TSTP Solution File: KRS111+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : KRS111+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n007.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 20:24:48 EDT 2024

% Result   : Unsatisfiable 0.19s 0.36s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   60 (  13 unt;   0 def)
%            Number of atoms       :  174 (  14 equ)
%            Maximal formula atoms :   14 (   2 avg)
%            Number of connectives :  195 (  81   ~;  72   |;  33   &)
%                                         (   5 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-1 aty)
%            Number of variables   :  120 ( 105   !;  15   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f24,axiom,
    ! [X] :
      ( cUnsatisfiable(X)
    <=> ( ? [Y] :
            ( rf1(X,Y)
            & cpxcomp(Y) )
        & ? [Y] :
            ( rs(X,Y)
            & cowlThing(Y) )
        & ? [Y] :
            ( rf(X,Y)
            & cp(Y) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f25,axiom,
    ! [X] :
      ( cp(X)
    <=> ~ ? [Y] : ra_Px1(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f26,axiom,
    ! [X] :
      ( cpxcomp(X)
    <=> ? [Y0] : ra_Px1(X,Y0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f27,axiom,
    ! [X,Y,Z] :
      ( ( rf(X,Y)
        & rf(X,Z) )
     => Y = Z ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f28,axiom,
    ! [X,Y,Z] :
      ( ( rf1(X,Y)
        & rf1(X,Z) )
     => Y = Z ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f31,axiom,
    ! [X,Y] :
      ( rinvS(X,Y)
    <=> rs(Y,X) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f33,axiom,
    cUnsatisfiable(i2003_11_14_17_21_15425),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f34,axiom,
    ! [X,Y] :
      ( rs(X,Y)
     => rf(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f35,axiom,
    ! [X,Y] :
      ( rs(X,Y)
     => rf1(X,Y) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).

fof(f106,plain,
    ! [X] :
      ( ( ~ cUnsatisfiable(X)
        | ( ? [Y] :
              ( rf1(X,Y)
              & cpxcomp(Y) )
          & ? [Y] :
              ( rs(X,Y)
              & cowlThing(Y) )
          & ? [Y] :
              ( rf(X,Y)
              & cp(Y) ) ) )
      & ( cUnsatisfiable(X)
        | ! [Y] :
            ( ~ rf1(X,Y)
            | ~ cpxcomp(Y) )
        | ! [Y] :
            ( ~ rs(X,Y)
            | ~ cowlThing(Y) )
        | ! [Y] :
            ( ~ rf(X,Y)
            | ~ cp(Y) ) ) ),
    inference(NNF_transformation,[status(esa)],[f24]) ).

fof(f107,plain,
    ( ! [X] :
        ( ~ cUnsatisfiable(X)
        | ( ? [Y] :
              ( rf1(X,Y)
              & cpxcomp(Y) )
          & ? [Y] :
              ( rs(X,Y)
              & cowlThing(Y) )
          & ? [Y] :
              ( rf(X,Y)
              & cp(Y) ) ) )
    & ! [X] :
        ( cUnsatisfiable(X)
        | ! [Y] :
            ( ~ rf1(X,Y)
            | ~ cpxcomp(Y) )
        | ! [Y] :
            ( ~ rs(X,Y)
            | ~ cowlThing(Y) )
        | ! [Y] :
            ( ~ rf(X,Y)
            | ~ cp(Y) ) ) ),
    inference(miniscoping,[status(esa)],[f106]) ).

fof(f108,plain,
    ( ! [X] :
        ( ~ cUnsatisfiable(X)
        | ( rf1(X,sk0_0(X))
          & cpxcomp(sk0_0(X))
          & rs(X,sk0_1(X))
          & cowlThing(sk0_1(X))
          & rf(X,sk0_2(X))
          & cp(sk0_2(X)) ) )
    & ! [X] :
        ( cUnsatisfiable(X)
        | ! [Y] :
            ( ~ rf1(X,Y)
            | ~ cpxcomp(Y) )
        | ! [Y] :
            ( ~ rs(X,Y)
            | ~ cowlThing(Y) )
        | ! [Y] :
            ( ~ rf(X,Y)
            | ~ cp(Y) ) ) ),
    inference(skolemization,[status(esa)],[f107]) ).

fof(f109,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | rf1(X0,sk0_0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f108]) ).

fof(f110,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | cpxcomp(sk0_0(X0)) ),
    inference(cnf_transformation,[status(esa)],[f108]) ).

fof(f111,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | rs(X0,sk0_1(X0)) ),
    inference(cnf_transformation,[status(esa)],[f108]) ).

fof(f113,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | rf(X0,sk0_2(X0)) ),
    inference(cnf_transformation,[status(esa)],[f108]) ).

fof(f114,plain,
    ! [X0] :
      ( ~ cUnsatisfiable(X0)
      | cp(sk0_2(X0)) ),
    inference(cnf_transformation,[status(esa)],[f108]) ).

fof(f116,plain,
    ! [X] :
      ( cp(X)
    <=> ! [Y] : ~ ra_Px1(X,Y) ),
    inference(pre_NNF_transformation,[status(esa)],[f25]) ).

fof(f117,plain,
    ! [X] :
      ( ( ~ cp(X)
        | ! [Y] : ~ ra_Px1(X,Y) )
      & ( cp(X)
        | ? [Y] : ra_Px1(X,Y) ) ),
    inference(NNF_transformation,[status(esa)],[f116]) ).

fof(f118,plain,
    ( ! [X] :
        ( ~ cp(X)
        | ! [Y] : ~ ra_Px1(X,Y) )
    & ! [X] :
        ( cp(X)
        | ? [Y] : ra_Px1(X,Y) ) ),
    inference(miniscoping,[status(esa)],[f117]) ).

fof(f119,plain,
    ( ! [X] :
        ( ~ cp(X)
        | ! [Y] : ~ ra_Px1(X,Y) )
    & ! [X] :
        ( cp(X)
        | ra_Px1(X,sk0_3(X)) ) ),
    inference(skolemization,[status(esa)],[f118]) ).

fof(f120,plain,
    ! [X0,X1] :
      ( ~ cp(X0)
      | ~ ra_Px1(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f119]) ).

fof(f122,plain,
    ! [X] :
      ( ( ~ cpxcomp(X)
        | ? [Y0] : ra_Px1(X,Y0) )
      & ( cpxcomp(X)
        | ! [Y0] : ~ ra_Px1(X,Y0) ) ),
    inference(NNF_transformation,[status(esa)],[f26]) ).

fof(f123,plain,
    ( ! [X] :
        ( ~ cpxcomp(X)
        | ? [Y0] : ra_Px1(X,Y0) )
    & ! [X] :
        ( cpxcomp(X)
        | ! [Y0] : ~ ra_Px1(X,Y0) ) ),
    inference(miniscoping,[status(esa)],[f122]) ).

fof(f124,plain,
    ( ! [X] :
        ( ~ cpxcomp(X)
        | ra_Px1(X,sk0_4(X)) )
    & ! [X] :
        ( cpxcomp(X)
        | ! [Y0] : ~ ra_Px1(X,Y0) ) ),
    inference(skolemization,[status(esa)],[f123]) ).

fof(f125,plain,
    ! [X0] :
      ( ~ cpxcomp(X0)
      | ra_Px1(X0,sk0_4(X0)) ),
    inference(cnf_transformation,[status(esa)],[f124]) ).

fof(f127,plain,
    ! [X,Y,Z] :
      ( ~ rf(X,Y)
      | ~ rf(X,Z)
      | Y = Z ),
    inference(pre_NNF_transformation,[status(esa)],[f27]) ).

fof(f128,plain,
    ! [Y,Z] :
      ( ! [X] :
          ( ~ rf(X,Y)
          | ~ rf(X,Z) )
      | Y = Z ),
    inference(miniscoping,[status(esa)],[f127]) ).

fof(f129,plain,
    ! [X0,X1,X2] :
      ( ~ rf(X0,X1)
      | ~ rf(X0,X2)
      | X1 = X2 ),
    inference(cnf_transformation,[status(esa)],[f128]) ).

fof(f130,plain,
    ! [X,Y,Z] :
      ( ~ rf1(X,Y)
      | ~ rf1(X,Z)
      | Y = Z ),
    inference(pre_NNF_transformation,[status(esa)],[f28]) ).

fof(f131,plain,
    ! [Y,Z] :
      ( ! [X] :
          ( ~ rf1(X,Y)
          | ~ rf1(X,Z) )
      | Y = Z ),
    inference(miniscoping,[status(esa)],[f130]) ).

fof(f132,plain,
    ! [X0,X1,X2] :
      ( ~ rf1(X0,X1)
      | ~ rf1(X0,X2)
      | X1 = X2 ),
    inference(cnf_transformation,[status(esa)],[f131]) ).

fof(f141,plain,
    ! [X,Y] :
      ( ( ~ rinvS(X,Y)
        | rs(Y,X) )
      & ( rinvS(X,Y)
        | ~ rs(Y,X) ) ),
    inference(NNF_transformation,[status(esa)],[f31]) ).

fof(f142,plain,
    ( ! [X,Y] :
        ( ~ rinvS(X,Y)
        | rs(Y,X) )
    & ! [X,Y] :
        ( rinvS(X,Y)
        | ~ rs(Y,X) ) ),
    inference(miniscoping,[status(esa)],[f141]) ).

fof(f143,plain,
    ! [X0,X1] :
      ( ~ rinvS(X0,X1)
      | rs(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f142]) ).

fof(f144,plain,
    ! [X0,X1] :
      ( rinvS(X0,X1)
      | ~ rs(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f142]) ).

fof(f148,plain,
    cUnsatisfiable(i2003_11_14_17_21_15425),
    inference(cnf_transformation,[status(esa)],[f33]) ).

fof(f149,plain,
    ! [X,Y] :
      ( ~ rs(X,Y)
      | rf(X,Y) ),
    inference(pre_NNF_transformation,[status(esa)],[f34]) ).

fof(f150,plain,
    ! [X0,X1] :
      ( ~ rs(X0,X1)
      | rf(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f149]) ).

fof(f151,plain,
    ! [X,Y] :
      ( ~ rs(X,Y)
      | rf1(X,Y) ),
    inference(pre_NNF_transformation,[status(esa)],[f35]) ).

fof(f152,plain,
    ! [X0,X1] :
      ( ~ rs(X0,X1)
      | rf1(X0,X1) ),
    inference(cnf_transformation,[status(esa)],[f151]) ).

fof(f154,plain,
    ! [X0,X1] :
      ( ~ cUnsatisfiable(X0)
      | ~ ra_Px1(sk0_2(X0),X1) ),
    inference(resolution,[status(thm)],[f114,f120]) ).

fof(f155,plain,
    ! [X0] :
      ( rinvS(sk0_1(X0),X0)
      | ~ cUnsatisfiable(X0) ),
    inference(resolution,[status(thm)],[f144,f111]) ).

fof(f157,plain,
    ! [X0,X1] :
      ( rf(X0,X1)
      | ~ rinvS(X1,X0) ),
    inference(resolution,[status(thm)],[f150,f143]) ).

fof(f159,plain,
    ! [X0,X1] :
      ( rf1(X0,X1)
      | ~ rinvS(X1,X0) ),
    inference(resolution,[status(thm)],[f152,f143]) ).

fof(f161,plain,
    ! [X0] : ~ ra_Px1(sk0_2(i2003_11_14_17_21_15425),X0),
    inference(resolution,[status(thm)],[f154,f148]) ).

fof(f162,plain,
    ~ cpxcomp(sk0_2(i2003_11_14_17_21_15425)),
    inference(resolution,[status(thm)],[f161,f125]) ).

fof(f166,plain,
    rinvS(sk0_1(i2003_11_14_17_21_15425),i2003_11_14_17_21_15425),
    inference(resolution,[status(thm)],[f155,f148]) ).

fof(f168,plain,
    ! [X0,X1] :
      ( ~ rf(X0,X1)
      | X1 = sk0_2(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(resolution,[status(thm)],[f129,f113]) ).

fof(f169,plain,
    ! [X0,X1] :
      ( ~ rf1(X0,X1)
      | X1 = sk0_0(X0)
      | ~ cUnsatisfiable(X0) ),
    inference(resolution,[status(thm)],[f132,f109]) ).

fof(f172,plain,
    rf1(i2003_11_14_17_21_15425,sk0_1(i2003_11_14_17_21_15425)),
    inference(resolution,[status(thm)],[f166,f159]) ).

fof(f173,plain,
    rf(i2003_11_14_17_21_15425,sk0_1(i2003_11_14_17_21_15425)),
    inference(resolution,[status(thm)],[f166,f157]) ).

fof(f214,plain,
    ! [X0] :
      ( ~ rf(i2003_11_14_17_21_15425,X0)
      | X0 = sk0_2(i2003_11_14_17_21_15425) ),
    inference(resolution,[status(thm)],[f168,f148]) ).

fof(f215,plain,
    sk0_1(i2003_11_14_17_21_15425) = sk0_2(i2003_11_14_17_21_15425),
    inference(resolution,[status(thm)],[f214,f173]) ).

fof(f223,plain,
    ~ cpxcomp(sk0_1(i2003_11_14_17_21_15425)),
    inference(backward_demodulation,[status(thm)],[f215,f162]) ).

fof(f244,plain,
    ! [X0] :
      ( ~ rf1(i2003_11_14_17_21_15425,X0)
      | X0 = sk0_0(i2003_11_14_17_21_15425) ),
    inference(resolution,[status(thm)],[f169,f148]) ).

fof(f246,plain,
    sk0_1(i2003_11_14_17_21_15425) = sk0_0(i2003_11_14_17_21_15425),
    inference(resolution,[status(thm)],[f244,f172]) ).

fof(f253,plain,
    ~ cpxcomp(sk0_0(i2003_11_14_17_21_15425)),
    inference(backward_demodulation,[status(thm)],[f246,f223]) ).

fof(f271,plain,
    ~ cUnsatisfiable(i2003_11_14_17_21_15425),
    inference(resolution,[status(thm)],[f253,f110]) ).

fof(f272,plain,
    $false,
    inference(forward_subsumption_resolution,[status(thm)],[f271,f148]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : KRS111+1 : TPTP v8.1.2. Released v3.1.0.
% 0.03/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.35  % Computer : n007.cluster.edu
% 0.12/0.35  % Model    : x86_64 x86_64
% 0.12/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.35  % Memory   : 8042.1875MB
% 0.12/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.35  % CPULimit : 300
% 0.12/0.35  % WCLimit  : 300
% 0.12/0.35  % DateTime : Mon Apr 29 23:17:02 EDT 2024
% 0.12/0.35  % CPUTime  : 
% 0.19/0.36  % Drodi V3.6.0
% 0.19/0.36  % Refutation found
% 0.19/0.36  % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.19/0.36  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.37  % Elapsed time: 0.013388 seconds
% 0.19/0.37  % CPU time: 0.025827 seconds
% 0.19/0.37  % Total memory used: 976.832 KB
% 0.19/0.37  % Net memory used: 858.080 KB
%------------------------------------------------------------------------------