%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU161+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n013.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 0.20s 0.44s
% Output   : Refutation 0.20s
% 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(1,axiom,
    in(skc2,skc3),
    file('SEU161+1.p',unknown),
    [] ).

cnf(3,axiom,
    ~ equal(set_union2(singleton(skc2),skc3),skc3),
    file('SEU161+1.p',unknown),
    [] ).

cnf(4,axiom,
    equal(set_union2(u,v),set_union2(v,u)),
    file('SEU161+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ in(u,v)
    | equal(set_union2(singleton(u),v),v) ),
    file('SEU161+1.p',unknown),
    [] ).

cnf(7,plain,
    ~ equal(set_union2(skc3,singleton(skc2)),skc3),
    inference(rew,[status(thm),theory(equality)],[4,3]),
    [iquote('0:Rew:4.0,3.0')] ).

cnf(8,plain,
    equal(set_union2(singleton(skc2),skc3),skc3),
    inference(res,[status(thm),theory(equality)],[1,6]),
    [iquote('0:Res:1.0,6.0')] ).

cnf(11,plain,
    equal(set_union2(skc3,singleton(skc2)),skc3),
    inference(rew,[status(thm),theory(equality)],[4,8]),
    [iquote('0:Rew:4.0,8.0')] ).

cnf(12,plain,
    $false,
    inference(mrr,[status(thm)],[11,7]),
    [iquote('0:MRR:11.0,7.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13  % Problem  : SEU161+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.14  % Command  : run_spass %d %s
% 0.14/0.35  % Computer : n013.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 Jun 19 12:36:44 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.20/0.44  
% 0.20/0.44  SPASS V 3.9 
% 0.20/0.44  SPASS beiseite: Proof found.
% 0.20/0.44  % SZS status Theorem
% 0.20/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.20/0.44  SPASS derived 3 clauses, backtracked 0 clauses, performed 0 splits and kept 8 clauses.
% 0.20/0.44  SPASS allocated 85060 KBytes.
% 0.20/0.44  SPASS spent	0:00:00.08 on the problem.
% 0.20/0.44  		0:00:00.03 for the input.
% 0.20/0.44  		0:00:00.02 for the FLOTTER CNF translation.
% 0.20/0.44  		0:00:00.00 for inferences.
% 0.20/0.44  		0:00:00.00 for the backtracking.
% 0.20/0.44  		0:00:00.00 for the reduction.
% 0.20/0.44  
% 0.20/0.44  
% 0.20/0.44  Here is a proof with depth 1, length 8 :
% 0.20/0.44  % SZS output start Refutation
% See solution above
% 0.20/0.44  Formulae used in the proof : t46_zfmisc_1 commutativity_k2_xboole_0 l23_zfmisc_1
% 0.20/0.44  
%------------------------------------------------------------------------------