%------------------------------------------------------------------------------
% File     : SPASS---3.9
% Problem  : NUM228-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm  : none
% Format   : tptp
% Command  : run_spass %d %s

% Computer : n014.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 : Mon Jul 18 14:24:45 EDT 2022

% Result   : Unsatisfiable 0.18s 0.44s
% Output   : Refutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    3
%            Number of leaves      :    4
% Syntax   : Number of clauses     :    7 (   5 unt;   1 nHn;   7 RR)
%            Number of literals    :    9 (   0 equ;   4 neg)
%            Maximal clause size   :    2 (   1 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-1 aty)
%            Number of variables   :    0 (   0 sgn)

% Comments : 
%------------------------------------------------------------------------------
cnf(1,axiom,
    ~ function(z__dfg),
    file('NUM228-1.p',unknown),
    [] ).

cnf(2,axiom,
    ~ equal(recursion_equation_functions(z__dfg),null_class),
    file('NUM228-1.p',unknown),
    [] ).

cnf(68,axiom,
    ( equal(u,null_class)
    | member(regular(u),u) ),
    file('NUM228-1.p',unknown),
    [] ).

cnf(149,axiom,
    ( ~ member(u,recursion_equation_functions(v))
    | function(v) ),
    file('NUM228-1.p',unknown),
    [] ).

cnf(169,plain,
    ~ member(u,recursion_equation_functions(z__dfg)),
    inference(res,[status(thm),theory(equality)],[149,1]),
    [iquote('0:Res:149.1,1.0')] ).

cnf(194,plain,
    equal(recursion_equation_functions(z__dfg),null_class),
    inference(res,[status(thm),theory(equality)],[68,169]),
    [iquote('0:Res:68.1,169.0')] ).

cnf(195,plain,
    $false,
    inference(mrr,[status(thm)],[194,2]),
    [iquote('0:MRR:194.0,2.0')] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem  : NUM228-1 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.11/0.13  % Command  : run_spass %d %s
% 0.12/0.33  % Computer : n014.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
% 0.12/0.34  % CPULimit : 300
% 0.12/0.34  % WCLimit  : 600
% 0.12/0.34  % DateTime : Thu Jul  7 07:37:22 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.18/0.44  
% 0.18/0.44  SPASS V 3.9 
% 0.18/0.44  SPASS beiseite: Proof found.
% 0.18/0.44  % SZS status Theorem
% 0.18/0.44  Problem: /export/starexec/sandbox/benchmark/theBenchmark.p 
% 0.18/0.44  SPASS derived 24 clauses, backtracked 0 clauses, performed 0 splits and kept 173 clauses.
% 0.18/0.44  SPASS allocated 75857 KBytes.
% 0.18/0.44  SPASS spent	0:00:00.09 on the problem.
% 0.18/0.44  		0:00:00.04 for the input.
% 0.18/0.44  		0:00:00.00 for the FLOTTER CNF translation.
% 0.18/0.44  		0:00:00.00 for inferences.
% 0.18/0.44  		0:00:00.00 for the backtracking.
% 0.18/0.44  		0:00:00.02 for the reduction.
% 0.18/0.44  
% 0.18/0.44  
% 0.18/0.44  Here is a proof with depth 2, length 7 :
% 0.18/0.44  % SZS output start Refutation
% See solution above
% 0.18/0.44  Formulae used in the proof : prove_corollary_1 prove_corollary_2 regularity1 recursion_equation_functions1
% 0.18/0.44  
%------------------------------------------------------------------------------