%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET063+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n024.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 05:23:23 EDT 2022

% Result   : Theorem 0.20s 0.43s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    6 (   4 unt;   0 nHn;   6 RR)
%            Number of literals    :    9 (   0 equ;   4 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   4 con; 0-0 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    subset(skc1,empty_set),
    file('SET063+3.p',unknown),
    [] ).

cnf(2,axiom,
    subset(empty_set,u),
    file('SET063+3.p',unknown),
    [] ).

cnf(4,axiom,
    ~ equal(skc1,empty_set),
    file('SET063+3.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ subset(u,v)
    | ~ subset(v,u)
    | equal(v,u) ),
    file('SET063+3.p',unknown),
    [] ).

cnf(14,plain,
    ( ~ subset(empty_set,skc1)
    | equal(skc1,empty_set) ),
    inference(res,[status(thm),theory(equality)],[1,13]),
    [iquote('0:Res:1.0,13.1')] ).

cnf(19,plain,
    $false,
    inference(mrr,[status(thm)],[14,2,4]),
    [iquote('0:MRR:14.0,14.1,2.0,4.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET063+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n024.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 21:47:58 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.20/0.43  
% 0.20/0.43  SPASS V 3.9 
% 0.20/0.43  SPASS beiseite: Proof found.
% 0.20/0.43  % SZS status Theorem
% 0.20/0.43  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.20/0.43  SPASS derived 5 clauses, backtracked 0 clauses, performed 0 splits and kept 13 clauses.
% 0.20/0.43  SPASS allocated 97678 KBytes.
% 0.20/0.43  SPASS spent	0:00:00.08 on the problem.
% 0.20/0.43  		0:00:00.03 for the input.
% 0.20/0.43  		0:00:00.03 for the FLOTTER CNF translation.
% 0.20/0.43  		0:00:00.00 for inferences.
% 0.20/0.43  		0:00:00.00 for the backtracking.
% 0.20/0.43  		0:00:00.00 for the reduction.
% 0.20/0.43  
% 0.20/0.43  
% 0.20/0.43  Here is a proof with depth 1, length 6 :
% 0.20/0.43  % SZS output start Refutation
% See solution above
% 0.20/0.43  Formulae used in the proof : prove_subset_of_empty_set_is_empty_set empty_set_subset equal_defn
% 0.20/0.43  
%------------------------------------------------------------------------------