TPTP Problem File: GEO286+1.p

View Solutions - Solve Problem

%------------------------------------------------------------------------------
% File     : GEO286+1 : TPTP v7.4.0. Released v4.1.0.
% Domain   : Geometry
% Problem  : 261-qe(261)
% Version  : Especial.
% English  :

% Refs     : [EucBC] Euclid (300 BC), Elements
%          : [Hea56] Heath (1956), The Thirteen Books of Euclid's Elements
%          : [ADM08] Avigad et al. (2008), A Formal System for Euclid's Ele
%          : [Kue10] Kuehlwein (2010), Email to Geoff Sutcliffe
%          : [KC+10] Kuehlwein et al. (2010), Premise Selection in the Napr
% Source   : [Kue10]
% Names    :

% Status   : Theorem
% Rating   : 0.59 v7.4.0, 0.60 v7.3.0, 0.66 v7.2.0, 0.62 v7.1.0, 0.65 v7.0.0, 0.67 v6.4.0, 0.62 v6.2.0, 0.68 v6.1.0, 0.77 v6.0.0, 0.83 v5.5.0, 0.85 v5.4.0, 0.86 v5.3.0, 0.89 v5.2.0, 0.85 v5.1.0, 0.86 v5.0.0, 0.96 v4.1.0
% Syntax   : Number of formulae    :  135 (   7 unit)
%            Number of atoms       : 1278 ( 521 equality)
%            Maximal formula depth :   46 (  12 average)
%            Number of connectives : 1304 ( 161   ~;  12   |; 994   &)
%                                         (   8 <=>; 129  =>;   0  <=;   0 <~>)
%                                         (   0  ~|;   0  ~&)
%            Number of predicates  :   15 (   0 propositional; 1-3 arity)
%            Number of functors    :   28 (  21 constant; 0-4 arity)
%            Number of variables   :  751 (   0 sgn; 483   !; 268   ?)
%            Maximal term depth    :    3 (   1 average)
% SPC      : FOF_THM_RFO_SEQ

% Comments : From the Euclid in Naproche 0.46 collection, using the [Hea56]
%            text, and axioms from [ADM08].
%------------------------------------------------------------------------------
fof('qe(261)',conjecture,(
    ? [Vd1153] :
      ( rR(Vd1153,vd1123,vd1125)
      & ron(Vd1153,vd1152)
      & ron(Vd1153,vd1151)
      & rpoint(Vd1153) ) )).

fof('neg(neg(comma_conjunct2(260)))',axiom,(
    ~ ron(vd1125,vd1152) )).

fof('neg(neg(260))',axiom,(
    ~ rinside(vd1125,vd1152) )).

fof('and(and(pred(comma_conjunct2(comma_conjunct2(comma_conjunct2(259))), 0), and(pred(comma_conjunct1(comma_conjunct2(comma_conjunct2(259))), 0), and(pred(comma_conjunct2(comma_conjunct2(259)), 0), pred(comma_conjunct1(comma_conjunct2(259)), 0)))), pred(comma_conjunct1(259), 0))',axiom,
    ( ron(vd1127,vd1152)
    & rcenter(vd1123,vd1152)
    & rcircle(vd1152)
    & ron(vd1125,vd1151)
    & ron(vd1123,vd1151) )).

fof('holds(258, 1150, 0)',axiom,(
    vd1123 = vd1129 )).

fof('and(and(and(and(holds(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1133, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(conjunct2(242)))))), 1132, 0), and(holds(conjunct1(conjunct2(conjunct2(conjunct2(conjunct2(242))))), 1131, 0), and(pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 2), pred(conjunct1(conjunct2(conjunct2(conjunct2(242)))), 1))))), and(pred(conjunct1(conjunct2(conjunct2(242))), 2), pred(conjunct1(conjunct2(conjunct2(242))), 1))), and(pred(conjunct1(conjunct2(242)), 2), pred(conjunct1(conjunct2(242)), 1))), and(pred(conjunct1(242), 2), pred(conjunct1(242), 1)))',axiom,
    ( rless(vf(vd1127,vd1129),vf(vd1123,vd1125))
    & vd1127 != vd1129
    & vd1123 != vd1125
    & vd1129 = vd1130
    & rpoint(vd1130)
    & vd1127 = vd1128
    & rpoint(vd1128)
    & vd1125 = vd1126
    & rpoint(vd1126)
    & vd1123 = vd1124
    & rpoint(vd1124) )).

fof('qu(cond(axiom(184), 0), imp(cond(axiom(184), 0)))',axiom,(
    ! [Vd847,Vd848,Vd849,Vd850,Vd851,Vd852] :
      ( ( ron(Vd851,Vd850)
        & Vd851 = Vd852
        & rpoint(Vd852)
        & rcenter(Vd849,Vd850)
        & Vd847 = Vd848
        & rpoint(Vd848) )
     => ( vf(Vd849,Vd847) = vf(Vd849,Vd851)
      <=> ron(Vd847,Vd850) ) ) )).

fof('qu(cond(axiom(166), 0), imp(cond(axiom(166), 0)))',axiom,(
    ! [Vd761,Vd762] :
      ( ( ? [Vd765] :
            ( Vd762 = Vd765
            & rpoint(Vd765) )
        & ? [Vd764] :
            ( Vd761 = Vd764
            & rpoint(Vd764) ) )
     => vf(Vd761,Vd762) = vf(Vd762,Vd761) ) )).

fof('qu(cond(axiom(160), 0), imp(cond(axiom(160), 0)))',axiom,(
    ! [Vd741,Vd742] :
      ( ( ? [Vd745] :
            ( Vd742 = Vd745
            & rpoint(Vd745) )
        & ? [Vd744] :
            ( Vd741 = Vd744
            & rpoint(Vd744) ) )
     => ? [Vd747] :
          ( vf(Vd741,Vd742) = Vd747
          & rreal(Vd747) ) ) )).

fof('qu(cond(axiom(149), 0), imp(cond(axiom(149), 0)))',axiom,(
    ! [Vd713,Vd714] :
      ( ( Vd713 = Vd714
        & rreal(Vd714) )
     => ~ rless(Vd713,Vd713) ) )).

fof('pred(259, 0)',axiom,(
    rline(vd1151) )).

fof('qu(cond(axiom(186), 0), imp(cond(axiom(186), 0)))',axiom,(
    ! [Vd854,Vd855,Vd859,Vd860] :
      ( ( ron(Vd855,Vd860)
        & rcenter(Vd859,Vd860)
        & ? [Vd858] :
            ( Vd855 = Vd858
            & rpoint(Vd858) )
        & ? [Vd857] :
            ( Vd854 = Vd857
            & rpoint(Vd857) ) )
     => ( rless(vf(Vd859,Vd854),vf(Vd859,Vd855))
      <=> rinside(Vd854,Vd860) ) ) )).

fof('qu(cond(axiom(135), 0), imp(cond(axiom(135), 0)))',axiom,(
    ! [Vd676,Vd677,Vd681,Vd682] :
      ( ( ron(Vd677,Vd682)
        & rinside(Vd676,Vd682)
        & rinside(Vd677,Vd681)
        & ron(Vd676,Vd681)
        & ? [Vd680] :
            ( Vd677 = Vd680
            & rpoint(Vd680) )
        & ? [Vd679] :
            ( Vd676 = Vd679
            & rpoint(Vd679) ) )
     => rintersect(Vd681,Vd682) ) )).

fof('qu(cond(axiom(133), 0), imp(cond(axiom(133), 0)))',axiom,(
    ! [Vd666,Vd667,Vd671,Vd672] :
      ( ( ~ rinside(Vd667,Vd672)
        & ~ ron(Vd667,Vd672)
        & rinside(Vd666,Vd672)
        & ( ron(Vd667,Vd671)
          | rinside(Vd667,Vd671) )
        & ron(Vd666,Vd671)
        & ? [Vd675] :
            ( Vd672 = Vd675
            & rcircle(Vd675) )
        & ? [Vd674] :
            ( Vd671 = Vd674
            & rcircle(Vd674) )
        & ? [Vd670] :
            ( Vd667 = Vd670
            & rpoint(Vd670) )
        & ? [Vd669] :
            ( Vd666 = Vd669
            & rpoint(Vd669) ) )
     => rintersect(Vd671,Vd672) ) )).

fof('qu(cond(axiom(79), 0), imp(cond(axiom(79), 0)))',axiom,(
    ! [Vd336,Vd337,Vd338,Vd339] :
      ( ( rinside(Vd336,Vd338)
        & Vd338 = Vd339
        & rcircle(Vd339)
        & Vd336 = Vd337
        & rpoint(Vd337) )
     => ~ ron(Vd336,Vd338) ) )).

fof('qu(cond(axiom(67), 0), imp(cond(axiom(67), 0)))',axiom,(
    ! [Vd280,Vd281] :
      ( ( rintersect(Vd280,Vd281)
        & ? [Vd284] :
            ( Vd281 = Vd284
            & rcircle(Vd284) )
        & ? [Vd283] :
            ( Vd280 = Vd283
            & rcircle(Vd283) ) )
     => ? [Vd285,Vd286] :
          ( Vd285 != Vd286
          & ron(Vd286,Vd281)
          & ron(Vd286,Vd280)
          & rpoint(Vd286)
          & ron(Vd285,Vd281)
          & ron(Vd285,Vd280)
          & rpoint(Vd285) ) ) )).

fof('qu(cond(axiom(61), 0), imp(cond(axiom(61), 0)))',axiom,(
    ! [Vd253,Vd254,Vd255,Vd256,Vd257,Vd258,Vd259,Vd260] :
      ( ( ron(Vd259,Vd255)
        & ~ ron(Vd259,Vd253)
        & ~ rinside(Vd259,Vd253)
        & Vd259 = Vd260
        & rpoint(Vd260)
        & ron(Vd257,Vd255)
        & rinside(Vd257,Vd253)
        & Vd257 = Vd258
        & rpoint(Vd258)
        & Vd255 = Vd256
        & rline(Vd256)
        & Vd253 = Vd254
        & rcircle(Vd254) )
     => ? [Vd261] :
          ( rR(Vd261,Vd257,Vd259)
          & ron(Vd261,Vd253)
          & ron(Vd261,Vd255)
          & rpoint(Vd261) ) ) )).

fof('qu(cond(axiom(53), 0), imp(cond(axiom(53), 0)))',axiom,(
    ! [Vd225,Vd226] :
      ( ( Vd225 != Vd226
        & ? [Vd230] :
            ( Vd226 = Vd230
            & rpoint(Vd230) )
        & ? [Vd229] :
            ( Vd225 = Vd229
            & rpoint(Vd229) ) )
     => ? [Vd231] :
          ( ron(Vd226,Vd231)
          & rcenter(Vd225,Vd231)
          & rcircle(Vd231) ) ) )).

fof('ass(cond(conseq(242), 1), 0)',axiom,
    ( vd1123 = vd1127
   => vf(vd1123,vskolem1147) = vf(vd1127,vd1129) )).

fof('ass(cond(conseq(242), 1), 1)',axiom,
    ( vd1123 = vd1127
   => rR(vskolem1147,vd1123,vd1125) )).

fof('ass(cond(conseq(242), 1), 2)',axiom,
    ( vd1123 = vd1127
   => ron(vskolem1147,vskolem1146) )).

fof('ass(cond(conseq(242), 1), 3)',axiom,
    ( vd1123 = vd1127
   => ron(vskolem1147,vskolem1145) )).

fof('ass(cond(conseq(242), 1), 4)',axiom,
    ( vd1123 = vd1127
   => rpoint(vskolem1147) )).

fof('ass(cond(conseq(242), 1), 5)',axiom,
    ( vd1123 = vd1127
   => ~ ron(vd1125,vskolem1146) )).

fof('ass(cond(conseq(242), 1), 6)',axiom,
    ( vd1123 = vd1127
   => ~ rinside(vd1125,vskolem1146) )).

fof('ass(cond(conseq(242), 1), 7)',axiom,
    ( vd1123 = vd1127
   => ( ron(vd1129,vskolem1146)
      & rcenter(vd1123,vskolem1146)
      & rcircle(vskolem1146)
      & ron(vd1125,vskolem1145)
      & ron(vd1123,vskolem1145) ) )).

fof('ass(cond(conseq(242), 1), 8)',axiom,
    ( vd1123 = vd1127
   => rline(vskolem1145) )).

fof('qu(cond(axiom(51), 0), imp(cond(axiom(51), 0)))',axiom,(
    ! [Vd217,Vd218] :
      ( ( Vd217 != Vd218
        & ? [Vd221] :
            ( Vd218 = Vd221
            & rpoint(Vd221) )
        & ? [Vd220] :
            ( Vd217 = Vd220
            & rpoint(Vd220) ) )
     => ? [Vd223] :
          ( ron(Vd218,Vd223)
          & ron(Vd217,Vd223)
          & rline(Vd223) ) ) )).

fof('qu(cond(axiom(1), 0), imp(cond(axiom(1), 0)))',axiom,(
    ! [Vd1,Vd2] :
      ( rcenter(Vd1,Vd2)
     => ? [Vd3,Vd4] :
          ( Vd2 = Vd4
          & rcircle(Vd4)
          & Vd1 = Vd3
          & rpoint(Vd3) ) ) )).

fof('ass(cond(conseq(242), 0), 0)',axiom,
    ( ( vd1123 != vd1129
      & vd1123 != vd1127 )
   => vf(vd1123,vskolem1140) = vf(vd1127,vd1129) )).

fof('ass(cond(conseq(242), 0), 1)',axiom,
    ( ( vd1123 != vd1129
      & vd1123 != vd1127 )
   => vf(vd1123,vskolem1140) = vf(vd1123,vskolem1136) )).

fof('ass(cond(conseq(242), 0), 2)',axiom,
    ( ( vd1123 != vd1129
      & vd1123 != vd1127 )
   => rR(vskolem1140,vd1123,vd1125) )).

fof('ass(cond(conseq(242), 0), 3)',axiom,
    ( ( vd1123 != vd1129
      & vd1123 != vd1127 )
   => ron(vskolem1140,vskolem1139) )).

fof('ass(cond(conseq(242), 0), 4)',axiom,
    ( ( vd1123 != vd1129
      & vd1123 != vd1127 )
   => ron(vskolem1140,vskolem1138) )).

fof('ass(cond(conseq(242), 0), 5)',axiom,
    ( ( vd1123 != vd1129
      & vd1123 != vd1127 )
   => rpoint(vskolem1140) )).

fof('ass(cond(conseq(242), 0), 6)',axiom,
    ( ( vd1123 != vd1129
      & vd1123 != vd1127 )
   => ~ ron(vd1125,vskolem1139) )).

fof('ass(cond(conseq(242), 0), 7)',axiom,
    ( ( vd1123 != vd1129
      & vd1123 != vd1127 )
   => ~ rinside(vd1125,vskolem1139) )).

fof('ass(cond(conseq(242), 0), 8)',axiom,
    ( ( vd1123 != vd1129
      & vd1123 != vd1127 )
   => ( ron(vskolem1136,vskolem1139)
      & rcenter(vd1123,vskolem1139)
      & rcircle(vskolem1139)
      & ron(vd1125,vskolem1138)
      & ron(vd1123,vskolem1138) ) )).

fof('ass(cond(conseq(242), 0), 9)',axiom,
    ( ( vd1123 != vd1129
      & vd1123 != vd1127 )
   => rline(vskolem1138) )).

fof('ass(cond(conseq(242), 0), 10)',axiom,
    ( ( vd1123 != vd1129
      & vd1123 != vd1127 )
   => vf(vd1127,vd1129) = vf(vd1123,vskolem1136) )).

fof('ass(cond(conseq(242), 0), 11)',axiom,
    ( ( vd1123 != vd1129
      & vd1123 != vd1127 )
   => rpoint(vskolem1136) )).

fof('ass(cond(156, 0), 0)',axiom,(
    ! [Vd733,Vd734,Vd735,Vd736,Vd737,Vd738] :
      ( ( vplus(Vd733,Vd737) = vplus(Vd735,Vd737)
        & Vd737 = Vd738
        & rreal(Vd738)
        & Vd735 = Vd736
        & rreal(Vd736)
        & Vd733 = Vd734
        & rreal(Vd734) )
     => Vd733 = Vd735 ) )).

fof('qu(cond(axiom(59), 0), imp(cond(axiom(59), 0)))',axiom,(
    ! [Vd244,Vd245,Vd246,Vd247] :
      ( ( rintersect(Vd246,Vd244)
        & Vd246 = Vd247
        & rline(Vd247)
        & Vd244 = Vd245
        & rcircle(Vd245) )
     => ? [Vd248,Vd250] :
          ( Vd248 != Vd250
          & ron(Vd250,Vd244)
          & ron(Vd250,Vd246)
          & rpoint(Vd250)
          & ron(Vd248,Vd244)
          & ron(Vd248,Vd246)
          & rpoint(Vd248) ) ) )).

fof('ass(cond(goal(219), 0), 0)',axiom,(
    ! [Vd1069,Vd1070] :
      ( ( Vd1069 != Vd1070
        & ? [Vd1073] :
            ( Vd1070 = Vd1073
            & rpoint(Vd1073) )
        & ? [Vd1072] :
            ( Vd1069 = Vd1072
            & rpoint(Vd1072) ) )
     => ! [Vd1074,Vd1075] :
          ( ( Vd1074 = Vd1075
            & Vd1074 != Vd1070
            & Vd1074 != Vd1069
            & rpoint(Vd1075) )
         => vf(Vd1069,Vd1070) = vf(Vd1074,vskolem1078(Vd1074,Vd1075,Vd1069,Vd1070)) ) ) )).

fof('ass(cond(goal(219), 0), 1)',axiom,(
    ! [Vd1069,Vd1070] :
      ( ( Vd1069 != Vd1070
        & ? [Vd1073] :
            ( Vd1070 = Vd1073
            & rpoint(Vd1073) )
        & ? [Vd1072] :
            ( Vd1069 = Vd1072
            & rpoint(Vd1072) ) )
     => ! [Vd1074,Vd1075] :
          ( ( Vd1074 = Vd1075
            & Vd1074 != Vd1070
            & Vd1074 != Vd1069
            & rpoint(Vd1075) )
         => rpoint(vskolem1078(Vd1074,Vd1075,Vd1069,Vd1070)) ) ) )).

fof('qu(cond(axiom(182), 0), imp(cond(axiom(182), 0)))',axiom,(
    ! [Vd837,Vd838,Vd842,Vd843,Vd844] :
      ( ( vf(Vd842,Vd837) = vf(Vd842,Vd838)
        & ron(Vd838,Vd844)
        & ron(Vd837,Vd843)
        & rcenter(Vd842,Vd844)
        & rcenter(Vd842,Vd843)
        & ? [Vd841] :
            ( Vd838 = Vd841
            & rpoint(Vd841) )
        & ? [Vd840] :
            ( Vd837 = Vd840
            & rpoint(Vd840) ) )
     => Vd843 = Vd844 ) )).

fof('qu(cond(axiom(164), 0), imp(cond(axiom(164), 0)))',axiom,(
    ! [Vd755,Vd756] :
      ( ( ? [Vd759] :
            ( Vd756 = Vd759
            & rpoint(Vd759) )
        & ? [Vd758] :
            ( Vd755 = Vd758
            & rpoint(Vd758) ) )
     => rleq(v0,vf(Vd755,Vd756)) ) )).

fof('qu(cond(axiom(153), 0), imp(cond(axiom(153), 0)))',axiom,(
    ! [Vd725,Vd726,Vd727,Vd728,Vd729,Vd730] :
      ( ( rless(Vd725,Vd727)
        & Vd729 = Vd730
        & rreal(Vd730)
        & Vd727 = Vd728
        & rreal(Vd728)
        & Vd725 = Vd726
        & rreal(Vd726) )
     => rless(vplus(Vd725,Vd729),vplus(Vd727,Vd729)) ) )).

fof('qu(cond(axiom(151), 0), imp(cond(axiom(151), 0)))',axiom,(
    ! [Vd716,Vd717,Vd718,Vd719,Vd720,Vd721] :
      ( ( rless(Vd718,Vd720)
        & rless(Vd716,Vd718)
        & Vd720 = Vd721
        & rreal(Vd721)
        & Vd718 = Vd719
        & rreal(Vd719)
        & Vd716 = Vd717
        & rreal(Vd717) )
     => rless(Vd716,Vd720) ) )).

fof('qu(cond(axiom(147), 0), imp(cond(axiom(147), 0)))',axiom,(
    ! [Vd706,Vd707,Vd708,Vd709] :
      ( ( rless(Vd706,Vd708)
        & Vd708 = Vd709
        & rreal(Vd709)
        & Vd706 = Vd707
        & rreal(Vd707) )
     => ( ~ rless(Vd708,Vd706)
        | Vd706 = Vd708 ) ) )).

fof('qu(cond(axiom(145), 0), imp(cond(axiom(145), 0)))',axiom,(
    ! [Vd699,Vd700,Vd701,Vd702] :
      ( ( Vd701 = Vd702
        & rreal(Vd702)
        & Vd699 = Vd700
        & rreal(Vd700) )
     => ( rless(Vd699,Vd701)
        | Vd699 = Vd701
        | rless(Vd701,Vd699) ) ) )).

fof('qu(cond(axiom(143), 0), imp(cond(axiom(143), 0)))',axiom,(
    ! [Vd694,Vd695,Vd696,Vd697] :
      ( ( Vd696 = Vd697
        & rreal(Vd697)
        & Vd694 = Vd695
        & rreal(Vd695) )
     => vplus(Vd694,Vd696) = vplus(Vd696,Vd694) ) )).

fof('qu(cond(axiom(141), 0), imp(cond(axiom(141), 0)))',axiom,(
    ! [Vd691,Vd692] :
      ( ( Vd691 = Vd692
        & rreal(Vd692) )
     => vplus(Vd691,v0) = Vd691 ) )).

fof('qu(cond(axiom(139), 0), imp(cond(axiom(139), 0)))',axiom,(
    ! [Vd685,Vd686,Vd687,Vd688] :
      ( ( Vd687 = Vd688
        & rreal(Vd688)
        & Vd685 = Vd686
        & rreal(Vd686) )
     => ? [Vd690] :
          ( vplus(Vd685,Vd687) = Vd690
          & rreal(Vd690) ) ) )).

fof('pred(axiom(137), 2)',axiom,(
    v0 = vd684 )).

fof('pred(axiom(137), 1)',axiom,(
    rreal(vd684) )).

fof('qu(cond(axiom(131), 0), imp(cond(axiom(131), 0)))',axiom,(
    ! [Vd660,Vd661,Vd662,Vd663,Vd664,Vd665] :
      ( ( ron(Vd660,Vd664)
        & rinside(Vd660,Vd662)
        & Vd664 = Vd665
        & rline(Vd665)
        & Vd662 = Vd663
        & rcircle(Vd663)
        & Vd660 = Vd661
        & rpoint(Vd661) )
     => rintersect(Vd664,Vd662) ) )).

fof('qu(cond(axiom(129), 0), imp(cond(axiom(129), 0)))',axiom,(
    ! [Vd647,Vd648,Vd652,Vd653] :
      ( ( ~ ? [Vd657] : rS(Vd647,Vd648,Vd657)
        & ( ron(Vd648,Vd652)
          | rinside(Vd648,Vd652) )
        & ( ron(Vd647,Vd652)
          | rinside(Vd647,Vd652) )
        & ? [Vd656] :
            ( Vd653 = Vd656
            & rcircle(Vd656) )
        & ? [Vd655] :
            ( Vd652 = Vd655
            & rcircle(Vd655) )
        & ? [Vd651] :
            ( Vd648 = Vd651
            & rpoint(Vd651) )
        & ? [Vd650] :
            ( Vd647 = Vd650
            & rpoint(Vd650) ) )
     => ? [Vd659] : rintersect(Vd659,Vd652) ) )).

fof('qu(cond(axiom(127), 0), imp(cond(axiom(127), 0)))',axiom,(
    ! [Vd636,Vd637,Vd641,Vd642,Vd644,Vd645] :
      ( ( Vd641 = Vd642
        & Vd644 = Vd645
        & ron(Vd637,Vd644)
        & ron(Vd636,Vd644)
        & rline(Vd645)
        & ~ rS(Vd636,Vd637,Vd641)
        & rline(Vd642)
        & ? [Vd640] :
            ( Vd637 = Vd640
            & rpoint(Vd640) )
        & ? [Vd639] :
            ( Vd636 = Vd639
            & rpoint(Vd639) ) )
     => rintersect(Vd641,Vd644) ) )).

fof('qu(cond(axiom(125), 0), imp(cond(axiom(125), 0)))',axiom,(
    ! [Vd616,Vd617,Vd622,Vd623,Vd630,Vd631,Vd632,Vd633] :
      ( ( ron(Vd631,Vd632)
        & ron(Vd630,Vd632)
        & Vd632 = Vd633
        & rline(Vd633)
        & rcenter(Vd631,Vd617)
        & rcenter(Vd630,Vd616)
        & Vd622 != Vd623
        & ron(Vd623,Vd617)
        & ron(Vd623,Vd616)
        & ron(Vd622,Vd617)
        & ron(Vd622,Vd616)
        & ? [Vd626] :
            ( Vd623 = Vd626
            & rpoint(Vd626) )
        & ? [Vd625] :
            ( Vd622 = Vd625
            & rpoint(Vd625) )
        & rintersect(Vd616,Vd617)
        & Vd616 != Vd617
        & ? [Vd620] :
            ( Vd617 = Vd620
            & rcircle(Vd620) )
        & ? [Vd619] :
            ( Vd616 = Vd619
            & rcircle(Vd619) ) )
     => ~ rS(Vd622,Vd623,Vd632) ) )).

fof('qu(cond(axiom(123), 0), imp(cond(axiom(123), 0)))',axiom,(
    ! [Vd606,Vd607,Vd608,Vd613,Vd614] :
      ( ( rR(Vd608,Vd606,Vd607)
        & ~ rinside(Vd608,Vd613)
        & ( ron(Vd606,Vd613)
          | rinside(Vd606,Vd613) )
        & Vd613 = Vd614
        & rcircle(Vd614)
        & ? [Vd612] :
            ( Vd608 = Vd612
            & rpoint(Vd612) )
        & ? [Vd611] :
            ( Vd607 = Vd611
            & rpoint(Vd611) )
        & ? [Vd610] :
            ( Vd606 = Vd610
            & rpoint(Vd610) ) )
     => ( ~ ron(Vd607,Vd613)
        & ~ ron(Vd607,Vd613) ) ) )).

fof('qu(cond(axiom(121), 0), imp(cond(axiom(121), 0)))',axiom,(
    ! [Vd594,Vd595,Vd596,Vd601,Vd602,Vd603,Vd604] :
      ( ( rR(Vd596,Vd594,Vd595)
        & ( ron(Vd595,Vd603)
          | rinside(Vd595,Vd603) )
        & ( ron(Vd594,Vd603)
          | rinside(Vd594,Vd603) )
        & Vd603 = Vd604
        & rcircle(Vd604)
        & Vd601 = Vd602
        & rline(Vd602)
        & ? [Vd600] :
            ( Vd596 = Vd600
            & rpoint(Vd600) )
        & ? [Vd599] :
            ( Vd595 = Vd599
            & rpoint(Vd599) )
        & ? [Vd598] :
            ( Vd594 = Vd598
            & rpoint(Vd598) ) )
     => rinside(Vd596,Vd603) ) )).

fof('qu(cond(axiom(119), 0), imp(cond(axiom(119), 0)))',axiom,(
    ! [Vd581,Vd582,Vd583,Vd588,Vd589,Vd590,Vd591] :
      ( ( Vd582 != Vd583
        & ron(Vd583,Vd590)
        & ron(Vd582,Vd590)
        & rinside(Vd581,Vd590)
        & ron(Vd583,Vd588)
        & ron(Vd582,Vd588)
        & ron(Vd581,Vd588)
        & Vd590 = Vd591
        & rcircle(Vd591)
        & Vd588 = Vd589
        & rline(Vd589)
        & ? [Vd587] :
            ( Vd583 = Vd587
            & rpoint(Vd587) )
        & ? [Vd586] :
            ( Vd582 = Vd586
            & rpoint(Vd586) )
        & ? [Vd585] :
            ( Vd581 = Vd585
            & rpoint(Vd585) ) )
     => rR(Vd581,Vd582,Vd583) ) )).

fof('qu(cond(axiom(117), 0), imp(cond(axiom(117), 0)))',axiom,(
    ! [Vd558,Vd559,Vd560,Vd565,Vd566,Vd567,Vd568,Vd577] :
      ( ( rS(Vd567,Vd577,Vd560)
        & rS(Vd568,Vd577,Vd559)
        & rS(Vd566,Vd567,Vd560)
        & rS(Vd567,Vd568,Vd558)
        & ron(Vd568,Vd560)
        & ron(Vd567,Vd559)
        & ron(Vd566,Vd558)
        & ron(Vd565,Vd560)
        & ron(Vd565,Vd559)
        & ron(Vd565,Vd558)
        & ? [Vd573] :
            ( Vd568 = Vd573
            & rpoint(Vd573) )
        & ? [Vd572] :
            ( Vd567 = Vd572
            & rpoint(Vd572) )
        & ? [Vd571] :
            ( Vd566 = Vd571
            & rpoint(Vd571) )
        & ? [Vd570] :
            ( Vd565 = Vd570
            & rpoint(Vd570) )
        & ? [Vd564] :
            ( Vd560 = Vd564
            & rline(Vd564) )
        & ? [Vd563] :
            ( Vd559 = Vd563
            & rline(Vd563) )
        & ? [Vd562] :
            ( Vd558 = Vd562
            & rline(Vd562) ) )
     => rS(Vd567,Vd577,Vd558) ) )).

fof('qu(cond(axiom(115), 0), imp(cond(axiom(115), 0)))',axiom,(
    ! [Vd537,Vd538,Vd539,Vd544,Vd545,Vd546,Vd547] :
      ( ( Vd545 != Vd544
        & ~ ron(Vd547,Vd538)
        & ~ rS(Vd545,Vd547,Vd538)
        & rS(Vd546,Vd547,Vd537)
        & ron(Vd547,Vd539)
        & ron(Vd546,Vd538)
        & ron(Vd545,Vd537)
        & ron(Vd544,Vd539)
        & ron(Vd544,Vd538)
        & ron(Vd544,Vd537)
        & ? [Vd552] :
            ( Vd547 = Vd552
            & rpoint(Vd552) )
        & ? [Vd551] :
            ( Vd546 = Vd551
            & rpoint(Vd551) )
        & ? [Vd550] :
            ( Vd545 = Vd550
            & rpoint(Vd550) )
        & ? [Vd549] :
            ( Vd544 = Vd549
            & rpoint(Vd549) )
        & ? [Vd543] :
            ( Vd539 = Vd543
            & rline(Vd543) )
        & ? [Vd542] :
            ( Vd538 = Vd542
            & rline(Vd542) )
        & ? [Vd541] :
            ( Vd537 = Vd541
            & rline(Vd541) ) )
     => rS(Vd545,Vd546,Vd539) ) )).

fof('qu(cond(axiom(113), 0), imp(cond(axiom(113), 0)))',axiom,(
    ! [Vd516,Vd517,Vd518,Vd523,Vd524,Vd525,Vd526] :
      ( ( rS(Vd524,Vd525,Vd518)
        & rS(Vd525,Vd526,Vd516)
        & ron(Vd526,Vd518)
        & ron(Vd525,Vd518)
        & ron(Vd524,Vd516)
        & ron(Vd523,Vd518)
        & ron(Vd523,Vd517)
        & ron(Vd523,Vd516)
        & ? [Vd531] :
            ( Vd526 = Vd531
            & rpoint(Vd531) )
        & ? [Vd530] :
            ( Vd525 = Vd530
            & rpoint(Vd530) )
        & ? [Vd529] :
            ( Vd524 = Vd529
            & rpoint(Vd529) )
        & ? [Vd528] :
            ( Vd523 = Vd528
            & rpoint(Vd528) )
        & ? [Vd522] :
            ( Vd518 = Vd522
            & rline(Vd522) )
        & ? [Vd521] :
            ( Vd517 = Vd521
            & rline(Vd521) )
        & ? [Vd520] :
            ( Vd516 = Vd520
            & rline(Vd520) ) )
     => ~ rS(Vd524,Vd526,Vd517) ) )).

fof('qu(cond(axiom(111), 0), imp(cond(axiom(111), 0)))',axiom,(
    ! [Vd500,Vd501,Vd502,Vd507,Vd508] :
      ( ( ron(Vd501,Vd507)
        & ron(Vd501,Vd508)
        & ~ rS(Vd500,Vd502,Vd507)
        & ron(Vd502,Vd508)
        & ron(Vd500,Vd508)
        & Vd507 != Vd508
        & ? [Vd511] :
            ( Vd508 = Vd511
            & rline(Vd511) )
        & ? [Vd510] :
            ( Vd507 = Vd510
            & rline(Vd510) )
        & Vd501 != Vd502
        & Vd500 != Vd502
        & Vd500 != Vd501
        & ? [Vd506] :
            ( Vd502 = Vd506
            & rpoint(Vd506) )
        & ? [Vd505] :
            ( Vd501 = Vd505
            & rpoint(Vd505) )
        & ? [Vd504] :
            ( Vd500 = Vd504
            & rpoint(Vd504) ) )
     => rR(Vd501,Vd500,Vd502) ) )).

fof('qu(cond(axiom(109), 0), imp(cond(axiom(109), 0)))',axiom,(
    ! [Vd489,Vd490,Vd491,Vd496,Vd497] :
      ( ( ron(Vd490,Vd496)
        & rR(Vd490,Vd489,Vd491)
        & Vd496 = Vd497
        & rline(Vd497)
        & ? [Vd495] :
            ( Vd491 = Vd495
            & rpoint(Vd495) )
        & ? [Vd494] :
            ( Vd490 = Vd494
            & rpoint(Vd494) )
        & ? [Vd493] :
            ( Vd489 = Vd493
            & rpoint(Vd493) ) )
     => ~ rS(Vd489,Vd491,Vd496) ) )).

fof('qu(cond(axiom(107), 0), imp(cond(axiom(107), 0)))',axiom,(
    ! [Vd478,Vd479,Vd480,Vd485,Vd486] :
      ( ( ~ ron(Vd479,Vd485)
        & ron(Vd478,Vd485)
        & rR(Vd479,Vd478,Vd480)
        & Vd485 = Vd486
        & rline(Vd486)
        & ? [Vd484] :
            ( Vd480 = Vd484
            & rpoint(Vd484) )
        & ? [Vd483] :
            ( Vd479 = Vd483
            & rpoint(Vd483) )
        & ? [Vd482] :
            ( Vd478 = Vd482
            & rpoint(Vd482) ) )
     => rS(Vd479,Vd480,Vd485) ) )).

fof('qu(cond(axiom(105), 0), imp(cond(axiom(105), 0)))',axiom,(
    ! [Vd466,Vd467,Vd468,Vd473,Vd474] :
      ( ( rS(Vd466,Vd468,Vd473)
        & rR(Vd467,Vd466,Vd468)
        & Vd473 = Vd474
        & rline(Vd474)
        & ? [Vd472] :
            ( Vd468 = Vd472
            & rpoint(Vd472) )
        & ? [Vd471] :
            ( Vd467 = Vd471
            & rpoint(Vd471) )
        & ? [Vd470] :
            ( Vd466 = Vd470
            & rpoint(Vd470) ) )
     => rS(Vd466,Vd467,Vd473) ) )).

fof('qu(cond(axiom(103), 0), imp(cond(axiom(103), 0)))',axiom,(
    ! [Vd454,Vd455,Vd456,Vd461,Vd462] :
      ( ( ~ rS(Vd454,Vd455,Vd461)
        & ~ ron(Vd456,Vd461)
        & ~ ron(Vd455,Vd461)
        & ~ ron(Vd454,Vd461)
        & Vd461 = Vd462
        & rline(Vd462)
        & ? [Vd460] :
            ( Vd456 = Vd460
            & rpoint(Vd460) )
        & ? [Vd459] :
            ( Vd455 = Vd459
            & rpoint(Vd459) )
        & ? [Vd458] :
            ( Vd454 = Vd458
            & rpoint(Vd458) ) )
     => ( rS(Vd454,Vd456,Vd461)
        | rS(Vd455,Vd456,Vd461) ) ) )).

fof('qu(cond(axiom(101), 0), imp(cond(axiom(101), 0)))',axiom,(
    ! [Vd442,Vd443,Vd444,Vd449,Vd450] :
      ( ( rS(Vd442,Vd444,Vd449)
        & rS(Vd442,Vd443,Vd449)
        & Vd449 = Vd450
        & rline(Vd450)
        & ? [Vd448] :
            ( Vd444 = Vd448
            & rpoint(Vd448) )
        & ? [Vd447] :
            ( Vd443 = Vd447
            & rpoint(Vd447) )
        & ? [Vd446] :
            ( Vd442 = Vd446
            & rpoint(Vd446) ) )
     => rS(Vd443,Vd444,Vd449) ) )).

fof('qu(cond(axiom(99), 0), imp(cond(axiom(99), 0)))',axiom,(
    ! [Vd434,Vd435,Vd439,Vd440] :
      ( ( rS(Vd434,Vd435,Vd439)
        & Vd439 = Vd440
        & rline(Vd440)
        & ? [Vd438] :
            ( Vd435 = Vd438
            & rpoint(Vd438) )
        & ? [Vd437] :
            ( Vd434 = Vd437
            & rpoint(Vd437) ) )
     => ~ ron(Vd434,Vd439) ) )).

fof('qu(cond(axiom(97), 0), imp(cond(axiom(97), 0)))',axiom,(
    ! [Vd425,Vd426,Vd430,Vd431] :
      ( ( rS(Vd425,Vd426,Vd430)
        & Vd430 = Vd431
        & rline(Vd431)
        & ? [Vd429] :
            ( Vd426 = Vd429
            & rpoint(Vd429) )
        & ? [Vd428] :
            ( Vd425 = Vd428
            & rpoint(Vd428) ) )
     => rS(Vd426,Vd425,Vd430) ) )).

fof('qu(cond(axiom(95), 0), imp(cond(axiom(95), 0)))',axiom,(
    ! [Vd420,Vd421,Vd422,Vd423] :
      ( ( ~ ron(Vd420,Vd422)
        & Vd422 = Vd423
        & rline(Vd423)
        & Vd420 = Vd421
        & rpoint(Vd421) )
     => rS(Vd420,Vd420,Vd422) ) )).

fof('qu(cond(axiom(93), 0), imp(cond(axiom(93), 0)))',axiom,(
    ! [Vd408,Vd409,Vd410,Vd411] :
      ( ( rR(Vd409,Vd408,Vd411)
        & rR(Vd409,Vd408,Vd410)
        & ? [Vd416] :
            ( Vd411 = Vd416
            & rpoint(Vd416) )
        & ? [Vd415] :
            ( Vd410 = Vd415
            & rpoint(Vd415) )
        & ? [Vd414] :
            ( Vd409 = Vd414
            & rpoint(Vd414) )
        & ? [Vd413] :
            ( Vd408 = Vd413
            & rpoint(Vd413) ) )
     => ~ rR(Vd409,Vd410,Vd411) ) )).

fof('qu(cond(axiom(91), 0), imp(cond(axiom(91), 0)))',axiom,(
    ! [Vd396,Vd397,Vd398,Vd403,Vd404] :
      ( ( Vd403 = Vd404
        & ron(Vd398,Vd403)
        & ron(Vd397,Vd403)
        & ron(Vd396,Vd403)
        & rline(Vd404)
        & Vd397 != Vd398
        & Vd396 != Vd398
        & Vd396 != Vd397
        & ? [Vd402] :
            ( Vd398 = Vd402
            & rpoint(Vd402) )
        & ? [Vd401] :
            ( Vd397 = Vd401
            & rpoint(Vd401) )
        & ? [Vd400] :
            ( Vd396 = Vd400
            & rpoint(Vd400) ) )
     => ( rR(Vd397,Vd396,Vd398)
        | rR(Vd396,Vd397,Vd398)
        | rR(Vd398,Vd396,Vd397) ) ) )).

fof('qu(cond(axiom(89), 0), imp(cond(axiom(89), 0)))',axiom,(
    ! [Vd384,Vd385,Vd386,Vd387] :
      ( ( rR(Vd386,Vd385,Vd387)
        & rR(Vd385,Vd384,Vd386)
        & ? [Vd392] :
            ( Vd387 = Vd392
            & rpoint(Vd392) )
        & ? [Vd391] :
            ( Vd386 = Vd391
            & rpoint(Vd391) )
        & ? [Vd390] :
            ( Vd385 = Vd390
            & rpoint(Vd390) )
        & ? [Vd389] :
            ( Vd384 = Vd389
            & rpoint(Vd389) ) )
     => rR(Vd385,Vd384,Vd387) ) )).

fof('qu(cond(axiom(87), 0), imp(cond(axiom(87), 0)))',axiom,(
    ! [Vd372,Vd373,Vd374,Vd375] :
      ( ( rR(Vd375,Vd372,Vd373)
        & rR(Vd373,Vd372,Vd374)
        & ? [Vd380] :
            ( Vd375 = Vd380
            & rpoint(Vd380) )
        & ? [Vd379] :
            ( Vd374 = Vd379
            & rpoint(Vd379) )
        & ? [Vd378] :
            ( Vd373 = Vd378
            & rpoint(Vd378) )
        & ? [Vd377] :
            ( Vd372 = Vd377
            & rpoint(Vd377) ) )
     => rR(Vd375,Vd372,Vd374) ) )).

fof('qu(cond(axiom(85), 0), imp(cond(axiom(85), 0)))',axiom,(
    ! [Vd362,Vd363,Vd364,Vd369,Vd370] :
      ( ( Vd369 = Vd370
        & ron(Vd364,Vd369)
        & ron(Vd362,Vd369)
        & rR(Vd363,Vd362,Vd364)
        & rline(Vd370)
        & ? [Vd368] :
            ( Vd364 = Vd368
            & rpoint(Vd368) )
        & ? [Vd367] :
            ( Vd363 = Vd367
            & rpoint(Vd367) )
        & ? [Vd366] :
            ( Vd362 = Vd366
            & rpoint(Vd366) ) )
     => ron(Vd363,Vd369) ) )).

fof('qu(cond(axiom(83), 0), imp(cond(axiom(83), 0)))',axiom,(
    ! [Vd352,Vd353,Vd354,Vd359,Vd360] :
      ( ( Vd359 = Vd360
        & ron(Vd353,Vd359)
        & ron(Vd352,Vd359)
        & rR(Vd353,Vd352,Vd354)
        & rline(Vd360)
        & ? [Vd358] :
            ( Vd354 = Vd358
            & rpoint(Vd358) )
        & ? [Vd357] :
            ( Vd353 = Vd357
            & rpoint(Vd357) )
        & ? [Vd356] :
            ( Vd352 = Vd356
            & rpoint(Vd356) ) )
     => ron(Vd354,Vd359) ) )).

fof('qu(cond(axiom(81), 0), imp(cond(axiom(81), 0)))',axiom,(
    ! [Vd340,Vd341,Vd342] :
      ( ( rR(Vd341,Vd340,Vd342)
        & ? [Vd346] :
            ( Vd342 = Vd346
            & rpoint(Vd346) )
        & ? [Vd345] :
            ( Vd341 = Vd345
            & rpoint(Vd345) )
        & ? [Vd344] :
            ( Vd340 = Vd344
            & rpoint(Vd344) ) )
     => ( ~ rR(Vd340,Vd341,Vd342)
        & Vd340 != Vd342
        & Vd340 != Vd341
        & rR(Vd341,Vd342,Vd340) ) ) )).

fof('qu(cond(axiom(77), 0), imp(cond(axiom(77), 0)))',axiom,(
    ! [Vd334,Vd335] :
      ( rcenter(Vd334,Vd335)
     => rinside(Vd334,Vd335) ) )).

fof('qu(cond(axiom(75), 0), imp(cond(axiom(75), 0)))',axiom,(
    ! [Vd328,Vd329,Vd331,Vd332] :
      ( ( rcenter(Vd332,Vd328)
        & rcenter(Vd331,Vd328)
        & Vd328 = Vd329
        & rcircle(Vd329) )
     => Vd331 = Vd332 ) )).

fof('qu(cond(axiom(73), 0), imp(cond(axiom(73), 0)))',axiom,(
    ! [Vd314,Vd315,Vd319,Vd320] :
      ( ( ron(Vd315,Vd320)
        & ron(Vd315,Vd319)
        & ron(Vd314,Vd320)
        & ron(Vd314,Vd319)
        & ? [Vd324] :
            ( Vd320 = Vd324
            & rline(Vd324) )
        & ? [Vd323] :
            ( Vd319 = Vd323
            & rline(Vd323) )
        & Vd314 != Vd315
        & ? [Vd318] :
            ( Vd315 = Vd318
            & rpoint(Vd318) )
        & ? [Vd317] :
            ( Vd314 = Vd317
            & rpoint(Vd317) ) )
     => Vd319 = Vd320 ) )).

fof('qu(cond(axiom(71), 0), imp(cond(axiom(71), 0)))',axiom,(
    ! [Vd301,Vd302,Vd306,Vd307,Vd308,Vd309,Vd311] :
      ( ( ~ ron(Vd311,Vd306)
        & ron(Vd309,Vd306)
        & ron(Vd308,Vd306)
        & rcenter(Vd309,Vd302)
        & rcenter(Vd308,Vd301)
        & rintersect(Vd301,Vd302)
        & Vd306 = Vd307
        & rline(Vd307)
        & ? [Vd305] :
            ( Vd302 = Vd305
            & rcircle(Vd305) )
        & ? [Vd304] :
            ( Vd301 = Vd304
            & rcircle(Vd304) ) )
     => ? [Vd312] :
          ( ~ rS(Vd312,Vd311,Vd306)
          & ron(Vd312,Vd302)
          & ron(Vd312,Vd301)
          & rpoint(Vd312) ) ) )).

fof('qu(cond(axiom(69), 0), imp(cond(axiom(69), 0)))',axiom,(
    ! [Vd288,Vd289,Vd293,Vd294,Vd295,Vd296,Vd298] :
      ( ( ~ ron(Vd298,Vd293)
        & ron(Vd296,Vd293)
        & ron(Vd295,Vd293)
        & rcenter(Vd296,Vd289)
        & rcenter(Vd295,Vd288)
        & rintersect(Vd288,Vd289)
        & Vd293 = Vd294
        & rline(Vd294)
        & ? [Vd292] :
            ( Vd289 = Vd292
            & rcircle(Vd292) )
        & ? [Vd291] :
            ( Vd288 = Vd291
            & rcircle(Vd291) ) )
     => ? [Vd299] :
          ( rS(Vd299,Vd298,Vd293)
          & ron(Vd299,Vd289)
          & ron(Vd299,Vd288)
          & rpoint(Vd299) ) ) )).

fof('qu(cond(axiom(65), 0), imp(cond(axiom(65), 0)))',axiom,(
    ! [Vd275,Vd276,Vd277,Vd278] :
      ( ( rintersect(Vd275,Vd277)
        & Vd277 = Vd278
        & rcircle(Vd278)
        & Vd275 = Vd276
        & rcircle(Vd276) )
     => ? [Vd279] :
          ( ron(Vd279,Vd277)
          & ron(Vd279,Vd275)
          & rpoint(Vd279) ) ) )).

fof('qu(cond(axiom(63), 0), imp(cond(axiom(63), 0)))',axiom,(
    ! [Vd263,Vd264,Vd265,Vd266,Vd267,Vd268,Vd269,Vd270] :
      ( ( Vd269 != Vd267
        & ron(Vd269,Vd265)
        & Vd269 = Vd270
        & rpoint(Vd270)
        & ron(Vd267,Vd265)
        & rinside(Vd267,Vd263)
        & Vd267 = Vd268
        & rpoint(Vd268)
        & Vd265 = Vd266
        & rline(Vd266)
        & Vd263 = Vd264
        & rcircle(Vd264) )
     => ? [Vd272] :
          ( rR(Vd267,Vd272,Vd269)
          & ron(Vd272,Vd265)
          & ron(Vd272,Vd263)
          & rpoint(Vd272) ) ) )).

fof('qu(cond(axiom(57), 0), imp(cond(axiom(57), 0)))',axiom,(
    ! [Vd238,Vd239,Vd240,Vd241] :
      ( ( rintersect(Vd240,Vd238)
        & Vd240 = Vd241
        & rline(Vd241)
        & Vd238 = Vd239
        & rcircle(Vd239) )
     => ? [Vd242] :
          ( ron(Vd242,Vd238)
          & ron(Vd242,Vd240)
          & rpoint(Vd242) ) ) )).

fof('qu(cond(axiom(55), 0), imp(cond(axiom(55), 0)))',axiom,(
    ! [Vd232,Vd233,Vd234,Vd235] :
      ( ( rintersect(Vd232,Vd234)
        & Vd234 = Vd235
        & rline(Vd235)
        & Vd232 = Vd233
        & rline(Vd233) )
     => ? [Vd236] :
          ( ron(Vd236,Vd234)
          & ron(Vd236,Vd232)
          & rpoint(Vd236) ) ) )).

fof('qu(cond(axiom(49), 0), imp(cond(axiom(49), 0)))',axiom,(
    ! [Vd214,Vd215] :
      ( ( Vd214 = Vd215
        & rcircle(Vd215) )
     => ? [Vd216] :
          ( ~ ron(Vd216,Vd214)
          & ~ rinside(Vd216,Vd214)
          & rpoint(Vd216) ) ) )).

fof('qu(cond(axiom(47), 0), imp(cond(axiom(47), 0)))',axiom,(
    ! [Vd211,Vd212] :
      ( ( Vd211 = Vd212
        & rcircle(Vd212) )
     => ? [Vd213] :
          ( rinside(Vd213,Vd211)
          & rpoint(Vd213) ) ) )).

fof('qu(cond(axiom(45), 0), imp(cond(axiom(45), 0)))',axiom,(
    ! [Vd200,Vd201,Vd202,Vd203] :
      ( ( ron(Vd203,Vd200)
        & ron(Vd202,Vd200)
        & ? [Vd206] :
            ( Vd203 = Vd206
            & rpoint(Vd206) )
        & ? [Vd205] :
            ( Vd202 = Vd205
            & rpoint(Vd205) )
        & Vd200 = Vd201
        & rcircle(Vd201) )
     => ? [Vd208] :
          ( Vd208 != Vd203
          & Vd208 != Vd202
          & ron(Vd208,Vd200)
          & rpoint(Vd208) ) ) )).

fof('qu(cond(axiom(43), 0), imp(cond(axiom(43), 0)))',axiom,(
    ! [Vd194,Vd195,Vd196,Vd197] :
      ( ( ron(Vd196,Vd194)
        & Vd196 = Vd197
        & rpoint(Vd197)
        & Vd194 = Vd195
        & rcircle(Vd195) )
     => ? [Vd198] :
          ( Vd198 != Vd196
          & ron(Vd198,Vd194)
          & rpoint(Vd198) ) ) )).

fof('qu(cond(axiom(41), 0), imp(cond(axiom(41), 0)))',axiom,(
    ! [Vd191,Vd192] :
      ( ( Vd191 = Vd192
        & rcircle(Vd192) )
     => ? [Vd193] :
          ( ron(Vd193,Vd191)
          & rpoint(Vd193) ) ) )).

fof('qu(cond(axiom(39), 0), imp(cond(axiom(39), 0)))',axiom,(
    ! [Vd185,Vd186,Vd187,Vd188] :
      ( ( Vd187 = Vd188
        & ~ ron(Vd187,Vd185)
        & rpoint(Vd188)
        & Vd185 = Vd186
        & rline(Vd186) )
     => ? [Vd189] :
          ( ~ rS(Vd189,Vd187,Vd185)
          & rpoint(Vd189) ) ) )).

fof('qu(cond(axiom(37), 0), imp(cond(axiom(37), 0)))',axiom,(
    ! [Vd170,Vd171,Vd172,Vd173,Vd174,Vd175,Vd177,Vd178] :
      ( ( Vd172 = Vd173
        & Vd174 = Vd175
        & Vd177 = Vd178
        & rS(Vd177,Vd172,Vd170)
        & rpoint(Vd178)
        & rS(Vd174,Vd172,Vd170)
        & rpoint(Vd175)
        & ~ ron(Vd172,Vd170)
        & rpoint(Vd173)
        & Vd170 = Vd171
        & rline(Vd171) )
     => ? [Vd180] :
          ( Vd180 != Vd177
          & Vd180 != Vd174
          & Vd180 != Vd172
          & rS(Vd180,Vd172,Vd170)
          & rpoint(Vd180) ) ) )).

fof('qu(cond(axiom(35), 0), imp(cond(axiom(35), 0)))',axiom,(
    ! [Vd159,Vd160,Vd161,Vd162,Vd163,Vd164] :
      ( ( Vd161 = Vd162
        & Vd163 = Vd164
        & rS(Vd163,Vd161,Vd159)
        & rpoint(Vd164)
        & ~ ron(Vd161,Vd159)
        & rpoint(Vd162)
        & Vd159 = Vd160
        & rline(Vd160) )
     => ? [Vd166] :
          ( Vd166 != Vd163
          & Vd166 != Vd161
          & rS(Vd166,Vd161,Vd159)
          & rpoint(Vd166) ) ) )).

fof('qu(cond(axiom(33), 0), imp(cond(axiom(33), 0)))',axiom,(
    ! [Vd152,Vd153,Vd154,Vd155] :
      ( ( Vd154 = Vd155
        & ~ ron(Vd154,Vd152)
        & rpoint(Vd155)
        & Vd152 = Vd153
        & rline(Vd153) )
     => ? [Vd156] :
          ( Vd156 != Vd154
          & rS(Vd156,Vd154,Vd152)
          & rpoint(Vd156) ) ) )).

fof('qu(cond(axiom(31), 0), imp(cond(axiom(31), 0)))',axiom,(
    ! [Vd138,Vd139,Vd140,Vd141,Vd146,Vd147] :
      ( ( Vd146 = Vd147
        & rR(Vd141,Vd140,Vd146)
        & rpoint(Vd147)
        & ron(Vd141,Vd138)
        & ron(Vd140,Vd138)
        & ? [Vd144] :
            ( Vd141 = Vd144
            & rpoint(Vd144) )
        & ? [Vd143] :
            ( Vd140 = Vd143
            & rpoint(Vd143) )
        & Vd138 = Vd139
        & rline(Vd139) )
     => ? [Vd149] :
          ( Vd149 != Vd146
          & rR(Vd141,Vd140,Vd149)
          & rpoint(Vd149) ) ) )).

fof('qu(cond(axiom(29), 0), imp(cond(axiom(29), 0)))',axiom,(
    ! [Vd127,Vd128,Vd129,Vd130] :
      ( ( Vd129 != Vd130
        & ron(Vd130,Vd127)
        & ron(Vd129,Vd127)
        & ? [Vd133] :
            ( Vd130 = Vd133
            & rpoint(Vd133) )
        & ? [Vd132] :
            ( Vd129 = Vd132
            & rpoint(Vd132) )
        & Vd127 = Vd128
        & rline(Vd128) )
     => ? [Vd136] :
          ( rR(Vd130,Vd129,Vd136)
          & rpoint(Vd136) ) ) )).

fof('qu(cond(axiom(27), 0), imp(cond(axiom(27), 0)))',axiom,(
    ! [Vd109,Vd110,Vd111,Vd112,Vd113,Vd114] :
      ( ( rR(Vd114,Vd111,Vd112)
        & rR(Vd113,Vd111,Vd112)
        & ron(Vd113,Vd109)
        & ron(Vd112,Vd109)
        & ron(Vd111,Vd109)
        & ? [Vd119] :
            ( Vd114 = Vd119
            & rpoint(Vd119) )
        & ? [Vd118] :
            ( Vd113 = Vd118
            & rpoint(Vd118) )
        & ? [Vd117] :
            ( Vd112 = Vd117
            & rpoint(Vd117) )
        & ? [Vd116] :
            ( Vd111 = Vd116
            & rpoint(Vd116) )
        & Vd109 = Vd110
        & rline(Vd110) )
     => ? [Vd123] :
          ( Vd123 != Vd114
          & Vd123 != Vd113
          & rR(Vd123,Vd111,Vd112)
          & rpoint(Vd123) ) ) )).

fof('qu(cond(axiom(25), 0), imp(cond(axiom(25), 0)))',axiom,(
    ! [Vd95,Vd96,Vd97,Vd98,Vd99] :
      ( ( rR(Vd99,Vd97,Vd98)
        & ron(Vd98,Vd95)
        & ron(Vd97,Vd95)
        & ? [Vd103] :
            ( Vd99 = Vd103
            & rpoint(Vd103) )
        & ? [Vd102] :
            ( Vd98 = Vd102
            & rpoint(Vd102) )
        & ? [Vd101] :
            ( Vd97 = Vd101
            & rpoint(Vd101) )
        & Vd95 = Vd96
        & rline(Vd96) )
     => ? [Vd106] :
          ( Vd106 != Vd99
          & rR(Vd106,Vd97,Vd98)
          & rpoint(Vd106) ) ) )).

fof('qu(cond(axiom(23), 0), imp(cond(axiom(23), 0)))',axiom,(
    ! [Vd84,Vd85,Vd86,Vd87] :
      ( ( Vd86 != Vd87
        & ron(Vd87,Vd84)
        & ron(Vd86,Vd84)
        & ? [Vd90] :
            ( Vd87 = Vd90
            & rpoint(Vd90) )
        & ? [Vd89] :
            ( Vd86 = Vd89
            & rpoint(Vd89) )
        & Vd84 = Vd85
        & rline(Vd85) )
     => ? [Vd93] :
          ( rR(Vd93,Vd86,Vd87)
          & rpoint(Vd93) ) ) )).

fof('qu(cond(axiom(21), 0), imp(cond(axiom(21), 0)))',axiom,(
    ! [Vd71,Vd72,Vd73,Vd74,Vd75] :
      ( ( ron(Vd75,Vd71)
        & ron(Vd74,Vd71)
        & ron(Vd73,Vd71)
        & ? [Vd79] :
            ( Vd75 = Vd79
            & rpoint(Vd79) )
        & ? [Vd78] :
            ( Vd74 = Vd78
            & rpoint(Vd78) )
        & ? [Vd77] :
            ( Vd73 = Vd77
            & rpoint(Vd77) )
        & Vd71 = Vd72
        & rline(Vd72) )
     => ? [Vd81] :
          ( Vd81 != Vd74
          & Vd81 != Vd73
          & ron(Vd81,Vd71)
          & rpoint(Vd81) ) ) )).

fof('qu(cond(axiom(19), 0), imp(cond(axiom(19), 0)))',axiom,(
    ! [Vd61,Vd62,Vd63,Vd64,Vd65,Vd66] :
      ( ( ron(Vd65,Vd61)
        & ron(Vd63,Vd61)
        & Vd65 = Vd66
        & rpoint(Vd66)
        & Vd63 = Vd64
        & rpoint(Vd64)
        & Vd61 = Vd62
        & rline(Vd62) )
     => ? [Vd68] :
          ( Vd68 != Vd65
          & Vd68 != Vd63
          & ron(Vd68,Vd61)
          & rpoint(Vd68) ) ) )).

fof('qu(cond(axiom(17), 0), imp(cond(axiom(17), 0)))',axiom,(
    ! [Vd55,Vd56,Vd57,Vd58] :
      ( ( ron(Vd57,Vd55)
        & Vd57 = Vd58
        & rpoint(Vd58)
        & Vd55 = Vd56
        & rline(Vd56) )
     => ? [Vd59] :
          ( Vd59 != Vd57
          & ron(Vd59,Vd55)
          & rpoint(Vd59) ) ) )).

fof('qu(cond(axiom(15), 0), imp(cond(axiom(15), 0)))',axiom,(
    ! [Vd52,Vd53] :
      ( ( Vd52 = Vd53
        & rline(Vd53) )
     => ? [Vd54] :
          ( ron(Vd54,Vd52)
          & rpoint(Vd54) ) ) )).

fof('qu(cond(axiom(13), 0), imp(cond(axiom(13), 0)))',axiom,(
    ! [Vd38,Vd39,Vd40,Vd41] :
      ( ( ? [Vd46] :
            ( Vd41 = Vd46
            & rpoint(Vd46) )
        & ? [Vd45] :
            ( Vd40 = Vd45
            & rpoint(Vd45) )
        & ? [Vd44] :
            ( Vd39 = Vd44
            & rpoint(Vd44) )
        & ? [Vd43] :
            ( Vd38 = Vd43
            & rpoint(Vd43) ) )
     => ? [Vd47] :
          ( Vd47 != Vd41
          & Vd47 != Vd40
          & Vd47 != Vd39
          & Vd47 != Vd38
          & rpoint(Vd47) ) ) )).

fof('qu(cond(axiom(11), 0), imp(cond(axiom(11), 0)))',axiom,(
    ! [Vd27,Vd28,Vd29] :
      ( ( ? [Vd33] :
            ( Vd29 = Vd33
            & rpoint(Vd33) )
        & ? [Vd32] :
            ( Vd28 = Vd32
            & rpoint(Vd32) )
        & ? [Vd31] :
            ( Vd27 = Vd31
            & rpoint(Vd31) ) )
     => ? [Vd34] :
          ( Vd34 != Vd29
          & Vd34 != Vd28
          & Vd34 != Vd27
          & rpoint(Vd34) ) ) )).

fof('qu(cond(axiom(9), 0), imp(cond(axiom(9), 0)))',axiom,(
    ! [Vd19,Vd20] :
      ( ( ? [Vd23] :
            ( Vd20 = Vd23
            & rpoint(Vd23) )
        & ? [Vd22] :
            ( Vd19 = Vd22
            & rpoint(Vd22) ) )
     => ? [Vd24] :
          ( Vd24 != Vd20
          & Vd24 != Vd19
          & rpoint(Vd24) ) ) )).

fof('qu(cond(axiom(7), 0), imp(cond(axiom(7), 0)))',axiom,(
    ! [Vd15,Vd16] :
      ( ( Vd15 = Vd16
        & rpoint(Vd16) )
     => ? [Vd17] :
          ( Vd17 != Vd15
          & rpoint(Vd17) ) ) )).

fof('pred(axiom(5), 0)',axiom,(
    rpoint(vd14) )).

fof('qu(cond(axiom(3), 0), imp(cond(axiom(3), 0)))',axiom,(
    ! [Vd5,Vd6,Vd7,Vd9] :
      ( ( vtriangle(Vd5,Vd6,Vd7) = Vd9
        & rtriangle(Vd9) )
     => ( Vd6 != Vd7
        & Vd5 != Vd7
        & Vd5 != Vd6
        & ? [Vd13] :
            ( Vd7 = Vd13
            & rpoint(Vd13) )
        & ? [Vd12] :
            ( Vd6 = Vd12
            & rpoint(Vd12) )
        & ? [Vd11] :
            ( Vd5 = Vd11
            & rpoint(Vd11) ) ) ) )).

fof('ass(cond(goal(206), 0), 0)',axiom,(
    ! [Vd1047,Vd1048,Vd1049,Vd1050] :
      ( ( Vd1049 = Vd1050
        & Vd1047 != Vd1049
        & rpoint(Vd1050)
        & Vd1047 = Vd1048
        & rpoint(Vd1048) )
     => vf(Vd1049,vskolem1052(Vd1047,Vd1048,Vd1049,Vd1050)) = vf(vskolem1052(Vd1047,Vd1048,Vd1049,Vd1050),Vd1047) ) )).

fof('ass(cond(goal(206), 0), 1)',axiom,(
    ! [Vd1047,Vd1048,Vd1049,Vd1050] :
      ( ( Vd1049 = Vd1050
        & Vd1047 != Vd1049
        & rpoint(Vd1050)
        & Vd1047 = Vd1048
        & rpoint(Vd1048) )
     => vf(Vd1047,Vd1049) = vf(Vd1049,vskolem1052(Vd1047,Vd1048,Vd1049,Vd1050)) ) )).

fof('ass(cond(goal(206), 0), 2)',axiom,(
    ! [Vd1047,Vd1048,Vd1049,Vd1050] :
      ( ( Vd1049 = Vd1050
        & Vd1047 != Vd1049
        & rpoint(Vd1050)
        & Vd1047 = Vd1048
        & rpoint(Vd1048) )
     => rpoint(vskolem1052(Vd1047,Vd1048,Vd1049,Vd1050)) ) )).

fof('qu(cond(axiom(190), 0), imp(cond(axiom(190), 0)))',axiom,(
    ! [Vd874,Vd875,Vd876,Vd877,Vd883,Vd884] :
      ( ( Vd883 != Vd884
        & ~ ron(Vd877,Vd884)
        & ~ ron(Vd877,Vd883)
        & Vd874 != Vd876
        & Vd874 != Vd875
        & ron(Vd876,Vd884)
        & ron(Vd875,Vd883)
        & ron(Vd874,Vd884)
        & ron(Vd874,Vd883)
        & ? [Vd887] :
            ( Vd884 = Vd887
            & rline(Vd887) )
        & ? [Vd886] :
            ( Vd883 = Vd886
            & rline(Vd886) )
        & ? [Vd882] :
            ( Vd877 = Vd882
            & rpoint(Vd882) )
        & ? [Vd881] :
            ( Vd876 = Vd881
            & rpoint(Vd881) )
        & ? [Vd880] :
            ( Vd875 = Vd880
            & rpoint(Vd880) )
        & ? [Vd879] :
            ( Vd874 = Vd879
            & rpoint(Vd879) ) )
     => ( vangle(Vd875,Vd874,Vd876) = vplus(vangle(Vd875,Vd874,Vd877),vangle(Vd877,Vd874,Vd876))
      <=> ( rS(Vd876,Vd877,Vd883)
          & rS(Vd875,Vd877,Vd884) ) ) ) )).

fof('qu(cond(axiom(188), 0), imp(cond(axiom(188), 0)))',axiom,(
    ! [Vd862,Vd863,Vd864,Vd865,Vd866,Vd867,Vd868,Vd869] :
      ( ( ron(Vd864,Vd868)
        & ron(Vd862,Vd868)
        & Vd862 != Vd866
        & Vd862 != Vd864
        & Vd868 = Vd869
        & rline(Vd869)
        & Vd866 = Vd867
        & rpoint(Vd867)
        & Vd864 = Vd865
        & rpoint(Vd865)
        & Vd862 = Vd863
        & rpoint(Vd863) )
     => ( ( ~ rR(Vd862,Vd864,Vd866)
          & ron(Vd866,Vd868) )
      <=> vangle(Vd864,Vd862,Vd866) = v0 ) ) )).

fof('qu(cond(axiom(180), 0), imp(cond(axiom(180), 0)))',axiom,(
    ! [Vd828,Vd829,Vd830] :
      ( ( rR(Vd829,Vd828,Vd830)
        & ? [Vd834] :
            ( Vd830 = Vd834
            & rpoint(Vd834) )
        & ? [Vd833] :
            ( Vd829 = Vd833
            & rpoint(Vd833) )
        & ? [Vd832] :
            ( Vd828 = Vd832
            & rpoint(Vd832) ) )
     => vplus(vf(Vd828,Vd829),vf(Vd829,Vd830)) = vf(Vd828,Vd830) ) )).

fof('qu(cond(axiom(162), 0), imp(cond(axiom(162), 0)))',axiom,(
    ! [Vd748,Vd749] :
      ( ( ? [Vd752] :
            ( Vd749 = Vd752
            & rpoint(Vd752) )
        & ? [Vd751] :
            ( Vd748 = Vd751
            & rpoint(Vd751) ) )
     => ( vf(Vd748,Vd749) = v0
      <=> Vd748 = Vd749 ) ) )).

fof('qu(cond(axiom(204), 0), imp(cond(axiom(204), 0)))',axiom,(
    ! [Vd992,Vd993,Vd994,Vd999,Vd1000,Vd1001,Vd1006,Vd1007,Vd1008,Vd1009,Vd1010,Vd1011,Vd1012,Vd1013,Vd1014,Vd1015,Vd1027,Vd1028] :
      ( ( Vd1027 = Vd1028
        & ! [Vd1031,Vd1032,Vd1033] :
            ( ( rS(Vd1033,Vd1001,Vd1027)
              & ~ rR(Vd999,Vd1032,Vd1000)
              & ron(Vd1032,Vd1027)
              & vf(Vd992,Vd994) = vf(Vd1031,Vd1033)
              & vf(Vd993,Vd994) = vf(Vd1032,Vd1033)
              & vf(Vd992,Vd993) = vf(Vd1031,Vd1032)
              & vangle(Vd1031,Vd1033,Vd1032) = vangle(Vd992,Vd994,Vd993)
              & vangle(Vd1032,Vd1031,Vd1033) = vangle(Vd993,Vd992,Vd994)
              & vangle(Vd1033,Vd1032,Vd1031) = vangle(Vd994,Vd993,Vd992)
              & Vd1031 = Vd999
              & rpoint(Vd1033)
              & rpoint(Vd1032)
              & rpoint(Vd1031) )
           => ( vangle(Vd1010,Vd1011,Vd1012) = vangle(Vd1013,Vd1014,Vd1015)
              & vf(Vd1006,Vd1007) = vf(Vd1008,Vd1009) ) )
        & ~ ron(Vd1001,Vd1027)
        & ron(Vd1000,Vd1027)
        & ron(Vd999,Vd1027)
        & rline(Vd1028)
        & ? [Vd1026] :
            ( Vd1015 = Vd1026
            & rpoint(Vd1026) )
        & ? [Vd1025] :
            ( Vd1014 = Vd1025
            & rpoint(Vd1025) )
        & ? [Vd1024] :
            ( Vd1013 = Vd1024
            & rpoint(Vd1024) )
        & ? [Vd1023] :
            ( Vd1012 = Vd1023
            & rpoint(Vd1023) )
        & ? [Vd1022] :
            ( Vd1011 = Vd1022
            & rpoint(Vd1022) )
        & ? [Vd1021] :
            ( Vd1010 = Vd1021
            & rpoint(Vd1021) )
        & ? [Vd1020] :
            ( Vd1009 = Vd1020
            & rpoint(Vd1020) )
        & ? [Vd1019] :
            ( Vd1008 = Vd1019
            & rpoint(Vd1019) )
        & ? [Vd1018] :
            ( Vd1007 = Vd1018
            & rpoint(Vd1018) )
        & ? [Vd1017] :
            ( Vd1006 = Vd1017
            & rpoint(Vd1017) )
        & ? [Vd1005] :
            ( Vd1001 = Vd1005
            & rpoint(Vd1005) )
        & ? [Vd1004] :
            ( Vd1000 = Vd1004
            & rpoint(Vd1004) )
        & ? [Vd1003] :
            ( Vd999 = Vd1003
            & rpoint(Vd1003) )
        & Vd993 != Vd994
        & Vd992 != Vd994
        & Vd992 != Vd993
        & ? [Vd998] :
            ( Vd994 = Vd998
            & rpoint(Vd998) )
        & ? [Vd997] :
            ( Vd993 = Vd997
            & rpoint(Vd997) )
        & ? [Vd996] :
            ( Vd992 = Vd996
            & rpoint(Vd996) ) )
     => ( vangle(Vd1010,Vd1011,Vd1012) = vangle(Vd1013,Vd1014,Vd1015)
        & vf(Vd1006,Vd1007) = vf(Vd1008,Vd1009) ) ) )).

fof('qu(cond(axiom(194), 0), imp(cond(axiom(194), 0)))',axiom,(
    ! [Vd908,Vd909,Vd910,Vd911,Vd912,Vd919,Vd920] :
      ( ( ~ rR(Vd908,Vd910,Vd912)
        & ~ rR(Vd908,Vd909,Vd911)
        & Vd912 != Vd908
        & Vd911 != Vd908
        & Vd910 != Vd908
        & Vd909 != Vd908
        & ron(Vd912,Vd920)
        & ron(Vd910,Vd920)
        & ron(Vd911,Vd919)
        & ron(Vd909,Vd919)
        & ron(Vd908,Vd919)
        & ? [Vd923] :
            ( Vd920 = Vd923
            & rline(Vd923) )
        & ? [Vd922] :
            ( Vd919 = Vd922
            & rline(Vd922) )
        & ? [Vd918] :
            ( Vd912 = Vd918
            & rpoint(Vd918) )
        & ? [Vd917] :
            ( Vd911 = Vd917
            & rpoint(Vd917) )
        & ? [Vd916] :
            ( Vd910 = Vd916
            & rpoint(Vd916) )
        & ? [Vd915] :
            ( Vd909 = Vd915
            & rpoint(Vd915) )
        & ? [Vd914] :
            ( Vd908 = Vd914
            & rpoint(Vd914) ) )
     => vangle(Vd909,Vd908,Vd910) = vangle(Vd911,Vd908,Vd912) ) )).

fof('qu(cond(axiom(178), 0), imp(cond(axiom(178), 0)))',axiom,(
    ! [Vd808,Vd809,Vd810,Vd811,Vd812,Vd813] :
      ( ( vangle(Vd810,Vd808,Vd809) = vangle(Vd813,Vd811,Vd812)
        & vangle(Vd809,Vd810,Vd808) = vangle(Vd812,Vd813,Vd811)
        & vangle(Vd808,Vd809,Vd810) = vangle(Vd811,Vd812,Vd813)
        & vf(Vd810,Vd808) = vf(Vd813,Vd811)
        & vf(Vd809,Vd810) = vf(Vd812,Vd813)
        & vf(Vd808,Vd809) = vf(Vd811,Vd812)
        & ? [Vd820] :
            ( Vd813 = Vd820
            & rpoint(Vd820) )
        & ? [Vd819] :
            ( Vd812 = Vd819
            & rpoint(Vd819) )
        & ? [Vd818] :
            ( Vd811 = Vd818
            & rpoint(Vd818) )
        & ? [Vd817] :
            ( Vd810 = Vd817
            & rpoint(Vd817) )
        & ? [Vd816] :
            ( Vd809 = Vd816
            & rpoint(Vd816) )
        & ? [Vd815] :
            ( Vd808 = Vd815
            & rpoint(Vd815) ) )
     => vg(Vd808,Vd809,Vd810) = vg(Vd811,Vd812,Vd813) ) )).

fof('qu(cond(axiom(202), 0), imp(cond(axiom(202), 0)))',axiom,(
    ! [Vd979,Vd980,Vd981,Vd982,Vd988,Vd989] :
      ( ( ~ ron(Vd982,Vd988)
        & Vd988 = Vd989
        & rline(Vd989)
        & Vd981 != Vd982
        & Vd980 != Vd982
        & Vd980 != Vd981
        & Vd979 != Vd982
        & Vd979 != Vd981
        & Vd979 != Vd980
        & ? [Vd987] :
            ( Vd982 = Vd987
            & rpoint(Vd987) )
        & ? [Vd986] :
            ( Vd981 = Vd986
            & rpoint(Vd986) )
        & ? [Vd985] :
            ( Vd980 = Vd985
            & rpoint(Vd985) )
        & ? [Vd984] :
            ( Vd979 = Vd984
            & rpoint(Vd984) ) )
     => ( rR(Vd981,Vd979,Vd980)
      <=> vplus(vg(Vd979,Vd981,Vd982),vg(Vd982,Vd981,Vd980)) = vg(Vd979,Vd982,Vd980) ) ) )).

fof('qu(cond(axiom(176), 0), imp(cond(axiom(176), 0)))',axiom,(
    ! [Vd799,Vd800,Vd801] :
      ( ( ? [Vd805] :
            ( Vd801 = Vd805
            & rpoint(Vd805) )
        & ? [Vd804] :
            ( Vd800 = Vd804
            & rpoint(Vd804) )
        & ? [Vd803] :
            ( Vd799 = Vd803
            & rpoint(Vd803) ) )
     => ( vg(Vd799,Vd800,Vd801) = vg(Vd799,Vd801,Vd800)
        & vg(Vd799,Vd800,Vd801) = vg(Vd801,Vd799,Vd800) ) ) )).

fof('qu(cond(axiom(200), 0), imp(cond(axiom(200), 0)))',axiom,(
    ! [Vd967,Vd968,Vd969,Vd974,Vd975] :
      ( ( ron(Vd968,Vd974)
        & ron(Vd967,Vd974)
        & Vd967 != Vd968
        & Vd974 = Vd975
        & rline(Vd975)
        & ? [Vd973] :
            ( Vd969 = Vd973
            & rpoint(Vd973) )
        & ? [Vd972] :
            ( Vd968 = Vd972
            & rpoint(Vd972) )
        & ? [Vd971] :
            ( Vd967 = Vd971
            & rpoint(Vd971) ) )
     => ( vg(Vd967,Vd968,Vd969) = v0
      <=> ron(Vd969,Vd974) ) ) )).

fof('qu(cond(axiom(192), 0), imp(cond(axiom(192), 0)))',axiom,(
    ! [Vd894,Vd895,Vd896,Vd897,Vd903,Vd904] :
      ( ( ~ ron(Vd897,Vd903)
        & rR(Vd896,Vd894,Vd895)
        & Vd903 = Vd904
        & rline(Vd904)
        & ? [Vd902] :
            ( Vd897 = Vd902
            & rpoint(Vd902) )
        & ? [Vd901] :
            ( Vd896 = Vd901
            & rpoint(Vd901) )
        & ? [Vd900] :
            ( Vd895 = Vd900
            & rpoint(Vd900) )
        & ? [Vd899] :
            ( Vd894 = Vd899
            & rpoint(Vd899) ) )
     => ( vangle(Vd894,Vd896,Vd897) = vangle(Vd897,Vd896,Vd895)
      <=> vangle(Vd894,Vd896,Vd897) = vperp ) ) )).

fof('qu(cond(axiom(174), 0), imp(cond(axiom(174), 0)))',axiom,(
    ! [Vd792,Vd793,Vd794,Vd795,Vd796,Vd797] :
      ( ( Vd796 = Vd797
        & rpoint(Vd797)
        & Vd794 = Vd795
        & rpoint(Vd795)
        & Vd792 = Vd793
        & rpoint(Vd793) )
     => rgeq(vg(Vd792,Vd794,Vd796),v0) ) )).

fof('qu(cond(axiom(198), 0), imp(cond(axiom(198), 0)))',axiom,(
    ! [Vd958,Vd959,Vd960] :
      ( ( ? [Vd964] :
            ( Vd960 = Vd964
            & rpoint(Vd964) )
        & ? [Vd963] :
            ( Vd959 = Vd963
            & rpoint(Vd963) )
        & ? [Vd962] :
            ( Vd958 = Vd962
            & rpoint(Vd962) ) )
     => ? [Vd966] :
          ( vg(Vd958,Vd959,Vd960) = Vd966
          & rreal(Vd966) ) ) )).

fof('qu(cond(axiom(196), 0), imp(cond(axiom(196), 0)))',axiom,(
    ! [Vd933,Vd934,Vd935,Vd936,Vd937,Vd944,Vd945,Vd946] :
      ( ( rless(vplus(vangle(Vd933,Vd934,Vd935),vangle(Vd934,Vd935,Vd936)),vplus(vperp,vperp))
        & rS(Vd933,Vd936,Vd945)
        & Vd934 != Vd935
        & ron(Vd936,Vd946)
        & ron(Vd935,Vd946)
        & ron(Vd935,Vd945)
        & ron(Vd934,Vd945)
        & ron(Vd934,Vd944)
        & ron(Vd933,Vd944)
        & ? [Vd950] :
            ( Vd946 = Vd950
            & rline(Vd950) )
        & ? [Vd949] :
            ( Vd945 = Vd949
            & rline(Vd949) )
        & ? [Vd948] :
            ( Vd944 = Vd948
            & rline(Vd948) )
        & ? [Vd943] :
            ( Vd937 = Vd943
            & rpoint(Vd943) )
        & ? [Vd942] :
            ( Vd936 = Vd942
            & rpoint(Vd942) )
        & ? [Vd941] :
            ( Vd935 = Vd941
            & rpoint(Vd941) )
        & ? [Vd940] :
            ( Vd934 = Vd940
            & rpoint(Vd940) )
        & ? [Vd939] :
            ( Vd933 = Vd939
            & rpoint(Vd939) ) )
     => ( ( ( ron(Vd937,Vd945)
            & ron(Vd937,Vd944) )
         => rS(Vd937,Vd933,Vd945) )
        & rintersect(Vd944,Vd945) ) ) )).

fof('qu(cond(axiom(172), 0), imp(cond(axiom(172), 0)))',axiom,(
    ! [Vd786,Vd787] :
      ( ( ? [Vd790] :
            ( Vd787 = Vd790
            & rpoint(Vd790) )
        & ? [Vd789] :
            ( Vd786 = Vd789
            & rpoint(Vd789) ) )
     => vg(Vd786,Vd786,Vd787) = v0 ) )).

fof('qu(cond(axiom(170), 0), imp(cond(axiom(170), 0)))',axiom,(
    ! [Vd777,Vd778,Vd779] :
      ( ( ? [Vd783] :
            ( Vd779 = Vd783
            & rpoint(Vd783) )
        & ? [Vd782] :
            ( Vd778 = Vd782
            & rpoint(Vd782) )
        & ? [Vd781] :
            ( Vd777 = Vd781
            & rpoint(Vd781) ) )
     => ( rleq(vangle(Vd777,Vd778,Vd779),vplus(vperp,vperp))
        & rleq(v0,vangle(Vd777,Vd778,Vd779)) ) ) )).

fof('qu(cond(axiom(168), 0), imp(cond(axiom(168), 0)))',axiom,(
    ! [Vd767,Vd768,Vd769] :
      ( ( Vd767 != Vd769
        & Vd767 != Vd768
        & ? [Vd773] :
            ( Vd769 = Vd773
            & rpoint(Vd773) )
        & ? [Vd772] :
            ( Vd768 = Vd772
            & rpoint(Vd772) )
        & ? [Vd771] :
            ( Vd767 = Vd771
            & rpoint(Vd771) ) )
     => vangle(Vd767,Vd768,Vd769) = vangle(Vd769,Vd768,Vd767) ) )).

%------------------------------------------------------------------------------