%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET925+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n027.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 05:29:50 EDT 2022

% Result   : Theorem 0.22s 0.46s
% Output   : Refutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    9 (   4 unt;   1 nHn;   9 RR)
%            Number of literals    :   14 (   0 equ;   7 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    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(5,axiom,
    ( equal(set_difference(singleton(skc4),skc5),empty_set)
    | in(skc4,skc5) ),
    file('SET925+1.p',unknown),
    [] ).

cnf(6,axiom,
    ( ~ equal(set_difference(singleton(u),v),empty_set)
    | in(u,v) ),
    file('SET925+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ in(u,v)
    | equal(set_difference(singleton(u),v),empty_set) ),
    file('SET925+1.p',unknown),
    [] ).

cnf(8,axiom,
    ( ~ equal(set_difference(singleton(skc4),skc5),empty_set)
    | ~ in(skc4,skc5) ),
    file('SET925+1.p',unknown),
    [] ).

cnf(9,plain,
    equal(set_difference(singleton(skc4),skc5),empty_set),
    inference(mrr,[status(thm)],[5,7]),
    [iquote('0:MRR:5.1,7.0')] ).

cnf(10,plain,
    ( ~ equal(empty_set,empty_set)
    | ~ in(skc4,skc5) ),
    inference(rew,[status(thm),theory(equality)],[9,8]),
    [iquote('0:Rew:9.0,8.0')] ).

cnf(11,plain,
    ~ in(skc4,skc5),
    inference(obv,[status(thm),theory(equality)],[10]),
    [iquote('0:Obv:10.0')] ).

cnf(13,plain,
    in(skc4,skc5),
    inference(res,[status(thm),theory(equality)],[9,6]),
    [iquote('0:Res:9.0,6.0')] ).

cnf(14,plain,
    $false,
    inference(mrr,[status(thm)],[13,11]),
    [iquote('0:MRR:13.0,11.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.14  % Problem  : SET925+1 : TPTP v8.1.0. Released v3.2.0.
% 0.09/0.15  % Command  : run_spass %d %s
% 0.15/0.37  % Computer : n027.cluster.edu
% 0.15/0.37  % Model    : x86_64 x86_64
% 0.15/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37  % Memory   : 8042.1875MB
% 0.15/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37  % CPULimit : 300
% 0.15/0.37  % WCLimit  : 600
% 0.15/0.37  % DateTime : Mon Jul 11 04:32:48 EDT 2022
% 0.15/0.37  % CPUTime  : 
% 0.22/0.46  
% 0.22/0.46  SPASS V 3.9 
% 0.22/0.46  SPASS beiseite: Proof found.
% 0.22/0.46  % SZS status Theorem
% 0.22/0.46  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.22/0.46  SPASS derived 3 clauses, backtracked 0 clauses, performed 0 splits and kept 10 clauses.
% 0.22/0.46  SPASS allocated 85063 KBytes.
% 0.22/0.46  SPASS spent	0:00:00.08 on the problem.
% 0.22/0.46  		0:00:00.03 for the input.
% 0.22/0.46  		0:00:00.02 for the FLOTTER CNF translation.
% 0.22/0.46  		0:00:00.00 for inferences.
% 0.22/0.46  		0:00:00.00 for the backtracking.
% 0.22/0.46  		0:00:00.00 for the reduction.
% 0.22/0.46  
% 0.22/0.46  
% 0.22/0.46  Here is a proof with depth 1, length 9 :
% 0.22/0.46  % SZS output start Refutation
% See solution above
% 0.22/0.46  Formulae used in the proof : t68_zfmisc_1 l36_zfmisc_1
% 0.22/0.46  
%------------------------------------------------------------------------------