%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET838-1 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n020.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 05:29:06 EDT 2022

% Result   : Unsatisfiable 0.58s 0.76s
% Output   : Refutation 0.58s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :    4
% Syntax   : Number of clauses     :   12 (   4 unt;   0 nHn;  12 RR)
%            Number of literals    :   21 (   0 equ;  12 neg)
%            Maximal clause size   :    3 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :    2 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    equal(v(v_g(v_x)),v_x),
    file('SET838-1.p',unknown),
    [] ).

cnf(2,axiom,
    ( ~ equal(v(v_g(u)),u)
    | equal(u,v_x) ),
    file('SET838-1.p',unknown),
    [] ).

cnf(3,axiom,
    ( ~ equal(v_g(v(u)),u)
    | equal(v_g(v(v_xa(u))),v_xa(u)) ),
    file('SET838-1.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ equal(v_xa(u),u)
    | ~ equal(v_g(v(u)),u) ),
    file('SET838-1.p',unknown),
    [] ).

cnf(1437,plain,
    ( ~ equal(v_xa(v_g(v_x)),v_g(v_x))
    | ~ equal(v_g(v_x),v_g(v_x)) ),
    inference(spl,[status(thm),theory(equality)],[1,4]),
    [iquote('0:SpL:1.0,4.1')] ).

cnf(1438,plain,
    ~ equal(v_xa(v_g(v_x)),v_g(v_x)),
    inference(obv,[status(thm),theory(equality)],[1437]),
    [iquote('0:Obv:1437.1')] ).

cnf(1556,plain,
    ( ~ equal(v_g(v(u)),u)
    | ~ equal(v(v_xa(u)),v(v_xa(u)))
    | equal(v(v_xa(u)),v_x) ),
    inference(spl,[status(thm),theory(equality)],[3,2]),
    [iquote('0:SpL:3.1,2.0')] ).

cnf(1558,plain,
    ( ~ equal(v_g(v(u)),u)
    | equal(v(v_xa(u)),v_x) ),
    inference(obv,[status(thm),theory(equality)],[1556]),
    [iquote('0:Obv:1556.1')] ).

cnf(1559,plain,
    ( ~ equal(v_g(v(u)),u)
    | equal(v_xa(u),v_g(v_x)) ),
    inference(rew,[status(thm),theory(equality)],[1558,3]),
    [iquote('0:Rew:1558.1,3.1')] ).

cnf(1564,plain,
    ( ~ equal(v_g(v_x),v_g(v_x))
    | equal(v_xa(v_g(v_x)),v_g(v_x)) ),
    inference(spl,[status(thm),theory(equality)],[1,1559]),
    [iquote('0:SpL:1.0,1559.0')] ).

cnf(1565,plain,
    equal(v_xa(v_g(v_x)),v_g(v_x)),
    inference(obv,[status(thm),theory(equality)],[1564]),
    [iquote('0:Obv:1564.0')] ).

cnf(1566,plain,
    $false,
    inference(mrr,[status(thm)],[1565,1438]),
    [iquote('0:MRR:1565.0,1438.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : SET838-1 : TPTP v8.1.0. Released v3.2.0.
% 0.03/0.12  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n020.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 : Sat Jul  9 21:55:58 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.58/0.76  
% 0.58/0.76  SPASS V 3.9 
% 0.58/0.76  SPASS beiseite: Proof found.
% 0.58/0.76  % SZS status Theorem
% 0.58/0.76  Problem: /export/starexec/sandbox2/benchmark/theBenchmark.p 
% 0.58/0.76  SPASS derived 177 clauses, backtracked 0 clauses, performed 0 splits and kept 1362 clauses.
% 0.58/0.76  SPASS allocated 77966 KBytes.
% 0.58/0.76  SPASS spent	0:00:00.41 on the problem.
% 0.58/0.76  		0:00:00.09 for the input.
% 0.58/0.76  		0:00:00.00 for the FLOTTER CNF translation.
% 0.58/0.76  		0:00:00.03 for inferences.
% 0.58/0.76  		0:00:00.00 for the backtracking.
% 0.58/0.76  		0:00:00.08 for the reduction.
% 0.58/0.76  
% 0.58/0.76  
% 0.58/0.76  Here is a proof with depth 1, length 12 :
% 0.58/0.76  % SZS output start Refutation
% See solution above
% 0.58/0.76  Formulae used in the proof : cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3
% 0.58/0.76  
%------------------------------------------------------------------------------