%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET511-6 : 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 : n006.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 08:36:25 AM UTC 2026
% Result : Unsatisfiable 98.55s 13.93s
% Output : CNFRefutation 98.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 15
% Syntax : Number of formulae : 87 ( 30 unt; 0 def)
% Number of atoms : 158 ( 97 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 121 ( 50 ~; 71 |; 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 : 12 ( 12 usr; 3 con; 0-3 aty)
% Number of variables : 122 ( 8 sgn 31 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_1_to_property_1_of_ordered_pair_1,axiom,
unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,universal_class),
file('theBenchmark.p',prove_corollary_1_to_property_1_of_ordered_pair_1) ).
cnf(c_36,plain,
unordered_pair(singleton(x),unordered_pair(x,null_class)) != ordered_pair(x,universal_class),
inference(clausify,[status(thm)],[prove_corollary_1_to_property_1_of_ordered_pair_1]) ).
fof(regularity2,axiom,
! [VAR_0] :
( intersection(VAR_0,regular(VAR_0)) = null_class
| VAR_0 = null_class ),
file('theBenchmark.p',regularity2) ).
cnf(c_73,plain,
( intersection(A,regular(A)) = null_class
| A = null_class ),
inference(clausify,[status(thm)],[regularity2]) ).
cnf(c_74,plain,
( intersection(A,regular(A)) = null_class
| null_class = A ),
inference(copy,[status(thm)],[c_73]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_75,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_76,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_75]) ).
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_109,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_110,plain,
intersection(cross_product(A,B),C) = restrict(C,A,B),
inference(clausify,[status(thm)],[restriction2]) ).
cnf(c_111,plain,
restrict(A,B,C) = intersection(cross_product(B,C),A),
inference(copy,[status(thm)],[c_110]) ).
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_112,plain,
intersection(A,cross_product(B,C)) = restrict(A,B,C),
inference(clausify,[status(thm)],[restriction1]) ).
cnf(c_49337,plain,
intersection(A,cross_product(B,C)) = intersection(cross_product(B,C),A),
inference(paramod,[status(thm)],[c_111,c_112]) ).
cnf(c_113,plain,
intersection(cross_product(A,B),C) = intersection(C,cross_product(A,B)),
inference(copy,[status(thm)],[c_49337]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_119,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_120,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_121,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_122,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(ordered_pair,axiom,
! [VAR_0,VAR_1] : unordered_pair(singleton(VAR_0),unordered_pair(VAR_0,singleton(VAR_1))) = ordered_pair(VAR_0,VAR_1),
file('theBenchmark.p',ordered_pair) ).
cnf(c_130,plain,
unordered_pair(singleton(A),unordered_pair(A,singleton(B))) = ordered_pair(A,B),
inference(clausify,[status(thm)],[ordered_pair]) ).
cnf(c_131,plain,
ordered_pair(A,B) = unordered_pair(singleton(A),unordered_pair(A,singleton(B))),
inference(copy,[status(thm)],[c_130]) ).
fof(singleton_set,axiom,
! [VAR_0] : unordered_pair(VAR_0,VAR_0) = singleton(VAR_0),
file('theBenchmark.p',singleton_set) ).
cnf(c_132,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_133,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_132]) ).
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_137,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_141,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_144,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_49338,plain,
( ~ member(B,domain_of(A))
| restrict(A,unordered_pair(B,B),universal_class) != null_class ),
inference(paramod,[status(thm)],[c_133,c_109]) ).
cnf(c_225,plain,
( ~ member(A,domain_of(B))
| intersection(cross_product(unordered_pair(A,A),universal_class),B) != null_class ),
inference(paramod,[status(thm)],[c_111,c_49338]) ).
cnf(c_231,plain,
( member(A,intersection(B,B))
| ~ member(A,B) ),
inference(factor,[status(thm)],[c_120]) ).
cnf(c_49339,plain,
unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)) != ordered_pair(x,universal_class),
inference(paramod,[status(thm)],[c_133,c_36]) ).
cnf(c_49340,plain,
unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)) != unordered_pair(singleton(x),unordered_pair(x,singleton(universal_class))),
inference(paramod,[status(thm)],[c_131,c_49339]) ).
cnf(c_49341,plain,
unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)) != unordered_pair(unordered_pair(x,x),unordered_pair(x,singleton(universal_class))),
inference(paramod,[status(thm)],[c_133,c_49340]) ).
cnf(c_49342,plain,
unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)) != unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(universal_class,universal_class))),
inference(paramod,[status(thm)],[c_133,c_49341]) ).
cnf(c_250,plain,
unordered_pair(unordered_pair(x,x),unordered_pair(x,unordered_pair(universal_class,universal_class))) != unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)),
inference(copy,[status(thm)],[c_49342]) ).
cnf(c_49343,plain,
( null_class = complement(A)
| ~ member(regular(complement(A)),A) ),
inference(resolve,[status(thm)],[c_119,c_76]) ).
cnf(c_259,plain,
( complement(A) = null_class
| ~ member(regular(complement(A)),A) ),
inference(copy,[status(thm)],[c_49343]) ).
cnf(c_261,plain,
( null_class = A
| member(regular(A),intersection(A,B))
| ~ member(regular(A),B) ),
inference(resolve,[status(thm)],[c_120,c_76]) ).
cnf(c_49344,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),B) ),
inference(resolve,[status(thm)],[c_121,c_76]) ).
cnf(c_266,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),B) ),
inference(copy,[status(thm)],[c_49344]) ).
cnf(c_49345,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),A) ),
inference(resolve,[status(thm)],[c_122,c_76]) ).
cnf(c_269,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),A) ),
inference(copy,[status(thm)],[c_49345]) ).
cnf(c_49346,plain,
( null_class = unordered_pair(A,B)
| regular(unordered_pair(A,B)) = B
| regular(unordered_pair(A,B)) = A ),
inference(resolve,[status(thm)],[c_137,c_76]) ).
cnf(c_281,plain,
( unordered_pair(A,B) = null_class
| regular(unordered_pair(A,B)) = B
| regular(unordered_pair(A,B)) = A ),
inference(copy,[status(thm)],[c_49346]) ).
cnf(c_282,plain,
( unordered_pair(A,A) = null_class
| regular(unordered_pair(A,A)) = A ),
inference(factor,[status(thm)],[c_281]) ).
cnf(c_308,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_144,c_141]) ).
cnf(c_49347,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_225,c_76]) ).
cnf(c_49348,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_113,c_49347]) ).
cnf(c_366,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_49348]) ).
cnf(c_449,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_308,c_76]) ).
cnf(c_525,plain,
( member(regular(A),intersection(universal_class,universal_class))
| null_class = A ),
inference(resolve,[status(thm)],[c_449,c_231]) ).
cnf(c_49349,plain,
( null_class = A
| null_class = A
| member(regular(A),intersection(A,universal_class)) ),
inference(resolve,[status(thm)],[c_261,c_449]) ).
cnf(c_574,plain,
( null_class = A
| member(regular(A),intersection(A,universal_class)) ),
inference(copy,[status(thm)],[c_49349]) ).
cnf(c_49350,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_282,c_74]) ).
cnf(c_49351,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_49350]) ).
cnf(c_1151,plain,
( intersection(unordered_pair(A,A),A) = null_class
| unordered_pair(A,A) = null_class ),
inference(copy,[status(thm)],[c_49351]) ).
cnf(c_49352,plain,
( complement(intersection(universal_class,universal_class)) = null_class
| null_class = complement(intersection(universal_class,universal_class)) ),
inference(resolve,[status(thm)],[c_525,c_259]) ).
cnf(c_49353,plain,
( complement(intersection(universal_class,universal_class)) = null_class
| complement(intersection(universal_class,universal_class)) = null_class ),
inference(copy,[status(thm)],[c_49352]) ).
cnf(c_1229,plain,
complement(intersection(universal_class,universal_class)) = null_class,
inference(copy,[status(thm)],[c_49353]) ).
cnf(c_1238,plain,
( ~ member(A,intersection(universal_class,universal_class))
| ~ member(A,null_class) ),
inference(paramod,[status(thm)],[c_1229,c_119]) ).
cnf(c_1243,plain,
( null_class = A
| ~ member(regular(A),null_class) ),
inference(resolve,[status(thm)],[c_1238,c_525]) ).
cnf(c_49354,plain,
( intersection(null_class,A) = null_class
| null_class = intersection(null_class,A) ),
inference(resolve,[status(thm)],[c_1243,c_269]) ).
cnf(c_49355,plain,
( intersection(null_class,A) = null_class
| intersection(null_class,A) = null_class ),
inference(copy,[status(thm)],[c_49354]) ).
cnf(c_1250,plain,
intersection(null_class,A) = null_class,
inference(copy,[status(thm)],[c_49355]) ).
cnf(c_49356,plain,
( intersection(A,null_class) = null_class
| null_class = intersection(A,null_class) ),
inference(resolve,[status(thm)],[c_1243,c_266]) ).
cnf(c_49357,plain,
( intersection(A,null_class) = null_class
| intersection(A,null_class) = null_class ),
inference(copy,[status(thm)],[c_49356]) ).
cnf(c_1251,plain,
intersection(A,null_class) = null_class,
inference(copy,[status(thm)],[c_49357]) ).
cnf(c_5102,plain,
domain_of(null_class) = null_class,
inference(resolve,[status(thm)],[c_366,c_1250]) ).
cnf(c_49358,plain,
( ~ member(A,null_class)
| intersection(cross_product(unordered_pair(A,A),universal_class),null_class) != null_class ),
inference(paramod,[status(thm)],[c_5102,c_225]) ).
cnf(c_49359,plain,
( ~ member(A,null_class)
| null_class != null_class ),
inference(paramod,[status(thm)],[c_1251,c_49358]) ).
cnf(c_5120,plain,
~ member(A,null_class),
inference(copy,[status(thm)],[c_49359]) ).
cnf(c_49360,plain,
( null_class = unordered_pair(universal_class,universal_class)
| member(regular(unordered_pair(universal_class,universal_class)),null_class)
| unordered_pair(universal_class,universal_class) = null_class ),
inference(paramod,[status(thm)],[c_1151,c_574]) ).
cnf(c_49361,plain,
( unordered_pair(universal_class,universal_class) = null_class
| member(regular(unordered_pair(universal_class,universal_class)),null_class)
| unordered_pair(universal_class,universal_class) = null_class ),
inference(copy,[status(thm)],[c_49360]) ).
cnf(c_49362,plain,
( member(regular(unordered_pair(universal_class,universal_class)),null_class)
| unordered_pair(universal_class,universal_class) = null_class ),
inference(copy,[status(thm)],[c_49361]) ).
cnf(c_49335,plain,
unordered_pair(universal_class,universal_class) = null_class,
inference(resolve,[status(thm)],[c_5120,c_49362]) ).
cnf(c_49363,plain,
unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)) != unordered_pair(unordered_pair(x,x),unordered_pair(x,null_class)),
inference(paramod,[status(thm)],[c_49335,c_250]) ).
cnf(c_49336,plain,
$false,
inference(copy,[status(thm)],[c_49363]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET511-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n006.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 07:50:25 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 749989 was started by sandbox2 on n006,
% 0.10/0.36 % Sat Sep 26 07:50:25 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 98.55/13.93
% 98.55/13.93 % given #500 (F,wt=29): 4669 intersection(cross_product(unordered_pair(A,A),universal_class),domain_of(flip(cross_product(intersection(cross_product(B,universal_class),C),universal_class)))) != null_class | -member(A,domain_of(domain_of(flip(cross_product(intersection(C,cross_product(B,universal_class)),universal_class))))). [para(361(a,1),225(b,2))].
% 98.55/13.93
% 98.55/13.93 % given #1000 (T,wt=11): 2133 member(null_class,intersection(universal_class,intersection(intersection(unordered_pair(null_class,A),omega),universal_class))). [resolve(904,a,463,a)].
% 98.55/13.93
% 98.55/13.93 % given #1500 (T,wt=11): 4598 member(null_class,intersection(intersection(unordered_pair(A,null_class),omega),unordered_pair(null_class,B))). [resolve(475,a,679,a)].
% 98.55/13.93
% 98.55/13.93 % given #2000 (T,wt=10): 40393 intersection(singleton_relation,complement(complement(compose(element_relation,complement(identity_relation))))) = null_class. [para(43(a,1),40390(a,1,1))].
% 98.55/13.93
% 98.55/13.93 % SZS status Unsatisfiable for theBenchmark
% 98.55/13.93
% 98.55/13.93 % Proof 1 at 10.11 (+ 3.27) seconds.
% 98.55/13.93 % Length of proof is 45.
% 98.55/13.93 % Level of proof is 11.
% 98.55/13.93 % Maximum clause weight is 17.000.
% 98.55/13.93 % Given clauses 2448.
% 98.55/13.93
% 98.55/13.93 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------