%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET188-6 : 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 : n017.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 08:36:00 AM UTC 2026
% Result : Unsatisfiable 72.94s 10.77s
% Output : CNFRefutation 72.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 16 unt; 0 def)
% Number of atoms : 82 ( 13 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 61 ( 25 ~; 36 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 51 ( 5 sgn 16 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_subclass_property6_2,axiom,
~ subclass(x,y),
file('theBenchmark.p',prove_subclass_property6_2) ).
cnf(c_36,plain,
~ subclass(x,y),
inference(clausify,[status(thm)],[prove_subclass_property6_2]) ).
fof(prove_subclass_property6_1,axiom,
intersection(complement(y),x) = null_class,
file('theBenchmark.p',prove_subclass_property6_1) ).
cnf(c_37,plain,
intersection(complement(y),x) = null_class,
inference(clausify,[status(thm)],[prove_subclass_property6_1]) ).
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_77,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_76]) ).
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_119,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_120,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_121,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_142,plain,
subclass(A,universal_class),
inference(clausify,[status(thm)],[class_elements_are_sets]) ).
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]) ).
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_145,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_17192,plain,
( null_class = complement(A)
| ~ member(regular(complement(A)),A) ),
inference(resolve,[status(thm)],[c_120,c_77]) ).
cnf(c_257,plain,
( complement(A) = null_class
| ~ member(regular(complement(A)),A) ),
inference(copy,[status(thm)],[c_17192]) ).
cnf(c_311,plain,
( ~ member(not_subclass_element(complement(A),B),A)
| subclass(complement(A),B) ),
inference(resolve,[status(thm)],[c_144,c_120]) ).
cnf(c_315,plain,
member(not_subclass_element(x,y),x),
inference(resolve,[status(thm)],[c_144,c_36]) ).
cnf(c_318,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_145,c_142]) ).
cnf(c_439,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),universal_class) ),
inference(resolve,[status(thm)],[c_318,c_144]) ).
cnf(c_440,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_318,c_77]) ).
cnf(c_493,plain,
member(not_subclass_element(x,y),universal_class),
inference(resolve,[status(thm)],[c_315,c_318]) ).
cnf(c_498,plain,
( member(not_subclass_element(x,y),intersection(A,x))
| ~ member(not_subclass_element(x,y),A) ),
inference(resolve,[status(thm)],[c_315,c_121]) ).
cnf(c_558,plain,
( member(not_subclass_element(x,y),A)
| member(not_subclass_element(x,y),complement(A)) ),
inference(resolve,[status(thm)],[c_493,c_119]) ).
cnf(c_17193,plain,
( complement(universal_class) = null_class
| null_class = complement(universal_class) ),
inference(resolve,[status(thm)],[c_440,c_257]) ).
cnf(c_17194,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(copy,[status(thm)],[c_17193]) ).
cnf(c_659,plain,
complement(universal_class) = null_class,
inference(copy,[status(thm)],[c_17194]) ).
cnf(c_17195,plain,
( subclass(complement(universal_class),A)
| subclass(complement(universal_class),A) ),
inference(resolve,[status(thm)],[c_311,c_439]) ).
cnf(c_17196,plain,
( subclass(complement(universal_class),A)
| subclass(null_class,A) ),
inference(paramod,[status(thm)],[c_659,c_17195]) ).
cnf(c_17197,plain,
( subclass(null_class,A)
| subclass(null_class,A) ),
inference(paramod,[status(thm)],[c_659,c_17196]) ).
cnf(c_1513,plain,
subclass(null_class,A),
inference(copy,[status(thm)],[c_17197]) ).
cnf(c_1528,plain,
( member(A,B)
| ~ member(A,null_class) ),
inference(resolve,[status(thm)],[c_1513,c_145]) ).
cnf(c_17198,plain,
( subclass(x,y)
| member(not_subclass_element(x,y),complement(y)) ),
inference(resolve,[status(thm)],[c_558,c_143]) ).
cnf(c_17134,plain,
member(not_subclass_element(x,y),complement(y)),
inference(resolve,[status(thm)],[c_36,c_17198]) ).
cnf(c_17199,plain,
member(not_subclass_element(x,y),intersection(complement(y),x)),
inference(resolve,[status(thm)],[c_17134,c_498]) ).
cnf(c_17182,plain,
member(not_subclass_element(x,y),null_class),
inference(paramod,[status(thm)],[c_37,c_17199]) ).
cnf(c_17189,plain,
~ member(not_subclass_element(x,y),y),
inference(resolve,[status(thm)],[c_17134,c_120]) ).
cnf(c_17190,plain,
member(not_subclass_element(x,y),A),
inference(resolve,[status(thm)],[c_17182,c_1528]) ).
cnf(c_17191,plain,
$false,
inference(resolve,[status(thm)],[c_17190,c_17189]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET188-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n017.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Sat Sep 26 07:13:33 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.11/0.38 % Process 126787 was started by sandbox2 on n017,
% 0.11/0.38 % Sat Sep 26 07:13:33 2026
% 0.11/0.38 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.11/0.38
% 0.11/0.38 % From the command line: assign(max_seconds, 300).
% 72.94/10.77
% 72.94/10.77 % given #500 (T,wt=18): 7210 member(null_class,complement(identity_relation)) | member(regular(identity_relation),subset_relation). [resolve(6166,a,1505,a)].
% 72.94/10.77
% 72.94/10.77 % SZS status Unsatisfiable for theBenchmark
% 72.94/10.77
% 72.94/10.77 % Proof 1 at 1.84 (+ 0.36) seconds.
% 72.94/10.77 % Length of proof is 28.
% 72.94/10.77 % Level of proof is 7.
% 72.94/10.77 % Maximum clause weight is 25.000.
% 72.94/10.77 % Given clauses 762.
% 72.94/10.77
% 72.94/10.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------