%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET094-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n008.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   : Unsatisfiable 0.19s 0.51s
% Output   : Refutation 0.19s
% 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(1,axiom,
    equal(singleton(member_of(x__dfg)),x__dfg),
    file('SET094-6.p',unknown),
    [] ).

cnf(2,axiom,
    member(y__dfg,x__dfg),
    file('SET094-6.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(member_of(x__dfg),y__dfg),
    file('SET094-6.p',unknown),
    [] ).

cnf(11,axiom,
    ( ~ member(u,unordered_pair(v,w))
    | equal(u,w)
    | equal(u,v) ),
    file('SET094-6.p',unknown),
    [] ).

cnf(15,axiom,
    equal(unordered_pair(u,u),singleton(u)),
    file('SET094-6.p',unknown),
    [] ).

cnf(541,plain,
    ( ~ member(u,singleton(v))
    | equal(u,v)
    | equal(u,v) ),
    inference(spl,[status(thm),theory(equality)],[15,11]),
    [iquote('0:SpL:15.0,11.0')] ).

cnf(554,plain,
    ( ~ member(u,singleton(v))
    | equal(u,v) ),
    inference(obv,[status(thm),theory(equality)],[541]),
    [iquote('0:Obv:541.1')] ).

cnf(556,plain,
    ( ~ member(u,x__dfg)
    | equal(u,member_of(x__dfg)) ),
    inference(spl,[status(thm),theory(equality)],[1,554]),
    [iquote('0:SpL:1.0,554.0')] ).

cnf(570,plain,
    equal(member_of(x__dfg),y__dfg),
    inference(res,[status(thm),theory(equality)],[2,556]),
    [iquote('0:Res:2.0,556.0')] ).

cnf(580,plain,
    $false,
    inference(mrr,[status(thm)],[570,3]),
    [iquote('0:MRR:570.0,3.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem  : SET094-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.12/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n008.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 07:15:23 EDT 2022
% 0.19/0.33  % CPUTime  : 
% 0.19/0.51  
% 0.19/0.51  SPASS V 3.9 
% 0.19/0.51  SPASS beiseite: Proof found.
% 0.19/0.51  % SZS status Theorem
% 0.19/0.51  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.19/0.51  SPASS derived 451 clauses, backtracked 0 clauses, performed 0 splits and kept 434 clauses.
% 0.19/0.51  SPASS allocated 76260 KBytes.
% 0.19/0.51  SPASS spent	0:00:00.16 on the problem.
% 0.19/0.51  		0:00:00.04 for the input.
% 0.19/0.51  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.51  		0:00:00.01 for inferences.
% 0.19/0.51  		0:00:00.00 for the backtracking.
% 0.19/0.51  		0:00:00.08 for the reduction.
% 0.19/0.51  
% 0.19/0.51  
% 0.19/0.51  Here is a proof with depth 3, length 10 :
% 0.19/0.51  % SZS output start Refutation
% See solution above
% 0.19/0.51  Formulae used in the proof : prove_property_of_singletons1_1 prove_property_of_singletons1_2 prove_property_of_singletons1_3 unordered_pair_member singleton_set
% 0.19/0.51  
%------------------------------------------------------------------------------