%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : SET079-7 : 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 : n018.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 08:35:40 AM UTC 2026
% Result : Unsatisfiable 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 4
% Syntax : Number of formulae : 12 ( 10 unt; 0 def)
% Number of atoms : 14 ( 3 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 7 ( 5 ~; 2 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 4 ( 2 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-1 aty)
% Number of variables : 5 ( 2 sgn 2 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_corollary_to_set_in_its_singleton_2,axiom,
singleton(x) = null_class,
file('theBenchmark.p',prove_corollary_to_set_in_its_singleton_2) ).
cnf(c_33,plain,
singleton(x) = null_class,
inference(clausify,[status(thm)],[prove_corollary_to_set_in_its_singleton_2]) ).
cnf(c_34,plain,
null_class = singleton(x),
inference(copy,[status(thm)],[c_33]) ).
fof(prove_corollary_to_set_in_its_singleton_1,axiom,
member(x,universal_class),
file('theBenchmark.p',prove_corollary_to_set_in_its_singleton_1) ).
cnf(c_35,plain,
member(x,universal_class),
inference(clausify,[status(thm)],[prove_corollary_to_set_in_its_singleton_1]) ).
fof(set_in_its_singleton,axiom,
! [VAR_0] :
( member(VAR_0,singleton(VAR_0))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',set_in_its_singleton) ).
cnf(c_36,plain,
( member(A,singleton(A))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[set_in_its_singleton]) ).
fof(existence_of_null_class,axiom,
! [VAR_0] : ~ member(VAR_0,null_class),
file('theBenchmark.p',existence_of_null_class) ).
cnf(c_57,plain,
~ member(A,null_class),
inference(clausify,[status(thm)],[existence_of_null_class]) ).
cnf(c_182,plain,
member(x,singleton(x)),
inference(resolve,[status(thm)],[c_36,c_35]) ).
cnf(c_214,plain,
~ member(A,singleton(x)),
inference(paramod,[status(thm)],[c_34,c_57]) ).
cnf(c_215,plain,
$false,
inference(resolve,[status(thm)],[c_214,c_182]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET079-7 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n018.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 07:06:06 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 4007810 was started by sandbox2 on n018,
% 0.09/0.37 % Sat Sep 26 07:06:06 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 Unsatisfiable for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.09/0.40 % Length of proof is 8.
% 0.09/0.40 % Level of proof is 3.
% 0.09/0.40 % Maximum clause weight is 17.000.
% 0.09/0.40 % Given clauses 27.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------