%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET094+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n005.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 05:23:55 EDT 2022

% Result   : Theorem 0.45s 0.62s
% Output   : Refutation 0.45s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   6 unt;   2 nHn;  10 RR)
%            Number of literals    :   16 (   0 equ;   5 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 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,
    member(skc5,skc4),
    file('SET094+1.p',unknown),
    [] ).

cnf(9,axiom,
    ~ equal(member_of(skc4),skc5),
    file('SET094+1.p',unknown),
    [] ).

cnf(10,axiom,
    equal(singleton(member_of(skc4)),skc4),
    file('SET094+1.p',unknown),
    [] ).

cnf(14,axiom,
    equal(unordered_pair(u,u),singleton(u)),
    file('SET094+1.p',unknown),
    [] ).

cnf(68,axiom,
    ( ~ member(u,unordered_pair(v,w))
    | equal(u,w)
    | equal(u,v) ),
    file('SET094+1.p',unknown),
    [] ).

cnf(988,plain,
    ( ~ member(u,singleton(v))
    | equal(u,v)
    | equal(u,v) ),
    inference(spl,[status(thm),theory(equality)],[14,68]),
    [iquote('0:SpL:14.0,68.0')] ).

cnf(1005,plain,
    ( ~ member(u,singleton(v))
    | equal(u,v) ),
    inference(obv,[status(thm),theory(equality)],[988]),
    [iquote('0:Obv:988.1')] ).

cnf(1196,plain,
    ( ~ member(u,skc4)
    | equal(u,member_of(skc4)) ),
    inference(spl,[status(thm),theory(equality)],[10,1005]),
    [iquote('0:SpL:10.0,1005.0')] ).

cnf(1324,plain,
    equal(member_of(skc4),skc5),
    inference(res,[status(thm),theory(equality)],[3,1196]),
    [iquote('0:Res:3.0,1196.0')] ).

cnf(1326,plain,
    $false,
    inference(mrr,[status(thm)],[1324,9]),
    [iquote('0:MRR:1324.0,9.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET094+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n005.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 : Mon Jul 11 04:58:07 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.45/0.62  
% 0.45/0.62  SPASS V 3.9 
% 0.45/0.62  SPASS beiseite: Proof found.
% 0.45/0.62  % SZS status Theorem
% 0.45/0.62  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.45/0.62  SPASS derived 1129 clauses, backtracked 81 clauses, performed 1 splits and kept 897 clauses.
% 0.45/0.62  SPASS allocated 98651 KBytes.
% 0.45/0.62  SPASS spent	0:00:00.27 on the problem.
% 0.45/0.62  		0:00:00.03 for the input.
% 0.45/0.62  		0:00:00.06 for the FLOTTER CNF translation.
% 0.45/0.62  		0:00:00.01 for inferences.
% 0.45/0.62  		0:00:00.00 for the backtracking.
% 0.45/0.62  		0:00:00.13 for the reduction.
% 0.45/0.62  
% 0.45/0.62  
% 0.45/0.62  Here is a proof with depth 3, length 10 :
% 0.45/0.62  % SZS output start Refutation
% See solution above
% 0.45/0.62  Formulae used in the proof : property_of_singletons1_1 singleton_set_defn unordered_pair_defn
% 0.45/0.62  
%------------------------------------------------------------------------------