%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM183-1 : 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 : n014.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 08:16:15 AM UTC 2026
% Result : Unsatisfiable 2.50s 0.80s
% Output : CNFRefutation 2.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 8
% Syntax : Number of formulae : 25 ( 16 unt; 0 def)
% Number of atoms : 40 ( 3 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 32 ( 17 ~; 15 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 22 ( 2 sgn 9 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_ordinals_are_kind_1_or_limit_3,axiom,
~ member(x,limit_ordinals),
file('theBenchmark.p',prove_ordinals_are_kind_1_or_limit_3) ).
cnf(c_53,plain,
~ member(x,limit_ordinals),
inference(clausify,[status(thm)],[prove_ordinals_are_kind_1_or_limit_3]) ).
fof(prove_ordinals_are_kind_1_or_limit_2,axiom,
~ member(x,kind_1_ordinals),
file('theBenchmark.p',prove_ordinals_are_kind_1_or_limit_2) ).
cnf(c_54,plain,
~ member(x,kind_1_ordinals),
inference(clausify,[status(thm)],[prove_ordinals_are_kind_1_or_limit_2]) ).
fof(prove_ordinals_are_kind_1_or_limit_1,axiom,
member(x,ordinal_numbers),
file('theBenchmark.p',prove_ordinals_are_kind_1_or_limit_1) ).
cnf(c_55,plain,
member(x,ordinal_numbers),
inference(clausify,[status(thm)],[prove_ordinals_are_kind_1_or_limit_1]) ).
fof(limit_ordinals,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
file('theBenchmark.p',limit_ordinals) ).
cnf(c_77,plain,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
inference(clausify,[status(thm)],[limit_ordinals]) ).
cnf(c_78,plain,
limit_ordinals = intersection(complement(kind_1_ordinals),ordinal_numbers),
inference(copy,[status(thm)],[c_77]) ).
fof(complement2,axiom,
! [VAR_0,VAR_1] :
( member(VAR_0,VAR_1)
| member(VAR_0,complement(VAR_1))
| ~ member(VAR_0,universal_class) ),
file('theBenchmark.p',complement2) ).
cnf(c_180,plain,
( member(A,B)
| member(A,complement(B))
| ~ member(A,universal_class) ),
inference(clausify,[status(thm)],[complement2]) ).
fof(intersection3,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,intersection(VAR_1,VAR_2))
| ~ member(VAR_0,VAR_2)
| ~ member(VAR_0,VAR_1) ),
file('theBenchmark.p',intersection3) ).
cnf(c_182,plain,
( member(A,intersection(B,C))
| ~ member(A,C)
| ~ member(A,B) ),
inference(clausify,[status(thm)],[intersection3]) ).
fof(class_elements_are_sets,axiom,
! [VAR_0] : subclass(VAR_0,universal_class),
file('theBenchmark.p',class_elements_are_sets) ).
cnf(c_203,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_206,plain,
( member(C,B)
| ~ member(C,A)
| ~ subclass(A,B) ),
inference(clausify,[status(thm)],[subclass_members]) ).
cnf(c_221,plain,
~ member(x,intersection(complement(kind_1_ordinals),ordinal_numbers)),
inference(paramod,[status(thm)],[c_78,c_53]) ).
cnf(c_303,plain,
( member(x,intersection(A,ordinal_numbers))
| ~ member(x,A) ),
inference(resolve,[status(thm)],[c_182,c_55]) ).
cnf(c_469,plain,
( member(A,universal_class)
| ~ member(A,B) ),
inference(resolve,[status(thm)],[c_206,c_203]) ).
cnf(c_529,plain,
member(x,universal_class),
inference(resolve,[status(thm)],[c_469,c_55]) ).
cnf(c_539,plain,
( member(x,A)
| member(x,complement(A)) ),
inference(resolve,[status(thm)],[c_529,c_180]) ).
cnf(c_1424,plain,
member(x,complement(kind_1_ordinals)),
inference(resolve,[status(thm)],[c_539,c_54]) ).
cnf(c_1893,plain,
member(x,intersection(complement(kind_1_ordinals),ordinal_numbers)),
inference(resolve,[status(thm)],[c_303,c_1424]) ).
cnf(c_1892,plain,
$false,
inference(resolve,[status(thm)],[c_221,c_1893]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : NUM183-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n014.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.43 % CPULimit : 300
% 0.17/0.43 % WCLimit : 300
% 0.17/0.43 % DateTime : Sat Sep 26 02:10:18 UTC 2026
% 0.17/0.43 % CPUTime :
% 0.17/0.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.43 % Process 1890509 was started by sandbox on n014,
% 0.17/0.43 % Sat Sep 26 02:10:18 2026
% 0.17/0.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.45
% 0.17/0.45 % From the command line: assign(max_seconds, 300).
% 2.50/0.80
% 2.50/0.80 % SZS status Unsatisfiable for theBenchmark
% 2.50/0.80
% 2.50/0.80 % Proof 1 at 0.26 (+ 0.08) seconds.
% 2.50/0.80 % Length of proof is 16.
% 2.50/0.80 % Level of proof is 5.
% 2.50/0.80 % Maximum clause weight is 21.000.
% 2.50/0.80 % Given clauses 345.
% 2.50/0.80
% 2.50/0.80 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------