TSTP Solution File: COM016+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : COM016+1 : 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 : Wed May 31 12:03:55 EDT 2023

% Result   : Theorem 0.18s 0.37s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   88 (  17 unt;   2 def)
%            Number of atoms       :  262 (  16 equ)
%            Maximal formula atoms :   13 (   2 avg)
%            Number of connectives :  286 ( 112   ~; 127   |;  26   &)
%                                         (  19 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   24 (  22 usr;  16 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-3 aty)
%            Number of variables   :   48 (;  43   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f6,definition,
    ! [W0,W1,W2] :
      ( ( aElement0(W0)
        & aRewritingSystem0(W1)
        & aElement0(W2) )
     => ( sdtmndtplgtdt0(W0,W1,W2)
      <=> ( aReductOfIn0(W2,W0,W1)
          | ? [W3] :
              ( aElement0(W3)
              & aReductOfIn0(W3,W0,W1)
              & sdtmndtplgtdt0(W3,W1,W2) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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(f16,hypothesis,
    ( isLocallyConfluent0(xR)
    & isTerminating0(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,
    ( sdtmndtplgtdt0(xa,xR,xb)
    & sdtmndtplgtdt0(xa,xR,xc) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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

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

fof(f34,plain,
    ! [W0,W1,W2] :
      ( ~ aElement0(W0)
      | ~ aRewritingSystem0(W1)
      | ~ aElement0(W2)
      | ( sdtmndtplgtdt0(W0,W1,W2)
      <=> ( aReductOfIn0(W2,W0,W1)
          | ? [W3] :
              ( aElement0(W3)
              & aReductOfIn0(W3,W0,W1)
              & sdtmndtplgtdt0(W3,W1,W2) ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f35,plain,
    ! [W0,W1,W2] :
      ( ~ aElement0(W0)
      | ~ aRewritingSystem0(W1)
      | ~ aElement0(W2)
      | ( ( ~ sdtmndtplgtdt0(W0,W1,W2)
          | aReductOfIn0(W2,W0,W1)
          | ? [W3] :
              ( aElement0(W3)
              & aReductOfIn0(W3,W0,W1)
              & sdtmndtplgtdt0(W3,W1,W2) ) )
        & ( sdtmndtplgtdt0(W0,W1,W2)
          | ( ~ aReductOfIn0(W2,W0,W1)
            & ! [W3] :
                ( ~ aElement0(W3)
                | ~ aReductOfIn0(W3,W0,W1)
                | ~ sdtmndtplgtdt0(W3,W1,W2) ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f34]) ).

fof(f36,plain,
    ! [W0,W1,W2] :
      ( ~ aElement0(W0)
      | ~ aRewritingSystem0(W1)
      | ~ aElement0(W2)
      | ( ( ~ sdtmndtplgtdt0(W0,W1,W2)
          | aReductOfIn0(W2,W0,W1)
          | ( aElement0(sk0_0(W2,W1,W0))
            & aReductOfIn0(sk0_0(W2,W1,W0),W0,W1)
            & sdtmndtplgtdt0(sk0_0(W2,W1,W0),W1,W2) ) )
        & ( sdtmndtplgtdt0(W0,W1,W2)
          | ( ~ aReductOfIn0(W2,W0,W1)
            & ! [W3] :
                ( ~ aElement0(W3)
                | ~ aReductOfIn0(W3,W0,W1)
                | ~ sdtmndtplgtdt0(W3,W1,W2) ) ) ) ) ),
    inference(skolemization,[status(esa)],[f35]) ).

fof(f37,plain,
    ! [X0,X1,X2] :
      ( ~ aElement0(X0)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X2)
      | ~ sdtmndtplgtdt0(X0,X1,X2)
      | aReductOfIn0(X2,X0,X1)
      | aElement0(sk0_0(X2,X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ~ aElement0(X0)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X2)
      | ~ sdtmndtplgtdt0(X0,X1,X2)
      | aReductOfIn0(X2,X0,X1)
      | aReductOfIn0(sk0_0(X2,X1,X0),X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

fof(f39,plain,
    ! [X0,X1,X2] :
      ( ~ aElement0(X0)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X2)
      | ~ sdtmndtplgtdt0(X0,X1,X2)
      | aReductOfIn0(X2,X0,X1)
      | sdtmndtplgtdt0(sk0_0(X2,X1,X0),X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f36]) ).

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(f48,plain,
    ! [X0,X1,X2] :
      ( ~ aElement0(X0)
      | ~ aRewritingSystem0(X1)
      | ~ aElement0(X2)
      | sdtmndtasgtdt0(X0,X1,X2)
      | ~ sdtmndtplgtdt0(X0,X1,X2) ),
    inference(cnf_transformation,[status(esa)],[f45]) ).

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

fof(f98,plain,
    isTerminating0(xR),
    inference(cnf_transformation,[status(esa)],[f16]) ).

fof(f99,plain,
    aElement0(xa),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f100,plain,
    aElement0(xb),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f101,plain,
    aElement0(xc),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f107,plain,
    sdtmndtplgtdt0(xa,xR,xb),
    inference(cnf_transformation,[status(esa)],[f19]) ).

fof(f109,plain,
    ! [W0] :
      ( ~ aElement0(W0)
      | ~ aReductOfIn0(W0,xa,xR)
      | ~ sdtmndtasgtdt0(W0,xR,xb) ),
    inference(pre_NNF_transformation,[status(esa)],[f21]) ).

fof(f110,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | ~ aReductOfIn0(X0,xa,xR)
      | ~ sdtmndtasgtdt0(X0,xR,xb) ),
    inference(cnf_transformation,[status(esa)],[f109]) ).

fof(f111,plain,
    ! [X0,X1] :
      ( ~ aRewritingSystem0(X0)
      | ~ aElement0(X1)
      | sdtmndtasgtdt0(xb,X0,X1)
      | xb != X1 ),
    inference(resolution,[status(thm)],[f47,f100]) ).

fof(f113,plain,
    ! [X0] :
      ( ~ aElement0(X0)
      | sdtmndtasgtdt0(xb,xR,X0)
      | xb != X0 ),
    inference(resolution,[status(thm)],[f111,f96]) ).

fof(f115,plain,
    ( spl0_0
  <=> sdtmndtasgtdt0(xb,xR,xb) ),
    introduced(split_symbol_definition) ).

fof(f116,plain,
    ( sdtmndtasgtdt0(xb,xR,xb)
    | ~ spl0_0 ),
    inference(component_clause,[status(thm)],[f115]) ).

fof(f118,plain,
    ( spl0_1
  <=> xb = xb ),
    introduced(split_symbol_definition) ).

fof(f120,plain,
    ( xb != xb
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f118]) ).

fof(f121,plain,
    ( sdtmndtasgtdt0(xb,xR,xb)
    | xb != xb ),
    inference(resolution,[status(thm)],[f113,f100]) ).

fof(f122,plain,
    ( spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f121,f115,f118]) ).

fof(f131,plain,
    ( $false
    | spl0_1 ),
    inference(equality_resolution,[status(esa)],[f120]) ).

fof(f132,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f131]) ).

fof(f133,plain,
    ( spl0_4
  <=> aElement0(xb) ),
    introduced(split_symbol_definition) ).

fof(f135,plain,
    ( ~ aElement0(xb)
    | spl0_4 ),
    inference(component_clause,[status(thm)],[f133]) ).

fof(f136,plain,
    ( spl0_5
  <=> aReductOfIn0(xb,xa,xR) ),
    introduced(split_symbol_definition) ).

fof(f139,plain,
    ( ~ aElement0(xb)
    | ~ aReductOfIn0(xb,xa,xR)
    | ~ spl0_0 ),
    inference(resolution,[status(thm)],[f116,f110]) ).

fof(f140,plain,
    ( ~ spl0_4
    | ~ spl0_5
    | ~ spl0_0 ),
    inference(split_clause,[status(thm)],[f139,f133,f136,f115]) ).

fof(f141,plain,
    ( spl0_6
  <=> aRewritingSystem0(xR) ),
    introduced(split_symbol_definition) ).

fof(f143,plain,
    ( ~ aRewritingSystem0(xR)
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f141]) ).

fof(f149,plain,
    ( $false
    | spl0_6 ),
    inference(forward_subsumption_resolution,[status(thm)],[f143,f96]) ).

fof(f150,plain,
    spl0_6,
    inference(contradiction_clause,[status(thm)],[f149]) ).

fof(f151,plain,
    ( $false
    | spl0_4 ),
    inference(forward_subsumption_resolution,[status(thm)],[f135,f100]) ).

fof(f152,plain,
    spl0_4,
    inference(contradiction_clause,[status(thm)],[f151]) ).

fof(f168,plain,
    ( spl0_11
  <=> aElement0(xa) ),
    introduced(split_symbol_definition) ).

fof(f170,plain,
    ( ~ aElement0(xa)
    | spl0_11 ),
    inference(component_clause,[status(thm)],[f168]) ).

fof(f176,plain,
    ( $false
    | spl0_11 ),
    inference(forward_subsumption_resolution,[status(thm)],[f170,f99]) ).

fof(f177,plain,
    spl0_11,
    inference(contradiction_clause,[status(thm)],[f176]) ).

fof(f199,plain,
    ( spl0_18
  <=> xc = xc ),
    introduced(split_symbol_definition) ).

fof(f201,plain,
    ( xc != xc
    | spl0_18 ),
    inference(component_clause,[status(thm)],[f199]) ).

fof(f214,plain,
    ( $false
    | spl0_18 ),
    inference(equality_resolution,[status(esa)],[f201]) ).

fof(f215,plain,
    spl0_18,
    inference(contradiction_clause,[status(thm)],[f214]) ).

fof(f216,plain,
    ( spl0_21
  <=> aElement0(xc) ),
    introduced(split_symbol_definition) ).

fof(f218,plain,
    ( ~ aElement0(xc)
    | spl0_21 ),
    inference(component_clause,[status(thm)],[f216]) ).

fof(f224,plain,
    ( $false
    | spl0_21 ),
    inference(forward_subsumption_resolution,[status(thm)],[f218,f101]) ).

fof(f225,plain,
    spl0_21,
    inference(contradiction_clause,[status(thm)],[f224]) ).

fof(f226,plain,
    ( spl0_23
  <=> isTerminating0(xR) ),
    introduced(split_symbol_definition) ).

fof(f228,plain,
    ( ~ isTerminating0(xR)
    | spl0_23 ),
    inference(component_clause,[status(thm)],[f226]) ).

fof(f316,plain,
    ( $false
    | spl0_23 ),
    inference(forward_subsumption_resolution,[status(thm)],[f228,f98]) ).

fof(f317,plain,
    spl0_23,
    inference(contradiction_clause,[status(thm)],[f316]) ).

fof(f324,plain,
    ( spl0_39
  <=> sdtmndtplgtdt0(sk0_0(xb,xR,xa),xR,xb) ),
    introduced(split_symbol_definition) ).

fof(f325,plain,
    ( sdtmndtplgtdt0(sk0_0(xb,xR,xa),xR,xb)
    | ~ spl0_39 ),
    inference(component_clause,[status(thm)],[f324]) ).

fof(f327,plain,
    ( ~ aElement0(xa)
    | ~ aRewritingSystem0(xR)
    | ~ aElement0(xb)
    | aReductOfIn0(xb,xa,xR)
    | sdtmndtplgtdt0(sk0_0(xb,xR,xa),xR,xb) ),
    inference(resolution,[status(thm)],[f39,f107]) ).

fof(f328,plain,
    ( ~ spl0_11
    | ~ spl0_6
    | ~ spl0_4
    | spl0_5
    | spl0_39 ),
    inference(split_clause,[status(thm)],[f327,f168,f141,f133,f136,f324]) ).

fof(f329,plain,
    ( spl0_40
  <=> aElement0(sk0_0(xb,xR,xa)) ),
    introduced(split_symbol_definition) ).

fof(f350,plain,
    ( spl0_45
  <=> sdtmndtasgtdt0(sk0_0(xb,xR,xa),xR,xb) ),
    introduced(split_symbol_definition) ).

fof(f351,plain,
    ( sdtmndtasgtdt0(sk0_0(xb,xR,xa),xR,xb)
    | ~ spl0_45 ),
    inference(component_clause,[status(thm)],[f350]) ).

fof(f353,plain,
    ( ~ aElement0(sk0_0(xb,xR,xa))
    | ~ aRewritingSystem0(xR)
    | ~ aElement0(xb)
    | sdtmndtasgtdt0(sk0_0(xb,xR,xa),xR,xb)
    | ~ spl0_39 ),
    inference(resolution,[status(thm)],[f325,f48]) ).

fof(f354,plain,
    ( ~ spl0_40
    | ~ spl0_6
    | ~ spl0_4
    | spl0_45
    | ~ spl0_39 ),
    inference(split_clause,[status(thm)],[f353,f329,f141,f133,f350,f324]) ).

fof(f360,plain,
    ( ~ aElement0(xa)
    | ~ aRewritingSystem0(xR)
    | ~ aElement0(xb)
    | aReductOfIn0(xb,xa,xR)
    | aElement0(sk0_0(xb,xR,xa)) ),
    inference(resolution,[status(thm)],[f37,f107]) ).

fof(f361,plain,
    ( ~ spl0_11
    | ~ spl0_6
    | ~ spl0_4
    | spl0_5
    | spl0_40 ),
    inference(split_clause,[status(thm)],[f360,f168,f141,f133,f136,f329]) ).

fof(f393,plain,
    ( spl0_53
  <=> aReductOfIn0(sk0_0(xb,xR,xa),xa,xR) ),
    introduced(split_symbol_definition) ).

fof(f396,plain,
    ( ~ aElement0(sk0_0(xb,xR,xa))
    | ~ aReductOfIn0(sk0_0(xb,xR,xa),xa,xR)
    | ~ spl0_45 ),
    inference(resolution,[status(thm)],[f351,f110]) ).

fof(f397,plain,
    ( ~ spl0_40
    | ~ spl0_53
    | ~ spl0_45 ),
    inference(split_clause,[status(thm)],[f396,f329,f393,f350]) ).

fof(f423,plain,
    ( spl0_58
  <=> sk0_0(xb,xR,xa) = sk0_0(xb,xR,xa) ),
    introduced(split_symbol_definition) ).

fof(f425,plain,
    ( sk0_0(xb,xR,xa) != sk0_0(xb,xR,xa)
    | spl0_58 ),
    inference(component_clause,[status(thm)],[f423]) ).

fof(f440,plain,
    ( $false
    | spl0_58 ),
    inference(equality_resolution,[status(esa)],[f425]) ).

fof(f441,plain,
    spl0_58,
    inference(contradiction_clause,[status(thm)],[f440]) ).

fof(f533,plain,
    ( spl0_82
  <=> sk0_13(xb,xb,xb) = sk0_13(xb,xb,xb) ),
    introduced(split_symbol_definition) ).

fof(f535,plain,
    ( sk0_13(xb,xb,xb) != sk0_13(xb,xb,xb)
    | spl0_82 ),
    inference(component_clause,[status(thm)],[f533]) ).

fof(f558,plain,
    ( $false
    | spl0_82 ),
    inference(equality_resolution,[status(esa)],[f535]) ).

fof(f559,plain,
    spl0_82,
    inference(contradiction_clause,[status(thm)],[f558]) ).

fof(f1296,plain,
    ( ~ aElement0(xa)
    | ~ aRewritingSystem0(xR)
    | ~ aElement0(xb)
    | aReductOfIn0(xb,xa,xR)
    | aReductOfIn0(sk0_0(xb,xR,xa),xa,xR) ),
    inference(resolution,[status(thm)],[f38,f107]) ).

fof(f1297,plain,
    ( ~ spl0_11
    | ~ spl0_6
    | ~ spl0_4
    | spl0_5
    | spl0_53 ),
    inference(split_clause,[status(thm)],[f1296,f168,f141,f133,f136,f393]) ).

fof(f1298,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f122,f132,f140,f150,f152,f177,f215,f225,f317,f328,f354,f361,f397,f441,f559,f1297]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : COM016+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33  % Computer : n026.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 300
% 0.13/0.33  % DateTime : Tue May 30 12:05:28 EDT 2023
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  % Drodi V3.5.1
% 0.18/0.37  % Refutation found
% 0.18/0.37  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.18/0.37  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.18/0.39  % Elapsed time: 0.050777 seconds
% 0.18/0.39  % CPU time: 0.247438 seconds
% 0.18/0.39  % Memory used: 21.881 MB
%------------------------------------------------------------------------------