TSTP Solution File: COM018+4 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : COM018+4 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n011.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 12:03:56 EDT 2023

% Result   : Theorem 0.19s 0.40s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   35 (   9 unt;   0 def)
%            Number of atoms       :  249 (  17 equ)
%            Maximal formula atoms :   30 (   7 avg)
%            Number of connectives :  299 (  85   ~;  97   |; 109   &)
%                                         (   3 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   14 (  12 usr;   4 prp; 0-3 aty)
%            Number of functors    :   11 (  11 usr;   6 con; 0-2 aty)
%            Number of variables   :   62 (;  40   !;  22   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f14,axiom,
    ! [W0] :
      ( ( aRewritingSystem0(W0)
        & isTerminating0(W0) )
     => ! [W1] :
          ( aElement0(W1)
         => ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

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

fof(f16,hypothesis,
    ( ! [W0,W1,W2] :
        ( ( aElement0(W0)
          & aElement0(W1)
          & aElement0(W2)
          & aReductOfIn0(W1,W0,xR)
          & aReductOfIn0(W2,W0,xR) )
       => ? [W3] :
            ( aElement0(W3)
            & ( W1 = W3
              | ( ( aReductOfIn0(W3,W1,xR)
                  | ? [W4] :
                      ( aElement0(W4)
                      & aReductOfIn0(W4,W1,xR)
                      & sdtmndtplgtdt0(W4,xR,W3) ) )
                & sdtmndtplgtdt0(W1,xR,W3) ) )
            & sdtmndtasgtdt0(W1,xR,W3)
            & ( W2 = W3
              | ( ( aReductOfIn0(W3,W2,xR)
                  | ? [W4] :
                      ( aElement0(W4)
                      & aReductOfIn0(W4,W2,xR)
                      & sdtmndtplgtdt0(W4,xR,W3) ) )
                & sdtmndtplgtdt0(W2,xR,W3) ) )
            & sdtmndtasgtdt0(W2,xR,W3) ) )
    & isLocallyConfluent0(xR)
    & ! [W0,W1] :
        ( ( aElement0(W0)
          & aElement0(W1) )
       => ( ( aReductOfIn0(W1,W0,xR)
            | ? [W2] :
                ( aElement0(W2)
                & aReductOfIn0(W2,W0,xR)
                & sdtmndtplgtdt0(W2,xR,W1) )
            | sdtmndtplgtdt0(W0,xR,W1) )
         => iLess0(W1,W0) ) )
    & isTerminating0(xR) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,hypothesis,
    ( aElement0(xw)
    & ( xu = xw
      | ( ( aReductOfIn0(xw,xu,xR)
          | ? [W0] :
              ( aElement0(W0)
              & aReductOfIn0(W0,xu,xR)
              & sdtmndtplgtdt0(W0,xR,xw) ) )
        & sdtmndtplgtdt0(xu,xR,xw) ) )
    & sdtmndtasgtdt0(xu,xR,xw)
    & ( xv = xw
      | ( ( aReductOfIn0(xw,xv,xR)
          | ? [W0] :
              ( aElement0(W0)
              & aReductOfIn0(W0,xv,xR)
              & sdtmndtplgtdt0(W0,xR,xw) ) )
        & sdtmndtplgtdt0(xv,xR,xw) ) )
    & sdtmndtasgtdt0(xv,xR,xw) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f23,conjecture,
    ? [W0] :
      ( ( aElement0(W0)
        & ( xw = W0
          | aReductOfIn0(W0,xw,xR)
          | ? [W1] :
              ( aElement0(W1)
              & aReductOfIn0(W1,xw,xR)
              & sdtmndtplgtdt0(W1,xR,W0) )
          | sdtmndtplgtdt0(xw,xR,W0)
          | sdtmndtasgtdt0(xw,xR,W0) )
        & ~ ? [W1] : aReductOfIn0(W1,W0,xR) )
      | aNormalFormOfIn0(W0,xw,xR) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f24,negated_conjecture,
    ~ ? [W0] :
        ( ( aElement0(W0)
          & ( xw = W0
            | aReductOfIn0(W0,xw,xR)
            | ? [W1] :
                ( aElement0(W1)
                & aReductOfIn0(W1,xw,xR)
                & sdtmndtplgtdt0(W1,xR,W0) )
            | sdtmndtplgtdt0(xw,xR,W0)
            | sdtmndtasgtdt0(xw,xR,W0) )
          & ~ ? [W1] : aReductOfIn0(W1,W0,xR) )
        | aNormalFormOfIn0(W0,xw,xR) ),
    inference(negated_conjecture,[status(cth)],[f23]) ).

fof(f96,plain,
    ! [W0] :
      ( ~ aRewritingSystem0(W0)
      | ~ isTerminating0(W0)
      | ! [W1] :
          ( ~ aElement0(W1)
          | ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f14]) ).

fof(f97,plain,
    ! [W0] :
      ( ~ aRewritingSystem0(W0)
      | ~ isTerminating0(W0)
      | ! [W1] :
          ( ~ aElement0(W1)
          | aNormalFormOfIn0(sk0_12(W1,W0),W1,W0) ) ),
    inference(skolemization,[status(esa)],[f96]) ).

fof(f98,plain,
    ! [X0,X1] :
      ( ~ aRewritingSystem0(X0)
      | ~ isTerminating0(X0)
      | ~ aElement0(X1)
      | aNormalFormOfIn0(sk0_12(X1,X0),X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f97]) ).

fof(f99,plain,
    aRewritingSystem0(xR),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f100,plain,
    ( ! [W0,W1,W2] :
        ( ~ aElement0(W0)
        | ~ aElement0(W1)
        | ~ aElement0(W2)
        | ~ aReductOfIn0(W1,W0,xR)
        | ~ aReductOfIn0(W2,W0,xR)
        | ? [W3] :
            ( aElement0(W3)
            & ( W1 = W3
              | ( ( aReductOfIn0(W3,W1,xR)
                  | ? [W4] :
                      ( aElement0(W4)
                      & aReductOfIn0(W4,W1,xR)
                      & sdtmndtplgtdt0(W4,xR,W3) ) )
                & sdtmndtplgtdt0(W1,xR,W3) ) )
            & sdtmndtasgtdt0(W1,xR,W3)
            & ( W2 = W3
              | ( ( aReductOfIn0(W3,W2,xR)
                  | ? [W4] :
                      ( aElement0(W4)
                      & aReductOfIn0(W4,W2,xR)
                      & sdtmndtplgtdt0(W4,xR,W3) ) )
                & sdtmndtplgtdt0(W2,xR,W3) ) )
            & sdtmndtasgtdt0(W2,xR,W3) ) )
    & isLocallyConfluent0(xR)
    & ! [W0,W1] :
        ( ~ aElement0(W0)
        | ~ aElement0(W1)
        | ( ~ aReductOfIn0(W1,W0,xR)
          & ! [W2] :
              ( ~ aElement0(W2)
              | ~ aReductOfIn0(W2,W0,xR)
              | ~ sdtmndtplgtdt0(W2,xR,W1) )
          & ~ sdtmndtplgtdt0(W0,xR,W1) )
        | iLess0(W1,W0) )
    & isTerminating0(xR) ),
    inference(pre_NNF_transformation,[status(esa)],[f16]) ).

fof(f101,plain,
    ( ! [W1,W2] :
        ( ! [W0] :
            ( ~ aElement0(W0)
            | ~ aElement0(W1)
            | ~ aElement0(W2)
            | ~ aReductOfIn0(W1,W0,xR)
            | ~ aReductOfIn0(W2,W0,xR) )
        | ? [W3] :
            ( aElement0(W3)
            & ( W1 = W3
              | ( ( aReductOfIn0(W3,W1,xR)
                  | ? [W4] :
                      ( aElement0(W4)
                      & aReductOfIn0(W4,W1,xR)
                      & sdtmndtplgtdt0(W4,xR,W3) ) )
                & sdtmndtplgtdt0(W1,xR,W3) ) )
            & sdtmndtasgtdt0(W1,xR,W3)
            & ( W2 = W3
              | ( ( aReductOfIn0(W3,W2,xR)
                  | ? [W4] :
                      ( aElement0(W4)
                      & aReductOfIn0(W4,W2,xR)
                      & sdtmndtplgtdt0(W4,xR,W3) ) )
                & sdtmndtplgtdt0(W2,xR,W3) ) )
            & sdtmndtasgtdt0(W2,xR,W3) ) )
    & isLocallyConfluent0(xR)
    & ! [W0,W1] :
        ( ~ aElement0(W0)
        | ~ aElement0(W1)
        | ( ~ aReductOfIn0(W1,W0,xR)
          & ! [W2] :
              ( ~ aElement0(W2)
              | ~ aReductOfIn0(W2,W0,xR)
              | ~ sdtmndtplgtdt0(W2,xR,W1) )
          & ~ sdtmndtplgtdt0(W0,xR,W1) )
        | iLess0(W1,W0) )
    & isTerminating0(xR) ),
    inference(miniscoping,[status(esa)],[f100]) ).

fof(f102,plain,
    ( ! [W1,W2] :
        ( ! [W0] :
            ( ~ aElement0(W0)
            | ~ aElement0(W1)
            | ~ aElement0(W2)
            | ~ aReductOfIn0(W1,W0,xR)
            | ~ aReductOfIn0(W2,W0,xR) )
        | ( aElement0(sk0_13(W2,W1))
          & ( W1 = sk0_13(W2,W1)
            | ( ( aReductOfIn0(sk0_13(W2,W1),W1,xR)
                | ( aElement0(sk0_14(W2,W1))
                  & aReductOfIn0(sk0_14(W2,W1),W1,xR)
                  & sdtmndtplgtdt0(sk0_14(W2,W1),xR,sk0_13(W2,W1)) ) )
              & sdtmndtplgtdt0(W1,xR,sk0_13(W2,W1)) ) )
          & sdtmndtasgtdt0(W1,xR,sk0_13(W2,W1))
          & ( W2 = sk0_13(W2,W1)
            | ( ( aReductOfIn0(sk0_13(W2,W1),W2,xR)
                | ( aElement0(sk0_15(W2,W1))
                  & aReductOfIn0(sk0_15(W2,W1),W2,xR)
                  & sdtmndtplgtdt0(sk0_15(W2,W1),xR,sk0_13(W2,W1)) ) )
              & sdtmndtplgtdt0(W2,xR,sk0_13(W2,W1)) ) )
          & sdtmndtasgtdt0(W2,xR,sk0_13(W2,W1)) ) )
    & isLocallyConfluent0(xR)
    & ! [W0,W1] :
        ( ~ aElement0(W0)
        | ~ aElement0(W1)
        | ( ~ aReductOfIn0(W1,W0,xR)
          & ! [W2] :
              ( ~ aElement0(W2)
              | ~ aReductOfIn0(W2,W0,xR)
              | ~ sdtmndtplgtdt0(W2,xR,W1) )
          & ~ sdtmndtplgtdt0(W0,xR,W1) )
        | iLess0(W1,W0) )
    & isTerminating0(xR) ),
    inference(skolemization,[status(esa)],[f101]) ).

fof(f118,plain,
    isTerminating0(xR),
    inference(cnf_transformation,[status(esa)],[f102]) ).

fof(f206,plain,
    ( aElement0(xw)
    & ( xu = xw
      | ( ( aReductOfIn0(xw,xu,xR)
          | ( aElement0(sk0_23)
            & aReductOfIn0(sk0_23,xu,xR)
            & sdtmndtplgtdt0(sk0_23,xR,xw) ) )
        & sdtmndtplgtdt0(xu,xR,xw) ) )
    & sdtmndtasgtdt0(xu,xR,xw)
    & ( xv = xw
      | ( ( aReductOfIn0(xw,xv,xR)
          | ( aElement0(sk0_24)
            & aReductOfIn0(sk0_24,xv,xR)
            & sdtmndtplgtdt0(sk0_24,xR,xw) ) )
        & sdtmndtplgtdt0(xv,xR,xw) ) )
    & sdtmndtasgtdt0(xv,xR,xw) ),
    inference(skolemization,[status(esa)],[f22]) ).

fof(f207,plain,
    aElement0(xw),
    inference(cnf_transformation,[status(esa)],[f206]) ).

fof(f218,plain,
    ! [W0] :
      ( ( ~ aElement0(W0)
        | ( xw != W0
          & ~ aReductOfIn0(W0,xw,xR)
          & ! [W1] :
              ( ~ aElement0(W1)
              | ~ aReductOfIn0(W1,xw,xR)
              | ~ sdtmndtplgtdt0(W1,xR,W0) )
          & ~ sdtmndtplgtdt0(xw,xR,W0)
          & ~ sdtmndtasgtdt0(xw,xR,W0) )
        | ? [W1] : aReductOfIn0(W1,W0,xR) )
      & ~ aNormalFormOfIn0(W0,xw,xR) ),
    inference(pre_NNF_transformation,[status(esa)],[f24]) ).

fof(f219,plain,
    ( ! [W0] :
        ( ~ aElement0(W0)
        | ( xw != W0
          & ~ aReductOfIn0(W0,xw,xR)
          & ! [W1] :
              ( ~ aElement0(W1)
              | ~ aReductOfIn0(W1,xw,xR)
              | ~ sdtmndtplgtdt0(W1,xR,W0) )
          & ~ sdtmndtplgtdt0(xw,xR,W0)
          & ~ sdtmndtasgtdt0(xw,xR,W0) )
        | ? [W1] : aReductOfIn0(W1,W0,xR) )
    & ! [W0] : ~ aNormalFormOfIn0(W0,xw,xR) ),
    inference(miniscoping,[status(esa)],[f218]) ).

fof(f220,plain,
    ( ! [W0] :
        ( ~ aElement0(W0)
        | ( xw != W0
          & ~ aReductOfIn0(W0,xw,xR)
          & ! [W1] :
              ( ~ aElement0(W1)
              | ~ aReductOfIn0(W1,xw,xR)
              | ~ sdtmndtplgtdt0(W1,xR,W0) )
          & ~ sdtmndtplgtdt0(xw,xR,W0)
          & ~ sdtmndtasgtdt0(xw,xR,W0) )
        | aReductOfIn0(sk0_25(W0),W0,xR) )
    & ! [W0] : ~ aNormalFormOfIn0(W0,xw,xR) ),
    inference(skolemization,[status(esa)],[f219]) ).

fof(f226,plain,
    ! [X0] : ~ aNormalFormOfIn0(X0,xw,xR),
    inference(cnf_transformation,[status(esa)],[f220]) ).

fof(f386,plain,
    ( spl0_33
  <=> aRewritingSystem0(xR) ),
    introduced(split_symbol_definition) ).

fof(f388,plain,
    ( ~ aRewritingSystem0(xR)
    | spl0_33 ),
    inference(component_clause,[status(thm)],[f386]) ).

fof(f399,plain,
    ( spl0_36
  <=> aElement0(xw) ),
    introduced(split_symbol_definition) ).

fof(f401,plain,
    ( ~ aElement0(xw)
    | spl0_36 ),
    inference(component_clause,[status(thm)],[f399]) ).

fof(f427,plain,
    ( $false
    | spl0_33 ),
    inference(forward_subsumption_resolution,[status(thm)],[f388,f99]) ).

fof(f428,plain,
    spl0_33,
    inference(contradiction_clause,[status(thm)],[f427]) ).

fof(f429,plain,
    ( $false
    | spl0_36 ),
    inference(forward_subsumption_resolution,[status(thm)],[f401,f207]) ).

fof(f430,plain,
    spl0_36,
    inference(contradiction_clause,[status(thm)],[f429]) ).

fof(f1114,plain,
    ( spl0_128
  <=> isTerminating0(xR) ),
    introduced(split_symbol_definition) ).

fof(f1116,plain,
    ( ~ isTerminating0(xR)
    | spl0_128 ),
    inference(component_clause,[status(thm)],[f1114]) ).

fof(f1772,plain,
    ( ~ aRewritingSystem0(xR)
    | ~ isTerminating0(xR)
    | ~ aElement0(xw) ),
    inference(resolution,[status(thm)],[f98,f226]) ).

fof(f1773,plain,
    ( ~ spl0_33
    | ~ spl0_128
    | ~ spl0_36 ),
    inference(split_clause,[status(thm)],[f1772,f386,f1114,f399]) ).

fof(f1780,plain,
    ( $false
    | spl0_128 ),
    inference(forward_subsumption_resolution,[status(thm)],[f1116,f118]) ).

fof(f1781,plain,
    spl0_128,
    inference(contradiction_clause,[status(thm)],[f1780]) ).

fof(f1782,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f428,f430,f1773,f1781]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : COM018+4 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n011.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue May 30 11:48:42 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 0.19/0.40  % Refutation found
% 0.19/0.40  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.40  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.42  % Elapsed time: 0.071412 seconds
% 0.19/0.42  % CPU time: 0.404317 seconds
% 0.19/0.42  % Memory used: 29.154 MB
%------------------------------------------------------------------------------