TSTP Solution File: GEO201+2 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO201+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n008.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 05:25:16 EDT 2022

% Result   : Theorem 2.92s 3.09s
% Output   : CNFRefutation 2.92s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   73 (  20 unt;   0 def)
%            Number of atoms       :  183 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  178 (  68   ~;  96   |;   6   &)
%                                         (   0 <=>;   8  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   95 (   0 sgn  57   !;   2   ?)

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

fof(apart3,axiom,
    ! [X] : ~ convergent_lines(X,X) ).

fof(apart6,axiom,
    ! [X,Y,Z] :
      ( convergent_lines(X,Y)
     => ( convergent_lines(X,Z)
        | convergent_lines(Y,Z) ) ) ).

fof(con2,axiom,
    ! [X,Y,Z] :
      ( convergent_lines(X,Y)
     => ( ( apart_point_and_line(Z,X)
          | apart_point_and_line(Z,Y) )
       => distinct_points(Z,intersection_point(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(ceq3,axiom,
    ! [X,Y] :
      ( convergent_lines(X,Y)
     => distinct_lines(X,Y) ) ).

fof(con,conjecture,
    ! [X,Y] :
      ( convergent_lines(X,Y)
     => ~ distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ) ).

fof(subgoal_0,plain,
    ! [X,Y] :
      ( convergent_lines(X,Y)
     => ~ distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ),
    inference(strip,[],[con]) ).

fof(negate_0_0,plain,
    ~ ! [X,Y] :
        ( convergent_lines(X,Y)
       => ~ distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ),
    inference(negate,[],[subgoal_0]) ).

fof(normalize_0_0,plain,
    ? [X,Y] :
      ( convergent_lines(X,Y)
      & distinct_points(intersection_point(X,Y),intersection_point(Y,X)) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_1,plain,
    ( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
    & distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) ),
    inference(skolemize,[],[normalize_0_0]) ).

fof(normalize_0_2,plain,
    convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
    inference(conjunct,[],[normalize_0_1]) ).

fof(normalize_0_3,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | distinct_points(Z,intersection_point(X,Y))
      | ( ~ apart_point_and_line(Z,X)
        & ~ apart_point_and_line(Z,Y) ) ),
    inference(canonicalize,[],[con2]) ).

fof(normalize_0_4,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | distinct_points(Z,intersection_point(X,Y))
      | ( ~ apart_point_and_line(Z,X)
        & ~ apart_point_and_line(Z,Y) ) ),
    inference(specialize,[],[normalize_0_3]) ).

fof(normalize_0_5,plain,
    ! [X,Y,Z] :
      ( ( ~ apart_point_and_line(Z,X)
        | ~ convergent_lines(X,Y)
        | distinct_points(Z,intersection_point(X,Y)) )
      & ( ~ apart_point_and_line(Z,Y)
        | ~ convergent_lines(X,Y)
        | distinct_points(Z,intersection_point(X,Y)) ) ),
    inference(clausify,[],[normalize_0_4]) ).

fof(normalize_0_6,plain,
    ! [X,Y,Z] :
      ( ~ apart_point_and_line(Z,X)
      | ~ convergent_lines(X,Y)
      | distinct_points(Z,intersection_point(X,Y)) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_7,plain,
    ! [X,Y,Z] :
      ( ~ apart_point_and_line(Z,Y)
      | ~ convergent_lines(X,Y)
      | distinct_points(Z,intersection_point(X,Y)) ),
    inference(conjunct,[],[normalize_0_5]) ).

fof(normalize_0_8,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | convergent_lines(X,Z)
      | convergent_lines(Y,Z) ),
    inference(canonicalize,[],[apart6]) ).

fof(normalize_0_9,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | convergent_lines(X,Z)
      | convergent_lines(Y,Z) ),
    inference(specialize,[],[normalize_0_8]) ).

fof(normalize_0_10,plain,
    ! [X] : ~ convergent_lines(X,X),
    inference(canonicalize,[],[apart3]) ).

fof(normalize_0_11,plain,
    ! [X] : ~ convergent_lines(X,X),
    inference(specialize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
      | distinct_lines(X,Y) ),
    inference(canonicalize,[],[ceq3]) ).

fof(normalize_0_13,plain,
    ! [X,Y] :
      ( ~ convergent_lines(X,Y)
      | distinct_lines(X,Y) ),
    inference(specialize,[],[normalize_0_12]) ).

fof(normalize_0_14,plain,
    distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)),
    inference(conjunct,[],[normalize_0_1]) ).

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

fof(normalize_0_18,plain,
    ! [X] : ~ distinct_points(X,X),
    inference(specialize,[],[normalize_0_17]) ).

cnf(refute_0_0,plain,
    convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
    inference(canonicalize,[],[normalize_0_2]) ).

cnf(refute_0_1,plain,
    ( ~ apart_point_and_line(Z,X)
    | ~ convergent_lines(X,Y)
    | distinct_points(Z,intersection_point(X,Y)) ),
    inference(canonicalize,[],[normalize_0_6]) ).

cnf(refute_0_2,plain,
    ( ~ apart_point_and_line(X_46,skolemFOFtoCNF_X)
    | ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
    | distinct_points(X_46,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_46))]]) ).

cnf(refute_0_3,plain,
    ( ~ apart_point_and_line(X_46,skolemFOFtoCNF_X)
    | distinct_points(X_46,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_0,refute_0_2]) ).

cnf(refute_0_4,plain,
    ( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
    | distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(subst,[],[refute_0_3:[bind(X_46,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).

cnf(refute_0_5,plain,
    ( ~ apart_point_and_line(Z,Y)
    | ~ convergent_lines(X,Y)
    | distinct_points(Z,intersection_point(X,Y)) ),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_6,plain,
    ( ~ apart_point_and_line(X_51,skolemFOFtoCNF_Y)
    | ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
    | distinct_points(X_51,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_51))]]) ).

cnf(refute_0_7,plain,
    ( ~ apart_point_and_line(X_51,skolemFOFtoCNF_Y)
    | distinct_points(X_51,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_0,refute_0_6]) ).

cnf(refute_0_8,plain,
    ( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
    | distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(subst,[],[refute_0_7:[bind(X_51,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).

cnf(refute_0_9,plain,
    ( ~ convergent_lines(X,Y)
    | convergent_lines(X,Z)
    | convergent_lines(Y,Z) ),
    inference(canonicalize,[],[normalize_0_9]) ).

cnf(refute_0_10,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_Y,X_23)
    | convergent_lines(X_23,Z)
    | convergent_lines(skolemFOFtoCNF_Y,Z) ),
    inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(X_23))]]) ).

cnf(refute_0_11,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
    | convergent_lines(skolemFOFtoCNF_X,X_22)
    | convergent_lines(skolemFOFtoCNF_Y,X_22) ),
    inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_22))]]) ).

cnf(refute_0_12,plain,
    ( convergent_lines(skolemFOFtoCNF_X,X_22)
    | convergent_lines(skolemFOFtoCNF_Y,X_22) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_0,refute_0_11]) ).

cnf(refute_0_13,plain,
    ( convergent_lines(skolemFOFtoCNF_X,X_23)
    | convergent_lines(skolemFOFtoCNF_Y,X_23) ),
    inference(subst,[],[refute_0_12:[bind(X_22,$fot(X_23))]]) ).

cnf(refute_0_14,plain,
    ( convergent_lines(X_23,Z)
    | convergent_lines(skolemFOFtoCNF_X,X_23)
    | convergent_lines(skolemFOFtoCNF_Y,Z) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Y,X_23) )],[refute_0_13,refute_0_10]) ).

cnf(refute_0_15,plain,
    ( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X)
    | convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_X) ),
    inference(subst,[],[refute_0_14:[bind(Z,$fot(skolemFOFtoCNF_X)),bind(X_23,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_16,plain,
    ~ convergent_lines(X,X),
    inference(canonicalize,[],[normalize_0_11]) ).

cnf(refute_0_17,plain,
    ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
    inference(subst,[],[refute_0_16:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_18,plain,
    convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_15,refute_0_17]) ).

cnf(refute_0_19,plain,
    ( ~ apart_point_and_line(X_51,skolemFOFtoCNF_X)
    | ~ convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)
    | distinct_points(X_51,intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) ),
    inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_X)),bind(Z,$fot(X_51))]]) ).

cnf(refute_0_20,plain,
    ( ~ apart_point_and_line(X_51,skolemFOFtoCNF_X)
    | distinct_points(X_51,intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_X) )],[refute_0_18,refute_0_19]) ).

cnf(refute_0_21,plain,
    ( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_X)
    | distinct_points(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) ),
    inference(subst,[],[refute_0_20:[bind(X_51,$fot(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)))]]) ).

cnf(refute_0_22,plain,
    ( ~ apart_point_and_line(X_46,skolemFOFtoCNF_Y)
    | ~ convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)
    | distinct_points(X_46,intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) ),
    inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_X)),bind(Z,$fot(X_46))]]) ).

cnf(refute_0_23,plain,
    ( ~ apart_point_and_line(X_46,skolemFOFtoCNF_Y)
    | distinct_points(X_46,intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_X) )],[refute_0_18,refute_0_22]) ).

cnf(refute_0_24,plain,
    ( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_Y)
    | distinct_points(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) ),
    inference(subst,[],[refute_0_23:[bind(X_46,$fot(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)))]]) ).

cnf(refute_0_25,plain,
    ( ~ convergent_lines(X,Y)
    | distinct_lines(X,Y) ),
    inference(canonicalize,[],[normalize_0_13]) ).

cnf(refute_0_26,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
    | distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
    inference(subst,[],[refute_0_25:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).

cnf(refute_0_27,plain,
    distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_0,refute_0_26]) ).

cnf(refute_0_28,plain,
    distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_29,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_30,plain,
    ( ~ distinct_lines(X_293,X_294)
    | ~ distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_293)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_294)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),X_293)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),X_294) ),
    inference(subst,[],[refute_0_29:[bind(U,$fot(X_293)),bind(V,$fot(X_294)),bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)))]]) ).

cnf(refute_0_31,plain,
    ( ~ distinct_lines(X_293,X_294)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_293)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_294)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),X_293)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),X_294) ),
    inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) )],[refute_0_28,refute_0_30]) ).

cnf(refute_0_32,plain,
    ( ~ distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_X)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_Y) ),
    inference(subst,[],[refute_0_31:[bind(X_293,$fot(skolemFOFtoCNF_X)),bind(X_294,$fot(skolemFOFtoCNF_Y))]]) ).

cnf(refute_0_33,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_X)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_Y) ),
    inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_27,refute_0_32]) ).

cnf(refute_0_34,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_X)
    | distinct_points(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) ),
    inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_Y) )],[refute_0_33,refute_0_24]) ).

cnf(refute_0_35,plain,
    ~ distinct_points(X,X),
    inference(canonicalize,[],[normalize_0_18]) ).

cnf(refute_0_36,plain,
    ~ distinct_points(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)),
    inference(subst,[],[refute_0_35:[bind(X,$fot(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)))]]) ).

cnf(refute_0_37,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_X) ),
    inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) )],[refute_0_34,refute_0_36]) ).

cnf(refute_0_38,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y)
    | distinct_points(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) ),
    inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),skolemFOFtoCNF_X) )],[refute_0_37,refute_0_21]) ).

cnf(refute_0_39,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y) ),
    inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),intersection_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) )],[refute_0_38,refute_0_36]) ).

cnf(refute_0_40,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
    | distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
    inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Y) )],[refute_0_39,refute_0_8]) ).

cnf(refute_0_41,plain,
    ~ distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
    inference(subst,[],[refute_0_35:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).

cnf(refute_0_42,plain,
    apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X),
    inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_40,refute_0_41]) ).

cnf(refute_0_43,plain,
    distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
    inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X) )],[refute_0_42,refute_0_4]) ).

cnf(refute_0_44,plain,
    $false,
    inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_43,refute_0_41]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : GEO201+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13  % Command  : metis --show proof --show saturation %s
% 0.13/0.34  % Computer : n008.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 600
% 0.13/0.34  % DateTime : Fri Jun 17 17:06:22 EDT 2022
% 0.13/0.35  % CPUTime  : 
% 0.13/0.35  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.92/3.09  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.92/3.09  
% 2.92/3.09  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.92/3.09  
%------------------------------------------------------------------------------