%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET061-7 : 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 : n020.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 08:35:33 AM UTC 2026
% Result : Unsatisfiable 0.15s 5.46s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 3
% Syntax : Number of formulae : 11 ( 8 unt; 0 def)
% Number of atoms : 14 ( 5 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 6 ( 3 ~; 3 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 10 ( 2 sgn 3 !; 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_33,plain,
member(z,null_class),
inference(clausify,[status(thm)],[prove_existence_of_null_class_1]) ).
fof(special_classes_lemma,axiom,
! [VAR_0,VAR_1] : ~ member(VAR_0,intersection(complement(VAR_1),VAR_1)),
file('theBenchmark.p',special_classes_lemma) ).
cnf(c_34,plain,
~ member(A,intersection(complement(B),B)),
inference(clausify,[status(thm)],[special_classes_lemma]) ).
fof(regularity1,axiom,
! [VAR_0] :
( member(regular(VAR_0),VAR_0)
| VAR_0 = null_class ),
file('theBenchmark.p',regularity1) ).
cnf(c_61,plain,
( member(regular(A),A)
| A = null_class ),
inference(clausify,[status(thm)],[regularity1]) ).
cnf(c_62,plain,
( member(regular(A),A)
| null_class = A ),
inference(copy,[status(thm)],[c_61]) ).
cnf(c_268,plain,
null_class = intersection(complement(A),A),
inference(resolve,[status(thm)],[c_62,c_34]) ).
cnf(c_239,plain,
intersection(complement(A),A) = null_class,
inference(copy,[status(thm)],[c_268]) ).
cnf(c_266,plain,
~ member(A,null_class),
inference(paramod,[status(thm)],[c_239,c_34]) ).
cnf(c_267,plain,
$false,
inference(resolve,[status(thm)],[c_266,c_33]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET061-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/5.41 % Computer : n020.cluster.edu
% 0.15/5.41 % Model : x86_64 x86_64
% 0.15/5.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.41 % Memory : 8046.5625MB
% 0.15/5.41 % OS : Linux 6.8.0-71-generic
% 0.15/5.41 % CPULimit : 300
% 0.15/5.41 % WCLimit : 300
% 0.15/5.41 % DateTime : Sat Sep 26 07:02:10 UTC 2026
% 0.15/5.41 % CPUTime :
% 0.15/5.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.15/5.41 % Process 926206 was started by sandbox on n020,
% 0.15/5.41 % Sat Sep 26 07:02:10 2026
% 0.15/5.41 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.15/5.42
% 0.15/5.42 % From the command line: assign(max_seconds, 300).
% 0.15/5.46
% 0.15/5.46 % SZS status Unsatisfiable for theBenchmark
% 0.15/5.46
% 0.15/5.46 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.15/5.46 % Length of proof is 7.
% 0.15/5.46 % Level of proof is 4.
% 0.15/5.46 % Maximum clause weight is 12.000.
% 0.15/5.46 % Given clauses 14.
% 0.15/5.46
% 0.15/5.46 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------