TSTP Solution File: GEO191+3 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO191+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n020.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 05:25:08 EDT 2022

% Result   : Theorem 0.57s 0.77s
% Output   : CNFRefutation 0.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :    7
% Syntax   : Number of formulae    :   70 (  25 unt;   0 def)
%            Number of atoms       :  157 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  128 (  41   ~;  65   |;  16   &)
%                                         (   0 <=>;   6  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :  113 (  21 sgn  51   !;   4   ?)

% 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(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,U,V] :
      ( ( convergent_lines(X,Y)
        & convergent_lines(U,V)
        & ( apart_point_and_line(intersection_point(X,Y),U)
          | apart_point_and_line(intersection_point(X,Y),V) ) )
     => ( apart_point_and_line(intersection_point(U,V),X)
        | apart_point_and_line(intersection_point(U,V),Y) ) ) ).

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

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

fof(normalize_0_0,plain,
    ! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
    inference(canonicalize,[],[cp1]) ).

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

fof(normalize_0_2,plain,
    ! [X,Y] :
      ( ~ distinct_lines(X,Y)
      | convergent_lines(X,Y) ),
    inference(canonicalize,[],[p1]) ).

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

fof(normalize_0_4,plain,
    ! [X,Y,Z] :
      ( ~ distinct_lines(X,Y)
      | distinct_lines(X,Z)
      | distinct_lines(Y,Z) ),
    inference(canonicalize,[],[apart5]) ).

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

fof(normalize_0_6,plain,
    ! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
    inference(canonicalize,[],[cp2]) ).

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

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(canonicalize,[],[ceq2]) ).

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

fof(normalize_0_10,plain,
    ? [U,V,X,Y] :
      ( ~ apart_point_and_line(intersection_point(U,V),X)
      & ~ apart_point_and_line(intersection_point(U,V),Y)
      & convergent_lines(U,V)
      & convergent_lines(X,Y)
      & ( apart_point_and_line(intersection_point(X,Y),U)
        | apart_point_and_line(intersection_point(X,Y),V) ) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_11,plain,
    ( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_X)
    & ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_Y)
    & convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
    & convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
    & ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
      | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_V) ) ),
    inference(skolemize,[],[normalize_0_10]) ).

fof(normalize_0_12,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_V) ),
    inference(conjunct,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [X] : ~ distinct_lines(X,X),
    inference(canonicalize,[],[apart2]) ).

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

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

cnf(refute_0_1,plain,
    ~ convergent_lines(parallel_through_point(skolemFOFtoCNF_U,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U),
    inference(subst,[],[refute_0_0:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(skolemFOFtoCNF_U))]]) ).

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

cnf(refute_0_3,plain,
    ( ~ distinct_lines(parallel_through_point(X_649,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U)
    | convergent_lines(parallel_through_point(X_649,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(parallel_through_point(X_649,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))),bind(Y,$fot(skolemFOFtoCNF_U))]]) ).

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

cnf(refute_0_5,plain,
    ( ~ distinct_lines(parallel_through_point(X_648,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),X_647)
    | distinct_lines(X_647,Z)
    | distinct_lines(parallel_through_point(X_648,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),Z) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(parallel_through_point(X_648,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))),bind(Y,$fot(X_647))]]) ).

cnf(refute_0_6,plain,
    ( ~ distinct_lines(skolemFOFtoCNF_U,parallel_through_point(X_585,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))
    | distinct_lines(parallel_through_point(X_585,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),Z)
    | distinct_lines(skolemFOFtoCNF_U,Z) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(parallel_through_point(X_585,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))))]]) ).

cnf(refute_0_7,plain,
    ~ apart_point_and_line(X,parallel_through_point(Y,X)),
    inference(canonicalize,[],[normalize_0_7]) ).

cnf(refute_0_8,plain,
    ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),
    inference(subst,[],[refute_0_7:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).

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_9]) ).

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

cnf(refute_0_11,plain,
    ~ convergent_lines(parallel_through_point(skolemFOFtoCNF_V,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V),
    inference(subst,[],[refute_0_0:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(skolemFOFtoCNF_V))]]) ).

cnf(refute_0_12,plain,
    ( ~ distinct_lines(parallel_through_point(X_581,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V)
    | convergent_lines(parallel_through_point(X_581,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V) ),
    inference(subst,[],[refute_0_2:[bind(X,$fot(parallel_through_point(X_581,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))),bind(Y,$fot(skolemFOFtoCNF_V))]]) ).

cnf(refute_0_13,plain,
    ( ~ distinct_lines(parallel_through_point(X_580,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),X_579)
    | distinct_lines(X_579,Z)
    | distinct_lines(parallel_through_point(X_580,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),Z) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(parallel_through_point(X_580,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))),bind(Y,$fot(X_579))]]) ).

cnf(refute_0_14,plain,
    ( ~ distinct_lines(skolemFOFtoCNF_V,parallel_through_point(X_92,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))
    | distinct_lines(parallel_through_point(X_92,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),Z)
    | distinct_lines(skolemFOFtoCNF_V,Z) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_V)),bind(Y,$fot(parallel_through_point(X_92,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))))]]) ).

cnf(refute_0_15,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_V) ),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_16,plain,
    ( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_V)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_89)
    | distinct_lines(skolemFOFtoCNF_V,X_89) ),
    inference(subst,[],[refute_0_9:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(skolemFOFtoCNF_V)),bind(Z,$fot(X_89))]]) ).

cnf(refute_0_17,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_89)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
    | distinct_lines(skolemFOFtoCNF_V,X_89) ),
    inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_V) )],[refute_0_15,refute_0_16]) ).

cnf(refute_0_18,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
    | distinct_lines(skolemFOFtoCNF_V,parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))) ),
    inference(subst,[],[refute_0_17:[bind(X_89,$fot(parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))))]]) ).

cnf(refute_0_19,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
    | distinct_lines(skolemFOFtoCNF_V,parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))) ),
    inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))) )],[refute_0_18,refute_0_8]) ).

cnf(refute_0_20,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
    | distinct_lines(skolemFOFtoCNF_V,parallel_through_point(X_92,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))) ),
    inference(subst,[],[refute_0_19:[bind(Y,$fot(X_92))]]) ).

cnf(refute_0_21,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
    | distinct_lines(parallel_through_point(X_92,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),Z)
    | distinct_lines(skolemFOFtoCNF_V,Z) ),
    inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_V,parallel_through_point(X_92,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))) )],[refute_0_20,refute_0_14]) ).

cnf(refute_0_22,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
    | distinct_lines(parallel_through_point(X_580,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),X_579)
    | distinct_lines(skolemFOFtoCNF_V,X_579) ),
    inference(subst,[],[refute_0_21:[bind(Z,$fot(X_579)),bind(X_92,$fot(X_580))]]) ).

cnf(refute_0_23,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
    | distinct_lines(X_579,Z)
    | distinct_lines(parallel_through_point(X_580,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),Z)
    | distinct_lines(skolemFOFtoCNF_V,X_579) ),
    inference(resolve,[$cnf( distinct_lines(parallel_through_point(X_580,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),X_579) )],[refute_0_22,refute_0_13]) ).

cnf(refute_0_24,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
    | distinct_lines(parallel_through_point(X_580,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V)
    | distinct_lines(skolemFOFtoCNF_V,skolemFOFtoCNF_V) ),
    inference(subst,[],[refute_0_23:[bind(Z,$fot(skolemFOFtoCNF_V)),bind(X_579,$fot(skolemFOFtoCNF_V))]]) ).

cnf(refute_0_25,plain,
    ~ distinct_lines(X,X),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_26,plain,
    ~ distinct_lines(skolemFOFtoCNF_V,skolemFOFtoCNF_V),
    inference(subst,[],[refute_0_25:[bind(X,$fot(skolemFOFtoCNF_V))]]) ).

cnf(refute_0_27,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
    | distinct_lines(parallel_through_point(X_580,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V) ),
    inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_V,skolemFOFtoCNF_V) )],[refute_0_24,refute_0_26]) ).

cnf(refute_0_28,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
    | distinct_lines(parallel_through_point(X_581,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V) ),
    inference(subst,[],[refute_0_27:[bind(X_580,$fot(X_581))]]) ).

cnf(refute_0_29,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
    | convergent_lines(parallel_through_point(X_581,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V) ),
    inference(resolve,[$cnf( distinct_lines(parallel_through_point(X_581,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V) )],[refute_0_28,refute_0_12]) ).

cnf(refute_0_30,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)
    | convergent_lines(parallel_through_point(skolemFOFtoCNF_V,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V) ),
    inference(subst,[],[refute_0_29:[bind(X_581,$fot(skolemFOFtoCNF_V))]]) ).

cnf(refute_0_31,plain,
    apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U),
    inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_V,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_V) )],[refute_0_30,refute_0_11]) ).

cnf(refute_0_32,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z)
    | distinct_lines(skolemFOFtoCNF_U,Z) ),
    inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U) )],[refute_0_31,refute_0_10]) ).

cnf(refute_0_33,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))
    | distinct_lines(skolemFOFtoCNF_U,parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))) ),
    inference(subst,[],[refute_0_32:[bind(Z,$fot(parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))))]]) ).

cnf(refute_0_34,plain,
    distinct_lines(skolemFOFtoCNF_U,parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),
    inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),parallel_through_point(Y,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))) )],[refute_0_33,refute_0_8]) ).

cnf(refute_0_35,plain,
    distinct_lines(skolemFOFtoCNF_U,parallel_through_point(X_585,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),
    inference(subst,[],[refute_0_34:[bind(Y,$fot(X_585))]]) ).

cnf(refute_0_36,plain,
    ( distinct_lines(parallel_through_point(X_585,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),Z)
    | distinct_lines(skolemFOFtoCNF_U,Z) ),
    inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_U,parallel_through_point(X_585,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))) )],[refute_0_35,refute_0_6]) ).

cnf(refute_0_37,plain,
    ( distinct_lines(parallel_through_point(X_648,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),X_647)
    | distinct_lines(skolemFOFtoCNF_U,X_647) ),
    inference(subst,[],[refute_0_36:[bind(Z,$fot(X_647)),bind(X_585,$fot(X_648))]]) ).

cnf(refute_0_38,plain,
    ( distinct_lines(X_647,Z)
    | distinct_lines(parallel_through_point(X_648,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),Z)
    | distinct_lines(skolemFOFtoCNF_U,X_647) ),
    inference(resolve,[$cnf( distinct_lines(parallel_through_point(X_648,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),X_647) )],[refute_0_37,refute_0_5]) ).

cnf(refute_0_39,plain,
    ( distinct_lines(parallel_through_point(X_648,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U)
    | distinct_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
    inference(subst,[],[refute_0_38:[bind(Z,$fot(skolemFOFtoCNF_U)),bind(X_647,$fot(skolemFOFtoCNF_U))]]) ).

cnf(refute_0_40,plain,
    ~ distinct_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_U),
    inference(subst,[],[refute_0_25:[bind(X,$fot(skolemFOFtoCNF_U))]]) ).

cnf(refute_0_41,plain,
    distinct_lines(parallel_through_point(X_648,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U),
    inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_U) )],[refute_0_39,refute_0_40]) ).

cnf(refute_0_42,plain,
    distinct_lines(parallel_through_point(X_649,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U),
    inference(subst,[],[refute_0_41:[bind(X_648,$fot(X_649))]]) ).

cnf(refute_0_43,plain,
    convergent_lines(parallel_through_point(X_649,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U),
    inference(resolve,[$cnf( distinct_lines(parallel_through_point(X_649,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U) )],[refute_0_42,refute_0_3]) ).

cnf(refute_0_44,plain,
    convergent_lines(parallel_through_point(skolemFOFtoCNF_U,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U),
    inference(subst,[],[refute_0_43:[bind(X_649,$fot(skolemFOFtoCNF_U))]]) ).

cnf(refute_0_45,plain,
    $false,
    inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_U,intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),skolemFOFtoCNF_U) )],[refute_0_44,refute_0_1]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : GEO191+3 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.14  % Command  : metis --show proof --show saturation %s
% 0.15/0.36  % Computer : n020.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 600
% 0.15/0.36  % DateTime : Sat Jun 18 06:06:49 EDT 2022
% 0.15/0.36  % CPUTime  : 
% 0.15/0.36  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.57/0.77  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.57/0.77  
% 0.57/0.77  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.57/0.78  
%------------------------------------------------------------------------------