TSTP Solution File: KRS077+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : KRS077+1 : TPTP v8.1.2. Released v3.1.0.
% 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 20:24:42 EDT 2024

% Result   : Unsatisfiable 0.14s 0.31s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   47 (   8 unt;   0 def)
%            Number of atoms       :  176 (  14 equ)
%            Maximal formula atoms :   18 (   3 avg)
%            Number of connectives :  206 (  77   ~;  72   |;  46   &)
%                                         (   8 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   4 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :   87 (  71   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f15,axiom,
    ! [X] :
      ( cUnsatisfiable(X)
    <=> ( ! [Y0,Y1] :
            ( ( rr(X,Y0)
              & rr(X,Y1) )
           => Y0 = Y1 )
        & ? [Y] :
            ( rr(X,Y)
            & ! [Z] :
                ( rinvS(Y,Z)
               => cp(Z) ) )
        & ~ cp(X)
        & ? [Y] :
            ( rs(X,Y)
            & cp(Y) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f16,axiom,
    ! [X,Y] :
      ( rinvS(X,Y)
    <=> rs(Y,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f17,axiom,
    cUnsatisfiable(i2003_11_14_17_19_09372),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,axiom,
    ! [X,Y] :
      ( rs(X,Y)
     => rr(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f62,plain,
    ! [X] :
      ( cUnsatisfiable(X)
    <=> ( ! [Y0,Y1] :
            ( ~ rr(X,Y0)
            | ~ rr(X,Y1)
            | Y0 = Y1 )
        & ? [Y] :
            ( rr(X,Y)
            & ! [Z] :
                ( ~ rinvS(Y,Z)
                | cp(Z) ) )
        & ~ cp(X)
        & ? [Y] :
            ( rs(X,Y)
            & cp(Y) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f63,plain,
    ! [Y,Z] :
      ( pd0_0(Z,Y)
    <=> ( ~ rinvS(Y,Z)
        | cp(Z) ) ),
    introduced(predicate_definition,[f62]) ).

fof(f64,plain,
    ! [X] :
      ( cUnsatisfiable(X)
    <=> ( ! [Y0,Y1] :
            ( ~ rr(X,Y0)
            | ~ rr(X,Y1)
            | Y0 = Y1 )
        & ? [Y] :
            ( rr(X,Y)
            & ! [Z] : pd0_0(Z,Y) )
        & ~ cp(X)
        & ? [Y] :
            ( rs(X,Y)
            & cp(Y) ) ) ),
    inference(formula_renaming,[status(thm)],[f62,f63]) ).

fof(f65,plain,
    ! [X] :
      ( ( ~ cUnsatisfiable(X)
        | ( ! [Y0,Y1] :
              ( ~ rr(X,Y0)
              | ~ rr(X,Y1)
              | Y0 = Y1 )
          & ? [Y] :
              ( rr(X,Y)
              & ! [Z] : pd0_0(Z,Y) )
          & ~ cp(X)
          & ? [Y] :
              ( rs(X,Y)
              & cp(Y) ) ) )
      & ( cUnsatisfiable(X)
        | ? [Y0,Y1] :
            ( rr(X,Y0)
            & rr(X,Y1)
            & Y0 != Y1 )
        | ! [Y] :
            ( ~ rr(X,Y)
            | ? [Z] : ~ pd0_0(Z,Y) )
        | cp(X)
        | ! [Y] :
            ( ~ rs(X,Y)
            | ~ cp(Y) ) ) ),
    inference(NNF_transformation,[status(esa)],[f64]) ).

fof(f66,plain,
    ( ! [X] :
        ( ~ cUnsatisfiable(X)
        | ( ! [Y0,Y1] :
              ( ~ rr(X,Y0)
              | ~ rr(X,Y1)
              | Y0 = Y1 )
          & ? [Y] :
              ( rr(X,Y)
              & ! [Z] : pd0_0(Z,Y) )
          & ~ cp(X)
          & ? [Y] :
              ( rs(X,Y)
              & cp(Y) ) ) )
    & ! [X] :
        ( cUnsatisfiable(X)
        | ? [Y0,Y1] :
            ( rr(X,Y0)
            & rr(X,Y1)
            & Y0 != Y1 )
        | ! [Y] :
            ( ~ rr(X,Y)
            | ? [Z] : ~ pd0_0(Z,Y) )
        | cp(X)
        | ! [Y] :
            ( ~ rs(X,Y)
            | ~ cp(Y) ) ) ),
    inference(miniscoping,[status(esa)],[f65]) ).

fof(f67,plain,
    ( ! [X] :
        ( ~ cUnsatisfiable(X)
        | ( ! [Y0,Y1] :
              ( ~ rr(X,Y0)
              | ~ rr(X,Y1)
              | Y0 = Y1 )
          & rr(X,sk0_0(X))
          & ! [Z] : pd0_0(Z,sk0_0(X))
          & ~ cp(X)
          & rs(X,sk0_1(X))
          & cp(sk0_1(X)) ) )
    & ! [X] :
        ( cUnsatisfiable(X)
        | ( rr(X,sk0_2(X))
          & rr(X,sk0_3(X))
          & sk0_2(X) != sk0_3(X) )
        | ! [Y] :
            ( ~ rr(X,Y)
            | ~ pd0_0(sk0_4(Y,X),Y) )
        | cp(X)
        | ! [Y] :
            ( ~ rs(X,Y)
            | ~ cp(Y) ) ) ),
    inference(skolemization,[status(esa)],[f66]) ).

fof(f68,plain,
    ! [X0,X1,X2] :
      ( ~ cUnsatisfiable(X0)
      | ~ rr(X0,X1)
      | ~ rr(X0,X2)
      | X1 = X2 ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f69,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | rr(X0,sk0_0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f70,plain,
    ! [X0,X1] :
      ( ~ cUnsatisfiable(X0)
      | pd0_0(X1,sk0_0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f71,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | ~ cp(X0) ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f72,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | rs(X0,sk0_1(X0)) ),
    inference(cnf_transformation,[status(esa)],[f67]) ).

fof(f77,plain,
    ! [X,Y] :
      ( ( ~ rinvS(X,Y)
        | rs(Y,X) )
      & ( rinvS(X,Y)
        | ~ rs(Y,X) ) ),
    inference(NNF_transformation,[status(esa)],[f16]) ).

fof(f78,plain,
    ( ! [X,Y] :
        ( ~ rinvS(X,Y)
        | rs(Y,X) )
    & ! [X,Y] :
        ( rinvS(X,Y)
        | ~ rs(Y,X) ) ),
    inference(miniscoping,[status(esa)],[f77]) ).

fof(f80,plain,
    ! [X0,X1] :
      ( rinvS(X0,X1)
      | ~ rs(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f78]) ).

fof(f81,plain,
    cUnsatisfiable(i2003_11_14_17_19_09372),
    inference(cnf_transformation,[status(esa)],[f17]) ).

fof(f82,plain,
    ! [X,Y] :
      ( ~ rs(X,Y)
      | rr(X,Y) ),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f83,plain,
    ! [X0,X1] :
      ( ~ rs(X0,X1)
      | rr(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f82]) ).

fof(f84,plain,
    ! [Y,Z] :
      ( ( ~ pd0_0(Z,Y)
        | ~ rinvS(Y,Z)
        | cp(Z) )
      & ( pd0_0(Z,Y)
        | ( rinvS(Y,Z)
          & ~ cp(Z) ) ) ),
    inference(NNF_transformation,[status(esa)],[f63]) ).

fof(f85,plain,
    ( ! [Y,Z] :
        ( ~ pd0_0(Z,Y)
        | ~ rinvS(Y,Z)
        | cp(Z) )
    & ! [Y,Z] :
        ( pd0_0(Z,Y)
        | ( rinvS(Y,Z)
          & ~ cp(Z) ) ) ),
    inference(miniscoping,[status(esa)],[f84]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ~ pd0_0(X0,X1)
      | ~ rinvS(X1,X0)
      | cp(X0) ),
    inference(cnf_transformation,[status(esa)],[f85]) ).

fof(f89,plain,
    ! [X0,X1] :
      ( ~ cUnsatisfiable(X0)
      | ~ cUnsatisfiable(X0)
      | ~ rr(X0,X1)
      | X1 = sk0_0(X0) ),
    inference(resolution,[status(thm)],[f69,f68]) ).

fof(f90,plain,
    ! [X0,X1] :
      ( ~ cUnsatisfiable(X0)
      | ~ rr(X0,X1)
      | X1 = sk0_0(X0) ),
    inference(duplicate_literals_removal,[status(esa)],[f89]) ).

fof(f96,plain,
    rs(i2003_11_14_17_19_09372,sk0_1(i2003_11_14_17_19_09372)),
    inference(resolution,[status(thm)],[f72,f81]) ).

fof(f97,plain,
    ( spl0_0
  <=> cUnsatisfiable(i2003_11_14_17_19_09372) ),
    introduced(split_symbol_definition) ).

fof(f99,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f97]) ).

fof(f106,plain,
    ( spl0_3
  <=> cp(i2003_11_14_17_19_09372) ),
    introduced(split_symbol_definition) ).

fof(f107,plain,
    ( cp(i2003_11_14_17_19_09372)
    | ~ spl0_3 ),
    inference(component_clause,[status(thm)],[f106]) ).

fof(f116,plain,
    rr(i2003_11_14_17_19_09372,sk0_1(i2003_11_14_17_19_09372)),
    inference(resolution,[status(thm)],[f96,f83]) ).

fof(f117,plain,
    rinvS(sk0_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372),
    inference(resolution,[status(thm)],[f96,f80]) ).

fof(f123,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f99,f81]) ).

fof(f124,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f123]) ).

fof(f126,plain,
    ( spl0_6
  <=> pd0_0(i2003_11_14_17_19_09372,sk0_1(i2003_11_14_17_19_09372)) ),
    introduced(split_symbol_definition) ).

fof(f128,plain,
    ( ~ pd0_0(i2003_11_14_17_19_09372,sk0_1(i2003_11_14_17_19_09372))
    | spl0_6 ),
    inference(component_clause,[status(thm)],[f126]) ).

fof(f129,plain,
    ( ~ pd0_0(i2003_11_14_17_19_09372,sk0_1(i2003_11_14_17_19_09372))
    | cp(i2003_11_14_17_19_09372) ),
    inference(resolution,[status(thm)],[f86,f117]) ).

fof(f130,plain,
    ( ~ spl0_6
    | spl0_3 ),
    inference(split_clause,[status(thm)],[f129,f126,f106]) ).

fof(f131,plain,
    ! [X0] :
      ( ~ rr(i2003_11_14_17_19_09372,X0)
      | X0 = sk0_0(i2003_11_14_17_19_09372) ),
    inference(resolution,[status(thm)],[f90,f81]) ).

fof(f132,plain,
    sk0_1(i2003_11_14_17_19_09372) = sk0_0(i2003_11_14_17_19_09372),
    inference(resolution,[status(thm)],[f131,f116]) ).

fof(f167,plain,
    ( ~ pd0_0(i2003_11_14_17_19_09372,sk0_0(i2003_11_14_17_19_09372))
    | spl0_6 ),
    inference(forward_demodulation,[status(thm)],[f132,f128]) ).

fof(f168,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
    | spl0_6 ),
    inference(resolution,[status(thm)],[f167,f70]) ).

fof(f169,plain,
    ( ~ spl0_0
    | spl0_6 ),
    inference(split_clause,[status(thm)],[f168,f97,f126]) ).

fof(f175,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
    | ~ spl0_3 ),
    inference(resolution,[status(thm)],[f107,f71]) ).

fof(f176,plain,
    ( ~ spl0_0
    | ~ spl0_3 ),
    inference(split_clause,[status(thm)],[f175,f97,f106]) ).

fof(f177,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f124,f130,f169,f176]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09  % Problem  : KRS077+1 : TPTP v8.1.2. Released v3.1.0.
% 0.00/0.10  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.08/0.30  % Computer : n012.cluster.edu
% 0.08/0.30  % Model    : x86_64 x86_64
% 0.08/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.30  % Memory   : 8042.1875MB
% 0.08/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.08/0.30  % CPULimit : 300
% 0.08/0.30  % WCLimit  : 300
% 0.08/0.30  % DateTime : Mon Apr 29 23:17:41 EDT 2024
% 0.08/0.30  % CPUTime  : 
% 0.14/0.30  % Drodi V3.6.0
% 0.14/0.31  % Refutation found
% 0.14/0.31  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.14/0.31  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.31  % Elapsed time: 0.010867 seconds
% 0.14/0.31  % CPU time: 0.019197 seconds
% 0.14/0.31  % Total memory used: 716.064 KB
% 0.14/0.31  % Net memory used: 692.064 KB
%------------------------------------------------------------------------------