%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET104-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n009.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 05:24:06 EDT 2022

% Result   : Unsatisfiable 0.20s 0.54s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    5
% Syntax   : Number of clauses     :   10 (   8 unt;   2 nHn;  10 RR)
%            Number of literals    :   12 (   0 equ;   2 neg)
%            Maximal clause size   :    2 (   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;   6 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(21,axiom,
    ( member(u,universal_class)
    | equal(unordered_pair(u,v),singleton(v)) ),
    file('SET104-7.p',unknown),
    [] ).

cnf(35,axiom,
    ( member(u,universal_class)
    | equal(singleton(u),null_class) ),
    file('SET104-7.p',unknown),
    [] ).

cnf(57,axiom,
    ~ equal(unordered_pair(null_class,singleton(singleton(y__dfg))),ordered_pair(x__dfg,y__dfg)),
    file('SET104-7.p',unknown),
    [] ).

cnf(58,axiom,
    ~ member(x__dfg,universal_class),
    file('SET104-7.p',unknown),
    [] ).

cnf(71,axiom,
    equal(unordered_pair(singleton(u),unordered_pair(u,singleton(v))),ordered_pair(u,v)),
    file('SET104-7.p',unknown),
    [] ).

cnf(157,plain,
    equal(unordered_pair(x__dfg,u),singleton(u)),
    inference(res,[status(thm),theory(equality)],[21,58]),
    [iquote('0:Res:21.0,58.0')] ).

cnf(159,plain,
    equal(singleton(x__dfg),null_class),
    inference(res,[status(thm),theory(equality)],[35,58]),
    [iquote('0:Res:35.0,58.0')] ).

cnf(1205,plain,
    equal(unordered_pair(null_class,unordered_pair(x__dfg,singleton(u))),ordered_pair(x__dfg,u)),
    inference(spr,[status(thm),theory(equality)],[159,71]),
    [iquote('0:SpR:159.0,71.0')] ).

cnf(1213,plain,
    equal(unordered_pair(null_class,singleton(singleton(u))),ordered_pair(x__dfg,u)),
    inference(rew,[status(thm),theory(equality)],[157,1205]),
    [iquote('0:Rew:157.0,1205.0')] ).

cnf(1214,plain,
    $false,
    inference(unc,[status(thm)],[1213,57]),
    [iquote('0:UnC:1213.0,57.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET104-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.13/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n009.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 17:54:37 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.20/0.54  
% 0.20/0.54  SPASS V 3.9 
% 0.20/0.54  SPASS beiseite: Proof found.
% 0.20/0.54  % SZS status Theorem
% 0.20/0.54  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.54  SPASS derived 874 clauses, backtracked 0 clauses, performed 2 splits and kept 478 clauses.
% 0.20/0.54  SPASS allocated 76718 KBytes.
% 0.20/0.54  SPASS spent	0:00:00.17 on the problem.
% 0.20/0.54  		0:00:00.04 for the input.
% 0.20/0.54  		0:00:00.00 for the FLOTTER CNF translation.
% 0.20/0.54  		0:00:00.01 for inferences.
% 0.20/0.54  		0:00:00.00 for the backtracking.
% 0.20/0.54  		0:00:00.09 for the reduction.
% 0.20/0.54  
% 0.20/0.54  
% 0.20/0.54  Here is a proof with depth 2, length 10 :
% 0.20/0.54  % SZS output start Refutation
% See solution above
% 0.20/0.54  Formulae used in the proof : unordered_pair_equals_singleton2 singleton_is_null_class prove_property_2_of_ordered_pair_2 prove_property_2_of_ordered_pair_3 ordered_pair
% 0.20/0.54  
%------------------------------------------------------------------------------