%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET261-6 : 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 : n019.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 08:36:07 AM UTC 2026
% Result : Unsatisfiable 0.68s 0.56s
% Output : CNFRefutation 0.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 46 ( 20 unt; 0 def)
% Number of atoms : 74 ( 39 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 56 ( 28 ~; 28 |; 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 : 10 ( 10 usr; 2 con; 0-3 aty)
% Number of variables : 70 ( 5 sgn 19 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_domain_of_null_class_1,axiom,
domain_of(null_class) != null_class,
file('theBenchmark.p',prove_domain_of_null_class_1) ).
cnf(c_36,plain,
domain_of(null_class) != null_class,
inference(clausify,[status(thm)],[prove_domain_of_null_class_1]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_75,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_76,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_75]) ).
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_109,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_110,plain,
intersection(cross_product(A,B),C) = restrict(C,A,B),
inference(clausify,[status(thm)],[restriction2]) ).
cnf(c_111,plain,
restrict(A,B,C) = intersection(cross_product(B,C),A),
inference(copy,[status(thm)],[c_110]) ).
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_112,plain,
intersection(A,cross_product(B,C)) = restrict(A,B,C),
inference(clausify,[status(thm)],[restriction1]) ).
cnf(c_836,plain,
intersection(A,cross_product(B,C)) = intersection(cross_product(B,C),A),
inference(paramod,[status(thm)],[c_111,c_112]) ).
cnf(c_113,plain,
intersection(cross_product(A,B),C) = intersection(C,cross_product(A,B)),
inference(copy,[status(thm)],[c_836]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_119,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_122,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_132,plain,
unordered_pair(A,A) = singleton(A),
inference(clausify,[status(thm)],[singleton_set]) ).
cnf(c_133,plain,
singleton(A) = unordered_pair(A,A),
inference(copy,[status(thm)],[c_132]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_141,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_144,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_837,plain,
( ~ member(B,domain_of(A))
| restrict(A,unordered_pair(B,B),universal_class) != null_class ),
inference(paramod,[status(thm)],[c_133,c_109]) ).
cnf(c_225,plain,
( ~ member(A,domain_of(B))
| intersection(cross_product(unordered_pair(A,A),universal_class),B) != null_class ),
inference(paramod,[status(thm)],[c_111,c_837]) ).
cnf(c_838,plain,
( null_class = complement(A)
| ~ member(regular(complement(A)),A) ),
inference(resolve,[status(thm)],[c_119,c_76]) ).
cnf(c_258,plain,
( complement(A) = null_class
| ~ member(regular(complement(A)),A) ),
inference(copy,[status(thm)],[c_838]) ).
cnf(c_839,plain,
( null_class = intersection(A,B)
| member(regular(intersection(A,B)),A) ),
inference(resolve,[status(thm)],[c_122,c_76]) ).
cnf(c_271,plain,
( intersection(A,B) = null_class
| member(regular(intersection(A,B)),A) ),
inference(copy,[status(thm)],[c_839]) ).
cnf(c_311,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_144,c_141]) ).
cnf(c_418,plain,
( ~ member(B,domain_of(A))
| intersection(A,cross_product(unordered_pair(B,B),universal_class)) != null_class ),
inference(paramod,[status(thm)],[c_113,c_225]) ).
cnf(c_479,plain,
( null_class = A
| member(regular(A),universal_class) ),
inference(resolve,[status(thm)],[c_311,c_76]) ).
cnf(c_840,plain,
( complement(universal_class) = null_class
| null_class = complement(universal_class) ),
inference(resolve,[status(thm)],[c_479,c_258]) ).
cnf(c_841,plain,
( complement(universal_class) = null_class
| complement(universal_class) = null_class ),
inference(copy,[status(thm)],[c_840]) ).
cnf(c_640,plain,
complement(universal_class) = null_class,
inference(copy,[status(thm)],[c_841]) ).
cnf(c_842,plain,
( ~ member(regular(A),complement(universal_class))
| null_class = A ),
inference(resolve,[status(thm)],[c_479,c_119]) ).
cnf(c_661,plain,
( ~ member(regular(A),null_class)
| null_class = A ),
inference(paramod,[status(thm)],[c_640,c_842]) ).
cnf(c_843,plain,
( intersection(null_class,A) = null_class
| null_class = intersection(null_class,A) ),
inference(resolve,[status(thm)],[c_661,c_271]) ).
cnf(c_844,plain,
( intersection(null_class,A) = null_class
| intersection(null_class,A) = null_class ),
inference(copy,[status(thm)],[c_843]) ).
cnf(c_827,plain,
intersection(null_class,A) = null_class,
inference(copy,[status(thm)],[c_844]) ).
cnf(c_831,plain,
~ member(A,domain_of(null_class)),
inference(resolve,[status(thm)],[c_827,c_418]) ).
cnf(c_845,plain,
null_class = domain_of(null_class),
inference(resolve,[status(thm)],[c_831,c_76]) ).
cnf(c_846,plain,
domain_of(null_class) = null_class,
inference(copy,[status(thm)],[c_845]) ).
cnf(c_835,plain,
$false,
inference(resolve,[status(thm)],[c_36,c_846]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET261-6 : 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 : n019.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 26 07:24:33 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/0.36 % Process 707050 was started by sandbox on n019,
% 0.10/0.36 % Sat Sep 26 07:24:33 2026
% 0.10/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.10/0.37
% 0.10/0.37 % From the command line: assign(max_seconds, 300).
% 0.68/0.56
% 0.68/0.56 % SZS status Unsatisfiable for theBenchmark
% 0.68/0.56
% 0.68/0.56 % Proof 1 at 0.15 (+ 0.03) seconds.
% 0.68/0.56 % Length of proof is 25.
% 0.68/0.56 % Level of proof is 7.
% 0.68/0.56 % Maximum clause weight is 33.000.
% 0.68/0.56 % Given clauses 196.
% 0.68/0.56
% 0.68/0.56 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------