%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO053-3 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 10:17:42 AM UTC 2026
% Result : Unsatisfiable 10.92s 2.07s
% Output : CNFRefutation 10.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 86
% Syntax : Number of formulae : 890 ( 500 unt; 0 typ; 0 def)
% Number of atoms : 6012 (1940 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 14424 (1418 ~;2226 |; 0 &;10780 @)
% ( 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 : 18 ( 15 usr; 8 con; 0-6 aty)
% Number of variables : 3850 ( 0 ^;3850 !; 0 ?;3850 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_between,type,
between: $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(1,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/sandbox2/benchmark/theBenchmark.p',t8) ).
thf(2,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/sandbox2/benchmark/theBenchmark.p',b14) ).
thf(3,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/sandbox2/benchmark/theBenchmark.p',t9) ).
thf(4,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/sandbox2/benchmark/theBenchmark.p',t7) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',b13) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',b12) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',b11) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',i4) ).
thf(9,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( V
= ( insertion @ U @ W @ U @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i3) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',i2_3) ).
thf(11,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/sandbox2/benchmark/theBenchmark.p',i2_2) ).
thf(12,axiom,
! [U: $i,V: $i,U1: $i,W1: $i] : ( equidistant @ U @ V @ U1 @ ( insertion @ U1 @ W1 @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i2_1) ).
thf(13,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/sandbox2/benchmark/theBenchmark.p',d15) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',d14) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',d13) ).
thf(16,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/sandbox2/benchmark/theBenchmark.p',d12) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',d11) ).
thf(18,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/sandbox2/benchmark/theBenchmark.p',b10) ).
thf(19,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e3_3) ).
thf(20,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/sandbox2/benchmark/theBenchmark.p',e3_2) ).
thf(21,axiom,
! [V: $i,U: $i] :
( V
!= ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e3_1) ).
thf(22,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_3) ).
thf(23,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_2) ).
thf(24,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_1) ).
thf(25,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ X )
| ( between @ U @ V @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b9) ).
thf(26,axiom,
! [U: $i,V: $i,X: $i,W: $i] :
( ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b8) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',b7) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',b6) ).
thf(29,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ X )
| ( between @ V @ W @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b5) ).
thf(30,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ V @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b4) ).
thf(31,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( U = V )
| ( V = W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_2) ).
thf(32,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V )
| ( V = W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_1) ).
thf(33,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b3) ).
thf(34,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).
thf(35,axiom,
! [U: $i,V: $i] : ( between @ U @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
thf(36,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
thf(37,axiom,
! [U: $i,W: $i,X: $i,V: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ( between @ V @ W @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).
thf(38,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
thf(39,axiom,
! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).
thf(40,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).
thf(41,axiom,
! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_3) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p',d10_2) ).
thf(43,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( U = V )
| ( W
= ( extension @ U @ V @ V @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_1) ).
thf(44,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/sandbox2/benchmark/theBenchmark.p',d9) ).
thf(45,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/sandbox2/benchmark/theBenchmark.p',d8) ).
thf(46,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
thf(47,axiom,
! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
thf(48,axiom,
! [U: $i] :
( U
= ( reflection @ U @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).
thf(49,axiom,
! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_1) ).
thf(50,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
thf(51,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).
thf(52,axiom,
! [Y: $i,U: $i,V: $i,W: $i,X: $i] :
( ( Y
!= ( extension @ U @ V @ W @ X ) )
| ( between @ U @ V @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b0) ).
thf(53,axiom,
! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
thf(54,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/sandbox2/benchmark/theBenchmark.p',d5) ).
thf(55,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_5) ).
thf(56,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_4) ).
thf(57,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_3) ).
thf(58,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_2) ).
thf(59,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_1) ).
thf(60,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3) ).
thf(61,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
thf(62,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
thf(63,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/sandbox2/benchmark/theBenchmark.p',insertion) ).
thf(64,axiom,
! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',continuity2) ).
thf(66,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/sandbox2/benchmark/theBenchmark.p',continuity1) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',euclid3) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',euclid2) ).
thf(69,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/sandbox2/benchmark/theBenchmark.p',euclid1) ).
thf(70,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/sandbox2/benchmark/theBenchmark.p',upper_dimension) ).
thf(71,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(72,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(73,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',inner_pasch2) ).
thf(75,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/sandbox2/benchmark/theBenchmark.p',inner_pasch1) ).
thf(76,axiom,
! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(77,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/sandbox2/benchmark/theBenchmark.p',outer_five_segment) ).
thf(78,axiom,
! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).
thf(79,axiom,
! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).
thf(80,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(81,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/sandbox2/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
thf(82,axiom,
! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(83,axiom,
equidistant @ u @ v @ u @ w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_u_to_w) ).
thf(84,axiom,
between @ u @ v @ w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
thf(85,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(86,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[85]) ).
thf(87,negated_conjecture,
v != w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_equals_w) ).
thf(88,plain,
$false = $false,
inference(unfold_def,[status(thm)],[86]) ).
thf(89,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)],[1]) ).
thf(90,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)],[2]) ).
thf(91,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)],[3]) ).
thf(92,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)],[4]) ).
thf(93,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)],[5]) ).
thf(94,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)],[6]) ).
thf(95,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)],[7]) ).
thf(96,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)],[8]) ).
thf(97,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( V
= ( insertion @ U @ W @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(98,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)],[10]) ).
thf(99,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)],[11]) ).
thf(100,plain,
( ( ! [U: $i,V: $i,U1: $i,W1: $i] : ( equidistant @ U @ V @ U1 @ ( insertion @ U1 @ W1 @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(101,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)],[13]) ).
thf(102,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)],[14]) ).
thf(103,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)],[15]) ).
thf(104,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)],[16]) ).
thf(105,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)],[17]) ).
thf(106,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)],[18]) ).
thf(107,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)],[19]) ).
thf(108,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)],[20]) ).
thf(109,plain,
( ( ! [V: $i,U: $i] :
( V
!= ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(110,plain,
( ( lower_dimension_point_1 != lower_dimension_point_3 )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(111,plain,
( ( lower_dimension_point_2 != lower_dimension_point_3 )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(112,plain,
( ( lower_dimension_point_1 != lower_dimension_point_2 )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(113,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)],[25]) ).
thf(114,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)],[26]) ).
thf(115,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)],[27]) ).
thf(116,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)],[28]) ).
thf(117,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)],[29]) ).
thf(118,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)],[30]) ).
thf(119,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)],[31]) ).
thf(120,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)],[32]) ).
thf(121,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(122,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(123,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(124,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(125,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)],[37]) ).
thf(126,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(127,plain,
( ( ! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(128,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(129,plain,
( ( ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(130,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)],[42]) ).
thf(131,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)],[43]) ).
thf(132,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)],[44]) ).
thf(133,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)],[45]) ).
thf(134,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(135,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(136,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(137,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(138,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(139,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(140,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)],[52]) ).
thf(141,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(142,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)],[54]) ).
thf(143,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)],[55]) ).
thf(144,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)],[56]) ).
thf(145,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)],[57]) ).
thf(146,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)],[58]) ).
thf(147,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)],[59]) ).
thf(148,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)],[60]) ).
thf(149,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)],[61]) ).
thf(150,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(151,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)],[63]) ).
thf(152,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(153,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)],[65]) ).
thf(154,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)],[66]) ).
thf(155,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)],[67]) ).
thf(156,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)],[68]) ).
thf(157,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)],[69]) ).
thf(158,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)],[70]) ).
thf(159,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(160,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[72]) ).
thf(161,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(162,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)],[74]) ).
thf(163,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)],[75]) ).
thf(164,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[76]) ).
thf(165,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)],[77]) ).
thf(166,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[78]) ).
thf(167,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[79]) ).
thf(168,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[80]) ).
thf(169,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)],[81]) ).
thf(170,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[82]) ).
thf(171,plain,
( ( equidistant @ u @ v @ u @ w )
= $true ),
inference(unfold_def,[status(thm)],[83]) ).
thf(172,plain,
( ( between @ u @ v @ w )
= $true ),
inference(unfold_def,[status(thm)],[84]) ).
thf(173,plain,
( ( v != w )
= $true ),
inference(unfold_def,[status(thm)],[87]) ).
thf(174,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[88]) ).
thf(175,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)],[89]) ).
thf(176,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)],[90]) ).
thf(177,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)],[91]) ).
thf(178,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)],[92]) ).
thf(179,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)],[93]) ).
thf(180,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)],[94]) ).
thf(181,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)],[95]) ).
thf(182,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)],[96]) ).
thf(183,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)],[98]) ).
thf(184,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)],[99]) ).
thf(185,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)],[101]) ).
thf(186,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)],[102]) ).
thf(187,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)],[103]) ).
thf(188,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)],[104]) ).
thf(189,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)],[105]) ).
thf(190,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)],[106]) ).
thf(191,plain,
( ( ! [V: $i,U: $i] :
( V
!= ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(192,plain,
( ( lower_dimension_point_1 != lower_dimension_point_3 )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(193,plain,
( ( lower_dimension_point_2 != lower_dimension_point_3 )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(194,plain,
( ( lower_dimension_point_1 != lower_dimension_point_2 )
= $true ),
inference(extcnf_combined,[status(esa)],[112]) ).
thf(195,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)],[113]) ).
thf(196,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)],[114]) ).
thf(197,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)],[115]) ).
thf(198,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)],[116]) ).
thf(199,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)],[117]) ).
thf(200,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)],[118]) ).
thf(201,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)],[125]) ).
thf(202,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)],[130]) ).
thf(203,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)],[132]) ).
thf(204,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)],[133]) ).
thf(205,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[135]) ).
thf(206,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[137]) ).
thf(207,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)],[140]) ).
thf(208,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)],[142]) ).
thf(209,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)],[153]) ).
thf(210,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)],[154]) ).
thf(211,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)],[155]) ).
thf(212,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)],[156]) ).
thf(213,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)],[157]) ).
thf(214,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)],[158]) ).
thf(215,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)],[162]) ).
thf(216,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)],[163]) ).
thf(217,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)],[165]) ).
thf(218,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[168]) ).
thf(219,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)],[169]) ).
thf(220,plain,
( ( v != w )
= $true ),
inference(extcnf_combined,[status(esa)],[173]) ).
thf(221,plain,
( ( v != w )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(222,plain,
( ( between @ u @ v @ w )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(223,plain,
( ( equidistant @ u @ v @ u @ w )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(224,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(225,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)],[219]) ).
thf(226,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(227,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[167]) ).
thf(228,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[166]) ).
thf(229,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)],[217]) ).
thf(230,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[164]) ).
thf(231,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)],[216]) ).
thf(232,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)],[215]) ).
thf(233,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[161]) ).
thf(234,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(copy,[status(thm)],[160]) ).
thf(235,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(copy,[status(thm)],[159]) ).
thf(236,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)],[214]) ).
thf(237,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)],[213]) ).
thf(238,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)],[212]) ).
thf(239,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)],[211]) ).
thf(240,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)],[210]) ).
thf(241,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)],[209]) ).
thf(242,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(243,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)],[151]) ).
thf(244,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(245,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(246,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(247,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(248,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(249,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(250,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(251,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(252,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)],[208]) ).
thf(253,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(254,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)],[207]) ).
thf(255,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(256,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(257,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(258,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(259,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(260,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(261,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)],[204]) ).
thf(262,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)],[203]) ).
thf(263,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( U = V )
| ( W
= ( extension @ U @ V @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(264,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)],[202]) ).
thf(265,plain,
( ( ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(266,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(267,plain,
( ( ! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(268,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(269,plain,
( ( ! [U: $i,W: $i,X: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ! [V: $i] : ( between @ V @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(270,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(271,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(272,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(273,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(274,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(275,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( U = V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(276,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)],[200]) ).
thf(277,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)],[199]) ).
thf(278,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)],[198]) ).
thf(279,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)],[197]) ).
thf(280,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)],[196]) ).
thf(281,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)],[195]) ).
thf(282,plain,
( ( lower_dimension_point_1 != lower_dimension_point_2 )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(283,plain,
( ( lower_dimension_point_2 != lower_dimension_point_3 )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(284,plain,
( ( lower_dimension_point_1 != lower_dimension_point_3 )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(285,plain,
( ( ! [V: $i,U: $i] :
( V
!= ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(286,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)],[108]) ).
thf(287,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(288,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)],[190]) ).
thf(289,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)],[189]) ).
thf(290,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)],[188]) ).
thf(291,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)],[187]) ).
thf(292,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)],[186]) ).
thf(293,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)],[185]) ).
thf(294,plain,
( ( ! [U: $i,V: $i,U1: $i,W1: $i] : ( equidistant @ U @ V @ U1 @ ( insertion @ U1 @ W1 @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(295,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)],[184]) ).
thf(296,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)],[183]) ).
thf(297,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( V
= ( insertion @ U @ W @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(298,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)],[182]) ).
thf(299,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)],[181]) ).
thf(300,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)],[180]) ).
thf(301,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)],[179]) ).
thf(302,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)],[178]) ).
thf(303,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)],[177]) ).
thf(304,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)],[176]) ).
thf(305,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)],[175]) ).
thf(306,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[174]) ).
thf(307,plain,
( ( v = w )
= $false ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(308,plain,
! [SV1: $i] :
( ( ! [SY302: $i] : ( equidistant @ SV1 @ SY302 @ SY302 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(309,plain,
! [SV2: $i] :
( ( ! [SY303: $i,SY304: $i,SY305: $i] :
( ~ ( equidistant @ SV2 @ SY303 @ SY304 @ SY305 )
| ! [SY306: $i,SY307: $i] :
( ~ ( equidistant @ SV2 @ SY303 @ SY306 @ SY307 )
| ( equidistant @ SY304 @ SY305 @ SY306 @ SY307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(310,plain,
! [SV3: $i] :
( ( ! [SY308: $i] :
( ! [SY309: $i] :
~ ( equidistant @ SV3 @ SY308 @ SY309 @ SY309 )
| ( SV3 = SY308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(311,plain,
! [SV4: $i] :
( ( ! [SY310: $i,SY311: $i,SY312: $i] : ( between @ SV4 @ SY310 @ ( extension @ SV4 @ SY310 @ SY311 @ SY312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(312,plain,
! [SV5: $i] :
( ( ! [SY313: $i,SY314: $i,SY315: $i] : ( equidistant @ SV5 @ ( extension @ SY313 @ SV5 @ SY314 @ SY315 ) @ SY314 @ SY315 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(313,plain,
! [SV6: $i] :
( ( ! [SY316: $i,SY317: $i,SY318: $i,SY319: $i,SY320: $i] :
( ~ ( equidistant @ SV6 @ SY316 @ SY317 @ SY318 )
| ~ ( equidistant @ SY316 @ SY319 @ SY318 @ SY320 )
| ! [SY321: $i,SY322: $i] :
( ~ ( equidistant @ SV6 @ SY321 @ SY317 @ SY322 )
| ~ ( equidistant @ SY316 @ SY321 @ SY318 @ SY322 )
| ~ ( between @ SV6 @ SY316 @ SY319 )
| ~ ( between @ SY317 @ SY318 @ SY320 )
| ( SV6 = SY316 )
| ( equidistant @ SY319 @ SY321 @ SY320 @ SY322 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(314,plain,
! [SV7: $i] :
( ( ! [SY323: $i] :
( ~ ( between @ SV7 @ SY323 @ SV7 )
| ( SV7 = SY323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(315,plain,
! [SV8: $i] :
( ( ! [SY324: $i,SY325: $i] :
( ~ ( between @ SV8 @ SY324 @ SY325 )
| ! [SY326: $i,SY327: $i] :
( ~ ( between @ SY326 @ SY327 @ SY325 )
| ( between @ SY324 @ ( inner_pasch @ SV8 @ SY324 @ SY325 @ SY327 @ SY326 ) @ SY326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(316,plain,
! [SV9: $i] :
( ( ! [SY328: $i,SY329: $i] :
( ~ ( between @ SV9 @ SY328 @ SY329 )
| ! [SY330: $i,SY331: $i] :
( ~ ( between @ SY330 @ SY331 @ SY329 )
| ( between @ SY331 @ ( inner_pasch @ SV9 @ SY328 @ SY329 @ SY331 @ SY330 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(317,plain,
( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(318,plain,
( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(319,plain,
( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(320,plain,
! [SV10: $i] :
( ( ! [SY332: $i,SY333: $i] :
( ~ ( equidistant @ SV10 @ SY332 @ SV10 @ SY333 )
| ! [SY334: $i] :
( ~ ( equidistant @ SY334 @ SY332 @ SY334 @ SY333 )
| ! [SY335: $i] :
( ~ ( equidistant @ SY335 @ SY332 @ SY335 @ SY333 )
| ( between @ SV10 @ SY334 @ SY335 )
| ( between @ SY334 @ SY335 @ SV10 )
| ( SY332 = SY333 )
| ( between @ SY335 @ SV10 @ SY334 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(321,plain,
! [SV11: $i] :
( ( ! [SY336: $i,SY337: $i] :
( ~ ( between @ SV11 @ SY336 @ SY337 )
| ! [SY338: $i,SY339: $i] :
( ~ ( between @ SY338 @ SY336 @ SY339 )
| ( SV11 = SY336 )
| ( between @ SV11 @ SY338 @ ( euclid1 @ SV11 @ SY338 @ SY336 @ SY339 @ SY337 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(322,plain,
! [SV12: $i] :
( ( ! [SY340: $i,SY341: $i] :
( ~ ( between @ SV12 @ SY340 @ SY341 )
| ! [SY342: $i,SY343: $i] :
( ~ ( between @ SY342 @ SY340 @ SY343 )
| ( SV12 = SY340 )
| ( between @ SV12 @ SY343 @ ( euclid2 @ SV12 @ SY342 @ SY340 @ SY343 @ SY341 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(323,plain,
! [SV13: $i] :
( ( ! [SY344: $i,SY345: $i] :
( ~ ( between @ SV13 @ SY344 @ SY345 )
| ! [SY346: $i,SY347: $i] :
( ~ ( between @ SY346 @ SY344 @ SY347 )
| ( SV13 = SY344 )
| ( between @ ( euclid1 @ SV13 @ SY346 @ SY344 @ SY347 @ SY345 ) @ SY345 @ ( euclid2 @ SV13 @ SY346 @ SY344 @ SY347 @ SY345 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(324,plain,
! [SV14: $i] :
( ( ! [SY348: $i,SY349: $i,SY350: $i] :
( ~ ( equidistant @ SV14 @ SY348 @ SV14 @ SY349 )
| ! [SY351: $i] :
( ~ ( equidistant @ SV14 @ SY350 @ SV14 @ SY351 )
| ~ ( between @ SV14 @ SY348 @ SY350 )
| ! [SY352: $i] :
( ~ ( between @ SY348 @ SY352 @ SY350 )
| ( between @ SY349 @ ( continuous @ SV14 @ SY348 @ SY349 @ SY352 @ SY350 @ SY351 ) @ SY351 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(325,plain,
! [SV15: $i] :
( ( ! [SY353: $i,SY354: $i,SY355: $i] :
( ~ ( equidistant @ SV15 @ SY353 @ SV15 @ SY354 )
| ! [SY356: $i] :
( ~ ( equidistant @ SV15 @ SY355 @ SV15 @ SY356 )
| ~ ( between @ SV15 @ SY353 @ SY355 )
| ! [SY357: $i] :
( ~ ( between @ SY353 @ SY357 @ SY355 )
| ( equidistant @ SV15 @ SY357 @ SV15 @ ( continuous @ SV15 @ SY353 @ SY354 @ SY357 @ SY355 @ SY356 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(326,plain,
! [SV16: $i] :
( ( ! [SY358: $i] :
( ( reflection @ SV16 @ SY358 )
= ( extension @ SV16 @ SY358 @ SV16 @ SY358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(327,plain,
! [SV17: $i] :
( ( ! [SY359: $i,SY360: $i,SY361: $i] :
( ( insertion @ SV17 @ SY359 @ SY360 @ SY361 )
= ( extension @ ( extension @ SY359 @ SV17 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV17 @ SY360 @ SY361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(328,plain,
! [SV18: $i] :
( ( ! [SY362: $i] : ( equidistant @ SV18 @ SY362 @ SV18 @ SY362 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(329,plain,
! [SV19: $i] :
( ( ! [SY363: $i,SY364: $i,SY365: $i] :
( ~ ( equidistant @ SV19 @ SY363 @ SY364 @ SY365 )
| ( equidistant @ SY364 @ SY365 @ SV19 @ SY363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(330,plain,
! [SV20: $i] :
( ( ! [SY366: $i,SY367: $i,SY368: $i] :
( ~ ( equidistant @ SV20 @ SY366 @ SY367 @ SY368 )
| ( equidistant @ SY366 @ SV20 @ SY367 @ SY368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(331,plain,
! [SV21: $i] :
( ( ! [SY369: $i,SY370: $i,SY371: $i] :
( ~ ( equidistant @ SV21 @ SY369 @ SY370 @ SY371 )
| ( equidistant @ SV21 @ SY369 @ SY371 @ SY370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(332,plain,
! [SV22: $i] :
( ( ! [SY372: $i,SY373: $i,SY374: $i] :
( ~ ( equidistant @ SV22 @ SY372 @ SY373 @ SY374 )
| ( equidistant @ SY372 @ SV22 @ SY374 @ SY373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(333,plain,
! [SV23: $i] :
( ( ! [SY375: $i,SY376: $i,SY377: $i] :
( ~ ( equidistant @ SV23 @ SY375 @ SY376 @ SY377 )
| ( equidistant @ SY376 @ SY377 @ SY375 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(334,plain,
! [SV24: $i] :
( ( ! [SY378: $i,SY379: $i,SY380: $i] :
( ~ ( equidistant @ SV24 @ SY378 @ SY379 @ SY380 )
| ( equidistant @ SY380 @ SY379 @ SV24 @ SY378 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(335,plain,
! [SV25: $i] :
( ( ! [SY381: $i,SY382: $i,SY383: $i] :
( ~ ( equidistant @ SV25 @ SY381 @ SY382 @ SY383 )
| ( equidistant @ SY383 @ SY382 @ SY381 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(336,plain,
! [SV26: $i] :
( ( ! [SY384: $i,SY385: $i,SY386: $i] :
( ~ ( equidistant @ SV26 @ SY384 @ SY385 @ SY386 )
| ! [SY387: $i,SY388: $i] :
( ~ ( equidistant @ SY385 @ SY386 @ SY387 @ SY388 )
| ( equidistant @ SV26 @ SY384 @ SY387 @ SY388 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(337,plain,
! [SV27: $i] :
( ( ! [SY389: $i,SY390: $i] :
( SV27
= ( extension @ SY389 @ SV27 @ SY390 @ SY390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(338,plain,
! [SV28: $i] :
( ( ! [SY391: $i,SY392: $i] :
( ! [SY393: $i,SY394: $i] :
( SV28
!= ( extension @ SY391 @ SY392 @ SY393 @ SY394 ) )
| ( between @ SY391 @ SY392 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(339,plain,
! [SV29: $i] :
( ( ! [SY395: $i] : ( between @ SV29 @ SY395 @ ( reflection @ SV29 @ SY395 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(340,plain,
! [SV30: $i] :
( ( ! [SY396: $i] : ( equidistant @ SV30 @ ( reflection @ SY396 @ SV30 ) @ SY396 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(341,plain,
! [SV31: $i] :
( ( ! [SY397: $i] :
( ( SV31 != SY397 )
| ( SY397
= ( reflection @ SV31 @ SY397 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(342,plain,
! [SV32: $i] :
( ( SV32
= ( reflection @ SV32 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(343,plain,
! [SV33: $i] :
( ( ! [SY398: $i] :
( ( SV33
!= ( reflection @ SY398 @ SV33 ) )
| ( SY398 = SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(344,plain,
! [SV34: $i] :
( ( ! [SY399: $i] : ( equidistant @ SV34 @ SV34 @ SY399 @ SY399 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(345,plain,
! [SV35: $i] :
( ( ! [SY400: $i,SY401: $i,SY402: $i] :
( ~ ( equidistant @ SV35 @ SY400 @ SY401 @ SY402 )
| ! [SY403: $i,SY404: $i] :
( ~ ( equidistant @ SY400 @ SY403 @ SY402 @ SY404 )
| ~ ( between @ SV35 @ SY400 @ SY403 )
| ~ ( between @ SY401 @ SY402 @ SY404 )
| ( equidistant @ SV35 @ SY403 @ SY401 @ SY404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(346,plain,
! [SV36: $i] :
( ( ! [SY405: $i,SY406: $i] :
( ~ ( between @ SV36 @ SY405 @ SY406 )
| ! [SY407: $i] :
( ~ ( between @ SV36 @ SY405 @ SY407 )
| ~ ( equidistant @ SY405 @ SY406 @ SY405 @ SY407 )
| ( SV36 = SY405 )
| ( SY406 = SY407 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(347,plain,
! [SV37: $i] :
( ( ! [SY408: $i,SY409: $i] :
( ~ ( between @ SV37 @ SY408 @ SY409 )
| ( SV37 = SY408 )
| ( SY409
= ( extension @ SV37 @ SY408 @ SY408 @ SY409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(348,plain,
! [SV38: $i] :
( ( ! [SY410: $i,SY411: $i,SY412: $i] :
( ~ ( equidistant @ SV38 @ SY410 @ SY411 @ SY412 )
| ! [SY413: $i,SY414: $i] :
( ( ( extension @ SY413 @ SY414 @ SV38 @ SY410 )
= ( extension @ SY413 @ SY414 @ SY411 @ SY412 ) )
| ( SY413 = SY414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(349,plain,
! [SV39: $i] :
( ( ! [SY415: $i] :
( ( ( extension @ SV39 @ SY415 @ SV39 @ SY415 )
= ( extension @ SV39 @ SY415 @ SY415 @ SV39 ) )
| ( SV39 = SY415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(350,plain,
! [SV40: $i] :
( ( ! [SY416: $i] : ( equidistant @ SV40 @ SY416 @ SV40 @ ( reflection @ ( reflection @ SY416 @ SV40 ) @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(351,plain,
! [SV41: $i] :
( ( ! [SY417: $i] :
( SV41
= ( reflection @ ( reflection @ SV41 @ SY417 ) @ SY417 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(352,plain,
! [SV42: $i] :
( ( ! [SY418: $i] : ( between @ SV42 @ SY418 @ SY418 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(353,plain,
! [SV43: $i] :
( ( ! [SY419: $i,SY420: $i] :
( ~ ( between @ SV43 @ SY419 @ SY420 )
| ( SV43 != SY420 )
| ! [V: $i] : ( between @ V @ SY419 @ SY420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(354,plain,
! [SV44: $i] :
( ( ! [SY422: $i,SY423: $i] :
( ~ ( between @ SV44 @ SY422 @ SY423 )
| ( between @ SY423 @ SY422 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(355,plain,
! [SV45: $i] :
( ( ! [SY424: $i] : ( between @ SV45 @ SV45 @ SY424 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(356,plain,
! [SV46: $i] :
( ( ! [SY425: $i,SY426: $i] :
( ~ ( between @ SV46 @ SY425 @ SY426 )
| ~ ( between @ SY425 @ SV46 @ SY426 )
| ( SV46 = SY425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(357,plain,
! [SV47: $i] :
( ( ! [SY427: $i,SY428: $i] :
( ~ ( between @ SV47 @ SY427 @ SY428 )
| ~ ( between @ SV47 @ SY428 @ SY427 )
| ( SY427 = SY428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(358,plain,
! [SV48: $i] :
( ( ! [SY429: $i,SY430: $i] :
( ~ ( between @ SV48 @ SY429 @ SY430 )
| ~ ( between @ SY429 @ SV48 @ SY430 )
| ( SV48 = SY429 )
| ( SY429 = SY430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(359,plain,
! [SV49: $i] :
( ( ! [SY431: $i,SY432: $i] :
( ~ ( between @ SV49 @ SY431 @ SY432 )
| ~ ( between @ SV49 @ SY432 @ SY431 )
| ( SV49 = SY431 )
| ( SY431 = SY432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(360,plain,
! [SV50: $i] :
( ( ! [SY433: $i,SY434: $i] :
( ~ ( between @ SV50 @ SY433 @ SY434 )
| ! [X: $i] :
~ ( between @ SY433 @ SY434 @ X )
| ( between @ SV50 @ SY433 @ SY434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(361,plain,
! [SV51: $i] :
( ( ! [SY436: $i,SY437: $i] :
( ~ ( between @ SV51 @ SY436 @ SY437 )
| ! [SY438: $i] :
( ~ ( between @ SV51 @ SY437 @ SY438 )
| ( between @ SY436 @ SY437 @ SY438 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(362,plain,
! [SV52: $i] :
( ( ! [SY439: $i,SY440: $i] :
( ~ ( between @ SV52 @ SY439 @ SY440 )
| ! [SY441: $i] :
( ~ ( between @ SY439 @ SY440 @ SY441 )
| ( SY439 = SY440 )
| ( between @ SV52 @ SY440 @ SY441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(363,plain,
! [SV53: $i] :
( ( ! [SY442: $i,SY443: $i] :
( ~ ( between @ SV53 @ SY442 @ SY443 )
| ! [SY444: $i] :
( ~ ( between @ SY442 @ SY443 @ SY444 )
| ( SY442 = SY443 )
| ( between @ SV53 @ SY442 @ SY444 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(364,plain,
! [SV54: $i] :
( ( ! [SY445: $i,SY446: $i] :
( ~ ( between @ SV54 @ SY445 @ SY446 )
| ! [SY447: $i] :
( ~ ( between @ SY445 @ SY447 @ SY446 )
| ( between @ SV54 @ SY447 @ SY446 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(365,plain,
! [SV55: $i] :
( ( ! [SY448: $i,SY449: $i] :
( ~ ( between @ SV55 @ SY448 @ SY449 )
| ! [SY450: $i] :
( ~ ( between @ SV55 @ SY449 @ SY450 )
| ( between @ SV55 @ SY448 @ SY450 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(366,plain,
( ( lower_dimension_point_1 = lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(367,plain,
( ( lower_dimension_point_2 = lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(368,plain,
( ( lower_dimension_point_1 = lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(369,plain,
! [SV56: $i] :
( ( ! [SY451: $i] :
( SV56
!= ( extension @ SY451 @ SV56 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(370,plain,
! [SV57: $i] :
( ( ! [SY452: $i,SY453: $i,SY454: $i] : ( equidistant @ SV57 @ ( extension @ SY452 @ SV57 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SY453 @ ( extension @ SY454 @ SY453 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(371,plain,
! [SV58: $i] :
( ( ! [SY455: $i] : ( between @ SV58 @ SY455 @ ( extension @ SV58 @ SY455 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(372,plain,
! [SV59: $i] :
( ( ! [SY456: $i,SY457: $i,SY458: $i] :
( ~ ( between @ SV59 @ SY456 @ SY457 )
| ! [SY459: $i] :
( ~ ( between @ SY458 @ SY459 @ SY457 )
| ! [SY460: $i] :
( ~ ( between @ SV59 @ SY460 @ SY458 )
| ( between @ SY460 @ ( inner_pasch @ SY459 @ ( inner_pasch @ SV59 @ SY460 @ SY458 @ SY459 @ SY457 ) @ SV59 @ SY456 @ SY457 ) @ SY457 )
| ( between @ SY456 @ ( inner_pasch @ SY459 @ ( inner_pasch @ SV59 @ SY460 @ SY458 @ SY459 @ SY457 ) @ SV59 @ SY456 @ SY457 ) @ SY459 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(373,plain,
! [SV60: $i] :
( ( ! [SY461: $i,SY462: $i] :
( ~ ( between @ SV60 @ SY461 @ SY462 )
| ! [SY463: $i] :
( ~ ( equidistant @ SV60 @ SY462 @ SV60 @ SY463 )
| ~ ( equidistant @ SY461 @ SY462 @ SY461 @ SY463 )
| ( SV60 = SY461 )
| ( SY462 = SY463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(374,plain,
! [SV61: $i] :
( ( ! [SY464: $i,SY465: $i,SY466: $i,SY467: $i,SY468: $i] :
( ~ ( equidistant @ SV61 @ SY464 @ SY465 @ SY466 )
| ~ ( equidistant @ SV61 @ SY467 @ SY465 @ SY468 )
| ! [SY469: $i,SY470: $i] :
( ~ ( equidistant @ SV61 @ SY469 @ SY465 @ SY470 )
| ~ ( equidistant @ SY467 @ SY469 @ SY468 @ SY470 )
| ~ ( between @ SV61 @ SY464 @ SY467 )
| ~ ( between @ SY465 @ SY466 @ SY468 )
| ( equidistant @ SY464 @ SY469 @ SY466 @ SY470 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(375,plain,
! [SV62: $i] :
( ( ! [SY471: $i,SY472: $i,SY473: $i] :
( ~ ( between @ SV62 @ SY471 @ SY472 )
| ! [SY474: $i,SY475: $i] :
( ~ ( between @ SY473 @ SY474 @ SY475 )
| ~ ( equidistant @ SV62 @ SY471 @ SY473 @ SY474 )
| ~ ( equidistant @ SV62 @ SY472 @ SY473 @ SY475 )
| ( equidistant @ SY471 @ SY472 @ SY474 @ SY475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(376,plain,
! [SV63: $i] :
( ( ! [SY476: $i,SY477: $i,SY478: $i,SY479: $i,SY480: $i] :
( ~ ( equidistant @ SV63 @ SY476 @ SY477 @ SY478 )
| ~ ( equidistant @ SY476 @ SY479 @ SY478 @ SY480 )
| ! [SY481: $i,SY482: $i] :
( ~ ( equidistant @ SV63 @ SY481 @ SY477 @ SY482 )
| ~ ( equidistant @ SY479 @ SY481 @ SY480 @ SY482 )
| ~ ( between @ SV63 @ SY476 @ SY479 )
| ~ ( between @ SY477 @ SY478 @ SY480 )
| ( equidistant @ SY476 @ SY481 @ SY478 @ SY482 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(377,plain,
! [SV64: $i] :
( ( ! [SY483: $i,SY484: $i] :
( ~ ( between @ SV64 @ SY483 @ SY484 )
| ! [SY485: $i] :
( ~ ( equidistant @ SV64 @ SY483 @ SV64 @ SY485 )
| ~ ( equidistant @ SY484 @ SY483 @ SY484 @ SY485 )
| ( SY483 = SY485 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(378,plain,
! [SV65: $i] :
( ( ! [SY486: $i,SY487: $i,SY488: $i] : ( equidistant @ SV65 @ SY486 @ SY487 @ ( insertion @ SY487 @ SY488 @ SV65 @ SY486 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(379,plain,
! [SV66: $i] :
( ( ! [SY489: $i,SY490: $i] :
( ~ ( between @ SV66 @ SY489 @ SY490 )
| ! [SY491: $i,SY492: $i] :
( ~ ( equidistant @ SV66 @ SY490 @ SY491 @ SY492 )
| ( between @ SY491 @ ( insertion @ SY491 @ SY492 @ SV66 @ SY489 ) @ SY492 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(380,plain,
! [SV67: $i] :
( ( ! [SY493: $i,SY494: $i] :
( ~ ( between @ SV67 @ SY493 @ SY494 )
| ! [SY495: $i,SY496: $i] :
( ~ ( equidistant @ SV67 @ SY494 @ SY495 @ SY496 )
| ( equidistant @ SY493 @ SY494 @ ( insertion @ SY495 @ SY496 @ SV67 @ SY493 ) @ SY496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(381,plain,
! [SV68: $i] :
( ( ! [SY497: $i,SY498: $i] :
( ~ ( between @ SV68 @ SY497 @ SY498 )
| ( SY497
= ( insertion @ SV68 @ SY498 @ SV68 @ SY497 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(382,plain,
! [SV69: $i] :
( ( ! [SY499: $i,SY500: $i,SY501: $i] :
( ~ ( equidistant @ SV69 @ SY499 @ SY500 @ SY501 )
| ! [SY502: $i,SY503: $i] :
( ( insertion @ SY502 @ SY503 @ SV69 @ SY499 )
= ( insertion @ SY502 @ SY503 @ SY500 @ SY501 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(383,plain,
! [SV70: $i] :
( ( ! [SY504: $i,SY505: $i,SY506: $i] :
( ~ ( equidistant @ SV70 @ SY504 @ SY505 @ SY506 )
| ! [SY507: $i,SY508: $i] :
( ~ ( equidistant @ SY504 @ SY507 @ SY506 @ SY508 )
| ~ ( equidistant @ SV70 @ SY507 @ SY505 @ SY508 )
| ~ ( between @ SV70 @ SY504 @ SY507 )
| ( between @ SY505 @ SY506 @ SY508 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(384,plain,
! [SV71: $i] :
( ( ! [SY509: $i,SY510: $i] :
( ~ ( between @ SV71 @ SY509 @ SY510 )
| ! [SY511: $i] :
( ~ ( between @ SV71 @ SY509 @ SY511 )
| ( SV71 = SY509 )
| ( between @ SV71 @ SY510 @ SY511 )
| ( between @ SV71 @ SY511 @ SY510 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(385,plain,
! [SV72: $i] :
( ( ! [SY512: $i,SY513: $i] :
( ~ ( between @ SV72 @ SY512 @ SY513 )
| ! [SY514: $i] :
( ~ ( between @ SV72 @ SY512 @ SY514 )
| ( SV72 = SY512 )
| ( between @ SY512 @ SY513 @ SY514 )
| ( between @ SY512 @ SY514 @ SY513 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(386,plain,
! [SV73: $i] :
( ( ! [SY515: $i,SY516: $i] :
( ~ ( between @ SV73 @ SY515 @ SY516 )
| ! [SY517: $i] :
( ~ ( between @ SY517 @ SY515 @ SY516 )
| ( SY515 = SY516 )
| ( between @ SV73 @ SY517 @ SY515 )
| ( between @ SY517 @ SV73 @ SY515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(387,plain,
! [SV74: $i] :
( ( ! [SY518: $i,SY519: $i] :
( ~ ( between @ SV74 @ SY518 @ SY519 )
| ! [SY520: $i] :
( ~ ( between @ SV74 @ SY520 @ SY519 )
| ( between @ SV74 @ SY518 @ SY520 )
| ( between @ SV74 @ SY520 @ SY518 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(388,plain,
! [SV75: $i] :
( ( ! [SY521: $i,SY522: $i] :
( ~ ( between @ SV75 @ SY521 @ SY522 )
| ! [SY523: $i] :
( ~ ( between @ SV75 @ SY523 @ SY522 )
| ( between @ SY521 @ SY523 @ SY522 )
| ( between @ SY523 @ SY521 @ SY522 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(389,plain,
! [SV76: $i] :
( ( ! [SY524: $i,SY525: $i] :
( ~ ( between @ SV76 @ SY524 @ SY525 )
| ! [SY526: $i,SY527: $i] :
( ~ ( between @ SY524 @ SY526 @ SY527 )
| ~ ( between @ SV76 @ SY527 @ SY525 )
| ( between @ SV76 @ SY526 @ SY525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(390,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(391,plain,
! [SV77: $i,SV1: $i] :
( ( equidistant @ SV1 @ SV77 @ SV77 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(392,plain,
! [SV78: $i,SV2: $i] :
( ( ! [SY528: $i,SY529: $i] :
( ~ ( equidistant @ SV2 @ SV78 @ SY528 @ SY529 )
| ! [SY530: $i,SY531: $i] :
( ~ ( equidistant @ SV2 @ SV78 @ SY530 @ SY531 )
| ( equidistant @ SY528 @ SY529 @ SY530 @ SY531 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(393,plain,
! [SV79: $i,SV3: $i] :
( ( ! [SY532: $i] :
~ ( equidistant @ SV3 @ SV79 @ SY532 @ SY532 )
| ( SV3 = SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(394,plain,
! [SV80: $i,SV4: $i] :
( ( ! [SY533: $i,SY534: $i] : ( between @ SV4 @ SV80 @ ( extension @ SV4 @ SV80 @ SY533 @ SY534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(395,plain,
! [SV81: $i,SV5: $i] :
( ( ! [SY535: $i,SY536: $i] : ( equidistant @ SV5 @ ( extension @ SV81 @ SV5 @ SY535 @ SY536 ) @ SY535 @ SY536 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(396,plain,
! [SV82: $i,SV6: $i] :
( ( ! [SY537: $i,SY538: $i,SY539: $i,SY540: $i] :
( ~ ( equidistant @ SV6 @ SV82 @ SY537 @ SY538 )
| ~ ( equidistant @ SV82 @ SY539 @ SY538 @ SY540 )
| ! [SY541: $i,SY542: $i] :
( ~ ( equidistant @ SV6 @ SY541 @ SY537 @ SY542 )
| ~ ( equidistant @ SV82 @ SY541 @ SY538 @ SY542 )
| ~ ( between @ SV6 @ SV82 @ SY539 )
| ~ ( between @ SY537 @ SY538 @ SY540 )
| ( SV6 = SV82 )
| ( equidistant @ SY539 @ SY541 @ SY540 @ SY542 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(397,plain,
! [SV83: $i,SV7: $i] :
( ( ~ ( between @ SV7 @ SV83 @ SV7 )
| ( SV7 = SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(398,plain,
! [SV84: $i,SV8: $i] :
( ( ! [SY543: $i] :
( ~ ( between @ SV8 @ SV84 @ SY543 )
| ! [SY544: $i,SY545: $i] :
( ~ ( between @ SY544 @ SY545 @ SY543 )
| ( between @ SV84 @ ( inner_pasch @ SV8 @ SV84 @ SY543 @ SY545 @ SY544 ) @ SY544 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(399,plain,
! [SV85: $i,SV9: $i] :
( ( ! [SY546: $i] :
( ~ ( between @ SV9 @ SV85 @ SY546 )
| ! [SY547: $i,SY548: $i] :
( ~ ( between @ SY547 @ SY548 @ SY546 )
| ( between @ SY548 @ ( inner_pasch @ SV9 @ SV85 @ SY546 @ SY548 @ SY547 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(400,plain,
! [SV86: $i,SV10: $i] :
( ( ! [SY549: $i] :
( ~ ( equidistant @ SV10 @ SV86 @ SV10 @ SY549 )
| ! [SY550: $i] :
( ~ ( equidistant @ SY550 @ SV86 @ SY550 @ SY549 )
| ! [SY551: $i] :
( ~ ( equidistant @ SY551 @ SV86 @ SY551 @ SY549 )
| ( between @ SV10 @ SY550 @ SY551 )
| ( between @ SY550 @ SY551 @ SV10 )
| ( SV86 = SY549 )
| ( between @ SY551 @ SV10 @ SY550 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(401,plain,
! [SV87: $i,SV11: $i] :
( ( ! [SY552: $i] :
( ~ ( between @ SV11 @ SV87 @ SY552 )
| ! [SY553: $i,SY554: $i] :
( ~ ( between @ SY553 @ SV87 @ SY554 )
| ( SV11 = SV87 )
| ( between @ SV11 @ SY553 @ ( euclid1 @ SV11 @ SY553 @ SV87 @ SY554 @ SY552 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(402,plain,
! [SV88: $i,SV12: $i] :
( ( ! [SY555: $i] :
( ~ ( between @ SV12 @ SV88 @ SY555 )
| ! [SY556: $i,SY557: $i] :
( ~ ( between @ SY556 @ SV88 @ SY557 )
| ( SV12 = SV88 )
| ( between @ SV12 @ SY557 @ ( euclid2 @ SV12 @ SY556 @ SV88 @ SY557 @ SY555 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(403,plain,
! [SV89: $i,SV13: $i] :
( ( ! [SY558: $i] :
( ~ ( between @ SV13 @ SV89 @ SY558 )
| ! [SY559: $i,SY560: $i] :
( ~ ( between @ SY559 @ SV89 @ SY560 )
| ( SV13 = SV89 )
| ( between @ ( euclid1 @ SV13 @ SY559 @ SV89 @ SY560 @ SY558 ) @ SY558 @ ( euclid2 @ SV13 @ SY559 @ SV89 @ SY560 @ SY558 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(404,plain,
! [SV90: $i,SV14: $i] :
( ( ! [SY561: $i,SY562: $i] :
( ~ ( equidistant @ SV14 @ SV90 @ SV14 @ SY561 )
| ! [SY563: $i] :
( ~ ( equidistant @ SV14 @ SY562 @ SV14 @ SY563 )
| ~ ( between @ SV14 @ SV90 @ SY562 )
| ! [SY564: $i] :
( ~ ( between @ SV90 @ SY564 @ SY562 )
| ( between @ SY561 @ ( continuous @ SV14 @ SV90 @ SY561 @ SY564 @ SY562 @ SY563 ) @ SY563 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(405,plain,
! [SV91: $i,SV15: $i] :
( ( ! [SY565: $i,SY566: $i] :
( ~ ( equidistant @ SV15 @ SV91 @ SV15 @ SY565 )
| ! [SY567: $i] :
( ~ ( equidistant @ SV15 @ SY566 @ SV15 @ SY567 )
| ~ ( between @ SV15 @ SV91 @ SY566 )
| ! [SY568: $i] :
( ~ ( between @ SV91 @ SY568 @ SY566 )
| ( equidistant @ SV15 @ SY568 @ SV15 @ ( continuous @ SV15 @ SV91 @ SY565 @ SY568 @ SY566 @ SY567 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(406,plain,
! [SV92: $i,SV16: $i] :
( ( ( reflection @ SV16 @ SV92 )
= ( extension @ SV16 @ SV92 @ SV16 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(407,plain,
! [SV93: $i,SV17: $i] :
( ( ! [SY569: $i,SY570: $i] :
( ( insertion @ SV17 @ SV93 @ SY569 @ SY570 )
= ( extension @ ( extension @ SV93 @ SV17 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV17 @ SY569 @ SY570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(408,plain,
! [SV94: $i,SV18: $i] :
( ( equidistant @ SV18 @ SV94 @ SV18 @ SV94 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(409,plain,
! [SV95: $i,SV19: $i] :
( ( ! [SY571: $i,SY572: $i] :
( ~ ( equidistant @ SV19 @ SV95 @ SY571 @ SY572 )
| ( equidistant @ SY571 @ SY572 @ SV19 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(410,plain,
! [SV96: $i,SV20: $i] :
( ( ! [SY573: $i,SY574: $i] :
( ~ ( equidistant @ SV20 @ SV96 @ SY573 @ SY574 )
| ( equidistant @ SV96 @ SV20 @ SY573 @ SY574 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(411,plain,
! [SV97: $i,SV21: $i] :
( ( ! [SY575: $i,SY576: $i] :
( ~ ( equidistant @ SV21 @ SV97 @ SY575 @ SY576 )
| ( equidistant @ SV21 @ SV97 @ SY576 @ SY575 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(412,plain,
! [SV98: $i,SV22: $i] :
( ( ! [SY577: $i,SY578: $i] :
( ~ ( equidistant @ SV22 @ SV98 @ SY577 @ SY578 )
| ( equidistant @ SV98 @ SV22 @ SY578 @ SY577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(413,plain,
! [SV99: $i,SV23: $i] :
( ( ! [SY579: $i,SY580: $i] :
( ~ ( equidistant @ SV23 @ SV99 @ SY579 @ SY580 )
| ( equidistant @ SY579 @ SY580 @ SV99 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(414,plain,
! [SV100: $i,SV24: $i] :
( ( ! [SY581: $i,SY582: $i] :
( ~ ( equidistant @ SV24 @ SV100 @ SY581 @ SY582 )
| ( equidistant @ SY582 @ SY581 @ SV24 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(415,plain,
! [SV101: $i,SV25: $i] :
( ( ! [SY583: $i,SY584: $i] :
( ~ ( equidistant @ SV25 @ SV101 @ SY583 @ SY584 )
| ( equidistant @ SY584 @ SY583 @ SV101 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(416,plain,
! [SV102: $i,SV26: $i] :
( ( ! [SY585: $i,SY586: $i] :
( ~ ( equidistant @ SV26 @ SV102 @ SY585 @ SY586 )
| ! [SY587: $i,SY588: $i] :
( ~ ( equidistant @ SY585 @ SY586 @ SY587 @ SY588 )
| ( equidistant @ SV26 @ SV102 @ SY587 @ SY588 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(417,plain,
! [SV103: $i,SV27: $i] :
( ( ! [SY589: $i] :
( SV27
= ( extension @ SV103 @ SV27 @ SY589 @ SY589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(418,plain,
! [SV104: $i,SV28: $i] :
( ( ! [SY590: $i] :
( ! [SY591: $i,SY592: $i] :
( SV28
!= ( extension @ SV104 @ SY590 @ SY591 @ SY592 ) )
| ( between @ SV104 @ SY590 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(419,plain,
! [SV105: $i,SV29: $i] :
( ( between @ SV29 @ SV105 @ ( reflection @ SV29 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(420,plain,
! [SV106: $i,SV30: $i] :
( ( equidistant @ SV30 @ ( reflection @ SV106 @ SV30 ) @ SV106 @ SV30 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(421,plain,
! [SV107: $i,SV31: $i] :
( ( ( SV31 != SV107 )
| ( SV107
= ( reflection @ SV31 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(422,plain,
! [SV108: $i,SV33: $i] :
( ( ( SV33
!= ( reflection @ SV108 @ SV33 ) )
| ( SV108 = SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(423,plain,
! [SV109: $i,SV34: $i] :
( ( equidistant @ SV34 @ SV34 @ SV109 @ SV109 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(424,plain,
! [SV110: $i,SV35: $i] :
( ( ! [SY593: $i,SY594: $i] :
( ~ ( equidistant @ SV35 @ SV110 @ SY593 @ SY594 )
| ! [SY595: $i,SY596: $i] :
( ~ ( equidistant @ SV110 @ SY595 @ SY594 @ SY596 )
| ~ ( between @ SV35 @ SV110 @ SY595 )
| ~ ( between @ SY593 @ SY594 @ SY596 )
| ( equidistant @ SV35 @ SY595 @ SY593 @ SY596 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(425,plain,
! [SV111: $i,SV36: $i] :
( ( ! [SY597: $i] :
( ~ ( between @ SV36 @ SV111 @ SY597 )
| ! [SY598: $i] :
( ~ ( between @ SV36 @ SV111 @ SY598 )
| ~ ( equidistant @ SV111 @ SY597 @ SV111 @ SY598 )
| ( SV36 = SV111 )
| ( SY597 = SY598 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(426,plain,
! [SV112: $i,SV37: $i] :
( ( ! [SY599: $i] :
( ~ ( between @ SV37 @ SV112 @ SY599 )
| ( SV37 = SV112 )
| ( SY599
= ( extension @ SV37 @ SV112 @ SV112 @ SY599 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(427,plain,
! [SV113: $i,SV38: $i] :
( ( ! [SY600: $i,SY601: $i] :
( ~ ( equidistant @ SV38 @ SV113 @ SY600 @ SY601 )
| ! [SY602: $i,SY603: $i] :
( ( ( extension @ SY602 @ SY603 @ SV38 @ SV113 )
= ( extension @ SY602 @ SY603 @ SY600 @ SY601 ) )
| ( SY602 = SY603 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(428,plain,
! [SV114: $i,SV39: $i] :
( ( ( ( extension @ SV39 @ SV114 @ SV39 @ SV114 )
= ( extension @ SV39 @ SV114 @ SV114 @ SV39 ) )
| ( SV39 = SV114 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(429,plain,
! [SV115: $i,SV40: $i] :
( ( equidistant @ SV40 @ SV115 @ SV40 @ ( reflection @ ( reflection @ SV115 @ SV40 ) @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(430,plain,
! [SV116: $i,SV41: $i] :
( ( SV41
= ( reflection @ ( reflection @ SV41 @ SV116 ) @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(431,plain,
! [SV117: $i,SV42: $i] :
( ( between @ SV42 @ SV117 @ SV117 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(432,plain,
! [SV118: $i,SV43: $i] :
( ( ! [SY604: $i] :
( ~ ( between @ SV43 @ SV118 @ SY604 )
| ( SV43 != SY604 )
| ! [SY605: $i] : ( between @ SY605 @ SV118 @ SY604 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(433,plain,
! [SV119: $i,SV44: $i] :
( ( ! [SY606: $i] :
( ~ ( between @ SV44 @ SV119 @ SY606 )
| ( between @ SY606 @ SV119 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(434,plain,
! [SV120: $i,SV45: $i] :
( ( between @ SV45 @ SV45 @ SV120 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(435,plain,
! [SV121: $i,SV46: $i] :
( ( ! [SY607: $i] :
( ~ ( between @ SV46 @ SV121 @ SY607 )
| ~ ( between @ SV121 @ SV46 @ SY607 )
| ( SV46 = SV121 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(436,plain,
! [SV122: $i,SV47: $i] :
( ( ! [SY608: $i] :
( ~ ( between @ SV47 @ SV122 @ SY608 )
| ~ ( between @ SV47 @ SY608 @ SV122 )
| ( SV122 = SY608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(437,plain,
! [SV123: $i,SV48: $i] :
( ( ! [SY609: $i] :
( ~ ( between @ SV48 @ SV123 @ SY609 )
| ~ ( between @ SV123 @ SV48 @ SY609 )
| ( SV48 = SV123 )
| ( SV123 = SY609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(438,plain,
! [SV124: $i,SV49: $i] :
( ( ! [SY610: $i] :
( ~ ( between @ SV49 @ SV124 @ SY610 )
| ~ ( between @ SV49 @ SY610 @ SV124 )
| ( SV49 = SV124 )
| ( SV124 = SY610 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(439,plain,
! [SV125: $i,SV50: $i] :
( ( ! [SY611: $i] :
( ~ ( between @ SV50 @ SV125 @ SY611 )
| ! [SY612: $i] :
~ ( between @ SV125 @ SY611 @ SY612 )
| ( between @ SV50 @ SV125 @ SY611 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(440,plain,
! [SV126: $i,SV51: $i] :
( ( ! [SY613: $i] :
( ~ ( between @ SV51 @ SV126 @ SY613 )
| ! [SY614: $i] :
( ~ ( between @ SV51 @ SY613 @ SY614 )
| ( between @ SV126 @ SY613 @ SY614 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(441,plain,
! [SV127: $i,SV52: $i] :
( ( ! [SY615: $i] :
( ~ ( between @ SV52 @ SV127 @ SY615 )
| ! [SY616: $i] :
( ~ ( between @ SV127 @ SY615 @ SY616 )
| ( SV127 = SY615 )
| ( between @ SV52 @ SY615 @ SY616 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(442,plain,
! [SV128: $i,SV53: $i] :
( ( ! [SY617: $i] :
( ~ ( between @ SV53 @ SV128 @ SY617 )
| ! [SY618: $i] :
( ~ ( between @ SV128 @ SY617 @ SY618 )
| ( SV128 = SY617 )
| ( between @ SV53 @ SV128 @ SY618 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(443,plain,
! [SV129: $i,SV54: $i] :
( ( ! [SY619: $i] :
( ~ ( between @ SV54 @ SV129 @ SY619 )
| ! [SY620: $i] :
( ~ ( between @ SV129 @ SY620 @ SY619 )
| ( between @ SV54 @ SY620 @ SY619 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(444,plain,
! [SV130: $i,SV55: $i] :
( ( ! [SY621: $i] :
( ~ ( between @ SV55 @ SV130 @ SY621 )
| ! [SY622: $i] :
( ~ ( between @ SV55 @ SY621 @ SY622 )
| ( between @ SV55 @ SV130 @ SY622 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(445,plain,
! [SV131: $i,SV56: $i] :
( ( SV56
!= ( extension @ SV131 @ SV56 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(446,plain,
! [SV132: $i,SV57: $i] :
( ( ! [SY623: $i,SY624: $i] : ( equidistant @ SV57 @ ( extension @ SV132 @ SV57 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SY623 @ ( extension @ SY624 @ SY623 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(447,plain,
! [SV133: $i,SV58: $i] :
( ( between @ SV58 @ SV133 @ ( extension @ SV58 @ SV133 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(448,plain,
! [SV134: $i,SV59: $i] :
( ( ! [SY625: $i,SY626: $i] :
( ~ ( between @ SV59 @ SV134 @ SY625 )
| ! [SY627: $i] :
( ~ ( between @ SY626 @ SY627 @ SY625 )
| ! [SY628: $i] :
( ~ ( between @ SV59 @ SY628 @ SY626 )
| ( between @ SY628 @ ( inner_pasch @ SY627 @ ( inner_pasch @ SV59 @ SY628 @ SY626 @ SY627 @ SY625 ) @ SV59 @ SV134 @ SY625 ) @ SY625 )
| ( between @ SV134 @ ( inner_pasch @ SY627 @ ( inner_pasch @ SV59 @ SY628 @ SY626 @ SY627 @ SY625 ) @ SV59 @ SV134 @ SY625 ) @ SY627 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(449,plain,
! [SV135: $i,SV60: $i] :
( ( ! [SY629: $i] :
( ~ ( between @ SV60 @ SV135 @ SY629 )
| ! [SY630: $i] :
( ~ ( equidistant @ SV60 @ SY629 @ SV60 @ SY630 )
| ~ ( equidistant @ SV135 @ SY629 @ SV135 @ SY630 )
| ( SV60 = SV135 )
| ( SY629 = SY630 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(450,plain,
! [SV136: $i,SV61: $i] :
( ( ! [SY631: $i,SY632: $i,SY633: $i,SY634: $i] :
( ~ ( equidistant @ SV61 @ SV136 @ SY631 @ SY632 )
| ~ ( equidistant @ SV61 @ SY633 @ SY631 @ SY634 )
| ! [SY635: $i,SY636: $i] :
( ~ ( equidistant @ SV61 @ SY635 @ SY631 @ SY636 )
| ~ ( equidistant @ SY633 @ SY635 @ SY634 @ SY636 )
| ~ ( between @ SV61 @ SV136 @ SY633 )
| ~ ( between @ SY631 @ SY632 @ SY634 )
| ( equidistant @ SV136 @ SY635 @ SY632 @ SY636 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(451,plain,
! [SV137: $i,SV62: $i] :
( ( ! [SY637: $i,SY638: $i] :
( ~ ( between @ SV62 @ SV137 @ SY637 )
| ! [SY639: $i,SY640: $i] :
( ~ ( between @ SY638 @ SY639 @ SY640 )
| ~ ( equidistant @ SV62 @ SV137 @ SY638 @ SY639 )
| ~ ( equidistant @ SV62 @ SY637 @ SY638 @ SY640 )
| ( equidistant @ SV137 @ SY637 @ SY639 @ SY640 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(452,plain,
! [SV138: $i,SV63: $i] :
( ( ! [SY641: $i,SY642: $i,SY643: $i,SY644: $i] :
( ~ ( equidistant @ SV63 @ SV138 @ SY641 @ SY642 )
| ~ ( equidistant @ SV138 @ SY643 @ SY642 @ SY644 )
| ! [SY645: $i,SY646: $i] :
( ~ ( equidistant @ SV63 @ SY645 @ SY641 @ SY646 )
| ~ ( equidistant @ SY643 @ SY645 @ SY644 @ SY646 )
| ~ ( between @ SV63 @ SV138 @ SY643 )
| ~ ( between @ SY641 @ SY642 @ SY644 )
| ( equidistant @ SV138 @ SY645 @ SY642 @ SY646 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(453,plain,
! [SV139: $i,SV64: $i] :
( ( ! [SY647: $i] :
( ~ ( between @ SV64 @ SV139 @ SY647 )
| ! [SY648: $i] :
( ~ ( equidistant @ SV64 @ SV139 @ SV64 @ SY648 )
| ~ ( equidistant @ SY647 @ SV139 @ SY647 @ SY648 )
| ( SV139 = SY648 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(454,plain,
! [SV140: $i,SV65: $i] :
( ( ! [SY649: $i,SY650: $i] : ( equidistant @ SV65 @ SV140 @ SY649 @ ( insertion @ SY649 @ SY650 @ SV65 @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(455,plain,
! [SV141: $i,SV66: $i] :
( ( ! [SY651: $i] :
( ~ ( between @ SV66 @ SV141 @ SY651 )
| ! [SY652: $i,SY653: $i] :
( ~ ( equidistant @ SV66 @ SY651 @ SY652 @ SY653 )
| ( between @ SY652 @ ( insertion @ SY652 @ SY653 @ SV66 @ SV141 ) @ SY653 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(456,plain,
! [SV142: $i,SV67: $i] :
( ( ! [SY654: $i] :
( ~ ( between @ SV67 @ SV142 @ SY654 )
| ! [SY655: $i,SY656: $i] :
( ~ ( equidistant @ SV67 @ SY654 @ SY655 @ SY656 )
| ( equidistant @ SV142 @ SY654 @ ( insertion @ SY655 @ SY656 @ SV67 @ SV142 ) @ SY656 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(457,plain,
! [SV143: $i,SV68: $i] :
( ( ! [SY657: $i] :
( ~ ( between @ SV68 @ SV143 @ SY657 )
| ( SV143
= ( insertion @ SV68 @ SY657 @ SV68 @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(458,plain,
! [SV144: $i,SV69: $i] :
( ( ! [SY658: $i,SY659: $i] :
( ~ ( equidistant @ SV69 @ SV144 @ SY658 @ SY659 )
| ! [SY660: $i,SY661: $i] :
( ( insertion @ SY660 @ SY661 @ SV69 @ SV144 )
= ( insertion @ SY660 @ SY661 @ SY658 @ SY659 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(459,plain,
! [SV145: $i,SV70: $i] :
( ( ! [SY662: $i,SY663: $i] :
( ~ ( equidistant @ SV70 @ SV145 @ SY662 @ SY663 )
| ! [SY664: $i,SY665: $i] :
( ~ ( equidistant @ SV145 @ SY664 @ SY663 @ SY665 )
| ~ ( equidistant @ SV70 @ SY664 @ SY662 @ SY665 )
| ~ ( between @ SV70 @ SV145 @ SY664 )
| ( between @ SY662 @ SY663 @ SY665 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(460,plain,
! [SV146: $i,SV71: $i] :
( ( ! [SY666: $i] :
( ~ ( between @ SV71 @ SV146 @ SY666 )
| ! [SY667: $i] :
( ~ ( between @ SV71 @ SV146 @ SY667 )
| ( SV71 = SV146 )
| ( between @ SV71 @ SY666 @ SY667 )
| ( between @ SV71 @ SY667 @ SY666 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(461,plain,
! [SV147: $i,SV72: $i] :
( ( ! [SY668: $i] :
( ~ ( between @ SV72 @ SV147 @ SY668 )
| ! [SY669: $i] :
( ~ ( between @ SV72 @ SV147 @ SY669 )
| ( SV72 = SV147 )
| ( between @ SV147 @ SY668 @ SY669 )
| ( between @ SV147 @ SY669 @ SY668 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(462,plain,
! [SV148: $i,SV73: $i] :
( ( ! [SY670: $i] :
( ~ ( between @ SV73 @ SV148 @ SY670 )
| ! [SY671: $i] :
( ~ ( between @ SY671 @ SV148 @ SY670 )
| ( SV148 = SY670 )
| ( between @ SV73 @ SY671 @ SV148 )
| ( between @ SY671 @ SV73 @ SV148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(463,plain,
! [SV149: $i,SV74: $i] :
( ( ! [SY672: $i] :
( ~ ( between @ SV74 @ SV149 @ SY672 )
| ! [SY673: $i] :
( ~ ( between @ SV74 @ SY673 @ SY672 )
| ( between @ SV74 @ SV149 @ SY673 )
| ( between @ SV74 @ SY673 @ SV149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(464,plain,
! [SV150: $i,SV75: $i] :
( ( ! [SY674: $i] :
( ~ ( between @ SV75 @ SV150 @ SY674 )
| ! [SY675: $i] :
( ~ ( between @ SV75 @ SY675 @ SY674 )
| ( between @ SV150 @ SY675 @ SY674 )
| ( between @ SY675 @ SV150 @ SY674 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(465,plain,
! [SV151: $i,SV76: $i] :
( ( ! [SY676: $i] :
( ~ ( between @ SV76 @ SV151 @ SY676 )
| ! [SY677: $i,SY678: $i] :
( ~ ( between @ SV151 @ SY677 @ SY678 )
| ~ ( between @ SV76 @ SY678 @ SY676 )
| ( between @ SV76 @ SY677 @ SY676 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(466,plain,
! [SV152: $i,SV78: $i,SV2: $i] :
( ( ! [SY679: $i] :
( ~ ( equidistant @ SV2 @ SV78 @ SV152 @ SY679 )
| ! [SY680: $i,SY681: $i] :
( ~ ( equidistant @ SV2 @ SV78 @ SY680 @ SY681 )
| ( equidistant @ SV152 @ SY679 @ SY680 @ SY681 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(467,plain,
! [SV79: $i,SV3: $i] :
( ( ( ! [SY532: $i] :
~ ( equidistant @ SV3 @ SV79 @ SY532 @ SY532 ) )
= $true )
| ( ( SV3 = SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(468,plain,
! [SV153: $i,SV80: $i,SV4: $i] :
( ( ! [SY682: $i] : ( between @ SV4 @ SV80 @ ( extension @ SV4 @ SV80 @ SV153 @ SY682 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(469,plain,
! [SV154: $i,SV81: $i,SV5: $i] :
( ( ! [SY683: $i] : ( equidistant @ SV5 @ ( extension @ SV81 @ SV5 @ SV154 @ SY683 ) @ SV154 @ SY683 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(470,plain,
! [SV155: $i,SV82: $i,SV6: $i] :
( ( ! [SY684: $i,SY685: $i,SY686: $i] :
( ~ ( equidistant @ SV6 @ SV82 @ SV155 @ SY684 )
| ~ ( equidistant @ SV82 @ SY685 @ SY684 @ SY686 )
| ! [SY687: $i,SY688: $i] :
( ~ ( equidistant @ SV6 @ SY687 @ SV155 @ SY688 )
| ~ ( equidistant @ SV82 @ SY687 @ SY684 @ SY688 )
| ~ ( between @ SV6 @ SV82 @ SY685 )
| ~ ( between @ SV155 @ SY684 @ SY686 )
| ( SV6 = SV82 )
| ( equidistant @ SY685 @ SY687 @ SY686 @ SY688 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(471,plain,
! [SV83: $i,SV7: $i] :
( ( ( ~ ( between @ SV7 @ SV83 @ SV7 ) )
= $true )
| ( ( SV7 = SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(472,plain,
! [SV156: $i,SV84: $i,SV8: $i] :
( ( ~ ( between @ SV8 @ SV84 @ SV156 )
| ! [SY689: $i,SY690: $i] :
( ~ ( between @ SY689 @ SY690 @ SV156 )
| ( between @ SV84 @ ( inner_pasch @ SV8 @ SV84 @ SV156 @ SY690 @ SY689 ) @ SY689 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(473,plain,
! [SV157: $i,SV85: $i,SV9: $i] :
( ( ~ ( between @ SV9 @ SV85 @ SV157 )
| ! [SY691: $i,SY692: $i] :
( ~ ( between @ SY691 @ SY692 @ SV157 )
| ( between @ SY692 @ ( inner_pasch @ SV9 @ SV85 @ SV157 @ SY692 @ SY691 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(474,plain,
! [SV158: $i,SV86: $i,SV10: $i] :
( ( ~ ( equidistant @ SV10 @ SV86 @ SV10 @ SV158 )
| ! [SY693: $i] :
( ~ ( equidistant @ SY693 @ SV86 @ SY693 @ SV158 )
| ! [SY694: $i] :
( ~ ( equidistant @ SY694 @ SV86 @ SY694 @ SV158 )
| ( between @ SV10 @ SY693 @ SY694 )
| ( between @ SY693 @ SY694 @ SV10 )
| ( SV86 = SV158 )
| ( between @ SY694 @ SV10 @ SY693 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(475,plain,
! [SV159: $i,SV87: $i,SV11: $i] :
( ( ~ ( between @ SV11 @ SV87 @ SV159 )
| ! [SY695: $i,SY696: $i] :
( ~ ( between @ SY695 @ SV87 @ SY696 )
| ( SV11 = SV87 )
| ( between @ SV11 @ SY695 @ ( euclid1 @ SV11 @ SY695 @ SV87 @ SY696 @ SV159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(476,plain,
! [SV160: $i,SV88: $i,SV12: $i] :
( ( ~ ( between @ SV12 @ SV88 @ SV160 )
| ! [SY697: $i,SY698: $i] :
( ~ ( between @ SY697 @ SV88 @ SY698 )
| ( SV12 = SV88 )
| ( between @ SV12 @ SY698 @ ( euclid2 @ SV12 @ SY697 @ SV88 @ SY698 @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(477,plain,
! [SV161: $i,SV89: $i,SV13: $i] :
( ( ~ ( between @ SV13 @ SV89 @ SV161 )
| ! [SY699: $i,SY700: $i] :
( ~ ( between @ SY699 @ SV89 @ SY700 )
| ( SV13 = SV89 )
| ( between @ ( euclid1 @ SV13 @ SY699 @ SV89 @ SY700 @ SV161 ) @ SV161 @ ( euclid2 @ SV13 @ SY699 @ SV89 @ SY700 @ SV161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(478,plain,
! [SV162: $i,SV90: $i,SV14: $i] :
( ( ! [SY701: $i] :
( ~ ( equidistant @ SV14 @ SV90 @ SV14 @ SV162 )
| ! [SY702: $i] :
( ~ ( equidistant @ SV14 @ SY701 @ SV14 @ SY702 )
| ~ ( between @ SV14 @ SV90 @ SY701 )
| ! [SY703: $i] :
( ~ ( between @ SV90 @ SY703 @ SY701 )
| ( between @ SV162 @ ( continuous @ SV14 @ SV90 @ SV162 @ SY703 @ SY701 @ SY702 ) @ SY702 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(479,plain,
! [SV163: $i,SV91: $i,SV15: $i] :
( ( ! [SY704: $i] :
( ~ ( equidistant @ SV15 @ SV91 @ SV15 @ SV163 )
| ! [SY705: $i] :
( ~ ( equidistant @ SV15 @ SY704 @ SV15 @ SY705 )
| ~ ( between @ SV15 @ SV91 @ SY704 )
| ! [SY706: $i] :
( ~ ( between @ SV91 @ SY706 @ SY704 )
| ( equidistant @ SV15 @ SY706 @ SV15 @ ( continuous @ SV15 @ SV91 @ SV163 @ SY706 @ SY704 @ SY705 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(480,plain,
! [SV164: $i,SV93: $i,SV17: $i] :
( ( ! [SY707: $i] :
( ( insertion @ SV17 @ SV93 @ SV164 @ SY707 )
= ( extension @ ( extension @ SV93 @ SV17 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV17 @ SV164 @ SY707 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(481,plain,
! [SV165: $i,SV95: $i,SV19: $i] :
( ( ! [SY708: $i] :
( ~ ( equidistant @ SV19 @ SV95 @ SV165 @ SY708 )
| ( equidistant @ SV165 @ SY708 @ SV19 @ SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(482,plain,
! [SV166: $i,SV96: $i,SV20: $i] :
( ( ! [SY709: $i] :
( ~ ( equidistant @ SV20 @ SV96 @ SV166 @ SY709 )
| ( equidistant @ SV96 @ SV20 @ SV166 @ SY709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(483,plain,
! [SV167: $i,SV97: $i,SV21: $i] :
( ( ! [SY710: $i] :
( ~ ( equidistant @ SV21 @ SV97 @ SV167 @ SY710 )
| ( equidistant @ SV21 @ SV97 @ SY710 @ SV167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(484,plain,
! [SV168: $i,SV98: $i,SV22: $i] :
( ( ! [SY711: $i] :
( ~ ( equidistant @ SV22 @ SV98 @ SV168 @ SY711 )
| ( equidistant @ SV98 @ SV22 @ SY711 @ SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(485,plain,
! [SV169: $i,SV99: $i,SV23: $i] :
( ( ! [SY712: $i] :
( ~ ( equidistant @ SV23 @ SV99 @ SV169 @ SY712 )
| ( equidistant @ SV169 @ SY712 @ SV99 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[413]) ).
thf(486,plain,
! [SV170: $i,SV100: $i,SV24: $i] :
( ( ! [SY713: $i] :
( ~ ( equidistant @ SV24 @ SV100 @ SV170 @ SY713 )
| ( equidistant @ SY713 @ SV170 @ SV24 @ SV100 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(487,plain,
! [SV171: $i,SV101: $i,SV25: $i] :
( ( ! [SY714: $i] :
( ~ ( equidistant @ SV25 @ SV101 @ SV171 @ SY714 )
| ( equidistant @ SY714 @ SV171 @ SV101 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(488,plain,
! [SV172: $i,SV102: $i,SV26: $i] :
( ( ! [SY715: $i] :
( ~ ( equidistant @ SV26 @ SV102 @ SV172 @ SY715 )
| ! [SY716: $i,SY717: $i] :
( ~ ( equidistant @ SV172 @ SY715 @ SY716 @ SY717 )
| ( equidistant @ SV26 @ SV102 @ SY716 @ SY717 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(489,plain,
! [SV173: $i,SV103: $i,SV27: $i] :
( ( SV27
= ( extension @ SV103 @ SV27 @ SV173 @ SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(490,plain,
! [SV174: $i,SV104: $i,SV28: $i] :
( ( ! [SY718: $i,SY719: $i] :
( SV28
!= ( extension @ SV104 @ SV174 @ SY718 @ SY719 ) )
| ( between @ SV104 @ SV174 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(491,plain,
! [SV107: $i,SV31: $i] :
( ( ( SV31 != SV107 )
= $true )
| ( ( SV107
= ( reflection @ SV31 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(492,plain,
! [SV108: $i,SV33: $i] :
( ( ( SV33
!= ( reflection @ SV108 @ SV33 ) )
= $true )
| ( ( SV108 = SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(493,plain,
! [SV175: $i,SV110: $i,SV35: $i] :
( ( ! [SY720: $i] :
( ~ ( equidistant @ SV35 @ SV110 @ SV175 @ SY720 )
| ! [SY721: $i,SY722: $i] :
( ~ ( equidistant @ SV110 @ SY721 @ SY720 @ SY722 )
| ~ ( between @ SV35 @ SV110 @ SY721 )
| ~ ( between @ SV175 @ SY720 @ SY722 )
| ( equidistant @ SV35 @ SY721 @ SV175 @ SY722 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(494,plain,
! [SV176: $i,SV111: $i,SV36: $i] :
( ( ~ ( between @ SV36 @ SV111 @ SV176 )
| ! [SY723: $i] :
( ~ ( between @ SV36 @ SV111 @ SY723 )
| ~ ( equidistant @ SV111 @ SV176 @ SV111 @ SY723 )
| ( SV36 = SV111 )
| ( SV176 = SY723 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(495,plain,
! [SV177: $i,SV112: $i,SV37: $i] :
( ( ~ ( between @ SV37 @ SV112 @ SV177 )
| ( SV37 = SV112 )
| ( SV177
= ( extension @ SV37 @ SV112 @ SV112 @ SV177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(496,plain,
! [SV178: $i,SV113: $i,SV38: $i] :
( ( ! [SY724: $i] :
( ~ ( equidistant @ SV38 @ SV113 @ SV178 @ SY724 )
| ! [SY725: $i,SY726: $i] :
( ( ( extension @ SY725 @ SY726 @ SV38 @ SV113 )
= ( extension @ SY725 @ SY726 @ SV178 @ SY724 ) )
| ( SY725 = SY726 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(497,plain,
! [SV114: $i,SV39: $i] :
( ( ( ( extension @ SV39 @ SV114 @ SV39 @ SV114 )
= ( extension @ SV39 @ SV114 @ SV114 @ SV39 ) )
= $true )
| ( ( SV39 = SV114 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(498,plain,
! [SV179: $i,SV118: $i,SV43: $i] :
( ( ~ ( between @ SV43 @ SV118 @ SV179 )
| ( SV43 != SV179 )
| ! [SY727: $i] : ( between @ SY727 @ SV118 @ SV179 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(499,plain,
! [SV180: $i,SV119: $i,SV44: $i] :
( ( ~ ( between @ SV44 @ SV119 @ SV180 )
| ( between @ SV180 @ SV119 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(500,plain,
! [SV181: $i,SV121: $i,SV46: $i] :
( ( ~ ( between @ SV46 @ SV121 @ SV181 )
| ~ ( between @ SV121 @ SV46 @ SV181 )
| ( SV46 = SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(501,plain,
! [SV182: $i,SV122: $i,SV47: $i] :
( ( ~ ( between @ SV47 @ SV122 @ SV182 )
| ~ ( between @ SV47 @ SV182 @ SV122 )
| ( SV122 = SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(502,plain,
! [SV183: $i,SV123: $i,SV48: $i] :
( ( ~ ( between @ SV48 @ SV123 @ SV183 )
| ~ ( between @ SV123 @ SV48 @ SV183 )
| ( SV48 = SV123 )
| ( SV123 = SV183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(503,plain,
! [SV184: $i,SV124: $i,SV49: $i] :
( ( ~ ( between @ SV49 @ SV124 @ SV184 )
| ~ ( between @ SV49 @ SV184 @ SV124 )
| ( SV49 = SV124 )
| ( SV124 = SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(504,plain,
! [SV185: $i,SV125: $i,SV50: $i] :
( ( ~ ( between @ SV50 @ SV125 @ SV185 )
| ! [SY728: $i] :
~ ( between @ SV125 @ SV185 @ SY728 )
| ( between @ SV50 @ SV125 @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(505,plain,
! [SV186: $i,SV126: $i,SV51: $i] :
( ( ~ ( between @ SV51 @ SV126 @ SV186 )
| ! [SY729: $i] :
( ~ ( between @ SV51 @ SV186 @ SY729 )
| ( between @ SV126 @ SV186 @ SY729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(506,plain,
! [SV187: $i,SV127: $i,SV52: $i] :
( ( ~ ( between @ SV52 @ SV127 @ SV187 )
| ! [SY730: $i] :
( ~ ( between @ SV127 @ SV187 @ SY730 )
| ( SV127 = SV187 )
| ( between @ SV52 @ SV187 @ SY730 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(507,plain,
! [SV188: $i,SV128: $i,SV53: $i] :
( ( ~ ( between @ SV53 @ SV128 @ SV188 )
| ! [SY731: $i] :
( ~ ( between @ SV128 @ SV188 @ SY731 )
| ( SV128 = SV188 )
| ( between @ SV53 @ SV128 @ SY731 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(508,plain,
! [SV189: $i,SV129: $i,SV54: $i] :
( ( ~ ( between @ SV54 @ SV129 @ SV189 )
| ! [SY732: $i] :
( ~ ( between @ SV129 @ SY732 @ SV189 )
| ( between @ SV54 @ SY732 @ SV189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(509,plain,
! [SV190: $i,SV130: $i,SV55: $i] :
( ( ~ ( between @ SV55 @ SV130 @ SV190 )
| ! [SY733: $i] :
( ~ ( between @ SV55 @ SV190 @ SY733 )
| ( between @ SV55 @ SV130 @ SY733 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(510,plain,
! [SV131: $i,SV56: $i] :
( ( SV56
= ( extension @ SV131 @ SV56 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(511,plain,
! [SV191: $i,SV132: $i,SV57: $i] :
( ( ! [SY734: $i] : ( equidistant @ SV57 @ ( extension @ SV132 @ SV57 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV191 @ ( extension @ SY734 @ SV191 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(512,plain,
! [SV192: $i,SV134: $i,SV59: $i] :
( ( ! [SY735: $i] :
( ~ ( between @ SV59 @ SV134 @ SV192 )
| ! [SY736: $i] :
( ~ ( between @ SY735 @ SY736 @ SV192 )
| ! [SY737: $i] :
( ~ ( between @ SV59 @ SY737 @ SY735 )
| ( between @ SY737 @ ( inner_pasch @ SY736 @ ( inner_pasch @ SV59 @ SY737 @ SY735 @ SY736 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV192 )
| ( between @ SV134 @ ( inner_pasch @ SY736 @ ( inner_pasch @ SV59 @ SY737 @ SY735 @ SY736 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SY736 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(513,plain,
! [SV193: $i,SV135: $i,SV60: $i] :
( ( ~ ( between @ SV60 @ SV135 @ SV193 )
| ! [SY738: $i] :
( ~ ( equidistant @ SV60 @ SV193 @ SV60 @ SY738 )
| ~ ( equidistant @ SV135 @ SV193 @ SV135 @ SY738 )
| ( SV60 = SV135 )
| ( SV193 = SY738 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(514,plain,
! [SV194: $i,SV136: $i,SV61: $i] :
( ( ! [SY739: $i,SY740: $i,SY741: $i] :
( ~ ( equidistant @ SV61 @ SV136 @ SV194 @ SY739 )
| ~ ( equidistant @ SV61 @ SY740 @ SV194 @ SY741 )
| ! [SY742: $i,SY743: $i] :
( ~ ( equidistant @ SV61 @ SY742 @ SV194 @ SY743 )
| ~ ( equidistant @ SY740 @ SY742 @ SY741 @ SY743 )
| ~ ( between @ SV61 @ SV136 @ SY740 )
| ~ ( between @ SV194 @ SY739 @ SY741 )
| ( equidistant @ SV136 @ SY742 @ SY739 @ SY743 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(515,plain,
! [SV195: $i,SV137: $i,SV62: $i] :
( ( ! [SY744: $i] :
( ~ ( between @ SV62 @ SV137 @ SV195 )
| ! [SY745: $i,SY746: $i] :
( ~ ( between @ SY744 @ SY745 @ SY746 )
| ~ ( equidistant @ SV62 @ SV137 @ SY744 @ SY745 )
| ~ ( equidistant @ SV62 @ SV195 @ SY744 @ SY746 )
| ( equidistant @ SV137 @ SV195 @ SY745 @ SY746 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(516,plain,
! [SV196: $i,SV138: $i,SV63: $i] :
( ( ! [SY747: $i,SY748: $i,SY749: $i] :
( ~ ( equidistant @ SV63 @ SV138 @ SV196 @ SY747 )
| ~ ( equidistant @ SV138 @ SY748 @ SY747 @ SY749 )
| ! [SY750: $i,SY751: $i] :
( ~ ( equidistant @ SV63 @ SY750 @ SV196 @ SY751 )
| ~ ( equidistant @ SY748 @ SY750 @ SY749 @ SY751 )
| ~ ( between @ SV63 @ SV138 @ SY748 )
| ~ ( between @ SV196 @ SY747 @ SY749 )
| ( equidistant @ SV138 @ SY750 @ SY747 @ SY751 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(517,plain,
! [SV197: $i,SV139: $i,SV64: $i] :
( ( ~ ( between @ SV64 @ SV139 @ SV197 )
| ! [SY752: $i] :
( ~ ( equidistant @ SV64 @ SV139 @ SV64 @ SY752 )
| ~ ( equidistant @ SV197 @ SV139 @ SV197 @ SY752 )
| ( SV139 = SY752 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(518,plain,
! [SV198: $i,SV140: $i,SV65: $i] :
( ( ! [SY753: $i] : ( equidistant @ SV65 @ SV140 @ SV198 @ ( insertion @ SV198 @ SY753 @ SV65 @ SV140 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(519,plain,
! [SV199: $i,SV141: $i,SV66: $i] :
( ( ~ ( between @ SV66 @ SV141 @ SV199 )
| ! [SY754: $i,SY755: $i] :
( ~ ( equidistant @ SV66 @ SV199 @ SY754 @ SY755 )
| ( between @ SY754 @ ( insertion @ SY754 @ SY755 @ SV66 @ SV141 ) @ SY755 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(520,plain,
! [SV200: $i,SV142: $i,SV67: $i] :
( ( ~ ( between @ SV67 @ SV142 @ SV200 )
| ! [SY756: $i,SY757: $i] :
( ~ ( equidistant @ SV67 @ SV200 @ SY756 @ SY757 )
| ( equidistant @ SV142 @ SV200 @ ( insertion @ SY756 @ SY757 @ SV67 @ SV142 ) @ SY757 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(521,plain,
! [SV201: $i,SV143: $i,SV68: $i] :
( ( ~ ( between @ SV68 @ SV143 @ SV201 )
| ( SV143
= ( insertion @ SV68 @ SV201 @ SV68 @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(522,plain,
! [SV202: $i,SV144: $i,SV69: $i] :
( ( ! [SY758: $i] :
( ~ ( equidistant @ SV69 @ SV144 @ SV202 @ SY758 )
| ! [SY759: $i,SY760: $i] :
( ( insertion @ SY759 @ SY760 @ SV69 @ SV144 )
= ( insertion @ SY759 @ SY760 @ SV202 @ SY758 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(523,plain,
! [SV203: $i,SV145: $i,SV70: $i] :
( ( ! [SY761: $i] :
( ~ ( equidistant @ SV70 @ SV145 @ SV203 @ SY761 )
| ! [SY762: $i,SY763: $i] :
( ~ ( equidistant @ SV145 @ SY762 @ SY761 @ SY763 )
| ~ ( equidistant @ SV70 @ SY762 @ SV203 @ SY763 )
| ~ ( between @ SV70 @ SV145 @ SY762 )
| ( between @ SV203 @ SY761 @ SY763 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(524,plain,
! [SV204: $i,SV146: $i,SV71: $i] :
( ( ~ ( between @ SV71 @ SV146 @ SV204 )
| ! [SY764: $i] :
( ~ ( between @ SV71 @ SV146 @ SY764 )
| ( SV71 = SV146 )
| ( between @ SV71 @ SV204 @ SY764 )
| ( between @ SV71 @ SY764 @ SV204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(525,plain,
! [SV205: $i,SV147: $i,SV72: $i] :
( ( ~ ( between @ SV72 @ SV147 @ SV205 )
| ! [SY765: $i] :
( ~ ( between @ SV72 @ SV147 @ SY765 )
| ( SV72 = SV147 )
| ( between @ SV147 @ SV205 @ SY765 )
| ( between @ SV147 @ SY765 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(526,plain,
! [SV206: $i,SV148: $i,SV73: $i] :
( ( ~ ( between @ SV73 @ SV148 @ SV206 )
| ! [SY766: $i] :
( ~ ( between @ SY766 @ SV148 @ SV206 )
| ( SV148 = SV206 )
| ( between @ SV73 @ SY766 @ SV148 )
| ( between @ SY766 @ SV73 @ SV148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(527,plain,
! [SV207: $i,SV149: $i,SV74: $i] :
( ( ~ ( between @ SV74 @ SV149 @ SV207 )
| ! [SY767: $i] :
( ~ ( between @ SV74 @ SY767 @ SV207 )
| ( between @ SV74 @ SV149 @ SY767 )
| ( between @ SV74 @ SY767 @ SV149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(528,plain,
! [SV208: $i,SV150: $i,SV75: $i] :
( ( ~ ( between @ SV75 @ SV150 @ SV208 )
| ! [SY768: $i] :
( ~ ( between @ SV75 @ SY768 @ SV208 )
| ( between @ SV150 @ SY768 @ SV208 )
| ( between @ SY768 @ SV150 @ SV208 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(529,plain,
! [SV209: $i,SV151: $i,SV76: $i] :
( ( ~ ( between @ SV76 @ SV151 @ SV209 )
| ! [SY769: $i,SY770: $i] :
( ~ ( between @ SV151 @ SY769 @ SY770 )
| ~ ( between @ SV76 @ SY770 @ SV209 )
| ( between @ SV76 @ SY769 @ SV209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(530,plain,
! [SV210: $i,SV152: $i,SV78: $i,SV2: $i] :
( ( ~ ( equidistant @ SV2 @ SV78 @ SV152 @ SV210 )
| ! [SY771: $i,SY772: $i] :
( ~ ( equidistant @ SV2 @ SV78 @ SY771 @ SY772 )
| ( equidistant @ SV152 @ SV210 @ SY771 @ SY772 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(531,plain,
! [SV211: $i,SV79: $i,SV3: $i] :
( ( ( ~ ( equidistant @ SV3 @ SV79 @ SV211 @ SV211 ) )
= $true )
| ( ( SV3 = SV79 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(532,plain,
! [SV212: $i,SV153: $i,SV80: $i,SV4: $i] :
( ( between @ SV4 @ SV80 @ ( extension @ SV4 @ SV80 @ SV153 @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(533,plain,
! [SV213: $i,SV154: $i,SV81: $i,SV5: $i] :
( ( equidistant @ SV5 @ ( extension @ SV81 @ SV5 @ SV154 @ SV213 ) @ SV154 @ SV213 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(534,plain,
! [SV214: $i,SV155: $i,SV82: $i,SV6: $i] :
( ( ! [SY773: $i,SY774: $i] :
( ~ ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
| ~ ( equidistant @ SV82 @ SY773 @ SV214 @ SY774 )
| ! [SY775: $i,SY776: $i] :
( ~ ( equidistant @ SV6 @ SY775 @ SV155 @ SY776 )
| ~ ( equidistant @ SV82 @ SY775 @ SV214 @ SY776 )
| ~ ( between @ SV6 @ SV82 @ SY773 )
| ~ ( between @ SV155 @ SV214 @ SY774 )
| ( SV6 = SV82 )
| ( equidistant @ SY773 @ SY775 @ SY774 @ SY776 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(535,plain,
! [SV83: $i,SV7: $i] :
( ( ( between @ SV7 @ SV83 @ SV7 )
= $false )
| ( ( SV7 = SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(536,plain,
! [SV156: $i,SV84: $i,SV8: $i] :
( ( ( ~ ( between @ SV8 @ SV84 @ SV156 ) )
= $true )
| ( ( ! [SY689: $i,SY690: $i] :
( ~ ( between @ SY689 @ SY690 @ SV156 )
| ( between @ SV84 @ ( inner_pasch @ SV8 @ SV84 @ SV156 @ SY690 @ SY689 ) @ SY689 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(537,plain,
! [SV157: $i,SV85: $i,SV9: $i] :
( ( ( ~ ( between @ SV9 @ SV85 @ SV157 ) )
= $true )
| ( ( ! [SY691: $i,SY692: $i] :
( ~ ( between @ SY691 @ SY692 @ SV157 )
| ( between @ SY692 @ ( inner_pasch @ SV9 @ SV85 @ SV157 @ SY692 @ SY691 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(538,plain,
! [SV158: $i,SV86: $i,SV10: $i] :
( ( ( ~ ( equidistant @ SV10 @ SV86 @ SV10 @ SV158 ) )
= $true )
| ( ( ! [SY693: $i] :
( ~ ( equidistant @ SY693 @ SV86 @ SY693 @ SV158 )
| ! [SY694: $i] :
( ~ ( equidistant @ SY694 @ SV86 @ SY694 @ SV158 )
| ( between @ SV10 @ SY693 @ SY694 )
| ( between @ SY693 @ SY694 @ SV10 )
| ( SV86 = SV158 )
| ( between @ SY694 @ SV10 @ SY693 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(539,plain,
! [SV159: $i,SV87: $i,SV11: $i] :
( ( ( ~ ( between @ SV11 @ SV87 @ SV159 ) )
= $true )
| ( ( ! [SY695: $i,SY696: $i] :
( ~ ( between @ SY695 @ SV87 @ SY696 )
| ( SV11 = SV87 )
| ( between @ SV11 @ SY695 @ ( euclid1 @ SV11 @ SY695 @ SV87 @ SY696 @ SV159 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(540,plain,
! [SV160: $i,SV88: $i,SV12: $i] :
( ( ( ~ ( between @ SV12 @ SV88 @ SV160 ) )
= $true )
| ( ( ! [SY697: $i,SY698: $i] :
( ~ ( between @ SY697 @ SV88 @ SY698 )
| ( SV12 = SV88 )
| ( between @ SV12 @ SY698 @ ( euclid2 @ SV12 @ SY697 @ SV88 @ SY698 @ SV160 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(541,plain,
! [SV161: $i,SV89: $i,SV13: $i] :
( ( ( ~ ( between @ SV13 @ SV89 @ SV161 ) )
= $true )
| ( ( ! [SY699: $i,SY700: $i] :
( ~ ( between @ SY699 @ SV89 @ SY700 )
| ( SV13 = SV89 )
| ( between @ ( euclid1 @ SV13 @ SY699 @ SV89 @ SY700 @ SV161 ) @ SV161 @ ( euclid2 @ SV13 @ SY699 @ SV89 @ SY700 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(542,plain,
! [SV215: $i,SV162: $i,SV90: $i,SV14: $i] :
( ( ~ ( equidistant @ SV14 @ SV90 @ SV14 @ SV162 )
| ! [SY777: $i] :
( ~ ( equidistant @ SV14 @ SV215 @ SV14 @ SY777 )
| ~ ( between @ SV14 @ SV90 @ SV215 )
| ! [SY778: $i] :
( ~ ( between @ SV90 @ SY778 @ SV215 )
| ( between @ SV162 @ ( continuous @ SV14 @ SV90 @ SV162 @ SY778 @ SV215 @ SY777 ) @ SY777 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(543,plain,
! [SV216: $i,SV163: $i,SV91: $i,SV15: $i] :
( ( ~ ( equidistant @ SV15 @ SV91 @ SV15 @ SV163 )
| ! [SY779: $i] :
( ~ ( equidistant @ SV15 @ SV216 @ SV15 @ SY779 )
| ~ ( between @ SV15 @ SV91 @ SV216 )
| ! [SY780: $i] :
( ~ ( between @ SV91 @ SY780 @ SV216 )
| ( equidistant @ SV15 @ SY780 @ SV15 @ ( continuous @ SV15 @ SV91 @ SV163 @ SY780 @ SV216 @ SY779 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(544,plain,
! [SV217: $i,SV164: $i,SV93: $i,SV17: $i] :
( ( ( insertion @ SV17 @ SV93 @ SV164 @ SV217 )
= ( extension @ ( extension @ SV93 @ SV17 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV17 @ SV164 @ SV217 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(545,plain,
! [SV218: $i,SV165: $i,SV95: $i,SV19: $i] :
( ( ~ ( equidistant @ SV19 @ SV95 @ SV165 @ SV218 )
| ( equidistant @ SV165 @ SV218 @ SV19 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(546,plain,
! [SV219: $i,SV166: $i,SV96: $i,SV20: $i] :
( ( ~ ( equidistant @ SV20 @ SV96 @ SV166 @ SV219 )
| ( equidistant @ SV96 @ SV20 @ SV166 @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(547,plain,
! [SV220: $i,SV167: $i,SV97: $i,SV21: $i] :
( ( ~ ( equidistant @ SV21 @ SV97 @ SV167 @ SV220 )
| ( equidistant @ SV21 @ SV97 @ SV220 @ SV167 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(548,plain,
! [SV221: $i,SV168: $i,SV98: $i,SV22: $i] :
( ( ~ ( equidistant @ SV22 @ SV98 @ SV168 @ SV221 )
| ( equidistant @ SV98 @ SV22 @ SV221 @ SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(549,plain,
! [SV222: $i,SV169: $i,SV99: $i,SV23: $i] :
( ( ~ ( equidistant @ SV23 @ SV99 @ SV169 @ SV222 )
| ( equidistant @ SV169 @ SV222 @ SV99 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(550,plain,
! [SV223: $i,SV170: $i,SV100: $i,SV24: $i] :
( ( ~ ( equidistant @ SV24 @ SV100 @ SV170 @ SV223 )
| ( equidistant @ SV223 @ SV170 @ SV24 @ SV100 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(551,plain,
! [SV224: $i,SV171: $i,SV101: $i,SV25: $i] :
( ( ~ ( equidistant @ SV25 @ SV101 @ SV171 @ SV224 )
| ( equidistant @ SV224 @ SV171 @ SV101 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(552,plain,
! [SV225: $i,SV172: $i,SV102: $i,SV26: $i] :
( ( ~ ( equidistant @ SV26 @ SV102 @ SV172 @ SV225 )
| ! [SY781: $i,SY782: $i] :
( ~ ( equidistant @ SV172 @ SV225 @ SY781 @ SY782 )
| ( equidistant @ SV26 @ SV102 @ SY781 @ SY782 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(553,plain,
! [SV174: $i,SV104: $i,SV28: $i] :
( ( ( ! [SY718: $i,SY719: $i] :
( SV28
!= ( extension @ SV104 @ SV174 @ SY718 @ SY719 ) ) )
= $true )
| ( ( between @ SV104 @ SV174 @ SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[490]) ).
thf(554,plain,
! [SV107: $i,SV31: $i] :
( ( ( SV31 = SV107 )
= $false )
| ( ( SV107
= ( reflection @ SV31 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(555,plain,
! [SV108: $i,SV33: $i] :
( ( ( SV33
= ( reflection @ SV108 @ SV33 ) )
= $false )
| ( ( SV108 = SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(556,plain,
! [SV226: $i,SV175: $i,SV110: $i,SV35: $i] :
( ( ~ ( equidistant @ SV35 @ SV110 @ SV175 @ SV226 )
| ! [SY783: $i,SY784: $i] :
( ~ ( equidistant @ SV110 @ SY783 @ SV226 @ SY784 )
| ~ ( between @ SV35 @ SV110 @ SY783 )
| ~ ( between @ SV175 @ SV226 @ SY784 )
| ( equidistant @ SV35 @ SY783 @ SV175 @ SY784 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(557,plain,
! [SV176: $i,SV111: $i,SV36: $i] :
( ( ( ~ ( between @ SV36 @ SV111 @ SV176 ) )
= $true )
| ( ( ! [SY723: $i] :
( ~ ( between @ SV36 @ SV111 @ SY723 )
| ~ ( equidistant @ SV111 @ SV176 @ SV111 @ SY723 )
| ( SV36 = SV111 )
| ( SV176 = SY723 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(558,plain,
! [SV177: $i,SV112: $i,SV37: $i] :
( ( ( ~ ( between @ SV37 @ SV112 @ SV177 ) )
= $true )
| ( ( ( SV37 = SV112 )
| ( SV177
= ( extension @ SV37 @ SV112 @ SV112 @ SV177 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(559,plain,
! [SV227: $i,SV178: $i,SV113: $i,SV38: $i] :
( ( ~ ( equidistant @ SV38 @ SV113 @ SV178 @ SV227 )
| ! [SY785: $i,SY786: $i] :
( ( ( extension @ SY785 @ SY786 @ SV38 @ SV113 )
= ( extension @ SY785 @ SY786 @ SV178 @ SV227 ) )
| ( SY785 = SY786 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(560,plain,
! [SV179: $i,SV118: $i,SV43: $i] :
( ( ( ~ ( between @ SV43 @ SV118 @ SV179 ) )
= $true )
| ( ( ( SV43 != SV179 )
| ! [SY727: $i] : ( between @ SY727 @ SV118 @ SV179 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[498]) ).
thf(561,plain,
! [SV180: $i,SV119: $i,SV44: $i] :
( ( ( ~ ( between @ SV44 @ SV119 @ SV180 ) )
= $true )
| ( ( between @ SV180 @ SV119 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(562,plain,
! [SV181: $i,SV121: $i,SV46: $i] :
( ( ( ~ ( between @ SV46 @ SV121 @ SV181 ) )
= $true )
| ( ( ~ ( between @ SV121 @ SV46 @ SV181 )
| ( SV46 = SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(563,plain,
! [SV182: $i,SV122: $i,SV47: $i] :
( ( ( ~ ( between @ SV47 @ SV122 @ SV182 ) )
= $true )
| ( ( ~ ( between @ SV47 @ SV182 @ SV122 )
| ( SV122 = SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(564,plain,
! [SV183: $i,SV123: $i,SV48: $i] :
( ( ( ~ ( between @ SV48 @ SV123 @ SV183 ) )
= $true )
| ( ( ~ ( between @ SV123 @ SV48 @ SV183 )
| ( SV48 = SV123 )
| ( SV123 = SV183 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(565,plain,
! [SV184: $i,SV124: $i,SV49: $i] :
( ( ( ~ ( between @ SV49 @ SV124 @ SV184 ) )
= $true )
| ( ( ~ ( between @ SV49 @ SV184 @ SV124 )
| ( SV49 = SV124 )
| ( SV124 = SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(566,plain,
! [SV185: $i,SV125: $i,SV50: $i] :
( ( ( ~ ( between @ SV50 @ SV125 @ SV185 ) )
= $true )
| ( ( ! [SY728: $i] :
~ ( between @ SV125 @ SV185 @ SY728 )
| ( between @ SV50 @ SV125 @ SV185 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(567,plain,
! [SV186: $i,SV126: $i,SV51: $i] :
( ( ( ~ ( between @ SV51 @ SV126 @ SV186 ) )
= $true )
| ( ( ! [SY729: $i] :
( ~ ( between @ SV51 @ SV186 @ SY729 )
| ( between @ SV126 @ SV186 @ SY729 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(568,plain,
! [SV187: $i,SV127: $i,SV52: $i] :
( ( ( ~ ( between @ SV52 @ SV127 @ SV187 ) )
= $true )
| ( ( ! [SY730: $i] :
( ~ ( between @ SV127 @ SV187 @ SY730 )
| ( SV127 = SV187 )
| ( between @ SV52 @ SV187 @ SY730 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(569,plain,
! [SV188: $i,SV128: $i,SV53: $i] :
( ( ( ~ ( between @ SV53 @ SV128 @ SV188 ) )
= $true )
| ( ( ! [SY731: $i] :
( ~ ( between @ SV128 @ SV188 @ SY731 )
| ( SV128 = SV188 )
| ( between @ SV53 @ SV128 @ SY731 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(570,plain,
! [SV189: $i,SV129: $i,SV54: $i] :
( ( ( ~ ( between @ SV54 @ SV129 @ SV189 ) )
= $true )
| ( ( ! [SY732: $i] :
( ~ ( between @ SV129 @ SY732 @ SV189 )
| ( between @ SV54 @ SY732 @ SV189 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[508]) ).
thf(571,plain,
! [SV190: $i,SV130: $i,SV55: $i] :
( ( ( ~ ( between @ SV55 @ SV130 @ SV190 ) )
= $true )
| ( ( ! [SY733: $i] :
( ~ ( between @ SV55 @ SV190 @ SY733 )
| ( between @ SV55 @ SV130 @ SY733 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(572,plain,
! [SV228: $i,SV191: $i,SV132: $i,SV57: $i] :
( ( equidistant @ SV57 @ ( extension @ SV132 @ SV57 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV191 @ ( extension @ SV228 @ SV191 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(573,plain,
! [SV229: $i,SV192: $i,SV134: $i,SV59: $i] :
( ( ~ ( between @ SV59 @ SV134 @ SV192 )
| ! [SY787: $i] :
( ~ ( between @ SV229 @ SY787 @ SV192 )
| ! [SY788: $i] :
( ~ ( between @ SV59 @ SY788 @ SV229 )
| ( between @ SY788 @ ( inner_pasch @ SY787 @ ( inner_pasch @ SV59 @ SY788 @ SV229 @ SY787 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV192 )
| ( between @ SV134 @ ( inner_pasch @ SY787 @ ( inner_pasch @ SV59 @ SY788 @ SV229 @ SY787 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SY787 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(574,plain,
! [SV193: $i,SV135: $i,SV60: $i] :
( ( ( ~ ( between @ SV60 @ SV135 @ SV193 ) )
= $true )
| ( ( ! [SY738: $i] :
( ~ ( equidistant @ SV60 @ SV193 @ SV60 @ SY738 )
| ~ ( equidistant @ SV135 @ SV193 @ SV135 @ SY738 )
| ( SV60 = SV135 )
| ( SV193 = SY738 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(575,plain,
! [SV230: $i,SV194: $i,SV136: $i,SV61: $i] :
( ( ! [SY789: $i,SY790: $i] :
( ~ ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 )
| ~ ( equidistant @ SV61 @ SY789 @ SV194 @ SY790 )
| ! [SY791: $i,SY792: $i] :
( ~ ( equidistant @ SV61 @ SY791 @ SV194 @ SY792 )
| ~ ( equidistant @ SY789 @ SY791 @ SY790 @ SY792 )
| ~ ( between @ SV61 @ SV136 @ SY789 )
| ~ ( between @ SV194 @ SV230 @ SY790 )
| ( equidistant @ SV136 @ SY791 @ SV230 @ SY792 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(576,plain,
! [SV231: $i,SV195: $i,SV137: $i,SV62: $i] :
( ( ~ ( between @ SV62 @ SV137 @ SV195 )
| ! [SY793: $i,SY794: $i] :
( ~ ( between @ SV231 @ SY793 @ SY794 )
| ~ ( equidistant @ SV62 @ SV137 @ SV231 @ SY793 )
| ~ ( equidistant @ SV62 @ SV195 @ SV231 @ SY794 )
| ( equidistant @ SV137 @ SV195 @ SY793 @ SY794 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(577,plain,
! [SV232: $i,SV196: $i,SV138: $i,SV63: $i] :
( ( ! [SY795: $i,SY796: $i] :
( ~ ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 )
| ~ ( equidistant @ SV138 @ SY795 @ SV232 @ SY796 )
| ! [SY797: $i,SY798: $i] :
( ~ ( equidistant @ SV63 @ SY797 @ SV196 @ SY798 )
| ~ ( equidistant @ SY795 @ SY797 @ SY796 @ SY798 )
| ~ ( between @ SV63 @ SV138 @ SY795 )
| ~ ( between @ SV196 @ SV232 @ SY796 )
| ( equidistant @ SV138 @ SY797 @ SV232 @ SY798 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(578,plain,
! [SV197: $i,SV139: $i,SV64: $i] :
( ( ( ~ ( between @ SV64 @ SV139 @ SV197 ) )
= $true )
| ( ( ! [SY752: $i] :
( ~ ( equidistant @ SV64 @ SV139 @ SV64 @ SY752 )
| ~ ( equidistant @ SV197 @ SV139 @ SV197 @ SY752 )
| ( SV139 = SY752 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(579,plain,
! [SV233: $i,SV198: $i,SV140: $i,SV65: $i] :
( ( equidistant @ SV65 @ SV140 @ SV198 @ ( insertion @ SV198 @ SV233 @ SV65 @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(580,plain,
! [SV199: $i,SV141: $i,SV66: $i] :
( ( ( ~ ( between @ SV66 @ SV141 @ SV199 ) )
= $true )
| ( ( ! [SY754: $i,SY755: $i] :
( ~ ( equidistant @ SV66 @ SV199 @ SY754 @ SY755 )
| ( between @ SY754 @ ( insertion @ SY754 @ SY755 @ SV66 @ SV141 ) @ SY755 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(581,plain,
! [SV200: $i,SV142: $i,SV67: $i] :
( ( ( ~ ( between @ SV67 @ SV142 @ SV200 ) )
= $true )
| ( ( ! [SY756: $i,SY757: $i] :
( ~ ( equidistant @ SV67 @ SV200 @ SY756 @ SY757 )
| ( equidistant @ SV142 @ SV200 @ ( insertion @ SY756 @ SY757 @ SV67 @ SV142 ) @ SY757 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(582,plain,
! [SV201: $i,SV143: $i,SV68: $i] :
( ( ( ~ ( between @ SV68 @ SV143 @ SV201 ) )
= $true )
| ( ( SV143
= ( insertion @ SV68 @ SV201 @ SV68 @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(583,plain,
! [SV234: $i,SV202: $i,SV144: $i,SV69: $i] :
( ( ~ ( equidistant @ SV69 @ SV144 @ SV202 @ SV234 )
| ! [SY799: $i,SY800: $i] :
( ( insertion @ SY799 @ SY800 @ SV69 @ SV144 )
= ( insertion @ SY799 @ SY800 @ SV202 @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(584,plain,
! [SV235: $i,SV203: $i,SV145: $i,SV70: $i] :
( ( ~ ( equidistant @ SV70 @ SV145 @ SV203 @ SV235 )
| ! [SY801: $i,SY802: $i] :
( ~ ( equidistant @ SV145 @ SY801 @ SV235 @ SY802 )
| ~ ( equidistant @ SV70 @ SY801 @ SV203 @ SY802 )
| ~ ( between @ SV70 @ SV145 @ SY801 )
| ( between @ SV203 @ SV235 @ SY802 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(585,plain,
! [SV204: $i,SV146: $i,SV71: $i] :
( ( ( ~ ( between @ SV71 @ SV146 @ SV204 ) )
= $true )
| ( ( ! [SY764: $i] :
( ~ ( between @ SV71 @ SV146 @ SY764 )
| ( SV71 = SV146 )
| ( between @ SV71 @ SV204 @ SY764 )
| ( between @ SV71 @ SY764 @ SV204 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(586,plain,
! [SV205: $i,SV147: $i,SV72: $i] :
( ( ( ~ ( between @ SV72 @ SV147 @ SV205 ) )
= $true )
| ( ( ! [SY765: $i] :
( ~ ( between @ SV72 @ SV147 @ SY765 )
| ( SV72 = SV147 )
| ( between @ SV147 @ SV205 @ SY765 )
| ( between @ SV147 @ SY765 @ SV205 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(587,plain,
! [SV206: $i,SV148: $i,SV73: $i] :
( ( ( ~ ( between @ SV73 @ SV148 @ SV206 ) )
= $true )
| ( ( ! [SY766: $i] :
( ~ ( between @ SY766 @ SV148 @ SV206 )
| ( SV148 = SV206 )
| ( between @ SV73 @ SY766 @ SV148 )
| ( between @ SY766 @ SV73 @ SV148 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[526]) ).
thf(588,plain,
! [SV207: $i,SV149: $i,SV74: $i] :
( ( ( ~ ( between @ SV74 @ SV149 @ SV207 ) )
= $true )
| ( ( ! [SY767: $i] :
( ~ ( between @ SV74 @ SY767 @ SV207 )
| ( between @ SV74 @ SV149 @ SY767 )
| ( between @ SV74 @ SY767 @ SV149 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(589,plain,
! [SV208: $i,SV150: $i,SV75: $i] :
( ( ( ~ ( between @ SV75 @ SV150 @ SV208 ) )
= $true )
| ( ( ! [SY768: $i] :
( ~ ( between @ SV75 @ SY768 @ SV208 )
| ( between @ SV150 @ SY768 @ SV208 )
| ( between @ SY768 @ SV150 @ SV208 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[528]) ).
thf(590,plain,
! [SV209: $i,SV151: $i,SV76: $i] :
( ( ( ~ ( between @ SV76 @ SV151 @ SV209 ) )
= $true )
| ( ( ! [SY769: $i,SY770: $i] :
( ~ ( between @ SV151 @ SY769 @ SY770 )
| ~ ( between @ SV76 @ SY770 @ SV209 )
| ( between @ SV76 @ SY769 @ SV209 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(591,plain,
! [SV210: $i,SV152: $i,SV78: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV78 @ SV152 @ SV210 ) )
= $true )
| ( ( ! [SY771: $i,SY772: $i] :
( ~ ( equidistant @ SV2 @ SV78 @ SY771 @ SY772 )
| ( equidistant @ SV152 @ SV210 @ SY771 @ SY772 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(592,plain,
! [SV211: $i,SV79: $i,SV3: $i] :
( ( ( equidistant @ SV3 @ SV79 @ SV211 @ SV211 )
= $false )
| ( ( SV3 = SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(593,plain,
! [SV236: $i,SV214: $i,SV155: $i,SV82: $i,SV6: $i] :
( ( ! [SY803: $i] :
( ~ ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
| ~ ( equidistant @ SV82 @ SV236 @ SV214 @ SY803 )
| ! [SY804: $i,SY805: $i] :
( ~ ( equidistant @ SV6 @ SY804 @ SV155 @ SY805 )
| ~ ( equidistant @ SV82 @ SY804 @ SV214 @ SY805 )
| ~ ( between @ SV6 @ SV82 @ SV236 )
| ~ ( between @ SV155 @ SV214 @ SY803 )
| ( SV6 = SV82 )
| ( equidistant @ SV236 @ SY804 @ SY803 @ SY805 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(594,plain,
! [SV156: $i,SV84: $i,SV8: $i] :
( ( ( between @ SV8 @ SV84 @ SV156 )
= $false )
| ( ( ! [SY689: $i,SY690: $i] :
( ~ ( between @ SY689 @ SY690 @ SV156 )
| ( between @ SV84 @ ( inner_pasch @ SV8 @ SV84 @ SV156 @ SY690 @ SY689 ) @ SY689 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(595,plain,
! [SV157: $i,SV85: $i,SV9: $i] :
( ( ( between @ SV9 @ SV85 @ SV157 )
= $false )
| ( ( ! [SY691: $i,SY692: $i] :
( ~ ( between @ SY691 @ SY692 @ SV157 )
| ( between @ SY692 @ ( inner_pasch @ SV9 @ SV85 @ SV157 @ SY692 @ SY691 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(596,plain,
! [SV158: $i,SV86: $i,SV10: $i] :
( ( ( equidistant @ SV10 @ SV86 @ SV10 @ SV158 )
= $false )
| ( ( ! [SY693: $i] :
( ~ ( equidistant @ SY693 @ SV86 @ SY693 @ SV158 )
| ! [SY694: $i] :
( ~ ( equidistant @ SY694 @ SV86 @ SY694 @ SV158 )
| ( between @ SV10 @ SY693 @ SY694 )
| ( between @ SY693 @ SY694 @ SV10 )
| ( SV86 = SV158 )
| ( between @ SY694 @ SV10 @ SY693 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(597,plain,
! [SV159: $i,SV87: $i,SV11: $i] :
( ( ( between @ SV11 @ SV87 @ SV159 )
= $false )
| ( ( ! [SY695: $i,SY696: $i] :
( ~ ( between @ SY695 @ SV87 @ SY696 )
| ( SV11 = SV87 )
| ( between @ SV11 @ SY695 @ ( euclid1 @ SV11 @ SY695 @ SV87 @ SY696 @ SV159 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(598,plain,
! [SV160: $i,SV88: $i,SV12: $i] :
( ( ( between @ SV12 @ SV88 @ SV160 )
= $false )
| ( ( ! [SY697: $i,SY698: $i] :
( ~ ( between @ SY697 @ SV88 @ SY698 )
| ( SV12 = SV88 )
| ( between @ SV12 @ SY698 @ ( euclid2 @ SV12 @ SY697 @ SV88 @ SY698 @ SV160 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(599,plain,
! [SV161: $i,SV89: $i,SV13: $i] :
( ( ( between @ SV13 @ SV89 @ SV161 )
= $false )
| ( ( ! [SY699: $i,SY700: $i] :
( ~ ( between @ SY699 @ SV89 @ SY700 )
| ( SV13 = SV89 )
| ( between @ ( euclid1 @ SV13 @ SY699 @ SV89 @ SY700 @ SV161 ) @ SV161 @ ( euclid2 @ SV13 @ SY699 @ SV89 @ SY700 @ SV161 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(600,plain,
! [SV215: $i,SV162: $i,SV90: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV90 @ SV14 @ SV162 ) )
= $true )
| ( ( ! [SY777: $i] :
( ~ ( equidistant @ SV14 @ SV215 @ SV14 @ SY777 )
| ~ ( between @ SV14 @ SV90 @ SV215 )
| ! [SY778: $i] :
( ~ ( between @ SV90 @ SY778 @ SV215 )
| ( between @ SV162 @ ( continuous @ SV14 @ SV90 @ SV162 @ SY778 @ SV215 @ SY777 ) @ SY777 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(601,plain,
! [SV216: $i,SV163: $i,SV91: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV91 @ SV15 @ SV163 ) )
= $true )
| ( ( ! [SY779: $i] :
( ~ ( equidistant @ SV15 @ SV216 @ SV15 @ SY779 )
| ~ ( between @ SV15 @ SV91 @ SV216 )
| ! [SY780: $i] :
( ~ ( between @ SV91 @ SY780 @ SV216 )
| ( equidistant @ SV15 @ SY780 @ SV15 @ ( continuous @ SV15 @ SV91 @ SV163 @ SY780 @ SV216 @ SY779 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(602,plain,
! [SV218: $i,SV165: $i,SV95: $i,SV19: $i] :
( ( ( ~ ( equidistant @ SV19 @ SV95 @ SV165 @ SV218 ) )
= $true )
| ( ( equidistant @ SV165 @ SV218 @ SV19 @ SV95 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(603,plain,
! [SV219: $i,SV166: $i,SV96: $i,SV20: $i] :
( ( ( ~ ( equidistant @ SV20 @ SV96 @ SV166 @ SV219 ) )
= $true )
| ( ( equidistant @ SV96 @ SV20 @ SV166 @ SV219 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[546]) ).
thf(604,plain,
! [SV220: $i,SV167: $i,SV97: $i,SV21: $i] :
( ( ( ~ ( equidistant @ SV21 @ SV97 @ SV167 @ SV220 ) )
= $true )
| ( ( equidistant @ SV21 @ SV97 @ SV220 @ SV167 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(605,plain,
! [SV221: $i,SV168: $i,SV98: $i,SV22: $i] :
( ( ( ~ ( equidistant @ SV22 @ SV98 @ SV168 @ SV221 ) )
= $true )
| ( ( equidistant @ SV98 @ SV22 @ SV221 @ SV168 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[548]) ).
thf(606,plain,
! [SV222: $i,SV169: $i,SV99: $i,SV23: $i] :
( ( ( ~ ( equidistant @ SV23 @ SV99 @ SV169 @ SV222 ) )
= $true )
| ( ( equidistant @ SV169 @ SV222 @ SV99 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(607,plain,
! [SV223: $i,SV170: $i,SV100: $i,SV24: $i] :
( ( ( ~ ( equidistant @ SV24 @ SV100 @ SV170 @ SV223 ) )
= $true )
| ( ( equidistant @ SV223 @ SV170 @ SV24 @ SV100 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(608,plain,
! [SV224: $i,SV171: $i,SV101: $i,SV25: $i] :
( ( ( ~ ( equidistant @ SV25 @ SV101 @ SV171 @ SV224 ) )
= $true )
| ( ( equidistant @ SV224 @ SV171 @ SV101 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(609,plain,
! [SV225: $i,SV172: $i,SV102: $i,SV26: $i] :
( ( ( ~ ( equidistant @ SV26 @ SV102 @ SV172 @ SV225 ) )
= $true )
| ( ( ! [SY781: $i,SY782: $i] :
( ~ ( equidistant @ SV172 @ SV225 @ SY781 @ SY782 )
| ( equidistant @ SV26 @ SV102 @ SY781 @ SY782 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(610,plain,
! [SV237: $i,SV174: $i,SV104: $i,SV28: $i] :
( ( ( ! [SY806: $i] :
( SV28
!= ( extension @ SV104 @ SV174 @ SV237 @ SY806 ) ) )
= $true )
| ( ( between @ SV104 @ SV174 @ SV28 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(611,plain,
! [SV226: $i,SV175: $i,SV110: $i,SV35: $i] :
( ( ( ~ ( equidistant @ SV35 @ SV110 @ SV175 @ SV226 ) )
= $true )
| ( ( ! [SY783: $i,SY784: $i] :
( ~ ( equidistant @ SV110 @ SY783 @ SV226 @ SY784 )
| ~ ( between @ SV35 @ SV110 @ SY783 )
| ~ ( between @ SV175 @ SV226 @ SY784 )
| ( equidistant @ SV35 @ SY783 @ SV175 @ SY784 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(612,plain,
! [SV176: $i,SV111: $i,SV36: $i] :
( ( ( between @ SV36 @ SV111 @ SV176 )
= $false )
| ( ( ! [SY723: $i] :
( ~ ( between @ SV36 @ SV111 @ SY723 )
| ~ ( equidistant @ SV111 @ SV176 @ SV111 @ SY723 )
| ( SV36 = SV111 )
| ( SV176 = SY723 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(613,plain,
! [SV177: $i,SV112: $i,SV37: $i] :
( ( ( between @ SV37 @ SV112 @ SV177 )
= $false )
| ( ( ( SV37 = SV112 )
| ( SV177
= ( extension @ SV37 @ SV112 @ SV112 @ SV177 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(614,plain,
! [SV227: $i,SV178: $i,SV113: $i,SV38: $i] :
( ( ( ~ ( equidistant @ SV38 @ SV113 @ SV178 @ SV227 ) )
= $true )
| ( ( ! [SY785: $i,SY786: $i] :
( ( ( extension @ SY785 @ SY786 @ SV38 @ SV113 )
= ( extension @ SY785 @ SY786 @ SV178 @ SV227 ) )
| ( SY785 = SY786 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(615,plain,
! [SV179: $i,SV118: $i,SV43: $i] :
( ( ( between @ SV43 @ SV118 @ SV179 )
= $false )
| ( ( ( SV43 != SV179 )
| ! [SY727: $i] : ( between @ SY727 @ SV118 @ SV179 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[560]) ).
thf(616,plain,
! [SV180: $i,SV119: $i,SV44: $i] :
( ( ( between @ SV44 @ SV119 @ SV180 )
= $false )
| ( ( between @ SV180 @ SV119 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[561]) ).
thf(617,plain,
! [SV181: $i,SV121: $i,SV46: $i] :
( ( ( between @ SV46 @ SV121 @ SV181 )
= $false )
| ( ( ~ ( between @ SV121 @ SV46 @ SV181 )
| ( SV46 = SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[562]) ).
thf(618,plain,
! [SV182: $i,SV122: $i,SV47: $i] :
( ( ( between @ SV47 @ SV122 @ SV182 )
= $false )
| ( ( ~ ( between @ SV47 @ SV182 @ SV122 )
| ( SV122 = SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[563]) ).
thf(619,plain,
! [SV183: $i,SV123: $i,SV48: $i] :
( ( ( between @ SV48 @ SV123 @ SV183 )
= $false )
| ( ( ~ ( between @ SV123 @ SV48 @ SV183 )
| ( SV48 = SV123 )
| ( SV123 = SV183 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[564]) ).
thf(620,plain,
! [SV184: $i,SV124: $i,SV49: $i] :
( ( ( between @ SV49 @ SV124 @ SV184 )
= $false )
| ( ( ~ ( between @ SV49 @ SV184 @ SV124 )
| ( SV49 = SV124 )
| ( SV124 = SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(621,plain,
! [SV185: $i,SV125: $i,SV50: $i] :
( ( ( between @ SV50 @ SV125 @ SV185 )
= $false )
| ( ( ! [SY728: $i] :
~ ( between @ SV125 @ SV185 @ SY728 )
| ( between @ SV50 @ SV125 @ SV185 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[566]) ).
thf(622,plain,
! [SV186: $i,SV126: $i,SV51: $i] :
( ( ( between @ SV51 @ SV126 @ SV186 )
= $false )
| ( ( ! [SY729: $i] :
( ~ ( between @ SV51 @ SV186 @ SY729 )
| ( between @ SV126 @ SV186 @ SY729 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(623,plain,
! [SV187: $i,SV127: $i,SV52: $i] :
( ( ( between @ SV52 @ SV127 @ SV187 )
= $false )
| ( ( ! [SY730: $i] :
( ~ ( between @ SV127 @ SV187 @ SY730 )
| ( SV127 = SV187 )
| ( between @ SV52 @ SV187 @ SY730 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(624,plain,
! [SV188: $i,SV128: $i,SV53: $i] :
( ( ( between @ SV53 @ SV128 @ SV188 )
= $false )
| ( ( ! [SY731: $i] :
( ~ ( between @ SV128 @ SV188 @ SY731 )
| ( SV128 = SV188 )
| ( between @ SV53 @ SV128 @ SY731 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(625,plain,
! [SV189: $i,SV129: $i,SV54: $i] :
( ( ( between @ SV54 @ SV129 @ SV189 )
= $false )
| ( ( ! [SY732: $i] :
( ~ ( between @ SV129 @ SY732 @ SV189 )
| ( between @ SV54 @ SY732 @ SV189 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(626,plain,
! [SV190: $i,SV130: $i,SV55: $i] :
( ( ( between @ SV55 @ SV130 @ SV190 )
= $false )
| ( ( ! [SY733: $i] :
( ~ ( between @ SV55 @ SV190 @ SY733 )
| ( between @ SV55 @ SV130 @ SY733 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(627,plain,
! [SV229: $i,SV192: $i,SV134: $i,SV59: $i] :
( ( ( ~ ( between @ SV59 @ SV134 @ SV192 ) )
= $true )
| ( ( ! [SY787: $i] :
( ~ ( between @ SV229 @ SY787 @ SV192 )
| ! [SY788: $i] :
( ~ ( between @ SV59 @ SY788 @ SV229 )
| ( between @ SY788 @ ( inner_pasch @ SY787 @ ( inner_pasch @ SV59 @ SY788 @ SV229 @ SY787 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV192 )
| ( between @ SV134 @ ( inner_pasch @ SY787 @ ( inner_pasch @ SV59 @ SY788 @ SV229 @ SY787 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SY787 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(628,plain,
! [SV193: $i,SV135: $i,SV60: $i] :
( ( ( between @ SV60 @ SV135 @ SV193 )
= $false )
| ( ( ! [SY738: $i] :
( ~ ( equidistant @ SV60 @ SV193 @ SV60 @ SY738 )
| ~ ( equidistant @ SV135 @ SV193 @ SV135 @ SY738 )
| ( SV60 = SV135 )
| ( SV193 = SY738 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(629,plain,
! [SV238: $i,SV230: $i,SV194: $i,SV136: $i,SV61: $i] :
( ( ! [SY807: $i] :
( ~ ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 )
| ~ ( equidistant @ SV61 @ SV238 @ SV194 @ SY807 )
| ! [SY808: $i,SY809: $i] :
( ~ ( equidistant @ SV61 @ SY808 @ SV194 @ SY809 )
| ~ ( equidistant @ SV238 @ SY808 @ SY807 @ SY809 )
| ~ ( between @ SV61 @ SV136 @ SV238 )
| ~ ( between @ SV194 @ SV230 @ SY807 )
| ( equidistant @ SV136 @ SY808 @ SV230 @ SY809 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(630,plain,
! [SV231: $i,SV195: $i,SV137: $i,SV62: $i] :
( ( ( ~ ( between @ SV62 @ SV137 @ SV195 ) )
= $true )
| ( ( ! [SY793: $i,SY794: $i] :
( ~ ( between @ SV231 @ SY793 @ SY794 )
| ~ ( equidistant @ SV62 @ SV137 @ SV231 @ SY793 )
| ~ ( equidistant @ SV62 @ SV195 @ SV231 @ SY794 )
| ( equidistant @ SV137 @ SV195 @ SY793 @ SY794 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[576]) ).
thf(631,plain,
! [SV239: $i,SV232: $i,SV196: $i,SV138: $i,SV63: $i] :
( ( ! [SY810: $i] :
( ~ ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 )
| ~ ( equidistant @ SV138 @ SV239 @ SV232 @ SY810 )
| ! [SY811: $i,SY812: $i] :
( ~ ( equidistant @ SV63 @ SY811 @ SV196 @ SY812 )
| ~ ( equidistant @ SV239 @ SY811 @ SY810 @ SY812 )
| ~ ( between @ SV63 @ SV138 @ SV239 )
| ~ ( between @ SV196 @ SV232 @ SY810 )
| ( equidistant @ SV138 @ SY811 @ SV232 @ SY812 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(632,plain,
! [SV197: $i,SV139: $i,SV64: $i] :
( ( ( between @ SV64 @ SV139 @ SV197 )
= $false )
| ( ( ! [SY752: $i] :
( ~ ( equidistant @ SV64 @ SV139 @ SV64 @ SY752 )
| ~ ( equidistant @ SV197 @ SV139 @ SV197 @ SY752 )
| ( SV139 = SY752 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(633,plain,
! [SV199: $i,SV141: $i,SV66: $i] :
( ( ( between @ SV66 @ SV141 @ SV199 )
= $false )
| ( ( ! [SY754: $i,SY755: $i] :
( ~ ( equidistant @ SV66 @ SV199 @ SY754 @ SY755 )
| ( between @ SY754 @ ( insertion @ SY754 @ SY755 @ SV66 @ SV141 ) @ SY755 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[580]) ).
thf(634,plain,
! [SV200: $i,SV142: $i,SV67: $i] :
( ( ( between @ SV67 @ SV142 @ SV200 )
= $false )
| ( ( ! [SY756: $i,SY757: $i] :
( ~ ( equidistant @ SV67 @ SV200 @ SY756 @ SY757 )
| ( equidistant @ SV142 @ SV200 @ ( insertion @ SY756 @ SY757 @ SV67 @ SV142 ) @ SY757 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[581]) ).
thf(635,plain,
! [SV201: $i,SV143: $i,SV68: $i] :
( ( ( between @ SV68 @ SV143 @ SV201 )
= $false )
| ( ( SV143
= ( insertion @ SV68 @ SV201 @ SV68 @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(636,plain,
! [SV234: $i,SV202: $i,SV144: $i,SV69: $i] :
( ( ( ~ ( equidistant @ SV69 @ SV144 @ SV202 @ SV234 ) )
= $true )
| ( ( ! [SY799: $i,SY800: $i] :
( ( insertion @ SY799 @ SY800 @ SV69 @ SV144 )
= ( insertion @ SY799 @ SY800 @ SV202 @ SV234 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[583]) ).
thf(637,plain,
! [SV235: $i,SV203: $i,SV145: $i,SV70: $i] :
( ( ( ~ ( equidistant @ SV70 @ SV145 @ SV203 @ SV235 ) )
= $true )
| ( ( ! [SY801: $i,SY802: $i] :
( ~ ( equidistant @ SV145 @ SY801 @ SV235 @ SY802 )
| ~ ( equidistant @ SV70 @ SY801 @ SV203 @ SY802 )
| ~ ( between @ SV70 @ SV145 @ SY801 )
| ( between @ SV203 @ SV235 @ SY802 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[584]) ).
thf(638,plain,
! [SV204: $i,SV146: $i,SV71: $i] :
( ( ( between @ SV71 @ SV146 @ SV204 )
= $false )
| ( ( ! [SY764: $i] :
( ~ ( between @ SV71 @ SV146 @ SY764 )
| ( SV71 = SV146 )
| ( between @ SV71 @ SV204 @ SY764 )
| ( between @ SV71 @ SY764 @ SV204 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(639,plain,
! [SV205: $i,SV147: $i,SV72: $i] :
( ( ( between @ SV72 @ SV147 @ SV205 )
= $false )
| ( ( ! [SY765: $i] :
( ~ ( between @ SV72 @ SV147 @ SY765 )
| ( SV72 = SV147 )
| ( between @ SV147 @ SV205 @ SY765 )
| ( between @ SV147 @ SY765 @ SV205 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(640,plain,
! [SV206: $i,SV148: $i,SV73: $i] :
( ( ( between @ SV73 @ SV148 @ SV206 )
= $false )
| ( ( ! [SY766: $i] :
( ~ ( between @ SY766 @ SV148 @ SV206 )
| ( SV148 = SV206 )
| ( between @ SV73 @ SY766 @ SV148 )
| ( between @ SY766 @ SV73 @ SV148 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(641,plain,
! [SV207: $i,SV149: $i,SV74: $i] :
( ( ( between @ SV74 @ SV149 @ SV207 )
= $false )
| ( ( ! [SY767: $i] :
( ~ ( between @ SV74 @ SY767 @ SV207 )
| ( between @ SV74 @ SV149 @ SY767 )
| ( between @ SV74 @ SY767 @ SV149 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[588]) ).
thf(642,plain,
! [SV208: $i,SV150: $i,SV75: $i] :
( ( ( between @ SV75 @ SV150 @ SV208 )
= $false )
| ( ( ! [SY768: $i] :
( ~ ( between @ SV75 @ SY768 @ SV208 )
| ( between @ SV150 @ SY768 @ SV208 )
| ( between @ SY768 @ SV150 @ SV208 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(643,plain,
! [SV209: $i,SV151: $i,SV76: $i] :
( ( ( between @ SV76 @ SV151 @ SV209 )
= $false )
| ( ( ! [SY769: $i,SY770: $i] :
( ~ ( between @ SV151 @ SY769 @ SY770 )
| ~ ( between @ SV76 @ SY770 @ SV209 )
| ( between @ SV76 @ SY769 @ SV209 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(644,plain,
! [SV210: $i,SV152: $i,SV78: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV78 @ SV152 @ SV210 )
= $false )
| ( ( ! [SY771: $i,SY772: $i] :
( ~ ( equidistant @ SV2 @ SV78 @ SY771 @ SY772 )
| ( equidistant @ SV152 @ SV210 @ SY771 @ SY772 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[591]) ).
thf(645,plain,
! [SV240: $i,SV236: $i,SV214: $i,SV155: $i,SV82: $i,SV6: $i] :
( ( ~ ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
| ~ ( equidistant @ SV82 @ SV236 @ SV214 @ SV240 )
| ! [SY813: $i,SY814: $i] :
( ~ ( equidistant @ SV6 @ SY813 @ SV155 @ SY814 )
| ~ ( equidistant @ SV82 @ SY813 @ SV214 @ SY814 )
| ~ ( between @ SV6 @ SV82 @ SV236 )
| ~ ( between @ SV155 @ SV214 @ SV240 )
| ( SV6 = SV82 )
| ( equidistant @ SV236 @ SY813 @ SV240 @ SY814 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(646,plain,
! [SV8: $i,SV84: $i,SV156: $i,SV241: $i] :
( ( ( ! [SY815: $i] :
( ~ ( between @ SV241 @ SY815 @ SV156 )
| ( between @ SV84 @ ( inner_pasch @ SV8 @ SV84 @ SV156 @ SY815 @ SV241 ) @ SV241 ) ) )
= $true )
| ( ( between @ SV8 @ SV84 @ SV156 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(647,plain,
! [SV85: $i,SV9: $i,SV157: $i,SV242: $i] :
( ( ( ! [SY816: $i] :
( ~ ( between @ SV242 @ SY816 @ SV157 )
| ( between @ SY816 @ ( inner_pasch @ SV9 @ SV85 @ SV157 @ SY816 @ SV242 ) @ SV9 ) ) )
= $true )
| ( ( between @ SV9 @ SV85 @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(648,plain,
! [SV10: $i,SV158: $i,SV86: $i,SV243: $i] :
( ( ( ~ ( equidistant @ SV243 @ SV86 @ SV243 @ SV158 )
| ! [SY817: $i] :
( ~ ( equidistant @ SY817 @ SV86 @ SY817 @ SV158 )
| ( between @ SV10 @ SV243 @ SY817 )
| ( between @ SV243 @ SY817 @ SV10 )
| ( SV86 = SV158 )
| ( between @ SY817 @ SV10 @ SV243 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV86 @ SV10 @ SV158 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(649,plain,
! [SV159: $i,SV11: $i,SV87: $i,SV244: $i] :
( ( ( ! [SY818: $i] :
( ~ ( between @ SV244 @ SV87 @ SY818 )
| ( SV11 = SV87 )
| ( between @ SV11 @ SV244 @ ( euclid1 @ SV11 @ SV244 @ SV87 @ SY818 @ SV159 ) ) ) )
= $true )
| ( ( between @ SV11 @ SV87 @ SV159 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(650,plain,
! [SV160: $i,SV12: $i,SV88: $i,SV245: $i] :
( ( ( ! [SY819: $i] :
( ~ ( between @ SV245 @ SV88 @ SY819 )
| ( SV12 = SV88 )
| ( between @ SV12 @ SY819 @ ( euclid2 @ SV12 @ SV245 @ SV88 @ SY819 @ SV160 ) ) ) )
= $true )
| ( ( between @ SV12 @ SV88 @ SV160 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(651,plain,
! [SV161: $i,SV13: $i,SV89: $i,SV246: $i] :
( ( ( ! [SY820: $i] :
( ~ ( between @ SV246 @ SV89 @ SY820 )
| ( SV13 = SV89 )
| ( between @ ( euclid1 @ SV13 @ SV246 @ SV89 @ SY820 @ SV161 ) @ SV161 @ ( euclid2 @ SV13 @ SV246 @ SV89 @ SY820 @ SV161 ) ) ) )
= $true )
| ( ( between @ SV13 @ SV89 @ SV161 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(652,plain,
! [SV215: $i,SV162: $i,SV90: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV90 @ SV14 @ SV162 )
= $false )
| ( ( ! [SY777: $i] :
( ~ ( equidistant @ SV14 @ SV215 @ SV14 @ SY777 )
| ~ ( between @ SV14 @ SV90 @ SV215 )
| ! [SY778: $i] :
( ~ ( between @ SV90 @ SY778 @ SV215 )
| ( between @ SV162 @ ( continuous @ SV14 @ SV90 @ SV162 @ SY778 @ SV215 @ SY777 ) @ SY777 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[600]) ).
thf(653,plain,
! [SV216: $i,SV163: $i,SV91: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV91 @ SV15 @ SV163 )
= $false )
| ( ( ! [SY779: $i] :
( ~ ( equidistant @ SV15 @ SV216 @ SV15 @ SY779 )
| ~ ( between @ SV15 @ SV91 @ SV216 )
| ! [SY780: $i] :
( ~ ( between @ SV91 @ SY780 @ SV216 )
| ( equidistant @ SV15 @ SY780 @ SV15 @ ( continuous @ SV15 @ SV91 @ SV163 @ SY780 @ SV216 @ SY779 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(654,plain,
! [SV218: $i,SV165: $i,SV95: $i,SV19: $i] :
( ( ( equidistant @ SV19 @ SV95 @ SV165 @ SV218 )
= $false )
| ( ( equidistant @ SV165 @ SV218 @ SV19 @ SV95 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[602]) ).
thf(655,plain,
! [SV219: $i,SV166: $i,SV96: $i,SV20: $i] :
( ( ( equidistant @ SV20 @ SV96 @ SV166 @ SV219 )
= $false )
| ( ( equidistant @ SV96 @ SV20 @ SV166 @ SV219 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(656,plain,
! [SV220: $i,SV167: $i,SV97: $i,SV21: $i] :
( ( ( equidistant @ SV21 @ SV97 @ SV167 @ SV220 )
= $false )
| ( ( equidistant @ SV21 @ SV97 @ SV220 @ SV167 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[604]) ).
thf(657,plain,
! [SV221: $i,SV168: $i,SV98: $i,SV22: $i] :
( ( ( equidistant @ SV22 @ SV98 @ SV168 @ SV221 )
= $false )
| ( ( equidistant @ SV98 @ SV22 @ SV221 @ SV168 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(658,plain,
! [SV222: $i,SV169: $i,SV99: $i,SV23: $i] :
( ( ( equidistant @ SV23 @ SV99 @ SV169 @ SV222 )
= $false )
| ( ( equidistant @ SV169 @ SV222 @ SV99 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(659,plain,
! [SV223: $i,SV170: $i,SV100: $i,SV24: $i] :
( ( ( equidistant @ SV24 @ SV100 @ SV170 @ SV223 )
= $false )
| ( ( equidistant @ SV223 @ SV170 @ SV24 @ SV100 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(660,plain,
! [SV224: $i,SV171: $i,SV101: $i,SV25: $i] :
( ( ( equidistant @ SV25 @ SV101 @ SV171 @ SV224 )
= $false )
| ( ( equidistant @ SV224 @ SV171 @ SV101 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(661,plain,
! [SV225: $i,SV172: $i,SV102: $i,SV26: $i] :
( ( ( equidistant @ SV26 @ SV102 @ SV172 @ SV225 )
= $false )
| ( ( ! [SY781: $i,SY782: $i] :
( ~ ( equidistant @ SV172 @ SV225 @ SY781 @ SY782 )
| ( equidistant @ SV26 @ SV102 @ SY781 @ SY782 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(662,plain,
! [SV247: $i,SV237: $i,SV174: $i,SV104: $i,SV28: $i] :
( ( ( SV28
!= ( extension @ SV104 @ SV174 @ SV237 @ SV247 ) )
= $true )
| ( ( between @ SV104 @ SV174 @ SV28 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(663,plain,
! [SV226: $i,SV175: $i,SV110: $i,SV35: $i] :
( ( ( equidistant @ SV35 @ SV110 @ SV175 @ SV226 )
= $false )
| ( ( ! [SY783: $i,SY784: $i] :
( ~ ( equidistant @ SV110 @ SY783 @ SV226 @ SY784 )
| ~ ( between @ SV35 @ SV110 @ SY783 )
| ~ ( between @ SV175 @ SV226 @ SY784 )
| ( equidistant @ SV35 @ SY783 @ SV175 @ SY784 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(664,plain,
! [SV176: $i,SV248: $i,SV111: $i,SV36: $i] :
( ( ( ~ ( between @ SV36 @ SV111 @ SV248 )
| ~ ( equidistant @ SV111 @ SV176 @ SV111 @ SV248 )
| ( SV36 = SV111 )
| ( SV176 = SV248 ) )
= $true )
| ( ( between @ SV36 @ SV111 @ SV176 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(665,plain,
! [SV177: $i,SV112: $i,SV37: $i] :
( ( ( SV37 = SV112 )
= $true )
| ( ( SV177
= ( extension @ SV37 @ SV112 @ SV112 @ SV177 ) )
= $true )
| ( ( between @ SV37 @ SV112 @ SV177 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[613]) ).
thf(666,plain,
! [SV227: $i,SV178: $i,SV113: $i,SV38: $i] :
( ( ( equidistant @ SV38 @ SV113 @ SV178 @ SV227 )
= $false )
| ( ( ! [SY785: $i,SY786: $i] :
( ( ( extension @ SY785 @ SY786 @ SV38 @ SV113 )
= ( extension @ SY785 @ SY786 @ SV178 @ SV227 ) )
| ( SY785 = SY786 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(667,plain,
! [SV118: $i,SV179: $i,SV43: $i] :
( ( ( SV43 != SV179 )
= $true )
| ( ( ! [SY727: $i] : ( between @ SY727 @ SV118 @ SV179 ) )
= $true )
| ( ( between @ SV43 @ SV118 @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[615]) ).
thf(668,plain,
! [SV181: $i,SV46: $i,SV121: $i] :
( ( ( ~ ( between @ SV121 @ SV46 @ SV181 ) )
= $true )
| ( ( SV46 = SV121 )
= $true )
| ( ( between @ SV46 @ SV121 @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(669,plain,
! [SV122: $i,SV182: $i,SV47: $i] :
( ( ( ~ ( between @ SV47 @ SV182 @ SV122 ) )
= $true )
| ( ( SV122 = SV182 )
= $true )
| ( ( between @ SV47 @ SV122 @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(670,plain,
! [SV183: $i,SV48: $i,SV123: $i] :
( ( ( ~ ( between @ SV123 @ SV48 @ SV183 ) )
= $true )
| ( ( ( SV48 = SV123 )
| ( SV123 = SV183 ) )
= $true )
| ( ( between @ SV48 @ SV123 @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(671,plain,
! [SV124: $i,SV184: $i,SV49: $i] :
( ( ( ~ ( between @ SV49 @ SV184 @ SV124 ) )
= $true )
| ( ( ( SV49 = SV124 )
| ( SV124 = SV184 ) )
= $true )
| ( ( between @ SV49 @ SV124 @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(672,plain,
! [SV50: $i,SV185: $i,SV125: $i] :
( ( ( ! [SY728: $i] :
~ ( between @ SV125 @ SV185 @ SY728 ) )
= $true )
| ( ( between @ SV50 @ SV125 @ SV185 )
= $true )
| ( ( between @ SV50 @ SV125 @ SV185 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(673,plain,
! [SV126: $i,SV249: $i,SV186: $i,SV51: $i] :
( ( ( ~ ( between @ SV51 @ SV186 @ SV249 )
| ( between @ SV126 @ SV186 @ SV249 ) )
= $true )
| ( ( between @ SV51 @ SV126 @ SV186 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(674,plain,
! [SV52: $i,SV250: $i,SV187: $i,SV127: $i] :
( ( ( ~ ( between @ SV127 @ SV187 @ SV250 )
| ( SV127 = SV187 )
| ( between @ SV52 @ SV187 @ SV250 ) )
= $true )
| ( ( between @ SV52 @ SV127 @ SV187 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(675,plain,
! [SV53: $i,SV251: $i,SV188: $i,SV128: $i] :
( ( ( ~ ( between @ SV128 @ SV188 @ SV251 )
| ( SV128 = SV188 )
| ( between @ SV53 @ SV128 @ SV251 ) )
= $true )
| ( ( between @ SV53 @ SV128 @ SV188 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(676,plain,
! [SV54: $i,SV189: $i,SV252: $i,SV129: $i] :
( ( ( ~ ( between @ SV129 @ SV252 @ SV189 )
| ( between @ SV54 @ SV252 @ SV189 ) )
= $true )
| ( ( between @ SV54 @ SV129 @ SV189 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(677,plain,
! [SV130: $i,SV253: $i,SV190: $i,SV55: $i] :
( ( ( ~ ( between @ SV55 @ SV190 @ SV253 )
| ( between @ SV55 @ SV130 @ SV253 ) )
= $true )
| ( ( between @ SV55 @ SV130 @ SV190 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(678,plain,
! [SV229: $i,SV192: $i,SV134: $i,SV59: $i] :
( ( ( between @ SV59 @ SV134 @ SV192 )
= $false )
| ( ( ! [SY787: $i] :
( ~ ( between @ SV229 @ SY787 @ SV192 )
| ! [SY788: $i] :
( ~ ( between @ SV59 @ SY788 @ SV229 )
| ( between @ SY788 @ ( inner_pasch @ SY787 @ ( inner_pasch @ SV59 @ SY788 @ SV229 @ SY787 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV192 )
| ( between @ SV134 @ ( inner_pasch @ SY787 @ ( inner_pasch @ SV59 @ SY788 @ SV229 @ SY787 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SY787 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[627]) ).
thf(679,plain,
! [SV135: $i,SV254: $i,SV193: $i,SV60: $i] :
( ( ( ~ ( equidistant @ SV60 @ SV193 @ SV60 @ SV254 )
| ~ ( equidistant @ SV135 @ SV193 @ SV135 @ SV254 )
| ( SV60 = SV135 )
| ( SV193 = SV254 ) )
= $true )
| ( ( between @ SV60 @ SV135 @ SV193 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(680,plain,
! [SV255: $i,SV238: $i,SV230: $i,SV194: $i,SV136: $i,SV61: $i] :
( ( ~ ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 )
| ~ ( equidistant @ SV61 @ SV238 @ SV194 @ SV255 )
| ! [SY821: $i,SY822: $i] :
( ~ ( equidistant @ SV61 @ SY821 @ SV194 @ SY822 )
| ~ ( equidistant @ SV238 @ SY821 @ SV255 @ SY822 )
| ~ ( between @ SV61 @ SV136 @ SV238 )
| ~ ( between @ SV194 @ SV230 @ SV255 )
| ( equidistant @ SV136 @ SY821 @ SV230 @ SY822 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(681,plain,
! [SV231: $i,SV195: $i,SV137: $i,SV62: $i] :
( ( ( between @ SV62 @ SV137 @ SV195 )
= $false )
| ( ( ! [SY793: $i,SY794: $i] :
( ~ ( between @ SV231 @ SY793 @ SY794 )
| ~ ( equidistant @ SV62 @ SV137 @ SV231 @ SY793 )
| ~ ( equidistant @ SV62 @ SV195 @ SV231 @ SY794 )
| ( equidistant @ SV137 @ SV195 @ SY793 @ SY794 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[630]) ).
thf(682,plain,
! [SV256: $i,SV239: $i,SV232: $i,SV196: $i,SV138: $i,SV63: $i] :
( ( ~ ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 )
| ~ ( equidistant @ SV138 @ SV239 @ SV232 @ SV256 )
| ! [SY823: $i,SY824: $i] :
( ~ ( equidistant @ SV63 @ SY823 @ SV196 @ SY824 )
| ~ ( equidistant @ SV239 @ SY823 @ SV256 @ SY824 )
| ~ ( between @ SV63 @ SV138 @ SV239 )
| ~ ( between @ SV196 @ SV232 @ SV256 )
| ( equidistant @ SV138 @ SY823 @ SV232 @ SY824 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(683,plain,
! [SV197: $i,SV257: $i,SV139: $i,SV64: $i] :
( ( ( ~ ( equidistant @ SV64 @ SV139 @ SV64 @ SV257 )
| ~ ( equidistant @ SV197 @ SV139 @ SV197 @ SV257 )
| ( SV139 = SV257 ) )
= $true )
| ( ( between @ SV64 @ SV139 @ SV197 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(684,plain,
! [SV141: $i,SV258: $i,SV199: $i,SV66: $i] :
( ( ( ! [SY825: $i] :
( ~ ( equidistant @ SV66 @ SV199 @ SV258 @ SY825 )
| ( between @ SV258 @ ( insertion @ SV258 @ SY825 @ SV66 @ SV141 ) @ SY825 ) ) )
= $true )
| ( ( between @ SV66 @ SV141 @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(685,plain,
! [SV142: $i,SV259: $i,SV200: $i,SV67: $i] :
( ( ( ! [SY826: $i] :
( ~ ( equidistant @ SV67 @ SV200 @ SV259 @ SY826 )
| ( equidistant @ SV142 @ SV200 @ ( insertion @ SV259 @ SY826 @ SV67 @ SV142 ) @ SY826 ) ) )
= $true )
| ( ( between @ SV67 @ SV142 @ SV200 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(686,plain,
! [SV234: $i,SV202: $i,SV144: $i,SV69: $i] :
( ( ( equidistant @ SV69 @ SV144 @ SV202 @ SV234 )
= $false )
| ( ( ! [SY799: $i,SY800: $i] :
( ( insertion @ SY799 @ SY800 @ SV69 @ SV144 )
= ( insertion @ SY799 @ SY800 @ SV202 @ SV234 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(687,plain,
! [SV235: $i,SV203: $i,SV145: $i,SV70: $i] :
( ( ( equidistant @ SV70 @ SV145 @ SV203 @ SV235 )
= $false )
| ( ( ! [SY801: $i,SY802: $i] :
( ~ ( equidistant @ SV145 @ SY801 @ SV235 @ SY802 )
| ~ ( equidistant @ SV70 @ SY801 @ SV203 @ SY802 )
| ~ ( between @ SV70 @ SV145 @ SY801 )
| ( between @ SV203 @ SV235 @ SY802 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(688,plain,
! [SV204: $i,SV260: $i,SV146: $i,SV71: $i] :
( ( ( ~ ( between @ SV71 @ SV146 @ SV260 )
| ( SV71 = SV146 )
| ( between @ SV71 @ SV204 @ SV260 )
| ( between @ SV71 @ SV260 @ SV204 ) )
= $true )
| ( ( between @ SV71 @ SV146 @ SV204 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(689,plain,
! [SV205: $i,SV261: $i,SV147: $i,SV72: $i] :
( ( ( ~ ( between @ SV72 @ SV147 @ SV261 )
| ( SV72 = SV147 )
| ( between @ SV147 @ SV205 @ SV261 )
| ( between @ SV147 @ SV261 @ SV205 ) )
= $true )
| ( ( between @ SV72 @ SV147 @ SV205 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(690,plain,
! [SV73: $i,SV206: $i,SV148: $i,SV262: $i] :
( ( ( ~ ( between @ SV262 @ SV148 @ SV206 )
| ( SV148 = SV206 )
| ( between @ SV73 @ SV262 @ SV148 )
| ( between @ SV262 @ SV73 @ SV148 ) )
= $true )
| ( ( between @ SV73 @ SV148 @ SV206 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(691,plain,
! [SV149: $i,SV207: $i,SV263: $i,SV74: $i] :
( ( ( ~ ( between @ SV74 @ SV263 @ SV207 )
| ( between @ SV74 @ SV149 @ SV263 )
| ( between @ SV74 @ SV263 @ SV149 ) )
= $true )
| ( ( between @ SV74 @ SV149 @ SV207 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(692,plain,
! [SV150: $i,SV208: $i,SV264: $i,SV75: $i] :
( ( ( ~ ( between @ SV75 @ SV264 @ SV208 )
| ( between @ SV150 @ SV264 @ SV208 )
| ( between @ SV264 @ SV150 @ SV208 ) )
= $true )
| ( ( between @ SV75 @ SV150 @ SV208 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(693,plain,
! [SV209: $i,SV76: $i,SV265: $i,SV151: $i] :
( ( ( ! [SY827: $i] :
( ~ ( between @ SV151 @ SV265 @ SY827 )
| ~ ( between @ SV76 @ SY827 @ SV209 )
| ( between @ SV76 @ SV265 @ SV209 ) ) )
= $true )
| ( ( between @ SV76 @ SV151 @ SV209 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(694,plain,
! [SV210: $i,SV152: $i,SV266: $i,SV78: $i,SV2: $i] :
( ( ( ! [SY828: $i] :
( ~ ( equidistant @ SV2 @ SV78 @ SV266 @ SY828 )
| ( equidistant @ SV152 @ SV210 @ SV266 @ SY828 ) ) )
= $true )
| ( ( equidistant @ SV2 @ SV78 @ SV152 @ SV210 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[644]) ).
thf(695,plain,
! [SV240: $i,SV236: $i,SV214: $i,SV155: $i,SV82: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 ) )
= $true )
| ( ( ~ ( equidistant @ SV82 @ SV236 @ SV214 @ SV240 )
| ! [SY813: $i,SY814: $i] :
( ~ ( equidistant @ SV6 @ SY813 @ SV155 @ SY814 )
| ~ ( equidistant @ SV82 @ SY813 @ SV214 @ SY814 )
| ~ ( between @ SV6 @ SV82 @ SV236 )
| ~ ( between @ SV155 @ SV214 @ SV240 )
| ( SV6 = SV82 )
| ( equidistant @ SV236 @ SY813 @ SV240 @ SY814 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[645]) ).
thf(696,plain,
! [SV8: $i,SV84: $i,SV156: $i,SV267: $i,SV241: $i] :
( ( ( ~ ( between @ SV241 @ SV267 @ SV156 )
| ( between @ SV84 @ ( inner_pasch @ SV8 @ SV84 @ SV156 @ SV267 @ SV241 ) @ SV241 ) )
= $true )
| ( ( between @ SV8 @ SV84 @ SV156 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(697,plain,
! [SV85: $i,SV9: $i,SV157: $i,SV268: $i,SV242: $i] :
( ( ( ~ ( between @ SV242 @ SV268 @ SV157 )
| ( between @ SV268 @ ( inner_pasch @ SV9 @ SV85 @ SV157 @ SV268 @ SV242 ) @ SV9 ) )
= $true )
| ( ( between @ SV9 @ SV85 @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(698,plain,
! [SV10: $i,SV158: $i,SV86: $i,SV243: $i] :
( ( ( ~ ( equidistant @ SV243 @ SV86 @ SV243 @ SV158 ) )
= $true )
| ( ( ! [SY817: $i] :
( ~ ( equidistant @ SY817 @ SV86 @ SY817 @ SV158 )
| ( between @ SV10 @ SV243 @ SY817 )
| ( between @ SV243 @ SY817 @ SV10 )
| ( SV86 = SV158 )
| ( between @ SY817 @ SV10 @ SV243 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV86 @ SV10 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[648]) ).
thf(699,plain,
! [SV159: $i,SV11: $i,SV269: $i,SV87: $i,SV244: $i] :
( ( ( ~ ( between @ SV244 @ SV87 @ SV269 )
| ( SV11 = SV87 )
| ( between @ SV11 @ SV244 @ ( euclid1 @ SV11 @ SV244 @ SV87 @ SV269 @ SV159 ) ) )
= $true )
| ( ( between @ SV11 @ SV87 @ SV159 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(700,plain,
! [SV160: $i,SV12: $i,SV270: $i,SV88: $i,SV245: $i] :
( ( ( ~ ( between @ SV245 @ SV88 @ SV270 )
| ( SV12 = SV88 )
| ( between @ SV12 @ SV270 @ ( euclid2 @ SV12 @ SV245 @ SV88 @ SV270 @ SV160 ) ) )
= $true )
| ( ( between @ SV12 @ SV88 @ SV160 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(701,plain,
! [SV161: $i,SV13: $i,SV271: $i,SV89: $i,SV246: $i] :
( ( ( ~ ( between @ SV246 @ SV89 @ SV271 )
| ( SV13 = SV89 )
| ( between @ ( euclid1 @ SV13 @ SV246 @ SV89 @ SV271 @ SV161 ) @ SV161 @ ( euclid2 @ SV13 @ SV246 @ SV89 @ SV271 @ SV161 ) ) )
= $true )
| ( ( between @ SV13 @ SV89 @ SV161 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(702,plain,
! [SV162: $i,SV90: $i,SV272: $i,SV215: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV215 @ SV14 @ SV272 )
| ~ ( between @ SV14 @ SV90 @ SV215 )
| ! [SY829: $i] :
( ~ ( between @ SV90 @ SY829 @ SV215 )
| ( between @ SV162 @ ( continuous @ SV14 @ SV90 @ SV162 @ SY829 @ SV215 @ SV272 ) @ SV272 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV90 @ SV14 @ SV162 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(703,plain,
! [SV163: $i,SV91: $i,SV273: $i,SV216: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV216 @ SV15 @ SV273 )
| ~ ( between @ SV15 @ SV91 @ SV216 )
| ! [SY830: $i] :
( ~ ( between @ SV91 @ SY830 @ SV216 )
| ( equidistant @ SV15 @ SY830 @ SV15 @ ( continuous @ SV15 @ SV91 @ SV163 @ SY830 @ SV216 @ SV273 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV91 @ SV15 @ SV163 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(704,plain,
! [SV102: $i,SV26: $i,SV274: $i,SV225: $i,SV172: $i] :
( ( ( ! [SY831: $i] :
( ~ ( equidistant @ SV172 @ SV225 @ SV274 @ SY831 )
| ( equidistant @ SV26 @ SV102 @ SV274 @ SY831 ) ) )
= $true )
| ( ( equidistant @ SV26 @ SV102 @ SV172 @ SV225 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(705,plain,
! [SV247: $i,SV237: $i,SV174: $i,SV104: $i,SV28: $i] :
( ( ( SV28
= ( extension @ SV104 @ SV174 @ SV237 @ SV247 ) )
= $false )
| ( ( between @ SV104 @ SV174 @ SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[662]) ).
thf(706,plain,
! [SV175: $i,SV35: $i,SV226: $i,SV275: $i,SV110: $i] :
( ( ( ! [SY832: $i] :
( ~ ( equidistant @ SV110 @ SV275 @ SV226 @ SY832 )
| ~ ( between @ SV35 @ SV110 @ SV275 )
| ~ ( between @ SV175 @ SV226 @ SY832 )
| ( equidistant @ SV35 @ SV275 @ SV175 @ SY832 ) ) )
= $true )
| ( ( equidistant @ SV35 @ SV110 @ SV175 @ SV226 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(707,plain,
! [SV176: $i,SV248: $i,SV111: $i,SV36: $i] :
( ( ( ~ ( between @ SV36 @ SV111 @ SV248 ) )
= $true )
| ( ( ~ ( equidistant @ SV111 @ SV176 @ SV111 @ SV248 )
| ( SV36 = SV111 )
| ( SV176 = SV248 ) )
= $true )
| ( ( between @ SV36 @ SV111 @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(708,plain,
! [SV227: $i,SV178: $i,SV113: $i,SV38: $i,SV276: $i] :
( ( ( ! [SY833: $i] :
( ( ( extension @ SV276 @ SY833 @ SV38 @ SV113 )
= ( extension @ SV276 @ SY833 @ SV178 @ SV227 ) )
| ( SV276 = SY833 ) ) )
= $true )
| ( ( equidistant @ SV38 @ SV113 @ SV178 @ SV227 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(709,plain,
! [SV118: $i,SV179: $i,SV43: $i] :
( ( ( SV43 = SV179 )
= $false )
| ( ( ! [SY727: $i] : ( between @ SY727 @ SV118 @ SV179 ) )
= $true )
| ( ( between @ SV43 @ SV118 @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[667]) ).
thf(710,plain,
! [SV181: $i,SV46: $i,SV121: $i] :
( ( ( between @ SV121 @ SV46 @ SV181 )
= $false )
| ( ( SV46 = SV121 )
= $true )
| ( ( between @ SV46 @ SV121 @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[668]) ).
thf(711,plain,
! [SV122: $i,SV182: $i,SV47: $i] :
( ( ( between @ SV47 @ SV182 @ SV122 )
= $false )
| ( ( SV122 = SV182 )
= $true )
| ( ( between @ SV47 @ SV122 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(712,plain,
! [SV183: $i,SV48: $i,SV123: $i] :
( ( ( between @ SV123 @ SV48 @ SV183 )
= $false )
| ( ( ( SV48 = SV123 )
| ( SV123 = SV183 ) )
= $true )
| ( ( between @ SV48 @ SV123 @ SV183 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[670]) ).
thf(713,plain,
! [SV124: $i,SV184: $i,SV49: $i] :
( ( ( between @ SV49 @ SV184 @ SV124 )
= $false )
| ( ( ( SV49 = SV124 )
| ( SV124 = SV184 ) )
= $true )
| ( ( between @ SV49 @ SV124 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[671]) ).
thf(714,plain,
! [SV50: $i,SV277: $i,SV185: $i,SV125: $i] :
( ( ( ~ ( between @ SV125 @ SV185 @ SV277 ) )
= $true )
| ( ( between @ SV50 @ SV125 @ SV185 )
= $true )
| ( ( between @ SV50 @ SV125 @ SV185 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(715,plain,
! [SV126: $i,SV249: $i,SV186: $i,SV51: $i] :
( ( ( ~ ( between @ SV51 @ SV186 @ SV249 ) )
= $true )
| ( ( between @ SV126 @ SV186 @ SV249 )
= $true )
| ( ( between @ SV51 @ SV126 @ SV186 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(716,plain,
! [SV52: $i,SV250: $i,SV187: $i,SV127: $i] :
( ( ( ~ ( between @ SV127 @ SV187 @ SV250 ) )
= $true )
| ( ( ( SV127 = SV187 )
| ( between @ SV52 @ SV187 @ SV250 ) )
= $true )
| ( ( between @ SV52 @ SV127 @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(717,plain,
! [SV53: $i,SV251: $i,SV188: $i,SV128: $i] :
( ( ( ~ ( between @ SV128 @ SV188 @ SV251 ) )
= $true )
| ( ( ( SV128 = SV188 )
| ( between @ SV53 @ SV128 @ SV251 ) )
= $true )
| ( ( between @ SV53 @ SV128 @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(718,plain,
! [SV54: $i,SV189: $i,SV252: $i,SV129: $i] :
( ( ( ~ ( between @ SV129 @ SV252 @ SV189 ) )
= $true )
| ( ( between @ SV54 @ SV252 @ SV189 )
= $true )
| ( ( between @ SV54 @ SV129 @ SV189 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(719,plain,
! [SV130: $i,SV253: $i,SV190: $i,SV55: $i] :
( ( ( ~ ( between @ SV55 @ SV190 @ SV253 ) )
= $true )
| ( ( between @ SV55 @ SV130 @ SV253 )
= $true )
| ( ( between @ SV55 @ SV130 @ SV190 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(720,plain,
! [SV134: $i,SV59: $i,SV192: $i,SV278: $i,SV229: $i] :
( ( ( ~ ( between @ SV229 @ SV278 @ SV192 )
| ! [SY834: $i] :
( ~ ( between @ SV59 @ SY834 @ SV229 )
| ( between @ SY834 @ ( inner_pasch @ SV278 @ ( inner_pasch @ SV59 @ SY834 @ SV229 @ SV278 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV192 )
| ( between @ SV134 @ ( inner_pasch @ SV278 @ ( inner_pasch @ SV59 @ SY834 @ SV229 @ SV278 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV278 ) ) )
= $true )
| ( ( between @ SV59 @ SV134 @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(721,plain,
! [SV135: $i,SV254: $i,SV193: $i,SV60: $i] :
( ( ( ~ ( equidistant @ SV60 @ SV193 @ SV60 @ SV254 ) )
= $true )
| ( ( ~ ( equidistant @ SV135 @ SV193 @ SV135 @ SV254 )
| ( SV60 = SV135 )
| ( SV193 = SV254 ) )
= $true )
| ( ( between @ SV60 @ SV135 @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(722,plain,
! [SV255: $i,SV238: $i,SV230: $i,SV194: $i,SV136: $i,SV61: $i] :
( ( ( ~ ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 ) )
= $true )
| ( ( ~ ( equidistant @ SV61 @ SV238 @ SV194 @ SV255 )
| ! [SY821: $i,SY822: $i] :
( ~ ( equidistant @ SV61 @ SY821 @ SV194 @ SY822 )
| ~ ( equidistant @ SV238 @ SY821 @ SV255 @ SY822 )
| ~ ( between @ SV61 @ SV136 @ SV238 )
| ~ ( between @ SV194 @ SV230 @ SV255 )
| ( equidistant @ SV136 @ SY821 @ SV230 @ SY822 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(723,plain,
! [SV195: $i,SV137: $i,SV62: $i,SV279: $i,SV231: $i] :
( ( ( ! [SY835: $i] :
( ~ ( between @ SV231 @ SV279 @ SY835 )
| ~ ( equidistant @ SV62 @ SV137 @ SV231 @ SV279 )
| ~ ( equidistant @ SV62 @ SV195 @ SV231 @ SY835 )
| ( equidistant @ SV137 @ SV195 @ SV279 @ SY835 ) ) )
= $true )
| ( ( between @ SV62 @ SV137 @ SV195 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(724,plain,
! [SV256: $i,SV239: $i,SV232: $i,SV196: $i,SV138: $i,SV63: $i] :
( ( ( ~ ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 ) )
= $true )
| ( ( ~ ( equidistant @ SV138 @ SV239 @ SV232 @ SV256 )
| ! [SY823: $i,SY824: $i] :
( ~ ( equidistant @ SV63 @ SY823 @ SV196 @ SY824 )
| ~ ( equidistant @ SV239 @ SY823 @ SV256 @ SY824 )
| ~ ( between @ SV63 @ SV138 @ SV239 )
| ~ ( between @ SV196 @ SV232 @ SV256 )
| ( equidistant @ SV138 @ SY823 @ SV232 @ SY824 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[682]) ).
thf(725,plain,
! [SV197: $i,SV257: $i,SV139: $i,SV64: $i] :
( ( ( ~ ( equidistant @ SV64 @ SV139 @ SV64 @ SV257 ) )
= $true )
| ( ( ~ ( equidistant @ SV197 @ SV139 @ SV197 @ SV257 )
| ( SV139 = SV257 ) )
= $true )
| ( ( between @ SV64 @ SV139 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[683]) ).
thf(726,plain,
! [SV141: $i,SV280: $i,SV258: $i,SV199: $i,SV66: $i] :
( ( ( ~ ( equidistant @ SV66 @ SV199 @ SV258 @ SV280 )
| ( between @ SV258 @ ( insertion @ SV258 @ SV280 @ SV66 @ SV141 ) @ SV280 ) )
= $true )
| ( ( between @ SV66 @ SV141 @ SV199 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(727,plain,
! [SV142: $i,SV281: $i,SV259: $i,SV200: $i,SV67: $i] :
( ( ( ~ ( equidistant @ SV67 @ SV200 @ SV259 @ SV281 )
| ( equidistant @ SV142 @ SV200 @ ( insertion @ SV259 @ SV281 @ SV67 @ SV142 ) @ SV281 ) )
= $true )
| ( ( between @ SV67 @ SV142 @ SV200 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[685]) ).
thf(728,plain,
! [SV234: $i,SV202: $i,SV144: $i,SV69: $i,SV282: $i] :
( ( ( ! [SY836: $i] :
( ( insertion @ SV282 @ SY836 @ SV69 @ SV144 )
= ( insertion @ SV282 @ SY836 @ SV202 @ SV234 ) ) )
= $true )
| ( ( equidistant @ SV69 @ SV144 @ SV202 @ SV234 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(729,plain,
! [SV203: $i,SV70: $i,SV235: $i,SV283: $i,SV145: $i] :
( ( ( ! [SY837: $i] :
( ~ ( equidistant @ SV145 @ SV283 @ SV235 @ SY837 )
| ~ ( equidistant @ SV70 @ SV283 @ SV203 @ SY837 )
| ~ ( between @ SV70 @ SV145 @ SV283 )
| ( between @ SV203 @ SV235 @ SY837 ) ) )
= $true )
| ( ( equidistant @ SV70 @ SV145 @ SV203 @ SV235 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(730,plain,
! [SV204: $i,SV260: $i,SV146: $i,SV71: $i] :
( ( ( ~ ( between @ SV71 @ SV146 @ SV260 ) )
= $true )
| ( ( ( SV71 = SV146 )
| ( between @ SV71 @ SV204 @ SV260 )
| ( between @ SV71 @ SV260 @ SV204 ) )
= $true )
| ( ( between @ SV71 @ SV146 @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[688]) ).
thf(731,plain,
! [SV205: $i,SV261: $i,SV147: $i,SV72: $i] :
( ( ( ~ ( between @ SV72 @ SV147 @ SV261 ) )
= $true )
| ( ( ( SV72 = SV147 )
| ( between @ SV147 @ SV205 @ SV261 )
| ( between @ SV147 @ SV261 @ SV205 ) )
= $true )
| ( ( between @ SV72 @ SV147 @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(732,plain,
! [SV73: $i,SV206: $i,SV148: $i,SV262: $i] :
( ( ( ~ ( between @ SV262 @ SV148 @ SV206 ) )
= $true )
| ( ( ( SV148 = SV206 )
| ( between @ SV73 @ SV262 @ SV148 )
| ( between @ SV262 @ SV73 @ SV148 ) )
= $true )
| ( ( between @ SV73 @ SV148 @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[690]) ).
thf(733,plain,
! [SV149: $i,SV207: $i,SV263: $i,SV74: $i] :
( ( ( ~ ( between @ SV74 @ SV263 @ SV207 ) )
= $true )
| ( ( ( between @ SV74 @ SV149 @ SV263 )
| ( between @ SV74 @ SV263 @ SV149 ) )
= $true )
| ( ( between @ SV74 @ SV149 @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(734,plain,
! [SV150: $i,SV208: $i,SV264: $i,SV75: $i] :
( ( ( ~ ( between @ SV75 @ SV264 @ SV208 ) )
= $true )
| ( ( ( between @ SV150 @ SV264 @ SV208 )
| ( between @ SV264 @ SV150 @ SV208 ) )
= $true )
| ( ( between @ SV75 @ SV150 @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[692]) ).
thf(735,plain,
! [SV209: $i,SV76: $i,SV284: $i,SV265: $i,SV151: $i] :
( ( ( ~ ( between @ SV151 @ SV265 @ SV284 )
| ~ ( between @ SV76 @ SV284 @ SV209 )
| ( between @ SV76 @ SV265 @ SV209 ) )
= $true )
| ( ( between @ SV76 @ SV151 @ SV209 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(736,plain,
! [SV210: $i,SV152: $i,SV285: $i,SV266: $i,SV78: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV78 @ SV266 @ SV285 )
| ( equidistant @ SV152 @ SV210 @ SV266 @ SV285 ) )
= $true )
| ( ( equidistant @ SV2 @ SV78 @ SV152 @ SV210 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[694]) ).
thf(737,plain,
! [SV240: $i,SV236: $i,SV214: $i,SV155: $i,SV82: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
= $false )
| ( ( ~ ( equidistant @ SV82 @ SV236 @ SV214 @ SV240 )
| ! [SY813: $i,SY814: $i] :
( ~ ( equidistant @ SV6 @ SY813 @ SV155 @ SY814 )
| ~ ( equidistant @ SV82 @ SY813 @ SV214 @ SY814 )
| ~ ( between @ SV6 @ SV82 @ SV236 )
| ~ ( between @ SV155 @ SV214 @ SV240 )
| ( SV6 = SV82 )
| ( equidistant @ SV236 @ SY813 @ SV240 @ SY814 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[695]) ).
thf(738,plain,
! [SV8: $i,SV84: $i,SV156: $i,SV267: $i,SV241: $i] :
( ( ( ~ ( between @ SV241 @ SV267 @ SV156 ) )
= $true )
| ( ( between @ SV84 @ ( inner_pasch @ SV8 @ SV84 @ SV156 @ SV267 @ SV241 ) @ SV241 )
= $true )
| ( ( between @ SV8 @ SV84 @ SV156 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(739,plain,
! [SV85: $i,SV9: $i,SV157: $i,SV268: $i,SV242: $i] :
( ( ( ~ ( between @ SV242 @ SV268 @ SV157 ) )
= $true )
| ( ( between @ SV268 @ ( inner_pasch @ SV9 @ SV85 @ SV157 @ SV268 @ SV242 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV85 @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(740,plain,
! [SV10: $i,SV158: $i,SV86: $i,SV243: $i] :
( ( ( equidistant @ SV243 @ SV86 @ SV243 @ SV158 )
= $false )
| ( ( ! [SY817: $i] :
( ~ ( equidistant @ SY817 @ SV86 @ SY817 @ SV158 )
| ( between @ SV10 @ SV243 @ SY817 )
| ( between @ SV243 @ SY817 @ SV10 )
| ( SV86 = SV158 )
| ( between @ SY817 @ SV10 @ SV243 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV86 @ SV10 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[698]) ).
thf(741,plain,
! [SV159: $i,SV11: $i,SV269: $i,SV87: $i,SV244: $i] :
( ( ( ~ ( between @ SV244 @ SV87 @ SV269 ) )
= $true )
| ( ( ( SV11 = SV87 )
| ( between @ SV11 @ SV244 @ ( euclid1 @ SV11 @ SV244 @ SV87 @ SV269 @ SV159 ) ) )
= $true )
| ( ( between @ SV11 @ SV87 @ SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(742,plain,
! [SV160: $i,SV12: $i,SV270: $i,SV88: $i,SV245: $i] :
( ( ( ~ ( between @ SV245 @ SV88 @ SV270 ) )
= $true )
| ( ( ( SV12 = SV88 )
| ( between @ SV12 @ SV270 @ ( euclid2 @ SV12 @ SV245 @ SV88 @ SV270 @ SV160 ) ) )
= $true )
| ( ( between @ SV12 @ SV88 @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[700]) ).
thf(743,plain,
! [SV161: $i,SV13: $i,SV271: $i,SV89: $i,SV246: $i] :
( ( ( ~ ( between @ SV246 @ SV89 @ SV271 ) )
= $true )
| ( ( ( SV13 = SV89 )
| ( between @ ( euclid1 @ SV13 @ SV246 @ SV89 @ SV271 @ SV161 ) @ SV161 @ ( euclid2 @ SV13 @ SV246 @ SV89 @ SV271 @ SV161 ) ) )
= $true )
| ( ( between @ SV13 @ SV89 @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(744,plain,
! [SV162: $i,SV90: $i,SV272: $i,SV215: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV215 @ SV14 @ SV272 ) )
= $true )
| ( ( ~ ( between @ SV14 @ SV90 @ SV215 )
| ! [SY829: $i] :
( ~ ( between @ SV90 @ SY829 @ SV215 )
| ( between @ SV162 @ ( continuous @ SV14 @ SV90 @ SV162 @ SY829 @ SV215 @ SV272 ) @ SV272 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV90 @ SV14 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[702]) ).
thf(745,plain,
! [SV163: $i,SV91: $i,SV273: $i,SV216: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV216 @ SV15 @ SV273 ) )
= $true )
| ( ( ~ ( between @ SV15 @ SV91 @ SV216 )
| ! [SY830: $i] :
( ~ ( between @ SV91 @ SY830 @ SV216 )
| ( equidistant @ SV15 @ SY830 @ SV15 @ ( continuous @ SV15 @ SV91 @ SV163 @ SY830 @ SV216 @ SV273 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV91 @ SV15 @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(746,plain,
! [SV102: $i,SV26: $i,SV286: $i,SV274: $i,SV225: $i,SV172: $i] :
( ( ( ~ ( equidistant @ SV172 @ SV225 @ SV274 @ SV286 )
| ( equidistant @ SV26 @ SV102 @ SV274 @ SV286 ) )
= $true )
| ( ( equidistant @ SV26 @ SV102 @ SV172 @ SV225 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[704]) ).
thf(747,plain,
! [SV175: $i,SV35: $i,SV287: $i,SV226: $i,SV275: $i,SV110: $i] :
( ( ( ~ ( equidistant @ SV110 @ SV275 @ SV226 @ SV287 )
| ~ ( between @ SV35 @ SV110 @ SV275 )
| ~ ( between @ SV175 @ SV226 @ SV287 )
| ( equidistant @ SV35 @ SV275 @ SV175 @ SV287 ) )
= $true )
| ( ( equidistant @ SV35 @ SV110 @ SV175 @ SV226 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(748,plain,
! [SV176: $i,SV248: $i,SV111: $i,SV36: $i] :
( ( ( between @ SV36 @ SV111 @ SV248 )
= $false )
| ( ( ~ ( equidistant @ SV111 @ SV176 @ SV111 @ SV248 )
| ( SV36 = SV111 )
| ( SV176 = SV248 ) )
= $true )
| ( ( between @ SV36 @ SV111 @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(749,plain,
! [SV227: $i,SV178: $i,SV113: $i,SV38: $i,SV288: $i,SV276: $i] :
( ( ( ( ( extension @ SV276 @ SV288 @ SV38 @ SV113 )
= ( extension @ SV276 @ SV288 @ SV178 @ SV227 ) )
| ( SV276 = SV288 ) )
= $true )
| ( ( equidistant @ SV38 @ SV113 @ SV178 @ SV227 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(750,plain,
! [SV43: $i,SV179: $i,SV118: $i,SV289: $i] :
( ( ( between @ SV289 @ SV118 @ SV179 )
= $true )
| ( ( SV43 = SV179 )
= $false )
| ( ( between @ SV43 @ SV118 @ SV179 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(751,plain,
! [SV183: $i,SV123: $i,SV48: $i] :
( ( ( SV48 = SV123 )
= $true )
| ( ( SV123 = SV183 )
= $true )
| ( ( between @ SV123 @ SV48 @ SV183 )
= $false )
| ( ( between @ SV48 @ SV123 @ SV183 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[712]) ).
thf(752,plain,
! [SV184: $i,SV124: $i,SV49: $i] :
( ( ( SV49 = SV124 )
= $true )
| ( ( SV124 = SV184 )
= $true )
| ( ( between @ SV49 @ SV184 @ SV124 )
= $false )
| ( ( between @ SV49 @ SV124 @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[713]) ).
thf(753,plain,
! [SV50: $i,SV277: $i,SV185: $i,SV125: $i] :
( ( ( between @ SV125 @ SV185 @ SV277 )
= $false )
| ( ( between @ SV50 @ SV125 @ SV185 )
= $true )
| ( ( between @ SV50 @ SV125 @ SV185 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[714]) ).
thf(754,plain,
! [SV126: $i,SV249: $i,SV186: $i,SV51: $i] :
( ( ( between @ SV51 @ SV186 @ SV249 )
= $false )
| ( ( between @ SV126 @ SV186 @ SV249 )
= $true )
| ( ( between @ SV51 @ SV126 @ SV186 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[715]) ).
thf(755,plain,
! [SV52: $i,SV250: $i,SV187: $i,SV127: $i] :
( ( ( between @ SV127 @ SV187 @ SV250 )
= $false )
| ( ( ( SV127 = SV187 )
| ( between @ SV52 @ SV187 @ SV250 ) )
= $true )
| ( ( between @ SV52 @ SV127 @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[716]) ).
thf(756,plain,
! [SV53: $i,SV251: $i,SV188: $i,SV128: $i] :
( ( ( between @ SV128 @ SV188 @ SV251 )
= $false )
| ( ( ( SV128 = SV188 )
| ( between @ SV53 @ SV128 @ SV251 ) )
= $true )
| ( ( between @ SV53 @ SV128 @ SV188 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(757,plain,
! [SV54: $i,SV189: $i,SV252: $i,SV129: $i] :
( ( ( between @ SV129 @ SV252 @ SV189 )
= $false )
| ( ( between @ SV54 @ SV252 @ SV189 )
= $true )
| ( ( between @ SV54 @ SV129 @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(758,plain,
! [SV130: $i,SV253: $i,SV190: $i,SV55: $i] :
( ( ( between @ SV55 @ SV190 @ SV253 )
= $false )
| ( ( between @ SV55 @ SV130 @ SV253 )
= $true )
| ( ( between @ SV55 @ SV130 @ SV190 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(759,plain,
! [SV134: $i,SV59: $i,SV192: $i,SV278: $i,SV229: $i] :
( ( ( ~ ( between @ SV229 @ SV278 @ SV192 ) )
= $true )
| ( ( ! [SY834: $i] :
( ~ ( between @ SV59 @ SY834 @ SV229 )
| ( between @ SY834 @ ( inner_pasch @ SV278 @ ( inner_pasch @ SV59 @ SY834 @ SV229 @ SV278 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV192 )
| ( between @ SV134 @ ( inner_pasch @ SV278 @ ( inner_pasch @ SV59 @ SY834 @ SV229 @ SV278 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV278 ) ) )
= $true )
| ( ( between @ SV59 @ SV134 @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(760,plain,
! [SV135: $i,SV254: $i,SV193: $i,SV60: $i] :
( ( ( equidistant @ SV60 @ SV193 @ SV60 @ SV254 )
= $false )
| ( ( ~ ( equidistant @ SV135 @ SV193 @ SV135 @ SV254 )
| ( SV60 = SV135 )
| ( SV193 = SV254 ) )
= $true )
| ( ( between @ SV60 @ SV135 @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[721]) ).
thf(761,plain,
! [SV255: $i,SV238: $i,SV230: $i,SV194: $i,SV136: $i,SV61: $i] :
( ( ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 )
= $false )
| ( ( ~ ( equidistant @ SV61 @ SV238 @ SV194 @ SV255 )
| ! [SY821: $i,SY822: $i] :
( ~ ( equidistant @ SV61 @ SY821 @ SV194 @ SY822 )
| ~ ( equidistant @ SV238 @ SY821 @ SV255 @ SY822 )
| ~ ( between @ SV61 @ SV136 @ SV238 )
| ~ ( between @ SV194 @ SV230 @ SV255 )
| ( equidistant @ SV136 @ SY821 @ SV230 @ SY822 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[722]) ).
thf(762,plain,
! [SV195: $i,SV137: $i,SV62: $i,SV290: $i,SV279: $i,SV231: $i] :
( ( ( ~ ( between @ SV231 @ SV279 @ SV290 )
| ~ ( equidistant @ SV62 @ SV137 @ SV231 @ SV279 )
| ~ ( equidistant @ SV62 @ SV195 @ SV231 @ SV290 )
| ( equidistant @ SV137 @ SV195 @ SV279 @ SV290 ) )
= $true )
| ( ( between @ SV62 @ SV137 @ SV195 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(763,plain,
! [SV256: $i,SV239: $i,SV232: $i,SV196: $i,SV138: $i,SV63: $i] :
( ( ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 )
= $false )
| ( ( ~ ( equidistant @ SV138 @ SV239 @ SV232 @ SV256 )
| ! [SY823: $i,SY824: $i] :
( ~ ( equidistant @ SV63 @ SY823 @ SV196 @ SY824 )
| ~ ( equidistant @ SV239 @ SY823 @ SV256 @ SY824 )
| ~ ( between @ SV63 @ SV138 @ SV239 )
| ~ ( between @ SV196 @ SV232 @ SV256 )
| ( equidistant @ SV138 @ SY823 @ SV232 @ SY824 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(764,plain,
! [SV197: $i,SV257: $i,SV139: $i,SV64: $i] :
( ( ( equidistant @ SV64 @ SV139 @ SV64 @ SV257 )
= $false )
| ( ( ~ ( equidistant @ SV197 @ SV139 @ SV197 @ SV257 )
| ( SV139 = SV257 ) )
= $true )
| ( ( between @ SV64 @ SV139 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(765,plain,
! [SV141: $i,SV280: $i,SV258: $i,SV199: $i,SV66: $i] :
( ( ( ~ ( equidistant @ SV66 @ SV199 @ SV258 @ SV280 ) )
= $true )
| ( ( between @ SV258 @ ( insertion @ SV258 @ SV280 @ SV66 @ SV141 ) @ SV280 )
= $true )
| ( ( between @ SV66 @ SV141 @ SV199 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(766,plain,
! [SV142: $i,SV281: $i,SV259: $i,SV200: $i,SV67: $i] :
( ( ( ~ ( equidistant @ SV67 @ SV200 @ SV259 @ SV281 ) )
= $true )
| ( ( equidistant @ SV142 @ SV200 @ ( insertion @ SV259 @ SV281 @ SV67 @ SV142 ) @ SV281 )
= $true )
| ( ( between @ SV67 @ SV142 @ SV200 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(767,plain,
! [SV234: $i,SV202: $i,SV144: $i,SV69: $i,SV291: $i,SV282: $i] :
( ( ( ( insertion @ SV282 @ SV291 @ SV69 @ SV144 )
= ( insertion @ SV282 @ SV291 @ SV202 @ SV234 ) )
= $true )
| ( ( equidistant @ SV69 @ SV144 @ SV202 @ SV234 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(768,plain,
! [SV203: $i,SV70: $i,SV292: $i,SV235: $i,SV283: $i,SV145: $i] :
( ( ( ~ ( equidistant @ SV145 @ SV283 @ SV235 @ SV292 )
| ~ ( equidistant @ SV70 @ SV283 @ SV203 @ SV292 )
| ~ ( between @ SV70 @ SV145 @ SV283 )
| ( between @ SV203 @ SV235 @ SV292 ) )
= $true )
| ( ( equidistant @ SV70 @ SV145 @ SV203 @ SV235 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(769,plain,
! [SV204: $i,SV260: $i,SV146: $i,SV71: $i] :
( ( ( between @ SV71 @ SV146 @ SV260 )
= $false )
| ( ( ( SV71 = SV146 )
| ( between @ SV71 @ SV204 @ SV260 )
| ( between @ SV71 @ SV260 @ SV204 ) )
= $true )
| ( ( between @ SV71 @ SV146 @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(770,plain,
! [SV205: $i,SV261: $i,SV147: $i,SV72: $i] :
( ( ( between @ SV72 @ SV147 @ SV261 )
= $false )
| ( ( ( SV72 = SV147 )
| ( between @ SV147 @ SV205 @ SV261 )
| ( between @ SV147 @ SV261 @ SV205 ) )
= $true )
| ( ( between @ SV72 @ SV147 @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(771,plain,
! [SV73: $i,SV206: $i,SV148: $i,SV262: $i] :
( ( ( between @ SV262 @ SV148 @ SV206 )
= $false )
| ( ( ( SV148 = SV206 )
| ( between @ SV73 @ SV262 @ SV148 )
| ( between @ SV262 @ SV73 @ SV148 ) )
= $true )
| ( ( between @ SV73 @ SV148 @ SV206 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[732]) ).
thf(772,plain,
! [SV149: $i,SV207: $i,SV263: $i,SV74: $i] :
( ( ( between @ SV74 @ SV263 @ SV207 )
= $false )
| ( ( ( between @ SV74 @ SV149 @ SV263 )
| ( between @ SV74 @ SV263 @ SV149 ) )
= $true )
| ( ( between @ SV74 @ SV149 @ SV207 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[733]) ).
thf(773,plain,
! [SV150: $i,SV208: $i,SV264: $i,SV75: $i] :
( ( ( between @ SV75 @ SV264 @ SV208 )
= $false )
| ( ( ( between @ SV150 @ SV264 @ SV208 )
| ( between @ SV264 @ SV150 @ SV208 ) )
= $true )
| ( ( between @ SV75 @ SV150 @ SV208 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[734]) ).
thf(774,plain,
! [SV209: $i,SV76: $i,SV284: $i,SV265: $i,SV151: $i] :
( ( ( ~ ( between @ SV151 @ SV265 @ SV284 ) )
= $true )
| ( ( ~ ( between @ SV76 @ SV284 @ SV209 )
| ( between @ SV76 @ SV265 @ SV209 ) )
= $true )
| ( ( between @ SV76 @ SV151 @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(775,plain,
! [SV210: $i,SV152: $i,SV285: $i,SV266: $i,SV78: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV78 @ SV266 @ SV285 ) )
= $true )
| ( ( equidistant @ SV152 @ SV210 @ SV266 @ SV285 )
= $true )
| ( ( equidistant @ SV2 @ SV78 @ SV152 @ SV210 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(776,plain,
! [SV155: $i,SV6: $i,SV240: $i,SV214: $i,SV236: $i,SV82: $i] :
( ( ( ~ ( equidistant @ SV82 @ SV236 @ SV214 @ SV240 ) )
= $true )
| ( ( ! [SY813: $i,SY814: $i] :
( ~ ( equidistant @ SV6 @ SY813 @ SV155 @ SY814 )
| ~ ( equidistant @ SV82 @ SY813 @ SV214 @ SY814 )
| ~ ( between @ SV6 @ SV82 @ SV236 )
| ~ ( between @ SV155 @ SV214 @ SV240 )
| ( SV6 = SV82 )
| ( equidistant @ SV236 @ SY813 @ SV240 @ SY814 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(777,plain,
! [SV8: $i,SV84: $i,SV156: $i,SV267: $i,SV241: $i] :
( ( ( between @ SV241 @ SV267 @ SV156 )
= $false )
| ( ( between @ SV84 @ ( inner_pasch @ SV8 @ SV84 @ SV156 @ SV267 @ SV241 ) @ SV241 )
= $true )
| ( ( between @ SV8 @ SV84 @ SV156 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[738]) ).
thf(778,plain,
! [SV85: $i,SV9: $i,SV157: $i,SV268: $i,SV242: $i] :
( ( ( between @ SV242 @ SV268 @ SV157 )
= $false )
| ( ( between @ SV268 @ ( inner_pasch @ SV9 @ SV85 @ SV157 @ SV268 @ SV242 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV85 @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[739]) ).
thf(779,plain,
! [SV243: $i,SV10: $i,SV158: $i,SV86: $i,SV293: $i] :
( ( ( ~ ( equidistant @ SV293 @ SV86 @ SV293 @ SV158 )
| ( between @ SV10 @ SV243 @ SV293 )
| ( between @ SV243 @ SV293 @ SV10 )
| ( SV86 = SV158 )
| ( between @ SV293 @ SV10 @ SV243 ) )
= $true )
| ( ( equidistant @ SV243 @ SV86 @ SV243 @ SV158 )
= $false )
| ( ( equidistant @ SV10 @ SV86 @ SV10 @ SV158 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[740]) ).
thf(780,plain,
! [SV159: $i,SV11: $i,SV269: $i,SV87: $i,SV244: $i] :
( ( ( between @ SV244 @ SV87 @ SV269 )
= $false )
| ( ( ( SV11 = SV87 )
| ( between @ SV11 @ SV244 @ ( euclid1 @ SV11 @ SV244 @ SV87 @ SV269 @ SV159 ) ) )
= $true )
| ( ( between @ SV11 @ SV87 @ SV159 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[741]) ).
thf(781,plain,
! [SV160: $i,SV12: $i,SV270: $i,SV88: $i,SV245: $i] :
( ( ( between @ SV245 @ SV88 @ SV270 )
= $false )
| ( ( ( SV12 = SV88 )
| ( between @ SV12 @ SV270 @ ( euclid2 @ SV12 @ SV245 @ SV88 @ SV270 @ SV160 ) ) )
= $true )
| ( ( between @ SV12 @ SV88 @ SV160 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[742]) ).
thf(782,plain,
! [SV161: $i,SV13: $i,SV271: $i,SV89: $i,SV246: $i] :
( ( ( between @ SV246 @ SV89 @ SV271 )
= $false )
| ( ( ( SV13 = SV89 )
| ( between @ ( euclid1 @ SV13 @ SV246 @ SV89 @ SV271 @ SV161 ) @ SV161 @ ( euclid2 @ SV13 @ SV246 @ SV89 @ SV271 @ SV161 ) ) )
= $true )
| ( ( between @ SV13 @ SV89 @ SV161 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[743]) ).
thf(783,plain,
! [SV162: $i,SV90: $i,SV272: $i,SV215: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV215 @ SV14 @ SV272 )
= $false )
| ( ( ~ ( between @ SV14 @ SV90 @ SV215 )
| ! [SY829: $i] :
( ~ ( between @ SV90 @ SY829 @ SV215 )
| ( between @ SV162 @ ( continuous @ SV14 @ SV90 @ SV162 @ SY829 @ SV215 @ SV272 ) @ SV272 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV90 @ SV14 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[744]) ).
thf(784,plain,
! [SV163: $i,SV91: $i,SV273: $i,SV216: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV216 @ SV15 @ SV273 )
= $false )
| ( ( ~ ( between @ SV15 @ SV91 @ SV216 )
| ! [SY830: $i] :
( ~ ( between @ SV91 @ SY830 @ SV216 )
| ( equidistant @ SV15 @ SY830 @ SV15 @ ( continuous @ SV15 @ SV91 @ SV163 @ SY830 @ SV216 @ SV273 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV91 @ SV15 @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[745]) ).
thf(785,plain,
! [SV102: $i,SV26: $i,SV286: $i,SV274: $i,SV225: $i,SV172: $i] :
( ( ( ~ ( equidistant @ SV172 @ SV225 @ SV274 @ SV286 ) )
= $true )
| ( ( equidistant @ SV26 @ SV102 @ SV274 @ SV286 )
= $true )
| ( ( equidistant @ SV26 @ SV102 @ SV172 @ SV225 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(786,plain,
! [SV175: $i,SV35: $i,SV287: $i,SV226: $i,SV275: $i,SV110: $i] :
( ( ( ~ ( equidistant @ SV110 @ SV275 @ SV226 @ SV287 ) )
= $true )
| ( ( ~ ( between @ SV35 @ SV110 @ SV275 )
| ~ ( between @ SV175 @ SV226 @ SV287 )
| ( equidistant @ SV35 @ SV275 @ SV175 @ SV287 ) )
= $true )
| ( ( equidistant @ SV35 @ SV110 @ SV175 @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(787,plain,
! [SV36: $i,SV248: $i,SV176: $i,SV111: $i] :
( ( ( ~ ( equidistant @ SV111 @ SV176 @ SV111 @ SV248 ) )
= $true )
| ( ( ( SV36 = SV111 )
| ( SV176 = SV248 ) )
= $true )
| ( ( between @ SV36 @ SV111 @ SV248 )
= $false )
| ( ( between @ SV36 @ SV111 @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(788,plain,
! [SV227: $i,SV178: $i,SV113: $i,SV38: $i,SV288: $i,SV276: $i] :
( ( ( ( extension @ SV276 @ SV288 @ SV38 @ SV113 )
= ( extension @ SV276 @ SV288 @ SV178 @ SV227 ) )
= $true )
| ( ( SV276 = SV288 )
= $true )
| ( ( equidistant @ SV38 @ SV113 @ SV178 @ SV227 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(789,plain,
! [SV250: $i,SV52: $i,SV187: $i,SV127: $i] :
( ( ( SV127 = SV187 )
= $true )
| ( ( between @ SV52 @ SV187 @ SV250 )
= $true )
| ( ( between @ SV127 @ SV187 @ SV250 )
= $false )
| ( ( between @ SV52 @ SV127 @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[755]) ).
thf(790,plain,
! [SV251: $i,SV53: $i,SV188: $i,SV128: $i] :
( ( ( SV128 = SV188 )
= $true )
| ( ( between @ SV53 @ SV128 @ SV251 )
= $true )
| ( ( between @ SV128 @ SV188 @ SV251 )
= $false )
| ( ( between @ SV53 @ SV128 @ SV188 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[756]) ).
thf(791,plain,
! [SV134: $i,SV59: $i,SV192: $i,SV278: $i,SV229: $i] :
( ( ( between @ SV229 @ SV278 @ SV192 )
= $false )
| ( ( ! [SY834: $i] :
( ~ ( between @ SV59 @ SY834 @ SV229 )
| ( between @ SY834 @ ( inner_pasch @ SV278 @ ( inner_pasch @ SV59 @ SY834 @ SV229 @ SV278 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV192 )
| ( between @ SV134 @ ( inner_pasch @ SV278 @ ( inner_pasch @ SV59 @ SY834 @ SV229 @ SV278 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV278 ) ) )
= $true )
| ( ( between @ SV59 @ SV134 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[759]) ).
thf(792,plain,
! [SV60: $i,SV254: $i,SV193: $i,SV135: $i] :
( ( ( ~ ( equidistant @ SV135 @ SV193 @ SV135 @ SV254 ) )
= $true )
| ( ( ( SV60 = SV135 )
| ( SV193 = SV254 ) )
= $true )
| ( ( equidistant @ SV60 @ SV193 @ SV60 @ SV254 )
= $false )
| ( ( between @ SV60 @ SV135 @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[760]) ).
thf(793,plain,
! [SV230: $i,SV136: $i,SV255: $i,SV194: $i,SV238: $i,SV61: $i] :
( ( ( ~ ( equidistant @ SV61 @ SV238 @ SV194 @ SV255 ) )
= $true )
| ( ( ! [SY821: $i,SY822: $i] :
( ~ ( equidistant @ SV61 @ SY821 @ SV194 @ SY822 )
| ~ ( equidistant @ SV238 @ SY821 @ SV255 @ SY822 )
| ~ ( between @ SV61 @ SV136 @ SV238 )
| ~ ( between @ SV194 @ SV230 @ SV255 )
| ( equidistant @ SV136 @ SY821 @ SV230 @ SY822 ) ) )
= $true )
| ( ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[761]) ).
thf(794,plain,
! [SV195: $i,SV137: $i,SV62: $i,SV290: $i,SV279: $i,SV231: $i] :
( ( ( ~ ( between @ SV231 @ SV279 @ SV290 ) )
= $true )
| ( ( ~ ( equidistant @ SV62 @ SV137 @ SV231 @ SV279 )
| ~ ( equidistant @ SV62 @ SV195 @ SV231 @ SV290 )
| ( equidistant @ SV137 @ SV195 @ SV279 @ SV290 ) )
= $true )
| ( ( between @ SV62 @ SV137 @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[762]) ).
thf(795,plain,
! [SV196: $i,SV63: $i,SV256: $i,SV232: $i,SV239: $i,SV138: $i] :
( ( ( ~ ( equidistant @ SV138 @ SV239 @ SV232 @ SV256 ) )
= $true )
| ( ( ! [SY823: $i,SY824: $i] :
( ~ ( equidistant @ SV63 @ SY823 @ SV196 @ SY824 )
| ~ ( equidistant @ SV239 @ SY823 @ SV256 @ SY824 )
| ~ ( between @ SV63 @ SV138 @ SV239 )
| ~ ( between @ SV196 @ SV232 @ SV256 )
| ( equidistant @ SV138 @ SY823 @ SV232 @ SY824 ) ) )
= $true )
| ( ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(796,plain,
! [SV64: $i,SV257: $i,SV139: $i,SV197: $i] :
( ( ( ~ ( equidistant @ SV197 @ SV139 @ SV197 @ SV257 ) )
= $true )
| ( ( SV139 = SV257 )
= $true )
| ( ( equidistant @ SV64 @ SV139 @ SV64 @ SV257 )
= $false )
| ( ( between @ SV64 @ SV139 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(797,plain,
! [SV141: $i,SV280: $i,SV258: $i,SV199: $i,SV66: $i] :
( ( ( equidistant @ SV66 @ SV199 @ SV258 @ SV280 )
= $false )
| ( ( between @ SV258 @ ( insertion @ SV258 @ SV280 @ SV66 @ SV141 ) @ SV280 )
= $true )
| ( ( between @ SV66 @ SV141 @ SV199 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[765]) ).
thf(798,plain,
! [SV142: $i,SV281: $i,SV259: $i,SV200: $i,SV67: $i] :
( ( ( equidistant @ SV67 @ SV200 @ SV259 @ SV281 )
= $false )
| ( ( equidistant @ SV142 @ SV200 @ ( insertion @ SV259 @ SV281 @ SV67 @ SV142 ) @ SV281 )
= $true )
| ( ( between @ SV67 @ SV142 @ SV200 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[766]) ).
thf(799,plain,
! [SV203: $i,SV70: $i,SV292: $i,SV235: $i,SV283: $i,SV145: $i] :
( ( ( ~ ( equidistant @ SV145 @ SV283 @ SV235 @ SV292 ) )
= $true )
| ( ( ~ ( equidistant @ SV70 @ SV283 @ SV203 @ SV292 )
| ~ ( between @ SV70 @ SV145 @ SV283 )
| ( between @ SV203 @ SV235 @ SV292 ) )
= $true )
| ( ( equidistant @ SV70 @ SV145 @ SV203 @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(800,plain,
! [SV260: $i,SV204: $i,SV146: $i,SV71: $i] :
( ( ( SV71 = SV146 )
= $true )
| ( ( ( between @ SV71 @ SV204 @ SV260 )
| ( between @ SV71 @ SV260 @ SV204 ) )
= $true )
| ( ( between @ SV71 @ SV146 @ SV260 )
= $false )
| ( ( between @ SV71 @ SV146 @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[769]) ).
thf(801,plain,
! [SV261: $i,SV205: $i,SV147: $i,SV72: $i] :
( ( ( SV72 = SV147 )
= $true )
| ( ( ( between @ SV147 @ SV205 @ SV261 )
| ( between @ SV147 @ SV261 @ SV205 ) )
= $true )
| ( ( between @ SV72 @ SV147 @ SV261 )
= $false )
| ( ( between @ SV72 @ SV147 @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(802,plain,
! [SV262: $i,SV73: $i,SV206: $i,SV148: $i] :
( ( ( SV148 = SV206 )
= $true )
| ( ( ( between @ SV73 @ SV262 @ SV148 )
| ( between @ SV262 @ SV73 @ SV148 ) )
= $true )
| ( ( between @ SV262 @ SV148 @ SV206 )
= $false )
| ( ( between @ SV73 @ SV148 @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[771]) ).
thf(803,plain,
! [SV207: $i,SV263: $i,SV149: $i,SV74: $i] :
( ( ( between @ SV74 @ SV149 @ SV263 )
= $true )
| ( ( between @ SV74 @ SV263 @ SV149 )
= $true )
| ( ( between @ SV74 @ SV263 @ SV207 )
= $false )
| ( ( between @ SV74 @ SV149 @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[772]) ).
thf(804,plain,
! [SV75: $i,SV208: $i,SV264: $i,SV150: $i] :
( ( ( between @ SV150 @ SV264 @ SV208 )
= $true )
| ( ( between @ SV264 @ SV150 @ SV208 )
= $true )
| ( ( between @ SV75 @ SV264 @ SV208 )
= $false )
| ( ( between @ SV75 @ SV150 @ SV208 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[773]) ).
thf(805,plain,
! [SV209: $i,SV76: $i,SV284: $i,SV265: $i,SV151: $i] :
( ( ( between @ SV151 @ SV265 @ SV284 )
= $false )
| ( ( ~ ( between @ SV76 @ SV284 @ SV209 )
| ( between @ SV76 @ SV265 @ SV209 ) )
= $true )
| ( ( between @ SV76 @ SV151 @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[774]) ).
thf(806,plain,
! [SV210: $i,SV152: $i,SV285: $i,SV266: $i,SV78: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV78 @ SV266 @ SV285 )
= $false )
| ( ( equidistant @ SV152 @ SV210 @ SV266 @ SV285 )
= $true )
| ( ( equidistant @ SV2 @ SV78 @ SV152 @ SV210 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[775]) ).
thf(807,plain,
! [SV155: $i,SV6: $i,SV240: $i,SV214: $i,SV236: $i,SV82: $i] :
( ( ( equidistant @ SV82 @ SV236 @ SV214 @ SV240 )
= $false )
| ( ( ! [SY813: $i,SY814: $i] :
( ~ ( equidistant @ SV6 @ SY813 @ SV155 @ SY814 )
| ~ ( equidistant @ SV82 @ SY813 @ SV214 @ SY814 )
| ~ ( between @ SV6 @ SV82 @ SV236 )
| ~ ( between @ SV155 @ SV214 @ SV240 )
| ( SV6 = SV82 )
| ( equidistant @ SV236 @ SY813 @ SV240 @ SY814 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[776]) ).
thf(808,plain,
! [SV243: $i,SV10: $i,SV158: $i,SV86: $i,SV293: $i] :
( ( ( ~ ( equidistant @ SV293 @ SV86 @ SV293 @ SV158 ) )
= $true )
| ( ( ( between @ SV10 @ SV243 @ SV293 )
| ( between @ SV243 @ SV293 @ SV10 )
| ( SV86 = SV158 )
| ( between @ SV293 @ SV10 @ SV243 ) )
= $true )
| ( ( equidistant @ SV243 @ SV86 @ SV243 @ SV158 )
= $false )
| ( ( equidistant @ SV10 @ SV86 @ SV10 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[779]) ).
thf(809,plain,
! [SV159: $i,SV269: $i,SV244: $i,SV87: $i,SV11: $i] :
( ( ( SV11 = SV87 )
= $true )
| ( ( between @ SV11 @ SV244 @ ( euclid1 @ SV11 @ SV244 @ SV87 @ SV269 @ SV159 ) )
= $true )
| ( ( between @ SV244 @ SV87 @ SV269 )
= $false )
| ( ( between @ SV11 @ SV87 @ SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(810,plain,
! [SV160: $i,SV245: $i,SV270: $i,SV88: $i,SV12: $i] :
( ( ( SV12 = SV88 )
= $true )
| ( ( between @ SV12 @ SV270 @ ( euclid2 @ SV12 @ SV245 @ SV88 @ SV270 @ SV160 ) )
= $true )
| ( ( between @ SV245 @ SV88 @ SV270 )
= $false )
| ( ( between @ SV12 @ SV88 @ SV160 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[781]) ).
thf(811,plain,
! [SV161: $i,SV271: $i,SV246: $i,SV89: $i,SV13: $i] :
( ( ( SV13 = SV89 )
= $true )
| ( ( between @ ( euclid1 @ SV13 @ SV246 @ SV89 @ SV271 @ SV161 ) @ SV161 @ ( euclid2 @ SV13 @ SV246 @ SV89 @ SV271 @ SV161 ) )
= $true )
| ( ( between @ SV246 @ SV89 @ SV271 )
= $false )
| ( ( between @ SV13 @ SV89 @ SV161 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[782]) ).
thf(812,plain,
! [SV272: $i,SV162: $i,SV215: $i,SV90: $i,SV14: $i] :
( ( ( ~ ( between @ SV14 @ SV90 @ SV215 ) )
= $true )
| ( ( ! [SY829: $i] :
( ~ ( between @ SV90 @ SY829 @ SV215 )
| ( between @ SV162 @ ( continuous @ SV14 @ SV90 @ SV162 @ SY829 @ SV215 @ SV272 ) @ SV272 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV215 @ SV14 @ SV272 )
= $false )
| ( ( equidistant @ SV14 @ SV90 @ SV14 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[783]) ).
thf(813,plain,
! [SV273: $i,SV163: $i,SV216: $i,SV91: $i,SV15: $i] :
( ( ( ~ ( between @ SV15 @ SV91 @ SV216 ) )
= $true )
| ( ( ! [SY830: $i] :
( ~ ( between @ SV91 @ SY830 @ SV216 )
| ( equidistant @ SV15 @ SY830 @ SV15 @ ( continuous @ SV15 @ SV91 @ SV163 @ SY830 @ SV216 @ SV273 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV216 @ SV15 @ SV273 )
= $false )
| ( ( equidistant @ SV15 @ SV91 @ SV15 @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[784]) ).
thf(814,plain,
! [SV102: $i,SV26: $i,SV286: $i,SV274: $i,SV225: $i,SV172: $i] :
( ( ( equidistant @ SV172 @ SV225 @ SV274 @ SV286 )
= $false )
| ( ( equidistant @ SV26 @ SV102 @ SV274 @ SV286 )
= $true )
| ( ( equidistant @ SV26 @ SV102 @ SV172 @ SV225 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[785]) ).
thf(815,plain,
! [SV175: $i,SV35: $i,SV287: $i,SV226: $i,SV275: $i,SV110: $i] :
( ( ( equidistant @ SV110 @ SV275 @ SV226 @ SV287 )
= $false )
| ( ( ~ ( between @ SV35 @ SV110 @ SV275 )
| ~ ( between @ SV175 @ SV226 @ SV287 )
| ( equidistant @ SV35 @ SV275 @ SV175 @ SV287 ) )
= $true )
| ( ( equidistant @ SV35 @ SV110 @ SV175 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[786]) ).
thf(816,plain,
! [SV36: $i,SV248: $i,SV176: $i,SV111: $i] :
( ( ( equidistant @ SV111 @ SV176 @ SV111 @ SV248 )
= $false )
| ( ( ( SV36 = SV111 )
| ( SV176 = SV248 ) )
= $true )
| ( ( between @ SV36 @ SV111 @ SV248 )
= $false )
| ( ( between @ SV36 @ SV111 @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[787]) ).
thf(817,plain,
! [SV134: $i,SV192: $i,SV278: $i,SV229: $i,SV294: $i,SV59: $i] :
( ( ( ~ ( between @ SV59 @ SV294 @ SV229 )
| ( between @ SV294 @ ( inner_pasch @ SV278 @ ( inner_pasch @ SV59 @ SV294 @ SV229 @ SV278 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV192 )
| ( between @ SV134 @ ( inner_pasch @ SV278 @ ( inner_pasch @ SV59 @ SV294 @ SV229 @ SV278 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV278 ) )
= $true )
| ( ( between @ SV229 @ SV278 @ SV192 )
= $false )
| ( ( between @ SV59 @ SV134 @ SV192 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(818,plain,
! [SV60: $i,SV254: $i,SV193: $i,SV135: $i] :
( ( ( equidistant @ SV135 @ SV193 @ SV135 @ SV254 )
= $false )
| ( ( ( SV60 = SV135 )
| ( SV193 = SV254 ) )
= $true )
| ( ( equidistant @ SV60 @ SV193 @ SV60 @ SV254 )
= $false )
| ( ( between @ SV60 @ SV135 @ SV193 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[792]) ).
thf(819,plain,
! [SV230: $i,SV136: $i,SV255: $i,SV194: $i,SV238: $i,SV61: $i] :
( ( ( equidistant @ SV61 @ SV238 @ SV194 @ SV255 )
= $false )
| ( ( ! [SY821: $i,SY822: $i] :
( ~ ( equidistant @ SV61 @ SY821 @ SV194 @ SY822 )
| ~ ( equidistant @ SV238 @ SY821 @ SV255 @ SY822 )
| ~ ( between @ SV61 @ SV136 @ SV238 )
| ~ ( between @ SV194 @ SV230 @ SV255 )
| ( equidistant @ SV136 @ SY821 @ SV230 @ SY822 ) ) )
= $true )
| ( ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[793]) ).
thf(820,plain,
! [SV195: $i,SV137: $i,SV62: $i,SV290: $i,SV279: $i,SV231: $i] :
( ( ( between @ SV231 @ SV279 @ SV290 )
= $false )
| ( ( ~ ( equidistant @ SV62 @ SV137 @ SV231 @ SV279 )
| ~ ( equidistant @ SV62 @ SV195 @ SV231 @ SV290 )
| ( equidistant @ SV137 @ SV195 @ SV279 @ SV290 ) )
= $true )
| ( ( between @ SV62 @ SV137 @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[794]) ).
thf(821,plain,
! [SV196: $i,SV63: $i,SV256: $i,SV232: $i,SV239: $i,SV138: $i] :
( ( ( equidistant @ SV138 @ SV239 @ SV232 @ SV256 )
= $false )
| ( ( ! [SY823: $i,SY824: $i] :
( ~ ( equidistant @ SV63 @ SY823 @ SV196 @ SY824 )
| ~ ( equidistant @ SV239 @ SY823 @ SV256 @ SY824 )
| ~ ( between @ SV63 @ SV138 @ SV239 )
| ~ ( between @ SV196 @ SV232 @ SV256 )
| ( equidistant @ SV138 @ SY823 @ SV232 @ SY824 ) ) )
= $true )
| ( ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[795]) ).
thf(822,plain,
! [SV64: $i,SV257: $i,SV139: $i,SV197: $i] :
( ( ( equidistant @ SV197 @ SV139 @ SV197 @ SV257 )
= $false )
| ( ( SV139 = SV257 )
= $true )
| ( ( equidistant @ SV64 @ SV139 @ SV64 @ SV257 )
= $false )
| ( ( between @ SV64 @ SV139 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[796]) ).
thf(823,plain,
! [SV203: $i,SV70: $i,SV292: $i,SV235: $i,SV283: $i,SV145: $i] :
( ( ( equidistant @ SV145 @ SV283 @ SV235 @ SV292 )
= $false )
| ( ( ~ ( equidistant @ SV70 @ SV283 @ SV203 @ SV292 )
| ~ ( between @ SV70 @ SV145 @ SV283 )
| ( between @ SV203 @ SV235 @ SV292 ) )
= $true )
| ( ( equidistant @ SV70 @ SV145 @ SV203 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[799]) ).
thf(824,plain,
! [SV146: $i,SV260: $i,SV204: $i,SV71: $i] :
( ( ( between @ SV71 @ SV204 @ SV260 )
= $true )
| ( ( between @ SV71 @ SV260 @ SV204 )
= $true )
| ( ( SV71 = SV146 )
= $true )
| ( ( between @ SV71 @ SV146 @ SV260 )
= $false )
| ( ( between @ SV71 @ SV146 @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[800]) ).
thf(825,plain,
! [SV72: $i,SV261: $i,SV205: $i,SV147: $i] :
( ( ( between @ SV147 @ SV205 @ SV261 )
= $true )
| ( ( between @ SV147 @ SV261 @ SV205 )
= $true )
| ( ( SV72 = SV147 )
= $true )
| ( ( between @ SV72 @ SV147 @ SV261 )
= $false )
| ( ( between @ SV72 @ SV147 @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(826,plain,
! [SV206: $i,SV148: $i,SV262: $i,SV73: $i] :
( ( ( between @ SV73 @ SV262 @ SV148 )
= $true )
| ( ( between @ SV262 @ SV73 @ SV148 )
= $true )
| ( ( SV148 = SV206 )
= $true )
| ( ( between @ SV262 @ SV148 @ SV206 )
= $false )
| ( ( between @ SV73 @ SV148 @ SV206 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[802]) ).
thf(827,plain,
! [SV151: $i,SV265: $i,SV209: $i,SV284: $i,SV76: $i] :
( ( ( ~ ( between @ SV76 @ SV284 @ SV209 ) )
= $true )
| ( ( between @ SV76 @ SV265 @ SV209 )
= $true )
| ( ( between @ SV151 @ SV265 @ SV284 )
= $false )
| ( ( between @ SV76 @ SV151 @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[805]) ).
thf(828,plain,
! [SV240: $i,SV236: $i,SV214: $i,SV82: $i,SV155: $i,SV295: $i,SV6: $i] :
( ( ( ! [SY838: $i] :
( ~ ( equidistant @ SV6 @ SV295 @ SV155 @ SY838 )
| ~ ( equidistant @ SV82 @ SV295 @ SV214 @ SY838 )
| ~ ( between @ SV6 @ SV82 @ SV236 )
| ~ ( between @ SV155 @ SV214 @ SV240 )
| ( SV6 = SV82 )
| ( equidistant @ SV236 @ SV295 @ SV240 @ SY838 ) ) )
= $true )
| ( ( equidistant @ SV82 @ SV236 @ SV214 @ SV240 )
= $false )
| ( ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(829,plain,
! [SV243: $i,SV10: $i,SV158: $i,SV86: $i,SV293: $i] :
( ( ( equidistant @ SV293 @ SV86 @ SV293 @ SV158 )
= $false )
| ( ( ( between @ SV10 @ SV243 @ SV293 )
| ( between @ SV243 @ SV293 @ SV10 )
| ( SV86 = SV158 )
| ( between @ SV293 @ SV10 @ SV243 ) )
= $true )
| ( ( equidistant @ SV243 @ SV86 @ SV243 @ SV158 )
= $false )
| ( ( equidistant @ SV10 @ SV86 @ SV10 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[808]) ).
thf(830,plain,
! [SV272: $i,SV162: $i,SV215: $i,SV90: $i,SV14: $i] :
( ( ( between @ SV14 @ SV90 @ SV215 )
= $false )
| ( ( ! [SY829: $i] :
( ~ ( between @ SV90 @ SY829 @ SV215 )
| ( between @ SV162 @ ( continuous @ SV14 @ SV90 @ SV162 @ SY829 @ SV215 @ SV272 ) @ SV272 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV215 @ SV14 @ SV272 )
= $false )
| ( ( equidistant @ SV14 @ SV90 @ SV14 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[812]) ).
thf(831,plain,
! [SV273: $i,SV163: $i,SV216: $i,SV91: $i,SV15: $i] :
( ( ( between @ SV15 @ SV91 @ SV216 )
= $false )
| ( ( ! [SY830: $i] :
( ~ ( between @ SV91 @ SY830 @ SV216 )
| ( equidistant @ SV15 @ SY830 @ SV15 @ ( continuous @ SV15 @ SV91 @ SV163 @ SY830 @ SV216 @ SV273 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV216 @ SV15 @ SV273 )
= $false )
| ( ( equidistant @ SV15 @ SV91 @ SV15 @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[813]) ).
thf(832,plain,
! [SV287: $i,SV226: $i,SV175: $i,SV275: $i,SV110: $i,SV35: $i] :
( ( ( ~ ( between @ SV35 @ SV110 @ SV275 ) )
= $true )
| ( ( ~ ( between @ SV175 @ SV226 @ SV287 )
| ( equidistant @ SV35 @ SV275 @ SV175 @ SV287 ) )
= $true )
| ( ( equidistant @ SV110 @ SV275 @ SV226 @ SV287 )
= $false )
| ( ( equidistant @ SV35 @ SV110 @ SV175 @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(833,plain,
! [SV248: $i,SV176: $i,SV111: $i,SV36: $i] :
( ( ( SV36 = SV111 )
= $true )
| ( ( SV176 = SV248 )
= $true )
| ( ( equidistant @ SV111 @ SV176 @ SV111 @ SV248 )
= $false )
| ( ( between @ SV36 @ SV111 @ SV248 )
= $false )
| ( ( between @ SV36 @ SV111 @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(834,plain,
! [SV134: $i,SV192: $i,SV278: $i,SV229: $i,SV294: $i,SV59: $i] :
( ( ( ~ ( between @ SV59 @ SV294 @ SV229 ) )
= $true )
| ( ( ( between @ SV294 @ ( inner_pasch @ SV278 @ ( inner_pasch @ SV59 @ SV294 @ SV229 @ SV278 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV192 )
| ( between @ SV134 @ ( inner_pasch @ SV278 @ ( inner_pasch @ SV59 @ SV294 @ SV229 @ SV278 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV278 ) )
= $true )
| ( ( between @ SV229 @ SV278 @ SV192 )
= $false )
| ( ( between @ SV59 @ SV134 @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(835,plain,
! [SV254: $i,SV193: $i,SV135: $i,SV60: $i] :
( ( ( SV60 = SV135 )
= $true )
| ( ( SV193 = SV254 )
= $true )
| ( ( equidistant @ SV135 @ SV193 @ SV135 @ SV254 )
= $false )
| ( ( equidistant @ SV60 @ SV193 @ SV60 @ SV254 )
= $false )
| ( ( between @ SV60 @ SV135 @ SV193 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[818]) ).
thf(836,plain,
! [SV230: $i,SV136: $i,SV255: $i,SV238: $i,SV194: $i,SV296: $i,SV61: $i] :
( ( ( ! [SY839: $i] :
( ~ ( equidistant @ SV61 @ SV296 @ SV194 @ SY839 )
| ~ ( equidistant @ SV238 @ SV296 @ SV255 @ SY839 )
| ~ ( between @ SV61 @ SV136 @ SV238 )
| ~ ( between @ SV194 @ SV230 @ SV255 )
| ( equidistant @ SV136 @ SV296 @ SV230 @ SY839 ) ) )
= $true )
| ( ( equidistant @ SV61 @ SV238 @ SV194 @ SV255 )
= $false )
| ( ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(837,plain,
! [SV290: $i,SV195: $i,SV279: $i,SV231: $i,SV137: $i,SV62: $i] :
( ( ( ~ ( equidistant @ SV62 @ SV137 @ SV231 @ SV279 ) )
= $true )
| ( ( ~ ( equidistant @ SV62 @ SV195 @ SV231 @ SV290 )
| ( equidistant @ SV137 @ SV195 @ SV279 @ SV290 ) )
= $true )
| ( ( between @ SV231 @ SV279 @ SV290 )
= $false )
| ( ( between @ SV62 @ SV137 @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[820]) ).
thf(838,plain,
! [SV232: $i,SV138: $i,SV256: $i,SV239: $i,SV196: $i,SV297: $i,SV63: $i] :
( ( ( ! [SY840: $i] :
( ~ ( equidistant @ SV63 @ SV297 @ SV196 @ SY840 )
| ~ ( equidistant @ SV239 @ SV297 @ SV256 @ SY840 )
| ~ ( between @ SV63 @ SV138 @ SV239 )
| ~ ( between @ SV196 @ SV232 @ SV256 )
| ( equidistant @ SV138 @ SV297 @ SV232 @ SY840 ) ) )
= $true )
| ( ( equidistant @ SV138 @ SV239 @ SV232 @ SV256 )
= $false )
| ( ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[821]) ).
thf(839,plain,
! [SV235: $i,SV145: $i,SV292: $i,SV203: $i,SV283: $i,SV70: $i] :
( ( ( ~ ( equidistant @ SV70 @ SV283 @ SV203 @ SV292 ) )
= $true )
| ( ( ~ ( between @ SV70 @ SV145 @ SV283 )
| ( between @ SV203 @ SV235 @ SV292 ) )
= $true )
| ( ( equidistant @ SV145 @ SV283 @ SV235 @ SV292 )
= $false )
| ( ( equidistant @ SV70 @ SV145 @ SV203 @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(840,plain,
! [SV151: $i,SV265: $i,SV209: $i,SV284: $i,SV76: $i] :
( ( ( between @ SV76 @ SV284 @ SV209 )
= $false )
| ( ( between @ SV76 @ SV265 @ SV209 )
= $true )
| ( ( between @ SV151 @ SV265 @ SV284 )
= $false )
| ( ( between @ SV76 @ SV151 @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[827]) ).
thf(841,plain,
! [SV240: $i,SV236: $i,SV214: $i,SV82: $i,SV298: $i,SV155: $i,SV295: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV295 @ SV155 @ SV298 )
| ~ ( equidistant @ SV82 @ SV295 @ SV214 @ SV298 )
| ~ ( between @ SV6 @ SV82 @ SV236 )
| ~ ( between @ SV155 @ SV214 @ SV240 )
| ( SV6 = SV82 )
| ( equidistant @ SV236 @ SV295 @ SV240 @ SV298 ) )
= $true )
| ( ( equidistant @ SV82 @ SV236 @ SV214 @ SV240 )
= $false )
| ( ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(842,plain,
! [SV158: $i,SV86: $i,SV293: $i,SV243: $i,SV10: $i] :
( ( ( between @ SV10 @ SV243 @ SV293 )
= $true )
| ( ( ( between @ SV243 @ SV293 @ SV10 )
| ( SV86 = SV158 )
| ( between @ SV293 @ SV10 @ SV243 ) )
= $true )
| ( ( equidistant @ SV293 @ SV86 @ SV293 @ SV158 )
= $false )
| ( ( equidistant @ SV243 @ SV86 @ SV243 @ SV158 )
= $false )
| ( ( equidistant @ SV10 @ SV86 @ SV10 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(843,plain,
! [SV272: $i,SV14: $i,SV162: $i,SV215: $i,SV299: $i,SV90: $i] :
( ( ( ~ ( between @ SV90 @ SV299 @ SV215 )
| ( between @ SV162 @ ( continuous @ SV14 @ SV90 @ SV162 @ SV299 @ SV215 @ SV272 ) @ SV272 ) )
= $true )
| ( ( between @ SV14 @ SV90 @ SV215 )
= $false )
| ( ( equidistant @ SV14 @ SV215 @ SV14 @ SV272 )
= $false )
| ( ( equidistant @ SV14 @ SV90 @ SV14 @ SV162 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(844,plain,
! [SV273: $i,SV163: $i,SV15: $i,SV216: $i,SV300: $i,SV91: $i] :
( ( ( ~ ( between @ SV91 @ SV300 @ SV216 )
| ( equidistant @ SV15 @ SV300 @ SV15 @ ( continuous @ SV15 @ SV91 @ SV163 @ SV300 @ SV216 @ SV273 ) ) )
= $true )
| ( ( between @ SV15 @ SV91 @ SV216 )
= $false )
| ( ( equidistant @ SV15 @ SV216 @ SV15 @ SV273 )
= $false )
| ( ( equidistant @ SV15 @ SV91 @ SV15 @ SV163 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(845,plain,
! [SV287: $i,SV226: $i,SV175: $i,SV275: $i,SV110: $i,SV35: $i] :
( ( ( between @ SV35 @ SV110 @ SV275 )
= $false )
| ( ( ~ ( between @ SV175 @ SV226 @ SV287 )
| ( equidistant @ SV35 @ SV275 @ SV175 @ SV287 ) )
= $true )
| ( ( equidistant @ SV110 @ SV275 @ SV226 @ SV287 )
= $false )
| ( ( equidistant @ SV35 @ SV110 @ SV175 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[832]) ).
thf(846,plain,
! [SV134: $i,SV192: $i,SV278: $i,SV229: $i,SV294: $i,SV59: $i] :
( ( ( between @ SV59 @ SV294 @ SV229 )
= $false )
| ( ( ( between @ SV294 @ ( inner_pasch @ SV278 @ ( inner_pasch @ SV59 @ SV294 @ SV229 @ SV278 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV192 )
| ( between @ SV134 @ ( inner_pasch @ SV278 @ ( inner_pasch @ SV59 @ SV294 @ SV229 @ SV278 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV278 ) )
= $true )
| ( ( between @ SV229 @ SV278 @ SV192 )
= $false )
| ( ( between @ SV59 @ SV134 @ SV192 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(847,plain,
! [SV230: $i,SV136: $i,SV255: $i,SV238: $i,SV301: $i,SV194: $i,SV296: $i,SV61: $i] :
( ( ( ~ ( equidistant @ SV61 @ SV296 @ SV194 @ SV301 )
| ~ ( equidistant @ SV238 @ SV296 @ SV255 @ SV301 )
| ~ ( between @ SV61 @ SV136 @ SV238 )
| ~ ( between @ SV194 @ SV230 @ SV255 )
| ( equidistant @ SV136 @ SV296 @ SV230 @ SV301 ) )
= $true )
| ( ( equidistant @ SV61 @ SV238 @ SV194 @ SV255 )
= $false )
| ( ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[836]) ).
thf(848,plain,
! [SV290: $i,SV195: $i,SV279: $i,SV231: $i,SV137: $i,SV62: $i] :
( ( ( equidistant @ SV62 @ SV137 @ SV231 @ SV279 )
= $false )
| ( ( ~ ( equidistant @ SV62 @ SV195 @ SV231 @ SV290 )
| ( equidistant @ SV137 @ SV195 @ SV279 @ SV290 ) )
= $true )
| ( ( between @ SV231 @ SV279 @ SV290 )
= $false )
| ( ( between @ SV62 @ SV137 @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[837]) ).
thf(849,plain,
! [SV232: $i,SV138: $i,SV256: $i,SV239: $i,SV302: $i,SV196: $i,SV297: $i,SV63: $i] :
( ( ( ~ ( equidistant @ SV63 @ SV297 @ SV196 @ SV302 )
| ~ ( equidistant @ SV239 @ SV297 @ SV256 @ SV302 )
| ~ ( between @ SV63 @ SV138 @ SV239 )
| ~ ( between @ SV196 @ SV232 @ SV256 )
| ( equidistant @ SV138 @ SV297 @ SV232 @ SV302 ) )
= $true )
| ( ( equidistant @ SV138 @ SV239 @ SV232 @ SV256 )
= $false )
| ( ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(850,plain,
! [SV235: $i,SV145: $i,SV292: $i,SV203: $i,SV283: $i,SV70: $i] :
( ( ( equidistant @ SV70 @ SV283 @ SV203 @ SV292 )
= $false )
| ( ( ~ ( between @ SV70 @ SV145 @ SV283 )
| ( between @ SV203 @ SV235 @ SV292 ) )
= $true )
| ( ( equidistant @ SV145 @ SV283 @ SV235 @ SV292 )
= $false )
| ( ( equidistant @ SV70 @ SV145 @ SV203 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[839]) ).
thf(851,plain,
! [SV240: $i,SV236: $i,SV214: $i,SV82: $i,SV298: $i,SV155: $i,SV295: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV295 @ SV155 @ SV298 ) )
= $true )
| ( ( ~ ( equidistant @ SV82 @ SV295 @ SV214 @ SV298 )
| ~ ( between @ SV6 @ SV82 @ SV236 )
| ~ ( between @ SV155 @ SV214 @ SV240 )
| ( SV6 = SV82 )
| ( equidistant @ SV236 @ SV295 @ SV240 @ SV298 ) )
= $true )
| ( ( equidistant @ SV82 @ SV236 @ SV214 @ SV240 )
= $false )
| ( ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(852,plain,
! [SV158: $i,SV86: $i,SV10: $i,SV293: $i,SV243: $i] :
( ( ( between @ SV243 @ SV293 @ SV10 )
= $true )
| ( ( ( SV86 = SV158 )
| ( between @ SV293 @ SV10 @ SV243 ) )
= $true )
| ( ( between @ SV10 @ SV243 @ SV293 )
= $true )
| ( ( equidistant @ SV293 @ SV86 @ SV293 @ SV158 )
= $false )
| ( ( equidistant @ SV243 @ SV86 @ SV243 @ SV158 )
= $false )
| ( ( equidistant @ SV10 @ SV86 @ SV10 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(853,plain,
! [SV272: $i,SV14: $i,SV162: $i,SV215: $i,SV299: $i,SV90: $i] :
( ( ( ~ ( between @ SV90 @ SV299 @ SV215 ) )
= $true )
| ( ( between @ SV162 @ ( continuous @ SV14 @ SV90 @ SV162 @ SV299 @ SV215 @ SV272 ) @ SV272 )
= $true )
| ( ( between @ SV14 @ SV90 @ SV215 )
= $false )
| ( ( equidistant @ SV14 @ SV215 @ SV14 @ SV272 )
= $false )
| ( ( equidistant @ SV14 @ SV90 @ SV14 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(854,plain,
! [SV273: $i,SV163: $i,SV15: $i,SV216: $i,SV300: $i,SV91: $i] :
( ( ( ~ ( between @ SV91 @ SV300 @ SV216 ) )
= $true )
| ( ( equidistant @ SV15 @ SV300 @ SV15 @ ( continuous @ SV15 @ SV91 @ SV163 @ SV300 @ SV216 @ SV273 ) )
= $true )
| ( ( between @ SV15 @ SV91 @ SV216 )
= $false )
| ( ( equidistant @ SV15 @ SV216 @ SV15 @ SV273 )
= $false )
| ( ( equidistant @ SV15 @ SV91 @ SV15 @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(855,plain,
! [SV110: $i,SV275: $i,SV35: $i,SV287: $i,SV226: $i,SV175: $i] :
( ( ( ~ ( between @ SV175 @ SV226 @ SV287 ) )
= $true )
| ( ( equidistant @ SV35 @ SV275 @ SV175 @ SV287 )
= $true )
| ( ( between @ SV35 @ SV110 @ SV275 )
= $false )
| ( ( equidistant @ SV110 @ SV275 @ SV226 @ SV287 )
= $false )
| ( ( equidistant @ SV35 @ SV110 @ SV175 @ SV226 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[845]) ).
thf(856,plain,
! [SV134: $i,SV192: $i,SV229: $i,SV59: $i,SV278: $i,SV294: $i] :
( ( ( between @ SV294 @ ( inner_pasch @ SV278 @ ( inner_pasch @ SV59 @ SV294 @ SV229 @ SV278 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV192 )
= $true )
| ( ( between @ SV134 @ ( inner_pasch @ SV278 @ ( inner_pasch @ SV59 @ SV294 @ SV229 @ SV278 @ SV192 ) @ SV59 @ SV134 @ SV192 ) @ SV278 )
= $true )
| ( ( between @ SV59 @ SV294 @ SV229 )
= $false )
| ( ( between @ SV229 @ SV278 @ SV192 )
= $false )
| ( ( between @ SV59 @ SV134 @ SV192 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[846]) ).
thf(857,plain,
! [SV230: $i,SV136: $i,SV255: $i,SV238: $i,SV301: $i,SV194: $i,SV296: $i,SV61: $i] :
( ( ( ~ ( equidistant @ SV61 @ SV296 @ SV194 @ SV301 ) )
= $true )
| ( ( ~ ( equidistant @ SV238 @ SV296 @ SV255 @ SV301 )
| ~ ( between @ SV61 @ SV136 @ SV238 )
| ~ ( between @ SV194 @ SV230 @ SV255 )
| ( equidistant @ SV136 @ SV296 @ SV230 @ SV301 ) )
= $true )
| ( ( equidistant @ SV61 @ SV238 @ SV194 @ SV255 )
= $false )
| ( ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(858,plain,
! [SV279: $i,SV137: $i,SV290: $i,SV231: $i,SV195: $i,SV62: $i] :
( ( ( ~ ( equidistant @ SV62 @ SV195 @ SV231 @ SV290 ) )
= $true )
| ( ( equidistant @ SV137 @ SV195 @ SV279 @ SV290 )
= $true )
| ( ( equidistant @ SV62 @ SV137 @ SV231 @ SV279 )
= $false )
| ( ( between @ SV231 @ SV279 @ SV290 )
= $false )
| ( ( between @ SV62 @ SV137 @ SV195 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(859,plain,
! [SV232: $i,SV138: $i,SV256: $i,SV239: $i,SV302: $i,SV196: $i,SV297: $i,SV63: $i] :
( ( ( ~ ( equidistant @ SV63 @ SV297 @ SV196 @ SV302 ) )
= $true )
| ( ( ~ ( equidistant @ SV239 @ SV297 @ SV256 @ SV302 )
| ~ ( between @ SV63 @ SV138 @ SV239 )
| ~ ( between @ SV196 @ SV232 @ SV256 )
| ( equidistant @ SV138 @ SV297 @ SV232 @ SV302 ) )
= $true )
| ( ( equidistant @ SV138 @ SV239 @ SV232 @ SV256 )
= $false )
| ( ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(860,plain,
! [SV292: $i,SV235: $i,SV203: $i,SV283: $i,SV145: $i,SV70: $i] :
( ( ( ~ ( between @ SV70 @ SV145 @ SV283 ) )
= $true )
| ( ( between @ SV203 @ SV235 @ SV292 )
= $true )
| ( ( equidistant @ SV70 @ SV283 @ SV203 @ SV292 )
= $false )
| ( ( equidistant @ SV145 @ SV283 @ SV235 @ SV292 )
= $false )
| ( ( equidistant @ SV70 @ SV145 @ SV203 @ SV235 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(861,plain,
! [SV240: $i,SV236: $i,SV214: $i,SV82: $i,SV298: $i,SV155: $i,SV295: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV295 @ SV155 @ SV298 )
= $false )
| ( ( ~ ( equidistant @ SV82 @ SV295 @ SV214 @ SV298 )
| ~ ( between @ SV6 @ SV82 @ SV236 )
| ~ ( between @ SV155 @ SV214 @ SV240 )
| ( SV6 = SV82 )
| ( equidistant @ SV236 @ SV295 @ SV240 @ SV298 ) )
= $true )
| ( ( equidistant @ SV82 @ SV236 @ SV214 @ SV240 )
= $false )
| ( ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[851]) ).
thf(862,plain,
! [SV243: $i,SV10: $i,SV293: $i,SV158: $i,SV86: $i] :
( ( ( SV86 = SV158 )
= $true )
| ( ( between @ SV293 @ SV10 @ SV243 )
= $true )
| ( ( between @ SV243 @ SV293 @ SV10 )
= $true )
| ( ( between @ SV10 @ SV243 @ SV293 )
= $true )
| ( ( equidistant @ SV293 @ SV86 @ SV293 @ SV158 )
= $false )
| ( ( equidistant @ SV243 @ SV86 @ SV243 @ SV158 )
= $false )
| ( ( equidistant @ SV10 @ SV86 @ SV10 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(863,plain,
! [SV272: $i,SV14: $i,SV162: $i,SV215: $i,SV299: $i,SV90: $i] :
( ( ( between @ SV90 @ SV299 @ SV215 )
= $false )
| ( ( between @ SV162 @ ( continuous @ SV14 @ SV90 @ SV162 @ SV299 @ SV215 @ SV272 ) @ SV272 )
= $true )
| ( ( between @ SV14 @ SV90 @ SV215 )
= $false )
| ( ( equidistant @ SV14 @ SV215 @ SV14 @ SV272 )
= $false )
| ( ( equidistant @ SV14 @ SV90 @ SV14 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[853]) ).
thf(864,plain,
! [SV273: $i,SV163: $i,SV15: $i,SV216: $i,SV300: $i,SV91: $i] :
( ( ( between @ SV91 @ SV300 @ SV216 )
= $false )
| ( ( equidistant @ SV15 @ SV300 @ SV15 @ ( continuous @ SV15 @ SV91 @ SV163 @ SV300 @ SV216 @ SV273 ) )
= $true )
| ( ( between @ SV15 @ SV91 @ SV216 )
= $false )
| ( ( equidistant @ SV15 @ SV216 @ SV15 @ SV273 )
= $false )
| ( ( equidistant @ SV15 @ SV91 @ SV15 @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(865,plain,
! [SV110: $i,SV275: $i,SV35: $i,SV287: $i,SV226: $i,SV175: $i] :
( ( ( between @ SV175 @ SV226 @ SV287 )
= $false )
| ( ( equidistant @ SV35 @ SV275 @ SV175 @ SV287 )
= $true )
| ( ( between @ SV35 @ SV110 @ SV275 )
= $false )
| ( ( equidistant @ SV110 @ SV275 @ SV226 @ SV287 )
= $false )
| ( ( equidistant @ SV35 @ SV110 @ SV175 @ SV226 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[855]) ).
thf(866,plain,
! [SV230: $i,SV136: $i,SV255: $i,SV238: $i,SV301: $i,SV194: $i,SV296: $i,SV61: $i] :
( ( ( equidistant @ SV61 @ SV296 @ SV194 @ SV301 )
= $false )
| ( ( ~ ( equidistant @ SV238 @ SV296 @ SV255 @ SV301 )
| ~ ( between @ SV61 @ SV136 @ SV238 )
| ~ ( between @ SV194 @ SV230 @ SV255 )
| ( equidistant @ SV136 @ SV296 @ SV230 @ SV301 ) )
= $true )
| ( ( equidistant @ SV61 @ SV238 @ SV194 @ SV255 )
= $false )
| ( ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[857]) ).
thf(867,plain,
! [SV279: $i,SV137: $i,SV290: $i,SV231: $i,SV195: $i,SV62: $i] :
( ( ( equidistant @ SV62 @ SV195 @ SV231 @ SV290 )
= $false )
| ( ( equidistant @ SV137 @ SV195 @ SV279 @ SV290 )
= $true )
| ( ( equidistant @ SV62 @ SV137 @ SV231 @ SV279 )
= $false )
| ( ( between @ SV231 @ SV279 @ SV290 )
= $false )
| ( ( between @ SV62 @ SV137 @ SV195 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[858]) ).
thf(868,plain,
! [SV232: $i,SV138: $i,SV256: $i,SV239: $i,SV302: $i,SV196: $i,SV297: $i,SV63: $i] :
( ( ( equidistant @ SV63 @ SV297 @ SV196 @ SV302 )
= $false )
| ( ( ~ ( equidistant @ SV239 @ SV297 @ SV256 @ SV302 )
| ~ ( between @ SV63 @ SV138 @ SV239 )
| ~ ( between @ SV196 @ SV232 @ SV256 )
| ( equidistant @ SV138 @ SV297 @ SV232 @ SV302 ) )
= $true )
| ( ( equidistant @ SV138 @ SV239 @ SV232 @ SV256 )
= $false )
| ( ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[859]) ).
thf(869,plain,
! [SV292: $i,SV235: $i,SV203: $i,SV283: $i,SV145: $i,SV70: $i] :
( ( ( between @ SV70 @ SV145 @ SV283 )
= $false )
| ( ( between @ SV203 @ SV235 @ SV292 )
= $true )
| ( ( equidistant @ SV70 @ SV283 @ SV203 @ SV292 )
= $false )
| ( ( equidistant @ SV145 @ SV283 @ SV235 @ SV292 )
= $false )
| ( ( equidistant @ SV70 @ SV145 @ SV203 @ SV235 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(870,plain,
! [SV240: $i,SV155: $i,SV236: $i,SV6: $i,SV298: $i,SV214: $i,SV295: $i,SV82: $i] :
( ( ( ~ ( equidistant @ SV82 @ SV295 @ SV214 @ SV298 ) )
= $true )
| ( ( ~ ( between @ SV6 @ SV82 @ SV236 )
| ~ ( between @ SV155 @ SV214 @ SV240 )
| ( SV6 = SV82 )
| ( equidistant @ SV236 @ SV295 @ SV240 @ SV298 ) )
= $true )
| ( ( equidistant @ SV6 @ SV295 @ SV155 @ SV298 )
= $false )
| ( ( equidistant @ SV82 @ SV236 @ SV214 @ SV240 )
= $false )
| ( ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[861]) ).
thf(871,plain,
! [SV230: $i,SV194: $i,SV136: $i,SV61: $i,SV301: $i,SV255: $i,SV296: $i,SV238: $i] :
( ( ( ~ ( equidistant @ SV238 @ SV296 @ SV255 @ SV301 ) )
= $true )
| ( ( ~ ( between @ SV61 @ SV136 @ SV238 )
| ~ ( between @ SV194 @ SV230 @ SV255 )
| ( equidistant @ SV136 @ SV296 @ SV230 @ SV301 ) )
= $true )
| ( ( equidistant @ SV61 @ SV296 @ SV194 @ SV301 )
= $false )
| ( ( equidistant @ SV61 @ SV238 @ SV194 @ SV255 )
= $false )
| ( ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(872,plain,
! [SV232: $i,SV196: $i,SV138: $i,SV63: $i,SV302: $i,SV256: $i,SV297: $i,SV239: $i] :
( ( ( ~ ( equidistant @ SV239 @ SV297 @ SV256 @ SV302 ) )
= $true )
| ( ( ~ ( between @ SV63 @ SV138 @ SV239 )
| ~ ( between @ SV196 @ SV232 @ SV256 )
| ( equidistant @ SV138 @ SV297 @ SV232 @ SV302 ) )
= $true )
| ( ( equidistant @ SV63 @ SV297 @ SV196 @ SV302 )
= $false )
| ( ( equidistant @ SV138 @ SV239 @ SV232 @ SV256 )
= $false )
| ( ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(873,plain,
! [SV240: $i,SV155: $i,SV236: $i,SV6: $i,SV298: $i,SV214: $i,SV295: $i,SV82: $i] :
( ( ( equidistant @ SV82 @ SV295 @ SV214 @ SV298 )
= $false )
| ( ( ~ ( between @ SV6 @ SV82 @ SV236 )
| ~ ( between @ SV155 @ SV214 @ SV240 )
| ( SV6 = SV82 )
| ( equidistant @ SV236 @ SV295 @ SV240 @ SV298 ) )
= $true )
| ( ( equidistant @ SV6 @ SV295 @ SV155 @ SV298 )
= $false )
| ( ( equidistant @ SV82 @ SV236 @ SV214 @ SV240 )
= $false )
| ( ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(874,plain,
! [SV230: $i,SV194: $i,SV136: $i,SV61: $i,SV301: $i,SV255: $i,SV296: $i,SV238: $i] :
( ( ( equidistant @ SV238 @ SV296 @ SV255 @ SV301 )
= $false )
| ( ( ~ ( between @ SV61 @ SV136 @ SV238 )
| ~ ( between @ SV194 @ SV230 @ SV255 )
| ( equidistant @ SV136 @ SV296 @ SV230 @ SV301 ) )
= $true )
| ( ( equidistant @ SV61 @ SV296 @ SV194 @ SV301 )
= $false )
| ( ( equidistant @ SV61 @ SV238 @ SV194 @ SV255 )
= $false )
| ( ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(875,plain,
! [SV232: $i,SV196: $i,SV138: $i,SV63: $i,SV302: $i,SV256: $i,SV297: $i,SV239: $i] :
( ( ( equidistant @ SV239 @ SV297 @ SV256 @ SV302 )
= $false )
| ( ( ~ ( between @ SV63 @ SV138 @ SV239 )
| ~ ( between @ SV196 @ SV232 @ SV256 )
| ( equidistant @ SV138 @ SV297 @ SV232 @ SV302 ) )
= $true )
| ( ( equidistant @ SV63 @ SV297 @ SV196 @ SV302 )
= $false )
| ( ( equidistant @ SV138 @ SV239 @ SV232 @ SV256 )
= $false )
| ( ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[872]) ).
thf(876,plain,
! [SV298: $i,SV295: $i,SV240: $i,SV214: $i,SV155: $i,SV236: $i,SV82: $i,SV6: $i] :
( ( ( ~ ( between @ SV6 @ SV82 @ SV236 ) )
= $true )
| ( ( ~ ( between @ SV155 @ SV214 @ SV240 )
| ( SV6 = SV82 )
| ( equidistant @ SV236 @ SV295 @ SV240 @ SV298 ) )
= $true )
| ( ( equidistant @ SV82 @ SV295 @ SV214 @ SV298 )
= $false )
| ( ( equidistant @ SV6 @ SV295 @ SV155 @ SV298 )
= $false )
| ( ( equidistant @ SV82 @ SV236 @ SV214 @ SV240 )
= $false )
| ( ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(877,plain,
! [SV301: $i,SV296: $i,SV255: $i,SV230: $i,SV194: $i,SV238: $i,SV136: $i,SV61: $i] :
( ( ( ~ ( between @ SV61 @ SV136 @ SV238 ) )
= $true )
| ( ( ~ ( between @ SV194 @ SV230 @ SV255 )
| ( equidistant @ SV136 @ SV296 @ SV230 @ SV301 ) )
= $true )
| ( ( equidistant @ SV238 @ SV296 @ SV255 @ SV301 )
= $false )
| ( ( equidistant @ SV61 @ SV296 @ SV194 @ SV301 )
= $false )
| ( ( equidistant @ SV61 @ SV238 @ SV194 @ SV255 )
= $false )
| ( ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[874]) ).
thf(878,plain,
! [SV302: $i,SV297: $i,SV256: $i,SV232: $i,SV196: $i,SV239: $i,SV138: $i,SV63: $i] :
( ( ( ~ ( between @ SV63 @ SV138 @ SV239 ) )
= $true )
| ( ( ~ ( between @ SV196 @ SV232 @ SV256 )
| ( equidistant @ SV138 @ SV297 @ SV232 @ SV302 ) )
= $true )
| ( ( equidistant @ SV239 @ SV297 @ SV256 @ SV302 )
= $false )
| ( ( equidistant @ SV63 @ SV297 @ SV196 @ SV302 )
= $false )
| ( ( equidistant @ SV138 @ SV239 @ SV232 @ SV256 )
= $false )
| ( ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(879,plain,
! [SV298: $i,SV295: $i,SV240: $i,SV214: $i,SV155: $i,SV236: $i,SV82: $i,SV6: $i] :
( ( ( between @ SV6 @ SV82 @ SV236 )
= $false )
| ( ( ~ ( between @ SV155 @ SV214 @ SV240 )
| ( SV6 = SV82 )
| ( equidistant @ SV236 @ SV295 @ SV240 @ SV298 ) )
= $true )
| ( ( equidistant @ SV82 @ SV295 @ SV214 @ SV298 )
= $false )
| ( ( equidistant @ SV6 @ SV295 @ SV155 @ SV298 )
= $false )
| ( ( equidistant @ SV82 @ SV236 @ SV214 @ SV240 )
= $false )
| ( ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[876]) ).
thf(880,plain,
! [SV301: $i,SV296: $i,SV255: $i,SV230: $i,SV194: $i,SV238: $i,SV136: $i,SV61: $i] :
( ( ( between @ SV61 @ SV136 @ SV238 )
= $false )
| ( ( ~ ( between @ SV194 @ SV230 @ SV255 )
| ( equidistant @ SV136 @ SV296 @ SV230 @ SV301 ) )
= $true )
| ( ( equidistant @ SV238 @ SV296 @ SV255 @ SV301 )
= $false )
| ( ( equidistant @ SV61 @ SV296 @ SV194 @ SV301 )
= $false )
| ( ( equidistant @ SV61 @ SV238 @ SV194 @ SV255 )
= $false )
| ( ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[877]) ).
thf(881,plain,
! [SV302: $i,SV297: $i,SV256: $i,SV232: $i,SV196: $i,SV239: $i,SV138: $i,SV63: $i] :
( ( ( between @ SV63 @ SV138 @ SV239 )
= $false )
| ( ( ~ ( between @ SV196 @ SV232 @ SV256 )
| ( equidistant @ SV138 @ SV297 @ SV232 @ SV302 ) )
= $true )
| ( ( equidistant @ SV239 @ SV297 @ SV256 @ SV302 )
= $false )
| ( ( equidistant @ SV63 @ SV297 @ SV196 @ SV302 )
= $false )
| ( ( equidistant @ SV138 @ SV239 @ SV232 @ SV256 )
= $false )
| ( ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[878]) ).
thf(882,plain,
! [SV298: $i,SV295: $i,SV236: $i,SV82: $i,SV6: $i,SV240: $i,SV214: $i,SV155: $i] :
( ( ( ~ ( between @ SV155 @ SV214 @ SV240 ) )
= $true )
| ( ( ( SV6 = SV82 )
| ( equidistant @ SV236 @ SV295 @ SV240 @ SV298 ) )
= $true )
| ( ( between @ SV6 @ SV82 @ SV236 )
= $false )
| ( ( equidistant @ SV82 @ SV295 @ SV214 @ SV298 )
= $false )
| ( ( equidistant @ SV6 @ SV295 @ SV155 @ SV298 )
= $false )
| ( ( equidistant @ SV82 @ SV236 @ SV214 @ SV240 )
= $false )
| ( ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(883,plain,
! [SV238: $i,SV61: $i,SV301: $i,SV296: $i,SV136: $i,SV255: $i,SV230: $i,SV194: $i] :
( ( ( ~ ( between @ SV194 @ SV230 @ SV255 ) )
= $true )
| ( ( equidistant @ SV136 @ SV296 @ SV230 @ SV301 )
= $true )
| ( ( between @ SV61 @ SV136 @ SV238 )
= $false )
| ( ( equidistant @ SV238 @ SV296 @ SV255 @ SV301 )
= $false )
| ( ( equidistant @ SV61 @ SV296 @ SV194 @ SV301 )
= $false )
| ( ( equidistant @ SV61 @ SV238 @ SV194 @ SV255 )
= $false )
| ( ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(884,plain,
! [SV239: $i,SV63: $i,SV302: $i,SV297: $i,SV138: $i,SV256: $i,SV232: $i,SV196: $i] :
( ( ( ~ ( between @ SV196 @ SV232 @ SV256 ) )
= $true )
| ( ( equidistant @ SV138 @ SV297 @ SV232 @ SV302 )
= $true )
| ( ( between @ SV63 @ SV138 @ SV239 )
= $false )
| ( ( equidistant @ SV239 @ SV297 @ SV256 @ SV302 )
= $false )
| ( ( equidistant @ SV63 @ SV297 @ SV196 @ SV302 )
= $false )
| ( ( equidistant @ SV138 @ SV239 @ SV232 @ SV256 )
= $false )
| ( ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[881]) ).
thf(885,plain,
! [SV298: $i,SV295: $i,SV236: $i,SV82: $i,SV6: $i,SV240: $i,SV214: $i,SV155: $i] :
( ( ( between @ SV155 @ SV214 @ SV240 )
= $false )
| ( ( ( SV6 = SV82 )
| ( equidistant @ SV236 @ SV295 @ SV240 @ SV298 ) )
= $true )
| ( ( between @ SV6 @ SV82 @ SV236 )
= $false )
| ( ( equidistant @ SV82 @ SV295 @ SV214 @ SV298 )
= $false )
| ( ( equidistant @ SV6 @ SV295 @ SV155 @ SV298 )
= $false )
| ( ( equidistant @ SV82 @ SV236 @ SV214 @ SV240 )
= $false )
| ( ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(886,plain,
! [SV238: $i,SV61: $i,SV301: $i,SV296: $i,SV136: $i,SV255: $i,SV230: $i,SV194: $i] :
( ( ( between @ SV194 @ SV230 @ SV255 )
= $false )
| ( ( equidistant @ SV136 @ SV296 @ SV230 @ SV301 )
= $true )
| ( ( between @ SV61 @ SV136 @ SV238 )
= $false )
| ( ( equidistant @ SV238 @ SV296 @ SV255 @ SV301 )
= $false )
| ( ( equidistant @ SV61 @ SV296 @ SV194 @ SV301 )
= $false )
| ( ( equidistant @ SV61 @ SV238 @ SV194 @ SV255 )
= $false )
| ( ( equidistant @ SV61 @ SV136 @ SV194 @ SV230 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(887,plain,
! [SV239: $i,SV63: $i,SV302: $i,SV297: $i,SV138: $i,SV256: $i,SV232: $i,SV196: $i] :
( ( ( between @ SV196 @ SV232 @ SV256 )
= $false )
| ( ( equidistant @ SV138 @ SV297 @ SV232 @ SV302 )
= $true )
| ( ( between @ SV63 @ SV138 @ SV239 )
= $false )
| ( ( equidistant @ SV239 @ SV297 @ SV256 @ SV302 )
= $false )
| ( ( equidistant @ SV63 @ SV297 @ SV196 @ SV302 )
= $false )
| ( ( equidistant @ SV138 @ SV239 @ SV232 @ SV256 )
= $false )
| ( ( equidistant @ SV63 @ SV138 @ SV196 @ SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[884]) ).
thf(888,plain,
! [SV214: $i,SV155: $i,SV298: $i,SV240: $i,SV295: $i,SV236: $i,SV82: $i,SV6: $i] :
( ( ( SV6 = SV82 )
= $true )
| ( ( equidistant @ SV236 @ SV295 @ SV240 @ SV298 )
= $true )
| ( ( between @ SV155 @ SV214 @ SV240 )
= $false )
| ( ( between @ SV6 @ SV82 @ SV236 )
= $false )
| ( ( equidistant @ SV82 @ SV295 @ SV214 @ SV298 )
= $false )
| ( ( equidistant @ SV6 @ SV295 @ SV155 @ SV298 )
= $false )
| ( ( equidistant @ SV82 @ SV236 @ SV214 @ SV240 )
= $false )
| ( ( equidistant @ SV6 @ SV82 @ SV155 @ SV214 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(889,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[222,888,887,886,869,867,865,864,863,862,856,840,835,833,826,825,824,822,814,811,810,809,806,804,803,798,797,790,789,788,778,777,767,758,757,754,753,752,751,750,711,710,705,665,660,659,658,657,656,655,654,635,616,592,579,572,555,554,544,535,533,532,510,497,489,447,434,431,430,429,423,420,419,408,406,391,390,368,367,366,342,319,318,317,307,223]) ).
thf(890,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[889]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO053-3 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n011.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 10:00:51 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 10.92/2.07
% 10.92/2.07 No.of.Axioms: 85
% 10.92/2.07
% 10.92/2.07 Length.of.Defs: 0
% 10.92/2.07
% 10.92/2.07 Contains.Choice.Funs: false
% 10.92/2.07 ....................................
% 10.92/2.07
% 10.92/2.07 ********************************
% 10.92/2.07 * All subproblems solved! *
% 10.92/2.07 ********************************
% 10.92/2.07 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:85,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:889,loop_count:0,foatp_calls:1,translation:fof_full)
% 10.92/2.07
% 10.92/2.07 %**** Beginning of derivation protocol ****
% 10.92/2.07 % SZS output start CNFRefutation
% See solution above
% 10.92/2.08
% 10.92/2.08 %**** End of derivation protocol ****
% 10.92/2.08 %**** no. of clauses in derivation: 890 ****
% 10.92/2.08 %**** clause counter: 889 ****
% 10.92/2.08
% 10.92/2.08 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:85,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:889,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------