%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET063-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n010.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 : Unsatisfiable 0.23s 0.58s
% Output : CNFRefutation 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 34 ( 15 unt; 0 def)
% Number of atoms : 55 ( 15 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 40 ( 19 ~; 21 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 26 ( 2 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_of_null_class_is_subclass_2,axiom,
x != null_class,
file('theBenchmark.p',prove_corollary_of_null_class_is_subclass_2) ).
cnf(c_34,plain,
x != null_class,
inference(clausify,[status(thm)],[prove_corollary_of_null_class_is_subclass_2]) ).
fof(prove_corollary_of_null_class_is_subclass_1,axiom,
subclass(x,null_class),
file('theBenchmark.p',prove_corollary_of_null_class_is_subclass_1) ).
cnf(c_35,plain,
subclass(x,null_class),
inference(clausify,[status(thm)],[prove_corollary_of_null_class_is_subclass_1]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_52,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_53,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_52]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_96,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_118,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
fof(not_subclass_members1,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| member(not_subclass_element(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',not_subclass_members1) ).
cnf(c_120,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
fof(subclass_members,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_2,VAR_1)
| ~ member(VAR_2,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_members) ).
cnf(c_121,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_849,plain,
( null_class = complement(A)
| ~ member(regular(complement(A)),A) ),
inference(resolve,[status(thm)],[c_96,c_53]) ).
cnf(c_203,plain,
( complement(A) = null_class
| ~ member(regular(complement(A)),A) ),
inference(copy,[status(thm)],[c_849]) ).
cnf(c_251,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_121,c_118]) ).
cnf(c_257,plain,
( member(A,null_class)
| ~ member(A,x) ),
inference(resolve,[status(thm)],[c_121,c_35]) ).
cnf(c_410,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_251,c_53]) ).
cnf(c_850,plain,
( null_class = x
| member(regular(x),null_class) ),
inference(resolve,[status(thm)],[c_257,c_53]) ).
cnf(c_851,plain,
( x = null_class
| member(regular(x),null_class) ),
inference(copy,[status(thm)],[c_850]) ).
cnf(c_547,plain,
member(regular(x),null_class),
inference(resolve,[status(thm)],[c_34,c_851]) ).
cnf(c_555,plain,
~ member(regular(x),complement(null_class)),
inference(resolve,[status(thm)],[c_96,c_547]) ).
cnf(c_852,plain,
( member(regular(x),A)
| ~ subclass(null_class,A) ),
inference(resolve,[status(thm)],[c_121,c_547]) ).
cnf(c_698,plain,
~ subclass(null_class,complement(null_class)),
inference(resolve,[status(thm)],[c_852,c_555]) ).
cnf(c_704,plain,
member(not_subclass_element(null_class,complement(null_class)),null_class),
inference(resolve,[status(thm)],[c_698,c_120]) ).
cnf(c_754,plain,
member(not_subclass_element(null_class,complement(null_class)),universal_class),
inference(resolve,[status(thm)],[c_704,c_251]) ).
cnf(c_814,plain,
~ member(not_subclass_element(null_class,complement(null_class)),complement(universal_class)),
inference(resolve,[status(thm)],[c_96,c_754]) ).
cnf(c_853,plain,
( complement(universal_class) = null_class
| null_class = complement(universal_class) ),
inference(resolve,[status(thm)],[c_410,c_203]) ).
cnf(c_854,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(copy,[status(thm)],[c_853]) ).
cnf(c_832,plain,
complement(universal_class) = null_class,
inference(copy,[status(thm)],[c_854]) ).
cnf(c_855,plain,
~ member(not_subclass_element(null_class,complement(null_class)),null_class),
inference(paramod,[status(thm)],[c_832,c_814]) ).
cnf(c_848,plain,
$false,
inference(resolve,[status(thm)],[c_704,c_855]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET063-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n010.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.46 % CPULimit : 300
% 0.18/0.46 % WCLimit : 300
% 0.18/0.46 % DateTime : Sat Sep 26 07:01:49 UTC 2026
% 0.18/0.46 % CPUTime :
% 0.18/0.46 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.46 % Process 2738701 was started by sandbox2 on n010,
% 0.18/0.46 % Sat Sep 26 07:01:49 2026
% 0.18/0.46 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.47
% 0.18/0.47 % From the command line: assign(max_seconds, 300).
% 0.23/0.58
% 0.23/0.58 % SZS status Unsatisfiable for theBenchmark
% 0.23/0.58
% 0.23/0.58 % Proof 1 at 0.08 (+ 0.02) seconds.
% 0.23/0.58 % Length of proof is 20.
% 0.23/0.58 % Level of proof is 8.
% 0.23/0.58 % Maximum clause weight is 9.000.
% 0.23/0.58 % Given clauses 170.
% 0.23/0.58
% 0.23/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------