%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET098-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n006.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 05:24:00 EDT 2022

% Result   : Unsatisfiable 0.19s 0.45s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    8 (   5 unt;   2 nHn;   8 RR)
%            Number of literals    :   12 (   0 equ;   5 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(50,axiom,
    ( equal(u,null_class)
    | equal(singleton(not_subclass_element(u,null_class)),u)
    | member(not_subclass_element(intersection(complement(singleton(not_subclass_element(u,null_class))),u),null_class),intersection(complement(singleton(not_subclass_element(u,null_class))),u)) ),
    file('SET098-7.p',unknown),
    [] ).

cnf(51,axiom,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x__dfg,null_class))),x__dfg),null_class),x__dfg),
    file('SET098-7.p',unknown),
    [] ).

cnf(52,axiom,
    ~ equal(singleton(not_subclass_element(x__dfg,null_class)),x__dfg),
    file('SET098-7.p',unknown),
    [] ).

cnf(53,axiom,
    ~ equal(null_class,x__dfg),
    file('SET098-7.p',unknown),
    [] ).

cnf(75,axiom,
    ( ~ member(u,intersection(v,w))
    | member(u,w) ),
    file('SET098-7.p',unknown),
    [] ).

cnf(182,plain,
    ( member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x__dfg,null_class))),x__dfg),null_class),intersection(complement(singleton(not_subclass_element(x__dfg,null_class))),x__dfg))
    | equal(null_class,x__dfg) ),
    inference(res,[status(thm),theory(equality)],[50,52]),
    [iquote('0:Res:50.1,52.0')] ).

cnf(211,plain,
    ~ member(not_subclass_element(intersection(complement(singleton(not_subclass_element(x__dfg,null_class))),x__dfg),null_class),intersection(u,x__dfg)),
    inference(res,[status(thm),theory(equality)],[75,51]),
    [iquote('0:Res:75.1,51.0')] ).

cnf(218,plain,
    $false,
    inference(mrr,[status(thm)],[182,211,53]),
    [iquote('0:MRR:182.0,182.1,211.0,53.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET098-7 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n006.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 : Sun Jul 10 02:57:06 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.45  
% 0.19/0.45  SPASS V 3.9 
% 0.19/0.45  SPASS beiseite: Proof found.
% 0.19/0.45  % SZS status Theorem
% 0.19/0.45  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.45  SPASS derived 42 clauses, backtracked 0 clauses, performed 0 splits and kept 166 clauses.
% 0.19/0.45  SPASS allocated 75834 KBytes.
% 0.19/0.45  SPASS spent	0:00:00.09 on the problem.
% 0.19/0.45  		0:00:00.04 for the input.
% 0.19/0.45  		0:00:00.00 for the FLOTTER CNF translation.
% 0.19/0.45  		0:00:00.00 for inferences.
% 0.19/0.45  		0:00:00.00 for the backtracking.
% 0.19/0.45  		0:00:00.01 for the reduction.
% 0.19/0.45  
% 0.19/0.45  
% 0.19/0.45  Here is a proof with depth 1, length 8 :
% 0.19/0.45  % SZS output start Refutation
% See solution above
% 0.19/0.45  Formulae used in the proof : number_of_elements_in_class prove_corollary_1_to_number_of_elements_in_class_1 prove_corollary_1_to_number_of_elements_in_class_2 prove_corollary_1_to_number_of_elements_in_class_3 intersection2
% 0.19/0.45  
%------------------------------------------------------------------------------