%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET098-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n019.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 08:35:46 AM UTC 2026
% Result : Unsatisfiable 0.66s 0.49s
% Output : CNFRefutation 0.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 16 ( 9 unt; 0 def)
% Number of atoms : 26 ( 12 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 18 ( 8 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 9 ( 1 sgn 4 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_1_to_number_of_elements_in_class_3,axiom,
x != null_class,
file('theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_3) ).
cnf(c_33,plain,
x != null_class,
inference(clausify,[status(thm)],[prove_corollary_1_to_number_of_elements_in_class_3]) ).
fof(prove_corollary_1_to_number_of_elements_in_class_2,axiom,
singleton(not_subclass_element(x,null_class)) != x,
file('theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_2) ).
cnf(c_34,plain,
singleton(not_subclass_element(x,null_class)) != x,
inference(clausify,[status(thm)],[prove_corollary_1_to_number_of_elements_in_class_2]) ).
fof(prove_corollary_1_to_number_of_elements_in_class_1,axiom,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
file('theBenchmark.p',prove_corollary_1_to_number_of_elements_in_class_1) ).
cnf(c_35,plain,
~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
inference(clausify,[status(thm)],[prove_corollary_1_to_number_of_elements_in_class_1]) ).
fof(number_of_elements_in_class,axiom,
! [VAR_0] :
( VAR_0 = null_class
| singleton(not_subclass_element(VAR_0,null_class)) = VAR_0
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(VAR_0,null_class))),VAR_0),null_class),intersection(complement(singleton(not_subclass_element(VAR_0,null_class))),VAR_0)) ),
file('theBenchmark.p',number_of_elements_in_class) ).
cnf(c_36,plain,
( A = null_class
| singleton(not_subclass_element(A,null_class)) = A
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(A,null_class))),A),null_class),intersection(complement(singleton(not_subclass_element(A,null_class))),A)) ),
inference(clausify,[status(thm)],[number_of_elements_in_class]) ).
cnf(c_37,plain,
( null_class = A
| singleton(not_subclass_element(A,null_class)) = A
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(A,null_class))),A),null_class),intersection(complement(singleton(not_subclass_element(A,null_class))),A)) ),
inference(copy,[status(thm)],[c_36]) ).
fof(intersection2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection2) ).
cnf(c_153,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection2]) ).
cnf(c_952,plain,
( null_class = x
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)) ),
inference(resolve,[status(thm)],[c_37,c_34]) ).
cnf(c_953,plain,
( x = null_class
| member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)) ),
inference(copy,[status(thm)],[c_952]) ).
cnf(c_204,plain,
member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),intersection(complement(singleton(not_subclass_element(x,null_class))),x)),
inference(resolve,[status(thm)],[c_33,c_953]) ).
cnf(c_954,plain,
member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class),x),
inference(resolve,[status(thm)],[c_204,c_153]) ).
cnf(c_951,plain,
$false,
inference(resolve,[status(thm)],[c_35,c_954]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET098-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sat Sep 26 07:07:20 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 671767 was started by sandbox on n019,
% 0.09/0.37 % Sat Sep 26 07:07:20 2026
% 0.09/0.37 % 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).
% 0.66/0.49
% 0.66/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.66/0.49
% 0.66/0.49 % Proof 1 at 0.07 (+ 0.03) seconds.
% 0.66/0.49 % Length of proof is 8.
% 0.66/0.49 % Level of proof is 3.
% 0.66/0.49 % Maximum clause weight is 56.000.
% 0.66/0.49 % Given clauses 152.
% 0.66/0.49
% 0.66/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------