%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU161+3 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n022.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 14:34:32 EDT 2022

% Result   : Theorem 0.19s 0.42s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   7 unt;   0 nHn;   8 RR)
%            Number of literals    :    9 (   0 equ;   3 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(2,axiom,
    in(skc4,skc5),
    file('SEU161+3.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(set_union2(singleton(skc4),skc5),skc5),
    file('SEU161+3.p',unknown),
    [] ).

cnf(8,axiom,
    equal(set_union2(u,v),set_union2(v,u)),
    file('SEU161+3.p',unknown),
    [] ).

cnf(10,axiom,
    ( ~ in(u,v)
    | equal(set_union2(singleton(u),v),v) ),
    file('SEU161+3.p',unknown),
    [] ).

cnf(11,plain,
    ~ equal(set_union2(skc5,singleton(skc4)),skc5),
    inference(rew,[status(thm),theory(equality)],[8,5]),
    [iquote('0:Rew:8.0,5.0')] ).

cnf(12,plain,
    equal(set_union2(singleton(skc4),skc5),skc5),
    inference(res,[status(thm),theory(equality)],[2,10]),
    [iquote('0:Res:2.0,10.0')] ).

cnf(15,plain,
    equal(set_union2(skc5,singleton(skc4)),skc5),
    inference(rew,[status(thm),theory(equality)],[8,12]),
    [iquote('0:Rew:8.0,12.0')] ).

cnf(16,plain,
    $false,
    inference(mrr,[status(thm)],[15,11]),
    [iquote('0:MRR:15.0,11.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SEU161+3 : TPTP v8.1.0. Released v3.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n022.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 : Sun Jun 19 17:20:16 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.42  
% 0.19/0.42  SPASS V 3.9 
% 0.19/0.42  SPASS beiseite: Proof found.
% 0.19/0.42  % SZS status Theorem
% 0.19/0.42  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.42  SPASS derived 3 clauses, backtracked 0 clauses, performed 0 splits and kept 12 clauses.
% 0.19/0.42  SPASS allocated 85070 KBytes.
% 0.19/0.42  SPASS spent	0:00:00.08 on the problem.
% 0.19/0.42  		0:00:00.03 for the input.
% 0.19/0.42  		0:00:00.02 for the FLOTTER CNF translation.
% 0.19/0.42  		0:00:00.00 for inferences.
% 0.19/0.42  		0:00:00.00 for the backtracking.
% 0.19/0.42  		0:00:00.00 for the reduction.
% 0.19/0.42  
% 0.19/0.42  
% 0.19/0.42  Here is a proof with depth 1, length 8 :
% 0.19/0.42  % SZS output start Refutation
% See solution above
% 0.19/0.42  Formulae used in the proof : t46_zfmisc_1 commutativity_k2_xboole_0 l23_zfmisc_1
% 0.19/0.43  
%------------------------------------------------------------------------------