%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM183-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n016.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 14:24:32 EDT 2022

% Result   : Unsatisfiable 0.17s 0.46s
% Output   : Refutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    8
% Syntax   : Number of clauses     :   15 (   8 unt;   1 nHn;  15 RR)
%            Number of literals    :   25 (   0 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    member(x__dfg,ordinal_numbers),
    file('NUM183-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ member(x__dfg,kind_1_ordinals),
    file('NUM183-1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ member(x__dfg,limit_ordinals),
    file('NUM183-1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ member(u,v)
    | ~ subclass(v,w)
    | member(u,w) ),
    file('NUM183-1.p',unknown),
    [] ).

cnf(7,axiom,
    subclass(u,universal_class),
    file('NUM183-1.p',unknown),
    [] ).

cnf(26,axiom,
    ( ~ member(u,v)
    | ~ member(u,w)
    | member(u,intersection(w,v)) ),
    file('NUM183-1.p',unknown),
    [] ).

cnf(28,axiom,
    ( ~ member(u,universal_class)
    | member(u,v)
    | member(u,complement(v)) ),
    file('NUM183-1.p',unknown),
    [] ).

cnf(142,axiom,
    equal(intersection(complement(kind_1_ordinals),ordinal_numbers),limit_ordinals),
    file('NUM183-1.p',unknown),
    [] ).

cnf(164,plain,
    ( ~ subclass(ordinal_numbers,u)
    | member(x__dfg,u) ),
    inference(res,[status(thm),theory(equality)],[1,4]),
    [iquote('0:Res:1.0,4.1')] ).

cnf(171,plain,
    ( ~ member(x__dfg,u)
    | member(x__dfg,intersection(u,ordinal_numbers)) ),
    inference(res,[status(thm),theory(equality)],[1,26]),
    [iquote('0:Res:1.0,26.1')] ).

cnf(182,plain,
    ( ~ member(x__dfg,universal_class)
    | member(x__dfg,complement(kind_1_ordinals)) ),
    inference(res,[status(thm),theory(equality)],[28,2]),
    [iquote('0:Res:28.2,2.0')] ).

cnf(202,plain,
    member(x__dfg,universal_class),
    inference(res,[status(thm),theory(equality)],[7,164]),
    [iquote('0:Res:7.0,164.0')] ).

cnf(203,plain,
    member(x__dfg,complement(kind_1_ordinals)),
    inference(mrr,[status(thm)],[182,202]),
    [iquote('0:MRR:182.0,202.0')] ).

cnf(424,plain,
    ( ~ member(x__dfg,complement(kind_1_ordinals))
    | member(x__dfg,limit_ordinals) ),
    inference(spr,[status(thm),theory(equality)],[142,171]),
    [iquote('0:SpR:142.0,171.1')] ).

cnf(429,plain,
    $false,
    inference(mrr,[status(thm)],[424,203,3]),
    [iquote('0:MRR:424.0,424.1,203.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11  % Problem  : NUM183-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.06/0.11  % Command  : run_spass %d %s
% 0.11/0.32  % Computer : n016.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 600
% 0.11/0.32  % DateTime : Tue Jul  5 06:53:03 EDT 2022
% 0.11/0.32  % CPUTime  : 
% 0.17/0.46  
% 0.17/0.46  SPASS V 3.9 
% 0.17/0.46  SPASS beiseite: Proof found.
% 0.17/0.46  % SZS status Theorem
% 0.17/0.46  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.17/0.46  SPASS derived 251 clauses, backtracked 0 clauses, performed 2 splits and kept 313 clauses.
% 0.17/0.46  SPASS allocated 76054 KBytes.
% 0.17/0.46  SPASS spent	0:00:00.13 on the problem.
% 0.17/0.46  		0:00:00.04 for the input.
% 0.17/0.46  		0:00:00.00 for the FLOTTER CNF translation.
% 0.17/0.46  		0:00:00.01 for inferences.
% 0.17/0.46  		0:00:00.00 for the backtracking.
% 0.17/0.46  		0:00:00.04 for the reduction.
% 0.17/0.46  
% 0.17/0.46  
% 0.17/0.46  Here is a proof with depth 2, length 15 :
% 0.17/0.46  % SZS output start Refutation
% See solution above
% 0.17/0.46  Formulae used in the proof : prove_ordinals_are_kind_1_or_limit_1 prove_ordinals_are_kind_1_or_limit_2 prove_ordinals_are_kind_1_or_limit_3 subclass_members class_elements_are_sets intersection3 complement2 limit_ordinals
% 0.17/0.46  
%------------------------------------------------------------------------------