TSTP Solution File: KRS072+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : KRS072+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n020.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 03:18:36 EDT 2022

% Result   : Unsatisfiable 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   55 (  14 unt;   0 def)
%            Number of atoms       :  168 (  22 equ)
%            Maximal formula atoms :   30 (   3 avg)
%            Number of connectives :  212 (  99   ~;  79   |;  26   &)
%                                         (   6 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   11 (   8 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-1 aty)
%            Number of variables   :   60 (   0 sgn  36   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
    ! [X] :
      ( cUnsatisfiable(X)
    <=> ( ? [Y] :
            ( rinvR(X,Y)
            & ! [Z0,Z1] :
                ( ( rr(Y,Z0)
                  & rr(Y,Z1) )
               => Z0 = Z1 )
            & ? [Z] :
                ( rr(Y,Z)
                & cp1(Z) ) )
        & cp2(X) ) ) ).

fof(axiom_3,axiom,
    ! [X] :
      ( cp1(X)
     => ~ ( cp3(X)
          | cp2(X)
          | cp4(X)
          | cp5(X) ) ) ).

fof(axiom_7,axiom,
    ! [X,Y] :
      ( rinvR(X,Y)
    <=> rr(Y,X) ) ).

fof(axiom_8,axiom,
    cUnsatisfiable(i2003_11_14_17_18_50190) ).

fof(normalize_0_0,plain,
    cUnsatisfiable(i2003_11_14_17_18_50190),
    inference(canonicalize,[],[axiom_8]) ).

fof(normalize_0_1,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
    <=> ( ~ cp2(X)
        | ! [Y] :
            ( ~ rinvR(X,Y)
            | ? [Z0,Z1] :
                ( Z0 != Z1
                & rr(Y,Z0)
                & rr(Y,Z1) )
            | ! [Z] :
                ( ~ cp1(Z)
                | ~ rr(Y,Z) ) ) ) ),
    inference(canonicalize,[],[axiom_2]) ).

fof(normalize_0_2,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
    <=> ( ~ cp2(X)
        | ! [Y] :
            ( ~ rinvR(X,Y)
            | ? [Z0,Z1] :
                ( Z0 != Z1
                & rr(Y,Z0)
                & rr(Y,Z1) )
            | ! [Z] :
                ( ~ cp1(Z)
                | ~ rr(Y,Z) ) ) ) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X,Y,Z,Z0,Z1] :
      ( ( ~ cUnsatisfiable(X)
        | cp1(skolemFOFtoCNF_Z(X)) )
      & ( ~ cUnsatisfiable(X)
        | cp2(X) )
      & ( ~ cUnsatisfiable(X)
        | rinvR(X,skolemFOFtoCNF_Y(X)) )
      & ( ~ cUnsatisfiable(X)
        | rr(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) )
      & ( ~ cUnsatisfiable(X)
        | ~ rr(skolemFOFtoCNF_Y(X),Z0)
        | ~ rr(skolemFOFtoCNF_Y(X),Z1)
        | Z0 = Z1 )
      & ( skolemFOFtoCNF_Z0(Y) != skolemFOFtoCNF_Z1(Y)
        | ~ cp1(Z)
        | ~ cp2(X)
        | ~ rinvR(X,Y)
        | ~ rr(Y,Z)
        | cUnsatisfiable(X) )
      & ( ~ cp1(Z)
        | ~ cp2(X)
        | ~ rinvR(X,Y)
        | ~ rr(Y,Z)
        | cUnsatisfiable(X)
        | rr(Y,skolemFOFtoCNF_Z0(Y)) )
      & ( ~ cp1(Z)
        | ~ cp2(X)
        | ~ rinvR(X,Y)
        | ~ rr(Y,Z)
        | cUnsatisfiable(X)
        | rr(Y,skolemFOFtoCNF_Z1(Y)) ) ),
    inference(clausify,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
      | cp1(skolemFOFtoCNF_Z(X)) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
      | rr(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_6,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
      | rinvR(X,skolemFOFtoCNF_Y(X)) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_7,plain,
    ! [X,Y] :
      ( ~ rinvR(X,Y)
    <=> ~ rr(Y,X) ),
    inference(canonicalize,[],[axiom_7]) ).

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

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

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

fof(normalize_0_11,plain,
    ! [X,Z0,Z1] :
      ( ~ cUnsatisfiable(X)
      | ~ rr(skolemFOFtoCNF_Y(X),Z0)
      | ~ rr(skolemFOFtoCNF_Y(X),Z1)
      | Z0 = Z1 ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_12,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
      | cp2(X) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_13,plain,
    ! [X] :
      ( ~ cp1(X)
      | ( ~ cp2(X)
        & ~ cp3(X)
        & ~ cp4(X)
        & ~ cp5(X) ) ),
    inference(canonicalize,[],[axiom_3]) ).

fof(normalize_0_14,plain,
    ! [X] :
      ( ~ cp1(X)
      | ( ~ cp2(X)
        & ~ cp3(X)
        & ~ cp4(X)
        & ~ cp5(X) ) ),
    inference(specialize,[],[normalize_0_13]) ).

fof(normalize_0_15,plain,
    ! [X] :
      ( ( ~ cp1(X)
        | ~ cp2(X) )
      & ( ~ cp1(X)
        | ~ cp3(X) )
      & ( ~ cp1(X)
        | ~ cp4(X) )
      & ( ~ cp1(X)
        | ~ cp5(X) ) ),
    inference(clausify,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
    ! [X] :
      ( ~ cp1(X)
      | ~ cp2(X) ),
    inference(conjunct,[],[normalize_0_15]) ).

cnf(refute_0_0,plain,
    cUnsatisfiable(i2003_11_14_17_18_50190),
    inference(canonicalize,[],[normalize_0_0]) ).

cnf(refute_0_1,plain,
    ( ~ cUnsatisfiable(X)
    | cp1(skolemFOFtoCNF_Z(X)) ),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_2,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
    | cp1(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)) ),
    inference(subst,[],[refute_0_1:[bind(X,$fot(i2003_11_14_17_18_50190))]]) ).

cnf(refute_0_3,plain,
    cp1(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)),
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_50190) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ cUnsatisfiable(X)
    | rr(skolemFOFtoCNF_Y(X),skolemFOFtoCNF_Z(X)) ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_5,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
    | rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(i2003_11_14_17_18_50190))]]) ).

cnf(refute_0_6,plain,
    rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)),
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_50190) )],[refute_0_0,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( ~ cUnsatisfiable(X)
    | rinvR(X,skolemFOFtoCNF_Y(X)) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_8,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
    | rinvR(i2003_11_14_17_18_50190,skolemFOFtoCNF_Y(i2003_11_14_17_18_50190)) ),
    inference(subst,[],[refute_0_7:[bind(X,$fot(i2003_11_14_17_18_50190))]]) ).

cnf(refute_0_9,plain,
    rinvR(i2003_11_14_17_18_50190,skolemFOFtoCNF_Y(i2003_11_14_17_18_50190)),
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_50190) )],[refute_0_0,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( ~ rinvR(X,Y)
    | rr(Y,X) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_11,plain,
    ( ~ rinvR(i2003_11_14_17_18_50190,skolemFOFtoCNF_Y(i2003_11_14_17_18_50190))
    | rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) ),
    inference(subst,[],[refute_0_10:[bind(X,$fot(i2003_11_14_17_18_50190)),bind(Y,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190)))]]) ).

cnf(refute_0_12,plain,
    rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190),
    inference(resolve,[$cnf( rinvR(i2003_11_14_17_18_50190,skolemFOFtoCNF_Y(i2003_11_14_17_18_50190)) )],[refute_0_9,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ cUnsatisfiable(X)
    | ~ rr(skolemFOFtoCNF_Y(X),Z0)
    | ~ rr(skolemFOFtoCNF_Y(X),Z1)
    | Z0 = Z1 ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_14,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
    | ~ rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),X_24)
    | ~ rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190)
    | i2003_11_14_17_18_50190 = X_24 ),
    inference(subst,[],[refute_0_13:[bind(X,$fot(i2003_11_14_17_18_50190)),bind(Z0,$fot(i2003_11_14_17_18_50190)),bind(Z1,$fot(X_24))]]) ).

cnf(refute_0_15,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
    | ~ rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),X_24)
    | i2003_11_14_17_18_50190 = X_24 ),
    inference(resolve,[$cnf( rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) )],[refute_0_12,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( ~ rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),X_24)
    | i2003_11_14_17_18_50190 = X_24 ),
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_50190) )],[refute_0_0,refute_0_15]) ).

cnf(refute_0_17,plain,
    ( ~ rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),skolemFOFtoCNF_Z(i2003_11_14_17_18_50190))
    | i2003_11_14_17_18_50190 = skolemFOFtoCNF_Z(i2003_11_14_17_18_50190) ),
    inference(subst,[],[refute_0_16:[bind(X_24,$fot(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)))]]) ).

cnf(refute_0_18,plain,
    i2003_11_14_17_18_50190 = skolemFOFtoCNF_Z(i2003_11_14_17_18_50190),
    inference(resolve,[$cnf( rr(skolemFOFtoCNF_Y(i2003_11_14_17_18_50190),skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)) )],[refute_0_6,refute_0_17]) ).

cnf(refute_0_19,plain,
    X0 = X0,
    introduced(tautology,[refl,[$fot(X0)]]) ).

cnf(refute_0_20,plain,
    ( X0 != X0
    | X0 != Y0
    | Y0 = X0 ),
    introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).

cnf(refute_0_21,plain,
    ( X0 != Y0
    | Y0 = X0 ),
    inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_19,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( i2003_11_14_17_18_50190 != skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)
    | skolemFOFtoCNF_Z(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190 ),
    inference(subst,[],[refute_0_21:[bind(X0,$fot(i2003_11_14_17_18_50190)),bind(Y0,$fot(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)))]]) ).

cnf(refute_0_23,plain,
    skolemFOFtoCNF_Z(i2003_11_14_17_18_50190) = i2003_11_14_17_18_50190,
    inference(resolve,[$cnf( $equal(i2003_11_14_17_18_50190,skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)) )],[refute_0_18,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( skolemFOFtoCNF_Z(i2003_11_14_17_18_50190) != i2003_11_14_17_18_50190
    | ~ cp1(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190))
    | cp1(i2003_11_14_17_18_50190) ),
    introduced(tautology,[equality,[$cnf( cp1(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)) ),[0],$fot(i2003_11_14_17_18_50190)]]) ).

cnf(refute_0_25,plain,
    ( ~ cp1(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190))
    | cp1(i2003_11_14_17_18_50190) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190),i2003_11_14_17_18_50190) )],[refute_0_23,refute_0_24]) ).

cnf(refute_0_26,plain,
    cp1(i2003_11_14_17_18_50190),
    inference(resolve,[$cnf( cp1(skolemFOFtoCNF_Z(i2003_11_14_17_18_50190)) )],[refute_0_3,refute_0_25]) ).

cnf(refute_0_27,plain,
    ( ~ cUnsatisfiable(X)
    | cp2(X) ),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_28,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_18_50190)
    | cp2(i2003_11_14_17_18_50190) ),
    inference(subst,[],[refute_0_27:[bind(X,$fot(i2003_11_14_17_18_50190))]]) ).

cnf(refute_0_29,plain,
    cp2(i2003_11_14_17_18_50190),
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_18_50190) )],[refute_0_0,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( ~ cp1(X)
    | ~ cp2(X) ),
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_31,plain,
    ( ~ cp1(i2003_11_14_17_18_50190)
    | ~ cp2(i2003_11_14_17_18_50190) ),
    inference(subst,[],[refute_0_30:[bind(X,$fot(i2003_11_14_17_18_50190))]]) ).

cnf(refute_0_32,plain,
    ~ cp1(i2003_11_14_17_18_50190),
    inference(resolve,[$cnf( cp2(i2003_11_14_17_18_50190) )],[refute_0_29,refute_0_31]) ).

cnf(refute_0_33,plain,
    $false,
    inference(resolve,[$cnf( cp1(i2003_11_14_17_18_50190) )],[refute_0_26,refute_0_32]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KRS072+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n020.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Tue Jun  7 20:24:51 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36  
% 0.13/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37  
%------------------------------------------------------------------------------