TSTP Solution File: KRS179+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : KRS179+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n017.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  : 600s
% DateTime : Sun Jul 17 03:19:05 EDT 2022

% Result   : Theorem 0.21s 0.41s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   35 (   8 unt;   0 def)
%            Number of atoms       :   83 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   75 (  27   ~;  30   |;  11   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :   61 (   0 sgn  29   !;   7   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(isa,axiom,
    ! [S1,S2] :
      ( ! [Ax,C] :
          ( status(Ax,C,S1)
         => status(Ax,C,S2) )
    <=> isa(S1,S2) ) ).

fof(isa_transitive,conjecture,
    ! [S1,S2,S3] :
      ( ( isa(S1,S2)
        & isa(S2,S3) )
     => isa(S1,S3) ) ).

fof(subgoal_0,plain,
    ! [S1,S2,S3] :
      ( ( isa(S1,S2)
        & isa(S2,S3) )
     => isa(S1,S3) ),
    inference(strip,[],[isa_transitive]) ).

fof(negate_0_0,plain,
    ~ ! [S1,S2,S3] :
        ( ( isa(S1,S2)
          & isa(S2,S3) )
       => isa(S1,S3) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [S1,S2] :
      ( ~ isa(S1,S2)
    <=> ? [Ax,C] :
          ( ~ status(Ax,C,S2)
          & status(Ax,C,S1) ) ),
    inference(canonicalize,[],[isa]) ).

fof(normalize_0_1,plain,
    ! [S1,S2] :
      ( ~ isa(S1,S2)
    <=> ? [Ax,C] :
          ( ~ status(Ax,C,S2)
          & status(Ax,C,S1) ) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [Ax,C,S1,S2] :
      ( ( ~ status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S2)
        | isa(S1,S2) )
      & ( isa(S1,S2)
        | status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S1) )
      & ( ~ isa(S1,S2)
        | ~ status(Ax,C,S1)
        | status(Ax,C,S2) ) ),
    inference(clausify,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [S1,S2] :
      ( ~ status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S2)
      | isa(S1,S2) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ? [S1,S2,S3] :
      ( ~ isa(S1,S3)
      & isa(S1,S2)
      & isa(S2,S3) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_5,plain,
    ( ~ isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S3)
    & isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2)
    & isa(skolemFOFtoCNF_S2,skolemFOFtoCNF_S3) ),
    inference(skolemize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    isa(skolemFOFtoCNF_S2,skolemFOFtoCNF_S3),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [Ax,C,S1,S2] :
      ( ~ isa(S1,S2)
      | ~ status(Ax,C,S1)
      | status(Ax,C,S2) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_8,plain,
    isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_9,plain,
    ! [S1,S2] :
      ( isa(S1,S2)
      | status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S1) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_10,plain,
    ~ isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S3),
    inference(conjunct,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    ( ~ status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S2)
    | isa(S1,S2) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( ~ status(skolemFOFtoCNF_Ax_1(skolemFOFtoCNF_S1,skolemFOFtoCNF_S3),skolemFOFtoCNF_C_1(skolemFOFtoCNF_S1,skolemFOFtoCNF_S3),skolemFOFtoCNF_S3)
    | isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S3) ),
    inference(subst,[],[refute_0_0:[bind(S1,$fot(skolemFOFtoCNF_S1)),bind(S2,$fot(skolemFOFtoCNF_S3))]]) ).

cnf(refute_0_2,plain,
    isa(skolemFOFtoCNF_S2,skolemFOFtoCNF_S3),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_3,plain,
    ( ~ isa(S1,S2)
    | ~ status(Ax,C,S1)
    | status(Ax,C,S2) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_4,plain,
    ( ~ isa(skolemFOFtoCNF_S2,S2)
    | ~ status(skolemFOFtoCNF_Ax_1(skolemFOFtoCNF_S1,X_89),skolemFOFtoCNF_C_1(skolemFOFtoCNF_S1,X_89),skolemFOFtoCNF_S2)
    | status(skolemFOFtoCNF_Ax_1(skolemFOFtoCNF_S1,X_89),skolemFOFtoCNF_C_1(skolemFOFtoCNF_S1,X_89),S2) ),
    inference(subst,[],[refute_0_3:[bind(Ax,$fot(skolemFOFtoCNF_Ax_1(skolemFOFtoCNF_S1,X_89))),bind(C,$fot(skolemFOFtoCNF_C_1(skolemFOFtoCNF_S1,X_89))),bind(S1,$fot(skolemFOFtoCNF_S2))]]) ).

cnf(refute_0_5,plain,
    isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_6,plain,
    ( isa(S1,S2)
    | status(skolemFOFtoCNF_Ax_1(S1,S2),skolemFOFtoCNF_C_1(S1,S2),S1) ),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_7,plain,
    ( isa(X_42,S2)
    | status(skolemFOFtoCNF_Ax_1(X_42,S2),skolemFOFtoCNF_C_1(X_42,S2),X_42) ),
    inference(subst,[],[refute_0_6:[bind(S1,$fot(X_42))]]) ).

cnf(refute_0_8,plain,
    ( ~ isa(X_42,X_43)
    | ~ status(skolemFOFtoCNF_Ax_1(X_42,S2),skolemFOFtoCNF_C_1(X_42,S2),X_42)
    | status(skolemFOFtoCNF_Ax_1(X_42,S2),skolemFOFtoCNF_C_1(X_42,S2),X_43) ),
    inference(subst,[],[refute_0_3:[bind(Ax,$fot(skolemFOFtoCNF_Ax_1(X_42,S2))),bind(C,$fot(skolemFOFtoCNF_C_1(X_42,S2))),bind(S1,$fot(X_42)),bind(S2,$fot(X_43))]]) ).

cnf(refute_0_9,plain,
    ( ~ isa(X_42,X_43)
    | isa(X_42,S2)
    | status(skolemFOFtoCNF_Ax_1(X_42,S2),skolemFOFtoCNF_C_1(X_42,S2),X_43) ),
    inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax_1(X_42,S2),skolemFOFtoCNF_C_1(X_42,S2),X_42) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( ~ isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2)
    | isa(skolemFOFtoCNF_S1,X_86)
    | status(skolemFOFtoCNF_Ax_1(skolemFOFtoCNF_S1,X_86),skolemFOFtoCNF_C_1(skolemFOFtoCNF_S1,X_86),skolemFOFtoCNF_S2) ),
    inference(subst,[],[refute_0_9:[bind(S2,$fot(X_86)),bind(X_42,$fot(skolemFOFtoCNF_S1)),bind(X_43,$fot(skolemFOFtoCNF_S2))]]) ).

cnf(refute_0_11,plain,
    ( isa(skolemFOFtoCNF_S1,X_86)
    | status(skolemFOFtoCNF_Ax_1(skolemFOFtoCNF_S1,X_86),skolemFOFtoCNF_C_1(skolemFOFtoCNF_S1,X_86),skolemFOFtoCNF_S2) ),
    inference(resolve,[$cnf( isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S2) )],[refute_0_5,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( isa(skolemFOFtoCNF_S1,X_89)
    | status(skolemFOFtoCNF_Ax_1(skolemFOFtoCNF_S1,X_89),skolemFOFtoCNF_C_1(skolemFOFtoCNF_S1,X_89),skolemFOFtoCNF_S2) ),
    inference(subst,[],[refute_0_11:[bind(X_86,$fot(X_89))]]) ).

cnf(refute_0_13,plain,
    ( ~ isa(skolemFOFtoCNF_S2,S2)
    | isa(skolemFOFtoCNF_S1,X_89)
    | status(skolemFOFtoCNF_Ax_1(skolemFOFtoCNF_S1,X_89),skolemFOFtoCNF_C_1(skolemFOFtoCNF_S1,X_89),S2) ),
    inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax_1(skolemFOFtoCNF_S1,X_89),skolemFOFtoCNF_C_1(skolemFOFtoCNF_S1,X_89),skolemFOFtoCNF_S2) )],[refute_0_12,refute_0_4]) ).

cnf(refute_0_14,plain,
    ( ~ isa(skolemFOFtoCNF_S2,skolemFOFtoCNF_S3)
    | isa(skolemFOFtoCNF_S1,X_135)
    | status(skolemFOFtoCNF_Ax_1(skolemFOFtoCNF_S1,X_135),skolemFOFtoCNF_C_1(skolemFOFtoCNF_S1,X_135),skolemFOFtoCNF_S3) ),
    inference(subst,[],[refute_0_13:[bind(S2,$fot(skolemFOFtoCNF_S3)),bind(X_89,$fot(X_135))]]) ).

cnf(refute_0_15,plain,
    ( isa(skolemFOFtoCNF_S1,X_135)
    | status(skolemFOFtoCNF_Ax_1(skolemFOFtoCNF_S1,X_135),skolemFOFtoCNF_C_1(skolemFOFtoCNF_S1,X_135),skolemFOFtoCNF_S3) ),
    inference(resolve,[$cnf( isa(skolemFOFtoCNF_S2,skolemFOFtoCNF_S3) )],[refute_0_2,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S3)
    | status(skolemFOFtoCNF_Ax_1(skolemFOFtoCNF_S1,skolemFOFtoCNF_S3),skolemFOFtoCNF_C_1(skolemFOFtoCNF_S1,skolemFOFtoCNF_S3),skolemFOFtoCNF_S3) ),
    inference(subst,[],[refute_0_15:[bind(X_135,$fot(skolemFOFtoCNF_S3))]]) ).

cnf(refute_0_17,plain,
    isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S3),
    inference(resolve,[$cnf( status(skolemFOFtoCNF_Ax_1(skolemFOFtoCNF_S1,skolemFOFtoCNF_S3),skolemFOFtoCNF_C_1(skolemFOFtoCNF_S1,skolemFOFtoCNF_S3),skolemFOFtoCNF_S3) )],[refute_0_16,refute_0_1]) ).

cnf(refute_0_18,plain,
    ~ isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S3),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_19,plain,
    $false,
    inference(resolve,[$cnf( isa(skolemFOFtoCNF_S1,skolemFOFtoCNF_S3) )],[refute_0_17,refute_0_18]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KRS179+1 : TPTP v8.1.0. Bugfixed v5.4.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.14/0.34  % Computer : n017.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 600
% 0.14/0.34  % DateTime : Tue Jun  7 05:27:32 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.41  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.41  
% 0.21/0.41  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.21/0.42  
%------------------------------------------------------------------------------