TSTP Solution File: GEO186+1 by Metis---2.4

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Metis---2.4
% Problem  : GEO186+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : metis --show proof --show saturation %s

% Computer : n029.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 05:25:03 EDT 2022

% Result   : Theorem 1.21s 1.40s
% Output   : CNFRefutation 1.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   24
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   82 (  24 unt;   0 def)
%            Number of atoms       :  209 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  201 (  74   ~; 100   |;  18   &)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :  125 (   0 sgn  69   !;   4   ?)

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

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

fof(apart4,axiom,
    ! [X,Y,Z] :
      ( distinct_points(X,Y)
     => ( distinct_points(X,Z)
        | distinct_points(Y,Z) ) ) ).

fof(ax6,axiom,
    ! [X,Y,Z] :
      ( convergent_lines(X,Y)
     => ( convergent_lines(X,Z)
        | convergent_lines(Y,Z) ) ) ).

fof(ci3,axiom,
    ! [X,Y] :
      ( convergent_lines(X,Y)
     => ~ apart_point_and_line(intersection_point(X,Y),X) ) ).

fof(ci4,axiom,
    ! [X,Y] :
      ( convergent_lines(X,Y)
     => ~ apart_point_and_line(intersection_point(X,Y),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,Z] :
      ( convergent_lines(X,Y)
     => ( distinct_lines(Y,Z)
        | convergent_lines(X,Z) ) ) ).

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

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

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

fof(normalize_0_0,plain,
    ! [X,Y] :
      ( ~ apart_point_and_line(intersection_point(X,Y),X)
      | ~ convergent_lines(X,Y) ),
    inference(canonicalize,[],[ci3]) ).

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

fof(normalize_0_2,plain,
    ! [X,Y] :
      ( ~ apart_point_and_line(intersection_point(X,Y),Y)
      | ~ convergent_lines(X,Y) ),
    inference(canonicalize,[],[ci4]) ).

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

fof(normalize_0_4,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | convergent_lines(X,Z)
      | convergent_lines(Y,Z) ),
    inference(canonicalize,[],[ax6]) ).

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

fof(normalize_0_6,plain,
    ? [U,V,X,Y] :
      ( ~ apart_point_and_line(X,U)
      & ~ apart_point_and_line(X,V)
      & convergent_lines(U,V)
      & distinct_points(X,Y)
      & distinct_points(X,intersection_point(U,V)) ),
    inference(canonicalize,[],[negate_0_0]) ).

fof(normalize_0_7,plain,
    ( ~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
    & ~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V)
    & convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
    & distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    & distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
    inference(skolemize,[],[normalize_0_6]) ).

fof(normalize_0_8,plain,
    convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_9,plain,
    ! [X] : ~ convergent_lines(X,X),
    inference(canonicalize,[],[apart3]) ).

fof(normalize_0_10,plain,
    ! [X] : ~ convergent_lines(X,X),
    inference(specialize,[],[normalize_0_9]) ).

fof(normalize_0_11,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | convergent_lines(X,Z)
      | distinct_lines(Y,Z) ),
    inference(canonicalize,[],[ceq3]) ).

fof(normalize_0_12,plain,
    ! [X,Y,Z] :
      ( ~ convergent_lines(X,Y)
      | convergent_lines(X,Z)
      | distinct_lines(Y,Z) ),
    inference(specialize,[],[normalize_0_11]) ).

fof(normalize_0_13,plain,
    ! [X,Y,Z] :
      ( ~ distinct_points(X,Y)
      | distinct_points(X,Z)
      | distinct_points(Y,Z) ),
    inference(canonicalize,[],[apart4]) ).

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

fof(normalize_0_15,plain,
    distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_16,plain,
    ! [X] : ~ distinct_points(X,X),
    inference(canonicalize,[],[apart1]) ).

fof(normalize_0_17,plain,
    ! [X] : ~ distinct_points(X,X),
    inference(specialize,[],[normalize_0_16]) ).

fof(normalize_0_18,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_19,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_18]) ).

fof(normalize_0_20,plain,
    ~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U),
    inference(conjunct,[],[normalize_0_7]) ).

fof(normalize_0_21,plain,
    ~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V),
    inference(conjunct,[],[normalize_0_7]) ).

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

cnf(refute_0_1,plain,
    ( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
    | ~ convergent_lines(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(intersection_point(X,Y),Y)
    | ~ convergent_lines(X,Y) ),
    inference(canonicalize,[],[normalize_0_3]) ).

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

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

cnf(refute_0_5,plain,
    ( ~ convergent_lines(X_31,X_30)
    | convergent_lines(X_30,Z)
    | convergent_lines(X_31,Z) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(X_31)),bind(Y,$fot(X_30))]]) ).

cnf(refute_0_6,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_V,X_29)
    | convergent_lines(X_29,Z)
    | convergent_lines(skolemFOFtoCNF_V,Z) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_V)),bind(Y,$fot(X_29))]]) ).

cnf(refute_0_7,plain,
    convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
    inference(canonicalize,[],[normalize_0_8]) ).

cnf(refute_0_8,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
    | convergent_lines(skolemFOFtoCNF_U,X_28)
    | convergent_lines(skolemFOFtoCNF_V,X_28) ),
    inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(skolemFOFtoCNF_V)),bind(Z,$fot(X_28))]]) ).

cnf(refute_0_9,plain,
    ( convergent_lines(skolemFOFtoCNF_U,X_28)
    | convergent_lines(skolemFOFtoCNF_V,X_28) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_7,refute_0_8]) ).

cnf(refute_0_10,plain,
    ( convergent_lines(skolemFOFtoCNF_U,X_29)
    | convergent_lines(skolemFOFtoCNF_V,X_29) ),
    inference(subst,[],[refute_0_9:[bind(X_28,$fot(X_29))]]) ).

cnf(refute_0_11,plain,
    ( convergent_lines(X_29,Z)
    | convergent_lines(skolemFOFtoCNF_U,X_29)
    | convergent_lines(skolemFOFtoCNF_V,Z) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_V,X_29) )],[refute_0_10,refute_0_6]) ).

cnf(refute_0_12,plain,
    ( convergent_lines(X_31,X_30)
    | convergent_lines(skolemFOFtoCNF_U,X_31)
    | convergent_lines(skolemFOFtoCNF_V,X_30) ),
    inference(subst,[],[refute_0_11:[bind(Z,$fot(X_30)),bind(X_29,$fot(X_31))]]) ).

cnf(refute_0_13,plain,
    ( convergent_lines(X_30,Z)
    | convergent_lines(X_31,Z)
    | convergent_lines(skolemFOFtoCNF_U,X_31)
    | convergent_lines(skolemFOFtoCNF_V,X_30) ),
    inference(resolve,[$cnf( convergent_lines(X_31,X_30) )],[refute_0_12,refute_0_5]) ).

cnf(refute_0_14,plain,
    ( convergent_lines(X_30,skolemFOFtoCNF_U)
    | convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_U)
    | convergent_lines(skolemFOFtoCNF_V,X_30) ),
    inference(subst,[],[refute_0_13:[bind(Z,$fot(skolemFOFtoCNF_U)),bind(X_31,$fot(skolemFOFtoCNF_U))]]) ).

cnf(refute_0_15,plain,
    ~ convergent_lines(X,X),
    inference(canonicalize,[],[normalize_0_10]) ).

cnf(refute_0_16,plain,
    ~ convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_U),
    inference(subst,[],[refute_0_15:[bind(X,$fot(skolemFOFtoCNF_U))]]) ).

cnf(refute_0_17,plain,
    ( convergent_lines(X_30,skolemFOFtoCNF_U)
    | convergent_lines(skolemFOFtoCNF_V,X_30) ),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_U) )],[refute_0_14,refute_0_16]) ).

cnf(refute_0_18,plain,
    ( convergent_lines(X_37,skolemFOFtoCNF_U)
    | convergent_lines(skolemFOFtoCNF_V,X_37) ),
    inference(subst,[],[refute_0_17:[bind(X_30,$fot(X_37))]]) ).

cnf(refute_0_19,plain,
    ( ~ convergent_lines(X,Y)
    | convergent_lines(X,Z)
    | distinct_lines(Y,Z) ),
    inference(canonicalize,[],[normalize_0_12]) ).

cnf(refute_0_20,plain,
    ( ~ convergent_lines(X_37,skolemFOFtoCNF_U)
    | convergent_lines(X_37,X_39)
    | distinct_lines(skolemFOFtoCNF_U,X_39) ),
    inference(subst,[],[refute_0_19:[bind(X,$fot(X_37)),bind(Y,$fot(skolemFOFtoCNF_U)),bind(Z,$fot(X_39))]]) ).

cnf(refute_0_21,plain,
    ( convergent_lines(X_37,X_39)
    | convergent_lines(skolemFOFtoCNF_V,X_37)
    | distinct_lines(skolemFOFtoCNF_U,X_39) ),
    inference(resolve,[$cnf( convergent_lines(X_37,skolemFOFtoCNF_U) )],[refute_0_18,refute_0_20]) ).

cnf(refute_0_22,plain,
    ( convergent_lines(skolemFOFtoCNF_V,skolemFOFtoCNF_V)
    | distinct_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V) ),
    inference(subst,[],[refute_0_21:[bind(X_37,$fot(skolemFOFtoCNF_V)),bind(X_39,$fot(skolemFOFtoCNF_V))]]) ).

cnf(refute_0_23,plain,
    ~ convergent_lines(skolemFOFtoCNF_V,skolemFOFtoCNF_V),
    inference(subst,[],[refute_0_15:[bind(X,$fot(skolemFOFtoCNF_V))]]) ).

cnf(refute_0_24,plain,
    distinct_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_V,skolemFOFtoCNF_V) )],[refute_0_22,refute_0_23]) ).

cnf(refute_0_25,plain,
    ( ~ distinct_points(X,Y)
    | distinct_points(X,Z)
    | distinct_points(Y,Z) ),
    inference(canonicalize,[],[normalize_0_14]) ).

cnf(refute_0_26,plain,
    ( ~ distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_18)
    | distinct_points(X_18,Z)
    | distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z) ),
    inference(subst,[],[refute_0_25:[bind(X,$fot(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(Y,$fot(X_18))]]) ).

cnf(refute_0_27,plain,
    distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
    inference(canonicalize,[],[normalize_0_15]) ).

cnf(refute_0_28,plain,
    ( ~ distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
    | distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_16)
    | distinct_points(skolemFOFtoCNF_X,X_16) ),
    inference(subst,[],[refute_0_25:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(Z,$fot(X_16))]]) ).

cnf(refute_0_29,plain,
    ( distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_16)
    | distinct_points(skolemFOFtoCNF_X,X_16) ),
    inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_27,refute_0_28]) ).

cnf(refute_0_30,plain,
    ( distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_18)
    | distinct_points(skolemFOFtoCNF_X,X_18) ),
    inference(subst,[],[refute_0_29:[bind(X_16,$fot(X_18))]]) ).

cnf(refute_0_31,plain,
    ( distinct_points(X_18,Z)
    | distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z)
    | distinct_points(skolemFOFtoCNF_X,X_18) ),
    inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_18) )],[refute_0_30,refute_0_26]) ).

cnf(refute_0_32,plain,
    ( distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_X)
    | distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
    inference(subst,[],[refute_0_31:[bind(Z,$fot(skolemFOFtoCNF_X)),bind(X_18,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_33,plain,
    ~ distinct_points(X,X),
    inference(canonicalize,[],[normalize_0_17]) ).

cnf(refute_0_34,plain,
    ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
    inference(subst,[],[refute_0_33:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_35,plain,
    distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_X),
    inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_32,refute_0_34]) ).

cnf(refute_0_36,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_19]) ).

cnf(refute_0_37,plain,
    ( ~ distinct_lines(X_363,X_364)
    | ~ distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_X)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_363)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_364)
    | apart_point_and_line(skolemFOFtoCNF_X,X_363)
    | apart_point_and_line(skolemFOFtoCNF_X,X_364) ),
    inference(subst,[],[refute_0_36:[bind(U,$fot(X_363)),bind(V,$fot(X_364)),bind(X,$fot(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(Y,$fot(skolemFOFtoCNF_X))]]) ).

cnf(refute_0_38,plain,
    ( ~ distinct_lines(X_363,X_364)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_363)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_364)
    | apart_point_and_line(skolemFOFtoCNF_X,X_363)
    | apart_point_and_line(skolemFOFtoCNF_X,X_364) ),
    inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_X) )],[refute_0_35,refute_0_37]) ).

cnf(refute_0_39,plain,
    ( ~ distinct_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_V)
    | apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
    | apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V) ),
    inference(subst,[],[refute_0_38:[bind(X_363,$fot(skolemFOFtoCNF_U)),bind(X_364,$fot(skolemFOFtoCNF_V))]]) ).

cnf(refute_0_40,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_V)
    | apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
    | apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V) ),
    inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_24,refute_0_39]) ).

cnf(refute_0_41,plain,
    ~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U),
    inference(canonicalize,[],[normalize_0_20]) ).

cnf(refute_0_42,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_V)
    | apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V) ),
    inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U) )],[refute_0_40,refute_0_41]) ).

cnf(refute_0_43,plain,
    ~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V),
    inference(canonicalize,[],[normalize_0_21]) ).

cnf(refute_0_44,plain,
    ( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_V) ),
    inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_V) )],[refute_0_42,refute_0_43]) ).

cnf(refute_0_45,plain,
    ( ~ convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
    | apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U) ),
    inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_V) )],[refute_0_44,refute_0_3]) ).

cnf(refute_0_46,plain,
    apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U),
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_7,refute_0_45]) ).

cnf(refute_0_47,plain,
    ~ convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
    inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U) )],[refute_0_46,refute_0_1]) ).

cnf(refute_0_48,plain,
    $false,
    inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_7,refute_0_47]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem  : GEO186+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12  % Command  : metis --show proof --show saturation %s
% 0.12/0.33  % Computer : n029.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit : 300
% 0.12/0.33  % WCLimit  : 600
% 0.12/0.34  % DateTime : Fri Jun 17 17:06:43 EDT 2022
% 0.12/0.34  % CPUTime  : 
% 0.12/0.34  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.21/1.40  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.21/1.40  
% 1.21/1.40  % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.21/1.41  
%------------------------------------------------------------------------------