%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET134-6 : 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 : n009.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 08:35:52 AM UTC 2026
% Result : Unsatisfiable 0.91s 0.49s
% Output : CNFRefutation 0.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 31 unt; 0 def)
% Number of atoms : 63 ( 29 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 34 ( 17 ~; 17 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 5 con; 0-2 aty)
% Number of variables : 42 ( 7 sgn 15 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_2_to_member_of_triple_2,axiom,
set_builder(u,set_builder(y,set_builder(z,null_class))) = null_class,
file('theBenchmark.p',prove_corollary_2_to_member_of_triple_2) ).
cnf(c_34,plain,
set_builder(u,set_builder(y,set_builder(z,null_class))) = null_class,
inference(clausify,[status(thm)],[prove_corollary_2_to_member_of_triple_2]) ).
fof(prove_corollary_2_to_member_of_triple_1,axiom,
member(u,universal_class),
file('theBenchmark.p',prove_corollary_2_to_member_of_triple_1) ).
cnf(c_35,plain,
member(u,universal_class),
inference(clausify,[status(thm)],[prove_corollary_2_to_member_of_triple_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_36,plain,
union(singleton(A),B) = set_builder(A,B),
inference(clausify,[status(thm)],[definition_of_set_builder]) ).
cnf(c_37,plain,
set_builder(A,B) = union(singleton(A),B),
inference(copy,[status(thm)],[c_36]) ).
fof(regularity2,axiom,
! [VAR_0] :
( intersection(VAR_0,regular(VAR_0)) = null_class
| VAR_0 = null_class ),
file('theBenchmark.p',regularity2) ).
cnf(c_52,plain,
( intersection(A,regular(A)) = null_class
| A = null_class ),
inference(clausify,[status(thm)],[regularity2]) ).
cnf(c_53,plain,
( intersection(A,regular(A)) = null_class
| null_class = A ),
inference(copy,[status(thm)],[c_52]) ).
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_95,plain,
complement(intersection(complement(A),complement(B))) = union(A,B),
inference(clausify,[status(thm)],[union]) ).
cnf(c_96,plain,
union(A,B) = complement(intersection(complement(A),complement(B))),
inference(copy,[status(thm)],[c_95]) ).
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_97,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_98,plain,
( ~ member(A,B)
| ~ member(A,complement(B)) ),
inference(clausify,[status(thm)],[complement1]) ).
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_101,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_111,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_112,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_111]) ).
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_114,plain,
( member(A,unordered_pair(B,A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair3]) ).
cnf(c_852,plain,
set_builder(u,set_builder(y,union(singleton(z),null_class))) = null_class,
inference(paramod,[status(thm)],[c_37,c_34]) ).
cnf(c_853,plain,
set_builder(u,set_builder(y,union(unordered_pair(z,z),null_class))) = null_class,
inference(paramod,[status(thm)],[c_112,c_852]) ).
cnf(c_854,plain,
set_builder(u,set_builder(y,complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))) = null_class,
inference(paramod,[status(thm)],[c_96,c_853]) ).
cnf(c_855,plain,
set_builder(u,union(singleton(y),complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))) = null_class,
inference(paramod,[status(thm)],[c_37,c_854]) ).
cnf(c_856,plain,
set_builder(u,union(unordered_pair(y,y),complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))) = null_class,
inference(paramod,[status(thm)],[c_112,c_855]) ).
cnf(c_857,plain,
set_builder(u,complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))) = null_class,
inference(paramod,[status(thm)],[c_96,c_856]) ).
cnf(c_858,plain,
union(singleton(u),complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))) = null_class,
inference(paramod,[status(thm)],[c_37,c_857]) ).
cnf(c_859,plain,
union(unordered_pair(u,u),complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))) = null_class,
inference(paramod,[status(thm)],[c_112,c_858]) ).
cnf(c_157,plain,
complement(intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class))))))))) = null_class,
inference(paramod,[status(thm)],[c_96,c_859]) ).
cnf(c_207,plain,
( member(u,A)
| member(u,complement(A)) ),
inference(resolve,[status(thm)],[c_97,c_35]) ).
cnf(c_210,plain,
~ member(u,complement(universal_class)),
inference(resolve,[status(thm)],[c_98,c_35]) ).
cnf(c_231,plain,
member(u,unordered_pair(A,u)),
inference(resolve,[status(thm)],[c_114,c_35]) ).
cnf(c_356,plain,
~ member(u,intersection(complement(universal_class),A)),
inference(resolve,[status(thm)],[c_101,c_210]) ).
cnf(c_385,plain,
~ member(u,complement(unordered_pair(A,u))),
inference(resolve,[status(thm)],[c_98,c_231]) ).
cnf(c_860,plain,
( ~ member(u,null_class)
| null_class = complement(universal_class) ),
inference(paramod,[status(thm)],[c_53,c_356]) ).
cnf(c_481,plain,
( ~ member(u,null_class)
| complement(universal_class) = null_class ),
inference(copy,[status(thm)],[c_860]) ).
cnf(c_692,plain,
~ member(u,intersection(complement(unordered_pair(A,u)),B)),
inference(resolve,[status(thm)],[c_101,c_385]) ).
cnf(c_861,plain,
( member(u,intersection(complement(unordered_pair(u,u)),complement(complement(intersection(complement(unordered_pair(y,y)),complement(complement(intersection(complement(unordered_pair(z,z)),complement(null_class)))))))))
| member(u,null_class) ),
inference(paramod,[status(thm)],[c_157,c_207]) ).
cnf(c_718,plain,
member(u,null_class),
inference(resolve,[status(thm)],[c_692,c_861]) ).
cnf(c_719,plain,
complement(universal_class) = null_class,
inference(resolve,[status(thm)],[c_718,c_481]) ).
cnf(c_862,plain,
~ member(u,null_class),
inference(paramod,[status(thm)],[c_719,c_210]) ).
cnf(c_851,plain,
$false,
inference(resolve,[status(thm)],[c_718,c_862]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET134-6 : 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 : n009.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 07:11:45 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 3650571 was started by sandbox2 on n009,
% 0.09/0.35 % Sat Sep 26 07:11:45 2026
% 0.09/0.35 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.13/0.36
% 0.13/0.36 % From the command line: assign(max_seconds, 300).
% 0.91/0.49
% 0.91/0.49 % SZS status Unsatisfiable for theBenchmark
% 0.91/0.49
% 0.91/0.49 % Proof 1 at 0.09 (+ 0.03) seconds.
% 0.91/0.49 % Length of proof is 25.
% 0.91/0.49 % Level of proof is 6.
% 0.91/0.49 % Maximum clause weight is 24.000.
% 0.91/0.49 % Given clauses 151.
% 0.91/0.49
% 0.91/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------