%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO037-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n008.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 10:17:38 AM UTC 2026
% Result : Unsatisfiable 55.20s 9.56s
% Output : CNFRefutation 55.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 62
% Syntax : Number of formulae : 573 ( 363 unt; 0 typ; 0 def)
% Number of atoms : 3451 (1195 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 7979 ( 808 ~;1212 |; 0 &;5959 @)
% ( 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; 9 con; 0-6 aty)
% Number of variables : 2246 ( 0 ^;2246 !; 0 ?;2246 :)
% 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_lower_dimension_point_1,type,
lower_dimension_point_1: $i ).
thf(tp_lower_dimension_point_2,type,
lower_dimension_point_2: $i ).
thf(tp_lower_dimension_point_3,type,
lower_dimension_point_3: $i ).
thf(tp_reflection,type,
reflection: $i > $i > $i ).
thf(tp_u,type,
u: $i ).
thf(tp_v,type,
v: $i ).
thf(tp_w,type,
w: $i ).
thf(tp_x,type,
x: $i ).
thf(1,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_3) ).
thf(2,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_2) ).
thf(3,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_1) ).
thf(4,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ X )
| ( between @ U @ V @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b9) ).
thf(5,axiom,
! [U: $i,V: $i,X: $i,W: $i] :
( ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b8) ).
thf(6,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ V @ X )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b7) ).
thf(7,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b6) ).
thf(8,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ X )
| ( between @ V @ W @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b5) ).
thf(9,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ V @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b4) ).
thf(10,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( U = V )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_2) ).
thf(11,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_1) ).
thf(12,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b3) ).
thf(13,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
thf(14,axiom,
! [U: $i,V: $i] : ( between @ U @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2) ).
thf(15,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
thf(16,axiom,
! [U: $i,W: $i,X: $i,V: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ( between @ V @ W @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b1) ).
thf(17,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3) ).
thf(18,axiom,
! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r6) ).
thf(19,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r5) ).
thf(20,axiom,
! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_3) ).
thf(21,axiom,
! [W: $i,X: $i,Y: $i,Z: $i,U: $i,V: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ( ( extension @ U @ V @ W @ X )
= ( extension @ U @ V @ Y @ Z ) )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_2) ).
thf(22,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( U = V )
| ( W
= ( extension @ U @ V @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_1) ).
thf(23,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ V @ X )
| ~ ( equidistant @ V @ W @ V @ X )
| ( U = V )
| ( W = X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9) ).
thf(24,axiom,
! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ U @ W @ U1 @ W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8) ).
thf(25,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7) ).
thf(26,axiom,
! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).
thf(27,axiom,
! [U: $i] :
( U
= ( reflection @ U @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3_2) ).
thf(28,axiom,
! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3_1) ).
thf(29,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_2) ).
thf(30,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_1) ).
thf(31,axiom,
! [Y: $i,U: $i,V: $i,W: $i,X: $i] :
( ( Y
!= ( extension @ U @ V @ W @ X ) )
| ( between @ U @ V @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b0) ).
thf(32,axiom,
! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e1) ).
thf(33,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ~ ( equidistant @ W @ X @ Y @ Z )
| ( equidistant @ U @ V @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5) ).
thf(34,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_5) ).
thf(35,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_4) ).
thf(36,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_3) ).
thf(37,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_2) ).
thf(38,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_1) ).
thf(39,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3) ).
thf(40,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
thf(41,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
thf(42,axiom,
! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflection) ).
thf(43,axiom,
! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity2) ).
thf(44,axiom,
! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity1) ).
thf(45,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid3) ).
thf(46,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid2) ).
thf(47,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid1) ).
thf(48,axiom,
! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ W @ X @ V )
| ~ ( equidistant @ Y @ W @ Y @ V )
| ~ ( equidistant @ Z @ W @ Z @ V )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y )
| ( W = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_dimension) ).
thf(49,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
thf(50,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).
thf(51,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).
thf(52,axiom,
! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ Y @ X @ W )
| ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch2) ).
thf(53,axiom,
! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ Y @ X @ W )
| ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch1) ).
thf(54,axiom,
! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(55,axiom,
! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i,V: $i,V1: $i] :
( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
| ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
| ~ ( equidistant @ X @ V @ X1 @ V1 )
| ~ ( equidistant @ Y @ V @ Y1 @ V1 )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equidistant @ Z @ V @ Z1 @ V1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).
thf(56,axiom,
! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
thf(57,axiom,
! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
thf(58,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(59,axiom,
! [X: $i,Y: $i,Z: $i,V: $i,V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
thf(60,axiom,
! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(61,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(62,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[61]) ).
thf(63,negated_conjecture,
( ( v
= ( extension @ u @ v @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
| ~ ( 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 ) )
| ~ ( between @ u @ v @ ( extension @ u @ v @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lengthen) ).
thf(64,plain,
$false = $false,
inference(unfold_def,[status(thm)],[62]) ).
thf(65,plain,
( ( lower_dimension_point_1 != lower_dimension_point_3 )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(66,plain,
( ( lower_dimension_point_2 != lower_dimension_point_3 )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(67,plain,
( ( lower_dimension_point_1 != lower_dimension_point_2 )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(68,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)],[4]) ).
thf(69,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)],[5]) ).
thf(70,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)],[6]) ).
thf(71,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)],[7]) ).
thf(72,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)],[8]) ).
thf(73,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)],[9]) ).
thf(74,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)],[10]) ).
thf(75,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)],[11]) ).
thf(76,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(77,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(78,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(79,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(80,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)],[16]) ).
thf(81,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(82,plain,
( ( ! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(83,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(84,plain,
( ( ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(85,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)],[21]) ).
thf(86,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)],[22]) ).
thf(87,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)],[23]) ).
thf(88,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)],[24]) ).
thf(89,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(90,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(91,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(92,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(93,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(94,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(95,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)],[31]) ).
thf(96,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(97,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)],[33]) ).
thf(98,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)],[34]) ).
thf(99,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)],[35]) ).
thf(100,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)],[36]) ).
thf(101,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)],[37]) ).
thf(102,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)],[38]) ).
thf(103,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)],[39]) ).
thf(104,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)],[40]) ).
thf(105,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[41]) ).
thf(106,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(107,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)],[43]) ).
thf(108,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)],[44]) ).
thf(109,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)],[45]) ).
thf(110,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)],[46]) ).
thf(111,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)],[47]) ).
thf(112,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)],[48]) ).
thf(113,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(114,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(115,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(116,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)],[52]) ).
thf(117,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)],[53]) ).
thf(118,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(119,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)],[55]) ).
thf(120,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(121,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(122,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[58]) ).
thf(123,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)],[59]) ).
thf(124,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(125,plain,
( ( ( v
= ( extension @ u @ v @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
| ~ ( 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 ) )
| ~ ( between @ u @ v @ ( extension @ u @ v @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(126,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[64]) ).
thf(127,plain,
( ( ( v
= ( extension @ u @ v @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
| ~ ( 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 ) )
| ~ ( between @ u @ v @ ( extension @ u @ v @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(128,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(129,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)],[123]) ).
thf(130,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(131,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(132,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(133,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)],[119]) ).
thf(134,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(135,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)],[117]) ).
thf(136,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)],[116]) ).
thf(137,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(138,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(139,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(140,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)],[112]) ).
thf(141,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)],[111]) ).
thf(142,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)],[110]) ).
thf(143,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)],[109]) ).
thf(144,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)],[108]) ).
thf(145,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)],[107]) ).
thf(146,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(147,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(148,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(149,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(150,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(151,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(152,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(153,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(154,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(155,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)],[97]) ).
thf(156,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(157,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)],[95]) ).
thf(158,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(159,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(160,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(161,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(162,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(163,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(164,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)],[88]) ).
thf(165,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)],[87]) ).
thf(166,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( U = V )
| ( W
= ( extension @ U @ V @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(167,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)],[85]) ).
thf(168,plain,
( ( ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(169,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(170,plain,
( ( ! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(171,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(172,plain,
( ( ! [U: $i,W: $i,X: $i,V: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ( between @ V @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(173,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(174,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(175,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(176,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(177,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(178,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( U = V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(179,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)],[73]) ).
thf(180,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)],[72]) ).
thf(181,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)],[71]) ).
thf(182,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)],[70]) ).
thf(183,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)],[69]) ).
thf(184,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)],[68]) ).
thf(185,plain,
( ( lower_dimension_point_1 != lower_dimension_point_2 )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(186,plain,
( ( lower_dimension_point_2 != lower_dimension_point_3 )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(187,plain,
( ( lower_dimension_point_1 != lower_dimension_point_3 )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(188,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[126]) ).
thf(189,plain,
( ( lower_dimension_point_1 != lower_dimension_point_2 )
= $true ),
inference(unfold_def,[status(thm)],[185]) ).
thf(190,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( reflection @ SX1 @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[162]) ).
thf(191,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)],[157]) ).
thf(192,plain,
( ( lower_dimension_point_1 != lower_dimension_point_3 )
= $true ),
inference(unfold_def,[status(thm)],[187]) ).
thf(193,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)],[172]) ).
thf(194,plain,
( ( lower_dimension_point_2 != lower_dimension_point_3 )
= $true ),
inference(unfold_def,[status(thm)],[186]) ).
thf(195,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( SX1
= ( reflection @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[160]) ).
thf(196,plain,
( ( ( v
= ( extension @ u @ v @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true )
| ( ( ~ ( 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 ) )
| ~ ( between @ u @ v @ ( extension @ u @ v @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(197,plain,
! [SV1: $i] :
( ( ! [SY200: $i] : ( equidistant @ SV1 @ SY200 @ SY200 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(198,plain,
! [SV2: $i] :
( ( ! [SY201: $i,SY202: $i,SY203: $i,SY204: $i,SY205: $i] :
( ~ ( equidistant @ SV2 @ SY201 @ SY202 @ SY203 )
| ~ ( equidistant @ SV2 @ SY201 @ SY204 @ SY205 )
| ( equidistant @ SY202 @ SY203 @ SY204 @ SY205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(199,plain,
! [SV3: $i] :
( ( ! [SY206: $i,SY207: $i] :
( ~ ( equidistant @ SV3 @ SY206 @ SY207 @ SY207 )
| ( SV3 = SY206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(200,plain,
! [SV4: $i] :
( ( ! [SY208: $i,SY209: $i,SY210: $i] : ( between @ SV4 @ SY208 @ ( extension @ SV4 @ SY208 @ SY209 @ SY210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(201,plain,
! [SV5: $i] :
( ( ! [SY211: $i,SY212: $i,SY213: $i] : ( equidistant @ SV5 @ ( extension @ SY211 @ SV5 @ SY212 @ SY213 ) @ SY212 @ SY213 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(202,plain,
! [SV6: $i] :
( ( ! [SY214: $i,SY215: $i,SY216: $i,SY217: $i,SY218: $i,SY219: $i,SY220: $i] :
( ~ ( equidistant @ SV6 @ SY214 @ SY215 @ SY216 )
| ~ ( equidistant @ SY214 @ SY217 @ SY216 @ SY218 )
| ~ ( equidistant @ SV6 @ SY219 @ SY215 @ SY220 )
| ~ ( equidistant @ SY214 @ SY219 @ SY216 @ SY220 )
| ~ ( between @ SV6 @ SY214 @ SY217 )
| ~ ( between @ SY215 @ SY216 @ SY218 )
| ( SV6 = SY214 )
| ( equidistant @ SY217 @ SY219 @ SY218 @ SY220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(203,plain,
! [SV7: $i] :
( ( ! [SY221: $i] :
( ~ ( between @ SV7 @ SY221 @ SV7 )
| ( SV7 = SY221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(204,plain,
! [SV8: $i] :
( ( ! [SY222: $i,SY223: $i,SY224: $i,SY225: $i] :
( ~ ( between @ SV8 @ SY222 @ SY223 )
| ~ ( between @ SY224 @ SY225 @ SY223 )
| ( between @ SY222 @ ( inner_pasch @ SV8 @ SY222 @ SY223 @ SY225 @ SY224 ) @ SY224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(205,plain,
! [SV9: $i] :
( ( ! [SY226: $i,SY227: $i,SY228: $i,SY229: $i] :
( ~ ( between @ SV9 @ SY226 @ SY227 )
| ~ ( between @ SY228 @ SY229 @ SY227 )
| ( between @ SY229 @ ( inner_pasch @ SV9 @ SY226 @ SY227 @ SY229 @ SY228 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(206,plain,
( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(207,plain,
( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(208,plain,
( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(209,plain,
! [SV10: $i] :
( ( ! [SY230: $i,SY231: $i,SY232: $i,SY233: $i] :
( ~ ( equidistant @ SV10 @ SY230 @ SV10 @ SY231 )
| ~ ( equidistant @ SY232 @ SY230 @ SY232 @ SY231 )
| ~ ( equidistant @ SY233 @ SY230 @ SY233 @ SY231 )
| ( between @ SV10 @ SY232 @ SY233 )
| ( between @ SY232 @ SY233 @ SV10 )
| ( between @ SY233 @ SV10 @ SY232 )
| ( SY230 = SY231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(210,plain,
! [SV11: $i] :
( ( ! [SY234: $i,SY235: $i,SY236: $i,SY237: $i] :
( ~ ( between @ SV11 @ SY234 @ SY235 )
| ~ ( between @ SY236 @ SY234 @ SY237 )
| ( SV11 = SY234 )
| ( between @ SV11 @ SY236 @ ( euclid1 @ SV11 @ SY236 @ SY234 @ SY237 @ SY235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(211,plain,
! [SV12: $i] :
( ( ! [SY238: $i,SY239: $i,SY240: $i,SY241: $i] :
( ~ ( between @ SV12 @ SY238 @ SY239 )
| ~ ( between @ SY240 @ SY238 @ SY241 )
| ( SV12 = SY238 )
| ( between @ SV12 @ SY241 @ ( euclid2 @ SV12 @ SY240 @ SY238 @ SY241 @ SY239 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(212,plain,
! [SV13: $i] :
( ( ! [SY242: $i,SY243: $i,SY244: $i,SY245: $i] :
( ~ ( between @ SV13 @ SY242 @ SY243 )
| ~ ( between @ SY244 @ SY242 @ SY245 )
| ( SV13 = SY242 )
| ( between @ ( euclid1 @ SV13 @ SY244 @ SY242 @ SY245 @ SY243 ) @ SY243 @ ( euclid2 @ SV13 @ SY244 @ SY242 @ SY245 @ SY243 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(213,plain,
! [SV14: $i] :
( ( ! [SY246: $i,SY247: $i,SY248: $i,SY249: $i,SY250: $i] :
( ~ ( equidistant @ SV14 @ SY246 @ SV14 @ SY247 )
| ~ ( equidistant @ SV14 @ SY248 @ SV14 @ SY249 )
| ~ ( between @ SV14 @ SY246 @ SY248 )
| ~ ( between @ SY246 @ SY250 @ SY248 )
| ( between @ SY247 @ ( continuous @ SV14 @ SY246 @ SY247 @ SY250 @ SY248 @ SY249 ) @ SY249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(214,plain,
! [SV15: $i] :
( ( ! [SY251: $i,SY252: $i,SY253: $i,SY254: $i,SY255: $i] :
( ~ ( equidistant @ SV15 @ SY251 @ SV15 @ SY252 )
| ~ ( equidistant @ SV15 @ SY253 @ SV15 @ SY254 )
| ~ ( between @ SV15 @ SY251 @ SY253 )
| ~ ( between @ SY251 @ SY255 @ SY253 )
| ( equidistant @ SV15 @ SY255 @ SV15 @ ( continuous @ SV15 @ SY251 @ SY252 @ SY255 @ SY253 @ SY254 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(215,plain,
! [SV16: $i] :
( ( ! [SY256: $i] :
( ( reflection @ SV16 @ SY256 )
= ( extension @ SV16 @ SY256 @ SV16 @ SY256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(216,plain,
! [SV17: $i] :
( ( ! [SY257: $i] : ( equidistant @ SV17 @ SY257 @ SV17 @ SY257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(217,plain,
! [SV18: $i] :
( ( ! [SY258: $i,SY259: $i,SY260: $i] :
( ~ ( equidistant @ SV18 @ SY258 @ SY259 @ SY260 )
| ( equidistant @ SY259 @ SY260 @ SV18 @ SY258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(218,plain,
! [SV19: $i] :
( ( ! [SY261: $i,SY262: $i,SY263: $i] :
( ~ ( equidistant @ SV19 @ SY261 @ SY262 @ SY263 )
| ( equidistant @ SY261 @ SV19 @ SY262 @ SY263 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(219,plain,
! [SV20: $i] :
( ( ! [SY264: $i,SY265: $i,SY266: $i] :
( ~ ( equidistant @ SV20 @ SY264 @ SY265 @ SY266 )
| ( equidistant @ SV20 @ SY264 @ SY266 @ SY265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(220,plain,
! [SV21: $i] :
( ( ! [SY267: $i,SY268: $i,SY269: $i] :
( ~ ( equidistant @ SV21 @ SY267 @ SY268 @ SY269 )
| ( equidistant @ SY267 @ SV21 @ SY269 @ SY268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(221,plain,
! [SV22: $i] :
( ( ! [SY270: $i,SY271: $i,SY272: $i] :
( ~ ( equidistant @ SV22 @ SY270 @ SY271 @ SY272 )
| ( equidistant @ SY271 @ SY272 @ SY270 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(222,plain,
! [SV23: $i] :
( ( ! [SY273: $i,SY274: $i,SY275: $i] :
( ~ ( equidistant @ SV23 @ SY273 @ SY274 @ SY275 )
| ( equidistant @ SY275 @ SY274 @ SV23 @ SY273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(223,plain,
! [SV24: $i] :
( ( ! [SY276: $i,SY277: $i,SY278: $i] :
( ~ ( equidistant @ SV24 @ SY276 @ SY277 @ SY278 )
| ( equidistant @ SY278 @ SY277 @ SY276 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(224,plain,
! [SV25: $i] :
( ( ! [SY279: $i,SY280: $i,SY281: $i,SY282: $i,SY283: $i] :
( ~ ( equidistant @ SV25 @ SY279 @ SY280 @ SY281 )
| ~ ( equidistant @ SY280 @ SY281 @ SY282 @ SY283 )
| ( equidistant @ SV25 @ SY279 @ SY282 @ SY283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(225,plain,
! [SV26: $i] :
( ( ! [SY284: $i,SY285: $i] :
( SV26
= ( extension @ SY284 @ SV26 @ SY285 @ SY285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(226,plain,
! [SV27: $i] :
( ( ! [SY286: $i] : ( between @ SV27 @ SY286 @ ( reflection @ SV27 @ SY286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(227,plain,
! [SV28: $i] :
( ( ! [SY287: $i] : ( equidistant @ SV28 @ ( reflection @ SY287 @ SV28 ) @ SY287 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(228,plain,
! [SV29: $i] :
( ( SV29
= ( reflection @ SV29 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(229,plain,
! [SV30: $i] :
( ( ! [SY288: $i] : ( equidistant @ SV30 @ SV30 @ SY288 @ SY288 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(230,plain,
! [SV31: $i] :
( ( ! [SY289: $i,SY290: $i,SY291: $i,SY292: $i,SY293: $i] :
( ~ ( equidistant @ SV31 @ SY289 @ SY290 @ SY291 )
| ~ ( equidistant @ SY289 @ SY292 @ SY291 @ SY293 )
| ~ ( between @ SV31 @ SY289 @ SY292 )
| ~ ( between @ SY290 @ SY291 @ SY293 )
| ( equidistant @ SV31 @ SY292 @ SY290 @ SY293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(231,plain,
! [SV32: $i] :
( ( ! [SY294: $i,SY295: $i,SY296: $i] :
( ~ ( between @ SV32 @ SY294 @ SY295 )
| ~ ( between @ SV32 @ SY294 @ SY296 )
| ~ ( equidistant @ SY294 @ SY295 @ SY294 @ SY296 )
| ( SV32 = SY294 )
| ( SY295 = SY296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(232,plain,
! [SV33: $i] :
( ( ! [SY297: $i,SY298: $i] :
( ~ ( between @ SV33 @ SY297 @ SY298 )
| ( SV33 = SY297 )
| ( SY298
= ( extension @ SV33 @ SY297 @ SY297 @ SY298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(233,plain,
! [SV34: $i] :
( ( ! [SY299: $i,SY300: $i,SY301: $i,SY302: $i,SY303: $i] :
( ~ ( equidistant @ SV34 @ SY299 @ SY300 @ SY301 )
| ( ( extension @ SY302 @ SY303 @ SV34 @ SY299 )
= ( extension @ SY302 @ SY303 @ SY300 @ SY301 ) )
| ( SY302 = SY303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(234,plain,
! [SV35: $i] :
( ( ! [SY304: $i] :
( ( ( extension @ SV35 @ SY304 @ SV35 @ SY304 )
= ( extension @ SV35 @ SY304 @ SY304 @ SV35 ) )
| ( SV35 = SY304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(235,plain,
! [SV36: $i] :
( ( ! [SY305: $i] : ( equidistant @ SV36 @ SY305 @ SV36 @ ( reflection @ ( reflection @ SY305 @ SV36 ) @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(236,plain,
! [SV37: $i] :
( ( ! [SY306: $i] :
( SV37
= ( reflection @ ( reflection @ SV37 @ SY306 ) @ SY306 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(237,plain,
! [SV38: $i] :
( ( ! [SY307: $i] : ( between @ SV38 @ SY307 @ SY307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(238,plain,
! [SV39: $i] :
( ( ! [SY308: $i,SY309: $i] :
( ~ ( between @ SV39 @ SY308 @ SY309 )
| ( between @ SY309 @ SY308 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(239,plain,
! [SV40: $i] :
( ( ! [SY310: $i] : ( between @ SV40 @ SV40 @ SY310 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(240,plain,
! [SV41: $i] :
( ( ! [SY311: $i,SY312: $i] :
( ~ ( between @ SV41 @ SY311 @ SY312 )
| ~ ( between @ SY311 @ SV41 @ SY312 )
| ( SV41 = SY311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(241,plain,
! [SV42: $i] :
( ( ! [SY313: $i,SY314: $i] :
( ~ ( between @ SV42 @ SY313 @ SY314 )
| ~ ( between @ SV42 @ SY314 @ SY313 )
| ( SY313 = SY314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(242,plain,
! [SV43: $i] :
( ( ! [SY315: $i,SY316: $i] :
( ~ ( between @ SV43 @ SY315 @ SY316 )
| ~ ( between @ SY315 @ SV43 @ SY316 )
| ( SV43 = SY315 )
| ( SY315 = SY316 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(243,plain,
! [SV44: $i] :
( ( ! [SY317: $i,SY318: $i] :
( ~ ( between @ SV44 @ SY317 @ SY318 )
| ~ ( between @ SV44 @ SY318 @ SY317 )
| ( SV44 = SY317 )
| ( SY317 = SY318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(244,plain,
! [SV45: $i] :
( ( ! [SY319: $i,SY320: $i,SY321: $i] :
( ~ ( between @ SV45 @ SY319 @ SY320 )
| ~ ( between @ SY319 @ SY320 @ SY321 )
| ( between @ SV45 @ SY319 @ SY320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(245,plain,
! [SV46: $i] :
( ( ! [SY322: $i,SY323: $i,SY324: $i] :
( ~ ( between @ SV46 @ SY322 @ SY323 )
| ~ ( between @ SV46 @ SY323 @ SY324 )
| ( between @ SY322 @ SY323 @ SY324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(246,plain,
! [SV47: $i] :
( ( ! [SY325: $i,SY326: $i,SY327: $i] :
( ~ ( between @ SV47 @ SY325 @ SY326 )
| ~ ( between @ SY325 @ SY326 @ SY327 )
| ( between @ SV47 @ SY326 @ SY327 )
| ( SY325 = SY326 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(247,plain,
! [SV48: $i] :
( ( ! [SY328: $i,SY329: $i,SY330: $i] :
( ~ ( between @ SV48 @ SY328 @ SY329 )
| ~ ( between @ SY328 @ SY329 @ SY330 )
| ( between @ SV48 @ SY328 @ SY330 )
| ( SY328 = SY329 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(248,plain,
! [SV49: $i] :
( ( ! [SY331: $i,SY332: $i,SY333: $i] :
( ~ ( between @ SV49 @ SY331 @ SY332 )
| ~ ( between @ SY331 @ SY333 @ SY332 )
| ( between @ SV49 @ SY333 @ SY332 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(249,plain,
! [SV50: $i] :
( ( ! [SY334: $i,SY335: $i,SY336: $i] :
( ~ ( between @ SV50 @ SY334 @ SY335 )
| ~ ( between @ SV50 @ SY335 @ SY336 )
| ( between @ SV50 @ SY334 @ SY336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(250,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(251,plain,
( ( lower_dimension_point_1 = lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(252,plain,
! [SV51: $i] :
( ( ! [SY337: $i] :
( ( SV51
!= ( reflection @ SY337 @ SV51 ) )
| ( SY337 = SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(253,plain,
! [SV52: $i] :
( ( ! [SY338: $i,SY339: $i,SY340: $i,SY341: $i] :
( ( SV52
!= ( extension @ SY338 @ SY339 @ SY340 @ SY341 ) )
| ( between @ SY338 @ SY339 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(254,plain,
( ( lower_dimension_point_1 = lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(255,plain,
! [SV53: $i] :
( ( ! [SY342: $i,SY343: $i,SY344: $i] :
( ~ ( between @ SV53 @ SY342 @ SY343 )
| ( SV53 != SY343 )
| ( between @ SY344 @ SY342 @ SY343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(256,plain,
( ( lower_dimension_point_2 = lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(257,plain,
! [SV54: $i] :
( ( ! [SY345: $i] :
( ( SV54 != SY345 )
| ( SY345
= ( reflection @ SV54 @ SY345 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(258,plain,
( ( ( ~ ( 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 )
| ( ( ~ ( between @ u @ v @ ( extension @ u @ v @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true )
| ( ( v
= ( extension @ u @ v @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(259,plain,
! [SV55: $i,SV1: $i] :
( ( equidistant @ SV1 @ SV55 @ SV55 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(260,plain,
! [SV56: $i,SV2: $i] :
( ( ! [SY346: $i,SY347: $i,SY348: $i,SY349: $i] :
( ~ ( equidistant @ SV2 @ SV56 @ SY346 @ SY347 )
| ~ ( equidistant @ SV2 @ SV56 @ SY348 @ SY349 )
| ( equidistant @ SY346 @ SY347 @ SY348 @ SY349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(261,plain,
! [SV57: $i,SV3: $i] :
( ( ! [SY350: $i] :
( ~ ( equidistant @ SV3 @ SV57 @ SY350 @ SY350 )
| ( SV3 = SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(262,plain,
! [SV58: $i,SV4: $i] :
( ( ! [SY351: $i,SY352: $i] : ( between @ SV4 @ SV58 @ ( extension @ SV4 @ SV58 @ SY351 @ SY352 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(263,plain,
! [SV59: $i,SV5: $i] :
( ( ! [SY353: $i,SY354: $i] : ( equidistant @ SV5 @ ( extension @ SV59 @ SV5 @ SY353 @ SY354 ) @ SY353 @ SY354 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(264,plain,
! [SV60: $i,SV6: $i] :
( ( ! [SY355: $i,SY356: $i,SY357: $i,SY358: $i,SY359: $i,SY360: $i] :
( ~ ( equidistant @ SV6 @ SV60 @ SY355 @ SY356 )
| ~ ( equidistant @ SV60 @ SY357 @ SY356 @ SY358 )
| ~ ( equidistant @ SV6 @ SY359 @ SY355 @ SY360 )
| ~ ( equidistant @ SV60 @ SY359 @ SY356 @ SY360 )
| ~ ( between @ SV6 @ SV60 @ SY357 )
| ~ ( between @ SY355 @ SY356 @ SY358 )
| ( SV6 = SV60 )
| ( equidistant @ SY357 @ SY359 @ SY358 @ SY360 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(265,plain,
! [SV61: $i,SV7: $i] :
( ( ~ ( between @ SV7 @ SV61 @ SV7 )
| ( SV7 = SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(266,plain,
! [SV62: $i,SV8: $i] :
( ( ! [SY361: $i,SY362: $i,SY363: $i] :
( ~ ( between @ SV8 @ SV62 @ SY361 )
| ~ ( between @ SY362 @ SY363 @ SY361 )
| ( between @ SV62 @ ( inner_pasch @ SV8 @ SV62 @ SY361 @ SY363 @ SY362 ) @ SY362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(267,plain,
! [SV63: $i,SV9: $i] :
( ( ! [SY364: $i,SY365: $i,SY366: $i] :
( ~ ( between @ SV9 @ SV63 @ SY364 )
| ~ ( between @ SY365 @ SY366 @ SY364 )
| ( between @ SY366 @ ( inner_pasch @ SV9 @ SV63 @ SY364 @ SY366 @ SY365 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(268,plain,
! [SV64: $i,SV10: $i] :
( ( ! [SY367: $i,SY368: $i,SY369: $i] :
( ~ ( equidistant @ SV10 @ SV64 @ SV10 @ SY367 )
| ~ ( equidistant @ SY368 @ SV64 @ SY368 @ SY367 )
| ~ ( equidistant @ SY369 @ SV64 @ SY369 @ SY367 )
| ( between @ SV10 @ SY368 @ SY369 )
| ( between @ SY368 @ SY369 @ SV10 )
| ( between @ SY369 @ SV10 @ SY368 )
| ( SV64 = SY367 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(269,plain,
! [SV65: $i,SV11: $i] :
( ( ! [SY370: $i,SY371: $i,SY372: $i] :
( ~ ( between @ SV11 @ SV65 @ SY370 )
| ~ ( between @ SY371 @ SV65 @ SY372 )
| ( SV11 = SV65 )
| ( between @ SV11 @ SY371 @ ( euclid1 @ SV11 @ SY371 @ SV65 @ SY372 @ SY370 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(270,plain,
! [SV66: $i,SV12: $i] :
( ( ! [SY373: $i,SY374: $i,SY375: $i] :
( ~ ( between @ SV12 @ SV66 @ SY373 )
| ~ ( between @ SY374 @ SV66 @ SY375 )
| ( SV12 = SV66 )
| ( between @ SV12 @ SY375 @ ( euclid2 @ SV12 @ SY374 @ SV66 @ SY375 @ SY373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(271,plain,
! [SV67: $i,SV13: $i] :
( ( ! [SY376: $i,SY377: $i,SY378: $i] :
( ~ ( between @ SV13 @ SV67 @ SY376 )
| ~ ( between @ SY377 @ SV67 @ SY378 )
| ( SV13 = SV67 )
| ( between @ ( euclid1 @ SV13 @ SY377 @ SV67 @ SY378 @ SY376 ) @ SY376 @ ( euclid2 @ SV13 @ SY377 @ SV67 @ SY378 @ SY376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(272,plain,
! [SV68: $i,SV14: $i] :
( ( ! [SY379: $i,SY380: $i,SY381: $i,SY382: $i] :
( ~ ( equidistant @ SV14 @ SV68 @ SV14 @ SY379 )
| ~ ( equidistant @ SV14 @ SY380 @ SV14 @ SY381 )
| ~ ( between @ SV14 @ SV68 @ SY380 )
| ~ ( between @ SV68 @ SY382 @ SY380 )
| ( between @ SY379 @ ( continuous @ SV14 @ SV68 @ SY379 @ SY382 @ SY380 @ SY381 ) @ SY381 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(273,plain,
! [SV69: $i,SV15: $i] :
( ( ! [SY383: $i,SY384: $i,SY385: $i,SY386: $i] :
( ~ ( equidistant @ SV15 @ SV69 @ SV15 @ SY383 )
| ~ ( equidistant @ SV15 @ SY384 @ SV15 @ SY385 )
| ~ ( between @ SV15 @ SV69 @ SY384 )
| ~ ( between @ SV69 @ SY386 @ SY384 )
| ( equidistant @ SV15 @ SY386 @ SV15 @ ( continuous @ SV15 @ SV69 @ SY383 @ SY386 @ SY384 @ SY385 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(274,plain,
! [SV70: $i,SV16: $i] :
( ( ( reflection @ SV16 @ SV70 )
= ( extension @ SV16 @ SV70 @ SV16 @ SV70 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(275,plain,
! [SV71: $i,SV17: $i] :
( ( equidistant @ SV17 @ SV71 @ SV17 @ SV71 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(276,plain,
! [SV72: $i,SV18: $i] :
( ( ! [SY387: $i,SY388: $i] :
( ~ ( equidistant @ SV18 @ SV72 @ SY387 @ SY388 )
| ( equidistant @ SY387 @ SY388 @ SV18 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(277,plain,
! [SV73: $i,SV19: $i] :
( ( ! [SY389: $i,SY390: $i] :
( ~ ( equidistant @ SV19 @ SV73 @ SY389 @ SY390 )
| ( equidistant @ SV73 @ SV19 @ SY389 @ SY390 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(278,plain,
! [SV74: $i,SV20: $i] :
( ( ! [SY391: $i,SY392: $i] :
( ~ ( equidistant @ SV20 @ SV74 @ SY391 @ SY392 )
| ( equidistant @ SV20 @ SV74 @ SY392 @ SY391 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(279,plain,
! [SV75: $i,SV21: $i] :
( ( ! [SY393: $i,SY394: $i] :
( ~ ( equidistant @ SV21 @ SV75 @ SY393 @ SY394 )
| ( equidistant @ SV75 @ SV21 @ SY394 @ SY393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(280,plain,
! [SV76: $i,SV22: $i] :
( ( ! [SY395: $i,SY396: $i] :
( ~ ( equidistant @ SV22 @ SV76 @ SY395 @ SY396 )
| ( equidistant @ SY395 @ SY396 @ SV76 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(281,plain,
! [SV77: $i,SV23: $i] :
( ( ! [SY397: $i,SY398: $i] :
( ~ ( equidistant @ SV23 @ SV77 @ SY397 @ SY398 )
| ( equidistant @ SY398 @ SY397 @ SV23 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(282,plain,
! [SV78: $i,SV24: $i] :
( ( ! [SY399: $i,SY400: $i] :
( ~ ( equidistant @ SV24 @ SV78 @ SY399 @ SY400 )
| ( equidistant @ SY400 @ SY399 @ SV78 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(283,plain,
! [SV79: $i,SV25: $i] :
( ( ! [SY401: $i,SY402: $i,SY403: $i,SY404: $i] :
( ~ ( equidistant @ SV25 @ SV79 @ SY401 @ SY402 )
| ~ ( equidistant @ SY401 @ SY402 @ SY403 @ SY404 )
| ( equidistant @ SV25 @ SV79 @ SY403 @ SY404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(284,plain,
! [SV80: $i,SV26: $i] :
( ( ! [SY405: $i] :
( SV26
= ( extension @ SV80 @ SV26 @ SY405 @ SY405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(285,plain,
! [SV81: $i,SV27: $i] :
( ( between @ SV27 @ SV81 @ ( reflection @ SV27 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(286,plain,
! [SV82: $i,SV28: $i] :
( ( equidistant @ SV28 @ ( reflection @ SV82 @ SV28 ) @ SV82 @ SV28 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(287,plain,
! [SV83: $i,SV30: $i] :
( ( equidistant @ SV30 @ SV30 @ SV83 @ SV83 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(288,plain,
! [SV84: $i,SV31: $i] :
( ( ! [SY406: $i,SY407: $i,SY408: $i,SY409: $i] :
( ~ ( equidistant @ SV31 @ SV84 @ SY406 @ SY407 )
| ~ ( equidistant @ SV84 @ SY408 @ SY407 @ SY409 )
| ~ ( between @ SV31 @ SV84 @ SY408 )
| ~ ( between @ SY406 @ SY407 @ SY409 )
| ( equidistant @ SV31 @ SY408 @ SY406 @ SY409 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(289,plain,
! [SV85: $i,SV32: $i] :
( ( ! [SY410: $i,SY411: $i] :
( ~ ( between @ SV32 @ SV85 @ SY410 )
| ~ ( between @ SV32 @ SV85 @ SY411 )
| ~ ( equidistant @ SV85 @ SY410 @ SV85 @ SY411 )
| ( SV32 = SV85 )
| ( SY410 = SY411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(290,plain,
! [SV86: $i,SV33: $i] :
( ( ! [SY412: $i] :
( ~ ( between @ SV33 @ SV86 @ SY412 )
| ( SV33 = SV86 )
| ( SY412
= ( extension @ SV33 @ SV86 @ SV86 @ SY412 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(291,plain,
! [SV87: $i,SV34: $i] :
( ( ! [SY413: $i,SY414: $i,SY415: $i,SY416: $i] :
( ~ ( equidistant @ SV34 @ SV87 @ SY413 @ SY414 )
| ( ( extension @ SY415 @ SY416 @ SV34 @ SV87 )
= ( extension @ SY415 @ SY416 @ SY413 @ SY414 ) )
| ( SY415 = SY416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(292,plain,
! [SV88: $i,SV35: $i] :
( ( ( ( extension @ SV35 @ SV88 @ SV35 @ SV88 )
= ( extension @ SV35 @ SV88 @ SV88 @ SV35 ) )
| ( SV35 = SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(293,plain,
! [SV89: $i,SV36: $i] :
( ( equidistant @ SV36 @ SV89 @ SV36 @ ( reflection @ ( reflection @ SV89 @ SV36 ) @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(294,plain,
! [SV90: $i,SV37: $i] :
( ( SV37
= ( reflection @ ( reflection @ SV37 @ SV90 ) @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(295,plain,
! [SV91: $i,SV38: $i] :
( ( between @ SV38 @ SV91 @ SV91 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(296,plain,
! [SV92: $i,SV39: $i] :
( ( ! [SY417: $i] :
( ~ ( between @ SV39 @ SV92 @ SY417 )
| ( between @ SY417 @ SV92 @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(297,plain,
! [SV93: $i,SV40: $i] :
( ( between @ SV40 @ SV40 @ SV93 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(298,plain,
! [SV94: $i,SV41: $i] :
( ( ! [SY418: $i] :
( ~ ( between @ SV41 @ SV94 @ SY418 )
| ~ ( between @ SV94 @ SV41 @ SY418 )
| ( SV41 = SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(299,plain,
! [SV95: $i,SV42: $i] :
( ( ! [SY419: $i] :
( ~ ( between @ SV42 @ SV95 @ SY419 )
| ~ ( between @ SV42 @ SY419 @ SV95 )
| ( SV95 = SY419 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(300,plain,
! [SV96: $i,SV43: $i] :
( ( ! [SY420: $i] :
( ~ ( between @ SV43 @ SV96 @ SY420 )
| ~ ( between @ SV96 @ SV43 @ SY420 )
| ( SV43 = SV96 )
| ( SV96 = SY420 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(301,plain,
! [SV97: $i,SV44: $i] :
( ( ! [SY421: $i] :
( ~ ( between @ SV44 @ SV97 @ SY421 )
| ~ ( between @ SV44 @ SY421 @ SV97 )
| ( SV44 = SV97 )
| ( SV97 = SY421 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(302,plain,
! [SV98: $i,SV45: $i] :
( ( ! [SY422: $i,SY423: $i] :
( ~ ( between @ SV45 @ SV98 @ SY422 )
| ~ ( between @ SV98 @ SY422 @ SY423 )
| ( between @ SV45 @ SV98 @ SY422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(303,plain,
! [SV99: $i,SV46: $i] :
( ( ! [SY424: $i,SY425: $i] :
( ~ ( between @ SV46 @ SV99 @ SY424 )
| ~ ( between @ SV46 @ SY424 @ SY425 )
| ( between @ SV99 @ SY424 @ SY425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(304,plain,
! [SV100: $i,SV47: $i] :
( ( ! [SY426: $i,SY427: $i] :
( ~ ( between @ SV47 @ SV100 @ SY426 )
| ~ ( between @ SV100 @ SY426 @ SY427 )
| ( between @ SV47 @ SY426 @ SY427 )
| ( SV100 = SY426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(305,plain,
! [SV101: $i,SV48: $i] :
( ( ! [SY428: $i,SY429: $i] :
( ~ ( between @ SV48 @ SV101 @ SY428 )
| ~ ( between @ SV101 @ SY428 @ SY429 )
| ( between @ SV48 @ SV101 @ SY429 )
| ( SV101 = SY428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(306,plain,
! [SV102: $i,SV49: $i] :
( ( ! [SY430: $i,SY431: $i] :
( ~ ( between @ SV49 @ SV102 @ SY430 )
| ~ ( between @ SV102 @ SY431 @ SY430 )
| ( between @ SV49 @ SY431 @ SY430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(307,plain,
! [SV103: $i,SV50: $i] :
( ( ! [SY432: $i,SY433: $i] :
( ~ ( between @ SV50 @ SV103 @ SY432 )
| ~ ( between @ SV50 @ SY432 @ SY433 )
| ( between @ SV50 @ SV103 @ SY433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(308,plain,
! [SV104: $i,SV51: $i] :
( ( ( SV51
!= ( reflection @ SV104 @ SV51 ) )
| ( SV104 = SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(309,plain,
! [SV105: $i,SV52: $i] :
( ( ! [SY434: $i,SY435: $i,SY436: $i] :
( ( SV52
!= ( extension @ SV105 @ SY434 @ SY435 @ SY436 ) )
| ( between @ SV105 @ SY434 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(310,plain,
! [SV106: $i,SV53: $i] :
( ( ! [SY437: $i,SY438: $i] :
( ~ ( between @ SV53 @ SV106 @ SY437 )
| ( SV53 != SY437 )
| ( between @ SY438 @ SV106 @ SY437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(311,plain,
! [SV107: $i,SV54: $i] :
( ( ( SV54 != SV107 )
| ( SV107
= ( reflection @ SV54 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(312,plain,
( ( ( 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 ) )
= $false )
| ( ( ~ ( between @ u @ v @ ( extension @ u @ v @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true )
| ( ( v
= ( extension @ u @ v @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(313,plain,
! [SV108: $i,SV56: $i,SV2: $i] :
( ( ! [SY439: $i,SY440: $i,SY441: $i] :
( ~ ( equidistant @ SV2 @ SV56 @ SV108 @ SY439 )
| ~ ( equidistant @ SV2 @ SV56 @ SY440 @ SY441 )
| ( equidistant @ SV108 @ SY439 @ SY440 @ SY441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(314,plain,
! [SV109: $i,SV57: $i,SV3: $i] :
( ( ~ ( equidistant @ SV3 @ SV57 @ SV109 @ SV109 )
| ( SV3 = SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(315,plain,
! [SV110: $i,SV58: $i,SV4: $i] :
( ( ! [SY442: $i] : ( between @ SV4 @ SV58 @ ( extension @ SV4 @ SV58 @ SV110 @ SY442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(316,plain,
! [SV111: $i,SV59: $i,SV5: $i] :
( ( ! [SY443: $i] : ( equidistant @ SV5 @ ( extension @ SV59 @ SV5 @ SV111 @ SY443 ) @ SV111 @ SY443 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(317,plain,
! [SV112: $i,SV60: $i,SV6: $i] :
( ( ! [SY444: $i,SY445: $i,SY446: $i,SY447: $i,SY448: $i] :
( ~ ( equidistant @ SV6 @ SV60 @ SV112 @ SY444 )
| ~ ( equidistant @ SV60 @ SY445 @ SY444 @ SY446 )
| ~ ( equidistant @ SV6 @ SY447 @ SV112 @ SY448 )
| ~ ( equidistant @ SV60 @ SY447 @ SY444 @ SY448 )
| ~ ( between @ SV6 @ SV60 @ SY445 )
| ~ ( between @ SV112 @ SY444 @ SY446 )
| ( SV6 = SV60 )
| ( equidistant @ SY445 @ SY447 @ SY446 @ SY448 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(318,plain,
! [SV61: $i,SV7: $i] :
( ( ( ~ ( between @ SV7 @ SV61 @ SV7 ) )
= $true )
| ( ( SV7 = SV61 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(319,plain,
! [SV113: $i,SV62: $i,SV8: $i] :
( ( ! [SY449: $i,SY450: $i] :
( ~ ( between @ SV8 @ SV62 @ SV113 )
| ~ ( between @ SY449 @ SY450 @ SV113 )
| ( between @ SV62 @ ( inner_pasch @ SV8 @ SV62 @ SV113 @ SY450 @ SY449 ) @ SY449 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(320,plain,
! [SV114: $i,SV63: $i,SV9: $i] :
( ( ! [SY451: $i,SY452: $i] :
( ~ ( between @ SV9 @ SV63 @ SV114 )
| ~ ( between @ SY451 @ SY452 @ SV114 )
| ( between @ SY452 @ ( inner_pasch @ SV9 @ SV63 @ SV114 @ SY452 @ SY451 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(321,plain,
! [SV115: $i,SV64: $i,SV10: $i] :
( ( ! [SY453: $i,SY454: $i] :
( ~ ( equidistant @ SV10 @ SV64 @ SV10 @ SV115 )
| ~ ( equidistant @ SY453 @ SV64 @ SY453 @ SV115 )
| ~ ( equidistant @ SY454 @ SV64 @ SY454 @ SV115 )
| ( between @ SV10 @ SY453 @ SY454 )
| ( between @ SY453 @ SY454 @ SV10 )
| ( between @ SY454 @ SV10 @ SY453 )
| ( SV64 = SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(322,plain,
! [SV116: $i,SV65: $i,SV11: $i] :
( ( ! [SY455: $i,SY456: $i] :
( ~ ( between @ SV11 @ SV65 @ SV116 )
| ~ ( between @ SY455 @ SV65 @ SY456 )
| ( SV11 = SV65 )
| ( between @ SV11 @ SY455 @ ( euclid1 @ SV11 @ SY455 @ SV65 @ SY456 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(323,plain,
! [SV117: $i,SV66: $i,SV12: $i] :
( ( ! [SY457: $i,SY458: $i] :
( ~ ( between @ SV12 @ SV66 @ SV117 )
| ~ ( between @ SY457 @ SV66 @ SY458 )
| ( SV12 = SV66 )
| ( between @ SV12 @ SY458 @ ( euclid2 @ SV12 @ SY457 @ SV66 @ SY458 @ SV117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(324,plain,
! [SV118: $i,SV67: $i,SV13: $i] :
( ( ! [SY459: $i,SY460: $i] :
( ~ ( between @ SV13 @ SV67 @ SV118 )
| ~ ( between @ SY459 @ SV67 @ SY460 )
| ( SV13 = SV67 )
| ( between @ ( euclid1 @ SV13 @ SY459 @ SV67 @ SY460 @ SV118 ) @ SV118 @ ( euclid2 @ SV13 @ SY459 @ SV67 @ SY460 @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(325,plain,
! [SV119: $i,SV68: $i,SV14: $i] :
( ( ! [SY461: $i,SY462: $i,SY463: $i] :
( ~ ( equidistant @ SV14 @ SV68 @ SV14 @ SV119 )
| ~ ( equidistant @ SV14 @ SY461 @ SV14 @ SY462 )
| ~ ( between @ SV14 @ SV68 @ SY461 )
| ~ ( between @ SV68 @ SY463 @ SY461 )
| ( between @ SV119 @ ( continuous @ SV14 @ SV68 @ SV119 @ SY463 @ SY461 @ SY462 ) @ SY462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(326,plain,
! [SV120: $i,SV69: $i,SV15: $i] :
( ( ! [SY464: $i,SY465: $i,SY466: $i] :
( ~ ( equidistant @ SV15 @ SV69 @ SV15 @ SV120 )
| ~ ( equidistant @ SV15 @ SY464 @ SV15 @ SY465 )
| ~ ( between @ SV15 @ SV69 @ SY464 )
| ~ ( between @ SV69 @ SY466 @ SY464 )
| ( equidistant @ SV15 @ SY466 @ SV15 @ ( continuous @ SV15 @ SV69 @ SV120 @ SY466 @ SY464 @ SY465 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(327,plain,
! [SV121: $i,SV72: $i,SV18: $i] :
( ( ! [SY467: $i] :
( ~ ( equidistant @ SV18 @ SV72 @ SV121 @ SY467 )
| ( equidistant @ SV121 @ SY467 @ SV18 @ SV72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(328,plain,
! [SV122: $i,SV73: $i,SV19: $i] :
( ( ! [SY468: $i] :
( ~ ( equidistant @ SV19 @ SV73 @ SV122 @ SY468 )
| ( equidistant @ SV73 @ SV19 @ SV122 @ SY468 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(329,plain,
! [SV123: $i,SV74: $i,SV20: $i] :
( ( ! [SY469: $i] :
( ~ ( equidistant @ SV20 @ SV74 @ SV123 @ SY469 )
| ( equidistant @ SV20 @ SV74 @ SY469 @ SV123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(330,plain,
! [SV124: $i,SV75: $i,SV21: $i] :
( ( ! [SY470: $i] :
( ~ ( equidistant @ SV21 @ SV75 @ SV124 @ SY470 )
| ( equidistant @ SV75 @ SV21 @ SY470 @ SV124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(331,plain,
! [SV125: $i,SV76: $i,SV22: $i] :
( ( ! [SY471: $i] :
( ~ ( equidistant @ SV22 @ SV76 @ SV125 @ SY471 )
| ( equidistant @ SV125 @ SY471 @ SV76 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(332,plain,
! [SV126: $i,SV77: $i,SV23: $i] :
( ( ! [SY472: $i] :
( ~ ( equidistant @ SV23 @ SV77 @ SV126 @ SY472 )
| ( equidistant @ SY472 @ SV126 @ SV23 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(333,plain,
! [SV127: $i,SV78: $i,SV24: $i] :
( ( ! [SY473: $i] :
( ~ ( equidistant @ SV24 @ SV78 @ SV127 @ SY473 )
| ( equidistant @ SY473 @ SV127 @ SV78 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(334,plain,
! [SV128: $i,SV79: $i,SV25: $i] :
( ( ! [SY474: $i,SY475: $i,SY476: $i] :
( ~ ( equidistant @ SV25 @ SV79 @ SV128 @ SY474 )
| ~ ( equidistant @ SV128 @ SY474 @ SY475 @ SY476 )
| ( equidistant @ SV25 @ SV79 @ SY475 @ SY476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(335,plain,
! [SV129: $i,SV80: $i,SV26: $i] :
( ( SV26
= ( extension @ SV80 @ SV26 @ SV129 @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(336,plain,
! [SV130: $i,SV84: $i,SV31: $i] :
( ( ! [SY477: $i,SY478: $i,SY479: $i] :
( ~ ( equidistant @ SV31 @ SV84 @ SV130 @ SY477 )
| ~ ( equidistant @ SV84 @ SY478 @ SY477 @ SY479 )
| ~ ( between @ SV31 @ SV84 @ SY478 )
| ~ ( between @ SV130 @ SY477 @ SY479 )
| ( equidistant @ SV31 @ SY478 @ SV130 @ SY479 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(337,plain,
! [SV131: $i,SV85: $i,SV32: $i] :
( ( ! [SY480: $i] :
( ~ ( between @ SV32 @ SV85 @ SV131 )
| ~ ( between @ SV32 @ SV85 @ SY480 )
| ~ ( equidistant @ SV85 @ SV131 @ SV85 @ SY480 )
| ( SV32 = SV85 )
| ( SV131 = SY480 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(338,plain,
! [SV132: $i,SV86: $i,SV33: $i] :
( ( ~ ( between @ SV33 @ SV86 @ SV132 )
| ( SV33 = SV86 )
| ( SV132
= ( extension @ SV33 @ SV86 @ SV86 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(339,plain,
! [SV133: $i,SV87: $i,SV34: $i] :
( ( ! [SY481: $i,SY482: $i,SY483: $i] :
( ~ ( equidistant @ SV34 @ SV87 @ SV133 @ SY481 )
| ( ( extension @ SY482 @ SY483 @ SV34 @ SV87 )
= ( extension @ SY482 @ SY483 @ SV133 @ SY481 ) )
| ( SY482 = SY483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(340,plain,
! [SV88: $i,SV35: $i] :
( ( ( ( extension @ SV35 @ SV88 @ SV35 @ SV88 )
= ( extension @ SV35 @ SV88 @ SV88 @ SV35 ) )
= $true )
| ( ( SV35 = SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(341,plain,
! [SV134: $i,SV92: $i,SV39: $i] :
( ( ~ ( between @ SV39 @ SV92 @ SV134 )
| ( between @ SV134 @ SV92 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(342,plain,
! [SV135: $i,SV94: $i,SV41: $i] :
( ( ~ ( between @ SV41 @ SV94 @ SV135 )
| ~ ( between @ SV94 @ SV41 @ SV135 )
| ( SV41 = SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[298]) ).
thf(343,plain,
! [SV136: $i,SV95: $i,SV42: $i] :
( ( ~ ( between @ SV42 @ SV95 @ SV136 )
| ~ ( between @ SV42 @ SV136 @ SV95 )
| ( SV95 = SV136 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(344,plain,
! [SV137: $i,SV96: $i,SV43: $i] :
( ( ~ ( between @ SV43 @ SV96 @ SV137 )
| ~ ( between @ SV96 @ SV43 @ SV137 )
| ( SV43 = SV96 )
| ( SV96 = SV137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(345,plain,
! [SV138: $i,SV97: $i,SV44: $i] :
( ( ~ ( between @ SV44 @ SV97 @ SV138 )
| ~ ( between @ SV44 @ SV138 @ SV97 )
| ( SV44 = SV97 )
| ( SV97 = SV138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(346,plain,
! [SV139: $i,SV98: $i,SV45: $i] :
( ( ! [SY484: $i] :
( ~ ( between @ SV45 @ SV98 @ SV139 )
| ~ ( between @ SV98 @ SV139 @ SY484 )
| ( between @ SV45 @ SV98 @ SV139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(347,plain,
! [SV140: $i,SV99: $i,SV46: $i] :
( ( ! [SY485: $i] :
( ~ ( between @ SV46 @ SV99 @ SV140 )
| ~ ( between @ SV46 @ SV140 @ SY485 )
| ( between @ SV99 @ SV140 @ SY485 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(348,plain,
! [SV141: $i,SV100: $i,SV47: $i] :
( ( ! [SY486: $i] :
( ~ ( between @ SV47 @ SV100 @ SV141 )
| ~ ( between @ SV100 @ SV141 @ SY486 )
| ( between @ SV47 @ SV141 @ SY486 )
| ( SV100 = SV141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(349,plain,
! [SV142: $i,SV101: $i,SV48: $i] :
( ( ! [SY487: $i] :
( ~ ( between @ SV48 @ SV101 @ SV142 )
| ~ ( between @ SV101 @ SV142 @ SY487 )
| ( between @ SV48 @ SV101 @ SY487 )
| ( SV101 = SV142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(350,plain,
! [SV143: $i,SV102: $i,SV49: $i] :
( ( ! [SY488: $i] :
( ~ ( between @ SV49 @ SV102 @ SV143 )
| ~ ( between @ SV102 @ SY488 @ SV143 )
| ( between @ SV49 @ SY488 @ SV143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(351,plain,
! [SV144: $i,SV103: $i,SV50: $i] :
( ( ! [SY489: $i] :
( ~ ( between @ SV50 @ SV103 @ SV144 )
| ~ ( between @ SV50 @ SV144 @ SY489 )
| ( between @ SV50 @ SV103 @ SY489 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(352,plain,
! [SV104: $i,SV51: $i] :
( ( ( SV51
!= ( reflection @ SV104 @ SV51 ) )
= $true )
| ( ( SV104 = SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(353,plain,
! [SV145: $i,SV105: $i,SV52: $i] :
( ( ! [SY490: $i,SY491: $i] :
( ( SV52
!= ( extension @ SV105 @ SV145 @ SY490 @ SY491 ) )
| ( between @ SV105 @ SV145 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(354,plain,
! [SV146: $i,SV106: $i,SV53: $i] :
( ( ! [SY492: $i] :
( ~ ( between @ SV53 @ SV106 @ SV146 )
| ( SV53 != SV146 )
| ( between @ SY492 @ SV106 @ SV146 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(355,plain,
! [SV107: $i,SV54: $i] :
( ( ( SV54 != SV107 )
= $true )
| ( ( SV107
= ( reflection @ SV54 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(356,plain,
( ( ( between @ u @ v @ ( extension @ u @ v @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $false )
| ( ( 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 ) )
= $false )
| ( ( v
= ( extension @ u @ v @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[312]) ).
thf(357,plain,
! [SV147: $i,SV108: $i,SV56: $i,SV2: $i] :
( ( ! [SY493: $i,SY494: $i] :
( ~ ( equidistant @ SV2 @ SV56 @ SV108 @ SV147 )
| ~ ( equidistant @ SV2 @ SV56 @ SY493 @ SY494 )
| ( equidistant @ SV108 @ SV147 @ SY493 @ SY494 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(358,plain,
! [SV109: $i,SV57: $i,SV3: $i] :
( ( ( ~ ( equidistant @ SV3 @ SV57 @ SV109 @ SV109 ) )
= $true )
| ( ( SV3 = SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(359,plain,
! [SV148: $i,SV110: $i,SV58: $i,SV4: $i] :
( ( between @ SV4 @ SV58 @ ( extension @ SV4 @ SV58 @ SV110 @ SV148 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(360,plain,
! [SV149: $i,SV111: $i,SV59: $i,SV5: $i] :
( ( equidistant @ SV5 @ ( extension @ SV59 @ SV5 @ SV111 @ SV149 ) @ SV111 @ SV149 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(361,plain,
! [SV150: $i,SV112: $i,SV60: $i,SV6: $i] :
( ( ! [SY495: $i,SY496: $i,SY497: $i,SY498: $i] :
( ~ ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
| ~ ( equidistant @ SV60 @ SY495 @ SV150 @ SY496 )
| ~ ( equidistant @ SV6 @ SY497 @ SV112 @ SY498 )
| ~ ( equidistant @ SV60 @ SY497 @ SV150 @ SY498 )
| ~ ( between @ SV6 @ SV60 @ SY495 )
| ~ ( between @ SV112 @ SV150 @ SY496 )
| ( SV6 = SV60 )
| ( equidistant @ SY495 @ SY497 @ SY496 @ SY498 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(362,plain,
! [SV61: $i,SV7: $i] :
( ( ( between @ SV7 @ SV61 @ SV7 )
= $false )
| ( ( SV7 = SV61 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(363,plain,
! [SV151: $i,SV113: $i,SV62: $i,SV8: $i] :
( ( ! [SY499: $i] :
( ~ ( between @ SV8 @ SV62 @ SV113 )
| ~ ( between @ SV151 @ SY499 @ SV113 )
| ( between @ SV62 @ ( inner_pasch @ SV8 @ SV62 @ SV113 @ SY499 @ SV151 ) @ SV151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(364,plain,
! [SV152: $i,SV114: $i,SV63: $i,SV9: $i] :
( ( ! [SY500: $i] :
( ~ ( between @ SV9 @ SV63 @ SV114 )
| ~ ( between @ SV152 @ SY500 @ SV114 )
| ( between @ SY500 @ ( inner_pasch @ SV9 @ SV63 @ SV114 @ SY500 @ SV152 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(365,plain,
! [SV153: $i,SV115: $i,SV64: $i,SV10: $i] :
( ( ! [SY501: $i] :
( ~ ( equidistant @ SV10 @ SV64 @ SV10 @ SV115 )
| ~ ( equidistant @ SV153 @ SV64 @ SV153 @ SV115 )
| ~ ( equidistant @ SY501 @ SV64 @ SY501 @ SV115 )
| ( between @ SV10 @ SV153 @ SY501 )
| ( between @ SV153 @ SY501 @ SV10 )
| ( between @ SY501 @ SV10 @ SV153 )
| ( SV64 = SV115 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(366,plain,
! [SV154: $i,SV116: $i,SV65: $i,SV11: $i] :
( ( ! [SY502: $i] :
( ~ ( between @ SV11 @ SV65 @ SV116 )
| ~ ( between @ SV154 @ SV65 @ SY502 )
| ( SV11 = SV65 )
| ( between @ SV11 @ SV154 @ ( euclid1 @ SV11 @ SV154 @ SV65 @ SY502 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(367,plain,
! [SV155: $i,SV117: $i,SV66: $i,SV12: $i] :
( ( ! [SY503: $i] :
( ~ ( between @ SV12 @ SV66 @ SV117 )
| ~ ( between @ SV155 @ SV66 @ SY503 )
| ( SV12 = SV66 )
| ( between @ SV12 @ SY503 @ ( euclid2 @ SV12 @ SV155 @ SV66 @ SY503 @ SV117 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(368,plain,
! [SV156: $i,SV118: $i,SV67: $i,SV13: $i] :
( ( ! [SY504: $i] :
( ~ ( between @ SV13 @ SV67 @ SV118 )
| ~ ( between @ SV156 @ SV67 @ SY504 )
| ( SV13 = SV67 )
| ( between @ ( euclid1 @ SV13 @ SV156 @ SV67 @ SY504 @ SV118 ) @ SV118 @ ( euclid2 @ SV13 @ SV156 @ SV67 @ SY504 @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(369,plain,
! [SV157: $i,SV119: $i,SV68: $i,SV14: $i] :
( ( ! [SY505: $i,SY506: $i] :
( ~ ( equidistant @ SV14 @ SV68 @ SV14 @ SV119 )
| ~ ( equidistant @ SV14 @ SV157 @ SV14 @ SY505 )
| ~ ( between @ SV14 @ SV68 @ SV157 )
| ~ ( between @ SV68 @ SY506 @ SV157 )
| ( between @ SV119 @ ( continuous @ SV14 @ SV68 @ SV119 @ SY506 @ SV157 @ SY505 ) @ SY505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(370,plain,
! [SV158: $i,SV120: $i,SV69: $i,SV15: $i] :
( ( ! [SY507: $i,SY508: $i] :
( ~ ( equidistant @ SV15 @ SV69 @ SV15 @ SV120 )
| ~ ( equidistant @ SV15 @ SV158 @ SV15 @ SY507 )
| ~ ( between @ SV15 @ SV69 @ SV158 )
| ~ ( between @ SV69 @ SY508 @ SV158 )
| ( equidistant @ SV15 @ SY508 @ SV15 @ ( continuous @ SV15 @ SV69 @ SV120 @ SY508 @ SV158 @ SY507 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(371,plain,
! [SV159: $i,SV121: $i,SV72: $i,SV18: $i] :
( ( ~ ( equidistant @ SV18 @ SV72 @ SV121 @ SV159 )
| ( equidistant @ SV121 @ SV159 @ SV18 @ SV72 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(372,plain,
! [SV160: $i,SV122: $i,SV73: $i,SV19: $i] :
( ( ~ ( equidistant @ SV19 @ SV73 @ SV122 @ SV160 )
| ( equidistant @ SV73 @ SV19 @ SV122 @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(373,plain,
! [SV161: $i,SV123: $i,SV74: $i,SV20: $i] :
( ( ~ ( equidistant @ SV20 @ SV74 @ SV123 @ SV161 )
| ( equidistant @ SV20 @ SV74 @ SV161 @ SV123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(374,plain,
! [SV162: $i,SV124: $i,SV75: $i,SV21: $i] :
( ( ~ ( equidistant @ SV21 @ SV75 @ SV124 @ SV162 )
| ( equidistant @ SV75 @ SV21 @ SV162 @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(375,plain,
! [SV163: $i,SV125: $i,SV76: $i,SV22: $i] :
( ( ~ ( equidistant @ SV22 @ SV76 @ SV125 @ SV163 )
| ( equidistant @ SV125 @ SV163 @ SV76 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(376,plain,
! [SV164: $i,SV126: $i,SV77: $i,SV23: $i] :
( ( ~ ( equidistant @ SV23 @ SV77 @ SV126 @ SV164 )
| ( equidistant @ SV164 @ SV126 @ SV23 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(377,plain,
! [SV165: $i,SV127: $i,SV78: $i,SV24: $i] :
( ( ~ ( equidistant @ SV24 @ SV78 @ SV127 @ SV165 )
| ( equidistant @ SV165 @ SV127 @ SV78 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(378,plain,
! [SV166: $i,SV128: $i,SV79: $i,SV25: $i] :
( ( ! [SY509: $i,SY510: $i] :
( ~ ( equidistant @ SV25 @ SV79 @ SV128 @ SV166 )
| ~ ( equidistant @ SV128 @ SV166 @ SY509 @ SY510 )
| ( equidistant @ SV25 @ SV79 @ SY509 @ SY510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(379,plain,
! [SV167: $i,SV130: $i,SV84: $i,SV31: $i] :
( ( ! [SY511: $i,SY512: $i] :
( ~ ( equidistant @ SV31 @ SV84 @ SV130 @ SV167 )
| ~ ( equidistant @ SV84 @ SY511 @ SV167 @ SY512 )
| ~ ( between @ SV31 @ SV84 @ SY511 )
| ~ ( between @ SV130 @ SV167 @ SY512 )
| ( equidistant @ SV31 @ SY511 @ SV130 @ SY512 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(380,plain,
! [SV168: $i,SV131: $i,SV85: $i,SV32: $i] :
( ( ~ ( between @ SV32 @ SV85 @ SV131 )
| ~ ( between @ SV32 @ SV85 @ SV168 )
| ~ ( equidistant @ SV85 @ SV131 @ SV85 @ SV168 )
| ( SV32 = SV85 )
| ( SV131 = SV168 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(381,plain,
! [SV132: $i,SV86: $i,SV33: $i] :
( ( ( ~ ( between @ SV33 @ SV86 @ SV132 ) )
= $true )
| ( ( ( SV33 = SV86 )
| ( SV132
= ( extension @ SV33 @ SV86 @ SV86 @ SV132 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(382,plain,
! [SV169: $i,SV133: $i,SV87: $i,SV34: $i] :
( ( ! [SY513: $i,SY514: $i] :
( ~ ( equidistant @ SV34 @ SV87 @ SV133 @ SV169 )
| ( ( extension @ SY513 @ SY514 @ SV34 @ SV87 )
= ( extension @ SY513 @ SY514 @ SV133 @ SV169 ) )
| ( SY513 = SY514 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(383,plain,
! [SV134: $i,SV92: $i,SV39: $i] :
( ( ( ~ ( between @ SV39 @ SV92 @ SV134 ) )
= $true )
| ( ( between @ SV134 @ SV92 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(384,plain,
! [SV135: $i,SV94: $i,SV41: $i] :
( ( ( ~ ( between @ SV41 @ SV94 @ SV135 ) )
= $true )
| ( ( ~ ( between @ SV94 @ SV41 @ SV135 )
| ( SV41 = SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(385,plain,
! [SV136: $i,SV95: $i,SV42: $i] :
( ( ( ~ ( between @ SV42 @ SV95 @ SV136 ) )
= $true )
| ( ( ~ ( between @ SV42 @ SV136 @ SV95 )
| ( SV95 = SV136 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(386,plain,
! [SV137: $i,SV96: $i,SV43: $i] :
( ( ( ~ ( between @ SV43 @ SV96 @ SV137 ) )
= $true )
| ( ( ~ ( between @ SV96 @ SV43 @ SV137 )
| ( SV43 = SV96 )
| ( SV96 = SV137 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(387,plain,
! [SV138: $i,SV97: $i,SV44: $i] :
( ( ( ~ ( between @ SV44 @ SV97 @ SV138 ) )
= $true )
| ( ( ~ ( between @ SV44 @ SV138 @ SV97 )
| ( SV44 = SV97 )
| ( SV97 = SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(388,plain,
! [SV170: $i,SV139: $i,SV98: $i,SV45: $i] :
( ( ~ ( between @ SV45 @ SV98 @ SV139 )
| ~ ( between @ SV98 @ SV139 @ SV170 )
| ( between @ SV45 @ SV98 @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(389,plain,
! [SV171: $i,SV140: $i,SV99: $i,SV46: $i] :
( ( ~ ( between @ SV46 @ SV99 @ SV140 )
| ~ ( between @ SV46 @ SV140 @ SV171 )
| ( between @ SV99 @ SV140 @ SV171 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(390,plain,
! [SV172: $i,SV141: $i,SV100: $i,SV47: $i] :
( ( ~ ( between @ SV47 @ SV100 @ SV141 )
| ~ ( between @ SV100 @ SV141 @ SV172 )
| ( between @ SV47 @ SV141 @ SV172 )
| ( SV100 = SV141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(391,plain,
! [SV173: $i,SV142: $i,SV101: $i,SV48: $i] :
( ( ~ ( between @ SV48 @ SV101 @ SV142 )
| ~ ( between @ SV101 @ SV142 @ SV173 )
| ( between @ SV48 @ SV101 @ SV173 )
| ( SV101 = SV142 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(392,plain,
! [SV174: $i,SV143: $i,SV102: $i,SV49: $i] :
( ( ~ ( between @ SV49 @ SV102 @ SV143 )
| ~ ( between @ SV102 @ SV174 @ SV143 )
| ( between @ SV49 @ SV174 @ SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(393,plain,
! [SV175: $i,SV144: $i,SV103: $i,SV50: $i] :
( ( ~ ( between @ SV50 @ SV103 @ SV144 )
| ~ ( between @ SV50 @ SV144 @ SV175 )
| ( between @ SV50 @ SV103 @ SV175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(394,plain,
! [SV104: $i,SV51: $i] :
( ( ( SV51
= ( reflection @ SV104 @ SV51 ) )
= $false )
| ( ( SV104 = SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(395,plain,
! [SV176: $i,SV145: $i,SV105: $i,SV52: $i] :
( ( ! [SY515: $i] :
( ( SV52
!= ( extension @ SV105 @ SV145 @ SV176 @ SY515 ) )
| ( between @ SV105 @ SV145 @ SV52 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(396,plain,
! [SV177: $i,SV146: $i,SV106: $i,SV53: $i] :
( ( ~ ( between @ SV53 @ SV106 @ SV146 )
| ( SV53 != SV146 )
| ( between @ SV177 @ SV106 @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(397,plain,
! [SV107: $i,SV54: $i] :
( ( ( SV54 = SV107 )
= $false )
| ( ( SV107
= ( reflection @ SV54 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(398,plain,
! [SV178: $i,SV147: $i,SV108: $i,SV56: $i,SV2: $i] :
( ( ! [SY516: $i] :
( ~ ( equidistant @ SV2 @ SV56 @ SV108 @ SV147 )
| ~ ( equidistant @ SV2 @ SV56 @ SV178 @ SY516 )
| ( equidistant @ SV108 @ SV147 @ SV178 @ SY516 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(399,plain,
! [SV109: $i,SV57: $i,SV3: $i] :
( ( ( equidistant @ SV3 @ SV57 @ SV109 @ SV109 )
= $false )
| ( ( SV3 = SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(400,plain,
! [SV179: $i,SV150: $i,SV112: $i,SV60: $i,SV6: $i] :
( ( ! [SY517: $i,SY518: $i,SY519: $i] :
( ~ ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
| ~ ( equidistant @ SV60 @ SV179 @ SV150 @ SY517 )
| ~ ( equidistant @ SV6 @ SY518 @ SV112 @ SY519 )
| ~ ( equidistant @ SV60 @ SY518 @ SV150 @ SY519 )
| ~ ( between @ SV6 @ SV60 @ SV179 )
| ~ ( between @ SV112 @ SV150 @ SY517 )
| ( SV6 = SV60 )
| ( equidistant @ SV179 @ SY518 @ SY517 @ SY519 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(401,plain,
! [SV180: $i,SV151: $i,SV113: $i,SV62: $i,SV8: $i] :
( ( ~ ( between @ SV8 @ SV62 @ SV113 )
| ~ ( between @ SV151 @ SV180 @ SV113 )
| ( between @ SV62 @ ( inner_pasch @ SV8 @ SV62 @ SV113 @ SV180 @ SV151 ) @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(402,plain,
! [SV181: $i,SV152: $i,SV114: $i,SV63: $i,SV9: $i] :
( ( ~ ( between @ SV9 @ SV63 @ SV114 )
| ~ ( between @ SV152 @ SV181 @ SV114 )
| ( between @ SV181 @ ( inner_pasch @ SV9 @ SV63 @ SV114 @ SV181 @ SV152 ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(403,plain,
! [SV182: $i,SV153: $i,SV115: $i,SV64: $i,SV10: $i] :
( ( ~ ( equidistant @ SV10 @ SV64 @ SV10 @ SV115 )
| ~ ( equidistant @ SV153 @ SV64 @ SV153 @ SV115 )
| ~ ( equidistant @ SV182 @ SV64 @ SV182 @ SV115 )
| ( between @ SV10 @ SV153 @ SV182 )
| ( between @ SV153 @ SV182 @ SV10 )
| ( between @ SV182 @ SV10 @ SV153 )
| ( SV64 = SV115 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(404,plain,
! [SV183: $i,SV154: $i,SV116: $i,SV65: $i,SV11: $i] :
( ( ~ ( between @ SV11 @ SV65 @ SV116 )
| ~ ( between @ SV154 @ SV65 @ SV183 )
| ( SV11 = SV65 )
| ( between @ SV11 @ SV154 @ ( euclid1 @ SV11 @ SV154 @ SV65 @ SV183 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(405,plain,
! [SV184: $i,SV155: $i,SV117: $i,SV66: $i,SV12: $i] :
( ( ~ ( between @ SV12 @ SV66 @ SV117 )
| ~ ( between @ SV155 @ SV66 @ SV184 )
| ( SV12 = SV66 )
| ( between @ SV12 @ SV184 @ ( euclid2 @ SV12 @ SV155 @ SV66 @ SV184 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(406,plain,
! [SV185: $i,SV156: $i,SV118: $i,SV67: $i,SV13: $i] :
( ( ~ ( between @ SV13 @ SV67 @ SV118 )
| ~ ( between @ SV156 @ SV67 @ SV185 )
| ( SV13 = SV67 )
| ( between @ ( euclid1 @ SV13 @ SV156 @ SV67 @ SV185 @ SV118 ) @ SV118 @ ( euclid2 @ SV13 @ SV156 @ SV67 @ SV185 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(407,plain,
! [SV186: $i,SV157: $i,SV119: $i,SV68: $i,SV14: $i] :
( ( ! [SY520: $i] :
( ~ ( equidistant @ SV14 @ SV68 @ SV14 @ SV119 )
| ~ ( equidistant @ SV14 @ SV157 @ SV14 @ SV186 )
| ~ ( between @ SV14 @ SV68 @ SV157 )
| ~ ( between @ SV68 @ SY520 @ SV157 )
| ( between @ SV119 @ ( continuous @ SV14 @ SV68 @ SV119 @ SY520 @ SV157 @ SV186 ) @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(408,plain,
! [SV187: $i,SV158: $i,SV120: $i,SV69: $i,SV15: $i] :
( ( ! [SY521: $i] :
( ~ ( equidistant @ SV15 @ SV69 @ SV15 @ SV120 )
| ~ ( equidistant @ SV15 @ SV158 @ SV15 @ SV187 )
| ~ ( between @ SV15 @ SV69 @ SV158 )
| ~ ( between @ SV69 @ SY521 @ SV158 )
| ( equidistant @ SV15 @ SY521 @ SV15 @ ( continuous @ SV15 @ SV69 @ SV120 @ SY521 @ SV158 @ SV187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(409,plain,
! [SV159: $i,SV121: $i,SV72: $i,SV18: $i] :
( ( ( ~ ( equidistant @ SV18 @ SV72 @ SV121 @ SV159 ) )
= $true )
| ( ( equidistant @ SV121 @ SV159 @ SV18 @ SV72 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(410,plain,
! [SV160: $i,SV122: $i,SV73: $i,SV19: $i] :
( ( ( ~ ( equidistant @ SV19 @ SV73 @ SV122 @ SV160 ) )
= $true )
| ( ( equidistant @ SV73 @ SV19 @ SV122 @ SV160 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(411,plain,
! [SV161: $i,SV123: $i,SV74: $i,SV20: $i] :
( ( ( ~ ( equidistant @ SV20 @ SV74 @ SV123 @ SV161 ) )
= $true )
| ( ( equidistant @ SV20 @ SV74 @ SV161 @ SV123 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[373]) ).
thf(412,plain,
! [SV162: $i,SV124: $i,SV75: $i,SV21: $i] :
( ( ( ~ ( equidistant @ SV21 @ SV75 @ SV124 @ SV162 ) )
= $true )
| ( ( equidistant @ SV75 @ SV21 @ SV162 @ SV124 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[374]) ).
thf(413,plain,
! [SV163: $i,SV125: $i,SV76: $i,SV22: $i] :
( ( ( ~ ( equidistant @ SV22 @ SV76 @ SV125 @ SV163 ) )
= $true )
| ( ( equidistant @ SV125 @ SV163 @ SV76 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(414,plain,
! [SV164: $i,SV126: $i,SV77: $i,SV23: $i] :
( ( ( ~ ( equidistant @ SV23 @ SV77 @ SV126 @ SV164 ) )
= $true )
| ( ( equidistant @ SV164 @ SV126 @ SV23 @ SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[376]) ).
thf(415,plain,
! [SV165: $i,SV127: $i,SV78: $i,SV24: $i] :
( ( ( ~ ( equidistant @ SV24 @ SV78 @ SV127 @ SV165 ) )
= $true )
| ( ( equidistant @ SV165 @ SV127 @ SV78 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[377]) ).
thf(416,plain,
! [SV188: $i,SV166: $i,SV128: $i,SV79: $i,SV25: $i] :
( ( ! [SY522: $i] :
( ~ ( equidistant @ SV25 @ SV79 @ SV128 @ SV166 )
| ~ ( equidistant @ SV128 @ SV166 @ SV188 @ SY522 )
| ( equidistant @ SV25 @ SV79 @ SV188 @ SY522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(417,plain,
! [SV189: $i,SV167: $i,SV130: $i,SV84: $i,SV31: $i] :
( ( ! [SY523: $i] :
( ~ ( equidistant @ SV31 @ SV84 @ SV130 @ SV167 )
| ~ ( equidistant @ SV84 @ SV189 @ SV167 @ SY523 )
| ~ ( between @ SV31 @ SV84 @ SV189 )
| ~ ( between @ SV130 @ SV167 @ SY523 )
| ( equidistant @ SV31 @ SV189 @ SV130 @ SY523 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(418,plain,
! [SV168: $i,SV131: $i,SV85: $i,SV32: $i] :
( ( ( ~ ( between @ SV32 @ SV85 @ SV131 ) )
= $true )
| ( ( ~ ( between @ SV32 @ SV85 @ SV168 )
| ~ ( equidistant @ SV85 @ SV131 @ SV85 @ SV168 )
| ( SV32 = SV85 )
| ( SV131 = SV168 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[380]) ).
thf(419,plain,
! [SV132: $i,SV86: $i,SV33: $i] :
( ( ( between @ SV33 @ SV86 @ SV132 )
= $false )
| ( ( ( SV33 = SV86 )
| ( SV132
= ( extension @ SV33 @ SV86 @ SV86 @ SV132 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(420,plain,
! [SV190: $i,SV169: $i,SV133: $i,SV87: $i,SV34: $i] :
( ( ! [SY524: $i] :
( ~ ( equidistant @ SV34 @ SV87 @ SV133 @ SV169 )
| ( ( extension @ SV190 @ SY524 @ SV34 @ SV87 )
= ( extension @ SV190 @ SY524 @ SV133 @ SV169 ) )
| ( SV190 = SY524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(421,plain,
! [SV134: $i,SV92: $i,SV39: $i] :
( ( ( between @ SV39 @ SV92 @ SV134 )
= $false )
| ( ( between @ SV134 @ SV92 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(422,plain,
! [SV135: $i,SV94: $i,SV41: $i] :
( ( ( between @ SV41 @ SV94 @ SV135 )
= $false )
| ( ( ~ ( between @ SV94 @ SV41 @ SV135 )
| ( SV41 = SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(423,plain,
! [SV136: $i,SV95: $i,SV42: $i] :
( ( ( between @ SV42 @ SV95 @ SV136 )
= $false )
| ( ( ~ ( between @ SV42 @ SV136 @ SV95 )
| ( SV95 = SV136 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(424,plain,
! [SV137: $i,SV96: $i,SV43: $i] :
( ( ( between @ SV43 @ SV96 @ SV137 )
= $false )
| ( ( ~ ( between @ SV96 @ SV43 @ SV137 )
| ( SV43 = SV96 )
| ( SV96 = SV137 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(425,plain,
! [SV138: $i,SV97: $i,SV44: $i] :
( ( ( between @ SV44 @ SV97 @ SV138 )
= $false )
| ( ( ~ ( between @ SV44 @ SV138 @ SV97 )
| ( SV44 = SV97 )
| ( SV97 = SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(426,plain,
! [SV170: $i,SV139: $i,SV98: $i,SV45: $i] :
( ( ( ~ ( between @ SV45 @ SV98 @ SV139 ) )
= $true )
| ( ( ~ ( between @ SV98 @ SV139 @ SV170 )
| ( between @ SV45 @ SV98 @ SV139 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(427,plain,
! [SV171: $i,SV140: $i,SV99: $i,SV46: $i] :
( ( ( ~ ( between @ SV46 @ SV99 @ SV140 ) )
= $true )
| ( ( ~ ( between @ SV46 @ SV140 @ SV171 )
| ( between @ SV99 @ SV140 @ SV171 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(428,plain,
! [SV172: $i,SV141: $i,SV100: $i,SV47: $i] :
( ( ( ~ ( between @ SV47 @ SV100 @ SV141 ) )
= $true )
| ( ( ~ ( between @ SV100 @ SV141 @ SV172 )
| ( between @ SV47 @ SV141 @ SV172 )
| ( SV100 = SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[390]) ).
thf(429,plain,
! [SV173: $i,SV142: $i,SV101: $i,SV48: $i] :
( ( ( ~ ( between @ SV48 @ SV101 @ SV142 ) )
= $true )
| ( ( ~ ( between @ SV101 @ SV142 @ SV173 )
| ( between @ SV48 @ SV101 @ SV173 )
| ( SV101 = SV142 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[391]) ).
thf(430,plain,
! [SV174: $i,SV143: $i,SV102: $i,SV49: $i] :
( ( ( ~ ( between @ SV49 @ SV102 @ SV143 ) )
= $true )
| ( ( ~ ( between @ SV102 @ SV174 @ SV143 )
| ( between @ SV49 @ SV174 @ SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(431,plain,
! [SV175: $i,SV144: $i,SV103: $i,SV50: $i] :
( ( ( ~ ( between @ SV50 @ SV103 @ SV144 ) )
= $true )
| ( ( ~ ( between @ SV50 @ SV144 @ SV175 )
| ( between @ SV50 @ SV103 @ SV175 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(432,plain,
! [SV191: $i,SV176: $i,SV145: $i,SV105: $i,SV52: $i] :
( ( ( SV52
!= ( extension @ SV105 @ SV145 @ SV176 @ SV191 ) )
| ( between @ SV105 @ SV145 @ SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(433,plain,
! [SV177: $i,SV146: $i,SV106: $i,SV53: $i] :
( ( ( ~ ( between @ SV53 @ SV106 @ SV146 ) )
= $true )
| ( ( ( SV53 != SV146 )
| ( between @ SV177 @ SV106 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(434,plain,
! [SV192: $i,SV178: $i,SV147: $i,SV108: $i,SV56: $i,SV2: $i] :
( ( ~ ( equidistant @ SV2 @ SV56 @ SV108 @ SV147 )
| ~ ( equidistant @ SV2 @ SV56 @ SV178 @ SV192 )
| ( equidistant @ SV108 @ SV147 @ SV178 @ SV192 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[398]) ).
thf(435,plain,
! [SV193: $i,SV179: $i,SV150: $i,SV112: $i,SV60: $i,SV6: $i] :
( ( ! [SY525: $i,SY526: $i] :
( ~ ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
| ~ ( equidistant @ SV60 @ SV179 @ SV150 @ SV193 )
| ~ ( equidistant @ SV6 @ SY525 @ SV112 @ SY526 )
| ~ ( equidistant @ SV60 @ SY525 @ SV150 @ SY526 )
| ~ ( between @ SV6 @ SV60 @ SV179 )
| ~ ( between @ SV112 @ SV150 @ SV193 )
| ( SV6 = SV60 )
| ( equidistant @ SV179 @ SY525 @ SV193 @ SY526 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[400]) ).
thf(436,plain,
! [SV180: $i,SV151: $i,SV113: $i,SV62: $i,SV8: $i] :
( ( ( ~ ( between @ SV8 @ SV62 @ SV113 ) )
= $true )
| ( ( ~ ( between @ SV151 @ SV180 @ SV113 )
| ( between @ SV62 @ ( inner_pasch @ SV8 @ SV62 @ SV113 @ SV180 @ SV151 ) @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(437,plain,
! [SV181: $i,SV152: $i,SV114: $i,SV63: $i,SV9: $i] :
( ( ( ~ ( between @ SV9 @ SV63 @ SV114 ) )
= $true )
| ( ( ~ ( between @ SV152 @ SV181 @ SV114 )
| ( between @ SV181 @ ( inner_pasch @ SV9 @ SV63 @ SV114 @ SV181 @ SV152 ) @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(438,plain,
! [SV182: $i,SV153: $i,SV115: $i,SV64: $i,SV10: $i] :
( ( ( ~ ( equidistant @ SV10 @ SV64 @ SV10 @ SV115 ) )
= $true )
| ( ( ~ ( equidistant @ SV153 @ SV64 @ SV153 @ SV115 )
| ~ ( equidistant @ SV182 @ SV64 @ SV182 @ SV115 )
| ( between @ SV10 @ SV153 @ SV182 )
| ( between @ SV153 @ SV182 @ SV10 )
| ( between @ SV182 @ SV10 @ SV153 )
| ( SV64 = SV115 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(439,plain,
! [SV183: $i,SV154: $i,SV116: $i,SV65: $i,SV11: $i] :
( ( ( ~ ( between @ SV11 @ SV65 @ SV116 ) )
= $true )
| ( ( ~ ( between @ SV154 @ SV65 @ SV183 )
| ( SV11 = SV65 )
| ( between @ SV11 @ SV154 @ ( euclid1 @ SV11 @ SV154 @ SV65 @ SV183 @ SV116 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[404]) ).
thf(440,plain,
! [SV184: $i,SV155: $i,SV117: $i,SV66: $i,SV12: $i] :
( ( ( ~ ( between @ SV12 @ SV66 @ SV117 ) )
= $true )
| ( ( ~ ( between @ SV155 @ SV66 @ SV184 )
| ( SV12 = SV66 )
| ( between @ SV12 @ SV184 @ ( euclid2 @ SV12 @ SV155 @ SV66 @ SV184 @ SV117 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(441,plain,
! [SV185: $i,SV156: $i,SV118: $i,SV67: $i,SV13: $i] :
( ( ( ~ ( between @ SV13 @ SV67 @ SV118 ) )
= $true )
| ( ( ~ ( between @ SV156 @ SV67 @ SV185 )
| ( SV13 = SV67 )
| ( between @ ( euclid1 @ SV13 @ SV156 @ SV67 @ SV185 @ SV118 ) @ SV118 @ ( euclid2 @ SV13 @ SV156 @ SV67 @ SV185 @ SV118 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(442,plain,
! [SV194: $i,SV186: $i,SV157: $i,SV119: $i,SV68: $i,SV14: $i] :
( ( ~ ( equidistant @ SV14 @ SV68 @ SV14 @ SV119 )
| ~ ( equidistant @ SV14 @ SV157 @ SV14 @ SV186 )
| ~ ( between @ SV14 @ SV68 @ SV157 )
| ~ ( between @ SV68 @ SV194 @ SV157 )
| ( between @ SV119 @ ( continuous @ SV14 @ SV68 @ SV119 @ SV194 @ SV157 @ SV186 ) @ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(443,plain,
! [SV195: $i,SV187: $i,SV158: $i,SV120: $i,SV69: $i,SV15: $i] :
( ( ~ ( equidistant @ SV15 @ SV69 @ SV15 @ SV120 )
| ~ ( equidistant @ SV15 @ SV158 @ SV15 @ SV187 )
| ~ ( between @ SV15 @ SV69 @ SV158 )
| ~ ( between @ SV69 @ SV195 @ SV158 )
| ( equidistant @ SV15 @ SV195 @ SV15 @ ( continuous @ SV15 @ SV69 @ SV120 @ SV195 @ SV158 @ SV187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[408]) ).
thf(444,plain,
! [SV159: $i,SV121: $i,SV72: $i,SV18: $i] :
( ( ( equidistant @ SV18 @ SV72 @ SV121 @ SV159 )
= $false )
| ( ( equidistant @ SV121 @ SV159 @ SV18 @ SV72 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(445,plain,
! [SV160: $i,SV122: $i,SV73: $i,SV19: $i] :
( ( ( equidistant @ SV19 @ SV73 @ SV122 @ SV160 )
= $false )
| ( ( equidistant @ SV73 @ SV19 @ SV122 @ SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(446,plain,
! [SV161: $i,SV123: $i,SV74: $i,SV20: $i] :
( ( ( equidistant @ SV20 @ SV74 @ SV123 @ SV161 )
= $false )
| ( ( equidistant @ SV20 @ SV74 @ SV161 @ SV123 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(447,plain,
! [SV162: $i,SV124: $i,SV75: $i,SV21: $i] :
( ( ( equidistant @ SV21 @ SV75 @ SV124 @ SV162 )
= $false )
| ( ( equidistant @ SV75 @ SV21 @ SV162 @ SV124 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(448,plain,
! [SV163: $i,SV125: $i,SV76: $i,SV22: $i] :
( ( ( equidistant @ SV22 @ SV76 @ SV125 @ SV163 )
= $false )
| ( ( equidistant @ SV125 @ SV163 @ SV76 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(449,plain,
! [SV164: $i,SV126: $i,SV77: $i,SV23: $i] :
( ( ( equidistant @ SV23 @ SV77 @ SV126 @ SV164 )
= $false )
| ( ( equidistant @ SV164 @ SV126 @ SV23 @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(450,plain,
! [SV165: $i,SV127: $i,SV78: $i,SV24: $i] :
( ( ( equidistant @ SV24 @ SV78 @ SV127 @ SV165 )
= $false )
| ( ( equidistant @ SV165 @ SV127 @ SV78 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(451,plain,
! [SV196: $i,SV188: $i,SV166: $i,SV128: $i,SV79: $i,SV25: $i] :
( ( ~ ( equidistant @ SV25 @ SV79 @ SV128 @ SV166 )
| ~ ( equidistant @ SV128 @ SV166 @ SV188 @ SV196 )
| ( equidistant @ SV25 @ SV79 @ SV188 @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(452,plain,
! [SV197: $i,SV189: $i,SV167: $i,SV130: $i,SV84: $i,SV31: $i] :
( ( ~ ( equidistant @ SV31 @ SV84 @ SV130 @ SV167 )
| ~ ( equidistant @ SV84 @ SV189 @ SV167 @ SV197 )
| ~ ( between @ SV31 @ SV84 @ SV189 )
| ~ ( between @ SV130 @ SV167 @ SV197 )
| ( equidistant @ SV31 @ SV189 @ SV130 @ SV197 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(453,plain,
! [SV168: $i,SV131: $i,SV85: $i,SV32: $i] :
( ( ( between @ SV32 @ SV85 @ SV131 )
= $false )
| ( ( ~ ( between @ SV32 @ SV85 @ SV168 )
| ~ ( equidistant @ SV85 @ SV131 @ SV85 @ SV168 )
| ( SV32 = SV85 )
| ( SV131 = SV168 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[418]) ).
thf(454,plain,
! [SV132: $i,SV86: $i,SV33: $i] :
( ( ( SV33 = SV86 )
= $true )
| ( ( SV132
= ( extension @ SV33 @ SV86 @ SV86 @ SV132 ) )
= $true )
| ( ( between @ SV33 @ SV86 @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(455,plain,
! [SV198: $i,SV190: $i,SV169: $i,SV133: $i,SV87: $i,SV34: $i] :
( ( ~ ( equidistant @ SV34 @ SV87 @ SV133 @ SV169 )
| ( ( extension @ SV190 @ SV198 @ SV34 @ SV87 )
= ( extension @ SV190 @ SV198 @ SV133 @ SV169 ) )
| ( SV190 = SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(456,plain,
! [SV135: $i,SV41: $i,SV94: $i] :
( ( ( ~ ( between @ SV94 @ SV41 @ SV135 ) )
= $true )
| ( ( SV41 = SV94 )
= $true )
| ( ( between @ SV41 @ SV94 @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(457,plain,
! [SV95: $i,SV136: $i,SV42: $i] :
( ( ( ~ ( between @ SV42 @ SV136 @ SV95 ) )
= $true )
| ( ( SV95 = SV136 )
= $true )
| ( ( between @ SV42 @ SV95 @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(458,plain,
! [SV137: $i,SV43: $i,SV96: $i] :
( ( ( ~ ( between @ SV96 @ SV43 @ SV137 ) )
= $true )
| ( ( ( SV43 = SV96 )
| ( SV96 = SV137 ) )
= $true )
| ( ( between @ SV43 @ SV96 @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(459,plain,
! [SV97: $i,SV138: $i,SV44: $i] :
( ( ( ~ ( between @ SV44 @ SV138 @ SV97 ) )
= $true )
| ( ( ( SV44 = SV97 )
| ( SV97 = SV138 ) )
= $true )
| ( ( between @ SV44 @ SV97 @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(460,plain,
! [SV170: $i,SV139: $i,SV98: $i,SV45: $i] :
( ( ( between @ SV45 @ SV98 @ SV139 )
= $false )
| ( ( ~ ( between @ SV98 @ SV139 @ SV170 )
| ( between @ SV45 @ SV98 @ SV139 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[426]) ).
thf(461,plain,
! [SV171: $i,SV140: $i,SV99: $i,SV46: $i] :
( ( ( between @ SV46 @ SV99 @ SV140 )
= $false )
| ( ( ~ ( between @ SV46 @ SV140 @ SV171 )
| ( between @ SV99 @ SV140 @ SV171 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[427]) ).
thf(462,plain,
! [SV172: $i,SV141: $i,SV100: $i,SV47: $i] :
( ( ( between @ SV47 @ SV100 @ SV141 )
= $false )
| ( ( ~ ( between @ SV100 @ SV141 @ SV172 )
| ( between @ SV47 @ SV141 @ SV172 )
| ( SV100 = SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[428]) ).
thf(463,plain,
! [SV173: $i,SV142: $i,SV101: $i,SV48: $i] :
( ( ( between @ SV48 @ SV101 @ SV142 )
= $false )
| ( ( ~ ( between @ SV101 @ SV142 @ SV173 )
| ( between @ SV48 @ SV101 @ SV173 )
| ( SV101 = SV142 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[429]) ).
thf(464,plain,
! [SV174: $i,SV143: $i,SV102: $i,SV49: $i] :
( ( ( between @ SV49 @ SV102 @ SV143 )
= $false )
| ( ( ~ ( between @ SV102 @ SV174 @ SV143 )
| ( between @ SV49 @ SV174 @ SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[430]) ).
thf(465,plain,
! [SV175: $i,SV144: $i,SV103: $i,SV50: $i] :
( ( ( between @ SV50 @ SV103 @ SV144 )
= $false )
| ( ( ~ ( between @ SV50 @ SV144 @ SV175 )
| ( between @ SV50 @ SV103 @ SV175 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(466,plain,
! [SV191: $i,SV176: $i,SV145: $i,SV105: $i,SV52: $i] :
( ( ( SV52
!= ( extension @ SV105 @ SV145 @ SV176 @ SV191 ) )
= $true )
| ( ( between @ SV105 @ SV145 @ SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(467,plain,
! [SV177: $i,SV146: $i,SV106: $i,SV53: $i] :
( ( ( between @ SV53 @ SV106 @ SV146 )
= $false )
| ( ( ( SV53 != SV146 )
| ( between @ SV177 @ SV106 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(468,plain,
! [SV192: $i,SV178: $i,SV147: $i,SV108: $i,SV56: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV56 @ SV108 @ SV147 ) )
= $true )
| ( ( ~ ( equidistant @ SV2 @ SV56 @ SV178 @ SV192 )
| ( equidistant @ SV108 @ SV147 @ SV178 @ SV192 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(469,plain,
! [SV199: $i,SV193: $i,SV179: $i,SV150: $i,SV112: $i,SV60: $i,SV6: $i] :
( ( ! [SY527: $i] :
( ~ ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
| ~ ( equidistant @ SV60 @ SV179 @ SV150 @ SV193 )
| ~ ( equidistant @ SV6 @ SV199 @ SV112 @ SY527 )
| ~ ( equidistant @ SV60 @ SV199 @ SV150 @ SY527 )
| ~ ( between @ SV6 @ SV60 @ SV179 )
| ~ ( between @ SV112 @ SV150 @ SV193 )
| ( SV6 = SV60 )
| ( equidistant @ SV179 @ SV199 @ SV193 @ SY527 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(470,plain,
! [SV180: $i,SV151: $i,SV113: $i,SV62: $i,SV8: $i] :
( ( ( between @ SV8 @ SV62 @ SV113 )
= $false )
| ( ( ~ ( between @ SV151 @ SV180 @ SV113 )
| ( between @ SV62 @ ( inner_pasch @ SV8 @ SV62 @ SV113 @ SV180 @ SV151 ) @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(471,plain,
! [SV181: $i,SV152: $i,SV114: $i,SV63: $i,SV9: $i] :
( ( ( between @ SV9 @ SV63 @ SV114 )
= $false )
| ( ( ~ ( between @ SV152 @ SV181 @ SV114 )
| ( between @ SV181 @ ( inner_pasch @ SV9 @ SV63 @ SV114 @ SV181 @ SV152 ) @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(472,plain,
! [SV182: $i,SV153: $i,SV115: $i,SV64: $i,SV10: $i] :
( ( ( equidistant @ SV10 @ SV64 @ SV10 @ SV115 )
= $false )
| ( ( ~ ( equidistant @ SV153 @ SV64 @ SV153 @ SV115 )
| ~ ( equidistant @ SV182 @ SV64 @ SV182 @ SV115 )
| ( between @ SV10 @ SV153 @ SV182 )
| ( between @ SV153 @ SV182 @ SV10 )
| ( between @ SV182 @ SV10 @ SV153 )
| ( SV64 = SV115 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(473,plain,
! [SV183: $i,SV154: $i,SV116: $i,SV65: $i,SV11: $i] :
( ( ( between @ SV11 @ SV65 @ SV116 )
= $false )
| ( ( ~ ( between @ SV154 @ SV65 @ SV183 )
| ( SV11 = SV65 )
| ( between @ SV11 @ SV154 @ ( euclid1 @ SV11 @ SV154 @ SV65 @ SV183 @ SV116 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(474,plain,
! [SV184: $i,SV155: $i,SV117: $i,SV66: $i,SV12: $i] :
( ( ( between @ SV12 @ SV66 @ SV117 )
= $false )
| ( ( ~ ( between @ SV155 @ SV66 @ SV184 )
| ( SV12 = SV66 )
| ( between @ SV12 @ SV184 @ ( euclid2 @ SV12 @ SV155 @ SV66 @ SV184 @ SV117 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(475,plain,
! [SV185: $i,SV156: $i,SV118: $i,SV67: $i,SV13: $i] :
( ( ( between @ SV13 @ SV67 @ SV118 )
= $false )
| ( ( ~ ( between @ SV156 @ SV67 @ SV185 )
| ( SV13 = SV67 )
| ( between @ ( euclid1 @ SV13 @ SV156 @ SV67 @ SV185 @ SV118 ) @ SV118 @ ( euclid2 @ SV13 @ SV156 @ SV67 @ SV185 @ SV118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(476,plain,
! [SV194: $i,SV186: $i,SV157: $i,SV119: $i,SV68: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV68 @ SV14 @ SV119 ) )
= $true )
| ( ( ~ ( equidistant @ SV14 @ SV157 @ SV14 @ SV186 )
| ~ ( between @ SV14 @ SV68 @ SV157 )
| ~ ( between @ SV68 @ SV194 @ SV157 )
| ( between @ SV119 @ ( continuous @ SV14 @ SV68 @ SV119 @ SV194 @ SV157 @ SV186 ) @ SV186 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(477,plain,
! [SV195: $i,SV187: $i,SV158: $i,SV120: $i,SV69: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV69 @ SV15 @ SV120 ) )
= $true )
| ( ( ~ ( equidistant @ SV15 @ SV158 @ SV15 @ SV187 )
| ~ ( between @ SV15 @ SV69 @ SV158 )
| ~ ( between @ SV69 @ SV195 @ SV158 )
| ( equidistant @ SV15 @ SV195 @ SV15 @ ( continuous @ SV15 @ SV69 @ SV120 @ SV195 @ SV158 @ SV187 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[443]) ).
thf(478,plain,
! [SV196: $i,SV188: $i,SV166: $i,SV128: $i,SV79: $i,SV25: $i] :
( ( ( ~ ( equidistant @ SV25 @ SV79 @ SV128 @ SV166 ) )
= $true )
| ( ( ~ ( equidistant @ SV128 @ SV166 @ SV188 @ SV196 )
| ( equidistant @ SV25 @ SV79 @ SV188 @ SV196 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(479,plain,
! [SV197: $i,SV189: $i,SV167: $i,SV130: $i,SV84: $i,SV31: $i] :
( ( ( ~ ( equidistant @ SV31 @ SV84 @ SV130 @ SV167 ) )
= $true )
| ( ( ~ ( equidistant @ SV84 @ SV189 @ SV167 @ SV197 )
| ~ ( between @ SV31 @ SV84 @ SV189 )
| ~ ( between @ SV130 @ SV167 @ SV197 )
| ( equidistant @ SV31 @ SV189 @ SV130 @ SV197 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(480,plain,
! [SV131: $i,SV168: $i,SV85: $i,SV32: $i] :
( ( ( ~ ( between @ SV32 @ SV85 @ SV168 ) )
= $true )
| ( ( ~ ( equidistant @ SV85 @ SV131 @ SV85 @ SV168 )
| ( SV32 = SV85 )
| ( SV131 = SV168 ) )
= $true )
| ( ( between @ SV32 @ SV85 @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(481,plain,
! [SV198: $i,SV190: $i,SV169: $i,SV133: $i,SV87: $i,SV34: $i] :
( ( ( ~ ( equidistant @ SV34 @ SV87 @ SV133 @ SV169 ) )
= $true )
| ( ( ( ( extension @ SV190 @ SV198 @ SV34 @ SV87 )
= ( extension @ SV190 @ SV198 @ SV133 @ SV169 ) )
| ( SV190 = SV198 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(482,plain,
! [SV135: $i,SV41: $i,SV94: $i] :
( ( ( between @ SV94 @ SV41 @ SV135 )
= $false )
| ( ( SV41 = SV94 )
= $true )
| ( ( between @ SV41 @ SV94 @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(483,plain,
! [SV95: $i,SV136: $i,SV42: $i] :
( ( ( between @ SV42 @ SV136 @ SV95 )
= $false )
| ( ( SV95 = SV136 )
= $true )
| ( ( between @ SV42 @ SV95 @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(484,plain,
! [SV137: $i,SV43: $i,SV96: $i] :
( ( ( between @ SV96 @ SV43 @ SV137 )
= $false )
| ( ( ( SV43 = SV96 )
| ( SV96 = SV137 ) )
= $true )
| ( ( between @ SV43 @ SV96 @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(485,plain,
! [SV97: $i,SV138: $i,SV44: $i] :
( ( ( between @ SV44 @ SV138 @ SV97 )
= $false )
| ( ( ( SV44 = SV97 )
| ( SV97 = SV138 ) )
= $true )
| ( ( between @ SV44 @ SV97 @ SV138 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(486,plain,
! [SV45: $i,SV170: $i,SV139: $i,SV98: $i] :
( ( ( ~ ( between @ SV98 @ SV139 @ SV170 ) )
= $true )
| ( ( between @ SV45 @ SV98 @ SV139 )
= $true )
| ( ( between @ SV45 @ SV98 @ SV139 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(487,plain,
! [SV99: $i,SV171: $i,SV140: $i,SV46: $i] :
( ( ( ~ ( between @ SV46 @ SV140 @ SV171 ) )
= $true )
| ( ( between @ SV99 @ SV140 @ SV171 )
= $true )
| ( ( between @ SV46 @ SV99 @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(488,plain,
! [SV47: $i,SV172: $i,SV141: $i,SV100: $i] :
( ( ( ~ ( between @ SV100 @ SV141 @ SV172 ) )
= $true )
| ( ( ( between @ SV47 @ SV141 @ SV172 )
| ( SV100 = SV141 ) )
= $true )
| ( ( between @ SV47 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[462]) ).
thf(489,plain,
! [SV48: $i,SV173: $i,SV142: $i,SV101: $i] :
( ( ( ~ ( between @ SV101 @ SV142 @ SV173 ) )
= $true )
| ( ( ( between @ SV48 @ SV101 @ SV173 )
| ( SV101 = SV142 ) )
= $true )
| ( ( between @ SV48 @ SV101 @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[463]) ).
thf(490,plain,
! [SV49: $i,SV143: $i,SV174: $i,SV102: $i] :
( ( ( ~ ( between @ SV102 @ SV174 @ SV143 ) )
= $true )
| ( ( between @ SV49 @ SV174 @ SV143 )
= $true )
| ( ( between @ SV49 @ SV102 @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(491,plain,
! [SV103: $i,SV175: $i,SV144: $i,SV50: $i] :
( ( ( ~ ( between @ SV50 @ SV144 @ SV175 ) )
= $true )
| ( ( between @ SV50 @ SV103 @ SV175 )
= $true )
| ( ( between @ SV50 @ SV103 @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[465]) ).
thf(492,plain,
! [SV191: $i,SV176: $i,SV145: $i,SV105: $i,SV52: $i] :
( ( ( SV52
= ( extension @ SV105 @ SV145 @ SV176 @ SV191 ) )
= $false )
| ( ( between @ SV105 @ SV145 @ SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(493,plain,
! [SV106: $i,SV177: $i,SV146: $i,SV53: $i] :
( ( ( SV53 != SV146 )
= $true )
| ( ( between @ SV177 @ SV106 @ SV146 )
= $true )
| ( ( between @ SV53 @ SV106 @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(494,plain,
! [SV192: $i,SV178: $i,SV147: $i,SV108: $i,SV56: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV56 @ SV108 @ SV147 )
= $false )
| ( ( ~ ( equidistant @ SV2 @ SV56 @ SV178 @ SV192 )
| ( equidistant @ SV108 @ SV147 @ SV178 @ SV192 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(495,plain,
! [SV200: $i,SV199: $i,SV193: $i,SV179: $i,SV150: $i,SV112: $i,SV60: $i,SV6: $i] :
( ( ~ ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
| ~ ( equidistant @ SV60 @ SV179 @ SV150 @ SV193 )
| ~ ( equidistant @ SV6 @ SV199 @ SV112 @ SV200 )
| ~ ( equidistant @ SV60 @ SV199 @ SV150 @ SV200 )
| ~ ( between @ SV6 @ SV60 @ SV179 )
| ~ ( between @ SV112 @ SV150 @ SV193 )
| ( SV6 = SV60 )
| ( equidistant @ SV179 @ SV199 @ SV193 @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(496,plain,
! [SV8: $i,SV62: $i,SV113: $i,SV180: $i,SV151: $i] :
( ( ( ~ ( between @ SV151 @ SV180 @ SV113 ) )
= $true )
| ( ( between @ SV62 @ ( inner_pasch @ SV8 @ SV62 @ SV113 @ SV180 @ SV151 ) @ SV151 )
= $true )
| ( ( between @ SV8 @ SV62 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(497,plain,
! [SV63: $i,SV9: $i,SV114: $i,SV181: $i,SV152: $i] :
( ( ( ~ ( between @ SV152 @ SV181 @ SV114 ) )
= $true )
| ( ( between @ SV181 @ ( inner_pasch @ SV9 @ SV63 @ SV114 @ SV181 @ SV152 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV63 @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(498,plain,
! [SV10: $i,SV182: $i,SV115: $i,SV64: $i,SV153: $i] :
( ( ( ~ ( equidistant @ SV153 @ SV64 @ SV153 @ SV115 ) )
= $true )
| ( ( ~ ( equidistant @ SV182 @ SV64 @ SV182 @ SV115 )
| ( between @ SV10 @ SV153 @ SV182 )
| ( between @ SV153 @ SV182 @ SV10 )
| ( between @ SV182 @ SV10 @ SV153 )
| ( SV64 = SV115 ) )
= $true )
| ( ( equidistant @ SV10 @ SV64 @ SV10 @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(499,plain,
! [SV116: $i,SV11: $i,SV183: $i,SV65: $i,SV154: $i] :
( ( ( ~ ( between @ SV154 @ SV65 @ SV183 ) )
= $true )
| ( ( ( SV11 = SV65 )
| ( between @ SV11 @ SV154 @ ( euclid1 @ SV11 @ SV154 @ SV65 @ SV183 @ SV116 ) ) )
= $true )
| ( ( between @ SV11 @ SV65 @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[473]) ).
thf(500,plain,
! [SV117: $i,SV12: $i,SV184: $i,SV66: $i,SV155: $i] :
( ( ( ~ ( between @ SV155 @ SV66 @ SV184 ) )
= $true )
| ( ( ( SV12 = SV66 )
| ( between @ SV12 @ SV184 @ ( euclid2 @ SV12 @ SV155 @ SV66 @ SV184 @ SV117 ) ) )
= $true )
| ( ( between @ SV12 @ SV66 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(501,plain,
! [SV118: $i,SV13: $i,SV185: $i,SV67: $i,SV156: $i] :
( ( ( ~ ( between @ SV156 @ SV67 @ SV185 ) )
= $true )
| ( ( ( SV13 = SV67 )
| ( between @ ( euclid1 @ SV13 @ SV156 @ SV67 @ SV185 @ SV118 ) @ SV118 @ ( euclid2 @ SV13 @ SV156 @ SV67 @ SV185 @ SV118 ) ) )
= $true )
| ( ( between @ SV13 @ SV67 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(502,plain,
! [SV194: $i,SV186: $i,SV157: $i,SV119: $i,SV68: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV68 @ SV14 @ SV119 )
= $false )
| ( ( ~ ( equidistant @ SV14 @ SV157 @ SV14 @ SV186 )
| ~ ( between @ SV14 @ SV68 @ SV157 )
| ~ ( between @ SV68 @ SV194 @ SV157 )
| ( between @ SV119 @ ( continuous @ SV14 @ SV68 @ SV119 @ SV194 @ SV157 @ SV186 ) @ SV186 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[476]) ).
thf(503,plain,
! [SV195: $i,SV187: $i,SV158: $i,SV120: $i,SV69: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV69 @ SV15 @ SV120 )
= $false )
| ( ( ~ ( equidistant @ SV15 @ SV158 @ SV15 @ SV187 )
| ~ ( between @ SV15 @ SV69 @ SV158 )
| ~ ( between @ SV69 @ SV195 @ SV158 )
| ( equidistant @ SV15 @ SV195 @ SV15 @ ( continuous @ SV15 @ SV69 @ SV120 @ SV195 @ SV158 @ SV187 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(504,plain,
! [SV196: $i,SV188: $i,SV166: $i,SV128: $i,SV79: $i,SV25: $i] :
( ( ( equidistant @ SV25 @ SV79 @ SV128 @ SV166 )
= $false )
| ( ( ~ ( equidistant @ SV128 @ SV166 @ SV188 @ SV196 )
| ( equidistant @ SV25 @ SV79 @ SV188 @ SV196 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(505,plain,
! [SV197: $i,SV189: $i,SV167: $i,SV130: $i,SV84: $i,SV31: $i] :
( ( ( equidistant @ SV31 @ SV84 @ SV130 @ SV167 )
= $false )
| ( ( ~ ( equidistant @ SV84 @ SV189 @ SV167 @ SV197 )
| ~ ( between @ SV31 @ SV84 @ SV189 )
| ~ ( between @ SV130 @ SV167 @ SV197 )
| ( equidistant @ SV31 @ SV189 @ SV130 @ SV197 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[479]) ).
thf(506,plain,
! [SV131: $i,SV168: $i,SV85: $i,SV32: $i] :
( ( ( between @ SV32 @ SV85 @ SV168 )
= $false )
| ( ( ~ ( equidistant @ SV85 @ SV131 @ SV85 @ SV168 )
| ( SV32 = SV85 )
| ( SV131 = SV168 ) )
= $true )
| ( ( between @ SV32 @ SV85 @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(507,plain,
! [SV198: $i,SV190: $i,SV169: $i,SV133: $i,SV87: $i,SV34: $i] :
( ( ( equidistant @ SV34 @ SV87 @ SV133 @ SV169 )
= $false )
| ( ( ( ( extension @ SV190 @ SV198 @ SV34 @ SV87 )
= ( extension @ SV190 @ SV198 @ SV133 @ SV169 ) )
| ( SV190 = SV198 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(508,plain,
! [SV137: $i,SV96: $i,SV43: $i] :
( ( ( SV43 = SV96 )
= $true )
| ( ( SV96 = SV137 )
= $true )
| ( ( between @ SV96 @ SV43 @ SV137 )
= $false )
| ( ( between @ SV43 @ SV96 @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[484]) ).
thf(509,plain,
! [SV138: $i,SV97: $i,SV44: $i] :
( ( ( SV44 = SV97 )
= $true )
| ( ( SV97 = SV138 )
= $true )
| ( ( between @ SV44 @ SV138 @ SV97 )
= $false )
| ( ( between @ SV44 @ SV97 @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(510,plain,
! [SV45: $i,SV170: $i,SV139: $i,SV98: $i] :
( ( ( between @ SV98 @ SV139 @ SV170 )
= $false )
| ( ( between @ SV45 @ SV98 @ SV139 )
= $true )
| ( ( between @ SV45 @ SV98 @ SV139 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[486]) ).
thf(511,plain,
! [SV99: $i,SV171: $i,SV140: $i,SV46: $i] :
( ( ( between @ SV46 @ SV140 @ SV171 )
= $false )
| ( ( between @ SV99 @ SV140 @ SV171 )
= $true )
| ( ( between @ SV46 @ SV99 @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[487]) ).
thf(512,plain,
! [SV47: $i,SV172: $i,SV141: $i,SV100: $i] :
( ( ( between @ SV100 @ SV141 @ SV172 )
= $false )
| ( ( ( between @ SV47 @ SV141 @ SV172 )
| ( SV100 = SV141 ) )
= $true )
| ( ( between @ SV47 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[488]) ).
thf(513,plain,
! [SV48: $i,SV173: $i,SV142: $i,SV101: $i] :
( ( ( between @ SV101 @ SV142 @ SV173 )
= $false )
| ( ( ( between @ SV48 @ SV101 @ SV173 )
| ( SV101 = SV142 ) )
= $true )
| ( ( between @ SV48 @ SV101 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[489]) ).
thf(514,plain,
! [SV49: $i,SV143: $i,SV174: $i,SV102: $i] :
( ( ( between @ SV102 @ SV174 @ SV143 )
= $false )
| ( ( between @ SV49 @ SV174 @ SV143 )
= $true )
| ( ( between @ SV49 @ SV102 @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(515,plain,
! [SV103: $i,SV175: $i,SV144: $i,SV50: $i] :
( ( ( between @ SV50 @ SV144 @ SV175 )
= $false )
| ( ( between @ SV50 @ SV103 @ SV175 )
= $true )
| ( ( between @ SV50 @ SV103 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[491]) ).
thf(516,plain,
! [SV106: $i,SV177: $i,SV146: $i,SV53: $i] :
( ( ( SV53 = SV146 )
= $false )
| ( ( between @ SV177 @ SV106 @ SV146 )
= $true )
| ( ( between @ SV53 @ SV106 @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[493]) ).
thf(517,plain,
! [SV147: $i,SV108: $i,SV192: $i,SV178: $i,SV56: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV56 @ SV178 @ SV192 ) )
= $true )
| ( ( equidistant @ SV108 @ SV147 @ SV178 @ SV192 )
= $true )
| ( ( equidistant @ SV2 @ SV56 @ SV108 @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(518,plain,
! [SV200: $i,SV199: $i,SV193: $i,SV179: $i,SV150: $i,SV112: $i,SV60: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 ) )
= $true )
| ( ( ~ ( equidistant @ SV60 @ SV179 @ SV150 @ SV193 )
| ~ ( equidistant @ SV6 @ SV199 @ SV112 @ SV200 )
| ~ ( equidistant @ SV60 @ SV199 @ SV150 @ SV200 )
| ~ ( between @ SV6 @ SV60 @ SV179 )
| ~ ( between @ SV112 @ SV150 @ SV193 )
| ( SV6 = SV60 )
| ( equidistant @ SV179 @ SV199 @ SV193 @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(519,plain,
! [SV8: $i,SV62: $i,SV113: $i,SV180: $i,SV151: $i] :
( ( ( between @ SV151 @ SV180 @ SV113 )
= $false )
| ( ( between @ SV62 @ ( inner_pasch @ SV8 @ SV62 @ SV113 @ SV180 @ SV151 ) @ SV151 )
= $true )
| ( ( between @ SV8 @ SV62 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(520,plain,
! [SV63: $i,SV9: $i,SV114: $i,SV181: $i,SV152: $i] :
( ( ( between @ SV152 @ SV181 @ SV114 )
= $false )
| ( ( between @ SV181 @ ( inner_pasch @ SV9 @ SV63 @ SV114 @ SV181 @ SV152 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV63 @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[497]) ).
thf(521,plain,
! [SV10: $i,SV182: $i,SV115: $i,SV64: $i,SV153: $i] :
( ( ( equidistant @ SV153 @ SV64 @ SV153 @ SV115 )
= $false )
| ( ( ~ ( equidistant @ SV182 @ SV64 @ SV182 @ SV115 )
| ( between @ SV10 @ SV153 @ SV182 )
| ( between @ SV153 @ SV182 @ SV10 )
| ( between @ SV182 @ SV10 @ SV153 )
| ( SV64 = SV115 ) )
= $true )
| ( ( equidistant @ SV10 @ SV64 @ SV10 @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[498]) ).
thf(522,plain,
! [SV116: $i,SV11: $i,SV183: $i,SV65: $i,SV154: $i] :
( ( ( between @ SV154 @ SV65 @ SV183 )
= $false )
| ( ( ( SV11 = SV65 )
| ( between @ SV11 @ SV154 @ ( euclid1 @ SV11 @ SV154 @ SV65 @ SV183 @ SV116 ) ) )
= $true )
| ( ( between @ SV11 @ SV65 @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[499]) ).
thf(523,plain,
! [SV117: $i,SV12: $i,SV184: $i,SV66: $i,SV155: $i] :
( ( ( between @ SV155 @ SV66 @ SV184 )
= $false )
| ( ( ( SV12 = SV66 )
| ( between @ SV12 @ SV184 @ ( euclid2 @ SV12 @ SV155 @ SV66 @ SV184 @ SV117 ) ) )
= $true )
| ( ( between @ SV12 @ SV66 @ SV117 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(524,plain,
! [SV118: $i,SV13: $i,SV185: $i,SV67: $i,SV156: $i] :
( ( ( between @ SV156 @ SV67 @ SV185 )
= $false )
| ( ( ( SV13 = SV67 )
| ( between @ ( euclid1 @ SV13 @ SV156 @ SV67 @ SV185 @ SV118 ) @ SV118 @ ( euclid2 @ SV13 @ SV156 @ SV67 @ SV185 @ SV118 ) ) )
= $true )
| ( ( between @ SV13 @ SV67 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[501]) ).
thf(525,plain,
! [SV119: $i,SV194: $i,SV68: $i,SV186: $i,SV157: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV157 @ SV14 @ SV186 ) )
= $true )
| ( ( ~ ( between @ SV14 @ SV68 @ SV157 )
| ~ ( between @ SV68 @ SV194 @ SV157 )
| ( between @ SV119 @ ( continuous @ SV14 @ SV68 @ SV119 @ SV194 @ SV157 @ SV186 ) @ SV186 ) )
= $true )
| ( ( equidistant @ SV14 @ SV68 @ SV14 @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(526,plain,
! [SV120: $i,SV195: $i,SV69: $i,SV187: $i,SV158: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV158 @ SV15 @ SV187 ) )
= $true )
| ( ( ~ ( between @ SV15 @ SV69 @ SV158 )
| ~ ( between @ SV69 @ SV195 @ SV158 )
| ( equidistant @ SV15 @ SV195 @ SV15 @ ( continuous @ SV15 @ SV69 @ SV120 @ SV195 @ SV158 @ SV187 ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV69 @ SV15 @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(527,plain,
! [SV79: $i,SV25: $i,SV196: $i,SV188: $i,SV166: $i,SV128: $i] :
( ( ( ~ ( equidistant @ SV128 @ SV166 @ SV188 @ SV196 ) )
= $true )
| ( ( equidistant @ SV25 @ SV79 @ SV188 @ SV196 )
= $true )
| ( ( equidistant @ SV25 @ SV79 @ SV128 @ SV166 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(528,plain,
! [SV130: $i,SV31: $i,SV197: $i,SV167: $i,SV189: $i,SV84: $i] :
( ( ( ~ ( equidistant @ SV84 @ SV189 @ SV167 @ SV197 ) )
= $true )
| ( ( ~ ( between @ SV31 @ SV84 @ SV189 )
| ~ ( between @ SV130 @ SV167 @ SV197 )
| ( equidistant @ SV31 @ SV189 @ SV130 @ SV197 ) )
= $true )
| ( ( equidistant @ SV31 @ SV84 @ SV130 @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[505]) ).
thf(529,plain,
! [SV32: $i,SV168: $i,SV131: $i,SV85: $i] :
( ( ( ~ ( equidistant @ SV85 @ SV131 @ SV85 @ SV168 ) )
= $true )
| ( ( ( SV32 = SV85 )
| ( SV131 = SV168 ) )
= $true )
| ( ( between @ SV32 @ SV85 @ SV168 )
= $false )
| ( ( between @ SV32 @ SV85 @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[506]) ).
thf(530,plain,
! [SV169: $i,SV133: $i,SV87: $i,SV34: $i,SV198: $i,SV190: $i] :
( ( ( ( extension @ SV190 @ SV198 @ SV34 @ SV87 )
= ( extension @ SV190 @ SV198 @ SV133 @ SV169 ) )
= $true )
| ( ( SV190 = SV198 )
= $true )
| ( ( equidistant @ SV34 @ SV87 @ SV133 @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[507]) ).
thf(531,plain,
! [SV100: $i,SV172: $i,SV141: $i,SV47: $i] :
( ( ( between @ SV47 @ SV141 @ SV172 )
= $true )
| ( ( SV100 = SV141 )
= $true )
| ( ( between @ SV100 @ SV141 @ SV172 )
= $false )
| ( ( between @ SV47 @ SV100 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[512]) ).
thf(532,plain,
! [SV142: $i,SV173: $i,SV101: $i,SV48: $i] :
( ( ( between @ SV48 @ SV101 @ SV173 )
= $true )
| ( ( SV101 = SV142 )
= $true )
| ( ( between @ SV101 @ SV142 @ SV173 )
= $false )
| ( ( between @ SV48 @ SV101 @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(533,plain,
! [SV147: $i,SV108: $i,SV192: $i,SV178: $i,SV56: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV56 @ SV178 @ SV192 )
= $false )
| ( ( equidistant @ SV108 @ SV147 @ SV178 @ SV192 )
= $true )
| ( ( equidistant @ SV2 @ SV56 @ SV108 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(534,plain,
! [SV200: $i,SV199: $i,SV193: $i,SV179: $i,SV150: $i,SV112: $i,SV60: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
= $false )
| ( ( ~ ( equidistant @ SV60 @ SV179 @ SV150 @ SV193 )
| ~ ( equidistant @ SV6 @ SV199 @ SV112 @ SV200 )
| ~ ( equidistant @ SV60 @ SV199 @ SV150 @ SV200 )
| ~ ( between @ SV6 @ SV60 @ SV179 )
| ~ ( between @ SV112 @ SV150 @ SV193 )
| ( SV6 = SV60 )
| ( equidistant @ SV179 @ SV199 @ SV193 @ SV200 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[518]) ).
thf(535,plain,
! [SV153: $i,SV10: $i,SV115: $i,SV64: $i,SV182: $i] :
( ( ( ~ ( equidistant @ SV182 @ SV64 @ SV182 @ SV115 ) )
= $true )
| ( ( ( between @ SV10 @ SV153 @ SV182 )
| ( between @ SV153 @ SV182 @ SV10 )
| ( between @ SV182 @ SV10 @ SV153 )
| ( SV64 = SV115 ) )
= $true )
| ( ( equidistant @ SV153 @ SV64 @ SV153 @ SV115 )
= $false )
| ( ( equidistant @ SV10 @ SV64 @ SV10 @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(536,plain,
! [SV116: $i,SV183: $i,SV154: $i,SV65: $i,SV11: $i] :
( ( ( SV11 = SV65 )
= $true )
| ( ( between @ SV11 @ SV154 @ ( euclid1 @ SV11 @ SV154 @ SV65 @ SV183 @ SV116 ) )
= $true )
| ( ( between @ SV154 @ SV65 @ SV183 )
= $false )
| ( ( between @ SV11 @ SV65 @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(537,plain,
! [SV117: $i,SV155: $i,SV184: $i,SV66: $i,SV12: $i] :
( ( ( SV12 = SV66 )
= $true )
| ( ( between @ SV12 @ SV184 @ ( euclid2 @ SV12 @ SV155 @ SV66 @ SV184 @ SV117 ) )
= $true )
| ( ( between @ SV155 @ SV66 @ SV184 )
= $false )
| ( ( between @ SV12 @ SV66 @ SV117 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(538,plain,
! [SV118: $i,SV185: $i,SV156: $i,SV67: $i,SV13: $i] :
( ( ( SV13 = SV67 )
= $true )
| ( ( between @ ( euclid1 @ SV13 @ SV156 @ SV67 @ SV185 @ SV118 ) @ SV118 @ ( euclid2 @ SV13 @ SV156 @ SV67 @ SV185 @ SV118 ) )
= $true )
| ( ( between @ SV156 @ SV67 @ SV185 )
= $false )
| ( ( between @ SV13 @ SV67 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(539,plain,
! [SV119: $i,SV194: $i,SV68: $i,SV186: $i,SV157: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV157 @ SV14 @ SV186 )
= $false )
| ( ( ~ ( between @ SV14 @ SV68 @ SV157 )
| ~ ( between @ SV68 @ SV194 @ SV157 )
| ( between @ SV119 @ ( continuous @ SV14 @ SV68 @ SV119 @ SV194 @ SV157 @ SV186 ) @ SV186 ) )
= $true )
| ( ( equidistant @ SV14 @ SV68 @ SV14 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(540,plain,
! [SV120: $i,SV195: $i,SV69: $i,SV187: $i,SV158: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV158 @ SV15 @ SV187 )
= $false )
| ( ( ~ ( between @ SV15 @ SV69 @ SV158 )
| ~ ( between @ SV69 @ SV195 @ SV158 )
| ( equidistant @ SV15 @ SV195 @ SV15 @ ( continuous @ SV15 @ SV69 @ SV120 @ SV195 @ SV158 @ SV187 ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV69 @ SV15 @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[526]) ).
thf(541,plain,
! [SV79: $i,SV25: $i,SV196: $i,SV188: $i,SV166: $i,SV128: $i] :
( ( ( equidistant @ SV128 @ SV166 @ SV188 @ SV196 )
= $false )
| ( ( equidistant @ SV25 @ SV79 @ SV188 @ SV196 )
= $true )
| ( ( equidistant @ SV25 @ SV79 @ SV128 @ SV166 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[527]) ).
thf(542,plain,
! [SV130: $i,SV31: $i,SV197: $i,SV167: $i,SV189: $i,SV84: $i] :
( ( ( equidistant @ SV84 @ SV189 @ SV167 @ SV197 )
= $false )
| ( ( ~ ( between @ SV31 @ SV84 @ SV189 )
| ~ ( between @ SV130 @ SV167 @ SV197 )
| ( equidistant @ SV31 @ SV189 @ SV130 @ SV197 ) )
= $true )
| ( ( equidistant @ SV31 @ SV84 @ SV130 @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[528]) ).
thf(543,plain,
! [SV32: $i,SV168: $i,SV131: $i,SV85: $i] :
( ( ( equidistant @ SV85 @ SV131 @ SV85 @ SV168 )
= $false )
| ( ( ( SV32 = SV85 )
| ( SV131 = SV168 ) )
= $true )
| ( ( between @ SV32 @ SV85 @ SV168 )
= $false )
| ( ( between @ SV32 @ SV85 @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[529]) ).
thf(544,plain,
! [SV200: $i,SV112: $i,SV199: $i,SV6: $i,SV193: $i,SV150: $i,SV179: $i,SV60: $i] :
( ( ( ~ ( equidistant @ SV60 @ SV179 @ SV150 @ SV193 ) )
= $true )
| ( ( ~ ( equidistant @ SV6 @ SV199 @ SV112 @ SV200 )
| ~ ( equidistant @ SV60 @ SV199 @ SV150 @ SV200 )
| ~ ( between @ SV6 @ SV60 @ SV179 )
| ~ ( between @ SV112 @ SV150 @ SV193 )
| ( SV6 = SV60 )
| ( equidistant @ SV179 @ SV199 @ SV193 @ SV200 ) )
= $true )
| ( ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[534]) ).
thf(545,plain,
! [SV153: $i,SV10: $i,SV115: $i,SV64: $i,SV182: $i] :
( ( ( equidistant @ SV182 @ SV64 @ SV182 @ SV115 )
= $false )
| ( ( ( between @ SV10 @ SV153 @ SV182 )
| ( between @ SV153 @ SV182 @ SV10 )
| ( between @ SV182 @ SV10 @ SV153 )
| ( SV64 = SV115 ) )
= $true )
| ( ( equidistant @ SV153 @ SV64 @ SV153 @ SV115 )
= $false )
| ( ( equidistant @ SV10 @ SV64 @ SV10 @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(546,plain,
! [SV186: $i,SV119: $i,SV194: $i,SV157: $i,SV68: $i,SV14: $i] :
( ( ( ~ ( between @ SV14 @ SV68 @ SV157 ) )
= $true )
| ( ( ~ ( between @ SV68 @ SV194 @ SV157 )
| ( between @ SV119 @ ( continuous @ SV14 @ SV68 @ SV119 @ SV194 @ SV157 @ SV186 ) @ SV186 ) )
= $true )
| ( ( equidistant @ SV14 @ SV157 @ SV14 @ SV186 )
= $false )
| ( ( equidistant @ SV14 @ SV68 @ SV14 @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[539]) ).
thf(547,plain,
! [SV187: $i,SV120: $i,SV195: $i,SV158: $i,SV69: $i,SV15: $i] :
( ( ( ~ ( between @ SV15 @ SV69 @ SV158 ) )
= $true )
| ( ( ~ ( between @ SV69 @ SV195 @ SV158 )
| ( equidistant @ SV15 @ SV195 @ SV15 @ ( continuous @ SV15 @ SV69 @ SV120 @ SV195 @ SV158 @ SV187 ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV158 @ SV15 @ SV187 )
= $false )
| ( ( equidistant @ SV15 @ SV69 @ SV15 @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[540]) ).
thf(548,plain,
! [SV197: $i,SV167: $i,SV130: $i,SV189: $i,SV84: $i,SV31: $i] :
( ( ( ~ ( between @ SV31 @ SV84 @ SV189 ) )
= $true )
| ( ( ~ ( between @ SV130 @ SV167 @ SV197 )
| ( equidistant @ SV31 @ SV189 @ SV130 @ SV197 ) )
= $true )
| ( ( equidistant @ SV84 @ SV189 @ SV167 @ SV197 )
= $false )
| ( ( equidistant @ SV31 @ SV84 @ SV130 @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[542]) ).
thf(549,plain,
! [SV168: $i,SV131: $i,SV85: $i,SV32: $i] :
( ( ( SV32 = SV85 )
= $true )
| ( ( SV131 = SV168 )
= $true )
| ( ( equidistant @ SV85 @ SV131 @ SV85 @ SV168 )
= $false )
| ( ( between @ SV32 @ SV85 @ SV168 )
= $false )
| ( ( between @ SV32 @ SV85 @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(550,plain,
! [SV200: $i,SV112: $i,SV199: $i,SV6: $i,SV193: $i,SV150: $i,SV179: $i,SV60: $i] :
( ( ( equidistant @ SV60 @ SV179 @ SV150 @ SV193 )
= $false )
| ( ( ~ ( equidistant @ SV6 @ SV199 @ SV112 @ SV200 )
| ~ ( equidistant @ SV60 @ SV199 @ SV150 @ SV200 )
| ~ ( between @ SV6 @ SV60 @ SV179 )
| ~ ( between @ SV112 @ SV150 @ SV193 )
| ( SV6 = SV60 )
| ( equidistant @ SV179 @ SV199 @ SV193 @ SV200 ) )
= $true )
| ( ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(551,plain,
! [SV115: $i,SV64: $i,SV182: $i,SV153: $i,SV10: $i] :
( ( ( between @ SV10 @ SV153 @ SV182 )
= $true )
| ( ( ( between @ SV153 @ SV182 @ SV10 )
| ( between @ SV182 @ SV10 @ SV153 )
| ( SV64 = SV115 ) )
= $true )
| ( ( equidistant @ SV182 @ SV64 @ SV182 @ SV115 )
= $false )
| ( ( equidistant @ SV153 @ SV64 @ SV153 @ SV115 )
= $false )
| ( ( equidistant @ SV10 @ SV64 @ SV10 @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(552,plain,
! [SV186: $i,SV119: $i,SV194: $i,SV157: $i,SV68: $i,SV14: $i] :
( ( ( between @ SV14 @ SV68 @ SV157 )
= $false )
| ( ( ~ ( between @ SV68 @ SV194 @ SV157 )
| ( between @ SV119 @ ( continuous @ SV14 @ SV68 @ SV119 @ SV194 @ SV157 @ SV186 ) @ SV186 ) )
= $true )
| ( ( equidistant @ SV14 @ SV157 @ SV14 @ SV186 )
= $false )
| ( ( equidistant @ SV14 @ SV68 @ SV14 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(553,plain,
! [SV187: $i,SV120: $i,SV195: $i,SV158: $i,SV69: $i,SV15: $i] :
( ( ( between @ SV15 @ SV69 @ SV158 )
= $false )
| ( ( ~ ( between @ SV69 @ SV195 @ SV158 )
| ( equidistant @ SV15 @ SV195 @ SV15 @ ( continuous @ SV15 @ SV69 @ SV120 @ SV195 @ SV158 @ SV187 ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV158 @ SV15 @ SV187 )
= $false )
| ( ( equidistant @ SV15 @ SV69 @ SV15 @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(554,plain,
! [SV197: $i,SV167: $i,SV130: $i,SV189: $i,SV84: $i,SV31: $i] :
( ( ( between @ SV31 @ SV84 @ SV189 )
= $false )
| ( ( ~ ( between @ SV130 @ SV167 @ SV197 )
| ( equidistant @ SV31 @ SV189 @ SV130 @ SV197 ) )
= $true )
| ( ( equidistant @ SV84 @ SV189 @ SV167 @ SV197 )
= $false )
| ( ( equidistant @ SV31 @ SV84 @ SV130 @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[548]) ).
thf(555,plain,
! [SV193: $i,SV179: $i,SV150: $i,SV60: $i,SV200: $i,SV112: $i,SV199: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV199 @ SV112 @ SV200 ) )
= $true )
| ( ( ~ ( equidistant @ SV60 @ SV199 @ SV150 @ SV200 )
| ~ ( between @ SV6 @ SV60 @ SV179 )
| ~ ( between @ SV112 @ SV150 @ SV193 )
| ( SV6 = SV60 )
| ( equidistant @ SV179 @ SV199 @ SV193 @ SV200 ) )
= $true )
| ( ( equidistant @ SV60 @ SV179 @ SV150 @ SV193 )
= $false )
| ( ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[550]) ).
thf(556,plain,
! [SV115: $i,SV64: $i,SV10: $i,SV182: $i,SV153: $i] :
( ( ( between @ SV153 @ SV182 @ SV10 )
= $true )
| ( ( ( between @ SV182 @ SV10 @ SV153 )
| ( SV64 = SV115 ) )
= $true )
| ( ( between @ SV10 @ SV153 @ SV182 )
= $true )
| ( ( equidistant @ SV182 @ SV64 @ SV182 @ SV115 )
= $false )
| ( ( equidistant @ SV153 @ SV64 @ SV153 @ SV115 )
= $false )
| ( ( equidistant @ SV10 @ SV64 @ SV10 @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[551]) ).
thf(557,plain,
! [SV186: $i,SV14: $i,SV119: $i,SV157: $i,SV194: $i,SV68: $i] :
( ( ( ~ ( between @ SV68 @ SV194 @ SV157 ) )
= $true )
| ( ( between @ SV119 @ ( continuous @ SV14 @ SV68 @ SV119 @ SV194 @ SV157 @ SV186 ) @ SV186 )
= $true )
| ( ( between @ SV14 @ SV68 @ SV157 )
= $false )
| ( ( equidistant @ SV14 @ SV157 @ SV14 @ SV186 )
= $false )
| ( ( equidistant @ SV14 @ SV68 @ SV14 @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[552]) ).
thf(558,plain,
! [SV187: $i,SV120: $i,SV15: $i,SV158: $i,SV195: $i,SV69: $i] :
( ( ( ~ ( between @ SV69 @ SV195 @ SV158 ) )
= $true )
| ( ( equidistant @ SV15 @ SV195 @ SV15 @ ( continuous @ SV15 @ SV69 @ SV120 @ SV195 @ SV158 @ SV187 ) )
= $true )
| ( ( between @ SV15 @ SV69 @ SV158 )
= $false )
| ( ( equidistant @ SV15 @ SV158 @ SV15 @ SV187 )
= $false )
| ( ( equidistant @ SV15 @ SV69 @ SV15 @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[553]) ).
thf(559,plain,
! [SV84: $i,SV189: $i,SV31: $i,SV197: $i,SV167: $i,SV130: $i] :
( ( ( ~ ( between @ SV130 @ SV167 @ SV197 ) )
= $true )
| ( ( equidistant @ SV31 @ SV189 @ SV130 @ SV197 )
= $true )
| ( ( between @ SV31 @ SV84 @ SV189 )
= $false )
| ( ( equidistant @ SV84 @ SV189 @ SV167 @ SV197 )
= $false )
| ( ( equidistant @ SV31 @ SV84 @ SV130 @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(560,plain,
! [SV193: $i,SV179: $i,SV150: $i,SV60: $i,SV200: $i,SV112: $i,SV199: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV199 @ SV112 @ SV200 )
= $false )
| ( ( ~ ( equidistant @ SV60 @ SV199 @ SV150 @ SV200 )
| ~ ( between @ SV6 @ SV60 @ SV179 )
| ~ ( between @ SV112 @ SV150 @ SV193 )
| ( SV6 = SV60 )
| ( equidistant @ SV179 @ SV199 @ SV193 @ SV200 ) )
= $true )
| ( ( equidistant @ SV60 @ SV179 @ SV150 @ SV193 )
= $false )
| ( ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[555]) ).
thf(561,plain,
! [SV115: $i,SV64: $i,SV153: $i,SV10: $i,SV182: $i] :
( ( ( between @ SV182 @ SV10 @ SV153 )
= $true )
| ( ( SV64 = SV115 )
= $true )
| ( ( between @ SV153 @ SV182 @ SV10 )
= $true )
| ( ( between @ SV10 @ SV153 @ SV182 )
= $true )
| ( ( equidistant @ SV182 @ SV64 @ SV182 @ SV115 )
= $false )
| ( ( equidistant @ SV153 @ SV64 @ SV153 @ SV115 )
= $false )
| ( ( equidistant @ SV10 @ SV64 @ SV10 @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(562,plain,
! [SV186: $i,SV14: $i,SV119: $i,SV157: $i,SV194: $i,SV68: $i] :
( ( ( between @ SV68 @ SV194 @ SV157 )
= $false )
| ( ( between @ SV119 @ ( continuous @ SV14 @ SV68 @ SV119 @ SV194 @ SV157 @ SV186 ) @ SV186 )
= $true )
| ( ( between @ SV14 @ SV68 @ SV157 )
= $false )
| ( ( equidistant @ SV14 @ SV157 @ SV14 @ SV186 )
= $false )
| ( ( equidistant @ SV14 @ SV68 @ SV14 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[557]) ).
thf(563,plain,
! [SV187: $i,SV120: $i,SV15: $i,SV158: $i,SV195: $i,SV69: $i] :
( ( ( between @ SV69 @ SV195 @ SV158 )
= $false )
| ( ( equidistant @ SV15 @ SV195 @ SV15 @ ( continuous @ SV15 @ SV69 @ SV120 @ SV195 @ SV158 @ SV187 ) )
= $true )
| ( ( between @ SV15 @ SV69 @ SV158 )
= $false )
| ( ( equidistant @ SV15 @ SV158 @ SV15 @ SV187 )
= $false )
| ( ( equidistant @ SV15 @ SV69 @ SV15 @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[558]) ).
thf(564,plain,
! [SV84: $i,SV189: $i,SV31: $i,SV197: $i,SV167: $i,SV130: $i] :
( ( ( between @ SV130 @ SV167 @ SV197 )
= $false )
| ( ( equidistant @ SV31 @ SV189 @ SV130 @ SV197 )
= $true )
| ( ( between @ SV31 @ SV84 @ SV189 )
= $false )
| ( ( equidistant @ SV84 @ SV189 @ SV167 @ SV197 )
= $false )
| ( ( equidistant @ SV31 @ SV84 @ SV130 @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[559]) ).
thf(565,plain,
! [SV193: $i,SV112: $i,SV179: $i,SV6: $i,SV200: $i,SV150: $i,SV199: $i,SV60: $i] :
( ( ( ~ ( equidistant @ SV60 @ SV199 @ SV150 @ SV200 ) )
= $true )
| ( ( ~ ( between @ SV6 @ SV60 @ SV179 )
| ~ ( between @ SV112 @ SV150 @ SV193 )
| ( SV6 = SV60 )
| ( equidistant @ SV179 @ SV199 @ SV193 @ SV200 ) )
= $true )
| ( ( equidistant @ SV6 @ SV199 @ SV112 @ SV200 )
= $false )
| ( ( equidistant @ SV60 @ SV179 @ SV150 @ SV193 )
= $false )
| ( ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[560]) ).
thf(566,plain,
! [SV193: $i,SV112: $i,SV179: $i,SV6: $i,SV200: $i,SV150: $i,SV199: $i,SV60: $i] :
( ( ( equidistant @ SV60 @ SV199 @ SV150 @ SV200 )
= $false )
| ( ( ~ ( between @ SV6 @ SV60 @ SV179 )
| ~ ( between @ SV112 @ SV150 @ SV193 )
| ( SV6 = SV60 )
| ( equidistant @ SV179 @ SV199 @ SV193 @ SV200 ) )
= $true )
| ( ( equidistant @ SV6 @ SV199 @ SV112 @ SV200 )
= $false )
| ( ( equidistant @ SV60 @ SV179 @ SV150 @ SV193 )
= $false )
| ( ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[565]) ).
thf(567,plain,
! [SV200: $i,SV199: $i,SV193: $i,SV150: $i,SV112: $i,SV179: $i,SV60: $i,SV6: $i] :
( ( ( ~ ( between @ SV6 @ SV60 @ SV179 ) )
= $true )
| ( ( ~ ( between @ SV112 @ SV150 @ SV193 )
| ( SV6 = SV60 )
| ( equidistant @ SV179 @ SV199 @ SV193 @ SV200 ) )
= $true )
| ( ( equidistant @ SV60 @ SV199 @ SV150 @ SV200 )
= $false )
| ( ( equidistant @ SV6 @ SV199 @ SV112 @ SV200 )
= $false )
| ( ( equidistant @ SV60 @ SV179 @ SV150 @ SV193 )
= $false )
| ( ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[566]) ).
thf(568,plain,
! [SV200: $i,SV199: $i,SV193: $i,SV150: $i,SV112: $i,SV179: $i,SV60: $i,SV6: $i] :
( ( ( between @ SV6 @ SV60 @ SV179 )
= $false )
| ( ( ~ ( between @ SV112 @ SV150 @ SV193 )
| ( SV6 = SV60 )
| ( equidistant @ SV179 @ SV199 @ SV193 @ SV200 ) )
= $true )
| ( ( equidistant @ SV60 @ SV199 @ SV150 @ SV200 )
= $false )
| ( ( equidistant @ SV6 @ SV199 @ SV112 @ SV200 )
= $false )
| ( ( equidistant @ SV60 @ SV179 @ SV150 @ SV193 )
= $false )
| ( ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(569,plain,
! [SV200: $i,SV199: $i,SV179: $i,SV60: $i,SV6: $i,SV193: $i,SV150: $i,SV112: $i] :
( ( ( ~ ( between @ SV112 @ SV150 @ SV193 ) )
= $true )
| ( ( ( SV6 = SV60 )
| ( equidistant @ SV179 @ SV199 @ SV193 @ SV200 ) )
= $true )
| ( ( between @ SV6 @ SV60 @ SV179 )
= $false )
| ( ( equidistant @ SV60 @ SV199 @ SV150 @ SV200 )
= $false )
| ( ( equidistant @ SV6 @ SV199 @ SV112 @ SV200 )
= $false )
| ( ( equidistant @ SV60 @ SV179 @ SV150 @ SV193 )
= $false )
| ( ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[568]) ).
thf(570,plain,
! [SV200: $i,SV199: $i,SV179: $i,SV60: $i,SV6: $i,SV193: $i,SV150: $i,SV112: $i] :
( ( ( between @ SV112 @ SV150 @ SV193 )
= $false )
| ( ( ( SV6 = SV60 )
| ( equidistant @ SV179 @ SV199 @ SV193 @ SV200 ) )
= $true )
| ( ( between @ SV6 @ SV60 @ SV179 )
= $false )
| ( ( equidistant @ SV60 @ SV199 @ SV150 @ SV200 )
= $false )
| ( ( equidistant @ SV6 @ SV199 @ SV112 @ SV200 )
= $false )
| ( ( equidistant @ SV60 @ SV179 @ SV150 @ SV193 )
= $false )
| ( ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[569]) ).
thf(571,plain,
! [SV150: $i,SV112: $i,SV200: $i,SV193: $i,SV199: $i,SV179: $i,SV60: $i,SV6: $i] :
( ( ( SV6 = SV60 )
= $true )
| ( ( equidistant @ SV179 @ SV199 @ SV193 @ SV200 )
= $true )
| ( ( between @ SV112 @ SV150 @ SV193 )
= $false )
| ( ( between @ SV6 @ SV60 @ SV179 )
= $false )
| ( ( equidistant @ SV60 @ SV199 @ SV150 @ SV200 )
= $false )
| ( ( equidistant @ SV6 @ SV199 @ SV112 @ SV200 )
= $false )
| ( ( equidistant @ SV60 @ SV179 @ SV150 @ SV193 )
= $false )
| ( ( equidistant @ SV6 @ SV60 @ SV112 @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[570]) ).
thf(572,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[206,571,564,563,562,561,549,541,538,537,536,533,532,531,530,520,519,516,515,514,511,510,509,508,492,483,482,454,450,449,448,447,446,445,444,421,399,397,394,362,360,359,356,340,335,297,295,294,293,287,286,285,275,274,259,256,254,251,250,228,208,207]) ).
thf(573,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[572]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO037-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.06/0.19 % Computer : n008.cluster.edu
% 0.06/0.19 % Model : x86_64 x86_64
% 0.06/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.19 % Memory : 8046.5625MB
% 0.06/0.19 % OS : Linux 6.8.0-71-generic
% 0.06/0.19 % CPULimit : 300
% 0.06/0.19 % WCLimit : 300
% 0.06/0.19 % DateTime : Tue Oct 6 10:01:12 UTC 2026
% 0.06/0.19 % CPUTime :
% 0.06/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 55.20/9.56
% 55.20/9.56 No.of.Axioms: 61
% 55.20/9.56
% 55.20/9.56 Length.of.Defs: 0
% 55.20/9.56
% 55.20/9.56 Contains.Choice.Funs: false
% 55.20/9.56 ..................
% 55.20/9.56
% 55.20/9.56 ********************************
% 55.20/9.56 * All subproblems solved! *
% 55.20/9.56 ********************************
% 55.20/9.56 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:61,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:572,loop_count:0,foatp_calls:1,translation:fof_full)
% 55.20/9.56
% 55.20/9.56 %**** Beginning of derivation protocol ****
% 55.20/9.56 % SZS output start CNFRefutation
% See solution above
% 55.20/9.56
% 55.20/9.56 %**** End of derivation protocol ****
% 55.20/9.56 %**** no. of clauses in derivation: 573 ****
% 55.20/9.56 %**** clause counter: 572 ****
% 55.20/9.56
% 55.20/9.56 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:1,axioms:61,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:572,loop_count:0,foatp_calls:1,translation:fof_full)
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