%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET510-6 : 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 : 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 11.44s 3.72s
% Output : CNFRefutation 11.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 16
% Syntax : Number of formulae : 88 ( 24 unt; 0 def)
% Number of atoms : 164 ( 95 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 128 ( 52 ~; 76 |; 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 : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 123 ( 8 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_to_singleton_is_null_class_1,axiom,
singleton(universal_class) != null_class,
file('theBenchmark.p',prove_corollary_to_singleton_is_null_class_1) ).
cnf(c_36,plain,
singleton(universal_class) != null_class,
inference(clausify,[status(thm)],[prove_corollary_to_singleton_is_null_class_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_12171,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_12171]) ).
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(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(subclass_implies_equal,axiom,
! [VAR_0,VAR_1] :
( VAR_0 = VAR_1
| ~ subclass(VAR_1,VAR_0)
| ~ subclass(VAR_0,VAR_1) ),
file('theBenchmark.p',subclass_implies_equal) ).
cnf(c_138,plain,
( A = B
| ~ subclass(B,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_implies_equal]) ).
fof(equal_implies_subclass2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_1,VAR_0)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',equal_implies_subclass2) ).
cnf(c_139,plain,
( subclass(B,A)
| A != B ),
inference(clausify,[status(thm)],[equal_implies_subclass2]) ).
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_12172,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_12172]) ).
cnf(c_231,plain,
( member(A,intersection(B,B))
| ~ member(A,B) ),
inference(factor,[status(thm)],[c_120]) ).
cnf(c_251,plain,
unordered_pair(universal_class,universal_class) != null_class,
inference(paramod,[status(thm)],[c_133,c_36]) ).
cnf(c_12173,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_12173]) ).
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_12174,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_12174]) ).
cnf(c_12175,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_12175]) ).
cnf(c_12176,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_12176]) ).
cnf(c_282,plain,
( unordered_pair(A,A) = null_class
| regular(unordered_pair(A,A)) = A ),
inference(factor,[status(thm)],[c_281]) ).
cnf(c_304,plain,
( universal_class = A
| ~ subclass(universal_class,A) ),
inference(resolve,[status(thm)],[c_141,c_138]) ).
cnf(c_308,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_144,c_141]) ).
cnf(c_12177,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_12178,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_12177]) ).
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_12178]) ).
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_12179,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_12179]) ).
cnf(c_1150,plain,
( subclass(A,regular(unordered_pair(A,A)))
| unordered_pair(A,A) = null_class ),
inference(resolve,[status(thm)],[c_282,c_139]) ).
cnf(c_12180,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_12181,plain,
( complement(intersection(universal_class,universal_class)) = null_class
| complement(intersection(universal_class,universal_class)) = null_class ),
inference(copy,[status(thm)],[c_12180]) ).
cnf(c_1229,plain,
complement(intersection(universal_class,universal_class)) = null_class,
inference(copy,[status(thm)],[c_12181]) ).
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_12182,plain,
( intersection(null_class,A) = null_class
| null_class = intersection(null_class,A) ),
inference(resolve,[status(thm)],[c_1243,c_269]) ).
cnf(c_12183,plain,
( intersection(null_class,A) = null_class
| intersection(null_class,A) = null_class ),
inference(copy,[status(thm)],[c_12182]) ).
cnf(c_1250,plain,
intersection(null_class,A) = null_class,
inference(copy,[status(thm)],[c_12183]) ).
cnf(c_12184,plain,
( intersection(A,null_class) = null_class
| null_class = intersection(A,null_class) ),
inference(resolve,[status(thm)],[c_1243,c_266]) ).
cnf(c_12185,plain,
( intersection(A,null_class) = null_class
| intersection(A,null_class) = null_class ),
inference(copy,[status(thm)],[c_12184]) ).
cnf(c_1251,plain,
intersection(A,null_class) = null_class,
inference(copy,[status(thm)],[c_12185]) ).
cnf(c_5102,plain,
domain_of(null_class) = null_class,
inference(resolve,[status(thm)],[c_366,c_1250]) ).
cnf(c_12186,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_12187,plain,
( ~ member(A,null_class)
| null_class != null_class ),
inference(paramod,[status(thm)],[c_1251,c_12186]) ).
cnf(c_5120,plain,
~ member(A,null_class),
inference(copy,[status(thm)],[c_12187]) ).
cnf(c_12188,plain,
( universal_class = regular(unordered_pair(universal_class,universal_class))
| unordered_pair(universal_class,universal_class) = null_class ),
inference(resolve,[status(thm)],[c_1150,c_304]) ).
cnf(c_12189,plain,
( regular(unordered_pair(universal_class,universal_class)) = universal_class
| unordered_pair(universal_class,universal_class) = null_class ),
inference(copy,[status(thm)],[c_12188]) ).
cnf(c_12159,plain,
regular(unordered_pair(universal_class,universal_class)) = universal_class,
inference(resolve,[status(thm)],[c_251,c_12189]) ).
cnf(c_12190,plain,
( intersection(unordered_pair(universal_class,universal_class),universal_class) = null_class
| null_class = unordered_pair(universal_class,universal_class) ),
inference(paramod,[status(thm)],[c_12159,c_74]) ).
cnf(c_12191,plain,
( intersection(unordered_pair(universal_class,universal_class),universal_class) = null_class
| unordered_pair(universal_class,universal_class) = null_class ),
inference(copy,[status(thm)],[c_12190]) ).
cnf(c_12164,plain,
intersection(unordered_pair(universal_class,universal_class),universal_class) = null_class,
inference(resolve,[status(thm)],[c_251,c_12191]) ).
cnf(c_12192,plain,
( null_class = unordered_pair(universal_class,universal_class)
| member(universal_class,intersection(unordered_pair(universal_class,universal_class),universal_class)) ),
inference(paramod,[status(thm)],[c_12159,c_574]) ).
cnf(c_12193,plain,
( null_class = unordered_pair(universal_class,universal_class)
| member(universal_class,null_class) ),
inference(paramod,[status(thm)],[c_12164,c_12192]) ).
cnf(c_12194,plain,
( unordered_pair(universal_class,universal_class) = null_class
| member(universal_class,null_class) ),
inference(copy,[status(thm)],[c_12193]) ).
cnf(c_12195,plain,
unordered_pair(universal_class,universal_class) = null_class,
inference(resolve,[status(thm)],[c_5120,c_12194]) ).
cnf(c_12170,plain,
$false,
inference(resolve,[status(thm)],[c_251,c_12195]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET510-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n006.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 07:50:10 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.37 % Process 748845 was started by sandbox on n006,
% 0.11/0.37 % Sat Sep 26 07:50:10 2026
% 0.11/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 11.44/3.72
% 11.44/3.72 % 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))].
% 11.44/3.72
% 11.44/3.72 % SZS status Unsatisfiable for theBenchmark
% 11.44/3.72
% 11.44/3.72 % Proof 1 at 1.26 (+ 0.25) seconds.
% 11.44/3.72 % Length of proof is 47.
% 11.44/3.72 % Level of proof is 10.
% 11.44/3.72 % Maximum clause weight is 17.000.
% 11.44/3.72 % Given clauses 701.
% 11.44/3.72
% 11.44/3.72 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------