TSTP Solution File: KRS105+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : KRS105+1 : TPTP v8.1.0. Released v3.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n024.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 03:18:44 EDT 2022

% Result   : Unsatisfiable 0.07s 0.27s
% Output   : CNFRefutation 0.07s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   58 (  10 unt;   0 def)
%            Number of atoms       :  126 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  123 (  55   ~;  47   |;   6   &)
%                                         (   9 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   1 con; 0-1 aty)
%            Number of variables   :   59 (   1 sgn  40   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(axiom_2,axiom,
    ! [X] :
      ( cUnsatisfiable(X)
     => cdxcomp(X) ) ).

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

fof(axiom_4,axiom,
    ! [X] :
      ( cc(X)
     => ! [Y] :
          ( rr(X,Y)
         => cc(Y) ) ) ).

fof(axiom_5,axiom,
    ! [X] :
      ( cd(X)
    <=> ~ ? [Y] : ra_Px1(X,Y) ) ).

fof(axiom_6,axiom,
    ! [X] :
      ( cdxcomp(X)
    <=> ? [Y0] : ra_Px1(X,Y0) ) ).

fof(axiom_7,axiom,
    ! [X] :
      ( ca_Ax2(X)
    <=> ! [Y] :
          ( rr(X,Y)
         => cc(Y) ) ) ).

fof(axiom_8,axiom,
    ! [X] :
      ( ca_Ax2(X)
     => cd(X) ) ).

fof(axiom_9,axiom,
    cUnsatisfiable(i2003_11_14_17_20_53634) ).

fof(normalize_0_0,plain,
    ! [X] :
      ( ~ ca_Ax2(X)
      | cd(X) ),
    inference(canonicalize,[],[axiom_8]) ).

fof(normalize_0_1,plain,
    ! [X] :
      ( ~ ca_Ax2(X)
      | cd(X) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X] :
      ( ~ ca_Ax2(X)
    <=> ? [Y] :
          ( ~ cc(Y)
          & rr(X,Y) ) ),
    inference(canonicalize,[],[axiom_7]) ).

fof(normalize_0_3,plain,
    ! [X] :
      ( ~ ca_Ax2(X)
    <=> ? [Y] :
          ( ~ cc(Y)
          & rr(X,Y) ) ),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X,Y] :
      ( ( ~ cc(skolemFOFtoCNF_Y_1(X))
        | ca_Ax2(X) )
      & ( ca_Ax2(X)
        | rr(X,skolemFOFtoCNF_Y_1(X)) )
      & ( ~ ca_Ax2(X)
        | ~ rr(X,Y)
        | cc(Y) ) ),
    inference(clausify,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [X] :
      ( ~ cc(skolemFOFtoCNF_Y_1(X))
      | ca_Ax2(X) ),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    cUnsatisfiable(i2003_11_14_17_20_53634),
    inference(canonicalize,[],[axiom_9]) ).

fof(normalize_0_7,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
      | cc(X) ),
    inference(canonicalize,[],[axiom_3]) ).

fof(normalize_0_8,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
      | cc(X) ),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [X] :
      ( ca_Ax2(X)
      | rr(X,skolemFOFtoCNF_Y_1(X)) ),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_10,plain,
    ! [X] :
      ( ~ cc(X)
      | ! [Y] :
          ( ~ rr(X,Y)
          | cc(Y) ) ),
    inference(canonicalize,[],[axiom_4]) ).

fof(normalize_0_11,plain,
    ! [X] :
      ( ~ cc(X)
      | ! [Y] :
          ( ~ rr(X,Y)
          | cc(Y) ) ),
    inference(specialize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [X,Y] :
      ( ~ cc(X)
      | ~ rr(X,Y)
      | cc(Y) ),
    inference(clausify,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
      | cdxcomp(X) ),
    inference(canonicalize,[],[axiom_2]) ).

fof(normalize_0_14,plain,
    ! [X] :
      ( ~ cUnsatisfiable(X)
      | cdxcomp(X) ),
    inference(specialize,[],[normalize_0_13]) ).

fof(normalize_0_15,plain,
    ! [X] :
      ( ~ cdxcomp(X)
    <=> ! [Y0] : ~ ra_Px1(X,Y0) ),
    inference(canonicalize,[],[axiom_6]) ).

fof(normalize_0_16,plain,
    ! [X] :
      ( ~ cdxcomp(X)
    <=> ! [Y0] : ~ ra_Px1(X,Y0) ),
    inference(specialize,[],[normalize_0_15]) ).

fof(normalize_0_17,plain,
    ! [X,Y0] :
      ( ( ~ cdxcomp(X)
        | ra_Px1(X,skolemFOFtoCNF_Y0(X)) )
      & ( ~ ra_Px1(X,Y0)
        | cdxcomp(X) ) ),
    inference(clausify,[],[normalize_0_16]) ).

fof(normalize_0_18,plain,
    ! [X] :
      ( ~ cdxcomp(X)
      | ra_Px1(X,skolemFOFtoCNF_Y0(X)) ),
    inference(conjunct,[],[normalize_0_17]) ).

fof(normalize_0_19,plain,
    ! [X] :
      ( ~ cd(X)
    <=> ? [Y] : ra_Px1(X,Y) ),
    inference(canonicalize,[],[axiom_5]) ).

fof(normalize_0_20,plain,
    ! [X] :
      ( ~ cd(X)
    <=> ? [Y] : ra_Px1(X,Y) ),
    inference(specialize,[],[normalize_0_19]) ).

fof(normalize_0_21,plain,
    ! [X,Y] :
      ( ( ~ cd(X)
        | ~ ra_Px1(X,Y) )
      & ( cd(X)
        | ra_Px1(X,skolemFOFtoCNF_Y(X)) ) ),
    inference(clausify,[],[normalize_0_20]) ).

fof(normalize_0_22,plain,
    ! [X,Y] :
      ( ~ cd(X)
      | ~ ra_Px1(X,Y) ),
    inference(conjunct,[],[normalize_0_21]) ).

cnf(refute_0_0,plain,
    ( ~ ca_Ax2(X)
    | cd(X) ),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    ( ~ ca_Ax2(i2003_11_14_17_20_53634)
    | cd(i2003_11_14_17_20_53634) ),
    inference(subst,[],[refute_0_0:[bind(X,$fot(i2003_11_14_17_20_53634))]]) ).

cnf(refute_0_2,plain,
    ( ~ cc(skolemFOFtoCNF_Y_1(X))
    | ca_Ax2(X) ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_3,plain,
    ( ~ cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_53634))
    | ca_Ax2(i2003_11_14_17_20_53634) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(i2003_11_14_17_20_53634))]]) ).

cnf(refute_0_4,plain,
    cUnsatisfiable(i2003_11_14_17_20_53634),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_5,plain,
    ( ~ cUnsatisfiable(X)
    | cc(X) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_6,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_20_53634)
    | cc(i2003_11_14_17_20_53634) ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(i2003_11_14_17_20_53634))]]) ).

cnf(refute_0_7,plain,
    cc(i2003_11_14_17_20_53634),
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_53634) )],[refute_0_4,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( ca_Ax2(X)
    | rr(X,skolemFOFtoCNF_Y_1(X)) ),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_9,plain,
    ( ca_Ax2(X_17)
    | rr(X_17,skolemFOFtoCNF_Y_1(X_17)) ),
    inference(subst,[],[refute_0_8:[bind(X,$fot(X_17))]]) ).

cnf(refute_0_10,plain,
    ( ~ cc(X)
    | ~ rr(X,Y)
    | cc(Y) ),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_11,plain,
    ( ~ cc(X_17)
    | ~ rr(X_17,skolemFOFtoCNF_Y_1(X_17))
    | cc(skolemFOFtoCNF_Y_1(X_17)) ),
    inference(subst,[],[refute_0_10:[bind(X,$fot(X_17)),bind(Y,$fot(skolemFOFtoCNF_Y_1(X_17)))]]) ).

cnf(refute_0_12,plain,
    ( ~ cc(X_17)
    | ca_Ax2(X_17)
    | cc(skolemFOFtoCNF_Y_1(X_17)) ),
    inference(resolve,[$cnf( rr(X_17,skolemFOFtoCNF_Y_1(X_17)) )],[refute_0_9,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ cc(i2003_11_14_17_20_53634)
    | ca_Ax2(i2003_11_14_17_20_53634)
    | cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_53634)) ),
    inference(subst,[],[refute_0_12:[bind(X_17,$fot(i2003_11_14_17_20_53634))]]) ).

cnf(refute_0_14,plain,
    ( ca_Ax2(i2003_11_14_17_20_53634)
    | cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_53634)) ),
    inference(resolve,[$cnf( cc(i2003_11_14_17_20_53634) )],[refute_0_7,refute_0_13]) ).

cnf(refute_0_15,plain,
    ca_Ax2(i2003_11_14_17_20_53634),
    inference(resolve,[$cnf( cc(skolemFOFtoCNF_Y_1(i2003_11_14_17_20_53634)) )],[refute_0_14,refute_0_3]) ).

cnf(refute_0_16,plain,
    cd(i2003_11_14_17_20_53634),
    inference(resolve,[$cnf( ca_Ax2(i2003_11_14_17_20_53634) )],[refute_0_15,refute_0_1]) ).

cnf(refute_0_17,plain,
    ( ~ cUnsatisfiable(X)
    | cdxcomp(X) ),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_18,plain,
    ( ~ cUnsatisfiable(i2003_11_14_17_20_53634)
    | cdxcomp(i2003_11_14_17_20_53634) ),
    inference(subst,[],[refute_0_17:[bind(X,$fot(i2003_11_14_17_20_53634))]]) ).

cnf(refute_0_19,plain,
    cdxcomp(i2003_11_14_17_20_53634),
    inference(resolve,[$cnf( cUnsatisfiable(i2003_11_14_17_20_53634) )],[refute_0_4,refute_0_18]) ).

cnf(refute_0_20,plain,
    ( ~ cdxcomp(X)
    | ra_Px1(X,skolemFOFtoCNF_Y0(X)) ),
    inference(canonicalize,[],[normalize_0_18]) ).

cnf(refute_0_21,plain,
    ( ~ cdxcomp(i2003_11_14_17_20_53634)
    | ra_Px1(i2003_11_14_17_20_53634,skolemFOFtoCNF_Y0(i2003_11_14_17_20_53634)) ),
    inference(subst,[],[refute_0_20:[bind(X,$fot(i2003_11_14_17_20_53634))]]) ).

cnf(refute_0_22,plain,
    ra_Px1(i2003_11_14_17_20_53634,skolemFOFtoCNF_Y0(i2003_11_14_17_20_53634)),
    inference(resolve,[$cnf( cdxcomp(i2003_11_14_17_20_53634) )],[refute_0_19,refute_0_21]) ).

cnf(refute_0_23,plain,
    ( ~ cd(X)
    | ~ ra_Px1(X,Y) ),
    inference(canonicalize,[],[normalize_0_22]) ).

cnf(refute_0_24,plain,
    ( ~ cd(i2003_11_14_17_20_53634)
    | ~ ra_Px1(i2003_11_14_17_20_53634,skolemFOFtoCNF_Y0(i2003_11_14_17_20_53634)) ),
    inference(subst,[],[refute_0_23:[bind(X,$fot(i2003_11_14_17_20_53634)),bind(Y,$fot(skolemFOFtoCNF_Y0(i2003_11_14_17_20_53634)))]]) ).

cnf(refute_0_25,plain,
    ~ cd(i2003_11_14_17_20_53634),
    inference(resolve,[$cnf( ra_Px1(i2003_11_14_17_20_53634,skolemFOFtoCNF_Y0(i2003_11_14_17_20_53634)) )],[refute_0_22,refute_0_24]) ).

cnf(refute_0_26,plain,
    $false,
    inference(resolve,[$cnf( cd(i2003_11_14_17_20_53634) )],[refute_0_16,refute_0_25]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07  % Problem  : KRS105+1 : TPTP v8.1.0. Released v3.1.0.
% 0.00/0.08  % Command  : metis --show proof --show saturation %s
% 0.07/0.27  % Computer : n024.cluster.edu
% 0.07/0.27  % Model    : x86_64 x86_64
% 0.07/0.27  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.27  % Memory   : 8042.1875MB
% 0.07/0.27  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.07/0.27  % CPULimit : 300
% 0.07/0.27  % WCLimit  : 600
% 0.07/0.27  % DateTime : Tue Jun  7 17:31:49 EDT 2022
% 0.07/0.27  % CPUTime  : 
% 0.07/0.27  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.07/0.27  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.27  
% 0.07/0.27  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.07/0.28  
%------------------------------------------------------------------------------