%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM180-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n013.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 600s
% DateTime : Mon Jul 18 14:24:31 EDT 2022

% Result   : Unsatisfiable 0.21s 0.47s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   6 unt;   1 nHn;  10 RR)
%            Number of literals    :   14 (   0 equ;   6 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ subclass(limit_ordinals,ordinal_numbers),
    file('NUM180-1.p',unknown),
    [] ).

cnf(3,axiom,
    ( subclass(u,v)
    | member(not_subclass_element(u,v),u) ),
    file('NUM180-1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ member(not_subclass_element(u,v),v)
    | subclass(u,v) ),
    file('NUM180-1.p',unknown),
    [] ).

cnf(23,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,w) ),
    file('NUM180-1.p',unknown),
    [] ).

cnf(140,axiom,
    equal(intersection(complement(kind_1_ordinals),ordinal_numbers),limit_ordinals),
    file('NUM180-1.p',unknown),
    [] ).

cnf(162,plain,
    ~ member(not_subclass_element(limit_ordinals,ordinal_numbers),ordinal_numbers),
    inference(res,[status(thm),theory(equality)],[4,1]),
    [iquote('0:Res:4.1,1.0')] ).

cnf(163,plain,
    member(not_subclass_element(limit_ordinals,ordinal_numbers),limit_ordinals),
    inference(res,[status(thm),theory(equality)],[3,1]),
    [iquote('0:Res:3.1,1.0')] ).

cnf(291,plain,
    ( ~ member(u,limit_ordinals)
    | member(u,ordinal_numbers) ),
    inference(spl,[status(thm),theory(equality)],[140,23]),
    [iquote('0:SpL:140.0,23.0')] ).

cnf(298,plain,
    ~ member(not_subclass_element(limit_ordinals,ordinal_numbers),limit_ordinals),
    inference(res,[status(thm),theory(equality)],[291,162]),
    [iquote('0:Res:291.1,162.0')] ).

cnf(300,plain,
    $false,
    inference(mrr,[status(thm)],[298,163]),
    [iquote('0:MRR:298.0,163.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : NUM180-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n013.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Wed Jul  6 05:33:14 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.21/0.47  
% 0.21/0.47  SPASS V 3.9 
% 0.21/0.47  SPASS beiseite: Proof found.
% 0.21/0.47  % SZS status Theorem
% 0.21/0.47  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.21/0.47  SPASS derived 131 clauses, backtracked 0 clauses, performed 2 splits and kept 237 clauses.
% 0.21/0.47  SPASS allocated 75979 KBytes.
% 0.21/0.47  SPASS spent	0:00:00.11 on the problem.
% 0.21/0.47  		0:00:00.04 for the input.
% 0.21/0.47  		0:00:00.00 for the FLOTTER CNF translation.
% 0.21/0.47  		0:00:00.00 for inferences.
% 0.21/0.47  		0:00:00.00 for the backtracking.
% 0.21/0.47  		0:00:00.03 for the reduction.
% 0.21/0.47  
% 0.21/0.47  
% 0.21/0.47  Here is a proof with depth 2, length 10 :
% 0.21/0.47  % SZS output start Refutation
% See solution above
% 0.21/0.47  Formulae used in the proof : prove_limit_ordinals_are_ordinals_1 not_subclass_members1 not_subclass_members2 intersection2 limit_ordinals
% 0.21/0.47  
%------------------------------------------------------------------------------