%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET517-6 : 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 08:36:26 AM UTC 2026
% Result : Unsatisfiable 3.46s 0.88s
% Output : CNFRefutation 3.46s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 18
% Syntax : Number of formulae : 97 ( 34 unt; 0 def)
% Number of atoms : 171 ( 83 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 117 ( 43 ~; 74 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 3 con; 0-3 aty)
% Number of variables : 127 ( 13 sgn 35 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_not_singleton_of_set_2,axiom,
member_of(x) = x,
file('theBenchmark.p',prove_not_singleton_of_set_2) ).
cnf(c_36,plain,
member_of(x) = x,
inference(clausify,[status(thm)],[prove_not_singleton_of_set_2]) ).
fof(prove_not_singleton_of_set_1,axiom,
singleton(member_of(x)) = x,
file('theBenchmark.p',prove_not_singleton_of_set_1) ).
cnf(c_37,plain,
singleton(member_of(x)) = x,
inference(clausify,[status(thm)],[prove_not_singleton_of_set_1]) ).
cnf(c_38,plain,
singleton(x) = x,
inference(paramod,[status(thm)],[c_36,c_37]) ).
fof(regularity2,axiom,
! [VAR_0] :
( intersection(VAR_0,regular(VAR_0)) = null_class
| VAR_0 = null_class ),
file('theBenchmark.p',regularity2) ).
cnf(c_75,plain,
( intersection(A,regular(A)) = null_class
| A = null_class ),
inference(clausify,[status(thm)],[regularity2]) ).
cnf(c_76,plain,
( intersection(A,regular(A)) = null_class
| null_class = A ),
inference(copy,[status(thm)],[c_75]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_77,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_78,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_77]) ).
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_111,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_112,plain,
intersection(cross_product(A,B),C) = restrict(C,A,B),
inference(clausify,[status(thm)],[restriction2]) ).
cnf(c_113,plain,
restrict(A,B,C) = intersection(cross_product(B,C),A),
inference(copy,[status(thm)],[c_112]) ).
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_114,plain,
intersection(A,cross_product(B,C)) = restrict(A,B,C),
inference(clausify,[status(thm)],[restriction1]) ).
cnf(c_1526,plain,
intersection(A,cross_product(B,C)) = intersection(cross_product(B,C),A),
inference(paramod,[status(thm)],[c_113,c_114]) ).
cnf(c_115,plain,
intersection(cross_product(A,B),C) = intersection(C,cross_product(A,B)),
inference(copy,[status(thm)],[c_1526]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_121,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_122,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_123,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_124,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_134,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_135,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_134]) ).
fof(unordered_pairs_in_universal,axiom,
! [VAR_0,VAR_1] : member(unordered_pair(VAR_0,VAR_1),universal_class),
file('theBenchmark.p',unordered_pairs_in_universal) ).
cnf(c_136,plain,
member(unordered_pair(A,B),universal_class),
inference(clausify,[status(thm)],[unordered_pairs_in_universal]) ).
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_138,plain,
( member(A,unordered_pair(A,B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[unordered_pair2]) ).
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_139,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_143,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
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_145,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_146,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_1527,plain,
( ~ member(B,domain_of(A))
| restrict(A,unordered_pair(B,B),universal_class) != null_class ),
inference(paramod,[status(thm)],[c_135,c_111]) ).
cnf(c_227,plain,
( ~ member(A,domain_of(B))
| intersection(cross_product(unordered_pair(A,A),universal_class),B) != null_class ),
inference(paramod,[status(thm)],[c_113,c_1527]) ).
cnf(c_233,plain,
( member(A,intersection(B,B))
| ~ member(A,B) ),
inference(factor,[status(thm)],[c_122]) ).
cnf(c_253,plain,
unordered_pair(x,x) = x,
inference(paramod,[status(thm)],[c_135,c_38]) ).
cnf(c_1528,plain,
( null_class = complement(A)
| ~ member(regular(complement(A)),A) ),
inference(resolve,[status(thm)],[c_121,c_78]) ).
cnf(c_261,plain,
( complement(A) = null_class
| ~ member(regular(complement(A)),A) ),
inference(copy,[status(thm)],[c_1528]) ).
cnf(c_1529,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),B) ),
inference(resolve,[status(thm)],[c_123,c_78]) ).
cnf(c_271,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),B) ),
inference(copy,[status(thm)],[c_1529]) ).
cnf(c_1530,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),A) ),
inference(resolve,[status(thm)],[c_124,c_78]) ).
cnf(c_274,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),A) ),
inference(copy,[status(thm)],[c_1530]) ).
cnf(c_315,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_146,c_143]) ).
cnf(c_422,plain,
( ~ member(B,domain_of(A))
| intersection(A,cross_product(unordered_pair(B,B),universal_class)) != null_class ),
inference(paramod,[status(thm)],[c_115,c_227]) ).
cnf(c_454,plain,
member(x,universal_class),
inference(paramod,[status(thm)],[c_253,c_136]) ).
cnf(c_1531,plain,
( A = x
| A = x
| ~ member(A,x) ),
inference(paramod,[status(thm)],[c_253,c_139]) ).
cnf(c_1532,plain,
( A = x
| x = A
| ~ member(A,x) ),
inference(copy,[status(thm)],[c_1531]) ).
cnf(c_1533,plain,
( x = A
| x = A
| ~ member(A,x) ),
inference(copy,[status(thm)],[c_1532]) ).
cnf(c_455,plain,
( x = A
| ~ member(A,x) ),
inference(copy,[status(thm)],[c_1533]) ).
cnf(c_521,plain,
member(x,unordered_pair(x,A)),
inference(resolve,[status(thm)],[c_454,c_138]) ).
cnf(c_528,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_315,c_78]) ).
cnf(c_1534,plain,
( null_class = x
| x = regular(x) ),
inference(resolve,[status(thm)],[c_455,c_78]) ).
cnf(c_1535,plain,
( null_class = x
| regular(x) = x ),
inference(copy,[status(thm)],[c_1534]) ).
cnf(c_582,plain,
( x = null_class
| regular(x) = x ),
inference(copy,[status(thm)],[c_1535]) ).
cnf(c_659,plain,
member(x,x),
inference(paramod,[status(thm)],[c_253,c_521]) ).
cnf(c_664,plain,
member(x,intersection(x,x)),
inference(resolve,[status(thm)],[c_659,c_233]) ).
cnf(c_665,plain,
( member(x,A)
| ~ subclass(x,A) ),
inference(resolve,[status(thm)],[c_659,c_146]) ).
cnf(c_678,plain,
( member(not_subclass_element(x,A),x)
| member(x,A) ),
inference(resolve,[status(thm)],[c_665,c_145]) ).
cnf(c_1536,plain,
( complement(universal_class) = null_class
| null_class = complement(universal_class) ),
inference(resolve,[status(thm)],[c_528,c_261]) ).
cnf(c_1537,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(copy,[status(thm)],[c_1536]) ).
cnf(c_918,plain,
complement(universal_class) = null_class,
inference(copy,[status(thm)],[c_1537]) ).
cnf(c_1538,plain,
( ~ member(regular(A),complement(universal_class))
| null_class = A ),
inference(resolve,[status(thm)],[c_528,c_121]) ).
cnf(c_939,plain,
( ~ member(regular(A),null_class)
| null_class = A ),
inference(paramod,[status(thm)],[c_918,c_1538]) ).
cnf(c_1539,plain,
( intersection(x,x) = null_class
| null_class = x
| x = null_class ),
inference(paramod,[status(thm)],[c_582,c_76]) ).
cnf(c_1540,plain,
( intersection(x,x) = null_class
| x = null_class
| x = null_class ),
inference(copy,[status(thm)],[c_1539]) ).
cnf(c_1019,plain,
( intersection(x,x) = null_class
| x = null_class ),
inference(copy,[status(thm)],[c_1540]) ).
cnf(c_1541,plain,
( intersection(null_class,A) = null_class
| null_class = intersection(null_class,A) ),
inference(resolve,[status(thm)],[c_939,c_274]) ).
cnf(c_1542,plain,
( intersection(null_class,A) = null_class
| intersection(null_class,A) = null_class ),
inference(copy,[status(thm)],[c_1541]) ).
cnf(c_1063,plain,
intersection(null_class,A) = null_class,
inference(copy,[status(thm)],[c_1542]) ).
cnf(c_1543,plain,
( intersection(A,null_class) = null_class
| null_class = intersection(A,null_class) ),
inference(resolve,[status(thm)],[c_939,c_271]) ).
cnf(c_1544,plain,
( intersection(A,null_class) = null_class
| intersection(A,null_class) = null_class ),
inference(copy,[status(thm)],[c_1543]) ).
cnf(c_1064,plain,
intersection(A,null_class) = null_class,
inference(copy,[status(thm)],[c_1544]) ).
cnf(c_1071,plain,
~ member(A,domain_of(null_class)),
inference(resolve,[status(thm)],[c_1063,c_422]) ).
cnf(c_1545,plain,
null_class = domain_of(null_class),
inference(resolve,[status(thm)],[c_1071,c_78]) ).
cnf(c_1075,plain,
domain_of(null_class) = null_class,
inference(copy,[status(thm)],[c_1545]) ).
cnf(c_1076,plain,
~ member(A,null_class),
inference(paramod,[status(thm)],[c_1075,c_1071]) ).
cnf(c_1478,plain,
( member(not_subclass_element(x,A),intersection(x,x))
| member(x,A) ),
inference(resolve,[status(thm)],[c_678,c_233]) ).
cnf(c_1546,plain,
( member(x,null_class)
| x = null_class ),
inference(paramod,[status(thm)],[c_1019,c_664]) ).
cnf(c_1508,plain,
x = null_class,
inference(resolve,[status(thm)],[c_1076,c_1546]) ).
cnf(c_1547,plain,
( member(not_subclass_element(x,A),intersection(x,x))
| member(null_class,A) ),
inference(paramod,[status(thm)],[c_1508,c_1478]) ).
cnf(c_1548,plain,
( member(not_subclass_element(null_class,A),intersection(x,x))
| member(null_class,A) ),
inference(paramod,[status(thm)],[c_1508,c_1547]) ).
cnf(c_1549,plain,
( member(not_subclass_element(null_class,A),intersection(null_class,x))
| member(null_class,A) ),
inference(paramod,[status(thm)],[c_1508,c_1548]) ).
cnf(c_1550,plain,
( member(not_subclass_element(null_class,A),intersection(null_class,null_class))
| member(null_class,A) ),
inference(paramod,[status(thm)],[c_1508,c_1549]) ).
cnf(c_1551,plain,
( member(not_subclass_element(null_class,A),null_class)
| member(null_class,A) ),
inference(paramod,[status(thm)],[c_1064,c_1550]) ).
cnf(c_1524,plain,
member(null_class,A),
inference(resolve,[status(thm)],[c_1076,c_1551]) ).
cnf(c_1525,plain,
$false,
inference(resolve,[status(thm)],[c_1524,c_1076]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET517-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n014.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 26 07:50:47 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2558829 was started by sandbox2 on n014,
% 0.09/0.37 % Sat Sep 26 07:50:47 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 3.46/0.88
% 3.46/0.88 % SZS status Unsatisfiable for theBenchmark
% 3.46/0.88
% 3.46/0.88 % Proof 1 at 0.41 (+ 0.07) seconds.
% 3.46/0.88 % Length of proof is 53.
% 3.46/0.88 % Level of proof is 11.
% 3.46/0.88 % Maximum clause weight is 33.000.
% 3.46/0.88 % Given clauses 327.
% 3.46/0.88
% 3.46/0.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------