TSTP Solution File: KRS077+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : KRS077+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n026.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 03:18:37 EDT 2022

% Result   : Unsatisfiable 0.12s 0.34s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   18
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   49 (  12 unt;   0 def)
%            Number of atoms       :  178 (  14 equ)
%            Maximal formula atoms :   57 (   3 avg)
%            Number of connectives :  224 (  95   ~;  96   |;  24   &)
%                                         (   6 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   24 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   5 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-1 aty)
%            Number of variables   :   63 (   0 sgn  40   !;   8   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
    ! [X] :
      ( cUnsatisfiable(X)
    <=> ( ! [Y1,Y2] :
            ( ( rr(X,Y1)
              & rr(X,Y2) )
           => Y1 = Y2 )
        & ? [Y] :
            ( rr(X,Y)
            & ! [Z] :
                ( rinvS(Y,Z)
               => cp(Z) ) )
        & ~ cp(X)
        & ? [Y] :
            ( rs(X,Y)
            & cp(Y) ) ) ) ).

fof(axiom_3,axiom,
    ! [X,Y] :
      ( rinvS(X,Y)
    <=> rs(Y,X) ) ).

fof(axiom_4,axiom,
    cUnsatisfiable(i2003_11_14_17_19_09372) ).

fof(axiom_5,axiom,
    ! [X,Y] :
      ( rs(X,Y)
     => rr(X,Y) ) ).

fof(normalize_0_0,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
    <=> ( cp(X)
        | ? [Y1,Y2] :
            ( Y1 != Y2
            & rr(X,Y1)
            & rr(X,Y2) )
        | ! [Y] :
            ( ~ cp(Y)
            | ~ rs(X,Y) )
        | ! [Y] :
            ( ~ rr(X,Y)
            | ? [Z] :
                ( ~ cp(Z)
                & rinvS(Y,Z) ) ) ) ),
    inference(canonicalize,[],[axiom_2]) ).

fof(normalize_0_1,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
    <=> ( cp(X)
        | ? [Y1,Y2] :
            ( Y1 != Y2
            & rr(X,Y1)
            & rr(X,Y2) )
        | ! [Y] :
            ( ~ cp(Y)
            | ~ rs(X,Y) )
        | ! [Y] :
            ( ~ rr(X,Y)
            | ? [Z] :
                ( ~ cp(Z)
                & rinvS(Y,Z) ) ) ) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X,Y,Y0,Y1,Y2,Z] :
      ( ( ~ cUnsatisfiable(X)
        | ~ cp(X) )
      & ( ~ cUnsatisfiable(X)
        | cp(skolemFOFtoCNF_Y_1(X)) )
      & ( ~ cUnsatisfiable(X)
        | rr(X,skolemFOFtoCNF_Y(X)) )
      & ( ~ cUnsatisfiable(X)
        | rs(X,skolemFOFtoCNF_Y_1(X)) )
      & ( ~ cUnsatisfiable(X)
        | ~ rinvS(skolemFOFtoCNF_Y(X),Z)
        | cp(Z) )
      & ( ~ cUnsatisfiable(X)
        | ~ rr(X,Y1)
        | ~ rr(X,Y2)
        | Y1 = Y2 )
      & ( skolemFOFtoCNF_Y0(X) != skolemFOFtoCNF_Y1(X)
        | ~ cp(Y)
        | ~ cp(skolemFOFtoCNF_Z(Y0))
        | ~ rr(X,Y0)
        | ~ rs(X,Y)
        | cUnsatisfiable(X)
        | cp(X) )
      & ( skolemFOFtoCNF_Y0(X) != skolemFOFtoCNF_Y1(X)
        | ~ cp(Y)
        | ~ rr(X,Y0)
        | ~ rs(X,Y)
        | cUnsatisfiable(X)
        | cp(X)
        | rinvS(Y0,skolemFOFtoCNF_Z(Y0)) )
      & ( ~ cp(Y)
        | ~ cp(skolemFOFtoCNF_Z(Y0))
        | ~ rr(X,Y0)
        | ~ rs(X,Y)
        | cUnsatisfiable(X)
        | cp(X)
        | rr(X,skolemFOFtoCNF_Y0(X)) )
      & ( ~ cp(Y)
        | ~ cp(skolemFOFtoCNF_Z(Y0))
        | ~ rr(X,Y0)
        | ~ rs(X,Y)
        | cUnsatisfiable(X)
        | cp(X)
        | rr(X,skolemFOFtoCNF_Y1(X)) )
      & ( ~ cp(Y)
        | ~ rr(X,Y0)
        | ~ rs(X,Y)
        | cUnsatisfiable(X)
        | cp(X)
        | rinvS(Y0,skolemFOFtoCNF_Z(Y0))
        | rr(X,skolemFOFtoCNF_Y0(X)) )
      & ( ~ cp(Y)
        | ~ rr(X,Y0)
        | ~ rs(X,Y)
        | cUnsatisfiable(X)
        | cp(X)
        | rinvS(Y0,skolemFOFtoCNF_Z(Y0))
        | rr(X,skolemFOFtoCNF_Y1(X)) ) ),
    inference(clausify,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
      | ~ cp(X) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X,Z] :
      ( ~ cUnsatisfiable(X)
      | ~ rinvS(skolemFOFtoCNF_Y(X),Z)
      | cp(Z) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_5,plain,
    cUnsatisfiable(i2003_11_14_17_19_09372),
    inference(canonicalize,[],[axiom_4]) ).

fof(normalize_0_6,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
      | rs(X,skolemFOFtoCNF_Y_1(X)) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_7,plain,
    ! [X,Y] :
      ( ~ rinvS(X,Y)
    <=> ~ rs(Y,X) ),
    inference(canonicalize,[],[axiom_3]) ).

fof(normalize_0_8,plain,
    ! [X,Y] :
      ( ~ rinvS(X,Y)
    <=> ~ rs(Y,X) ),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [X,Y] :
      ( ( ~ rinvS(X,Y)
        | rs(Y,X) )
      & ( ~ rs(Y,X)
        | rinvS(X,Y) ) ),
    inference(clausify,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [X,Y] :
      ( ~ rs(Y,X)
      | rinvS(X,Y) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
      | rr(X,skolemFOFtoCNF_Y(X)) ),
    inference(conjunct,[],[normalize_0_2]) ).

fof(normalize_0_12,plain,
    ! [X,Y] :
      ( ~ rs(X,Y)
      | rr(X,Y) ),
    inference(canonicalize,[],[axiom_5]) ).

fof(normalize_0_13,plain,
    ! [X,Y] :
      ( ~ rs(X,Y)
      | rr(X,Y) ),
    inference(specialize,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    ! [X,Y1,Y2] :
      ( ~ cUnsatisfiable(X)
      | ~ rr(X,Y1)
      | ~ rr(X,Y2)
      | Y1 = Y2 ),
    inference(conjunct,[],[normalize_0_2]) ).

cnf(refute_0_0,plain,
    ( ~ cUnsatisfiable(X)
    | ~ cp(X) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_1,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
    | ~ cp(i2003_11_14_17_19_09372) ),
    inference(subst,[],[refute_0_0:[bind(X,$fot(i2003_11_14_17_19_09372))]]) ).

cnf(refute_0_2,plain,
    ( ~ cUnsatisfiable(X)
    | ~ rinvS(skolemFOFtoCNF_Y(X),Z)
    | cp(Z) ),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_3,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
    | ~ rinvS(skolemFOFtoCNF_Y(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
    | cp(i2003_11_14_17_19_09372) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(i2003_11_14_17_19_09372)),bind(Z,$fot(i2003_11_14_17_19_09372))]]) ).

cnf(refute_0_4,plain,
    cUnsatisfiable(i2003_11_14_17_19_09372),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_5,plain,
    ( ~ cUnsatisfiable(X)
    | rs(X,skolemFOFtoCNF_Y_1(X)) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_6,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
    | rs(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372)) ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(i2003_11_14_17_19_09372))]]) ).

cnf(refute_0_7,plain,
    rs(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372)),
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_09372) )],[refute_0_4,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( ~ rs(Y,X)
    | rinvS(X,Y) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_9,plain,
    ( ~ rs(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372))
    | rinvS(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ),
    inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372))),bind(Y,$fot(i2003_11_14_17_19_09372))]]) ).

cnf(refute_0_10,plain,
    rinvS(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372),
    inference(resolve,[$cnf( rs(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372)) )],[refute_0_7,refute_0_9]) ).

cnf(refute_0_11,plain,
    ( ~ cUnsatisfiable(X)
    | rr(X,skolemFOFtoCNF_Y(X)) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_12,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
    | rr(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y(i2003_11_14_17_19_09372)) ),
    inference(subst,[],[refute_0_11:[bind(X,$fot(i2003_11_14_17_19_09372))]]) ).

cnf(refute_0_13,plain,
    rr(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y(i2003_11_14_17_19_09372)),
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_09372) )],[refute_0_4,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( ~ rs(X,Y)
    | rr(X,Y) ),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_15,plain,
    ( ~ rs(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372))
    | rr(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372)) ),
    inference(subst,[],[refute_0_14:[bind(X,$fot(i2003_11_14_17_19_09372)),bind(Y,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372)))]]) ).

cnf(refute_0_16,plain,
    rr(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372)),
    inference(resolve,[$cnf( rs(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372)) )],[refute_0_7,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( ~ cUnsatisfiable(X)
    | ~ rr(X,Y1)
    | ~ rr(X,Y2)
    | Y1 = Y2 ),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_18,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
    | ~ rr(i2003_11_14_17_19_09372,X_18)
    | ~ rr(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372))
    | skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372) = X_18 ),
    inference(subst,[],[refute_0_17:[bind(X,$fot(i2003_11_14_17_19_09372)),bind(Y1,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372))),bind(Y2,$fot(X_18))]]) ).

cnf(refute_0_19,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
    | ~ rr(i2003_11_14_17_19_09372,X_18)
    | skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372) = X_18 ),
    inference(resolve,[$cnf( rr(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372)) )],[refute_0_16,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( ~ rr(i2003_11_14_17_19_09372,X_18)
    | skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372) = X_18 ),
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_09372) )],[refute_0_4,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( ~ rr(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y(i2003_11_14_17_19_09372))
    | skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372) = skolemFOFtoCNF_Y(i2003_11_14_17_19_09372) ),
    inference(subst,[],[refute_0_20:[bind(X_18,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_19_09372)))]]) ).

cnf(refute_0_22,plain,
    skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372) = skolemFOFtoCNF_Y(i2003_11_14_17_19_09372),
    inference(resolve,[$cnf( rr(i2003_11_14_17_19_09372,skolemFOFtoCNF_Y(i2003_11_14_17_19_09372)) )],[refute_0_13,refute_0_21]) ).

cnf(refute_0_23,plain,
    ( skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372) != skolemFOFtoCNF_Y(i2003_11_14_17_19_09372)
    | ~ rinvS(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
    | rinvS(skolemFOFtoCNF_Y(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ),
    introduced(tautology,[equality,[$cnf( rinvS(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ),[0],$fot(skolemFOFtoCNF_Y(i2003_11_14_17_19_09372))]]) ).

cnf(refute_0_24,plain,
    ( ~ rinvS(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372)
    | rinvS(skolemFOFtoCNF_Y(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372),skolemFOFtoCNF_Y(i2003_11_14_17_19_09372)) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    rinvS(skolemFOFtoCNF_Y(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372),
    inference(resolve,[$cnf( rinvS(skolemFOFtoCNF_Y_1(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) )],[refute_0_10,refute_0_24]) ).

cnf(refute_0_26,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_19_09372)
    | cp(i2003_11_14_17_19_09372) ),
    inference(resolve,[$cnf( rinvS(skolemFOFtoCNF_Y(i2003_11_14_17_19_09372),i2003_11_14_17_19_09372) )],[refute_0_25,refute_0_3]) ).

cnf(refute_0_27,plain,
    cp(i2003_11_14_17_19_09372),
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_09372) )],[refute_0_4,refute_0_26]) ).

cnf(refute_0_28,plain,
    ~ cUnsatisfiable(i2003_11_14_17_19_09372),
    inference(resolve,[$cnf( cp(i2003_11_14_17_19_09372) )],[refute_0_27,refute_0_1]) ).

cnf(refute_0_29,plain,
    $false,
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_19_09372) )],[refute_0_4,refute_0_28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : KRS077+1 : TPTP v8.1.0. Released v3.1.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n026.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.33  % DateTime : Tue Jun  7 13:27:31 EDT 2022
% 0.12/0.33  % CPUTime  : 
% 0.12/0.33  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.34  
% 0.12/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.35  
%------------------------------------------------------------------------------