%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET079+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n015.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 : Tue Jul 19 05:23:41 EDT 2022

% Result   : Theorem 0.18s 0.48s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   6 unt;   0 nHn;  10 RR)
%            Number of literals    :   15 (   0 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    member(skc3,universal_class),
    file('SET079+1.p',unknown),
    [] ).

cnf(6,axiom,
    equal(singleton(skc3),null_class),
    file('SET079+1.p',unknown),
    [] ).

cnf(7,axiom,
    ~ member(u,null_class),
    file('SET079+1.p',unknown),
    [] ).

cnf(13,axiom,
    equal(unordered_pair(u,u),singleton(u)),
    file('SET079+1.p',unknown),
    [] ).

cnf(72,axiom,
    ( ~ equal(u,v)
    | ~ member(u,universal_class)
    | member(u,unordered_pair(w,v)) ),
    file('SET079+1.p',unknown),
    [] ).

cnf(97,plain,
    ( ~ equal(skc3,u)
    | member(skc3,unordered_pair(v,u)) ),
    inference(res,[status(thm),theory(equality)],[3,72]),
    [iquote('0:Res:3.0,72.1')] ).

cnf(318,plain,
    ( ~ equal(skc3,u)
    | member(skc3,singleton(u)) ),
    inference(spr,[status(thm),theory(equality)],[13,97]),
    [iquote('0:SpR:13.0,97.1')] ).

cnf(321,plain,
    ( ~ equal(skc3,skc3)
    | member(skc3,null_class) ),
    inference(spr,[status(thm),theory(equality)],[6,318]),
    [iquote('0:SpR:6.0,318.1')] ).

cnf(324,plain,
    member(skc3,null_class),
    inference(obv,[status(thm),theory(equality)],[321]),
    [iquote('0:Obv:321.0')] ).

cnf(325,plain,
    $false,
    inference(mrr,[status(thm)],[324,7]),
    [iquote('0:MRR:324.0,7.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem  : SET079+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.12/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n015.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 05:40:22 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.48  
% 0.18/0.48  SPASS V 3.9 
% 0.18/0.48  SPASS beiseite: Proof found.
% 0.18/0.48  % SZS status Theorem
% 0.18/0.48  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.18/0.48  SPASS derived 206 clauses, backtracked 41 clauses, performed 1 splits and kept 281 clauses.
% 0.18/0.48  SPASS allocated 98311 KBytes.
% 0.18/0.48  SPASS spent	0:00:00.14 on the problem.
% 0.18/0.48  		0:00:00.04 for the input.
% 0.18/0.48  		0:00:00.06 for the FLOTTER CNF translation.
% 0.18/0.48  		0:00:00.00 for inferences.
% 0.18/0.48  		0:00:00.00 for the backtracking.
% 0.18/0.48  		0:00:00.02 for the reduction.
% 0.18/0.48  
% 0.18/0.48  
% 0.18/0.48  Here is a proof with depth 3, length 10 :
% 0.18/0.48  % SZS output start Refutation
% See solution above
% 0.18/0.48  Formulae used in the proof : corollary_to_set_in_its_singleton null_class_defn singleton_set_defn unordered_pair_defn
% 0.18/0.48  
%------------------------------------------------------------------------------