%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO257+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n009.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 05:25:57 EDT 2022

% Result   : Theorem 0.12s 0.36s
% Output   : CNFRefutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   15 (   8 unt;   0 def)
%            Number of atoms       :   47 (   0 equ)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives :   42 (  10   ~;   1   |;  27   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   5 con; 0-1 aty)
%            Number of variables   :   34 (   2 sgn  25   !;   7   ?)

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

fof(con,conjecture,
    ! [L,A,B,C,D] :
      ( ( distinct_points(A,C)
        & distinct_points(B,C)
        & incident_point_and_line(C,L)
        & left_apart_point(D,L) )
     => ( ( before_on_line(L,A,B)
          & before_on_line(L,B,C) )
       => before_on_line(L,A,C) ) ) ).

fof(subgoal_0,plain,
    ! [L,A,B,C,D] :
      ( ( distinct_points(A,C)
        & distinct_points(B,C)
        & incident_point_and_line(C,L)
        & left_apart_point(D,L)
        & before_on_line(L,A,B)
        & before_on_line(L,B,C) )
     => before_on_line(L,A,C) ),
    inference(strip,[],[con]) ).

fof(negate_0_0,plain,
    ~ ! [L,A,B,C,D] :
        ( ( distinct_points(A,C)
          & distinct_points(B,C)
          & incident_point_and_line(C,L)
          & left_apart_point(D,L)
          & before_on_line(L,A,B)
          & before_on_line(L,B,C) )
       => before_on_line(L,A,C) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [A,B,C,L] :
      ( ~ before_on_line(L,A,C)
      & before_on_line(L,A,B)
      & before_on_line(L,B,C)
      & distinct_points(A,C)
      & distinct_points(B,C)
      & incident_point_and_line(C,L)
      & ? [D] : left_apart_point(D,L) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ~ before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_C)
    & before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
    & before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
    & distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_C)
    & distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_C)
    & incident_point_and_line(skolemFOFtoCNF_C,skolemFOFtoCNF_L)
    & ? [D] : left_apart_point(D,skolemFOFtoCNF_L) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ? [D] : left_apart_point(D,skolemFOFtoCNF_L),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    left_apart_point(skolemFOFtoCNF_D,skolemFOFtoCNF_L),
    inference(skolemize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ( ! [A,L] : ~ left_apart_point(A,L)
    & ! [A,L] : ~ left_apart_point(A,reverse_line(L)) ),
    inference(canonicalize,[],[ax10_basics]) ).

fof(normalize_0_5,plain,
    ! [A,L] : ~ left_apart_point(A,L),
    inference(conjunct,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [A,L] : ~ left_apart_point(A,L),
    inference(specialize,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    left_apart_point(skolemFOFtoCNF_D,skolemFOFtoCNF_L),
    inference(canonicalize,[],[normalize_0_3]) ).

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

cnf(refute_0_2,plain,
    ~ left_apart_point(skolemFOFtoCNF_D,skolemFOFtoCNF_L),
    inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_D)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).

cnf(refute_0_3,plain,
    $false,
    inference(resolve,[$cnf( left_apart_point(skolemFOFtoCNF_D,skolemFOFtoCNF_L) )],[refute_0_0,refute_0_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO257+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n009.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 Jun 18 00:47:07 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.36  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36  
% 0.12/0.36  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.36  
%------------------------------------------------------------------------------