TPTP Problem File: GEO280+1.p

View Solutions - Solve Problem

```%------------------------------------------------------------------------------
% File     : GEO280+1 : TPTP v8.0.0. Released v4.1.0.
% Domain   : Geometry
% Problem  : neg(247)-neg(neg(247))
% 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   : 0.56 v7.5.0, 0.62 v7.4.0, 0.43 v7.3.0, 0.55 v7.1.0, 0.52 v7.0.0, 0.50 v6.4.0, 0.58 v6.3.0, 0.54 v6.2.0, 0.64 v6.1.0, 0.70 v5.5.0, 0.78 v5.4.0, 0.79 v5.3.0, 0.81 v5.2.0, 0.65 v5.1.0, 0.67 v5.0.0, 0.79 v4.1.0
% Syntax   : Number of formulae    :  115 (   9 unt;   0 def)
%            Number of atoms       : 1214 ( 486 equ)
%            Maximal formula atoms :   57 (  10 avg)
%            Number of connectives : 1233 ( 134   ~;  12   |; 971   &)
%                                         (   8 <=>; 108  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   46 (  13 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of predicates  :   15 (  14 usr;   0 prp; 1-3 aty)
%            Number of functors    :   22 (  22 usr;  15 con; 0-4 aty)
%            Number of variables   :  750 ( 483   !; 267   ?)
% SPC      : FOF_THM_RFO_SEQ

% Comments : From the Euclid in Naproche 0.46 collection, using the [Hea56]
%            text, and axioms from [ADM08].
%------------------------------------------------------------------------------
fof('neg(neg(247))',conjecture,
~ rinside(vd1125,vd1139) ).

fof('and(and(pred(comma_conjunct2(comma_conjunct2(comma_conjunct2(246))), 0), and(pred(comma_conjunct1(comma_conjunct2(comma_conjunct2(246))), 0), and(pred(comma_conjunct2(comma_conjunct2(246)), 0), pred(comma_conjunct1(comma_conjunct2(246)), 0)))), pred(comma_conjunct1(246), 0))',axiom,
( ron(vd1136,vd1139)
& rcenter(vd1123,vd1139)
& rcircle(vd1139)
& ron(vd1125,vd1138)
& ron(vd1123,vd1138) ) ).

fof('pred(246, 0)',axiom,
rline(vd1138) ).

fof('holds(245, 1137, 0)',axiom,
vf(vd1127,vd1129) = vf(vd1123,vd1136) ).

fof('pred(245, 0)',axiom,
rpoint(vd1136) ).

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(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(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('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('holds(conjunct2(244), 1135, 0)',axiom,
vd1123 != vd1129 ).

fof('holds(conjunct1(244), 1134, 0)',axiom,
vd1123 != vd1127 ).

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

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

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(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(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(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(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(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(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(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(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(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('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(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('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(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(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(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(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(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(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(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(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(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) ) ).

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)) ) ).

%------------------------------------------------------------------------------
```