TSTP Solution File: KRS128+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : KRS128+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n009.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 20:24:50 EDT 2024

% Result   : Unsatisfiable 0.11s 0.34s
% Output   : CNFRefutation 0.11s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   53 (   7 unt;   0 def)
%            Number of atoms       :  172 (   0 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  193 (  74   ~;  71   |;  35   &)
%                                         (  11 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   13 (  12 usr;   6 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-1 aty)
%            Number of variables   :   68 (  54   !;  14   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f3,axiom,
    ! [X] :
      ( cUnsatisfiable(X)
    <=> ( ? [Y] :
            ( rr(X,Y)
            & cexcomp(Y) )
        & ! [Y] :
            ( rr(X,Y)
           => cd(Y) )
        & ! [Y] :
            ( rr(X,Y)
           => ca_Cx4(Y) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X] :
      ( ca_Cx4(X)
    <=> ? [Y0] : ra_Px4(X,Y0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X] :
      ( ca_Cx4xcomp(X)
    <=> ~ ? [Y] : ra_Px4(X,Y) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X] :
      ( ca_Cx4xcomp(X)
    <=> ( cd(X)
        & cexcomp(X) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    cUnsatisfiable(i2003_11_14_17_22_31584),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f20,plain,
    ! [X] :
      ( cUnsatisfiable(X)
    <=> ( ? [Y] :
            ( rr(X,Y)
            & cexcomp(Y) )
        & ! [Y] :
            ( ~ rr(X,Y)
            | cd(Y) )
        & ! [Y] :
            ( ~ rr(X,Y)
            | ca_Cx4(Y) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

fof(f21,plain,
    ! [X] :
      ( ( ~ cUnsatisfiable(X)
        | ( ? [Y] :
              ( rr(X,Y)
              & cexcomp(Y) )
          & ! [Y] :
              ( ~ rr(X,Y)
              | cd(Y) )
          & ! [Y] :
              ( ~ rr(X,Y)
              | ca_Cx4(Y) ) ) )
      & ( cUnsatisfiable(X)
        | ! [Y] :
            ( ~ rr(X,Y)
            | ~ cexcomp(Y) )
        | ? [Y] :
            ( rr(X,Y)
            & ~ cd(Y) )
        | ? [Y] :
            ( rr(X,Y)
            & ~ ca_Cx4(Y) ) ) ),
    inference(NNF_transformation,[status(esa)],[f20]) ).

fof(f22,plain,
    ( ! [X] :
        ( ~ cUnsatisfiable(X)
        | ( ? [Y] :
              ( rr(X,Y)
              & cexcomp(Y) )
          & ! [Y] :
              ( ~ rr(X,Y)
              | cd(Y) )
          & ! [Y] :
              ( ~ rr(X,Y)
              | ca_Cx4(Y) ) ) )
    & ! [X] :
        ( cUnsatisfiable(X)
        | ! [Y] :
            ( ~ rr(X,Y)
            | ~ cexcomp(Y) )
        | ? [Y] :
            ( rr(X,Y)
            & ~ cd(Y) )
        | ? [Y] :
            ( rr(X,Y)
            & ~ ca_Cx4(Y) ) ) ),
    inference(miniscoping,[status(esa)],[f21]) ).

fof(f23,plain,
    ( ! [X] :
        ( ~ cUnsatisfiable(X)
        | ( rr(X,sk0_0(X))
          & cexcomp(sk0_0(X))
          & ! [Y] :
              ( ~ rr(X,Y)
              | cd(Y) )
          & ! [Y] :
              ( ~ rr(X,Y)
              | ca_Cx4(Y) ) ) )
    & ! [X] :
        ( cUnsatisfiable(X)
        | ! [Y] :
            ( ~ rr(X,Y)
            | ~ cexcomp(Y) )
        | ( rr(X,sk0_1(X))
          & ~ cd(sk0_1(X)) )
        | ( rr(X,sk0_2(X))
          & ~ ca_Cx4(sk0_2(X)) ) ) ),
    inference(skolemization,[status(esa)],[f22]) ).

fof(f24,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | rr(X0,sk0_0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f25,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | cexcomp(sk0_0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f26,plain,
    ! [X0,X1] :
      ( ~ cUnsatisfiable(X0)
      | ~ rr(X0,X1)
      | cd(X1) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f27,plain,
    ! [X0,X1] :
      ( ~ cUnsatisfiable(X0)
      | ~ rr(X0,X1)
      | ca_Cx4(X1) ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f56,plain,
    ! [X] :
      ( ( ~ ca_Cx4(X)
        | ? [Y0] : ra_Px4(X,Y0) )
      & ( ca_Cx4(X)
        | ! [Y0] : ~ ra_Px4(X,Y0) ) ),
    inference(NNF_transformation,[status(esa)],[f9]) ).

fof(f57,plain,
    ( ! [X] :
        ( ~ ca_Cx4(X)
        | ? [Y0] : ra_Px4(X,Y0) )
    & ! [X] :
        ( ca_Cx4(X)
        | ! [Y0] : ~ ra_Px4(X,Y0) ) ),
    inference(miniscoping,[status(esa)],[f56]) ).

fof(f58,plain,
    ( ! [X] :
        ( ~ ca_Cx4(X)
        | ra_Px4(X,sk0_7(X)) )
    & ! [X] :
        ( ca_Cx4(X)
        | ! [Y0] : ~ ra_Px4(X,Y0) ) ),
    inference(skolemization,[status(esa)],[f57]) ).

fof(f59,plain,
    ! [X0] :
      ( ~ ca_Cx4(X0)
      | ra_Px4(X0,sk0_7(X0)) ),
    inference(cnf_transformation,[status(esa)],[f58]) ).

fof(f61,plain,
    ! [X] :
      ( ca_Cx4xcomp(X)
    <=> ! [Y] : ~ ra_Px4(X,Y) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f62,plain,
    ! [X] :
      ( ( ~ ca_Cx4xcomp(X)
        | ! [Y] : ~ ra_Px4(X,Y) )
      & ( ca_Cx4xcomp(X)
        | ? [Y] : ra_Px4(X,Y) ) ),
    inference(NNF_transformation,[status(esa)],[f61]) ).

fof(f63,plain,
    ( ! [X] :
        ( ~ ca_Cx4xcomp(X)
        | ! [Y] : ~ ra_Px4(X,Y) )
    & ! [X] :
        ( ca_Cx4xcomp(X)
        | ? [Y] : ra_Px4(X,Y) ) ),
    inference(miniscoping,[status(esa)],[f62]) ).

fof(f64,plain,
    ( ! [X] :
        ( ~ ca_Cx4xcomp(X)
        | ! [Y] : ~ ra_Px4(X,Y) )
    & ! [X] :
        ( ca_Cx4xcomp(X)
        | ra_Px4(X,sk0_8(X)) ) ),
    inference(skolemization,[status(esa)],[f63]) ).

fof(f65,plain,
    ! [X0,X1] :
      ( ~ ca_Cx4xcomp(X0)
      | ~ ra_Px4(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f64]) ).

fof(f67,plain,
    ! [X] :
      ( ( ~ ca_Cx4xcomp(X)
        | ( cd(X)
          & cexcomp(X) ) )
      & ( ca_Cx4xcomp(X)
        | ~ cd(X)
        | ~ cexcomp(X) ) ),
    inference(NNF_transformation,[status(esa)],[f11]) ).

fof(f68,plain,
    ( ! [X] :
        ( ~ ca_Cx4xcomp(X)
        | ( cd(X)
          & cexcomp(X) ) )
    & ! [X] :
        ( ca_Cx4xcomp(X)
        | ~ cd(X)
        | ~ cexcomp(X) ) ),
    inference(miniscoping,[status(esa)],[f67]) ).

fof(f71,plain,
    ! [X0] :
      ( ca_Cx4xcomp(X0)
      | ~ cd(X0)
      | ~ cexcomp(X0) ),
    inference(cnf_transformation,[status(esa)],[f68]) ).

fof(f72,plain,
    cUnsatisfiable(i2003_11_14_17_22_31584),
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f73,plain,
    rr(i2003_11_14_17_22_31584,sk0_0(i2003_11_14_17_22_31584)),
    inference(resolution,[status(thm)],[f24,f72]) ).

fof(f79,plain,
    cexcomp(sk0_0(i2003_11_14_17_22_31584)),
    inference(resolution,[status(thm)],[f25,f72]) ).

fof(f80,plain,
    ( spl0_0
  <=> cUnsatisfiable(i2003_11_14_17_22_31584) ),
    introduced(split_symbol_definition) ).

fof(f82,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f80]) ).

fof(f83,plain,
    ( spl0_1
  <=> cexcomp(sk0_0(i2003_11_14_17_22_31584)) ),
    introduced(split_symbol_definition) ).

fof(f85,plain,
    ( ~ cexcomp(sk0_0(i2003_11_14_17_22_31584))
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f83]) ).

fof(f104,plain,
    ( $false
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f85,f79]) ).

fof(f105,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f104]) ).

fof(f113,plain,
    ( spl0_6
  <=> cd(sk0_0(i2003_11_14_17_22_31584)) ),
    introduced(split_symbol_definition) ).

fof(f114,plain,
    ( cd(sk0_0(i2003_11_14_17_22_31584))
    | ~ spl0_6 ),
    inference(component_clause,[status(thm)],[f113]) ).

fof(f116,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
    | cd(sk0_0(i2003_11_14_17_22_31584)) ),
    inference(resolution,[status(thm)],[f26,f73]) ).

fof(f117,plain,
    ( ~ spl0_0
    | spl0_6 ),
    inference(split_clause,[status(thm)],[f116,f80,f113]) ).

fof(f118,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f82,f72]) ).

fof(f119,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f118]) ).

fof(f120,plain,
    ( spl0_7
  <=> ca_Cx4(sk0_0(i2003_11_14_17_22_31584)) ),
    introduced(split_symbol_definition) ).

fof(f121,plain,
    ( ca_Cx4(sk0_0(i2003_11_14_17_22_31584))
    | ~ spl0_7 ),
    inference(component_clause,[status(thm)],[f120]) ).

fof(f123,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_22_31584)
    | ca_Cx4(sk0_0(i2003_11_14_17_22_31584)) ),
    inference(resolution,[status(thm)],[f27,f73]) ).

fof(f124,plain,
    ( ~ spl0_0
    | spl0_7 ),
    inference(split_clause,[status(thm)],[f123,f80,f120]) ).

fof(f130,plain,
    ( spl0_8
  <=> ca_Cx4xcomp(sk0_0(i2003_11_14_17_22_31584)) ),
    introduced(split_symbol_definition) ).

fof(f131,plain,
    ( ca_Cx4xcomp(sk0_0(i2003_11_14_17_22_31584))
    | ~ spl0_8 ),
    inference(component_clause,[status(thm)],[f130]) ).

fof(f133,plain,
    ( ca_Cx4xcomp(sk0_0(i2003_11_14_17_22_31584))
    | ~ cexcomp(sk0_0(i2003_11_14_17_22_31584))
    | ~ spl0_6 ),
    inference(resolution,[status(thm)],[f114,f71]) ).

fof(f134,plain,
    ( spl0_8
    | ~ spl0_1
    | ~ spl0_6 ),
    inference(split_clause,[status(thm)],[f133,f130,f83,f113]) ).

fof(f136,plain,
    ( ra_Px4(sk0_0(i2003_11_14_17_22_31584),sk0_7(sk0_0(i2003_11_14_17_22_31584)))
    | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f121,f59]) ).

fof(f141,plain,
    ( ~ ca_Cx4xcomp(sk0_0(i2003_11_14_17_22_31584))
    | ~ spl0_7 ),
    inference(resolution,[status(thm)],[f136,f65]) ).

fof(f142,plain,
    ( $false
    | ~ spl0_8
    | ~ spl0_7 ),
    inference(forward_subsumption_resolution,[status(thm)],[f141,f131]) ).

fof(f143,plain,
    ( ~ spl0_8
    | ~ spl0_7 ),
    inference(contradiction_clause,[status(thm)],[f142]) ).

fof(f144,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f105,f117,f119,f124,f134,f143]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : KRS128+1 : TPTP v8.1.2. Released v3.1.0.
% 0.03/0.12  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.33  % Computer : n009.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit : 300
% 0.11/0.33  % WCLimit  : 300
% 0.11/0.33  % DateTime : Mon Apr 29 23:20:11 EDT 2024
% 0.11/0.33  % CPUTime  : 
% 0.11/0.34  % Drodi V3.6.0
% 0.11/0.34  % Refutation found
% 0.11/0.34  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.34  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.36  % Elapsed time: 0.009616 seconds
% 0.11/0.36  % CPU time: 0.018406 seconds
% 0.11/0.36  % Total memory used: 692.608 KB
% 0.11/0.36  % Net memory used: 672.352 KB
%------------------------------------------------------------------------------