%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET599+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n007.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 05:27:17 EDT 2022

% Result   : Theorem 0.19s 0.45s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    5
% Syntax   : Number of clauses     :    9 (   9 unt;   0 nHn;   9 RR)
%            Number of literals    :    9 (   0 equ;   2 neg)
%            Maximal clause size   :    1 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    3 (   2 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(2,axiom,
    subset(u,union(u,v)),
    file('SET599+3.p',unknown),
    [] ).

cnf(3,axiom,
    equal(union(u,v),union(v,u)),
    file('SET599+3.p',unknown),
    [] ).

cnf(4,axiom,
    equal(symmetric_difference(u,v),symmetric_difference(v,u)),
    file('SET599+3.p',unknown),
    [] ).

cnf(5,axiom,
    ~ subset(difference(skc3,skc2),symmetric_difference(skc3,skc2)),
    file('SET599+3.p',unknown),
    [] ).

cnf(10,axiom,
    equal(union(difference(u,v),difference(v,u)),symmetric_difference(u,v)),
    file('SET599+3.p',unknown),
    [] ).

cnf(17,plain,
    ~ subset(difference(skc3,skc2),symmetric_difference(skc2,skc3)),
    inference(rew,[status(thm),theory(equality)],[4,5]),
    [iquote('0:Rew:4.0,5.0')] ).

cnf(24,plain,
    subset(u,union(v,u)),
    inference(spr,[status(thm),theory(equality)],[3,2]),
    [iquote('0:SpR:3.0,2.0')] ).

cnf(39,plain,
    subset(difference(u,v),symmetric_difference(v,u)),
    inference(spr,[status(thm),theory(equality)],[10,24]),
    [iquote('0:SpR:10.0,24.0')] ).

cnf(41,plain,
    $false,
    inference(unc,[status(thm)],[39,17]),
    [iquote('0:UnC:39.0,17.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : SET599+3 : TPTP v8.1.0. Released v2.2.0.
% 0.07/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n007.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 21:15:47 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.19/0.45  
% 0.19/0.45  SPASS V 3.9 
% 0.19/0.45  SPASS beiseite: Proof found.
% 0.19/0.45  % SZS status Theorem
% 0.19/0.45  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.45  SPASS derived 20 clauses, backtracked 0 clauses, performed 0 splits and kept 20 clauses.
% 0.19/0.45  SPASS allocated 85290 KBytes.
% 0.19/0.45  SPASS spent	0:00:00.10 on the problem.
% 0.19/0.45  		0:00:00.04 for the input.
% 0.19/0.45  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.45  		0:00:00.00 for inferences.
% 0.19/0.45  		0:00:00.00 for the backtracking.
% 0.19/0.45  		0:00:00.00 for the reduction.
% 0.19/0.45  
% 0.19/0.45  
% 0.19/0.45  Here is a proof with depth 2, length 9 :
% 0.19/0.45  % SZS output start Refutation
% See solution above
% 0.19/0.45  Formulae used in the proof : subset_of_union commutativity_of_union commutativity_of_symmetric_difference prove_th58 symmetric_difference_defn
% 0.19/0.45  
%------------------------------------------------------------------------------