TSTP Solution File: GEO237+3 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO237+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n025.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 : Sat Jul 16 05:25:45 EDT 2022

% Result   : Theorem 0.13s 0.36s
% Output   : CNFRefutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   31 (  11 unt;   0 def)
%            Number of atoms       :   73 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   80 (  38   ~;  16   |;  16   &)
%                                         (   6 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-1 aty)
%            Number of variables   :   62 (  10 sgn  42   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(a2_defns,axiom,
    ! [X,Y] :
      ( right_apart_point(X,Y)
    <=> left_apart_point(X,reverse_line(Y)) ) ).

fof(a6_defns,axiom,
    ! [A,L] :
      ( apart_point_and_line(A,L)
    <=> ( left_apart_point(A,L)
        | right_apart_point(A,L) ) ) ).

fof(ax10_basics,axiom,
    ! [A,L] :
      ~ ( left_apart_point(A,L)
        | left_apart_point(A,reverse_line(L)) ) ).

fof(con,conjecture,
    ! [A,B,C,L] :
      ( apart_point_and_line(C,L)
     => ( divides_points(L,A,B)
       => ( divides_points(L,A,C)
          | divides_points(L,B,C) ) ) ) ).

fof(subgoal_0,plain,
    ! [A,B,C,L] :
      ( ( apart_point_and_line(C,L)
        & divides_points(L,A,B)
        & ~ divides_points(L,A,C) )
     => divides_points(L,B,C) ),
    inference(strip,[],[con]) ).

fof(negate_0_0,plain,
    ~ ! [A,B,C,L] :
        ( ( apart_point_and_line(C,L)
          & divides_points(L,A,B)
          & ~ divides_points(L,A,C) )
       => divides_points(L,B,C) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [A,B,C,L] :
      ( ~ divides_points(L,A,C)
      & ~ divides_points(L,B,C)
      & apart_point_and_line(C,L)
      & divides_points(L,A,B) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ~ divides_points(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_C)
    & ~ divides_points(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
    & apart_point_and_line(skolemFOFtoCNF_C,skolemFOFtoCNF_L)
    & divides_points(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    apart_point_and_line(skolemFOFtoCNF_C,skolemFOFtoCNF_L),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [A,L] :
      ( ~ apart_point_and_line(A,L)
    <=> ( ~ left_apart_point(A,L)
        & ~ right_apart_point(A,L) ) ),
    inference(canonicalize,[],[a6_defns]) ).

fof(normalize_0_4,plain,
    ! [A,L] :
      ( ~ apart_point_and_line(A,L)
    <=> ( ~ left_apart_point(A,L)
        & ~ right_apart_point(A,L) ) ),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [A,L] :
      ( ( ~ left_apart_point(A,L)
        | apart_point_and_line(A,L) )
      & ( ~ right_apart_point(A,L)
        | apart_point_and_line(A,L) )
      & ( ~ apart_point_and_line(A,L)
        | left_apart_point(A,L)
        | right_apart_point(A,L) ) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [A,L] :
      ( ~ apart_point_and_line(A,L)
      | left_apart_point(A,L)
      | right_apart_point(A,L) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ( ! [A,L] : ~ left_apart_point(A,L)
    & ! [A,L] : ~ left_apart_point(A,reverse_line(L)) ),
    inference(canonicalize,[],[ax10_basics]) ).

fof(normalize_0_8,plain,
    ! [A,L] : ~ left_apart_point(A,L),
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [A,L] : ~ left_apart_point(A,L),
    inference(specialize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [X,Y] :
      ( ~ left_apart_point(X,reverse_line(Y))
    <=> ~ right_apart_point(X,Y) ),
    inference(canonicalize,[],[a2_defns]) ).

fof(normalize_0_11,plain,
    ! [X,Y] :
      ( ~ left_apart_point(X,reverse_line(Y))
    <=> ~ right_apart_point(X,Y) ),
    inference(specialize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [X,Y] :
      ( ( ~ left_apart_point(X,reverse_line(Y))
        | right_apart_point(X,Y) )
      & ( ~ right_apart_point(X,Y)
        | left_apart_point(X,reverse_line(Y)) ) ),
    inference(clausify,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [X,Y] :
      ( ~ right_apart_point(X,Y)
      | left_apart_point(X,reverse_line(Y)) ),
    inference(conjunct,[],[normalize_0_12]) ).

cnf(refute_0_0,plain,
    apart_point_and_line(skolemFOFtoCNF_C,skolemFOFtoCNF_L),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    ( ~ apart_point_and_line(A,L)
    | left_apart_point(A,L)
    | right_apart_point(A,L) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_2,plain,
    ~ left_apart_point(A,L),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_3,plain,
    ( ~ apart_point_and_line(A,L)
    | right_apart_point(A,L) ),
    inference(resolve,[$cnf( left_apart_point(A,L) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ right_apart_point(X,Y)
    | left_apart_point(X,reverse_line(Y)) ),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_5,plain,
    ~ left_apart_point(X,reverse_line(Y)),
    inference(subst,[],[refute_0_2:[bind(A,$fot(X)),bind(L,$fot(reverse_line(Y)))]]) ).

cnf(refute_0_6,plain,
    ~ right_apart_point(X,Y),
    inference(resolve,[$cnf( left_apart_point(X,reverse_line(Y)) )],[refute_0_4,refute_0_5]) ).

cnf(refute_0_7,plain,
    ~ right_apart_point(A,L),
    inference(subst,[],[refute_0_6:[bind(X,$fot(A)),bind(Y,$fot(L))]]) ).

cnf(refute_0_8,plain,
    ~ apart_point_and_line(A,L),
    inference(resolve,[$cnf( right_apart_point(A,L) )],[refute_0_3,refute_0_7]) ).

cnf(refute_0_9,plain,
    ~ apart_point_and_line(skolemFOFtoCNF_C,skolemFOFtoCNF_L),
    inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_C)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).

cnf(refute_0_10,plain,
    $false,
    inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_C,skolemFOFtoCNF_L) )],[refute_0_0,refute_0_9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO237+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.33  % Computer : n025.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
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Sat Jun 18 14:06:58 EDT 2022
% 0.13/0.34  % CPUTime  : 
% 0.13/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36  % SZS status Theorem 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  
%------------------------------------------------------------------------------