TSTP Solution File: GEO177+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO177+1 : TPTP v8.1.0. Released v3.3.0.
% 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 05:24:55 EDT 2022

% Result   : Theorem 2.91s 3.15s
% Output   : CNFRefutation 2.91s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   68 (  16 unt;   0 def)
%            Number of atoms       :  199 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  193 (  62   ~; 106   |;  16   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   98 (   0 sgn  57   !;   4   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(apart1,axiom,
    ! [X] : ~ distinct_points(X,X) ).

fof(ci1,axiom,
    ! [X,Y] :
      ( distinct_points(X,Y)
     => ~ apart_point_and_line(X,line_connecting(X,Y)) ) ).

fof(ci2,axiom,
    ! [X,Y] :
      ( distinct_points(X,Y)
     => ~ apart_point_and_line(Y,line_connecting(X,Y)) ) ).

fof(cu1,axiom,
    ! [X,Y,U,V] :
      ( ( distinct_points(X,Y)
        & distinct_lines(U,V) )
     => ( apart_point_and_line(X,U)
        | apart_point_and_line(X,V)
        | apart_point_and_line(Y,U)
        | apart_point_and_line(Y,V) ) ) ).

fof(ceq1,axiom,
    ! [X,Y,Z] :
      ( apart_point_and_line(X,Y)
     => ( distinct_points(X,Z)
        | apart_point_and_line(Z,Y) ) ) ).

fof(ceq2,axiom,
    ! [X,Y,Z] :
      ( apart_point_and_line(X,Y)
     => ( distinct_lines(Y,Z)
        | apart_point_and_line(X,Z) ) ) ).

fof(con,conjecture,
    ! [X,Y,U,V] :
      ( ( distinct_points(X,Y)
        & distinct_points(U,V) )
     => ( ( apart_point_and_line(X,line_connecting(U,V))
          | apart_point_and_line(Y,line_connecting(U,V)) )
       => ( apart_point_and_line(U,line_connecting(X,Y))
          | apart_point_and_line(V,line_connecting(X,Y)) ) ) ) ).

fof(subgoal_0,plain,
    ! [X,Y,U,V] :
      ( ( distinct_points(X,Y)
        & distinct_points(U,V)
        & ( apart_point_and_line(X,line_connecting(U,V))
          | apart_point_and_line(Y,line_connecting(U,V)) )
        & ~ apart_point_and_line(U,line_connecting(X,Y)) )
     => apart_point_and_line(V,line_connecting(X,Y)) ),
    inference(strip,[],[con]) ).

fof(negate_0_0,plain,
    ~ ! [X,Y,U,V] :
        ( ( distinct_points(X,Y)
          & distinct_points(U,V)
          & ( apart_point_and_line(X,line_connecting(U,V))
            | apart_point_and_line(Y,line_connecting(U,V)) )
          & ~ apart_point_and_line(U,line_connecting(X,Y)) )
       => apart_point_and_line(V,line_connecting(X,Y)) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ! [X,Y] :
      ( ~ apart_point_and_line(X,line_connecting(X,Y))
      | ~ distinct_points(X,Y) ),
    inference(canonicalize,[],[ci1]) ).

fof(normalize_0_1,plain,
    ! [X,Y] :
      ( ~ apart_point_and_line(X,line_connecting(X,Y))
      | ~ distinct_points(X,Y) ),
    inference(specialize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    ! [X,Y] :
      ( ~ apart_point_and_line(Y,line_connecting(X,Y))
      | ~ distinct_points(X,Y) ),
    inference(canonicalize,[],[ci2]) ).

fof(normalize_0_3,plain,
    ! [X,Y] :
      ( ~ apart_point_and_line(Y,line_connecting(X,Y))
      | ~ distinct_points(X,Y) ),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ? [U,V,X,Y] :
      ( ~ apart_point_and_line(U,line_connecting(X,Y))
      & ~ apart_point_and_line(V,line_connecting(X,Y))
      & distinct_points(U,V)
      & distinct_points(X,Y)
      & ( apart_point_and_line(X,line_connecting(U,V))
        | apart_point_and_line(Y,line_connecting(U,V)) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_5,plain,
    ( ~ apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    & ~ apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    & distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
    & distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
    & ( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
      | apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ) ),
    inference(skolemize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X,Y,Z] :
      ( ~ apart_point_and_line(X,Y)
      | apart_point_and_line(X,Z)
      | distinct_lines(Y,Z) ),
    inference(canonicalize,[],[ceq2]) ).

fof(normalize_0_8,plain,
    ! [X,Y,Z] :
      ( ~ apart_point_and_line(X,Y)
      | apart_point_and_line(X,Z)
      | distinct_lines(Y,Z) ),
    inference(specialize,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_10,plain,
    ! [X,Y,Z] :
      ( ~ apart_point_and_line(X,Y)
      | apart_point_and_line(Z,Y)
      | distinct_points(X,Z) ),
    inference(canonicalize,[],[ceq1]) ).

fof(normalize_0_11,plain,
    ! [X,Y,Z] :
      ( ~ apart_point_and_line(X,Y)
      | apart_point_and_line(Z,Y)
      | distinct_points(X,Z) ),
    inference(specialize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [X] : ~ distinct_points(X,X),
    inference(canonicalize,[],[apart1]) ).

fof(normalize_0_13,plain,
    ! [X] : ~ distinct_points(X,X),
    inference(specialize,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_15,plain,
    ! [U,V,X,Y] :
      ( ~ distinct_lines(U,V)
      | ~ distinct_points(X,Y)
      | apart_point_and_line(X,U)
      | apart_point_and_line(X,V)
      | apart_point_and_line(Y,U)
      | apart_point_and_line(Y,V) ),
    inference(canonicalize,[],[cu1]) ).

fof(normalize_0_16,plain,
    ! [U,V,X,Y] :
      ( ~ distinct_lines(U,V)
      | ~ distinct_points(X,Y)
      | apart_point_and_line(X,U)
      | apart_point_and_line(X,V)
      | apart_point_and_line(Y,U)
      | apart_point_and_line(Y,V) ),
    inference(specialize,[],[normalize_0_15]) ).

fof(normalize_0_17,plain,
    ~ apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_18,plain,
    ~ apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
    inference(conjunct,[],[normalize_0_5]) ).

cnf(refute_0_0,plain,
    ( ~ apart_point_and_line(X,line_connecting(X,Y))
    | ~ distinct_points(X,Y) ),
    inference(canonicalize,[],[normalize_0_1]) ).

cnf(refute_0_1,plain,
    ( ~ apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | ~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V) ),
    inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(skolemFOFtoCNF_V))]]) ).

cnf(refute_0_2,plain,
    ( ~ apart_point_and_line(Y,line_connecting(X,Y))
    | ~ distinct_points(X,Y) ),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_3,plain,
    ( ~ apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | ~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(skolemFOFtoCNF_V))]]) ).

cnf(refute_0_4,plain,
    ( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    | ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
    inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).

cnf(refute_0_5,plain,
    distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_6,plain,
    ( ~ apart_point_and_line(X_99,line_connecting(X,X_99))
    | ~ distinct_points(X,X_99) ),
    inference(subst,[],[refute_0_2:[bind(Y,$fot(X_99))]]) ).

cnf(refute_0_7,plain,
    ( ~ apart_point_and_line(X,Y)
    | apart_point_and_line(X,Z)
    | distinct_lines(Y,Z) ),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_8,plain,
    ( ~ apart_point_and_line(X_58,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(X_58,Z)
    | distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z) ),
    inference(subst,[],[refute_0_7:[bind(X,$fot(X_58)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).

cnf(refute_0_9,plain,
    ( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_10,plain,
    ( ~ apart_point_and_line(X,Y)
    | apart_point_and_line(Z,Y)
    | distinct_points(X,Z) ),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_11,plain,
    ( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(X_24,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | distinct_points(skolemFOFtoCNF_Y,X_24) ),
    inference(subst,[],[refute_0_10:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(Z,$fot(X_24))]]) ).

cnf(refute_0_12,plain,
    ( apart_point_and_line(X_24,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | distinct_points(skolemFOFtoCNF_Y,X_24) ),
    inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_9,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(skolemFOFtoCNF_X,X_29)
    | distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_29) ),
    inference(subst,[],[refute_0_7:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(Z,$fot(X_29))]]) ).

cnf(refute_0_14,plain,
    ( apart_point_and_line(X_24,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(skolemFOFtoCNF_X,X_29)
    | distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_29)
    | distinct_points(skolemFOFtoCNF_Y,X_24) ),
    inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_12,refute_0_13]) ).

cnf(refute_0_15,plain,
    ( apart_point_and_line(X_58,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(skolemFOFtoCNF_X,X_59)
    | distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_59)
    | distinct_points(skolemFOFtoCNF_Y,X_58) ),
    inference(subst,[],[refute_0_14:[bind(X_24,$fot(X_58)),bind(X_29,$fot(X_59))]]) ).

cnf(refute_0_16,plain,
    ( apart_point_and_line(X_58,Z)
    | apart_point_and_line(skolemFOFtoCNF_X,X_59)
    | distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z)
    | distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_59)
    | distinct_points(skolemFOFtoCNF_Y,X_58) ),
    inference(resolve,[$cnf( apart_point_and_line(X_58,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_15,refute_0_8]) ).

cnf(refute_0_17,plain,
    ( apart_point_and_line(X_99,line_connecting(X,X_99))
    | apart_point_and_line(skolemFOFtoCNF_X,line_connecting(X,X_99))
    | distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(X,X_99))
    | distinct_points(skolemFOFtoCNF_Y,X_99) ),
    inference(subst,[],[refute_0_16:[bind(Z,$fot(line_connecting(X,X_99))),bind(X_58,$fot(X_99)),bind(X_59,$fot(line_connecting(X,X_99)))]]) ).

cnf(refute_0_18,plain,
    ( ~ distinct_points(X,X_99)
    | apart_point_and_line(skolemFOFtoCNF_X,line_connecting(X,X_99))
    | distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(X,X_99))
    | distinct_points(skolemFOFtoCNF_Y,X_99) ),
    inference(resolve,[$cnf( apart_point_and_line(X_99,line_connecting(X,X_99)) )],[refute_0_17,refute_0_6]) ).

cnf(refute_0_19,plain,
    ( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
    | apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    | distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    | distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
    inference(subst,[],[refute_0_18:[bind(X,$fot(skolemFOFtoCNF_X)),bind(X_99,$fot(skolemFOFtoCNF_Y))]]) ).

cnf(refute_0_20,plain,
    ( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    | distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    | distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
    inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_5,refute_0_19]) ).

cnf(refute_0_21,plain,
    ~ distinct_points(X,X),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_22,plain,
    ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
    inference(subst,[],[refute_0_21:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).

cnf(refute_0_23,plain,
    ( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    | distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_20,refute_0_22]) ).

cnf(refute_0_24,plain,
    distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_25,plain,
    ( ~ distinct_lines(U,V)
    | ~ distinct_points(X,Y)
    | apart_point_and_line(X,U)
    | apart_point_and_line(X,V)
    | apart_point_and_line(Y,U)
    | apart_point_and_line(Y,V) ),
    inference(canonicalize,[],[normalize_0_16]) ).

cnf(refute_0_26,plain,
    ( ~ distinct_lines(X_332,X_333)
    | ~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
    | apart_point_and_line(skolemFOFtoCNF_U,X_332)
    | apart_point_and_line(skolemFOFtoCNF_U,X_333)
    | apart_point_and_line(skolemFOFtoCNF_V,X_332)
    | apart_point_and_line(skolemFOFtoCNF_V,X_333) ),
    inference(subst,[],[refute_0_25:[bind(U,$fot(X_332)),bind(V,$fot(X_333)),bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(skolemFOFtoCNF_V))]]) ).

cnf(refute_0_27,plain,
    ( ~ distinct_lines(X_332,X_333)
    | apart_point_and_line(skolemFOFtoCNF_U,X_332)
    | apart_point_and_line(skolemFOFtoCNF_U,X_333)
    | apart_point_and_line(skolemFOFtoCNF_V,X_332)
    | apart_point_and_line(skolemFOFtoCNF_V,X_333) ),
    inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_24,refute_0_26]) ).

cnf(refute_0_28,plain,
    ( ~ distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    | apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    | apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(subst,[],[refute_0_27:[bind(X_332,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(X_333,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).

cnf(refute_0_29,plain,
    ( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    | apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    | apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_23,refute_0_28]) ).

cnf(refute_0_30,plain,
    ~ apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
    inference(canonicalize,[],[normalize_0_17]) ).

cnf(refute_0_31,plain,
    ( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    | apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_29,refute_0_30]) ).

cnf(refute_0_32,plain,
    ~ apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
    inference(canonicalize,[],[normalize_0_18]) ).

cnf(refute_0_33,plain,
    ( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_31,refute_0_32]) ).

cnf(refute_0_34,plain,
    ( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
    | apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
    inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_33,refute_0_4]) ).

cnf(refute_0_35,plain,
    ( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
    inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_5,refute_0_34]) ).

cnf(refute_0_36,plain,
    ( ~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
    | apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
    inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_35,refute_0_3]) ).

cnf(refute_0_37,plain,
    apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
    inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_24,refute_0_36]) ).

cnf(refute_0_38,plain,
    ~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
    inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_37,refute_0_1]) ).

cnf(refute_0_39,plain,
    $false,
    inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_24,refute_0_38]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.21  % Problem  : GEO177+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.21  % Command  : metis --show proof --show saturation %s
% 0.13/0.42  % Computer : n007.cluster.edu
% 0.13/0.42  % Model    : x86_64 x86_64
% 0.13/0.42  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.42  % Memory   : 8042.1875MB
% 0.13/0.42  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.42  % CPULimit : 300
% 0.13/0.42  % WCLimit  : 600
% 0.13/0.42  % DateTime : Fri Jun 17 23:11:13 EDT 2022
% 0.13/0.42  % CPUTime  : 
% 0.13/0.43  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.91/3.15  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.91/3.15  
% 2.91/3.15  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.91/3.15  
%------------------------------------------------------------------------------