TSTP Solution File: PUZ001+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : PUZ001+1 : TPTP v8.1.0. Released v2.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n023.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 : Mon Jul 18 18:20:24 EDT 2022

% Result   : Theorem 0.12s 0.35s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   82 (  27 unt;   0 def)
%            Number of atoms       :  156 (  44 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  134 (  60   ~;  64   |;   3   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    7 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-1 aty)
%            Number of variables   :   52 (   0 sgn  31   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(pel55_1,axiom,
    ? [X] :
      ( lives(X)
      & killed(X,agatha) ) ).

fof(pel55_3,axiom,
    ! [X] :
      ( lives(X)
     => ( X = agatha
        | X = butler
        | X = charles ) ) ).

fof(pel55_4,axiom,
    ! [X,Y] :
      ( killed(X,Y)
     => hates(X,Y) ) ).

fof(pel55_5,axiom,
    ! [X,Y] :
      ( killed(X,Y)
     => ~ richer(X,Y) ) ).

fof(pel55_6,axiom,
    ! [X] :
      ( hates(agatha,X)
     => ~ hates(charles,X) ) ).

fof(pel55_7,axiom,
    ! [X] :
      ( X != butler
     => hates(agatha,X) ) ).

fof(pel55_8,axiom,
    ! [X] :
      ( ~ richer(X,agatha)
     => hates(butler,X) ) ).

fof(pel55_9,axiom,
    ! [X] :
      ( hates(agatha,X)
     => hates(butler,X) ) ).

fof(pel55_10,axiom,
    ! [X] :
    ? [Y] : ~ hates(X,Y) ).

fof(pel55_11,axiom,
    agatha != butler ).

fof(pel55,conjecture,
    killed(agatha,agatha) ).

fof(subgoal_0,plain,
    killed(agatha,agatha),
    inference(strip,[],[pel55]) ).

fof(negate_0_0,plain,
    ~ killed(agatha,agatha),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [X] :
      ( X = butler
      | hates(agatha,X) ),
    inference(canonicalize,[],[pel55_7]) ).

fof(normalize_0_1,plain,
    ! [X] :
      ( X = butler
      | hates(agatha,X) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X] :
      ( ~ hates(agatha,X)
      | ~ hates(charles,X) ),
    inference(canonicalize,[],[pel55_6]) ).

fof(normalize_0_3,plain,
    ! [X] :
      ( ~ hates(agatha,X)
      | ~ hates(charles,X) ),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ? [X] :
      ( killed(X,agatha)
      & lives(X) ),
    inference(canonicalize,[],[pel55_1]) ).

fof(normalize_0_5,plain,
    ( killed(skolemFOFtoCNF_X,agatha)
    & lives(skolemFOFtoCNF_X) ),
    inference(skolemize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    killed(skolemFOFtoCNF_X,agatha),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X,Y] :
      ( ~ killed(X,Y)
      | hates(X,Y) ),
    inference(canonicalize,[],[pel55_4]) ).

fof(normalize_0_8,plain,
    ! [X,Y] :
      ( ~ killed(X,Y)
      | hates(X,Y) ),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [X] :
      ( hates(butler,X)
      | richer(X,agatha) ),
    inference(canonicalize,[],[pel55_8]) ).

fof(normalize_0_10,plain,
    ! [X] :
      ( hates(butler,X)
      | richer(X,agatha) ),
    inference(specialize,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [X,Y] :
      ( ~ killed(X,Y)
      | ~ richer(X,Y) ),
    inference(canonicalize,[],[pel55_5]) ).

fof(normalize_0_12,plain,
    ! [X,Y] :
      ( ~ killed(X,Y)
      | ~ richer(X,Y) ),
    inference(specialize,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    lives(skolemFOFtoCNF_X),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_14,plain,
    ! [X] :
      ( ~ lives(X)
      | X = agatha
      | X = butler
      | X = charles ),
    inference(canonicalize,[],[pel55_3]) ).

fof(normalize_0_15,plain,
    ! [X] :
      ( ~ lives(X)
      | X = agatha
      | X = butler
      | X = charles ),
    inference(specialize,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
    ~ killed(agatha,agatha),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_17,plain,
    ! [X] :
    ? [Y] : ~ hates(X,Y),
    inference(canonicalize,[],[pel55_10]) ).

fof(normalize_0_18,plain,
    ! [X] :
    ? [Y] : ~ hates(X,Y),
    inference(specialize,[],[normalize_0_17]) ).

fof(normalize_0_19,plain,
    ! [X] : ~ hates(X,skolemFOFtoCNF_Y(X)),
    inference(skolemize,[],[normalize_0_18]) ).

fof(normalize_0_20,plain,
    ! [X] :
      ( ~ hates(agatha,X)
      | hates(butler,X) ),
    inference(canonicalize,[],[pel55_9]) ).

fof(normalize_0_21,plain,
    ! [X] :
      ( ~ hates(agatha,X)
      | hates(butler,X) ),
    inference(specialize,[],[normalize_0_20]) ).

fof(normalize_0_22,plain,
    agatha != butler,
    inference(canonicalize,[],[pel55_11]) ).

cnf(refute_0_0,plain,
    ( X = butler
    | hates(agatha,X) ),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    ( agatha = butler
    | hates(agatha,agatha) ),
    inference(subst,[],[refute_0_0:[bind(X,$fot(agatha))]]) ).

cnf(refute_0_2,plain,
    ( ~ hates(agatha,X)
    | ~ hates(charles,X) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_3,plain,
    ( ~ hates(agatha,agatha)
    | ~ hates(charles,agatha) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(agatha))]]) ).

cnf(refute_0_4,plain,
    killed(skolemFOFtoCNF_X,agatha),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_5,plain,
    ( ~ killed(X,Y)
    | hates(X,Y) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_6,plain,
    ( ~ killed(skolemFOFtoCNF_X,agatha)
    | hates(skolemFOFtoCNF_X,agatha) ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(agatha))]]) ).

cnf(refute_0_7,plain,
    hates(skolemFOFtoCNF_X,agatha),
    inference(resolve,[$cnf( killed(skolemFOFtoCNF_X,agatha) )],[refute_0_4,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( hates(butler,X)
    | richer(X,agatha) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_9,plain,
    ( hates(butler,X_8)
    | richer(X_8,agatha) ),
    inference(subst,[],[refute_0_8:[bind(X,$fot(X_8))]]) ).

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

cnf(refute_0_11,plain,
    ( ~ killed(X_8,agatha)
    | ~ richer(X_8,agatha) ),
    inference(subst,[],[refute_0_10:[bind(X,$fot(X_8)),bind(Y,$fot(agatha))]]) ).

cnf(refute_0_12,plain,
    ( ~ killed(X_8,agatha)
    | hates(butler,X_8) ),
    inference(resolve,[$cnf( richer(X_8,agatha) )],[refute_0_9,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ killed(skolemFOFtoCNF_X,agatha)
    | hates(butler,skolemFOFtoCNF_X) ),
    inference(subst,[],[refute_0_12:[bind(X_8,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_14,plain,
    hates(butler,skolemFOFtoCNF_X),
    inference(resolve,[$cnf( killed(skolemFOFtoCNF_X,agatha) )],[refute_0_4,refute_0_13]) ).

cnf(refute_0_15,plain,
    lives(skolemFOFtoCNF_X),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_16,plain,
    ( ~ lives(X)
    | X = agatha
    | X = butler
    | X = charles ),
    inference(canonicalize,[],[normalize_0_15]) ).

cnf(refute_0_17,plain,
    ( ~ lives(skolemFOFtoCNF_X)
    | skolemFOFtoCNF_X = agatha
    | skolemFOFtoCNF_X = butler
    | skolemFOFtoCNF_X = charles ),
    inference(subst,[],[refute_0_16:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_18,plain,
    ( skolemFOFtoCNF_X = agatha
    | skolemFOFtoCNF_X = butler
    | skolemFOFtoCNF_X = charles ),
    inference(resolve,[$cnf( lives(skolemFOFtoCNF_X) )],[refute_0_15,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( skolemFOFtoCNF_X != agatha
    | ~ killed(skolemFOFtoCNF_X,agatha)
    | killed(agatha,agatha) ),
    introduced(tautology,[equality,[$cnf( killed(skolemFOFtoCNF_X,agatha) ),[0],$fot(agatha)]]) ).

cnf(refute_0_20,plain,
    ( ~ killed(skolemFOFtoCNF_X,agatha)
    | skolemFOFtoCNF_X = butler
    | skolemFOFtoCNF_X = charles
    | killed(agatha,agatha) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,agatha) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( skolemFOFtoCNF_X = butler
    | skolemFOFtoCNF_X = charles
    | killed(agatha,agatha) ),
    inference(resolve,[$cnf( killed(skolemFOFtoCNF_X,agatha) )],[refute_0_4,refute_0_20]) ).

cnf(refute_0_22,plain,
    ~ killed(agatha,agatha),
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_23,plain,
    ( skolemFOFtoCNF_X = butler
    | skolemFOFtoCNF_X = charles ),
    inference(resolve,[$cnf( killed(agatha,agatha) )],[refute_0_21,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( skolemFOFtoCNF_X != butler
    | ~ hates(butler,skolemFOFtoCNF_X)
    | hates(butler,butler) ),
    introduced(tautology,[equality,[$cnf( hates(butler,skolemFOFtoCNF_X) ),[1],$fot(butler)]]) ).

cnf(refute_0_25,plain,
    ( ~ hates(butler,skolemFOFtoCNF_X)
    | skolemFOFtoCNF_X = charles
    | hates(butler,butler) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,butler) )],[refute_0_23,refute_0_24]) ).

cnf(refute_0_26,plain,
    ( skolemFOFtoCNF_X = charles
    | hates(butler,butler) ),
    inference(resolve,[$cnf( hates(butler,skolemFOFtoCNF_X) )],[refute_0_14,refute_0_25]) ).

cnf(refute_0_27,plain,
    ~ hates(X,skolemFOFtoCNF_Y(X)),
    inference(canonicalize,[],[normalize_0_19]) ).

cnf(refute_0_28,plain,
    ~ hates(butler,skolemFOFtoCNF_Y(butler)),
    inference(subst,[],[refute_0_27:[bind(X,$fot(butler))]]) ).

cnf(refute_0_29,plain,
    ( X_4 = butler
    | hates(agatha,X_4) ),
    inference(subst,[],[refute_0_0:[bind(X,$fot(X_4))]]) ).

cnf(refute_0_30,plain,
    ( ~ hates(agatha,X)
    | hates(butler,X) ),
    inference(canonicalize,[],[normalize_0_21]) ).

cnf(refute_0_31,plain,
    ( ~ hates(agatha,X_4)
    | hates(butler,X_4) ),
    inference(subst,[],[refute_0_30:[bind(X,$fot(X_4))]]) ).

cnf(refute_0_32,plain,
    ( X_4 = butler
    | hates(butler,X_4) ),
    inference(resolve,[$cnf( hates(agatha,X_4) )],[refute_0_29,refute_0_31]) ).

cnf(refute_0_33,plain,
    ( skolemFOFtoCNF_Y(butler) = butler
    | hates(butler,skolemFOFtoCNF_Y(butler)) ),
    inference(subst,[],[refute_0_32:[bind(X_4,$fot(skolemFOFtoCNF_Y(butler)))]]) ).

cnf(refute_0_34,plain,
    skolemFOFtoCNF_Y(butler) = butler,
    inference(resolve,[$cnf( hates(butler,skolemFOFtoCNF_Y(butler)) )],[refute_0_33,refute_0_28]) ).

cnf(refute_0_35,plain,
    ( skolemFOFtoCNF_Y(butler) != butler
    | ~ hates(butler,butler)
    | hates(butler,skolemFOFtoCNF_Y(butler)) ),
    introduced(tautology,[equality,[$cnf( ~ hates(butler,skolemFOFtoCNF_Y(butler)) ),[1],$fot(butler)]]) ).

cnf(refute_0_36,plain,
    ( ~ hates(butler,butler)
    | hates(butler,skolemFOFtoCNF_Y(butler)) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_Y(butler),butler) )],[refute_0_34,refute_0_35]) ).

cnf(refute_0_37,plain,
    ~ hates(butler,butler),
    inference(resolve,[$cnf( hates(butler,skolemFOFtoCNF_Y(butler)) )],[refute_0_36,refute_0_28]) ).

cnf(refute_0_38,plain,
    skolemFOFtoCNF_X = charles,
    inference(resolve,[$cnf( hates(butler,butler) )],[refute_0_26,refute_0_37]) ).

cnf(refute_0_39,plain,
    ( skolemFOFtoCNF_X != charles
    | ~ hates(skolemFOFtoCNF_X,agatha)
    | hates(charles,agatha) ),
    introduced(tautology,[equality,[$cnf( hates(skolemFOFtoCNF_X,agatha) ),[0],$fot(charles)]]) ).

cnf(refute_0_40,plain,
    ( ~ hates(skolemFOFtoCNF_X,agatha)
    | hates(charles,agatha) ),
    inference(resolve,[$cnf( $equal(skolemFOFtoCNF_X,charles) )],[refute_0_38,refute_0_39]) ).

cnf(refute_0_41,plain,
    hates(charles,agatha),
    inference(resolve,[$cnf( hates(skolemFOFtoCNF_X,agatha) )],[refute_0_7,refute_0_40]) ).

cnf(refute_0_42,plain,
    ~ hates(agatha,agatha),
    inference(resolve,[$cnf( hates(charles,agatha) )],[refute_0_41,refute_0_3]) ).

cnf(refute_0_43,plain,
    agatha = butler,
    inference(resolve,[$cnf( hates(agatha,agatha) )],[refute_0_1,refute_0_42]) ).

cnf(refute_0_44,plain,
    agatha != butler,
    inference(canonicalize,[],[normalize_0_22]) ).

cnf(refute_0_45,plain,
    $false,
    inference(resolve,[$cnf( $equal(agatha,butler) )],[refute_0_43,refute_0_44]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : PUZ001+1 : TPTP v8.1.0. Released v2.0.0.
% 0.06/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n023.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 : Sat May 28 22:42:27 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.35  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.35  
% 0.12/0.35  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.12/0.35  
%------------------------------------------------------------------------------