%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET090+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n026.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 05:23:51 EDT 2022

% Result   : Theorem 0.48s 0.66s
% Output   : Refutation 0.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   15 (   8 unt;   0 nHn;  15 RR)
%            Number of literals    :   25 (   0 equ;  11 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    member(skc3,universal_class),
    file('SET090+1.p',unknown),
    [] ).

cnf(12,axiom,
    ~ equal(member_of(singleton(skc3)),skc3),
    file('SET090+1.p',unknown),
    [] ).

cnf(38,axiom,
    ( ~ member(u,universal_class)
    | member(member_of(singleton(u)),universal_class) ),
    file('SET090+1.p',unknown),
    [] ).

cnf(58,axiom,
    ( ~ member(u,universal_class)
    | equal(singleton(member_of(singleton(u))),singleton(u)) ),
    file('SET090+1.p',unknown),
    [] ).

cnf(61,axiom,
    equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
    file('SET090+1.p',unknown),
    [] ).

cnf(83,axiom,
    ( ~ member(u,universal_class)
    | ~ member(v,universal_class)
    | equal(second(ordered_pair(v,u)),u) ),
    file('SET090+1.p',unknown),
    [] ).

cnf(105,plain,
    equal(singleton(member_of(singleton(skc3))),singleton(skc3)),
    inference(res,[status(thm),theory(equality)],[3,58]),
    [iquote('0:Res:3.0,58.0')] ).

cnf(107,plain,
    member(member_of(singleton(skc3)),universal_class),
    inference(res,[status(thm),theory(equality)],[3,38]),
    [iquote('0:Res:3.0,38.0')] ).

cnf(112,plain,
    ( ~ member(u,universal_class)
    | equal(second(ordered_pair(u,skc3)),skc3) ),
    inference(res,[status(thm),theory(equality)],[3,83]),
    [iquote('0:Res:3.0,83.1')] ).

cnf(645,plain,
    equal(unordered_pair(singleton(u),unordered_pair(u,singleton(skc3))),ordered_pair(u,member_of(singleton(skc3)))),
    inference(spr,[status(thm),theory(equality)],[105,61]),
    [iquote('0:SpR:105.0,61.0')] ).

cnf(648,plain,
    equal(ordered_pair(u,member_of(singleton(skc3))),ordered_pair(u,skc3)),
    inference(rew,[status(thm),theory(equality)],[61,645]),
    [iquote('0:Rew:61.0,645.0')] ).

cnf(1471,plain,
    ( ~ member(member_of(singleton(skc3)),universal_class)
    | ~ member(u,universal_class)
    | equal(second(ordered_pair(u,skc3)),member_of(singleton(skc3))) ),
    inference(spr,[status(thm),theory(equality)],[648,83]),
    [iquote('0:SpR:648.0,83.2')] ).

cnf(1488,plain,
    ( ~ member(member_of(singleton(skc3)),universal_class)
    | ~ member(u,universal_class)
    | equal(member_of(singleton(skc3)),skc3) ),
    inference(rew,[status(thm),theory(equality)],[112,1471]),
    [iquote('0:Rew:112.1,1471.2')] ).

cnf(1489,plain,
    ( ~ member(member_of(singleton(skc3)),universal_class)
    | equal(member_of(singleton(skc3)),skc3) ),
    inference(con,[status(thm)],[1488]),
    [iquote('0:Con:1488.1')] ).

cnf(1490,plain,
    $false,
    inference(mrr,[status(thm)],[1489,107,12]),
    [iquote('0:MRR:1489.0,1489.1,107.0,12.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET090+1 : TPTP v8.1.0. Bugfixed v7.3.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n026.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jul  9 21:55:26 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.48/0.66  
% 0.48/0.66  SPASS V 3.9 
% 0.48/0.66  SPASS beiseite: Proof found.
% 0.48/0.66  % SZS status Theorem
% 0.48/0.66  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.48/0.66  SPASS derived 1285 clauses, backtracked 58 clauses, performed 4 splits and kept 987 clauses.
% 0.48/0.66  SPASS allocated 98813 KBytes.
% 0.48/0.66  SPASS spent	0:00:00.30 on the problem.
% 0.48/0.66  		0:00:00.04 for the input.
% 0.48/0.66  		0:00:00.06 for the FLOTTER CNF translation.
% 0.48/0.66  		0:00:00.01 for inferences.
% 0.48/0.66  		0:00:00.00 for the backtracking.
% 0.48/0.66  		0:00:00.16 for the reduction.
% 0.48/0.66  
% 0.48/0.66  
% 0.48/0.66  Here is a proof with depth 3, length 15 :
% 0.48/0.66  % SZS output start Refutation
% See solution above
% 0.48/0.66  Formulae used in the proof : member_of_singleton member_singleton_universal member_singleton_singleton ordered_pair_defn first_second
% 0.48/0.66  
%------------------------------------------------------------------------------