%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET151-6 : 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 : n014.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 08:35:55 AM UTC 2026
% Result : Unsatisfiable 51.35s 7.81s
% Output : CNFRefutation 51.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 16
% Syntax : Number of formulae : 83 ( 24 unt; 0 def)
% Number of atoms : 155 ( 70 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 122 ( 50 ~; 72 |; 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; 2 con; 0-3 aty)
% Number of variables : 122 ( 8 sgn 33 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_complement_of_null_class_1,axiom,
complement(null_class) != universal_class,
file('theBenchmark.p',prove_complement_of_null_class_1) ).
cnf(c_36,plain,
complement(null_class) != universal_class,
inference(clausify,[status(thm)],[prove_complement_of_null_class_1]) ).
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_44965,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_44965]) ).
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_118,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_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(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(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(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_142,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_143,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_144,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_44966,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_44966]) ).
cnf(c_231,plain,
( member(A,intersection(B,B))
| ~ member(A,B) ),
inference(factor,[status(thm)],[c_120]) ).
cnf(c_44967,plain,
( null_class = complement(A)
| ~ member(regular(complement(A)),A) ),
inference(resolve,[status(thm)],[c_119,c_76]) ).
cnf(c_258,plain,
( complement(A) = null_class
| ~ member(regular(complement(A)),A) ),
inference(copy,[status(thm)],[c_44967]) ).
cnf(c_44968,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),B) ),
inference(resolve,[status(thm)],[c_121,c_76]) ).
cnf(c_265,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),B) ),
inference(copy,[status(thm)],[c_44968]) ).
cnf(c_44969,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),A) ),
inference(resolve,[status(thm)],[c_122,c_76]) ).
cnf(c_268,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),A) ),
inference(copy,[status(thm)],[c_44969]) ).
cnf(c_303,plain,
( universal_class = A
| ~ subclass(universal_class,A) ),
inference(resolve,[status(thm)],[c_141,c_138]) ).
cnf(c_307,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_144,c_141]) ).
cnf(c_44970,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_44971,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_44970]) ).
cnf(c_365,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_44971]) ).
cnf(c_437,plain,
( member(not_subclass_element(universal_class,A),universal_class)
| universal_class = A ),
inference(resolve,[status(thm)],[c_303,c_143]) ).
cnf(c_448,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_307,c_76]) ).
cnf(c_524,plain,
( member(regular(A),intersection(universal_class,universal_class))
| null_class = A ),
inference(resolve,[status(thm)],[c_448,c_231]) ).
cnf(c_535,plain,
( member(regular(A),B)
| member(regular(A),complement(B))
| null_class = A ),
inference(resolve,[status(thm)],[c_448,c_118]) ).
cnf(c_879,plain,
( member(not_subclass_element(universal_class,A),B)
| member(not_subclass_element(universal_class,A),complement(B))
| universal_class = A ),
inference(resolve,[status(thm)],[c_437,c_118]) ).
cnf(c_44972,plain,
( complement(intersection(universal_class,universal_class)) = null_class
| null_class = complement(intersection(universal_class,universal_class)) ),
inference(resolve,[status(thm)],[c_524,c_258]) ).
cnf(c_44973,plain,
( complement(intersection(universal_class,universal_class)) = null_class
| complement(intersection(universal_class,universal_class)) = null_class ),
inference(copy,[status(thm)],[c_44972]) ).
cnf(c_1228,plain,
complement(intersection(universal_class,universal_class)) = null_class,
inference(copy,[status(thm)],[c_44973]) ).
cnf(c_1237,plain,
( ~ member(A,intersection(universal_class,universal_class))
| ~ member(A,null_class) ),
inference(paramod,[status(thm)],[c_1228,c_119]) ).
cnf(c_1242,plain,
( null_class = A
| ~ member(regular(A),null_class) ),
inference(resolve,[status(thm)],[c_1237,c_524]) ).
cnf(c_44974,plain,
( intersection(null_class,A) = null_class
| null_class = intersection(null_class,A) ),
inference(resolve,[status(thm)],[c_1242,c_268]) ).
cnf(c_44975,plain,
( intersection(null_class,A) = null_class
| intersection(null_class,A) = null_class ),
inference(copy,[status(thm)],[c_44974]) ).
cnf(c_1249,plain,
intersection(null_class,A) = null_class,
inference(copy,[status(thm)],[c_44975]) ).
cnf(c_44976,plain,
( intersection(A,null_class) = null_class
| null_class = intersection(A,null_class) ),
inference(resolve,[status(thm)],[c_1242,c_265]) ).
cnf(c_44977,plain,
( intersection(A,null_class) = null_class
| intersection(A,null_class) = null_class ),
inference(copy,[status(thm)],[c_44976]) ).
cnf(c_1250,plain,
intersection(A,null_class) = null_class,
inference(copy,[status(thm)],[c_44977]) ).
cnf(c_5101,plain,
domain_of(null_class) = null_class,
inference(resolve,[status(thm)],[c_365,c_1249]) ).
cnf(c_44978,plain,
( ~ member(A,null_class)
| intersection(cross_product(unordered_pair(A,A),universal_class),null_class) != null_class ),
inference(paramod,[status(thm)],[c_5101,c_225]) ).
cnf(c_44979,plain,
( ~ member(A,null_class)
| null_class != null_class ),
inference(paramod,[status(thm)],[c_1250,c_44978]) ).
cnf(c_5119,plain,
~ member(A,null_class),
inference(copy,[status(thm)],[c_44979]) ).
cnf(c_44980,plain,
( complement(complement(A)) = null_class
| member(regular(complement(complement(A))),A)
| null_class = complement(complement(A)) ),
inference(resolve,[status(thm)],[c_535,c_258]) ).
cnf(c_44981,plain,
( complement(complement(A)) = null_class
| member(regular(complement(complement(A))),A)
| complement(complement(A)) = null_class ),
inference(copy,[status(thm)],[c_44980]) ).
cnf(c_20422,plain,
( member(regular(complement(complement(A))),A)
| complement(complement(A)) = null_class ),
inference(copy,[status(thm)],[c_44981]) ).
cnf(c_40543,plain,
complement(complement(null_class)) = null_class,
inference(resolve,[status(thm)],[c_20422,c_5119]) ).
cnf(c_44982,plain,
( member(not_subclass_element(universal_class,A),complement(null_class))
| member(not_subclass_element(universal_class,A),null_class)
| universal_class = A ),
inference(paramod,[status(thm)],[c_40543,c_879]) ).
cnf(c_44956,plain,
( member(not_subclass_element(universal_class,A),complement(null_class))
| universal_class = A ),
inference(resolve,[status(thm)],[c_5119,c_44982]) ).
cnf(c_44983,plain,
( subclass(universal_class,complement(null_class))
| universal_class = complement(null_class) ),
inference(resolve,[status(thm)],[c_44956,c_142]) ).
cnf(c_44984,plain,
( subclass(universal_class,complement(null_class))
| complement(null_class) = universal_class ),
inference(copy,[status(thm)],[c_44983]) ).
cnf(c_44962,plain,
subclass(universal_class,complement(null_class)),
inference(resolve,[status(thm)],[c_36,c_44984]) ).
cnf(c_44985,plain,
universal_class = complement(null_class),
inference(resolve,[status(thm)],[c_44962,c_303]) ).
cnf(c_44986,plain,
complement(null_class) = universal_class,
inference(copy,[status(thm)],[c_44985]) ).
cnf(c_44964,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_44986]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET151-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n014.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 07:13:46 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.35 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.35 % Process 2487208 was started by sandbox2 on n014,
% 0.09/0.35 % Sat Sep 26 07:13:46 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.36
% 0.09/0.36 % From the command line: assign(max_seconds, 300).
% 51.35/7.81
% 51.35/7.81 % given #500 (F,wt=29): 4668 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(360(a,1),225(b,2))].
% 51.35/7.81
% 51.35/7.81 % given #1000 (T,wt=11): 2132 member(null_class,intersection(universal_class,intersection(intersection(unordered_pair(null_class,A),omega),universal_class))). [resolve(903,a,462,a)].
% 51.35/7.81
% 51.35/7.81 % given #1500 (T,wt=11): 4597 member(null_class,intersection(intersection(unordered_pair(A,null_class),omega),unordered_pair(null_class,B))). [resolve(474,a,678,a)].
% 51.35/7.81
% 51.35/7.81 % given #2000 (T,wt=10): 40392 intersection(singleton_relation,complement(complement(compose(element_relation,complement(identity_relation))))) = null_class. [para(43(a,1),40389(a,1,1))].
% 51.35/7.81
% 51.35/7.81 % SZS status Unsatisfiable for theBenchmark
% 51.35/7.81
% 51.35/7.81 % Proof 1 at 5.54 (+ 1.84) seconds.
% 51.35/7.81 % Length of proof is 45.
% 51.35/7.81 % Level of proof is 13.
% 51.35/7.81 % Maximum clause weight is 17.000.
% 51.35/7.81 % Given clauses 2239.
% 51.35/7.81
% 51.35/7.81 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------