%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET867+1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n016.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 05:29:28 EDT 2022

% Result   : Theorem 0.13s 0.37s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    3
% Syntax   : Number of clauses     :    8 (   4 unt;   2 nHn;   8 RR)
%            Number of literals    :   13 (   0 equ;   5 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   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(4,axiom,
    ~ equal(union(empty_set),empty_set),
    file('SET867+1.p',unknown),
    [] ).

cnf(7,axiom,
    ( ~ in(u,v)
    | ~ equal(v,empty_set) ),
    file('SET867+1.p',unknown),
    [] ).

cnf(10,axiom,
    ( equal(u,union(v))
    | in(skf7(v,u),u)
    | in(skf8(v,w),v) ),
    file('SET867+1.p',unknown),
    [] ).

cnf(15,plain,
    ( in(skf8(empty_set,u),empty_set)
    | in(skf7(empty_set,empty_set),empty_set) ),
    inference(res,[status(thm),theory(equality)],[10,4]),
    [iquote('0:Res:10.2,4.0')] ).

cnf(20,plain,
    ( ~ equal(empty_set,empty_set)
    | in(skf7(empty_set,empty_set),empty_set) ),
    inference(res,[status(thm),theory(equality)],[15,7]),
    [iquote('0:Res:15.0,7.0')] ).

cnf(21,plain,
    in(skf7(empty_set,empty_set),empty_set),
    inference(obv,[status(thm),theory(equality)],[20]),
    [iquote('0:Obv:20.0')] ).

cnf(24,plain,
    ~ equal(empty_set,empty_set),
    inference(res,[status(thm),theory(equality)],[21,7]),
    [iquote('0:Res:21.0,7.0')] ).

cnf(25,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[24]),
    [iquote('0:Obv:24.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.08  % Problem  : SET867+1 : TPTP v8.1.0. Released v3.2.0.
% 0.02/0.09  % Command  : run_spass %d %s
% 0.09/0.28  % Computer : n016.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 600
% 0.09/0.28  % DateTime : Mon Jul 11 02:43:27 EDT 2022
% 0.09/0.28  % CPUTime  : 
% 0.13/0.37  
% 0.13/0.37  SPASS V 3.9 
% 0.13/0.37  SPASS beiseite: Proof found.
% 0.13/0.37  % SZS status Theorem
% 0.13/0.37  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.13/0.37  SPASS derived 9 clauses, backtracked 0 clauses, performed 0 splits and kept 20 clauses.
% 0.13/0.37  SPASS allocated 85249 KBytes.
% 0.13/0.37  SPASS spent	0:00:00.07 on the problem.
% 0.13/0.37  		0:00:00.03 for the input.
% 0.13/0.37  		0:00:00.03 for the FLOTTER CNF translation.
% 0.13/0.37  		0:00:00.00 for inferences.
% 0.13/0.37  		0:00:00.00 for the backtracking.
% 0.13/0.37  		0:00:00.00 for the reduction.
% 0.13/0.37  
% 0.13/0.37  
% 0.13/0.37  Here is a proof with depth 3, length 8 :
% 0.13/0.37  % SZS output start Refutation
% See solution above
% 0.13/0.37  Formulae used in the proof : t2_zfmisc_1 d1_xboole_0 d4_tarski antisymmetry_r2_hidden
% 0.13/0.37  
%------------------------------------------------------------------------------