%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET095-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n003.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 05:23:57 EDT 2022

% Result   : Unsatisfiable 0.44s 0.62s
% Output   : Refutation 0.44s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   13 (   5 unt;   5 nHn;  13 RR)
%            Number of literals    :   24 (   0 equ;   8 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(1,axiom,
    member(x__dfg,y__dfg),
    file('SET095-6.p',unknown),
    [] ).

cnf(2,axiom,
    ~ subclass(singleton(x__dfg),y__dfg),
    file('SET095-6.p',unknown),
    [] ).

cnf(4,axiom,
    ( subclass(u,v)
    | member(not_subclass_element(u,v),u) ),
    file('SET095-6.p',unknown),
    [] ).

cnf(5,axiom,
    ( ~ member(not_subclass_element(u,v),v)
    | subclass(u,v) ),
    file('SET095-6.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ member(u,unordered_pair(v,w))
    | equal(u,w)
    | equal(u,v) ),
    file('SET095-6.p',unknown),
    [] ).

cnf(14,axiom,
    equal(unordered_pair(u,u),singleton(u)),
    file('SET095-6.p',unknown),
    [] ).

cnf(555,plain,
    ( ~ member(u,singleton(v))
    | equal(u,v)
    | equal(u,v) ),
    inference(spl,[status(thm),theory(equality)],[14,10]),
    [iquote('0:SpL:14.0,10.0')] ).

cnf(567,plain,
    ( ~ member(u,singleton(v))
    | equal(u,v) ),
    inference(obv,[status(thm),theory(equality)],[555]),
    [iquote('0:Obv:555.1')] ).

cnf(573,plain,
    ( subclass(singleton(u),v)
    | equal(not_subclass_element(singleton(u),v),u) ),
    inference(res,[status(thm),theory(equality)],[4,567]),
    [iquote('0:Res:4.1,567.0')] ).

cnf(1439,plain,
    ( ~ member(u,v)
    | subclass(singleton(u),v)
    | subclass(singleton(u),v) ),
    inference(spl,[status(thm),theory(equality)],[573,5]),
    [iquote('0:SpL:573.1,5.0')] ).

cnf(1444,plain,
    ( ~ member(u,v)
    | subclass(singleton(u),v) ),
    inference(obv,[status(thm),theory(equality)],[1439]),
    [iquote('0:Obv:1439.1')] ).

cnf(1461,plain,
    ~ member(x__dfg,y__dfg),
    inference(res,[status(thm),theory(equality)],[1444,2]),
    [iquote('0:Res:1444.1,2.0')] ).

cnf(1462,plain,
    $false,
    inference(mrr,[status(thm)],[1461,1]),
    [iquote('0:MRR:1461.0,1.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET095-6 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n003.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 01:26:29 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.44/0.62  
% 0.44/0.62  SPASS V 3.9 
% 0.44/0.62  SPASS beiseite: Proof found.
% 0.44/0.62  % SZS status Theorem
% 0.44/0.62  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.44/0.62  SPASS derived 1256 clauses, backtracked 0 clauses, performed 1 splits and kept 823 clauses.
% 0.44/0.62  SPASS allocated 77070 KBytes.
% 0.44/0.62  SPASS spent	0:00:00.26 on the problem.
% 0.44/0.62  		0:00:00.04 for the input.
% 0.44/0.62  		0:00:00.00 for the FLOTTER CNF translation.
% 0.44/0.62  		0:00:00.02 for inferences.
% 0.44/0.62  		0:00:00.00 for the backtracking.
% 0.44/0.62  		0:00:00.17 for the reduction.
% 0.44/0.62  
% 0.44/0.62  
% 0.44/0.62  Here is a proof with depth 4, length 13 :
% 0.44/0.62  % SZS output start Refutation
% See solution above
% 0.44/0.62  Formulae used in the proof : prove_property_of_singletons2_1 prove_property_of_singletons2_2 not_subclass_members1 not_subclass_members2 unordered_pair_member singleton_set
% 0.44/0.62  
%------------------------------------------------------------------------------