%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET099-7 : 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 : n001.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 236.55s 54.91s
% Output : CNFRefutation 236.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 42 ( 20 unt; 0 def)
% Number of atoms : 73 ( 32 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 51 ( 20 ~; 31 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 6 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_2_to_number_of_elements_in_class_3,axiom,
x != null_class,
file('theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_3) ).
cnf(c_33,plain,
x != null_class,
inference(clausify,[status(thm)],[prove_corollary_2_to_number_of_elements_in_class_3]) ).
fof(prove_corollary_2_to_number_of_elements_in_class_2,axiom,
singleton(not_subclass_element(x,null_class)) != x,
file('theBenchmark.p',prove_corollary_2_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_2_to_number_of_elements_in_class_2]) ).
fof(prove_corollary_2_to_number_of_elements_in_class_1,axiom,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
file('theBenchmark.p',prove_corollary_2_to_number_of_elements_in_class_1) ).
cnf(c_35,plain,
not_subclass_element(intersection(complement(singleton(not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
inference(clausify,[status(thm)],[prove_corollary_2_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(null_class_is_unique,axiom,
! [VAR_0] :
( member(not_subclass_element(VAR_0,null_class),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',null_class_is_unique) ).
cnf(c_74,plain,
( member(not_subclass_element(A,null_class),A)
| A = null_class ),
inference(clausify,[status(thm)],[null_class_is_unique]) ).
cnf(c_75,plain,
( member(not_subclass_element(A,null_class),A)
| null_class = A ),
inference(copy,[status(thm)],[c_74]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_151,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
fof(intersection1,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_1)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection1) ).
cnf(c_154,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_164,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_165,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_164]) ).
fof(unordered_pair3,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_1,VAR_0))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair3) ).
cnf(c_167,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_173,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
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_176,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_23485,plain,
( null_class = A
| singleton(not_subclass_element(A,null_class)) = A
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(A,null_class),not_subclass_element(A,null_class))),A),null_class),intersection(complement(singleton(not_subclass_element(A,null_class))),A)) ),
inference(paramod,[status(thm)],[c_165,c_37]) ).
cnf(c_23486,plain,
( null_class = A
| singleton(not_subclass_element(A,null_class)) = A
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(A,null_class),not_subclass_element(A,null_class))),A),null_class),intersection(complement(unordered_pair(not_subclass_element(A,null_class),not_subclass_element(A,null_class))),A)) ),
inference(paramod,[status(thm)],[c_165,c_23485]) ).
cnf(c_278,plain,
( null_class = A
| unordered_pair(not_subclass_element(A,null_class),not_subclass_element(A,null_class)) = A
| member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(A,null_class),not_subclass_element(A,null_class))),A),null_class),intersection(complement(unordered_pair(not_subclass_element(A,null_class),not_subclass_element(A,null_class))),A)) ),
inference(paramod,[status(thm)],[c_165,c_23486]) ).
cnf(c_279,plain,
not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class) = not_subclass_element(x,null_class),
inference(paramod,[status(thm)],[c_165,c_35]) ).
cnf(c_280,plain,
unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)) != x,
inference(paramod,[status(thm)],[c_165,c_34]) ).
cnf(c_23487,plain,
null_class != x,
inference(copy,[status(thm)],[c_33]) ).
cnf(c_296,plain,
member(not_subclass_element(x,null_class),x),
inference(resolve,[status(thm)],[c_75,c_23487]) ).
cnf(c_461,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_176,c_173]) ).
cnf(c_950,plain,
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(A,null_class),not_subclass_element(A,null_class))),A),null_class),complement(unordered_pair(not_subclass_element(A,null_class),not_subclass_element(A,null_class))))
| null_class = A
| unordered_pair(not_subclass_element(A,null_class),not_subclass_element(A,null_class)) = A ),
inference(resolve,[status(thm)],[c_278,c_154]) ).
cnf(c_1140,plain,
member(not_subclass_element(x,null_class),universal_class),
inference(resolve,[status(thm)],[c_461,c_296]) ).
cnf(c_1192,plain,
member(not_subclass_element(x,null_class),unordered_pair(A,not_subclass_element(x,null_class))),
inference(resolve,[status(thm)],[c_1140,c_167]) ).
cnf(c_20977,plain,
~ member(not_subclass_element(x,null_class),complement(unordered_pair(A,not_subclass_element(x,null_class)))),
inference(resolve,[status(thm)],[c_1192,c_151]) ).
cnf(c_23488,plain,
( member(not_subclass_element(intersection(complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))),x),null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
| null_class = x ),
inference(resolve,[status(thm)],[c_950,c_280]) ).
cnf(c_23489,plain,
( member(not_subclass_element(x,null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
| null_class = x ),
inference(paramod,[status(thm)],[c_279,c_23488]) ).
cnf(c_23490,plain,
( member(not_subclass_element(x,null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class))))
| x = null_class ),
inference(copy,[status(thm)],[c_23489]) ).
cnf(c_23491,plain,
member(not_subclass_element(x,null_class),complement(unordered_pair(not_subclass_element(x,null_class),not_subclass_element(x,null_class)))),
inference(resolve,[status(thm)],[c_33,c_23490]) ).
cnf(c_23484,plain,
$false,
inference(resolve,[status(thm)],[c_20977,c_23491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET099-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.38 % Computer : n001.cluster.edu
% 0.08/0.38 % Model : x86_64 x86_64
% 0.08/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.38 % Memory : 8046.5625MB
% 0.08/0.38 % OS : Linux 6.8.0-71-generic
% 0.08/0.38 % CPULimit : 300
% 0.08/0.38 % WCLimit : 300
% 0.08/0.38 % DateTime : Sat Sep 26 07:12:42 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.39 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.39 % Process 1204454 was started by sandbox on n001,
% 0.08/0.39 % Sat Sep 26 07:12:42 2026
% 0.08/0.39 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.39
% 0.08/0.39 % From the command line: assign(max_seconds, 300).
% 236.55/54.91
% 236.55/54.91 % given #500 (F,wt=8): 4508 -member(null_class,complement(intersection(complement(complement(omega)),universal_class))). [resolve(4376,a,151,b)].
% 236.55/54.91
% 236.55/54.91 % given #1000 (W,wt=8): 2437 member(regular(A),A) | member(null_class,complement(A)). [resolve(1519,b,341,b)].
% 236.55/54.91
% 236.55/54.91 % given #1500 (T,wt=8): 9271 -subclass(omega,A) | member(not_subclass_element(omega,successor_relation),A). [resolve(9118,a,176,b)].
% 236.55/54.91
% 236.55/54.91 % given #2000 (F,wt=9): 17986 unordered_pair(regular(complement(intersection(identity_relation,A))),B) != null_class. [resolve(17951,a,64,a)].
% 236.55/54.91
% 236.55/54.91 % given #2500 (W,wt=8): 17636 identity_relation = null_class | member(not_subclass_element(identity_relation,null_class),universal_class). [resolve(10276,a,461,a)].
% 236.55/54.91
% 236.55/54.91 % given #3000 (T,wt=8): 21399 member(not_subclass_element(omega,intersection(complement(omega),A)),universal_class). [resolve(21387,a,7930,b)].
% 236.55/54.91
% 236.55/54.91 % SZS status Unsatisfiable for theBenchmark
% 236.55/54.91
% 236.55/54.91 % Proof 1 at 4.68 (+ 1.51) seconds.
% 236.55/54.91 % Length of proof is 24.
% 236.55/54.91 % Level of proof is 6.
% 236.55/54.91 % Maximum clause weight is 35.000.
% 236.55/54.91 % Given clauses 3365.
% 236.55/54.91
% 236.55/54.91 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------