%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SEU148+3 : TPTP v8.1.0. Released v3.2.0.
% 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 14:34:21 EDT 2022

% Result   : Theorem 0.19s 0.43s
% Output   : Refutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :    6
% Syntax   : Number of clauses     :   13 (   5 unt;   2 nHn;  13 RR)
%            Number of literals    :   24 (   0 equ;  13 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    7 (   7 usr;   6 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(5,axiom,
    ~ equal(skc5,skc4),
    file('SEU148+3.p',unknown),
    [] ).

cnf(6,axiom,
    subset(singleton(skc4),singleton(skc5)),
    file('SEU148+3.p',unknown),
    [] ).

cnf(7,axiom,
    ~ equal(singleton(u),empty_set),
    file('SEU148+3.p',unknown),
    [] ).

cnf(12,axiom,
    ( ~ in(u,v)
    | ~ equal(v,singleton(w))
    | equal(u,w) ),
    file('SEU148+3.p',unknown),
    [] ).

cnf(13,axiom,
    ( ~ equal(u,v)
    | ~ equal(w,singleton(v))
    | in(u,w) ),
    file('SEU148+3.p',unknown),
    [] ).

cnf(14,axiom,
    ( ~ subset(u,singleton(v))
    | equal(u,empty_set)
    | equal(u,singleton(v)) ),
    file('SEU148+3.p',unknown),
    [] ).

cnf(16,plain,
    ( ~ equal(u,singleton(skc4))
    | ~ in(skc5,u) ),
    inference(res,[status(thm),theory(equality)],[12,5]),
    [iquote('0:Res:12.2,5.0')] ).

cnf(18,plain,
    ( equal(singleton(skc5),singleton(skc4))
    | equal(singleton(skc4),empty_set) ),
    inference(res,[status(thm),theory(equality)],[6,14]),
    [iquote('0:Res:6.0,14.0')] ).

cnf(19,plain,
    equal(singleton(skc5),singleton(skc4)),
    inference(mrr,[status(thm)],[18,7]),
    [iquote('0:MRR:18.1,7.0')] ).

cnf(32,plain,
    ( ~ equal(u,v)
    | in(u,singleton(v)) ),
    inference(eqr,[status(thm),theory(equality)],[13]),
    [iquote('0:EqR:13.1')] ).

cnf(34,plain,
    ( ~ equal(u,skc5)
    | in(u,singleton(skc4)) ),
    inference(spr,[status(thm),theory(equality)],[19,32]),
    [iquote('0:SpR:19.0,32.1')] ).

cnf(41,plain,
    ( ~ equal(skc5,skc5)
    | ~ equal(singleton(skc4),singleton(skc4)) ),
    inference(res,[status(thm),theory(equality)],[34,16]),
    [iquote('0:Res:34.1,16.1')] ).

cnf(43,plain,
    $false,
    inference(obv,[status(thm),theory(equality)],[41]),
    [iquote('0:Obv:41.1')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem  : SEU148+3 : TPTP v8.1.0. Released v3.2.0.
% 0.08/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n007.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 Jun 19 12:35:29 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.19/0.43  
% 0.19/0.43  SPASS V 3.9 
% 0.19/0.43  SPASS beiseite: Proof found.
% 0.19/0.43  % SZS status Theorem
% 0.19/0.43  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.19/0.43  SPASS derived 24 clauses, backtracked 0 clauses, performed 0 splits and kept 29 clauses.
% 0.19/0.43  SPASS allocated 85200 KBytes.
% 0.19/0.43  SPASS spent	0:00:00.08 on the problem.
% 0.19/0.43  		0:00:00.03 for the input.
% 0.19/0.43  		0:00:00.03 for the FLOTTER CNF translation.
% 0.19/0.43  		0:00:00.00 for inferences.
% 0.19/0.43  		0:00:00.00 for the backtracking.
% 0.19/0.43  		0:00:00.00 for the reduction.
% 0.19/0.43  
% 0.19/0.43  
% 0.19/0.43  Here is a proof with depth 3, length 13 :
% 0.19/0.43  % SZS output start Refutation
% See solution above
% 0.19/0.43  Formulae used in the proof : t6_zfmisc_1 l1_zfmisc_1 d1_tarski antisymmetry_r2_hidden l4_zfmisc_1
% 0.19/0.43  
%------------------------------------------------------------------------------