TSTP Solution File: GEO262+1 by Metis---2.4

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%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO262+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n013.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 0.20s 0.37s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :    4
% Syntax   : Number of formulae    :   25 (   9 unt;   0 def)
%            Number of atoms       :   76 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :   85 (  34   ~;  14   |;  30   &)
%                                         (   3 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   5 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    6 (   5 usr;   1 prp; 0-4 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :   58 (   6 sgn  42   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(con_def,axiom,
    ! [L,M] :
      ( convergent_lines(L,M)
    <=> ( unequally_directed_lines(L,M)
        & unequally_directed_lines(L,reverse_line(M)) ) ) ).

fof(oag9,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(oag11,axiom,
    ! [L,M] :
      ~ ( left_convergent_lines(L,M)
        | left_convergent_lines(L,reverse_line(M)) ) ).

fof(con,conjecture,
    ! [L,M,N,A,B,C] :
      ( ( between_on_line(L,A,B,C)
        & convergent_lines(L,M)
        & ~ apart_point_and_line(B,M)
        & convergent_lines(L,N)
        & convergent_lines(M,N)
        & ~ apart_point_and_line(B,N) )
     => between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C))) ) ).

fof(subgoal_0,plain,
    ! [L,M,N,A,B,C] :
      ( ( between_on_line(L,A,B,C)
        & convergent_lines(L,M)
        & ~ apart_point_and_line(B,M)
        & convergent_lines(L,N)
        & convergent_lines(M,N)
        & ~ apart_point_and_line(B,N) )
     => between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C))) ),
    inference(strip,[],[con]) ).

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

fof(normalize_0_0,plain,
    ? [A,B,C,L,M,N] :
      ( ~ apart_point_and_line(B,M)
      & ~ apart_point_and_line(B,N)
      & ~ between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C)))
      & between_on_line(L,A,B,C)
      & convergent_lines(L,M)
      & convergent_lines(L,N)
      & convergent_lines(M,N) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ~ apart_point_and_line(skolemFOFtoCNF_B,skolemFOFtoCNF_M)
    & ~ apart_point_and_line(skolemFOFtoCNF_B,skolemFOFtoCNF_N)
    & ~ between_on_line(skolemFOFtoCNF_M,intersection_point(skolemFOFtoCNF_M,parallel_through_point(skolemFOFtoCNF_N,skolemFOFtoCNF_A)),skolemFOFtoCNF_B,intersection_point(skolemFOFtoCNF_M,parallel_through_point(skolemFOFtoCNF_N,skolemFOFtoCNF_C)))
    & between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
    & convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
    & convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
    & convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) ),
    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] :
      ( ~ 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,[],[oag9]) ).

fof(normalize_0_4,plain,
    ! [L,M] :
      ( ~ convergent_lines(L,M)
    <=> ( ~ unequally_directed_lines(L,M)
        | ~ unequally_directed_lines(L,reverse_line(M)) ) ),
    inference(canonicalize,[],[con_def]) ).

fof(normalize_0_5,plain,
    ! [L,M] :
      ( ~ convergent_lines(L,M)
    <=> ( ~ unequally_directed_lines(L,M)
        | ~ unequally_directed_lines(L,reverse_line(M)) ) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [L,M] :
      ( ~ convergent_lines(L,M)
      | left_convergent_lines(L,M)
      | left_convergent_lines(L,reverse_line(M)) ),
    inference(simplify,[],[normalize_0_3,normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [L,M] :
      ( ~ convergent_lines(L,M)
      | left_convergent_lines(L,M)
      | left_convergent_lines(L,reverse_line(M)) ),
    inference(specialize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ( ! [L,M] : ~ left_convergent_lines(L,M)
    & ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
    inference(canonicalize,[],[oag11]) ).

fof(normalize_0_9,plain,
    ! [L,M] : ~ left_convergent_lines(L,M),
    inference(conjunct,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [L,M] : ~ left_convergent_lines(L,M),
    inference(specialize,[],[normalize_0_9]) ).

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)
    | left_convergent_lines(L,M)
    | left_convergent_lines(L,reverse_line(M)) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_2,plain,
    ~ left_convergent_lines(L,M),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_3,plain,
    ( ~ convergent_lines(L,M)
    | left_convergent_lines(L,reverse_line(M)) ),
    inference(resolve,[$cnf( left_convergent_lines(L,M) )],[refute_0_1,refute_0_2]) ).

cnf(refute_0_4,plain,
    ~ left_convergent_lines(L,reverse_line(M)),
    inference(subst,[],[refute_0_2:[bind(M,$fot(reverse_line(M)))]]) ).

cnf(refute_0_5,plain,
    ~ convergent_lines(L,M),
    inference(resolve,[$cnf( left_convergent_lines(L,reverse_line(M)) )],[refute_0_3,refute_0_4]) ).

cnf(refute_0_6,plain,
    ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
    inference(subst,[],[refute_0_5:[bind(L,$fot(skolemFOFtoCNF_L)),bind(M,$fot(skolemFOFtoCNF_M))]]) ).

cnf(refute_0_7,plain,
    $false,
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_0,refute_0_6]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13  % Problem  : GEO262+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.13/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.35  % Computer : n013.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.20/0.35  % WCLimit  : 600
% 0.20/0.35  % DateTime : Sat Jun 18 12:34:59 EDT 2022
% 0.20/0.35  % CPUTime  : 
% 0.20/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.37  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.37  
% 0.20/0.37  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.37  
%------------------------------------------------------------------------------