%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET093+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n014.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 05:23:54 EDT 2022

% Result   : Theorem 0.18s 0.46s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (   9 unt;   0 nHn;  11 RR)
%            Number of literals    :   14 (   0 equ;   6 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    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    subclass(u,universal_class),
    file('SET093+1.p',unknown),
    [] ).

cnf(5,axiom,
    ~ member(skc3,universal_class),
    file('SET093+1.p',unknown),
    [] ).

cnf(9,axiom,
    equal(singleton(member_of(skc3)),skc3),
    file('SET093+1.p',unknown),
    [] ).

cnf(10,axiom,
    member(unordered_pair(u,v),universal_class),
    file('SET093+1.p',unknown),
    [] ).

cnf(14,axiom,
    equal(unordered_pair(u,u),singleton(u)),
    file('SET093+1.p',unknown),
    [] ).

cnf(59,axiom,
    ( ~ member(u,v)
    | ~ subclass(v,w)
    | member(u,w) ),
    file('SET093+1.p',unknown),
    [] ).

cnf(111,plain,
    ( ~ subclass(u,universal_class)
    | ~ member(skc3,u) ),
    inference(res,[status(thm),theory(equality)],[59,5]),
    [iquote('0:Res:59.2,5.0')] ).

cnf(121,plain,
    ~ member(skc3,u),
    inference(mrr,[status(thm)],[111,3]),
    [iquote('0:MRR:111.0,3.0')] ).

cnf(127,plain,
    member(singleton(u),universal_class),
    inference(spr,[status(thm),theory(equality)],[14,10]),
    [iquote('0:SpR:14.0,10.0')] ).

cnf(129,plain,
    member(skc3,universal_class),
    inference(spr,[status(thm),theory(equality)],[9,127]),
    [iquote('0:SpR:9.0,127.0')] ).

cnf(130,plain,
    $false,
    inference(mrr,[status(thm)],[129,121]),
    [iquote('0:MRR:129.0,121.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11  % Problem  : SET093+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n014.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 01:24:35 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.18/0.46  
% 0.18/0.46  SPASS V 3.9 
% 0.18/0.46  SPASS beiseite: Proof found.
% 0.18/0.46  % SZS status Theorem
% 0.18/0.46  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.46  SPASS derived 27 clauses, backtracked 0 clauses, performed 0 splits and kept 112 clauses.
% 0.18/0.46  SPASS allocated 98242 KBytes.
% 0.18/0.46  SPASS spent	0:00:00.12 on the problem.
% 0.18/0.46  		0:00:00.04 for the input.
% 0.18/0.46  		0:00:00.05 for the FLOTTER CNF translation.
% 0.18/0.46  		0:00:00.00 for inferences.
% 0.18/0.46  		0:00:00.00 for the backtracking.
% 0.18/0.46  		0:00:00.01 for the reduction.
% 0.18/0.46  
% 0.18/0.46  
% 0.18/0.46  Here is a proof with depth 2, length 11 :
% 0.18/0.46  % SZS output start Refutation
% See solution above
% 0.18/0.46  Formulae used in the proof : class_elements_are_sets corollary_2_to_singletons_are_sets unordered_pair singleton_set_defn subclass_defn
% 0.18/0.46  
%------------------------------------------------------------------------------