%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET617+3 : TPTP v8.1.0. Released v2.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n029.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 0.19s 0.45s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    7
% Syntax   : Number of clauses     :   15 (  12 unt;   0 nHn;  15 RR)
%            Number of literals    :   18 (   0 equ;   8 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    equal(union(u,empty_set),u),
    file('SET617+3.p',unknown),
    [] ).

cnf(4,axiom,
    equal(difference(u,empty_set),u),
    file('SET617+3.p',unknown),
    [] ).

cnf(5,axiom,
    equal(difference(empty_set,u),empty_set),
    file('SET617+3.p',unknown),
    [] ).

cnf(9,axiom,
    equal(union(u,v),union(v,u)),
    file('SET617+3.p',unknown),
    [] ).

cnf(10,axiom,
    equal(symmetric_difference(u,v),symmetric_difference(v,u)),
    file('SET617+3.p',unknown),
    [] ).

cnf(14,axiom,
    equal(union(difference(u,v),difference(v,u)),symmetric_difference(u,v)),
    file('SET617+3.p',unknown),
    [] ).

cnf(19,axiom,
    ( ~ equal(symmetric_difference(skc2,empty_set),skc2)
    | ~ equal(symmetric_difference(empty_set,skc3),skc3) ),
    file('SET617+3.p',unknown),
    [] ).

cnf(22,plain,
    ( ~ equal(symmetric_difference(empty_set,skc3),skc3)
    | ~ equal(symmetric_difference(empty_set,skc2),skc2) ),
    inference(rew,[status(thm),theory(equality)],[10,19]),
    [iquote('0:Rew:10.0,19.0')] ).

cnf(33,plain,
    equal(union(empty_set,u),u),
    inference(spr,[status(thm),theory(equality)],[9,3]),
    [iquote('0:SpR:9.0,3.0')] ).

cnf(51,plain,
    equal(union(difference(empty_set,u),u),symmetric_difference(empty_set,u)),
    inference(spr,[status(thm),theory(equality)],[4,14]),
    [iquote('0:SpR:4.0,14.0')] ).

cnf(55,plain,
    equal(symmetric_difference(empty_set,u),u),
    inference(rew,[status(thm),theory(equality)],[33,51,5]),
    [iquote('0:Rew:33.0,51.0,5.0,51.0')] ).

cnf(56,plain,
    ( ~ equal(symmetric_difference(empty_set,skc3),skc3)
    | ~ equal(skc2,skc2) ),
    inference(rew,[status(thm),theory(equality)],[55,22]),
    [iquote('0:Rew:55.0,22.1')] ).

cnf(59,plain,
    ~ equal(symmetric_difference(empty_set,skc3),skc3),
    inference(obv,[status(thm),theory(equality)],[56]),
    [iquote('0:Obv:56.1')] ).

cnf(60,plain,
    ~ equal(skc3,skc3),
    inference(rew,[status(thm),theory(equality)],[55,59]),
    [iquote('0:Rew:55.0,59.0')] ).

cnf(61,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[60]),
    [iquote('0:Obv:60.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : SET617+3 : TPTP v8.1.0. Released v2.2.0.
% 0.03/0.13  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n029.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 08:07:31 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 31 clauses, backtracked 0 clauses, performed 0 splits and kept 26 clauses.
% 0.19/0.45  SPASS allocated 97830 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  		0:00:00.04 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 1, length 15 :
% 0.19/0.45  % SZS output start Refutation
% See solution above
% 0.19/0.45  Formulae used in the proof : union_empty_set no_difference_with_empty_set1 no_difference_with_empty_set2 commutativity_of_union commutativity_of_symmetric_difference symmetric_difference_defn prove_th92
% 0.19/0.45  
%------------------------------------------------------------------------------