%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO069-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:17:48 AM UTC 2026
% Result : Unsatisfiable 6.57s 1.42s
% Output : CNFRefutation 6.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 108
% Syntax : Number of formulae : 1076 ( 610 unt; 0 typ; 0 def)
% Number of atoms : 6995 (2232 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 16331 (1629 ~;2529 |; 0 &;12173 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 9 con; 0-6 aty)
% Number of variables : 4443 ( 0 ^;4443 !; 0 ?;4443 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_between,type,
between: $i > $i > $i > $o ).
thf(tp_colinear,type,
colinear: $i > $i > $i > $o ).
thf(tp_continuous,type,
continuous: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_equidistant,type,
equidistant: $i > $i > $i > $i > $o ).
thf(tp_euclid1,type,
euclid1: $i > $i > $i > $i > $i > $i ).
thf(tp_euclid2,type,
euclid2: $i > $i > $i > $i > $i > $i ).
thf(tp_extension,type,
extension: $i > $i > $i > $i > $i ).
thf(tp_inner_pasch,type,
inner_pasch: $i > $i > $i > $i > $i > $i ).
thf(tp_insertion,type,
insertion: $i > $i > $i > $i > $i ).
thf(tp_lower_dimension_point_1,type,
lower_dimension_point_1: $i ).
thf(tp_lower_dimension_point_2,type,
lower_dimension_point_2: $i ).
thf(tp_lower_dimension_point_3,type,
lower_dimension_point_3: $i ).
thf(tp_reflection,type,
reflection: $i > $i > $i ).
thf(tp_u,type,
u: $i ).
thf(tp_v,type,
v: $i ).
thf(tp_w,type,
w: $i ).
thf(tp_x,type,
x: $i ).
thf(1,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( colinear @ U @ V @ W )
| ~ ( colinear @ U @ V @ X )
| ( colinear @ V @ W @ X )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_2) ).
thf(2,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( colinear @ U @ V @ W )
| ~ ( colinear @ U @ V @ X )
| ( colinear @ U @ W @ X )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t12_1) ).
thf(3,axiom,
! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ~ ( colinear @ U @ V @ W )
| ( colinear @ U1 @ V1 @ W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c4) ).
thf(4,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( X != Y )
| ( colinear @ X @ Z @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c3_4) ).
thf(5,axiom,
! [Y: $i,X: $i] : ( colinear @ Y @ X @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c3_3) ).
thf(6,axiom,
! [X: $i,Y: $i] : ( colinear @ X @ Y @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c3_2) ).
thf(7,axiom,
! [X: $i,Y: $i] : ( colinear @ X @ X @ Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c3_1) ).
thf(8,axiom,
~ ( colinear @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t11) ).
thf(9,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ( colinear @ V @ U @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_5) ).
thf(10,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ( colinear @ W @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_4) ).
thf(11,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ( colinear @ U @ W @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_3) ).
thf(12,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ( colinear @ V @ W @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_2) ).
thf(13,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ( colinear @ W @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t10_1) ).
thf(14,axiom,
! [V: $i,U: $i,W: $i] :
( ~ ( between @ V @ U @ W )
| ( colinear @ U @ V @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2_3) ).
thf(15,axiom,
! [U: $i,W: $i,V: $i] :
( ~ ( between @ U @ W @ V )
| ( colinear @ U @ V @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2_2) ).
thf(16,axiom,
! [W: $i,V: $i,U: $i] :
( ~ ( between @ W @ V @ U )
| ( colinear @ U @ V @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',c2_1) ).
thf(17,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( equidistant @ U @ V @ U @ W )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b15) ).
thf(18,axiom,
! [U: $i,V: $i,Y: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ Y )
| ~ ( between @ V @ W @ X )
| ~ ( between @ U @ X @ Y )
| ( between @ U @ W @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8) ).
thf(19,axiom,
! [U: $i,V: $i,X: $i,W: $i] :
( ~ ( between @ U @ V @ X )
| ~ ( between @ U @ W @ X )
| ( between @ V @ W @ X )
| ( between @ W @ V @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b14) ).
thf(20,axiom,
! [U: $i,V: $i,X: $i,W: $i] :
( ~ ( between @ U @ V @ X )
| ~ ( between @ U @ W @ X )
| ( between @ U @ V @ W )
| ( between @ U @ W @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t9) ).
thf(21,axiom,
! [U: $i,W: $i,X: $i,V: $i] :
( ~ ( between @ U @ W @ X )
| ~ ( between @ V @ W @ X )
| ( W = X )
| ( between @ U @ V @ W )
| ( between @ V @ U @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7) ).
thf(22,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ V @ X )
| ( U = V )
| ( between @ V @ W @ X )
| ( between @ V @ X @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b13) ).
thf(23,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ V @ X )
| ( U = V )
| ( between @ U @ W @ X )
| ( between @ U @ X @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b12) ).
thf(24,axiom,
! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ~ ( between @ U @ V @ W )
| ( between @ U1 @ V1 @ W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b11) ).
thf(25,axiom,
! [W: $i,X: $i,Y: $i,Z: $i,U: $i,V: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ( ( insertion @ U @ V @ W @ X )
= ( insertion @ U @ V @ Y @ Z ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i4) ).
thf(26,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( V
= ( insertion @ U @ W @ U @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i3) ).
thf(27,axiom,
! [U: $i,V: $i,W: $i,U1: $i,W1: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ( equidistant @ V @ W @ ( insertion @ U1 @ W1 @ U @ V ) @ W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i2_3) ).
thf(28,axiom,
! [U: $i,V: $i,W: $i,U1: $i,W1: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ( between @ U1 @ ( insertion @ U1 @ W1 @ U @ V ) @ W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i2_2) ).
thf(29,axiom,
! [U: $i,V: $i,U1: $i,W1: $i] : ( equidistant @ U @ V @ U1 @ ( insertion @ U1 @ W1 @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',i2_1) ).
thf(30,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( equidistant @ U @ V @ U @ X )
| ~ ( equidistant @ W @ V @ W @ X )
| ( V = X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d15) ).
thf(31,axiom,
! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i,X: $i,X1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( equidistant @ U @ X @ U1 @ X1 )
| ~ ( equidistant @ W @ X @ W1 @ X1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ V @ X @ V1 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d14) ).
thf(32,axiom,
! [U: $i,V: $i,W: $i,U1: $i,V1: $i,W1: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ( equidistant @ V @ W @ V1 @ W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d13) ).
thf(33,axiom,
! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i,X: $i,X1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ~ ( equidistant @ U @ X @ U1 @ X1 )
| ~ ( equidistant @ W @ X @ W1 @ X1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ V @ X @ V1 @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d12) ).
thf(34,axiom,
! [U: $i,V: $i,W: $i,W1: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( equidistant @ U @ W @ U @ W1 )
| ~ ( equidistant @ V @ W @ V @ W1 )
| ( U = V )
| ( W = W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d11) ).
thf(35,axiom,
! [U: $i,V: $i,W: $i,U1: $i,V1: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W )
| ~ ( between @ U @ X @ U1 )
| ( between @ X @ ( inner_pasch @ V1 @ ( inner_pasch @ U @ X @ U1 @ V1 @ W ) @ U @ V @ W ) @ W )
| ( between @ V @ ( inner_pasch @ V1 @ ( inner_pasch @ U @ X @ U1 @ V1 @ W ) @ U @ V @ W ) @ V1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b10) ).
thf(36,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_3) ).
thf(37,axiom,
! [V: $i,U: $i,X: $i,W: $i] : ( equidistant @ V @ ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ X @ ( extension @ W @ X @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_2) ).
thf(38,axiom,
! [V: $i,U: $i] :
( V
!= ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_1) ).
thf(39,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_3) ).
thf(40,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_2) ).
thf(41,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_1) ).
thf(42,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ X )
| ( between @ U @ V @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b9) ).
thf(43,axiom,
! [U: $i,V: $i,X: $i,W: $i] :
( ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b8) ).
thf(44,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ V @ X )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b7) ).
thf(45,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b6) ).
thf(46,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ X )
| ( between @ V @ W @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b5) ).
thf(47,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ V @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b4) ).
thf(48,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( U = V )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_2) ).
thf(49,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_1) ).
thf(50,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b3) ).
thf(51,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
thf(52,axiom,
! [U: $i,V: $i] : ( between @ U @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2) ).
thf(53,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
thf(54,axiom,
! [U: $i,W: $i,X: $i,V: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ( between @ V @ W @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b1) ).
thf(55,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3) ).
thf(56,axiom,
! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r6) ).
thf(57,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r5) ).
thf(58,axiom,
! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_3) ).
thf(59,axiom,
! [W: $i,X: $i,Y: $i,Z: $i,U: $i,V: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ( ( extension @ U @ V @ W @ X )
= ( extension @ U @ V @ Y @ Z ) )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_2) ).
thf(60,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( U = V )
| ( W
= ( extension @ U @ V @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_1) ).
thf(61,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ V @ X )
| ~ ( equidistant @ V @ W @ V @ X )
| ( U = V )
| ( W = X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9) ).
thf(62,axiom,
! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ U @ W @ U1 @ W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8) ).
thf(63,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7) ).
thf(64,axiom,
! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).
thf(65,axiom,
! [U: $i] :
( U
= ( reflection @ U @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3_2) ).
thf(66,axiom,
! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3_1) ).
thf(67,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_2) ).
thf(68,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_1) ).
thf(69,axiom,
! [Y: $i,U: $i,V: $i,W: $i,X: $i] :
( ( Y
!= ( extension @ U @ V @ W @ X ) )
| ( between @ U @ V @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b0) ).
thf(70,axiom,
! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e1) ).
thf(71,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ~ ( equidistant @ W @ X @ Y @ Z )
| ( equidistant @ U @ V @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5) ).
thf(72,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_5) ).
thf(73,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_4) ).
thf(74,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_3) ).
thf(75,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_2) ).
thf(76,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_1) ).
thf(77,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3) ).
thf(78,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
thf(79,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
thf(80,axiom,
! [U1: $i,W1: $i,U: $i,V: $i] :
( ( insertion @ U1 @ W1 @ U @ V )
= ( extension @ ( extension @ W1 @ U1 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ U1 @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',insertion) ).
thf(81,axiom,
! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflection) ).
thf(82,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( colinear @ X @ Y @ Z )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity4) ).
thf(83,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( between @ Z @ X @ Y )
| ( colinear @ X @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity3) ).
thf(84,axiom,
! [Y: $i,Z: $i,X: $i] :
( ~ ( between @ Y @ Z @ X )
| ( colinear @ X @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity2) ).
thf(85,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ Y @ Z )
| ( colinear @ X @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity1) ).
thf(86,axiom,
! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity2) ).
thf(87,axiom,
! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity1) ).
thf(88,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid3) ).
thf(89,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid2) ).
thf(90,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid1) ).
thf(91,axiom,
! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ W @ X @ V )
| ~ ( equidistant @ Y @ W @ Y @ V )
| ~ ( equidistant @ Z @ W @ Z @ V )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y )
| ( W = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_dimension) ).
thf(92,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
thf(93,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).
thf(94,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).
thf(95,axiom,
! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ Y @ X @ W )
| ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch2) ).
thf(96,axiom,
! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ Y @ X @ W )
| ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch1) ).
thf(97,axiom,
! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(98,axiom,
! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i,V: $i,V1: $i] :
( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
| ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
| ~ ( equidistant @ X @ V @ X1 @ V1 )
| ~ ( equidistant @ Y @ V @ Y1 @ V1 )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equidistant @ Z @ V @ Z1 @ V1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).
thf(99,axiom,
! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
thf(100,axiom,
! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
thf(101,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(102,axiom,
! [X: $i,Y: $i,Z: $i,V: $i,V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
thf(103,axiom,
! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(104,axiom,
colinear @ x @ v @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',xvu_colinear) ).
thf(105,axiom,
colinear @ w @ v @ u,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wvu_colinear) ).
thf(106,axiom,
u != v,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',u_not_v) ).
thf(107,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(108,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[107]) ).
thf(109,negated_conjecture,
( ~ ( colinear @ x @ w @ u )
| ~ ( colinear @ x @ w @ v ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_xwu_and_xwv_colinear) ).
thf(110,plain,
$false = $false,
inference(unfold_def,[status(thm)],[108]) ).
thf(111,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( colinear @ U @ V @ W )
| ~ ( colinear @ U @ V @ X )
| ( colinear @ V @ W @ X )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(112,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( colinear @ U @ V @ W )
| ~ ( colinear @ U @ V @ X )
| ( colinear @ U @ W @ X )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(113,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ~ ( colinear @ U @ V @ W )
| ( colinear @ U1 @ V1 @ W1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(114,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ( X != Y )
| ( colinear @ X @ Z @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(115,plain,
( ( ! [Y: $i,X: $i] : ( colinear @ Y @ X @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(116,plain,
( ( ! [X: $i,Y: $i] : ( colinear @ X @ Y @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(117,plain,
( ( ! [X: $i,Y: $i] : ( colinear @ X @ X @ Y ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(118,plain,
( ( ~ ( colinear @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(119,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ( colinear @ V @ U @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(120,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ( colinear @ W @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(121,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ( colinear @ U @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(122,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ( colinear @ V @ W @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(123,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ( colinear @ W @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(124,plain,
( ( ! [V: $i,U: $i,W: $i] :
( ~ ( between @ V @ U @ W )
| ( colinear @ U @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(125,plain,
( ( ! [U: $i,W: $i,V: $i] :
( ~ ( between @ U @ W @ V )
| ( colinear @ U @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(126,plain,
( ( ! [W: $i,V: $i,U: $i] :
( ~ ( between @ W @ V @ U )
| ( colinear @ U @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(127,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( equidistant @ U @ V @ U @ W )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(128,plain,
( ( ! [U: $i,V: $i,Y: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ Y )
| ~ ( between @ V @ W @ X )
| ~ ( between @ U @ X @ Y )
| ( between @ U @ W @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(129,plain,
( ( ! [U: $i,V: $i,X: $i,W: $i] :
( ~ ( between @ U @ V @ X )
| ~ ( between @ U @ W @ X )
| ( between @ V @ W @ X )
| ( between @ W @ V @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(130,plain,
( ( ! [U: $i,V: $i,X: $i,W: $i] :
( ~ ( between @ U @ V @ X )
| ~ ( between @ U @ W @ X )
| ( between @ U @ V @ W )
| ( between @ U @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(131,plain,
( ( ! [U: $i,W: $i,X: $i,V: $i] :
( ~ ( between @ U @ W @ X )
| ~ ( between @ V @ W @ X )
| ( W = X )
| ( between @ U @ V @ W )
| ( between @ V @ U @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(132,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ V @ X )
| ( U = V )
| ( between @ V @ W @ X )
| ( between @ V @ X @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(133,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ V @ X )
| ( U = V )
| ( between @ U @ W @ X )
| ( between @ U @ X @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(134,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ~ ( between @ U @ V @ W )
| ( between @ U1 @ V1 @ W1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(135,plain,
( ( ! [W: $i,X: $i,Y: $i,Z: $i,U: $i,V: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ( ( insertion @ U @ V @ W @ X )
= ( insertion @ U @ V @ Y @ Z ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(136,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( V
= ( insertion @ U @ W @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(137,plain,
( ( ! [U: $i,V: $i,W: $i,U1: $i,W1: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ( equidistant @ V @ W @ ( insertion @ U1 @ W1 @ U @ V ) @ W1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(138,plain,
( ( ! [U: $i,V: $i,W: $i,U1: $i,W1: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ( between @ U1 @ ( insertion @ U1 @ W1 @ U @ V ) @ W1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(139,plain,
( ( ! [U: $i,V: $i,U1: $i,W1: $i] : ( equidistant @ U @ V @ U1 @ ( insertion @ U1 @ W1 @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(140,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( equidistant @ U @ V @ U @ X )
| ~ ( equidistant @ W @ V @ W @ X )
| ( V = X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(141,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i,X: $i,X1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( equidistant @ U @ X @ U1 @ X1 )
| ~ ( equidistant @ W @ X @ W1 @ X1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ V @ X @ V1 @ X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(142,plain,
( ( ! [U: $i,V: $i,W: $i,U1: $i,V1: $i,W1: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ( equidistant @ V @ W @ V1 @ W1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(143,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i,X: $i,X1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ~ ( equidistant @ U @ X @ U1 @ X1 )
| ~ ( equidistant @ W @ X @ W1 @ X1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ V @ X @ V1 @ X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(144,plain,
( ( ! [U: $i,V: $i,W: $i,W1: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( equidistant @ U @ W @ U @ W1 )
| ~ ( equidistant @ V @ W @ V @ W1 )
| ( U = V )
| ( W = W1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(145,plain,
( ( ! [U: $i,V: $i,W: $i,U1: $i,V1: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W )
| ~ ( between @ U @ X @ U1 )
| ( between @ X @ ( inner_pasch @ V1 @ ( inner_pasch @ U @ X @ U1 @ V1 @ W ) @ U @ V @ W ) @ W )
| ( between @ V @ ( inner_pasch @ V1 @ ( inner_pasch @ U @ X @ U1 @ V1 @ W ) @ U @ V @ W ) @ V1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(146,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(147,plain,
( ( ! [V: $i,U: $i,X: $i,W: $i] : ( equidistant @ V @ ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ X @ ( extension @ W @ X @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(148,plain,
( ( ! [V: $i,U: $i] :
( V
!= ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(149,plain,
( ( lower_dimension_point_1 != lower_dimension_point_3 )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(150,plain,
( ( lower_dimension_point_2 != lower_dimension_point_3 )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(151,plain,
( ( lower_dimension_point_1 != lower_dimension_point_2 )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(152,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ X )
| ( between @ U @ V @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(153,plain,
( ( ! [U: $i,V: $i,X: $i,W: $i] :
( ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(154,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ V @ X )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(155,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(156,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ X )
| ( between @ V @ W @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(157,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(158,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( U = V )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(159,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(160,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(161,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(162,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(163,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(164,plain,
( ( ! [U: $i,W: $i,X: $i,V: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ( between @ V @ W @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(165,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(166,plain,
( ( ! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(167,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(168,plain,
( ( ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(169,plain,
( ( ! [W: $i,X: $i,Y: $i,Z: $i,U: $i,V: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ( ( extension @ U @ V @ W @ X )
= ( extension @ U @ V @ Y @ Z ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(170,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( U = V )
| ( W
= ( extension @ U @ V @ V @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(171,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ V @ X )
| ~ ( equidistant @ V @ W @ V @ X )
| ( U = V )
| ( W = X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(172,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ U @ W @ U1 @ W1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(173,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(174,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(175,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(176,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(177,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(178,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[68]) ).
thf(179,plain,
( ( ! [Y: $i,U: $i,V: $i,W: $i,X: $i] :
( ( Y
!= ( extension @ U @ V @ W @ X ) )
| ( between @ U @ V @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(180,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(181,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ~ ( equidistant @ W @ X @ Y @ Z )
| ( equidistant @ U @ V @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(182,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(183,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(184,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(185,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[75]) ).
thf(186,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(187,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(188,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(189,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(190,plain,
( ( ! [U1: $i,W1: $i,U: $i,V: $i] :
( ( insertion @ U1 @ W1 @ U @ V )
= ( extension @ ( extension @ W1 @ U1 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ U1 @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(191,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[81]) ).
thf(192,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( colinear @ X @ Y @ Z )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(193,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( between @ Z @ X @ Y )
| ( colinear @ X @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(194,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ~ ( between @ Y @ Z @ X )
| ( colinear @ X @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(195,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ Y @ Z )
| ( colinear @ X @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[85]) ).
thf(196,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[86]) ).
thf(197,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(198,plain,
( ( ! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[88]) ).
thf(199,plain,
( ( ! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[89]) ).
thf(200,plain,
( ( ! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[90]) ).
thf(201,plain,
( ( ! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ W @ X @ V )
| ~ ( equidistant @ Y @ W @ Y @ V )
| ~ ( equidistant @ Z @ W @ Z @ V )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y )
| ( W = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[91]) ).
thf(202,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[92]) ).
thf(203,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[93]) ).
thf(204,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[94]) ).
thf(205,plain,
( ( ! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ Y @ X @ W )
| ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[95]) ).
thf(206,plain,
( ( ! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ Y @ X @ W )
| ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[96]) ).
thf(207,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[97]) ).
thf(208,plain,
( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i,V: $i,V1: $i] :
( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
| ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
| ~ ( equidistant @ X @ V @ X1 @ V1 )
| ~ ( equidistant @ Y @ V @ Y1 @ V1 )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equidistant @ Z @ V @ Z1 @ V1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[98]) ).
thf(209,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[99]) ).
thf(210,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[100]) ).
thf(211,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[101]) ).
thf(212,plain,
( ( ! [X: $i,Y: $i,Z: $i,V: $i,V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[102]) ).
thf(213,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[103]) ).
thf(214,plain,
( ( colinear @ x @ v @ u )
= $true ),
inference(unfold_def,[status(thm)],[104]) ).
thf(215,plain,
( ( colinear @ w @ v @ u )
= $true ),
inference(unfold_def,[status(thm)],[105]) ).
thf(216,plain,
( ( u != v )
= $true ),
inference(unfold_def,[status(thm)],[106]) ).
thf(217,plain,
( ( ~ ( colinear @ x @ w @ u )
| ~ ( colinear @ x @ w @ v ) )
= $true ),
inference(unfold_def,[status(thm)],[109]) ).
thf(218,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[110]) ).
thf(219,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ! [X: $i] :
( ~ ( colinear @ U @ V @ X )
| ( U = V )
| ( colinear @ V @ W @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(220,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ! [X: $i] :
( ~ ( colinear @ U @ V @ X )
| ( U = V )
| ( colinear @ U @ W @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[112]) ).
thf(221,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ! [W: $i,W1: $i] :
( ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ~ ( colinear @ U @ V @ W )
| ( colinear @ U1 @ V1 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[113]) ).
thf(222,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ! [Z: $i] : ( colinear @ X @ Z @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[114]) ).
thf(223,plain,
( ( ! [U: $i,V: $i,Y: $i] :
( ~ ( between @ U @ V @ Y )
| ! [W: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ~ ( between @ U @ X @ Y )
| ( between @ U @ W @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[128]) ).
thf(224,plain,
( ( ! [U: $i,V: $i,X: $i] :
( ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ U @ W @ X )
| ( between @ V @ W @ X )
| ( between @ W @ V @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[129]) ).
thf(225,plain,
( ( ! [U: $i,V: $i,X: $i] :
( ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ U @ W @ X )
| ( between @ U @ V @ W )
| ( between @ U @ W @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[130]) ).
thf(226,plain,
( ( ! [U: $i,W: $i,X: $i] :
( ~ ( between @ U @ W @ X )
| ! [V: $i] :
( ~ ( between @ V @ W @ X )
| ( W = X )
| ( between @ U @ V @ W )
| ( between @ V @ U @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[131]) ).
thf(227,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ U @ V @ X )
| ( U = V )
| ( between @ V @ W @ X )
| ( between @ V @ X @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[132]) ).
thf(228,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ U @ V @ X )
| ( U = V )
| ( between @ U @ W @ X )
| ( between @ U @ X @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[133]) ).
thf(229,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ! [W: $i,W1: $i] :
( ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ~ ( between @ U @ V @ W )
| ( between @ U1 @ V1 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[134]) ).
thf(230,plain,
( ( ! [W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ! [U: $i,V: $i] :
( ( insertion @ U @ V @ W @ X )
= ( insertion @ U @ V @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[135]) ).
thf(231,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [U1: $i,W1: $i] :
( ~ ( equidistant @ U @ W @ U1 @ W1 )
| ( equidistant @ V @ W @ ( insertion @ U1 @ W1 @ U @ V ) @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[137]) ).
thf(232,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [U1: $i,W1: $i] :
( ~ ( equidistant @ U @ W @ U1 @ W1 )
| ( between @ U1 @ ( insertion @ U1 @ W1 @ U @ V ) @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[138]) ).
thf(233,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( equidistant @ U @ V @ U @ X )
| ~ ( equidistant @ W @ V @ W @ X )
| ( V = X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[140]) ).
thf(234,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ V @ W @ V1 @ W1 )
| ! [X: $i,X1: $i] :
( ~ ( equidistant @ U @ X @ U1 @ X1 )
| ~ ( equidistant @ W @ X @ W1 @ X1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ V @ X @ V1 @ X1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[141]) ).
thf(235,plain,
( ( ! [U: $i,V: $i,W: $i,U1: $i] :
( ~ ( between @ U @ V @ W )
| ! [V1: $i,W1: $i] :
( ~ ( between @ U1 @ V1 @ W1 )
| ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ( equidistant @ V @ W @ V1 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[142]) ).
thf(236,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ! [X: $i,X1: $i] :
( ~ ( equidistant @ U @ X @ U1 @ X1 )
| ~ ( equidistant @ W @ X @ W1 @ X1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ V @ X @ V1 @ X1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[143]) ).
thf(237,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [W1: $i] :
( ~ ( equidistant @ U @ W @ U @ W1 )
| ~ ( equidistant @ V @ W @ V @ W1 )
| ( U = V )
| ( W = W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[144]) ).
thf(238,plain,
( ( ! [U: $i,V: $i,W: $i,U1: $i] :
( ~ ( between @ U @ V @ W )
| ! [V1: $i] :
( ~ ( between @ U1 @ V1 @ W )
| ! [X: $i] :
( ~ ( between @ U @ X @ U1 )
| ( between @ X @ ( inner_pasch @ V1 @ ( inner_pasch @ U @ X @ U1 @ V1 @ W ) @ U @ V @ W ) @ W )
| ( between @ V @ ( inner_pasch @ V1 @ ( inner_pasch @ U @ X @ U1 @ V1 @ W ) @ U @ V @ W ) @ V1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[145]) ).
thf(239,plain,
( ( ! [V: $i,U: $i] :
( V
!= ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[148]) ).
thf(240,plain,
( ( lower_dimension_point_1 != lower_dimension_point_3 )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(241,plain,
( ( lower_dimension_point_2 != lower_dimension_point_3 )
= $true ),
inference(extcnf_combined,[status(esa)],[150]) ).
thf(242,plain,
( ( lower_dimension_point_1 != lower_dimension_point_2 )
= $true ),
inference(extcnf_combined,[status(esa)],[151]) ).
thf(243,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ U @ W @ X )
| ( between @ U @ V @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[152]) ).
thf(244,plain,
( ( ! [U: $i,V: $i,X: $i] :
( ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[153]) ).
thf(245,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ V @ W @ X )
| ( V = W )
| ( between @ U @ V @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[154]) ).
thf(246,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ V @ W @ X )
| ( V = W )
| ( between @ U @ W @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[155]) ).
thf(247,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ U @ W @ X )
| ( between @ V @ W @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[156]) ).
thf(248,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
~ ( between @ V @ W @ X )
| ( between @ U @ V @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[157]) ).
thf(249,plain,
( ( ! [U: $i,W: $i,X: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ! [V: $i] : ( between @ V @ W @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[164]) ).
thf(250,plain,
( ( ! [W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ W @ X )
= ( extension @ U @ V @ Y @ Z ) )
| ( U = V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[169]) ).
thf(251,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ U @ V @ X )
| ~ ( equidistant @ V @ W @ V @ X )
| ( U = V )
| ( W = X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[171]) ).
thf(252,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ! [W: $i,W1: $i] :
( ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ U @ W @ U1 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[172]) ).
thf(253,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[174]) ).
thf(254,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[176]) ).
thf(255,plain,
( ( ! [Y: $i,U: $i,V: $i] :
( ! [W: $i,X: $i] :
( Y
!= ( extension @ U @ V @ W @ X ) )
| ( between @ U @ V @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[179]) ).
thf(256,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ! [Y: $i,Z: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ( equidistant @ U @ V @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[181]) ).
thf(257,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ! [X1: $i] :
( ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[196]) ).
thf(258,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ! [X1: $i] :
( ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[197]) ).
thf(259,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[198]) ).
thf(260,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[199]) ).
thf(261,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[200]) ).
thf(262,plain,
( ( ! [X: $i,W: $i,V: $i] :
( ~ ( equidistant @ X @ W @ X @ V )
| ! [Y: $i] :
( ~ ( equidistant @ Y @ W @ Y @ V )
| ! [Z: $i] :
( ~ ( equidistant @ Z @ W @ Z @ V )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( W = V )
| ( between @ Z @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[201]) ).
thf(263,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [Y: $i,X: $i] :
( ~ ( between @ Y @ X @ W )
| ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[205]) ).
thf(264,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [Y: $i,X: $i] :
( ~ ( between @ Y @ X @ W )
| ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[206]) ).
thf(265,plain,
( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i] :
( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
| ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
| ! [V: $i,V1: $i] :
( ~ ( equidistant @ X @ V @ X1 @ V1 )
| ~ ( equidistant @ Y @ V @ Y1 @ V1 )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equidistant @ Z @ V @ Z1 @ V1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[208]) ).
thf(266,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[211]) ).
thf(267,plain,
( ( ! [X: $i,Y: $i,Z: $i,V: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ! [V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[212]) ).
thf(268,plain,
( ( u != v )
= $true ),
inference(extcnf_combined,[status(esa)],[216]) ).
thf(269,plain,
( ( ~ ( colinear @ x @ w @ u )
| ~ ( colinear @ x @ w @ v ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(270,plain,
( ( u != v )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(271,plain,
( ( colinear @ w @ v @ u )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(272,plain,
( ( colinear @ x @ v @ u )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(273,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(274,plain,
( ( ! [X: $i,Y: $i,Z: $i,V: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ! [V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(275,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(276,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(277,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(278,plain,
( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i] :
( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
| ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
| ! [V: $i,V1: $i] :
( ~ ( equidistant @ X @ V @ X1 @ V1 )
| ~ ( equidistant @ Y @ V @ Y1 @ V1 )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equidistant @ Z @ V @ Z1 @ V1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(279,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(280,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [Y: $i,X: $i] :
( ~ ( between @ Y @ X @ W )
| ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(281,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [Y: $i,X: $i] :
( ~ ( between @ Y @ X @ W )
| ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(282,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(283,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(284,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(285,plain,
( ( ! [X: $i,W: $i,V: $i] :
( ~ ( equidistant @ X @ W @ X @ V )
| ! [Y: $i] :
( ~ ( equidistant @ Y @ W @ Y @ V )
| ! [Z: $i] :
( ~ ( equidistant @ Z @ W @ Z @ V )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( W = V )
| ( between @ Z @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(286,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(287,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(288,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(289,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ! [X1: $i] :
( ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(290,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ! [X1: $i] :
( ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(291,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ Y @ Z )
| ( colinear @ X @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(292,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ~ ( between @ Y @ Z @ X )
| ( colinear @ X @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(293,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( between @ Z @ X @ Y )
| ( colinear @ X @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(294,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( colinear @ X @ Y @ Z )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(295,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(296,plain,
( ( ! [U1: $i,W1: $i,U: $i,V: $i] :
( ( insertion @ U1 @ W1 @ U @ V )
= ( extension @ ( extension @ W1 @ U1 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ U1 @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(297,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(298,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(299,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(300,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(301,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(302,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(303,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(304,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(305,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ! [Y: $i,Z: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ( equidistant @ U @ V @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(306,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(307,plain,
( ( ! [Y: $i,U: $i,V: $i] :
( ! [W: $i,X: $i] :
( Y
!= ( extension @ U @ V @ W @ X ) )
| ( between @ U @ V @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(308,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(309,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(310,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(311,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(312,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(313,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(314,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ! [W: $i,W1: $i] :
( ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ U @ W @ U1 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(315,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ U @ V @ X )
| ~ ( equidistant @ V @ W @ V @ X )
| ( U = V )
| ( W = X ) ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(316,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( U = V )
| ( W
= ( extension @ U @ V @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(317,plain,
( ( ! [W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ W @ X )
= ( extension @ U @ V @ Y @ Z ) )
| ( U = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(318,plain,
( ( ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(319,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(320,plain,
( ( ! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(321,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(322,plain,
( ( ! [U: $i,W: $i,X: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ! [V: $i] : ( between @ V @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(323,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[163]) ).
thf(324,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[162]) ).
thf(325,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(326,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(327,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(328,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( U = V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[158]) ).
thf(329,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
~ ( between @ V @ W @ X )
| ( between @ U @ V @ W ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(330,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ U @ W @ X )
| ( between @ V @ W @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(331,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ V @ W @ X )
| ( V = W )
| ( between @ U @ W @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(332,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ V @ W @ X )
| ( V = W )
| ( between @ U @ V @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(333,plain,
( ( ! [U: $i,V: $i,X: $i] :
( ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(334,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ U @ W @ X )
| ( between @ U @ V @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(335,plain,
( ( lower_dimension_point_1 != lower_dimension_point_2 )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(336,plain,
( ( lower_dimension_point_2 != lower_dimension_point_3 )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(337,plain,
( ( lower_dimension_point_1 != lower_dimension_point_3 )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(338,plain,
( ( ! [V: $i,U: $i] :
( V
!= ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(339,plain,
( ( ! [V: $i,U: $i,X: $i,W: $i] : ( equidistant @ V @ ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ X @ ( extension @ W @ X @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(340,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(341,plain,
( ( ! [U: $i,V: $i,W: $i,U1: $i] :
( ~ ( between @ U @ V @ W )
| ! [V1: $i] :
( ~ ( between @ U1 @ V1 @ W )
| ! [X: $i] :
( ~ ( between @ U @ X @ U1 )
| ( between @ X @ ( inner_pasch @ V1 @ ( inner_pasch @ U @ X @ U1 @ V1 @ W ) @ U @ V @ W ) @ W )
| ( between @ V @ ( inner_pasch @ V1 @ ( inner_pasch @ U @ X @ U1 @ V1 @ W ) @ U @ V @ W ) @ V1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(342,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [W1: $i] :
( ~ ( equidistant @ U @ W @ U @ W1 )
| ~ ( equidistant @ V @ W @ V @ W1 )
| ( U = V )
| ( W = W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(343,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ! [X: $i,X1: $i] :
( ~ ( equidistant @ U @ X @ U1 @ X1 )
| ~ ( equidistant @ W @ X @ W1 @ X1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ V @ X @ V1 @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(344,plain,
( ( ! [U: $i,V: $i,W: $i,U1: $i] :
( ~ ( between @ U @ V @ W )
| ! [V1: $i,W1: $i] :
( ~ ( between @ U1 @ V1 @ W1 )
| ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ( equidistant @ V @ W @ V1 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(345,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ V @ W @ V1 @ W1 )
| ! [X: $i,X1: $i] :
( ~ ( equidistant @ U @ X @ U1 @ X1 )
| ~ ( equidistant @ W @ X @ W1 @ X1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ V @ X @ V1 @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(346,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( equidistant @ U @ V @ U @ X )
| ~ ( equidistant @ W @ V @ W @ X )
| ( V = X ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(347,plain,
( ( ! [U: $i,V: $i,U1: $i,W1: $i] : ( equidistant @ U @ V @ U1 @ ( insertion @ U1 @ W1 @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(348,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [U1: $i,W1: $i] :
( ~ ( equidistant @ U @ W @ U1 @ W1 )
| ( between @ U1 @ ( insertion @ U1 @ W1 @ U @ V ) @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(349,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [U1: $i,W1: $i] :
( ~ ( equidistant @ U @ W @ U1 @ W1 )
| ( equidistant @ V @ W @ ( insertion @ U1 @ W1 @ U @ V ) @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[231]) ).
thf(350,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( V
= ( insertion @ U @ W @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(351,plain,
( ( ! [W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ! [U: $i,V: $i] :
( ( insertion @ U @ V @ W @ X )
= ( insertion @ U @ V @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(352,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ! [W: $i,W1: $i] :
( ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ~ ( between @ U @ V @ W )
| ( between @ U1 @ V1 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(353,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ U @ V @ X )
| ( U = V )
| ( between @ U @ W @ X )
| ( between @ U @ X @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(354,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ U @ V @ X )
| ( U = V )
| ( between @ V @ W @ X )
| ( between @ V @ X @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[227]) ).
thf(355,plain,
( ( ! [U: $i,W: $i,X: $i] :
( ~ ( between @ U @ W @ X )
| ! [V: $i] :
( ~ ( between @ V @ W @ X )
| ( W = X )
| ( between @ U @ V @ W )
| ( between @ V @ U @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(356,plain,
( ( ! [U: $i,V: $i,X: $i] :
( ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ U @ W @ X )
| ( between @ U @ V @ W )
| ( between @ U @ W @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(357,plain,
( ( ! [U: $i,V: $i,X: $i] :
( ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ U @ W @ X )
| ( between @ V @ W @ X )
| ( between @ W @ V @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(358,plain,
( ( ! [U: $i,V: $i,Y: $i] :
( ~ ( between @ U @ V @ Y )
| ! [W: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ~ ( between @ U @ X @ Y )
| ( between @ U @ W @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(359,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( equidistant @ U @ V @ U @ W )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(360,plain,
( ( ! [W: $i,V: $i,U: $i] :
( ~ ( between @ W @ V @ U )
| ( colinear @ U @ V @ W ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(361,plain,
( ( ! [U: $i,W: $i,V: $i] :
( ~ ( between @ U @ W @ V )
| ( colinear @ U @ V @ W ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(362,plain,
( ( ! [V: $i,U: $i,W: $i] :
( ~ ( between @ V @ U @ W )
| ( colinear @ U @ V @ W ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(363,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ( colinear @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(364,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ( colinear @ V @ W @ U ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(365,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ( colinear @ U @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(366,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ( colinear @ W @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(367,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ( colinear @ V @ U @ W ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(368,plain,
( ( ~ ( colinear @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(369,plain,
( ( ! [X: $i,Y: $i] : ( colinear @ X @ X @ Y ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(370,plain,
( ( ! [X: $i,Y: $i] : ( colinear @ X @ Y @ X ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(371,plain,
( ( ! [Y: $i,X: $i] : ( colinear @ Y @ X @ X ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(372,plain,
( ( ! [X: $i,Y: $i] :
( ( X != Y )
| ! [Z: $i] : ( colinear @ X @ Z @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(373,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ! [W: $i,W1: $i] :
( ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( equidistant @ U @ W @ U1 @ W1 )
| ~ ( colinear @ U @ V @ W )
| ( colinear @ U1 @ V1 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(374,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ! [X: $i] :
( ~ ( colinear @ U @ V @ X )
| ( U = V )
| ( colinear @ U @ W @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(375,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( colinear @ U @ V @ W )
| ! [X: $i] :
( ~ ( colinear @ U @ V @ X )
| ( U = V )
| ( colinear @ V @ W @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(376,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[218]) ).
thf(377,plain,
( ( ( ~ ( colinear @ x @ w @ u ) )
= $true )
| ( ( ~ ( colinear @ x @ w @ v ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[269]) ).
thf(378,plain,
( ( u = v )
= $false ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(379,plain,
! [SV1: $i] :
( ( ! [SY364: $i] : ( equidistant @ SV1 @ SY364 @ SY364 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(380,plain,
! [SV2: $i] :
( ( ! [SY365: $i,SY366: $i,SY367: $i] :
( ~ ( equidistant @ SV2 @ SY365 @ SY366 @ SY367 )
| ! [SY368: $i,SY369: $i] :
( ~ ( equidistant @ SV2 @ SY365 @ SY368 @ SY369 )
| ( equidistant @ SY366 @ SY367 @ SY368 @ SY369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(381,plain,
! [SV3: $i] :
( ( ! [SY370: $i] :
( ! [SY371: $i] :
~ ( equidistant @ SV3 @ SY370 @ SY371 @ SY371 )
| ( SV3 = SY370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(382,plain,
! [SV4: $i] :
( ( ! [SY372: $i,SY373: $i,SY374: $i] : ( between @ SV4 @ SY372 @ ( extension @ SV4 @ SY372 @ SY373 @ SY374 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(383,plain,
! [SV5: $i] :
( ( ! [SY375: $i,SY376: $i,SY377: $i] : ( equidistant @ SV5 @ ( extension @ SY375 @ SV5 @ SY376 @ SY377 ) @ SY376 @ SY377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(384,plain,
! [SV6: $i] :
( ( ! [SY378: $i,SY379: $i,SY380: $i,SY381: $i,SY382: $i] :
( ~ ( equidistant @ SV6 @ SY378 @ SY379 @ SY380 )
| ~ ( equidistant @ SY378 @ SY381 @ SY380 @ SY382 )
| ! [SY383: $i,SY384: $i] :
( ~ ( equidistant @ SV6 @ SY383 @ SY379 @ SY384 )
| ~ ( equidistant @ SY378 @ SY383 @ SY380 @ SY384 )
| ~ ( between @ SV6 @ SY378 @ SY381 )
| ~ ( between @ SY379 @ SY380 @ SY382 )
| ( SV6 = SY378 )
| ( equidistant @ SY381 @ SY383 @ SY382 @ SY384 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(385,plain,
! [SV7: $i] :
( ( ! [SY385: $i] :
( ~ ( between @ SV7 @ SY385 @ SV7 )
| ( SV7 = SY385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(386,plain,
! [SV8: $i] :
( ( ! [SY386: $i,SY387: $i] :
( ~ ( between @ SV8 @ SY386 @ SY387 )
| ! [SY388: $i,SY389: $i] :
( ~ ( between @ SY388 @ SY389 @ SY387 )
| ( between @ SY386 @ ( inner_pasch @ SV8 @ SY386 @ SY387 @ SY389 @ SY388 ) @ SY388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(387,plain,
! [SV9: $i] :
( ( ! [SY390: $i,SY391: $i] :
( ~ ( between @ SV9 @ SY390 @ SY391 )
| ! [SY392: $i,SY393: $i] :
( ~ ( between @ SY392 @ SY393 @ SY391 )
| ( between @ SY393 @ ( inner_pasch @ SV9 @ SY390 @ SY391 @ SY393 @ SY392 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(388,plain,
( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(389,plain,
( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(390,plain,
( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(391,plain,
! [SV10: $i] :
( ( ! [SY394: $i,SY395: $i] :
( ~ ( equidistant @ SV10 @ SY394 @ SV10 @ SY395 )
| ! [SY396: $i] :
( ~ ( equidistant @ SY396 @ SY394 @ SY396 @ SY395 )
| ! [SY397: $i] :
( ~ ( equidistant @ SY397 @ SY394 @ SY397 @ SY395 )
| ( between @ SV10 @ SY396 @ SY397 )
| ( between @ SY396 @ SY397 @ SV10 )
| ( SY394 = SY395 )
| ( between @ SY397 @ SV10 @ SY396 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(392,plain,
! [SV11: $i] :
( ( ! [SY398: $i,SY399: $i] :
( ~ ( between @ SV11 @ SY398 @ SY399 )
| ! [SY400: $i,SY401: $i] :
( ~ ( between @ SY400 @ SY398 @ SY401 )
| ( SV11 = SY398 )
| ( between @ SV11 @ SY400 @ ( euclid1 @ SV11 @ SY400 @ SY398 @ SY401 @ SY399 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(393,plain,
! [SV12: $i] :
( ( ! [SY402: $i,SY403: $i] :
( ~ ( between @ SV12 @ SY402 @ SY403 )
| ! [SY404: $i,SY405: $i] :
( ~ ( between @ SY404 @ SY402 @ SY405 )
| ( SV12 = SY402 )
| ( between @ SV12 @ SY405 @ ( euclid2 @ SV12 @ SY404 @ SY402 @ SY405 @ SY403 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(394,plain,
! [SV13: $i] :
( ( ! [SY406: $i,SY407: $i] :
( ~ ( between @ SV13 @ SY406 @ SY407 )
| ! [SY408: $i,SY409: $i] :
( ~ ( between @ SY408 @ SY406 @ SY409 )
| ( SV13 = SY406 )
| ( between @ ( euclid1 @ SV13 @ SY408 @ SY406 @ SY409 @ SY407 ) @ SY407 @ ( euclid2 @ SV13 @ SY408 @ SY406 @ SY409 @ SY407 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(395,plain,
! [SV14: $i] :
( ( ! [SY410: $i,SY411: $i,SY412: $i] :
( ~ ( equidistant @ SV14 @ SY410 @ SV14 @ SY411 )
| ! [SY413: $i] :
( ~ ( equidistant @ SV14 @ SY412 @ SV14 @ SY413 )
| ~ ( between @ SV14 @ SY410 @ SY412 )
| ! [SY414: $i] :
( ~ ( between @ SY410 @ SY414 @ SY412 )
| ( between @ SY411 @ ( continuous @ SV14 @ SY410 @ SY411 @ SY414 @ SY412 @ SY413 ) @ SY413 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(396,plain,
! [SV15: $i] :
( ( ! [SY415: $i,SY416: $i,SY417: $i] :
( ~ ( equidistant @ SV15 @ SY415 @ SV15 @ SY416 )
| ! [SY418: $i] :
( ~ ( equidistant @ SV15 @ SY417 @ SV15 @ SY418 )
| ~ ( between @ SV15 @ SY415 @ SY417 )
| ! [SY419: $i] :
( ~ ( between @ SY415 @ SY419 @ SY417 )
| ( equidistant @ SV15 @ SY419 @ SV15 @ ( continuous @ SV15 @ SY415 @ SY416 @ SY419 @ SY417 @ SY418 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(397,plain,
! [SV16: $i] :
( ( ! [SY420: $i,SY421: $i] :
( ~ ( between @ SV16 @ SY420 @ SY421 )
| ( colinear @ SV16 @ SY420 @ SY421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(398,plain,
! [SV17: $i] :
( ( ! [SY422: $i,SY423: $i] :
( ~ ( between @ SV17 @ SY422 @ SY423 )
| ( colinear @ SY423 @ SV17 @ SY422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(399,plain,
! [SV18: $i] :
( ( ! [SY424: $i,SY425: $i] :
( ~ ( between @ SV18 @ SY424 @ SY425 )
| ( colinear @ SY424 @ SY425 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(400,plain,
! [SV19: $i] :
( ( ! [SY426: $i,SY427: $i] :
( ~ ( colinear @ SV19 @ SY426 @ SY427 )
| ( between @ SV19 @ SY426 @ SY427 )
| ( between @ SY426 @ SY427 @ SV19 )
| ( between @ SY427 @ SV19 @ SY426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(401,plain,
! [SV20: $i] :
( ( ! [SY428: $i] :
( ( reflection @ SV20 @ SY428 )
= ( extension @ SV20 @ SY428 @ SV20 @ SY428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(402,plain,
! [SV21: $i] :
( ( ! [SY429: $i,SY430: $i,SY431: $i] :
( ( insertion @ SV21 @ SY429 @ SY430 @ SY431 )
= ( extension @ ( extension @ SY429 @ SV21 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV21 @ SY430 @ SY431 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(403,plain,
! [SV22: $i] :
( ( ! [SY432: $i] : ( equidistant @ SV22 @ SY432 @ SV22 @ SY432 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(404,plain,
! [SV23: $i] :
( ( ! [SY433: $i,SY434: $i,SY435: $i] :
( ~ ( equidistant @ SV23 @ SY433 @ SY434 @ SY435 )
| ( equidistant @ SY434 @ SY435 @ SV23 @ SY433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(405,plain,
! [SV24: $i] :
( ( ! [SY436: $i,SY437: $i,SY438: $i] :
( ~ ( equidistant @ SV24 @ SY436 @ SY437 @ SY438 )
| ( equidistant @ SY436 @ SV24 @ SY437 @ SY438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(406,plain,
! [SV25: $i] :
( ( ! [SY439: $i,SY440: $i,SY441: $i] :
( ~ ( equidistant @ SV25 @ SY439 @ SY440 @ SY441 )
| ( equidistant @ SV25 @ SY439 @ SY441 @ SY440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(407,plain,
! [SV26: $i] :
( ( ! [SY442: $i,SY443: $i,SY444: $i] :
( ~ ( equidistant @ SV26 @ SY442 @ SY443 @ SY444 )
| ( equidistant @ SY442 @ SV26 @ SY444 @ SY443 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(408,plain,
! [SV27: $i] :
( ( ! [SY445: $i,SY446: $i,SY447: $i] :
( ~ ( equidistant @ SV27 @ SY445 @ SY446 @ SY447 )
| ( equidistant @ SY446 @ SY447 @ SY445 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(409,plain,
! [SV28: $i] :
( ( ! [SY448: $i,SY449: $i,SY450: $i] :
( ~ ( equidistant @ SV28 @ SY448 @ SY449 @ SY450 )
| ( equidistant @ SY450 @ SY449 @ SV28 @ SY448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(410,plain,
! [SV29: $i] :
( ( ! [SY451: $i,SY452: $i,SY453: $i] :
( ~ ( equidistant @ SV29 @ SY451 @ SY452 @ SY453 )
| ( equidistant @ SY453 @ SY452 @ SY451 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(411,plain,
! [SV30: $i] :
( ( ! [SY454: $i,SY455: $i,SY456: $i] :
( ~ ( equidistant @ SV30 @ SY454 @ SY455 @ SY456 )
| ! [SY457: $i,SY458: $i] :
( ~ ( equidistant @ SY455 @ SY456 @ SY457 @ SY458 )
| ( equidistant @ SV30 @ SY454 @ SY457 @ SY458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(412,plain,
! [SV31: $i] :
( ( ! [SY459: $i,SY460: $i] :
( SV31
= ( extension @ SY459 @ SV31 @ SY460 @ SY460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(413,plain,
! [SV32: $i] :
( ( ! [SY461: $i,SY462: $i] :
( ! [SY463: $i,SY464: $i] :
( SV32
!= ( extension @ SY461 @ SY462 @ SY463 @ SY464 ) )
| ( between @ SY461 @ SY462 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(414,plain,
! [SV33: $i] :
( ( ! [SY465: $i] : ( between @ SV33 @ SY465 @ ( reflection @ SV33 @ SY465 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(415,plain,
! [SV34: $i] :
( ( ! [SY466: $i] : ( equidistant @ SV34 @ ( reflection @ SY466 @ SV34 ) @ SY466 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(416,plain,
! [SV35: $i] :
( ( ! [SY467: $i] :
( ( SV35 != SY467 )
| ( SY467
= ( reflection @ SV35 @ SY467 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(417,plain,
! [SV36: $i] :
( ( SV36
= ( reflection @ SV36 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(418,plain,
! [SV37: $i] :
( ( ! [SY468: $i] :
( ( SV37
!= ( reflection @ SY468 @ SV37 ) )
| ( SY468 = SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(419,plain,
! [SV38: $i] :
( ( ! [SY469: $i] : ( equidistant @ SV38 @ SV38 @ SY469 @ SY469 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(420,plain,
! [SV39: $i] :
( ( ! [SY470: $i,SY471: $i,SY472: $i] :
( ~ ( equidistant @ SV39 @ SY470 @ SY471 @ SY472 )
| ! [SY473: $i,SY474: $i] :
( ~ ( equidistant @ SY470 @ SY473 @ SY472 @ SY474 )
| ~ ( between @ SV39 @ SY470 @ SY473 )
| ~ ( between @ SY471 @ SY472 @ SY474 )
| ( equidistant @ SV39 @ SY473 @ SY471 @ SY474 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(421,plain,
! [SV40: $i] :
( ( ! [SY475: $i,SY476: $i] :
( ~ ( between @ SV40 @ SY475 @ SY476 )
| ! [SY477: $i] :
( ~ ( between @ SV40 @ SY475 @ SY477 )
| ~ ( equidistant @ SY475 @ SY476 @ SY475 @ SY477 )
| ( SV40 = SY475 )
| ( SY476 = SY477 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(422,plain,
! [SV41: $i] :
( ( ! [SY478: $i,SY479: $i] :
( ~ ( between @ SV41 @ SY478 @ SY479 )
| ( SV41 = SY478 )
| ( SY479
= ( extension @ SV41 @ SY478 @ SY478 @ SY479 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(423,plain,
! [SV42: $i] :
( ( ! [SY480: $i,SY481: $i,SY482: $i] :
( ~ ( equidistant @ SV42 @ SY480 @ SY481 @ SY482 )
| ! [SY483: $i,SY484: $i] :
( ( ( extension @ SY483 @ SY484 @ SV42 @ SY480 )
= ( extension @ SY483 @ SY484 @ SY481 @ SY482 ) )
| ( SY483 = SY484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(424,plain,
! [SV43: $i] :
( ( ! [SY485: $i] :
( ( ( extension @ SV43 @ SY485 @ SV43 @ SY485 )
= ( extension @ SV43 @ SY485 @ SY485 @ SV43 ) )
| ( SV43 = SY485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(425,plain,
! [SV44: $i] :
( ( ! [SY486: $i] : ( equidistant @ SV44 @ SY486 @ SV44 @ ( reflection @ ( reflection @ SY486 @ SV44 ) @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(426,plain,
! [SV45: $i] :
( ( ! [SY487: $i] :
( SV45
= ( reflection @ ( reflection @ SV45 @ SY487 ) @ SY487 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(427,plain,
! [SV46: $i] :
( ( ! [SY488: $i] : ( between @ SV46 @ SY488 @ SY488 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(428,plain,
! [SV47: $i] :
( ( ! [SY489: $i,SY490: $i] :
( ~ ( between @ SV47 @ SY489 @ SY490 )
| ( SV47 != SY490 )
| ! [V: $i] : ( between @ V @ SY489 @ SY490 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(429,plain,
! [SV48: $i] :
( ( ! [SY492: $i,SY493: $i] :
( ~ ( between @ SV48 @ SY492 @ SY493 )
| ( between @ SY493 @ SY492 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(430,plain,
! [SV49: $i] :
( ( ! [SY494: $i] : ( between @ SV49 @ SV49 @ SY494 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(431,plain,
! [SV50: $i] :
( ( ! [SY495: $i,SY496: $i] :
( ~ ( between @ SV50 @ SY495 @ SY496 )
| ~ ( between @ SY495 @ SV50 @ SY496 )
| ( SV50 = SY495 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(432,plain,
! [SV51: $i] :
( ( ! [SY497: $i,SY498: $i] :
( ~ ( between @ SV51 @ SY497 @ SY498 )
| ~ ( between @ SV51 @ SY498 @ SY497 )
| ( SY497 = SY498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(433,plain,
! [SV52: $i] :
( ( ! [SY499: $i,SY500: $i] :
( ~ ( between @ SV52 @ SY499 @ SY500 )
| ~ ( between @ SY499 @ SV52 @ SY500 )
| ( SV52 = SY499 )
| ( SY499 = SY500 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(434,plain,
! [SV53: $i] :
( ( ! [SY501: $i,SY502: $i] :
( ~ ( between @ SV53 @ SY501 @ SY502 )
| ~ ( between @ SV53 @ SY502 @ SY501 )
| ( SV53 = SY501 )
| ( SY501 = SY502 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(435,plain,
! [SV54: $i] :
( ( ! [SY503: $i,SY504: $i] :
( ~ ( between @ SV54 @ SY503 @ SY504 )
| ! [X: $i] :
~ ( between @ SY503 @ SY504 @ X )
| ( between @ SV54 @ SY503 @ SY504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(436,plain,
! [SV55: $i] :
( ( ! [SY506: $i,SY507: $i] :
( ~ ( between @ SV55 @ SY506 @ SY507 )
| ! [SY508: $i] :
( ~ ( between @ SV55 @ SY507 @ SY508 )
| ( between @ SY506 @ SY507 @ SY508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(437,plain,
! [SV56: $i] :
( ( ! [SY509: $i,SY510: $i] :
( ~ ( between @ SV56 @ SY509 @ SY510 )
| ! [SY511: $i] :
( ~ ( between @ SY509 @ SY510 @ SY511 )
| ( SY509 = SY510 )
| ( between @ SV56 @ SY510 @ SY511 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(438,plain,
! [SV57: $i] :
( ( ! [SY512: $i,SY513: $i] :
( ~ ( between @ SV57 @ SY512 @ SY513 )
| ! [SY514: $i] :
( ~ ( between @ SY512 @ SY513 @ SY514 )
| ( SY512 = SY513 )
| ( between @ SV57 @ SY512 @ SY514 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(439,plain,
! [SV58: $i] :
( ( ! [SY515: $i,SY516: $i] :
( ~ ( between @ SV58 @ SY515 @ SY516 )
| ! [SY517: $i] :
( ~ ( between @ SY515 @ SY517 @ SY516 )
| ( between @ SV58 @ SY517 @ SY516 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(440,plain,
! [SV59: $i] :
( ( ! [SY518: $i,SY519: $i] :
( ~ ( between @ SV59 @ SY518 @ SY519 )
| ! [SY520: $i] :
( ~ ( between @ SV59 @ SY519 @ SY520 )
| ( between @ SV59 @ SY518 @ SY520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(441,plain,
( ( lower_dimension_point_1 = lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(442,plain,
( ( lower_dimension_point_2 = lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(443,plain,
( ( lower_dimension_point_1 = lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(444,plain,
! [SV60: $i] :
( ( ! [SY521: $i] :
( SV60
!= ( extension @ SY521 @ SV60 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(445,plain,
! [SV61: $i] :
( ( ! [SY522: $i,SY523: $i,SY524: $i] : ( equidistant @ SV61 @ ( extension @ SY522 @ SV61 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SY523 @ ( extension @ SY524 @ SY523 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(446,plain,
! [SV62: $i] :
( ( ! [SY525: $i] : ( between @ SV62 @ SY525 @ ( extension @ SV62 @ SY525 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(447,plain,
! [SV63: $i] :
( ( ! [SY526: $i,SY527: $i,SY528: $i] :
( ~ ( between @ SV63 @ SY526 @ SY527 )
| ! [SY529: $i] :
( ~ ( between @ SY528 @ SY529 @ SY527 )
| ! [SY530: $i] :
( ~ ( between @ SV63 @ SY530 @ SY528 )
| ( between @ SY530 @ ( inner_pasch @ SY529 @ ( inner_pasch @ SV63 @ SY530 @ SY528 @ SY529 @ SY527 ) @ SV63 @ SY526 @ SY527 ) @ SY527 )
| ( between @ SY526 @ ( inner_pasch @ SY529 @ ( inner_pasch @ SV63 @ SY530 @ SY528 @ SY529 @ SY527 ) @ SV63 @ SY526 @ SY527 ) @ SY529 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(448,plain,
! [SV64: $i] :
( ( ! [SY531: $i,SY532: $i] :
( ~ ( between @ SV64 @ SY531 @ SY532 )
| ! [SY533: $i] :
( ~ ( equidistant @ SV64 @ SY532 @ SV64 @ SY533 )
| ~ ( equidistant @ SY531 @ SY532 @ SY531 @ SY533 )
| ( SV64 = SY531 )
| ( SY532 = SY533 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(449,plain,
! [SV65: $i] :
( ( ! [SY534: $i,SY535: $i,SY536: $i,SY537: $i,SY538: $i] :
( ~ ( equidistant @ SV65 @ SY534 @ SY535 @ SY536 )
| ~ ( equidistant @ SV65 @ SY537 @ SY535 @ SY538 )
| ! [SY539: $i,SY540: $i] :
( ~ ( equidistant @ SV65 @ SY539 @ SY535 @ SY540 )
| ~ ( equidistant @ SY537 @ SY539 @ SY538 @ SY540 )
| ~ ( between @ SV65 @ SY534 @ SY537 )
| ~ ( between @ SY535 @ SY536 @ SY538 )
| ( equidistant @ SY534 @ SY539 @ SY536 @ SY540 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(450,plain,
! [SV66: $i] :
( ( ! [SY541: $i,SY542: $i,SY543: $i] :
( ~ ( between @ SV66 @ SY541 @ SY542 )
| ! [SY544: $i,SY545: $i] :
( ~ ( between @ SY543 @ SY544 @ SY545 )
| ~ ( equidistant @ SV66 @ SY541 @ SY543 @ SY544 )
| ~ ( equidistant @ SV66 @ SY542 @ SY543 @ SY545 )
| ( equidistant @ SY541 @ SY542 @ SY544 @ SY545 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(451,plain,
! [SV67: $i] :
( ( ! [SY546: $i,SY547: $i,SY548: $i,SY549: $i,SY550: $i] :
( ~ ( equidistant @ SV67 @ SY546 @ SY547 @ SY548 )
| ~ ( equidistant @ SY546 @ SY549 @ SY548 @ SY550 )
| ! [SY551: $i,SY552: $i] :
( ~ ( equidistant @ SV67 @ SY551 @ SY547 @ SY552 )
| ~ ( equidistant @ SY549 @ SY551 @ SY550 @ SY552 )
| ~ ( between @ SV67 @ SY546 @ SY549 )
| ~ ( between @ SY547 @ SY548 @ SY550 )
| ( equidistant @ SY546 @ SY551 @ SY548 @ SY552 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(452,plain,
! [SV68: $i] :
( ( ! [SY553: $i,SY554: $i] :
( ~ ( between @ SV68 @ SY553 @ SY554 )
| ! [SY555: $i] :
( ~ ( equidistant @ SV68 @ SY553 @ SV68 @ SY555 )
| ~ ( equidistant @ SY554 @ SY553 @ SY554 @ SY555 )
| ( SY553 = SY555 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(453,plain,
! [SV69: $i] :
( ( ! [SY556: $i,SY557: $i,SY558: $i] : ( equidistant @ SV69 @ SY556 @ SY557 @ ( insertion @ SY557 @ SY558 @ SV69 @ SY556 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(454,plain,
! [SV70: $i] :
( ( ! [SY559: $i,SY560: $i] :
( ~ ( between @ SV70 @ SY559 @ SY560 )
| ! [SY561: $i,SY562: $i] :
( ~ ( equidistant @ SV70 @ SY560 @ SY561 @ SY562 )
| ( between @ SY561 @ ( insertion @ SY561 @ SY562 @ SV70 @ SY559 ) @ SY562 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(455,plain,
! [SV71: $i] :
( ( ! [SY563: $i,SY564: $i] :
( ~ ( between @ SV71 @ SY563 @ SY564 )
| ! [SY565: $i,SY566: $i] :
( ~ ( equidistant @ SV71 @ SY564 @ SY565 @ SY566 )
| ( equidistant @ SY563 @ SY564 @ ( insertion @ SY565 @ SY566 @ SV71 @ SY563 ) @ SY566 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(456,plain,
! [SV72: $i] :
( ( ! [SY567: $i,SY568: $i] :
( ~ ( between @ SV72 @ SY567 @ SY568 )
| ( SY567
= ( insertion @ SV72 @ SY568 @ SV72 @ SY567 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(457,plain,
! [SV73: $i] :
( ( ! [SY569: $i,SY570: $i,SY571: $i] :
( ~ ( equidistant @ SV73 @ SY569 @ SY570 @ SY571 )
| ! [SY572: $i,SY573: $i] :
( ( insertion @ SY572 @ SY573 @ SV73 @ SY569 )
= ( insertion @ SY572 @ SY573 @ SY570 @ SY571 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(458,plain,
! [SV74: $i] :
( ( ! [SY574: $i,SY575: $i,SY576: $i] :
( ~ ( equidistant @ SV74 @ SY574 @ SY575 @ SY576 )
| ! [SY577: $i,SY578: $i] :
( ~ ( equidistant @ SY574 @ SY577 @ SY576 @ SY578 )
| ~ ( equidistant @ SV74 @ SY577 @ SY575 @ SY578 )
| ~ ( between @ SV74 @ SY574 @ SY577 )
| ( between @ SY575 @ SY576 @ SY578 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(459,plain,
! [SV75: $i] :
( ( ! [SY579: $i,SY580: $i] :
( ~ ( between @ SV75 @ SY579 @ SY580 )
| ! [SY581: $i] :
( ~ ( between @ SV75 @ SY579 @ SY581 )
| ( SV75 = SY579 )
| ( between @ SV75 @ SY580 @ SY581 )
| ( between @ SV75 @ SY581 @ SY580 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(460,plain,
! [SV76: $i] :
( ( ! [SY582: $i,SY583: $i] :
( ~ ( between @ SV76 @ SY582 @ SY583 )
| ! [SY584: $i] :
( ~ ( between @ SV76 @ SY582 @ SY584 )
| ( SV76 = SY582 )
| ( between @ SY582 @ SY583 @ SY584 )
| ( between @ SY582 @ SY584 @ SY583 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(461,plain,
! [SV77: $i] :
( ( ! [SY585: $i,SY586: $i] :
( ~ ( between @ SV77 @ SY585 @ SY586 )
| ! [SY587: $i] :
( ~ ( between @ SY587 @ SY585 @ SY586 )
| ( SY585 = SY586 )
| ( between @ SV77 @ SY587 @ SY585 )
| ( between @ SY587 @ SV77 @ SY585 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(462,plain,
! [SV78: $i] :
( ( ! [SY588: $i,SY589: $i] :
( ~ ( between @ SV78 @ SY588 @ SY589 )
| ! [SY590: $i] :
( ~ ( between @ SV78 @ SY590 @ SY589 )
| ( between @ SV78 @ SY588 @ SY590 )
| ( between @ SV78 @ SY590 @ SY588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(463,plain,
! [SV79: $i] :
( ( ! [SY591: $i,SY592: $i] :
( ~ ( between @ SV79 @ SY591 @ SY592 )
| ! [SY593: $i] :
( ~ ( between @ SV79 @ SY593 @ SY592 )
| ( between @ SY591 @ SY593 @ SY592 )
| ( between @ SY593 @ SY591 @ SY592 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(464,plain,
! [SV80: $i] :
( ( ! [SY594: $i,SY595: $i] :
( ~ ( between @ SV80 @ SY594 @ SY595 )
| ! [SY596: $i,SY597: $i] :
( ~ ( between @ SY594 @ SY596 @ SY597 )
| ~ ( between @ SV80 @ SY597 @ SY595 )
| ( between @ SV80 @ SY596 @ SY595 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(465,plain,
! [SV81: $i] :
( ( ! [SY598: $i,SY599: $i] :
( ~ ( between @ SV81 @ SY598 @ SY599 )
| ~ ( equidistant @ SV81 @ SY598 @ SV81 @ SY599 )
| ( SY598 = SY599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(466,plain,
! [SV82: $i] :
( ( ! [SY600: $i,SY601: $i] :
( ~ ( between @ SV82 @ SY600 @ SY601 )
| ( colinear @ SY601 @ SY600 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(467,plain,
! [SV83: $i] :
( ( ! [SY602: $i,SY603: $i] :
( ~ ( between @ SV83 @ SY602 @ SY603 )
| ( colinear @ SV83 @ SY603 @ SY602 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(468,plain,
! [SV84: $i] :
( ( ! [SY604: $i,SY605: $i] :
( ~ ( between @ SV84 @ SY604 @ SY605 )
| ( colinear @ SY604 @ SV84 @ SY605 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(469,plain,
! [SV85: $i] :
( ( ! [SY606: $i,SY607: $i] :
( ~ ( colinear @ SV85 @ SY606 @ SY607 )
| ( colinear @ SY607 @ SY606 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(470,plain,
! [SV86: $i] :
( ( ! [SY608: $i,SY609: $i] :
( ~ ( colinear @ SV86 @ SY608 @ SY609 )
| ( colinear @ SY608 @ SY609 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(471,plain,
! [SV87: $i] :
( ( ! [SY610: $i,SY611: $i] :
( ~ ( colinear @ SV87 @ SY610 @ SY611 )
| ( colinear @ SV87 @ SY611 @ SY610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(472,plain,
! [SV88: $i] :
( ( ! [SY612: $i,SY613: $i] :
( ~ ( colinear @ SV88 @ SY612 @ SY613 )
| ( colinear @ SY613 @ SV88 @ SY612 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(473,plain,
! [SV89: $i] :
( ( ! [SY614: $i,SY615: $i] :
( ~ ( colinear @ SV89 @ SY614 @ SY615 )
| ( colinear @ SY614 @ SV89 @ SY615 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(474,plain,
( ( colinear @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(475,plain,
! [SV90: $i] :
( ( ! [SY616: $i] : ( colinear @ SV90 @ SV90 @ SY616 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(476,plain,
! [SV91: $i] :
( ( ! [SY617: $i] : ( colinear @ SV91 @ SY617 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(477,plain,
! [SV92: $i] :
( ( ! [SY618: $i] : ( colinear @ SV92 @ SY618 @ SY618 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(478,plain,
! [SV93: $i] :
( ( ! [SY619: $i] :
( ( SV93 != SY619 )
| ! [SY620: $i] : ( colinear @ SV93 @ SY620 @ SY619 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(479,plain,
! [SV94: $i] :
( ( ! [SY621: $i,SY622: $i,SY623: $i] :
( ~ ( equidistant @ SV94 @ SY621 @ SY622 @ SY623 )
| ! [SY624: $i,SY625: $i] :
( ~ ( equidistant @ SY621 @ SY624 @ SY623 @ SY625 )
| ~ ( equidistant @ SV94 @ SY624 @ SY622 @ SY625 )
| ~ ( colinear @ SV94 @ SY621 @ SY624 )
| ( colinear @ SY622 @ SY623 @ SY625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(480,plain,
! [SV95: $i] :
( ( ! [SY626: $i,SY627: $i] :
( ~ ( colinear @ SV95 @ SY626 @ SY627 )
| ! [SY628: $i] :
( ~ ( colinear @ SV95 @ SY626 @ SY628 )
| ( SV95 = SY626 )
| ( colinear @ SV95 @ SY627 @ SY628 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(481,plain,
! [SV96: $i] :
( ( ! [SY629: $i,SY630: $i] :
( ~ ( colinear @ SV96 @ SY629 @ SY630 )
| ! [SY631: $i] :
( ~ ( colinear @ SV96 @ SY629 @ SY631 )
| ( SV96 = SY629 )
| ( colinear @ SY629 @ SY630 @ SY631 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(482,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(483,plain,
( ( ( colinear @ x @ w @ u )
= $false )
| ( ( ~ ( colinear @ x @ w @ v ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(484,plain,
! [SV97: $i,SV1: $i] :
( ( equidistant @ SV1 @ SV97 @ SV97 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(485,plain,
! [SV98: $i,SV2: $i] :
( ( ! [SY632: $i,SY633: $i] :
( ~ ( equidistant @ SV2 @ SV98 @ SY632 @ SY633 )
| ! [SY634: $i,SY635: $i] :
( ~ ( equidistant @ SV2 @ SV98 @ SY634 @ SY635 )
| ( equidistant @ SY632 @ SY633 @ SY634 @ SY635 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(486,plain,
! [SV99: $i,SV3: $i] :
( ( ! [SY636: $i] :
~ ( equidistant @ SV3 @ SV99 @ SY636 @ SY636 )
| ( SV3 = SV99 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(487,plain,
! [SV100: $i,SV4: $i] :
( ( ! [SY637: $i,SY638: $i] : ( between @ SV4 @ SV100 @ ( extension @ SV4 @ SV100 @ SY637 @ SY638 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(488,plain,
! [SV101: $i,SV5: $i] :
( ( ! [SY639: $i,SY640: $i] : ( equidistant @ SV5 @ ( extension @ SV101 @ SV5 @ SY639 @ SY640 ) @ SY639 @ SY640 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(489,plain,
! [SV102: $i,SV6: $i] :
( ( ! [SY641: $i,SY642: $i,SY643: $i,SY644: $i] :
( ~ ( equidistant @ SV6 @ SV102 @ SY641 @ SY642 )
| ~ ( equidistant @ SV102 @ SY643 @ SY642 @ SY644 )
| ! [SY645: $i,SY646: $i] :
( ~ ( equidistant @ SV6 @ SY645 @ SY641 @ SY646 )
| ~ ( equidistant @ SV102 @ SY645 @ SY642 @ SY646 )
| ~ ( between @ SV6 @ SV102 @ SY643 )
| ~ ( between @ SY641 @ SY642 @ SY644 )
| ( SV6 = SV102 )
| ( equidistant @ SY643 @ SY645 @ SY644 @ SY646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(490,plain,
! [SV103: $i,SV7: $i] :
( ( ~ ( between @ SV7 @ SV103 @ SV7 )
| ( SV7 = SV103 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(491,plain,
! [SV104: $i,SV8: $i] :
( ( ! [SY647: $i] :
( ~ ( between @ SV8 @ SV104 @ SY647 )
| ! [SY648: $i,SY649: $i] :
( ~ ( between @ SY648 @ SY649 @ SY647 )
| ( between @ SV104 @ ( inner_pasch @ SV8 @ SV104 @ SY647 @ SY649 @ SY648 ) @ SY648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(492,plain,
! [SV105: $i,SV9: $i] :
( ( ! [SY650: $i] :
( ~ ( between @ SV9 @ SV105 @ SY650 )
| ! [SY651: $i,SY652: $i] :
( ~ ( between @ SY651 @ SY652 @ SY650 )
| ( between @ SY652 @ ( inner_pasch @ SV9 @ SV105 @ SY650 @ SY652 @ SY651 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(493,plain,
! [SV106: $i,SV10: $i] :
( ( ! [SY653: $i] :
( ~ ( equidistant @ SV10 @ SV106 @ SV10 @ SY653 )
| ! [SY654: $i] :
( ~ ( equidistant @ SY654 @ SV106 @ SY654 @ SY653 )
| ! [SY655: $i] :
( ~ ( equidistant @ SY655 @ SV106 @ SY655 @ SY653 )
| ( between @ SV10 @ SY654 @ SY655 )
| ( between @ SY654 @ SY655 @ SV10 )
| ( SV106 = SY653 )
| ( between @ SY655 @ SV10 @ SY654 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(494,plain,
! [SV107: $i,SV11: $i] :
( ( ! [SY656: $i] :
( ~ ( between @ SV11 @ SV107 @ SY656 )
| ! [SY657: $i,SY658: $i] :
( ~ ( between @ SY657 @ SV107 @ SY658 )
| ( SV11 = SV107 )
| ( between @ SV11 @ SY657 @ ( euclid1 @ SV11 @ SY657 @ SV107 @ SY658 @ SY656 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(495,plain,
! [SV108: $i,SV12: $i] :
( ( ! [SY659: $i] :
( ~ ( between @ SV12 @ SV108 @ SY659 )
| ! [SY660: $i,SY661: $i] :
( ~ ( between @ SY660 @ SV108 @ SY661 )
| ( SV12 = SV108 )
| ( between @ SV12 @ SY661 @ ( euclid2 @ SV12 @ SY660 @ SV108 @ SY661 @ SY659 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(496,plain,
! [SV109: $i,SV13: $i] :
( ( ! [SY662: $i] :
( ~ ( between @ SV13 @ SV109 @ SY662 )
| ! [SY663: $i,SY664: $i] :
( ~ ( between @ SY663 @ SV109 @ SY664 )
| ( SV13 = SV109 )
| ( between @ ( euclid1 @ SV13 @ SY663 @ SV109 @ SY664 @ SY662 ) @ SY662 @ ( euclid2 @ SV13 @ SY663 @ SV109 @ SY664 @ SY662 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(497,plain,
! [SV110: $i,SV14: $i] :
( ( ! [SY665: $i,SY666: $i] :
( ~ ( equidistant @ SV14 @ SV110 @ SV14 @ SY665 )
| ! [SY667: $i] :
( ~ ( equidistant @ SV14 @ SY666 @ SV14 @ SY667 )
| ~ ( between @ SV14 @ SV110 @ SY666 )
| ! [SY668: $i] :
( ~ ( between @ SV110 @ SY668 @ SY666 )
| ( between @ SY665 @ ( continuous @ SV14 @ SV110 @ SY665 @ SY668 @ SY666 @ SY667 ) @ SY667 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(498,plain,
! [SV111: $i,SV15: $i] :
( ( ! [SY669: $i,SY670: $i] :
( ~ ( equidistant @ SV15 @ SV111 @ SV15 @ SY669 )
| ! [SY671: $i] :
( ~ ( equidistant @ SV15 @ SY670 @ SV15 @ SY671 )
| ~ ( between @ SV15 @ SV111 @ SY670 )
| ! [SY672: $i] :
( ~ ( between @ SV111 @ SY672 @ SY670 )
| ( equidistant @ SV15 @ SY672 @ SV15 @ ( continuous @ SV15 @ SV111 @ SY669 @ SY672 @ SY670 @ SY671 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(499,plain,
! [SV112: $i,SV16: $i] :
( ( ! [SY673: $i] :
( ~ ( between @ SV16 @ SV112 @ SY673 )
| ( colinear @ SV16 @ SV112 @ SY673 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(500,plain,
! [SV113: $i,SV17: $i] :
( ( ! [SY674: $i] :
( ~ ( between @ SV17 @ SV113 @ SY674 )
| ( colinear @ SY674 @ SV17 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(501,plain,
! [SV114: $i,SV18: $i] :
( ( ! [SY675: $i] :
( ~ ( between @ SV18 @ SV114 @ SY675 )
| ( colinear @ SV114 @ SY675 @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(502,plain,
! [SV115: $i,SV19: $i] :
( ( ! [SY676: $i] :
( ~ ( colinear @ SV19 @ SV115 @ SY676 )
| ( between @ SV19 @ SV115 @ SY676 )
| ( between @ SV115 @ SY676 @ SV19 )
| ( between @ SY676 @ SV19 @ SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(503,plain,
! [SV116: $i,SV20: $i] :
( ( ( reflection @ SV20 @ SV116 )
= ( extension @ SV20 @ SV116 @ SV20 @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(504,plain,
! [SV117: $i,SV21: $i] :
( ( ! [SY677: $i,SY678: $i] :
( ( insertion @ SV21 @ SV117 @ SY677 @ SY678 )
= ( extension @ ( extension @ SV117 @ SV21 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV21 @ SY677 @ SY678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(505,plain,
! [SV118: $i,SV22: $i] :
( ( equidistant @ SV22 @ SV118 @ SV22 @ SV118 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(506,plain,
! [SV119: $i,SV23: $i] :
( ( ! [SY679: $i,SY680: $i] :
( ~ ( equidistant @ SV23 @ SV119 @ SY679 @ SY680 )
| ( equidistant @ SY679 @ SY680 @ SV23 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(507,plain,
! [SV120: $i,SV24: $i] :
( ( ! [SY681: $i,SY682: $i] :
( ~ ( equidistant @ SV24 @ SV120 @ SY681 @ SY682 )
| ( equidistant @ SV120 @ SV24 @ SY681 @ SY682 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(508,plain,
! [SV121: $i,SV25: $i] :
( ( ! [SY683: $i,SY684: $i] :
( ~ ( equidistant @ SV25 @ SV121 @ SY683 @ SY684 )
| ( equidistant @ SV25 @ SV121 @ SY684 @ SY683 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(509,plain,
! [SV122: $i,SV26: $i] :
( ( ! [SY685: $i,SY686: $i] :
( ~ ( equidistant @ SV26 @ SV122 @ SY685 @ SY686 )
| ( equidistant @ SV122 @ SV26 @ SY686 @ SY685 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(510,plain,
! [SV123: $i,SV27: $i] :
( ( ! [SY687: $i,SY688: $i] :
( ~ ( equidistant @ SV27 @ SV123 @ SY687 @ SY688 )
| ( equidistant @ SY687 @ SY688 @ SV123 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(511,plain,
! [SV124: $i,SV28: $i] :
( ( ! [SY689: $i,SY690: $i] :
( ~ ( equidistant @ SV28 @ SV124 @ SY689 @ SY690 )
| ( equidistant @ SY690 @ SY689 @ SV28 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(512,plain,
! [SV125: $i,SV29: $i] :
( ( ! [SY691: $i,SY692: $i] :
( ~ ( equidistant @ SV29 @ SV125 @ SY691 @ SY692 )
| ( equidistant @ SY692 @ SY691 @ SV125 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(513,plain,
! [SV126: $i,SV30: $i] :
( ( ! [SY693: $i,SY694: $i] :
( ~ ( equidistant @ SV30 @ SV126 @ SY693 @ SY694 )
| ! [SY695: $i,SY696: $i] :
( ~ ( equidistant @ SY693 @ SY694 @ SY695 @ SY696 )
| ( equidistant @ SV30 @ SV126 @ SY695 @ SY696 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(514,plain,
! [SV127: $i,SV31: $i] :
( ( ! [SY697: $i] :
( SV31
= ( extension @ SV127 @ SV31 @ SY697 @ SY697 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(515,plain,
! [SV128: $i,SV32: $i] :
( ( ! [SY698: $i] :
( ! [SY699: $i,SY700: $i] :
( SV32
!= ( extension @ SV128 @ SY698 @ SY699 @ SY700 ) )
| ( between @ SV128 @ SY698 @ SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(516,plain,
! [SV129: $i,SV33: $i] :
( ( between @ SV33 @ SV129 @ ( reflection @ SV33 @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(517,plain,
! [SV130: $i,SV34: $i] :
( ( equidistant @ SV34 @ ( reflection @ SV130 @ SV34 ) @ SV130 @ SV34 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(518,plain,
! [SV131: $i,SV35: $i] :
( ( ( SV35 != SV131 )
| ( SV131
= ( reflection @ SV35 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(519,plain,
! [SV132: $i,SV37: $i] :
( ( ( SV37
!= ( reflection @ SV132 @ SV37 ) )
| ( SV132 = SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(520,plain,
! [SV133: $i,SV38: $i] :
( ( equidistant @ SV38 @ SV38 @ SV133 @ SV133 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(521,plain,
! [SV134: $i,SV39: $i] :
( ( ! [SY701: $i,SY702: $i] :
( ~ ( equidistant @ SV39 @ SV134 @ SY701 @ SY702 )
| ! [SY703: $i,SY704: $i] :
( ~ ( equidistant @ SV134 @ SY703 @ SY702 @ SY704 )
| ~ ( between @ SV39 @ SV134 @ SY703 )
| ~ ( between @ SY701 @ SY702 @ SY704 )
| ( equidistant @ SV39 @ SY703 @ SY701 @ SY704 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(522,plain,
! [SV135: $i,SV40: $i] :
( ( ! [SY705: $i] :
( ~ ( between @ SV40 @ SV135 @ SY705 )
| ! [SY706: $i] :
( ~ ( between @ SV40 @ SV135 @ SY706 )
| ~ ( equidistant @ SV135 @ SY705 @ SV135 @ SY706 )
| ( SV40 = SV135 )
| ( SY705 = SY706 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(523,plain,
! [SV136: $i,SV41: $i] :
( ( ! [SY707: $i] :
( ~ ( between @ SV41 @ SV136 @ SY707 )
| ( SV41 = SV136 )
| ( SY707
= ( extension @ SV41 @ SV136 @ SV136 @ SY707 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(524,plain,
! [SV137: $i,SV42: $i] :
( ( ! [SY708: $i,SY709: $i] :
( ~ ( equidistant @ SV42 @ SV137 @ SY708 @ SY709 )
| ! [SY710: $i,SY711: $i] :
( ( ( extension @ SY710 @ SY711 @ SV42 @ SV137 )
= ( extension @ SY710 @ SY711 @ SY708 @ SY709 ) )
| ( SY710 = SY711 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(525,plain,
! [SV138: $i,SV43: $i] :
( ( ( ( extension @ SV43 @ SV138 @ SV43 @ SV138 )
= ( extension @ SV43 @ SV138 @ SV138 @ SV43 ) )
| ( SV43 = SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(526,plain,
! [SV139: $i,SV44: $i] :
( ( equidistant @ SV44 @ SV139 @ SV44 @ ( reflection @ ( reflection @ SV139 @ SV44 ) @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(527,plain,
! [SV140: $i,SV45: $i] :
( ( SV45
= ( reflection @ ( reflection @ SV45 @ SV140 ) @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(528,plain,
! [SV141: $i,SV46: $i] :
( ( between @ SV46 @ SV141 @ SV141 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(529,plain,
! [SV142: $i,SV47: $i] :
( ( ! [SY712: $i] :
( ~ ( between @ SV47 @ SV142 @ SY712 )
| ( SV47 != SY712 )
| ! [SY713: $i] : ( between @ SY713 @ SV142 @ SY712 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(530,plain,
! [SV143: $i,SV48: $i] :
( ( ! [SY714: $i] :
( ~ ( between @ SV48 @ SV143 @ SY714 )
| ( between @ SY714 @ SV143 @ SV48 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(531,plain,
! [SV144: $i,SV49: $i] :
( ( between @ SV49 @ SV49 @ SV144 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(532,plain,
! [SV145: $i,SV50: $i] :
( ( ! [SY715: $i] :
( ~ ( between @ SV50 @ SV145 @ SY715 )
| ~ ( between @ SV145 @ SV50 @ SY715 )
| ( SV50 = SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(533,plain,
! [SV146: $i,SV51: $i] :
( ( ! [SY716: $i] :
( ~ ( between @ SV51 @ SV146 @ SY716 )
| ~ ( between @ SV51 @ SY716 @ SV146 )
| ( SV146 = SY716 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(534,plain,
! [SV147: $i,SV52: $i] :
( ( ! [SY717: $i] :
( ~ ( between @ SV52 @ SV147 @ SY717 )
| ~ ( between @ SV147 @ SV52 @ SY717 )
| ( SV52 = SV147 )
| ( SV147 = SY717 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(535,plain,
! [SV148: $i,SV53: $i] :
( ( ! [SY718: $i] :
( ~ ( between @ SV53 @ SV148 @ SY718 )
| ~ ( between @ SV53 @ SY718 @ SV148 )
| ( SV53 = SV148 )
| ( SV148 = SY718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(536,plain,
! [SV149: $i,SV54: $i] :
( ( ! [SY719: $i] :
( ~ ( between @ SV54 @ SV149 @ SY719 )
| ! [SY720: $i] :
~ ( between @ SV149 @ SY719 @ SY720 )
| ( between @ SV54 @ SV149 @ SY719 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(537,plain,
! [SV150: $i,SV55: $i] :
( ( ! [SY721: $i] :
( ~ ( between @ SV55 @ SV150 @ SY721 )
| ! [SY722: $i] :
( ~ ( between @ SV55 @ SY721 @ SY722 )
| ( between @ SV150 @ SY721 @ SY722 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(538,plain,
! [SV151: $i,SV56: $i] :
( ( ! [SY723: $i] :
( ~ ( between @ SV56 @ SV151 @ SY723 )
| ! [SY724: $i] :
( ~ ( between @ SV151 @ SY723 @ SY724 )
| ( SV151 = SY723 )
| ( between @ SV56 @ SY723 @ SY724 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(539,plain,
! [SV152: $i,SV57: $i] :
( ( ! [SY725: $i] :
( ~ ( between @ SV57 @ SV152 @ SY725 )
| ! [SY726: $i] :
( ~ ( between @ SV152 @ SY725 @ SY726 )
| ( SV152 = SY725 )
| ( between @ SV57 @ SV152 @ SY726 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(540,plain,
! [SV153: $i,SV58: $i] :
( ( ! [SY727: $i] :
( ~ ( between @ SV58 @ SV153 @ SY727 )
| ! [SY728: $i] :
( ~ ( between @ SV153 @ SY728 @ SY727 )
| ( between @ SV58 @ SY728 @ SY727 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(541,plain,
! [SV154: $i,SV59: $i] :
( ( ! [SY729: $i] :
( ~ ( between @ SV59 @ SV154 @ SY729 )
| ! [SY730: $i] :
( ~ ( between @ SV59 @ SY729 @ SY730 )
| ( between @ SV59 @ SV154 @ SY730 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(542,plain,
! [SV155: $i,SV60: $i] :
( ( SV60
!= ( extension @ SV155 @ SV60 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(543,plain,
! [SV156: $i,SV61: $i] :
( ( ! [SY731: $i,SY732: $i] : ( equidistant @ SV61 @ ( extension @ SV156 @ SV61 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SY731 @ ( extension @ SY732 @ SY731 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(544,plain,
! [SV157: $i,SV62: $i] :
( ( between @ SV62 @ SV157 @ ( extension @ SV62 @ SV157 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(545,plain,
! [SV158: $i,SV63: $i] :
( ( ! [SY733: $i,SY734: $i] :
( ~ ( between @ SV63 @ SV158 @ SY733 )
| ! [SY735: $i] :
( ~ ( between @ SY734 @ SY735 @ SY733 )
| ! [SY736: $i] :
( ~ ( between @ SV63 @ SY736 @ SY734 )
| ( between @ SY736 @ ( inner_pasch @ SY735 @ ( inner_pasch @ SV63 @ SY736 @ SY734 @ SY735 @ SY733 ) @ SV63 @ SV158 @ SY733 ) @ SY733 )
| ( between @ SV158 @ ( inner_pasch @ SY735 @ ( inner_pasch @ SV63 @ SY736 @ SY734 @ SY735 @ SY733 ) @ SV63 @ SV158 @ SY733 ) @ SY735 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(546,plain,
! [SV159: $i,SV64: $i] :
( ( ! [SY737: $i] :
( ~ ( between @ SV64 @ SV159 @ SY737 )
| ! [SY738: $i] :
( ~ ( equidistant @ SV64 @ SY737 @ SV64 @ SY738 )
| ~ ( equidistant @ SV159 @ SY737 @ SV159 @ SY738 )
| ( SV64 = SV159 )
| ( SY737 = SY738 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(547,plain,
! [SV160: $i,SV65: $i] :
( ( ! [SY739: $i,SY740: $i,SY741: $i,SY742: $i] :
( ~ ( equidistant @ SV65 @ SV160 @ SY739 @ SY740 )
| ~ ( equidistant @ SV65 @ SY741 @ SY739 @ SY742 )
| ! [SY743: $i,SY744: $i] :
( ~ ( equidistant @ SV65 @ SY743 @ SY739 @ SY744 )
| ~ ( equidistant @ SY741 @ SY743 @ SY742 @ SY744 )
| ~ ( between @ SV65 @ SV160 @ SY741 )
| ~ ( between @ SY739 @ SY740 @ SY742 )
| ( equidistant @ SV160 @ SY743 @ SY740 @ SY744 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(548,plain,
! [SV161: $i,SV66: $i] :
( ( ! [SY745: $i,SY746: $i] :
( ~ ( between @ SV66 @ SV161 @ SY745 )
| ! [SY747: $i,SY748: $i] :
( ~ ( between @ SY746 @ SY747 @ SY748 )
| ~ ( equidistant @ SV66 @ SV161 @ SY746 @ SY747 )
| ~ ( equidistant @ SV66 @ SY745 @ SY746 @ SY748 )
| ( equidistant @ SV161 @ SY745 @ SY747 @ SY748 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(549,plain,
! [SV162: $i,SV67: $i] :
( ( ! [SY749: $i,SY750: $i,SY751: $i,SY752: $i] :
( ~ ( equidistant @ SV67 @ SV162 @ SY749 @ SY750 )
| ~ ( equidistant @ SV162 @ SY751 @ SY750 @ SY752 )
| ! [SY753: $i,SY754: $i] :
( ~ ( equidistant @ SV67 @ SY753 @ SY749 @ SY754 )
| ~ ( equidistant @ SY751 @ SY753 @ SY752 @ SY754 )
| ~ ( between @ SV67 @ SV162 @ SY751 )
| ~ ( between @ SY749 @ SY750 @ SY752 )
| ( equidistant @ SV162 @ SY753 @ SY750 @ SY754 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(550,plain,
! [SV163: $i,SV68: $i] :
( ( ! [SY755: $i] :
( ~ ( between @ SV68 @ SV163 @ SY755 )
| ! [SY756: $i] :
( ~ ( equidistant @ SV68 @ SV163 @ SV68 @ SY756 )
| ~ ( equidistant @ SY755 @ SV163 @ SY755 @ SY756 )
| ( SV163 = SY756 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(551,plain,
! [SV164: $i,SV69: $i] :
( ( ! [SY757: $i,SY758: $i] : ( equidistant @ SV69 @ SV164 @ SY757 @ ( insertion @ SY757 @ SY758 @ SV69 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(552,plain,
! [SV165: $i,SV70: $i] :
( ( ! [SY759: $i] :
( ~ ( between @ SV70 @ SV165 @ SY759 )
| ! [SY760: $i,SY761: $i] :
( ~ ( equidistant @ SV70 @ SY759 @ SY760 @ SY761 )
| ( between @ SY760 @ ( insertion @ SY760 @ SY761 @ SV70 @ SV165 ) @ SY761 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(553,plain,
! [SV166: $i,SV71: $i] :
( ( ! [SY762: $i] :
( ~ ( between @ SV71 @ SV166 @ SY762 )
| ! [SY763: $i,SY764: $i] :
( ~ ( equidistant @ SV71 @ SY762 @ SY763 @ SY764 )
| ( equidistant @ SV166 @ SY762 @ ( insertion @ SY763 @ SY764 @ SV71 @ SV166 ) @ SY764 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(554,plain,
! [SV167: $i,SV72: $i] :
( ( ! [SY765: $i] :
( ~ ( between @ SV72 @ SV167 @ SY765 )
| ( SV167
= ( insertion @ SV72 @ SY765 @ SV72 @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(555,plain,
! [SV168: $i,SV73: $i] :
( ( ! [SY766: $i,SY767: $i] :
( ~ ( equidistant @ SV73 @ SV168 @ SY766 @ SY767 )
| ! [SY768: $i,SY769: $i] :
( ( insertion @ SY768 @ SY769 @ SV73 @ SV168 )
= ( insertion @ SY768 @ SY769 @ SY766 @ SY767 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(556,plain,
! [SV169: $i,SV74: $i] :
( ( ! [SY770: $i,SY771: $i] :
( ~ ( equidistant @ SV74 @ SV169 @ SY770 @ SY771 )
| ! [SY772: $i,SY773: $i] :
( ~ ( equidistant @ SV169 @ SY772 @ SY771 @ SY773 )
| ~ ( equidistant @ SV74 @ SY772 @ SY770 @ SY773 )
| ~ ( between @ SV74 @ SV169 @ SY772 )
| ( between @ SY770 @ SY771 @ SY773 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(557,plain,
! [SV170: $i,SV75: $i] :
( ( ! [SY774: $i] :
( ~ ( between @ SV75 @ SV170 @ SY774 )
| ! [SY775: $i] :
( ~ ( between @ SV75 @ SV170 @ SY775 )
| ( SV75 = SV170 )
| ( between @ SV75 @ SY774 @ SY775 )
| ( between @ SV75 @ SY775 @ SY774 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(558,plain,
! [SV171: $i,SV76: $i] :
( ( ! [SY776: $i] :
( ~ ( between @ SV76 @ SV171 @ SY776 )
| ! [SY777: $i] :
( ~ ( between @ SV76 @ SV171 @ SY777 )
| ( SV76 = SV171 )
| ( between @ SV171 @ SY776 @ SY777 )
| ( between @ SV171 @ SY777 @ SY776 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(559,plain,
! [SV172: $i,SV77: $i] :
( ( ! [SY778: $i] :
( ~ ( between @ SV77 @ SV172 @ SY778 )
| ! [SY779: $i] :
( ~ ( between @ SY779 @ SV172 @ SY778 )
| ( SV172 = SY778 )
| ( between @ SV77 @ SY779 @ SV172 )
| ( between @ SY779 @ SV77 @ SV172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(560,plain,
! [SV173: $i,SV78: $i] :
( ( ! [SY780: $i] :
( ~ ( between @ SV78 @ SV173 @ SY780 )
| ! [SY781: $i] :
( ~ ( between @ SV78 @ SY781 @ SY780 )
| ( between @ SV78 @ SV173 @ SY781 )
| ( between @ SV78 @ SY781 @ SV173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(561,plain,
! [SV174: $i,SV79: $i] :
( ( ! [SY782: $i] :
( ~ ( between @ SV79 @ SV174 @ SY782 )
| ! [SY783: $i] :
( ~ ( between @ SV79 @ SY783 @ SY782 )
| ( between @ SV174 @ SY783 @ SY782 )
| ( between @ SY783 @ SV174 @ SY782 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(562,plain,
! [SV175: $i,SV80: $i] :
( ( ! [SY784: $i] :
( ~ ( between @ SV80 @ SV175 @ SY784 )
| ! [SY785: $i,SY786: $i] :
( ~ ( between @ SV175 @ SY785 @ SY786 )
| ~ ( between @ SV80 @ SY786 @ SY784 )
| ( between @ SV80 @ SY785 @ SY784 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(563,plain,
! [SV176: $i,SV81: $i] :
( ( ! [SY787: $i] :
( ~ ( between @ SV81 @ SV176 @ SY787 )
| ~ ( equidistant @ SV81 @ SV176 @ SV81 @ SY787 )
| ( SV176 = SY787 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(564,plain,
! [SV177: $i,SV82: $i] :
( ( ! [SY788: $i] :
( ~ ( between @ SV82 @ SV177 @ SY788 )
| ( colinear @ SY788 @ SV177 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(565,plain,
! [SV178: $i,SV83: $i] :
( ( ! [SY789: $i] :
( ~ ( between @ SV83 @ SV178 @ SY789 )
| ( colinear @ SV83 @ SY789 @ SV178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(566,plain,
! [SV179: $i,SV84: $i] :
( ( ! [SY790: $i] :
( ~ ( between @ SV84 @ SV179 @ SY790 )
| ( colinear @ SV179 @ SV84 @ SY790 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(567,plain,
! [SV180: $i,SV85: $i] :
( ( ! [SY791: $i] :
( ~ ( colinear @ SV85 @ SV180 @ SY791 )
| ( colinear @ SY791 @ SV180 @ SV85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(568,plain,
! [SV181: $i,SV86: $i] :
( ( ! [SY792: $i] :
( ~ ( colinear @ SV86 @ SV181 @ SY792 )
| ( colinear @ SV181 @ SY792 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(569,plain,
! [SV182: $i,SV87: $i] :
( ( ! [SY793: $i] :
( ~ ( colinear @ SV87 @ SV182 @ SY793 )
| ( colinear @ SV87 @ SY793 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(570,plain,
! [SV183: $i,SV88: $i] :
( ( ! [SY794: $i] :
( ~ ( colinear @ SV88 @ SV183 @ SY794 )
| ( colinear @ SY794 @ SV88 @ SV183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(571,plain,
! [SV184: $i,SV89: $i] :
( ( ! [SY795: $i] :
( ~ ( colinear @ SV89 @ SV184 @ SY795 )
| ( colinear @ SV184 @ SV89 @ SY795 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[473]) ).
thf(572,plain,
! [SV185: $i,SV90: $i] :
( ( colinear @ SV90 @ SV90 @ SV185 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(573,plain,
! [SV186: $i,SV91: $i] :
( ( colinear @ SV91 @ SV186 @ SV91 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(574,plain,
! [SV187: $i,SV92: $i] :
( ( colinear @ SV92 @ SV187 @ SV187 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(575,plain,
! [SV188: $i,SV93: $i] :
( ( ( SV93 != SV188 )
| ! [SY796: $i] : ( colinear @ SV93 @ SY796 @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(576,plain,
! [SV189: $i,SV94: $i] :
( ( ! [SY797: $i,SY798: $i] :
( ~ ( equidistant @ SV94 @ SV189 @ SY797 @ SY798 )
| ! [SY799: $i,SY800: $i] :
( ~ ( equidistant @ SV189 @ SY799 @ SY798 @ SY800 )
| ~ ( equidistant @ SV94 @ SY799 @ SY797 @ SY800 )
| ~ ( colinear @ SV94 @ SV189 @ SY799 )
| ( colinear @ SY797 @ SY798 @ SY800 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(577,plain,
! [SV190: $i,SV95: $i] :
( ( ! [SY801: $i] :
( ~ ( colinear @ SV95 @ SV190 @ SY801 )
| ! [SY802: $i] :
( ~ ( colinear @ SV95 @ SV190 @ SY802 )
| ( SV95 = SV190 )
| ( colinear @ SV95 @ SY801 @ SY802 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(578,plain,
! [SV191: $i,SV96: $i] :
( ( ! [SY803: $i] :
( ~ ( colinear @ SV96 @ SV191 @ SY803 )
| ! [SY804: $i] :
( ~ ( colinear @ SV96 @ SV191 @ SY804 )
| ( SV96 = SV191 )
| ( colinear @ SV191 @ SY803 @ SY804 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(579,plain,
( ( ( colinear @ x @ w @ v )
= $false )
| ( ( colinear @ x @ w @ u )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(580,plain,
! [SV192: $i,SV98: $i,SV2: $i] :
( ( ! [SY805: $i] :
( ~ ( equidistant @ SV2 @ SV98 @ SV192 @ SY805 )
| ! [SY806: $i,SY807: $i] :
( ~ ( equidistant @ SV2 @ SV98 @ SY806 @ SY807 )
| ( equidistant @ SV192 @ SY805 @ SY806 @ SY807 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(581,plain,
! [SV99: $i,SV3: $i] :
( ( ( ! [SY636: $i] :
~ ( equidistant @ SV3 @ SV99 @ SY636 @ SY636 ) )
= $true )
| ( ( SV3 = SV99 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(582,plain,
! [SV193: $i,SV100: $i,SV4: $i] :
( ( ! [SY808: $i] : ( between @ SV4 @ SV100 @ ( extension @ SV4 @ SV100 @ SV193 @ SY808 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(583,plain,
! [SV194: $i,SV101: $i,SV5: $i] :
( ( ! [SY809: $i] : ( equidistant @ SV5 @ ( extension @ SV101 @ SV5 @ SV194 @ SY809 ) @ SV194 @ SY809 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(584,plain,
! [SV195: $i,SV102: $i,SV6: $i] :
( ( ! [SY810: $i,SY811: $i,SY812: $i] :
( ~ ( equidistant @ SV6 @ SV102 @ SV195 @ SY810 )
| ~ ( equidistant @ SV102 @ SY811 @ SY810 @ SY812 )
| ! [SY813: $i,SY814: $i] :
( ~ ( equidistant @ SV6 @ SY813 @ SV195 @ SY814 )
| ~ ( equidistant @ SV102 @ SY813 @ SY810 @ SY814 )
| ~ ( between @ SV6 @ SV102 @ SY811 )
| ~ ( between @ SV195 @ SY810 @ SY812 )
| ( SV6 = SV102 )
| ( equidistant @ SY811 @ SY813 @ SY812 @ SY814 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(585,plain,
! [SV103: $i,SV7: $i] :
( ( ( ~ ( between @ SV7 @ SV103 @ SV7 ) )
= $true )
| ( ( SV7 = SV103 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(586,plain,
! [SV196: $i,SV104: $i,SV8: $i] :
( ( ~ ( between @ SV8 @ SV104 @ SV196 )
| ! [SY815: $i,SY816: $i] :
( ~ ( between @ SY815 @ SY816 @ SV196 )
| ( between @ SV104 @ ( inner_pasch @ SV8 @ SV104 @ SV196 @ SY816 @ SY815 ) @ SY815 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(587,plain,
! [SV197: $i,SV105: $i,SV9: $i] :
( ( ~ ( between @ SV9 @ SV105 @ SV197 )
| ! [SY817: $i,SY818: $i] :
( ~ ( between @ SY817 @ SY818 @ SV197 )
| ( between @ SY818 @ ( inner_pasch @ SV9 @ SV105 @ SV197 @ SY818 @ SY817 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(588,plain,
! [SV198: $i,SV106: $i,SV10: $i] :
( ( ~ ( equidistant @ SV10 @ SV106 @ SV10 @ SV198 )
| ! [SY819: $i] :
( ~ ( equidistant @ SY819 @ SV106 @ SY819 @ SV198 )
| ! [SY820: $i] :
( ~ ( equidistant @ SY820 @ SV106 @ SY820 @ SV198 )
| ( between @ SV10 @ SY819 @ SY820 )
| ( between @ SY819 @ SY820 @ SV10 )
| ( SV106 = SV198 )
| ( between @ SY820 @ SV10 @ SY819 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(589,plain,
! [SV199: $i,SV107: $i,SV11: $i] :
( ( ~ ( between @ SV11 @ SV107 @ SV199 )
| ! [SY821: $i,SY822: $i] :
( ~ ( between @ SY821 @ SV107 @ SY822 )
| ( SV11 = SV107 )
| ( between @ SV11 @ SY821 @ ( euclid1 @ SV11 @ SY821 @ SV107 @ SY822 @ SV199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(590,plain,
! [SV200: $i,SV108: $i,SV12: $i] :
( ( ~ ( between @ SV12 @ SV108 @ SV200 )
| ! [SY823: $i,SY824: $i] :
( ~ ( between @ SY823 @ SV108 @ SY824 )
| ( SV12 = SV108 )
| ( between @ SV12 @ SY824 @ ( euclid2 @ SV12 @ SY823 @ SV108 @ SY824 @ SV200 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(591,plain,
! [SV201: $i,SV109: $i,SV13: $i] :
( ( ~ ( between @ SV13 @ SV109 @ SV201 )
| ! [SY825: $i,SY826: $i] :
( ~ ( between @ SY825 @ SV109 @ SY826 )
| ( SV13 = SV109 )
| ( between @ ( euclid1 @ SV13 @ SY825 @ SV109 @ SY826 @ SV201 ) @ SV201 @ ( euclid2 @ SV13 @ SY825 @ SV109 @ SY826 @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(592,plain,
! [SV202: $i,SV110: $i,SV14: $i] :
( ( ! [SY827: $i] :
( ~ ( equidistant @ SV14 @ SV110 @ SV14 @ SV202 )
| ! [SY828: $i] :
( ~ ( equidistant @ SV14 @ SY827 @ SV14 @ SY828 )
| ~ ( between @ SV14 @ SV110 @ SY827 )
| ! [SY829: $i] :
( ~ ( between @ SV110 @ SY829 @ SY827 )
| ( between @ SV202 @ ( continuous @ SV14 @ SV110 @ SV202 @ SY829 @ SY827 @ SY828 ) @ SY828 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(593,plain,
! [SV203: $i,SV111: $i,SV15: $i] :
( ( ! [SY830: $i] :
( ~ ( equidistant @ SV15 @ SV111 @ SV15 @ SV203 )
| ! [SY831: $i] :
( ~ ( equidistant @ SV15 @ SY830 @ SV15 @ SY831 )
| ~ ( between @ SV15 @ SV111 @ SY830 )
| ! [SY832: $i] :
( ~ ( between @ SV111 @ SY832 @ SY830 )
| ( equidistant @ SV15 @ SY832 @ SV15 @ ( continuous @ SV15 @ SV111 @ SV203 @ SY832 @ SY830 @ SY831 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(594,plain,
! [SV204: $i,SV112: $i,SV16: $i] :
( ( ~ ( between @ SV16 @ SV112 @ SV204 )
| ( colinear @ SV16 @ SV112 @ SV204 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(595,plain,
! [SV205: $i,SV113: $i,SV17: $i] :
( ( ~ ( between @ SV17 @ SV113 @ SV205 )
| ( colinear @ SV205 @ SV17 @ SV113 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(596,plain,
! [SV206: $i,SV114: $i,SV18: $i] :
( ( ~ ( between @ SV18 @ SV114 @ SV206 )
| ( colinear @ SV114 @ SV206 @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(597,plain,
! [SV207: $i,SV115: $i,SV19: $i] :
( ( ~ ( colinear @ SV19 @ SV115 @ SV207 )
| ( between @ SV19 @ SV115 @ SV207 )
| ( between @ SV115 @ SV207 @ SV19 )
| ( between @ SV207 @ SV19 @ SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(598,plain,
! [SV208: $i,SV117: $i,SV21: $i] :
( ( ! [SY833: $i] :
( ( insertion @ SV21 @ SV117 @ SV208 @ SY833 )
= ( extension @ ( extension @ SV117 @ SV21 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV21 @ SV208 @ SY833 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(599,plain,
! [SV209: $i,SV119: $i,SV23: $i] :
( ( ! [SY834: $i] :
( ~ ( equidistant @ SV23 @ SV119 @ SV209 @ SY834 )
| ( equidistant @ SV209 @ SY834 @ SV23 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(600,plain,
! [SV210: $i,SV120: $i,SV24: $i] :
( ( ! [SY835: $i] :
( ~ ( equidistant @ SV24 @ SV120 @ SV210 @ SY835 )
| ( equidistant @ SV120 @ SV24 @ SV210 @ SY835 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(601,plain,
! [SV211: $i,SV121: $i,SV25: $i] :
( ( ! [SY836: $i] :
( ~ ( equidistant @ SV25 @ SV121 @ SV211 @ SY836 )
| ( equidistant @ SV25 @ SV121 @ SY836 @ SV211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(602,plain,
! [SV212: $i,SV122: $i,SV26: $i] :
( ( ! [SY837: $i] :
( ~ ( equidistant @ SV26 @ SV122 @ SV212 @ SY837 )
| ( equidistant @ SV122 @ SV26 @ SY837 @ SV212 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(603,plain,
! [SV213: $i,SV123: $i,SV27: $i] :
( ( ! [SY838: $i] :
( ~ ( equidistant @ SV27 @ SV123 @ SV213 @ SY838 )
| ( equidistant @ SV213 @ SY838 @ SV123 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(604,plain,
! [SV214: $i,SV124: $i,SV28: $i] :
( ( ! [SY839: $i] :
( ~ ( equidistant @ SV28 @ SV124 @ SV214 @ SY839 )
| ( equidistant @ SY839 @ SV214 @ SV28 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(605,plain,
! [SV215: $i,SV125: $i,SV29: $i] :
( ( ! [SY840: $i] :
( ~ ( equidistant @ SV29 @ SV125 @ SV215 @ SY840 )
| ( equidistant @ SY840 @ SV215 @ SV125 @ SV29 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(606,plain,
! [SV216: $i,SV126: $i,SV30: $i] :
( ( ! [SY841: $i] :
( ~ ( equidistant @ SV30 @ SV126 @ SV216 @ SY841 )
| ! [SY842: $i,SY843: $i] :
( ~ ( equidistant @ SV216 @ SY841 @ SY842 @ SY843 )
| ( equidistant @ SV30 @ SV126 @ SY842 @ SY843 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(607,plain,
! [SV217: $i,SV127: $i,SV31: $i] :
( ( SV31
= ( extension @ SV127 @ SV31 @ SV217 @ SV217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(608,plain,
! [SV218: $i,SV128: $i,SV32: $i] :
( ( ! [SY844: $i,SY845: $i] :
( SV32
!= ( extension @ SV128 @ SV218 @ SY844 @ SY845 ) )
| ( between @ SV128 @ SV218 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(609,plain,
! [SV131: $i,SV35: $i] :
( ( ( SV35 != SV131 )
= $true )
| ( ( SV131
= ( reflection @ SV35 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[518]) ).
thf(610,plain,
! [SV132: $i,SV37: $i] :
( ( ( SV37
!= ( reflection @ SV132 @ SV37 ) )
= $true )
| ( ( SV132 = SV37 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(611,plain,
! [SV219: $i,SV134: $i,SV39: $i] :
( ( ! [SY846: $i] :
( ~ ( equidistant @ SV39 @ SV134 @ SV219 @ SY846 )
| ! [SY847: $i,SY848: $i] :
( ~ ( equidistant @ SV134 @ SY847 @ SY846 @ SY848 )
| ~ ( between @ SV39 @ SV134 @ SY847 )
| ~ ( between @ SV219 @ SY846 @ SY848 )
| ( equidistant @ SV39 @ SY847 @ SV219 @ SY848 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(612,plain,
! [SV220: $i,SV135: $i,SV40: $i] :
( ( ~ ( between @ SV40 @ SV135 @ SV220 )
| ! [SY849: $i] :
( ~ ( between @ SV40 @ SV135 @ SY849 )
| ~ ( equidistant @ SV135 @ SV220 @ SV135 @ SY849 )
| ( SV40 = SV135 )
| ( SV220 = SY849 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(613,plain,
! [SV221: $i,SV136: $i,SV41: $i] :
( ( ~ ( between @ SV41 @ SV136 @ SV221 )
| ( SV41 = SV136 )
| ( SV221
= ( extension @ SV41 @ SV136 @ SV136 @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(614,plain,
! [SV222: $i,SV137: $i,SV42: $i] :
( ( ! [SY850: $i] :
( ~ ( equidistant @ SV42 @ SV137 @ SV222 @ SY850 )
| ! [SY851: $i,SY852: $i] :
( ( ( extension @ SY851 @ SY852 @ SV42 @ SV137 )
= ( extension @ SY851 @ SY852 @ SV222 @ SY850 ) )
| ( SY851 = SY852 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(615,plain,
! [SV138: $i,SV43: $i] :
( ( ( ( extension @ SV43 @ SV138 @ SV43 @ SV138 )
= ( extension @ SV43 @ SV138 @ SV138 @ SV43 ) )
= $true )
| ( ( SV43 = SV138 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(616,plain,
! [SV223: $i,SV142: $i,SV47: $i] :
( ( ~ ( between @ SV47 @ SV142 @ SV223 )
| ( SV47 != SV223 )
| ! [SY853: $i] : ( between @ SY853 @ SV142 @ SV223 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(617,plain,
! [SV224: $i,SV143: $i,SV48: $i] :
( ( ~ ( between @ SV48 @ SV143 @ SV224 )
| ( between @ SV224 @ SV143 @ SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(618,plain,
! [SV225: $i,SV145: $i,SV50: $i] :
( ( ~ ( between @ SV50 @ SV145 @ SV225 )
| ~ ( between @ SV145 @ SV50 @ SV225 )
| ( SV50 = SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(619,plain,
! [SV226: $i,SV146: $i,SV51: $i] :
( ( ~ ( between @ SV51 @ SV146 @ SV226 )
| ~ ( between @ SV51 @ SV226 @ SV146 )
| ( SV146 = SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(620,plain,
! [SV227: $i,SV147: $i,SV52: $i] :
( ( ~ ( between @ SV52 @ SV147 @ SV227 )
| ~ ( between @ SV147 @ SV52 @ SV227 )
| ( SV52 = SV147 )
| ( SV147 = SV227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(621,plain,
! [SV228: $i,SV148: $i,SV53: $i] :
( ( ~ ( between @ SV53 @ SV148 @ SV228 )
| ~ ( between @ SV53 @ SV228 @ SV148 )
| ( SV53 = SV148 )
| ( SV148 = SV228 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(622,plain,
! [SV229: $i,SV149: $i,SV54: $i] :
( ( ~ ( between @ SV54 @ SV149 @ SV229 )
| ! [SY854: $i] :
~ ( between @ SV149 @ SV229 @ SY854 )
| ( between @ SV54 @ SV149 @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(623,plain,
! [SV230: $i,SV150: $i,SV55: $i] :
( ( ~ ( between @ SV55 @ SV150 @ SV230 )
| ! [SY855: $i] :
( ~ ( between @ SV55 @ SV230 @ SY855 )
| ( between @ SV150 @ SV230 @ SY855 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(624,plain,
! [SV231: $i,SV151: $i,SV56: $i] :
( ( ~ ( between @ SV56 @ SV151 @ SV231 )
| ! [SY856: $i] :
( ~ ( between @ SV151 @ SV231 @ SY856 )
| ( SV151 = SV231 )
| ( between @ SV56 @ SV231 @ SY856 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(625,plain,
! [SV232: $i,SV152: $i,SV57: $i] :
( ( ~ ( between @ SV57 @ SV152 @ SV232 )
| ! [SY857: $i] :
( ~ ( between @ SV152 @ SV232 @ SY857 )
| ( SV152 = SV232 )
| ( between @ SV57 @ SV152 @ SY857 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(626,plain,
! [SV233: $i,SV153: $i,SV58: $i] :
( ( ~ ( between @ SV58 @ SV153 @ SV233 )
| ! [SY858: $i] :
( ~ ( between @ SV153 @ SY858 @ SV233 )
| ( between @ SV58 @ SY858 @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(627,plain,
! [SV234: $i,SV154: $i,SV59: $i] :
( ( ~ ( between @ SV59 @ SV154 @ SV234 )
| ! [SY859: $i] :
( ~ ( between @ SV59 @ SV234 @ SY859 )
| ( between @ SV59 @ SV154 @ SY859 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(628,plain,
! [SV155: $i,SV60: $i] :
( ( SV60
= ( extension @ SV155 @ SV60 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(629,plain,
! [SV235: $i,SV156: $i,SV61: $i] :
( ( ! [SY860: $i] : ( equidistant @ SV61 @ ( extension @ SV156 @ SV61 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV235 @ ( extension @ SY860 @ SV235 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(630,plain,
! [SV236: $i,SV158: $i,SV63: $i] :
( ( ! [SY861: $i] :
( ~ ( between @ SV63 @ SV158 @ SV236 )
| ! [SY862: $i] :
( ~ ( between @ SY861 @ SY862 @ SV236 )
| ! [SY863: $i] :
( ~ ( between @ SV63 @ SY863 @ SY861 )
| ( between @ SY863 @ ( inner_pasch @ SY862 @ ( inner_pasch @ SV63 @ SY863 @ SY861 @ SY862 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV236 )
| ( between @ SV158 @ ( inner_pasch @ SY862 @ ( inner_pasch @ SV63 @ SY863 @ SY861 @ SY862 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SY862 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(631,plain,
! [SV237: $i,SV159: $i,SV64: $i] :
( ( ~ ( between @ SV64 @ SV159 @ SV237 )
| ! [SY864: $i] :
( ~ ( equidistant @ SV64 @ SV237 @ SV64 @ SY864 )
| ~ ( equidistant @ SV159 @ SV237 @ SV159 @ SY864 )
| ( SV64 = SV159 )
| ( SV237 = SY864 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(632,plain,
! [SV238: $i,SV160: $i,SV65: $i] :
( ( ! [SY865: $i,SY866: $i,SY867: $i] :
( ~ ( equidistant @ SV65 @ SV160 @ SV238 @ SY865 )
| ~ ( equidistant @ SV65 @ SY866 @ SV238 @ SY867 )
| ! [SY868: $i,SY869: $i] :
( ~ ( equidistant @ SV65 @ SY868 @ SV238 @ SY869 )
| ~ ( equidistant @ SY866 @ SY868 @ SY867 @ SY869 )
| ~ ( between @ SV65 @ SV160 @ SY866 )
| ~ ( between @ SV238 @ SY865 @ SY867 )
| ( equidistant @ SV160 @ SY868 @ SY865 @ SY869 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(633,plain,
! [SV239: $i,SV161: $i,SV66: $i] :
( ( ! [SY870: $i] :
( ~ ( between @ SV66 @ SV161 @ SV239 )
| ! [SY871: $i,SY872: $i] :
( ~ ( between @ SY870 @ SY871 @ SY872 )
| ~ ( equidistant @ SV66 @ SV161 @ SY870 @ SY871 )
| ~ ( equidistant @ SV66 @ SV239 @ SY870 @ SY872 )
| ( equidistant @ SV161 @ SV239 @ SY871 @ SY872 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(634,plain,
! [SV240: $i,SV162: $i,SV67: $i] :
( ( ! [SY873: $i,SY874: $i,SY875: $i] :
( ~ ( equidistant @ SV67 @ SV162 @ SV240 @ SY873 )
| ~ ( equidistant @ SV162 @ SY874 @ SY873 @ SY875 )
| ! [SY876: $i,SY877: $i] :
( ~ ( equidistant @ SV67 @ SY876 @ SV240 @ SY877 )
| ~ ( equidistant @ SY874 @ SY876 @ SY875 @ SY877 )
| ~ ( between @ SV67 @ SV162 @ SY874 )
| ~ ( between @ SV240 @ SY873 @ SY875 )
| ( equidistant @ SV162 @ SY876 @ SY873 @ SY877 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(635,plain,
! [SV241: $i,SV163: $i,SV68: $i] :
( ( ~ ( between @ SV68 @ SV163 @ SV241 )
| ! [SY878: $i] :
( ~ ( equidistant @ SV68 @ SV163 @ SV68 @ SY878 )
| ~ ( equidistant @ SV241 @ SV163 @ SV241 @ SY878 )
| ( SV163 = SY878 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(636,plain,
! [SV242: $i,SV164: $i,SV69: $i] :
( ( ! [SY879: $i] : ( equidistant @ SV69 @ SV164 @ SV242 @ ( insertion @ SV242 @ SY879 @ SV69 @ SV164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(637,plain,
! [SV243: $i,SV165: $i,SV70: $i] :
( ( ~ ( between @ SV70 @ SV165 @ SV243 )
| ! [SY880: $i,SY881: $i] :
( ~ ( equidistant @ SV70 @ SV243 @ SY880 @ SY881 )
| ( between @ SY880 @ ( insertion @ SY880 @ SY881 @ SV70 @ SV165 ) @ SY881 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(638,plain,
! [SV244: $i,SV166: $i,SV71: $i] :
( ( ~ ( between @ SV71 @ SV166 @ SV244 )
| ! [SY882: $i,SY883: $i] :
( ~ ( equidistant @ SV71 @ SV244 @ SY882 @ SY883 )
| ( equidistant @ SV166 @ SV244 @ ( insertion @ SY882 @ SY883 @ SV71 @ SV166 ) @ SY883 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(639,plain,
! [SV245: $i,SV167: $i,SV72: $i] :
( ( ~ ( between @ SV72 @ SV167 @ SV245 )
| ( SV167
= ( insertion @ SV72 @ SV245 @ SV72 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(640,plain,
! [SV246: $i,SV168: $i,SV73: $i] :
( ( ! [SY884: $i] :
( ~ ( equidistant @ SV73 @ SV168 @ SV246 @ SY884 )
| ! [SY885: $i,SY886: $i] :
( ( insertion @ SY885 @ SY886 @ SV73 @ SV168 )
= ( insertion @ SY885 @ SY886 @ SV246 @ SY884 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(641,plain,
! [SV247: $i,SV169: $i,SV74: $i] :
( ( ! [SY887: $i] :
( ~ ( equidistant @ SV74 @ SV169 @ SV247 @ SY887 )
| ! [SY888: $i,SY889: $i] :
( ~ ( equidistant @ SV169 @ SY888 @ SY887 @ SY889 )
| ~ ( equidistant @ SV74 @ SY888 @ SV247 @ SY889 )
| ~ ( between @ SV74 @ SV169 @ SY888 )
| ( between @ SV247 @ SY887 @ SY889 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(642,plain,
! [SV248: $i,SV170: $i,SV75: $i] :
( ( ~ ( between @ SV75 @ SV170 @ SV248 )
| ! [SY890: $i] :
( ~ ( between @ SV75 @ SV170 @ SY890 )
| ( SV75 = SV170 )
| ( between @ SV75 @ SV248 @ SY890 )
| ( between @ SV75 @ SY890 @ SV248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(643,plain,
! [SV249: $i,SV171: $i,SV76: $i] :
( ( ~ ( between @ SV76 @ SV171 @ SV249 )
| ! [SY891: $i] :
( ~ ( between @ SV76 @ SV171 @ SY891 )
| ( SV76 = SV171 )
| ( between @ SV171 @ SV249 @ SY891 )
| ( between @ SV171 @ SY891 @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(644,plain,
! [SV250: $i,SV172: $i,SV77: $i] :
( ( ~ ( between @ SV77 @ SV172 @ SV250 )
| ! [SY892: $i] :
( ~ ( between @ SY892 @ SV172 @ SV250 )
| ( SV172 = SV250 )
| ( between @ SV77 @ SY892 @ SV172 )
| ( between @ SY892 @ SV77 @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(645,plain,
! [SV251: $i,SV173: $i,SV78: $i] :
( ( ~ ( between @ SV78 @ SV173 @ SV251 )
| ! [SY893: $i] :
( ~ ( between @ SV78 @ SY893 @ SV251 )
| ( between @ SV78 @ SV173 @ SY893 )
| ( between @ SV78 @ SY893 @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(646,plain,
! [SV252: $i,SV174: $i,SV79: $i] :
( ( ~ ( between @ SV79 @ SV174 @ SV252 )
| ! [SY894: $i] :
( ~ ( between @ SV79 @ SY894 @ SV252 )
| ( between @ SV174 @ SY894 @ SV252 )
| ( between @ SY894 @ SV174 @ SV252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(647,plain,
! [SV253: $i,SV175: $i,SV80: $i] :
( ( ~ ( between @ SV80 @ SV175 @ SV253 )
| ! [SY895: $i,SY896: $i] :
( ~ ( between @ SV175 @ SY895 @ SY896 )
| ~ ( between @ SV80 @ SY896 @ SV253 )
| ( between @ SV80 @ SY895 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(648,plain,
! [SV254: $i,SV176: $i,SV81: $i] :
( ( ~ ( between @ SV81 @ SV176 @ SV254 )
| ~ ( equidistant @ SV81 @ SV176 @ SV81 @ SV254 )
| ( SV176 = SV254 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(649,plain,
! [SV255: $i,SV177: $i,SV82: $i] :
( ( ~ ( between @ SV82 @ SV177 @ SV255 )
| ( colinear @ SV255 @ SV177 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(650,plain,
! [SV256: $i,SV178: $i,SV83: $i] :
( ( ~ ( between @ SV83 @ SV178 @ SV256 )
| ( colinear @ SV83 @ SV256 @ SV178 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(651,plain,
! [SV257: $i,SV179: $i,SV84: $i] :
( ( ~ ( between @ SV84 @ SV179 @ SV257 )
| ( colinear @ SV179 @ SV84 @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(652,plain,
! [SV258: $i,SV180: $i,SV85: $i] :
( ( ~ ( colinear @ SV85 @ SV180 @ SV258 )
| ( colinear @ SV258 @ SV180 @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(653,plain,
! [SV259: $i,SV181: $i,SV86: $i] :
( ( ~ ( colinear @ SV86 @ SV181 @ SV259 )
| ( colinear @ SV181 @ SV259 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(654,plain,
! [SV260: $i,SV182: $i,SV87: $i] :
( ( ~ ( colinear @ SV87 @ SV182 @ SV260 )
| ( colinear @ SV87 @ SV260 @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(655,plain,
! [SV261: $i,SV183: $i,SV88: $i] :
( ( ~ ( colinear @ SV88 @ SV183 @ SV261 )
| ( colinear @ SV261 @ SV88 @ SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(656,plain,
! [SV262: $i,SV184: $i,SV89: $i] :
( ( ~ ( colinear @ SV89 @ SV184 @ SV262 )
| ( colinear @ SV184 @ SV89 @ SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(657,plain,
! [SV188: $i,SV93: $i] :
( ( ( SV93 != SV188 )
= $true )
| ( ( ! [SY796: $i] : ( colinear @ SV93 @ SY796 @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[575]) ).
thf(658,plain,
! [SV263: $i,SV189: $i,SV94: $i] :
( ( ! [SY897: $i] :
( ~ ( equidistant @ SV94 @ SV189 @ SV263 @ SY897 )
| ! [SY898: $i,SY899: $i] :
( ~ ( equidistant @ SV189 @ SY898 @ SY897 @ SY899 )
| ~ ( equidistant @ SV94 @ SY898 @ SV263 @ SY899 )
| ~ ( colinear @ SV94 @ SV189 @ SY898 )
| ( colinear @ SV263 @ SY897 @ SY899 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(659,plain,
! [SV264: $i,SV190: $i,SV95: $i] :
( ( ~ ( colinear @ SV95 @ SV190 @ SV264 )
| ! [SY900: $i] :
( ~ ( colinear @ SV95 @ SV190 @ SY900 )
| ( SV95 = SV190 )
| ( colinear @ SV95 @ SV264 @ SY900 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(660,plain,
! [SV265: $i,SV191: $i,SV96: $i] :
( ( ~ ( colinear @ SV96 @ SV191 @ SV265 )
| ! [SY901: $i] :
( ~ ( colinear @ SV96 @ SV191 @ SY901 )
| ( SV96 = SV191 )
| ( colinear @ SV191 @ SV265 @ SY901 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(661,plain,
! [SV266: $i,SV192: $i,SV98: $i,SV2: $i] :
( ( ~ ( equidistant @ SV2 @ SV98 @ SV192 @ SV266 )
| ! [SY902: $i,SY903: $i] :
( ~ ( equidistant @ SV2 @ SV98 @ SY902 @ SY903 )
| ( equidistant @ SV192 @ SV266 @ SY902 @ SY903 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(662,plain,
! [SV267: $i,SV99: $i,SV3: $i] :
( ( ( ~ ( equidistant @ SV3 @ SV99 @ SV267 @ SV267 ) )
= $true )
| ( ( SV3 = SV99 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(663,plain,
! [SV268: $i,SV193: $i,SV100: $i,SV4: $i] :
( ( between @ SV4 @ SV100 @ ( extension @ SV4 @ SV100 @ SV193 @ SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(664,plain,
! [SV269: $i,SV194: $i,SV101: $i,SV5: $i] :
( ( equidistant @ SV5 @ ( extension @ SV101 @ SV5 @ SV194 @ SV269 ) @ SV194 @ SV269 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(665,plain,
! [SV270: $i,SV195: $i,SV102: $i,SV6: $i] :
( ( ! [SY904: $i,SY905: $i] :
( ~ ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
| ~ ( equidistant @ SV102 @ SY904 @ SV270 @ SY905 )
| ! [SY906: $i,SY907: $i] :
( ~ ( equidistant @ SV6 @ SY906 @ SV195 @ SY907 )
| ~ ( equidistant @ SV102 @ SY906 @ SV270 @ SY907 )
| ~ ( between @ SV6 @ SV102 @ SY904 )
| ~ ( between @ SV195 @ SV270 @ SY905 )
| ( SV6 = SV102 )
| ( equidistant @ SY904 @ SY906 @ SY905 @ SY907 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(666,plain,
! [SV103: $i,SV7: $i] :
( ( ( between @ SV7 @ SV103 @ SV7 )
= $false )
| ( ( SV7 = SV103 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(667,plain,
! [SV196: $i,SV104: $i,SV8: $i] :
( ( ( ~ ( between @ SV8 @ SV104 @ SV196 ) )
= $true )
| ( ( ! [SY815: $i,SY816: $i] :
( ~ ( between @ SY815 @ SY816 @ SV196 )
| ( between @ SV104 @ ( inner_pasch @ SV8 @ SV104 @ SV196 @ SY816 @ SY815 ) @ SY815 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[586]) ).
thf(668,plain,
! [SV197: $i,SV105: $i,SV9: $i] :
( ( ( ~ ( between @ SV9 @ SV105 @ SV197 ) )
= $true )
| ( ( ! [SY817: $i,SY818: $i] :
( ~ ( between @ SY817 @ SY818 @ SV197 )
| ( between @ SY818 @ ( inner_pasch @ SV9 @ SV105 @ SV197 @ SY818 @ SY817 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[587]) ).
thf(669,plain,
! [SV198: $i,SV106: $i,SV10: $i] :
( ( ( ~ ( equidistant @ SV10 @ SV106 @ SV10 @ SV198 ) )
= $true )
| ( ( ! [SY819: $i] :
( ~ ( equidistant @ SY819 @ SV106 @ SY819 @ SV198 )
| ! [SY820: $i] :
( ~ ( equidistant @ SY820 @ SV106 @ SY820 @ SV198 )
| ( between @ SV10 @ SY819 @ SY820 )
| ( between @ SY819 @ SY820 @ SV10 )
| ( SV106 = SV198 )
| ( between @ SY820 @ SV10 @ SY819 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[588]) ).
thf(670,plain,
! [SV199: $i,SV107: $i,SV11: $i] :
( ( ( ~ ( between @ SV11 @ SV107 @ SV199 ) )
= $true )
| ( ( ! [SY821: $i,SY822: $i] :
( ~ ( between @ SY821 @ SV107 @ SY822 )
| ( SV11 = SV107 )
| ( between @ SV11 @ SY821 @ ( euclid1 @ SV11 @ SY821 @ SV107 @ SY822 @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[589]) ).
thf(671,plain,
! [SV200: $i,SV108: $i,SV12: $i] :
( ( ( ~ ( between @ SV12 @ SV108 @ SV200 ) )
= $true )
| ( ( ! [SY823: $i,SY824: $i] :
( ~ ( between @ SY823 @ SV108 @ SY824 )
| ( SV12 = SV108 )
| ( between @ SV12 @ SY824 @ ( euclid2 @ SV12 @ SY823 @ SV108 @ SY824 @ SV200 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(672,plain,
! [SV201: $i,SV109: $i,SV13: $i] :
( ( ( ~ ( between @ SV13 @ SV109 @ SV201 ) )
= $true )
| ( ( ! [SY825: $i,SY826: $i] :
( ~ ( between @ SY825 @ SV109 @ SY826 )
| ( SV13 = SV109 )
| ( between @ ( euclid1 @ SV13 @ SY825 @ SV109 @ SY826 @ SV201 ) @ SV201 @ ( euclid2 @ SV13 @ SY825 @ SV109 @ SY826 @ SV201 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(673,plain,
! [SV271: $i,SV202: $i,SV110: $i,SV14: $i] :
( ( ~ ( equidistant @ SV14 @ SV110 @ SV14 @ SV202 )
| ! [SY908: $i] :
( ~ ( equidistant @ SV14 @ SV271 @ SV14 @ SY908 )
| ~ ( between @ SV14 @ SV110 @ SV271 )
| ! [SY909: $i] :
( ~ ( between @ SV110 @ SY909 @ SV271 )
| ( between @ SV202 @ ( continuous @ SV14 @ SV110 @ SV202 @ SY909 @ SV271 @ SY908 ) @ SY908 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(674,plain,
! [SV272: $i,SV203: $i,SV111: $i,SV15: $i] :
( ( ~ ( equidistant @ SV15 @ SV111 @ SV15 @ SV203 )
| ! [SY910: $i] :
( ~ ( equidistant @ SV15 @ SV272 @ SV15 @ SY910 )
| ~ ( between @ SV15 @ SV111 @ SV272 )
| ! [SY911: $i] :
( ~ ( between @ SV111 @ SY911 @ SV272 )
| ( equidistant @ SV15 @ SY911 @ SV15 @ ( continuous @ SV15 @ SV111 @ SV203 @ SY911 @ SV272 @ SY910 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(675,plain,
! [SV204: $i,SV112: $i,SV16: $i] :
( ( ( ~ ( between @ SV16 @ SV112 @ SV204 ) )
= $true )
| ( ( colinear @ SV16 @ SV112 @ SV204 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(676,plain,
! [SV205: $i,SV113: $i,SV17: $i] :
( ( ( ~ ( between @ SV17 @ SV113 @ SV205 ) )
= $true )
| ( ( colinear @ SV205 @ SV17 @ SV113 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(677,plain,
! [SV206: $i,SV114: $i,SV18: $i] :
( ( ( ~ ( between @ SV18 @ SV114 @ SV206 ) )
= $true )
| ( ( colinear @ SV114 @ SV206 @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(678,plain,
! [SV207: $i,SV115: $i,SV19: $i] :
( ( ( ~ ( colinear @ SV19 @ SV115 @ SV207 ) )
= $true )
| ( ( ( between @ SV19 @ SV115 @ SV207 )
| ( between @ SV115 @ SV207 @ SV19 )
| ( between @ SV207 @ SV19 @ SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(679,plain,
! [SV273: $i,SV208: $i,SV117: $i,SV21: $i] :
( ( ( insertion @ SV21 @ SV117 @ SV208 @ SV273 )
= ( extension @ ( extension @ SV117 @ SV21 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV21 @ SV208 @ SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(680,plain,
! [SV274: $i,SV209: $i,SV119: $i,SV23: $i] :
( ( ~ ( equidistant @ SV23 @ SV119 @ SV209 @ SV274 )
| ( equidistant @ SV209 @ SV274 @ SV23 @ SV119 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(681,plain,
! [SV275: $i,SV210: $i,SV120: $i,SV24: $i] :
( ( ~ ( equidistant @ SV24 @ SV120 @ SV210 @ SV275 )
| ( equidistant @ SV120 @ SV24 @ SV210 @ SV275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(682,plain,
! [SV276: $i,SV211: $i,SV121: $i,SV25: $i] :
( ( ~ ( equidistant @ SV25 @ SV121 @ SV211 @ SV276 )
| ( equidistant @ SV25 @ SV121 @ SV276 @ SV211 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(683,plain,
! [SV277: $i,SV212: $i,SV122: $i,SV26: $i] :
( ( ~ ( equidistant @ SV26 @ SV122 @ SV212 @ SV277 )
| ( equidistant @ SV122 @ SV26 @ SV277 @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(684,plain,
! [SV278: $i,SV213: $i,SV123: $i,SV27: $i] :
( ( ~ ( equidistant @ SV27 @ SV123 @ SV213 @ SV278 )
| ( equidistant @ SV213 @ SV278 @ SV123 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(685,plain,
! [SV279: $i,SV214: $i,SV124: $i,SV28: $i] :
( ( ~ ( equidistant @ SV28 @ SV124 @ SV214 @ SV279 )
| ( equidistant @ SV279 @ SV214 @ SV28 @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(686,plain,
! [SV280: $i,SV215: $i,SV125: $i,SV29: $i] :
( ( ~ ( equidistant @ SV29 @ SV125 @ SV215 @ SV280 )
| ( equidistant @ SV280 @ SV215 @ SV125 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(687,plain,
! [SV281: $i,SV216: $i,SV126: $i,SV30: $i] :
( ( ~ ( equidistant @ SV30 @ SV126 @ SV216 @ SV281 )
| ! [SY912: $i,SY913: $i] :
( ~ ( equidistant @ SV216 @ SV281 @ SY912 @ SY913 )
| ( equidistant @ SV30 @ SV126 @ SY912 @ SY913 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(688,plain,
! [SV218: $i,SV128: $i,SV32: $i] :
( ( ( ! [SY844: $i,SY845: $i] :
( SV32
!= ( extension @ SV128 @ SV218 @ SY844 @ SY845 ) ) )
= $true )
| ( ( between @ SV128 @ SV218 @ SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(689,plain,
! [SV131: $i,SV35: $i] :
( ( ( SV35 = SV131 )
= $false )
| ( ( SV131
= ( reflection @ SV35 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(690,plain,
! [SV132: $i,SV37: $i] :
( ( ( SV37
= ( reflection @ SV132 @ SV37 ) )
= $false )
| ( ( SV132 = SV37 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(691,plain,
! [SV282: $i,SV219: $i,SV134: $i,SV39: $i] :
( ( ~ ( equidistant @ SV39 @ SV134 @ SV219 @ SV282 )
| ! [SY914: $i,SY915: $i] :
( ~ ( equidistant @ SV134 @ SY914 @ SV282 @ SY915 )
| ~ ( between @ SV39 @ SV134 @ SY914 )
| ~ ( between @ SV219 @ SV282 @ SY915 )
| ( equidistant @ SV39 @ SY914 @ SV219 @ SY915 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(692,plain,
! [SV220: $i,SV135: $i,SV40: $i] :
( ( ( ~ ( between @ SV40 @ SV135 @ SV220 ) )
= $true )
| ( ( ! [SY849: $i] :
( ~ ( between @ SV40 @ SV135 @ SY849 )
| ~ ( equidistant @ SV135 @ SV220 @ SV135 @ SY849 )
| ( SV40 = SV135 )
| ( SV220 = SY849 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[612]) ).
thf(693,plain,
! [SV221: $i,SV136: $i,SV41: $i] :
( ( ( ~ ( between @ SV41 @ SV136 @ SV221 ) )
= $true )
| ( ( ( SV41 = SV136 )
| ( SV221
= ( extension @ SV41 @ SV136 @ SV136 @ SV221 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(694,plain,
! [SV283: $i,SV222: $i,SV137: $i,SV42: $i] :
( ( ~ ( equidistant @ SV42 @ SV137 @ SV222 @ SV283 )
| ! [SY916: $i,SY917: $i] :
( ( ( extension @ SY916 @ SY917 @ SV42 @ SV137 )
= ( extension @ SY916 @ SY917 @ SV222 @ SV283 ) )
| ( SY916 = SY917 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(695,plain,
! [SV223: $i,SV142: $i,SV47: $i] :
( ( ( ~ ( between @ SV47 @ SV142 @ SV223 ) )
= $true )
| ( ( ( SV47 != SV223 )
| ! [SY853: $i] : ( between @ SY853 @ SV142 @ SV223 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(696,plain,
! [SV224: $i,SV143: $i,SV48: $i] :
( ( ( ~ ( between @ SV48 @ SV143 @ SV224 ) )
= $true )
| ( ( between @ SV224 @ SV143 @ SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(697,plain,
! [SV225: $i,SV145: $i,SV50: $i] :
( ( ( ~ ( between @ SV50 @ SV145 @ SV225 ) )
= $true )
| ( ( ~ ( between @ SV145 @ SV50 @ SV225 )
| ( SV50 = SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(698,plain,
! [SV226: $i,SV146: $i,SV51: $i] :
( ( ( ~ ( between @ SV51 @ SV146 @ SV226 ) )
= $true )
| ( ( ~ ( between @ SV51 @ SV226 @ SV146 )
| ( SV146 = SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(699,plain,
! [SV227: $i,SV147: $i,SV52: $i] :
( ( ( ~ ( between @ SV52 @ SV147 @ SV227 ) )
= $true )
| ( ( ~ ( between @ SV147 @ SV52 @ SV227 )
| ( SV52 = SV147 )
| ( SV147 = SV227 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(700,plain,
! [SV228: $i,SV148: $i,SV53: $i] :
( ( ( ~ ( between @ SV53 @ SV148 @ SV228 ) )
= $true )
| ( ( ~ ( between @ SV53 @ SV228 @ SV148 )
| ( SV53 = SV148 )
| ( SV148 = SV228 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(701,plain,
! [SV229: $i,SV149: $i,SV54: $i] :
( ( ( ~ ( between @ SV54 @ SV149 @ SV229 ) )
= $true )
| ( ( ! [SY854: $i] :
~ ( between @ SV149 @ SV229 @ SY854 )
| ( between @ SV54 @ SV149 @ SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[622]) ).
thf(702,plain,
! [SV230: $i,SV150: $i,SV55: $i] :
( ( ( ~ ( between @ SV55 @ SV150 @ SV230 ) )
= $true )
| ( ( ! [SY855: $i] :
( ~ ( between @ SV55 @ SV230 @ SY855 )
| ( between @ SV150 @ SV230 @ SY855 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[623]) ).
thf(703,plain,
! [SV231: $i,SV151: $i,SV56: $i] :
( ( ( ~ ( between @ SV56 @ SV151 @ SV231 ) )
= $true )
| ( ( ! [SY856: $i] :
( ~ ( between @ SV151 @ SV231 @ SY856 )
| ( SV151 = SV231 )
| ( between @ SV56 @ SV231 @ SY856 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[624]) ).
thf(704,plain,
! [SV232: $i,SV152: $i,SV57: $i] :
( ( ( ~ ( between @ SV57 @ SV152 @ SV232 ) )
= $true )
| ( ( ! [SY857: $i] :
( ~ ( between @ SV152 @ SV232 @ SY857 )
| ( SV152 = SV232 )
| ( between @ SV57 @ SV152 @ SY857 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(705,plain,
! [SV233: $i,SV153: $i,SV58: $i] :
( ( ( ~ ( between @ SV58 @ SV153 @ SV233 ) )
= $true )
| ( ( ! [SY858: $i] :
( ~ ( between @ SV153 @ SY858 @ SV233 )
| ( between @ SV58 @ SY858 @ SV233 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(706,plain,
! [SV234: $i,SV154: $i,SV59: $i] :
( ( ( ~ ( between @ SV59 @ SV154 @ SV234 ) )
= $true )
| ( ( ! [SY859: $i] :
( ~ ( between @ SV59 @ SV234 @ SY859 )
| ( between @ SV59 @ SV154 @ SY859 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(707,plain,
! [SV284: $i,SV235: $i,SV156: $i,SV61: $i] :
( ( equidistant @ SV61 @ ( extension @ SV156 @ SV61 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV235 @ ( extension @ SV284 @ SV235 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(708,plain,
! [SV285: $i,SV236: $i,SV158: $i,SV63: $i] :
( ( ~ ( between @ SV63 @ SV158 @ SV236 )
| ! [SY918: $i] :
( ~ ( between @ SV285 @ SY918 @ SV236 )
| ! [SY919: $i] :
( ~ ( between @ SV63 @ SY919 @ SV285 )
| ( between @ SY919 @ ( inner_pasch @ SY918 @ ( inner_pasch @ SV63 @ SY919 @ SV285 @ SY918 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV236 )
| ( between @ SV158 @ ( inner_pasch @ SY918 @ ( inner_pasch @ SV63 @ SY919 @ SV285 @ SY918 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SY918 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(709,plain,
! [SV237: $i,SV159: $i,SV64: $i] :
( ( ( ~ ( between @ SV64 @ SV159 @ SV237 ) )
= $true )
| ( ( ! [SY864: $i] :
( ~ ( equidistant @ SV64 @ SV237 @ SV64 @ SY864 )
| ~ ( equidistant @ SV159 @ SV237 @ SV159 @ SY864 )
| ( SV64 = SV159 )
| ( SV237 = SY864 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[631]) ).
thf(710,plain,
! [SV286: $i,SV238: $i,SV160: $i,SV65: $i] :
( ( ! [SY920: $i,SY921: $i] :
( ~ ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 )
| ~ ( equidistant @ SV65 @ SY920 @ SV238 @ SY921 )
| ! [SY922: $i,SY923: $i] :
( ~ ( equidistant @ SV65 @ SY922 @ SV238 @ SY923 )
| ~ ( equidistant @ SY920 @ SY922 @ SY921 @ SY923 )
| ~ ( between @ SV65 @ SV160 @ SY920 )
| ~ ( between @ SV238 @ SV286 @ SY921 )
| ( equidistant @ SV160 @ SY922 @ SV286 @ SY923 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(711,plain,
! [SV287: $i,SV239: $i,SV161: $i,SV66: $i] :
( ( ~ ( between @ SV66 @ SV161 @ SV239 )
| ! [SY924: $i,SY925: $i] :
( ~ ( between @ SV287 @ SY924 @ SY925 )
| ~ ( equidistant @ SV66 @ SV161 @ SV287 @ SY924 )
| ~ ( equidistant @ SV66 @ SV239 @ SV287 @ SY925 )
| ( equidistant @ SV161 @ SV239 @ SY924 @ SY925 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(712,plain,
! [SV288: $i,SV240: $i,SV162: $i,SV67: $i] :
( ( ! [SY926: $i,SY927: $i] :
( ~ ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 )
| ~ ( equidistant @ SV162 @ SY926 @ SV288 @ SY927 )
| ! [SY928: $i,SY929: $i] :
( ~ ( equidistant @ SV67 @ SY928 @ SV240 @ SY929 )
| ~ ( equidistant @ SY926 @ SY928 @ SY927 @ SY929 )
| ~ ( between @ SV67 @ SV162 @ SY926 )
| ~ ( between @ SV240 @ SV288 @ SY927 )
| ( equidistant @ SV162 @ SY928 @ SV288 @ SY929 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(713,plain,
! [SV241: $i,SV163: $i,SV68: $i] :
( ( ( ~ ( between @ SV68 @ SV163 @ SV241 ) )
= $true )
| ( ( ! [SY878: $i] :
( ~ ( equidistant @ SV68 @ SV163 @ SV68 @ SY878 )
| ~ ( equidistant @ SV241 @ SV163 @ SV241 @ SY878 )
| ( SV163 = SY878 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(714,plain,
! [SV289: $i,SV242: $i,SV164: $i,SV69: $i] :
( ( equidistant @ SV69 @ SV164 @ SV242 @ ( insertion @ SV242 @ SV289 @ SV69 @ SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(715,plain,
! [SV243: $i,SV165: $i,SV70: $i] :
( ( ( ~ ( between @ SV70 @ SV165 @ SV243 ) )
= $true )
| ( ( ! [SY880: $i,SY881: $i] :
( ~ ( equidistant @ SV70 @ SV243 @ SY880 @ SY881 )
| ( between @ SY880 @ ( insertion @ SY880 @ SY881 @ SV70 @ SV165 ) @ SY881 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(716,plain,
! [SV244: $i,SV166: $i,SV71: $i] :
( ( ( ~ ( between @ SV71 @ SV166 @ SV244 ) )
= $true )
| ( ( ! [SY882: $i,SY883: $i] :
( ~ ( equidistant @ SV71 @ SV244 @ SY882 @ SY883 )
| ( equidistant @ SV166 @ SV244 @ ( insertion @ SY882 @ SY883 @ SV71 @ SV166 ) @ SY883 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[638]) ).
thf(717,plain,
! [SV245: $i,SV167: $i,SV72: $i] :
( ( ( ~ ( between @ SV72 @ SV167 @ SV245 ) )
= $true )
| ( ( SV167
= ( insertion @ SV72 @ SV245 @ SV72 @ SV167 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[639]) ).
thf(718,plain,
! [SV290: $i,SV246: $i,SV168: $i,SV73: $i] :
( ( ~ ( equidistant @ SV73 @ SV168 @ SV246 @ SV290 )
| ! [SY930: $i,SY931: $i] :
( ( insertion @ SY930 @ SY931 @ SV73 @ SV168 )
= ( insertion @ SY930 @ SY931 @ SV246 @ SV290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(719,plain,
! [SV291: $i,SV247: $i,SV169: $i,SV74: $i] :
( ( ~ ( equidistant @ SV74 @ SV169 @ SV247 @ SV291 )
| ! [SY932: $i,SY933: $i] :
( ~ ( equidistant @ SV169 @ SY932 @ SV291 @ SY933 )
| ~ ( equidistant @ SV74 @ SY932 @ SV247 @ SY933 )
| ~ ( between @ SV74 @ SV169 @ SY932 )
| ( between @ SV247 @ SV291 @ SY933 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(720,plain,
! [SV248: $i,SV170: $i,SV75: $i] :
( ( ( ~ ( between @ SV75 @ SV170 @ SV248 ) )
= $true )
| ( ( ! [SY890: $i] :
( ~ ( between @ SV75 @ SV170 @ SY890 )
| ( SV75 = SV170 )
| ( between @ SV75 @ SV248 @ SY890 )
| ( between @ SV75 @ SY890 @ SV248 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[642]) ).
thf(721,plain,
! [SV249: $i,SV171: $i,SV76: $i] :
( ( ( ~ ( between @ SV76 @ SV171 @ SV249 ) )
= $true )
| ( ( ! [SY891: $i] :
( ~ ( between @ SV76 @ SV171 @ SY891 )
| ( SV76 = SV171 )
| ( between @ SV171 @ SV249 @ SY891 )
| ( between @ SV171 @ SY891 @ SV249 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(722,plain,
! [SV250: $i,SV172: $i,SV77: $i] :
( ( ( ~ ( between @ SV77 @ SV172 @ SV250 ) )
= $true )
| ( ( ! [SY892: $i] :
( ~ ( between @ SY892 @ SV172 @ SV250 )
| ( SV172 = SV250 )
| ( between @ SV77 @ SY892 @ SV172 )
| ( between @ SY892 @ SV77 @ SV172 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(723,plain,
! [SV251: $i,SV173: $i,SV78: $i] :
( ( ( ~ ( between @ SV78 @ SV173 @ SV251 ) )
= $true )
| ( ( ! [SY893: $i] :
( ~ ( between @ SV78 @ SY893 @ SV251 )
| ( between @ SV78 @ SV173 @ SY893 )
| ( between @ SV78 @ SY893 @ SV173 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[645]) ).
thf(724,plain,
! [SV252: $i,SV174: $i,SV79: $i] :
( ( ( ~ ( between @ SV79 @ SV174 @ SV252 ) )
= $true )
| ( ( ! [SY894: $i] :
( ~ ( between @ SV79 @ SY894 @ SV252 )
| ( between @ SV174 @ SY894 @ SV252 )
| ( between @ SY894 @ SV174 @ SV252 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(725,plain,
! [SV253: $i,SV175: $i,SV80: $i] :
( ( ( ~ ( between @ SV80 @ SV175 @ SV253 ) )
= $true )
| ( ( ! [SY895: $i,SY896: $i] :
( ~ ( between @ SV175 @ SY895 @ SY896 )
| ~ ( between @ SV80 @ SY896 @ SV253 )
| ( between @ SV80 @ SY895 @ SV253 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(726,plain,
! [SV254: $i,SV176: $i,SV81: $i] :
( ( ( ~ ( between @ SV81 @ SV176 @ SV254 ) )
= $true )
| ( ( ~ ( equidistant @ SV81 @ SV176 @ SV81 @ SV254 )
| ( SV176 = SV254 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(727,plain,
! [SV255: $i,SV177: $i,SV82: $i] :
( ( ( ~ ( between @ SV82 @ SV177 @ SV255 ) )
= $true )
| ( ( colinear @ SV255 @ SV177 @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[649]) ).
thf(728,plain,
! [SV256: $i,SV178: $i,SV83: $i] :
( ( ( ~ ( between @ SV83 @ SV178 @ SV256 ) )
= $true )
| ( ( colinear @ SV83 @ SV256 @ SV178 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(729,plain,
! [SV257: $i,SV179: $i,SV84: $i] :
( ( ( ~ ( between @ SV84 @ SV179 @ SV257 ) )
= $true )
| ( ( colinear @ SV179 @ SV84 @ SV257 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(730,plain,
! [SV258: $i,SV180: $i,SV85: $i] :
( ( ( ~ ( colinear @ SV85 @ SV180 @ SV258 ) )
= $true )
| ( ( colinear @ SV258 @ SV180 @ SV85 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(731,plain,
! [SV259: $i,SV181: $i,SV86: $i] :
( ( ( ~ ( colinear @ SV86 @ SV181 @ SV259 ) )
= $true )
| ( ( colinear @ SV181 @ SV259 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[653]) ).
thf(732,plain,
! [SV260: $i,SV182: $i,SV87: $i] :
( ( ( ~ ( colinear @ SV87 @ SV182 @ SV260 ) )
= $true )
| ( ( colinear @ SV87 @ SV260 @ SV182 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[654]) ).
thf(733,plain,
! [SV261: $i,SV183: $i,SV88: $i] :
( ( ( ~ ( colinear @ SV88 @ SV183 @ SV261 ) )
= $true )
| ( ( colinear @ SV261 @ SV88 @ SV183 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[655]) ).
thf(734,plain,
! [SV262: $i,SV184: $i,SV89: $i] :
( ( ( ~ ( colinear @ SV89 @ SV184 @ SV262 ) )
= $true )
| ( ( colinear @ SV184 @ SV89 @ SV262 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(735,plain,
! [SV188: $i,SV93: $i] :
( ( ( SV93 = SV188 )
= $false )
| ( ( ! [SY796: $i] : ( colinear @ SV93 @ SY796 @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(736,plain,
! [SV292: $i,SV263: $i,SV189: $i,SV94: $i] :
( ( ~ ( equidistant @ SV94 @ SV189 @ SV263 @ SV292 )
| ! [SY934: $i,SY935: $i] :
( ~ ( equidistant @ SV189 @ SY934 @ SV292 @ SY935 )
| ~ ( equidistant @ SV94 @ SY934 @ SV263 @ SY935 )
| ~ ( colinear @ SV94 @ SV189 @ SY934 )
| ( colinear @ SV263 @ SV292 @ SY935 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(737,plain,
! [SV264: $i,SV190: $i,SV95: $i] :
( ( ( ~ ( colinear @ SV95 @ SV190 @ SV264 ) )
= $true )
| ( ( ! [SY900: $i] :
( ~ ( colinear @ SV95 @ SV190 @ SY900 )
| ( SV95 = SV190 )
| ( colinear @ SV95 @ SV264 @ SY900 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(738,plain,
! [SV265: $i,SV191: $i,SV96: $i] :
( ( ( ~ ( colinear @ SV96 @ SV191 @ SV265 ) )
= $true )
| ( ( ! [SY901: $i] :
( ~ ( colinear @ SV96 @ SV191 @ SY901 )
| ( SV96 = SV191 )
| ( colinear @ SV191 @ SV265 @ SY901 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[660]) ).
thf(739,plain,
! [SV266: $i,SV192: $i,SV98: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV98 @ SV192 @ SV266 ) )
= $true )
| ( ( ! [SY902: $i,SY903: $i] :
( ~ ( equidistant @ SV2 @ SV98 @ SY902 @ SY903 )
| ( equidistant @ SV192 @ SV266 @ SY902 @ SY903 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[661]) ).
thf(740,plain,
! [SV267: $i,SV99: $i,SV3: $i] :
( ( ( equidistant @ SV3 @ SV99 @ SV267 @ SV267 )
= $false )
| ( ( SV3 = SV99 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(741,plain,
! [SV293: $i,SV270: $i,SV195: $i,SV102: $i,SV6: $i] :
( ( ! [SY936: $i] :
( ~ ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
| ~ ( equidistant @ SV102 @ SV293 @ SV270 @ SY936 )
| ! [SY937: $i,SY938: $i] :
( ~ ( equidistant @ SV6 @ SY937 @ SV195 @ SY938 )
| ~ ( equidistant @ SV102 @ SY937 @ SV270 @ SY938 )
| ~ ( between @ SV6 @ SV102 @ SV293 )
| ~ ( between @ SV195 @ SV270 @ SY936 )
| ( SV6 = SV102 )
| ( equidistant @ SV293 @ SY937 @ SY936 @ SY938 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(742,plain,
! [SV196: $i,SV104: $i,SV8: $i] :
( ( ( between @ SV8 @ SV104 @ SV196 )
= $false )
| ( ( ! [SY815: $i,SY816: $i] :
( ~ ( between @ SY815 @ SY816 @ SV196 )
| ( between @ SV104 @ ( inner_pasch @ SV8 @ SV104 @ SV196 @ SY816 @ SY815 ) @ SY815 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(743,plain,
! [SV197: $i,SV105: $i,SV9: $i] :
( ( ( between @ SV9 @ SV105 @ SV197 )
= $false )
| ( ( ! [SY817: $i,SY818: $i] :
( ~ ( between @ SY817 @ SY818 @ SV197 )
| ( between @ SY818 @ ( inner_pasch @ SV9 @ SV105 @ SV197 @ SY818 @ SY817 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(744,plain,
! [SV198: $i,SV106: $i,SV10: $i] :
( ( ( equidistant @ SV10 @ SV106 @ SV10 @ SV198 )
= $false )
| ( ( ! [SY819: $i] :
( ~ ( equidistant @ SY819 @ SV106 @ SY819 @ SV198 )
| ! [SY820: $i] :
( ~ ( equidistant @ SY820 @ SV106 @ SY820 @ SV198 )
| ( between @ SV10 @ SY819 @ SY820 )
| ( between @ SY819 @ SY820 @ SV10 )
| ( SV106 = SV198 )
| ( between @ SY820 @ SV10 @ SY819 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(745,plain,
! [SV199: $i,SV107: $i,SV11: $i] :
( ( ( between @ SV11 @ SV107 @ SV199 )
= $false )
| ( ( ! [SY821: $i,SY822: $i] :
( ~ ( between @ SY821 @ SV107 @ SY822 )
| ( SV11 = SV107 )
| ( between @ SV11 @ SY821 @ ( euclid1 @ SV11 @ SY821 @ SV107 @ SY822 @ SV199 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(746,plain,
! [SV200: $i,SV108: $i,SV12: $i] :
( ( ( between @ SV12 @ SV108 @ SV200 )
= $false )
| ( ( ! [SY823: $i,SY824: $i] :
( ~ ( between @ SY823 @ SV108 @ SY824 )
| ( SV12 = SV108 )
| ( between @ SV12 @ SY824 @ ( euclid2 @ SV12 @ SY823 @ SV108 @ SY824 @ SV200 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(747,plain,
! [SV201: $i,SV109: $i,SV13: $i] :
( ( ( between @ SV13 @ SV109 @ SV201 )
= $false )
| ( ( ! [SY825: $i,SY826: $i] :
( ~ ( between @ SY825 @ SV109 @ SY826 )
| ( SV13 = SV109 )
| ( between @ ( euclid1 @ SV13 @ SY825 @ SV109 @ SY826 @ SV201 ) @ SV201 @ ( euclid2 @ SV13 @ SY825 @ SV109 @ SY826 @ SV201 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[672]) ).
thf(748,plain,
! [SV271: $i,SV202: $i,SV110: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV110 @ SV14 @ SV202 ) )
= $true )
| ( ( ! [SY908: $i] :
( ~ ( equidistant @ SV14 @ SV271 @ SV14 @ SY908 )
| ~ ( between @ SV14 @ SV110 @ SV271 )
| ! [SY909: $i] :
( ~ ( between @ SV110 @ SY909 @ SV271 )
| ( between @ SV202 @ ( continuous @ SV14 @ SV110 @ SV202 @ SY909 @ SV271 @ SY908 ) @ SY908 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(749,plain,
! [SV272: $i,SV203: $i,SV111: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV111 @ SV15 @ SV203 ) )
= $true )
| ( ( ! [SY910: $i] :
( ~ ( equidistant @ SV15 @ SV272 @ SV15 @ SY910 )
| ~ ( between @ SV15 @ SV111 @ SV272 )
| ! [SY911: $i] :
( ~ ( between @ SV111 @ SY911 @ SV272 )
| ( equidistant @ SV15 @ SY911 @ SV15 @ ( continuous @ SV15 @ SV111 @ SV203 @ SY911 @ SV272 @ SY910 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(750,plain,
! [SV204: $i,SV112: $i,SV16: $i] :
( ( ( between @ SV16 @ SV112 @ SV204 )
= $false )
| ( ( colinear @ SV16 @ SV112 @ SV204 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(751,plain,
! [SV205: $i,SV113: $i,SV17: $i] :
( ( ( between @ SV17 @ SV113 @ SV205 )
= $false )
| ( ( colinear @ SV205 @ SV17 @ SV113 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[676]) ).
thf(752,plain,
! [SV206: $i,SV114: $i,SV18: $i] :
( ( ( between @ SV18 @ SV114 @ SV206 )
= $false )
| ( ( colinear @ SV114 @ SV206 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[677]) ).
thf(753,plain,
! [SV207: $i,SV115: $i,SV19: $i] :
( ( ( colinear @ SV19 @ SV115 @ SV207 )
= $false )
| ( ( ( between @ SV19 @ SV115 @ SV207 )
| ( between @ SV115 @ SV207 @ SV19 )
| ( between @ SV207 @ SV19 @ SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[678]) ).
thf(754,plain,
! [SV274: $i,SV209: $i,SV119: $i,SV23: $i] :
( ( ( ~ ( equidistant @ SV23 @ SV119 @ SV209 @ SV274 ) )
= $true )
| ( ( equidistant @ SV209 @ SV274 @ SV23 @ SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(755,plain,
! [SV275: $i,SV210: $i,SV120: $i,SV24: $i] :
( ( ( ~ ( equidistant @ SV24 @ SV120 @ SV210 @ SV275 ) )
= $true )
| ( ( equidistant @ SV120 @ SV24 @ SV210 @ SV275 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(756,plain,
! [SV276: $i,SV211: $i,SV121: $i,SV25: $i] :
( ( ( ~ ( equidistant @ SV25 @ SV121 @ SV211 @ SV276 ) )
= $true )
| ( ( equidistant @ SV25 @ SV121 @ SV276 @ SV211 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(757,plain,
! [SV277: $i,SV212: $i,SV122: $i,SV26: $i] :
( ( ( ~ ( equidistant @ SV26 @ SV122 @ SV212 @ SV277 ) )
= $true )
| ( ( equidistant @ SV122 @ SV26 @ SV277 @ SV212 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(758,plain,
! [SV278: $i,SV213: $i,SV123: $i,SV27: $i] :
( ( ( ~ ( equidistant @ SV27 @ SV123 @ SV213 @ SV278 ) )
= $true )
| ( ( equidistant @ SV213 @ SV278 @ SV123 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[684]) ).
thf(759,plain,
! [SV279: $i,SV214: $i,SV124: $i,SV28: $i] :
( ( ( ~ ( equidistant @ SV28 @ SV124 @ SV214 @ SV279 ) )
= $true )
| ( ( equidistant @ SV279 @ SV214 @ SV28 @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(760,plain,
! [SV280: $i,SV215: $i,SV125: $i,SV29: $i] :
( ( ( ~ ( equidistant @ SV29 @ SV125 @ SV215 @ SV280 ) )
= $true )
| ( ( equidistant @ SV280 @ SV215 @ SV125 @ SV29 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[686]) ).
thf(761,plain,
! [SV281: $i,SV216: $i,SV126: $i,SV30: $i] :
( ( ( ~ ( equidistant @ SV30 @ SV126 @ SV216 @ SV281 ) )
= $true )
| ( ( ! [SY912: $i,SY913: $i] :
( ~ ( equidistant @ SV216 @ SV281 @ SY912 @ SY913 )
| ( equidistant @ SV30 @ SV126 @ SY912 @ SY913 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(762,plain,
! [SV294: $i,SV218: $i,SV128: $i,SV32: $i] :
( ( ( ! [SY939: $i] :
( SV32
!= ( extension @ SV128 @ SV218 @ SV294 @ SY939 ) ) )
= $true )
| ( ( between @ SV128 @ SV218 @ SV32 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(763,plain,
! [SV282: $i,SV219: $i,SV134: $i,SV39: $i] :
( ( ( ~ ( equidistant @ SV39 @ SV134 @ SV219 @ SV282 ) )
= $true )
| ( ( ! [SY914: $i,SY915: $i] :
( ~ ( equidistant @ SV134 @ SY914 @ SV282 @ SY915 )
| ~ ( between @ SV39 @ SV134 @ SY914 )
| ~ ( between @ SV219 @ SV282 @ SY915 )
| ( equidistant @ SV39 @ SY914 @ SV219 @ SY915 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(764,plain,
! [SV220: $i,SV135: $i,SV40: $i] :
( ( ( between @ SV40 @ SV135 @ SV220 )
= $false )
| ( ( ! [SY849: $i] :
( ~ ( between @ SV40 @ SV135 @ SY849 )
| ~ ( equidistant @ SV135 @ SV220 @ SV135 @ SY849 )
| ( SV40 = SV135 )
| ( SV220 = SY849 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[692]) ).
thf(765,plain,
! [SV221: $i,SV136: $i,SV41: $i] :
( ( ( between @ SV41 @ SV136 @ SV221 )
= $false )
| ( ( ( SV41 = SV136 )
| ( SV221
= ( extension @ SV41 @ SV136 @ SV136 @ SV221 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[693]) ).
thf(766,plain,
! [SV283: $i,SV222: $i,SV137: $i,SV42: $i] :
( ( ( ~ ( equidistant @ SV42 @ SV137 @ SV222 @ SV283 ) )
= $true )
| ( ( ! [SY916: $i,SY917: $i] :
( ( ( extension @ SY916 @ SY917 @ SV42 @ SV137 )
= ( extension @ SY916 @ SY917 @ SV222 @ SV283 ) )
| ( SY916 = SY917 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(767,plain,
! [SV223: $i,SV142: $i,SV47: $i] :
( ( ( between @ SV47 @ SV142 @ SV223 )
= $false )
| ( ( ( SV47 != SV223 )
| ! [SY853: $i] : ( between @ SY853 @ SV142 @ SV223 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(768,plain,
! [SV224: $i,SV143: $i,SV48: $i] :
( ( ( between @ SV48 @ SV143 @ SV224 )
= $false )
| ( ( between @ SV224 @ SV143 @ SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[696]) ).
thf(769,plain,
! [SV225: $i,SV145: $i,SV50: $i] :
( ( ( between @ SV50 @ SV145 @ SV225 )
= $false )
| ( ( ~ ( between @ SV145 @ SV50 @ SV225 )
| ( SV50 = SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[697]) ).
thf(770,plain,
! [SV226: $i,SV146: $i,SV51: $i] :
( ( ( between @ SV51 @ SV146 @ SV226 )
= $false )
| ( ( ~ ( between @ SV51 @ SV226 @ SV146 )
| ( SV146 = SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(771,plain,
! [SV227: $i,SV147: $i,SV52: $i] :
( ( ( between @ SV52 @ SV147 @ SV227 )
= $false )
| ( ( ~ ( between @ SV147 @ SV52 @ SV227 )
| ( SV52 = SV147 )
| ( SV147 = SV227 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(772,plain,
! [SV228: $i,SV148: $i,SV53: $i] :
( ( ( between @ SV53 @ SV148 @ SV228 )
= $false )
| ( ( ~ ( between @ SV53 @ SV228 @ SV148 )
| ( SV53 = SV148 )
| ( SV148 = SV228 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(773,plain,
! [SV229: $i,SV149: $i,SV54: $i] :
( ( ( between @ SV54 @ SV149 @ SV229 )
= $false )
| ( ( ! [SY854: $i] :
~ ( between @ SV149 @ SV229 @ SY854 )
| ( between @ SV54 @ SV149 @ SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[701]) ).
thf(774,plain,
! [SV230: $i,SV150: $i,SV55: $i] :
( ( ( between @ SV55 @ SV150 @ SV230 )
= $false )
| ( ( ! [SY855: $i] :
( ~ ( between @ SV55 @ SV230 @ SY855 )
| ( between @ SV150 @ SV230 @ SY855 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(775,plain,
! [SV231: $i,SV151: $i,SV56: $i] :
( ( ( between @ SV56 @ SV151 @ SV231 )
= $false )
| ( ( ! [SY856: $i] :
( ~ ( between @ SV151 @ SV231 @ SY856 )
| ( SV151 = SV231 )
| ( between @ SV56 @ SV231 @ SY856 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(776,plain,
! [SV232: $i,SV152: $i,SV57: $i] :
( ( ( between @ SV57 @ SV152 @ SV232 )
= $false )
| ( ( ! [SY857: $i] :
( ~ ( between @ SV152 @ SV232 @ SY857 )
| ( SV152 = SV232 )
| ( between @ SV57 @ SV152 @ SY857 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(777,plain,
! [SV233: $i,SV153: $i,SV58: $i] :
( ( ( between @ SV58 @ SV153 @ SV233 )
= $false )
| ( ( ! [SY858: $i] :
( ~ ( between @ SV153 @ SY858 @ SV233 )
| ( between @ SV58 @ SY858 @ SV233 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[705]) ).
thf(778,plain,
! [SV234: $i,SV154: $i,SV59: $i] :
( ( ( between @ SV59 @ SV154 @ SV234 )
= $false )
| ( ( ! [SY859: $i] :
( ~ ( between @ SV59 @ SV234 @ SY859 )
| ( between @ SV59 @ SV154 @ SY859 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(779,plain,
! [SV285: $i,SV236: $i,SV158: $i,SV63: $i] :
( ( ( ~ ( between @ SV63 @ SV158 @ SV236 ) )
= $true )
| ( ( ! [SY918: $i] :
( ~ ( between @ SV285 @ SY918 @ SV236 )
| ! [SY919: $i] :
( ~ ( between @ SV63 @ SY919 @ SV285 )
| ( between @ SY919 @ ( inner_pasch @ SY918 @ ( inner_pasch @ SV63 @ SY919 @ SV285 @ SY918 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV236 )
| ( between @ SV158 @ ( inner_pasch @ SY918 @ ( inner_pasch @ SV63 @ SY919 @ SV285 @ SY918 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SY918 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[708]) ).
thf(780,plain,
! [SV237: $i,SV159: $i,SV64: $i] :
( ( ( between @ SV64 @ SV159 @ SV237 )
= $false )
| ( ( ! [SY864: $i] :
( ~ ( equidistant @ SV64 @ SV237 @ SV64 @ SY864 )
| ~ ( equidistant @ SV159 @ SV237 @ SV159 @ SY864 )
| ( SV64 = SV159 )
| ( SV237 = SY864 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[709]) ).
thf(781,plain,
! [SV295: $i,SV286: $i,SV238: $i,SV160: $i,SV65: $i] :
( ( ! [SY940: $i] :
( ~ ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 )
| ~ ( equidistant @ SV65 @ SV295 @ SV238 @ SY940 )
| ! [SY941: $i,SY942: $i] :
( ~ ( equidistant @ SV65 @ SY941 @ SV238 @ SY942 )
| ~ ( equidistant @ SV295 @ SY941 @ SY940 @ SY942 )
| ~ ( between @ SV65 @ SV160 @ SV295 )
| ~ ( between @ SV238 @ SV286 @ SY940 )
| ( equidistant @ SV160 @ SY941 @ SV286 @ SY942 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(782,plain,
! [SV287: $i,SV239: $i,SV161: $i,SV66: $i] :
( ( ( ~ ( between @ SV66 @ SV161 @ SV239 ) )
= $true )
| ( ( ! [SY924: $i,SY925: $i] :
( ~ ( between @ SV287 @ SY924 @ SY925 )
| ~ ( equidistant @ SV66 @ SV161 @ SV287 @ SY924 )
| ~ ( equidistant @ SV66 @ SV239 @ SV287 @ SY925 )
| ( equidistant @ SV161 @ SV239 @ SY924 @ SY925 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[711]) ).
thf(783,plain,
! [SV296: $i,SV288: $i,SV240: $i,SV162: $i,SV67: $i] :
( ( ! [SY943: $i] :
( ~ ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 )
| ~ ( equidistant @ SV162 @ SV296 @ SV288 @ SY943 )
| ! [SY944: $i,SY945: $i] :
( ~ ( equidistant @ SV67 @ SY944 @ SV240 @ SY945 )
| ~ ( equidistant @ SV296 @ SY944 @ SY943 @ SY945 )
| ~ ( between @ SV67 @ SV162 @ SV296 )
| ~ ( between @ SV240 @ SV288 @ SY943 )
| ( equidistant @ SV162 @ SY944 @ SV288 @ SY945 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(784,plain,
! [SV241: $i,SV163: $i,SV68: $i] :
( ( ( between @ SV68 @ SV163 @ SV241 )
= $false )
| ( ( ! [SY878: $i] :
( ~ ( equidistant @ SV68 @ SV163 @ SV68 @ SY878 )
| ~ ( equidistant @ SV241 @ SV163 @ SV241 @ SY878 )
| ( SV163 = SY878 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[713]) ).
thf(785,plain,
! [SV243: $i,SV165: $i,SV70: $i] :
( ( ( between @ SV70 @ SV165 @ SV243 )
= $false )
| ( ( ! [SY880: $i,SY881: $i] :
( ~ ( equidistant @ SV70 @ SV243 @ SY880 @ SY881 )
| ( between @ SY880 @ ( insertion @ SY880 @ SY881 @ SV70 @ SV165 ) @ SY881 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(786,plain,
! [SV244: $i,SV166: $i,SV71: $i] :
( ( ( between @ SV71 @ SV166 @ SV244 )
= $false )
| ( ( ! [SY882: $i,SY883: $i] :
( ~ ( equidistant @ SV71 @ SV244 @ SY882 @ SY883 )
| ( equidistant @ SV166 @ SV244 @ ( insertion @ SY882 @ SY883 @ SV71 @ SV166 ) @ SY883 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(787,plain,
! [SV245: $i,SV167: $i,SV72: $i] :
( ( ( between @ SV72 @ SV167 @ SV245 )
= $false )
| ( ( SV167
= ( insertion @ SV72 @ SV245 @ SV72 @ SV167 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(788,plain,
! [SV290: $i,SV246: $i,SV168: $i,SV73: $i] :
( ( ( ~ ( equidistant @ SV73 @ SV168 @ SV246 @ SV290 ) )
= $true )
| ( ( ! [SY930: $i,SY931: $i] :
( ( insertion @ SY930 @ SY931 @ SV73 @ SV168 )
= ( insertion @ SY930 @ SY931 @ SV246 @ SV290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(789,plain,
! [SV291: $i,SV247: $i,SV169: $i,SV74: $i] :
( ( ( ~ ( equidistant @ SV74 @ SV169 @ SV247 @ SV291 ) )
= $true )
| ( ( ! [SY932: $i,SY933: $i] :
( ~ ( equidistant @ SV169 @ SY932 @ SV291 @ SY933 )
| ~ ( equidistant @ SV74 @ SY932 @ SV247 @ SY933 )
| ~ ( between @ SV74 @ SV169 @ SY932 )
| ( between @ SV247 @ SV291 @ SY933 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(790,plain,
! [SV248: $i,SV170: $i,SV75: $i] :
( ( ( between @ SV75 @ SV170 @ SV248 )
= $false )
| ( ( ! [SY890: $i] :
( ~ ( between @ SV75 @ SV170 @ SY890 )
| ( SV75 = SV170 )
| ( between @ SV75 @ SV248 @ SY890 )
| ( between @ SV75 @ SY890 @ SV248 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[720]) ).
thf(791,plain,
! [SV249: $i,SV171: $i,SV76: $i] :
( ( ( between @ SV76 @ SV171 @ SV249 )
= $false )
| ( ( ! [SY891: $i] :
( ~ ( between @ SV76 @ SV171 @ SY891 )
| ( SV76 = SV171 )
| ( between @ SV171 @ SV249 @ SY891 )
| ( between @ SV171 @ SY891 @ SV249 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(792,plain,
! [SV250: $i,SV172: $i,SV77: $i] :
( ( ( between @ SV77 @ SV172 @ SV250 )
= $false )
| ( ( ! [SY892: $i] :
( ~ ( between @ SY892 @ SV172 @ SV250 )
| ( SV172 = SV250 )
| ( between @ SV77 @ SY892 @ SV172 )
| ( between @ SY892 @ SV77 @ SV172 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(793,plain,
! [SV251: $i,SV173: $i,SV78: $i] :
( ( ( between @ SV78 @ SV173 @ SV251 )
= $false )
| ( ( ! [SY893: $i] :
( ~ ( between @ SV78 @ SY893 @ SV251 )
| ( between @ SV78 @ SV173 @ SY893 )
| ( between @ SV78 @ SY893 @ SV173 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(794,plain,
! [SV252: $i,SV174: $i,SV79: $i] :
( ( ( between @ SV79 @ SV174 @ SV252 )
= $false )
| ( ( ! [SY894: $i] :
( ~ ( between @ SV79 @ SY894 @ SV252 )
| ( between @ SV174 @ SY894 @ SV252 )
| ( between @ SY894 @ SV174 @ SV252 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(795,plain,
! [SV253: $i,SV175: $i,SV80: $i] :
( ( ( between @ SV80 @ SV175 @ SV253 )
= $false )
| ( ( ! [SY895: $i,SY896: $i] :
( ~ ( between @ SV175 @ SY895 @ SY896 )
| ~ ( between @ SV80 @ SY896 @ SV253 )
| ( between @ SV80 @ SY895 @ SV253 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(796,plain,
! [SV254: $i,SV176: $i,SV81: $i] :
( ( ( between @ SV81 @ SV176 @ SV254 )
= $false )
| ( ( ~ ( equidistant @ SV81 @ SV176 @ SV81 @ SV254 )
| ( SV176 = SV254 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[726]) ).
thf(797,plain,
! [SV255: $i,SV177: $i,SV82: $i] :
( ( ( between @ SV82 @ SV177 @ SV255 )
= $false )
| ( ( colinear @ SV255 @ SV177 @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[727]) ).
thf(798,plain,
! [SV256: $i,SV178: $i,SV83: $i] :
( ( ( between @ SV83 @ SV178 @ SV256 )
= $false )
| ( ( colinear @ SV83 @ SV256 @ SV178 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[728]) ).
thf(799,plain,
! [SV257: $i,SV179: $i,SV84: $i] :
( ( ( between @ SV84 @ SV179 @ SV257 )
= $false )
| ( ( colinear @ SV179 @ SV84 @ SV257 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(800,plain,
! [SV258: $i,SV180: $i,SV85: $i] :
( ( ( colinear @ SV85 @ SV180 @ SV258 )
= $false )
| ( ( colinear @ SV258 @ SV180 @ SV85 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(801,plain,
! [SV259: $i,SV181: $i,SV86: $i] :
( ( ( colinear @ SV86 @ SV181 @ SV259 )
= $false )
| ( ( colinear @ SV181 @ SV259 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(802,plain,
! [SV260: $i,SV182: $i,SV87: $i] :
( ( ( colinear @ SV87 @ SV182 @ SV260 )
= $false )
| ( ( colinear @ SV87 @ SV260 @ SV182 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(803,plain,
! [SV261: $i,SV183: $i,SV88: $i] :
( ( ( colinear @ SV88 @ SV183 @ SV261 )
= $false )
| ( ( colinear @ SV261 @ SV88 @ SV183 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(804,plain,
! [SV262: $i,SV184: $i,SV89: $i] :
( ( ( colinear @ SV89 @ SV184 @ SV262 )
= $false )
| ( ( colinear @ SV184 @ SV89 @ SV262 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(805,plain,
! [SV188: $i,SV297: $i,SV93: $i] :
( ( ( colinear @ SV93 @ SV297 @ SV188 )
= $true )
| ( ( SV93 = SV188 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[735]) ).
thf(806,plain,
! [SV292: $i,SV263: $i,SV189: $i,SV94: $i] :
( ( ( ~ ( equidistant @ SV94 @ SV189 @ SV263 @ SV292 ) )
= $true )
| ( ( ! [SY934: $i,SY935: $i] :
( ~ ( equidistant @ SV189 @ SY934 @ SV292 @ SY935 )
| ~ ( equidistant @ SV94 @ SY934 @ SV263 @ SY935 )
| ~ ( colinear @ SV94 @ SV189 @ SY934 )
| ( colinear @ SV263 @ SV292 @ SY935 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(807,plain,
! [SV264: $i,SV190: $i,SV95: $i] :
( ( ( colinear @ SV95 @ SV190 @ SV264 )
= $false )
| ( ( ! [SY900: $i] :
( ~ ( colinear @ SV95 @ SV190 @ SY900 )
| ( SV95 = SV190 )
| ( colinear @ SV95 @ SV264 @ SY900 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[737]) ).
thf(808,plain,
! [SV265: $i,SV191: $i,SV96: $i] :
( ( ( colinear @ SV96 @ SV191 @ SV265 )
= $false )
| ( ( ! [SY901: $i] :
( ~ ( colinear @ SV96 @ SV191 @ SY901 )
| ( SV96 = SV191 )
| ( colinear @ SV191 @ SV265 @ SY901 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(809,plain,
! [SV266: $i,SV192: $i,SV98: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV98 @ SV192 @ SV266 )
= $false )
| ( ( ! [SY902: $i,SY903: $i] :
( ~ ( equidistant @ SV2 @ SV98 @ SY902 @ SY903 )
| ( equidistant @ SV192 @ SV266 @ SY902 @ SY903 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(810,plain,
! [SV298: $i,SV293: $i,SV270: $i,SV195: $i,SV102: $i,SV6: $i] :
( ( ~ ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
| ~ ( equidistant @ SV102 @ SV293 @ SV270 @ SV298 )
| ! [SY946: $i,SY947: $i] :
( ~ ( equidistant @ SV6 @ SY946 @ SV195 @ SY947 )
| ~ ( equidistant @ SV102 @ SY946 @ SV270 @ SY947 )
| ~ ( between @ SV6 @ SV102 @ SV293 )
| ~ ( between @ SV195 @ SV270 @ SV298 )
| ( SV6 = SV102 )
| ( equidistant @ SV293 @ SY946 @ SV298 @ SY947 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(811,plain,
! [SV8: $i,SV104: $i,SV196: $i,SV299: $i] :
( ( ( ! [SY948: $i] :
( ~ ( between @ SV299 @ SY948 @ SV196 )
| ( between @ SV104 @ ( inner_pasch @ SV8 @ SV104 @ SV196 @ SY948 @ SV299 ) @ SV299 ) ) )
= $true )
| ( ( between @ SV8 @ SV104 @ SV196 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(812,plain,
! [SV105: $i,SV9: $i,SV197: $i,SV300: $i] :
( ( ( ! [SY949: $i] :
( ~ ( between @ SV300 @ SY949 @ SV197 )
| ( between @ SY949 @ ( inner_pasch @ SV9 @ SV105 @ SV197 @ SY949 @ SV300 ) @ SV9 ) ) )
= $true )
| ( ( between @ SV9 @ SV105 @ SV197 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(813,plain,
! [SV10: $i,SV198: $i,SV106: $i,SV301: $i] :
( ( ( ~ ( equidistant @ SV301 @ SV106 @ SV301 @ SV198 )
| ! [SY950: $i] :
( ~ ( equidistant @ SY950 @ SV106 @ SY950 @ SV198 )
| ( between @ SV10 @ SV301 @ SY950 )
| ( between @ SV301 @ SY950 @ SV10 )
| ( SV106 = SV198 )
| ( between @ SY950 @ SV10 @ SV301 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV106 @ SV10 @ SV198 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(814,plain,
! [SV199: $i,SV11: $i,SV107: $i,SV302: $i] :
( ( ( ! [SY951: $i] :
( ~ ( between @ SV302 @ SV107 @ SY951 )
| ( SV11 = SV107 )
| ( between @ SV11 @ SV302 @ ( euclid1 @ SV11 @ SV302 @ SV107 @ SY951 @ SV199 ) ) ) )
= $true )
| ( ( between @ SV11 @ SV107 @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(815,plain,
! [SV200: $i,SV12: $i,SV108: $i,SV303: $i] :
( ( ( ! [SY952: $i] :
( ~ ( between @ SV303 @ SV108 @ SY952 )
| ( SV12 = SV108 )
| ( between @ SV12 @ SY952 @ ( euclid2 @ SV12 @ SV303 @ SV108 @ SY952 @ SV200 ) ) ) )
= $true )
| ( ( between @ SV12 @ SV108 @ SV200 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(816,plain,
! [SV201: $i,SV13: $i,SV109: $i,SV304: $i] :
( ( ( ! [SY953: $i] :
( ~ ( between @ SV304 @ SV109 @ SY953 )
| ( SV13 = SV109 )
| ( between @ ( euclid1 @ SV13 @ SV304 @ SV109 @ SY953 @ SV201 ) @ SV201 @ ( euclid2 @ SV13 @ SV304 @ SV109 @ SY953 @ SV201 ) ) ) )
= $true )
| ( ( between @ SV13 @ SV109 @ SV201 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(817,plain,
! [SV271: $i,SV202: $i,SV110: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV110 @ SV14 @ SV202 )
= $false )
| ( ( ! [SY908: $i] :
( ~ ( equidistant @ SV14 @ SV271 @ SV14 @ SY908 )
| ~ ( between @ SV14 @ SV110 @ SV271 )
| ! [SY909: $i] :
( ~ ( between @ SV110 @ SY909 @ SV271 )
| ( between @ SV202 @ ( continuous @ SV14 @ SV110 @ SV202 @ SY909 @ SV271 @ SY908 ) @ SY908 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[748]) ).
thf(818,plain,
! [SV272: $i,SV203: $i,SV111: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV111 @ SV15 @ SV203 )
= $false )
| ( ( ! [SY910: $i] :
( ~ ( equidistant @ SV15 @ SV272 @ SV15 @ SY910 )
| ~ ( between @ SV15 @ SV111 @ SV272 )
| ! [SY911: $i] :
( ~ ( between @ SV111 @ SY911 @ SV272 )
| ( equidistant @ SV15 @ SY911 @ SV15 @ ( continuous @ SV15 @ SV111 @ SV203 @ SY911 @ SV272 @ SY910 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[749]) ).
thf(819,plain,
! [SV207: $i,SV115: $i,SV19: $i] :
( ( ( between @ SV19 @ SV115 @ SV207 )
= $true )
| ( ( ( between @ SV115 @ SV207 @ SV19 )
| ( between @ SV207 @ SV19 @ SV115 ) )
= $true )
| ( ( colinear @ SV19 @ SV115 @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[753]) ).
thf(820,plain,
! [SV274: $i,SV209: $i,SV119: $i,SV23: $i] :
( ( ( equidistant @ SV23 @ SV119 @ SV209 @ SV274 )
= $false )
| ( ( equidistant @ SV209 @ SV274 @ SV23 @ SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(821,plain,
! [SV275: $i,SV210: $i,SV120: $i,SV24: $i] :
( ( ( equidistant @ SV24 @ SV120 @ SV210 @ SV275 )
= $false )
| ( ( equidistant @ SV120 @ SV24 @ SV210 @ SV275 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(822,plain,
! [SV276: $i,SV211: $i,SV121: $i,SV25: $i] :
( ( ( equidistant @ SV25 @ SV121 @ SV211 @ SV276 )
= $false )
| ( ( equidistant @ SV25 @ SV121 @ SV276 @ SV211 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(823,plain,
! [SV277: $i,SV212: $i,SV122: $i,SV26: $i] :
( ( ( equidistant @ SV26 @ SV122 @ SV212 @ SV277 )
= $false )
| ( ( equidistant @ SV122 @ SV26 @ SV277 @ SV212 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(824,plain,
! [SV278: $i,SV213: $i,SV123: $i,SV27: $i] :
( ( ( equidistant @ SV27 @ SV123 @ SV213 @ SV278 )
= $false )
| ( ( equidistant @ SV213 @ SV278 @ SV123 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[758]) ).
thf(825,plain,
! [SV279: $i,SV214: $i,SV124: $i,SV28: $i] :
( ( ( equidistant @ SV28 @ SV124 @ SV214 @ SV279 )
= $false )
| ( ( equidistant @ SV279 @ SV214 @ SV28 @ SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(826,plain,
! [SV280: $i,SV215: $i,SV125: $i,SV29: $i] :
( ( ( equidistant @ SV29 @ SV125 @ SV215 @ SV280 )
= $false )
| ( ( equidistant @ SV280 @ SV215 @ SV125 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[760]) ).
thf(827,plain,
! [SV281: $i,SV216: $i,SV126: $i,SV30: $i] :
( ( ( equidistant @ SV30 @ SV126 @ SV216 @ SV281 )
= $false )
| ( ( ! [SY912: $i,SY913: $i] :
( ~ ( equidistant @ SV216 @ SV281 @ SY912 @ SY913 )
| ( equidistant @ SV30 @ SV126 @ SY912 @ SY913 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[761]) ).
thf(828,plain,
! [SV305: $i,SV294: $i,SV218: $i,SV128: $i,SV32: $i] :
( ( ( SV32
!= ( extension @ SV128 @ SV218 @ SV294 @ SV305 ) )
= $true )
| ( ( between @ SV128 @ SV218 @ SV32 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(829,plain,
! [SV282: $i,SV219: $i,SV134: $i,SV39: $i] :
( ( ( equidistant @ SV39 @ SV134 @ SV219 @ SV282 )
= $false )
| ( ( ! [SY914: $i,SY915: $i] :
( ~ ( equidistant @ SV134 @ SY914 @ SV282 @ SY915 )
| ~ ( between @ SV39 @ SV134 @ SY914 )
| ~ ( between @ SV219 @ SV282 @ SY915 )
| ( equidistant @ SV39 @ SY914 @ SV219 @ SY915 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[763]) ).
thf(830,plain,
! [SV220: $i,SV306: $i,SV135: $i,SV40: $i] :
( ( ( ~ ( between @ SV40 @ SV135 @ SV306 )
| ~ ( equidistant @ SV135 @ SV220 @ SV135 @ SV306 )
| ( SV40 = SV135 )
| ( SV220 = SV306 ) )
= $true )
| ( ( between @ SV40 @ SV135 @ SV220 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[764]) ).
thf(831,plain,
! [SV221: $i,SV136: $i,SV41: $i] :
( ( ( SV41 = SV136 )
= $true )
| ( ( SV221
= ( extension @ SV41 @ SV136 @ SV136 @ SV221 ) )
= $true )
| ( ( between @ SV41 @ SV136 @ SV221 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(832,plain,
! [SV283: $i,SV222: $i,SV137: $i,SV42: $i] :
( ( ( equidistant @ SV42 @ SV137 @ SV222 @ SV283 )
= $false )
| ( ( ! [SY916: $i,SY917: $i] :
( ( ( extension @ SY916 @ SY917 @ SV42 @ SV137 )
= ( extension @ SY916 @ SY917 @ SV222 @ SV283 ) )
| ( SY916 = SY917 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(833,plain,
! [SV142: $i,SV223: $i,SV47: $i] :
( ( ( SV47 != SV223 )
= $true )
| ( ( ! [SY853: $i] : ( between @ SY853 @ SV142 @ SV223 ) )
= $true )
| ( ( between @ SV47 @ SV142 @ SV223 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[767]) ).
thf(834,plain,
! [SV225: $i,SV50: $i,SV145: $i] :
( ( ( ~ ( between @ SV145 @ SV50 @ SV225 ) )
= $true )
| ( ( SV50 = SV145 )
= $true )
| ( ( between @ SV50 @ SV145 @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(835,plain,
! [SV146: $i,SV226: $i,SV51: $i] :
( ( ( ~ ( between @ SV51 @ SV226 @ SV146 ) )
= $true )
| ( ( SV146 = SV226 )
= $true )
| ( ( between @ SV51 @ SV146 @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(836,plain,
! [SV227: $i,SV52: $i,SV147: $i] :
( ( ( ~ ( between @ SV147 @ SV52 @ SV227 ) )
= $true )
| ( ( ( SV52 = SV147 )
| ( SV147 = SV227 ) )
= $true )
| ( ( between @ SV52 @ SV147 @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(837,plain,
! [SV148: $i,SV228: $i,SV53: $i] :
( ( ( ~ ( between @ SV53 @ SV228 @ SV148 ) )
= $true )
| ( ( ( SV53 = SV148 )
| ( SV148 = SV228 ) )
= $true )
| ( ( between @ SV53 @ SV148 @ SV228 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[772]) ).
thf(838,plain,
! [SV54: $i,SV229: $i,SV149: $i] :
( ( ( ! [SY854: $i] :
~ ( between @ SV149 @ SV229 @ SY854 ) )
= $true )
| ( ( between @ SV54 @ SV149 @ SV229 )
= $true )
| ( ( between @ SV54 @ SV149 @ SV229 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[773]) ).
thf(839,plain,
! [SV150: $i,SV307: $i,SV230: $i,SV55: $i] :
( ( ( ~ ( between @ SV55 @ SV230 @ SV307 )
| ( between @ SV150 @ SV230 @ SV307 ) )
= $true )
| ( ( between @ SV55 @ SV150 @ SV230 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(840,plain,
! [SV56: $i,SV308: $i,SV231: $i,SV151: $i] :
( ( ( ~ ( between @ SV151 @ SV231 @ SV308 )
| ( SV151 = SV231 )
| ( between @ SV56 @ SV231 @ SV308 ) )
= $true )
| ( ( between @ SV56 @ SV151 @ SV231 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(841,plain,
! [SV57: $i,SV309: $i,SV232: $i,SV152: $i] :
( ( ( ~ ( between @ SV152 @ SV232 @ SV309 )
| ( SV152 = SV232 )
| ( between @ SV57 @ SV152 @ SV309 ) )
= $true )
| ( ( between @ SV57 @ SV152 @ SV232 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[776]) ).
thf(842,plain,
! [SV58: $i,SV233: $i,SV310: $i,SV153: $i] :
( ( ( ~ ( between @ SV153 @ SV310 @ SV233 )
| ( between @ SV58 @ SV310 @ SV233 ) )
= $true )
| ( ( between @ SV58 @ SV153 @ SV233 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(843,plain,
! [SV154: $i,SV311: $i,SV234: $i,SV59: $i] :
( ( ( ~ ( between @ SV59 @ SV234 @ SV311 )
| ( between @ SV59 @ SV154 @ SV311 ) )
= $true )
| ( ( between @ SV59 @ SV154 @ SV234 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(844,plain,
! [SV285: $i,SV236: $i,SV158: $i,SV63: $i] :
( ( ( between @ SV63 @ SV158 @ SV236 )
= $false )
| ( ( ! [SY918: $i] :
( ~ ( between @ SV285 @ SY918 @ SV236 )
| ! [SY919: $i] :
( ~ ( between @ SV63 @ SY919 @ SV285 )
| ( between @ SY919 @ ( inner_pasch @ SY918 @ ( inner_pasch @ SV63 @ SY919 @ SV285 @ SY918 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV236 )
| ( between @ SV158 @ ( inner_pasch @ SY918 @ ( inner_pasch @ SV63 @ SY919 @ SV285 @ SY918 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SY918 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[779]) ).
thf(845,plain,
! [SV159: $i,SV312: $i,SV237: $i,SV64: $i] :
( ( ( ~ ( equidistant @ SV64 @ SV237 @ SV64 @ SV312 )
| ~ ( equidistant @ SV159 @ SV237 @ SV159 @ SV312 )
| ( SV64 = SV159 )
| ( SV237 = SV312 ) )
= $true )
| ( ( between @ SV64 @ SV159 @ SV237 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[780]) ).
thf(846,plain,
! [SV313: $i,SV295: $i,SV286: $i,SV238: $i,SV160: $i,SV65: $i] :
( ( ~ ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 )
| ~ ( equidistant @ SV65 @ SV295 @ SV238 @ SV313 )
| ! [SY954: $i,SY955: $i] :
( ~ ( equidistant @ SV65 @ SY954 @ SV238 @ SY955 )
| ~ ( equidistant @ SV295 @ SY954 @ SV313 @ SY955 )
| ~ ( between @ SV65 @ SV160 @ SV295 )
| ~ ( between @ SV238 @ SV286 @ SV313 )
| ( equidistant @ SV160 @ SY954 @ SV286 @ SY955 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[781]) ).
thf(847,plain,
! [SV287: $i,SV239: $i,SV161: $i,SV66: $i] :
( ( ( between @ SV66 @ SV161 @ SV239 )
= $false )
| ( ( ! [SY924: $i,SY925: $i] :
( ~ ( between @ SV287 @ SY924 @ SY925 )
| ~ ( equidistant @ SV66 @ SV161 @ SV287 @ SY924 )
| ~ ( equidistant @ SV66 @ SV239 @ SV287 @ SY925 )
| ( equidistant @ SV161 @ SV239 @ SY924 @ SY925 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[782]) ).
thf(848,plain,
! [SV314: $i,SV296: $i,SV288: $i,SV240: $i,SV162: $i,SV67: $i] :
( ( ~ ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 )
| ~ ( equidistant @ SV162 @ SV296 @ SV288 @ SV314 )
| ! [SY956: $i,SY957: $i] :
( ~ ( equidistant @ SV67 @ SY956 @ SV240 @ SY957 )
| ~ ( equidistant @ SV296 @ SY956 @ SV314 @ SY957 )
| ~ ( between @ SV67 @ SV162 @ SV296 )
| ~ ( between @ SV240 @ SV288 @ SV314 )
| ( equidistant @ SV162 @ SY956 @ SV288 @ SY957 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(849,plain,
! [SV241: $i,SV315: $i,SV163: $i,SV68: $i] :
( ( ( ~ ( equidistant @ SV68 @ SV163 @ SV68 @ SV315 )
| ~ ( equidistant @ SV241 @ SV163 @ SV241 @ SV315 )
| ( SV163 = SV315 ) )
= $true )
| ( ( between @ SV68 @ SV163 @ SV241 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(850,plain,
! [SV165: $i,SV316: $i,SV243: $i,SV70: $i] :
( ( ( ! [SY958: $i] :
( ~ ( equidistant @ SV70 @ SV243 @ SV316 @ SY958 )
| ( between @ SV316 @ ( insertion @ SV316 @ SY958 @ SV70 @ SV165 ) @ SY958 ) ) )
= $true )
| ( ( between @ SV70 @ SV165 @ SV243 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(851,plain,
! [SV166: $i,SV317: $i,SV244: $i,SV71: $i] :
( ( ( ! [SY959: $i] :
( ~ ( equidistant @ SV71 @ SV244 @ SV317 @ SY959 )
| ( equidistant @ SV166 @ SV244 @ ( insertion @ SV317 @ SY959 @ SV71 @ SV166 ) @ SY959 ) ) )
= $true )
| ( ( between @ SV71 @ SV166 @ SV244 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(852,plain,
! [SV290: $i,SV246: $i,SV168: $i,SV73: $i] :
( ( ( equidistant @ SV73 @ SV168 @ SV246 @ SV290 )
= $false )
| ( ( ! [SY930: $i,SY931: $i] :
( ( insertion @ SY930 @ SY931 @ SV73 @ SV168 )
= ( insertion @ SY930 @ SY931 @ SV246 @ SV290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(853,plain,
! [SV291: $i,SV247: $i,SV169: $i,SV74: $i] :
( ( ( equidistant @ SV74 @ SV169 @ SV247 @ SV291 )
= $false )
| ( ( ! [SY932: $i,SY933: $i] :
( ~ ( equidistant @ SV169 @ SY932 @ SV291 @ SY933 )
| ~ ( equidistant @ SV74 @ SY932 @ SV247 @ SY933 )
| ~ ( between @ SV74 @ SV169 @ SY932 )
| ( between @ SV247 @ SV291 @ SY933 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[789]) ).
thf(854,plain,
! [SV248: $i,SV318: $i,SV170: $i,SV75: $i] :
( ( ( ~ ( between @ SV75 @ SV170 @ SV318 )
| ( SV75 = SV170 )
| ( between @ SV75 @ SV248 @ SV318 )
| ( between @ SV75 @ SV318 @ SV248 ) )
= $true )
| ( ( between @ SV75 @ SV170 @ SV248 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(855,plain,
! [SV249: $i,SV319: $i,SV171: $i,SV76: $i] :
( ( ( ~ ( between @ SV76 @ SV171 @ SV319 )
| ( SV76 = SV171 )
| ( between @ SV171 @ SV249 @ SV319 )
| ( between @ SV171 @ SV319 @ SV249 ) )
= $true )
| ( ( between @ SV76 @ SV171 @ SV249 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(856,plain,
! [SV77: $i,SV250: $i,SV172: $i,SV320: $i] :
( ( ( ~ ( between @ SV320 @ SV172 @ SV250 )
| ( SV172 = SV250 )
| ( between @ SV77 @ SV320 @ SV172 )
| ( between @ SV320 @ SV77 @ SV172 ) )
= $true )
| ( ( between @ SV77 @ SV172 @ SV250 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[792]) ).
thf(857,plain,
! [SV173: $i,SV251: $i,SV321: $i,SV78: $i] :
( ( ( ~ ( between @ SV78 @ SV321 @ SV251 )
| ( between @ SV78 @ SV173 @ SV321 )
| ( between @ SV78 @ SV321 @ SV173 ) )
= $true )
| ( ( between @ SV78 @ SV173 @ SV251 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[793]) ).
thf(858,plain,
! [SV174: $i,SV252: $i,SV322: $i,SV79: $i] :
( ( ( ~ ( between @ SV79 @ SV322 @ SV252 )
| ( between @ SV174 @ SV322 @ SV252 )
| ( between @ SV322 @ SV174 @ SV252 ) )
= $true )
| ( ( between @ SV79 @ SV174 @ SV252 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[794]) ).
thf(859,plain,
! [SV253: $i,SV80: $i,SV323: $i,SV175: $i] :
( ( ( ! [SY960: $i] :
( ~ ( between @ SV175 @ SV323 @ SY960 )
| ~ ( between @ SV80 @ SY960 @ SV253 )
| ( between @ SV80 @ SV323 @ SV253 ) ) )
= $true )
| ( ( between @ SV80 @ SV175 @ SV253 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(860,plain,
! [SV254: $i,SV176: $i,SV81: $i] :
( ( ( ~ ( equidistant @ SV81 @ SV176 @ SV81 @ SV254 ) )
= $true )
| ( ( SV176 = SV254 )
= $true )
| ( ( between @ SV81 @ SV176 @ SV254 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(861,plain,
! [SV292: $i,SV263: $i,SV189: $i,SV94: $i] :
( ( ( equidistant @ SV94 @ SV189 @ SV263 @ SV292 )
= $false )
| ( ( ! [SY934: $i,SY935: $i] :
( ~ ( equidistant @ SV189 @ SY934 @ SV292 @ SY935 )
| ~ ( equidistant @ SV94 @ SY934 @ SV263 @ SY935 )
| ~ ( colinear @ SV94 @ SV189 @ SY934 )
| ( colinear @ SV263 @ SV292 @ SY935 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[806]) ).
thf(862,plain,
! [SV264: $i,SV324: $i,SV190: $i,SV95: $i] :
( ( ( ~ ( colinear @ SV95 @ SV190 @ SV324 )
| ( SV95 = SV190 )
| ( colinear @ SV95 @ SV264 @ SV324 ) )
= $true )
| ( ( colinear @ SV95 @ SV190 @ SV264 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(863,plain,
! [SV265: $i,SV325: $i,SV191: $i,SV96: $i] :
( ( ( ~ ( colinear @ SV96 @ SV191 @ SV325 )
| ( SV96 = SV191 )
| ( colinear @ SV191 @ SV265 @ SV325 ) )
= $true )
| ( ( colinear @ SV96 @ SV191 @ SV265 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(864,plain,
! [SV266: $i,SV192: $i,SV326: $i,SV98: $i,SV2: $i] :
( ( ( ! [SY961: $i] :
( ~ ( equidistant @ SV2 @ SV98 @ SV326 @ SY961 )
| ( equidistant @ SV192 @ SV266 @ SV326 @ SY961 ) ) )
= $true )
| ( ( equidistant @ SV2 @ SV98 @ SV192 @ SV266 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(865,plain,
! [SV298: $i,SV293: $i,SV270: $i,SV195: $i,SV102: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 ) )
= $true )
| ( ( ~ ( equidistant @ SV102 @ SV293 @ SV270 @ SV298 )
| ! [SY946: $i,SY947: $i] :
( ~ ( equidistant @ SV6 @ SY946 @ SV195 @ SY947 )
| ~ ( equidistant @ SV102 @ SY946 @ SV270 @ SY947 )
| ~ ( between @ SV6 @ SV102 @ SV293 )
| ~ ( between @ SV195 @ SV270 @ SV298 )
| ( SV6 = SV102 )
| ( equidistant @ SV293 @ SY946 @ SV298 @ SY947 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[810]) ).
thf(866,plain,
! [SV8: $i,SV104: $i,SV196: $i,SV327: $i,SV299: $i] :
( ( ( ~ ( between @ SV299 @ SV327 @ SV196 )
| ( between @ SV104 @ ( inner_pasch @ SV8 @ SV104 @ SV196 @ SV327 @ SV299 ) @ SV299 ) )
= $true )
| ( ( between @ SV8 @ SV104 @ SV196 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(867,plain,
! [SV105: $i,SV9: $i,SV197: $i,SV328: $i,SV300: $i] :
( ( ( ~ ( between @ SV300 @ SV328 @ SV197 )
| ( between @ SV328 @ ( inner_pasch @ SV9 @ SV105 @ SV197 @ SV328 @ SV300 ) @ SV9 ) )
= $true )
| ( ( between @ SV9 @ SV105 @ SV197 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(868,plain,
! [SV10: $i,SV198: $i,SV106: $i,SV301: $i] :
( ( ( ~ ( equidistant @ SV301 @ SV106 @ SV301 @ SV198 ) )
= $true )
| ( ( ! [SY950: $i] :
( ~ ( equidistant @ SY950 @ SV106 @ SY950 @ SV198 )
| ( between @ SV10 @ SV301 @ SY950 )
| ( between @ SV301 @ SY950 @ SV10 )
| ( SV106 = SV198 )
| ( between @ SY950 @ SV10 @ SV301 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV106 @ SV10 @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[813]) ).
thf(869,plain,
! [SV199: $i,SV11: $i,SV329: $i,SV107: $i,SV302: $i] :
( ( ( ~ ( between @ SV302 @ SV107 @ SV329 )
| ( SV11 = SV107 )
| ( between @ SV11 @ SV302 @ ( euclid1 @ SV11 @ SV302 @ SV107 @ SV329 @ SV199 ) ) )
= $true )
| ( ( between @ SV11 @ SV107 @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(870,plain,
! [SV200: $i,SV12: $i,SV330: $i,SV108: $i,SV303: $i] :
( ( ( ~ ( between @ SV303 @ SV108 @ SV330 )
| ( SV12 = SV108 )
| ( between @ SV12 @ SV330 @ ( euclid2 @ SV12 @ SV303 @ SV108 @ SV330 @ SV200 ) ) )
= $true )
| ( ( between @ SV12 @ SV108 @ SV200 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(871,plain,
! [SV201: $i,SV13: $i,SV331: $i,SV109: $i,SV304: $i] :
( ( ( ~ ( between @ SV304 @ SV109 @ SV331 )
| ( SV13 = SV109 )
| ( between @ ( euclid1 @ SV13 @ SV304 @ SV109 @ SV331 @ SV201 ) @ SV201 @ ( euclid2 @ SV13 @ SV304 @ SV109 @ SV331 @ SV201 ) ) )
= $true )
| ( ( between @ SV13 @ SV109 @ SV201 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[816]) ).
thf(872,plain,
! [SV202: $i,SV110: $i,SV332: $i,SV271: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV271 @ SV14 @ SV332 )
| ~ ( between @ SV14 @ SV110 @ SV271 )
| ! [SY962: $i] :
( ~ ( between @ SV110 @ SY962 @ SV271 )
| ( between @ SV202 @ ( continuous @ SV14 @ SV110 @ SV202 @ SY962 @ SV271 @ SV332 ) @ SV332 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV110 @ SV14 @ SV202 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[817]) ).
thf(873,plain,
! [SV203: $i,SV111: $i,SV333: $i,SV272: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV272 @ SV15 @ SV333 )
| ~ ( between @ SV15 @ SV111 @ SV272 )
| ! [SY963: $i] :
( ~ ( between @ SV111 @ SY963 @ SV272 )
| ( equidistant @ SV15 @ SY963 @ SV15 @ ( continuous @ SV15 @ SV111 @ SV203 @ SY963 @ SV272 @ SV333 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV111 @ SV15 @ SV203 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(874,plain,
! [SV19: $i,SV207: $i,SV115: $i] :
( ( ( between @ SV115 @ SV207 @ SV19 )
= $true )
| ( ( between @ SV207 @ SV19 @ SV115 )
= $true )
| ( ( between @ SV19 @ SV115 @ SV207 )
= $true )
| ( ( colinear @ SV19 @ SV115 @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(875,plain,
! [SV126: $i,SV30: $i,SV334: $i,SV281: $i,SV216: $i] :
( ( ( ! [SY964: $i] :
( ~ ( equidistant @ SV216 @ SV281 @ SV334 @ SY964 )
| ( equidistant @ SV30 @ SV126 @ SV334 @ SY964 ) ) )
= $true )
| ( ( equidistant @ SV30 @ SV126 @ SV216 @ SV281 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(876,plain,
! [SV305: $i,SV294: $i,SV218: $i,SV128: $i,SV32: $i] :
( ( ( SV32
= ( extension @ SV128 @ SV218 @ SV294 @ SV305 ) )
= $false )
| ( ( between @ SV128 @ SV218 @ SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[828]) ).
thf(877,plain,
! [SV219: $i,SV39: $i,SV282: $i,SV335: $i,SV134: $i] :
( ( ( ! [SY965: $i] :
( ~ ( equidistant @ SV134 @ SV335 @ SV282 @ SY965 )
| ~ ( between @ SV39 @ SV134 @ SV335 )
| ~ ( between @ SV219 @ SV282 @ SY965 )
| ( equidistant @ SV39 @ SV335 @ SV219 @ SY965 ) ) )
= $true )
| ( ( equidistant @ SV39 @ SV134 @ SV219 @ SV282 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(878,plain,
! [SV220: $i,SV306: $i,SV135: $i,SV40: $i] :
( ( ( ~ ( between @ SV40 @ SV135 @ SV306 ) )
= $true )
| ( ( ~ ( equidistant @ SV135 @ SV220 @ SV135 @ SV306 )
| ( SV40 = SV135 )
| ( SV220 = SV306 ) )
= $true )
| ( ( between @ SV40 @ SV135 @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[830]) ).
thf(879,plain,
! [SV283: $i,SV222: $i,SV137: $i,SV42: $i,SV336: $i] :
( ( ( ! [SY966: $i] :
( ( ( extension @ SV336 @ SY966 @ SV42 @ SV137 )
= ( extension @ SV336 @ SY966 @ SV222 @ SV283 ) )
| ( SV336 = SY966 ) ) )
= $true )
| ( ( equidistant @ SV42 @ SV137 @ SV222 @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(880,plain,
! [SV142: $i,SV223: $i,SV47: $i] :
( ( ( SV47 = SV223 )
= $false )
| ( ( ! [SY853: $i] : ( between @ SY853 @ SV142 @ SV223 ) )
= $true )
| ( ( between @ SV47 @ SV142 @ SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(881,plain,
! [SV225: $i,SV50: $i,SV145: $i] :
( ( ( between @ SV145 @ SV50 @ SV225 )
= $false )
| ( ( SV50 = SV145 )
= $true )
| ( ( between @ SV50 @ SV145 @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(882,plain,
! [SV146: $i,SV226: $i,SV51: $i] :
( ( ( between @ SV51 @ SV226 @ SV146 )
= $false )
| ( ( SV146 = SV226 )
= $true )
| ( ( between @ SV51 @ SV146 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[835]) ).
thf(883,plain,
! [SV227: $i,SV52: $i,SV147: $i] :
( ( ( between @ SV147 @ SV52 @ SV227 )
= $false )
| ( ( ( SV52 = SV147 )
| ( SV147 = SV227 ) )
= $true )
| ( ( between @ SV52 @ SV147 @ SV227 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[836]) ).
thf(884,plain,
! [SV148: $i,SV228: $i,SV53: $i] :
( ( ( between @ SV53 @ SV228 @ SV148 )
= $false )
| ( ( ( SV53 = SV148 )
| ( SV148 = SV228 ) )
= $true )
| ( ( between @ SV53 @ SV148 @ SV228 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(885,plain,
! [SV54: $i,SV337: $i,SV229: $i,SV149: $i] :
( ( ( ~ ( between @ SV149 @ SV229 @ SV337 ) )
= $true )
| ( ( between @ SV54 @ SV149 @ SV229 )
= $true )
| ( ( between @ SV54 @ SV149 @ SV229 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(886,plain,
! [SV150: $i,SV307: $i,SV230: $i,SV55: $i] :
( ( ( ~ ( between @ SV55 @ SV230 @ SV307 ) )
= $true )
| ( ( between @ SV150 @ SV230 @ SV307 )
= $true )
| ( ( between @ SV55 @ SV150 @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(887,plain,
! [SV56: $i,SV308: $i,SV231: $i,SV151: $i] :
( ( ( ~ ( between @ SV151 @ SV231 @ SV308 ) )
= $true )
| ( ( ( SV151 = SV231 )
| ( between @ SV56 @ SV231 @ SV308 ) )
= $true )
| ( ( between @ SV56 @ SV151 @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[840]) ).
thf(888,plain,
! [SV57: $i,SV309: $i,SV232: $i,SV152: $i] :
( ( ( ~ ( between @ SV152 @ SV232 @ SV309 ) )
= $true )
| ( ( ( SV152 = SV232 )
| ( between @ SV57 @ SV152 @ SV309 ) )
= $true )
| ( ( between @ SV57 @ SV152 @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(889,plain,
! [SV58: $i,SV233: $i,SV310: $i,SV153: $i] :
( ( ( ~ ( between @ SV153 @ SV310 @ SV233 ) )
= $true )
| ( ( between @ SV58 @ SV310 @ SV233 )
= $true )
| ( ( between @ SV58 @ SV153 @ SV233 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(890,plain,
! [SV154: $i,SV311: $i,SV234: $i,SV59: $i] :
( ( ( ~ ( between @ SV59 @ SV234 @ SV311 ) )
= $true )
| ( ( between @ SV59 @ SV154 @ SV311 )
= $true )
| ( ( between @ SV59 @ SV154 @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(891,plain,
! [SV158: $i,SV63: $i,SV236: $i,SV338: $i,SV285: $i] :
( ( ( ~ ( between @ SV285 @ SV338 @ SV236 )
| ! [SY967: $i] :
( ~ ( between @ SV63 @ SY967 @ SV285 )
| ( between @ SY967 @ ( inner_pasch @ SV338 @ ( inner_pasch @ SV63 @ SY967 @ SV285 @ SV338 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV236 )
| ( between @ SV158 @ ( inner_pasch @ SV338 @ ( inner_pasch @ SV63 @ SY967 @ SV285 @ SV338 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV338 ) ) )
= $true )
| ( ( between @ SV63 @ SV158 @ SV236 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(892,plain,
! [SV159: $i,SV312: $i,SV237: $i,SV64: $i] :
( ( ( ~ ( equidistant @ SV64 @ SV237 @ SV64 @ SV312 ) )
= $true )
| ( ( ~ ( equidistant @ SV159 @ SV237 @ SV159 @ SV312 )
| ( SV64 = SV159 )
| ( SV237 = SV312 ) )
= $true )
| ( ( between @ SV64 @ SV159 @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[845]) ).
thf(893,plain,
! [SV313: $i,SV295: $i,SV286: $i,SV238: $i,SV160: $i,SV65: $i] :
( ( ( ~ ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 ) )
= $true )
| ( ( ~ ( equidistant @ SV65 @ SV295 @ SV238 @ SV313 )
| ! [SY954: $i,SY955: $i] :
( ~ ( equidistant @ SV65 @ SY954 @ SV238 @ SY955 )
| ~ ( equidistant @ SV295 @ SY954 @ SV313 @ SY955 )
| ~ ( between @ SV65 @ SV160 @ SV295 )
| ~ ( between @ SV238 @ SV286 @ SV313 )
| ( equidistant @ SV160 @ SY954 @ SV286 @ SY955 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[846]) ).
thf(894,plain,
! [SV239: $i,SV161: $i,SV66: $i,SV339: $i,SV287: $i] :
( ( ( ! [SY968: $i] :
( ~ ( between @ SV287 @ SV339 @ SY968 )
| ~ ( equidistant @ SV66 @ SV161 @ SV287 @ SV339 )
| ~ ( equidistant @ SV66 @ SV239 @ SV287 @ SY968 )
| ( equidistant @ SV161 @ SV239 @ SV339 @ SY968 ) ) )
= $true )
| ( ( between @ SV66 @ SV161 @ SV239 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(895,plain,
! [SV314: $i,SV296: $i,SV288: $i,SV240: $i,SV162: $i,SV67: $i] :
( ( ( ~ ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 ) )
= $true )
| ( ( ~ ( equidistant @ SV162 @ SV296 @ SV288 @ SV314 )
| ! [SY956: $i,SY957: $i] :
( ~ ( equidistant @ SV67 @ SY956 @ SV240 @ SY957 )
| ~ ( equidistant @ SV296 @ SY956 @ SV314 @ SY957 )
| ~ ( between @ SV67 @ SV162 @ SV296 )
| ~ ( between @ SV240 @ SV288 @ SV314 )
| ( equidistant @ SV162 @ SY956 @ SV288 @ SY957 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(896,plain,
! [SV241: $i,SV315: $i,SV163: $i,SV68: $i] :
( ( ( ~ ( equidistant @ SV68 @ SV163 @ SV68 @ SV315 ) )
= $true )
| ( ( ~ ( equidistant @ SV241 @ SV163 @ SV241 @ SV315 )
| ( SV163 = SV315 ) )
= $true )
| ( ( between @ SV68 @ SV163 @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(897,plain,
! [SV165: $i,SV340: $i,SV316: $i,SV243: $i,SV70: $i] :
( ( ( ~ ( equidistant @ SV70 @ SV243 @ SV316 @ SV340 )
| ( between @ SV316 @ ( insertion @ SV316 @ SV340 @ SV70 @ SV165 ) @ SV340 ) )
= $true )
| ( ( between @ SV70 @ SV165 @ SV243 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[850]) ).
thf(898,plain,
! [SV166: $i,SV341: $i,SV317: $i,SV244: $i,SV71: $i] :
( ( ( ~ ( equidistant @ SV71 @ SV244 @ SV317 @ SV341 )
| ( equidistant @ SV166 @ SV244 @ ( insertion @ SV317 @ SV341 @ SV71 @ SV166 ) @ SV341 ) )
= $true )
| ( ( between @ SV71 @ SV166 @ SV244 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[851]) ).
thf(899,plain,
! [SV290: $i,SV246: $i,SV168: $i,SV73: $i,SV342: $i] :
( ( ( ! [SY969: $i] :
( ( insertion @ SV342 @ SY969 @ SV73 @ SV168 )
= ( insertion @ SV342 @ SY969 @ SV246 @ SV290 ) ) )
= $true )
| ( ( equidistant @ SV73 @ SV168 @ SV246 @ SV290 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(900,plain,
! [SV247: $i,SV74: $i,SV291: $i,SV343: $i,SV169: $i] :
( ( ( ! [SY970: $i] :
( ~ ( equidistant @ SV169 @ SV343 @ SV291 @ SY970 )
| ~ ( equidistant @ SV74 @ SV343 @ SV247 @ SY970 )
| ~ ( between @ SV74 @ SV169 @ SV343 )
| ( between @ SV247 @ SV291 @ SY970 ) ) )
= $true )
| ( ( equidistant @ SV74 @ SV169 @ SV247 @ SV291 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[853]) ).
thf(901,plain,
! [SV248: $i,SV318: $i,SV170: $i,SV75: $i] :
( ( ( ~ ( between @ SV75 @ SV170 @ SV318 ) )
= $true )
| ( ( ( SV75 = SV170 )
| ( between @ SV75 @ SV248 @ SV318 )
| ( between @ SV75 @ SV318 @ SV248 ) )
= $true )
| ( ( between @ SV75 @ SV170 @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[854]) ).
thf(902,plain,
! [SV249: $i,SV319: $i,SV171: $i,SV76: $i] :
( ( ( ~ ( between @ SV76 @ SV171 @ SV319 ) )
= $true )
| ( ( ( SV76 = SV171 )
| ( between @ SV171 @ SV249 @ SV319 )
| ( between @ SV171 @ SV319 @ SV249 ) )
= $true )
| ( ( between @ SV76 @ SV171 @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[855]) ).
thf(903,plain,
! [SV77: $i,SV250: $i,SV172: $i,SV320: $i] :
( ( ( ~ ( between @ SV320 @ SV172 @ SV250 ) )
= $true )
| ( ( ( SV172 = SV250 )
| ( between @ SV77 @ SV320 @ SV172 )
| ( between @ SV320 @ SV77 @ SV172 ) )
= $true )
| ( ( between @ SV77 @ SV172 @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[856]) ).
thf(904,plain,
! [SV173: $i,SV251: $i,SV321: $i,SV78: $i] :
( ( ( ~ ( between @ SV78 @ SV321 @ SV251 ) )
= $true )
| ( ( ( between @ SV78 @ SV173 @ SV321 )
| ( between @ SV78 @ SV321 @ SV173 ) )
= $true )
| ( ( between @ SV78 @ SV173 @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[857]) ).
thf(905,plain,
! [SV174: $i,SV252: $i,SV322: $i,SV79: $i] :
( ( ( ~ ( between @ SV79 @ SV322 @ SV252 ) )
= $true )
| ( ( ( between @ SV174 @ SV322 @ SV252 )
| ( between @ SV322 @ SV174 @ SV252 ) )
= $true )
| ( ( between @ SV79 @ SV174 @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[858]) ).
thf(906,plain,
! [SV253: $i,SV80: $i,SV344: $i,SV323: $i,SV175: $i] :
( ( ( ~ ( between @ SV175 @ SV323 @ SV344 )
| ~ ( between @ SV80 @ SV344 @ SV253 )
| ( between @ SV80 @ SV323 @ SV253 ) )
= $true )
| ( ( between @ SV80 @ SV175 @ SV253 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(907,plain,
! [SV254: $i,SV176: $i,SV81: $i] :
( ( ( equidistant @ SV81 @ SV176 @ SV81 @ SV254 )
= $false )
| ( ( SV176 = SV254 )
= $true )
| ( ( between @ SV81 @ SV176 @ SV254 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(908,plain,
! [SV263: $i,SV94: $i,SV292: $i,SV345: $i,SV189: $i] :
( ( ( ! [SY971: $i] :
( ~ ( equidistant @ SV189 @ SV345 @ SV292 @ SY971 )
| ~ ( equidistant @ SV94 @ SV345 @ SV263 @ SY971 )
| ~ ( colinear @ SV94 @ SV189 @ SV345 )
| ( colinear @ SV263 @ SV292 @ SY971 ) ) )
= $true )
| ( ( equidistant @ SV94 @ SV189 @ SV263 @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(909,plain,
! [SV264: $i,SV324: $i,SV190: $i,SV95: $i] :
( ( ( ~ ( colinear @ SV95 @ SV190 @ SV324 ) )
= $true )
| ( ( ( SV95 = SV190 )
| ( colinear @ SV95 @ SV264 @ SV324 ) )
= $true )
| ( ( colinear @ SV95 @ SV190 @ SV264 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(910,plain,
! [SV265: $i,SV325: $i,SV191: $i,SV96: $i] :
( ( ( ~ ( colinear @ SV96 @ SV191 @ SV325 ) )
= $true )
| ( ( ( SV96 = SV191 )
| ( colinear @ SV191 @ SV265 @ SV325 ) )
= $true )
| ( ( colinear @ SV96 @ SV191 @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(911,plain,
! [SV266: $i,SV192: $i,SV346: $i,SV326: $i,SV98: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV98 @ SV326 @ SV346 )
| ( equidistant @ SV192 @ SV266 @ SV326 @ SV346 ) )
= $true )
| ( ( equidistant @ SV2 @ SV98 @ SV192 @ SV266 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(912,plain,
! [SV298: $i,SV293: $i,SV270: $i,SV195: $i,SV102: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
= $false )
| ( ( ~ ( equidistant @ SV102 @ SV293 @ SV270 @ SV298 )
| ! [SY946: $i,SY947: $i] :
( ~ ( equidistant @ SV6 @ SY946 @ SV195 @ SY947 )
| ~ ( equidistant @ SV102 @ SY946 @ SV270 @ SY947 )
| ~ ( between @ SV6 @ SV102 @ SV293 )
| ~ ( between @ SV195 @ SV270 @ SV298 )
| ( SV6 = SV102 )
| ( equidistant @ SV293 @ SY946 @ SV298 @ SY947 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(913,plain,
! [SV8: $i,SV104: $i,SV196: $i,SV327: $i,SV299: $i] :
( ( ( ~ ( between @ SV299 @ SV327 @ SV196 ) )
= $true )
| ( ( between @ SV104 @ ( inner_pasch @ SV8 @ SV104 @ SV196 @ SV327 @ SV299 ) @ SV299 )
= $true )
| ( ( between @ SV8 @ SV104 @ SV196 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(914,plain,
! [SV105: $i,SV9: $i,SV197: $i,SV328: $i,SV300: $i] :
( ( ( ~ ( between @ SV300 @ SV328 @ SV197 ) )
= $true )
| ( ( between @ SV328 @ ( inner_pasch @ SV9 @ SV105 @ SV197 @ SV328 @ SV300 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV105 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(915,plain,
! [SV10: $i,SV198: $i,SV106: $i,SV301: $i] :
( ( ( equidistant @ SV301 @ SV106 @ SV301 @ SV198 )
= $false )
| ( ( ! [SY950: $i] :
( ~ ( equidistant @ SY950 @ SV106 @ SY950 @ SV198 )
| ( between @ SV10 @ SV301 @ SY950 )
| ( between @ SV301 @ SY950 @ SV10 )
| ( SV106 = SV198 )
| ( between @ SY950 @ SV10 @ SV301 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV106 @ SV10 @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[868]) ).
thf(916,plain,
! [SV199: $i,SV11: $i,SV329: $i,SV107: $i,SV302: $i] :
( ( ( ~ ( between @ SV302 @ SV107 @ SV329 ) )
= $true )
| ( ( ( SV11 = SV107 )
| ( between @ SV11 @ SV302 @ ( euclid1 @ SV11 @ SV302 @ SV107 @ SV329 @ SV199 ) ) )
= $true )
| ( ( between @ SV11 @ SV107 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[869]) ).
thf(917,plain,
! [SV200: $i,SV12: $i,SV330: $i,SV108: $i,SV303: $i] :
( ( ( ~ ( between @ SV303 @ SV108 @ SV330 ) )
= $true )
| ( ( ( SV12 = SV108 )
| ( between @ SV12 @ SV330 @ ( euclid2 @ SV12 @ SV303 @ SV108 @ SV330 @ SV200 ) ) )
= $true )
| ( ( between @ SV12 @ SV108 @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[870]) ).
thf(918,plain,
! [SV201: $i,SV13: $i,SV331: $i,SV109: $i,SV304: $i] :
( ( ( ~ ( between @ SV304 @ SV109 @ SV331 ) )
= $true )
| ( ( ( SV13 = SV109 )
| ( between @ ( euclid1 @ SV13 @ SV304 @ SV109 @ SV331 @ SV201 ) @ SV201 @ ( euclid2 @ SV13 @ SV304 @ SV109 @ SV331 @ SV201 ) ) )
= $true )
| ( ( between @ SV13 @ SV109 @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[871]) ).
thf(919,plain,
! [SV202: $i,SV110: $i,SV332: $i,SV271: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV271 @ SV14 @ SV332 ) )
= $true )
| ( ( ~ ( between @ SV14 @ SV110 @ SV271 )
| ! [SY962: $i] :
( ~ ( between @ SV110 @ SY962 @ SV271 )
| ( between @ SV202 @ ( continuous @ SV14 @ SV110 @ SV202 @ SY962 @ SV271 @ SV332 ) @ SV332 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV110 @ SV14 @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(920,plain,
! [SV203: $i,SV111: $i,SV333: $i,SV272: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV272 @ SV15 @ SV333 ) )
= $true )
| ( ( ~ ( between @ SV15 @ SV111 @ SV272 )
| ! [SY963: $i] :
( ~ ( between @ SV111 @ SY963 @ SV272 )
| ( equidistant @ SV15 @ SY963 @ SV15 @ ( continuous @ SV15 @ SV111 @ SV203 @ SY963 @ SV272 @ SV333 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV111 @ SV15 @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(921,plain,
! [SV126: $i,SV30: $i,SV347: $i,SV334: $i,SV281: $i,SV216: $i] :
( ( ( ~ ( equidistant @ SV216 @ SV281 @ SV334 @ SV347 )
| ( equidistant @ SV30 @ SV126 @ SV334 @ SV347 ) )
= $true )
| ( ( equidistant @ SV30 @ SV126 @ SV216 @ SV281 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(922,plain,
! [SV219: $i,SV39: $i,SV348: $i,SV282: $i,SV335: $i,SV134: $i] :
( ( ( ~ ( equidistant @ SV134 @ SV335 @ SV282 @ SV348 )
| ~ ( between @ SV39 @ SV134 @ SV335 )
| ~ ( between @ SV219 @ SV282 @ SV348 )
| ( equidistant @ SV39 @ SV335 @ SV219 @ SV348 ) )
= $true )
| ( ( equidistant @ SV39 @ SV134 @ SV219 @ SV282 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[877]) ).
thf(923,plain,
! [SV220: $i,SV306: $i,SV135: $i,SV40: $i] :
( ( ( between @ SV40 @ SV135 @ SV306 )
= $false )
| ( ( ~ ( equidistant @ SV135 @ SV220 @ SV135 @ SV306 )
| ( SV40 = SV135 )
| ( SV220 = SV306 ) )
= $true )
| ( ( between @ SV40 @ SV135 @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(924,plain,
! [SV283: $i,SV222: $i,SV137: $i,SV42: $i,SV349: $i,SV336: $i] :
( ( ( ( ( extension @ SV336 @ SV349 @ SV42 @ SV137 )
= ( extension @ SV336 @ SV349 @ SV222 @ SV283 ) )
| ( SV336 = SV349 ) )
= $true )
| ( ( equidistant @ SV42 @ SV137 @ SV222 @ SV283 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[879]) ).
thf(925,plain,
! [SV47: $i,SV223: $i,SV142: $i,SV350: $i] :
( ( ( between @ SV350 @ SV142 @ SV223 )
= $true )
| ( ( SV47 = SV223 )
= $false )
| ( ( between @ SV47 @ SV142 @ SV223 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(926,plain,
! [SV227: $i,SV147: $i,SV52: $i] :
( ( ( SV52 = SV147 )
= $true )
| ( ( SV147 = SV227 )
= $true )
| ( ( between @ SV147 @ SV52 @ SV227 )
= $false )
| ( ( between @ SV52 @ SV147 @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[883]) ).
thf(927,plain,
! [SV228: $i,SV148: $i,SV53: $i] :
( ( ( SV53 = SV148 )
= $true )
| ( ( SV148 = SV228 )
= $true )
| ( ( between @ SV53 @ SV228 @ SV148 )
= $false )
| ( ( between @ SV53 @ SV148 @ SV228 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[884]) ).
thf(928,plain,
! [SV54: $i,SV337: $i,SV229: $i,SV149: $i] :
( ( ( between @ SV149 @ SV229 @ SV337 )
= $false )
| ( ( between @ SV54 @ SV149 @ SV229 )
= $true )
| ( ( between @ SV54 @ SV149 @ SV229 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(929,plain,
! [SV150: $i,SV307: $i,SV230: $i,SV55: $i] :
( ( ( between @ SV55 @ SV230 @ SV307 )
= $false )
| ( ( between @ SV150 @ SV230 @ SV307 )
= $true )
| ( ( between @ SV55 @ SV150 @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(930,plain,
! [SV56: $i,SV308: $i,SV231: $i,SV151: $i] :
( ( ( between @ SV151 @ SV231 @ SV308 )
= $false )
| ( ( ( SV151 = SV231 )
| ( between @ SV56 @ SV231 @ SV308 ) )
= $true )
| ( ( between @ SV56 @ SV151 @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[887]) ).
thf(931,plain,
! [SV57: $i,SV309: $i,SV232: $i,SV152: $i] :
( ( ( between @ SV152 @ SV232 @ SV309 )
= $false )
| ( ( ( SV152 = SV232 )
| ( between @ SV57 @ SV152 @ SV309 ) )
= $true )
| ( ( between @ SV57 @ SV152 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(932,plain,
! [SV58: $i,SV233: $i,SV310: $i,SV153: $i] :
( ( ( between @ SV153 @ SV310 @ SV233 )
= $false )
| ( ( between @ SV58 @ SV310 @ SV233 )
= $true )
| ( ( between @ SV58 @ SV153 @ SV233 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[889]) ).
thf(933,plain,
! [SV154: $i,SV311: $i,SV234: $i,SV59: $i] :
( ( ( between @ SV59 @ SV234 @ SV311 )
= $false )
| ( ( between @ SV59 @ SV154 @ SV311 )
= $true )
| ( ( between @ SV59 @ SV154 @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(934,plain,
! [SV158: $i,SV63: $i,SV236: $i,SV338: $i,SV285: $i] :
( ( ( ~ ( between @ SV285 @ SV338 @ SV236 ) )
= $true )
| ( ( ! [SY967: $i] :
( ~ ( between @ SV63 @ SY967 @ SV285 )
| ( between @ SY967 @ ( inner_pasch @ SV338 @ ( inner_pasch @ SV63 @ SY967 @ SV285 @ SV338 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV236 )
| ( between @ SV158 @ ( inner_pasch @ SV338 @ ( inner_pasch @ SV63 @ SY967 @ SV285 @ SV338 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV338 ) ) )
= $true )
| ( ( between @ SV63 @ SV158 @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(935,plain,
! [SV159: $i,SV312: $i,SV237: $i,SV64: $i] :
( ( ( equidistant @ SV64 @ SV237 @ SV64 @ SV312 )
= $false )
| ( ( ~ ( equidistant @ SV159 @ SV237 @ SV159 @ SV312 )
| ( SV64 = SV159 )
| ( SV237 = SV312 ) )
= $true )
| ( ( between @ SV64 @ SV159 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(936,plain,
! [SV313: $i,SV295: $i,SV286: $i,SV238: $i,SV160: $i,SV65: $i] :
( ( ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 )
= $false )
| ( ( ~ ( equidistant @ SV65 @ SV295 @ SV238 @ SV313 )
| ! [SY954: $i,SY955: $i] :
( ~ ( equidistant @ SV65 @ SY954 @ SV238 @ SY955 )
| ~ ( equidistant @ SV295 @ SY954 @ SV313 @ SY955 )
| ~ ( between @ SV65 @ SV160 @ SV295 )
| ~ ( between @ SV238 @ SV286 @ SV313 )
| ( equidistant @ SV160 @ SY954 @ SV286 @ SY955 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(937,plain,
! [SV239: $i,SV161: $i,SV66: $i,SV351: $i,SV339: $i,SV287: $i] :
( ( ( ~ ( between @ SV287 @ SV339 @ SV351 )
| ~ ( equidistant @ SV66 @ SV161 @ SV287 @ SV339 )
| ~ ( equidistant @ SV66 @ SV239 @ SV287 @ SV351 )
| ( equidistant @ SV161 @ SV239 @ SV339 @ SV351 ) )
= $true )
| ( ( between @ SV66 @ SV161 @ SV239 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(938,plain,
! [SV314: $i,SV296: $i,SV288: $i,SV240: $i,SV162: $i,SV67: $i] :
( ( ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 )
= $false )
| ( ( ~ ( equidistant @ SV162 @ SV296 @ SV288 @ SV314 )
| ! [SY956: $i,SY957: $i] :
( ~ ( equidistant @ SV67 @ SY956 @ SV240 @ SY957 )
| ~ ( equidistant @ SV296 @ SY956 @ SV314 @ SY957 )
| ~ ( between @ SV67 @ SV162 @ SV296 )
| ~ ( between @ SV240 @ SV288 @ SV314 )
| ( equidistant @ SV162 @ SY956 @ SV288 @ SY957 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(939,plain,
! [SV241: $i,SV315: $i,SV163: $i,SV68: $i] :
( ( ( equidistant @ SV68 @ SV163 @ SV68 @ SV315 )
= $false )
| ( ( ~ ( equidistant @ SV241 @ SV163 @ SV241 @ SV315 )
| ( SV163 = SV315 ) )
= $true )
| ( ( between @ SV68 @ SV163 @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(940,plain,
! [SV165: $i,SV340: $i,SV316: $i,SV243: $i,SV70: $i] :
( ( ( ~ ( equidistant @ SV70 @ SV243 @ SV316 @ SV340 ) )
= $true )
| ( ( between @ SV316 @ ( insertion @ SV316 @ SV340 @ SV70 @ SV165 ) @ SV340 )
= $true )
| ( ( between @ SV70 @ SV165 @ SV243 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[897]) ).
thf(941,plain,
! [SV166: $i,SV341: $i,SV317: $i,SV244: $i,SV71: $i] :
( ( ( ~ ( equidistant @ SV71 @ SV244 @ SV317 @ SV341 ) )
= $true )
| ( ( equidistant @ SV166 @ SV244 @ ( insertion @ SV317 @ SV341 @ SV71 @ SV166 ) @ SV341 )
= $true )
| ( ( between @ SV71 @ SV166 @ SV244 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[898]) ).
thf(942,plain,
! [SV290: $i,SV246: $i,SV168: $i,SV73: $i,SV352: $i,SV342: $i] :
( ( ( ( insertion @ SV342 @ SV352 @ SV73 @ SV168 )
= ( insertion @ SV342 @ SV352 @ SV246 @ SV290 ) )
= $true )
| ( ( equidistant @ SV73 @ SV168 @ SV246 @ SV290 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(943,plain,
! [SV247: $i,SV74: $i,SV353: $i,SV291: $i,SV343: $i,SV169: $i] :
( ( ( ~ ( equidistant @ SV169 @ SV343 @ SV291 @ SV353 )
| ~ ( equidistant @ SV74 @ SV343 @ SV247 @ SV353 )
| ~ ( between @ SV74 @ SV169 @ SV343 )
| ( between @ SV247 @ SV291 @ SV353 ) )
= $true )
| ( ( equidistant @ SV74 @ SV169 @ SV247 @ SV291 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[900]) ).
thf(944,plain,
! [SV248: $i,SV318: $i,SV170: $i,SV75: $i] :
( ( ( between @ SV75 @ SV170 @ SV318 )
= $false )
| ( ( ( SV75 = SV170 )
| ( between @ SV75 @ SV248 @ SV318 )
| ( between @ SV75 @ SV318 @ SV248 ) )
= $true )
| ( ( between @ SV75 @ SV170 @ SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[901]) ).
thf(945,plain,
! [SV249: $i,SV319: $i,SV171: $i,SV76: $i] :
( ( ( between @ SV76 @ SV171 @ SV319 )
= $false )
| ( ( ( SV76 = SV171 )
| ( between @ SV171 @ SV249 @ SV319 )
| ( between @ SV171 @ SV319 @ SV249 ) )
= $true )
| ( ( between @ SV76 @ SV171 @ SV249 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[902]) ).
thf(946,plain,
! [SV77: $i,SV250: $i,SV172: $i,SV320: $i] :
( ( ( between @ SV320 @ SV172 @ SV250 )
= $false )
| ( ( ( SV172 = SV250 )
| ( between @ SV77 @ SV320 @ SV172 )
| ( between @ SV320 @ SV77 @ SV172 ) )
= $true )
| ( ( between @ SV77 @ SV172 @ SV250 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[903]) ).
thf(947,plain,
! [SV173: $i,SV251: $i,SV321: $i,SV78: $i] :
( ( ( between @ SV78 @ SV321 @ SV251 )
= $false )
| ( ( ( between @ SV78 @ SV173 @ SV321 )
| ( between @ SV78 @ SV321 @ SV173 ) )
= $true )
| ( ( between @ SV78 @ SV173 @ SV251 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[904]) ).
thf(948,plain,
! [SV174: $i,SV252: $i,SV322: $i,SV79: $i] :
( ( ( between @ SV79 @ SV322 @ SV252 )
= $false )
| ( ( ( between @ SV174 @ SV322 @ SV252 )
| ( between @ SV322 @ SV174 @ SV252 ) )
= $true )
| ( ( between @ SV79 @ SV174 @ SV252 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[905]) ).
thf(949,plain,
! [SV253: $i,SV80: $i,SV344: $i,SV323: $i,SV175: $i] :
( ( ( ~ ( between @ SV175 @ SV323 @ SV344 ) )
= $true )
| ( ( ~ ( between @ SV80 @ SV344 @ SV253 )
| ( between @ SV80 @ SV323 @ SV253 ) )
= $true )
| ( ( between @ SV80 @ SV175 @ SV253 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(950,plain,
! [SV263: $i,SV94: $i,SV354: $i,SV292: $i,SV345: $i,SV189: $i] :
( ( ( ~ ( equidistant @ SV189 @ SV345 @ SV292 @ SV354 )
| ~ ( equidistant @ SV94 @ SV345 @ SV263 @ SV354 )
| ~ ( colinear @ SV94 @ SV189 @ SV345 )
| ( colinear @ SV263 @ SV292 @ SV354 ) )
= $true )
| ( ( equidistant @ SV94 @ SV189 @ SV263 @ SV292 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(951,plain,
! [SV264: $i,SV324: $i,SV190: $i,SV95: $i] :
( ( ( colinear @ SV95 @ SV190 @ SV324 )
= $false )
| ( ( ( SV95 = SV190 )
| ( colinear @ SV95 @ SV264 @ SV324 ) )
= $true )
| ( ( colinear @ SV95 @ SV190 @ SV264 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(952,plain,
! [SV265: $i,SV325: $i,SV191: $i,SV96: $i] :
( ( ( colinear @ SV96 @ SV191 @ SV325 )
= $false )
| ( ( ( SV96 = SV191 )
| ( colinear @ SV191 @ SV265 @ SV325 ) )
= $true )
| ( ( colinear @ SV96 @ SV191 @ SV265 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(953,plain,
! [SV266: $i,SV192: $i,SV346: $i,SV326: $i,SV98: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV98 @ SV326 @ SV346 ) )
= $true )
| ( ( equidistant @ SV192 @ SV266 @ SV326 @ SV346 )
= $true )
| ( ( equidistant @ SV2 @ SV98 @ SV192 @ SV266 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[911]) ).
thf(954,plain,
! [SV195: $i,SV6: $i,SV298: $i,SV270: $i,SV293: $i,SV102: $i] :
( ( ( ~ ( equidistant @ SV102 @ SV293 @ SV270 @ SV298 ) )
= $true )
| ( ( ! [SY946: $i,SY947: $i] :
( ~ ( equidistant @ SV6 @ SY946 @ SV195 @ SY947 )
| ~ ( equidistant @ SV102 @ SY946 @ SV270 @ SY947 )
| ~ ( between @ SV6 @ SV102 @ SV293 )
| ~ ( between @ SV195 @ SV270 @ SV298 )
| ( SV6 = SV102 )
| ( equidistant @ SV293 @ SY946 @ SV298 @ SY947 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(955,plain,
! [SV8: $i,SV104: $i,SV196: $i,SV327: $i,SV299: $i] :
( ( ( between @ SV299 @ SV327 @ SV196 )
= $false )
| ( ( between @ SV104 @ ( inner_pasch @ SV8 @ SV104 @ SV196 @ SV327 @ SV299 ) @ SV299 )
= $true )
| ( ( between @ SV8 @ SV104 @ SV196 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(956,plain,
! [SV105: $i,SV9: $i,SV197: $i,SV328: $i,SV300: $i] :
( ( ( between @ SV300 @ SV328 @ SV197 )
= $false )
| ( ( between @ SV328 @ ( inner_pasch @ SV9 @ SV105 @ SV197 @ SV328 @ SV300 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV105 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[914]) ).
thf(957,plain,
! [SV301: $i,SV10: $i,SV198: $i,SV106: $i,SV355: $i] :
( ( ( ~ ( equidistant @ SV355 @ SV106 @ SV355 @ SV198 )
| ( between @ SV10 @ SV301 @ SV355 )
| ( between @ SV301 @ SV355 @ SV10 )
| ( SV106 = SV198 )
| ( between @ SV355 @ SV10 @ SV301 ) )
= $true )
| ( ( equidistant @ SV301 @ SV106 @ SV301 @ SV198 )
= $false )
| ( ( equidistant @ SV10 @ SV106 @ SV10 @ SV198 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[915]) ).
thf(958,plain,
! [SV199: $i,SV11: $i,SV329: $i,SV107: $i,SV302: $i] :
( ( ( between @ SV302 @ SV107 @ SV329 )
= $false )
| ( ( ( SV11 = SV107 )
| ( between @ SV11 @ SV302 @ ( euclid1 @ SV11 @ SV302 @ SV107 @ SV329 @ SV199 ) ) )
= $true )
| ( ( between @ SV11 @ SV107 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[916]) ).
thf(959,plain,
! [SV200: $i,SV12: $i,SV330: $i,SV108: $i,SV303: $i] :
( ( ( between @ SV303 @ SV108 @ SV330 )
= $false )
| ( ( ( SV12 = SV108 )
| ( between @ SV12 @ SV330 @ ( euclid2 @ SV12 @ SV303 @ SV108 @ SV330 @ SV200 ) ) )
= $true )
| ( ( between @ SV12 @ SV108 @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[917]) ).
thf(960,plain,
! [SV201: $i,SV13: $i,SV331: $i,SV109: $i,SV304: $i] :
( ( ( between @ SV304 @ SV109 @ SV331 )
= $false )
| ( ( ( SV13 = SV109 )
| ( between @ ( euclid1 @ SV13 @ SV304 @ SV109 @ SV331 @ SV201 ) @ SV201 @ ( euclid2 @ SV13 @ SV304 @ SV109 @ SV331 @ SV201 ) ) )
= $true )
| ( ( between @ SV13 @ SV109 @ SV201 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(961,plain,
! [SV202: $i,SV110: $i,SV332: $i,SV271: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV271 @ SV14 @ SV332 )
= $false )
| ( ( ~ ( between @ SV14 @ SV110 @ SV271 )
| ! [SY962: $i] :
( ~ ( between @ SV110 @ SY962 @ SV271 )
| ( between @ SV202 @ ( continuous @ SV14 @ SV110 @ SV202 @ SY962 @ SV271 @ SV332 ) @ SV332 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV110 @ SV14 @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[919]) ).
thf(962,plain,
! [SV203: $i,SV111: $i,SV333: $i,SV272: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV272 @ SV15 @ SV333 )
= $false )
| ( ( ~ ( between @ SV15 @ SV111 @ SV272 )
| ! [SY963: $i] :
( ~ ( between @ SV111 @ SY963 @ SV272 )
| ( equidistant @ SV15 @ SY963 @ SV15 @ ( continuous @ SV15 @ SV111 @ SV203 @ SY963 @ SV272 @ SV333 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV111 @ SV15 @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[920]) ).
thf(963,plain,
! [SV126: $i,SV30: $i,SV347: $i,SV334: $i,SV281: $i,SV216: $i] :
( ( ( ~ ( equidistant @ SV216 @ SV281 @ SV334 @ SV347 ) )
= $true )
| ( ( equidistant @ SV30 @ SV126 @ SV334 @ SV347 )
= $true )
| ( ( equidistant @ SV30 @ SV126 @ SV216 @ SV281 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[921]) ).
thf(964,plain,
! [SV219: $i,SV39: $i,SV348: $i,SV282: $i,SV335: $i,SV134: $i] :
( ( ( ~ ( equidistant @ SV134 @ SV335 @ SV282 @ SV348 ) )
= $true )
| ( ( ~ ( between @ SV39 @ SV134 @ SV335 )
| ~ ( between @ SV219 @ SV282 @ SV348 )
| ( equidistant @ SV39 @ SV335 @ SV219 @ SV348 ) )
= $true )
| ( ( equidistant @ SV39 @ SV134 @ SV219 @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[922]) ).
thf(965,plain,
! [SV40: $i,SV306: $i,SV220: $i,SV135: $i] :
( ( ( ~ ( equidistant @ SV135 @ SV220 @ SV135 @ SV306 ) )
= $true )
| ( ( ( SV40 = SV135 )
| ( SV220 = SV306 ) )
= $true )
| ( ( between @ SV40 @ SV135 @ SV306 )
= $false )
| ( ( between @ SV40 @ SV135 @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[923]) ).
thf(966,plain,
! [SV283: $i,SV222: $i,SV137: $i,SV42: $i,SV349: $i,SV336: $i] :
( ( ( ( extension @ SV336 @ SV349 @ SV42 @ SV137 )
= ( extension @ SV336 @ SV349 @ SV222 @ SV283 ) )
= $true )
| ( ( SV336 = SV349 )
= $true )
| ( ( equidistant @ SV42 @ SV137 @ SV222 @ SV283 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(967,plain,
! [SV308: $i,SV56: $i,SV231: $i,SV151: $i] :
( ( ( SV151 = SV231 )
= $true )
| ( ( between @ SV56 @ SV231 @ SV308 )
= $true )
| ( ( between @ SV151 @ SV231 @ SV308 )
= $false )
| ( ( between @ SV56 @ SV151 @ SV231 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[930]) ).
thf(968,plain,
! [SV309: $i,SV57: $i,SV232: $i,SV152: $i] :
( ( ( SV152 = SV232 )
= $true )
| ( ( between @ SV57 @ SV152 @ SV309 )
= $true )
| ( ( between @ SV152 @ SV232 @ SV309 )
= $false )
| ( ( between @ SV57 @ SV152 @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[931]) ).
thf(969,plain,
! [SV158: $i,SV63: $i,SV236: $i,SV338: $i,SV285: $i] :
( ( ( between @ SV285 @ SV338 @ SV236 )
= $false )
| ( ( ! [SY967: $i] :
( ~ ( between @ SV63 @ SY967 @ SV285 )
| ( between @ SY967 @ ( inner_pasch @ SV338 @ ( inner_pasch @ SV63 @ SY967 @ SV285 @ SV338 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV236 )
| ( between @ SV158 @ ( inner_pasch @ SV338 @ ( inner_pasch @ SV63 @ SY967 @ SV285 @ SV338 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV338 ) ) )
= $true )
| ( ( between @ SV63 @ SV158 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[934]) ).
thf(970,plain,
! [SV64: $i,SV312: $i,SV237: $i,SV159: $i] :
( ( ( ~ ( equidistant @ SV159 @ SV237 @ SV159 @ SV312 ) )
= $true )
| ( ( ( SV64 = SV159 )
| ( SV237 = SV312 ) )
= $true )
| ( ( equidistant @ SV64 @ SV237 @ SV64 @ SV312 )
= $false )
| ( ( between @ SV64 @ SV159 @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[935]) ).
thf(971,plain,
! [SV286: $i,SV160: $i,SV313: $i,SV238: $i,SV295: $i,SV65: $i] :
( ( ( ~ ( equidistant @ SV65 @ SV295 @ SV238 @ SV313 ) )
= $true )
| ( ( ! [SY954: $i,SY955: $i] :
( ~ ( equidistant @ SV65 @ SY954 @ SV238 @ SY955 )
| ~ ( equidistant @ SV295 @ SY954 @ SV313 @ SY955 )
| ~ ( between @ SV65 @ SV160 @ SV295 )
| ~ ( between @ SV238 @ SV286 @ SV313 )
| ( equidistant @ SV160 @ SY954 @ SV286 @ SY955 ) ) )
= $true )
| ( ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[936]) ).
thf(972,plain,
! [SV239: $i,SV161: $i,SV66: $i,SV351: $i,SV339: $i,SV287: $i] :
( ( ( ~ ( between @ SV287 @ SV339 @ SV351 ) )
= $true )
| ( ( ~ ( equidistant @ SV66 @ SV161 @ SV287 @ SV339 )
| ~ ( equidistant @ SV66 @ SV239 @ SV287 @ SV351 )
| ( equidistant @ SV161 @ SV239 @ SV339 @ SV351 ) )
= $true )
| ( ( between @ SV66 @ SV161 @ SV239 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[937]) ).
thf(973,plain,
! [SV240: $i,SV67: $i,SV314: $i,SV288: $i,SV296: $i,SV162: $i] :
( ( ( ~ ( equidistant @ SV162 @ SV296 @ SV288 @ SV314 ) )
= $true )
| ( ( ! [SY956: $i,SY957: $i] :
( ~ ( equidistant @ SV67 @ SY956 @ SV240 @ SY957 )
| ~ ( equidistant @ SV296 @ SY956 @ SV314 @ SY957 )
| ~ ( between @ SV67 @ SV162 @ SV296 )
| ~ ( between @ SV240 @ SV288 @ SV314 )
| ( equidistant @ SV162 @ SY956 @ SV288 @ SY957 ) ) )
= $true )
| ( ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(974,plain,
! [SV68: $i,SV315: $i,SV163: $i,SV241: $i] :
( ( ( ~ ( equidistant @ SV241 @ SV163 @ SV241 @ SV315 ) )
= $true )
| ( ( SV163 = SV315 )
= $true )
| ( ( equidistant @ SV68 @ SV163 @ SV68 @ SV315 )
= $false )
| ( ( between @ SV68 @ SV163 @ SV241 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(975,plain,
! [SV165: $i,SV340: $i,SV316: $i,SV243: $i,SV70: $i] :
( ( ( equidistant @ SV70 @ SV243 @ SV316 @ SV340 )
= $false )
| ( ( between @ SV316 @ ( insertion @ SV316 @ SV340 @ SV70 @ SV165 ) @ SV340 )
= $true )
| ( ( between @ SV70 @ SV165 @ SV243 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(976,plain,
! [SV166: $i,SV341: $i,SV317: $i,SV244: $i,SV71: $i] :
( ( ( equidistant @ SV71 @ SV244 @ SV317 @ SV341 )
= $false )
| ( ( equidistant @ SV166 @ SV244 @ ( insertion @ SV317 @ SV341 @ SV71 @ SV166 ) @ SV341 )
= $true )
| ( ( between @ SV71 @ SV166 @ SV244 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[941]) ).
thf(977,plain,
! [SV247: $i,SV74: $i,SV353: $i,SV291: $i,SV343: $i,SV169: $i] :
( ( ( ~ ( equidistant @ SV169 @ SV343 @ SV291 @ SV353 ) )
= $true )
| ( ( ~ ( equidistant @ SV74 @ SV343 @ SV247 @ SV353 )
| ~ ( between @ SV74 @ SV169 @ SV343 )
| ( between @ SV247 @ SV291 @ SV353 ) )
= $true )
| ( ( equidistant @ SV74 @ SV169 @ SV247 @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[943]) ).
thf(978,plain,
! [SV318: $i,SV248: $i,SV170: $i,SV75: $i] :
( ( ( SV75 = SV170 )
= $true )
| ( ( ( between @ SV75 @ SV248 @ SV318 )
| ( between @ SV75 @ SV318 @ SV248 ) )
= $true )
| ( ( between @ SV75 @ SV170 @ SV318 )
= $false )
| ( ( between @ SV75 @ SV170 @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(979,plain,
! [SV319: $i,SV249: $i,SV171: $i,SV76: $i] :
( ( ( SV76 = SV171 )
= $true )
| ( ( ( between @ SV171 @ SV249 @ SV319 )
| ( between @ SV171 @ SV319 @ SV249 ) )
= $true )
| ( ( between @ SV76 @ SV171 @ SV319 )
= $false )
| ( ( between @ SV76 @ SV171 @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[945]) ).
thf(980,plain,
! [SV320: $i,SV77: $i,SV250: $i,SV172: $i] :
( ( ( SV172 = SV250 )
= $true )
| ( ( ( between @ SV77 @ SV320 @ SV172 )
| ( between @ SV320 @ SV77 @ SV172 ) )
= $true )
| ( ( between @ SV320 @ SV172 @ SV250 )
= $false )
| ( ( between @ SV77 @ SV172 @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[946]) ).
thf(981,plain,
! [SV251: $i,SV321: $i,SV173: $i,SV78: $i] :
( ( ( between @ SV78 @ SV173 @ SV321 )
= $true )
| ( ( between @ SV78 @ SV321 @ SV173 )
= $true )
| ( ( between @ SV78 @ SV321 @ SV251 )
= $false )
| ( ( between @ SV78 @ SV173 @ SV251 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(982,plain,
! [SV79: $i,SV252: $i,SV322: $i,SV174: $i] :
( ( ( between @ SV174 @ SV322 @ SV252 )
= $true )
| ( ( between @ SV322 @ SV174 @ SV252 )
= $true )
| ( ( between @ SV79 @ SV322 @ SV252 )
= $false )
| ( ( between @ SV79 @ SV174 @ SV252 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(983,plain,
! [SV253: $i,SV80: $i,SV344: $i,SV323: $i,SV175: $i] :
( ( ( between @ SV175 @ SV323 @ SV344 )
= $false )
| ( ( ~ ( between @ SV80 @ SV344 @ SV253 )
| ( between @ SV80 @ SV323 @ SV253 ) )
= $true )
| ( ( between @ SV80 @ SV175 @ SV253 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[949]) ).
thf(984,plain,
! [SV263: $i,SV94: $i,SV354: $i,SV292: $i,SV345: $i,SV189: $i] :
( ( ( ~ ( equidistant @ SV189 @ SV345 @ SV292 @ SV354 ) )
= $true )
| ( ( ~ ( equidistant @ SV94 @ SV345 @ SV263 @ SV354 )
| ~ ( colinear @ SV94 @ SV189 @ SV345 )
| ( colinear @ SV263 @ SV292 @ SV354 ) )
= $true )
| ( ( equidistant @ SV94 @ SV189 @ SV263 @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(985,plain,
! [SV324: $i,SV264: $i,SV190: $i,SV95: $i] :
( ( ( SV95 = SV190 )
= $true )
| ( ( colinear @ SV95 @ SV264 @ SV324 )
= $true )
| ( ( colinear @ SV95 @ SV190 @ SV324 )
= $false )
| ( ( colinear @ SV95 @ SV190 @ SV264 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[951]) ).
thf(986,plain,
! [SV325: $i,SV265: $i,SV191: $i,SV96: $i] :
( ( ( SV96 = SV191 )
= $true )
| ( ( colinear @ SV191 @ SV265 @ SV325 )
= $true )
| ( ( colinear @ SV96 @ SV191 @ SV325 )
= $false )
| ( ( colinear @ SV96 @ SV191 @ SV265 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[952]) ).
thf(987,plain,
! [SV266: $i,SV192: $i,SV346: $i,SV326: $i,SV98: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV98 @ SV326 @ SV346 )
= $false )
| ( ( equidistant @ SV192 @ SV266 @ SV326 @ SV346 )
= $true )
| ( ( equidistant @ SV2 @ SV98 @ SV192 @ SV266 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[953]) ).
thf(988,plain,
! [SV195: $i,SV6: $i,SV298: $i,SV270: $i,SV293: $i,SV102: $i] :
( ( ( equidistant @ SV102 @ SV293 @ SV270 @ SV298 )
= $false )
| ( ( ! [SY946: $i,SY947: $i] :
( ~ ( equidistant @ SV6 @ SY946 @ SV195 @ SY947 )
| ~ ( equidistant @ SV102 @ SY946 @ SV270 @ SY947 )
| ~ ( between @ SV6 @ SV102 @ SV293 )
| ~ ( between @ SV195 @ SV270 @ SV298 )
| ( SV6 = SV102 )
| ( equidistant @ SV293 @ SY946 @ SV298 @ SY947 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(989,plain,
! [SV301: $i,SV10: $i,SV198: $i,SV106: $i,SV355: $i] :
( ( ( ~ ( equidistant @ SV355 @ SV106 @ SV355 @ SV198 ) )
= $true )
| ( ( ( between @ SV10 @ SV301 @ SV355 )
| ( between @ SV301 @ SV355 @ SV10 )
| ( SV106 = SV198 )
| ( between @ SV355 @ SV10 @ SV301 ) )
= $true )
| ( ( equidistant @ SV301 @ SV106 @ SV301 @ SV198 )
= $false )
| ( ( equidistant @ SV10 @ SV106 @ SV10 @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[957]) ).
thf(990,plain,
! [SV199: $i,SV329: $i,SV302: $i,SV107: $i,SV11: $i] :
( ( ( SV11 = SV107 )
= $true )
| ( ( between @ SV11 @ SV302 @ ( euclid1 @ SV11 @ SV302 @ SV107 @ SV329 @ SV199 ) )
= $true )
| ( ( between @ SV302 @ SV107 @ SV329 )
= $false )
| ( ( between @ SV11 @ SV107 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(991,plain,
! [SV200: $i,SV303: $i,SV330: $i,SV108: $i,SV12: $i] :
( ( ( SV12 = SV108 )
= $true )
| ( ( between @ SV12 @ SV330 @ ( euclid2 @ SV12 @ SV303 @ SV108 @ SV330 @ SV200 ) )
= $true )
| ( ( between @ SV303 @ SV108 @ SV330 )
= $false )
| ( ( between @ SV12 @ SV108 @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[959]) ).
thf(992,plain,
! [SV201: $i,SV331: $i,SV304: $i,SV109: $i,SV13: $i] :
( ( ( SV13 = SV109 )
= $true )
| ( ( between @ ( euclid1 @ SV13 @ SV304 @ SV109 @ SV331 @ SV201 ) @ SV201 @ ( euclid2 @ SV13 @ SV304 @ SV109 @ SV331 @ SV201 ) )
= $true )
| ( ( between @ SV304 @ SV109 @ SV331 )
= $false )
| ( ( between @ SV13 @ SV109 @ SV201 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(993,plain,
! [SV332: $i,SV202: $i,SV271: $i,SV110: $i,SV14: $i] :
( ( ( ~ ( between @ SV14 @ SV110 @ SV271 ) )
= $true )
| ( ( ! [SY962: $i] :
( ~ ( between @ SV110 @ SY962 @ SV271 )
| ( between @ SV202 @ ( continuous @ SV14 @ SV110 @ SV202 @ SY962 @ SV271 @ SV332 ) @ SV332 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV271 @ SV14 @ SV332 )
= $false )
| ( ( equidistant @ SV14 @ SV110 @ SV14 @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[961]) ).
thf(994,plain,
! [SV333: $i,SV203: $i,SV272: $i,SV111: $i,SV15: $i] :
( ( ( ~ ( between @ SV15 @ SV111 @ SV272 ) )
= $true )
| ( ( ! [SY963: $i] :
( ~ ( between @ SV111 @ SY963 @ SV272 )
| ( equidistant @ SV15 @ SY963 @ SV15 @ ( continuous @ SV15 @ SV111 @ SV203 @ SY963 @ SV272 @ SV333 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV272 @ SV15 @ SV333 )
= $false )
| ( ( equidistant @ SV15 @ SV111 @ SV15 @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[962]) ).
thf(995,plain,
! [SV126: $i,SV30: $i,SV347: $i,SV334: $i,SV281: $i,SV216: $i] :
( ( ( equidistant @ SV216 @ SV281 @ SV334 @ SV347 )
= $false )
| ( ( equidistant @ SV30 @ SV126 @ SV334 @ SV347 )
= $true )
| ( ( equidistant @ SV30 @ SV126 @ SV216 @ SV281 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(996,plain,
! [SV219: $i,SV39: $i,SV348: $i,SV282: $i,SV335: $i,SV134: $i] :
( ( ( equidistant @ SV134 @ SV335 @ SV282 @ SV348 )
= $false )
| ( ( ~ ( between @ SV39 @ SV134 @ SV335 )
| ~ ( between @ SV219 @ SV282 @ SV348 )
| ( equidistant @ SV39 @ SV335 @ SV219 @ SV348 ) )
= $true )
| ( ( equidistant @ SV39 @ SV134 @ SV219 @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(997,plain,
! [SV40: $i,SV306: $i,SV220: $i,SV135: $i] :
( ( ( equidistant @ SV135 @ SV220 @ SV135 @ SV306 )
= $false )
| ( ( ( SV40 = SV135 )
| ( SV220 = SV306 ) )
= $true )
| ( ( between @ SV40 @ SV135 @ SV306 )
= $false )
| ( ( between @ SV40 @ SV135 @ SV220 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(998,plain,
! [SV158: $i,SV236: $i,SV338: $i,SV285: $i,SV356: $i,SV63: $i] :
( ( ( ~ ( between @ SV63 @ SV356 @ SV285 )
| ( between @ SV356 @ ( inner_pasch @ SV338 @ ( inner_pasch @ SV63 @ SV356 @ SV285 @ SV338 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV236 )
| ( between @ SV158 @ ( inner_pasch @ SV338 @ ( inner_pasch @ SV63 @ SV356 @ SV285 @ SV338 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV338 ) )
= $true )
| ( ( between @ SV285 @ SV338 @ SV236 )
= $false )
| ( ( between @ SV63 @ SV158 @ SV236 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[969]) ).
thf(999,plain,
! [SV64: $i,SV312: $i,SV237: $i,SV159: $i] :
( ( ( equidistant @ SV159 @ SV237 @ SV159 @ SV312 )
= $false )
| ( ( ( SV64 = SV159 )
| ( SV237 = SV312 ) )
= $true )
| ( ( equidistant @ SV64 @ SV237 @ SV64 @ SV312 )
= $false )
| ( ( between @ SV64 @ SV159 @ SV237 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[970]) ).
thf(1000,plain,
! [SV286: $i,SV160: $i,SV313: $i,SV238: $i,SV295: $i,SV65: $i] :
( ( ( equidistant @ SV65 @ SV295 @ SV238 @ SV313 )
= $false )
| ( ( ! [SY954: $i,SY955: $i] :
( ~ ( equidistant @ SV65 @ SY954 @ SV238 @ SY955 )
| ~ ( equidistant @ SV295 @ SY954 @ SV313 @ SY955 )
| ~ ( between @ SV65 @ SV160 @ SV295 )
| ~ ( between @ SV238 @ SV286 @ SV313 )
| ( equidistant @ SV160 @ SY954 @ SV286 @ SY955 ) ) )
= $true )
| ( ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[971]) ).
thf(1001,plain,
! [SV239: $i,SV161: $i,SV66: $i,SV351: $i,SV339: $i,SV287: $i] :
( ( ( between @ SV287 @ SV339 @ SV351 )
= $false )
| ( ( ~ ( equidistant @ SV66 @ SV161 @ SV287 @ SV339 )
| ~ ( equidistant @ SV66 @ SV239 @ SV287 @ SV351 )
| ( equidistant @ SV161 @ SV239 @ SV339 @ SV351 ) )
= $true )
| ( ( between @ SV66 @ SV161 @ SV239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1002,plain,
! [SV240: $i,SV67: $i,SV314: $i,SV288: $i,SV296: $i,SV162: $i] :
( ( ( equidistant @ SV162 @ SV296 @ SV288 @ SV314 )
= $false )
| ( ( ! [SY956: $i,SY957: $i] :
( ~ ( equidistant @ SV67 @ SY956 @ SV240 @ SY957 )
| ~ ( equidistant @ SV296 @ SY956 @ SV314 @ SY957 )
| ~ ( between @ SV67 @ SV162 @ SV296 )
| ~ ( between @ SV240 @ SV288 @ SV314 )
| ( equidistant @ SV162 @ SY956 @ SV288 @ SY957 ) ) )
= $true )
| ( ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[973]) ).
thf(1003,plain,
! [SV68: $i,SV315: $i,SV163: $i,SV241: $i] :
( ( ( equidistant @ SV241 @ SV163 @ SV241 @ SV315 )
= $false )
| ( ( SV163 = SV315 )
= $true )
| ( ( equidistant @ SV68 @ SV163 @ SV68 @ SV315 )
= $false )
| ( ( between @ SV68 @ SV163 @ SV241 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1004,plain,
! [SV247: $i,SV74: $i,SV353: $i,SV291: $i,SV343: $i,SV169: $i] :
( ( ( equidistant @ SV169 @ SV343 @ SV291 @ SV353 )
= $false )
| ( ( ~ ( equidistant @ SV74 @ SV343 @ SV247 @ SV353 )
| ~ ( between @ SV74 @ SV169 @ SV343 )
| ( between @ SV247 @ SV291 @ SV353 ) )
= $true )
| ( ( equidistant @ SV74 @ SV169 @ SV247 @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1005,plain,
! [SV170: $i,SV318: $i,SV248: $i,SV75: $i] :
( ( ( between @ SV75 @ SV248 @ SV318 )
= $true )
| ( ( between @ SV75 @ SV318 @ SV248 )
= $true )
| ( ( SV75 = SV170 )
= $true )
| ( ( between @ SV75 @ SV170 @ SV318 )
= $false )
| ( ( between @ SV75 @ SV170 @ SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1006,plain,
! [SV76: $i,SV319: $i,SV249: $i,SV171: $i] :
( ( ( between @ SV171 @ SV249 @ SV319 )
= $true )
| ( ( between @ SV171 @ SV319 @ SV249 )
= $true )
| ( ( SV76 = SV171 )
= $true )
| ( ( between @ SV76 @ SV171 @ SV319 )
= $false )
| ( ( between @ SV76 @ SV171 @ SV249 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1007,plain,
! [SV250: $i,SV172: $i,SV320: $i,SV77: $i] :
( ( ( between @ SV77 @ SV320 @ SV172 )
= $true )
| ( ( between @ SV320 @ SV77 @ SV172 )
= $true )
| ( ( SV172 = SV250 )
= $true )
| ( ( between @ SV320 @ SV172 @ SV250 )
= $false )
| ( ( between @ SV77 @ SV172 @ SV250 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1008,plain,
! [SV175: $i,SV323: $i,SV253: $i,SV344: $i,SV80: $i] :
( ( ( ~ ( between @ SV80 @ SV344 @ SV253 ) )
= $true )
| ( ( between @ SV80 @ SV323 @ SV253 )
= $true )
| ( ( between @ SV175 @ SV323 @ SV344 )
= $false )
| ( ( between @ SV80 @ SV175 @ SV253 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[983]) ).
thf(1009,plain,
! [SV263: $i,SV94: $i,SV354: $i,SV292: $i,SV345: $i,SV189: $i] :
( ( ( equidistant @ SV189 @ SV345 @ SV292 @ SV354 )
= $false )
| ( ( ~ ( equidistant @ SV94 @ SV345 @ SV263 @ SV354 )
| ~ ( colinear @ SV94 @ SV189 @ SV345 )
| ( colinear @ SV263 @ SV292 @ SV354 ) )
= $true )
| ( ( equidistant @ SV94 @ SV189 @ SV263 @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1010,plain,
! [SV298: $i,SV293: $i,SV270: $i,SV102: $i,SV195: $i,SV357: $i,SV6: $i] :
( ( ( ! [SY972: $i] :
( ~ ( equidistant @ SV6 @ SV357 @ SV195 @ SY972 )
| ~ ( equidistant @ SV102 @ SV357 @ SV270 @ SY972 )
| ~ ( between @ SV6 @ SV102 @ SV293 )
| ~ ( between @ SV195 @ SV270 @ SV298 )
| ( SV6 = SV102 )
| ( equidistant @ SV293 @ SV357 @ SV298 @ SY972 ) ) )
= $true )
| ( ( equidistant @ SV102 @ SV293 @ SV270 @ SV298 )
= $false )
| ( ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[988]) ).
thf(1011,plain,
! [SV301: $i,SV10: $i,SV198: $i,SV106: $i,SV355: $i] :
( ( ( equidistant @ SV355 @ SV106 @ SV355 @ SV198 )
= $false )
| ( ( ( between @ SV10 @ SV301 @ SV355 )
| ( between @ SV301 @ SV355 @ SV10 )
| ( SV106 = SV198 )
| ( between @ SV355 @ SV10 @ SV301 ) )
= $true )
| ( ( equidistant @ SV301 @ SV106 @ SV301 @ SV198 )
= $false )
| ( ( equidistant @ SV10 @ SV106 @ SV10 @ SV198 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1012,plain,
! [SV332: $i,SV202: $i,SV271: $i,SV110: $i,SV14: $i] :
( ( ( between @ SV14 @ SV110 @ SV271 )
= $false )
| ( ( ! [SY962: $i] :
( ~ ( between @ SV110 @ SY962 @ SV271 )
| ( between @ SV202 @ ( continuous @ SV14 @ SV110 @ SV202 @ SY962 @ SV271 @ SV332 ) @ SV332 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV271 @ SV14 @ SV332 )
= $false )
| ( ( equidistant @ SV14 @ SV110 @ SV14 @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1013,plain,
! [SV333: $i,SV203: $i,SV272: $i,SV111: $i,SV15: $i] :
( ( ( between @ SV15 @ SV111 @ SV272 )
= $false )
| ( ( ! [SY963: $i] :
( ~ ( between @ SV111 @ SY963 @ SV272 )
| ( equidistant @ SV15 @ SY963 @ SV15 @ ( continuous @ SV15 @ SV111 @ SV203 @ SY963 @ SV272 @ SV333 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV272 @ SV15 @ SV333 )
= $false )
| ( ( equidistant @ SV15 @ SV111 @ SV15 @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1014,plain,
! [SV348: $i,SV282: $i,SV219: $i,SV335: $i,SV134: $i,SV39: $i] :
( ( ( ~ ( between @ SV39 @ SV134 @ SV335 ) )
= $true )
| ( ( ~ ( between @ SV219 @ SV282 @ SV348 )
| ( equidistant @ SV39 @ SV335 @ SV219 @ SV348 ) )
= $true )
| ( ( equidistant @ SV134 @ SV335 @ SV282 @ SV348 )
= $false )
| ( ( equidistant @ SV39 @ SV134 @ SV219 @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[996]) ).
thf(1015,plain,
! [SV306: $i,SV220: $i,SV135: $i,SV40: $i] :
( ( ( SV40 = SV135 )
= $true )
| ( ( SV220 = SV306 )
= $true )
| ( ( equidistant @ SV135 @ SV220 @ SV135 @ SV306 )
= $false )
| ( ( between @ SV40 @ SV135 @ SV306 )
= $false )
| ( ( between @ SV40 @ SV135 @ SV220 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1016,plain,
! [SV158: $i,SV236: $i,SV338: $i,SV285: $i,SV356: $i,SV63: $i] :
( ( ( ~ ( between @ SV63 @ SV356 @ SV285 ) )
= $true )
| ( ( ( between @ SV356 @ ( inner_pasch @ SV338 @ ( inner_pasch @ SV63 @ SV356 @ SV285 @ SV338 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV236 )
| ( between @ SV158 @ ( inner_pasch @ SV338 @ ( inner_pasch @ SV63 @ SV356 @ SV285 @ SV338 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV338 ) )
= $true )
| ( ( between @ SV285 @ SV338 @ SV236 )
= $false )
| ( ( between @ SV63 @ SV158 @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[998]) ).
thf(1017,plain,
! [SV312: $i,SV237: $i,SV159: $i,SV64: $i] :
( ( ( SV64 = SV159 )
= $true )
| ( ( SV237 = SV312 )
= $true )
| ( ( equidistant @ SV159 @ SV237 @ SV159 @ SV312 )
= $false )
| ( ( equidistant @ SV64 @ SV237 @ SV64 @ SV312 )
= $false )
| ( ( between @ SV64 @ SV159 @ SV237 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1018,plain,
! [SV286: $i,SV160: $i,SV313: $i,SV295: $i,SV238: $i,SV358: $i,SV65: $i] :
( ( ( ! [SY973: $i] :
( ~ ( equidistant @ SV65 @ SV358 @ SV238 @ SY973 )
| ~ ( equidistant @ SV295 @ SV358 @ SV313 @ SY973 )
| ~ ( between @ SV65 @ SV160 @ SV295 )
| ~ ( between @ SV238 @ SV286 @ SV313 )
| ( equidistant @ SV160 @ SV358 @ SV286 @ SY973 ) ) )
= $true )
| ( ( equidistant @ SV65 @ SV295 @ SV238 @ SV313 )
= $false )
| ( ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1000]) ).
thf(1019,plain,
! [SV351: $i,SV239: $i,SV339: $i,SV287: $i,SV161: $i,SV66: $i] :
( ( ( ~ ( equidistant @ SV66 @ SV161 @ SV287 @ SV339 ) )
= $true )
| ( ( ~ ( equidistant @ SV66 @ SV239 @ SV287 @ SV351 )
| ( equidistant @ SV161 @ SV239 @ SV339 @ SV351 ) )
= $true )
| ( ( between @ SV287 @ SV339 @ SV351 )
= $false )
| ( ( between @ SV66 @ SV161 @ SV239 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1001]) ).
thf(1020,plain,
! [SV288: $i,SV162: $i,SV314: $i,SV296: $i,SV240: $i,SV359: $i,SV67: $i] :
( ( ( ! [SY974: $i] :
( ~ ( equidistant @ SV67 @ SV359 @ SV240 @ SY974 )
| ~ ( equidistant @ SV296 @ SV359 @ SV314 @ SY974 )
| ~ ( between @ SV67 @ SV162 @ SV296 )
| ~ ( between @ SV240 @ SV288 @ SV314 )
| ( equidistant @ SV162 @ SV359 @ SV288 @ SY974 ) ) )
= $true )
| ( ( equidistant @ SV162 @ SV296 @ SV288 @ SV314 )
= $false )
| ( ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1021,plain,
! [SV291: $i,SV169: $i,SV353: $i,SV247: $i,SV343: $i,SV74: $i] :
( ( ( ~ ( equidistant @ SV74 @ SV343 @ SV247 @ SV353 ) )
= $true )
| ( ( ~ ( between @ SV74 @ SV169 @ SV343 )
| ( between @ SV247 @ SV291 @ SV353 ) )
= $true )
| ( ( equidistant @ SV169 @ SV343 @ SV291 @ SV353 )
= $false )
| ( ( equidistant @ SV74 @ SV169 @ SV247 @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1022,plain,
! [SV175: $i,SV323: $i,SV253: $i,SV344: $i,SV80: $i] :
( ( ( between @ SV80 @ SV344 @ SV253 )
= $false )
| ( ( between @ SV80 @ SV323 @ SV253 )
= $true )
| ( ( between @ SV175 @ SV323 @ SV344 )
= $false )
| ( ( between @ SV80 @ SV175 @ SV253 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1023,plain,
! [SV292: $i,SV189: $i,SV354: $i,SV263: $i,SV345: $i,SV94: $i] :
( ( ( ~ ( equidistant @ SV94 @ SV345 @ SV263 @ SV354 ) )
= $true )
| ( ( ~ ( colinear @ SV94 @ SV189 @ SV345 )
| ( colinear @ SV263 @ SV292 @ SV354 ) )
= $true )
| ( ( equidistant @ SV189 @ SV345 @ SV292 @ SV354 )
= $false )
| ( ( equidistant @ SV94 @ SV189 @ SV263 @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1009]) ).
thf(1024,plain,
! [SV298: $i,SV293: $i,SV270: $i,SV102: $i,SV360: $i,SV195: $i,SV357: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV357 @ SV195 @ SV360 )
| ~ ( equidistant @ SV102 @ SV357 @ SV270 @ SV360 )
| ~ ( between @ SV6 @ SV102 @ SV293 )
| ~ ( between @ SV195 @ SV270 @ SV298 )
| ( SV6 = SV102 )
| ( equidistant @ SV293 @ SV357 @ SV298 @ SV360 ) )
= $true )
| ( ( equidistant @ SV102 @ SV293 @ SV270 @ SV298 )
= $false )
| ( ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1010]) ).
thf(1025,plain,
! [SV198: $i,SV106: $i,SV355: $i,SV301: $i,SV10: $i] :
( ( ( between @ SV10 @ SV301 @ SV355 )
= $true )
| ( ( ( between @ SV301 @ SV355 @ SV10 )
| ( SV106 = SV198 )
| ( between @ SV355 @ SV10 @ SV301 ) )
= $true )
| ( ( equidistant @ SV355 @ SV106 @ SV355 @ SV198 )
= $false )
| ( ( equidistant @ SV301 @ SV106 @ SV301 @ SV198 )
= $false )
| ( ( equidistant @ SV10 @ SV106 @ SV10 @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1026,plain,
! [SV332: $i,SV14: $i,SV202: $i,SV271: $i,SV361: $i,SV110: $i] :
( ( ( ~ ( between @ SV110 @ SV361 @ SV271 )
| ( between @ SV202 @ ( continuous @ SV14 @ SV110 @ SV202 @ SV361 @ SV271 @ SV332 ) @ SV332 ) )
= $true )
| ( ( between @ SV14 @ SV110 @ SV271 )
= $false )
| ( ( equidistant @ SV14 @ SV271 @ SV14 @ SV332 )
= $false )
| ( ( equidistant @ SV14 @ SV110 @ SV14 @ SV202 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1012]) ).
thf(1027,plain,
! [SV333: $i,SV203: $i,SV15: $i,SV272: $i,SV362: $i,SV111: $i] :
( ( ( ~ ( between @ SV111 @ SV362 @ SV272 )
| ( equidistant @ SV15 @ SV362 @ SV15 @ ( continuous @ SV15 @ SV111 @ SV203 @ SV362 @ SV272 @ SV333 ) ) )
= $true )
| ( ( between @ SV15 @ SV111 @ SV272 )
= $false )
| ( ( equidistant @ SV15 @ SV272 @ SV15 @ SV333 )
= $false )
| ( ( equidistant @ SV15 @ SV111 @ SV15 @ SV203 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1028,plain,
! [SV348: $i,SV282: $i,SV219: $i,SV335: $i,SV134: $i,SV39: $i] :
( ( ( between @ SV39 @ SV134 @ SV335 )
= $false )
| ( ( ~ ( between @ SV219 @ SV282 @ SV348 )
| ( equidistant @ SV39 @ SV335 @ SV219 @ SV348 ) )
= $true )
| ( ( equidistant @ SV134 @ SV335 @ SV282 @ SV348 )
= $false )
| ( ( equidistant @ SV39 @ SV134 @ SV219 @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1014]) ).
thf(1029,plain,
! [SV158: $i,SV236: $i,SV338: $i,SV285: $i,SV356: $i,SV63: $i] :
( ( ( between @ SV63 @ SV356 @ SV285 )
= $false )
| ( ( ( between @ SV356 @ ( inner_pasch @ SV338 @ ( inner_pasch @ SV63 @ SV356 @ SV285 @ SV338 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV236 )
| ( between @ SV158 @ ( inner_pasch @ SV338 @ ( inner_pasch @ SV63 @ SV356 @ SV285 @ SV338 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV338 ) )
= $true )
| ( ( between @ SV285 @ SV338 @ SV236 )
= $false )
| ( ( between @ SV63 @ SV158 @ SV236 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1016]) ).
thf(1030,plain,
! [SV286: $i,SV160: $i,SV313: $i,SV295: $i,SV363: $i,SV238: $i,SV358: $i,SV65: $i] :
( ( ( ~ ( equidistant @ SV65 @ SV358 @ SV238 @ SV363 )
| ~ ( equidistant @ SV295 @ SV358 @ SV313 @ SV363 )
| ~ ( between @ SV65 @ SV160 @ SV295 )
| ~ ( between @ SV238 @ SV286 @ SV313 )
| ( equidistant @ SV160 @ SV358 @ SV286 @ SV363 ) )
= $true )
| ( ( equidistant @ SV65 @ SV295 @ SV238 @ SV313 )
= $false )
| ( ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1018]) ).
thf(1031,plain,
! [SV351: $i,SV239: $i,SV339: $i,SV287: $i,SV161: $i,SV66: $i] :
( ( ( equidistant @ SV66 @ SV161 @ SV287 @ SV339 )
= $false )
| ( ( ~ ( equidistant @ SV66 @ SV239 @ SV287 @ SV351 )
| ( equidistant @ SV161 @ SV239 @ SV339 @ SV351 ) )
= $true )
| ( ( between @ SV287 @ SV339 @ SV351 )
= $false )
| ( ( between @ SV66 @ SV161 @ SV239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1032,plain,
! [SV288: $i,SV162: $i,SV314: $i,SV296: $i,SV364: $i,SV240: $i,SV359: $i,SV67: $i] :
( ( ( ~ ( equidistant @ SV67 @ SV359 @ SV240 @ SV364 )
| ~ ( equidistant @ SV296 @ SV359 @ SV314 @ SV364 )
| ~ ( between @ SV67 @ SV162 @ SV296 )
| ~ ( between @ SV240 @ SV288 @ SV314 )
| ( equidistant @ SV162 @ SV359 @ SV288 @ SV364 ) )
= $true )
| ( ( equidistant @ SV162 @ SV296 @ SV288 @ SV314 )
= $false )
| ( ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1020]) ).
thf(1033,plain,
! [SV291: $i,SV169: $i,SV353: $i,SV247: $i,SV343: $i,SV74: $i] :
( ( ( equidistant @ SV74 @ SV343 @ SV247 @ SV353 )
= $false )
| ( ( ~ ( between @ SV74 @ SV169 @ SV343 )
| ( between @ SV247 @ SV291 @ SV353 ) )
= $true )
| ( ( equidistant @ SV169 @ SV343 @ SV291 @ SV353 )
= $false )
| ( ( equidistant @ SV74 @ SV169 @ SV247 @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1021]) ).
thf(1034,plain,
! [SV292: $i,SV189: $i,SV354: $i,SV263: $i,SV345: $i,SV94: $i] :
( ( ( equidistant @ SV94 @ SV345 @ SV263 @ SV354 )
= $false )
| ( ( ~ ( colinear @ SV94 @ SV189 @ SV345 )
| ( colinear @ SV263 @ SV292 @ SV354 ) )
= $true )
| ( ( equidistant @ SV189 @ SV345 @ SV292 @ SV354 )
= $false )
| ( ( equidistant @ SV94 @ SV189 @ SV263 @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1023]) ).
thf(1035,plain,
! [SV298: $i,SV293: $i,SV270: $i,SV102: $i,SV360: $i,SV195: $i,SV357: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV357 @ SV195 @ SV360 ) )
= $true )
| ( ( ~ ( equidistant @ SV102 @ SV357 @ SV270 @ SV360 )
| ~ ( between @ SV6 @ SV102 @ SV293 )
| ~ ( between @ SV195 @ SV270 @ SV298 )
| ( SV6 = SV102 )
| ( equidistant @ SV293 @ SV357 @ SV298 @ SV360 ) )
= $true )
| ( ( equidistant @ SV102 @ SV293 @ SV270 @ SV298 )
= $false )
| ( ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1036,plain,
! [SV198: $i,SV106: $i,SV10: $i,SV355: $i,SV301: $i] :
( ( ( between @ SV301 @ SV355 @ SV10 )
= $true )
| ( ( ( SV106 = SV198 )
| ( between @ SV355 @ SV10 @ SV301 ) )
= $true )
| ( ( between @ SV10 @ SV301 @ SV355 )
= $true )
| ( ( equidistant @ SV355 @ SV106 @ SV355 @ SV198 )
= $false )
| ( ( equidistant @ SV301 @ SV106 @ SV301 @ SV198 )
= $false )
| ( ( equidistant @ SV10 @ SV106 @ SV10 @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1025]) ).
thf(1037,plain,
! [SV332: $i,SV14: $i,SV202: $i,SV271: $i,SV361: $i,SV110: $i] :
( ( ( ~ ( between @ SV110 @ SV361 @ SV271 ) )
= $true )
| ( ( between @ SV202 @ ( continuous @ SV14 @ SV110 @ SV202 @ SV361 @ SV271 @ SV332 ) @ SV332 )
= $true )
| ( ( between @ SV14 @ SV110 @ SV271 )
= $false )
| ( ( equidistant @ SV14 @ SV271 @ SV14 @ SV332 )
= $false )
| ( ( equidistant @ SV14 @ SV110 @ SV14 @ SV202 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1026]) ).
thf(1038,plain,
! [SV333: $i,SV203: $i,SV15: $i,SV272: $i,SV362: $i,SV111: $i] :
( ( ( ~ ( between @ SV111 @ SV362 @ SV272 ) )
= $true )
| ( ( equidistant @ SV15 @ SV362 @ SV15 @ ( continuous @ SV15 @ SV111 @ SV203 @ SV362 @ SV272 @ SV333 ) )
= $true )
| ( ( between @ SV15 @ SV111 @ SV272 )
= $false )
| ( ( equidistant @ SV15 @ SV272 @ SV15 @ SV333 )
= $false )
| ( ( equidistant @ SV15 @ SV111 @ SV15 @ SV203 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1039,plain,
! [SV134: $i,SV335: $i,SV39: $i,SV348: $i,SV282: $i,SV219: $i] :
( ( ( ~ ( between @ SV219 @ SV282 @ SV348 ) )
= $true )
| ( ( equidistant @ SV39 @ SV335 @ SV219 @ SV348 )
= $true )
| ( ( between @ SV39 @ SV134 @ SV335 )
= $false )
| ( ( equidistant @ SV134 @ SV335 @ SV282 @ SV348 )
= $false )
| ( ( equidistant @ SV39 @ SV134 @ SV219 @ SV282 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1028]) ).
thf(1040,plain,
! [SV158: $i,SV236: $i,SV285: $i,SV63: $i,SV338: $i,SV356: $i] :
( ( ( between @ SV356 @ ( inner_pasch @ SV338 @ ( inner_pasch @ SV63 @ SV356 @ SV285 @ SV338 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV236 )
= $true )
| ( ( between @ SV158 @ ( inner_pasch @ SV338 @ ( inner_pasch @ SV63 @ SV356 @ SV285 @ SV338 @ SV236 ) @ SV63 @ SV158 @ SV236 ) @ SV338 )
= $true )
| ( ( between @ SV63 @ SV356 @ SV285 )
= $false )
| ( ( between @ SV285 @ SV338 @ SV236 )
= $false )
| ( ( between @ SV63 @ SV158 @ SV236 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1029]) ).
thf(1041,plain,
! [SV286: $i,SV160: $i,SV313: $i,SV295: $i,SV363: $i,SV238: $i,SV358: $i,SV65: $i] :
( ( ( ~ ( equidistant @ SV65 @ SV358 @ SV238 @ SV363 ) )
= $true )
| ( ( ~ ( equidistant @ SV295 @ SV358 @ SV313 @ SV363 )
| ~ ( between @ SV65 @ SV160 @ SV295 )
| ~ ( between @ SV238 @ SV286 @ SV313 )
| ( equidistant @ SV160 @ SV358 @ SV286 @ SV363 ) )
= $true )
| ( ( equidistant @ SV65 @ SV295 @ SV238 @ SV313 )
= $false )
| ( ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1030]) ).
thf(1042,plain,
! [SV339: $i,SV161: $i,SV351: $i,SV287: $i,SV239: $i,SV66: $i] :
( ( ( ~ ( equidistant @ SV66 @ SV239 @ SV287 @ SV351 ) )
= $true )
| ( ( equidistant @ SV161 @ SV239 @ SV339 @ SV351 )
= $true )
| ( ( equidistant @ SV66 @ SV161 @ SV287 @ SV339 )
= $false )
| ( ( between @ SV287 @ SV339 @ SV351 )
= $false )
| ( ( between @ SV66 @ SV161 @ SV239 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1031]) ).
thf(1043,plain,
! [SV288: $i,SV162: $i,SV314: $i,SV296: $i,SV364: $i,SV240: $i,SV359: $i,SV67: $i] :
( ( ( ~ ( equidistant @ SV67 @ SV359 @ SV240 @ SV364 ) )
= $true )
| ( ( ~ ( equidistant @ SV296 @ SV359 @ SV314 @ SV364 )
| ~ ( between @ SV67 @ SV162 @ SV296 )
| ~ ( between @ SV240 @ SV288 @ SV314 )
| ( equidistant @ SV162 @ SV359 @ SV288 @ SV364 ) )
= $true )
| ( ( equidistant @ SV162 @ SV296 @ SV288 @ SV314 )
= $false )
| ( ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1032]) ).
thf(1044,plain,
! [SV353: $i,SV291: $i,SV247: $i,SV343: $i,SV169: $i,SV74: $i] :
( ( ( ~ ( between @ SV74 @ SV169 @ SV343 ) )
= $true )
| ( ( between @ SV247 @ SV291 @ SV353 )
= $true )
| ( ( equidistant @ SV74 @ SV343 @ SV247 @ SV353 )
= $false )
| ( ( equidistant @ SV169 @ SV343 @ SV291 @ SV353 )
= $false )
| ( ( equidistant @ SV74 @ SV169 @ SV247 @ SV291 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1033]) ).
thf(1045,plain,
! [SV354: $i,SV292: $i,SV263: $i,SV345: $i,SV189: $i,SV94: $i] :
( ( ( ~ ( colinear @ SV94 @ SV189 @ SV345 ) )
= $true )
| ( ( colinear @ SV263 @ SV292 @ SV354 )
= $true )
| ( ( equidistant @ SV94 @ SV345 @ SV263 @ SV354 )
= $false )
| ( ( equidistant @ SV189 @ SV345 @ SV292 @ SV354 )
= $false )
| ( ( equidistant @ SV94 @ SV189 @ SV263 @ SV292 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1046,plain,
! [SV298: $i,SV293: $i,SV270: $i,SV102: $i,SV360: $i,SV195: $i,SV357: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV357 @ SV195 @ SV360 )
= $false )
| ( ( ~ ( equidistant @ SV102 @ SV357 @ SV270 @ SV360 )
| ~ ( between @ SV6 @ SV102 @ SV293 )
| ~ ( between @ SV195 @ SV270 @ SV298 )
| ( SV6 = SV102 )
| ( equidistant @ SV293 @ SV357 @ SV298 @ SV360 ) )
= $true )
| ( ( equidistant @ SV102 @ SV293 @ SV270 @ SV298 )
= $false )
| ( ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1035]) ).
thf(1047,plain,
! [SV301: $i,SV10: $i,SV355: $i,SV198: $i,SV106: $i] :
( ( ( SV106 = SV198 )
= $true )
| ( ( between @ SV355 @ SV10 @ SV301 )
= $true )
| ( ( between @ SV301 @ SV355 @ SV10 )
= $true )
| ( ( between @ SV10 @ SV301 @ SV355 )
= $true )
| ( ( equidistant @ SV355 @ SV106 @ SV355 @ SV198 )
= $false )
| ( ( equidistant @ SV301 @ SV106 @ SV301 @ SV198 )
= $false )
| ( ( equidistant @ SV10 @ SV106 @ SV10 @ SV198 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1048,plain,
! [SV332: $i,SV14: $i,SV202: $i,SV271: $i,SV361: $i,SV110: $i] :
( ( ( between @ SV110 @ SV361 @ SV271 )
= $false )
| ( ( between @ SV202 @ ( continuous @ SV14 @ SV110 @ SV202 @ SV361 @ SV271 @ SV332 ) @ SV332 )
= $true )
| ( ( between @ SV14 @ SV110 @ SV271 )
= $false )
| ( ( equidistant @ SV14 @ SV271 @ SV14 @ SV332 )
= $false )
| ( ( equidistant @ SV14 @ SV110 @ SV14 @ SV202 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1037]) ).
thf(1049,plain,
! [SV333: $i,SV203: $i,SV15: $i,SV272: $i,SV362: $i,SV111: $i] :
( ( ( between @ SV111 @ SV362 @ SV272 )
= $false )
| ( ( equidistant @ SV15 @ SV362 @ SV15 @ ( continuous @ SV15 @ SV111 @ SV203 @ SV362 @ SV272 @ SV333 ) )
= $true )
| ( ( between @ SV15 @ SV111 @ SV272 )
= $false )
| ( ( equidistant @ SV15 @ SV272 @ SV15 @ SV333 )
= $false )
| ( ( equidistant @ SV15 @ SV111 @ SV15 @ SV203 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1038]) ).
thf(1050,plain,
! [SV134: $i,SV335: $i,SV39: $i,SV348: $i,SV282: $i,SV219: $i] :
( ( ( between @ SV219 @ SV282 @ SV348 )
= $false )
| ( ( equidistant @ SV39 @ SV335 @ SV219 @ SV348 )
= $true )
| ( ( between @ SV39 @ SV134 @ SV335 )
= $false )
| ( ( equidistant @ SV134 @ SV335 @ SV282 @ SV348 )
= $false )
| ( ( equidistant @ SV39 @ SV134 @ SV219 @ SV282 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1039]) ).
thf(1051,plain,
! [SV286: $i,SV160: $i,SV313: $i,SV295: $i,SV363: $i,SV238: $i,SV358: $i,SV65: $i] :
( ( ( equidistant @ SV65 @ SV358 @ SV238 @ SV363 )
= $false )
| ( ( ~ ( equidistant @ SV295 @ SV358 @ SV313 @ SV363 )
| ~ ( between @ SV65 @ SV160 @ SV295 )
| ~ ( between @ SV238 @ SV286 @ SV313 )
| ( equidistant @ SV160 @ SV358 @ SV286 @ SV363 ) )
= $true )
| ( ( equidistant @ SV65 @ SV295 @ SV238 @ SV313 )
= $false )
| ( ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1052,plain,
! [SV339: $i,SV161: $i,SV351: $i,SV287: $i,SV239: $i,SV66: $i] :
( ( ( equidistant @ SV66 @ SV239 @ SV287 @ SV351 )
= $false )
| ( ( equidistant @ SV161 @ SV239 @ SV339 @ SV351 )
= $true )
| ( ( equidistant @ SV66 @ SV161 @ SV287 @ SV339 )
= $false )
| ( ( between @ SV287 @ SV339 @ SV351 )
= $false )
| ( ( between @ SV66 @ SV161 @ SV239 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1042]) ).
thf(1053,plain,
! [SV288: $i,SV162: $i,SV314: $i,SV296: $i,SV364: $i,SV240: $i,SV359: $i,SV67: $i] :
( ( ( equidistant @ SV67 @ SV359 @ SV240 @ SV364 )
= $false )
| ( ( ~ ( equidistant @ SV296 @ SV359 @ SV314 @ SV364 )
| ~ ( between @ SV67 @ SV162 @ SV296 )
| ~ ( between @ SV240 @ SV288 @ SV314 )
| ( equidistant @ SV162 @ SV359 @ SV288 @ SV364 ) )
= $true )
| ( ( equidistant @ SV162 @ SV296 @ SV288 @ SV314 )
= $false )
| ( ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1043]) ).
thf(1054,plain,
! [SV353: $i,SV291: $i,SV247: $i,SV343: $i,SV169: $i,SV74: $i] :
( ( ( between @ SV74 @ SV169 @ SV343 )
= $false )
| ( ( between @ SV247 @ SV291 @ SV353 )
= $true )
| ( ( equidistant @ SV74 @ SV343 @ SV247 @ SV353 )
= $false )
| ( ( equidistant @ SV169 @ SV343 @ SV291 @ SV353 )
= $false )
| ( ( equidistant @ SV74 @ SV169 @ SV247 @ SV291 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1044]) ).
thf(1055,plain,
! [SV354: $i,SV292: $i,SV263: $i,SV345: $i,SV189: $i,SV94: $i] :
( ( ( colinear @ SV94 @ SV189 @ SV345 )
= $false )
| ( ( colinear @ SV263 @ SV292 @ SV354 )
= $true )
| ( ( equidistant @ SV94 @ SV345 @ SV263 @ SV354 )
= $false )
| ( ( equidistant @ SV189 @ SV345 @ SV292 @ SV354 )
= $false )
| ( ( equidistant @ SV94 @ SV189 @ SV263 @ SV292 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1045]) ).
thf(1056,plain,
! [SV298: $i,SV195: $i,SV293: $i,SV6: $i,SV360: $i,SV270: $i,SV357: $i,SV102: $i] :
( ( ( ~ ( equidistant @ SV102 @ SV357 @ SV270 @ SV360 ) )
= $true )
| ( ( ~ ( between @ SV6 @ SV102 @ SV293 )
| ~ ( between @ SV195 @ SV270 @ SV298 )
| ( SV6 = SV102 )
| ( equidistant @ SV293 @ SV357 @ SV298 @ SV360 ) )
= $true )
| ( ( equidistant @ SV6 @ SV357 @ SV195 @ SV360 )
= $false )
| ( ( equidistant @ SV102 @ SV293 @ SV270 @ SV298 )
= $false )
| ( ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1046]) ).
thf(1057,plain,
! [SV286: $i,SV238: $i,SV160: $i,SV65: $i,SV363: $i,SV313: $i,SV358: $i,SV295: $i] :
( ( ( ~ ( equidistant @ SV295 @ SV358 @ SV313 @ SV363 ) )
= $true )
| ( ( ~ ( between @ SV65 @ SV160 @ SV295 )
| ~ ( between @ SV238 @ SV286 @ SV313 )
| ( equidistant @ SV160 @ SV358 @ SV286 @ SV363 ) )
= $true )
| ( ( equidistant @ SV65 @ SV358 @ SV238 @ SV363 )
= $false )
| ( ( equidistant @ SV65 @ SV295 @ SV238 @ SV313 )
= $false )
| ( ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1051]) ).
thf(1058,plain,
! [SV288: $i,SV240: $i,SV162: $i,SV67: $i,SV364: $i,SV314: $i,SV359: $i,SV296: $i] :
( ( ( ~ ( equidistant @ SV296 @ SV359 @ SV314 @ SV364 ) )
= $true )
| ( ( ~ ( between @ SV67 @ SV162 @ SV296 )
| ~ ( between @ SV240 @ SV288 @ SV314 )
| ( equidistant @ SV162 @ SV359 @ SV288 @ SV364 ) )
= $true )
| ( ( equidistant @ SV67 @ SV359 @ SV240 @ SV364 )
= $false )
| ( ( equidistant @ SV162 @ SV296 @ SV288 @ SV314 )
= $false )
| ( ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1059,plain,
! [SV298: $i,SV195: $i,SV293: $i,SV6: $i,SV360: $i,SV270: $i,SV357: $i,SV102: $i] :
( ( ( equidistant @ SV102 @ SV357 @ SV270 @ SV360 )
= $false )
| ( ( ~ ( between @ SV6 @ SV102 @ SV293 )
| ~ ( between @ SV195 @ SV270 @ SV298 )
| ( SV6 = SV102 )
| ( equidistant @ SV293 @ SV357 @ SV298 @ SV360 ) )
= $true )
| ( ( equidistant @ SV6 @ SV357 @ SV195 @ SV360 )
= $false )
| ( ( equidistant @ SV102 @ SV293 @ SV270 @ SV298 )
= $false )
| ( ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1056]) ).
thf(1060,plain,
! [SV286: $i,SV238: $i,SV160: $i,SV65: $i,SV363: $i,SV313: $i,SV358: $i,SV295: $i] :
( ( ( equidistant @ SV295 @ SV358 @ SV313 @ SV363 )
= $false )
| ( ( ~ ( between @ SV65 @ SV160 @ SV295 )
| ~ ( between @ SV238 @ SV286 @ SV313 )
| ( equidistant @ SV160 @ SV358 @ SV286 @ SV363 ) )
= $true )
| ( ( equidistant @ SV65 @ SV358 @ SV238 @ SV363 )
= $false )
| ( ( equidistant @ SV65 @ SV295 @ SV238 @ SV313 )
= $false )
| ( ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1057]) ).
thf(1061,plain,
! [SV288: $i,SV240: $i,SV162: $i,SV67: $i,SV364: $i,SV314: $i,SV359: $i,SV296: $i] :
( ( ( equidistant @ SV296 @ SV359 @ SV314 @ SV364 )
= $false )
| ( ( ~ ( between @ SV67 @ SV162 @ SV296 )
| ~ ( between @ SV240 @ SV288 @ SV314 )
| ( equidistant @ SV162 @ SV359 @ SV288 @ SV364 ) )
= $true )
| ( ( equidistant @ SV67 @ SV359 @ SV240 @ SV364 )
= $false )
| ( ( equidistant @ SV162 @ SV296 @ SV288 @ SV314 )
= $false )
| ( ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1062,plain,
! [SV360: $i,SV357: $i,SV298: $i,SV270: $i,SV195: $i,SV293: $i,SV102: $i,SV6: $i] :
( ( ( ~ ( between @ SV6 @ SV102 @ SV293 ) )
= $true )
| ( ( ~ ( between @ SV195 @ SV270 @ SV298 )
| ( SV6 = SV102 )
| ( equidistant @ SV293 @ SV357 @ SV298 @ SV360 ) )
= $true )
| ( ( equidistant @ SV102 @ SV357 @ SV270 @ SV360 )
= $false )
| ( ( equidistant @ SV6 @ SV357 @ SV195 @ SV360 )
= $false )
| ( ( equidistant @ SV102 @ SV293 @ SV270 @ SV298 )
= $false )
| ( ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1059]) ).
thf(1063,plain,
! [SV363: $i,SV358: $i,SV313: $i,SV286: $i,SV238: $i,SV295: $i,SV160: $i,SV65: $i] :
( ( ( ~ ( between @ SV65 @ SV160 @ SV295 ) )
= $true )
| ( ( ~ ( between @ SV238 @ SV286 @ SV313 )
| ( equidistant @ SV160 @ SV358 @ SV286 @ SV363 ) )
= $true )
| ( ( equidistant @ SV295 @ SV358 @ SV313 @ SV363 )
= $false )
| ( ( equidistant @ SV65 @ SV358 @ SV238 @ SV363 )
= $false )
| ( ( equidistant @ SV65 @ SV295 @ SV238 @ SV313 )
= $false )
| ( ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1060]) ).
thf(1064,plain,
! [SV364: $i,SV359: $i,SV314: $i,SV288: $i,SV240: $i,SV296: $i,SV162: $i,SV67: $i] :
( ( ( ~ ( between @ SV67 @ SV162 @ SV296 ) )
= $true )
| ( ( ~ ( between @ SV240 @ SV288 @ SV314 )
| ( equidistant @ SV162 @ SV359 @ SV288 @ SV364 ) )
= $true )
| ( ( equidistant @ SV296 @ SV359 @ SV314 @ SV364 )
= $false )
| ( ( equidistant @ SV67 @ SV359 @ SV240 @ SV364 )
= $false )
| ( ( equidistant @ SV162 @ SV296 @ SV288 @ SV314 )
= $false )
| ( ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1065,plain,
! [SV360: $i,SV357: $i,SV298: $i,SV270: $i,SV195: $i,SV293: $i,SV102: $i,SV6: $i] :
( ( ( between @ SV6 @ SV102 @ SV293 )
= $false )
| ( ( ~ ( between @ SV195 @ SV270 @ SV298 )
| ( SV6 = SV102 )
| ( equidistant @ SV293 @ SV357 @ SV298 @ SV360 ) )
= $true )
| ( ( equidistant @ SV102 @ SV357 @ SV270 @ SV360 )
= $false )
| ( ( equidistant @ SV6 @ SV357 @ SV195 @ SV360 )
= $false )
| ( ( equidistant @ SV102 @ SV293 @ SV270 @ SV298 )
= $false )
| ( ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1062]) ).
thf(1066,plain,
! [SV363: $i,SV358: $i,SV313: $i,SV286: $i,SV238: $i,SV295: $i,SV160: $i,SV65: $i] :
( ( ( between @ SV65 @ SV160 @ SV295 )
= $false )
| ( ( ~ ( between @ SV238 @ SV286 @ SV313 )
| ( equidistant @ SV160 @ SV358 @ SV286 @ SV363 ) )
= $true )
| ( ( equidistant @ SV295 @ SV358 @ SV313 @ SV363 )
= $false )
| ( ( equidistant @ SV65 @ SV358 @ SV238 @ SV363 )
= $false )
| ( ( equidistant @ SV65 @ SV295 @ SV238 @ SV313 )
= $false )
| ( ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1063]) ).
thf(1067,plain,
! [SV364: $i,SV359: $i,SV314: $i,SV288: $i,SV240: $i,SV296: $i,SV162: $i,SV67: $i] :
( ( ( between @ SV67 @ SV162 @ SV296 )
= $false )
| ( ( ~ ( between @ SV240 @ SV288 @ SV314 )
| ( equidistant @ SV162 @ SV359 @ SV288 @ SV364 ) )
= $true )
| ( ( equidistant @ SV296 @ SV359 @ SV314 @ SV364 )
= $false )
| ( ( equidistant @ SV67 @ SV359 @ SV240 @ SV364 )
= $false )
| ( ( equidistant @ SV162 @ SV296 @ SV288 @ SV314 )
= $false )
| ( ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1068,plain,
! [SV360: $i,SV357: $i,SV293: $i,SV102: $i,SV6: $i,SV298: $i,SV270: $i,SV195: $i] :
( ( ( ~ ( between @ SV195 @ SV270 @ SV298 ) )
= $true )
| ( ( ( SV6 = SV102 )
| ( equidistant @ SV293 @ SV357 @ SV298 @ SV360 ) )
= $true )
| ( ( between @ SV6 @ SV102 @ SV293 )
= $false )
| ( ( equidistant @ SV102 @ SV357 @ SV270 @ SV360 )
= $false )
| ( ( equidistant @ SV6 @ SV357 @ SV195 @ SV360 )
= $false )
| ( ( equidistant @ SV102 @ SV293 @ SV270 @ SV298 )
= $false )
| ( ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1069,plain,
! [SV295: $i,SV65: $i,SV363: $i,SV358: $i,SV160: $i,SV313: $i,SV286: $i,SV238: $i] :
( ( ( ~ ( between @ SV238 @ SV286 @ SV313 ) )
= $true )
| ( ( equidistant @ SV160 @ SV358 @ SV286 @ SV363 )
= $true )
| ( ( between @ SV65 @ SV160 @ SV295 )
= $false )
| ( ( equidistant @ SV295 @ SV358 @ SV313 @ SV363 )
= $false )
| ( ( equidistant @ SV65 @ SV358 @ SV238 @ SV363 )
= $false )
| ( ( equidistant @ SV65 @ SV295 @ SV238 @ SV313 )
= $false )
| ( ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1066]) ).
thf(1070,plain,
! [SV296: $i,SV67: $i,SV364: $i,SV359: $i,SV162: $i,SV314: $i,SV288: $i,SV240: $i] :
( ( ( ~ ( between @ SV240 @ SV288 @ SV314 ) )
= $true )
| ( ( equidistant @ SV162 @ SV359 @ SV288 @ SV364 )
= $true )
| ( ( between @ SV67 @ SV162 @ SV296 )
= $false )
| ( ( equidistant @ SV296 @ SV359 @ SV314 @ SV364 )
= $false )
| ( ( equidistant @ SV67 @ SV359 @ SV240 @ SV364 )
= $false )
| ( ( equidistant @ SV162 @ SV296 @ SV288 @ SV314 )
= $false )
| ( ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1067]) ).
thf(1071,plain,
! [SV360: $i,SV357: $i,SV293: $i,SV102: $i,SV6: $i,SV298: $i,SV270: $i,SV195: $i] :
( ( ( between @ SV195 @ SV270 @ SV298 )
= $false )
| ( ( ( SV6 = SV102 )
| ( equidistant @ SV293 @ SV357 @ SV298 @ SV360 ) )
= $true )
| ( ( between @ SV6 @ SV102 @ SV293 )
= $false )
| ( ( equidistant @ SV102 @ SV357 @ SV270 @ SV360 )
= $false )
| ( ( equidistant @ SV6 @ SV357 @ SV195 @ SV360 )
= $false )
| ( ( equidistant @ SV102 @ SV293 @ SV270 @ SV298 )
= $false )
| ( ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1068]) ).
thf(1072,plain,
! [SV295: $i,SV65: $i,SV363: $i,SV358: $i,SV160: $i,SV313: $i,SV286: $i,SV238: $i] :
( ( ( between @ SV238 @ SV286 @ SV313 )
= $false )
| ( ( equidistant @ SV160 @ SV358 @ SV286 @ SV363 )
= $true )
| ( ( between @ SV65 @ SV160 @ SV295 )
= $false )
| ( ( equidistant @ SV295 @ SV358 @ SV313 @ SV363 )
= $false )
| ( ( equidistant @ SV65 @ SV358 @ SV238 @ SV363 )
= $false )
| ( ( equidistant @ SV65 @ SV295 @ SV238 @ SV313 )
= $false )
| ( ( equidistant @ SV65 @ SV160 @ SV238 @ SV286 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1073,plain,
! [SV296: $i,SV67: $i,SV364: $i,SV359: $i,SV162: $i,SV314: $i,SV288: $i,SV240: $i] :
( ( ( between @ SV240 @ SV288 @ SV314 )
= $false )
| ( ( equidistant @ SV162 @ SV359 @ SV288 @ SV364 )
= $true )
| ( ( between @ SV67 @ SV162 @ SV296 )
= $false )
| ( ( equidistant @ SV296 @ SV359 @ SV314 @ SV364 )
= $false )
| ( ( equidistant @ SV67 @ SV359 @ SV240 @ SV364 )
= $false )
| ( ( equidistant @ SV162 @ SV296 @ SV288 @ SV314 )
= $false )
| ( ( equidistant @ SV67 @ SV162 @ SV240 @ SV288 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1070]) ).
thf(1074,plain,
! [SV270: $i,SV195: $i,SV360: $i,SV298: $i,SV357: $i,SV293: $i,SV102: $i,SV6: $i] :
( ( ( SV6 = SV102 )
= $true )
| ( ( equidistant @ SV293 @ SV357 @ SV298 @ SV360 )
= $true )
| ( ( between @ SV195 @ SV270 @ SV298 )
= $false )
| ( ( between @ SV6 @ SV102 @ SV293 )
= $false )
| ( ( equidistant @ SV102 @ SV357 @ SV270 @ SV360 )
= $false )
| ( ( equidistant @ SV6 @ SV357 @ SV195 @ SV360 )
= $false )
| ( ( equidistant @ SV102 @ SV293 @ SV270 @ SV298 )
= $false )
| ( ( equidistant @ SV6 @ SV102 @ SV195 @ SV270 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1071]) ).
thf(1075,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[271,1074,1073,1072,1055,1054,1052,1050,1049,1048,1047,1040,1022,1017,1015,1007,1006,1005,1003,995,992,991,990,987,986,985,982,981,976,975,968,967,966,956,955,942,933,932,929,928,927,926,925,907,882,881,876,874,831,826,825,824,823,822,821,820,805,804,803,802,801,800,799,798,797,787,768,752,751,750,740,714,707,690,689,679,666,664,663,628,615,607,579,574,573,572,544,531,528,527,526,520,517,516,505,503,484,482,474,443,442,441,417,390,389,388,378,272]) ).
thf(1076,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[1075]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO069-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.18 % Computer : n001.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Oct 6 10:08:39 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 6.57/1.42
% 6.57/1.42 No.of.Axioms: 107
% 6.57/1.42
% 6.57/1.42 Length.of.Defs: 0
% 6.57/1.42
% 6.57/1.42 Contains.Choice.Funs: false
% 6.57/1.42 ...........................................
% 6.57/1.42
% 6.57/1.42 ********************************
% 6.57/1.42 * All subproblems solved! *
% 6.57/1.42 ********************************
% 6.57/1.42 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:107,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1075,loop_count:0,foatp_calls:1,translation:fof_full)
% 6.57/1.42
% 6.57/1.42 %**** Beginning of derivation protocol ****
% 6.57/1.42 % SZS output start CNFRefutation
% See solution above
% 6.57/1.43
% 6.57/1.43 %**** End of derivation protocol ****
% 6.57/1.43 %**** no. of clauses in derivation: 1076 ****
% 6.57/1.43 %**** clause counter: 1075 ****
% 6.57/1.43
% 6.57/1.43 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:107,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:1075,loop_count:0,foatp_calls:1,translation:fof_full)
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