%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWV041+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n018.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  : 300s
% DateTime : Wed May 31 12:40:31 EDT 2023

% Result   : Theorem 0.16s 0.51s
% Output   : CNFRefutation 0.16s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   38 (  15 unt;   0 def)
%            Number of atoms       :   88 (  14 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   73 (  23   ~;  18   |;  21   &)
%                                         (   3 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    7 (   5 usr;   3 prp; 0-2 aty)
%            Number of functors    :   16 (  16 usr;  10 con; 0-3 aty)
%            Number of variables   :   31 (;  29   !;   2   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X] : ~ gt(X,X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X,Y] :
      ( leq(X,pred(Y))
    <=> gt(Y,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [X,Y] :
      ( leq(X,Y)
     => leq(X,succ(Y)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f39,axiom,
    ! [X] : minus(X,n1) = pred(X),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f41,axiom,
    ! [X] : succ(pred(X)) = X,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f53,conjecture,
    ( ( geq(minus(n330,n1),n0)
      & geq(minus(n410,n1),n0) )
   => ! [A] :
        ( ( leq(n0,A)
          & leq(A,n2) )
       => ! [B] :
            ( ( leq(n0,B)
              & leq(B,minus(n0,n1)) )
           => a_select3(tptp_const_array2(dim(n0,n3),dim(n0,n2),uninit),B,A) = init ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f54,negated_conjecture,
    ~ ( ( geq(minus(n330,n1),n0)
        & geq(minus(n410,n1),n0) )
     => ! [A] :
          ( ( leq(n0,A)
            & leq(A,n2) )
         => ! [B] :
              ( ( leq(n0,B)
                & leq(B,minus(n0,n1)) )
             => a_select3(tptp_const_array2(dim(n0,n3),dim(n0,n2),uninit),B,A) = init ) ) ),
    inference(negated_conjecture,[status(cth)],[f53]) ).

fof(f93,axiom,
    ! [X] :
      ( ( leq(n0,X)
        & leq(X,n0) )
     => X = n0 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f106,plain,
    ! [X0] : ~ gt(X0,X0),
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f123,plain,
    ! [X,Y] :
      ( ( ~ leq(X,pred(Y))
        | gt(Y,X) )
      & ( leq(X,pred(Y))
        | ~ gt(Y,X) ) ),
    inference(NNF_transformation,[status(esa)],[f10]) ).

fof(f124,plain,
    ( ! [X,Y] :
        ( ~ leq(X,pred(Y))
        | gt(Y,X) )
    & ! [X,Y] :
        ( leq(X,pred(Y))
        | ~ gt(Y,X) ) ),
    inference(miniscoping,[status(esa)],[f123]) ).

fof(f125,plain,
    ! [X0,X1] :
      ( ~ leq(X0,pred(X1))
      | gt(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f124]) ).

fof(f128,plain,
    ! [X,Y] :
      ( ~ leq(X,Y)
      | leq(X,succ(Y)) ),
    inference(pre_NNF_transformation,[status(esa)],[f12]) ).

fof(f129,plain,
    ! [X0,X1] :
      ( ~ leq(X0,X1)
      | leq(X0,succ(X1)) ),
    inference(cnf_transformation,[status(esa)],[f128]) ).

fof(f225,plain,
    ! [X0] : minus(X0,n1) = pred(X0),
    inference(cnf_transformation,[status(esa)],[f39]) ).

fof(f227,plain,
    ! [X0] : succ(pred(X0)) = X0,
    inference(cnf_transformation,[status(esa)],[f41]) ).

fof(f259,plain,
    ( geq(minus(n330,n1),n0)
    & geq(minus(n410,n1),n0)
    & ? [A] :
        ( leq(n0,A)
        & leq(A,n2)
        & ? [B] :
            ( leq(n0,B)
            & leq(B,minus(n0,n1))
            & a_select3(tptp_const_array2(dim(n0,n3),dim(n0,n2),uninit),B,A) != init ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f54]) ).

fof(f260,plain,
    ( geq(minus(n330,n1),n0)
    & geq(minus(n410,n1),n0)
    & leq(n0,sk0_23)
    & leq(sk0_23,n2)
    & leq(n0,sk0_24)
    & leq(sk0_24,minus(n0,n1))
    & a_select3(tptp_const_array2(dim(n0,n3),dim(n0,n2),uninit),sk0_24,sk0_23) != init ),
    inference(skolemization,[status(esa)],[f259]) ).

fof(f265,plain,
    leq(n0,sk0_24),
    inference(cnf_transformation,[status(esa)],[f260]) ).

fof(f266,plain,
    leq(sk0_24,minus(n0,n1)),
    inference(cnf_transformation,[status(esa)],[f260]) ).

fof(f308,plain,
    ! [X] :
      ( ~ leq(n0,X)
      | ~ leq(X,n0)
      | X = n0 ),
    inference(pre_NNF_transformation,[status(esa)],[f93]) ).

fof(f309,plain,
    ! [X0] :
      ( ~ leq(n0,X0)
      | ~ leq(X0,n0)
      | X0 = n0 ),
    inference(cnf_transformation,[status(esa)],[f308]) ).

fof(f362,plain,
    leq(sk0_24,pred(n0)),
    inference(forward_demodulation,[status(thm)],[f225,f266]) ).

fof(f633,plain,
    ( spl0_25
  <=> leq(sk0_24,n0) ),
    introduced(split_symbol_definition) ).

fof(f635,plain,
    ( ~ leq(sk0_24,n0)
    | spl0_25 ),
    inference(component_clause,[status(thm)],[f633]) ).

fof(f636,plain,
    ( spl0_26
  <=> sk0_24 = n0 ),
    introduced(split_symbol_definition) ).

fof(f637,plain,
    ( sk0_24 = n0
    | ~ spl0_26 ),
    inference(component_clause,[status(thm)],[f636]) ).

fof(f639,plain,
    ( ~ leq(sk0_24,n0)
    | sk0_24 = n0 ),
    inference(resolution,[status(thm)],[f309,f265]) ).

fof(f640,plain,
    ( ~ spl0_25
    | spl0_26 ),
    inference(split_clause,[status(thm)],[f639,f633,f636]) ).

fof(f1323,plain,
    gt(n0,sk0_24),
    inference(resolution,[status(thm)],[f362,f125]) ).

fof(f1512,plain,
    leq(sk0_24,succ(pred(n0))),
    inference(resolution,[status(thm)],[f129,f362]) ).

fof(f1513,plain,
    leq(sk0_24,n0),
    inference(forward_demodulation,[status(thm)],[f227,f1512]) ).

fof(f1514,plain,
    ( $false
    | spl0_25 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1513,f635]) ).

fof(f1515,plain,
    spl0_25,
    inference(contradiction_clause,[status(thm)],[f1514]) ).

fof(f1530,plain,
    ( gt(n0,n0)
    | ~ spl0_26 ),
    inference(backward_demodulation,[status(thm)],[f637,f1323]) ).

fof(f1531,plain,
    ( $false
    | ~ spl0_26 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1530,f106]) ).

fof(f1532,plain,
    ~ spl0_26,
    inference(contradiction_clause,[status(thm)],[f1531]) ).

fof(f1533,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f640,f1515,f1532]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11  % Problem  : SWV041+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.05/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32  % Computer : n018.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Tue May 30 11:51:25 EDT 2023
% 0.11/0.32  % CPUTime  : 
% 0.11/0.33  % Drodi V3.5.1
% 0.16/0.51  % Refutation found
% 0.16/0.51  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.51  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.52  % Elapsed time: 0.200477 seconds
% 0.16/0.52  % CPU time: 0.620977 seconds
% 0.16/0.52  % Memory used: 67.669 MB
%------------------------------------------------------------------------------