%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : NUM180-1 : 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 : n003.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 08:16:14 AM UTC 2026
% Result : Unsatisfiable 1.94s 0.64s
% Output : CNFRefutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 5
% Number of leaves : 5
% Syntax : Number of formulae : 15 ( 8 unt; 0 def)
% Number of atoms : 22 ( 2 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 14 ( 7 ~; 7 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 15 ( 1 sgn 7 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(prove_limit_ordinals_are_ordinals_1,axiom,
~ subclass(limit_ordinals,ordinal_numbers),
file('theBenchmark.p',prove_limit_ordinals_are_ordinals_1) ).
cnf(c_53,plain,
~ subclass(limit_ordinals,ordinal_numbers),
inference(clausify,[status(thm)],[prove_limit_ordinals_are_ordinals_1]) ).
fof(limit_ordinals,axiom,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
file('theBenchmark.p',limit_ordinals) ).
cnf(c_75,plain,
intersection(complement(kind_1_ordinals),ordinal_numbers) = limit_ordinals,
inference(clausify,[status(thm)],[limit_ordinals]) ).
fof(intersection2,axiom,
! [VAR_0,VAR_1,VAR_2] :
( member(VAR_0,VAR_2)
| ~ member(VAR_0,intersection(VAR_1,VAR_2)) ),
file('theBenchmark.p',intersection2) ).
cnf(c_177,plain,
( member(A,C)
| ~ member(A,intersection(B,C)) ),
inference(clausify,[status(thm)],[intersection2]) ).
fof(not_subclass_members2,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| ~ member(not_subclass_element(VAR_0,VAR_1),VAR_1) ),
file('theBenchmark.p',not_subclass_members2) ).
cnf(c_198,plain,
( subclass(A,B)
| ~ member(not_subclass_element(A,B),B) ),
inference(clausify,[status(thm)],[not_subclass_members2]) ).
fof(not_subclass_members1,axiom,
! [VAR_0,VAR_1] :
( subclass(VAR_0,VAR_1)
| member(not_subclass_element(VAR_0,VAR_1),VAR_0) ),
file('theBenchmark.p',not_subclass_members1) ).
cnf(c_199,plain,
( subclass(A,B)
| member(not_subclass_element(A,B),A) ),
inference(clausify,[status(thm)],[not_subclass_members1]) ).
cnf(c_321,plain,
( member(A,ordinal_numbers)
| ~ member(A,limit_ordinals) ),
inference(paramod,[status(thm)],[c_75,c_177]) ).
cnf(c_371,plain,
member(not_subclass_element(limit_ordinals,ordinal_numbers),limit_ordinals),
inference(resolve,[status(thm)],[c_199,c_53]) ).
cnf(c_696,plain,
member(not_subclass_element(limit_ordinals,ordinal_numbers),ordinal_numbers),
inference(resolve,[status(thm)],[c_371,c_321]) ).
cnf(c_1022,plain,
subclass(limit_ordinals,ordinal_numbers),
inference(resolve,[status(thm)],[c_696,c_198]) ).
cnf(c_1021,plain,
$false,
inference(resolve,[status(thm)],[c_53,c_1022]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM180-1 : TPTP v9.3.1. Bugfixed v2.1.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n003.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Sat Sep 26 02:11:54 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.36 % Process 1795278 was started by sandbox on n003,
% 0.09/0.36 % Sat Sep 26 02:11:54 2026
% 0.09/0.36 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.14/0.36
% 0.14/0.36 % From the command line: assign(max_seconds, 300).
% 1.94/0.64
% 1.94/0.64 % SZS status Unsatisfiable for theBenchmark
% 1.94/0.64
% 1.94/0.64 % Proof 1 at 0.21 (+ 0.05) seconds.
% 1.94/0.64 % Length of proof is 9.
% 1.94/0.64 % Level of proof is 3.
% 1.94/0.64 % Maximum clause weight is 21.000.
% 1.94/0.64 % Given clauses 164.
% 1.94/0.64
% 1.94/0.64 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------