%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET813+4 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n025.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 05:28:49 EDT 2022

% Result   : Theorem 0.36s 0.52s
% Output   : Refutation 0.36s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    8 (   5 unt;   0 nHn;   8 RR)
%            Number of literals    :   11 (   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;   4 con; 0-2 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(3,axiom,
    ~ member(skc1,suc(skc1)),
    file('SET813+4.p',unknown),
    [] ).

cnf(17,axiom,
    ( ~ equal(u,v)
    | member(u,singleton(v)) ),
    file('SET813+4.p',unknown),
    [] ).

cnf(27,axiom,
    ( ~ member(u,v)
    | member(u,union(w,v)) ),
    file('SET813+4.p',unknown),
    [] ).

cnf(43,axiom,
    ( ~ member(u,union(v,singleton(v)))
    | member(u,suc(v)) ),
    file('SET813+4.p',unknown),
    [] ).

cnf(105,plain,
    ~ member(skc1,union(skc1,singleton(skc1))),
    inference(res,[status(thm),theory(equality)],[43,3]),
    [iquote('0:Res:43.1,3.0')] ).

cnf(177,plain,
    ~ member(skc1,singleton(skc1)),
    inference(res,[status(thm),theory(equality)],[27,105]),
    [iquote('0:Res:27.1,105.0')] ).

cnf(179,plain,
    ~ equal(skc1,skc1),
    inference(res,[status(thm),theory(equality)],[17,177]),
    [iquote('0:Res:17.1,177.0')] ).

cnf(180,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[179]),
    [iquote('0:Obv:179.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SET813+4 : TPTP v8.1.0. Released v3.2.0.
% 0.06/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n025.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Sun Jul 10 16:42:01 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.36/0.52  
% 0.36/0.52  SPASS V 3.9 
% 0.36/0.52  SPASS beiseite: Proof found.
% 0.36/0.52  % SZS status Theorem
% 0.36/0.52  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.36/0.52  SPASS derived 103 clauses, backtracked 0 clauses, performed 2 splits and kept 143 clauses.
% 0.36/0.52  SPASS allocated 99000 KBytes.
% 0.36/0.52  SPASS spent	0:00:00.17 on the problem.
% 0.36/0.52  		0:00:00.04 for the input.
% 0.36/0.52  		0:00:00.09 for the FLOTTER CNF translation.
% 0.36/0.52  		0:00:00.00 for inferences.
% 0.36/0.52  		0:00:00.00 for the backtracking.
% 0.36/0.52  		0:00:00.01 for the reduction.
% 0.36/0.52  
% 0.36/0.52  
% 0.36/0.52  Here is a proof with depth 3, length 8 :
% 0.36/0.52  % SZS output start Refutation
% See solution above
% 0.36/0.52  Formulae used in the proof : thV12 singleton union successor
% 0.36/0.52  
%------------------------------------------------------------------------------