%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% 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 05:27:13 EDT 2022

% Result   : Theorem 0.21s 0.45s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   11 (   8 unt;   0 nHn;  11 RR)
%            Number of literals    :   15 (   0 equ;   6 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   7 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    subset(skc5,skc3),
    file('SET592+3.p',unknown),
    [] ).

cnf(2,axiom,
    subset(skc5,skc4),
    file('SET592+3.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(skc5,empty_set),
    file('SET592+3.p',unknown),
    [] ).

cnf(6,axiom,
    equal(intersection(skc3,skc4),empty_set),
    file('SET592+3.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ subset(u,empty_set)
    | equal(u,empty_set) ),
    file('SET592+3.p',unknown),
    [] ).

cnf(21,axiom,
    ( ~ subset(u,v)
    | ~ subset(u,w)
    | subset(u,intersection(w,v)) ),
    file('SET592+3.p',unknown),
    [] ).

cnf(29,plain,
    ( ~ subset(skc5,u)
    | subset(skc5,intersection(u,skc4)) ),
    inference(res,[status(thm),theory(equality)],[2,21]),
    [iquote('0:Res:2.0,21.1')] ).

cnf(35,plain,
    ~ subset(skc5,empty_set),
    inference(res,[status(thm),theory(equality)],[8,4]),
    [iquote('0:Res:8.1,4.0')] ).

cnf(53,plain,
    subset(skc5,intersection(skc3,skc4)),
    inference(res,[status(thm),theory(equality)],[1,29]),
    [iquote('0:Res:1.0,29.0')] ).

cnf(55,plain,
    subset(skc5,empty_set),
    inference(rew,[status(thm),theory(equality)],[6,53]),
    [iquote('0:Rew:6.0,53.0')] ).

cnf(56,plain,
    $false,
    inference(mrr,[status(thm)],[55,35]),
    [iquote('0:MRR:55.0,35.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13  % Problem  : SET592+3 : TPTP v8.1.0. Released v2.2.0.
% 0.04/0.13  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n009.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sun Jul 10 09:49:22 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.21/0.45  
% 0.21/0.45  SPASS V 3.9 
% 0.21/0.45  SPASS beiseite: Proof found.
% 0.21/0.45  % SZS status Theorem
% 0.21/0.45  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.21/0.45  SPASS derived 25 clauses, backtracked 0 clauses, performed 0 splits and kept 35 clauses.
% 0.21/0.45  SPASS allocated 97873 KBytes.
% 0.21/0.45  SPASS spent	0:00:00.09 on the problem.
% 0.21/0.45  		0:00:00.03 for the input.
% 0.21/0.45  		0:00:00.04 for the FLOTTER CNF translation.
% 0.21/0.45  		0:00:00.00 for inferences.
% 0.21/0.45  		0:00:00.00 for the backtracking.
% 0.21/0.45  		0:00:00.00 for the reduction.
% 0.21/0.45  
% 0.21/0.45  
% 0.21/0.45  Here is a proof with depth 2, length 11 :
% 0.21/0.45  % SZS output start Refutation
% See solution above
% 0.21/0.45  Formulae used in the proof : prove_th51 subset_of_empty_set_is_empty_set intersection_of_subsets
% 0.21/0.45  
%------------------------------------------------------------------------------