%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : SET838-2 : TPTP v8.1.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n003.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 0.13s 0.41s
% Output   : Refutation 0.13s
% 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('SET838-2.p',unknown),
    [] ).

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

cnf(3,axiom,
    ( ~ equal(v_g(v(u)),u)
    | equal(v_g(v(v_xa(u))),v_xa(u)) ),
    file('SET838-2.p',unknown),
    [] ).

cnf(4,axiom,
    ( ~ equal(v_xa(u),u)
    | ~ equal(v_g(v(u)),u) ),
    file('SET838-2.p',unknown),
    [] ).

cnf(7,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(8,plain,
    ~ equal(v_xa(v_g(v_x)),v_g(v_x)),
    inference(obv,[status(thm),theory(equality)],[7]),
    [iquote('0:Obv:7.1')] ).

cnf(10,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(12,plain,
    ( ~ equal(v_g(v(u)),u)
    | equal(v(v_xa(u)),v_x) ),
    inference(obv,[status(thm),theory(equality)],[10]),
    [iquote('0:Obv:10.1')] ).

cnf(13,plain,
    ( ~ equal(v_g(v(u)),u)
    | equal(v_xa(u),v_g(v_x)) ),
    inference(rew,[status(thm),theory(equality)],[12,3]),
    [iquote('0:Rew:12.1,3.1')] ).

cnf(18,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)],[1,13]),
    [iquote('0:SpL:1.0,13.0')] ).

cnf(19,plain,
    equal(v_xa(v_g(v_x)),v_g(v_x)),
    inference(obv,[status(thm),theory(equality)],[18]),
    [iquote('0:Obv:18.0')] ).

cnf(20,plain,
    $false,
    inference(mrr,[status(thm)],[19,8]),
    [iquote('0:MRR:19.0,8.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : SET838-2 : TPTP v8.1.0. Released v3.2.0.
% 0.11/0.12  % Command  : run_spass %d %s
% 0.13/0.34  % Computer : n003.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Mon Jul 11 09:45:15 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.41  
% 0.13/0.41  SPASS V 3.9 
% 0.13/0.41  SPASS beiseite: Proof found.
% 0.13/0.41  % SZS status Theorem
% 0.13/0.41  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.13/0.41  SPASS derived 10 clauses, backtracked 0 clauses, performed 0 splits and kept 9 clauses.
% 0.13/0.41  SPASS allocated 63093 KBytes.
% 0.13/0.41  SPASS spent	0:00:00.06 on the problem.
% 0.13/0.41  		0:00:00.04 for the input.
% 0.13/0.41  		0:00:00.00 for the FLOTTER CNF translation.
% 0.13/0.41  		0:00:00.00 for inferences.
% 0.13/0.41  		0:00:00.00 for the backtracking.
% 0.13/0.41  		0:00:00.00 for the reduction.
% 0.13/0.41  
% 0.13/0.41  
% 0.13/0.41  Here is a proof with depth 1, length 12 :
% 0.13/0.41  % SZS output start Refutation
% See solution above
% 0.13/0.41  Formulae used in the proof : cls_conjecture_0 cls_conjecture_1 cls_conjecture_2 cls_conjecture_3
% 0.13/0.41  
%------------------------------------------------------------------------------