%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 05:27:31 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     :    7 (   7 unt;   0 nHn;   7 RR)
%            Number of literals    :    7 (   0 equ;   1 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    equal(union(u,u),u),
    file('SET618+3.p',unknown),
    [] ).

cnf(4,axiom,
    equal(difference(u,u),empty_set),
    file('SET618+3.p',unknown),
    [] ).

cnf(5,axiom,
    ~ equal(symmetric_difference(skc1,skc1),empty_set),
    file('SET618+3.p',unknown),
    [] ).

cnf(14,axiom,
    equal(union(difference(u,v),difference(v,u)),symmetric_difference(u,v)),
    file('SET618+3.p',unknown),
    [] ).

cnf(52,plain,
    equal(difference(u,u),symmetric_difference(u,u)),
    inference(spr,[status(thm),theory(equality)],[14,3]),
    [iquote('0:SpR:14.0,3.0')] ).

cnf(58,plain,
    equal(symmetric_difference(u,u),empty_set),
    inference(rew,[status(thm),theory(equality)],[4,52]),
    [iquote('0:Rew:4.0,52.0')] ).

cnf(59,plain,
    $false,
    inference(unc,[status(thm)],[58,5]),
    [iquote('0:UnC:58.0,5.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11  % Problem  : SET618+3 : TPTP v8.1.0. Released v2.2.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.13/0.33  % Computer : n020.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Sun Jul 10 06:46:13 EDT 2022
% 0.13/0.33  % 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 32 clauses, backtracked 0 clauses, performed 0 splits and kept 27 clauses.
% 0.20/0.44  SPASS allocated 97823 KBytes.
% 0.20/0.44  SPASS spent	0:00:00.10 on the problem.
% 0.20/0.44  		0:00:00.04 for the input.
% 0.20/0.44  		0:00:00.03 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 7 :
% 0.20/0.44  % SZS output start Refutation
% See solution above
% 0.20/0.44  Formulae used in the proof : idempotency_of_union self_difference_is_empty_set prove_th93 symmetric_difference_defn
% 0.20/0.44  
%------------------------------------------------------------------------------