%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET137-6 : 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 : n013.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 08:35:53 AM UTC 2026
% Result : Unsatisfiable 11.33s 12.40s
% Output : CNFRefutation 11.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 13
% Syntax : Number of formulae : 58 ( 34 unt; 0 def)
% Number of atoms : 88 ( 31 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 26 ~; 30 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 62 ( 8 sgn 22 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_member_of_triple_kludge1_4,axiom,
set_builder(u,set_builder(v,set_builder(w,null_class))) = null_class,
file('theBenchmark.p',prove_member_of_triple_kludge1_4) ).
cnf(c_34,plain,
set_builder(u,set_builder(v,set_builder(w,null_class))) = null_class,
inference(clausify,[status(thm)],[prove_member_of_triple_kludge1_4]) ).
fof(prove_member_of_triple_kludge1_1,axiom,
member(u,x),
file('theBenchmark.p',prove_member_of_triple_kludge1_1) ).
cnf(c_37,plain,
member(u,x),
inference(clausify,[status(thm)],[prove_member_of_triple_kludge1_1]) ).
fof(definition_of_set_builder,axiom,
! [VAR_0,VAR_1] : union(singleton(VAR_0),VAR_1) = set_builder(VAR_0,VAR_1),
file('theBenchmark.p',definition_of_set_builder) ).
cnf(c_38,plain,
union(singleton(A),B) = set_builder(A,B),
inference(clausify,[status(thm)],[definition_of_set_builder]) ).
cnf(c_39,plain,
set_builder(A,B) = union(singleton(A),B),
inference(copy,[status(thm)],[c_38]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_56,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_57,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_56]) ).
fof(union,axiom,
! [VAR_0,VAR_1] : complement(intersection(complement(VAR_0),complement(VAR_1))) = union(VAR_0,VAR_1),
file('theBenchmark.p',union) ).
cnf(c_97,plain,
complement(intersection(complement(A),complement(B))) = union(A,B),
inference(clausify,[status(thm)],[union]) ).
cnf(c_98,plain,
union(A,B) = complement(intersection(complement(A),complement(B))),
inference(copy,[status(thm)],[c_97]) ).
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_99,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_100,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_101,plain,
( member(A,intersection(B,C))
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[intersection3]) ).
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_103,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_113,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_114,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_113]) ).
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_117,plain,
( member(A,unordered_pair(A,B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair2]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_122,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_125,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_5788,plain,
set_builder(u,set_builder(v,union(singleton(w),null_class))) = null_class,
inference(paramod,[status(thm)],[c_39,c_34]) ).
cnf(c_5789,plain,
set_builder(u,set_builder(v,union(unordered_pair(w,w),null_class))) = null_class,
inference(paramod,[status(thm)],[c_114,c_5788]) ).
cnf(c_5790,plain,
set_builder(u,set_builder(v,complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))) = null_class,
inference(paramod,[status(thm)],[c_98,c_5789]) ).
cnf(c_5791,plain,
set_builder(u,union(singleton(v),complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))) = null_class,
inference(paramod,[status(thm)],[c_39,c_5790]) ).
cnf(c_5792,plain,
set_builder(u,union(unordered_pair(v,v),complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))) = null_class,
inference(paramod,[status(thm)],[c_114,c_5791]) ).
cnf(c_5793,plain,
set_builder(u,complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))) = null_class,
inference(paramod,[status(thm)],[c_98,c_5792]) ).
cnf(c_5794,plain,
union(singleton(u),complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))) = null_class,
inference(paramod,[status(thm)],[c_39,c_5793]) ).
cnf(c_5795,plain,
union(unordered_pair(u,u),complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))) = null_class,
inference(paramod,[status(thm)],[c_114,c_5794]) ).
cnf(c_159,plain,
complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))) = null_class,
inference(paramod,[status(thm)],[c_98,c_5795]) ).
cnf(c_189,plain,
( member(A,intersection(B,B))
| ~ member(A,B) ),
inference(factor,[status(thm)],[c_101]) ).
cnf(c_5796,plain,
( null_class = complement(A)
| ~ member(regular(complement(A)),A) ),
inference(resolve,[status(thm)],[c_100,c_57]) ).
cnf(c_209,plain,
( complement(A) = null_class
| ~ member(regular(complement(A)),A) ),
inference(copy,[status(thm)],[c_5796]) ).
cnf(c_263,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_125,c_122]) ).
cnf(c_321,plain,
member(u,intersection(x,x)),
inference(resolve,[status(thm)],[c_189,c_37]) ).
cnf(c_481,plain,
member(u,universal_class),
inference(resolve,[status(thm)],[c_263,c_321]) ).
cnf(c_482,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_263,c_57]) ).
cnf(c_573,plain,
member(u,unordered_pair(u,A)),
inference(resolve,[status(thm)],[c_481,c_117]) ).
cnf(c_577,plain,
( member(u,A)
| member(u,complement(A)) ),
inference(resolve,[status(thm)],[c_481,c_99]) ).
cnf(c_578,plain,
~ member(u,complement(universal_class)),
inference(resolve,[status(thm)],[c_100,c_481]) ).
cnf(c_769,plain,
~ member(u,complement(unordered_pair(u,A))),
inference(resolve,[status(thm)],[c_100,c_573]) ).
cnf(c_5797,plain,
( complement(universal_class) = null_class
| null_class = complement(universal_class) ),
inference(resolve,[status(thm)],[c_482,c_209]) ).
cnf(c_5798,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(copy,[status(thm)],[c_5797]) ).
cnf(c_1084,plain,
complement(universal_class) = null_class,
inference(copy,[status(thm)],[c_5798]) ).
cnf(c_1235,plain,
~ member(u,null_class),
inference(paramod,[status(thm)],[c_1084,c_578]) ).
cnf(c_5799,plain,
( member(u,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class)))))))))
| member(u,null_class) ),
inference(paramod,[status(thm)],[c_159,c_577]) ).
cnf(c_1356,plain,
member(u,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(v,v)),complement(complement(intersection(complement(unordered_pair(w,w)),complement(null_class))))))))),
inference(resolve,[status(thm)],[c_1235,c_5799]) ).
cnf(c_5786,plain,
~ member(u,intersection(complement(unordered_pair(u,A)),B)),
inference(resolve,[status(thm)],[c_103,c_769]) ).
cnf(c_5787,plain,
$false,
inference(resolve,[status(thm)],[c_5786,c_1356]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET137-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.07 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/10.88 % Computer : n013.cluster.edu
% 0.19/10.88 % Model : x86_64 x86_64
% 0.19/10.88 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/10.88 % Memory : 8046.5625MB
% 0.19/10.88 % OS : Linux 6.8.0-71-generic
% 0.19/10.88 % CPULimit : 300
% 0.19/10.89 % WCLimit : 300
% 0.19/10.89 % DateTime : Sat Sep 26 07:11:55 UTC 2026
% 0.19/10.89 % CPUTime :
% 0.19/10.89 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/10.89 % Process 2187812 was started by sandbox2 on n013,
% 0.19/10.89 % Sat Sep 26 07:11:55 2026
% 0.19/10.89 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.24/10.90
% 0.24/10.90 % From the command line: assign(max_seconds, 300).
% 11.33/12.40
% 11.33/12.40 % given #500 (F,wt=6): 586 -member(null_class,complement(intersection(universal_class,universal_class))). [ur(100,b,486,a)].
% 11.33/12.40
% 11.33/12.40 % SZS status Unsatisfiable for theBenchmark
% 11.33/12.40
% 11.33/12.40 % Proof 1 at 1.03 (+ 0.29) seconds.
% 11.33/12.40 % Length of proof is 33.
% 11.33/12.40 % Level of proof is 7.
% 11.33/12.40 % Maximum clause weight is 24.000.
% 11.33/12.40 % Given clauses 563.
% 11.33/12.40
% 11.33/12.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------