TSTP Solution File: GEO261+3 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO261+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n011.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 05:26:00 EDT 2022

% Result   : Theorem 0.19s 0.37s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   42 (  11 unt;   0 def)
%            Number of atoms       :  102 (   0 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :  108 (  48   ~;  32   |;  18   &)
%                                         (   6 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    8 (   7 usr;   1 prp; 0-4 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-1 aty)
%            Number of variables   :   74 (   4 sgn  53   !;   5   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(a1_defns,axiom,
    ! [X,Y] :
      ( unequally_directed_opposite_lines(X,Y)
    <=> unequally_directed_lines(X,reverse_line(Y)) ) ).

fof(a7_defns,axiom,
    ! [L,M] :
      ( convergent_lines(L,M)
    <=> ( unequally_directed_lines(L,M)
        & unequally_directed_opposite_lines(L,M) ) ) ).

fof(ax9_basics,axiom,
    ! [L,M] :
      ( ( unequally_directed_lines(L,M)
        & unequally_directed_lines(L,reverse_line(M)) )
     => ( left_convergent_lines(L,M)
        | left_convergent_lines(L,reverse_line(M)) ) ) ).

fof(ax11_basics,axiom,
    ! [L,M] :
      ~ ( left_convergent_lines(L,M)
        | left_convergent_lines(L,reverse_line(M)) ) ).

fof(con,conjecture,
    ! [L,M,A,B,C] :
      ( ( between_on_line(L,A,B,C)
        & convergent_lines(L,M)
        & incident_point_and_line(B,M) )
     => divides_points(M,A,C) ) ).

fof(subgoal_0,plain,
    ! [L,M,A,B,C] :
      ( ( between_on_line(L,A,B,C)
        & convergent_lines(L,M)
        & incident_point_and_line(B,M) )
     => divides_points(M,A,C) ),
    inference(strip,[],[con]) ).

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

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

fof(normalize_0_1,plain,
    ( ~ divides_points(skolemFOFtoCNF_M,skolemFOFtoCNF_A,skolemFOFtoCNF_C)
    & between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
    & convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
    & incident_point_and_line(skolemFOFtoCNF_B,skolemFOFtoCNF_M) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [L,M] :
      ( ~ convergent_lines(L,M)
    <=> ( ~ unequally_directed_lines(L,M)
        | ~ unequally_directed_opposite_lines(L,M) ) ),
    inference(canonicalize,[],[a7_defns]) ).

fof(normalize_0_4,plain,
    ! [L,M] :
      ( ~ convergent_lines(L,M)
    <=> ( ~ unequally_directed_lines(L,M)
        | ~ unequally_directed_opposite_lines(L,M) ) ),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [L,M] :
      ( ( ~ convergent_lines(L,M)
        | unequally_directed_lines(L,M) )
      & ( ~ convergent_lines(L,M)
        | unequally_directed_opposite_lines(L,M) )
      & ( ~ unequally_directed_lines(L,M)
        | ~ unequally_directed_opposite_lines(L,M)
        | convergent_lines(L,M) ) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [L,M] :
      ( ~ convergent_lines(L,M)
      | unequally_directed_opposite_lines(L,M) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X,Y] :
      ( ~ unequally_directed_lines(X,reverse_line(Y))
    <=> ~ unequally_directed_opposite_lines(X,Y) ),
    inference(canonicalize,[],[a1_defns]) ).

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

fof(normalize_0_9,plain,
    ! [X,Y] :
      ( ( ~ unequally_directed_lines(X,reverse_line(Y))
        | unequally_directed_opposite_lines(X,Y) )
      & ( ~ unequally_directed_opposite_lines(X,Y)
        | unequally_directed_lines(X,reverse_line(Y)) ) ),
    inference(clausify,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [X,Y] :
      ( ~ unequally_directed_opposite_lines(X,Y)
      | unequally_directed_lines(X,reverse_line(Y)) ),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [L,M] :
      ( ~ unequally_directed_lines(L,M)
      | ~ unequally_directed_lines(L,reverse_line(M))
      | left_convergent_lines(L,M)
      | left_convergent_lines(L,reverse_line(M)) ),
    inference(canonicalize,[],[ax9_basics]) ).

fof(normalize_0_12,plain,
    ! [L,M] :
      ( ~ unequally_directed_lines(L,M)
      | ~ unequally_directed_lines(L,reverse_line(M))
      | left_convergent_lines(L,M)
      | left_convergent_lines(L,reverse_line(M)) ),
    inference(specialize,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ( ! [L,M] : ~ left_convergent_lines(L,M)
    & ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
    inference(canonicalize,[],[ax11_basics]) ).

fof(normalize_0_14,plain,
    ! [L,M] : ~ left_convergent_lines(L,M),
    inference(conjunct,[],[normalize_0_13]) ).

fof(normalize_0_15,plain,
    ! [L,M] : ~ left_convergent_lines(L,M),
    inference(specialize,[],[normalize_0_14]) ).

fof(normalize_0_16,plain,
    ! [L,M] :
      ( ~ convergent_lines(L,M)
      | unequally_directed_lines(L,M) ),
    inference(conjunct,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    ( ~ convergent_lines(L,M)
    | unequally_directed_opposite_lines(L,M) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_2,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
    | unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
    inference(subst,[],[refute_0_1:[bind(L,$fot(skolemFOFtoCNF_L)),bind(M,$fot(skolemFOFtoCNF_M))]]) ).

cnf(refute_0_3,plain,
    unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ unequally_directed_opposite_lines(X,Y)
    | unequally_directed_lines(X,reverse_line(Y)) ),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_5,plain,
    ( ~ unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
    | unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_M))]]) ).

cnf(refute_0_6,plain,
    unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)),
    inference(resolve,[$cnf( unequally_directed_opposite_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_3,refute_0_5]) ).

cnf(refute_0_7,plain,
    ( ~ unequally_directed_lines(L,M)
    | ~ unequally_directed_lines(L,reverse_line(M))
    | left_convergent_lines(L,M)
    | left_convergent_lines(L,reverse_line(M)) ),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_8,plain,
    ~ left_convergent_lines(L,M),
    inference(canonicalize,[],[normalize_0_15]) ).

cnf(refute_0_9,plain,
    ( ~ unequally_directed_lines(L,M)
    | ~ unequally_directed_lines(L,reverse_line(M))
    | left_convergent_lines(L,reverse_line(M)) ),
    inference(resolve,[$cnf( left_convergent_lines(L,M) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    ~ left_convergent_lines(L,reverse_line(M)),
    inference(subst,[],[refute_0_8:[bind(M,$fot(reverse_line(M)))]]) ).

cnf(refute_0_11,plain,
    ( ~ unequally_directed_lines(L,M)
    | ~ unequally_directed_lines(L,reverse_line(M)) ),
    inference(resolve,[$cnf( left_convergent_lines(L,reverse_line(M)) )],[refute_0_9,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( ~ unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M))
    | ~ unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
    inference(subst,[],[refute_0_11:[bind(L,$fot(skolemFOFtoCNF_L)),bind(M,$fot(skolemFOFtoCNF_M))]]) ).

cnf(refute_0_13,plain,
    ~ unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L,reverse_line(skolemFOFtoCNF_M)) )],[refute_0_6,refute_0_12]) ).

cnf(refute_0_14,plain,
    ( ~ convergent_lines(L,M)
    | unequally_directed_lines(L,M) ),
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_15,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
    | unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
    inference(subst,[],[refute_0_14:[bind(L,$fot(skolemFOFtoCNF_L)),bind(M,$fot(skolemFOFtoCNF_M))]]) ).

cnf(refute_0_16,plain,
    unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_0,refute_0_15]) ).

cnf(refute_0_17,plain,
    $false,
    inference(resolve,[$cnf( unequally_directed_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_16,refute_0_13]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : GEO261+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n011.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 : Sat Jun 18 18:25:38 EDT 2022
% 0.19/0.34  % CPUTime  : 
% 0.19/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.37  
% 0.19/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.19/0.38  
%------------------------------------------------------------------------------