%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO062-3 : 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 : n020.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 10:17:45 AM UTC 2026
% Result : Unsatisfiable 129.08s 21.84s
% Output : CNFRefutation 129.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 76
% Syntax : Number of formulae : 737 ( 464 unt; 0 typ; 0 def)
% Number of atoms : 4758 (1551 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 11769 (1199 ~;1749 |; 0 &;8821 @)
% ( 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 : 3148 ( 0 ^;3148 !; 0 ?;3148 :)
% 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,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(2,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(3,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(4,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(5,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(6,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(7,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(8,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(9,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(10,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(11,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(12,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(13,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_3) ).
thf(14,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_2) ).
thf(15,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_1) ).
thf(16,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(17,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(18,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(19,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(20,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(21,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(22,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(23,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(24,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(25,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(26,axiom,
! [U: $i,V: $i] : ( between @ U @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
thf(27,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
thf(28,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(29,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
thf(30,axiom,
! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).
thf(31,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).
thf(32,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(33,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(34,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(35,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(36,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(37,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
thf(38,axiom,
! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
thf(39,axiom,
! [U: $i] :
( U
= ( reflection @ U @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).
thf(40,axiom,
! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_1) ).
thf(41,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
thf(42,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).
thf(43,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(44,axiom,
! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
thf(45,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(46,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(47,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(48,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(49,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(50,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(51,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(52,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(53,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
thf(54,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(55,axiom,
! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
thf(56,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(57,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(58,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(59,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(60,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(61,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(62,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(63,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(64,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(65,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(66,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(67,axiom,
! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(68,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(69,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(70,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(71,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(72,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(73,axiom,
! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(74,axiom,
between @ u @ v @ w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
thf(75,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(76,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[75]) ).
thf(77,negated_conjecture,
( v
!= ( insertion @ u @ w @ u @ v ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_equals_insertion) ).
thf(78,plain,
$false = $false,
inference(unfold_def,[status(thm)],[76]) ).
thf(79,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)],[1]) ).
thf(80,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)],[2]) ).
thf(81,plain,
( ( ! [U: $i,V: $i,U1: $i,W1: $i] : ( equidistant @ U @ V @ U1 @ ( insertion @ U1 @ W1 @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(82,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)],[4]) ).
thf(83,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)],[5]) ).
thf(84,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)],[6]) ).
thf(85,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)],[7]) ).
thf(86,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)],[8]) ).
thf(87,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)],[9]) ).
thf(88,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)],[10]) ).
thf(89,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)],[11]) ).
thf(90,plain,
( ( ! [V: $i,U: $i] :
( V
!= ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(91,plain,
( ( lower_dimension_point_1 != lower_dimension_point_3 )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(92,plain,
( ( lower_dimension_point_2 != lower_dimension_point_3 )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(93,plain,
( ( lower_dimension_point_1 != lower_dimension_point_2 )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(94,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)],[16]) ).
thf(95,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)],[17]) ).
thf(96,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)],[18]) ).
thf(97,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)],[19]) ).
thf(98,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)],[20]) ).
thf(99,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)],[21]) ).
thf(100,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)],[22]) ).
thf(101,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)],[23]) ).
thf(102,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(103,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(104,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(105,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(106,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)],[28]) ).
thf(107,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(108,plain,
( ( ! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(109,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(110,plain,
( ( ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(111,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)],[33]) ).
thf(112,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)],[34]) ).
thf(113,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)],[35]) ).
thf(114,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)],[36]) ).
thf(115,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(116,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(117,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(118,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(119,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(120,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(121,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)],[43]) ).
thf(122,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(123,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)],[45]) ).
thf(124,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)],[46]) ).
thf(125,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)],[47]) ).
thf(126,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)],[48]) ).
thf(127,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)],[49]) ).
thf(128,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)],[50]) ).
thf(129,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)],[51]) ).
thf(130,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)],[52]) ).
thf(131,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(132,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)],[54]) ).
thf(133,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(134,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)],[56]) ).
thf(135,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)],[57]) ).
thf(136,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)],[58]) ).
thf(137,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)],[59]) ).
thf(138,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)],[60]) ).
thf(139,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)],[61]) ).
thf(140,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[62]) ).
thf(141,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(142,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(143,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)],[65]) ).
thf(144,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)],[66]) ).
thf(145,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[67]) ).
thf(146,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)],[68]) ).
thf(147,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(148,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(149,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[71]) ).
thf(150,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)],[72]) ).
thf(151,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[73]) ).
thf(152,plain,
( ( between @ u @ v @ w )
= $true ),
inference(unfold_def,[status(thm)],[74]) ).
thf(153,plain,
( ( v
!= ( insertion @ u @ w @ u @ v ) )
= $true ),
inference(unfold_def,[status(thm)],[77]) ).
thf(154,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[78]) ).
thf(155,plain,
( ( v
!= ( insertion @ u @ w @ u @ v ) )
= $true ),
inference(copy,[status(thm)],[153]) ).
thf(156,plain,
( ( between @ u @ v @ w )
= $true ),
inference(copy,[status(thm)],[152]) ).
thf(157,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(158,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(copy,[status(thm)],[150]) ).
thf(159,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(160,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(161,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(162,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(copy,[status(thm)],[146]) ).
thf(163,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(164,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(copy,[status(thm)],[144]) ).
thf(165,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(copy,[status(thm)],[143]) ).
thf(166,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(167,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(168,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(169,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(copy,[status(thm)],[139]) ).
thf(170,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(copy,[status(thm)],[138]) ).
thf(171,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(copy,[status(thm)],[137]) ).
thf(172,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(copy,[status(thm)],[136]) ).
thf(173,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(copy,[status(thm)],[135]) ).
thf(174,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(copy,[status(thm)],[134]) ).
thf(175,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(176,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)],[132]) ).
thf(177,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(178,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(179,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(180,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(181,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[127]) ).
thf(182,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(183,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(184,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(185,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(copy,[status(thm)],[123]) ).
thf(186,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(187,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)],[121]) ).
thf(188,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(189,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(190,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(191,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(192,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(193,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(194,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(copy,[status(thm)],[114]) ).
thf(195,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(copy,[status(thm)],[113]) ).
thf(196,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( U = V )
| ( W
= ( extension @ U @ V @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(197,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(copy,[status(thm)],[111]) ).
thf(198,plain,
( ( ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(199,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(200,plain,
( ( ! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(201,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(202,plain,
( ( ! [U: $i,W: $i,X: $i,V: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ( between @ V @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(203,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(204,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(205,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(206,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(207,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(208,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( U = V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(209,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ V @ W ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(210,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ X )
| ( between @ V @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(211,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(copy,[status(thm)],[97]) ).
thf(212,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(copy,[status(thm)],[96]) ).
thf(213,plain,
( ( ! [U: $i,V: $i,X: $i,W: $i] :
( ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(214,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ X )
| ( between @ U @ V @ X ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(215,plain,
( ( lower_dimension_point_1 != lower_dimension_point_2 )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(216,plain,
( ( lower_dimension_point_2 != lower_dimension_point_3 )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(217,plain,
( ( lower_dimension_point_1 != lower_dimension_point_3 )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(218,plain,
( ( ! [V: $i,U: $i] :
( V
!= ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(219,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)],[89]) ).
thf(220,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(221,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(copy,[status(thm)],[87]) ).
thf(222,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(copy,[status(thm)],[86]) ).
thf(223,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(copy,[status(thm)],[85]) ).
thf(224,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(copy,[status(thm)],[84]) ).
thf(225,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(copy,[status(thm)],[83]) ).
thf(226,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(copy,[status(thm)],[82]) ).
thf(227,plain,
( ( ! [U: $i,V: $i,U1: $i,W1: $i] : ( equidistant @ U @ V @ U1 @ ( insertion @ U1 @ W1 @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(228,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(copy,[status(thm)],[80]) ).
thf(229,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(copy,[status(thm)],[79]) ).
thf(230,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[154]) ).
thf(231,plain,
( ( ! [SX0: $i,SX1: $i] :
( SX0
!= ( extension @ SX1 @ SX0 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218]) ).
thf(232,plain,
( ( v
!= ( insertion @ u @ w @ u @ v ) )
= $true ),
inference(unfold_def,[status(thm)],[155]) ).
thf(233,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( between @ SX0 @ SX1 @ SX2 )
| ( SX0 != SX2 )
| ( between @ SX3 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[202]) ).
thf(234,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( SX1
= ( reflection @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[190]) ).
thf(235,plain,
( ( lower_dimension_point_1 != lower_dimension_point_3 )
= $true ),
inference(unfold_def,[status(thm)],[217]) ).
thf(236,plain,
( ( lower_dimension_point_1 != lower_dimension_point_2 )
= $true ),
inference(unfold_def,[status(thm)],[215]) ).
thf(237,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( SX0
!= ( extension @ SX1 @ SX2 @ SX3 @ SX4 ) )
| ( between @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(238,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( reflection @ SX1 @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[192]) ).
thf(239,plain,
( ( lower_dimension_point_2 != lower_dimension_point_3 )
= $true ),
inference(unfold_def,[status(thm)],[216]) ).
thf(240,plain,
! [SV1: $i] :
( ( ! [SY262: $i] : ( equidistant @ SV1 @ SY262 @ SY262 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(241,plain,
! [SV2: $i] :
( ( ! [SY263: $i,SY264: $i,SY265: $i,SY266: $i,SY267: $i] :
( ~ ( equidistant @ SV2 @ SY263 @ SY264 @ SY265 )
| ~ ( equidistant @ SV2 @ SY263 @ SY266 @ SY267 )
| ( equidistant @ SY264 @ SY265 @ SY266 @ SY267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(242,plain,
! [SV3: $i] :
( ( ! [SY268: $i,SY269: $i] :
( ~ ( equidistant @ SV3 @ SY268 @ SY269 @ SY269 )
| ( SV3 = SY268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(243,plain,
! [SV4: $i] :
( ( ! [SY270: $i,SY271: $i,SY272: $i] : ( between @ SV4 @ SY270 @ ( extension @ SV4 @ SY270 @ SY271 @ SY272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(244,plain,
! [SV5: $i] :
( ( ! [SY273: $i,SY274: $i,SY275: $i] : ( equidistant @ SV5 @ ( extension @ SY273 @ SV5 @ SY274 @ SY275 ) @ SY274 @ SY275 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(245,plain,
! [SV6: $i] :
( ( ! [SY276: $i,SY277: $i,SY278: $i,SY279: $i,SY280: $i,SY281: $i,SY282: $i] :
( ~ ( equidistant @ SV6 @ SY276 @ SY277 @ SY278 )
| ~ ( equidistant @ SY276 @ SY279 @ SY278 @ SY280 )
| ~ ( equidistant @ SV6 @ SY281 @ SY277 @ SY282 )
| ~ ( equidistant @ SY276 @ SY281 @ SY278 @ SY282 )
| ~ ( between @ SV6 @ SY276 @ SY279 )
| ~ ( between @ SY277 @ SY278 @ SY280 )
| ( SV6 = SY276 )
| ( equidistant @ SY279 @ SY281 @ SY280 @ SY282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(246,plain,
! [SV7: $i] :
( ( ! [SY283: $i] :
( ~ ( between @ SV7 @ SY283 @ SV7 )
| ( SV7 = SY283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(247,plain,
! [SV8: $i] :
( ( ! [SY284: $i,SY285: $i,SY286: $i,SY287: $i] :
( ~ ( between @ SV8 @ SY284 @ SY285 )
| ~ ( between @ SY286 @ SY287 @ SY285 )
| ( between @ SY284 @ ( inner_pasch @ SV8 @ SY284 @ SY285 @ SY287 @ SY286 ) @ SY286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(248,plain,
! [SV9: $i] :
( ( ! [SY288: $i,SY289: $i,SY290: $i,SY291: $i] :
( ~ ( between @ SV9 @ SY288 @ SY289 )
| ~ ( between @ SY290 @ SY291 @ SY289 )
| ( between @ SY291 @ ( inner_pasch @ SV9 @ SY288 @ SY289 @ SY291 @ SY290 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(249,plain,
( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(250,plain,
( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(251,plain,
( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(252,plain,
! [SV10: $i] :
( ( ! [SY292: $i,SY293: $i,SY294: $i,SY295: $i] :
( ~ ( equidistant @ SV10 @ SY292 @ SV10 @ SY293 )
| ~ ( equidistant @ SY294 @ SY292 @ SY294 @ SY293 )
| ~ ( equidistant @ SY295 @ SY292 @ SY295 @ SY293 )
| ( between @ SV10 @ SY294 @ SY295 )
| ( between @ SY294 @ SY295 @ SV10 )
| ( between @ SY295 @ SV10 @ SY294 )
| ( SY292 = SY293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(253,plain,
! [SV11: $i] :
( ( ! [SY296: $i,SY297: $i,SY298: $i,SY299: $i] :
( ~ ( between @ SV11 @ SY296 @ SY297 )
| ~ ( between @ SY298 @ SY296 @ SY299 )
| ( SV11 = SY296 )
| ( between @ SV11 @ SY298 @ ( euclid1 @ SV11 @ SY298 @ SY296 @ SY299 @ SY297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(254,plain,
! [SV12: $i] :
( ( ! [SY300: $i,SY301: $i,SY302: $i,SY303: $i] :
( ~ ( between @ SV12 @ SY300 @ SY301 )
| ~ ( between @ SY302 @ SY300 @ SY303 )
| ( SV12 = SY300 )
| ( between @ SV12 @ SY303 @ ( euclid2 @ SV12 @ SY302 @ SY300 @ SY303 @ SY301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(255,plain,
! [SV13: $i] :
( ( ! [SY304: $i,SY305: $i,SY306: $i,SY307: $i] :
( ~ ( between @ SV13 @ SY304 @ SY305 )
| ~ ( between @ SY306 @ SY304 @ SY307 )
| ( SV13 = SY304 )
| ( between @ ( euclid1 @ SV13 @ SY306 @ SY304 @ SY307 @ SY305 ) @ SY305 @ ( euclid2 @ SV13 @ SY306 @ SY304 @ SY307 @ SY305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(256,plain,
! [SV14: $i] :
( ( ! [SY308: $i,SY309: $i,SY310: $i,SY311: $i,SY312: $i] :
( ~ ( equidistant @ SV14 @ SY308 @ SV14 @ SY309 )
| ~ ( equidistant @ SV14 @ SY310 @ SV14 @ SY311 )
| ~ ( between @ SV14 @ SY308 @ SY310 )
| ~ ( between @ SY308 @ SY312 @ SY310 )
| ( between @ SY309 @ ( continuous @ SV14 @ SY308 @ SY309 @ SY312 @ SY310 @ SY311 ) @ SY311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(257,plain,
! [SV15: $i] :
( ( ! [SY313: $i,SY314: $i,SY315: $i,SY316: $i,SY317: $i] :
( ~ ( equidistant @ SV15 @ SY313 @ SV15 @ SY314 )
| ~ ( equidistant @ SV15 @ SY315 @ SV15 @ SY316 )
| ~ ( between @ SV15 @ SY313 @ SY315 )
| ~ ( between @ SY313 @ SY317 @ SY315 )
| ( equidistant @ SV15 @ SY317 @ SV15 @ ( continuous @ SV15 @ SY313 @ SY314 @ SY317 @ SY315 @ SY316 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(258,plain,
! [SV16: $i] :
( ( ! [SY318: $i] :
( ( reflection @ SV16 @ SY318 )
= ( extension @ SV16 @ SY318 @ SV16 @ SY318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(259,plain,
! [SV17: $i] :
( ( ! [SY319: $i,SY320: $i,SY321: $i] :
( ( insertion @ SV17 @ SY319 @ SY320 @ SY321 )
= ( extension @ ( extension @ SY319 @ SV17 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV17 @ SY320 @ SY321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(260,plain,
! [SV18: $i] :
( ( ! [SY322: $i] : ( equidistant @ SV18 @ SY322 @ SV18 @ SY322 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(261,plain,
! [SV19: $i] :
( ( ! [SY323: $i,SY324: $i,SY325: $i] :
( ~ ( equidistant @ SV19 @ SY323 @ SY324 @ SY325 )
| ( equidistant @ SY324 @ SY325 @ SV19 @ SY323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(262,plain,
! [SV20: $i] :
( ( ! [SY326: $i,SY327: $i,SY328: $i] :
( ~ ( equidistant @ SV20 @ SY326 @ SY327 @ SY328 )
| ( equidistant @ SY326 @ SV20 @ SY327 @ SY328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(263,plain,
! [SV21: $i] :
( ( ! [SY329: $i,SY330: $i,SY331: $i] :
( ~ ( equidistant @ SV21 @ SY329 @ SY330 @ SY331 )
| ( equidistant @ SV21 @ SY329 @ SY331 @ SY330 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(264,plain,
! [SV22: $i] :
( ( ! [SY332: $i,SY333: $i,SY334: $i] :
( ~ ( equidistant @ SV22 @ SY332 @ SY333 @ SY334 )
| ( equidistant @ SY332 @ SV22 @ SY334 @ SY333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(265,plain,
! [SV23: $i] :
( ( ! [SY335: $i,SY336: $i,SY337: $i] :
( ~ ( equidistant @ SV23 @ SY335 @ SY336 @ SY337 )
| ( equidistant @ SY336 @ SY337 @ SY335 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(266,plain,
! [SV24: $i] :
( ( ! [SY338: $i,SY339: $i,SY340: $i] :
( ~ ( equidistant @ SV24 @ SY338 @ SY339 @ SY340 )
| ( equidistant @ SY340 @ SY339 @ SV24 @ SY338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(267,plain,
! [SV25: $i] :
( ( ! [SY341: $i,SY342: $i,SY343: $i] :
( ~ ( equidistant @ SV25 @ SY341 @ SY342 @ SY343 )
| ( equidistant @ SY343 @ SY342 @ SY341 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(268,plain,
! [SV26: $i] :
( ( ! [SY344: $i,SY345: $i,SY346: $i,SY347: $i,SY348: $i] :
( ~ ( equidistant @ SV26 @ SY344 @ SY345 @ SY346 )
| ~ ( equidistant @ SY345 @ SY346 @ SY347 @ SY348 )
| ( equidistant @ SV26 @ SY344 @ SY347 @ SY348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(269,plain,
! [SV27: $i] :
( ( ! [SY349: $i,SY350: $i] :
( SV27
= ( extension @ SY349 @ SV27 @ SY350 @ SY350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(270,plain,
! [SV28: $i] :
( ( ! [SY351: $i] : ( between @ SV28 @ SY351 @ ( reflection @ SV28 @ SY351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(271,plain,
! [SV29: $i] :
( ( ! [SY352: $i] : ( equidistant @ SV29 @ ( reflection @ SY352 @ SV29 ) @ SY352 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(272,plain,
! [SV30: $i] :
( ( SV30
= ( reflection @ SV30 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(273,plain,
! [SV31: $i] :
( ( ! [SY353: $i] : ( equidistant @ SV31 @ SV31 @ SY353 @ SY353 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(274,plain,
! [SV32: $i] :
( ( ! [SY354: $i,SY355: $i,SY356: $i,SY357: $i,SY358: $i] :
( ~ ( equidistant @ SV32 @ SY354 @ SY355 @ SY356 )
| ~ ( equidistant @ SY354 @ SY357 @ SY356 @ SY358 )
| ~ ( between @ SV32 @ SY354 @ SY357 )
| ~ ( between @ SY355 @ SY356 @ SY358 )
| ( equidistant @ SV32 @ SY357 @ SY355 @ SY358 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(275,plain,
! [SV33: $i] :
( ( ! [SY359: $i,SY360: $i,SY361: $i] :
( ~ ( between @ SV33 @ SY359 @ SY360 )
| ~ ( between @ SV33 @ SY359 @ SY361 )
| ~ ( equidistant @ SY359 @ SY360 @ SY359 @ SY361 )
| ( SV33 = SY359 )
| ( SY360 = SY361 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(276,plain,
! [SV34: $i] :
( ( ! [SY362: $i,SY363: $i] :
( ~ ( between @ SV34 @ SY362 @ SY363 )
| ( SV34 = SY362 )
| ( SY363
= ( extension @ SV34 @ SY362 @ SY362 @ SY363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(277,plain,
! [SV35: $i] :
( ( ! [SY364: $i,SY365: $i,SY366: $i,SY367: $i,SY368: $i] :
( ~ ( equidistant @ SV35 @ SY364 @ SY365 @ SY366 )
| ( ( extension @ SY367 @ SY368 @ SV35 @ SY364 )
= ( extension @ SY367 @ SY368 @ SY365 @ SY366 ) )
| ( SY367 = SY368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(278,plain,
! [SV36: $i] :
( ( ! [SY369: $i] :
( ( ( extension @ SV36 @ SY369 @ SV36 @ SY369 )
= ( extension @ SV36 @ SY369 @ SY369 @ SV36 ) )
| ( SV36 = SY369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(279,plain,
! [SV37: $i] :
( ( ! [SY370: $i] : ( equidistant @ SV37 @ SY370 @ SV37 @ ( reflection @ ( reflection @ SY370 @ SV37 ) @ SV37 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(280,plain,
! [SV38: $i] :
( ( ! [SY371: $i] :
( SV38
= ( reflection @ ( reflection @ SV38 @ SY371 ) @ SY371 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(281,plain,
! [SV39: $i] :
( ( ! [SY372: $i] : ( between @ SV39 @ SY372 @ SY372 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(282,plain,
! [SV40: $i] :
( ( ! [SY373: $i,SY374: $i] :
( ~ ( between @ SV40 @ SY373 @ SY374 )
| ( between @ SY374 @ SY373 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(283,plain,
! [SV41: $i] :
( ( ! [SY375: $i] : ( between @ SV41 @ SV41 @ SY375 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(284,plain,
! [SV42: $i] :
( ( ! [SY376: $i,SY377: $i] :
( ~ ( between @ SV42 @ SY376 @ SY377 )
| ~ ( between @ SY376 @ SV42 @ SY377 )
| ( SV42 = SY376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(285,plain,
! [SV43: $i] :
( ( ! [SY378: $i,SY379: $i] :
( ~ ( between @ SV43 @ SY378 @ SY379 )
| ~ ( between @ SV43 @ SY379 @ SY378 )
| ( SY378 = SY379 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(286,plain,
! [SV44: $i] :
( ( ! [SY380: $i,SY381: $i] :
( ~ ( between @ SV44 @ SY380 @ SY381 )
| ~ ( between @ SY380 @ SV44 @ SY381 )
| ( SV44 = SY380 )
| ( SY380 = SY381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(287,plain,
! [SV45: $i] :
( ( ! [SY382: $i,SY383: $i] :
( ~ ( between @ SV45 @ SY382 @ SY383 )
| ~ ( between @ SV45 @ SY383 @ SY382 )
| ( SV45 = SY382 )
| ( SY382 = SY383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(288,plain,
! [SV46: $i] :
( ( ! [SY384: $i,SY385: $i,SY386: $i] :
( ~ ( between @ SV46 @ SY384 @ SY385 )
| ~ ( between @ SY384 @ SY385 @ SY386 )
| ( between @ SV46 @ SY384 @ SY385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(289,plain,
! [SV47: $i] :
( ( ! [SY387: $i,SY388: $i,SY389: $i] :
( ~ ( between @ SV47 @ SY387 @ SY388 )
| ~ ( between @ SV47 @ SY388 @ SY389 )
| ( between @ SY387 @ SY388 @ SY389 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(290,plain,
! [SV48: $i] :
( ( ! [SY390: $i,SY391: $i,SY392: $i] :
( ~ ( between @ SV48 @ SY390 @ SY391 )
| ~ ( between @ SY390 @ SY391 @ SY392 )
| ( between @ SV48 @ SY391 @ SY392 )
| ( SY390 = SY391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(291,plain,
! [SV49: $i] :
( ( ! [SY393: $i,SY394: $i,SY395: $i] :
( ~ ( between @ SV49 @ SY393 @ SY394 )
| ~ ( between @ SY393 @ SY394 @ SY395 )
| ( between @ SV49 @ SY393 @ SY395 )
| ( SY393 = SY394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(292,plain,
! [SV50: $i] :
( ( ! [SY396: $i,SY397: $i,SY398: $i] :
( ~ ( between @ SV50 @ SY396 @ SY397 )
| ~ ( between @ SY396 @ SY398 @ SY397 )
| ( between @ SV50 @ SY398 @ SY397 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(293,plain,
! [SV51: $i] :
( ( ! [SY399: $i,SY400: $i,SY401: $i] :
( ~ ( between @ SV51 @ SY399 @ SY400 )
| ~ ( between @ SV51 @ SY400 @ SY401 )
| ( between @ SV51 @ SY399 @ SY401 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(294,plain,
! [SV52: $i] :
( ( ! [SY402: $i,SY403: $i,SY404: $i] : ( equidistant @ SV52 @ ( extension @ SY402 @ SV52 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SY403 @ ( extension @ SY404 @ SY403 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(295,plain,
! [SV53: $i] :
( ( ! [SY405: $i] : ( between @ SV53 @ SY405 @ ( extension @ SV53 @ SY405 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(296,plain,
! [SV54: $i] :
( ( ! [SY406: $i,SY407: $i,SY408: $i,SY409: $i,SY410: $i] :
( ~ ( between @ SV54 @ SY406 @ SY407 )
| ~ ( between @ SY408 @ SY409 @ SY407 )
| ~ ( between @ SV54 @ SY410 @ SY408 )
| ( between @ SY410 @ ( inner_pasch @ SY409 @ ( inner_pasch @ SV54 @ SY410 @ SY408 @ SY409 @ SY407 ) @ SV54 @ SY406 @ SY407 ) @ SY407 )
| ( between @ SY406 @ ( inner_pasch @ SY409 @ ( inner_pasch @ SV54 @ SY410 @ SY408 @ SY409 @ SY407 ) @ SV54 @ SY406 @ SY407 ) @ SY409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(297,plain,
! [SV55: $i] :
( ( ! [SY411: $i,SY412: $i,SY413: $i] :
( ~ ( between @ SV55 @ SY411 @ SY412 )
| ~ ( equidistant @ SV55 @ SY412 @ SV55 @ SY413 )
| ~ ( equidistant @ SY411 @ SY412 @ SY411 @ SY413 )
| ( SV55 = SY411 )
| ( SY412 = SY413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(298,plain,
! [SV56: $i] :
( ( ! [SY414: $i,SY415: $i,SY416: $i,SY417: $i,SY418: $i,SY419: $i,SY420: $i] :
( ~ ( equidistant @ SV56 @ SY414 @ SY415 @ SY416 )
| ~ ( equidistant @ SV56 @ SY417 @ SY415 @ SY418 )
| ~ ( equidistant @ SV56 @ SY419 @ SY415 @ SY420 )
| ~ ( equidistant @ SY417 @ SY419 @ SY418 @ SY420 )
| ~ ( between @ SV56 @ SY414 @ SY417 )
| ~ ( between @ SY415 @ SY416 @ SY418 )
| ( equidistant @ SY414 @ SY419 @ SY416 @ SY420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(299,plain,
! [SV57: $i] :
( ( ! [SY421: $i,SY422: $i,SY423: $i,SY424: $i,SY425: $i] :
( ~ ( between @ SV57 @ SY421 @ SY422 )
| ~ ( between @ SY423 @ SY424 @ SY425 )
| ~ ( equidistant @ SV57 @ SY421 @ SY423 @ SY424 )
| ~ ( equidistant @ SV57 @ SY422 @ SY423 @ SY425 )
| ( equidistant @ SY421 @ SY422 @ SY424 @ SY425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(300,plain,
! [SV58: $i] :
( ( ! [SY426: $i,SY427: $i,SY428: $i,SY429: $i,SY430: $i,SY431: $i,SY432: $i] :
( ~ ( equidistant @ SV58 @ SY426 @ SY427 @ SY428 )
| ~ ( equidistant @ SY426 @ SY429 @ SY428 @ SY430 )
| ~ ( equidistant @ SV58 @ SY431 @ SY427 @ SY432 )
| ~ ( equidistant @ SY429 @ SY431 @ SY430 @ SY432 )
| ~ ( between @ SV58 @ SY426 @ SY429 )
| ~ ( between @ SY427 @ SY428 @ SY430 )
| ( equidistant @ SY426 @ SY431 @ SY428 @ SY432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(301,plain,
! [SV59: $i] :
( ( ! [SY433: $i,SY434: $i,SY435: $i] :
( ~ ( between @ SV59 @ SY433 @ SY434 )
| ~ ( equidistant @ SV59 @ SY433 @ SV59 @ SY435 )
| ~ ( equidistant @ SY434 @ SY433 @ SY434 @ SY435 )
| ( SY433 = SY435 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(302,plain,
! [SV60: $i] :
( ( ! [SY436: $i,SY437: $i,SY438: $i] : ( equidistant @ SV60 @ SY436 @ SY437 @ ( insertion @ SY437 @ SY438 @ SV60 @ SY436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(303,plain,
! [SV61: $i] :
( ( ! [SY439: $i,SY440: $i,SY441: $i,SY442: $i] :
( ~ ( between @ SV61 @ SY439 @ SY440 )
| ~ ( equidistant @ SV61 @ SY440 @ SY441 @ SY442 )
| ( between @ SY441 @ ( insertion @ SY441 @ SY442 @ SV61 @ SY439 ) @ SY442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(304,plain,
! [SV62: $i] :
( ( ! [SY443: $i,SY444: $i,SY445: $i,SY446: $i] :
( ~ ( between @ SV62 @ SY443 @ SY444 )
| ~ ( equidistant @ SV62 @ SY444 @ SY445 @ SY446 )
| ( equidistant @ SY443 @ SY444 @ ( insertion @ SY445 @ SY446 @ SV62 @ SY443 ) @ SY446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(305,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(306,plain,
! [SV63: $i] :
( ( ! [SY447: $i] :
( SV63
!= ( extension @ SY447 @ SV63 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(307,plain,
( ( v
= ( insertion @ u @ w @ u @ v ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(308,plain,
! [SV64: $i] :
( ( ! [SY448: $i,SY449: $i,SY450: $i] :
( ~ ( between @ SV64 @ SY448 @ SY449 )
| ( SV64 != SY449 )
| ( between @ SY450 @ SY448 @ SY449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(309,plain,
! [SV65: $i] :
( ( ! [SY451: $i] :
( ( SV65 != SY451 )
| ( SY451
= ( reflection @ SV65 @ SY451 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(310,plain,
( ( lower_dimension_point_1 = lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(311,plain,
( ( lower_dimension_point_1 = lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[236]) ).
thf(312,plain,
! [SV66: $i] :
( ( ! [SY452: $i,SY453: $i,SY454: $i,SY455: $i] :
( ( SV66
!= ( extension @ SY452 @ SY453 @ SY454 @ SY455 ) )
| ( between @ SY452 @ SY453 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(313,plain,
! [SV67: $i] :
( ( ! [SY456: $i] :
( ( SV67
!= ( reflection @ SY456 @ SV67 ) )
| ( SY456 = SV67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(314,plain,
( ( lower_dimension_point_2 = lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(315,plain,
! [SV68: $i,SV1: $i] :
( ( equidistant @ SV1 @ SV68 @ SV68 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(316,plain,
! [SV69: $i,SV2: $i] :
( ( ! [SY457: $i,SY458: $i,SY459: $i,SY460: $i] :
( ~ ( equidistant @ SV2 @ SV69 @ SY457 @ SY458 )
| ~ ( equidistant @ SV2 @ SV69 @ SY459 @ SY460 )
| ( equidistant @ SY457 @ SY458 @ SY459 @ SY460 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(317,plain,
! [SV70: $i,SV3: $i] :
( ( ! [SY461: $i] :
( ~ ( equidistant @ SV3 @ SV70 @ SY461 @ SY461 )
| ( SV3 = SV70 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(318,plain,
! [SV71: $i,SV4: $i] :
( ( ! [SY462: $i,SY463: $i] : ( between @ SV4 @ SV71 @ ( extension @ SV4 @ SV71 @ SY462 @ SY463 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(319,plain,
! [SV72: $i,SV5: $i] :
( ( ! [SY464: $i,SY465: $i] : ( equidistant @ SV5 @ ( extension @ SV72 @ SV5 @ SY464 @ SY465 ) @ SY464 @ SY465 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(320,plain,
! [SV73: $i,SV6: $i] :
( ( ! [SY466: $i,SY467: $i,SY468: $i,SY469: $i,SY470: $i,SY471: $i] :
( ~ ( equidistant @ SV6 @ SV73 @ SY466 @ SY467 )
| ~ ( equidistant @ SV73 @ SY468 @ SY467 @ SY469 )
| ~ ( equidistant @ SV6 @ SY470 @ SY466 @ SY471 )
| ~ ( equidistant @ SV73 @ SY470 @ SY467 @ SY471 )
| ~ ( between @ SV6 @ SV73 @ SY468 )
| ~ ( between @ SY466 @ SY467 @ SY469 )
| ( SV6 = SV73 )
| ( equidistant @ SY468 @ SY470 @ SY469 @ SY471 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(321,plain,
! [SV74: $i,SV7: $i] :
( ( ~ ( between @ SV7 @ SV74 @ SV7 )
| ( SV7 = SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(322,plain,
! [SV75: $i,SV8: $i] :
( ( ! [SY472: $i,SY473: $i,SY474: $i] :
( ~ ( between @ SV8 @ SV75 @ SY472 )
| ~ ( between @ SY473 @ SY474 @ SY472 )
| ( between @ SV75 @ ( inner_pasch @ SV8 @ SV75 @ SY472 @ SY474 @ SY473 ) @ SY473 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(323,plain,
! [SV76: $i,SV9: $i] :
( ( ! [SY475: $i,SY476: $i,SY477: $i] :
( ~ ( between @ SV9 @ SV76 @ SY475 )
| ~ ( between @ SY476 @ SY477 @ SY475 )
| ( between @ SY477 @ ( inner_pasch @ SV9 @ SV76 @ SY475 @ SY477 @ SY476 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(324,plain,
! [SV77: $i,SV10: $i] :
( ( ! [SY478: $i,SY479: $i,SY480: $i] :
( ~ ( equidistant @ SV10 @ SV77 @ SV10 @ SY478 )
| ~ ( equidistant @ SY479 @ SV77 @ SY479 @ SY478 )
| ~ ( equidistant @ SY480 @ SV77 @ SY480 @ SY478 )
| ( between @ SV10 @ SY479 @ SY480 )
| ( between @ SY479 @ SY480 @ SV10 )
| ( between @ SY480 @ SV10 @ SY479 )
| ( SV77 = SY478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(325,plain,
! [SV78: $i,SV11: $i] :
( ( ! [SY481: $i,SY482: $i,SY483: $i] :
( ~ ( between @ SV11 @ SV78 @ SY481 )
| ~ ( between @ SY482 @ SV78 @ SY483 )
| ( SV11 = SV78 )
| ( between @ SV11 @ SY482 @ ( euclid1 @ SV11 @ SY482 @ SV78 @ SY483 @ SY481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(326,plain,
! [SV79: $i,SV12: $i] :
( ( ! [SY484: $i,SY485: $i,SY486: $i] :
( ~ ( between @ SV12 @ SV79 @ SY484 )
| ~ ( between @ SY485 @ SV79 @ SY486 )
| ( SV12 = SV79 )
| ( between @ SV12 @ SY486 @ ( euclid2 @ SV12 @ SY485 @ SV79 @ SY486 @ SY484 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(327,plain,
! [SV80: $i,SV13: $i] :
( ( ! [SY487: $i,SY488: $i,SY489: $i] :
( ~ ( between @ SV13 @ SV80 @ SY487 )
| ~ ( between @ SY488 @ SV80 @ SY489 )
| ( SV13 = SV80 )
| ( between @ ( euclid1 @ SV13 @ SY488 @ SV80 @ SY489 @ SY487 ) @ SY487 @ ( euclid2 @ SV13 @ SY488 @ SV80 @ SY489 @ SY487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(328,plain,
! [SV81: $i,SV14: $i] :
( ( ! [SY490: $i,SY491: $i,SY492: $i,SY493: $i] :
( ~ ( equidistant @ SV14 @ SV81 @ SV14 @ SY490 )
| ~ ( equidistant @ SV14 @ SY491 @ SV14 @ SY492 )
| ~ ( between @ SV14 @ SV81 @ SY491 )
| ~ ( between @ SV81 @ SY493 @ SY491 )
| ( between @ SY490 @ ( continuous @ SV14 @ SV81 @ SY490 @ SY493 @ SY491 @ SY492 ) @ SY492 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(329,plain,
! [SV82: $i,SV15: $i] :
( ( ! [SY494: $i,SY495: $i,SY496: $i,SY497: $i] :
( ~ ( equidistant @ SV15 @ SV82 @ SV15 @ SY494 )
| ~ ( equidistant @ SV15 @ SY495 @ SV15 @ SY496 )
| ~ ( between @ SV15 @ SV82 @ SY495 )
| ~ ( between @ SV82 @ SY497 @ SY495 )
| ( equidistant @ SV15 @ SY497 @ SV15 @ ( continuous @ SV15 @ SV82 @ SY494 @ SY497 @ SY495 @ SY496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(330,plain,
! [SV83: $i,SV16: $i] :
( ( ( reflection @ SV16 @ SV83 )
= ( extension @ SV16 @ SV83 @ SV16 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(331,plain,
! [SV84: $i,SV17: $i] :
( ( ! [SY498: $i,SY499: $i] :
( ( insertion @ SV17 @ SV84 @ SY498 @ SY499 )
= ( extension @ ( extension @ SV84 @ SV17 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV17 @ SY498 @ SY499 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(332,plain,
! [SV85: $i,SV18: $i] :
( ( equidistant @ SV18 @ SV85 @ SV18 @ SV85 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(333,plain,
! [SV86: $i,SV19: $i] :
( ( ! [SY500: $i,SY501: $i] :
( ~ ( equidistant @ SV19 @ SV86 @ SY500 @ SY501 )
| ( equidistant @ SY500 @ SY501 @ SV19 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(334,plain,
! [SV87: $i,SV20: $i] :
( ( ! [SY502: $i,SY503: $i] :
( ~ ( equidistant @ SV20 @ SV87 @ SY502 @ SY503 )
| ( equidistant @ SV87 @ SV20 @ SY502 @ SY503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(335,plain,
! [SV88: $i,SV21: $i] :
( ( ! [SY504: $i,SY505: $i] :
( ~ ( equidistant @ SV21 @ SV88 @ SY504 @ SY505 )
| ( equidistant @ SV21 @ SV88 @ SY505 @ SY504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(336,plain,
! [SV89: $i,SV22: $i] :
( ( ! [SY506: $i,SY507: $i] :
( ~ ( equidistant @ SV22 @ SV89 @ SY506 @ SY507 )
| ( equidistant @ SV89 @ SV22 @ SY507 @ SY506 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(337,plain,
! [SV90: $i,SV23: $i] :
( ( ! [SY508: $i,SY509: $i] :
( ~ ( equidistant @ SV23 @ SV90 @ SY508 @ SY509 )
| ( equidistant @ SY508 @ SY509 @ SV90 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(338,plain,
! [SV91: $i,SV24: $i] :
( ( ! [SY510: $i,SY511: $i] :
( ~ ( equidistant @ SV24 @ SV91 @ SY510 @ SY511 )
| ( equidistant @ SY511 @ SY510 @ SV24 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(339,plain,
! [SV92: $i,SV25: $i] :
( ( ! [SY512: $i,SY513: $i] :
( ~ ( equidistant @ SV25 @ SV92 @ SY512 @ SY513 )
| ( equidistant @ SY513 @ SY512 @ SV92 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(340,plain,
! [SV93: $i,SV26: $i] :
( ( ! [SY514: $i,SY515: $i,SY516: $i,SY517: $i] :
( ~ ( equidistant @ SV26 @ SV93 @ SY514 @ SY515 )
| ~ ( equidistant @ SY514 @ SY515 @ SY516 @ SY517 )
| ( equidistant @ SV26 @ SV93 @ SY516 @ SY517 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(341,plain,
! [SV94: $i,SV27: $i] :
( ( ! [SY518: $i] :
( SV27
= ( extension @ SV94 @ SV27 @ SY518 @ SY518 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(342,plain,
! [SV95: $i,SV28: $i] :
( ( between @ SV28 @ SV95 @ ( reflection @ SV28 @ SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(343,plain,
! [SV96: $i,SV29: $i] :
( ( equidistant @ SV29 @ ( reflection @ SV96 @ SV29 ) @ SV96 @ SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(344,plain,
! [SV97: $i,SV31: $i] :
( ( equidistant @ SV31 @ SV31 @ SV97 @ SV97 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(345,plain,
! [SV98: $i,SV32: $i] :
( ( ! [SY519: $i,SY520: $i,SY521: $i,SY522: $i] :
( ~ ( equidistant @ SV32 @ SV98 @ SY519 @ SY520 )
| ~ ( equidistant @ SV98 @ SY521 @ SY520 @ SY522 )
| ~ ( between @ SV32 @ SV98 @ SY521 )
| ~ ( between @ SY519 @ SY520 @ SY522 )
| ( equidistant @ SV32 @ SY521 @ SY519 @ SY522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(346,plain,
! [SV99: $i,SV33: $i] :
( ( ! [SY523: $i,SY524: $i] :
( ~ ( between @ SV33 @ SV99 @ SY523 )
| ~ ( between @ SV33 @ SV99 @ SY524 )
| ~ ( equidistant @ SV99 @ SY523 @ SV99 @ SY524 )
| ( SV33 = SV99 )
| ( SY523 = SY524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(347,plain,
! [SV100: $i,SV34: $i] :
( ( ! [SY525: $i] :
( ~ ( between @ SV34 @ SV100 @ SY525 )
| ( SV34 = SV100 )
| ( SY525
= ( extension @ SV34 @ SV100 @ SV100 @ SY525 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(348,plain,
! [SV101: $i,SV35: $i] :
( ( ! [SY526: $i,SY527: $i,SY528: $i,SY529: $i] :
( ~ ( equidistant @ SV35 @ SV101 @ SY526 @ SY527 )
| ( ( extension @ SY528 @ SY529 @ SV35 @ SV101 )
= ( extension @ SY528 @ SY529 @ SY526 @ SY527 ) )
| ( SY528 = SY529 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(349,plain,
! [SV102: $i,SV36: $i] :
( ( ( ( extension @ SV36 @ SV102 @ SV36 @ SV102 )
= ( extension @ SV36 @ SV102 @ SV102 @ SV36 ) )
| ( SV36 = SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(350,plain,
! [SV103: $i,SV37: $i] :
( ( equidistant @ SV37 @ SV103 @ SV37 @ ( reflection @ ( reflection @ SV103 @ SV37 ) @ SV37 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(351,plain,
! [SV104: $i,SV38: $i] :
( ( SV38
= ( reflection @ ( reflection @ SV38 @ SV104 ) @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(352,plain,
! [SV105: $i,SV39: $i] :
( ( between @ SV39 @ SV105 @ SV105 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(353,plain,
! [SV106: $i,SV40: $i] :
( ( ! [SY530: $i] :
( ~ ( between @ SV40 @ SV106 @ SY530 )
| ( between @ SY530 @ SV106 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(354,plain,
! [SV107: $i,SV41: $i] :
( ( between @ SV41 @ SV41 @ SV107 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(355,plain,
! [SV108: $i,SV42: $i] :
( ( ! [SY531: $i] :
( ~ ( between @ SV42 @ SV108 @ SY531 )
| ~ ( between @ SV108 @ SV42 @ SY531 )
| ( SV42 = SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(356,plain,
! [SV109: $i,SV43: $i] :
( ( ! [SY532: $i] :
( ~ ( between @ SV43 @ SV109 @ SY532 )
| ~ ( between @ SV43 @ SY532 @ SV109 )
| ( SV109 = SY532 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(357,plain,
! [SV110: $i,SV44: $i] :
( ( ! [SY533: $i] :
( ~ ( between @ SV44 @ SV110 @ SY533 )
| ~ ( between @ SV110 @ SV44 @ SY533 )
| ( SV44 = SV110 )
| ( SV110 = SY533 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(358,plain,
! [SV111: $i,SV45: $i] :
( ( ! [SY534: $i] :
( ~ ( between @ SV45 @ SV111 @ SY534 )
| ~ ( between @ SV45 @ SY534 @ SV111 )
| ( SV45 = SV111 )
| ( SV111 = SY534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(359,plain,
! [SV112: $i,SV46: $i] :
( ( ! [SY535: $i,SY536: $i] :
( ~ ( between @ SV46 @ SV112 @ SY535 )
| ~ ( between @ SV112 @ SY535 @ SY536 )
| ( between @ SV46 @ SV112 @ SY535 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(360,plain,
! [SV113: $i,SV47: $i] :
( ( ! [SY537: $i,SY538: $i] :
( ~ ( between @ SV47 @ SV113 @ SY537 )
| ~ ( between @ SV47 @ SY537 @ SY538 )
| ( between @ SV113 @ SY537 @ SY538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(361,plain,
! [SV114: $i,SV48: $i] :
( ( ! [SY539: $i,SY540: $i] :
( ~ ( between @ SV48 @ SV114 @ SY539 )
| ~ ( between @ SV114 @ SY539 @ SY540 )
| ( between @ SV48 @ SY539 @ SY540 )
| ( SV114 = SY539 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(362,plain,
! [SV115: $i,SV49: $i] :
( ( ! [SY541: $i,SY542: $i] :
( ~ ( between @ SV49 @ SV115 @ SY541 )
| ~ ( between @ SV115 @ SY541 @ SY542 )
| ( between @ SV49 @ SV115 @ SY542 )
| ( SV115 = SY541 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(363,plain,
! [SV116: $i,SV50: $i] :
( ( ! [SY543: $i,SY544: $i] :
( ~ ( between @ SV50 @ SV116 @ SY543 )
| ~ ( between @ SV116 @ SY544 @ SY543 )
| ( between @ SV50 @ SY544 @ SY543 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(364,plain,
! [SV117: $i,SV51: $i] :
( ( ! [SY545: $i,SY546: $i] :
( ~ ( between @ SV51 @ SV117 @ SY545 )
| ~ ( between @ SV51 @ SY545 @ SY546 )
| ( between @ SV51 @ SV117 @ SY546 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(365,plain,
! [SV118: $i,SV52: $i] :
( ( ! [SY547: $i,SY548: $i] : ( equidistant @ SV52 @ ( extension @ SV118 @ SV52 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SY547 @ ( extension @ SY548 @ SY547 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(366,plain,
! [SV119: $i,SV53: $i] :
( ( between @ SV53 @ SV119 @ ( extension @ SV53 @ SV119 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(367,plain,
! [SV120: $i,SV54: $i] :
( ( ! [SY549: $i,SY550: $i,SY551: $i,SY552: $i] :
( ~ ( between @ SV54 @ SV120 @ SY549 )
| ~ ( between @ SY550 @ SY551 @ SY549 )
| ~ ( between @ SV54 @ SY552 @ SY550 )
| ( between @ SY552 @ ( inner_pasch @ SY551 @ ( inner_pasch @ SV54 @ SY552 @ SY550 @ SY551 @ SY549 ) @ SV54 @ SV120 @ SY549 ) @ SY549 )
| ( between @ SV120 @ ( inner_pasch @ SY551 @ ( inner_pasch @ SV54 @ SY552 @ SY550 @ SY551 @ SY549 ) @ SV54 @ SV120 @ SY549 ) @ SY551 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(368,plain,
! [SV121: $i,SV55: $i] :
( ( ! [SY553: $i,SY554: $i] :
( ~ ( between @ SV55 @ SV121 @ SY553 )
| ~ ( equidistant @ SV55 @ SY553 @ SV55 @ SY554 )
| ~ ( equidistant @ SV121 @ SY553 @ SV121 @ SY554 )
| ( SV55 = SV121 )
| ( SY553 = SY554 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(369,plain,
! [SV122: $i,SV56: $i] :
( ( ! [SY555: $i,SY556: $i,SY557: $i,SY558: $i,SY559: $i,SY560: $i] :
( ~ ( equidistant @ SV56 @ SV122 @ SY555 @ SY556 )
| ~ ( equidistant @ SV56 @ SY557 @ SY555 @ SY558 )
| ~ ( equidistant @ SV56 @ SY559 @ SY555 @ SY560 )
| ~ ( equidistant @ SY557 @ SY559 @ SY558 @ SY560 )
| ~ ( between @ SV56 @ SV122 @ SY557 )
| ~ ( between @ SY555 @ SY556 @ SY558 )
| ( equidistant @ SV122 @ SY559 @ SY556 @ SY560 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(370,plain,
! [SV123: $i,SV57: $i] :
( ( ! [SY561: $i,SY562: $i,SY563: $i,SY564: $i] :
( ~ ( between @ SV57 @ SV123 @ SY561 )
| ~ ( between @ SY562 @ SY563 @ SY564 )
| ~ ( equidistant @ SV57 @ SV123 @ SY562 @ SY563 )
| ~ ( equidistant @ SV57 @ SY561 @ SY562 @ SY564 )
| ( equidistant @ SV123 @ SY561 @ SY563 @ SY564 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(371,plain,
! [SV124: $i,SV58: $i] :
( ( ! [SY565: $i,SY566: $i,SY567: $i,SY568: $i,SY569: $i,SY570: $i] :
( ~ ( equidistant @ SV58 @ SV124 @ SY565 @ SY566 )
| ~ ( equidistant @ SV124 @ SY567 @ SY566 @ SY568 )
| ~ ( equidistant @ SV58 @ SY569 @ SY565 @ SY570 )
| ~ ( equidistant @ SY567 @ SY569 @ SY568 @ SY570 )
| ~ ( between @ SV58 @ SV124 @ SY567 )
| ~ ( between @ SY565 @ SY566 @ SY568 )
| ( equidistant @ SV124 @ SY569 @ SY566 @ SY570 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(372,plain,
! [SV125: $i,SV59: $i] :
( ( ! [SY571: $i,SY572: $i] :
( ~ ( between @ SV59 @ SV125 @ SY571 )
| ~ ( equidistant @ SV59 @ SV125 @ SV59 @ SY572 )
| ~ ( equidistant @ SY571 @ SV125 @ SY571 @ SY572 )
| ( SV125 = SY572 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(373,plain,
! [SV126: $i,SV60: $i] :
( ( ! [SY573: $i,SY574: $i] : ( equidistant @ SV60 @ SV126 @ SY573 @ ( insertion @ SY573 @ SY574 @ SV60 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(374,plain,
! [SV127: $i,SV61: $i] :
( ( ! [SY575: $i,SY576: $i,SY577: $i] :
( ~ ( between @ SV61 @ SV127 @ SY575 )
| ~ ( equidistant @ SV61 @ SY575 @ SY576 @ SY577 )
| ( between @ SY576 @ ( insertion @ SY576 @ SY577 @ SV61 @ SV127 ) @ SY577 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(375,plain,
! [SV128: $i,SV62: $i] :
( ( ! [SY578: $i,SY579: $i,SY580: $i] :
( ~ ( between @ SV62 @ SV128 @ SY578 )
| ~ ( equidistant @ SV62 @ SY578 @ SY579 @ SY580 )
| ( equidistant @ SV128 @ SY578 @ ( insertion @ SY579 @ SY580 @ SV62 @ SV128 ) @ SY580 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(376,plain,
! [SV129: $i,SV63: $i] :
( ( SV63
!= ( extension @ SV129 @ SV63 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(377,plain,
! [SV130: $i,SV64: $i] :
( ( ! [SY581: $i,SY582: $i] :
( ~ ( between @ SV64 @ SV130 @ SY581 )
| ( SV64 != SY581 )
| ( between @ SY582 @ SV130 @ SY581 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(378,plain,
! [SV131: $i,SV65: $i] :
( ( ( SV65 != SV131 )
| ( SV131
= ( reflection @ SV65 @ SV131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(379,plain,
! [SV132: $i,SV66: $i] :
( ( ! [SY583: $i,SY584: $i,SY585: $i] :
( ( SV66
!= ( extension @ SV132 @ SY583 @ SY584 @ SY585 ) )
| ( between @ SV132 @ SY583 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(380,plain,
! [SV133: $i,SV67: $i] :
( ( ( SV67
!= ( reflection @ SV133 @ SV67 ) )
| ( SV133 = SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(381,plain,
! [SV134: $i,SV69: $i,SV2: $i] :
( ( ! [SY586: $i,SY587: $i,SY588: $i] :
( ~ ( equidistant @ SV2 @ SV69 @ SV134 @ SY586 )
| ~ ( equidistant @ SV2 @ SV69 @ SY587 @ SY588 )
| ( equidistant @ SV134 @ SY586 @ SY587 @ SY588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(382,plain,
! [SV135: $i,SV70: $i,SV3: $i] :
( ( ~ ( equidistant @ SV3 @ SV70 @ SV135 @ SV135 )
| ( SV3 = SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(383,plain,
! [SV136: $i,SV71: $i,SV4: $i] :
( ( ! [SY589: $i] : ( between @ SV4 @ SV71 @ ( extension @ SV4 @ SV71 @ SV136 @ SY589 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(384,plain,
! [SV137: $i,SV72: $i,SV5: $i] :
( ( ! [SY590: $i] : ( equidistant @ SV5 @ ( extension @ SV72 @ SV5 @ SV137 @ SY590 ) @ SV137 @ SY590 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(385,plain,
! [SV138: $i,SV73: $i,SV6: $i] :
( ( ! [SY591: $i,SY592: $i,SY593: $i,SY594: $i,SY595: $i] :
( ~ ( equidistant @ SV6 @ SV73 @ SV138 @ SY591 )
| ~ ( equidistant @ SV73 @ SY592 @ SY591 @ SY593 )
| ~ ( equidistant @ SV6 @ SY594 @ SV138 @ SY595 )
| ~ ( equidistant @ SV73 @ SY594 @ SY591 @ SY595 )
| ~ ( between @ SV6 @ SV73 @ SY592 )
| ~ ( between @ SV138 @ SY591 @ SY593 )
| ( SV6 = SV73 )
| ( equidistant @ SY592 @ SY594 @ SY593 @ SY595 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(386,plain,
! [SV74: $i,SV7: $i] :
( ( ( ~ ( between @ SV7 @ SV74 @ SV7 ) )
= $true )
| ( ( SV7 = SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(387,plain,
! [SV139: $i,SV75: $i,SV8: $i] :
( ( ! [SY596: $i,SY597: $i] :
( ~ ( between @ SV8 @ SV75 @ SV139 )
| ~ ( between @ SY596 @ SY597 @ SV139 )
| ( between @ SV75 @ ( inner_pasch @ SV8 @ SV75 @ SV139 @ SY597 @ SY596 ) @ SY596 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(388,plain,
! [SV140: $i,SV76: $i,SV9: $i] :
( ( ! [SY598: $i,SY599: $i] :
( ~ ( between @ SV9 @ SV76 @ SV140 )
| ~ ( between @ SY598 @ SY599 @ SV140 )
| ( between @ SY599 @ ( inner_pasch @ SV9 @ SV76 @ SV140 @ SY599 @ SY598 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(389,plain,
! [SV141: $i,SV77: $i,SV10: $i] :
( ( ! [SY600: $i,SY601: $i] :
( ~ ( equidistant @ SV10 @ SV77 @ SV10 @ SV141 )
| ~ ( equidistant @ SY600 @ SV77 @ SY600 @ SV141 )
| ~ ( equidistant @ SY601 @ SV77 @ SY601 @ SV141 )
| ( between @ SV10 @ SY600 @ SY601 )
| ( between @ SY600 @ SY601 @ SV10 )
| ( between @ SY601 @ SV10 @ SY600 )
| ( SV77 = SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(390,plain,
! [SV142: $i,SV78: $i,SV11: $i] :
( ( ! [SY602: $i,SY603: $i] :
( ~ ( between @ SV11 @ SV78 @ SV142 )
| ~ ( between @ SY602 @ SV78 @ SY603 )
| ( SV11 = SV78 )
| ( between @ SV11 @ SY602 @ ( euclid1 @ SV11 @ SY602 @ SV78 @ SY603 @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(391,plain,
! [SV143: $i,SV79: $i,SV12: $i] :
( ( ! [SY604: $i,SY605: $i] :
( ~ ( between @ SV12 @ SV79 @ SV143 )
| ~ ( between @ SY604 @ SV79 @ SY605 )
| ( SV12 = SV79 )
| ( between @ SV12 @ SY605 @ ( euclid2 @ SV12 @ SY604 @ SV79 @ SY605 @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(392,plain,
! [SV144: $i,SV80: $i,SV13: $i] :
( ( ! [SY606: $i,SY607: $i] :
( ~ ( between @ SV13 @ SV80 @ SV144 )
| ~ ( between @ SY606 @ SV80 @ SY607 )
| ( SV13 = SV80 )
| ( between @ ( euclid1 @ SV13 @ SY606 @ SV80 @ SY607 @ SV144 ) @ SV144 @ ( euclid2 @ SV13 @ SY606 @ SV80 @ SY607 @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(393,plain,
! [SV145: $i,SV81: $i,SV14: $i] :
( ( ! [SY608: $i,SY609: $i,SY610: $i] :
( ~ ( equidistant @ SV14 @ SV81 @ SV14 @ SV145 )
| ~ ( equidistant @ SV14 @ SY608 @ SV14 @ SY609 )
| ~ ( between @ SV14 @ SV81 @ SY608 )
| ~ ( between @ SV81 @ SY610 @ SY608 )
| ( between @ SV145 @ ( continuous @ SV14 @ SV81 @ SV145 @ SY610 @ SY608 @ SY609 ) @ SY609 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(394,plain,
! [SV146: $i,SV82: $i,SV15: $i] :
( ( ! [SY611: $i,SY612: $i,SY613: $i] :
( ~ ( equidistant @ SV15 @ SV82 @ SV15 @ SV146 )
| ~ ( equidistant @ SV15 @ SY611 @ SV15 @ SY612 )
| ~ ( between @ SV15 @ SV82 @ SY611 )
| ~ ( between @ SV82 @ SY613 @ SY611 )
| ( equidistant @ SV15 @ SY613 @ SV15 @ ( continuous @ SV15 @ SV82 @ SV146 @ SY613 @ SY611 @ SY612 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(395,plain,
! [SV147: $i,SV84: $i,SV17: $i] :
( ( ! [SY614: $i] :
( ( insertion @ SV17 @ SV84 @ SV147 @ SY614 )
= ( extension @ ( extension @ SV84 @ SV17 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV17 @ SV147 @ SY614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(396,plain,
! [SV148: $i,SV86: $i,SV19: $i] :
( ( ! [SY615: $i] :
( ~ ( equidistant @ SV19 @ SV86 @ SV148 @ SY615 )
| ( equidistant @ SV148 @ SY615 @ SV19 @ SV86 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(397,plain,
! [SV149: $i,SV87: $i,SV20: $i] :
( ( ! [SY616: $i] :
( ~ ( equidistant @ SV20 @ SV87 @ SV149 @ SY616 )
| ( equidistant @ SV87 @ SV20 @ SV149 @ SY616 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(398,plain,
! [SV150: $i,SV88: $i,SV21: $i] :
( ( ! [SY617: $i] :
( ~ ( equidistant @ SV21 @ SV88 @ SV150 @ SY617 )
| ( equidistant @ SV21 @ SV88 @ SY617 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(399,plain,
! [SV151: $i,SV89: $i,SV22: $i] :
( ( ! [SY618: $i] :
( ~ ( equidistant @ SV22 @ SV89 @ SV151 @ SY618 )
| ( equidistant @ SV89 @ SV22 @ SY618 @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(400,plain,
! [SV152: $i,SV90: $i,SV23: $i] :
( ( ! [SY619: $i] :
( ~ ( equidistant @ SV23 @ SV90 @ SV152 @ SY619 )
| ( equidistant @ SV152 @ SY619 @ SV90 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(401,plain,
! [SV153: $i,SV91: $i,SV24: $i] :
( ( ! [SY620: $i] :
( ~ ( equidistant @ SV24 @ SV91 @ SV153 @ SY620 )
| ( equidistant @ SY620 @ SV153 @ SV24 @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(402,plain,
! [SV154: $i,SV92: $i,SV25: $i] :
( ( ! [SY621: $i] :
( ~ ( equidistant @ SV25 @ SV92 @ SV154 @ SY621 )
| ( equidistant @ SY621 @ SV154 @ SV92 @ SV25 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(403,plain,
! [SV155: $i,SV93: $i,SV26: $i] :
( ( ! [SY622: $i,SY623: $i,SY624: $i] :
( ~ ( equidistant @ SV26 @ SV93 @ SV155 @ SY622 )
| ~ ( equidistant @ SV155 @ SY622 @ SY623 @ SY624 )
| ( equidistant @ SV26 @ SV93 @ SY623 @ SY624 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(404,plain,
! [SV156: $i,SV94: $i,SV27: $i] :
( ( SV27
= ( extension @ SV94 @ SV27 @ SV156 @ SV156 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(405,plain,
! [SV157: $i,SV98: $i,SV32: $i] :
( ( ! [SY625: $i,SY626: $i,SY627: $i] :
( ~ ( equidistant @ SV32 @ SV98 @ SV157 @ SY625 )
| ~ ( equidistant @ SV98 @ SY626 @ SY625 @ SY627 )
| ~ ( between @ SV32 @ SV98 @ SY626 )
| ~ ( between @ SV157 @ SY625 @ SY627 )
| ( equidistant @ SV32 @ SY626 @ SV157 @ SY627 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(406,plain,
! [SV158: $i,SV99: $i,SV33: $i] :
( ( ! [SY628: $i] :
( ~ ( between @ SV33 @ SV99 @ SV158 )
| ~ ( between @ SV33 @ SV99 @ SY628 )
| ~ ( equidistant @ SV99 @ SV158 @ SV99 @ SY628 )
| ( SV33 = SV99 )
| ( SV158 = SY628 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(407,plain,
! [SV159: $i,SV100: $i,SV34: $i] :
( ( ~ ( between @ SV34 @ SV100 @ SV159 )
| ( SV34 = SV100 )
| ( SV159
= ( extension @ SV34 @ SV100 @ SV100 @ SV159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(408,plain,
! [SV160: $i,SV101: $i,SV35: $i] :
( ( ! [SY629: $i,SY630: $i,SY631: $i] :
( ~ ( equidistant @ SV35 @ SV101 @ SV160 @ SY629 )
| ( ( extension @ SY630 @ SY631 @ SV35 @ SV101 )
= ( extension @ SY630 @ SY631 @ SV160 @ SY629 ) )
| ( SY630 = SY631 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(409,plain,
! [SV102: $i,SV36: $i] :
( ( ( ( extension @ SV36 @ SV102 @ SV36 @ SV102 )
= ( extension @ SV36 @ SV102 @ SV102 @ SV36 ) )
= $true )
| ( ( SV36 = SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(410,plain,
! [SV161: $i,SV106: $i,SV40: $i] :
( ( ~ ( between @ SV40 @ SV106 @ SV161 )
| ( between @ SV161 @ SV106 @ SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(411,plain,
! [SV162: $i,SV108: $i,SV42: $i] :
( ( ~ ( between @ SV42 @ SV108 @ SV162 )
| ~ ( between @ SV108 @ SV42 @ SV162 )
| ( SV42 = SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(412,plain,
! [SV163: $i,SV109: $i,SV43: $i] :
( ( ~ ( between @ SV43 @ SV109 @ SV163 )
| ~ ( between @ SV43 @ SV163 @ SV109 )
| ( SV109 = SV163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(413,plain,
! [SV164: $i,SV110: $i,SV44: $i] :
( ( ~ ( between @ SV44 @ SV110 @ SV164 )
| ~ ( between @ SV110 @ SV44 @ SV164 )
| ( SV44 = SV110 )
| ( SV110 = SV164 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(414,plain,
! [SV165: $i,SV111: $i,SV45: $i] :
( ( ~ ( between @ SV45 @ SV111 @ SV165 )
| ~ ( between @ SV45 @ SV165 @ SV111 )
| ( SV45 = SV111 )
| ( SV111 = SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(415,plain,
! [SV166: $i,SV112: $i,SV46: $i] :
( ( ! [SY632: $i] :
( ~ ( between @ SV46 @ SV112 @ SV166 )
| ~ ( between @ SV112 @ SV166 @ SY632 )
| ( between @ SV46 @ SV112 @ SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(416,plain,
! [SV167: $i,SV113: $i,SV47: $i] :
( ( ! [SY633: $i] :
( ~ ( between @ SV47 @ SV113 @ SV167 )
| ~ ( between @ SV47 @ SV167 @ SY633 )
| ( between @ SV113 @ SV167 @ SY633 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(417,plain,
! [SV168: $i,SV114: $i,SV48: $i] :
( ( ! [SY634: $i] :
( ~ ( between @ SV48 @ SV114 @ SV168 )
| ~ ( between @ SV114 @ SV168 @ SY634 )
| ( between @ SV48 @ SV168 @ SY634 )
| ( SV114 = SV168 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(418,plain,
! [SV169: $i,SV115: $i,SV49: $i] :
( ( ! [SY635: $i] :
( ~ ( between @ SV49 @ SV115 @ SV169 )
| ~ ( between @ SV115 @ SV169 @ SY635 )
| ( between @ SV49 @ SV115 @ SY635 )
| ( SV115 = SV169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(419,plain,
! [SV170: $i,SV116: $i,SV50: $i] :
( ( ! [SY636: $i] :
( ~ ( between @ SV50 @ SV116 @ SV170 )
| ~ ( between @ SV116 @ SY636 @ SV170 )
| ( between @ SV50 @ SY636 @ SV170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(420,plain,
! [SV171: $i,SV117: $i,SV51: $i] :
( ( ! [SY637: $i] :
( ~ ( between @ SV51 @ SV117 @ SV171 )
| ~ ( between @ SV51 @ SV171 @ SY637 )
| ( between @ SV51 @ SV117 @ SY637 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(421,plain,
! [SV172: $i,SV118: $i,SV52: $i] :
( ( ! [SY638: $i] : ( equidistant @ SV52 @ ( extension @ SV118 @ SV52 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV172 @ ( extension @ SY638 @ SV172 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(422,plain,
! [SV173: $i,SV120: $i,SV54: $i] :
( ( ! [SY639: $i,SY640: $i,SY641: $i] :
( ~ ( between @ SV54 @ SV120 @ SV173 )
| ~ ( between @ SY639 @ SY640 @ SV173 )
| ~ ( between @ SV54 @ SY641 @ SY639 )
| ( between @ SY641 @ ( inner_pasch @ SY640 @ ( inner_pasch @ SV54 @ SY641 @ SY639 @ SY640 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV173 )
| ( between @ SV120 @ ( inner_pasch @ SY640 @ ( inner_pasch @ SV54 @ SY641 @ SY639 @ SY640 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SY640 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(423,plain,
! [SV174: $i,SV121: $i,SV55: $i] :
( ( ! [SY642: $i] :
( ~ ( between @ SV55 @ SV121 @ SV174 )
| ~ ( equidistant @ SV55 @ SV174 @ SV55 @ SY642 )
| ~ ( equidistant @ SV121 @ SV174 @ SV121 @ SY642 )
| ( SV55 = SV121 )
| ( SV174 = SY642 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(424,plain,
! [SV175: $i,SV122: $i,SV56: $i] :
( ( ! [SY643: $i,SY644: $i,SY645: $i,SY646: $i,SY647: $i] :
( ~ ( equidistant @ SV56 @ SV122 @ SV175 @ SY643 )
| ~ ( equidistant @ SV56 @ SY644 @ SV175 @ SY645 )
| ~ ( equidistant @ SV56 @ SY646 @ SV175 @ SY647 )
| ~ ( equidistant @ SY644 @ SY646 @ SY645 @ SY647 )
| ~ ( between @ SV56 @ SV122 @ SY644 )
| ~ ( between @ SV175 @ SY643 @ SY645 )
| ( equidistant @ SV122 @ SY646 @ SY643 @ SY647 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(425,plain,
! [SV176: $i,SV123: $i,SV57: $i] :
( ( ! [SY648: $i,SY649: $i,SY650: $i] :
( ~ ( between @ SV57 @ SV123 @ SV176 )
| ~ ( between @ SY648 @ SY649 @ SY650 )
| ~ ( equidistant @ SV57 @ SV123 @ SY648 @ SY649 )
| ~ ( equidistant @ SV57 @ SV176 @ SY648 @ SY650 )
| ( equidistant @ SV123 @ SV176 @ SY649 @ SY650 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(426,plain,
! [SV177: $i,SV124: $i,SV58: $i] :
( ( ! [SY651: $i,SY652: $i,SY653: $i,SY654: $i,SY655: $i] :
( ~ ( equidistant @ SV58 @ SV124 @ SV177 @ SY651 )
| ~ ( equidistant @ SV124 @ SY652 @ SY651 @ SY653 )
| ~ ( equidistant @ SV58 @ SY654 @ SV177 @ SY655 )
| ~ ( equidistant @ SY652 @ SY654 @ SY653 @ SY655 )
| ~ ( between @ SV58 @ SV124 @ SY652 )
| ~ ( between @ SV177 @ SY651 @ SY653 )
| ( equidistant @ SV124 @ SY654 @ SY651 @ SY655 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(427,plain,
! [SV178: $i,SV125: $i,SV59: $i] :
( ( ! [SY656: $i] :
( ~ ( between @ SV59 @ SV125 @ SV178 )
| ~ ( equidistant @ SV59 @ SV125 @ SV59 @ SY656 )
| ~ ( equidistant @ SV178 @ SV125 @ SV178 @ SY656 )
| ( SV125 = SY656 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(428,plain,
! [SV179: $i,SV126: $i,SV60: $i] :
( ( ! [SY657: $i] : ( equidistant @ SV60 @ SV126 @ SV179 @ ( insertion @ SV179 @ SY657 @ SV60 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(429,plain,
! [SV180: $i,SV127: $i,SV61: $i] :
( ( ! [SY658: $i,SY659: $i] :
( ~ ( between @ SV61 @ SV127 @ SV180 )
| ~ ( equidistant @ SV61 @ SV180 @ SY658 @ SY659 )
| ( between @ SY658 @ ( insertion @ SY658 @ SY659 @ SV61 @ SV127 ) @ SY659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(430,plain,
! [SV181: $i,SV128: $i,SV62: $i] :
( ( ! [SY660: $i,SY661: $i] :
( ~ ( between @ SV62 @ SV128 @ SV181 )
| ~ ( equidistant @ SV62 @ SV181 @ SY660 @ SY661 )
| ( equidistant @ SV128 @ SV181 @ ( insertion @ SY660 @ SY661 @ SV62 @ SV128 ) @ SY661 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(431,plain,
! [SV129: $i,SV63: $i] :
( ( SV63
= ( extension @ SV129 @ SV63 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(432,plain,
! [SV182: $i,SV130: $i,SV64: $i] :
( ( ! [SY662: $i] :
( ~ ( between @ SV64 @ SV130 @ SV182 )
| ( SV64 != SV182 )
| ( between @ SY662 @ SV130 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(433,plain,
! [SV131: $i,SV65: $i] :
( ( ( SV65 != SV131 )
= $true )
| ( ( SV131
= ( reflection @ SV65 @ SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(434,plain,
! [SV183: $i,SV132: $i,SV66: $i] :
( ( ! [SY663: $i,SY664: $i] :
( ( SV66
!= ( extension @ SV132 @ SV183 @ SY663 @ SY664 ) )
| ( between @ SV132 @ SV183 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(435,plain,
! [SV133: $i,SV67: $i] :
( ( ( SV67
!= ( reflection @ SV133 @ SV67 ) )
= $true )
| ( ( SV133 = SV67 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(436,plain,
! [SV184: $i,SV134: $i,SV69: $i,SV2: $i] :
( ( ! [SY665: $i,SY666: $i] :
( ~ ( equidistant @ SV2 @ SV69 @ SV134 @ SV184 )
| ~ ( equidistant @ SV2 @ SV69 @ SY665 @ SY666 )
| ( equidistant @ SV134 @ SV184 @ SY665 @ SY666 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(437,plain,
! [SV135: $i,SV70: $i,SV3: $i] :
( ( ( ~ ( equidistant @ SV3 @ SV70 @ SV135 @ SV135 ) )
= $true )
| ( ( SV3 = SV70 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[382]) ).
thf(438,plain,
! [SV185: $i,SV136: $i,SV71: $i,SV4: $i] :
( ( between @ SV4 @ SV71 @ ( extension @ SV4 @ SV71 @ SV136 @ SV185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(439,plain,
! [SV186: $i,SV137: $i,SV72: $i,SV5: $i] :
( ( equidistant @ SV5 @ ( extension @ SV72 @ SV5 @ SV137 @ SV186 ) @ SV137 @ SV186 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(440,plain,
! [SV187: $i,SV138: $i,SV73: $i,SV6: $i] :
( ( ! [SY667: $i,SY668: $i,SY669: $i,SY670: $i] :
( ~ ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
| ~ ( equidistant @ SV73 @ SY667 @ SV187 @ SY668 )
| ~ ( equidistant @ SV6 @ SY669 @ SV138 @ SY670 )
| ~ ( equidistant @ SV73 @ SY669 @ SV187 @ SY670 )
| ~ ( between @ SV6 @ SV73 @ SY667 )
| ~ ( between @ SV138 @ SV187 @ SY668 )
| ( SV6 = SV73 )
| ( equidistant @ SY667 @ SY669 @ SY668 @ SY670 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(441,plain,
! [SV74: $i,SV7: $i] :
( ( ( between @ SV7 @ SV74 @ SV7 )
= $false )
| ( ( SV7 = SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(442,plain,
! [SV188: $i,SV139: $i,SV75: $i,SV8: $i] :
( ( ! [SY671: $i] :
( ~ ( between @ SV8 @ SV75 @ SV139 )
| ~ ( between @ SV188 @ SY671 @ SV139 )
| ( between @ SV75 @ ( inner_pasch @ SV8 @ SV75 @ SV139 @ SY671 @ SV188 ) @ SV188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(443,plain,
! [SV189: $i,SV140: $i,SV76: $i,SV9: $i] :
( ( ! [SY672: $i] :
( ~ ( between @ SV9 @ SV76 @ SV140 )
| ~ ( between @ SV189 @ SY672 @ SV140 )
| ( between @ SY672 @ ( inner_pasch @ SV9 @ SV76 @ SV140 @ SY672 @ SV189 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(444,plain,
! [SV190: $i,SV141: $i,SV77: $i,SV10: $i] :
( ( ! [SY673: $i] :
( ~ ( equidistant @ SV10 @ SV77 @ SV10 @ SV141 )
| ~ ( equidistant @ SV190 @ SV77 @ SV190 @ SV141 )
| ~ ( equidistant @ SY673 @ SV77 @ SY673 @ SV141 )
| ( between @ SV10 @ SV190 @ SY673 )
| ( between @ SV190 @ SY673 @ SV10 )
| ( between @ SY673 @ SV10 @ SV190 )
| ( SV77 = SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(445,plain,
! [SV191: $i,SV142: $i,SV78: $i,SV11: $i] :
( ( ! [SY674: $i] :
( ~ ( between @ SV11 @ SV78 @ SV142 )
| ~ ( between @ SV191 @ SV78 @ SY674 )
| ( SV11 = SV78 )
| ( between @ SV11 @ SV191 @ ( euclid1 @ SV11 @ SV191 @ SV78 @ SY674 @ SV142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(446,plain,
! [SV192: $i,SV143: $i,SV79: $i,SV12: $i] :
( ( ! [SY675: $i] :
( ~ ( between @ SV12 @ SV79 @ SV143 )
| ~ ( between @ SV192 @ SV79 @ SY675 )
| ( SV12 = SV79 )
| ( between @ SV12 @ SY675 @ ( euclid2 @ SV12 @ SV192 @ SV79 @ SY675 @ SV143 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(447,plain,
! [SV193: $i,SV144: $i,SV80: $i,SV13: $i] :
( ( ! [SY676: $i] :
( ~ ( between @ SV13 @ SV80 @ SV144 )
| ~ ( between @ SV193 @ SV80 @ SY676 )
| ( SV13 = SV80 )
| ( between @ ( euclid1 @ SV13 @ SV193 @ SV80 @ SY676 @ SV144 ) @ SV144 @ ( euclid2 @ SV13 @ SV193 @ SV80 @ SY676 @ SV144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(448,plain,
! [SV194: $i,SV145: $i,SV81: $i,SV14: $i] :
( ( ! [SY677: $i,SY678: $i] :
( ~ ( equidistant @ SV14 @ SV81 @ SV14 @ SV145 )
| ~ ( equidistant @ SV14 @ SV194 @ SV14 @ SY677 )
| ~ ( between @ SV14 @ SV81 @ SV194 )
| ~ ( between @ SV81 @ SY678 @ SV194 )
| ( between @ SV145 @ ( continuous @ SV14 @ SV81 @ SV145 @ SY678 @ SV194 @ SY677 ) @ SY677 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(449,plain,
! [SV195: $i,SV146: $i,SV82: $i,SV15: $i] :
( ( ! [SY679: $i,SY680: $i] :
( ~ ( equidistant @ SV15 @ SV82 @ SV15 @ SV146 )
| ~ ( equidistant @ SV15 @ SV195 @ SV15 @ SY679 )
| ~ ( between @ SV15 @ SV82 @ SV195 )
| ~ ( between @ SV82 @ SY680 @ SV195 )
| ( equidistant @ SV15 @ SY680 @ SV15 @ ( continuous @ SV15 @ SV82 @ SV146 @ SY680 @ SV195 @ SY679 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(450,plain,
! [SV196: $i,SV147: $i,SV84: $i,SV17: $i] :
( ( ( insertion @ SV17 @ SV84 @ SV147 @ SV196 )
= ( extension @ ( extension @ SV84 @ SV17 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV17 @ SV147 @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(451,plain,
! [SV197: $i,SV148: $i,SV86: $i,SV19: $i] :
( ( ~ ( equidistant @ SV19 @ SV86 @ SV148 @ SV197 )
| ( equidistant @ SV148 @ SV197 @ SV19 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(452,plain,
! [SV198: $i,SV149: $i,SV87: $i,SV20: $i] :
( ( ~ ( equidistant @ SV20 @ SV87 @ SV149 @ SV198 )
| ( equidistant @ SV87 @ SV20 @ SV149 @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(453,plain,
! [SV199: $i,SV150: $i,SV88: $i,SV21: $i] :
( ( ~ ( equidistant @ SV21 @ SV88 @ SV150 @ SV199 )
| ( equidistant @ SV21 @ SV88 @ SV199 @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(454,plain,
! [SV200: $i,SV151: $i,SV89: $i,SV22: $i] :
( ( ~ ( equidistant @ SV22 @ SV89 @ SV151 @ SV200 )
| ( equidistant @ SV89 @ SV22 @ SV200 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[399]) ).
thf(455,plain,
! [SV201: $i,SV152: $i,SV90: $i,SV23: $i] :
( ( ~ ( equidistant @ SV23 @ SV90 @ SV152 @ SV201 )
| ( equidistant @ SV152 @ SV201 @ SV90 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(456,plain,
! [SV202: $i,SV153: $i,SV91: $i,SV24: $i] :
( ( ~ ( equidistant @ SV24 @ SV91 @ SV153 @ SV202 )
| ( equidistant @ SV202 @ SV153 @ SV24 @ SV91 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(457,plain,
! [SV203: $i,SV154: $i,SV92: $i,SV25: $i] :
( ( ~ ( equidistant @ SV25 @ SV92 @ SV154 @ SV203 )
| ( equidistant @ SV203 @ SV154 @ SV92 @ SV25 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(458,plain,
! [SV204: $i,SV155: $i,SV93: $i,SV26: $i] :
( ( ! [SY681: $i,SY682: $i] :
( ~ ( equidistant @ SV26 @ SV93 @ SV155 @ SV204 )
| ~ ( equidistant @ SV155 @ SV204 @ SY681 @ SY682 )
| ( equidistant @ SV26 @ SV93 @ SY681 @ SY682 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(459,plain,
! [SV205: $i,SV157: $i,SV98: $i,SV32: $i] :
( ( ! [SY683: $i,SY684: $i] :
( ~ ( equidistant @ SV32 @ SV98 @ SV157 @ SV205 )
| ~ ( equidistant @ SV98 @ SY683 @ SV205 @ SY684 )
| ~ ( between @ SV32 @ SV98 @ SY683 )
| ~ ( between @ SV157 @ SV205 @ SY684 )
| ( equidistant @ SV32 @ SY683 @ SV157 @ SY684 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(460,plain,
! [SV206: $i,SV158: $i,SV99: $i,SV33: $i] :
( ( ~ ( between @ SV33 @ SV99 @ SV158 )
| ~ ( between @ SV33 @ SV99 @ SV206 )
| ~ ( equidistant @ SV99 @ SV158 @ SV99 @ SV206 )
| ( SV33 = SV99 )
| ( SV158 = SV206 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(461,plain,
! [SV159: $i,SV100: $i,SV34: $i] :
( ( ( ~ ( between @ SV34 @ SV100 @ SV159 ) )
= $true )
| ( ( ( SV34 = SV100 )
| ( SV159
= ( extension @ SV34 @ SV100 @ SV100 @ SV159 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[407]) ).
thf(462,plain,
! [SV207: $i,SV160: $i,SV101: $i,SV35: $i] :
( ( ! [SY685: $i,SY686: $i] :
( ~ ( equidistant @ SV35 @ SV101 @ SV160 @ SV207 )
| ( ( extension @ SY685 @ SY686 @ SV35 @ SV101 )
= ( extension @ SY685 @ SY686 @ SV160 @ SV207 ) )
| ( SY685 = SY686 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(463,plain,
! [SV161: $i,SV106: $i,SV40: $i] :
( ( ( ~ ( between @ SV40 @ SV106 @ SV161 ) )
= $true )
| ( ( between @ SV161 @ SV106 @ SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(464,plain,
! [SV162: $i,SV108: $i,SV42: $i] :
( ( ( ~ ( between @ SV42 @ SV108 @ SV162 ) )
= $true )
| ( ( ~ ( between @ SV108 @ SV42 @ SV162 )
| ( SV42 = SV108 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[411]) ).
thf(465,plain,
! [SV163: $i,SV109: $i,SV43: $i] :
( ( ( ~ ( between @ SV43 @ SV109 @ SV163 ) )
= $true )
| ( ( ~ ( between @ SV43 @ SV163 @ SV109 )
| ( SV109 = SV163 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(466,plain,
! [SV164: $i,SV110: $i,SV44: $i] :
( ( ( ~ ( between @ SV44 @ SV110 @ SV164 ) )
= $true )
| ( ( ~ ( between @ SV110 @ SV44 @ SV164 )
| ( SV44 = SV110 )
| ( SV110 = SV164 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(467,plain,
! [SV165: $i,SV111: $i,SV45: $i] :
( ( ( ~ ( between @ SV45 @ SV111 @ SV165 ) )
= $true )
| ( ( ~ ( between @ SV45 @ SV165 @ SV111 )
| ( SV45 = SV111 )
| ( SV111 = SV165 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(468,plain,
! [SV208: $i,SV166: $i,SV112: $i,SV46: $i] :
( ( ~ ( between @ SV46 @ SV112 @ SV166 )
| ~ ( between @ SV112 @ SV166 @ SV208 )
| ( between @ SV46 @ SV112 @ SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(469,plain,
! [SV209: $i,SV167: $i,SV113: $i,SV47: $i] :
( ( ~ ( between @ SV47 @ SV113 @ SV167 )
| ~ ( between @ SV47 @ SV167 @ SV209 )
| ( between @ SV113 @ SV167 @ SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(470,plain,
! [SV210: $i,SV168: $i,SV114: $i,SV48: $i] :
( ( ~ ( between @ SV48 @ SV114 @ SV168 )
| ~ ( between @ SV114 @ SV168 @ SV210 )
| ( between @ SV48 @ SV168 @ SV210 )
| ( SV114 = SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(471,plain,
! [SV211: $i,SV169: $i,SV115: $i,SV49: $i] :
( ( ~ ( between @ SV49 @ SV115 @ SV169 )
| ~ ( between @ SV115 @ SV169 @ SV211 )
| ( between @ SV49 @ SV115 @ SV211 )
| ( SV115 = SV169 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(472,plain,
! [SV212: $i,SV170: $i,SV116: $i,SV50: $i] :
( ( ~ ( between @ SV50 @ SV116 @ SV170 )
| ~ ( between @ SV116 @ SV212 @ SV170 )
| ( between @ SV50 @ SV212 @ SV170 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(473,plain,
! [SV213: $i,SV171: $i,SV117: $i,SV51: $i] :
( ( ~ ( between @ SV51 @ SV117 @ SV171 )
| ~ ( between @ SV51 @ SV171 @ SV213 )
| ( between @ SV51 @ SV117 @ SV213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(474,plain,
! [SV214: $i,SV172: $i,SV118: $i,SV52: $i] :
( ( equidistant @ SV52 @ ( extension @ SV118 @ SV52 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV172 @ ( extension @ SV214 @ SV172 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(475,plain,
! [SV215: $i,SV173: $i,SV120: $i,SV54: $i] :
( ( ! [SY687: $i,SY688: $i] :
( ~ ( between @ SV54 @ SV120 @ SV173 )
| ~ ( between @ SV215 @ SY687 @ SV173 )
| ~ ( between @ SV54 @ SY688 @ SV215 )
| ( between @ SY688 @ ( inner_pasch @ SY687 @ ( inner_pasch @ SV54 @ SY688 @ SV215 @ SY687 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV173 )
| ( between @ SV120 @ ( inner_pasch @ SY687 @ ( inner_pasch @ SV54 @ SY688 @ SV215 @ SY687 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SY687 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(476,plain,
! [SV216: $i,SV174: $i,SV121: $i,SV55: $i] :
( ( ~ ( between @ SV55 @ SV121 @ SV174 )
| ~ ( equidistant @ SV55 @ SV174 @ SV55 @ SV216 )
| ~ ( equidistant @ SV121 @ SV174 @ SV121 @ SV216 )
| ( SV55 = SV121 )
| ( SV174 = SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(477,plain,
! [SV217: $i,SV175: $i,SV122: $i,SV56: $i] :
( ( ! [SY689: $i,SY690: $i,SY691: $i,SY692: $i] :
( ~ ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 )
| ~ ( equidistant @ SV56 @ SY689 @ SV175 @ SY690 )
| ~ ( equidistant @ SV56 @ SY691 @ SV175 @ SY692 )
| ~ ( equidistant @ SY689 @ SY691 @ SY690 @ SY692 )
| ~ ( between @ SV56 @ SV122 @ SY689 )
| ~ ( between @ SV175 @ SV217 @ SY690 )
| ( equidistant @ SV122 @ SY691 @ SV217 @ SY692 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(478,plain,
! [SV218: $i,SV176: $i,SV123: $i,SV57: $i] :
( ( ! [SY693: $i,SY694: $i] :
( ~ ( between @ SV57 @ SV123 @ SV176 )
| ~ ( between @ SV218 @ SY693 @ SY694 )
| ~ ( equidistant @ SV57 @ SV123 @ SV218 @ SY693 )
| ~ ( equidistant @ SV57 @ SV176 @ SV218 @ SY694 )
| ( equidistant @ SV123 @ SV176 @ SY693 @ SY694 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(479,plain,
! [SV219: $i,SV177: $i,SV124: $i,SV58: $i] :
( ( ! [SY695: $i,SY696: $i,SY697: $i,SY698: $i] :
( ~ ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 )
| ~ ( equidistant @ SV124 @ SY695 @ SV219 @ SY696 )
| ~ ( equidistant @ SV58 @ SY697 @ SV177 @ SY698 )
| ~ ( equidistant @ SY695 @ SY697 @ SY696 @ SY698 )
| ~ ( between @ SV58 @ SV124 @ SY695 )
| ~ ( between @ SV177 @ SV219 @ SY696 )
| ( equidistant @ SV124 @ SY697 @ SV219 @ SY698 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(480,plain,
! [SV220: $i,SV178: $i,SV125: $i,SV59: $i] :
( ( ~ ( between @ SV59 @ SV125 @ SV178 )
| ~ ( equidistant @ SV59 @ SV125 @ SV59 @ SV220 )
| ~ ( equidistant @ SV178 @ SV125 @ SV178 @ SV220 )
| ( SV125 = SV220 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(481,plain,
! [SV221: $i,SV179: $i,SV126: $i,SV60: $i] :
( ( equidistant @ SV60 @ SV126 @ SV179 @ ( insertion @ SV179 @ SV221 @ SV60 @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(482,plain,
! [SV222: $i,SV180: $i,SV127: $i,SV61: $i] :
( ( ! [SY699: $i] :
( ~ ( between @ SV61 @ SV127 @ SV180 )
| ~ ( equidistant @ SV61 @ SV180 @ SV222 @ SY699 )
| ( between @ SV222 @ ( insertion @ SV222 @ SY699 @ SV61 @ SV127 ) @ SY699 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(483,plain,
! [SV223: $i,SV181: $i,SV128: $i,SV62: $i] :
( ( ! [SY700: $i] :
( ~ ( between @ SV62 @ SV128 @ SV181 )
| ~ ( equidistant @ SV62 @ SV181 @ SV223 @ SY700 )
| ( equidistant @ SV128 @ SV181 @ ( insertion @ SV223 @ SY700 @ SV62 @ SV128 ) @ SY700 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(484,plain,
! [SV224: $i,SV182: $i,SV130: $i,SV64: $i] :
( ( ~ ( between @ SV64 @ SV130 @ SV182 )
| ( SV64 != SV182 )
| ( between @ SV224 @ SV130 @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(485,plain,
! [SV131: $i,SV65: $i] :
( ( ( SV65 = SV131 )
= $false )
| ( ( SV131
= ( reflection @ SV65 @ SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(486,plain,
! [SV225: $i,SV183: $i,SV132: $i,SV66: $i] :
( ( ! [SY701: $i] :
( ( SV66
!= ( extension @ SV132 @ SV183 @ SV225 @ SY701 ) )
| ( between @ SV132 @ SV183 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(487,plain,
! [SV133: $i,SV67: $i] :
( ( ( SV67
= ( reflection @ SV133 @ SV67 ) )
= $false )
| ( ( SV133 = SV67 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(488,plain,
! [SV226: $i,SV184: $i,SV134: $i,SV69: $i,SV2: $i] :
( ( ! [SY702: $i] :
( ~ ( equidistant @ SV2 @ SV69 @ SV134 @ SV184 )
| ~ ( equidistant @ SV2 @ SV69 @ SV226 @ SY702 )
| ( equidistant @ SV134 @ SV184 @ SV226 @ SY702 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(489,plain,
! [SV135: $i,SV70: $i,SV3: $i] :
( ( ( equidistant @ SV3 @ SV70 @ SV135 @ SV135 )
= $false )
| ( ( SV3 = SV70 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(490,plain,
! [SV227: $i,SV187: $i,SV138: $i,SV73: $i,SV6: $i] :
( ( ! [SY703: $i,SY704: $i,SY705: $i] :
( ~ ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
| ~ ( equidistant @ SV73 @ SV227 @ SV187 @ SY703 )
| ~ ( equidistant @ SV6 @ SY704 @ SV138 @ SY705 )
| ~ ( equidistant @ SV73 @ SY704 @ SV187 @ SY705 )
| ~ ( between @ SV6 @ SV73 @ SV227 )
| ~ ( between @ SV138 @ SV187 @ SY703 )
| ( SV6 = SV73 )
| ( equidistant @ SV227 @ SY704 @ SY703 @ SY705 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(491,plain,
! [SV228: $i,SV188: $i,SV139: $i,SV75: $i,SV8: $i] :
( ( ~ ( between @ SV8 @ SV75 @ SV139 )
| ~ ( between @ SV188 @ SV228 @ SV139 )
| ( between @ SV75 @ ( inner_pasch @ SV8 @ SV75 @ SV139 @ SV228 @ SV188 ) @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(492,plain,
! [SV229: $i,SV189: $i,SV140: $i,SV76: $i,SV9: $i] :
( ( ~ ( between @ SV9 @ SV76 @ SV140 )
| ~ ( between @ SV189 @ SV229 @ SV140 )
| ( between @ SV229 @ ( inner_pasch @ SV9 @ SV76 @ SV140 @ SV229 @ SV189 ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(493,plain,
! [SV230: $i,SV190: $i,SV141: $i,SV77: $i,SV10: $i] :
( ( ~ ( equidistant @ SV10 @ SV77 @ SV10 @ SV141 )
| ~ ( equidistant @ SV190 @ SV77 @ SV190 @ SV141 )
| ~ ( equidistant @ SV230 @ SV77 @ SV230 @ SV141 )
| ( between @ SV10 @ SV190 @ SV230 )
| ( between @ SV190 @ SV230 @ SV10 )
| ( between @ SV230 @ SV10 @ SV190 )
| ( SV77 = SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(494,plain,
! [SV231: $i,SV191: $i,SV142: $i,SV78: $i,SV11: $i] :
( ( ~ ( between @ SV11 @ SV78 @ SV142 )
| ~ ( between @ SV191 @ SV78 @ SV231 )
| ( SV11 = SV78 )
| ( between @ SV11 @ SV191 @ ( euclid1 @ SV11 @ SV191 @ SV78 @ SV231 @ SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(495,plain,
! [SV232: $i,SV192: $i,SV143: $i,SV79: $i,SV12: $i] :
( ( ~ ( between @ SV12 @ SV79 @ SV143 )
| ~ ( between @ SV192 @ SV79 @ SV232 )
| ( SV12 = SV79 )
| ( between @ SV12 @ SV232 @ ( euclid2 @ SV12 @ SV192 @ SV79 @ SV232 @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(496,plain,
! [SV233: $i,SV193: $i,SV144: $i,SV80: $i,SV13: $i] :
( ( ~ ( between @ SV13 @ SV80 @ SV144 )
| ~ ( between @ SV193 @ SV80 @ SV233 )
| ( SV13 = SV80 )
| ( between @ ( euclid1 @ SV13 @ SV193 @ SV80 @ SV233 @ SV144 ) @ SV144 @ ( euclid2 @ SV13 @ SV193 @ SV80 @ SV233 @ SV144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(497,plain,
! [SV234: $i,SV194: $i,SV145: $i,SV81: $i,SV14: $i] :
( ( ! [SY706: $i] :
( ~ ( equidistant @ SV14 @ SV81 @ SV14 @ SV145 )
| ~ ( equidistant @ SV14 @ SV194 @ SV14 @ SV234 )
| ~ ( between @ SV14 @ SV81 @ SV194 )
| ~ ( between @ SV81 @ SY706 @ SV194 )
| ( between @ SV145 @ ( continuous @ SV14 @ SV81 @ SV145 @ SY706 @ SV194 @ SV234 ) @ SV234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(498,plain,
! [SV235: $i,SV195: $i,SV146: $i,SV82: $i,SV15: $i] :
( ( ! [SY707: $i] :
( ~ ( equidistant @ SV15 @ SV82 @ SV15 @ SV146 )
| ~ ( equidistant @ SV15 @ SV195 @ SV15 @ SV235 )
| ~ ( between @ SV15 @ SV82 @ SV195 )
| ~ ( between @ SV82 @ SY707 @ SV195 )
| ( equidistant @ SV15 @ SY707 @ SV15 @ ( continuous @ SV15 @ SV82 @ SV146 @ SY707 @ SV195 @ SV235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(499,plain,
! [SV197: $i,SV148: $i,SV86: $i,SV19: $i] :
( ( ( ~ ( equidistant @ SV19 @ SV86 @ SV148 @ SV197 ) )
= $true )
| ( ( equidistant @ SV148 @ SV197 @ SV19 @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(500,plain,
! [SV198: $i,SV149: $i,SV87: $i,SV20: $i] :
( ( ( ~ ( equidistant @ SV20 @ SV87 @ SV149 @ SV198 ) )
= $true )
| ( ( equidistant @ SV87 @ SV20 @ SV149 @ SV198 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(501,plain,
! [SV199: $i,SV150: $i,SV88: $i,SV21: $i] :
( ( ( ~ ( equidistant @ SV21 @ SV88 @ SV150 @ SV199 ) )
= $true )
| ( ( equidistant @ SV21 @ SV88 @ SV199 @ SV150 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(502,plain,
! [SV200: $i,SV151: $i,SV89: $i,SV22: $i] :
( ( ( ~ ( equidistant @ SV22 @ SV89 @ SV151 @ SV200 ) )
= $true )
| ( ( equidistant @ SV89 @ SV22 @ SV200 @ SV151 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(503,plain,
! [SV201: $i,SV152: $i,SV90: $i,SV23: $i] :
( ( ( ~ ( equidistant @ SV23 @ SV90 @ SV152 @ SV201 ) )
= $true )
| ( ( equidistant @ SV152 @ SV201 @ SV90 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(504,plain,
! [SV202: $i,SV153: $i,SV91: $i,SV24: $i] :
( ( ( ~ ( equidistant @ SV24 @ SV91 @ SV153 @ SV202 ) )
= $true )
| ( ( equidistant @ SV202 @ SV153 @ SV24 @ SV91 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(505,plain,
! [SV203: $i,SV154: $i,SV92: $i,SV25: $i] :
( ( ( ~ ( equidistant @ SV25 @ SV92 @ SV154 @ SV203 ) )
= $true )
| ( ( equidistant @ SV203 @ SV154 @ SV92 @ SV25 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(506,plain,
! [SV236: $i,SV204: $i,SV155: $i,SV93: $i,SV26: $i] :
( ( ! [SY708: $i] :
( ~ ( equidistant @ SV26 @ SV93 @ SV155 @ SV204 )
| ~ ( equidistant @ SV155 @ SV204 @ SV236 @ SY708 )
| ( equidistant @ SV26 @ SV93 @ SV236 @ SY708 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(507,plain,
! [SV237: $i,SV205: $i,SV157: $i,SV98: $i,SV32: $i] :
( ( ! [SY709: $i] :
( ~ ( equidistant @ SV32 @ SV98 @ SV157 @ SV205 )
| ~ ( equidistant @ SV98 @ SV237 @ SV205 @ SY709 )
| ~ ( between @ SV32 @ SV98 @ SV237 )
| ~ ( between @ SV157 @ SV205 @ SY709 )
| ( equidistant @ SV32 @ SV237 @ SV157 @ SY709 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(508,plain,
! [SV206: $i,SV158: $i,SV99: $i,SV33: $i] :
( ( ( ~ ( between @ SV33 @ SV99 @ SV158 ) )
= $true )
| ( ( ~ ( between @ SV33 @ SV99 @ SV206 )
| ~ ( equidistant @ SV99 @ SV158 @ SV99 @ SV206 )
| ( SV33 = SV99 )
| ( SV158 = SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(509,plain,
! [SV159: $i,SV100: $i,SV34: $i] :
( ( ( between @ SV34 @ SV100 @ SV159 )
= $false )
| ( ( ( SV34 = SV100 )
| ( SV159
= ( extension @ SV34 @ SV100 @ SV100 @ SV159 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(510,plain,
! [SV238: $i,SV207: $i,SV160: $i,SV101: $i,SV35: $i] :
( ( ! [SY710: $i] :
( ~ ( equidistant @ SV35 @ SV101 @ SV160 @ SV207 )
| ( ( extension @ SV238 @ SY710 @ SV35 @ SV101 )
= ( extension @ SV238 @ SY710 @ SV160 @ SV207 ) )
| ( SV238 = SY710 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(511,plain,
! [SV161: $i,SV106: $i,SV40: $i] :
( ( ( between @ SV40 @ SV106 @ SV161 )
= $false )
| ( ( between @ SV161 @ SV106 @ SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(512,plain,
! [SV162: $i,SV108: $i,SV42: $i] :
( ( ( between @ SV42 @ SV108 @ SV162 )
= $false )
| ( ( ~ ( between @ SV108 @ SV42 @ SV162 )
| ( SV42 = SV108 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(513,plain,
! [SV163: $i,SV109: $i,SV43: $i] :
( ( ( between @ SV43 @ SV109 @ SV163 )
= $false )
| ( ( ~ ( between @ SV43 @ SV163 @ SV109 )
| ( SV109 = SV163 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(514,plain,
! [SV164: $i,SV110: $i,SV44: $i] :
( ( ( between @ SV44 @ SV110 @ SV164 )
= $false )
| ( ( ~ ( between @ SV110 @ SV44 @ SV164 )
| ( SV44 = SV110 )
| ( SV110 = SV164 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(515,plain,
! [SV165: $i,SV111: $i,SV45: $i] :
( ( ( between @ SV45 @ SV111 @ SV165 )
= $false )
| ( ( ~ ( between @ SV45 @ SV165 @ SV111 )
| ( SV45 = SV111 )
| ( SV111 = SV165 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[467]) ).
thf(516,plain,
! [SV208: $i,SV166: $i,SV112: $i,SV46: $i] :
( ( ( ~ ( between @ SV46 @ SV112 @ SV166 ) )
= $true )
| ( ( ~ ( between @ SV112 @ SV166 @ SV208 )
| ( between @ SV46 @ SV112 @ SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(517,plain,
! [SV209: $i,SV167: $i,SV113: $i,SV47: $i] :
( ( ( ~ ( between @ SV47 @ SV113 @ SV167 ) )
= $true )
| ( ( ~ ( between @ SV47 @ SV167 @ SV209 )
| ( between @ SV113 @ SV167 @ SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[469]) ).
thf(518,plain,
! [SV210: $i,SV168: $i,SV114: $i,SV48: $i] :
( ( ( ~ ( between @ SV48 @ SV114 @ SV168 ) )
= $true )
| ( ( ~ ( between @ SV114 @ SV168 @ SV210 )
| ( between @ SV48 @ SV168 @ SV210 )
| ( SV114 = SV168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(519,plain,
! [SV211: $i,SV169: $i,SV115: $i,SV49: $i] :
( ( ( ~ ( between @ SV49 @ SV115 @ SV169 ) )
= $true )
| ( ( ~ ( between @ SV115 @ SV169 @ SV211 )
| ( between @ SV49 @ SV115 @ SV211 )
| ( SV115 = SV169 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(520,plain,
! [SV212: $i,SV170: $i,SV116: $i,SV50: $i] :
( ( ( ~ ( between @ SV50 @ SV116 @ SV170 ) )
= $true )
| ( ( ~ ( between @ SV116 @ SV212 @ SV170 )
| ( between @ SV50 @ SV212 @ SV170 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(521,plain,
! [SV213: $i,SV171: $i,SV117: $i,SV51: $i] :
( ( ( ~ ( between @ SV51 @ SV117 @ SV171 ) )
= $true )
| ( ( ~ ( between @ SV51 @ SV171 @ SV213 )
| ( between @ SV51 @ SV117 @ SV213 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(522,plain,
! [SV239: $i,SV215: $i,SV173: $i,SV120: $i,SV54: $i] :
( ( ! [SY711: $i] :
( ~ ( between @ SV54 @ SV120 @ SV173 )
| ~ ( between @ SV215 @ SV239 @ SV173 )
| ~ ( between @ SV54 @ SY711 @ SV215 )
| ( between @ SY711 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SY711 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV173 )
| ( between @ SV120 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SY711 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(523,plain,
! [SV216: $i,SV174: $i,SV121: $i,SV55: $i] :
( ( ( ~ ( between @ SV55 @ SV121 @ SV174 ) )
= $true )
| ( ( ~ ( equidistant @ SV55 @ SV174 @ SV55 @ SV216 )
| ~ ( equidistant @ SV121 @ SV174 @ SV121 @ SV216 )
| ( SV55 = SV121 )
| ( SV174 = SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(524,plain,
! [SV240: $i,SV217: $i,SV175: $i,SV122: $i,SV56: $i] :
( ( ! [SY712: $i,SY713: $i,SY714: $i] :
( ~ ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 )
| ~ ( equidistant @ SV56 @ SV240 @ SV175 @ SY712 )
| ~ ( equidistant @ SV56 @ SY713 @ SV175 @ SY714 )
| ~ ( equidistant @ SV240 @ SY713 @ SY712 @ SY714 )
| ~ ( between @ SV56 @ SV122 @ SV240 )
| ~ ( between @ SV175 @ SV217 @ SY712 )
| ( equidistant @ SV122 @ SY713 @ SV217 @ SY714 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(525,plain,
! [SV241: $i,SV218: $i,SV176: $i,SV123: $i,SV57: $i] :
( ( ! [SY715: $i] :
( ~ ( between @ SV57 @ SV123 @ SV176 )
| ~ ( between @ SV218 @ SV241 @ SY715 )
| ~ ( equidistant @ SV57 @ SV123 @ SV218 @ SV241 )
| ~ ( equidistant @ SV57 @ SV176 @ SV218 @ SY715 )
| ( equidistant @ SV123 @ SV176 @ SV241 @ SY715 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(526,plain,
! [SV242: $i,SV219: $i,SV177: $i,SV124: $i,SV58: $i] :
( ( ! [SY716: $i,SY717: $i,SY718: $i] :
( ~ ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 )
| ~ ( equidistant @ SV124 @ SV242 @ SV219 @ SY716 )
| ~ ( equidistant @ SV58 @ SY717 @ SV177 @ SY718 )
| ~ ( equidistant @ SV242 @ SY717 @ SY716 @ SY718 )
| ~ ( between @ SV58 @ SV124 @ SV242 )
| ~ ( between @ SV177 @ SV219 @ SY716 )
| ( equidistant @ SV124 @ SY717 @ SV219 @ SY718 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(527,plain,
! [SV220: $i,SV178: $i,SV125: $i,SV59: $i] :
( ( ( ~ ( between @ SV59 @ SV125 @ SV178 ) )
= $true )
| ( ( ~ ( equidistant @ SV59 @ SV125 @ SV59 @ SV220 )
| ~ ( equidistant @ SV178 @ SV125 @ SV178 @ SV220 )
| ( SV125 = SV220 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[480]) ).
thf(528,plain,
! [SV243: $i,SV222: $i,SV180: $i,SV127: $i,SV61: $i] :
( ( ~ ( between @ SV61 @ SV127 @ SV180 )
| ~ ( equidistant @ SV61 @ SV180 @ SV222 @ SV243 )
| ( between @ SV222 @ ( insertion @ SV222 @ SV243 @ SV61 @ SV127 ) @ SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(529,plain,
! [SV244: $i,SV223: $i,SV181: $i,SV128: $i,SV62: $i] :
( ( ~ ( between @ SV62 @ SV128 @ SV181 )
| ~ ( equidistant @ SV62 @ SV181 @ SV223 @ SV244 )
| ( equidistant @ SV128 @ SV181 @ ( insertion @ SV223 @ SV244 @ SV62 @ SV128 ) @ SV244 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(530,plain,
! [SV224: $i,SV182: $i,SV130: $i,SV64: $i] :
( ( ( ~ ( between @ SV64 @ SV130 @ SV182 ) )
= $true )
| ( ( ( SV64 != SV182 )
| ( between @ SV224 @ SV130 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(531,plain,
! [SV245: $i,SV225: $i,SV183: $i,SV132: $i,SV66: $i] :
( ( ( SV66
!= ( extension @ SV132 @ SV183 @ SV225 @ SV245 ) )
| ( between @ SV132 @ SV183 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(532,plain,
! [SV246: $i,SV226: $i,SV184: $i,SV134: $i,SV69: $i,SV2: $i] :
( ( ~ ( equidistant @ SV2 @ SV69 @ SV134 @ SV184 )
| ~ ( equidistant @ SV2 @ SV69 @ SV226 @ SV246 )
| ( equidistant @ SV134 @ SV184 @ SV226 @ SV246 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(533,plain,
! [SV247: $i,SV227: $i,SV187: $i,SV138: $i,SV73: $i,SV6: $i] :
( ( ! [SY719: $i,SY720: $i] :
( ~ ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
| ~ ( equidistant @ SV73 @ SV227 @ SV187 @ SV247 )
| ~ ( equidistant @ SV6 @ SY719 @ SV138 @ SY720 )
| ~ ( equidistant @ SV73 @ SY719 @ SV187 @ SY720 )
| ~ ( between @ SV6 @ SV73 @ SV227 )
| ~ ( between @ SV138 @ SV187 @ SV247 )
| ( SV6 = SV73 )
| ( equidistant @ SV227 @ SY719 @ SV247 @ SY720 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(534,plain,
! [SV228: $i,SV188: $i,SV139: $i,SV75: $i,SV8: $i] :
( ( ( ~ ( between @ SV8 @ SV75 @ SV139 ) )
= $true )
| ( ( ~ ( between @ SV188 @ SV228 @ SV139 )
| ( between @ SV75 @ ( inner_pasch @ SV8 @ SV75 @ SV139 @ SV228 @ SV188 ) @ SV188 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(535,plain,
! [SV229: $i,SV189: $i,SV140: $i,SV76: $i,SV9: $i] :
( ( ( ~ ( between @ SV9 @ SV76 @ SV140 ) )
= $true )
| ( ( ~ ( between @ SV189 @ SV229 @ SV140 )
| ( between @ SV229 @ ( inner_pasch @ SV9 @ SV76 @ SV140 @ SV229 @ SV189 ) @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[492]) ).
thf(536,plain,
! [SV230: $i,SV190: $i,SV141: $i,SV77: $i,SV10: $i] :
( ( ( ~ ( equidistant @ SV10 @ SV77 @ SV10 @ SV141 ) )
= $true )
| ( ( ~ ( equidistant @ SV190 @ SV77 @ SV190 @ SV141 )
| ~ ( equidistant @ SV230 @ SV77 @ SV230 @ SV141 )
| ( between @ SV10 @ SV190 @ SV230 )
| ( between @ SV190 @ SV230 @ SV10 )
| ( between @ SV230 @ SV10 @ SV190 )
| ( SV77 = SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(537,plain,
! [SV231: $i,SV191: $i,SV142: $i,SV78: $i,SV11: $i] :
( ( ( ~ ( between @ SV11 @ SV78 @ SV142 ) )
= $true )
| ( ( ~ ( between @ SV191 @ SV78 @ SV231 )
| ( SV11 = SV78 )
| ( between @ SV11 @ SV191 @ ( euclid1 @ SV11 @ SV191 @ SV78 @ SV231 @ SV142 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(538,plain,
! [SV232: $i,SV192: $i,SV143: $i,SV79: $i,SV12: $i] :
( ( ( ~ ( between @ SV12 @ SV79 @ SV143 ) )
= $true )
| ( ( ~ ( between @ SV192 @ SV79 @ SV232 )
| ( SV12 = SV79 )
| ( between @ SV12 @ SV232 @ ( euclid2 @ SV12 @ SV192 @ SV79 @ SV232 @ SV143 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(539,plain,
! [SV233: $i,SV193: $i,SV144: $i,SV80: $i,SV13: $i] :
( ( ( ~ ( between @ SV13 @ SV80 @ SV144 ) )
= $true )
| ( ( ~ ( between @ SV193 @ SV80 @ SV233 )
| ( SV13 = SV80 )
| ( between @ ( euclid1 @ SV13 @ SV193 @ SV80 @ SV233 @ SV144 ) @ SV144 @ ( euclid2 @ SV13 @ SV193 @ SV80 @ SV233 @ SV144 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[496]) ).
thf(540,plain,
! [SV248: $i,SV234: $i,SV194: $i,SV145: $i,SV81: $i,SV14: $i] :
( ( ~ ( equidistant @ SV14 @ SV81 @ SV14 @ SV145 )
| ~ ( equidistant @ SV14 @ SV194 @ SV14 @ SV234 )
| ~ ( between @ SV14 @ SV81 @ SV194 )
| ~ ( between @ SV81 @ SV248 @ SV194 )
| ( between @ SV145 @ ( continuous @ SV14 @ SV81 @ SV145 @ SV248 @ SV194 @ SV234 ) @ SV234 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(541,plain,
! [SV249: $i,SV235: $i,SV195: $i,SV146: $i,SV82: $i,SV15: $i] :
( ( ~ ( equidistant @ SV15 @ SV82 @ SV15 @ SV146 )
| ~ ( equidistant @ SV15 @ SV195 @ SV15 @ SV235 )
| ~ ( between @ SV15 @ SV82 @ SV195 )
| ~ ( between @ SV82 @ SV249 @ SV195 )
| ( equidistant @ SV15 @ SV249 @ SV15 @ ( continuous @ SV15 @ SV82 @ SV146 @ SV249 @ SV195 @ SV235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(542,plain,
! [SV197: $i,SV148: $i,SV86: $i,SV19: $i] :
( ( ( equidistant @ SV19 @ SV86 @ SV148 @ SV197 )
= $false )
| ( ( equidistant @ SV148 @ SV197 @ SV19 @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(543,plain,
! [SV198: $i,SV149: $i,SV87: $i,SV20: $i] :
( ( ( equidistant @ SV20 @ SV87 @ SV149 @ SV198 )
= $false )
| ( ( equidistant @ SV87 @ SV20 @ SV149 @ SV198 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(544,plain,
! [SV199: $i,SV150: $i,SV88: $i,SV21: $i] :
( ( ( equidistant @ SV21 @ SV88 @ SV150 @ SV199 )
= $false )
| ( ( equidistant @ SV21 @ SV88 @ SV199 @ SV150 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(545,plain,
! [SV200: $i,SV151: $i,SV89: $i,SV22: $i] :
( ( ( equidistant @ SV22 @ SV89 @ SV151 @ SV200 )
= $false )
| ( ( equidistant @ SV89 @ SV22 @ SV200 @ SV151 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(546,plain,
! [SV201: $i,SV152: $i,SV90: $i,SV23: $i] :
( ( ( equidistant @ SV23 @ SV90 @ SV152 @ SV201 )
= $false )
| ( ( equidistant @ SV152 @ SV201 @ SV90 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[503]) ).
thf(547,plain,
! [SV202: $i,SV153: $i,SV91: $i,SV24: $i] :
( ( ( equidistant @ SV24 @ SV91 @ SV153 @ SV202 )
= $false )
| ( ( equidistant @ SV202 @ SV153 @ SV24 @ SV91 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[504]) ).
thf(548,plain,
! [SV203: $i,SV154: $i,SV92: $i,SV25: $i] :
( ( ( equidistant @ SV25 @ SV92 @ SV154 @ SV203 )
= $false )
| ( ( equidistant @ SV203 @ SV154 @ SV92 @ SV25 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(549,plain,
! [SV250: $i,SV236: $i,SV204: $i,SV155: $i,SV93: $i,SV26: $i] :
( ( ~ ( equidistant @ SV26 @ SV93 @ SV155 @ SV204 )
| ~ ( equidistant @ SV155 @ SV204 @ SV236 @ SV250 )
| ( equidistant @ SV26 @ SV93 @ SV236 @ SV250 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(550,plain,
! [SV251: $i,SV237: $i,SV205: $i,SV157: $i,SV98: $i,SV32: $i] :
( ( ~ ( equidistant @ SV32 @ SV98 @ SV157 @ SV205 )
| ~ ( equidistant @ SV98 @ SV237 @ SV205 @ SV251 )
| ~ ( between @ SV32 @ SV98 @ SV237 )
| ~ ( between @ SV157 @ SV205 @ SV251 )
| ( equidistant @ SV32 @ SV237 @ SV157 @ SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(551,plain,
! [SV206: $i,SV158: $i,SV99: $i,SV33: $i] :
( ( ( between @ SV33 @ SV99 @ SV158 )
= $false )
| ( ( ~ ( between @ SV33 @ SV99 @ SV206 )
| ~ ( equidistant @ SV99 @ SV158 @ SV99 @ SV206 )
| ( SV33 = SV99 )
| ( SV158 = SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(552,plain,
! [SV159: $i,SV100: $i,SV34: $i] :
( ( ( SV34 = SV100 )
= $true )
| ( ( SV159
= ( extension @ SV34 @ SV100 @ SV100 @ SV159 ) )
= $true )
| ( ( between @ SV34 @ SV100 @ SV159 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[509]) ).
thf(553,plain,
! [SV252: $i,SV238: $i,SV207: $i,SV160: $i,SV101: $i,SV35: $i] :
( ( ~ ( equidistant @ SV35 @ SV101 @ SV160 @ SV207 )
| ( ( extension @ SV238 @ SV252 @ SV35 @ SV101 )
= ( extension @ SV238 @ SV252 @ SV160 @ SV207 ) )
| ( SV238 = SV252 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(554,plain,
! [SV162: $i,SV42: $i,SV108: $i] :
( ( ( ~ ( between @ SV108 @ SV42 @ SV162 ) )
= $true )
| ( ( SV42 = SV108 )
= $true )
| ( ( between @ SV42 @ SV108 @ SV162 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(555,plain,
! [SV109: $i,SV163: $i,SV43: $i] :
( ( ( ~ ( between @ SV43 @ SV163 @ SV109 ) )
= $true )
| ( ( SV109 = SV163 )
= $true )
| ( ( between @ SV43 @ SV109 @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(556,plain,
! [SV164: $i,SV44: $i,SV110: $i] :
( ( ( ~ ( between @ SV110 @ SV44 @ SV164 ) )
= $true )
| ( ( ( SV44 = SV110 )
| ( SV110 = SV164 ) )
= $true )
| ( ( between @ SV44 @ SV110 @ SV164 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(557,plain,
! [SV111: $i,SV165: $i,SV45: $i] :
( ( ( ~ ( between @ SV45 @ SV165 @ SV111 ) )
= $true )
| ( ( ( SV45 = SV111 )
| ( SV111 = SV165 ) )
= $true )
| ( ( between @ SV45 @ SV111 @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(558,plain,
! [SV208: $i,SV166: $i,SV112: $i,SV46: $i] :
( ( ( between @ SV46 @ SV112 @ SV166 )
= $false )
| ( ( ~ ( between @ SV112 @ SV166 @ SV208 )
| ( between @ SV46 @ SV112 @ SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(559,plain,
! [SV209: $i,SV167: $i,SV113: $i,SV47: $i] :
( ( ( between @ SV47 @ SV113 @ SV167 )
= $false )
| ( ( ~ ( between @ SV47 @ SV167 @ SV209 )
| ( between @ SV113 @ SV167 @ SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(560,plain,
! [SV210: $i,SV168: $i,SV114: $i,SV48: $i] :
( ( ( between @ SV48 @ SV114 @ SV168 )
= $false )
| ( ( ~ ( between @ SV114 @ SV168 @ SV210 )
| ( between @ SV48 @ SV168 @ SV210 )
| ( SV114 = SV168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(561,plain,
! [SV211: $i,SV169: $i,SV115: $i,SV49: $i] :
( ( ( between @ SV49 @ SV115 @ SV169 )
= $false )
| ( ( ~ ( between @ SV115 @ SV169 @ SV211 )
| ( between @ SV49 @ SV115 @ SV211 )
| ( SV115 = SV169 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(562,plain,
! [SV212: $i,SV170: $i,SV116: $i,SV50: $i] :
( ( ( between @ SV50 @ SV116 @ SV170 )
= $false )
| ( ( ~ ( between @ SV116 @ SV212 @ SV170 )
| ( between @ SV50 @ SV212 @ SV170 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[520]) ).
thf(563,plain,
! [SV213: $i,SV171: $i,SV117: $i,SV51: $i] :
( ( ( between @ SV51 @ SV117 @ SV171 )
= $false )
| ( ( ~ ( between @ SV51 @ SV171 @ SV213 )
| ( between @ SV51 @ SV117 @ SV213 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[521]) ).
thf(564,plain,
! [SV253: $i,SV239: $i,SV215: $i,SV173: $i,SV120: $i,SV54: $i] :
( ( ~ ( between @ SV54 @ SV120 @ SV173 )
| ~ ( between @ SV215 @ SV239 @ SV173 )
| ~ ( between @ SV54 @ SV253 @ SV215 )
| ( between @ SV253 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SV253 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV173 )
| ( between @ SV120 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SV253 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(565,plain,
! [SV216: $i,SV174: $i,SV121: $i,SV55: $i] :
( ( ( between @ SV55 @ SV121 @ SV174 )
= $false )
| ( ( ~ ( equidistant @ SV55 @ SV174 @ SV55 @ SV216 )
| ~ ( equidistant @ SV121 @ SV174 @ SV121 @ SV216 )
| ( SV55 = SV121 )
| ( SV174 = SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[523]) ).
thf(566,plain,
! [SV254: $i,SV240: $i,SV217: $i,SV175: $i,SV122: $i,SV56: $i] :
( ( ! [SY721: $i,SY722: $i] :
( ~ ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 )
| ~ ( equidistant @ SV56 @ SV240 @ SV175 @ SV254 )
| ~ ( equidistant @ SV56 @ SY721 @ SV175 @ SY722 )
| ~ ( equidistant @ SV240 @ SY721 @ SV254 @ SY722 )
| ~ ( between @ SV56 @ SV122 @ SV240 )
| ~ ( between @ SV175 @ SV217 @ SV254 )
| ( equidistant @ SV122 @ SY721 @ SV217 @ SY722 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(567,plain,
! [SV255: $i,SV241: $i,SV218: $i,SV176: $i,SV123: $i,SV57: $i] :
( ( ~ ( between @ SV57 @ SV123 @ SV176 )
| ~ ( between @ SV218 @ SV241 @ SV255 )
| ~ ( equidistant @ SV57 @ SV123 @ SV218 @ SV241 )
| ~ ( equidistant @ SV57 @ SV176 @ SV218 @ SV255 )
| ( equidistant @ SV123 @ SV176 @ SV241 @ SV255 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(568,plain,
! [SV256: $i,SV242: $i,SV219: $i,SV177: $i,SV124: $i,SV58: $i] :
( ( ! [SY723: $i,SY724: $i] :
( ~ ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 )
| ~ ( equidistant @ SV124 @ SV242 @ SV219 @ SV256 )
| ~ ( equidistant @ SV58 @ SY723 @ SV177 @ SY724 )
| ~ ( equidistant @ SV242 @ SY723 @ SV256 @ SY724 )
| ~ ( between @ SV58 @ SV124 @ SV242 )
| ~ ( between @ SV177 @ SV219 @ SV256 )
| ( equidistant @ SV124 @ SY723 @ SV219 @ SY724 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(569,plain,
! [SV220: $i,SV178: $i,SV125: $i,SV59: $i] :
( ( ( between @ SV59 @ SV125 @ SV178 )
= $false )
| ( ( ~ ( equidistant @ SV59 @ SV125 @ SV59 @ SV220 )
| ~ ( equidistant @ SV178 @ SV125 @ SV178 @ SV220 )
| ( SV125 = SV220 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(570,plain,
! [SV243: $i,SV222: $i,SV180: $i,SV127: $i,SV61: $i] :
( ( ( ~ ( between @ SV61 @ SV127 @ SV180 ) )
= $true )
| ( ( ~ ( equidistant @ SV61 @ SV180 @ SV222 @ SV243 )
| ( between @ SV222 @ ( insertion @ SV222 @ SV243 @ SV61 @ SV127 ) @ SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[528]) ).
thf(571,plain,
! [SV244: $i,SV223: $i,SV181: $i,SV128: $i,SV62: $i] :
( ( ( ~ ( between @ SV62 @ SV128 @ SV181 ) )
= $true )
| ( ( ~ ( equidistant @ SV62 @ SV181 @ SV223 @ SV244 )
| ( equidistant @ SV128 @ SV181 @ ( insertion @ SV223 @ SV244 @ SV62 @ SV128 ) @ SV244 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(572,plain,
! [SV224: $i,SV182: $i,SV130: $i,SV64: $i] :
( ( ( between @ SV64 @ SV130 @ SV182 )
= $false )
| ( ( ( SV64 != SV182 )
| ( between @ SV224 @ SV130 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[530]) ).
thf(573,plain,
! [SV245: $i,SV225: $i,SV183: $i,SV132: $i,SV66: $i] :
( ( ( SV66
!= ( extension @ SV132 @ SV183 @ SV225 @ SV245 ) )
= $true )
| ( ( between @ SV132 @ SV183 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(574,plain,
! [SV246: $i,SV226: $i,SV184: $i,SV134: $i,SV69: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV69 @ SV134 @ SV184 ) )
= $true )
| ( ( ~ ( equidistant @ SV2 @ SV69 @ SV226 @ SV246 )
| ( equidistant @ SV134 @ SV184 @ SV226 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[532]) ).
thf(575,plain,
! [SV257: $i,SV247: $i,SV227: $i,SV187: $i,SV138: $i,SV73: $i,SV6: $i] :
( ( ! [SY725: $i] :
( ~ ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
| ~ ( equidistant @ SV73 @ SV227 @ SV187 @ SV247 )
| ~ ( equidistant @ SV6 @ SV257 @ SV138 @ SY725 )
| ~ ( equidistant @ SV73 @ SV257 @ SV187 @ SY725 )
| ~ ( between @ SV6 @ SV73 @ SV227 )
| ~ ( between @ SV138 @ SV187 @ SV247 )
| ( SV6 = SV73 )
| ( equidistant @ SV227 @ SV257 @ SV247 @ SY725 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(576,plain,
! [SV228: $i,SV188: $i,SV139: $i,SV75: $i,SV8: $i] :
( ( ( between @ SV8 @ SV75 @ SV139 )
= $false )
| ( ( ~ ( between @ SV188 @ SV228 @ SV139 )
| ( between @ SV75 @ ( inner_pasch @ SV8 @ SV75 @ SV139 @ SV228 @ SV188 ) @ SV188 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(577,plain,
! [SV229: $i,SV189: $i,SV140: $i,SV76: $i,SV9: $i] :
( ( ( between @ SV9 @ SV76 @ SV140 )
= $false )
| ( ( ~ ( between @ SV189 @ SV229 @ SV140 )
| ( between @ SV229 @ ( inner_pasch @ SV9 @ SV76 @ SV140 @ SV229 @ SV189 ) @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(578,plain,
! [SV230: $i,SV190: $i,SV141: $i,SV77: $i,SV10: $i] :
( ( ( equidistant @ SV10 @ SV77 @ SV10 @ SV141 )
= $false )
| ( ( ~ ( equidistant @ SV190 @ SV77 @ SV190 @ SV141 )
| ~ ( equidistant @ SV230 @ SV77 @ SV230 @ SV141 )
| ( between @ SV10 @ SV190 @ SV230 )
| ( between @ SV190 @ SV230 @ SV10 )
| ( between @ SV230 @ SV10 @ SV190 )
| ( SV77 = SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(579,plain,
! [SV231: $i,SV191: $i,SV142: $i,SV78: $i,SV11: $i] :
( ( ( between @ SV11 @ SV78 @ SV142 )
= $false )
| ( ( ~ ( between @ SV191 @ SV78 @ SV231 )
| ( SV11 = SV78 )
| ( between @ SV11 @ SV191 @ ( euclid1 @ SV11 @ SV191 @ SV78 @ SV231 @ SV142 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[537]) ).
thf(580,plain,
! [SV232: $i,SV192: $i,SV143: $i,SV79: $i,SV12: $i] :
( ( ( between @ SV12 @ SV79 @ SV143 )
= $false )
| ( ( ~ ( between @ SV192 @ SV79 @ SV232 )
| ( SV12 = SV79 )
| ( between @ SV12 @ SV232 @ ( euclid2 @ SV12 @ SV192 @ SV79 @ SV232 @ SV143 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(581,plain,
! [SV233: $i,SV193: $i,SV144: $i,SV80: $i,SV13: $i] :
( ( ( between @ SV13 @ SV80 @ SV144 )
= $false )
| ( ( ~ ( between @ SV193 @ SV80 @ SV233 )
| ( SV13 = SV80 )
| ( between @ ( euclid1 @ SV13 @ SV193 @ SV80 @ SV233 @ SV144 ) @ SV144 @ ( euclid2 @ SV13 @ SV193 @ SV80 @ SV233 @ SV144 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(582,plain,
! [SV248: $i,SV234: $i,SV194: $i,SV145: $i,SV81: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV81 @ SV14 @ SV145 ) )
= $true )
| ( ( ~ ( equidistant @ SV14 @ SV194 @ SV14 @ SV234 )
| ~ ( between @ SV14 @ SV81 @ SV194 )
| ~ ( between @ SV81 @ SV248 @ SV194 )
| ( between @ SV145 @ ( continuous @ SV14 @ SV81 @ SV145 @ SV248 @ SV194 @ SV234 ) @ SV234 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(583,plain,
! [SV249: $i,SV235: $i,SV195: $i,SV146: $i,SV82: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV82 @ SV15 @ SV146 ) )
= $true )
| ( ( ~ ( equidistant @ SV15 @ SV195 @ SV15 @ SV235 )
| ~ ( between @ SV15 @ SV82 @ SV195 )
| ~ ( between @ SV82 @ SV249 @ SV195 )
| ( equidistant @ SV15 @ SV249 @ SV15 @ ( continuous @ SV15 @ SV82 @ SV146 @ SV249 @ SV195 @ SV235 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[541]) ).
thf(584,plain,
! [SV250: $i,SV236: $i,SV204: $i,SV155: $i,SV93: $i,SV26: $i] :
( ( ( ~ ( equidistant @ SV26 @ SV93 @ SV155 @ SV204 ) )
= $true )
| ( ( ~ ( equidistant @ SV155 @ SV204 @ SV236 @ SV250 )
| ( equidistant @ SV26 @ SV93 @ SV236 @ SV250 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[549]) ).
thf(585,plain,
! [SV251: $i,SV237: $i,SV205: $i,SV157: $i,SV98: $i,SV32: $i] :
( ( ( ~ ( equidistant @ SV32 @ SV98 @ SV157 @ SV205 ) )
= $true )
| ( ( ~ ( equidistant @ SV98 @ SV237 @ SV205 @ SV251 )
| ~ ( between @ SV32 @ SV98 @ SV237 )
| ~ ( between @ SV157 @ SV205 @ SV251 )
| ( equidistant @ SV32 @ SV237 @ SV157 @ SV251 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(586,plain,
! [SV158: $i,SV206: $i,SV99: $i,SV33: $i] :
( ( ( ~ ( between @ SV33 @ SV99 @ SV206 ) )
= $true )
| ( ( ~ ( equidistant @ SV99 @ SV158 @ SV99 @ SV206 )
| ( SV33 = SV99 )
| ( SV158 = SV206 ) )
= $true )
| ( ( between @ SV33 @ SV99 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(587,plain,
! [SV252: $i,SV238: $i,SV207: $i,SV160: $i,SV101: $i,SV35: $i] :
( ( ( ~ ( equidistant @ SV35 @ SV101 @ SV160 @ SV207 ) )
= $true )
| ( ( ( ( extension @ SV238 @ SV252 @ SV35 @ SV101 )
= ( extension @ SV238 @ SV252 @ SV160 @ SV207 ) )
| ( SV238 = SV252 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(588,plain,
! [SV162: $i,SV42: $i,SV108: $i] :
( ( ( between @ SV108 @ SV42 @ SV162 )
= $false )
| ( ( SV42 = SV108 )
= $true )
| ( ( between @ SV42 @ SV108 @ SV162 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[554]) ).
thf(589,plain,
! [SV109: $i,SV163: $i,SV43: $i] :
( ( ( between @ SV43 @ SV163 @ SV109 )
= $false )
| ( ( SV109 = SV163 )
= $true )
| ( ( between @ SV43 @ SV109 @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(590,plain,
! [SV164: $i,SV44: $i,SV110: $i] :
( ( ( between @ SV110 @ SV44 @ SV164 )
= $false )
| ( ( ( SV44 = SV110 )
| ( SV110 = SV164 ) )
= $true )
| ( ( between @ SV44 @ SV110 @ SV164 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[556]) ).
thf(591,plain,
! [SV111: $i,SV165: $i,SV45: $i] :
( ( ( between @ SV45 @ SV165 @ SV111 )
= $false )
| ( ( ( SV45 = SV111 )
| ( SV111 = SV165 ) )
= $true )
| ( ( between @ SV45 @ SV111 @ SV165 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(592,plain,
! [SV46: $i,SV208: $i,SV166: $i,SV112: $i] :
( ( ( ~ ( between @ SV112 @ SV166 @ SV208 ) )
= $true )
| ( ( between @ SV46 @ SV112 @ SV166 )
= $true )
| ( ( between @ SV46 @ SV112 @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[558]) ).
thf(593,plain,
! [SV113: $i,SV209: $i,SV167: $i,SV47: $i] :
( ( ( ~ ( between @ SV47 @ SV167 @ SV209 ) )
= $true )
| ( ( between @ SV113 @ SV167 @ SV209 )
= $true )
| ( ( between @ SV47 @ SV113 @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[559]) ).
thf(594,plain,
! [SV48: $i,SV210: $i,SV168: $i,SV114: $i] :
( ( ( ~ ( between @ SV114 @ SV168 @ SV210 ) )
= $true )
| ( ( ( between @ SV48 @ SV168 @ SV210 )
| ( SV114 = SV168 ) )
= $true )
| ( ( between @ SV48 @ SV114 @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(595,plain,
! [SV49: $i,SV211: $i,SV169: $i,SV115: $i] :
( ( ( ~ ( between @ SV115 @ SV169 @ SV211 ) )
= $true )
| ( ( ( between @ SV49 @ SV115 @ SV211 )
| ( SV115 = SV169 ) )
= $true )
| ( ( between @ SV49 @ SV115 @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[561]) ).
thf(596,plain,
! [SV50: $i,SV170: $i,SV212: $i,SV116: $i] :
( ( ( ~ ( between @ SV116 @ SV212 @ SV170 ) )
= $true )
| ( ( between @ SV50 @ SV212 @ SV170 )
= $true )
| ( ( between @ SV50 @ SV116 @ SV170 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[562]) ).
thf(597,plain,
! [SV117: $i,SV213: $i,SV171: $i,SV51: $i] :
( ( ( ~ ( between @ SV51 @ SV171 @ SV213 ) )
= $true )
| ( ( between @ SV51 @ SV117 @ SV213 )
= $true )
| ( ( between @ SV51 @ SV117 @ SV171 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(598,plain,
! [SV253: $i,SV239: $i,SV215: $i,SV173: $i,SV120: $i,SV54: $i] :
( ( ( ~ ( between @ SV54 @ SV120 @ SV173 ) )
= $true )
| ( ( ~ ( between @ SV215 @ SV239 @ SV173 )
| ~ ( between @ SV54 @ SV253 @ SV215 )
| ( between @ SV253 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SV253 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV173 )
| ( between @ SV120 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SV253 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV239 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(599,plain,
! [SV121: $i,SV216: $i,SV174: $i,SV55: $i] :
( ( ( ~ ( equidistant @ SV55 @ SV174 @ SV55 @ SV216 ) )
= $true )
| ( ( ~ ( equidistant @ SV121 @ SV174 @ SV121 @ SV216 )
| ( SV55 = SV121 )
| ( SV174 = SV216 ) )
= $true )
| ( ( between @ SV55 @ SV121 @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[565]) ).
thf(600,plain,
! [SV258: $i,SV254: $i,SV240: $i,SV217: $i,SV175: $i,SV122: $i,SV56: $i] :
( ( ! [SY726: $i] :
( ~ ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 )
| ~ ( equidistant @ SV56 @ SV240 @ SV175 @ SV254 )
| ~ ( equidistant @ SV56 @ SV258 @ SV175 @ SY726 )
| ~ ( equidistant @ SV240 @ SV258 @ SV254 @ SY726 )
| ~ ( between @ SV56 @ SV122 @ SV240 )
| ~ ( between @ SV175 @ SV217 @ SV254 )
| ( equidistant @ SV122 @ SV258 @ SV217 @ SY726 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(601,plain,
! [SV255: $i,SV241: $i,SV218: $i,SV176: $i,SV123: $i,SV57: $i] :
( ( ( ~ ( between @ SV57 @ SV123 @ SV176 ) )
= $true )
| ( ( ~ ( between @ SV218 @ SV241 @ SV255 )
| ~ ( equidistant @ SV57 @ SV123 @ SV218 @ SV241 )
| ~ ( equidistant @ SV57 @ SV176 @ SV218 @ SV255 )
| ( equidistant @ SV123 @ SV176 @ SV241 @ SV255 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[567]) ).
thf(602,plain,
! [SV259: $i,SV256: $i,SV242: $i,SV219: $i,SV177: $i,SV124: $i,SV58: $i] :
( ( ! [SY727: $i] :
( ~ ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 )
| ~ ( equidistant @ SV124 @ SV242 @ SV219 @ SV256 )
| ~ ( equidistant @ SV58 @ SV259 @ SV177 @ SY727 )
| ~ ( equidistant @ SV242 @ SV259 @ SV256 @ SY727 )
| ~ ( between @ SV58 @ SV124 @ SV242 )
| ~ ( between @ SV177 @ SV219 @ SV256 )
| ( equidistant @ SV124 @ SV259 @ SV219 @ SY727 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(603,plain,
! [SV178: $i,SV220: $i,SV125: $i,SV59: $i] :
( ( ( ~ ( equidistant @ SV59 @ SV125 @ SV59 @ SV220 ) )
= $true )
| ( ( ~ ( equidistant @ SV178 @ SV125 @ SV178 @ SV220 )
| ( SV125 = SV220 ) )
= $true )
| ( ( between @ SV59 @ SV125 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[569]) ).
thf(604,plain,
! [SV243: $i,SV222: $i,SV180: $i,SV127: $i,SV61: $i] :
( ( ( between @ SV61 @ SV127 @ SV180 )
= $false )
| ( ( ~ ( equidistant @ SV61 @ SV180 @ SV222 @ SV243 )
| ( between @ SV222 @ ( insertion @ SV222 @ SV243 @ SV61 @ SV127 ) @ SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[570]) ).
thf(605,plain,
! [SV244: $i,SV223: $i,SV181: $i,SV128: $i,SV62: $i] :
( ( ( between @ SV62 @ SV128 @ SV181 )
= $false )
| ( ( ~ ( equidistant @ SV62 @ SV181 @ SV223 @ SV244 )
| ( equidistant @ SV128 @ SV181 @ ( insertion @ SV223 @ SV244 @ SV62 @ SV128 ) @ SV244 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[571]) ).
thf(606,plain,
! [SV130: $i,SV224: $i,SV182: $i,SV64: $i] :
( ( ( SV64 != SV182 )
= $true )
| ( ( between @ SV224 @ SV130 @ SV182 )
= $true )
| ( ( between @ SV64 @ SV130 @ SV182 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(607,plain,
! [SV245: $i,SV225: $i,SV183: $i,SV132: $i,SV66: $i] :
( ( ( SV66
= ( extension @ SV132 @ SV183 @ SV225 @ SV245 ) )
= $false )
| ( ( between @ SV132 @ SV183 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[573]) ).
thf(608,plain,
! [SV246: $i,SV226: $i,SV184: $i,SV134: $i,SV69: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV69 @ SV134 @ SV184 )
= $false )
| ( ( ~ ( equidistant @ SV2 @ SV69 @ SV226 @ SV246 )
| ( equidistant @ SV134 @ SV184 @ SV226 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[574]) ).
thf(609,plain,
! [SV260: $i,SV257: $i,SV247: $i,SV227: $i,SV187: $i,SV138: $i,SV73: $i,SV6: $i] :
( ( ~ ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
| ~ ( equidistant @ SV73 @ SV227 @ SV187 @ SV247 )
| ~ ( equidistant @ SV6 @ SV257 @ SV138 @ SV260 )
| ~ ( equidistant @ SV73 @ SV257 @ SV187 @ SV260 )
| ~ ( between @ SV6 @ SV73 @ SV227 )
| ~ ( between @ SV138 @ SV187 @ SV247 )
| ( SV6 = SV73 )
| ( equidistant @ SV227 @ SV257 @ SV247 @ SV260 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(610,plain,
! [SV8: $i,SV75: $i,SV139: $i,SV228: $i,SV188: $i] :
( ( ( ~ ( between @ SV188 @ SV228 @ SV139 ) )
= $true )
| ( ( between @ SV75 @ ( inner_pasch @ SV8 @ SV75 @ SV139 @ SV228 @ SV188 ) @ SV188 )
= $true )
| ( ( between @ SV8 @ SV75 @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[576]) ).
thf(611,plain,
! [SV76: $i,SV9: $i,SV140: $i,SV229: $i,SV189: $i] :
( ( ( ~ ( between @ SV189 @ SV229 @ SV140 ) )
= $true )
| ( ( between @ SV229 @ ( inner_pasch @ SV9 @ SV76 @ SV140 @ SV229 @ SV189 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV76 @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[577]) ).
thf(612,plain,
! [SV10: $i,SV230: $i,SV141: $i,SV77: $i,SV190: $i] :
( ( ( ~ ( equidistant @ SV190 @ SV77 @ SV190 @ SV141 ) )
= $true )
| ( ( ~ ( equidistant @ SV230 @ SV77 @ SV230 @ SV141 )
| ( between @ SV10 @ SV190 @ SV230 )
| ( between @ SV190 @ SV230 @ SV10 )
| ( between @ SV230 @ SV10 @ SV190 )
| ( SV77 = SV141 ) )
= $true )
| ( ( equidistant @ SV10 @ SV77 @ SV10 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[578]) ).
thf(613,plain,
! [SV142: $i,SV11: $i,SV231: $i,SV78: $i,SV191: $i] :
( ( ( ~ ( between @ SV191 @ SV78 @ SV231 ) )
= $true )
| ( ( ( SV11 = SV78 )
| ( between @ SV11 @ SV191 @ ( euclid1 @ SV11 @ SV191 @ SV78 @ SV231 @ SV142 ) ) )
= $true )
| ( ( between @ SV11 @ SV78 @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[579]) ).
thf(614,plain,
! [SV143: $i,SV12: $i,SV232: $i,SV79: $i,SV192: $i] :
( ( ( ~ ( between @ SV192 @ SV79 @ SV232 ) )
= $true )
| ( ( ( SV12 = SV79 )
| ( between @ SV12 @ SV232 @ ( euclid2 @ SV12 @ SV192 @ SV79 @ SV232 @ SV143 ) ) )
= $true )
| ( ( between @ SV12 @ SV79 @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[580]) ).
thf(615,plain,
! [SV144: $i,SV13: $i,SV233: $i,SV80: $i,SV193: $i] :
( ( ( ~ ( between @ SV193 @ SV80 @ SV233 ) )
= $true )
| ( ( ( SV13 = SV80 )
| ( between @ ( euclid1 @ SV13 @ SV193 @ SV80 @ SV233 @ SV144 ) @ SV144 @ ( euclid2 @ SV13 @ SV193 @ SV80 @ SV233 @ SV144 ) ) )
= $true )
| ( ( between @ SV13 @ SV80 @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[581]) ).
thf(616,plain,
! [SV248: $i,SV234: $i,SV194: $i,SV145: $i,SV81: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV81 @ SV14 @ SV145 )
= $false )
| ( ( ~ ( equidistant @ SV14 @ SV194 @ SV14 @ SV234 )
| ~ ( between @ SV14 @ SV81 @ SV194 )
| ~ ( between @ SV81 @ SV248 @ SV194 )
| ( between @ SV145 @ ( continuous @ SV14 @ SV81 @ SV145 @ SV248 @ SV194 @ SV234 ) @ SV234 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[582]) ).
thf(617,plain,
! [SV249: $i,SV235: $i,SV195: $i,SV146: $i,SV82: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV82 @ SV15 @ SV146 )
= $false )
| ( ( ~ ( equidistant @ SV15 @ SV195 @ SV15 @ SV235 )
| ~ ( between @ SV15 @ SV82 @ SV195 )
| ~ ( between @ SV82 @ SV249 @ SV195 )
| ( equidistant @ SV15 @ SV249 @ SV15 @ ( continuous @ SV15 @ SV82 @ SV146 @ SV249 @ SV195 @ SV235 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[583]) ).
thf(618,plain,
! [SV250: $i,SV236: $i,SV204: $i,SV155: $i,SV93: $i,SV26: $i] :
( ( ( equidistant @ SV26 @ SV93 @ SV155 @ SV204 )
= $false )
| ( ( ~ ( equidistant @ SV155 @ SV204 @ SV236 @ SV250 )
| ( equidistant @ SV26 @ SV93 @ SV236 @ SV250 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[584]) ).
thf(619,plain,
! [SV251: $i,SV237: $i,SV205: $i,SV157: $i,SV98: $i,SV32: $i] :
( ( ( equidistant @ SV32 @ SV98 @ SV157 @ SV205 )
= $false )
| ( ( ~ ( equidistant @ SV98 @ SV237 @ SV205 @ SV251 )
| ~ ( between @ SV32 @ SV98 @ SV237 )
| ~ ( between @ SV157 @ SV205 @ SV251 )
| ( equidistant @ SV32 @ SV237 @ SV157 @ SV251 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(620,plain,
! [SV158: $i,SV206: $i,SV99: $i,SV33: $i] :
( ( ( between @ SV33 @ SV99 @ SV206 )
= $false )
| ( ( ~ ( equidistant @ SV99 @ SV158 @ SV99 @ SV206 )
| ( SV33 = SV99 )
| ( SV158 = SV206 ) )
= $true )
| ( ( between @ SV33 @ SV99 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[586]) ).
thf(621,plain,
! [SV252: $i,SV238: $i,SV207: $i,SV160: $i,SV101: $i,SV35: $i] :
( ( ( equidistant @ SV35 @ SV101 @ SV160 @ SV207 )
= $false )
| ( ( ( ( extension @ SV238 @ SV252 @ SV35 @ SV101 )
= ( extension @ SV238 @ SV252 @ SV160 @ SV207 ) )
| ( SV238 = SV252 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[587]) ).
thf(622,plain,
! [SV164: $i,SV110: $i,SV44: $i] :
( ( ( SV44 = SV110 )
= $true )
| ( ( SV110 = SV164 )
= $true )
| ( ( between @ SV110 @ SV44 @ SV164 )
= $false )
| ( ( between @ SV44 @ SV110 @ SV164 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[590]) ).
thf(623,plain,
! [SV165: $i,SV111: $i,SV45: $i] :
( ( ( SV45 = SV111 )
= $true )
| ( ( SV111 = SV165 )
= $true )
| ( ( between @ SV45 @ SV165 @ SV111 )
= $false )
| ( ( between @ SV45 @ SV111 @ SV165 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[591]) ).
thf(624,plain,
! [SV46: $i,SV208: $i,SV166: $i,SV112: $i] :
( ( ( between @ SV112 @ SV166 @ SV208 )
= $false )
| ( ( between @ SV46 @ SV112 @ SV166 )
= $true )
| ( ( between @ SV46 @ SV112 @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[592]) ).
thf(625,plain,
! [SV113: $i,SV209: $i,SV167: $i,SV47: $i] :
( ( ( between @ SV47 @ SV167 @ SV209 )
= $false )
| ( ( between @ SV113 @ SV167 @ SV209 )
= $true )
| ( ( between @ SV47 @ SV113 @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[593]) ).
thf(626,plain,
! [SV48: $i,SV210: $i,SV168: $i,SV114: $i] :
( ( ( between @ SV114 @ SV168 @ SV210 )
= $false )
| ( ( ( between @ SV48 @ SV168 @ SV210 )
| ( SV114 = SV168 ) )
= $true )
| ( ( between @ SV48 @ SV114 @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[594]) ).
thf(627,plain,
! [SV49: $i,SV211: $i,SV169: $i,SV115: $i] :
( ( ( between @ SV115 @ SV169 @ SV211 )
= $false )
| ( ( ( between @ SV49 @ SV115 @ SV211 )
| ( SV115 = SV169 ) )
= $true )
| ( ( between @ SV49 @ SV115 @ SV169 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[595]) ).
thf(628,plain,
! [SV50: $i,SV170: $i,SV212: $i,SV116: $i] :
( ( ( between @ SV116 @ SV212 @ SV170 )
= $false )
| ( ( between @ SV50 @ SV212 @ SV170 )
= $true )
| ( ( between @ SV50 @ SV116 @ SV170 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[596]) ).
thf(629,plain,
! [SV117: $i,SV213: $i,SV171: $i,SV51: $i] :
( ( ( between @ SV51 @ SV171 @ SV213 )
= $false )
| ( ( between @ SV51 @ SV117 @ SV213 )
= $true )
| ( ( between @ SV51 @ SV117 @ SV171 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[597]) ).
thf(630,plain,
! [SV253: $i,SV239: $i,SV215: $i,SV173: $i,SV120: $i,SV54: $i] :
( ( ( between @ SV54 @ SV120 @ SV173 )
= $false )
| ( ( ~ ( between @ SV215 @ SV239 @ SV173 )
| ~ ( between @ SV54 @ SV253 @ SV215 )
| ( between @ SV253 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SV253 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV173 )
| ( between @ SV120 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SV253 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV239 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(631,plain,
! [SV121: $i,SV216: $i,SV174: $i,SV55: $i] :
( ( ( equidistant @ SV55 @ SV174 @ SV55 @ SV216 )
= $false )
| ( ( ~ ( equidistant @ SV121 @ SV174 @ SV121 @ SV216 )
| ( SV55 = SV121 )
| ( SV174 = SV216 ) )
= $true )
| ( ( between @ SV55 @ SV121 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[599]) ).
thf(632,plain,
! [SV261: $i,SV258: $i,SV254: $i,SV240: $i,SV217: $i,SV175: $i,SV122: $i,SV56: $i] :
( ( ~ ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 )
| ~ ( equidistant @ SV56 @ SV240 @ SV175 @ SV254 )
| ~ ( equidistant @ SV56 @ SV258 @ SV175 @ SV261 )
| ~ ( equidistant @ SV240 @ SV258 @ SV254 @ SV261 )
| ~ ( between @ SV56 @ SV122 @ SV240 )
| ~ ( between @ SV175 @ SV217 @ SV254 )
| ( equidistant @ SV122 @ SV258 @ SV217 @ SV261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(633,plain,
! [SV255: $i,SV241: $i,SV218: $i,SV176: $i,SV123: $i,SV57: $i] :
( ( ( between @ SV57 @ SV123 @ SV176 )
= $false )
| ( ( ~ ( between @ SV218 @ SV241 @ SV255 )
| ~ ( equidistant @ SV57 @ SV123 @ SV218 @ SV241 )
| ~ ( equidistant @ SV57 @ SV176 @ SV218 @ SV255 )
| ( equidistant @ SV123 @ SV176 @ SV241 @ SV255 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[601]) ).
thf(634,plain,
! [SV262: $i,SV259: $i,SV256: $i,SV242: $i,SV219: $i,SV177: $i,SV124: $i,SV58: $i] :
( ( ~ ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 )
| ~ ( equidistant @ SV124 @ SV242 @ SV219 @ SV256 )
| ~ ( equidistant @ SV58 @ SV259 @ SV177 @ SV262 )
| ~ ( equidistant @ SV242 @ SV259 @ SV256 @ SV262 )
| ~ ( between @ SV58 @ SV124 @ SV242 )
| ~ ( between @ SV177 @ SV219 @ SV256 )
| ( equidistant @ SV124 @ SV259 @ SV219 @ SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(635,plain,
! [SV178: $i,SV220: $i,SV125: $i,SV59: $i] :
( ( ( equidistant @ SV59 @ SV125 @ SV59 @ SV220 )
= $false )
| ( ( ~ ( equidistant @ SV178 @ SV125 @ SV178 @ SV220 )
| ( SV125 = SV220 ) )
= $true )
| ( ( between @ SV59 @ SV125 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[603]) ).
thf(636,plain,
! [SV127: $i,SV243: $i,SV222: $i,SV180: $i,SV61: $i] :
( ( ( ~ ( equidistant @ SV61 @ SV180 @ SV222 @ SV243 ) )
= $true )
| ( ( between @ SV222 @ ( insertion @ SV222 @ SV243 @ SV61 @ SV127 ) @ SV243 )
= $true )
| ( ( between @ SV61 @ SV127 @ SV180 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(637,plain,
! [SV128: $i,SV244: $i,SV223: $i,SV181: $i,SV62: $i] :
( ( ( ~ ( equidistant @ SV62 @ SV181 @ SV223 @ SV244 ) )
= $true )
| ( ( equidistant @ SV128 @ SV181 @ ( insertion @ SV223 @ SV244 @ SV62 @ SV128 ) @ SV244 )
= $true )
| ( ( between @ SV62 @ SV128 @ SV181 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[605]) ).
thf(638,plain,
! [SV130: $i,SV224: $i,SV182: $i,SV64: $i] :
( ( ( SV64 = SV182 )
= $false )
| ( ( between @ SV224 @ SV130 @ SV182 )
= $true )
| ( ( between @ SV64 @ SV130 @ SV182 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[606]) ).
thf(639,plain,
! [SV184: $i,SV134: $i,SV246: $i,SV226: $i,SV69: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV69 @ SV226 @ SV246 ) )
= $true )
| ( ( equidistant @ SV134 @ SV184 @ SV226 @ SV246 )
= $true )
| ( ( equidistant @ SV2 @ SV69 @ SV134 @ SV184 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[608]) ).
thf(640,plain,
! [SV260: $i,SV257: $i,SV247: $i,SV227: $i,SV187: $i,SV138: $i,SV73: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 ) )
= $true )
| ( ( ~ ( equidistant @ SV73 @ SV227 @ SV187 @ SV247 )
| ~ ( equidistant @ SV6 @ SV257 @ SV138 @ SV260 )
| ~ ( equidistant @ SV73 @ SV257 @ SV187 @ SV260 )
| ~ ( between @ SV6 @ SV73 @ SV227 )
| ~ ( between @ SV138 @ SV187 @ SV247 )
| ( SV6 = SV73 )
| ( equidistant @ SV227 @ SV257 @ SV247 @ SV260 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[609]) ).
thf(641,plain,
! [SV8: $i,SV75: $i,SV139: $i,SV228: $i,SV188: $i] :
( ( ( between @ SV188 @ SV228 @ SV139 )
= $false )
| ( ( between @ SV75 @ ( inner_pasch @ SV8 @ SV75 @ SV139 @ SV228 @ SV188 ) @ SV188 )
= $true )
| ( ( between @ SV8 @ SV75 @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[610]) ).
thf(642,plain,
! [SV76: $i,SV9: $i,SV140: $i,SV229: $i,SV189: $i] :
( ( ( between @ SV189 @ SV229 @ SV140 )
= $false )
| ( ( between @ SV229 @ ( inner_pasch @ SV9 @ SV76 @ SV140 @ SV229 @ SV189 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV76 @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[611]) ).
thf(643,plain,
! [SV10: $i,SV230: $i,SV141: $i,SV77: $i,SV190: $i] :
( ( ( equidistant @ SV190 @ SV77 @ SV190 @ SV141 )
= $false )
| ( ( ~ ( equidistant @ SV230 @ SV77 @ SV230 @ SV141 )
| ( between @ SV10 @ SV190 @ SV230 )
| ( between @ SV190 @ SV230 @ SV10 )
| ( between @ SV230 @ SV10 @ SV190 )
| ( SV77 = SV141 ) )
= $true )
| ( ( equidistant @ SV10 @ SV77 @ SV10 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[612]) ).
thf(644,plain,
! [SV142: $i,SV11: $i,SV231: $i,SV78: $i,SV191: $i] :
( ( ( between @ SV191 @ SV78 @ SV231 )
= $false )
| ( ( ( SV11 = SV78 )
| ( between @ SV11 @ SV191 @ ( euclid1 @ SV11 @ SV191 @ SV78 @ SV231 @ SV142 ) ) )
= $true )
| ( ( between @ SV11 @ SV78 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[613]) ).
thf(645,plain,
! [SV143: $i,SV12: $i,SV232: $i,SV79: $i,SV192: $i] :
( ( ( between @ SV192 @ SV79 @ SV232 )
= $false )
| ( ( ( SV12 = SV79 )
| ( between @ SV12 @ SV232 @ ( euclid2 @ SV12 @ SV192 @ SV79 @ SV232 @ SV143 ) ) )
= $true )
| ( ( between @ SV12 @ SV79 @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[614]) ).
thf(646,plain,
! [SV144: $i,SV13: $i,SV233: $i,SV80: $i,SV193: $i] :
( ( ( between @ SV193 @ SV80 @ SV233 )
= $false )
| ( ( ( SV13 = SV80 )
| ( between @ ( euclid1 @ SV13 @ SV193 @ SV80 @ SV233 @ SV144 ) @ SV144 @ ( euclid2 @ SV13 @ SV193 @ SV80 @ SV233 @ SV144 ) ) )
= $true )
| ( ( between @ SV13 @ SV80 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(647,plain,
! [SV145: $i,SV248: $i,SV81: $i,SV234: $i,SV194: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV194 @ SV14 @ SV234 ) )
= $true )
| ( ( ~ ( between @ SV14 @ SV81 @ SV194 )
| ~ ( between @ SV81 @ SV248 @ SV194 )
| ( between @ SV145 @ ( continuous @ SV14 @ SV81 @ SV145 @ SV248 @ SV194 @ SV234 ) @ SV234 ) )
= $true )
| ( ( equidistant @ SV14 @ SV81 @ SV14 @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(648,plain,
! [SV146: $i,SV249: $i,SV82: $i,SV235: $i,SV195: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV195 @ SV15 @ SV235 ) )
= $true )
| ( ( ~ ( between @ SV15 @ SV82 @ SV195 )
| ~ ( between @ SV82 @ SV249 @ SV195 )
| ( equidistant @ SV15 @ SV249 @ SV15 @ ( continuous @ SV15 @ SV82 @ SV146 @ SV249 @ SV195 @ SV235 ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV82 @ SV15 @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(649,plain,
! [SV93: $i,SV26: $i,SV250: $i,SV236: $i,SV204: $i,SV155: $i] :
( ( ( ~ ( equidistant @ SV155 @ SV204 @ SV236 @ SV250 ) )
= $true )
| ( ( equidistant @ SV26 @ SV93 @ SV236 @ SV250 )
= $true )
| ( ( equidistant @ SV26 @ SV93 @ SV155 @ SV204 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(650,plain,
! [SV157: $i,SV32: $i,SV251: $i,SV205: $i,SV237: $i,SV98: $i] :
( ( ( ~ ( equidistant @ SV98 @ SV237 @ SV205 @ SV251 ) )
= $true )
| ( ( ~ ( between @ SV32 @ SV98 @ SV237 )
| ~ ( between @ SV157 @ SV205 @ SV251 )
| ( equidistant @ SV32 @ SV237 @ SV157 @ SV251 ) )
= $true )
| ( ( equidistant @ SV32 @ SV98 @ SV157 @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(651,plain,
! [SV33: $i,SV206: $i,SV158: $i,SV99: $i] :
( ( ( ~ ( equidistant @ SV99 @ SV158 @ SV99 @ SV206 ) )
= $true )
| ( ( ( SV33 = SV99 )
| ( SV158 = SV206 ) )
= $true )
| ( ( between @ SV33 @ SV99 @ SV206 )
= $false )
| ( ( between @ SV33 @ SV99 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(652,plain,
! [SV207: $i,SV160: $i,SV101: $i,SV35: $i,SV252: $i,SV238: $i] :
( ( ( ( extension @ SV238 @ SV252 @ SV35 @ SV101 )
= ( extension @ SV238 @ SV252 @ SV160 @ SV207 ) )
= $true )
| ( ( SV238 = SV252 )
= $true )
| ( ( equidistant @ SV35 @ SV101 @ SV160 @ SV207 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(653,plain,
! [SV114: $i,SV210: $i,SV168: $i,SV48: $i] :
( ( ( between @ SV48 @ SV168 @ SV210 )
= $true )
| ( ( SV114 = SV168 )
= $true )
| ( ( between @ SV114 @ SV168 @ SV210 )
= $false )
| ( ( between @ SV48 @ SV114 @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(654,plain,
! [SV169: $i,SV211: $i,SV115: $i,SV49: $i] :
( ( ( between @ SV49 @ SV115 @ SV211 )
= $true )
| ( ( SV115 = SV169 )
= $true )
| ( ( between @ SV115 @ SV169 @ SV211 )
= $false )
| ( ( between @ SV49 @ SV115 @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(655,plain,
! [SV120: $i,SV253: $i,SV54: $i,SV173: $i,SV239: $i,SV215: $i] :
( ( ( ~ ( between @ SV215 @ SV239 @ SV173 ) )
= $true )
| ( ( ~ ( between @ SV54 @ SV253 @ SV215 )
| ( between @ SV253 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SV253 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV173 )
| ( between @ SV120 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SV253 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV239 ) )
= $true )
| ( ( between @ SV54 @ SV120 @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[630]) ).
thf(656,plain,
! [SV55: $i,SV216: $i,SV174: $i,SV121: $i] :
( ( ( ~ ( equidistant @ SV121 @ SV174 @ SV121 @ SV216 ) )
= $true )
| ( ( ( SV55 = SV121 )
| ( SV174 = SV216 ) )
= $true )
| ( ( equidistant @ SV55 @ SV174 @ SV55 @ SV216 )
= $false )
| ( ( between @ SV55 @ SV121 @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[631]) ).
thf(657,plain,
! [SV261: $i,SV258: $i,SV254: $i,SV240: $i,SV217: $i,SV175: $i,SV122: $i,SV56: $i] :
( ( ( ~ ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 ) )
= $true )
| ( ( ~ ( equidistant @ SV56 @ SV240 @ SV175 @ SV254 )
| ~ ( equidistant @ SV56 @ SV258 @ SV175 @ SV261 )
| ~ ( equidistant @ SV240 @ SV258 @ SV254 @ SV261 )
| ~ ( between @ SV56 @ SV122 @ SV240 )
| ~ ( between @ SV175 @ SV217 @ SV254 )
| ( equidistant @ SV122 @ SV258 @ SV217 @ SV261 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[632]) ).
thf(658,plain,
! [SV176: $i,SV123: $i,SV57: $i,SV255: $i,SV241: $i,SV218: $i] :
( ( ( ~ ( between @ SV218 @ SV241 @ SV255 ) )
= $true )
| ( ( ~ ( equidistant @ SV57 @ SV123 @ SV218 @ SV241 )
| ~ ( equidistant @ SV57 @ SV176 @ SV218 @ SV255 )
| ( equidistant @ SV123 @ SV176 @ SV241 @ SV255 ) )
= $true )
| ( ( between @ SV57 @ SV123 @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[633]) ).
thf(659,plain,
! [SV262: $i,SV259: $i,SV256: $i,SV242: $i,SV219: $i,SV177: $i,SV124: $i,SV58: $i] :
( ( ( ~ ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 ) )
= $true )
| ( ( ~ ( equidistant @ SV124 @ SV242 @ SV219 @ SV256 )
| ~ ( equidistant @ SV58 @ SV259 @ SV177 @ SV262 )
| ~ ( equidistant @ SV242 @ SV259 @ SV256 @ SV262 )
| ~ ( between @ SV58 @ SV124 @ SV242 )
| ~ ( between @ SV177 @ SV219 @ SV256 )
| ( equidistant @ SV124 @ SV259 @ SV219 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[634]) ).
thf(660,plain,
! [SV59: $i,SV220: $i,SV125: $i,SV178: $i] :
( ( ( ~ ( equidistant @ SV178 @ SV125 @ SV178 @ SV220 ) )
= $true )
| ( ( SV125 = SV220 )
= $true )
| ( ( equidistant @ SV59 @ SV125 @ SV59 @ SV220 )
= $false )
| ( ( between @ SV59 @ SV125 @ SV178 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[635]) ).
thf(661,plain,
! [SV127: $i,SV243: $i,SV222: $i,SV180: $i,SV61: $i] :
( ( ( equidistant @ SV61 @ SV180 @ SV222 @ SV243 )
= $false )
| ( ( between @ SV222 @ ( insertion @ SV222 @ SV243 @ SV61 @ SV127 ) @ SV243 )
= $true )
| ( ( between @ SV61 @ SV127 @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[636]) ).
thf(662,plain,
! [SV128: $i,SV244: $i,SV223: $i,SV181: $i,SV62: $i] :
( ( ( equidistant @ SV62 @ SV181 @ SV223 @ SV244 )
= $false )
| ( ( equidistant @ SV128 @ SV181 @ ( insertion @ SV223 @ SV244 @ SV62 @ SV128 ) @ SV244 )
= $true )
| ( ( between @ SV62 @ SV128 @ SV181 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[637]) ).
thf(663,plain,
! [SV184: $i,SV134: $i,SV246: $i,SV226: $i,SV69: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV69 @ SV226 @ SV246 )
= $false )
| ( ( equidistant @ SV134 @ SV184 @ SV226 @ SV246 )
= $true )
| ( ( equidistant @ SV2 @ SV69 @ SV134 @ SV184 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[639]) ).
thf(664,plain,
! [SV260: $i,SV257: $i,SV247: $i,SV227: $i,SV187: $i,SV138: $i,SV73: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
= $false )
| ( ( ~ ( equidistant @ SV73 @ SV227 @ SV187 @ SV247 )
| ~ ( equidistant @ SV6 @ SV257 @ SV138 @ SV260 )
| ~ ( equidistant @ SV73 @ SV257 @ SV187 @ SV260 )
| ~ ( between @ SV6 @ SV73 @ SV227 )
| ~ ( between @ SV138 @ SV187 @ SV247 )
| ( SV6 = SV73 )
| ( equidistant @ SV227 @ SV257 @ SV247 @ SV260 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[640]) ).
thf(665,plain,
! [SV190: $i,SV10: $i,SV141: $i,SV77: $i,SV230: $i] :
( ( ( ~ ( equidistant @ SV230 @ SV77 @ SV230 @ SV141 ) )
= $true )
| ( ( ( between @ SV10 @ SV190 @ SV230 )
| ( between @ SV190 @ SV230 @ SV10 )
| ( between @ SV230 @ SV10 @ SV190 )
| ( SV77 = SV141 ) )
= $true )
| ( ( equidistant @ SV190 @ SV77 @ SV190 @ SV141 )
= $false )
| ( ( equidistant @ SV10 @ SV77 @ SV10 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(666,plain,
! [SV142: $i,SV231: $i,SV191: $i,SV78: $i,SV11: $i] :
( ( ( SV11 = SV78 )
= $true )
| ( ( between @ SV11 @ SV191 @ ( euclid1 @ SV11 @ SV191 @ SV78 @ SV231 @ SV142 ) )
= $true )
| ( ( between @ SV191 @ SV78 @ SV231 )
= $false )
| ( ( between @ SV11 @ SV78 @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(667,plain,
! [SV143: $i,SV192: $i,SV232: $i,SV79: $i,SV12: $i] :
( ( ( SV12 = SV79 )
= $true )
| ( ( between @ SV12 @ SV232 @ ( euclid2 @ SV12 @ SV192 @ SV79 @ SV232 @ SV143 ) )
= $true )
| ( ( between @ SV192 @ SV79 @ SV232 )
= $false )
| ( ( between @ SV12 @ SV79 @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[645]) ).
thf(668,plain,
! [SV144: $i,SV233: $i,SV193: $i,SV80: $i,SV13: $i] :
( ( ( SV13 = SV80 )
= $true )
| ( ( between @ ( euclid1 @ SV13 @ SV193 @ SV80 @ SV233 @ SV144 ) @ SV144 @ ( euclid2 @ SV13 @ SV193 @ SV80 @ SV233 @ SV144 ) )
= $true )
| ( ( between @ SV193 @ SV80 @ SV233 )
= $false )
| ( ( between @ SV13 @ SV80 @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[646]) ).
thf(669,plain,
! [SV145: $i,SV248: $i,SV81: $i,SV234: $i,SV194: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV194 @ SV14 @ SV234 )
= $false )
| ( ( ~ ( between @ SV14 @ SV81 @ SV194 )
| ~ ( between @ SV81 @ SV248 @ SV194 )
| ( between @ SV145 @ ( continuous @ SV14 @ SV81 @ SV145 @ SV248 @ SV194 @ SV234 ) @ SV234 ) )
= $true )
| ( ( equidistant @ SV14 @ SV81 @ SV14 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[647]) ).
thf(670,plain,
! [SV146: $i,SV249: $i,SV82: $i,SV235: $i,SV195: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV195 @ SV15 @ SV235 )
= $false )
| ( ( ~ ( between @ SV15 @ SV82 @ SV195 )
| ~ ( between @ SV82 @ SV249 @ SV195 )
| ( equidistant @ SV15 @ SV249 @ SV15 @ ( continuous @ SV15 @ SV82 @ SV146 @ SV249 @ SV195 @ SV235 ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV82 @ SV15 @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[648]) ).
thf(671,plain,
! [SV93: $i,SV26: $i,SV250: $i,SV236: $i,SV204: $i,SV155: $i] :
( ( ( equidistant @ SV155 @ SV204 @ SV236 @ SV250 )
= $false )
| ( ( equidistant @ SV26 @ SV93 @ SV236 @ SV250 )
= $true )
| ( ( equidistant @ SV26 @ SV93 @ SV155 @ SV204 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[649]) ).
thf(672,plain,
! [SV157: $i,SV32: $i,SV251: $i,SV205: $i,SV237: $i,SV98: $i] :
( ( ( equidistant @ SV98 @ SV237 @ SV205 @ SV251 )
= $false )
| ( ( ~ ( between @ SV32 @ SV98 @ SV237 )
| ~ ( between @ SV157 @ SV205 @ SV251 )
| ( equidistant @ SV32 @ SV237 @ SV157 @ SV251 ) )
= $true )
| ( ( equidistant @ SV32 @ SV98 @ SV157 @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[650]) ).
thf(673,plain,
! [SV33: $i,SV206: $i,SV158: $i,SV99: $i] :
( ( ( equidistant @ SV99 @ SV158 @ SV99 @ SV206 )
= $false )
| ( ( ( SV33 = SV99 )
| ( SV158 = SV206 ) )
= $true )
| ( ( between @ SV33 @ SV99 @ SV206 )
= $false )
| ( ( between @ SV33 @ SV99 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[651]) ).
thf(674,plain,
! [SV120: $i,SV253: $i,SV54: $i,SV173: $i,SV239: $i,SV215: $i] :
( ( ( between @ SV215 @ SV239 @ SV173 )
= $false )
| ( ( ~ ( between @ SV54 @ SV253 @ SV215 )
| ( between @ SV253 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SV253 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV173 )
| ( between @ SV120 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SV253 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV239 ) )
= $true )
| ( ( between @ SV54 @ SV120 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[655]) ).
thf(675,plain,
! [SV55: $i,SV216: $i,SV174: $i,SV121: $i] :
( ( ( equidistant @ SV121 @ SV174 @ SV121 @ SV216 )
= $false )
| ( ( ( SV55 = SV121 )
| ( SV174 = SV216 ) )
= $true )
| ( ( equidistant @ SV55 @ SV174 @ SV55 @ SV216 )
= $false )
| ( ( between @ SV55 @ SV121 @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[656]) ).
thf(676,plain,
! [SV261: $i,SV258: $i,SV254: $i,SV240: $i,SV217: $i,SV175: $i,SV122: $i,SV56: $i] :
( ( ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 )
= $false )
| ( ( ~ ( equidistant @ SV56 @ SV240 @ SV175 @ SV254 )
| ~ ( equidistant @ SV56 @ SV258 @ SV175 @ SV261 )
| ~ ( equidistant @ SV240 @ SV258 @ SV254 @ SV261 )
| ~ ( between @ SV56 @ SV122 @ SV240 )
| ~ ( between @ SV175 @ SV217 @ SV254 )
| ( equidistant @ SV122 @ SV258 @ SV217 @ SV261 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[657]) ).
thf(677,plain,
! [SV176: $i,SV123: $i,SV57: $i,SV255: $i,SV241: $i,SV218: $i] :
( ( ( between @ SV218 @ SV241 @ SV255 )
= $false )
| ( ( ~ ( equidistant @ SV57 @ SV123 @ SV218 @ SV241 )
| ~ ( equidistant @ SV57 @ SV176 @ SV218 @ SV255 )
| ( equidistant @ SV123 @ SV176 @ SV241 @ SV255 ) )
= $true )
| ( ( between @ SV57 @ SV123 @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[658]) ).
thf(678,plain,
! [SV262: $i,SV259: $i,SV256: $i,SV242: $i,SV219: $i,SV177: $i,SV124: $i,SV58: $i] :
( ( ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 )
= $false )
| ( ( ~ ( equidistant @ SV124 @ SV242 @ SV219 @ SV256 )
| ~ ( equidistant @ SV58 @ SV259 @ SV177 @ SV262 )
| ~ ( equidistant @ SV242 @ SV259 @ SV256 @ SV262 )
| ~ ( between @ SV58 @ SV124 @ SV242 )
| ~ ( between @ SV177 @ SV219 @ SV256 )
| ( equidistant @ SV124 @ SV259 @ SV219 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[659]) ).
thf(679,plain,
! [SV59: $i,SV220: $i,SV125: $i,SV178: $i] :
( ( ( equidistant @ SV178 @ SV125 @ SV178 @ SV220 )
= $false )
| ( ( SV125 = SV220 )
= $true )
| ( ( equidistant @ SV59 @ SV125 @ SV59 @ SV220 )
= $false )
| ( ( between @ SV59 @ SV125 @ SV178 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[660]) ).
thf(680,plain,
! [SV260: $i,SV138: $i,SV257: $i,SV6: $i,SV247: $i,SV187: $i,SV227: $i,SV73: $i] :
( ( ( ~ ( equidistant @ SV73 @ SV227 @ SV187 @ SV247 ) )
= $true )
| ( ( ~ ( equidistant @ SV6 @ SV257 @ SV138 @ SV260 )
| ~ ( equidistant @ SV73 @ SV257 @ SV187 @ SV260 )
| ~ ( between @ SV6 @ SV73 @ SV227 )
| ~ ( between @ SV138 @ SV187 @ SV247 )
| ( SV6 = SV73 )
| ( equidistant @ SV227 @ SV257 @ SV247 @ SV260 ) )
= $true )
| ( ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[664]) ).
thf(681,plain,
! [SV190: $i,SV10: $i,SV141: $i,SV77: $i,SV230: $i] :
( ( ( equidistant @ SV230 @ SV77 @ SV230 @ SV141 )
= $false )
| ( ( ( between @ SV10 @ SV190 @ SV230 )
| ( between @ SV190 @ SV230 @ SV10 )
| ( between @ SV230 @ SV10 @ SV190 )
| ( SV77 = SV141 ) )
= $true )
| ( ( equidistant @ SV190 @ SV77 @ SV190 @ SV141 )
= $false )
| ( ( equidistant @ SV10 @ SV77 @ SV10 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[665]) ).
thf(682,plain,
! [SV234: $i,SV145: $i,SV248: $i,SV194: $i,SV81: $i,SV14: $i] :
( ( ( ~ ( between @ SV14 @ SV81 @ SV194 ) )
= $true )
| ( ( ~ ( between @ SV81 @ SV248 @ SV194 )
| ( between @ SV145 @ ( continuous @ SV14 @ SV81 @ SV145 @ SV248 @ SV194 @ SV234 ) @ SV234 ) )
= $true )
| ( ( equidistant @ SV14 @ SV194 @ SV14 @ SV234 )
= $false )
| ( ( equidistant @ SV14 @ SV81 @ SV14 @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[669]) ).
thf(683,plain,
! [SV235: $i,SV146: $i,SV249: $i,SV195: $i,SV82: $i,SV15: $i] :
( ( ( ~ ( between @ SV15 @ SV82 @ SV195 ) )
= $true )
| ( ( ~ ( between @ SV82 @ SV249 @ SV195 )
| ( equidistant @ SV15 @ SV249 @ SV15 @ ( continuous @ SV15 @ SV82 @ SV146 @ SV249 @ SV195 @ SV235 ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV195 @ SV15 @ SV235 )
= $false )
| ( ( equidistant @ SV15 @ SV82 @ SV15 @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(684,plain,
! [SV251: $i,SV205: $i,SV157: $i,SV237: $i,SV98: $i,SV32: $i] :
( ( ( ~ ( between @ SV32 @ SV98 @ SV237 ) )
= $true )
| ( ( ~ ( between @ SV157 @ SV205 @ SV251 )
| ( equidistant @ SV32 @ SV237 @ SV157 @ SV251 ) )
= $true )
| ( ( equidistant @ SV98 @ SV237 @ SV205 @ SV251 )
= $false )
| ( ( equidistant @ SV32 @ SV98 @ SV157 @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[672]) ).
thf(685,plain,
! [SV206: $i,SV158: $i,SV99: $i,SV33: $i] :
( ( ( SV33 = SV99 )
= $true )
| ( ( SV158 = SV206 )
= $true )
| ( ( equidistant @ SV99 @ SV158 @ SV99 @ SV206 )
= $false )
| ( ( between @ SV33 @ SV99 @ SV206 )
= $false )
| ( ( between @ SV33 @ SV99 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[673]) ).
thf(686,plain,
! [SV120: $i,SV173: $i,SV239: $i,SV215: $i,SV253: $i,SV54: $i] :
( ( ( ~ ( between @ SV54 @ SV253 @ SV215 ) )
= $true )
| ( ( ( between @ SV253 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SV253 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV173 )
| ( between @ SV120 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SV253 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV239 ) )
= $true )
| ( ( between @ SV215 @ SV239 @ SV173 )
= $false )
| ( ( between @ SV54 @ SV120 @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(687,plain,
! [SV216: $i,SV174: $i,SV121: $i,SV55: $i] :
( ( ( SV55 = SV121 )
= $true )
| ( ( SV174 = SV216 )
= $true )
| ( ( equidistant @ SV121 @ SV174 @ SV121 @ SV216 )
= $false )
| ( ( equidistant @ SV55 @ SV174 @ SV55 @ SV216 )
= $false )
| ( ( between @ SV55 @ SV121 @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[675]) ).
thf(688,plain,
! [SV217: $i,SV122: $i,SV261: $i,SV258: $i,SV254: $i,SV175: $i,SV240: $i,SV56: $i] :
( ( ( ~ ( equidistant @ SV56 @ SV240 @ SV175 @ SV254 ) )
= $true )
| ( ( ~ ( equidistant @ SV56 @ SV258 @ SV175 @ SV261 )
| ~ ( equidistant @ SV240 @ SV258 @ SV254 @ SV261 )
| ~ ( between @ SV56 @ SV122 @ SV240 )
| ~ ( between @ SV175 @ SV217 @ SV254 )
| ( equidistant @ SV122 @ SV258 @ SV217 @ SV261 ) )
= $true )
| ( ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[676]) ).
thf(689,plain,
! [SV255: $i,SV176: $i,SV241: $i,SV218: $i,SV123: $i,SV57: $i] :
( ( ( ~ ( equidistant @ SV57 @ SV123 @ SV218 @ SV241 ) )
= $true )
| ( ( ~ ( equidistant @ SV57 @ SV176 @ SV218 @ SV255 )
| ( equidistant @ SV123 @ SV176 @ SV241 @ SV255 ) )
= $true )
| ( ( between @ SV218 @ SV241 @ SV255 )
= $false )
| ( ( between @ SV57 @ SV123 @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[677]) ).
thf(690,plain,
! [SV262: $i,SV177: $i,SV259: $i,SV58: $i,SV256: $i,SV219: $i,SV242: $i,SV124: $i] :
( ( ( ~ ( equidistant @ SV124 @ SV242 @ SV219 @ SV256 ) )
= $true )
| ( ( ~ ( equidistant @ SV58 @ SV259 @ SV177 @ SV262 )
| ~ ( equidistant @ SV242 @ SV259 @ SV256 @ SV262 )
| ~ ( between @ SV58 @ SV124 @ SV242 )
| ~ ( between @ SV177 @ SV219 @ SV256 )
| ( equidistant @ SV124 @ SV259 @ SV219 @ SV262 ) )
= $true )
| ( ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[678]) ).
thf(691,plain,
! [SV260: $i,SV138: $i,SV257: $i,SV6: $i,SV247: $i,SV187: $i,SV227: $i,SV73: $i] :
( ( ( equidistant @ SV73 @ SV227 @ SV187 @ SV247 )
= $false )
| ( ( ~ ( equidistant @ SV6 @ SV257 @ SV138 @ SV260 )
| ~ ( equidistant @ SV73 @ SV257 @ SV187 @ SV260 )
| ~ ( between @ SV6 @ SV73 @ SV227 )
| ~ ( between @ SV138 @ SV187 @ SV247 )
| ( SV6 = SV73 )
| ( equidistant @ SV227 @ SV257 @ SV247 @ SV260 ) )
= $true )
| ( ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[680]) ).
thf(692,plain,
! [SV141: $i,SV77: $i,SV230: $i,SV190: $i,SV10: $i] :
( ( ( between @ SV10 @ SV190 @ SV230 )
= $true )
| ( ( ( between @ SV190 @ SV230 @ SV10 )
| ( between @ SV230 @ SV10 @ SV190 )
| ( SV77 = SV141 ) )
= $true )
| ( ( equidistant @ SV230 @ SV77 @ SV230 @ SV141 )
= $false )
| ( ( equidistant @ SV190 @ SV77 @ SV190 @ SV141 )
= $false )
| ( ( equidistant @ SV10 @ SV77 @ SV10 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[681]) ).
thf(693,plain,
! [SV234: $i,SV145: $i,SV248: $i,SV194: $i,SV81: $i,SV14: $i] :
( ( ( between @ SV14 @ SV81 @ SV194 )
= $false )
| ( ( ~ ( between @ SV81 @ SV248 @ SV194 )
| ( between @ SV145 @ ( continuous @ SV14 @ SV81 @ SV145 @ SV248 @ SV194 @ SV234 ) @ SV234 ) )
= $true )
| ( ( equidistant @ SV14 @ SV194 @ SV14 @ SV234 )
= $false )
| ( ( equidistant @ SV14 @ SV81 @ SV14 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[682]) ).
thf(694,plain,
! [SV235: $i,SV146: $i,SV249: $i,SV195: $i,SV82: $i,SV15: $i] :
( ( ( between @ SV15 @ SV82 @ SV195 )
= $false )
| ( ( ~ ( between @ SV82 @ SV249 @ SV195 )
| ( equidistant @ SV15 @ SV249 @ SV15 @ ( continuous @ SV15 @ SV82 @ SV146 @ SV249 @ SV195 @ SV235 ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV195 @ SV15 @ SV235 )
= $false )
| ( ( equidistant @ SV15 @ SV82 @ SV15 @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[683]) ).
thf(695,plain,
! [SV251: $i,SV205: $i,SV157: $i,SV237: $i,SV98: $i,SV32: $i] :
( ( ( between @ SV32 @ SV98 @ SV237 )
= $false )
| ( ( ~ ( between @ SV157 @ SV205 @ SV251 )
| ( equidistant @ SV32 @ SV237 @ SV157 @ SV251 ) )
= $true )
| ( ( equidistant @ SV98 @ SV237 @ SV205 @ SV251 )
= $false )
| ( ( equidistant @ SV32 @ SV98 @ SV157 @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[684]) ).
thf(696,plain,
! [SV120: $i,SV173: $i,SV239: $i,SV215: $i,SV253: $i,SV54: $i] :
( ( ( between @ SV54 @ SV253 @ SV215 )
= $false )
| ( ( ( between @ SV253 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SV253 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV173 )
| ( between @ SV120 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SV253 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV239 ) )
= $true )
| ( ( between @ SV215 @ SV239 @ SV173 )
= $false )
| ( ( between @ SV54 @ SV120 @ SV173 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[686]) ).
thf(697,plain,
! [SV217: $i,SV122: $i,SV261: $i,SV258: $i,SV254: $i,SV175: $i,SV240: $i,SV56: $i] :
( ( ( equidistant @ SV56 @ SV240 @ SV175 @ SV254 )
= $false )
| ( ( ~ ( equidistant @ SV56 @ SV258 @ SV175 @ SV261 )
| ~ ( equidistant @ SV240 @ SV258 @ SV254 @ SV261 )
| ~ ( between @ SV56 @ SV122 @ SV240 )
| ~ ( between @ SV175 @ SV217 @ SV254 )
| ( equidistant @ SV122 @ SV258 @ SV217 @ SV261 ) )
= $true )
| ( ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[688]) ).
thf(698,plain,
! [SV255: $i,SV176: $i,SV241: $i,SV218: $i,SV123: $i,SV57: $i] :
( ( ( equidistant @ SV57 @ SV123 @ SV218 @ SV241 )
= $false )
| ( ( ~ ( equidistant @ SV57 @ SV176 @ SV218 @ SV255 )
| ( equidistant @ SV123 @ SV176 @ SV241 @ SV255 ) )
= $true )
| ( ( between @ SV218 @ SV241 @ SV255 )
= $false )
| ( ( between @ SV57 @ SV123 @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[689]) ).
thf(699,plain,
! [SV262: $i,SV177: $i,SV259: $i,SV58: $i,SV256: $i,SV219: $i,SV242: $i,SV124: $i] :
( ( ( equidistant @ SV124 @ SV242 @ SV219 @ SV256 )
= $false )
| ( ( ~ ( equidistant @ SV58 @ SV259 @ SV177 @ SV262 )
| ~ ( equidistant @ SV242 @ SV259 @ SV256 @ SV262 )
| ~ ( between @ SV58 @ SV124 @ SV242 )
| ~ ( between @ SV177 @ SV219 @ SV256 )
| ( equidistant @ SV124 @ SV259 @ SV219 @ SV262 ) )
= $true )
| ( ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[690]) ).
thf(700,plain,
! [SV247: $i,SV227: $i,SV187: $i,SV73: $i,SV260: $i,SV138: $i,SV257: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV257 @ SV138 @ SV260 ) )
= $true )
| ( ( ~ ( equidistant @ SV73 @ SV257 @ SV187 @ SV260 )
| ~ ( between @ SV6 @ SV73 @ SV227 )
| ~ ( between @ SV138 @ SV187 @ SV247 )
| ( SV6 = SV73 )
| ( equidistant @ SV227 @ SV257 @ SV247 @ SV260 ) )
= $true )
| ( ( equidistant @ SV73 @ SV227 @ SV187 @ SV247 )
= $false )
| ( ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[691]) ).
thf(701,plain,
! [SV141: $i,SV77: $i,SV10: $i,SV230: $i,SV190: $i] :
( ( ( between @ SV190 @ SV230 @ SV10 )
= $true )
| ( ( ( between @ SV230 @ SV10 @ SV190 )
| ( SV77 = SV141 ) )
= $true )
| ( ( between @ SV10 @ SV190 @ SV230 )
= $true )
| ( ( equidistant @ SV230 @ SV77 @ SV230 @ SV141 )
= $false )
| ( ( equidistant @ SV190 @ SV77 @ SV190 @ SV141 )
= $false )
| ( ( equidistant @ SV10 @ SV77 @ SV10 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[692]) ).
thf(702,plain,
! [SV234: $i,SV14: $i,SV145: $i,SV194: $i,SV248: $i,SV81: $i] :
( ( ( ~ ( between @ SV81 @ SV248 @ SV194 ) )
= $true )
| ( ( between @ SV145 @ ( continuous @ SV14 @ SV81 @ SV145 @ SV248 @ SV194 @ SV234 ) @ SV234 )
= $true )
| ( ( between @ SV14 @ SV81 @ SV194 )
= $false )
| ( ( equidistant @ SV14 @ SV194 @ SV14 @ SV234 )
= $false )
| ( ( equidistant @ SV14 @ SV81 @ SV14 @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[693]) ).
thf(703,plain,
! [SV235: $i,SV146: $i,SV15: $i,SV195: $i,SV249: $i,SV82: $i] :
( ( ( ~ ( between @ SV82 @ SV249 @ SV195 ) )
= $true )
| ( ( equidistant @ SV15 @ SV249 @ SV15 @ ( continuous @ SV15 @ SV82 @ SV146 @ SV249 @ SV195 @ SV235 ) )
= $true )
| ( ( between @ SV15 @ SV82 @ SV195 )
= $false )
| ( ( equidistant @ SV15 @ SV195 @ SV15 @ SV235 )
= $false )
| ( ( equidistant @ SV15 @ SV82 @ SV15 @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(704,plain,
! [SV98: $i,SV237: $i,SV32: $i,SV251: $i,SV205: $i,SV157: $i] :
( ( ( ~ ( between @ SV157 @ SV205 @ SV251 ) )
= $true )
| ( ( equidistant @ SV32 @ SV237 @ SV157 @ SV251 )
= $true )
| ( ( between @ SV32 @ SV98 @ SV237 )
= $false )
| ( ( equidistant @ SV98 @ SV237 @ SV205 @ SV251 )
= $false )
| ( ( equidistant @ SV32 @ SV98 @ SV157 @ SV205 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(705,plain,
! [SV120: $i,SV173: $i,SV215: $i,SV54: $i,SV239: $i,SV253: $i] :
( ( ( between @ SV253 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SV253 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV173 )
= $true )
| ( ( between @ SV120 @ ( inner_pasch @ SV239 @ ( inner_pasch @ SV54 @ SV253 @ SV215 @ SV239 @ SV173 ) @ SV54 @ SV120 @ SV173 ) @ SV239 )
= $true )
| ( ( between @ SV54 @ SV253 @ SV215 )
= $false )
| ( ( between @ SV215 @ SV239 @ SV173 )
= $false )
| ( ( between @ SV54 @ SV120 @ SV173 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[696]) ).
thf(706,plain,
! [SV217: $i,SV122: $i,SV254: $i,SV240: $i,SV261: $i,SV175: $i,SV258: $i,SV56: $i] :
( ( ( ~ ( equidistant @ SV56 @ SV258 @ SV175 @ SV261 ) )
= $true )
| ( ( ~ ( equidistant @ SV240 @ SV258 @ SV254 @ SV261 )
| ~ ( between @ SV56 @ SV122 @ SV240 )
| ~ ( between @ SV175 @ SV217 @ SV254 )
| ( equidistant @ SV122 @ SV258 @ SV217 @ SV261 ) )
= $true )
| ( ( equidistant @ SV56 @ SV240 @ SV175 @ SV254 )
= $false )
| ( ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[697]) ).
thf(707,plain,
! [SV241: $i,SV123: $i,SV255: $i,SV218: $i,SV176: $i,SV57: $i] :
( ( ( ~ ( equidistant @ SV57 @ SV176 @ SV218 @ SV255 ) )
= $true )
| ( ( equidistant @ SV123 @ SV176 @ SV241 @ SV255 )
= $true )
| ( ( equidistant @ SV57 @ SV123 @ SV218 @ SV241 )
= $false )
| ( ( between @ SV218 @ SV241 @ SV255 )
= $false )
| ( ( between @ SV57 @ SV123 @ SV176 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[698]) ).
thf(708,plain,
! [SV219: $i,SV124: $i,SV256: $i,SV242: $i,SV262: $i,SV177: $i,SV259: $i,SV58: $i] :
( ( ( ~ ( equidistant @ SV58 @ SV259 @ SV177 @ SV262 ) )
= $true )
| ( ( ~ ( equidistant @ SV242 @ SV259 @ SV256 @ SV262 )
| ~ ( between @ SV58 @ SV124 @ SV242 )
| ~ ( between @ SV177 @ SV219 @ SV256 )
| ( equidistant @ SV124 @ SV259 @ SV219 @ SV262 ) )
= $true )
| ( ( equidistant @ SV124 @ SV242 @ SV219 @ SV256 )
= $false )
| ( ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[699]) ).
thf(709,plain,
! [SV247: $i,SV227: $i,SV187: $i,SV73: $i,SV260: $i,SV138: $i,SV257: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV257 @ SV138 @ SV260 )
= $false )
| ( ( ~ ( equidistant @ SV73 @ SV257 @ SV187 @ SV260 )
| ~ ( between @ SV6 @ SV73 @ SV227 )
| ~ ( between @ SV138 @ SV187 @ SV247 )
| ( SV6 = SV73 )
| ( equidistant @ SV227 @ SV257 @ SV247 @ SV260 ) )
= $true )
| ( ( equidistant @ SV73 @ SV227 @ SV187 @ SV247 )
= $false )
| ( ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[700]) ).
thf(710,plain,
! [SV141: $i,SV77: $i,SV190: $i,SV10: $i,SV230: $i] :
( ( ( between @ SV230 @ SV10 @ SV190 )
= $true )
| ( ( SV77 = SV141 )
= $true )
| ( ( between @ SV190 @ SV230 @ SV10 )
= $true )
| ( ( between @ SV10 @ SV190 @ SV230 )
= $true )
| ( ( equidistant @ SV230 @ SV77 @ SV230 @ SV141 )
= $false )
| ( ( equidistant @ SV190 @ SV77 @ SV190 @ SV141 )
= $false )
| ( ( equidistant @ SV10 @ SV77 @ SV10 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[701]) ).
thf(711,plain,
! [SV234: $i,SV14: $i,SV145: $i,SV194: $i,SV248: $i,SV81: $i] :
( ( ( between @ SV81 @ SV248 @ SV194 )
= $false )
| ( ( between @ SV145 @ ( continuous @ SV14 @ SV81 @ SV145 @ SV248 @ SV194 @ SV234 ) @ SV234 )
= $true )
| ( ( between @ SV14 @ SV81 @ SV194 )
= $false )
| ( ( equidistant @ SV14 @ SV194 @ SV14 @ SV234 )
= $false )
| ( ( equidistant @ SV14 @ SV81 @ SV14 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[702]) ).
thf(712,plain,
! [SV235: $i,SV146: $i,SV15: $i,SV195: $i,SV249: $i,SV82: $i] :
( ( ( between @ SV82 @ SV249 @ SV195 )
= $false )
| ( ( equidistant @ SV15 @ SV249 @ SV15 @ ( continuous @ SV15 @ SV82 @ SV146 @ SV249 @ SV195 @ SV235 ) )
= $true )
| ( ( between @ SV15 @ SV82 @ SV195 )
= $false )
| ( ( equidistant @ SV15 @ SV195 @ SV15 @ SV235 )
= $false )
| ( ( equidistant @ SV15 @ SV82 @ SV15 @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[703]) ).
thf(713,plain,
! [SV98: $i,SV237: $i,SV32: $i,SV251: $i,SV205: $i,SV157: $i] :
( ( ( between @ SV157 @ SV205 @ SV251 )
= $false )
| ( ( equidistant @ SV32 @ SV237 @ SV157 @ SV251 )
= $true )
| ( ( between @ SV32 @ SV98 @ SV237 )
= $false )
| ( ( equidistant @ SV98 @ SV237 @ SV205 @ SV251 )
= $false )
| ( ( equidistant @ SV32 @ SV98 @ SV157 @ SV205 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[704]) ).
thf(714,plain,
! [SV217: $i,SV122: $i,SV254: $i,SV240: $i,SV261: $i,SV175: $i,SV258: $i,SV56: $i] :
( ( ( equidistant @ SV56 @ SV258 @ SV175 @ SV261 )
= $false )
| ( ( ~ ( equidistant @ SV240 @ SV258 @ SV254 @ SV261 )
| ~ ( between @ SV56 @ SV122 @ SV240 )
| ~ ( between @ SV175 @ SV217 @ SV254 )
| ( equidistant @ SV122 @ SV258 @ SV217 @ SV261 ) )
= $true )
| ( ( equidistant @ SV56 @ SV240 @ SV175 @ SV254 )
= $false )
| ( ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[706]) ).
thf(715,plain,
! [SV241: $i,SV123: $i,SV255: $i,SV218: $i,SV176: $i,SV57: $i] :
( ( ( equidistant @ SV57 @ SV176 @ SV218 @ SV255 )
= $false )
| ( ( equidistant @ SV123 @ SV176 @ SV241 @ SV255 )
= $true )
| ( ( equidistant @ SV57 @ SV123 @ SV218 @ SV241 )
= $false )
| ( ( between @ SV218 @ SV241 @ SV255 )
= $false )
| ( ( between @ SV57 @ SV123 @ SV176 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[707]) ).
thf(716,plain,
! [SV219: $i,SV124: $i,SV256: $i,SV242: $i,SV262: $i,SV177: $i,SV259: $i,SV58: $i] :
( ( ( equidistant @ SV58 @ SV259 @ SV177 @ SV262 )
= $false )
| ( ( ~ ( equidistant @ SV242 @ SV259 @ SV256 @ SV262 )
| ~ ( between @ SV58 @ SV124 @ SV242 )
| ~ ( between @ SV177 @ SV219 @ SV256 )
| ( equidistant @ SV124 @ SV259 @ SV219 @ SV262 ) )
= $true )
| ( ( equidistant @ SV124 @ SV242 @ SV219 @ SV256 )
= $false )
| ( ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[708]) ).
thf(717,plain,
! [SV247: $i,SV138: $i,SV227: $i,SV6: $i,SV260: $i,SV187: $i,SV257: $i,SV73: $i] :
( ( ( ~ ( equidistant @ SV73 @ SV257 @ SV187 @ SV260 ) )
= $true )
| ( ( ~ ( between @ SV6 @ SV73 @ SV227 )
| ~ ( between @ SV138 @ SV187 @ SV247 )
| ( SV6 = SV73 )
| ( equidistant @ SV227 @ SV257 @ SV247 @ SV260 ) )
= $true )
| ( ( equidistant @ SV6 @ SV257 @ SV138 @ SV260 )
= $false )
| ( ( equidistant @ SV73 @ SV227 @ SV187 @ SV247 )
= $false )
| ( ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(718,plain,
! [SV217: $i,SV175: $i,SV122: $i,SV56: $i,SV261: $i,SV254: $i,SV258: $i,SV240: $i] :
( ( ( ~ ( equidistant @ SV240 @ SV258 @ SV254 @ SV261 ) )
= $true )
| ( ( ~ ( between @ SV56 @ SV122 @ SV240 )
| ~ ( between @ SV175 @ SV217 @ SV254 )
| ( equidistant @ SV122 @ SV258 @ SV217 @ SV261 ) )
= $true )
| ( ( equidistant @ SV56 @ SV258 @ SV175 @ SV261 )
= $false )
| ( ( equidistant @ SV56 @ SV240 @ SV175 @ SV254 )
= $false )
| ( ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(719,plain,
! [SV219: $i,SV177: $i,SV124: $i,SV58: $i,SV262: $i,SV256: $i,SV259: $i,SV242: $i] :
( ( ( ~ ( equidistant @ SV242 @ SV259 @ SV256 @ SV262 ) )
= $true )
| ( ( ~ ( between @ SV58 @ SV124 @ SV242 )
| ~ ( between @ SV177 @ SV219 @ SV256 )
| ( equidistant @ SV124 @ SV259 @ SV219 @ SV262 ) )
= $true )
| ( ( equidistant @ SV58 @ SV259 @ SV177 @ SV262 )
= $false )
| ( ( equidistant @ SV124 @ SV242 @ SV219 @ SV256 )
= $false )
| ( ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[716]) ).
thf(720,plain,
! [SV247: $i,SV138: $i,SV227: $i,SV6: $i,SV260: $i,SV187: $i,SV257: $i,SV73: $i] :
( ( ( equidistant @ SV73 @ SV257 @ SV187 @ SV260 )
= $false )
| ( ( ~ ( between @ SV6 @ SV73 @ SV227 )
| ~ ( between @ SV138 @ SV187 @ SV247 )
| ( SV6 = SV73 )
| ( equidistant @ SV227 @ SV257 @ SV247 @ SV260 ) )
= $true )
| ( ( equidistant @ SV6 @ SV257 @ SV138 @ SV260 )
= $false )
| ( ( equidistant @ SV73 @ SV227 @ SV187 @ SV247 )
= $false )
| ( ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[717]) ).
thf(721,plain,
! [SV217: $i,SV175: $i,SV122: $i,SV56: $i,SV261: $i,SV254: $i,SV258: $i,SV240: $i] :
( ( ( equidistant @ SV240 @ SV258 @ SV254 @ SV261 )
= $false )
| ( ( ~ ( between @ SV56 @ SV122 @ SV240 )
| ~ ( between @ SV175 @ SV217 @ SV254 )
| ( equidistant @ SV122 @ SV258 @ SV217 @ SV261 ) )
= $true )
| ( ( equidistant @ SV56 @ SV258 @ SV175 @ SV261 )
= $false )
| ( ( equidistant @ SV56 @ SV240 @ SV175 @ SV254 )
= $false )
| ( ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[718]) ).
thf(722,plain,
! [SV219: $i,SV177: $i,SV124: $i,SV58: $i,SV262: $i,SV256: $i,SV259: $i,SV242: $i] :
( ( ( equidistant @ SV242 @ SV259 @ SV256 @ SV262 )
= $false )
| ( ( ~ ( between @ SV58 @ SV124 @ SV242 )
| ~ ( between @ SV177 @ SV219 @ SV256 )
| ( equidistant @ SV124 @ SV259 @ SV219 @ SV262 ) )
= $true )
| ( ( equidistant @ SV58 @ SV259 @ SV177 @ SV262 )
= $false )
| ( ( equidistant @ SV124 @ SV242 @ SV219 @ SV256 )
= $false )
| ( ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[719]) ).
thf(723,plain,
! [SV260: $i,SV257: $i,SV247: $i,SV187: $i,SV138: $i,SV227: $i,SV73: $i,SV6: $i] :
( ( ( ~ ( between @ SV6 @ SV73 @ SV227 ) )
= $true )
| ( ( ~ ( between @ SV138 @ SV187 @ SV247 )
| ( SV6 = SV73 )
| ( equidistant @ SV227 @ SV257 @ SV247 @ SV260 ) )
= $true )
| ( ( equidistant @ SV73 @ SV257 @ SV187 @ SV260 )
= $false )
| ( ( equidistant @ SV6 @ SV257 @ SV138 @ SV260 )
= $false )
| ( ( equidistant @ SV73 @ SV227 @ SV187 @ SV247 )
= $false )
| ( ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[720]) ).
thf(724,plain,
! [SV261: $i,SV258: $i,SV254: $i,SV217: $i,SV175: $i,SV240: $i,SV122: $i,SV56: $i] :
( ( ( ~ ( between @ SV56 @ SV122 @ SV240 ) )
= $true )
| ( ( ~ ( between @ SV175 @ SV217 @ SV254 )
| ( equidistant @ SV122 @ SV258 @ SV217 @ SV261 ) )
= $true )
| ( ( equidistant @ SV240 @ SV258 @ SV254 @ SV261 )
= $false )
| ( ( equidistant @ SV56 @ SV258 @ SV175 @ SV261 )
= $false )
| ( ( equidistant @ SV56 @ SV240 @ SV175 @ SV254 )
= $false )
| ( ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[721]) ).
thf(725,plain,
! [SV262: $i,SV259: $i,SV256: $i,SV219: $i,SV177: $i,SV242: $i,SV124: $i,SV58: $i] :
( ( ( ~ ( between @ SV58 @ SV124 @ SV242 ) )
= $true )
| ( ( ~ ( between @ SV177 @ SV219 @ SV256 )
| ( equidistant @ SV124 @ SV259 @ SV219 @ SV262 ) )
= $true )
| ( ( equidistant @ SV242 @ SV259 @ SV256 @ SV262 )
= $false )
| ( ( equidistant @ SV58 @ SV259 @ SV177 @ SV262 )
= $false )
| ( ( equidistant @ SV124 @ SV242 @ SV219 @ SV256 )
= $false )
| ( ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(726,plain,
! [SV260: $i,SV257: $i,SV247: $i,SV187: $i,SV138: $i,SV227: $i,SV73: $i,SV6: $i] :
( ( ( between @ SV6 @ SV73 @ SV227 )
= $false )
| ( ( ~ ( between @ SV138 @ SV187 @ SV247 )
| ( SV6 = SV73 )
| ( equidistant @ SV227 @ SV257 @ SV247 @ SV260 ) )
= $true )
| ( ( equidistant @ SV73 @ SV257 @ SV187 @ SV260 )
= $false )
| ( ( equidistant @ SV6 @ SV257 @ SV138 @ SV260 )
= $false )
| ( ( equidistant @ SV73 @ SV227 @ SV187 @ SV247 )
= $false )
| ( ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[723]) ).
thf(727,plain,
! [SV261: $i,SV258: $i,SV254: $i,SV217: $i,SV175: $i,SV240: $i,SV122: $i,SV56: $i] :
( ( ( between @ SV56 @ SV122 @ SV240 )
= $false )
| ( ( ~ ( between @ SV175 @ SV217 @ SV254 )
| ( equidistant @ SV122 @ SV258 @ SV217 @ SV261 ) )
= $true )
| ( ( equidistant @ SV240 @ SV258 @ SV254 @ SV261 )
= $false )
| ( ( equidistant @ SV56 @ SV258 @ SV175 @ SV261 )
= $false )
| ( ( equidistant @ SV56 @ SV240 @ SV175 @ SV254 )
= $false )
| ( ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[724]) ).
thf(728,plain,
! [SV262: $i,SV259: $i,SV256: $i,SV219: $i,SV177: $i,SV242: $i,SV124: $i,SV58: $i] :
( ( ( between @ SV58 @ SV124 @ SV242 )
= $false )
| ( ( ~ ( between @ SV177 @ SV219 @ SV256 )
| ( equidistant @ SV124 @ SV259 @ SV219 @ SV262 ) )
= $true )
| ( ( equidistant @ SV242 @ SV259 @ SV256 @ SV262 )
= $false )
| ( ( equidistant @ SV58 @ SV259 @ SV177 @ SV262 )
= $false )
| ( ( equidistant @ SV124 @ SV242 @ SV219 @ SV256 )
= $false )
| ( ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[725]) ).
thf(729,plain,
! [SV260: $i,SV257: $i,SV227: $i,SV73: $i,SV6: $i,SV247: $i,SV187: $i,SV138: $i] :
( ( ( ~ ( between @ SV138 @ SV187 @ SV247 ) )
= $true )
| ( ( ( SV6 = SV73 )
| ( equidistant @ SV227 @ SV257 @ SV247 @ SV260 ) )
= $true )
| ( ( between @ SV6 @ SV73 @ SV227 )
= $false )
| ( ( equidistant @ SV73 @ SV257 @ SV187 @ SV260 )
= $false )
| ( ( equidistant @ SV6 @ SV257 @ SV138 @ SV260 )
= $false )
| ( ( equidistant @ SV73 @ SV227 @ SV187 @ SV247 )
= $false )
| ( ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[726]) ).
thf(730,plain,
! [SV240: $i,SV56: $i,SV261: $i,SV258: $i,SV122: $i,SV254: $i,SV217: $i,SV175: $i] :
( ( ( ~ ( between @ SV175 @ SV217 @ SV254 ) )
= $true )
| ( ( equidistant @ SV122 @ SV258 @ SV217 @ SV261 )
= $true )
| ( ( between @ SV56 @ SV122 @ SV240 )
= $false )
| ( ( equidistant @ SV240 @ SV258 @ SV254 @ SV261 )
= $false )
| ( ( equidistant @ SV56 @ SV258 @ SV175 @ SV261 )
= $false )
| ( ( equidistant @ SV56 @ SV240 @ SV175 @ SV254 )
= $false )
| ( ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(731,plain,
! [SV242: $i,SV58: $i,SV262: $i,SV259: $i,SV124: $i,SV256: $i,SV219: $i,SV177: $i] :
( ( ( ~ ( between @ SV177 @ SV219 @ SV256 ) )
= $true )
| ( ( equidistant @ SV124 @ SV259 @ SV219 @ SV262 )
= $true )
| ( ( between @ SV58 @ SV124 @ SV242 )
= $false )
| ( ( equidistant @ SV242 @ SV259 @ SV256 @ SV262 )
= $false )
| ( ( equidistant @ SV58 @ SV259 @ SV177 @ SV262 )
= $false )
| ( ( equidistant @ SV124 @ SV242 @ SV219 @ SV256 )
= $false )
| ( ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[728]) ).
thf(732,plain,
! [SV260: $i,SV257: $i,SV227: $i,SV73: $i,SV6: $i,SV247: $i,SV187: $i,SV138: $i] :
( ( ( between @ SV138 @ SV187 @ SV247 )
= $false )
| ( ( ( SV6 = SV73 )
| ( equidistant @ SV227 @ SV257 @ SV247 @ SV260 ) )
= $true )
| ( ( between @ SV6 @ SV73 @ SV227 )
= $false )
| ( ( equidistant @ SV73 @ SV257 @ SV187 @ SV260 )
= $false )
| ( ( equidistant @ SV6 @ SV257 @ SV138 @ SV260 )
= $false )
| ( ( equidistant @ SV73 @ SV227 @ SV187 @ SV247 )
= $false )
| ( ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[729]) ).
thf(733,plain,
! [SV240: $i,SV56: $i,SV261: $i,SV258: $i,SV122: $i,SV254: $i,SV217: $i,SV175: $i] :
( ( ( between @ SV175 @ SV217 @ SV254 )
= $false )
| ( ( equidistant @ SV122 @ SV258 @ SV217 @ SV261 )
= $true )
| ( ( between @ SV56 @ SV122 @ SV240 )
= $false )
| ( ( equidistant @ SV240 @ SV258 @ SV254 @ SV261 )
= $false )
| ( ( equidistant @ SV56 @ SV258 @ SV175 @ SV261 )
= $false )
| ( ( equidistant @ SV56 @ SV240 @ SV175 @ SV254 )
= $false )
| ( ( equidistant @ SV56 @ SV122 @ SV175 @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[730]) ).
thf(734,plain,
! [SV242: $i,SV58: $i,SV262: $i,SV259: $i,SV124: $i,SV256: $i,SV219: $i,SV177: $i] :
( ( ( between @ SV177 @ SV219 @ SV256 )
= $false )
| ( ( equidistant @ SV124 @ SV259 @ SV219 @ SV262 )
= $true )
| ( ( between @ SV58 @ SV124 @ SV242 )
= $false )
| ( ( equidistant @ SV242 @ SV259 @ SV256 @ SV262 )
= $false )
| ( ( equidistant @ SV58 @ SV259 @ SV177 @ SV262 )
= $false )
| ( ( equidistant @ SV124 @ SV242 @ SV219 @ SV256 )
= $false )
| ( ( equidistant @ SV58 @ SV124 @ SV177 @ SV219 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[731]) ).
thf(735,plain,
! [SV187: $i,SV138: $i,SV260: $i,SV247: $i,SV257: $i,SV227: $i,SV73: $i,SV6: $i] :
( ( ( SV6 = SV73 )
= $true )
| ( ( equidistant @ SV227 @ SV257 @ SV247 @ SV260 )
= $true )
| ( ( between @ SV138 @ SV187 @ SV247 )
= $false )
| ( ( between @ SV6 @ SV73 @ SV227 )
= $false )
| ( ( equidistant @ SV73 @ SV257 @ SV187 @ SV260 )
= $false )
| ( ( equidistant @ SV6 @ SV257 @ SV138 @ SV260 )
= $false )
| ( ( equidistant @ SV73 @ SV227 @ SV187 @ SV247 )
= $false )
| ( ( equidistant @ SV6 @ SV73 @ SV138 @ SV187 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(736,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[156,735,734,733,715,713,712,711,710,705,687,685,679,671,668,667,666,663,662,661,654,653,652,642,641,638,629,628,625,624,623,622,607,589,588,552,548,547,546,545,544,543,542,511,489,487,485,481,474,450,441,439,438,431,409,404,366,354,352,351,350,344,343,342,332,330,315,314,311,310,307,305,272,251,250,249]) ).
thf(737,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[736]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO062-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.03 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.18 % Computer : n020.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Oct 6 10:03:06 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 129.08/21.84
% 129.08/21.84 No.of.Axioms: 75
% 129.08/21.84
% 129.08/21.84 Length.of.Defs: 0
% 129.08/21.84
% 129.08/21.84 Contains.Choice.Funs: false
% 129.08/21.84 ........................
% 129.08/21.84
% 129.08/21.84 ********************************
% 129.08/21.84 * All subproblems solved! *
% 129.08/21.84 ********************************
% 129.08/21.84 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:75,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:736,loop_count:0,foatp_calls:1,translation:fof_full)
% 129.08/21.84
% 129.08/21.84 %**** Beginning of derivation protocol ****
% 129.08/21.84 % SZS output start CNFRefutation
% See solution above
% 129.08/21.85
% 129.08/21.85 %**** End of derivation protocol ****
% 129.08/21.85 %**** no. of clauses in derivation: 737 ****
% 129.08/21.85 %**** clause counter: 736 ****
% 129.08/21.85
% 129.08/21.85 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:75,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:736,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------