%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO264+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n007.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 05:26:01 EDT 2022

% Result   : Theorem 0.14s 0.38s
% Output   : CNFRefutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :    2
% Syntax   : Number of formulae    :   14 (   7 unt;   0 def)
%            Number of atoms       :   31 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :   27 (  10   ~;   1   |;  12   &)
%                                         (   0 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   28 (   2 sgn  22   !;   4   ?)

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

fof(con,conjecture,
    ! [A,B,C,D] :
      ( left_apart_point(C,line_connecting(A,B))
     => ( ( right_apart_point(D,line_connecting(B,C))
          & right_apart_point(D,line_connecting(C,A)) )
       => left_apart_point(D,line_connecting(A,B)) ) ) ).

fof(subgoal_0,plain,
    ! [A,B,C,D] :
      ( ( left_apart_point(C,line_connecting(A,B))
        & right_apart_point(D,line_connecting(B,C))
        & right_apart_point(D,line_connecting(C,A)) )
     => left_apart_point(D,line_connecting(A,B)) ),
    inference(strip,[],[con]) ).

fof(negate_0_0,plain,
    ~ ! [A,B,C,D] :
        ( ( left_apart_point(C,line_connecting(A,B))
          & right_apart_point(D,line_connecting(B,C))
          & right_apart_point(D,line_connecting(C,A)) )
       => left_apart_point(D,line_connecting(A,B)) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [A,B,C,D] :
      ( ~ left_apart_point(D,line_connecting(A,B))
      & left_apart_point(C,line_connecting(A,B))
      & right_apart_point(D,line_connecting(B,C))
      & right_apart_point(D,line_connecting(C,A)) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( ~ left_apart_point(skolemFOFtoCNF_D,line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B))
    & left_apart_point(skolemFOFtoCNF_C,line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B))
    & right_apart_point(skolemFOFtoCNF_D,line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_C))
    & right_apart_point(skolemFOFtoCNF_D,line_connecting(skolemFOFtoCNF_C,skolemFOFtoCNF_A)) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    left_apart_point(skolemFOFtoCNF_C,line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B)),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ( ! [A,L] : ~ left_apart_point(A,L)
    & ! [A,L] : ~ left_apart_point(A,reverse_line(L)) ),
    inference(canonicalize,[],[ax10_basics]) ).

fof(normalize_0_4,plain,
    ! [A,L] : ~ left_apart_point(A,L),
    inference(conjunct,[],[normalize_0_3]) ).

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

cnf(refute_0_0,plain,
    left_apart_point(skolemFOFtoCNF_C,line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B)),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    ~ left_apart_point(A,L),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_2,plain,
    ~ left_apart_point(skolemFOFtoCNF_C,line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B)),
    inference(subst,[],[refute_0_1:[bind(A,$fot(skolemFOFtoCNF_C)),bind(L,$fot(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B)))]]) ).

cnf(refute_0_3,plain,
    $false,
    inference(resolve,[$cnf( left_apart_point(skolemFOFtoCNF_C,line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B)) )],[refute_0_0,refute_0_2]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : GEO264+3 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14  % Command  : metis --show proof --show saturation %s
% 0.14/0.35  % Computer : n007.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 600
% 0.14/0.35  % DateTime : Sat Jun 18 14:04:58 EDT 2022
% 0.14/0.35  % CPUTime  : 
% 0.14/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.14/0.38  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.38  
% 0.14/0.38  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.14/0.38  
%------------------------------------------------------------------------------