%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET506-6 : 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 : n008.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 08:36:24 AM UTC 2026
% Result : Unsatisfiable 0.10s 0.48s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 15
% Syntax : Number of formulae : 63 ( 35 unt; 0 def)
% Number of atoms : 95 ( 34 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 61 ( 29 ~; 32 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-3 aty)
% Number of variables : 77 ( 3 sgn 23 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(inductive1,axiom,
! [VAR_0] :
( member(null_class,VAR_0)
| ~ inductive(VAR_0) ),
file('theBenchmark.p',inductive1) ).
cnf(c_3,plain,
( member(null_class,A)
| ~ inductive(A) ),
inference(clausify,[status(thm)],[inductive1]) ).
fof(omega_is_inductive1,axiom,
inductive(omega),
file('theBenchmark.p',omega_is_inductive1) ).
cnf(c_4,plain,
inductive(omega),
inference(clausify,[status(thm)],[omega_is_inductive1]) ).
cnf(c_34,plain,
member(null_class,omega),
inference(resolve,[status(thm)],[c_4,c_3]) ).
fof(prove_universal_class_not_null_class_1,axiom,
universal_class = null_class,
file('theBenchmark.p',prove_universal_class_not_null_class_1) ).
cnf(c_36,plain,
universal_class = null_class,
inference(clausify,[status(thm)],[prove_universal_class_not_null_class_1]) ).
cnf(c_37,plain,
null_class = universal_class,
inference(copy,[status(thm)],[c_36]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_76,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_535,plain,
( member(regular(A),A)
| A = universal_class ),
inference(paramod,[status(thm)],[c_37,c_76]) ).
cnf(c_77,plain,
( member(regular(A),A)
| universal_class = A ),
inference(copy,[status(thm)],[c_535]) ).
fof(power_class2,axiom,
! [VAR_0] :
( member(power_class(VAR_0),universal_class)
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',power_class2) ).
cnf(c_81,plain,
( member(power_class(A),universal_class)
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[power_class2]) ).
fof(power_class_definition,axiom,
! [VAR_0] : complement(image(element_relation,complement(VAR_0))) = power_class(VAR_0),
file('theBenchmark.p',power_class_definition) ).
cnf(c_82,plain,
complement(image(element_relation,complement(A))) = power_class(A),
inference(clausify,[status(thm)],[power_class_definition]) ).
cnf(c_83,plain,
power_class(A) = complement(image(element_relation,complement(A))),
inference(copy,[status(thm)],[c_82]) ).
fof(image,axiom,
! [VAR_0,VAR_1] : range_of(restrict(VAR_0,VAR_1,universal_class)) = image(VAR_0,VAR_1),
file('theBenchmark.p',image) ).
cnf(c_93,plain,
range_of(restrict(A,B,universal_class)) = image(A,B),
inference(clausify,[status(thm)],[image]) ).
cnf(c_94,plain,
image(A,B) = range_of(restrict(A,B,universal_class)),
inference(copy,[status(thm)],[c_93]) ).
fof(range_of,axiom,
! [VAR_0] : domain_of(inverse(VAR_0)) = range_of(VAR_0),
file('theBenchmark.p',range_of) ).
cnf(c_99,plain,
domain_of(inverse(A)) = range_of(A),
inference(clausify,[status(thm)],[range_of]) ).
cnf(c_100,plain,
range_of(A) = domain_of(inverse(A)),
inference(copy,[status(thm)],[c_99]) ).
fof(inverse,axiom,
! [VAR_0] : domain_of(flip(cross_product(VAR_0,universal_class))) = inverse(VAR_0),
file('theBenchmark.p',inverse) ).
cnf(c_101,plain,
domain_of(flip(cross_product(A,universal_class))) = inverse(A),
inference(clausify,[status(thm)],[inverse]) ).
cnf(c_102,plain,
inverse(A) = domain_of(flip(cross_product(A,universal_class))),
inference(copy,[status(thm)],[c_101]) ).
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_113,plain,
intersection(cross_product(A,B),C) = restrict(C,A,B),
inference(clausify,[status(thm)],[restriction2]) ).
cnf(c_114,plain,
restrict(A,B,C) = intersection(cross_product(B,C),A),
inference(copy,[status(thm)],[c_113]) ).
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_115,plain,
intersection(A,cross_product(B,C)) = restrict(A,B,C),
inference(clausify,[status(thm)],[restriction1]) ).
cnf(c_536,plain,
intersection(A,cross_product(B,C)) = intersection(cross_product(B,C),A),
inference(paramod,[status(thm)],[c_114,c_115]) ).
cnf(c_116,plain,
intersection(cross_product(A,B),C) = intersection(C,cross_product(A,B)),
inference(copy,[status(thm)],[c_536]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_122,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_123,plain,
( member(A,intersection(B,C))
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[intersection3]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_144,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_147,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_200,plain,
member(universal_class,omega),
inference(paramod,[status(thm)],[c_37,c_34]) ).
cnf(c_537,plain,
( member(complement(image(element_relation,complement(A))),universal_class)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_83,c_81]) ).
cnf(c_538,plain,
( member(complement(range_of(restrict(element_relation,complement(A),universal_class))),universal_class)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_94,c_537]) ).
cnf(c_539,plain,
( member(complement(range_of(intersection(cross_product(complement(A),universal_class),element_relation))),universal_class)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_114,c_538]) ).
cnf(c_540,plain,
( member(complement(range_of(intersection(element_relation,cross_product(complement(A),universal_class)))),universal_class)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_116,c_539]) ).
cnf(c_541,plain,
( member(complement(domain_of(inverse(intersection(element_relation,cross_product(complement(A),universal_class))))),universal_class)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_100,c_540]) ).
cnf(c_209,plain,
( member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(A),universal_class)),universal_class))))),universal_class)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_102,c_541]) ).
cnf(c_235,plain,
( member(A,intersection(B,B))
| ~ member(A,B) ),
inference(factor,[status(thm)],[c_123]) ).
cnf(c_542,plain,
( universal_class = complement(A)
| ~ member(regular(complement(A)),A) ),
inference(resolve,[status(thm)],[c_122,c_77]) ).
cnf(c_261,plain,
( complement(A) = universal_class
| ~ member(regular(complement(A)),A) ),
inference(copy,[status(thm)],[c_542]) ).
cnf(c_305,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_147,c_144]) ).
cnf(c_367,plain,
member(universal_class,intersection(omega,omega)),
inference(resolve,[status(thm)],[c_235,c_200]) ).
cnf(c_439,plain,
member(universal_class,universal_class),
inference(resolve,[status(thm)],[c_305,c_367]) ).
cnf(c_440,plain,
( universal_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_305,c_77]) ).
cnf(c_448,plain,
member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(complement(universal_class),universal_class)),universal_class))))),universal_class),
inference(resolve,[status(thm)],[c_439,c_209]) ).
cnf(c_543,plain,
( complement(universal_class) = universal_class
| universal_class = complement(universal_class) ),
inference(resolve,[status(thm)],[c_440,c_261]) ).
cnf(c_544,plain,
( complement(universal_class) = universal_class
| complement(universal_class) = universal_class ),
inference(copy,[status(thm)],[c_543]) ).
cnf(c_506,plain,
complement(universal_class) = universal_class,
inference(copy,[status(thm)],[c_544]) ).
cnf(c_524,plain,
member(complement(domain_of(domain_of(flip(cross_product(intersection(element_relation,cross_product(universal_class,universal_class)),universal_class))))),universal_class),
inference(paramod,[status(thm)],[c_506,c_448]) ).
cnf(c_545,plain,
( ~ member(A,universal_class)
| ~ member(A,universal_class) ),
inference(paramod,[status(thm)],[c_506,c_122]) ).
cnf(c_533,plain,
~ member(A,universal_class),
inference(copy,[status(thm)],[c_545]) ).
cnf(c_534,plain,
$false,
inference(resolve,[status(thm)],[c_533,c_524]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET506-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Sat Sep 26 07:51:09 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.37 % Process 3127989 was started by sandbox on n008,
% 0.10/0.37 % Sat Sep 26 07:51:09 2026
% 0.10/0.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.38
% 0.10/0.38 % From the command line: assign(max_seconds, 300).
% 0.10/0.48
% 0.10/0.48 % SZS status Unsatisfiable for theBenchmark
% 0.10/0.48
% 0.10/0.48 % Proof 1 at 0.07 (+ 0.02) seconds.
% 0.10/0.48 % Length of proof is 37.
% 0.10/0.48 % Level of proof is 7.
% 0.10/0.48 % Maximum clause weight is 17.000.
% 0.10/0.48 % Given clauses 151.
% 0.10/0.48
% 0.10/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------