%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET061+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 2
% Syntax : Number of formulae : 8 ( 8 unt; 0 def)
% Number of atoms : 8 ( 0 equ)
% Maximal formula atoms : 1 ( 1 avg)
% Number of connectives : 5 ( 5 ~; 0 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 2 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 1 con; 0-1 aty)
% Number of variables : 10 ( 1 sgn 5 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(null_class_defn,axiom,
! [X] : ~ member(X,null_class),
file('theBenchmark.p',null_class_defn) ).
fof(existence_of_null_class,conjecture,
? [X] :
! [Z] : ~ member(Z,X),
file('theBenchmark.p',existence_of_null_class) ).
fof(existence_of_null_class_neg,negated_conjecture,
~ ? [X] :
! [Z] : ~ member(Z,X),
inference(assume_negation,[status(cth)],[existence_of_null_class]) ).
fof(nnf_42,plain,
! [X] :
? [Z] : member(Z,X),
inference(fof_nnf,[status(thm)],[existence_of_null_class_neg]) ).
fof(sk_existence_of_null_class_neg,plain,
! [X] : member(sK0(X),X),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(Z,sK0(X))],[nnf_42]) ).
cnf(c_64,negated_conjecture,
member(sK0(A),A),
inference(split_conjunct,[status(thm)],[sk_existence_of_null_class_neg]) ).
cnf(c_108,plain,
~ member(A,null_class),
inference(clausify,[status(thm)],[null_class_defn]) ).
cnf(c_109,plain,
$false,
inference(resolve,[status(thm)],[c_108,c_64]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET061+1 : TPTP v9.3.1. Bugfixed v5.4.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n011.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 07:00:59 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 4031857 was started by sandbox2 on n011,
% 0.09/0.37 % Sat Sep 26 07:00:59 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Theorem for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.09/0.40 % Length of proof is 5.
% 0.09/0.40 % Level of proof is 2.
% 0.09/0.40 % Maximum clause weight is 4.000.
% 0.09/0.40 % Given clauses 0.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------