TSTP Solution File: GEO179+3 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO179+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n015.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 05:24:57 EDT 2022

% Result   : Theorem 0.20s 0.39s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   86 (  30 unt;   0 def)
%            Number of atoms       :  177 (   0 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  154 (  63   ~;  62   |;  18   &)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    8 (   8 usr;   6 con; 0-2 aty)
%            Number of variables   :  129 (   4 sgn  81   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(apart2,axiom,
    ! [X] : ~ distinct_lines(X,X) ).

fof(apart5,axiom,
    ! [X,Y,Z] :
      ( distinct_lines(X,Y)
     => ( distinct_lines(X,Z)
        | distinct_lines(Y,Z) ) ) ).

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(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(p1,axiom,
    ! [X,Y] :
      ( distinct_lines(X,Y)
     => convergent_lines(X,Y) ) ).

fof(cp1,axiom,
    ! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) ).

fof(cp2,axiom,
    ! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) ).

fof(con,conjecture,
    ! [X,Y,Z] :
      ( ( distinct_points(X,Y)
        & apart_point_and_line(Z,line_connecting(X,Y)) )
     => ( distinct_lines(line_connecting(X,Y),line_connecting(Z,X))
        & distinct_lines(line_connecting(X,Y),line_connecting(Z,Y)) ) ) ).

fof(subgoal_0,plain,
    ! [X,Y,Z] :
      ( ( distinct_points(X,Y)
        & apart_point_and_line(Z,line_connecting(X,Y)) )
     => distinct_lines(line_connecting(X,Y),line_connecting(Z,X)) ),
    inference(strip,[],[con]) ).

fof(subgoal_1,plain,
    ! [X,Y,Z] :
      ( ( distinct_points(X,Y)
        & apart_point_and_line(Z,line_connecting(X,Y))
        & distinct_lines(line_connecting(X,Y),line_connecting(Z,X)) )
     => distinct_lines(line_connecting(X,Y),line_connecting(Z,Y)) ),
    inference(strip,[],[con]) ).

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

fof(normalize_0_0,plain,
    ! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
    inference(canonicalize,[],[cp2]) ).

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

fof(normalize_0_2,plain,
    ! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
    inference(canonicalize,[],[cp1]) ).

fof(normalize_0_3,plain,
    ! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
    inference(specialize,[],[normalize_0_2]) ).

fof(normalize_0_4,plain,
    ! [X,Y] :
      ( ~ distinct_lines(X,Y)
      | convergent_lines(X,Y) ),
    inference(canonicalize,[],[p1]) ).

fof(normalize_0_5,plain,
    ! [X,Y] :
      ( ~ distinct_lines(X,Y)
      | convergent_lines(X,Y) ),
    inference(specialize,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X] : ~ distinct_lines(X,X),
    inference(canonicalize,[],[apart2]) ).

fof(normalize_0_7,plain,
    ! [X] : ~ distinct_lines(X,X),
    inference(specialize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    ? [X,Y,Z] :
      ( ~ distinct_lines(line_connecting(X,Y),line_connecting(Z,X))
      & apart_point_and_line(Z,line_connecting(X,Y))
      & distinct_points(X,Y) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_9,plain,
    ( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
    & apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    & distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
    inference(skolemize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
    inference(conjunct,[],[normalize_0_9]) ).

fof(normalize_0_11,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_12,plain,
    ! [X,Y,Z] :
      ( ~ apart_point_and_line(X,Y)
      | apart_point_and_line(X,Z)
      | distinct_lines(Y,Z) ),
    inference(specialize,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [X,Y,Z] :
      ( ~ distinct_lines(X,Y)
      | distinct_lines(X,Z)
      | distinct_lines(Y,Z) ),
    inference(canonicalize,[],[apart5]) ).

fof(normalize_0_14,plain,
    ! [X,Y,Z] :
      ( ~ distinct_lines(X,Y)
      | distinct_lines(X,Z)
      | distinct_lines(Y,Z) ),
    inference(specialize,[],[normalize_0_13]) ).

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

cnf(refute_0_1,plain,
    ~ apart_point_and_line(skolemFOFtoCNF_Z,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)),
    inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).

cnf(refute_0_2,plain,
    ~ convergent_lines(parallel_through_point(Y,X),Y),
    inference(canonicalize,[],[normalize_0_3]) ).

cnf(refute_0_3,plain,
    ~ convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
    inference(subst,[],[refute_0_2:[bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).

cnf(refute_0_4,plain,
    ( ~ distinct_lines(X,Y)
    | convergent_lines(X,Y) ),
    inference(canonicalize,[],[normalize_0_5]) ).

cnf(refute_0_5,plain,
    ( ~ distinct_lines(X_78,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    | convergent_lines(X_78,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(X_78)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).

cnf(refute_0_6,plain,
    ~ distinct_lines(X,X),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_7,plain,
    ~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
    inference(subst,[],[refute_0_6:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).

cnf(refute_0_8,plain,
    apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_9,plain,
    ( ~ apart_point_and_line(X,Y)
    | apart_point_and_line(X,Z)
    | distinct_lines(Y,Z) ),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_10,plain,
    ( ~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    | apart_point_and_line(skolemFOFtoCNF_Z,X_55)
    | distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_55) ),
    inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Z,$fot(X_55))]]) ).

cnf(refute_0_11,plain,
    ( apart_point_and_line(skolemFOFtoCNF_Z,X_55)
    | distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_55) ),
    inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_8,refute_0_10]) ).

cnf(refute_0_12,plain,
    ( apart_point_and_line(skolemFOFtoCNF_Z,X_73)
    | distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_73) ),
    inference(subst,[],[refute_0_11:[bind(X_55,$fot(X_73))]]) ).

cnf(refute_0_13,plain,
    ( ~ distinct_lines(X,Y)
    | distinct_lines(X,Z)
    | distinct_lines(Y,Z) ),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_14,plain,
    ( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_73)
    | distinct_lines(X_73,X_74)
    | distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_74) ),
    inference(subst,[],[refute_0_13:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(X_73)),bind(Z,$fot(X_74))]]) ).

cnf(refute_0_15,plain,
    ( apart_point_and_line(skolemFOFtoCNF_Z,X_73)
    | distinct_lines(X_73,X_74)
    | distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_74) ),
    inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_73) )],[refute_0_12,refute_0_14]) ).

cnf(refute_0_16,plain,
    ( apart_point_and_line(skolemFOFtoCNF_Z,X_75)
    | distinct_lines(X_75,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
    | distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(subst,[],[refute_0_15:[bind(X_73,$fot(X_75)),bind(X_74,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).

cnf(refute_0_17,plain,
    ( apart_point_and_line(skolemFOFtoCNF_Z,X_75)
    | distinct_lines(X_75,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_16,refute_0_7]) ).

cnf(refute_0_18,plain,
    ( apart_point_and_line(skolemFOFtoCNF_Z,X_78)
    | distinct_lines(X_78,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(subst,[],[refute_0_17:[bind(X_75,$fot(X_78))]]) ).

cnf(refute_0_19,plain,
    ( apart_point_and_line(skolemFOFtoCNF_Z,X_78)
    | convergent_lines(X_78,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(resolve,[$cnf( distinct_lines(X_78,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_18,refute_0_5]) ).

cnf(refute_0_20,plain,
    ( apart_point_and_line(skolemFOFtoCNF_Z,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X))
    | convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(subst,[],[refute_0_19:[bind(X_78,$fot(parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X)))]]) ).

cnf(refute_0_21,plain,
    apart_point_and_line(skolemFOFtoCNF_Z,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X)),
    inference(resolve,[$cnf( convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_20,refute_0_3]) ).

cnf(refute_0_22,plain,
    apart_point_and_line(skolemFOFtoCNF_Z,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)),
    inference(subst,[],[refute_0_21:[bind(X,$fot(skolemFOFtoCNF_Z))]]) ).

cnf(refute_0_23,plain,
    $false,
    inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)) )],[refute_0_22,refute_0_1]) ).

fof(negate_1_0,plain,
    ~ ! [X,Y,Z] :
        ( ( distinct_points(X,Y)
          & apart_point_and_line(Z,line_connecting(X,Y))
          & distinct_lines(line_connecting(X,Y),line_connecting(Z,X)) )
       => distinct_lines(line_connecting(X,Y),line_connecting(Z,Y)) ),
    inference(negate,[],[subgoal_1]) ).

fof(normalize_1_0,plain,
    ! [X,Y] :
      ( ~ apart_point_and_line(X,line_connecting(X,Y))
      | ~ distinct_points(X,Y) ),
    inference(canonicalize,[],[ci1]) ).

fof(normalize_1_1,plain,
    ! [X,Y] :
      ( ~ apart_point_and_line(X,line_connecting(X,Y))
      | ~ distinct_points(X,Y) ),
    inference(specialize,[],[normalize_1_0]) ).

fof(normalize_1_2,plain,
    ? [X,Y,Z] :
      ( ~ distinct_lines(line_connecting(X,Y),line_connecting(Z,Y))
      & apart_point_and_line(Z,line_connecting(X,Y))
      & distinct_lines(line_connecting(X,Y),line_connecting(Z,X))
      & distinct_points(X,Y) ),
    inference(canonicalize,[],[negate_1_0]) ).

fof(normalize_1_3,plain,
    ( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1))
    & apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
    & distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_X_1))
    & distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
    inference(skolemize,[],[normalize_1_2]) ).

fof(normalize_1_4,plain,
    ~ distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)),
    inference(conjunct,[],[normalize_1_3]) ).

fof(normalize_1_5,plain,
    apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
    inference(conjunct,[],[normalize_1_3]) ).

fof(normalize_1_6,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_1_7,plain,
    ! [X,Y,Z] :
      ( ~ apart_point_and_line(X,Y)
      | apart_point_and_line(X,Z)
      | distinct_lines(Y,Z) ),
    inference(specialize,[],[normalize_1_6]) ).

fof(normalize_1_8,plain,
    ! [X,Y] :
      ( ~ apart_point_and_line(Y,line_connecting(X,Y))
      | ~ distinct_points(X,Y) ),
    inference(canonicalize,[],[ci2]) ).

fof(normalize_1_9,plain,
    ! [X,Y] :
      ( ~ apart_point_and_line(Y,line_connecting(X,Y))
      | ~ distinct_points(X,Y) ),
    inference(specialize,[],[normalize_1_8]) ).

fof(normalize_1_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_1_11,plain,
    ! [X,Y,Z] :
      ( ~ apart_point_and_line(X,Y)
      | apart_point_and_line(Z,Y)
      | distinct_points(X,Z) ),
    inference(specialize,[],[normalize_1_10]) ).

fof(normalize_1_12,plain,
    distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
    inference(conjunct,[],[normalize_1_3]) ).

cnf(refute_1_0,plain,
    ( ~ apart_point_and_line(X,line_connecting(X,Y))
    | ~ distinct_points(X,Y) ),
    inference(canonicalize,[],[normalize_1_1]) ).

cnf(refute_1_1,plain,
    ( ~ apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1))
    | ~ distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
    inference(subst,[],[refute_1_0:[bind(X,$fot(skolemFOFtoCNF_Z_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).

cnf(refute_1_2,plain,
    ~ distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)),
    inference(canonicalize,[],[normalize_1_4]) ).

cnf(refute_1_3,plain,
    apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
    inference(canonicalize,[],[normalize_1_5]) ).

cnf(refute_1_4,plain,
    ( ~ apart_point_and_line(X,Y)
    | apart_point_and_line(X,Z)
    | distinct_lines(Y,Z) ),
    inference(canonicalize,[],[normalize_1_7]) ).

cnf(refute_1_5,plain,
    ( ~ apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
    | apart_point_and_line(skolemFOFtoCNF_Z_1,X_176)
    | distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_176) ),
    inference(subst,[],[refute_1_4:[bind(X,$fot(skolemFOFtoCNF_Z_1)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Z,$fot(X_176))]]) ).

cnf(refute_1_6,plain,
    ( apart_point_and_line(skolemFOFtoCNF_Z_1,X_176)
    | distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_176) ),
    inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_3,refute_1_5]) ).

cnf(refute_1_7,plain,
    ( apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1))
    | distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)) ),
    inference(subst,[],[refute_1_6:[bind(X_176,$fot(line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)))]]) ).

cnf(refute_1_8,plain,
    apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)),
    inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)) )],[refute_1_7,refute_1_2]) ).

cnf(refute_1_9,plain,
    ~ distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1),
    inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)) )],[refute_1_8,refute_1_1]) ).

cnf(refute_1_10,plain,
    ( ~ apart_point_and_line(Y,line_connecting(X,Y))
    | ~ distinct_points(X,Y) ),
    inference(canonicalize,[],[normalize_1_9]) ).

cnf(refute_1_11,plain,
    ( ~ apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
    | ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
    inference(subst,[],[refute_1_10:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).

cnf(refute_1_12,plain,
    ( ~ apart_point_and_line(X,Y)
    | apart_point_and_line(Z,Y)
    | distinct_points(X,Z) ),
    inference(canonicalize,[],[normalize_1_11]) ).

cnf(refute_1_13,plain,
    ( ~ apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
    | apart_point_and_line(X_159,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
    | distinct_points(skolemFOFtoCNF_Z_1,X_159) ),
    inference(subst,[],[refute_1_12:[bind(X,$fot(skolemFOFtoCNF_Z_1)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Z,$fot(X_159))]]) ).

cnf(refute_1_14,plain,
    ( apart_point_and_line(X_159,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
    | distinct_points(skolemFOFtoCNF_Z_1,X_159) ),
    inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_3,refute_1_13]) ).

cnf(refute_1_15,plain,
    ( apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
    | distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
    inference(subst,[],[refute_1_14:[bind(X_159,$fot(skolemFOFtoCNF_Y_1))]]) ).

cnf(refute_1_16,plain,
    ( ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
    | distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
    inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_15,refute_1_11]) ).

cnf(refute_1_17,plain,
    distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
    inference(canonicalize,[],[normalize_1_12]) ).

cnf(refute_1_18,plain,
    distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1),
    inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_17,refute_1_16]) ).

cnf(refute_1_19,plain,
    $false,
    inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) )],[refute_1_18,refute_1_9]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem  : GEO179+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12  % Command  : metis --show proof --show saturation %s
% 0.14/0.33  % Computer : n015.cluster.edu
% 0.14/0.33  % Model    : x86_64 x86_64
% 0.14/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33  % Memory   : 8042.1875MB
% 0.14/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33  % CPULimit : 300
% 0.14/0.33  % WCLimit  : 600
% 0.14/0.33  % DateTime : Fri Jun 17 19:31:57 EDT 2022
% 0.14/0.34  % CPUTime  : 
% 0.14/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.39  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.39  
% 0.20/0.39  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.40  
%------------------------------------------------------------------------------