%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET454-6 : 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 : n003.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 08:36:20 AM UTC 2026
% Result : Unsatisfiable 180.67s 24.52s
% Output : CNFRefutation 180.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 9
% Syntax : Number of formulae : 32 ( 16 unt; 0 def)
% Number of atoms : 50 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 36 ( 18 ~; 18 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-2 aty)
% Number of variables : 30 ( 2 sgn 14 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_identity_alternate_defn1_1,axiom,
~ subclass(identity_relation,cross_product(universal_class,universal_class)),
file('theBenchmark.p',prove_identity_alternate_defn1_1) ).
cnf(c_36,plain,
~ subclass(identity_relation,cross_product(universal_class,universal_class)),
inference(clausify,[status(thm)],[prove_identity_alternate_defn1_1]) ).
fof(identity_relation,axiom,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
file('theBenchmark.p',identity_relation) ).
cnf(c_67,plain,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
inference(clausify,[status(thm)],[identity_relation]) ).
cnf(c_68,plain,
identity_relation = intersection(inverse(subset_relation),subset_relation),
inference(copy,[status(thm)],[c_67]) ).
fof(subset_relation,axiom,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
file('theBenchmark.p',subset_relation) ).
cnf(c_69,plain,
intersection(cross_product(universal_class,universal_class),intersection(cross_product(universal_class,universal_class),complement(compose(complement(element_relation),inverse(element_relation))))) = subset_relation,
inference(clausify,[status(thm)],[subset_relation]) ).
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_122,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_123,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
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_139,plain,
( A = B
| ~ subclass(B,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_implies_equal]) ).
fof(equal_implies_subclass2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_1,VAR_0)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',equal_implies_subclass2) ).
cnf(c_140,plain,
( subclass(B,A)
| A != B ),
inference(clausify,[status(thm)],[equal_implies_subclass2]) ).
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_143,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_144,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
cnf(c_247,plain,
( member(A,cross_product(universal_class,universal_class))
| ~ member(A,subset_relation) ),
inference(paramod,[status(thm)],[c_69,c_123]) ).
cnf(c_340,plain,
subclass(intersection(inverse(subset_relation),subset_relation),identity_relation),
inference(resolve,[status(thm)],[c_140,c_68]) ).
cnf(c_20284,plain,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
inference(copy,[status(thm)],[c_68]) ).
cnf(c_364,plain,
subclass(identity_relation,intersection(inverse(subset_relation),subset_relation)),
inference(resolve,[status(thm)],[c_140,c_20284]) ).
cnf(c_375,plain,
member(not_subclass_element(identity_relation,cross_product(universal_class,universal_class)),identity_relation),
inference(resolve,[status(thm)],[c_144,c_36]) ).
cnf(c_20285,plain,
( identity_relation = intersection(inverse(subset_relation),subset_relation)
| ~ subclass(identity_relation,intersection(inverse(subset_relation),subset_relation)) ),
inference(resolve,[status(thm)],[c_340,c_139]) ).
cnf(c_20286,plain,
( intersection(inverse(subset_relation),subset_relation) = identity_relation
| ~ subclass(identity_relation,intersection(inverse(subset_relation),subset_relation)) ),
inference(copy,[status(thm)],[c_20285]) ).
cnf(c_2202,plain,
intersection(inverse(subset_relation),subset_relation) = identity_relation,
inference(resolve,[status(thm)],[c_364,c_20286]) ).
cnf(c_4344,plain,
( member(A,subset_relation)
| ~ member(A,identity_relation) ),
inference(paramod,[status(thm)],[c_2202,c_122]) ).
cnf(c_5814,plain,
member(not_subclass_element(identity_relation,cross_product(universal_class,universal_class)),subset_relation),
inference(resolve,[status(thm)],[c_375,c_4344]) ).
cnf(c_8994,plain,
member(not_subclass_element(identity_relation,cross_product(universal_class,universal_class)),cross_product(universal_class,universal_class)),
inference(resolve,[status(thm)],[c_5814,c_247]) ).
cnf(c_20287,plain,
subclass(identity_relation,cross_product(universal_class,universal_class)),
inference(resolve,[status(thm)],[c_8994,c_143]) ).
cnf(c_20283,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_20287]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SET454-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.43 % Computer : n003.cluster.edu
% 0.15/0.43 % Model : x86_64 x86_64
% 0.15/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.43 % Memory : 8046.5625MB
% 0.15/0.43 % OS : Linux 6.8.0-71-generic
% 0.15/0.43 % CPULimit : 300
% 0.15/0.43 % WCLimit : 300
% 0.15/0.43 % DateTime : Sat Sep 26 07:46:53 UTC 2026
% 0.15/0.43 % CPUTime :
% 0.15/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/0.43 % Process 2357938 was started by sandbox2 on n003,
% 0.15/0.43 % Sat Sep 26 07:46:53 2026
% 0.15/0.43 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.15/0.44
% 0.15/0.44 % From the command line: assign(max_seconds, 300).
% 180.67/24.52
% 180.67/24.52 % given #500 (W,wt=22): 614 maps(choice,domain_of(choice),domain_of(inverse(choice))). [para(100(a,1),446(a,3))].
% 180.67/24.52
% 180.67/24.52 % given #1000 (T,wt=22): 13433 member(not_subclass_element(universal_class,null_class),universal_class) | complement(A) = null_class | null_class = A. [resolve(7789,c,2433,c),merge(c)].
% 180.67/24.52
% 180.67/24.52 % given #1500 (F,wt=20): 17467 -member(power_class(power_class(null_class)),null_class). [resolve(17296,b,1893,a)].
% 180.67/24.52
% 180.67/24.52 % given #2000 (F,wt=34): 18117 -member(range_of(intersection(cross_product(sum_class(null_class),universal_class),choice)),null_class). [para(112(a,1),17901(a,1,1))].
% 180.67/24.52
% 180.67/24.52 % given #2500 (F,wt=46): 18660 -member(power_class(complement(range_of(intersection(cross_product(complement(omega),universal_class),element_relation)))),null_class). [para(112(a,1),18332(a,1,1,1,1))].
% 180.67/24.52
% 180.67/24.52 % given #3000 (F,wt=35): 20078 -member(range_of(intersection(cross_product(image(choice,omega),universal_class),choice)),null_class). [para(112(a,1),20070(a,1,1))].
% 180.67/24.52
% 180.67/24.52 % SZS status Unsatisfiable for theBenchmark
% 180.67/24.52
% 180.67/24.52 % Proof 1 at 6.14 (+ 1.61) seconds.
% 180.67/24.52 % Length of proof is 19.
% 180.67/24.52 % Level of proof is 7.
% 180.67/24.52 % Maximum clause weight is 46.000.
% 180.67/24.52 % Given clauses 3186.
% 180.67/24.52
% 180.67/24.52 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------