TSTP Solution File: COM016+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% 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 : n012.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 0.17s 0.33s
% Output   : CNFRefutation 0.17s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   73 (  14 unt;   2 def)
%            Number of atoms       :  233 (   5 equ)
%            Maximal formula atoms :   13 (   3 avg)
%            Number of connectives :  267 ( 107   ~; 115   |;  27   &)
%                                         (  14 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   14 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   19 (  17 usr;  11 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-3 aty)
%            Number of variables   :   56 (  51   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [W0,W1] :
      ( ( aElement0(W0)
        & aRewritingSystem0(W1) )
     => ! [W2] :
          ( aReductOfIn0(W2,W0,W1)
         => aElement0(W2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

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(f28,plain,
    ! [W0,W1] :
      ( ~ aElement0(W0)
      | ~ aRewritingSystem0(W1)
      | ! [W2] :
          ( ~ aReductOfIn0(W2,W0,W1)
          | aElement0(W2) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

fof(f29,plain,
    ! [X0,X1,X2] :
      ( ~ aElement0(X0)
      | ~ aRewritingSystem0(X1)
      | ~ aReductOfIn0(X2,X0,X1)
      | aElement0(X2) ),
    inference(cnf_transformation,[status(esa)],[f28]) ).

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

fof(f112,plain,
    ! [X0,X1] :
      ( ~ aElement0(X0)
      | ~ aRewritingSystem0(X1)
      | sdtmndtasgtdt0(X0,X1,X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f111]) ).

fof(f113,plain,
    ! [X0] :
      ( ~ aRewritingSystem0(X0)
      | sdtmndtasgtdt0(xb,X0,xb) ),
    inference(resolution,[status(thm)],[f112,f100]) ).

fof(f115,plain,
    sdtmndtasgtdt0(xb,xR,xb),
    inference(resolution,[status(thm)],[f113,f96]) ).

fof(f116,plain,
    ( spl0_0
  <=> aElement0(xb) ),
    introduced(split_symbol_definition) ).

fof(f118,plain,
    ( ~ aElement0(xb)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f116]) ).

fof(f119,plain,
    ( spl0_1
  <=> aReductOfIn0(xb,xa,xR) ),
    introduced(split_symbol_definition) ).

fof(f122,plain,
    ( ~ aElement0(xb)
    | ~ aReductOfIn0(xb,xa,xR) ),
    inference(resolution,[status(thm)],[f115,f110]) ).

fof(f123,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f122,f116,f119]) ).

fof(f127,plain,
    ( spl0_3
  <=> aRewritingSystem0(xR) ),
    introduced(split_symbol_definition) ).

fof(f129,plain,
    ( ~ aRewritingSystem0(xR)
    | spl0_3 ),
    inference(component_clause,[status(thm)],[f127]) ).

fof(f132,plain,
    ( $false
    | spl0_3 ),
    inference(forward_subsumption_resolution,[status(thm)],[f129,f96]) ).

fof(f133,plain,
    spl0_3,
    inference(contradiction_clause,[status(thm)],[f132]) ).

fof(f134,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f118,f100]) ).

fof(f135,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f134]) ).

fof(f140,plain,
    ( spl0_5
  <=> aElement0(xa) ),
    introduced(split_symbol_definition) ).

fof(f142,plain,
    ( ~ aElement0(xa)
    | spl0_5 ),
    inference(component_clause,[status(thm)],[f140]) ).

fof(f145,plain,
    ( $false
    | spl0_5 ),
    inference(forward_subsumption_resolution,[status(thm)],[f142,f99]) ).

fof(f146,plain,
    spl0_5,
    inference(contradiction_clause,[status(thm)],[f145]) ).

fof(f152,plain,
    ( spl0_7
  <=> aElement0(xc) ),
    introduced(split_symbol_definition) ).

fof(f154,plain,
    ( ~ aElement0(xc)
    | spl0_7 ),
    inference(component_clause,[status(thm)],[f152]) ).

fof(f157,plain,
    ( $false
    | spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f154,f101]) ).

fof(f158,plain,
    spl0_7,
    inference(contradiction_clause,[status(thm)],[f157]) ).

fof(f237,plain,
    ( spl0_19
  <=> isTerminating0(xR) ),
    introduced(split_symbol_definition) ).

fof(f239,plain,
    ( ~ isTerminating0(xR)
    | spl0_19 ),
    inference(component_clause,[status(thm)],[f237]) ).

fof(f245,plain,
    ( $false
    | spl0_19 ),
    inference(forward_subsumption_resolution,[status(thm)],[f239,f98]) ).

fof(f246,plain,
    spl0_19,
    inference(contradiction_clause,[status(thm)],[f245]) ).

fof(f258,plain,
    ( spl0_23
  <=> aReductOfIn0(sk0_0(xb,xR,xa),xa,xR) ),
    introduced(split_symbol_definition) ).

fof(f259,plain,
    ( aReductOfIn0(sk0_0(xb,xR,xa),xa,xR)
    | ~ spl0_23 ),
    inference(component_clause,[status(thm)],[f258]) ).

fof(f261,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(f262,plain,
    ( ~ spl0_5
    | ~ spl0_3
    | ~ spl0_0
    | spl0_1
    | spl0_23 ),
    inference(split_clause,[status(thm)],[f261,f140,f127,f116,f119,f258]) ).

fof(f268,plain,
    ( spl0_25
  <=> aElement0(sk0_0(xb,xR,xa)) ),
    introduced(split_symbol_definition) ).

fof(f271,plain,
    ( ~ aElement0(xa)
    | ~ aRewritingSystem0(xR)
    | aElement0(sk0_0(xb,xR,xa))
    | ~ spl0_23 ),
    inference(resolution,[status(thm)],[f259,f29]) ).

fof(f272,plain,
    ( ~ spl0_5
    | ~ spl0_3
    | spl0_25
    | ~ spl0_23 ),
    inference(split_clause,[status(thm)],[f271,f140,f127,f268,f258]) ).

fof(f337,plain,
    ( spl0_38
  <=> sdtmndtplgtdt0(sk0_0(xb,xR,xa),xR,xb) ),
    introduced(split_symbol_definition) ).

fof(f338,plain,
    ( sdtmndtplgtdt0(sk0_0(xb,xR,xa),xR,xb)
    | ~ spl0_38 ),
    inference(component_clause,[status(thm)],[f337]) ).

fof(f340,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(f341,plain,
    ( ~ spl0_5
    | ~ spl0_3
    | ~ spl0_0
    | spl0_1
    | spl0_38 ),
    inference(split_clause,[status(thm)],[f340,f140,f127,f116,f119,f337]) ).

fof(f375,plain,
    ( spl0_46
  <=> sdtmndtasgtdt0(sk0_0(xb,xR,xa),xR,xb) ),
    introduced(split_symbol_definition) ).

fof(f376,plain,
    ( sdtmndtasgtdt0(sk0_0(xb,xR,xa),xR,xb)
    | ~ spl0_46 ),
    inference(component_clause,[status(thm)],[f375]) ).

fof(f378,plain,
    ( ~ aElement0(sk0_0(xb,xR,xa))
    | ~ aRewritingSystem0(xR)
    | ~ aElement0(xb)
    | sdtmndtasgtdt0(sk0_0(xb,xR,xa),xR,xb)
    | ~ spl0_38 ),
    inference(resolution,[status(thm)],[f338,f48]) ).

fof(f379,plain,
    ( ~ spl0_25
    | ~ spl0_3
    | ~ spl0_0
    | spl0_46
    | ~ spl0_38 ),
    inference(split_clause,[status(thm)],[f378,f268,f127,f116,f375,f337]) ).

fof(f384,plain,
    ( ~ aElement0(sk0_0(xb,xR,xa))
    | ~ aReductOfIn0(sk0_0(xb,xR,xa),xa,xR)
    | ~ spl0_46 ),
    inference(resolution,[status(thm)],[f376,f110]) ).

fof(f385,plain,
    ( ~ spl0_25
    | ~ spl0_23
    | ~ spl0_46 ),
    inference(split_clause,[status(thm)],[f384,f268,f258,f375]) ).

fof(f396,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f123,f133,f135,f146,f158,f246,f262,f272,f341,f379,f385]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem  : COM016+1 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31  % Computer : n012.cluster.edu
% 0.10/0.31  % Model    : x86_64 x86_64
% 0.10/0.31  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31  % Memory   : 8042.1875MB
% 0.10/0.31  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31  % CPULimit : 300
% 0.10/0.31  % WCLimit  : 300
% 0.10/0.31  % DateTime : Tue Apr 30 00:57:41 EDT 2024
% 0.10/0.31  % CPUTime  : 
% 0.17/0.32  % Drodi V3.6.0
% 0.17/0.33  % Refutation found
% 0.17/0.33  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.33  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.34  % Elapsed time: 0.022282 seconds
% 0.17/0.34  % CPU time: 0.067414 seconds
% 0.17/0.34  % Total memory used: 13.669 MB
% 0.17/0.34  % Net memory used: 13.638 MB
%------------------------------------------------------------------------------