%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET082-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n017.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 05:23:45 EDT 2022

% Result   : Unsatisfiable 0.20s 0.44s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   4 unt;   4 nHn;   8 RR)
%            Number of literals    :   14 (   0 equ;   2 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    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(20,axiom,
    ( member(u,universal_class)
    | equal(unordered_pair(v,u),singleton(v)) ),
    file('SET082-7.p',unknown),
    [] ).

cnf(22,axiom,
    ( equal(unordered_pair(u,v),null_class)
    | member(u,universal_class)
    | member(v,universal_class) ),
    file('SET082-7.p',unknown),
    [] ).

cnf(35,axiom,
    ~ member(x__dfg,universal_class),
    file('SET082-7.p',unknown),
    [] ).

cnf(36,axiom,
    ~ equal(singleton(x__dfg),null_class),
    file('SET082-7.p',unknown),
    [] ).

cnf(128,plain,
    ( equal(singleton(u),null_class)
    | member(u,universal_class)
    | member(v,universal_class) ),
    inference(rew,[status(thm),theory(equality)],[20,22]),
    [iquote('0:Rew:20.1,22.0')] ).

cnf(129,plain,
    ( member(u,universal_class)
    | equal(singleton(u),null_class) ),
    inference(con,[status(thm)],[128]),
    [iquote('0:Con:128.2')] ).

cnf(144,plain,
    member(x__dfg,universal_class),
    inference(res,[status(thm),theory(equality)],[129,36]),
    [iquote('0:Res:129.0,36.0')] ).

cnf(168,plain,
    $false,
    inference(mrr,[status(thm)],[144,35]),
    [iquote('0:MRR:144.0,35.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SET082-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.13/0.35  % Computer : n017.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 600
% 0.13/0.35  % DateTime : Mon Jul 11 04:41:03 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.44  
% 0.20/0.44  SPASS V 3.9 
% 0.20/0.44  SPASS beiseite: Proof found.
% 0.20/0.44  % SZS status Theorem
% 0.20/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.44  SPASS derived 19 clauses, backtracked 0 clauses, performed 0 splits and kept 125 clauses.
% 0.20/0.44  SPASS allocated 75779 KBytes.
% 0.20/0.44  SPASS spent	0:00:00.07 on the problem.
% 0.20/0.44  		0:00:00.04 for the input.
% 0.20/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.44  		0:00:00.00 for inferences.
% 0.20/0.44  		0:00:00.00 for the backtracking.
% 0.20/0.44  		0:00:00.01 for the reduction.
% 0.20/0.44  
% 0.20/0.44  
% 0.20/0.44  Here is a proof with depth 1, length 8 :
% 0.20/0.44  % SZS output start Refutation
% See solution above
% 0.20/0.44  Formulae used in the proof : unordered_pair_equals_singleton1 null_unordered_pair prove_singleton_is_null_class_1 prove_singleton_is_null_class_2
% 0.20/0.44  
%------------------------------------------------------------------------------