TSTP Solution File: SWB023+2 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : SWB023+2 : TPTP v8.1.2. Released v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n001.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 12:38:38 EDT 2023

% Result   : Theorem 0.09s 0.30s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   56 (  15 unt;   0 def)
%            Number of atoms       :  203 (  38 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  227 (  80   ~;  81   |;  54   &)
%                                         (  10 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   6 usr;   3 prp; 0-3 aty)
%            Number of functors    :   17 (  17 usr;  13 con; 0-3 aty)
%            Number of variables   :   97 (;  85   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f1,axiom,
    ! [X,C] :
      ( iext(uri_rdf_type,X,C)
    <=> icext(C,X) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f2,axiom,
    ! [Z,S1,A1] :
      ( ( iext(uri_rdf_first,S1,A1)
        & iext(uri_rdf_rest,S1,uri_rdf_nil) )
     => ( iext(uri_owl_oneOf,Z,S1)
      <=> ( ic(Z)
          & ! [X] :
              ( icext(Z,X)
            <=> X = A1 ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [P] :
      ( icext(uri_owl_FunctionalProperty,P)
    <=> ( ip(P)
        & ! [X,Y1,Y2] :
            ( ( iext(P,X,Y1)
              & iext(P,X,Y2) )
           => Y1 = Y2 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [X,Y] :
      ( iext(uri_owl_sameAs,X,Y)
    <=> X = Y ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,conjecture,
    ( iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
    & iext(uri_owl_sameAs,uri_ex_w,uri_ex_v) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,negated_conjecture,
    ~ ( iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
      & iext(uri_owl_sameAs,uri_ex_w,uri_ex_v) ),
    inference(negated_conjecture,[status(cth)],[f5]) ).

fof(f7,axiom,
    ? [BNODE_o,BNODE_l] :
      ( iext(uri_rdf_type,uri_rdf_first,uri_owl_FunctionalProperty)
      & iext(uri_rdf_type,uri_ex_w,BNODE_o)
      & iext(uri_rdf_type,BNODE_o,uri_owl_Class)
      & iext(uri_owl_oneOf,BNODE_o,BNODE_l)
      & iext(uri_rdf_first,BNODE_l,uri_ex_u)
      & iext(uri_rdf_first,BNODE_l,uri_ex_v)
      & iext(uri_rdf_rest,BNODE_l,uri_rdf_nil) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,plain,
    ! [X,C] :
      ( ( ~ iext(uri_rdf_type,X,C)
        | icext(C,X) )
      & ( iext(uri_rdf_type,X,C)
        | ~ icext(C,X) ) ),
    inference(NNF_transformation,[status(esa)],[f1]) ).

fof(f9,plain,
    ( ! [X,C] :
        ( ~ iext(uri_rdf_type,X,C)
        | icext(C,X) )
    & ! [X,C] :
        ( iext(uri_rdf_type,X,C)
        | ~ icext(C,X) ) ),
    inference(miniscoping,[status(esa)],[f8]) ).

fof(f10,plain,
    ! [X0,X1] :
      ( ~ iext(uri_rdf_type,X0,X1)
      | icext(X1,X0) ),
    inference(cnf_transformation,[status(esa)],[f9]) ).

fof(f12,plain,
    ! [Z,S1,A1] :
      ( ~ iext(uri_rdf_first,S1,A1)
      | ~ iext(uri_rdf_rest,S1,uri_rdf_nil)
      | ( iext(uri_owl_oneOf,Z,S1)
      <=> ( ic(Z)
          & ! [X] :
              ( icext(Z,X)
            <=> X = A1 ) ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f2]) ).

fof(f13,plain,
    ! [Z,S1,A1] :
      ( ~ iext(uri_rdf_first,S1,A1)
      | ~ iext(uri_rdf_rest,S1,uri_rdf_nil)
      | ( ( ~ iext(uri_owl_oneOf,Z,S1)
          | ( ic(Z)
            & ! [X] :
                ( ( ~ icext(Z,X)
                  | X = A1 )
                & ( icext(Z,X)
                  | X != A1 ) ) ) )
        & ( iext(uri_owl_oneOf,Z,S1)
          | ~ ic(Z)
          | ? [X] :
              ( ( ~ icext(Z,X)
                | X != A1 )
              & ( icext(Z,X)
                | X = A1 ) ) ) ) ),
    inference(NNF_transformation,[status(esa)],[f12]) ).

fof(f14,plain,
    ! [S1,A1] :
      ( ~ iext(uri_rdf_first,S1,A1)
      | ~ iext(uri_rdf_rest,S1,uri_rdf_nil)
      | ( ! [Z] :
            ( ~ iext(uri_owl_oneOf,Z,S1)
            | ( ic(Z)
              & ! [X] :
                  ( ~ icext(Z,X)
                  | X = A1 )
              & ! [X] :
                  ( icext(Z,X)
                  | X != A1 ) ) )
        & ! [Z] :
            ( iext(uri_owl_oneOf,Z,S1)
            | ~ ic(Z)
            | ? [X] :
                ( ( ~ icext(Z,X)
                  | X != A1 )
                & ( icext(Z,X)
                  | X = A1 ) ) ) ) ),
    inference(miniscoping,[status(esa)],[f13]) ).

fof(f15,plain,
    ! [S1,A1] :
      ( ~ iext(uri_rdf_first,S1,A1)
      | ~ iext(uri_rdf_rest,S1,uri_rdf_nil)
      | ( ! [Z] :
            ( ~ iext(uri_owl_oneOf,Z,S1)
            | ( ic(Z)
              & ! [X] :
                  ( ~ icext(Z,X)
                  | X = A1 )
              & ! [X] :
                  ( icext(Z,X)
                  | X != A1 ) ) )
        & ! [Z] :
            ( iext(uri_owl_oneOf,Z,S1)
            | ~ ic(Z)
            | ( ( ~ icext(Z,sk0_0(Z,A1,S1))
                | sk0_0(Z,A1,S1) != A1 )
              & ( icext(Z,sk0_0(Z,A1,S1))
                | sk0_0(Z,A1,S1) = A1 ) ) ) ) ),
    inference(skolemization,[status(esa)],[f14]) ).

fof(f17,plain,
    ! [X0,X1,X2,X3] :
      ( ~ iext(uri_rdf_first,X0,X1)
      | ~ iext(uri_rdf_rest,X0,uri_rdf_nil)
      | ~ iext(uri_owl_oneOf,X2,X0)
      | ~ icext(X2,X3)
      | X3 = X1 ),
    inference(cnf_transformation,[status(esa)],[f15]) ).

fof(f21,plain,
    ! [P] :
      ( icext(uri_owl_FunctionalProperty,P)
    <=> ( ip(P)
        & ! [X,Y1,Y2] :
            ( ~ iext(P,X,Y1)
            | ~ iext(P,X,Y2)
            | Y1 = Y2 ) ) ),
    inference(pre_NNF_transformation,[status(esa)],[f3]) ).

fof(f22,plain,
    ! [P] :
      ( ( ~ icext(uri_owl_FunctionalProperty,P)
        | ( ip(P)
          & ! [X,Y1,Y2] :
              ( ~ iext(P,X,Y1)
              | ~ iext(P,X,Y2)
              | Y1 = Y2 ) ) )
      & ( icext(uri_owl_FunctionalProperty,P)
        | ~ ip(P)
        | ? [X,Y1,Y2] :
            ( iext(P,X,Y1)
            & iext(P,X,Y2)
            & Y1 != Y2 ) ) ),
    inference(NNF_transformation,[status(esa)],[f21]) ).

fof(f23,plain,
    ( ! [P] :
        ( ~ icext(uri_owl_FunctionalProperty,P)
        | ( ip(P)
          & ! [Y1,Y2] :
              ( ! [X] :
                  ( ~ iext(P,X,Y1)
                  | ~ iext(P,X,Y2) )
              | Y1 = Y2 ) ) )
    & ! [P] :
        ( icext(uri_owl_FunctionalProperty,P)
        | ~ ip(P)
        | ? [Y1,Y2] :
            ( ? [X] :
                ( iext(P,X,Y1)
                & iext(P,X,Y2) )
            & Y1 != Y2 ) ) ),
    inference(miniscoping,[status(esa)],[f22]) ).

fof(f24,plain,
    ( ! [P] :
        ( ~ icext(uri_owl_FunctionalProperty,P)
        | ( ip(P)
          & ! [Y1,Y2] :
              ( ! [X] :
                  ( ~ iext(P,X,Y1)
                  | ~ iext(P,X,Y2) )
              | Y1 = Y2 ) ) )
    & ! [P] :
        ( icext(uri_owl_FunctionalProperty,P)
        | ~ ip(P)
        | ( iext(P,sk0_3(P),sk0_1(P))
          & iext(P,sk0_3(P),sk0_2(P))
          & sk0_1(P) != sk0_2(P) ) ) ),
    inference(skolemization,[status(esa)],[f23]) ).

fof(f26,plain,
    ! [X0,X1,X2,X3] :
      ( ~ icext(uri_owl_FunctionalProperty,X0)
      | ~ iext(X0,X1,X2)
      | ~ iext(X0,X1,X3)
      | X2 = X3 ),
    inference(cnf_transformation,[status(esa)],[f24]) ).

fof(f30,plain,
    ! [X,Y] :
      ( ( ~ iext(uri_owl_sameAs,X,Y)
        | X = Y )
      & ( iext(uri_owl_sameAs,X,Y)
        | X != Y ) ),
    inference(NNF_transformation,[status(esa)],[f4]) ).

fof(f31,plain,
    ( ! [X,Y] :
        ( ~ iext(uri_owl_sameAs,X,Y)
        | X = Y )
    & ! [X,Y] :
        ( iext(uri_owl_sameAs,X,Y)
        | X != Y ) ),
    inference(miniscoping,[status(esa)],[f30]) ).

fof(f33,plain,
    ! [X0,X1] :
      ( iext(uri_owl_sameAs,X0,X1)
      | X0 != X1 ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f34,plain,
    ( ~ iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
    | ~ iext(uri_owl_sameAs,uri_ex_w,uri_ex_v) ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f35,plain,
    ( ~ iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
    | ~ iext(uri_owl_sameAs,uri_ex_w,uri_ex_v) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f36,plain,
    ? [BNODE_l] :
      ( ? [BNODE_o] :
          ( iext(uri_rdf_type,uri_rdf_first,uri_owl_FunctionalProperty)
          & iext(uri_rdf_type,uri_ex_w,BNODE_o)
          & iext(uri_rdf_type,BNODE_o,uri_owl_Class)
          & iext(uri_owl_oneOf,BNODE_o,BNODE_l) )
      & iext(uri_rdf_first,BNODE_l,uri_ex_u)
      & iext(uri_rdf_first,BNODE_l,uri_ex_v)
      & iext(uri_rdf_rest,BNODE_l,uri_rdf_nil) ),
    inference(miniscoping,[status(esa)],[f7]) ).

fof(f37,plain,
    ( iext(uri_rdf_type,uri_rdf_first,uri_owl_FunctionalProperty)
    & iext(uri_rdf_type,uri_ex_w,sk0_5)
    & iext(uri_rdf_type,sk0_5,uri_owl_Class)
    & iext(uri_owl_oneOf,sk0_5,sk0_4)
    & iext(uri_rdf_first,sk0_4,uri_ex_u)
    & iext(uri_rdf_first,sk0_4,uri_ex_v)
    & iext(uri_rdf_rest,sk0_4,uri_rdf_nil) ),
    inference(skolemization,[status(esa)],[f36]) ).

fof(f38,plain,
    iext(uri_rdf_type,uri_rdf_first,uri_owl_FunctionalProperty),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f39,plain,
    iext(uri_rdf_type,uri_ex_w,sk0_5),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f41,plain,
    iext(uri_owl_oneOf,sk0_5,sk0_4),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f42,plain,
    iext(uri_rdf_first,sk0_4,uri_ex_u),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f43,plain,
    iext(uri_rdf_first,sk0_4,uri_ex_v),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f44,plain,
    iext(uri_rdf_rest,sk0_4,uri_rdf_nil),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f45,plain,
    ( spl0_0
  <=> iext(uri_owl_sameAs,uri_ex_w,uri_ex_u) ),
    introduced(split_symbol_definition) ).

fof(f47,plain,
    ( ~ iext(uri_owl_sameAs,uri_ex_w,uri_ex_u)
    | spl0_0 ),
    inference(component_clause,[status(thm)],[f45]) ).

fof(f48,plain,
    ( spl0_1
  <=> iext(uri_owl_sameAs,uri_ex_w,uri_ex_v) ),
    introduced(split_symbol_definition) ).

fof(f50,plain,
    ( ~ iext(uri_owl_sameAs,uri_ex_w,uri_ex_v)
    | spl0_1 ),
    inference(component_clause,[status(thm)],[f48]) ).

fof(f51,plain,
    ( ~ spl0_0
    | ~ spl0_1 ),
    inference(split_clause,[status(thm)],[f35,f45,f48]) ).

fof(f53,plain,
    ! [X0] : iext(uri_owl_sameAs,X0,X0),
    inference(destructive_equality_resolution,[status(esa)],[f33]) ).

fof(f54,plain,
    icext(sk0_5,uri_ex_w),
    inference(resolution,[status(thm)],[f10,f39]) ).

fof(f55,plain,
    icext(uri_owl_FunctionalProperty,uri_rdf_first),
    inference(resolution,[status(thm)],[f38,f10]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( ~ iext(uri_rdf_first,sk0_4,X0)
      | ~ iext(uri_owl_oneOf,X1,sk0_4)
      | ~ icext(X1,X2)
      | X2 = X0 ),
    inference(resolution,[status(thm)],[f17,f44]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( ~ iext(uri_rdf_first,X0,X1)
      | ~ iext(uri_rdf_first,X0,X2)
      | X1 = X2 ),
    inference(resolution,[status(thm)],[f26,f55]) ).

fof(f68,plain,
    ! [X0] :
      ( ~ iext(uri_rdf_first,sk0_4,X0)
      | X0 = uri_ex_v ),
    inference(resolution,[status(thm)],[f67,f43]) ).

fof(f70,plain,
    uri_ex_u = uri_ex_v,
    inference(resolution,[status(thm)],[f68,f42]) ).

fof(f86,plain,
    ! [X0,X1] :
      ( ~ iext(uri_rdf_first,sk0_4,X0)
      | ~ icext(sk0_5,X1)
      | X1 = X0 ),
    inference(resolution,[status(thm)],[f66,f41]) ).

fof(f87,plain,
    ! [X0] :
      ( ~ iext(uri_rdf_first,sk0_4,X0)
      | uri_ex_w = X0 ),
    inference(resolution,[status(thm)],[f86,f54]) ).

fof(f88,plain,
    uri_ex_w = uri_ex_u,
    inference(resolution,[status(thm)],[f87,f42]) ).

fof(f90,plain,
    uri_ex_w = uri_ex_v,
    inference(backward_demodulation,[status(thm)],[f88,f70]) ).

fof(f94,plain,
    ( ~ iext(uri_owl_sameAs,uri_ex_w,uri_ex_w)
    | spl0_0 ),
    inference(forward_demodulation,[status(thm)],[f88,f47]) ).

fof(f95,plain,
    ( $false
    | spl0_0 ),
    inference(forward_subsumption_resolution,[status(thm)],[f94,f53]) ).

fof(f96,plain,
    spl0_0,
    inference(contradiction_clause,[status(thm)],[f95]) ).

fof(f97,plain,
    ( ~ iext(uri_owl_sameAs,uri_ex_w,uri_ex_w)
    | spl0_1 ),
    inference(forward_demodulation,[status(thm)],[f90,f50]) ).

fof(f98,plain,
    ( $false
    | spl0_1 ),
    inference(forward_subsumption_resolution,[status(thm)],[f97,f53]) ).

fof(f99,plain,
    spl0_1,
    inference(contradiction_clause,[status(thm)],[f98]) ).

fof(f100,plain,
    $false,
    inference(sat_refutation,[status(thm)],[f51,f96,f99]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08  % Problem  : SWB023+2 : TPTP v8.1.2. Released v5.2.0.
% 0.04/0.09  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.28  % Computer : n001.cluster.edu
% 0.09/0.28  % Model    : x86_64 x86_64
% 0.09/0.28  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28  % Memory   : 8042.1875MB
% 0.09/0.28  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28  % CPULimit : 300
% 0.09/0.28  % WCLimit  : 300
% 0.09/0.28  % DateTime : Tue May 30 11:11:30 EDT 2023
% 0.09/0.29  % CPUTime  : 
% 0.09/0.29  % Drodi V3.5.1
% 0.09/0.30  % Refutation found
% 0.09/0.30  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.30  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.51  % Elapsed time: 0.012155 seconds
% 0.13/0.51  % CPU time: 0.011532 seconds
% 0.13/0.51  % Memory used: 2.911 MB
%------------------------------------------------------------------------------