%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET101+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n021.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 05:24:02 EDT 2022

% Result   : Theorem 1.68s 1.88s
% Output   : Refutation 1.68s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   7 unt;   0 nHn;  10 RR)
%            Number of literals    :   15 (   0 equ;   8 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(8,axiom,
    member(unordered_pair(u,v),universal_class),
    file('SET101+1.p',unknown),
    [] ).

cnf(11,axiom,
    equal(unordered_pair(u,u),singleton(u)),
    file('SET101+1.p',unknown),
    [] ).

cnf(15,axiom,
    ~ member(singleton(skc5),ordered_pair(skc5,skc4)),
    file('SET101+1.p',unknown),
    [] ).

cnf(56,axiom,
    equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
    file('SET101+1.p',unknown),
    [] ).

cnf(70,axiom,
    ( ~ equal(u,v)
    | ~ member(u,universal_class)
    | member(u,unordered_pair(v,w)) ),
    file('SET101+1.p',unknown),
    [] ).

cnf(102,plain,
    member(singleton(u),universal_class),
    inference(spr,[status(thm),theory(equality)],[11,8]),
    [iquote('0:SpR:11.0,8.0')] ).

cnf(950,plain,
    ( ~ equal(u,singleton(v))
    | ~ member(u,universal_class)
    | member(u,ordered_pair(v,w)) ),
    inference(spr,[status(thm),theory(equality)],[56,70]),
    [iquote('0:SpR:56.0,70.2')] ).

cnf(7344,plain,
    ( ~ equal(singleton(skc5),singleton(skc5))
    | ~ member(singleton(skc5),universal_class) ),
    inference(res,[status(thm),theory(equality)],[950,15]),
    [iquote('0:Res:950.2,15.0')] ).

cnf(7354,plain,
    ~ member(singleton(skc5),universal_class),
    inference(obv,[status(thm),theory(equality)],[7344]),
    [iquote('0:Obv:7344.0')] ).

cnf(7355,plain,
    $false,
    inference(mrr,[status(thm)],[7354,102]),
    [iquote('0:MRR:7354.0,102.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : SET101+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.04/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n021.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 07:08:23 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 1.68/1.88  
% 1.68/1.88  SPASS V 3.9 
% 1.68/1.88  SPASS beiseite: Proof found.
% 1.68/1.88  % SZS status Theorem
% 1.68/1.88  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 1.68/1.88  SPASS derived 6402 clauses, backtracked 122 clauses, performed 5 splits and kept 3303 clauses.
% 1.68/1.88  SPASS allocated 103064 KBytes.
% 1.68/1.88  SPASS spent	0:00:01.51 on the problem.
% 1.68/1.88  		0:00:00.04 for the input.
% 1.68/1.88  		0:00:00.06 for the FLOTTER CNF translation.
% 1.68/1.88  		0:00:00.06 for inferences.
% 1.68/1.88  		0:00:00.03 for the backtracking.
% 1.68/1.88  		0:00:01.25 for the reduction.
% 1.68/1.88  
% 1.68/1.88  
% 1.68/1.88  Here is a proof with depth 2, length 10 :
% 1.68/1.88  % SZS output start Refutation
% See solution above
% 1.68/1.88  Formulae used in the proof : unordered_pair singleton_set_defn singleton_member_of_ordered_pair ordered_pair_defn unordered_pair_defn
% 1.68/1.88  
%------------------------------------------------------------------------------