TSTP Solution File: KRS084+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : KRS084+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n004.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 20:24:44 EDT 2024

% Result   : Unsatisfiable 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   65 (  10 unt;   0 def)
%            Number of atoms       :  208 (   6 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  236 (  93   ~;  89   |;  42   &)
%                                         (   9 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   13 (  11 usr;   5 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-2 aty)
%            Number of variables   :   88 (  75   !;  13   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f18,axiom,
    ! [X] :
      ( cUnsatisfiable(X)
    <=> ( ? [Y] :
            ( rinvF(X,Y)
            & cd(Y) )
        & ! [Y] :
            ( rinvR(X,Y)
           => ? [Z] :
                ( rinvF(Y,Z)
                & cd(Z) ) )
        & ~ cc(X) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f19,axiom,
    ! [X] :
      ( cd(X)
    <=> ( ? [Y] :
            ( rf(X,Y)
            & ~ cc(Y) )
        & cc(X) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,axiom,
    ! [X,Y,Z] :
      ( ( rf(X,Y)
        & rf(X,Z) )
     => Y = Z ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f21,axiom,
    ! [X,Y] :
      ( rinvF(X,Y)
    <=> rf(Y,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f22,axiom,
    ! [X,Y] :
      ( rinvR(X,Y)
    <=> rr(Y,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f24,axiom,
    cUnsatisfiable(i2003_11_14_17_19_35232),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f25,axiom,
    ! [X,Y] :
      ( rf(X,Y)
     => rr(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f78,plain,
    ! [X] :
      ( cUnsatisfiable(X)
    <=> ( ? [Y] :
            ( rinvF(X,Y)
            & cd(Y) )
        & ! [Y] :
            ( ~ rinvR(X,Y)
            | ? [Z] :
                ( rinvF(Y,Z)
                & cd(Z) ) )
        & ~ cc(X) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f79,plain,
    ! [X] :
      ( ( ~ cUnsatisfiable(X)
        | ( ? [Y] :
              ( rinvF(X,Y)
              & cd(Y) )
          & ! [Y] :
              ( ~ rinvR(X,Y)
              | ? [Z] :
                  ( rinvF(Y,Z)
                  & cd(Z) ) )
          & ~ cc(X) ) )
      & ( cUnsatisfiable(X)
        | ! [Y] :
            ( ~ rinvF(X,Y)
            | ~ cd(Y) )
        | ? [Y] :
            ( rinvR(X,Y)
            & ! [Z] :
                ( ~ rinvF(Y,Z)
                | ~ cd(Z) ) )
        | cc(X) ) ),
    inference(NNF_transformation,[status(esa)],[f78]) ).

fof(f80,plain,
    ( ! [X] :
        ( ~ cUnsatisfiable(X)
        | ( ? [Y] :
              ( rinvF(X,Y)
              & cd(Y) )
          & ! [Y] :
              ( ~ rinvR(X,Y)
              | ? [Z] :
                  ( rinvF(Y,Z)
                  & cd(Z) ) )
          & ~ cc(X) ) )
    & ! [X] :
        ( cUnsatisfiable(X)
        | ! [Y] :
            ( ~ rinvF(X,Y)
            | ~ cd(Y) )
        | ? [Y] :
            ( rinvR(X,Y)
            & ! [Z] :
                ( ~ rinvF(Y,Z)
                | ~ cd(Z) ) )
        | cc(X) ) ),
    inference(miniscoping,[status(esa)],[f79]) ).

fof(f81,plain,
    ( ! [X] :
        ( ~ cUnsatisfiable(X)
        | ( rinvF(X,sk0_0(X))
          & cd(sk0_0(X))
          & ! [Y] :
              ( ~ rinvR(X,Y)
              | ( rinvF(Y,sk0_1(Y,X))
                & cd(sk0_1(Y,X)) ) )
          & ~ cc(X) ) )
    & ! [X] :
        ( cUnsatisfiable(X)
        | ! [Y] :
            ( ~ rinvF(X,Y)
            | ~ cd(Y) )
        | ( rinvR(X,sk0_2(X))
          & ! [Z] :
              ( ~ rinvF(sk0_2(X),Z)
              | ~ cd(Z) ) )
        | cc(X) ) ),
    inference(skolemization,[status(esa)],[f80]) ).

fof(f82,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | rinvF(X0,sk0_0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f81]) ).

fof(f83,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | cd(sk0_0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f81]) ).

fof(f84,plain,
    ! [X0,X1] :
      ( ~ cUnsatisfiable(X0)
      | ~ rinvR(X0,X1)
      | rinvF(X1,sk0_1(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f81]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ~ cUnsatisfiable(X0)
      | ~ rinvR(X0,X1)
      | cd(sk0_1(X1,X0)) ),
    inference(cnf_transformation,[status(esa)],[f81]) ).

fof(f89,plain,
    ! [X] :
      ( ( ~ cd(X)
        | ( ? [Y] :
              ( rf(X,Y)
              & ~ cc(Y) )
          & cc(X) ) )
      & ( cd(X)
        | ! [Y] :
            ( ~ rf(X,Y)
            | cc(Y) )
        | ~ cc(X) ) ),
    inference(NNF_transformation,[status(esa)],[f19]) ).

fof(f90,plain,
    ( ! [X] :
        ( ~ cd(X)
        | ( ? [Y] :
              ( rf(X,Y)
              & ~ cc(Y) )
          & cc(X) ) )
    & ! [X] :
        ( cd(X)
        | ! [Y] :
            ( ~ rf(X,Y)
            | cc(Y) )
        | ~ cc(X) ) ),
    inference(miniscoping,[status(esa)],[f89]) ).

fof(f91,plain,
    ( ! [X] :
        ( ~ cd(X)
        | ( rf(X,sk0_3(X))
          & ~ cc(sk0_3(X))
          & cc(X) ) )
    & ! [X] :
        ( cd(X)
        | ! [Y] :
            ( ~ rf(X,Y)
            | cc(Y) )
        | ~ cc(X) ) ),
    inference(skolemization,[status(esa)],[f90]) ).

fof(f92,plain,
    ! [X0] :
      ( ~ cd(X0)
      | rf(X0,sk0_3(X0)) ),
    inference(cnf_transformation,[status(esa)],[f91]) ).

fof(f93,plain,
    ! [X0] :
      ( ~ cd(X0)
      | ~ cc(sk0_3(X0)) ),
    inference(cnf_transformation,[status(esa)],[f91]) ).

fof(f94,plain,
    ! [X0] :
      ( ~ cd(X0)
      | cc(X0) ),
    inference(cnf_transformation,[status(esa)],[f91]) ).

fof(f96,plain,
    ! [X,Y,Z] :
      ( ~ rf(X,Y)
      | ~ rf(X,Z)
      | Y = Z ),
    inference(pre_NNF_transformation,[status(esa)],[f20]) ).

fof(f97,plain,
    ! [Y,Z] :
      ( ! [X] :
          ( ~ rf(X,Y)
          | ~ rf(X,Z) )
      | Y = Z ),
    inference(miniscoping,[status(esa)],[f96]) ).

fof(f98,plain,
    ! [X0,X1,X2] :
      ( ~ rf(X0,X1)
      | ~ rf(X0,X2)
      | X1 = X2 ),
    inference(cnf_transformation,[status(esa)],[f97]) ).

fof(f99,plain,
    ! [X,Y] :
      ( ( ~ rinvF(X,Y)
        | rf(Y,X) )
      & ( rinvF(X,Y)
        | ~ rf(Y,X) ) ),
    inference(NNF_transformation,[status(esa)],[f21]) ).

fof(f100,plain,
    ( ! [X,Y] :
        ( ~ rinvF(X,Y)
        | rf(Y,X) )
    & ! [X,Y] :
        ( rinvF(X,Y)
        | ~ rf(Y,X) ) ),
    inference(miniscoping,[status(esa)],[f99]) ).

fof(f101,plain,
    ! [X0,X1] :
      ( ~ rinvF(X0,X1)
      | rf(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f100]) ).

fof(f103,plain,
    ! [X,Y] :
      ( ( ~ rinvR(X,Y)
        | rr(Y,X) )
      & ( rinvR(X,Y)
        | ~ rr(Y,X) ) ),
    inference(NNF_transformation,[status(esa)],[f22]) ).

fof(f104,plain,
    ( ! [X,Y] :
        ( ~ rinvR(X,Y)
        | rr(Y,X) )
    & ! [X,Y] :
        ( rinvR(X,Y)
        | ~ rr(Y,X) ) ),
    inference(miniscoping,[status(esa)],[f103]) ).

fof(f106,plain,
    ! [X0,X1] :
      ( rinvR(X0,X1)
      | ~ rr(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f104]) ).

fof(f110,plain,
    cUnsatisfiable(i2003_11_14_17_19_35232),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f111,plain,
    ! [X,Y] :
      ( ~ rf(X,Y)
      | rr(X,Y) ),
    inference(pre_NNF_transformation,[status(esa)],[f25]) ).

fof(f112,plain,
    ! [X0,X1] :
      ( ~ rf(X0,X1)
      | rr(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f111]) ).

fof(f113,plain,
    rinvF(i2003_11_14_17_19_35232,sk0_0(i2003_11_14_17_19_35232)),
    inference(resolution,[status(thm)],[f82,f110]) ).

fof(f114,plain,
    cd(sk0_0(i2003_11_14_17_19_35232)),
    inference(resolution,[status(thm)],[f83,f110]) ).

fof(f115,plain,
    cc(sk0_0(i2003_11_14_17_19_35232)),
    inference(resolution,[status(thm)],[f114,f94]) ).

fof(f117,plain,
    rf(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),
    inference(resolution,[status(thm)],[f113,f101]) ).

fof(f118,plain,
    ( spl0_0
  <=> cUnsatisfiable(i2003_11_14_17_19_35232) ),
    introduced(split_symbol_definition) ).

fof(f120,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f118]) ).

fof(f139,plain,
    rr(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),
    inference(resolution,[status(thm)],[f117,f112]) ).

fof(f146,plain,
    rinvR(i2003_11_14_17_19_35232,sk0_0(i2003_11_14_17_19_35232)),
    inference(resolution,[status(thm)],[f139,f106]) ).

fof(f163,plain,
    ( spl0_7
  <=> rinvF(sk0_0(i2003_11_14_17_19_35232),sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)) ),
    introduced(split_symbol_definition) ).

fof(f164,plain,
    ( rinvF(sk0_0(i2003_11_14_17_19_35232),sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232))
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f163]) ).

fof(f166,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
    | rinvF(sk0_0(i2003_11_14_17_19_35232),sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)) ),
    inference(resolution,[status(thm)],[f84,f146]) ).

fof(f167,plain,
    ( ~ spl0_0
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f166,f118,f163]) ).

fof(f168,plain,
    ( spl0_8
  <=> cd(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)) ),
    introduced(split_symbol_definition) ).

fof(f169,plain,
    ( cd(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232))
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f168]) ).

fof(f171,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_19_35232)
    | cd(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)) ),
    inference(resolution,[status(thm)],[f85,f146]) ).

fof(f172,plain,
    ( ~ spl0_0
    | spl0_8 ),
    inference(split_clause,[status(thm)],[f171,f118,f168]) ).

fof(f187,plain,
    ( rf(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),sk0_3(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)))
    | ~ spl0_8 ),
    inference(resolution,[status(thm)],[f169,f92]) ).

fof(f190,plain,
    ( rf(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),sk0_0(i2003_11_14_17_19_35232))
    | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f164,f101]) ).

fof(f204,plain,
    ! [X0] :
      ( ~ rf(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232),X0)
      | sk0_0(i2003_11_14_17_19_35232) = X0
      | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f190,f98]) ).

fof(f247,plain,
    ( sk0_0(i2003_11_14_17_19_35232) = sk0_3(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232))
    | ~ spl0_8
    | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f187,f204]) ).

fof(f251,plain,
    ( spl0_19
  <=> cc(sk0_3(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232))) ),
    introduced(split_symbol_definition) ).

fof(f252,plain,
    ( cc(sk0_3(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)))
    | ~ spl0_19 ),
    inference(component_clause,[status(thm)],[f251]) ).

fof(f253,plain,
    ( ~ cc(sk0_3(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232)))
    | spl0_19 ),
    inference(component_clause,[status(thm)],[f251]) ).

fof(f273,plain,
    ( ~ cd(sk0_1(sk0_0(i2003_11_14_17_19_35232),i2003_11_14_17_19_35232))
    | ~ spl0_19 ),
    inference(resolution,[status(thm)],[f252,f93]) ).

fof(f274,plain,
    ( $false
    | ~ spl0_8
    | ~ spl0_19 ),
    inference(forward_subsumption_resolution,[status(thm)],[f273,f169]) ).

fof(f275,plain,
    ( ~ spl0_8
    | ~ spl0_19 ),
    inference(contradiction_clause,[status(thm)],[f274]) ).

fof(f278,plain,
    ( ~ cc(sk0_0(i2003_11_14_17_19_35232))
    | ~ spl0_8
    | ~ spl0_7
    | spl0_19 ),
    inference(backward_demodulation,[status(thm)],[f247,f253]) ).

fof(f279,plain,
    ( $false
    | ~ spl0_8
    | ~ spl0_7
    | spl0_19 ),
    inference(forward_subsumption_resolution,[status(thm)],[f278,f115]) ).

fof(f280,plain,
    ( ~ spl0_8
    | ~ spl0_7
    | spl0_19 ),
    inference(contradiction_clause,[status(thm)],[f279]) ).

fof(f281,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f120,f110]) ).

fof(f282,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f281]) ).

fof(f283,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f167,f172,f275,f280,f282]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem  : KRS084+1 : TPTP v8.1.2. Released v3.1.0.
% 0.10/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33  % Computer : n004.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 300
% 0.12/0.33  % DateTime : Mon Apr 29 23:51:48 EDT 2024
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  % Drodi V3.6.0
% 0.12/0.35  % Refutation found
% 0.12/0.35  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.35  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.35  % Elapsed time: 0.013517 seconds
% 0.12/0.35  % CPU time: 0.033533 seconds
% 0.12/0.35  % Total memory used: 1.120 MB
% 0.12/0.35  % Net memory used: 1.071 MB
%------------------------------------------------------------------------------