%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET090-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 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 05:23:52 EDT 2022

% Result   : Unsatisfiable 0.20s 0.46s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (   6 unt;   0 nHn;  11 RR)
%            Number of literals    :   16 (   0 equ;   7 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(31,axiom,
    ( ~ member(u,universal_class)
    | member(u,singleton(u)) ),
    file('SET090-7.p',unknown),
    [] ).

cnf(34,axiom,
    ( ~ member(u,singleton(v))
    | equal(u,v) ),
    file('SET090-7.p',unknown),
    [] ).

cnf(39,axiom,
    ( ~ member(u,universal_class)
    | member(member_of(singleton(u)),universal_class) ),
    file('SET090-7.p',unknown),
    [] ).

cnf(40,axiom,
    ( ~ member(u,universal_class)
    | equal(singleton(member_of(singleton(u))),singleton(u)) ),
    file('SET090-7.p',unknown),
    [] ).

cnf(43,axiom,
    member(u__dfg,universal_class),
    file('SET090-7.p',unknown),
    [] ).

cnf(44,axiom,
    ~ equal(member_of(singleton(u__dfg)),u__dfg),
    file('SET090-7.p',unknown),
    [] ).

cnf(141,plain,
    equal(singleton(member_of(singleton(u__dfg))),singleton(u__dfg)),
    inference(res,[status(thm),theory(equality)],[43,40]),
    [iquote('0:Res:43.0,40.0')] ).

cnf(146,plain,
    member(member_of(singleton(u__dfg)),universal_class),
    inference(res,[status(thm),theory(equality)],[43,39]),
    [iquote('0:Res:43.0,39.0')] ).

cnf(169,plain,
    ~ member(member_of(singleton(u__dfg)),singleton(u__dfg)),
    inference(res,[status(thm),theory(equality)],[34,44]),
    [iquote('0:Res:34.1,44.0')] ).

cnf(296,plain,
    ( ~ member(member_of(singleton(u__dfg)),universal_class)
    | member(member_of(singleton(u__dfg)),singleton(u__dfg)) ),
    inference(spr,[status(thm),theory(equality)],[141,31]),
    [iquote('0:SpR:141.0,31.1')] ).

cnf(297,plain,
    $false,
    inference(mrr,[status(thm)],[296,146,169]),
    [iquote('0:MRR:296.0,296.1,146.0,169.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET090-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.14/0.34  % Computer : n014.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Sun Jul 10 09:43:50 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.20/0.46  
% 0.20/0.46  SPASS V 3.9 
% 0.20/0.46  SPASS beiseite: Proof found.
% 0.20/0.46  % SZS status Theorem
% 0.20/0.46  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.46  SPASS derived 129 clauses, backtracked 0 clauses, performed 1 splits and kept 200 clauses.
% 0.20/0.46  SPASS allocated 75905 KBytes.
% 0.20/0.46  SPASS spent	0:00:00.10 on the problem.
% 0.20/0.46  		0:00:00.04 for the input.
% 0.20/0.46  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.46  		0:00:00.00 for inferences.
% 0.20/0.46  		0:00:00.00 for the backtracking.
% 0.20/0.46  		0:00:00.02 for the reduction.
% 0.20/0.46  
% 0.20/0.46  
% 0.20/0.46  Here is a proof with depth 2, length 11 :
% 0.20/0.46  % SZS output start Refutation
% See solution above
% 0.20/0.46  Formulae used in the proof : set_in_its_singleton only_member_in_singleton member_exists1 member_exists2 prove_member_of_singleton_is_unique_1 prove_member_of_singleton_is_unique_2
% 0.20/0.46  
%------------------------------------------------------------------------------