%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET287-6 : 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 : n008.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 08:36:09 AM UTC 2026
% Result : Unsatisfiable 53.22s 17.27s
% Output : CNFRefutation 53.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 12
% Syntax : Number of formulae : 59 ( 25 unt; 0 def)
% Number of atoms : 95 ( 48 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 70 ( 34 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 4 con; 0-3 aty)
% Number of variables : 84 ( 6 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_domain_property8_2,axiom,
domain_of(intersection(complement(y),x)) != null_class,
file('theBenchmark.p',prove_domain_property8_2) ).
cnf(c_36,plain,
domain_of(intersection(complement(y),x)) != null_class,
inference(clausify,[status(thm)],[prove_domain_property8_2]) ).
fof(prove_domain_property8_1,axiom,
subclass(x,y),
file('theBenchmark.p',prove_domain_property8_1) ).
cnf(c_37,plain,
subclass(x,y),
inference(clausify,[status(thm)],[prove_domain_property8_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_21041,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_21041]) ).
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(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(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_21042,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_21042]) ).
cnf(c_21043,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_21043]) ).
cnf(c_21044,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),B) ),
inference(resolve,[status(thm)],[c_122,c_77]) ).
cnf(c_269,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),B) ),
inference(copy,[status(thm)],[c_21044]) ).
cnf(c_21045,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),A) ),
inference(resolve,[status(thm)],[c_123,c_77]) ).
cnf(c_272,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),A) ),
inference(copy,[status(thm)],[c_21045]) ).
cnf(c_313,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_145,c_142]) ).
cnf(c_323,plain,
( member(A,y)
| ~ member(A,x) ),
inference(resolve,[status(thm)],[c_145,c_37]) ).
cnf(c_421,plain,
( ~ member(B,domain_of(A))
| intersection(A,cross_product(unordered_pair(B,B),universal_class)) != null_class ),
inference(paramod,[status(thm)],[c_114,c_226]) ).
cnf(c_483,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_313,c_77]) ).
cnf(c_654,plain,
( member(regular(intersection(A,x)),y)
| intersection(A,x) = null_class ),
inference(resolve,[status(thm)],[c_269,c_323]) ).
cnf(c_21046,plain,
( complement(universal_class) = null_class
| null_class = complement(universal_class) ),
inference(resolve,[status(thm)],[c_483,c_259]) ).
cnf(c_21047,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(copy,[status(thm)],[c_21046]) ).
cnf(c_707,plain,
complement(universal_class) = null_class,
inference(copy,[status(thm)],[c_21047]) ).
cnf(c_21048,plain,
( ~ member(regular(A),complement(universal_class))
| null_class = A ),
inference(resolve,[status(thm)],[c_483,c_120]) ).
cnf(c_728,plain,
( ~ member(regular(A),null_class)
| null_class = A ),
inference(paramod,[status(thm)],[c_707,c_21048]) ).
cnf(c_781,plain,
( ~ member(regular(intersection(complement(A),B)),A)
| intersection(complement(A),B) = null_class ),
inference(resolve,[status(thm)],[c_272,c_120]) ).
cnf(c_21049,plain,
( intersection(null_class,A) = null_class
| null_class = intersection(null_class,A) ),
inference(resolve,[status(thm)],[c_728,c_272]) ).
cnf(c_21050,plain,
( intersection(null_class,A) = null_class
| intersection(null_class,A) = null_class ),
inference(copy,[status(thm)],[c_21049]) ).
cnf(c_847,plain,
intersection(null_class,A) = null_class,
inference(copy,[status(thm)],[c_21050]) ).
cnf(c_851,plain,
~ member(A,domain_of(null_class)),
inference(resolve,[status(thm)],[c_847,c_421]) ).
cnf(c_21051,plain,
null_class = domain_of(null_class),
inference(resolve,[status(thm)],[c_851,c_77]) ).
cnf(c_868,plain,
domain_of(null_class) = null_class,
inference(copy,[status(thm)],[c_21051]) ).
cnf(c_21052,plain,
( intersection(complement(y),x) = null_class
| intersection(complement(y),x) = null_class ),
inference(resolve,[status(thm)],[c_781,c_654]) ).
cnf(c_21032,plain,
intersection(complement(y),x) = null_class,
inference(copy,[status(thm)],[c_21052]) ).
cnf(c_21053,plain,
domain_of(null_class) != null_class,
inference(paramod,[status(thm)],[c_21032,c_36]) ).
cnf(c_21054,plain,
null_class != null_class,
inference(paramod,[status(thm)],[c_868,c_21053]) ).
cnf(c_21040,plain,
$false,
inference(copy,[status(thm)],[c_21054]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET287-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/10.38 % Computer : n008.cluster.edu
% 0.10/10.38 % Model : x86_64 x86_64
% 0.10/10.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/10.38 % Memory : 8046.5625MB
% 0.10/10.38 % OS : Linux 6.8.0-71-generic
% 0.10/10.38 % CPULimit : 300
% 0.10/10.38 % WCLimit : 300
% 0.10/10.38 % DateTime : Sat Sep 26 07:27:38 UTC 2026
% 0.10/10.38 % CPUTime :
% 0.10/10.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/10.38 % Process 3085278 was started by sandbox2 on n008,
% 0.10/10.38 % Sat Sep 26 07:27:38 2026
% 0.10/10.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/10.39
% 0.10/10.39 % From the command line: assign(max_seconds, 300).
% 53.22/17.27
% 53.22/17.27 % given #500 (T,wt=22): 604 member(null_class,intersection(omega,unordered_pair(A,null_class))). [resolve(501,a,265,a)].
% 53.22/17.27
% 53.22/17.27 % given #1000 (W,wt=22): 6148 member(not_subclass_element(A,singleton_relation),A) | null_class = A | member(regular(A),element_relation). [resolve(1277,a,270,a)].
% 53.22/17.27
% 53.22/17.27 % SZS status Unsatisfiable for theBenchmark
% 53.22/17.27
% 53.22/17.27 % Proof 1 at 5.30 (+ 1.21) seconds.
% 53.22/17.27 % Length of proof is 33.
% 53.22/17.27 % Level of proof is 8.
% 53.22/17.27 % Maximum clause weight is 33.000.
% 53.22/17.27 % Given clauses 1317.
% 53.22/17.27
% 53.22/17.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------