TSTP Solution File: KRS096+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : KRS096+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 03:18:42 EDT 2022

% Result   : Unsatisfiable 0.13s 0.34s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   40 (  11 unt;   0 def)
%            Number of atoms       :  123 (  13 equ)
%            Maximal formula atoms :   30 (   3 avg)
%            Number of connectives :  153 (  70   ~;  62   |;  16   &)
%                                         (   3 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   1 con; 0-1 aty)
%            Number of variables   :   41 (   0 sgn  24   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
    ! [X] :
      ( cUnsatisfiable(X)
    <=> ( ? [Y] :
            ( rr(X,Y)
            & cc(Y) )
        & ? [Y] :
            ( rr(X,Y)
            & cd(Y) )
        & ! [Y1,Y2] :
            ( ( rr(X,Y1)
              & rr(X,Y2) )
           => Y1 = Y2 ) ) ) ).

fof(axiom_3,axiom,
    ! [X] :
      ( cc(X)
     => ~ cd(X) ) ).

fof(axiom_4,axiom,
    cUnsatisfiable(i2003_11_14_17_20_18265) ).

fof(normalize_0_0,plain,
    cUnsatisfiable(i2003_11_14_17_20_18265),
    inference(canonicalize,[],[axiom_4]) ).

fof(normalize_0_1,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
    <=> ( ? [Y1,Y2] :
            ( Y1 != Y2
            & rr(X,Y1)
            & rr(X,Y2) )
        | ! [Y] :
            ( ~ cc(Y)
            | ~ rr(X,Y) )
        | ! [Y] :
            ( ~ cd(Y)
            | ~ rr(X,Y) ) ) ),
    inference(canonicalize,[],[axiom_2]) ).

fof(normalize_0_2,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
    <=> ( ? [Y1,Y2] :
            ( Y1 != Y2
            & rr(X,Y1)
            & rr(X,Y2) )
        | ! [Y] :
            ( ~ cc(Y)
            | ~ rr(X,Y) )
        | ! [Y] :
            ( ~ cd(Y)
            | ~ rr(X,Y) ) ) ),
    inference(specialize,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X,Y,Y0,Y1,Y2] :
      ( ( ~ cUnsatisfiable(X)
        | cc(skolemFOFtoCNF_Y_1(X)) )
      & ( ~ cUnsatisfiable(X)
        | cd(skolemFOFtoCNF_Y(X)) )
      & ( ~ cUnsatisfiable(X)
        | rr(X,skolemFOFtoCNF_Y(X)) )
      & ( ~ cUnsatisfiable(X)
        | rr(X,skolemFOFtoCNF_Y_1(X)) )
      & ( ~ cUnsatisfiable(X)
        | ~ rr(X,Y1)
        | ~ rr(X,Y2)
        | Y1 = Y2 )
      & ( skolemFOFtoCNF_Y0(X) != skolemFOFtoCNF_Y1(X)
        | ~ cc(Y)
        | ~ cd(Y0)
        | ~ rr(X,Y)
        | ~ rr(X,Y0)
        | cUnsatisfiable(X) )
      & ( ~ cc(Y)
        | ~ cd(Y0)
        | ~ rr(X,Y)
        | ~ rr(X,Y0)
        | cUnsatisfiable(X)
        | rr(X,skolemFOFtoCNF_Y0(X)) )
      & ( ~ cc(Y)
        | ~ cd(Y0)
        | ~ rr(X,Y)
        | ~ rr(X,Y0)
        | cUnsatisfiable(X)
        | rr(X,skolemFOFtoCNF_Y1(X)) ) ),
    inference(clausify,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
      | cc(skolemFOFtoCNF_Y_1(X)) ),
    inference(conjunct,[],[normalize_0_3]) ).

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

fof(normalize_0_6,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
      | rr(X,skolemFOFtoCNF_Y_1(X)) ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_7,plain,
    ! [X,Y1,Y2] :
      ( ~ cUnsatisfiable(X)
      | ~ rr(X,Y1)
      | ~ rr(X,Y2)
      | Y1 = Y2 ),
    inference(conjunct,[],[normalize_0_3]) ).

fof(normalize_0_8,plain,
    ! [X] :
      ( ~ cc(X)
      | ~ cd(X) ),
    inference(canonicalize,[],[axiom_3]) ).

fof(normalize_0_9,plain,
    ! [X] :
      ( ~ cc(X)
      | ~ cd(X) ),
    inference(specialize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
      | cd(skolemFOFtoCNF_Y(X)) ),
    inference(conjunct,[],[normalize_0_3]) ).

cnf(refute_0_0,plain,
    cUnsatisfiable(i2003_11_14_17_20_18265),
    inference(canonicalize,[],[normalize_0_0]) ).

cnf(refute_0_1,plain,
    ( ~ cUnsatisfiable(X)
    | cc(skolemFOFtoCNF_Y_1(X)) ),
    inference(canonicalize,[],[normalize_0_4]) ).

cnf(refute_0_2,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
    | cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265)) ),
    inference(subst,[],[refute_0_1:[bind(X,$fot(i2003_11_14_17_20_18265))]]) ).

cnf(refute_0_3,plain,
    cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265)),
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_18265) )],[refute_0_0,refute_0_2]) ).

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

cnf(refute_0_5,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
    | rr(i2003_11_14_17_20_18265,skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(i2003_11_14_17_20_18265))]]) ).

cnf(refute_0_6,plain,
    rr(i2003_11_14_17_20_18265,skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)),
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_18265) )],[refute_0_0,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( ~ cUnsatisfiable(X)
    | rr(X,skolemFOFtoCNF_Y_1(X)) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_8,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
    | rr(i2003_11_14_17_20_18265,skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265)) ),
    inference(subst,[],[refute_0_7:[bind(X,$fot(i2003_11_14_17_20_18265))]]) ).

cnf(refute_0_9,plain,
    rr(i2003_11_14_17_20_18265,skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265)),
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_18265) )],[refute_0_0,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( ~ cUnsatisfiable(X)
    | ~ rr(X,Y1)
    | ~ rr(X,Y2)
    | Y1 = Y2 ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_11,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
    | ~ rr(i2003_11_14_17_20_18265,X_11)
    | ~ rr(i2003_11_14_17_20_18265,skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265))
    | skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265) = X_11 ),
    inference(subst,[],[refute_0_10:[bind(X,$fot(i2003_11_14_17_20_18265)),bind(Y1,$fot(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265))),bind(Y2,$fot(X_11))]]) ).

cnf(refute_0_12,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
    | ~ rr(i2003_11_14_17_20_18265,X_11)
    | skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265) = X_11 ),
    inference(resolve,[$cnf( rr(i2003_11_14_17_20_18265,skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265)) )],[refute_0_9,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ rr(i2003_11_14_17_20_18265,X_11)
    | skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265) = X_11 ),
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_18265) )],[refute_0_0,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( ~ rr(i2003_11_14_17_20_18265,skolemFOFtoCNF_Y(i2003_11_14_17_20_18265))
    | skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265) = skolemFOFtoCNF_Y(i2003_11_14_17_20_18265) ),
    inference(subst,[],[refute_0_13:[bind(X_11,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)))]]) ).

cnf(refute_0_15,plain,
    skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265) = skolemFOFtoCNF_Y(i2003_11_14_17_20_18265),
    inference(resolve,[$cnf( rr(i2003_11_14_17_20_18265,skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) )],[refute_0_6,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265) != skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)
    | ~ cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265))
    | cc(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) ),
    introduced(tautology,[equality,[$cnf( cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265)) ),[0],$fot(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265))]]) ).

cnf(refute_0_17,plain,
    ( ~ cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265))
    | cc(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265),skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) )],[refute_0_15,refute_0_16]) ).

cnf(refute_0_18,plain,
    cc(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)),
    inference(resolve,[$cnf( cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_18265)) )],[refute_0_3,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( ~ cc(X)
    | ~ cd(X) ),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_20,plain,
    ( ~ cc(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265))
    | ~ cd(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) ),
    inference(subst,[],[refute_0_19:[bind(X,$fot(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)))]]) ).

cnf(refute_0_21,plain,
    ( ~ cUnsatisfiable(X)
    | cd(skolemFOFtoCNF_Y(X)) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_22,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_20_18265)
    | cd(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) ),
    inference(subst,[],[refute_0_21:[bind(X,$fot(i2003_11_14_17_20_18265))]]) ).

cnf(refute_0_23,plain,
    cd(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)),
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_18265) )],[refute_0_0,refute_0_22]) ).

cnf(refute_0_24,plain,
    ~ cc(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)),
    inference(resolve,[$cnf( cd(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) )],[refute_0_23,refute_0_20]) ).

cnf(refute_0_25,plain,
    $false,
    inference(resolve,[$cnf( cc(skolemFOFtoCNF_Y(i2003_11_14_17_20_18265)) )],[refute_0_18,refute_0_24]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : KRS096+1 : TPTP v8.1.0. Released v3.1.0.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n020.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit : 300
% 0.13/0.33  % WCLimit  : 600
% 0.13/0.33  % DateTime : Tue Jun  7 15:52:21 EDT 2022
% 0.13/0.33  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.34  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.34  
% 0.13/0.34  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.35  
%------------------------------------------------------------------------------