%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET497-6 : 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 : n002.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 08:36:23 AM UTC 2026
% Result : Unsatisfiable 248.20s 33.24s
% Output : CNFRefutation 248.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 16
% Syntax : Number of formulae : 84 ( 27 unt; 0 def)
% Number of atoms : 151 ( 78 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 113 ( 46 ~; 67 |; 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 : 11 ( 11 usr; 3 con; 0-3 aty)
% Number of variables : 124 ( 13 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_russell_class1_2,axiom,
member(z,z),
file('theBenchmark.p',prove_russell_class1_2) ).
cnf(c_36,plain,
member(z,z),
inference(clausify,[status(thm)],[prove_russell_class1_2]) ).
fof(regularity2,axiom,
! [VAR_0] :
( intersection(VAR_0,regular(VAR_0)) = null_class
| VAR_0 = null_class ),
file('theBenchmark.p',regularity2) ).
cnf(c_74,plain,
( intersection(A,regular(A)) = null_class
| A = null_class ),
inference(clausify,[status(thm)],[regularity2]) ).
cnf(c_75,plain,
( intersection(A,regular(A)) = null_class
| null_class = A ),
inference(copy,[status(thm)],[c_74]) ).
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_53075,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_53075]) ).
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(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_136,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
fof(unordered_pair2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,unordered_pair(VAR_0,VAR_1))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',unordered_pair2) ).
cnf(c_137,plain,
( member(A,unordered_pair(A,B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair2]) ).
fof(unordered_pair_member,axiom,
! [VAR_0,VAR_1,VAR_2] :
( VAR_0 = VAR_2
| VAR_0 = VAR_1
| ~ member(VAR_0,unordered_pair(VAR_1,VAR_2)) ),
file('theBenchmark.p',unordered_pair_member) ).
cnf(c_138,plain,
( A = C
| A = B
| ~ member(A,unordered_pair(B,C)) ),
inference(clausify,[status(thm)],[unordered_pair_member]) ).
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_53076,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_227,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_53076]) ).
cnf(c_233,plain,
( member(A,intersection(B,B))
| ~ member(A,B) ),
inference(factor,[status(thm)],[c_121]) ).
cnf(c_53077,plain,
( null_class = complement(A)
| ~ member(regular(complement(A)),A) ),
inference(resolve,[status(thm)],[c_120,c_77]) ).
cnf(c_260,plain,
( complement(A) = null_class
| ~ member(regular(complement(A)),A) ),
inference(copy,[status(thm)],[c_53077]) ).
cnf(c_267,plain,
( member(z,intersection(A,z))
| ~ member(z,A) ),
inference(resolve,[status(thm)],[c_121,c_36]) ).
cnf(c_53078,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_53078]) ).
cnf(c_53079,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_53079]) ).
cnf(c_53080,plain,
( null_class = unordered_pair(A,B)
| regular(unordered_pair(A,B)) = B
| regular(unordered_pair(A,B)) = A ),
inference(resolve,[status(thm)],[c_138,c_77]) ).
cnf(c_284,plain,
( unordered_pair(A,B) = null_class
| regular(unordered_pair(A,B)) = B
| regular(unordered_pair(A,B)) = A ),
inference(copy,[status(thm)],[c_53080]) ).
cnf(c_285,plain,
( unordered_pair(A,A) = null_class
| regular(unordered_pair(A,A)) = A ),
inference(factor,[status(thm)],[c_284]) ).
cnf(c_311,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_145,c_142]) ).
cnf(c_53081,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_227,c_77]) ).
cnf(c_53082,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_53081]) ).
cnf(c_372,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_53082]) ).
cnf(c_384,plain,
member(z,intersection(z,z)),
inference(resolve,[status(thm)],[c_233,c_36]) ).
cnf(c_469,plain,
member(z,universal_class),
inference(resolve,[status(thm)],[c_311,c_384]) ).
cnf(c_470,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_311,c_77]) ).
cnf(c_497,plain,
member(z,unordered_pair(z,A)),
inference(resolve,[status(thm)],[c_469,c_137]) ).
cnf(c_498,plain,
member(z,unordered_pair(A,z)),
inference(resolve,[status(thm)],[c_469,c_136]) ).
cnf(c_580,plain,
( member(regular(A),intersection(universal_class,universal_class))
| null_class = A ),
inference(resolve,[status(thm)],[c_470,c_233]) ).
cnf(c_797,plain,
member(z,intersection(unordered_pair(A,z),z)),
inference(resolve,[status(thm)],[c_267,c_498]) ).
cnf(c_53083,plain,
( intersection(unordered_pair(A,A),A) = null_class
| null_class = unordered_pair(A,A)
| unordered_pair(A,A) = null_class ),
inference(paramod,[status(thm)],[c_285,c_75]) ).
cnf(c_53084,plain,
( intersection(unordered_pair(A,A),A) = null_class
| unordered_pair(A,A) = null_class
| unordered_pair(A,A) = null_class ),
inference(copy,[status(thm)],[c_53083]) ).
cnf(c_1420,plain,
( intersection(unordered_pair(A,A),A) = null_class
| unordered_pair(A,A) = null_class ),
inference(copy,[status(thm)],[c_53084]) ).
cnf(c_53085,plain,
( complement(intersection(universal_class,universal_class)) = null_class
| null_class = complement(intersection(universal_class,universal_class)) ),
inference(resolve,[status(thm)],[c_580,c_260]) ).
cnf(c_53086,plain,
( complement(intersection(universal_class,universal_class)) = null_class
| complement(intersection(universal_class,universal_class)) = null_class ),
inference(copy,[status(thm)],[c_53085]) ).
cnf(c_1636,plain,
complement(intersection(universal_class,universal_class)) = null_class,
inference(copy,[status(thm)],[c_53086]) ).
cnf(c_1645,plain,
( ~ member(A,intersection(universal_class,universal_class))
| ~ member(A,null_class) ),
inference(paramod,[status(thm)],[c_1636,c_120]) ).
cnf(c_1650,plain,
( null_class = A
| ~ member(regular(A),null_class) ),
inference(resolve,[status(thm)],[c_1645,c_580]) ).
cnf(c_53087,plain,
( intersection(null_class,A) = null_class
| null_class = intersection(null_class,A) ),
inference(resolve,[status(thm)],[c_1650,c_272]) ).
cnf(c_53088,plain,
( intersection(null_class,A) = null_class
| intersection(null_class,A) = null_class ),
inference(copy,[status(thm)],[c_53087]) ).
cnf(c_1658,plain,
intersection(null_class,A) = null_class,
inference(copy,[status(thm)],[c_53088]) ).
cnf(c_53089,plain,
( intersection(A,null_class) = null_class
| null_class = intersection(A,null_class) ),
inference(resolve,[status(thm)],[c_1650,c_269]) ).
cnf(c_53090,plain,
( intersection(A,null_class) = null_class
| intersection(A,null_class) = null_class ),
inference(copy,[status(thm)],[c_53089]) ).
cnf(c_1659,plain,
intersection(A,null_class) = null_class,
inference(copy,[status(thm)],[c_53090]) ).
cnf(c_4615,plain,
domain_of(null_class) = null_class,
inference(resolve,[status(thm)],[c_372,c_1658]) ).
cnf(c_53091,plain,
( ~ member(A,null_class)
| intersection(cross_product(unordered_pair(A,A),universal_class),null_class) != null_class ),
inference(paramod,[status(thm)],[c_4615,c_227]) ).
cnf(c_53092,plain,
( ~ member(A,null_class)
| null_class != null_class ),
inference(paramod,[status(thm)],[c_1659,c_53091]) ).
cnf(c_4633,plain,
~ member(A,null_class),
inference(copy,[status(thm)],[c_53092]) ).
cnf(c_53093,plain,
( member(z,null_class)
| unordered_pair(z,z) = null_class ),
inference(paramod,[status(thm)],[c_1420,c_797]) ).
cnf(c_52844,plain,
unordered_pair(z,z) = null_class,
inference(resolve,[status(thm)],[c_4633,c_53093]) ).
cnf(c_53094,plain,
member(z,null_class),
inference(paramod,[status(thm)],[c_52844,c_497]) ).
cnf(c_53074,plain,
$false,
inference(resolve,[status(thm)],[c_4633,c_53094]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET497-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n002.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 26 07:52:06 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.08/0.36 % Process 1178101 was started by sandbox on n002,
% 0.08/0.36 % Sat Sep 26 07:52:06 2026
% 0.08/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.08/0.36
% 0.08/0.36 % From the command line: assign(max_seconds, 300).
% 248.20/33.24
% 248.20/33.24 % given #500 (T,wt=9): 1226 member(null_class,intersection(universal_class,intersection(universal_class,unordered_pair(null_class,A)))). [resolve(1185,a,484,a)].
% 248.20/33.24
% 248.20/33.24 % given #1000 (T,wt=11): 1617 member(z,intersection(intersection(unordered_pair(A,z),unordered_pair(A,z)),universal_class)). [resolve(551,a,499,a)].
% 248.20/33.24
% 248.20/33.24 % given #1500 (A,wt=12): 646 -member(omega,A) | member(omega,intersection(intersection(universal_class,unordered_pair(omega,B)),A)). [resolve(630,a,121,a)].
% 248.20/33.24
% 248.20/33.24 % given #2000 (A,wt=27): 860 intersection(A,universal_class) = null_class | intersection(cross_product(unordered_pair(regular(intersection(A,universal_class)),regular(intersection(A,universal_class))),universal_class),B) = null_class | member(regular(intersection(A,universal_class)),domain_of(B)). [resolve(269,a,228,a)].
% 248.20/33.24
% 248.20/33.24 % given #2500 (A,wt=13): 1001 member(z,intersection(intersection(z,intersection(universal_class,z)),intersection(z,intersection(universal_class,z)))). [resolve(816,a,233,a)].
% 248.20/33.24
% 248.20/33.24 % given #3000 (A,wt=13): 1188 member(unordered_pair(A,B),C) | member(unordered_pair(A,B),intersection(universal_class,complement(C))). [resolve(277,a,276,a)].
% 248.20/33.24
% 248.20/33.24 % given #3500 (T,wt=11): 52700 null_class = universal_class | -member(A,complement(complement(domain_of(domain_of(regular(universal_class)))))). [resolve(52279,b,145,a),unit_del(c,4633)].
% 248.20/33.24
% 248.20/33.24 % SZS status Unsatisfiable for theBenchmark
% 248.20/33.24
% 248.20/33.24 % Proof 1 at 22.23 (+ 10.05) seconds.
% 248.20/33.24 % Length of proof is 48.
% 248.20/33.24 % Level of proof is 11.
% 248.20/33.24 % Maximum clause weight is 17.000.
% 248.20/33.24 % Given clauses 3515.
% 248.20/33.24
% 248.20/33.24 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------