%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET061-6 : 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 : n013.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 08:35:32 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.43s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 6
% Syntax : Number of formulae : 23 ( 9 unt; 0 def)
% Number of atoms : 40 ( 14 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 35 ( 18 ~; 17 |; 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 27 ( 1 sgn 11 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_existence_of_null_class_1,axiom,
member(z,null_class),
file('theBenchmark.p',prove_existence_of_null_class_1) ).
cnf(c_34,plain,
member(z,null_class),
inference(clausify,[status(thm)],[prove_existence_of_null_class_1]) ).
fof(regularity2,axiom,
! [VAR_0] :
( intersection(VAR_0,regular(VAR_0)) = null_class
| VAR_0 = null_class ),
file('theBenchmark.p',regularity2) ).
cnf(c_49,plain,
( intersection(A,regular(A)) = null_class
| A = null_class ),
inference(clausify,[status(thm)],[regularity2]) ).
cnf(c_50,plain,
( intersection(A,regular(A)) = null_class
| null_class = A ),
inference(copy,[status(thm)],[c_49]) ).
fof(complement1,axiom,
! [VAR_0,VAR_1] :
( ~ member(VAR_0,VAR_1)
| ~ member(VAR_0,complement(VAR_1)) ),
file('theBenchmark.p',complement1) ).
cnf(c_95,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_98,plain,
( member(A,B)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection1]) ).
fof(equal_implies_subclass1,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| VAR_0 != VAR_1 ),
file('theBenchmark.p',equal_implies_subclass1) ).
cnf(c_116,plain,
( subclass(A,B)
| A != B ),
inference(clausify,[status(thm)],[equal_implies_subclass1]) ).
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_120,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_187,plain,
~ member(z,complement(null_class)),
inference(resolve,[status(thm)],[c_95,c_34]) ).
cnf(c_204,plain,
( member(B,A)
| ~ member(B,null_class)
| null_class = A ),
inference(paramod,[status(thm)],[c_50,c_98]) ).
cnf(c_518,plain,
( member(z,A)
| ~ subclass(null_class,A) ),
inference(resolve,[status(thm)],[c_120,c_34]) ).
cnf(c_376,plain,
~ subclass(null_class,complement(null_class)),
inference(resolve,[status(thm)],[c_518,c_187]) ).
cnf(c_519,plain,
null_class != complement(null_class),
inference(resolve,[status(thm)],[c_116,c_376]) ).
cnf(c_472,plain,
complement(null_class) != null_class,
inference(copy,[status(thm)],[c_519]) ).
cnf(c_515,plain,
( member(z,A)
| null_class = A ),
inference(resolve,[status(thm)],[c_204,c_34]) ).
cnf(c_520,plain,
null_class = complement(null_class),
inference(resolve,[status(thm)],[c_515,c_187]) ).
cnf(c_521,plain,
complement(null_class) = null_class,
inference(copy,[status(thm)],[c_520]) ).
cnf(c_517,plain,
$false,
inference(resolve,[status(thm)],[c_472,c_521]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET061-6 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n013.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 07:00:23 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 2168471 was started by sandbox on n013,
% 0.09/0.36 % Sat Sep 26 07:00:23 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.09/0.37
% 0.09/0.37 % From the command line: assign(max_seconds, 300).
% 0.09/0.43
% 0.09/0.43 % SZS status Unsatisfiable for theBenchmark
% 0.09/0.43
% 0.09/0.43 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.09/0.43 % Length of proof is 13.
% 0.09/0.43 % Level of proof is 4.
% 0.09/0.43 % Maximum clause weight is 24.000.
% 0.09/0.43 % Given clauses 121.
% 0.09/0.43
% 0.09/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------