TSTP Solution File: COM016+4 by Drodi---3.6.0

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%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : COM016+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n026.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 : Tue Apr 30 20:14:02 EDT 2024

% Result   : Theorem 0.15s 0.31s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   42 (   6 unt;   1 def)
%            Number of atoms       :  142 (   8 equ)
%            Maximal formula atoms :   10 (   3 avg)
%            Number of connectives :  149 (  49   ~;  59   |;  32   &)
%                                         (   8 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    1 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   7 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   6 con; 0-0 aty)
%            Number of variables   :   27 (  21   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f8,definition,
    ! [W0,W1,W2] :
      ( ( aElement0(W0)
        & aRewritingSystem0(W1)
        & aElement0(W2) )
     => ( sdtmndtasgtdt0(W0,W1,W2)
      <=> ( W0 = W2
          | sdtmndtplgtdt0(W0,W1,W2) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f15,hypothesis,
    aRewritingSystem0(xR),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f17,hypothesis,
    ( aElement0(xa)
    & aElement0(xb)
    & aElement0(xc) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f19,hypothesis,
    ( ( aReductOfIn0(xb,xa,xR)
      | ? [W0] :
          ( aElement0(W0)
          & aReductOfIn0(W0,xa,xR)
          & sdtmndtplgtdt0(W0,xR,xb) ) )
    & sdtmndtplgtdt0(xa,xR,xb)
    & ( aReductOfIn0(xc,xa,xR)
      | ? [W0] :
          ( aElement0(W0)
          & aReductOfIn0(W0,xa,xR)
          & sdtmndtplgtdt0(W0,xR,xc) ) )
    & sdtmndtplgtdt0(xa,xR,xc) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f20,conjecture,
    ? [W0] :
      ( aElement0(W0)
      & aReductOfIn0(W0,xa,xR)
      & ( W0 = xb
        | aReductOfIn0(xb,W0,xR)
        | ? [W1] :
            ( aElement0(W1)
            & aReductOfIn0(W1,W0,xR)
            & sdtmndtplgtdt0(W1,xR,xb) )
        | sdtmndtplgtdt0(W0,xR,xb)
        | sdtmndtasgtdt0(W0,xR,xb) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f21,negated_conjecture,
    ~ ? [W0] :
        ( aElement0(W0)
        & aReductOfIn0(W0,xa,xR)
        & ( W0 = xb
          | aReductOfIn0(xb,W0,xR)
          | ? [W1] :
              ( aElement0(W1)
              & aReductOfIn0(W1,W0,xR)
              & sdtmndtplgtdt0(W1,xR,xb) )
          | sdtmndtplgtdt0(W0,xR,xb)
          | sdtmndtasgtdt0(W0,xR,xb) ) ),
    inference(negated_conjecture,[status(cth)],[f20]) ).

fof(f44,plain,
    ! [W0,W1,W2] :
      ( ~ aElement0(W0)
      | ~ aRewritingSystem0(W1)
      | ~ aElement0(W2)
      | ( sdtmndtasgtdt0(W0,W1,W2)
      <=> ( W0 = W2
          | sdtmndtplgtdt0(W0,W1,W2) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f8]) ).

fof(f45,plain,
    ! [W0,W1,W2] :
      ( ~ aElement0(W0)
      | ~ aRewritingSystem0(W1)
      | ~ aElement0(W2)
      | ( ( ~ sdtmndtasgtdt0(W0,W1,W2)
          | W0 = W2
          | sdtmndtplgtdt0(W0,W1,W2) )
        & ( sdtmndtasgtdt0(W0,W1,W2)
          | ( W0 != W2
            & ~ sdtmndtplgtdt0(W0,W1,W2) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f44]) ).

fof(f47,plain,
    ! [X0,X1,X2] :
      ( ~ aElement0(X0)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X2)
      | sdtmndtasgtdt0(X0,X1,X2)
      | X0 != X2 ),
    inference(cnf_transformation,[status(esa)],[f45]) ).

fof(f96,plain,
    aRewritingSystem0(xR),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f117,plain,
    aElement0(xb),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f178,plain,
    ( ( aReductOfIn0(xb,xa,xR)
      | ( aElement0(sk0_19)
        & aReductOfIn0(sk0_19,xa,xR)
        & sdtmndtplgtdt0(sk0_19,xR,xb) ) )
    & sdtmndtplgtdt0(xa,xR,xb)
    & ( aReductOfIn0(xc,xa,xR)
      | ( aElement0(sk0_20)
        & aReductOfIn0(sk0_20,xa,xR)
        & sdtmndtplgtdt0(sk0_20,xR,xc) ) )
    & sdtmndtplgtdt0(xa,xR,xc) ),
    inference(skolemization,[status(esa)],[f19]) ).

fof(f179,plain,
    ( aReductOfIn0(xb,xa,xR)
    | aElement0(sk0_19) ),
    inference(cnf_transformation,[status(esa)],[f178]) ).

fof(f180,plain,
    ( aReductOfIn0(xb,xa,xR)
    | aReductOfIn0(sk0_19,xa,xR) ),
    inference(cnf_transformation,[status(esa)],[f178]) ).

fof(f181,plain,
    ( aReductOfIn0(xb,xa,xR)
    | sdtmndtplgtdt0(sk0_19,xR,xb) ),
    inference(cnf_transformation,[status(esa)],[f178]) ).

fof(f187,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | ~ aReductOfIn0(W0,xa,xR)
      | ( W0 != xb
        & ~ aReductOfIn0(xb,W0,xR)
        & ! [W1] :
            ( ~ aElement0(W1)
            | ~ aReductOfIn0(W1,W0,xR)
            | ~ sdtmndtplgtdt0(W1,xR,xb) )
        & ~ sdtmndtplgtdt0(W0,xR,xb)
        & ~ sdtmndtasgtdt0(W0,xR,xb) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f21]) ).

fof(f191,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | ~ aReductOfIn0(X0,xa,xR)
      | ~ sdtmndtplgtdt0(X0,xR,xb) ),
    inference(cnf_transformation,[status(esa)],[f187]) ).

fof(f192,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | ~ aReductOfIn0(X0,xa,xR)
      | ~ sdtmndtasgtdt0(X0,xR,xb) ),
    inference(cnf_transformation,[status(esa)],[f187]) ).

fof(f199,plain,
    ( spl0_0
  <=> aReductOfIn0(xb,xa,xR) ),
    introduced(split_symbol_definition) ).

fof(f202,plain,
    ( spl0_1
  <=> aElement0(sk0_19) ),
    introduced(split_symbol_definition) ).

fof(f205,plain,
    ( spl0_0
    | spl0_1 ),
    inference(split_clause,[status(thm)],[f179,f199,f202]) ).

fof(f206,plain,
    ( spl0_2
  <=> aReductOfIn0(sk0_19,xa,xR) ),
    introduced(split_symbol_definition) ).

fof(f207,plain,
    ( aReductOfIn0(sk0_19,xa,xR)
    | ~ spl0_2 ),
    inference(component_clause,[status(thm)],[f206]) ).

fof(f209,plain,
    ( spl0_0
    | spl0_2 ),
    inference(split_clause,[status(thm)],[f180,f199,f206]) ).

fof(f210,plain,
    ( spl0_3
  <=> sdtmndtplgtdt0(sk0_19,xR,xb) ),
    introduced(split_symbol_definition) ).

fof(f213,plain,
    ( spl0_0
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f181,f199,f210]) ).

fof(f229,plain,
    ! [X2,X1] :
      ( ~ aElement0(X2)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X2)
      | sdtmndtasgtdt0(X2,X1,X2) ),
    inference(destructive_equality_resolution,[status(esa)],[f47]) ).

fof(f230,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | ~ aRewritingSystem0(X1)
      | sdtmndtasgtdt0(X0,X1,X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f229]) ).

fof(f292,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sdtmndtasgtdt0(X0,xR,X0) ),
    inference(resolution,[status(thm)],[f230,f96]) ).

fof(f293,plain,
    ( spl0_16
  <=> aElement0(xb) ),
    introduced(split_symbol_definition) ).

fof(f295,plain,
    ( ~ aElement0(xb)
    | spl0_16 ),
    inference(component_clause,[status(thm)],[f293]) ).

fof(f296,plain,
    ( ~ aElement0(xb)
    | ~ aElement0(xb)
    | ~ aReductOfIn0(xb,xa,xR) ),
    inference(resolution,[status(thm)],[f292,f192]) ).

fof(f297,plain,
    ( ~ spl0_16
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f296,f293,f199]) ).

fof(f298,plain,
    ( $false
    | spl0_16 ),
    inference(forward_subsumption_resolution,[status(thm)],[f295,f117]) ).

fof(f299,plain,
    spl0_16,
    inference(contradiction_clause,[status(thm)],[f298]) ).

fof(f332,plain,
    ( spl0_22
  <=> aRewritingSystem0(xR) ),
    introduced(split_symbol_definition) ).

fof(f334,plain,
    ( ~ aRewritingSystem0(xR)
    | spl0_22 ),
    inference(component_clause,[status(thm)],[f332]) ).

fof(f337,plain,
    ( $false
    | spl0_22 ),
    inference(forward_subsumption_resolution,[status(thm)],[f334,f96]) ).

fof(f338,plain,
    spl0_22,
    inference(contradiction_clause,[status(thm)],[f337]) ).

fof(f359,plain,
    ( ~ aElement0(sk0_19)
    | ~ sdtmndtplgtdt0(sk0_19,xR,xb)
    | ~ spl0_2 ),
    inference(resolution,[status(thm)],[f207,f191]) ).

fof(f360,plain,
    ( ~ spl0_1
    | ~ spl0_3
    | ~ spl0_2 ),
    inference(split_clause,[status(thm)],[f359,f202,f210,f206]) ).

fof(f368,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f205,f209,f213,f297,f299,f338,f360]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.09  % Problem  : COM016+4 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.09  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30  % Computer : n026.cluster.edu
% 0.09/0.30  % Model    : x86_64 x86_64
% 0.09/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30  % Memory   : 8042.1875MB
% 0.09/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30  % CPULimit : 300
% 0.09/0.30  % WCLimit  : 300
% 0.09/0.30  % DateTime : Tue Apr 30 01:23:49 EDT 2024
% 0.09/0.30  % CPUTime  : 
% 0.09/0.31  % Drodi V3.6.0
% 0.15/0.31  % Refutation found
% 0.15/0.31  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.31  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.32  % Elapsed time: 0.021307 seconds
% 0.15/0.32  % CPU time: 0.040607 seconds
% 0.15/0.32  % Total memory used: 15.853 MB
% 0.15/0.32  % Net memory used: 15.823 MB
%------------------------------------------------------------------------------