%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET192-6 : 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 : n009.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 65.43s 9.99s
% Output : CNFRefutation 65.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 16
% Syntax : Number of formulae : 81 ( 28 unt; 0 def)
% Number of atoms : 140 ( 55 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 107 ( 48 ~; 59 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 4 con; 0-3 aty)
% Number of variables : 113 ( 8 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_subclass_property9_2,axiom,
~ subclass(complement(y),complement(x)),
file('theBenchmark.p',prove_subclass_property9_2) ).
cnf(c_36,plain,
~ subclass(complement(y),complement(x)),
inference(clausify,[status(thm)],[prove_subclass_property9_2]) ).
fof(prove_subclass_property9_1,axiom,
subclass(x,y),
file('theBenchmark.p',prove_subclass_property9_1) ).
cnf(c_37,plain,
subclass(x,y),
inference(clausify,[status(thm)],[prove_subclass_property9_1]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_76,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_77,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_76]) ).
fof(domain1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_1,domain_of(VAR_0))
| restrict(VAR_0,singleton(VAR_1),universal_class) != null_class ),
file('theBenchmark.p',domain1) ).
cnf(c_110,plain,
( ~ member(B,domain_of(A))
| restrict(A,singleton(B),universal_class) != null_class ),
inference(clausify,[status(thm)],[domain1]) ).
fof(restriction2,axiom,
! [VAR_0,VAR_1,VAR_2] : intersection(cross_product(VAR_0,VAR_1),VAR_2) = restrict(VAR_2,VAR_0,VAR_1),
file('theBenchmark.p',restriction2) ).
cnf(c_111,plain,
intersection(cross_product(A,B),C) = restrict(C,A,B),
inference(clausify,[status(thm)],[restriction2]) ).
cnf(c_112,plain,
restrict(A,B,C) = intersection(cross_product(B,C),A),
inference(copy,[status(thm)],[c_111]) ).
fof(restriction1,axiom,
! [VAR_0,VAR_1,VAR_2] : intersection(VAR_0,cross_product(VAR_1,VAR_2)) = restrict(VAR_0,VAR_1,VAR_2),
file('theBenchmark.p',restriction1) ).
cnf(c_113,plain,
intersection(A,cross_product(B,C)) = restrict(A,B,C),
inference(clausify,[status(thm)],[restriction1]) ).
cnf(c_34487,plain,
intersection(A,cross_product(B,C)) = intersection(cross_product(B,C),A),
inference(paramod,[status(thm)],[c_112,c_113]) ).
cnf(c_114,plain,
intersection(cross_product(A,B),C) = intersection(C,cross_product(A,B)),
inference(copy,[status(thm)],[c_34487]) ).
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_119,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_120,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_121,plain,
( member(A,intersection(B,C))
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[intersection3]) ).
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_122,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection2]) ).
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_123,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_133,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_134,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_133]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_142,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_143,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_144,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_145,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_34488,plain,
( ~ member(B,domain_of(A))
| restrict(A,unordered_pair(B,B),universal_class) != null_class ),
inference(paramod,[status(thm)],[c_134,c_110]) ).
cnf(c_226,plain,
( ~ member(A,domain_of(B))
| intersection(cross_product(unordered_pair(A,A),universal_class),B) != null_class ),
inference(paramod,[status(thm)],[c_112,c_34488]) ).
cnf(c_232,plain,
( member(A,intersection(B,B))
| ~ member(A,B) ),
inference(factor,[status(thm)],[c_121]) ).
cnf(c_34489,plain,
( null_class = complement(A)
| ~ member(regular(complement(A)),A) ),
inference(resolve,[status(thm)],[c_120,c_77]) ).
cnf(c_259,plain,
( complement(A) = null_class
| ~ member(regular(complement(A)),A) ),
inference(copy,[status(thm)],[c_34489]) ).
cnf(c_34490,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),B) ),
inference(resolve,[status(thm)],[c_122,c_77]) ).
cnf(c_266,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),B) ),
inference(copy,[status(thm)],[c_34490]) ).
cnf(c_34491,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),A) ),
inference(resolve,[status(thm)],[c_123,c_77]) ).
cnf(c_269,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),A) ),
inference(copy,[status(thm)],[c_34491]) ).
cnf(c_308,plain,
member(not_subclass_element(complement(y),complement(x)),complement(y)),
inference(resolve,[status(thm)],[c_144,c_36]) ).
cnf(c_310,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_145,c_142]) ).
cnf(c_320,plain,
( member(A,y)
| ~ member(A,x) ),
inference(resolve,[status(thm)],[c_145,c_37]) ).
cnf(c_34492,plain,
( null_class = domain_of(A)
| intersection(cross_product(unordered_pair(regular(domain_of(A)),regular(domain_of(A))),universal_class),A) != null_class ),
inference(resolve,[status(thm)],[c_226,c_77]) ).
cnf(c_34493,plain,
( null_class = domain_of(A)
| intersection(A,cross_product(unordered_pair(regular(domain_of(A)),regular(domain_of(A))),universal_class)) != null_class ),
inference(paramod,[status(thm)],[c_114,c_34492]) ).
cnf(c_369,plain,
( domain_of(A) = null_class
| intersection(A,cross_product(unordered_pair(regular(domain_of(A)),regular(domain_of(A))),universal_class)) != null_class ),
inference(copy,[status(thm)],[c_34493]) ).
cnf(c_453,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_310,c_77]) ).
cnf(c_524,plain,
( member(regular(A),intersection(universal_class,universal_class))
| null_class = A ),
inference(resolve,[status(thm)],[c_453,c_232]) ).
cnf(c_720,plain,
( member(regular(intersection(A,x)),y)
| intersection(A,x) = null_class ),
inference(resolve,[status(thm)],[c_266,c_320]) ).
cnf(c_849,plain,
( ~ member(regular(intersection(complement(A),B)),A)
| intersection(complement(A),B) = null_class ),
inference(resolve,[status(thm)],[c_269,c_120]) ).
cnf(c_861,plain,
member(not_subclass_element(complement(y),complement(x)),universal_class),
inference(resolve,[status(thm)],[c_308,c_310]) ).
cnf(c_867,plain,
( member(not_subclass_element(complement(y),complement(x)),intersection(complement(y),A))
| ~ member(not_subclass_element(complement(y),complement(x)),A) ),
inference(resolve,[status(thm)],[c_308,c_121]) ).
cnf(c_884,plain,
( member(not_subclass_element(complement(y),complement(x)),A)
| member(not_subclass_element(complement(y),complement(x)),complement(A)) ),
inference(resolve,[status(thm)],[c_861,c_119]) ).
cnf(c_34494,plain,
( complement(intersection(universal_class,universal_class)) = null_class
| null_class = complement(intersection(universal_class,universal_class)) ),
inference(resolve,[status(thm)],[c_524,c_259]) ).
cnf(c_34495,plain,
( complement(intersection(universal_class,universal_class)) = null_class
| complement(intersection(universal_class,universal_class)) = null_class ),
inference(copy,[status(thm)],[c_34494]) ).
cnf(c_1305,plain,
complement(intersection(universal_class,universal_class)) = null_class,
inference(copy,[status(thm)],[c_34495]) ).
cnf(c_1314,plain,
( ~ member(A,intersection(universal_class,universal_class))
| ~ member(A,null_class) ),
inference(paramod,[status(thm)],[c_1305,c_120]) ).
cnf(c_1335,plain,
( null_class = A
| ~ member(regular(A),null_class) ),
inference(resolve,[status(thm)],[c_1314,c_524]) ).
cnf(c_34496,plain,
( intersection(null_class,A) = null_class
| null_class = intersection(null_class,A) ),
inference(resolve,[status(thm)],[c_1335,c_269]) ).
cnf(c_34497,plain,
( intersection(null_class,A) = null_class
| intersection(null_class,A) = null_class ),
inference(copy,[status(thm)],[c_34496]) ).
cnf(c_1342,plain,
intersection(null_class,A) = null_class,
inference(copy,[status(thm)],[c_34497]) ).
cnf(c_34498,plain,
( intersection(A,null_class) = null_class
| null_class = intersection(A,null_class) ),
inference(resolve,[status(thm)],[c_1335,c_266]) ).
cnf(c_34499,plain,
( intersection(A,null_class) = null_class
| intersection(A,null_class) = null_class ),
inference(copy,[status(thm)],[c_34498]) ).
cnf(c_1343,plain,
intersection(A,null_class) = null_class,
inference(copy,[status(thm)],[c_34499]) ).
cnf(c_4643,plain,
domain_of(null_class) = null_class,
inference(resolve,[status(thm)],[c_369,c_1342]) ).
cnf(c_34500,plain,
( ~ member(A,null_class)
| intersection(cross_product(unordered_pair(A,A),universal_class),null_class) != null_class ),
inference(paramod,[status(thm)],[c_4643,c_226]) ).
cnf(c_34501,plain,
( ~ member(A,null_class)
| null_class != null_class ),
inference(paramod,[status(thm)],[c_1343,c_34500]) ).
cnf(c_4661,plain,
~ member(A,null_class),
inference(copy,[status(thm)],[c_34501]) ).
cnf(c_34502,plain,
( intersection(complement(y),x) = null_class
| intersection(complement(y),x) = null_class ),
inference(resolve,[status(thm)],[c_849,c_720]) ).
cnf(c_33235,plain,
intersection(complement(y),x) = null_class,
inference(copy,[status(thm)],[c_34502]) ).
cnf(c_34503,plain,
( subclass(complement(y),complement(x))
| member(not_subclass_element(complement(y),complement(x)),x) ),
inference(resolve,[status(thm)],[c_884,c_143]) ).
cnf(c_34482,plain,
member(not_subclass_element(complement(y),complement(x)),x),
inference(resolve,[status(thm)],[c_36,c_34503]) ).
cnf(c_34504,plain,
member(not_subclass_element(complement(y),complement(x)),intersection(complement(y),x)),
inference(resolve,[status(thm)],[c_34482,c_867]) ).
cnf(c_34505,plain,
member(not_subclass_element(complement(y),complement(x)),null_class),
inference(paramod,[status(thm)],[c_33235,c_34504]) ).
cnf(c_34486,plain,
$false,
inference(resolve,[status(thm)],[c_4661,c_34505]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET192-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.02/0.36 % Computer : n009.cluster.edu
% 0.02/0.36 % Model : x86_64 x86_64
% 0.02/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.02/0.36 % Memory : 8046.5625MB
% 0.02/0.36 % OS : Linux 6.8.0-71-generic
% 0.02/0.36 % CPULimit : 300
% 0.02/0.36 % WCLimit : 300
% 0.02/0.36 % DateTime : Sat Sep 26 07:18:29 UTC 2026
% 0.02/0.37 % CPUTime :
% 0.02/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.02/0.37 % Process 3671491 was started by sandbox2 on n009,
% 0.02/0.37 % Sat Sep 26 07:18:29 2026
% 0.02/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.02/0.37
% 0.02/0.37 % From the command line: assign(max_seconds, 300).
% 65.43/9.99
% 65.43/9.99 % given #500 (T,wt=10): 439 -member(null_class,A) | member(null_class,intersection(intersection(omega,omega),A)). [resolve(380,a,121,a)].
% 65.43/9.99
% 65.43/9.99 % given #1000 (T,wt=7): 17370 application_function = null_class | member(regular(application_function),universal_class). [resolve(2054,a,310,a)].
% 65.43/9.99
% 65.43/9.99 % given #1500 (A,wt=20): 670 -member(A,B) | member(unordered_pair(unordered_pair(A,A),unordered_pair(A,unordered_pair(null_class,null_class))),cross_product(B,intersection(omega,intersection(omega,universal_class)))). [resolve(627,a,236,b)].
% 65.43/9.99
% 65.43/9.99 % given #2000 (A,wt=22): 838 intersection(universal_class,A) = null_class | member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(regular(intersection(universal_class,A))),universal_class)),universal_class))))),universal_class). [resolve(269,a,205,a)].
% 65.43/9.99
% 65.43/9.99 % SZS status Unsatisfiable for theBenchmark
% 65.43/9.99
% 65.43/9.99 % Proof 1 at 6.80 (+ 2.37) seconds.
% 65.43/9.99 % Length of proof is 46.
% 65.43/9.99 % Level of proof is 10.
% 65.43/9.99 % Maximum clause weight is 17.000.
% 65.43/9.99 % Given clauses 2202.
% 65.43/9.99
% 65.43/9.99 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------