%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET189-6 : 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 : n016.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 08:36:00 AM UTC 2026
% Result : Unsatisfiable 100.68s 13.89s
% Output : CNFRefutation 100.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 12
% Syntax : Number of formulae : 53 ( 20 unt; 0 def)
% Number of atoms : 94 ( 19 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 73 ( 32 ~; 41 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 55 ( 5 sgn 18 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_to_subclass_property6_3,axiom,
x != y,
file('theBenchmark.p',prove_corollary_to_subclass_property6_3) ).
cnf(c_36,plain,
x != y,
inference(clausify,[status(thm)],[prove_corollary_to_subclass_property6_3]) ).
cnf(c_37,plain,
y != x,
inference(copy,[status(thm)],[c_36]) ).
fof(prove_corollary_to_subclass_property6_2,axiom,
subclass(y,x),
file('theBenchmark.p',prove_corollary_to_subclass_property6_2) ).
cnf(c_38,plain,
subclass(y,x),
inference(clausify,[status(thm)],[prove_corollary_to_subclass_property6_2]) ).
fof(prove_corollary_to_subclass_property6_1,axiom,
intersection(complement(y),x) = null_class,
file('theBenchmark.p',prove_corollary_to_subclass_property6_1) ).
cnf(c_39,plain,
intersection(complement(y),x) = null_class,
inference(clausify,[status(thm)],[prove_corollary_to_subclass_property6_1]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_78,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_79,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_78]) ).
fof(complement2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,VAR_1)
| member(VAR_0,complement(VAR_1))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',complement2) ).
cnf(c_121,plain,
( member(A,B)
| member(A,complement(B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[complement2]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_122,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
fof(intersection3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,intersection(VAR_1,VAR_2))
| ~ member(VAR_0,VAR_2)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',intersection3) ).
cnf(c_123,plain,
( member(A,intersection(B,C))
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[intersection3]) ).
fof(subclass_implies_equal,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ subclass(VAR_1,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_implies_equal) ).
cnf(c_141,plain,
( A = B
| ~ subclass(B,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_implies_equal]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_144,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
fof(not_subclass_members2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| ~ member(not_subclass_element(VAR_0,VAR_1),VAR_1) ),
file('theBenchmark.p',not_subclass_members2) ).
cnf(c_145,plain,
( subclass(A,B)
| ~ member(not_subclass_element(A,B),B) ),
inference(clausify,[status(thm)],[not_subclass_members2]) ).
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_146,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_147,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_17370,plain,
( null_class = complement(A)
| ~ member(regular(complement(A)),A) ),
inference(resolve,[status(thm)],[c_122,c_79]) ).
cnf(c_259,plain,
( complement(A) = null_class
| ~ member(regular(complement(A)),A) ),
inference(copy,[status(thm)],[c_17370]) ).
cnf(c_17371,plain,
( y = x
| ~ subclass(x,y) ),
inference(resolve,[status(thm)],[c_141,c_38]) ).
cnf(c_288,plain,
~ subclass(x,y),
inference(resolve,[status(thm)],[c_37,c_17371]) ).
cnf(c_314,plain,
( ~ member(not_subclass_element(complement(A),B),A)
| subclass(complement(A),B) ),
inference(resolve,[status(thm)],[c_146,c_122]) ).
cnf(c_320,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_147,c_144]) ).
cnf(c_435,plain,
member(not_subclass_element(x,y),x),
inference(resolve,[status(thm)],[c_288,c_146]) ).
cnf(c_443,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),universal_class) ),
inference(resolve,[status(thm)],[c_320,c_146]) ).
cnf(c_444,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_320,c_79]) ).
cnf(c_514,plain,
member(not_subclass_element(x,y),universal_class),
inference(resolve,[status(thm)],[c_435,c_320]) ).
cnf(c_519,plain,
( member(not_subclass_element(x,y),intersection(A,x))
| ~ member(not_subclass_element(x,y),A) ),
inference(resolve,[status(thm)],[c_435,c_123]) ).
cnf(c_566,plain,
( member(not_subclass_element(x,y),A)
| member(not_subclass_element(x,y),complement(A)) ),
inference(resolve,[status(thm)],[c_514,c_121]) ).
cnf(c_17372,plain,
( complement(universal_class) = null_class
| null_class = complement(universal_class) ),
inference(resolve,[status(thm)],[c_444,c_259]) ).
cnf(c_17373,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(copy,[status(thm)],[c_17372]) ).
cnf(c_670,plain,
complement(universal_class) = null_class,
inference(copy,[status(thm)],[c_17373]) ).
cnf(c_17374,plain,
( subclass(complement(universal_class),A)
| subclass(complement(universal_class),A) ),
inference(resolve,[status(thm)],[c_314,c_443]) ).
cnf(c_17375,plain,
( subclass(complement(universal_class),A)
| subclass(null_class,A) ),
inference(paramod,[status(thm)],[c_670,c_17374]) ).
cnf(c_17376,plain,
( subclass(null_class,A)
| subclass(null_class,A) ),
inference(paramod,[status(thm)],[c_670,c_17375]) ).
cnf(c_1463,plain,
subclass(null_class,A),
inference(copy,[status(thm)],[c_17376]) ).
cnf(c_1479,plain,
( member(A,B)
| ~ member(A,null_class) ),
inference(resolve,[status(thm)],[c_1463,c_147]) ).
cnf(c_17377,plain,
( subclass(x,y)
| member(not_subclass_element(x,y),complement(y)) ),
inference(resolve,[status(thm)],[c_566,c_145]) ).
cnf(c_17346,plain,
member(not_subclass_element(x,y),complement(y)),
inference(resolve,[status(thm)],[c_288,c_17377]) ).
cnf(c_17378,plain,
member(not_subclass_element(x,y),intersection(complement(y),x)),
inference(resolve,[status(thm)],[c_17346,c_519]) ).
cnf(c_17360,plain,
member(not_subclass_element(x,y),null_class),
inference(paramod,[status(thm)],[c_39,c_17378]) ).
cnf(c_17367,plain,
~ member(not_subclass_element(x,y),y),
inference(resolve,[status(thm)],[c_17346,c_122]) ).
cnf(c_17368,plain,
member(not_subclass_element(x,y),A),
inference(resolve,[status(thm)],[c_17360,c_1479]) ).
cnf(c_17369,plain,
$false,
inference(resolve,[status(thm)],[c_17368,c_17367]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET189-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n016.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 07:23:00 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 280509 was started by sandbox on n016,
% 0.11/0.38 % Sat Sep 26 07:23:00 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 100.68/13.89
% 100.68/13.89 % given #500 (A,wt=34): 428 member(omega,complement(domain_of(A))) | intersection(cross_product(unordered_pair(omega,omega),universal_class),A) != null_class. [resolve(257,b,228,b)].
% 100.68/13.89
% 100.68/13.89 % SZS status Unsatisfiable for theBenchmark
% 100.68/13.89
% 100.68/13.89 % Proof 1 at 4.08 (+ 1.03) seconds.
% 100.68/13.89 % Length of proof is 32.
% 100.68/13.89 % Level of proof is 9.
% 100.68/13.89 % Maximum clause weight is 25.000.
% 100.68/13.89 % Given clauses 765.
% 100.68/13.89
% 100.68/13.89 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------