%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO041-3 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:17:39 AM UTC 2026
% Result : Unsatisfiable 1.86s 0.52s
% Output : CNFRefutation 1.86s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 52
% Syntax : Number of formulae : 477 ( 290 unt; 0 typ; 0 def)
% Number of atoms : 2904 ( 990 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 6887 ( 637 ~;1001 |; 0 &;5249 @)
% ( 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 : 17 ( 14 usr; 8 con; 0-6 aty)
% Number of variables : 1959 ( 0 ^;1959 !; 0 ?;1959 :)
% 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(1,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).
thf(2,axiom,
! [U: $i,V: $i] : ( between @ U @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
thf(3,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
thf(4,axiom,
! [U: $i,W: $i,X: $i,V: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ( between @ V @ W @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).
thf(5,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
thf(6,axiom,
! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).
thf(7,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).
thf(8,axiom,
! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_3) ).
thf(9,axiom,
! [W: $i,X: $i,Y: $i,Z: $i,U: $i,V: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ( ( extension @ U @ V @ W @ X )
= ( extension @ U @ V @ Y @ Z ) )
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_2) ).
thf(10,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( U = V )
| ( W
= ( extension @ U @ V @ V @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_1) ).
thf(11,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ V @ X )
| ~ ( equidistant @ V @ W @ V @ X )
| ( U = V )
| ( W = X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9) ).
thf(12,axiom,
! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ U @ W @ U1 @ W1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8) ).
thf(13,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
thf(14,axiom,
! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
thf(15,axiom,
! [U: $i] :
( U
= ( reflection @ U @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).
thf(16,axiom,
! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_1) ).
thf(17,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
thf(18,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).
thf(19,axiom,
! [Y: $i,U: $i,V: $i,W: $i,X: $i] :
( ( Y
!= ( extension @ U @ V @ W @ X ) )
| ( between @ U @ V @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b0) ).
thf(20,axiom,
! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
thf(21,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ~ ( equidistant @ W @ X @ Y @ Z )
| ( equidistant @ U @ V @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5) ).
thf(22,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_5) ).
thf(23,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_4) ).
thf(24,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_3) ).
thf(25,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_2) ).
thf(26,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_1) ).
thf(27,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3) ).
thf(28,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
thf(29,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
thf(30,axiom,
! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
thf(31,axiom,
! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).
thf(32,axiom,
! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity1) ).
thf(33,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid3) ).
thf(34,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid2) ).
thf(35,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid1) ).
thf(36,axiom,
! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ W @ X @ V )
| ~ ( equidistant @ Y @ W @ Y @ V )
| ~ ( equidistant @ Z @ W @ Z @ V )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y )
| ( W = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_dimension) ).
thf(37,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(38,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(39,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(40,axiom,
! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ Y @ X @ W )
| ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch2) ).
thf(41,axiom,
! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ Y @ X @ W )
| ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch1) ).
thf(42,axiom,
! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(43,axiom,
! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i,V: $i,V1: $i] :
( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
| ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
| ~ ( equidistant @ X @ V @ X1 @ V1 )
| ~ ( equidistant @ Y @ V @ Y1 @ V1 )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equidistant @ Z @ V @ Z1 @ V1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_five_segment) ).
thf(44,axiom,
! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).
thf(45,axiom,
! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).
thf(46,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(47,axiom,
! [X: $i,Y: $i,Z: $i,V: $i,V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
thf(48,axiom,
! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(49,axiom,
between @ u @ w @ v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_between_u_and_v) ).
thf(50,axiom,
between @ u @ v @ w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
thf(51,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(52,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[51]) ).
thf(53,negated_conjecture,
v != w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_is_w) ).
thf(54,plain,
$false = $false,
inference(unfold_def,[status(thm)],[52]) ).
thf(55,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(56,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(57,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(58,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)],[4]) ).
thf(59,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(60,plain,
( ( ! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(61,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(62,plain,
( ( ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(63,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)],[9]) ).
thf(64,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)],[10]) ).
thf(65,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)],[11]) ).
thf(66,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)],[12]) ).
thf(67,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(68,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(69,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(70,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(71,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(72,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(73,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)],[19]) ).
thf(74,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(75,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)],[21]) ).
thf(76,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)],[22]) ).
thf(77,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)],[23]) ).
thf(78,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)],[24]) ).
thf(79,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)],[25]) ).
thf(80,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)],[26]) ).
thf(81,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)],[27]) ).
thf(82,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)],[28]) ).
thf(83,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(84,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(85,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)],[31]) ).
thf(86,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)],[32]) ).
thf(87,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)],[33]) ).
thf(88,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)],[34]) ).
thf(89,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)],[35]) ).
thf(90,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)],[36]) ).
thf(91,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(92,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(93,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(94,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)],[40]) ).
thf(95,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)],[41]) ).
thf(96,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[42]) ).
thf(97,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)],[43]) ).
thf(98,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(99,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(100,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(101,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)],[47]) ).
thf(102,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(103,plain,
( ( between @ u @ w @ v )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(104,plain,
( ( between @ u @ v @ w )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(105,plain,
( ( v != w )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(106,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[54]) ).
thf(107,plain,
( ( ! [U: $i,W: $i,X: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ! [V: $i] : ( between @ V @ W @ X ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(108,plain,
( ( ! [W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ W @ X )
= ( extension @ U @ V @ Y @ Z ) )
| ( U = V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(109,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ U @ V @ X )
| ~ ( equidistant @ V @ W @ V @ X )
| ( U = V )
| ( W = X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(110,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ! [W: $i,W1: $i] :
( ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ U @ W @ U1 @ W1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(111,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(112,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(113,plain,
( ( ! [Y: $i,U: $i,V: $i] :
( ! [W: $i,X: $i] :
( Y
!= ( extension @ U @ V @ W @ X ) )
| ( between @ U @ V @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(114,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ! [Y: $i,Z: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ( equidistant @ U @ V @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(115,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ! [X1: $i] :
( ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(116,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ! [X1: $i] :
( ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(117,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(118,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(119,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[89]) ).
thf(120,plain,
( ( ! [X: $i,W: $i,V: $i] :
( ~ ( equidistant @ X @ W @ X @ V )
| ! [Y: $i] :
( ~ ( equidistant @ Y @ W @ Y @ V )
| ! [Z: $i] :
( ~ ( equidistant @ Z @ W @ Z @ V )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( W = V )
| ( between @ Z @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[90]) ).
thf(121,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [Y: $i,X: $i] :
( ~ ( between @ Y @ X @ W )
| ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
thf(122,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [Y: $i,X: $i] :
( ~ ( between @ Y @ X @ W )
| ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(123,plain,
( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i] :
( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
| ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
| ! [V: $i,V1: $i] :
( ~ ( equidistant @ X @ V @ X1 @ V1 )
| ~ ( equidistant @ Y @ V @ Y1 @ V1 )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equidistant @ Z @ V @ Z1 @ V1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[97]) ).
thf(124,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[100]) ).
thf(125,plain,
( ( ! [X: $i,Y: $i,Z: $i,V: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ! [V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[101]) ).
thf(126,plain,
( ( v != w )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(127,plain,
( ( v != w )
= $true ),
inference(copy,[status(thm)],[126]) ).
thf(128,plain,
( ( between @ u @ v @ w )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(129,plain,
( ( between @ u @ w @ v )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(130,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(131,plain,
( ( ! [X: $i,Y: $i,Z: $i,V: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ! [V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(132,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(133,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(134,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(135,plain,
( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i] :
( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
| ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
| ! [V: $i,V1: $i] :
( ~ ( equidistant @ X @ V @ X1 @ V1 )
| ~ ( equidistant @ Y @ V @ Y1 @ V1 )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equidistant @ Z @ V @ Z1 @ V1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(136,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(137,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [Y: $i,X: $i] :
( ~ ( between @ Y @ X @ W )
| ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[122]) ).
thf(138,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [Y: $i,X: $i] :
( ~ ( between @ Y @ X @ W )
| ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[121]) ).
thf(139,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(140,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(141,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(142,plain,
( ( ! [X: $i,W: $i,V: $i] :
( ~ ( equidistant @ X @ W @ X @ V )
| ! [Y: $i] :
( ~ ( equidistant @ Y @ W @ Y @ V )
| ! [Z: $i] :
( ~ ( equidistant @ Z @ W @ Z @ V )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( W = V )
| ( between @ Z @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(143,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(144,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(145,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(146,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ! [X1: $i] :
( ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(147,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ! [X1: $i] :
( ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(148,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(149,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(150,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(151,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(152,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(153,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(154,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(155,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(156,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(157,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ! [Y: $i,Z: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ( equidistant @ U @ V @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(158,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(159,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)],[113]) ).
thf(160,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(161,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(162,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(163,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(164,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(165,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(166,plain,
( ( ! [U: $i,V: $i,U1: $i,V1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ! [W: $i,W1: $i] :
( ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ U @ W @ U1 @ W1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(167,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ U @ V @ X )
| ~ ( equidistant @ V @ W @ V @ X )
| ( U = V )
| ( W = X ) ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(168,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( U = V )
| ( W
= ( extension @ U @ V @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(169,plain,
( ( ! [W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ W @ X )
= ( extension @ U @ V @ Y @ Z ) )
| ( U = V ) ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(170,plain,
( ( ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(171,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(172,plain,
( ( ! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(173,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(174,plain,
( ( ! [U: $i,W: $i,X: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ! [V: $i] : ( between @ V @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(175,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(176,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(177,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(178,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[106]) ).
thf(179,plain,
( ( v = w )
= $false ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(180,plain,
! [SV1: $i] :
( ( ! [SY167: $i] : ( equidistant @ SV1 @ SY167 @ SY167 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(181,plain,
! [SV2: $i] :
( ( ! [SY168: $i,SY169: $i,SY170: $i] :
( ~ ( equidistant @ SV2 @ SY168 @ SY169 @ SY170 )
| ! [SY171: $i,SY172: $i] :
( ~ ( equidistant @ SV2 @ SY168 @ SY171 @ SY172 )
| ( equidistant @ SY169 @ SY170 @ SY171 @ SY172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(182,plain,
! [SV3: $i] :
( ( ! [SY173: $i] :
( ! [SY174: $i] :
~ ( equidistant @ SV3 @ SY173 @ SY174 @ SY174 )
| ( SV3 = SY173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(183,plain,
! [SV4: $i] :
( ( ! [SY175: $i,SY176: $i,SY177: $i] : ( between @ SV4 @ SY175 @ ( extension @ SV4 @ SY175 @ SY176 @ SY177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(184,plain,
! [SV5: $i] :
( ( ! [SY178: $i,SY179: $i,SY180: $i] : ( equidistant @ SV5 @ ( extension @ SY178 @ SV5 @ SY179 @ SY180 ) @ SY179 @ SY180 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(185,plain,
! [SV6: $i] :
( ( ! [SY181: $i,SY182: $i,SY183: $i,SY184: $i,SY185: $i] :
( ~ ( equidistant @ SV6 @ SY181 @ SY182 @ SY183 )
| ~ ( equidistant @ SY181 @ SY184 @ SY183 @ SY185 )
| ! [SY186: $i,SY187: $i] :
( ~ ( equidistant @ SV6 @ SY186 @ SY182 @ SY187 )
| ~ ( equidistant @ SY181 @ SY186 @ SY183 @ SY187 )
| ~ ( between @ SV6 @ SY181 @ SY184 )
| ~ ( between @ SY182 @ SY183 @ SY185 )
| ( SV6 = SY181 )
| ( equidistant @ SY184 @ SY186 @ SY185 @ SY187 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(186,plain,
! [SV7: $i] :
( ( ! [SY188: $i] :
( ~ ( between @ SV7 @ SY188 @ SV7 )
| ( SV7 = SY188 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(187,plain,
! [SV8: $i] :
( ( ! [SY189: $i,SY190: $i] :
( ~ ( between @ SV8 @ SY189 @ SY190 )
| ! [SY191: $i,SY192: $i] :
( ~ ( between @ SY191 @ SY192 @ SY190 )
| ( between @ SY189 @ ( inner_pasch @ SV8 @ SY189 @ SY190 @ SY192 @ SY191 ) @ SY191 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(188,plain,
! [SV9: $i] :
( ( ! [SY193: $i,SY194: $i] :
( ~ ( between @ SV9 @ SY193 @ SY194 )
| ! [SY195: $i,SY196: $i] :
( ~ ( between @ SY195 @ SY196 @ SY194 )
| ( between @ SY196 @ ( inner_pasch @ SV9 @ SY193 @ SY194 @ SY196 @ SY195 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(189,plain,
( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(190,plain,
( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(191,plain,
( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(192,plain,
! [SV10: $i] :
( ( ! [SY197: $i,SY198: $i] :
( ~ ( equidistant @ SV10 @ SY197 @ SV10 @ SY198 )
| ! [SY199: $i] :
( ~ ( equidistant @ SY199 @ SY197 @ SY199 @ SY198 )
| ! [SY200: $i] :
( ~ ( equidistant @ SY200 @ SY197 @ SY200 @ SY198 )
| ( between @ SV10 @ SY199 @ SY200 )
| ( between @ SY199 @ SY200 @ SV10 )
| ( SY197 = SY198 )
| ( between @ SY200 @ SV10 @ SY199 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(193,plain,
! [SV11: $i] :
( ( ! [SY201: $i,SY202: $i] :
( ~ ( between @ SV11 @ SY201 @ SY202 )
| ! [SY203: $i,SY204: $i] :
( ~ ( between @ SY203 @ SY201 @ SY204 )
| ( SV11 = SY201 )
| ( between @ SV11 @ SY203 @ ( euclid1 @ SV11 @ SY203 @ SY201 @ SY204 @ SY202 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(194,plain,
! [SV12: $i] :
( ( ! [SY205: $i,SY206: $i] :
( ~ ( between @ SV12 @ SY205 @ SY206 )
| ! [SY207: $i,SY208: $i] :
( ~ ( between @ SY207 @ SY205 @ SY208 )
| ( SV12 = SY205 )
| ( between @ SV12 @ SY208 @ ( euclid2 @ SV12 @ SY207 @ SY205 @ SY208 @ SY206 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(195,plain,
! [SV13: $i] :
( ( ! [SY209: $i,SY210: $i] :
( ~ ( between @ SV13 @ SY209 @ SY210 )
| ! [SY211: $i,SY212: $i] :
( ~ ( between @ SY211 @ SY209 @ SY212 )
| ( SV13 = SY209 )
| ( between @ ( euclid1 @ SV13 @ SY211 @ SY209 @ SY212 @ SY210 ) @ SY210 @ ( euclid2 @ SV13 @ SY211 @ SY209 @ SY212 @ SY210 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(196,plain,
! [SV14: $i] :
( ( ! [SY213: $i,SY214: $i,SY215: $i] :
( ~ ( equidistant @ SV14 @ SY213 @ SV14 @ SY214 )
| ! [SY216: $i] :
( ~ ( equidistant @ SV14 @ SY215 @ SV14 @ SY216 )
| ~ ( between @ SV14 @ SY213 @ SY215 )
| ! [SY217: $i] :
( ~ ( between @ SY213 @ SY217 @ SY215 )
| ( between @ SY214 @ ( continuous @ SV14 @ SY213 @ SY214 @ SY217 @ SY215 @ SY216 ) @ SY216 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(197,plain,
! [SV15: $i] :
( ( ! [SY218: $i,SY219: $i,SY220: $i] :
( ~ ( equidistant @ SV15 @ SY218 @ SV15 @ SY219 )
| ! [SY221: $i] :
( ~ ( equidistant @ SV15 @ SY220 @ SV15 @ SY221 )
| ~ ( between @ SV15 @ SY218 @ SY220 )
| ! [SY222: $i] :
( ~ ( between @ SY218 @ SY222 @ SY220 )
| ( equidistant @ SV15 @ SY222 @ SV15 @ ( continuous @ SV15 @ SY218 @ SY219 @ SY222 @ SY220 @ SY221 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(198,plain,
! [SV16: $i] :
( ( ! [SY223: $i] :
( ( reflection @ SV16 @ SY223 )
= ( extension @ SV16 @ SY223 @ SV16 @ SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(199,plain,
! [SV17: $i] :
( ( ! [SY224: $i] : ( equidistant @ SV17 @ SY224 @ SV17 @ SY224 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(200,plain,
! [SV18: $i] :
( ( ! [SY225: $i,SY226: $i,SY227: $i] :
( ~ ( equidistant @ SV18 @ SY225 @ SY226 @ SY227 )
| ( equidistant @ SY226 @ SY227 @ SV18 @ SY225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(201,plain,
! [SV19: $i] :
( ( ! [SY228: $i,SY229: $i,SY230: $i] :
( ~ ( equidistant @ SV19 @ SY228 @ SY229 @ SY230 )
| ( equidistant @ SY228 @ SV19 @ SY229 @ SY230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(202,plain,
! [SV20: $i] :
( ( ! [SY231: $i,SY232: $i,SY233: $i] :
( ~ ( equidistant @ SV20 @ SY231 @ SY232 @ SY233 )
| ( equidistant @ SV20 @ SY231 @ SY233 @ SY232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(203,plain,
! [SV21: $i] :
( ( ! [SY234: $i,SY235: $i,SY236: $i] :
( ~ ( equidistant @ SV21 @ SY234 @ SY235 @ SY236 )
| ( equidistant @ SY234 @ SV21 @ SY236 @ SY235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(204,plain,
! [SV22: $i] :
( ( ! [SY237: $i,SY238: $i,SY239: $i] :
( ~ ( equidistant @ SV22 @ SY237 @ SY238 @ SY239 )
| ( equidistant @ SY238 @ SY239 @ SY237 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(205,plain,
! [SV23: $i] :
( ( ! [SY240: $i,SY241: $i,SY242: $i] :
( ~ ( equidistant @ SV23 @ SY240 @ SY241 @ SY242 )
| ( equidistant @ SY242 @ SY241 @ SV23 @ SY240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(206,plain,
! [SV24: $i] :
( ( ! [SY243: $i,SY244: $i,SY245: $i] :
( ~ ( equidistant @ SV24 @ SY243 @ SY244 @ SY245 )
| ( equidistant @ SY245 @ SY244 @ SY243 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(207,plain,
! [SV25: $i] :
( ( ! [SY246: $i,SY247: $i,SY248: $i] :
( ~ ( equidistant @ SV25 @ SY246 @ SY247 @ SY248 )
| ! [SY249: $i,SY250: $i] :
( ~ ( equidistant @ SY247 @ SY248 @ SY249 @ SY250 )
| ( equidistant @ SV25 @ SY246 @ SY249 @ SY250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(208,plain,
! [SV26: $i] :
( ( ! [SY251: $i,SY252: $i] :
( SV26
= ( extension @ SY251 @ SV26 @ SY252 @ SY252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(209,plain,
! [SV27: $i] :
( ( ! [SY253: $i,SY254: $i] :
( ! [SY255: $i,SY256: $i] :
( SV27
!= ( extension @ SY253 @ SY254 @ SY255 @ SY256 ) )
| ( between @ SY253 @ SY254 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(210,plain,
! [SV28: $i] :
( ( ! [SY257: $i] : ( between @ SV28 @ SY257 @ ( reflection @ SV28 @ SY257 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(211,plain,
! [SV29: $i] :
( ( ! [SY258: $i] : ( equidistant @ SV29 @ ( reflection @ SY258 @ SV29 ) @ SY258 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(212,plain,
! [SV30: $i] :
( ( ! [SY259: $i] :
( ( SV30 != SY259 )
| ( SY259
= ( reflection @ SV30 @ SY259 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(213,plain,
! [SV31: $i] :
( ( SV31
= ( reflection @ SV31 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(214,plain,
! [SV32: $i] :
( ( ! [SY260: $i] :
( ( SV32
!= ( reflection @ SY260 @ SV32 ) )
| ( SY260 = SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(215,plain,
! [SV33: $i] :
( ( ! [SY261: $i] : ( equidistant @ SV33 @ SV33 @ SY261 @ SY261 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(216,plain,
! [SV34: $i] :
( ( ! [SY262: $i,SY263: $i,SY264: $i] :
( ~ ( equidistant @ SV34 @ SY262 @ SY263 @ SY264 )
| ! [SY265: $i,SY266: $i] :
( ~ ( equidistant @ SY262 @ SY265 @ SY264 @ SY266 )
| ~ ( between @ SV34 @ SY262 @ SY265 )
| ~ ( between @ SY263 @ SY264 @ SY266 )
| ( equidistant @ SV34 @ SY265 @ SY263 @ SY266 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(217,plain,
! [SV35: $i] :
( ( ! [SY267: $i,SY268: $i] :
( ~ ( between @ SV35 @ SY267 @ SY268 )
| ! [SY269: $i] :
( ~ ( between @ SV35 @ SY267 @ SY269 )
| ~ ( equidistant @ SY267 @ SY268 @ SY267 @ SY269 )
| ( SV35 = SY267 )
| ( SY268 = SY269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(218,plain,
! [SV36: $i] :
( ( ! [SY270: $i,SY271: $i] :
( ~ ( between @ SV36 @ SY270 @ SY271 )
| ( SV36 = SY270 )
| ( SY271
= ( extension @ SV36 @ SY270 @ SY270 @ SY271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(219,plain,
! [SV37: $i] :
( ( ! [SY272: $i,SY273: $i,SY274: $i] :
( ~ ( equidistant @ SV37 @ SY272 @ SY273 @ SY274 )
| ! [SY275: $i,SY276: $i] :
( ( ( extension @ SY275 @ SY276 @ SV37 @ SY272 )
= ( extension @ SY275 @ SY276 @ SY273 @ SY274 ) )
| ( SY275 = SY276 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(220,plain,
! [SV38: $i] :
( ( ! [SY277: $i] :
( ( ( extension @ SV38 @ SY277 @ SV38 @ SY277 )
= ( extension @ SV38 @ SY277 @ SY277 @ SV38 ) )
| ( SV38 = SY277 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(221,plain,
! [SV39: $i] :
( ( ! [SY278: $i] : ( equidistant @ SV39 @ SY278 @ SV39 @ ( reflection @ ( reflection @ SY278 @ SV39 ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(222,plain,
! [SV40: $i] :
( ( ! [SY279: $i] :
( SV40
= ( reflection @ ( reflection @ SV40 @ SY279 ) @ SY279 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(223,plain,
! [SV41: $i] :
( ( ! [SY280: $i] : ( between @ SV41 @ SY280 @ SY280 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(224,plain,
! [SV42: $i] :
( ( ! [SY281: $i,SY282: $i] :
( ~ ( between @ SV42 @ SY281 @ SY282 )
| ( SV42 != SY282 )
| ! [V: $i] : ( between @ V @ SY281 @ SY282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(225,plain,
! [SV43: $i] :
( ( ! [SY284: $i,SY285: $i] :
( ~ ( between @ SV43 @ SY284 @ SY285 )
| ( between @ SY285 @ SY284 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(226,plain,
! [SV44: $i] :
( ( ! [SY286: $i] : ( between @ SV44 @ SV44 @ SY286 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(227,plain,
! [SV45: $i] :
( ( ! [SY287: $i,SY288: $i] :
( ~ ( between @ SV45 @ SY287 @ SY288 )
| ~ ( between @ SY287 @ SV45 @ SY288 )
| ( SV45 = SY287 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(228,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(229,plain,
! [SV46: $i,SV1: $i] :
( ( equidistant @ SV1 @ SV46 @ SV46 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(230,plain,
! [SV47: $i,SV2: $i] :
( ( ! [SY289: $i,SY290: $i] :
( ~ ( equidistant @ SV2 @ SV47 @ SY289 @ SY290 )
| ! [SY291: $i,SY292: $i] :
( ~ ( equidistant @ SV2 @ SV47 @ SY291 @ SY292 )
| ( equidistant @ SY289 @ SY290 @ SY291 @ SY292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(231,plain,
! [SV48: $i,SV3: $i] :
( ( ! [SY293: $i] :
~ ( equidistant @ SV3 @ SV48 @ SY293 @ SY293 )
| ( SV3 = SV48 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(232,plain,
! [SV49: $i,SV4: $i] :
( ( ! [SY294: $i,SY295: $i] : ( between @ SV4 @ SV49 @ ( extension @ SV4 @ SV49 @ SY294 @ SY295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(233,plain,
! [SV50: $i,SV5: $i] :
( ( ! [SY296: $i,SY297: $i] : ( equidistant @ SV5 @ ( extension @ SV50 @ SV5 @ SY296 @ SY297 ) @ SY296 @ SY297 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(234,plain,
! [SV51: $i,SV6: $i] :
( ( ! [SY298: $i,SY299: $i,SY300: $i,SY301: $i] :
( ~ ( equidistant @ SV6 @ SV51 @ SY298 @ SY299 )
| ~ ( equidistant @ SV51 @ SY300 @ SY299 @ SY301 )
| ! [SY302: $i,SY303: $i] :
( ~ ( equidistant @ SV6 @ SY302 @ SY298 @ SY303 )
| ~ ( equidistant @ SV51 @ SY302 @ SY299 @ SY303 )
| ~ ( between @ SV6 @ SV51 @ SY300 )
| ~ ( between @ SY298 @ SY299 @ SY301 )
| ( SV6 = SV51 )
| ( equidistant @ SY300 @ SY302 @ SY301 @ SY303 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(235,plain,
! [SV52: $i,SV7: $i] :
( ( ~ ( between @ SV7 @ SV52 @ SV7 )
| ( SV7 = SV52 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(236,plain,
! [SV53: $i,SV8: $i] :
( ( ! [SY304: $i] :
( ~ ( between @ SV8 @ SV53 @ SY304 )
| ! [SY305: $i,SY306: $i] :
( ~ ( between @ SY305 @ SY306 @ SY304 )
| ( between @ SV53 @ ( inner_pasch @ SV8 @ SV53 @ SY304 @ SY306 @ SY305 ) @ SY305 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(237,plain,
! [SV54: $i,SV9: $i] :
( ( ! [SY307: $i] :
( ~ ( between @ SV9 @ SV54 @ SY307 )
| ! [SY308: $i,SY309: $i] :
( ~ ( between @ SY308 @ SY309 @ SY307 )
| ( between @ SY309 @ ( inner_pasch @ SV9 @ SV54 @ SY307 @ SY309 @ SY308 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(238,plain,
! [SV55: $i,SV10: $i] :
( ( ! [SY310: $i] :
( ~ ( equidistant @ SV10 @ SV55 @ SV10 @ SY310 )
| ! [SY311: $i] :
( ~ ( equidistant @ SY311 @ SV55 @ SY311 @ SY310 )
| ! [SY312: $i] :
( ~ ( equidistant @ SY312 @ SV55 @ SY312 @ SY310 )
| ( between @ SV10 @ SY311 @ SY312 )
| ( between @ SY311 @ SY312 @ SV10 )
| ( SV55 = SY310 )
| ( between @ SY312 @ SV10 @ SY311 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(239,plain,
! [SV56: $i,SV11: $i] :
( ( ! [SY313: $i] :
( ~ ( between @ SV11 @ SV56 @ SY313 )
| ! [SY314: $i,SY315: $i] :
( ~ ( between @ SY314 @ SV56 @ SY315 )
| ( SV11 = SV56 )
| ( between @ SV11 @ SY314 @ ( euclid1 @ SV11 @ SY314 @ SV56 @ SY315 @ SY313 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(240,plain,
! [SV57: $i,SV12: $i] :
( ( ! [SY316: $i] :
( ~ ( between @ SV12 @ SV57 @ SY316 )
| ! [SY317: $i,SY318: $i] :
( ~ ( between @ SY317 @ SV57 @ SY318 )
| ( SV12 = SV57 )
| ( between @ SV12 @ SY318 @ ( euclid2 @ SV12 @ SY317 @ SV57 @ SY318 @ SY316 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(241,plain,
! [SV58: $i,SV13: $i] :
( ( ! [SY319: $i] :
( ~ ( between @ SV13 @ SV58 @ SY319 )
| ! [SY320: $i,SY321: $i] :
( ~ ( between @ SY320 @ SV58 @ SY321 )
| ( SV13 = SV58 )
| ( between @ ( euclid1 @ SV13 @ SY320 @ SV58 @ SY321 @ SY319 ) @ SY319 @ ( euclid2 @ SV13 @ SY320 @ SV58 @ SY321 @ SY319 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(242,plain,
! [SV59: $i,SV14: $i] :
( ( ! [SY322: $i,SY323: $i] :
( ~ ( equidistant @ SV14 @ SV59 @ SV14 @ SY322 )
| ! [SY324: $i] :
( ~ ( equidistant @ SV14 @ SY323 @ SV14 @ SY324 )
| ~ ( between @ SV14 @ SV59 @ SY323 )
| ! [SY325: $i] :
( ~ ( between @ SV59 @ SY325 @ SY323 )
| ( between @ SY322 @ ( continuous @ SV14 @ SV59 @ SY322 @ SY325 @ SY323 @ SY324 ) @ SY324 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(243,plain,
! [SV60: $i,SV15: $i] :
( ( ! [SY326: $i,SY327: $i] :
( ~ ( equidistant @ SV15 @ SV60 @ SV15 @ SY326 )
| ! [SY328: $i] :
( ~ ( equidistant @ SV15 @ SY327 @ SV15 @ SY328 )
| ~ ( between @ SV15 @ SV60 @ SY327 )
| ! [SY329: $i] :
( ~ ( between @ SV60 @ SY329 @ SY327 )
| ( equidistant @ SV15 @ SY329 @ SV15 @ ( continuous @ SV15 @ SV60 @ SY326 @ SY329 @ SY327 @ SY328 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(244,plain,
! [SV61: $i,SV16: $i] :
( ( ( reflection @ SV16 @ SV61 )
= ( extension @ SV16 @ SV61 @ SV16 @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(245,plain,
! [SV62: $i,SV17: $i] :
( ( equidistant @ SV17 @ SV62 @ SV17 @ SV62 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(246,plain,
! [SV63: $i,SV18: $i] :
( ( ! [SY330: $i,SY331: $i] :
( ~ ( equidistant @ SV18 @ SV63 @ SY330 @ SY331 )
| ( equidistant @ SY330 @ SY331 @ SV18 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(247,plain,
! [SV64: $i,SV19: $i] :
( ( ! [SY332: $i,SY333: $i] :
( ~ ( equidistant @ SV19 @ SV64 @ SY332 @ SY333 )
| ( equidistant @ SV64 @ SV19 @ SY332 @ SY333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(248,plain,
! [SV65: $i,SV20: $i] :
( ( ! [SY334: $i,SY335: $i] :
( ~ ( equidistant @ SV20 @ SV65 @ SY334 @ SY335 )
| ( equidistant @ SV20 @ SV65 @ SY335 @ SY334 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(249,plain,
! [SV66: $i,SV21: $i] :
( ( ! [SY336: $i,SY337: $i] :
( ~ ( equidistant @ SV21 @ SV66 @ SY336 @ SY337 )
| ( equidistant @ SV66 @ SV21 @ SY337 @ SY336 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(250,plain,
! [SV67: $i,SV22: $i] :
( ( ! [SY338: $i,SY339: $i] :
( ~ ( equidistant @ SV22 @ SV67 @ SY338 @ SY339 )
| ( equidistant @ SY338 @ SY339 @ SV67 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(251,plain,
! [SV68: $i,SV23: $i] :
( ( ! [SY340: $i,SY341: $i] :
( ~ ( equidistant @ SV23 @ SV68 @ SY340 @ SY341 )
| ( equidistant @ SY341 @ SY340 @ SV23 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(252,plain,
! [SV69: $i,SV24: $i] :
( ( ! [SY342: $i,SY343: $i] :
( ~ ( equidistant @ SV24 @ SV69 @ SY342 @ SY343 )
| ( equidistant @ SY343 @ SY342 @ SV69 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(253,plain,
! [SV70: $i,SV25: $i] :
( ( ! [SY344: $i,SY345: $i] :
( ~ ( equidistant @ SV25 @ SV70 @ SY344 @ SY345 )
| ! [SY346: $i,SY347: $i] :
( ~ ( equidistant @ SY344 @ SY345 @ SY346 @ SY347 )
| ( equidistant @ SV25 @ SV70 @ SY346 @ SY347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(254,plain,
! [SV71: $i,SV26: $i] :
( ( ! [SY348: $i] :
( SV26
= ( extension @ SV71 @ SV26 @ SY348 @ SY348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(255,plain,
! [SV72: $i,SV27: $i] :
( ( ! [SY349: $i] :
( ! [SY350: $i,SY351: $i] :
( SV27
!= ( extension @ SV72 @ SY349 @ SY350 @ SY351 ) )
| ( between @ SV72 @ SY349 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(256,plain,
! [SV73: $i,SV28: $i] :
( ( between @ SV28 @ SV73 @ ( reflection @ SV28 @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(257,plain,
! [SV74: $i,SV29: $i] :
( ( equidistant @ SV29 @ ( reflection @ SV74 @ SV29 ) @ SV74 @ SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(258,plain,
! [SV75: $i,SV30: $i] :
( ( ( SV30 != SV75 )
| ( SV75
= ( reflection @ SV30 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(259,plain,
! [SV76: $i,SV32: $i] :
( ( ( SV32
!= ( reflection @ SV76 @ SV32 ) )
| ( SV76 = SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(260,plain,
! [SV77: $i,SV33: $i] :
( ( equidistant @ SV33 @ SV33 @ SV77 @ SV77 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(261,plain,
! [SV78: $i,SV34: $i] :
( ( ! [SY352: $i,SY353: $i] :
( ~ ( equidistant @ SV34 @ SV78 @ SY352 @ SY353 )
| ! [SY354: $i,SY355: $i] :
( ~ ( equidistant @ SV78 @ SY354 @ SY353 @ SY355 )
| ~ ( between @ SV34 @ SV78 @ SY354 )
| ~ ( between @ SY352 @ SY353 @ SY355 )
| ( equidistant @ SV34 @ SY354 @ SY352 @ SY355 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(262,plain,
! [SV79: $i,SV35: $i] :
( ( ! [SY356: $i] :
( ~ ( between @ SV35 @ SV79 @ SY356 )
| ! [SY357: $i] :
( ~ ( between @ SV35 @ SV79 @ SY357 )
| ~ ( equidistant @ SV79 @ SY356 @ SV79 @ SY357 )
| ( SV35 = SV79 )
| ( SY356 = SY357 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(263,plain,
! [SV80: $i,SV36: $i] :
( ( ! [SY358: $i] :
( ~ ( between @ SV36 @ SV80 @ SY358 )
| ( SV36 = SV80 )
| ( SY358
= ( extension @ SV36 @ SV80 @ SV80 @ SY358 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(264,plain,
! [SV81: $i,SV37: $i] :
( ( ! [SY359: $i,SY360: $i] :
( ~ ( equidistant @ SV37 @ SV81 @ SY359 @ SY360 )
| ! [SY361: $i,SY362: $i] :
( ( ( extension @ SY361 @ SY362 @ SV37 @ SV81 )
= ( extension @ SY361 @ SY362 @ SY359 @ SY360 ) )
| ( SY361 = SY362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(265,plain,
! [SV82: $i,SV38: $i] :
( ( ( ( extension @ SV38 @ SV82 @ SV38 @ SV82 )
= ( extension @ SV38 @ SV82 @ SV82 @ SV38 ) )
| ( SV38 = SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(266,plain,
! [SV83: $i,SV39: $i] :
( ( equidistant @ SV39 @ SV83 @ SV39 @ ( reflection @ ( reflection @ SV83 @ SV39 ) @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(267,plain,
! [SV84: $i,SV40: $i] :
( ( SV40
= ( reflection @ ( reflection @ SV40 @ SV84 ) @ SV84 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(268,plain,
! [SV85: $i,SV41: $i] :
( ( between @ SV41 @ SV85 @ SV85 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(269,plain,
! [SV86: $i,SV42: $i] :
( ( ! [SY363: $i] :
( ~ ( between @ SV42 @ SV86 @ SY363 )
| ( SV42 != SY363 )
| ! [SY364: $i] : ( between @ SY364 @ SV86 @ SY363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(270,plain,
! [SV87: $i,SV43: $i] :
( ( ! [SY365: $i] :
( ~ ( between @ SV43 @ SV87 @ SY365 )
| ( between @ SY365 @ SV87 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(271,plain,
! [SV88: $i,SV44: $i] :
( ( between @ SV44 @ SV44 @ SV88 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(272,plain,
! [SV89: $i,SV45: $i] :
( ( ! [SY366: $i] :
( ~ ( between @ SV45 @ SV89 @ SY366 )
| ~ ( between @ SV89 @ SV45 @ SY366 )
| ( SV45 = SV89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(273,plain,
! [SV90: $i,SV47: $i,SV2: $i] :
( ( ! [SY367: $i] :
( ~ ( equidistant @ SV2 @ SV47 @ SV90 @ SY367 )
| ! [SY368: $i,SY369: $i] :
( ~ ( equidistant @ SV2 @ SV47 @ SY368 @ SY369 )
| ( equidistant @ SV90 @ SY367 @ SY368 @ SY369 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(274,plain,
! [SV48: $i,SV3: $i] :
( ( ( ! [SY293: $i] :
~ ( equidistant @ SV3 @ SV48 @ SY293 @ SY293 ) )
= $true )
| ( ( SV3 = SV48 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(275,plain,
! [SV91: $i,SV49: $i,SV4: $i] :
( ( ! [SY370: $i] : ( between @ SV4 @ SV49 @ ( extension @ SV4 @ SV49 @ SV91 @ SY370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(276,plain,
! [SV92: $i,SV50: $i,SV5: $i] :
( ( ! [SY371: $i] : ( equidistant @ SV5 @ ( extension @ SV50 @ SV5 @ SV92 @ SY371 ) @ SV92 @ SY371 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(277,plain,
! [SV93: $i,SV51: $i,SV6: $i] :
( ( ! [SY372: $i,SY373: $i,SY374: $i] :
( ~ ( equidistant @ SV6 @ SV51 @ SV93 @ SY372 )
| ~ ( equidistant @ SV51 @ SY373 @ SY372 @ SY374 )
| ! [SY375: $i,SY376: $i] :
( ~ ( equidistant @ SV6 @ SY375 @ SV93 @ SY376 )
| ~ ( equidistant @ SV51 @ SY375 @ SY372 @ SY376 )
| ~ ( between @ SV6 @ SV51 @ SY373 )
| ~ ( between @ SV93 @ SY372 @ SY374 )
| ( SV6 = SV51 )
| ( equidistant @ SY373 @ SY375 @ SY374 @ SY376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(278,plain,
! [SV52: $i,SV7: $i] :
( ( ( ~ ( between @ SV7 @ SV52 @ SV7 ) )
= $true )
| ( ( SV7 = SV52 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(279,plain,
! [SV94: $i,SV53: $i,SV8: $i] :
( ( ~ ( between @ SV8 @ SV53 @ SV94 )
| ! [SY377: $i,SY378: $i] :
( ~ ( between @ SY377 @ SY378 @ SV94 )
| ( between @ SV53 @ ( inner_pasch @ SV8 @ SV53 @ SV94 @ SY378 @ SY377 ) @ SY377 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(280,plain,
! [SV95: $i,SV54: $i,SV9: $i] :
( ( ~ ( between @ SV9 @ SV54 @ SV95 )
| ! [SY379: $i,SY380: $i] :
( ~ ( between @ SY379 @ SY380 @ SV95 )
| ( between @ SY380 @ ( inner_pasch @ SV9 @ SV54 @ SV95 @ SY380 @ SY379 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(281,plain,
! [SV96: $i,SV55: $i,SV10: $i] :
( ( ~ ( equidistant @ SV10 @ SV55 @ SV10 @ SV96 )
| ! [SY381: $i] :
( ~ ( equidistant @ SY381 @ SV55 @ SY381 @ SV96 )
| ! [SY382: $i] :
( ~ ( equidistant @ SY382 @ SV55 @ SY382 @ SV96 )
| ( between @ SV10 @ SY381 @ SY382 )
| ( between @ SY381 @ SY382 @ SV10 )
| ( SV55 = SV96 )
| ( between @ SY382 @ SV10 @ SY381 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(282,plain,
! [SV97: $i,SV56: $i,SV11: $i] :
( ( ~ ( between @ SV11 @ SV56 @ SV97 )
| ! [SY383: $i,SY384: $i] :
( ~ ( between @ SY383 @ SV56 @ SY384 )
| ( SV11 = SV56 )
| ( between @ SV11 @ SY383 @ ( euclid1 @ SV11 @ SY383 @ SV56 @ SY384 @ SV97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(283,plain,
! [SV98: $i,SV57: $i,SV12: $i] :
( ( ~ ( between @ SV12 @ SV57 @ SV98 )
| ! [SY385: $i,SY386: $i] :
( ~ ( between @ SY385 @ SV57 @ SY386 )
| ( SV12 = SV57 )
| ( between @ SV12 @ SY386 @ ( euclid2 @ SV12 @ SY385 @ SV57 @ SY386 @ SV98 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(284,plain,
! [SV99: $i,SV58: $i,SV13: $i] :
( ( ~ ( between @ SV13 @ SV58 @ SV99 )
| ! [SY387: $i,SY388: $i] :
( ~ ( between @ SY387 @ SV58 @ SY388 )
| ( SV13 = SV58 )
| ( between @ ( euclid1 @ SV13 @ SY387 @ SV58 @ SY388 @ SV99 ) @ SV99 @ ( euclid2 @ SV13 @ SY387 @ SV58 @ SY388 @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(285,plain,
! [SV100: $i,SV59: $i,SV14: $i] :
( ( ! [SY389: $i] :
( ~ ( equidistant @ SV14 @ SV59 @ SV14 @ SV100 )
| ! [SY390: $i] :
( ~ ( equidistant @ SV14 @ SY389 @ SV14 @ SY390 )
| ~ ( between @ SV14 @ SV59 @ SY389 )
| ! [SY391: $i] :
( ~ ( between @ SV59 @ SY391 @ SY389 )
| ( between @ SV100 @ ( continuous @ SV14 @ SV59 @ SV100 @ SY391 @ SY389 @ SY390 ) @ SY390 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(286,plain,
! [SV101: $i,SV60: $i,SV15: $i] :
( ( ! [SY392: $i] :
( ~ ( equidistant @ SV15 @ SV60 @ SV15 @ SV101 )
| ! [SY393: $i] :
( ~ ( equidistant @ SV15 @ SY392 @ SV15 @ SY393 )
| ~ ( between @ SV15 @ SV60 @ SY392 )
| ! [SY394: $i] :
( ~ ( between @ SV60 @ SY394 @ SY392 )
| ( equidistant @ SV15 @ SY394 @ SV15 @ ( continuous @ SV15 @ SV60 @ SV101 @ SY394 @ SY392 @ SY393 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(287,plain,
! [SV102: $i,SV63: $i,SV18: $i] :
( ( ! [SY395: $i] :
( ~ ( equidistant @ SV18 @ SV63 @ SV102 @ SY395 )
| ( equidistant @ SV102 @ SY395 @ SV18 @ SV63 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(288,plain,
! [SV103: $i,SV64: $i,SV19: $i] :
( ( ! [SY396: $i] :
( ~ ( equidistant @ SV19 @ SV64 @ SV103 @ SY396 )
| ( equidistant @ SV64 @ SV19 @ SV103 @ SY396 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(289,plain,
! [SV104: $i,SV65: $i,SV20: $i] :
( ( ! [SY397: $i] :
( ~ ( equidistant @ SV20 @ SV65 @ SV104 @ SY397 )
| ( equidistant @ SV20 @ SV65 @ SY397 @ SV104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(290,plain,
! [SV105: $i,SV66: $i,SV21: $i] :
( ( ! [SY398: $i] :
( ~ ( equidistant @ SV21 @ SV66 @ SV105 @ SY398 )
| ( equidistant @ SV66 @ SV21 @ SY398 @ SV105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(291,plain,
! [SV106: $i,SV67: $i,SV22: $i] :
( ( ! [SY399: $i] :
( ~ ( equidistant @ SV22 @ SV67 @ SV106 @ SY399 )
| ( equidistant @ SV106 @ SY399 @ SV67 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(292,plain,
! [SV107: $i,SV68: $i,SV23: $i] :
( ( ! [SY400: $i] :
( ~ ( equidistant @ SV23 @ SV68 @ SV107 @ SY400 )
| ( equidistant @ SY400 @ SV107 @ SV23 @ SV68 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(293,plain,
! [SV108: $i,SV69: $i,SV24: $i] :
( ( ! [SY401: $i] :
( ~ ( equidistant @ SV24 @ SV69 @ SV108 @ SY401 )
| ( equidistant @ SY401 @ SV108 @ SV69 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(294,plain,
! [SV109: $i,SV70: $i,SV25: $i] :
( ( ! [SY402: $i] :
( ~ ( equidistant @ SV25 @ SV70 @ SV109 @ SY402 )
| ! [SY403: $i,SY404: $i] :
( ~ ( equidistant @ SV109 @ SY402 @ SY403 @ SY404 )
| ( equidistant @ SV25 @ SV70 @ SY403 @ SY404 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(295,plain,
! [SV110: $i,SV71: $i,SV26: $i] :
( ( SV26
= ( extension @ SV71 @ SV26 @ SV110 @ SV110 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(296,plain,
! [SV111: $i,SV72: $i,SV27: $i] :
( ( ! [SY405: $i,SY406: $i] :
( SV27
!= ( extension @ SV72 @ SV111 @ SY405 @ SY406 ) )
| ( between @ SV72 @ SV111 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(297,plain,
! [SV75: $i,SV30: $i] :
( ( ( SV30 != SV75 )
= $true )
| ( ( SV75
= ( reflection @ SV30 @ SV75 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(298,plain,
! [SV76: $i,SV32: $i] :
( ( ( SV32
!= ( reflection @ SV76 @ SV32 ) )
= $true )
| ( ( SV76 = SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(299,plain,
! [SV112: $i,SV78: $i,SV34: $i] :
( ( ! [SY407: $i] :
( ~ ( equidistant @ SV34 @ SV78 @ SV112 @ SY407 )
| ! [SY408: $i,SY409: $i] :
( ~ ( equidistant @ SV78 @ SY408 @ SY407 @ SY409 )
| ~ ( between @ SV34 @ SV78 @ SY408 )
| ~ ( between @ SV112 @ SY407 @ SY409 )
| ( equidistant @ SV34 @ SY408 @ SV112 @ SY409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(300,plain,
! [SV113: $i,SV79: $i,SV35: $i] :
( ( ~ ( between @ SV35 @ SV79 @ SV113 )
| ! [SY410: $i] :
( ~ ( between @ SV35 @ SV79 @ SY410 )
| ~ ( equidistant @ SV79 @ SV113 @ SV79 @ SY410 )
| ( SV35 = SV79 )
| ( SV113 = SY410 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(301,plain,
! [SV114: $i,SV80: $i,SV36: $i] :
( ( ~ ( between @ SV36 @ SV80 @ SV114 )
| ( SV36 = SV80 )
| ( SV114
= ( extension @ SV36 @ SV80 @ SV80 @ SV114 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(302,plain,
! [SV115: $i,SV81: $i,SV37: $i] :
( ( ! [SY411: $i] :
( ~ ( equidistant @ SV37 @ SV81 @ SV115 @ SY411 )
| ! [SY412: $i,SY413: $i] :
( ( ( extension @ SY412 @ SY413 @ SV37 @ SV81 )
= ( extension @ SY412 @ SY413 @ SV115 @ SY411 ) )
| ( SY412 = SY413 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(303,plain,
! [SV82: $i,SV38: $i] :
( ( ( ( extension @ SV38 @ SV82 @ SV38 @ SV82 )
= ( extension @ SV38 @ SV82 @ SV82 @ SV38 ) )
= $true )
| ( ( SV38 = SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(304,plain,
! [SV116: $i,SV86: $i,SV42: $i] :
( ( ~ ( between @ SV42 @ SV86 @ SV116 )
| ( SV42 != SV116 )
| ! [SY414: $i] : ( between @ SY414 @ SV86 @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(305,plain,
! [SV117: $i,SV87: $i,SV43: $i] :
( ( ~ ( between @ SV43 @ SV87 @ SV117 )
| ( between @ SV117 @ SV87 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(306,plain,
! [SV118: $i,SV89: $i,SV45: $i] :
( ( ~ ( between @ SV45 @ SV89 @ SV118 )
| ~ ( between @ SV89 @ SV45 @ SV118 )
| ( SV45 = SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(307,plain,
! [SV119: $i,SV90: $i,SV47: $i,SV2: $i] :
( ( ~ ( equidistant @ SV2 @ SV47 @ SV90 @ SV119 )
| ! [SY415: $i,SY416: $i] :
( ~ ( equidistant @ SV2 @ SV47 @ SY415 @ SY416 )
| ( equidistant @ SV90 @ SV119 @ SY415 @ SY416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(308,plain,
! [SV120: $i,SV48: $i,SV3: $i] :
( ( ( ~ ( equidistant @ SV3 @ SV48 @ SV120 @ SV120 ) )
= $true )
| ( ( SV3 = SV48 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(309,plain,
! [SV121: $i,SV91: $i,SV49: $i,SV4: $i] :
( ( between @ SV4 @ SV49 @ ( extension @ SV4 @ SV49 @ SV91 @ SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(310,plain,
! [SV122: $i,SV92: $i,SV50: $i,SV5: $i] :
( ( equidistant @ SV5 @ ( extension @ SV50 @ SV5 @ SV92 @ SV122 ) @ SV92 @ SV122 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(311,plain,
! [SV123: $i,SV93: $i,SV51: $i,SV6: $i] :
( ( ! [SY417: $i,SY418: $i] :
( ~ ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
| ~ ( equidistant @ SV51 @ SY417 @ SV123 @ SY418 )
| ! [SY419: $i,SY420: $i] :
( ~ ( equidistant @ SV6 @ SY419 @ SV93 @ SY420 )
| ~ ( equidistant @ SV51 @ SY419 @ SV123 @ SY420 )
| ~ ( between @ SV6 @ SV51 @ SY417 )
| ~ ( between @ SV93 @ SV123 @ SY418 )
| ( SV6 = SV51 )
| ( equidistant @ SY417 @ SY419 @ SY418 @ SY420 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(312,plain,
! [SV52: $i,SV7: $i] :
( ( ( between @ SV7 @ SV52 @ SV7 )
= $false )
| ( ( SV7 = SV52 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(313,plain,
! [SV94: $i,SV53: $i,SV8: $i] :
( ( ( ~ ( between @ SV8 @ SV53 @ SV94 ) )
= $true )
| ( ( ! [SY377: $i,SY378: $i] :
( ~ ( between @ SY377 @ SY378 @ SV94 )
| ( between @ SV53 @ ( inner_pasch @ SV8 @ SV53 @ SV94 @ SY378 @ SY377 ) @ SY377 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(314,plain,
! [SV95: $i,SV54: $i,SV9: $i] :
( ( ( ~ ( between @ SV9 @ SV54 @ SV95 ) )
= $true )
| ( ( ! [SY379: $i,SY380: $i] :
( ~ ( between @ SY379 @ SY380 @ SV95 )
| ( between @ SY380 @ ( inner_pasch @ SV9 @ SV54 @ SV95 @ SY380 @ SY379 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(315,plain,
! [SV96: $i,SV55: $i,SV10: $i] :
( ( ( ~ ( equidistant @ SV10 @ SV55 @ SV10 @ SV96 ) )
= $true )
| ( ( ! [SY381: $i] :
( ~ ( equidistant @ SY381 @ SV55 @ SY381 @ SV96 )
| ! [SY382: $i] :
( ~ ( equidistant @ SY382 @ SV55 @ SY382 @ SV96 )
| ( between @ SV10 @ SY381 @ SY382 )
| ( between @ SY381 @ SY382 @ SV10 )
| ( SV55 = SV96 )
| ( between @ SY382 @ SV10 @ SY381 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(316,plain,
! [SV97: $i,SV56: $i,SV11: $i] :
( ( ( ~ ( between @ SV11 @ SV56 @ SV97 ) )
= $true )
| ( ( ! [SY383: $i,SY384: $i] :
( ~ ( between @ SY383 @ SV56 @ SY384 )
| ( SV11 = SV56 )
| ( between @ SV11 @ SY383 @ ( euclid1 @ SV11 @ SY383 @ SV56 @ SY384 @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(317,plain,
! [SV98: $i,SV57: $i,SV12: $i] :
( ( ( ~ ( between @ SV12 @ SV57 @ SV98 ) )
= $true )
| ( ( ! [SY385: $i,SY386: $i] :
( ~ ( between @ SY385 @ SV57 @ SY386 )
| ( SV12 = SV57 )
| ( between @ SV12 @ SY386 @ ( euclid2 @ SV12 @ SY385 @ SV57 @ SY386 @ SV98 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[283]) ).
thf(318,plain,
! [SV99: $i,SV58: $i,SV13: $i] :
( ( ( ~ ( between @ SV13 @ SV58 @ SV99 ) )
= $true )
| ( ( ! [SY387: $i,SY388: $i] :
( ~ ( between @ SY387 @ SV58 @ SY388 )
| ( SV13 = SV58 )
| ( between @ ( euclid1 @ SV13 @ SY387 @ SV58 @ SY388 @ SV99 ) @ SV99 @ ( euclid2 @ SV13 @ SY387 @ SV58 @ SY388 @ SV99 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(319,plain,
! [SV124: $i,SV100: $i,SV59: $i,SV14: $i] :
( ( ~ ( equidistant @ SV14 @ SV59 @ SV14 @ SV100 )
| ! [SY421: $i] :
( ~ ( equidistant @ SV14 @ SV124 @ SV14 @ SY421 )
| ~ ( between @ SV14 @ SV59 @ SV124 )
| ! [SY422: $i] :
( ~ ( between @ SV59 @ SY422 @ SV124 )
| ( between @ SV100 @ ( continuous @ SV14 @ SV59 @ SV100 @ SY422 @ SV124 @ SY421 ) @ SY421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(320,plain,
! [SV125: $i,SV101: $i,SV60: $i,SV15: $i] :
( ( ~ ( equidistant @ SV15 @ SV60 @ SV15 @ SV101 )
| ! [SY423: $i] :
( ~ ( equidistant @ SV15 @ SV125 @ SV15 @ SY423 )
| ~ ( between @ SV15 @ SV60 @ SV125 )
| ! [SY424: $i] :
( ~ ( between @ SV60 @ SY424 @ SV125 )
| ( equidistant @ SV15 @ SY424 @ SV15 @ ( continuous @ SV15 @ SV60 @ SV101 @ SY424 @ SV125 @ SY423 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(321,plain,
! [SV126: $i,SV102: $i,SV63: $i,SV18: $i] :
( ( ~ ( equidistant @ SV18 @ SV63 @ SV102 @ SV126 )
| ( equidistant @ SV102 @ SV126 @ SV18 @ SV63 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(322,plain,
! [SV127: $i,SV103: $i,SV64: $i,SV19: $i] :
( ( ~ ( equidistant @ SV19 @ SV64 @ SV103 @ SV127 )
| ( equidistant @ SV64 @ SV19 @ SV103 @ SV127 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(323,plain,
! [SV128: $i,SV104: $i,SV65: $i,SV20: $i] :
( ( ~ ( equidistant @ SV20 @ SV65 @ SV104 @ SV128 )
| ( equidistant @ SV20 @ SV65 @ SV128 @ SV104 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(324,plain,
! [SV129: $i,SV105: $i,SV66: $i,SV21: $i] :
( ( ~ ( equidistant @ SV21 @ SV66 @ SV105 @ SV129 )
| ( equidistant @ SV66 @ SV21 @ SV129 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(325,plain,
! [SV130: $i,SV106: $i,SV67: $i,SV22: $i] :
( ( ~ ( equidistant @ SV22 @ SV67 @ SV106 @ SV130 )
| ( equidistant @ SV106 @ SV130 @ SV67 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(326,plain,
! [SV131: $i,SV107: $i,SV68: $i,SV23: $i] :
( ( ~ ( equidistant @ SV23 @ SV68 @ SV107 @ SV131 )
| ( equidistant @ SV131 @ SV107 @ SV23 @ SV68 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(327,plain,
! [SV132: $i,SV108: $i,SV69: $i,SV24: $i] :
( ( ~ ( equidistant @ SV24 @ SV69 @ SV108 @ SV132 )
| ( equidistant @ SV132 @ SV108 @ SV69 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(328,plain,
! [SV133: $i,SV109: $i,SV70: $i,SV25: $i] :
( ( ~ ( equidistant @ SV25 @ SV70 @ SV109 @ SV133 )
| ! [SY425: $i,SY426: $i] :
( ~ ( equidistant @ SV109 @ SV133 @ SY425 @ SY426 )
| ( equidistant @ SV25 @ SV70 @ SY425 @ SY426 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(329,plain,
! [SV111: $i,SV72: $i,SV27: $i] :
( ( ( ! [SY405: $i,SY406: $i] :
( SV27
!= ( extension @ SV72 @ SV111 @ SY405 @ SY406 ) ) )
= $true )
| ( ( between @ SV72 @ SV111 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(330,plain,
! [SV75: $i,SV30: $i] :
( ( ( SV30 = SV75 )
= $false )
| ( ( SV75
= ( reflection @ SV30 @ SV75 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(331,plain,
! [SV76: $i,SV32: $i] :
( ( ( SV32
= ( reflection @ SV76 @ SV32 ) )
= $false )
| ( ( SV76 = SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(332,plain,
! [SV134: $i,SV112: $i,SV78: $i,SV34: $i] :
( ( ~ ( equidistant @ SV34 @ SV78 @ SV112 @ SV134 )
| ! [SY427: $i,SY428: $i] :
( ~ ( equidistant @ SV78 @ SY427 @ SV134 @ SY428 )
| ~ ( between @ SV34 @ SV78 @ SY427 )
| ~ ( between @ SV112 @ SV134 @ SY428 )
| ( equidistant @ SV34 @ SY427 @ SV112 @ SY428 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(333,plain,
! [SV113: $i,SV79: $i,SV35: $i] :
( ( ( ~ ( between @ SV35 @ SV79 @ SV113 ) )
= $true )
| ( ( ! [SY410: $i] :
( ~ ( between @ SV35 @ SV79 @ SY410 )
| ~ ( equidistant @ SV79 @ SV113 @ SV79 @ SY410 )
| ( SV35 = SV79 )
| ( SV113 = SY410 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(334,plain,
! [SV114: $i,SV80: $i,SV36: $i] :
( ( ( ~ ( between @ SV36 @ SV80 @ SV114 ) )
= $true )
| ( ( ( SV36 = SV80 )
| ( SV114
= ( extension @ SV36 @ SV80 @ SV80 @ SV114 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[301]) ).
thf(335,plain,
! [SV135: $i,SV115: $i,SV81: $i,SV37: $i] :
( ( ~ ( equidistant @ SV37 @ SV81 @ SV115 @ SV135 )
| ! [SY429: $i,SY430: $i] :
( ( ( extension @ SY429 @ SY430 @ SV37 @ SV81 )
= ( extension @ SY429 @ SY430 @ SV115 @ SV135 ) )
| ( SY429 = SY430 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(336,plain,
! [SV116: $i,SV86: $i,SV42: $i] :
( ( ( ~ ( between @ SV42 @ SV86 @ SV116 ) )
= $true )
| ( ( ( SV42 != SV116 )
| ! [SY414: $i] : ( between @ SY414 @ SV86 @ SV116 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(337,plain,
! [SV117: $i,SV87: $i,SV43: $i] :
( ( ( ~ ( between @ SV43 @ SV87 @ SV117 ) )
= $true )
| ( ( between @ SV117 @ SV87 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(338,plain,
! [SV118: $i,SV89: $i,SV45: $i] :
( ( ( ~ ( between @ SV45 @ SV89 @ SV118 ) )
= $true )
| ( ( ~ ( between @ SV89 @ SV45 @ SV118 )
| ( SV45 = SV89 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(339,plain,
! [SV119: $i,SV90: $i,SV47: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV47 @ SV90 @ SV119 ) )
= $true )
| ( ( ! [SY415: $i,SY416: $i] :
( ~ ( equidistant @ SV2 @ SV47 @ SY415 @ SY416 )
| ( equidistant @ SV90 @ SV119 @ SY415 @ SY416 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(340,plain,
! [SV120: $i,SV48: $i,SV3: $i] :
( ( ( equidistant @ SV3 @ SV48 @ SV120 @ SV120 )
= $false )
| ( ( SV3 = SV48 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(341,plain,
! [SV136: $i,SV123: $i,SV93: $i,SV51: $i,SV6: $i] :
( ( ! [SY431: $i] :
( ~ ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
| ~ ( equidistant @ SV51 @ SV136 @ SV123 @ SY431 )
| ! [SY432: $i,SY433: $i] :
( ~ ( equidistant @ SV6 @ SY432 @ SV93 @ SY433 )
| ~ ( equidistant @ SV51 @ SY432 @ SV123 @ SY433 )
| ~ ( between @ SV6 @ SV51 @ SV136 )
| ~ ( between @ SV93 @ SV123 @ SY431 )
| ( SV6 = SV51 )
| ( equidistant @ SV136 @ SY432 @ SY431 @ SY433 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(342,plain,
! [SV94: $i,SV53: $i,SV8: $i] :
( ( ( between @ SV8 @ SV53 @ SV94 )
= $false )
| ( ( ! [SY377: $i,SY378: $i] :
( ~ ( between @ SY377 @ SY378 @ SV94 )
| ( between @ SV53 @ ( inner_pasch @ SV8 @ SV53 @ SV94 @ SY378 @ SY377 ) @ SY377 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(343,plain,
! [SV95: $i,SV54: $i,SV9: $i] :
( ( ( between @ SV9 @ SV54 @ SV95 )
= $false )
| ( ( ! [SY379: $i,SY380: $i] :
( ~ ( between @ SY379 @ SY380 @ SV95 )
| ( between @ SY380 @ ( inner_pasch @ SV9 @ SV54 @ SV95 @ SY380 @ SY379 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(344,plain,
! [SV96: $i,SV55: $i,SV10: $i] :
( ( ( equidistant @ SV10 @ SV55 @ SV10 @ SV96 )
= $false )
| ( ( ! [SY381: $i] :
( ~ ( equidistant @ SY381 @ SV55 @ SY381 @ SV96 )
| ! [SY382: $i] :
( ~ ( equidistant @ SY382 @ SV55 @ SY382 @ SV96 )
| ( between @ SV10 @ SY381 @ SY382 )
| ( between @ SY381 @ SY382 @ SV10 )
| ( SV55 = SV96 )
| ( between @ SY382 @ SV10 @ SY381 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(345,plain,
! [SV97: $i,SV56: $i,SV11: $i] :
( ( ( between @ SV11 @ SV56 @ SV97 )
= $false )
| ( ( ! [SY383: $i,SY384: $i] :
( ~ ( between @ SY383 @ SV56 @ SY384 )
| ( SV11 = SV56 )
| ( between @ SV11 @ SY383 @ ( euclid1 @ SV11 @ SY383 @ SV56 @ SY384 @ SV97 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(346,plain,
! [SV98: $i,SV57: $i,SV12: $i] :
( ( ( between @ SV12 @ SV57 @ SV98 )
= $false )
| ( ( ! [SY385: $i,SY386: $i] :
( ~ ( between @ SY385 @ SV57 @ SY386 )
| ( SV12 = SV57 )
| ( between @ SV12 @ SY386 @ ( euclid2 @ SV12 @ SY385 @ SV57 @ SY386 @ SV98 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[317]) ).
thf(347,plain,
! [SV99: $i,SV58: $i,SV13: $i] :
( ( ( between @ SV13 @ SV58 @ SV99 )
= $false )
| ( ( ! [SY387: $i,SY388: $i] :
( ~ ( between @ SY387 @ SV58 @ SY388 )
| ( SV13 = SV58 )
| ( between @ ( euclid1 @ SV13 @ SY387 @ SV58 @ SY388 @ SV99 ) @ SV99 @ ( euclid2 @ SV13 @ SY387 @ SV58 @ SY388 @ SV99 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[318]) ).
thf(348,plain,
! [SV124: $i,SV100: $i,SV59: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV59 @ SV14 @ SV100 ) )
= $true )
| ( ( ! [SY421: $i] :
( ~ ( equidistant @ SV14 @ SV124 @ SV14 @ SY421 )
| ~ ( between @ SV14 @ SV59 @ SV124 )
| ! [SY422: $i] :
( ~ ( between @ SV59 @ SY422 @ SV124 )
| ( between @ SV100 @ ( continuous @ SV14 @ SV59 @ SV100 @ SY422 @ SV124 @ SY421 ) @ SY421 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(349,plain,
! [SV125: $i,SV101: $i,SV60: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV60 @ SV15 @ SV101 ) )
= $true )
| ( ( ! [SY423: $i] :
( ~ ( equidistant @ SV15 @ SV125 @ SV15 @ SY423 )
| ~ ( between @ SV15 @ SV60 @ SV125 )
| ! [SY424: $i] :
( ~ ( between @ SV60 @ SY424 @ SV125 )
| ( equidistant @ SV15 @ SY424 @ SV15 @ ( continuous @ SV15 @ SV60 @ SV101 @ SY424 @ SV125 @ SY423 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(350,plain,
! [SV126: $i,SV102: $i,SV63: $i,SV18: $i] :
( ( ( ~ ( equidistant @ SV18 @ SV63 @ SV102 @ SV126 ) )
= $true )
| ( ( equidistant @ SV102 @ SV126 @ SV18 @ SV63 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(351,plain,
! [SV127: $i,SV103: $i,SV64: $i,SV19: $i] :
( ( ( ~ ( equidistant @ SV19 @ SV64 @ SV103 @ SV127 ) )
= $true )
| ( ( equidistant @ SV64 @ SV19 @ SV103 @ SV127 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(352,plain,
! [SV128: $i,SV104: $i,SV65: $i,SV20: $i] :
( ( ( ~ ( equidistant @ SV20 @ SV65 @ SV104 @ SV128 ) )
= $true )
| ( ( equidistant @ SV20 @ SV65 @ SV128 @ SV104 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(353,plain,
! [SV129: $i,SV105: $i,SV66: $i,SV21: $i] :
( ( ( ~ ( equidistant @ SV21 @ SV66 @ SV105 @ SV129 ) )
= $true )
| ( ( equidistant @ SV66 @ SV21 @ SV129 @ SV105 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(354,plain,
! [SV130: $i,SV106: $i,SV67: $i,SV22: $i] :
( ( ( ~ ( equidistant @ SV22 @ SV67 @ SV106 @ SV130 ) )
= $true )
| ( ( equidistant @ SV106 @ SV130 @ SV67 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[325]) ).
thf(355,plain,
! [SV131: $i,SV107: $i,SV68: $i,SV23: $i] :
( ( ( ~ ( equidistant @ SV23 @ SV68 @ SV107 @ SV131 ) )
= $true )
| ( ( equidistant @ SV131 @ SV107 @ SV23 @ SV68 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[326]) ).
thf(356,plain,
! [SV132: $i,SV108: $i,SV69: $i,SV24: $i] :
( ( ( ~ ( equidistant @ SV24 @ SV69 @ SV108 @ SV132 ) )
= $true )
| ( ( equidistant @ SV132 @ SV108 @ SV69 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(357,plain,
! [SV133: $i,SV109: $i,SV70: $i,SV25: $i] :
( ( ( ~ ( equidistant @ SV25 @ SV70 @ SV109 @ SV133 ) )
= $true )
| ( ( ! [SY425: $i,SY426: $i] :
( ~ ( equidistant @ SV109 @ SV133 @ SY425 @ SY426 )
| ( equidistant @ SV25 @ SV70 @ SY425 @ SY426 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[328]) ).
thf(358,plain,
! [SV137: $i,SV111: $i,SV72: $i,SV27: $i] :
( ( ( ! [SY434: $i] :
( SV27
!= ( extension @ SV72 @ SV111 @ SV137 @ SY434 ) ) )
= $true )
| ( ( between @ SV72 @ SV111 @ SV27 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(359,plain,
! [SV134: $i,SV112: $i,SV78: $i,SV34: $i] :
( ( ( ~ ( equidistant @ SV34 @ SV78 @ SV112 @ SV134 ) )
= $true )
| ( ( ! [SY427: $i,SY428: $i] :
( ~ ( equidistant @ SV78 @ SY427 @ SV134 @ SY428 )
| ~ ( between @ SV34 @ SV78 @ SY427 )
| ~ ( between @ SV112 @ SV134 @ SY428 )
| ( equidistant @ SV34 @ SY427 @ SV112 @ SY428 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(360,plain,
! [SV113: $i,SV79: $i,SV35: $i] :
( ( ( between @ SV35 @ SV79 @ SV113 )
= $false )
| ( ( ! [SY410: $i] :
( ~ ( between @ SV35 @ SV79 @ SY410 )
| ~ ( equidistant @ SV79 @ SV113 @ SV79 @ SY410 )
| ( SV35 = SV79 )
| ( SV113 = SY410 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(361,plain,
! [SV114: $i,SV80: $i,SV36: $i] :
( ( ( between @ SV36 @ SV80 @ SV114 )
= $false )
| ( ( ( SV36 = SV80 )
| ( SV114
= ( extension @ SV36 @ SV80 @ SV80 @ SV114 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(362,plain,
! [SV135: $i,SV115: $i,SV81: $i,SV37: $i] :
( ( ( ~ ( equidistant @ SV37 @ SV81 @ SV115 @ SV135 ) )
= $true )
| ( ( ! [SY429: $i,SY430: $i] :
( ( ( extension @ SY429 @ SY430 @ SV37 @ SV81 )
= ( extension @ SY429 @ SY430 @ SV115 @ SV135 ) )
| ( SY429 = SY430 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(363,plain,
! [SV116: $i,SV86: $i,SV42: $i] :
( ( ( between @ SV42 @ SV86 @ SV116 )
= $false )
| ( ( ( SV42 != SV116 )
| ! [SY414: $i] : ( between @ SY414 @ SV86 @ SV116 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(364,plain,
! [SV117: $i,SV87: $i,SV43: $i] :
( ( ( between @ SV43 @ SV87 @ SV117 )
= $false )
| ( ( between @ SV117 @ SV87 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(365,plain,
! [SV118: $i,SV89: $i,SV45: $i] :
( ( ( between @ SV45 @ SV89 @ SV118 )
= $false )
| ( ( ~ ( between @ SV89 @ SV45 @ SV118 )
| ( SV45 = SV89 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(366,plain,
! [SV119: $i,SV90: $i,SV47: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV47 @ SV90 @ SV119 )
= $false )
| ( ( ! [SY415: $i,SY416: $i] :
( ~ ( equidistant @ SV2 @ SV47 @ SY415 @ SY416 )
| ( equidistant @ SV90 @ SV119 @ SY415 @ SY416 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[339]) ).
thf(367,plain,
! [SV138: $i,SV136: $i,SV123: $i,SV93: $i,SV51: $i,SV6: $i] :
( ( ~ ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
| ~ ( equidistant @ SV51 @ SV136 @ SV123 @ SV138 )
| ! [SY435: $i,SY436: $i] :
( ~ ( equidistant @ SV6 @ SY435 @ SV93 @ SY436 )
| ~ ( equidistant @ SV51 @ SY435 @ SV123 @ SY436 )
| ~ ( between @ SV6 @ SV51 @ SV136 )
| ~ ( between @ SV93 @ SV123 @ SV138 )
| ( SV6 = SV51 )
| ( equidistant @ SV136 @ SY435 @ SV138 @ SY436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(368,plain,
! [SV8: $i,SV53: $i,SV94: $i,SV139: $i] :
( ( ( ! [SY437: $i] :
( ~ ( between @ SV139 @ SY437 @ SV94 )
| ( between @ SV53 @ ( inner_pasch @ SV8 @ SV53 @ SV94 @ SY437 @ SV139 ) @ SV139 ) ) )
= $true )
| ( ( between @ SV8 @ SV53 @ SV94 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(369,plain,
! [SV54: $i,SV9: $i,SV95: $i,SV140: $i] :
( ( ( ! [SY438: $i] :
( ~ ( between @ SV140 @ SY438 @ SV95 )
| ( between @ SY438 @ ( inner_pasch @ SV9 @ SV54 @ SV95 @ SY438 @ SV140 ) @ SV9 ) ) )
= $true )
| ( ( between @ SV9 @ SV54 @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(370,plain,
! [SV10: $i,SV96: $i,SV55: $i,SV141: $i] :
( ( ( ~ ( equidistant @ SV141 @ SV55 @ SV141 @ SV96 )
| ! [SY439: $i] :
( ~ ( equidistant @ SY439 @ SV55 @ SY439 @ SV96 )
| ( between @ SV10 @ SV141 @ SY439 )
| ( between @ SV141 @ SY439 @ SV10 )
| ( SV55 = SV96 )
| ( between @ SY439 @ SV10 @ SV141 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV55 @ SV10 @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(371,plain,
! [SV97: $i,SV11: $i,SV56: $i,SV142: $i] :
( ( ( ! [SY440: $i] :
( ~ ( between @ SV142 @ SV56 @ SY440 )
| ( SV11 = SV56 )
| ( between @ SV11 @ SV142 @ ( euclid1 @ SV11 @ SV142 @ SV56 @ SY440 @ SV97 ) ) ) )
= $true )
| ( ( between @ SV11 @ SV56 @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(372,plain,
! [SV98: $i,SV12: $i,SV57: $i,SV143: $i] :
( ( ( ! [SY441: $i] :
( ~ ( between @ SV143 @ SV57 @ SY441 )
| ( SV12 = SV57 )
| ( between @ SV12 @ SY441 @ ( euclid2 @ SV12 @ SV143 @ SV57 @ SY441 @ SV98 ) ) ) )
= $true )
| ( ( between @ SV12 @ SV57 @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(373,plain,
! [SV99: $i,SV13: $i,SV58: $i,SV144: $i] :
( ( ( ! [SY442: $i] :
( ~ ( between @ SV144 @ SV58 @ SY442 )
| ( SV13 = SV58 )
| ( between @ ( euclid1 @ SV13 @ SV144 @ SV58 @ SY442 @ SV99 ) @ SV99 @ ( euclid2 @ SV13 @ SV144 @ SV58 @ SY442 @ SV99 ) ) ) )
= $true )
| ( ( between @ SV13 @ SV58 @ SV99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(374,plain,
! [SV124: $i,SV100: $i,SV59: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV59 @ SV14 @ SV100 )
= $false )
| ( ( ! [SY421: $i] :
( ~ ( equidistant @ SV14 @ SV124 @ SV14 @ SY421 )
| ~ ( between @ SV14 @ SV59 @ SV124 )
| ! [SY422: $i] :
( ~ ( between @ SV59 @ SY422 @ SV124 )
| ( between @ SV100 @ ( continuous @ SV14 @ SV59 @ SV100 @ SY422 @ SV124 @ SY421 ) @ SY421 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[348]) ).
thf(375,plain,
! [SV125: $i,SV101: $i,SV60: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV60 @ SV15 @ SV101 )
= $false )
| ( ( ! [SY423: $i] :
( ~ ( equidistant @ SV15 @ SV125 @ SV15 @ SY423 )
| ~ ( between @ SV15 @ SV60 @ SV125 )
| ! [SY424: $i] :
( ~ ( between @ SV60 @ SY424 @ SV125 )
| ( equidistant @ SV15 @ SY424 @ SV15 @ ( continuous @ SV15 @ SV60 @ SV101 @ SY424 @ SV125 @ SY423 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[349]) ).
thf(376,plain,
! [SV126: $i,SV102: $i,SV63: $i,SV18: $i] :
( ( ( equidistant @ SV18 @ SV63 @ SV102 @ SV126 )
= $false )
| ( ( equidistant @ SV102 @ SV126 @ SV18 @ SV63 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(377,plain,
! [SV127: $i,SV103: $i,SV64: $i,SV19: $i] :
( ( ( equidistant @ SV19 @ SV64 @ SV103 @ SV127 )
= $false )
| ( ( equidistant @ SV64 @ SV19 @ SV103 @ SV127 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(378,plain,
! [SV128: $i,SV104: $i,SV65: $i,SV20: $i] :
( ( ( equidistant @ SV20 @ SV65 @ SV104 @ SV128 )
= $false )
| ( ( equidistant @ SV20 @ SV65 @ SV128 @ SV104 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[352]) ).
thf(379,plain,
! [SV129: $i,SV105: $i,SV66: $i,SV21: $i] :
( ( ( equidistant @ SV21 @ SV66 @ SV105 @ SV129 )
= $false )
| ( ( equidistant @ SV66 @ SV21 @ SV129 @ SV105 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(380,plain,
! [SV130: $i,SV106: $i,SV67: $i,SV22: $i] :
( ( ( equidistant @ SV22 @ SV67 @ SV106 @ SV130 )
= $false )
| ( ( equidistant @ SV106 @ SV130 @ SV67 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(381,plain,
! [SV131: $i,SV107: $i,SV68: $i,SV23: $i] :
( ( ( equidistant @ SV23 @ SV68 @ SV107 @ SV131 )
= $false )
| ( ( equidistant @ SV131 @ SV107 @ SV23 @ SV68 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(382,plain,
! [SV132: $i,SV108: $i,SV69: $i,SV24: $i] :
( ( ( equidistant @ SV24 @ SV69 @ SV108 @ SV132 )
= $false )
| ( ( equidistant @ SV132 @ SV108 @ SV69 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(383,plain,
! [SV133: $i,SV109: $i,SV70: $i,SV25: $i] :
( ( ( equidistant @ SV25 @ SV70 @ SV109 @ SV133 )
= $false )
| ( ( ! [SY425: $i,SY426: $i] :
( ~ ( equidistant @ SV109 @ SV133 @ SY425 @ SY426 )
| ( equidistant @ SV25 @ SV70 @ SY425 @ SY426 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(384,plain,
! [SV145: $i,SV137: $i,SV111: $i,SV72: $i,SV27: $i] :
( ( ( SV27
!= ( extension @ SV72 @ SV111 @ SV137 @ SV145 ) )
= $true )
| ( ( between @ SV72 @ SV111 @ SV27 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(385,plain,
! [SV134: $i,SV112: $i,SV78: $i,SV34: $i] :
( ( ( equidistant @ SV34 @ SV78 @ SV112 @ SV134 )
= $false )
| ( ( ! [SY427: $i,SY428: $i] :
( ~ ( equidistant @ SV78 @ SY427 @ SV134 @ SY428 )
| ~ ( between @ SV34 @ SV78 @ SY427 )
| ~ ( between @ SV112 @ SV134 @ SY428 )
| ( equidistant @ SV34 @ SY427 @ SV112 @ SY428 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(386,plain,
! [SV113: $i,SV146: $i,SV79: $i,SV35: $i] :
( ( ( ~ ( between @ SV35 @ SV79 @ SV146 )
| ~ ( equidistant @ SV79 @ SV113 @ SV79 @ SV146 )
| ( SV35 = SV79 )
| ( SV113 = SV146 ) )
= $true )
| ( ( between @ SV35 @ SV79 @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(387,plain,
! [SV114: $i,SV80: $i,SV36: $i] :
( ( ( SV36 = SV80 )
= $true )
| ( ( SV114
= ( extension @ SV36 @ SV80 @ SV80 @ SV114 ) )
= $true )
| ( ( between @ SV36 @ SV80 @ SV114 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[361]) ).
thf(388,plain,
! [SV135: $i,SV115: $i,SV81: $i,SV37: $i] :
( ( ( equidistant @ SV37 @ SV81 @ SV115 @ SV135 )
= $false )
| ( ( ! [SY429: $i,SY430: $i] :
( ( ( extension @ SY429 @ SY430 @ SV37 @ SV81 )
= ( extension @ SY429 @ SY430 @ SV115 @ SV135 ) )
| ( SY429 = SY430 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[362]) ).
thf(389,plain,
! [SV86: $i,SV116: $i,SV42: $i] :
( ( ( SV42 != SV116 )
= $true )
| ( ( ! [SY414: $i] : ( between @ SY414 @ SV86 @ SV116 ) )
= $true )
| ( ( between @ SV42 @ SV86 @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(390,plain,
! [SV118: $i,SV45: $i,SV89: $i] :
( ( ( ~ ( between @ SV89 @ SV45 @ SV118 ) )
= $true )
| ( ( SV45 = SV89 )
= $true )
| ( ( between @ SV45 @ SV89 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(391,plain,
! [SV119: $i,SV90: $i,SV147: $i,SV47: $i,SV2: $i] :
( ( ( ! [SY443: $i] :
( ~ ( equidistant @ SV2 @ SV47 @ SV147 @ SY443 )
| ( equidistant @ SV90 @ SV119 @ SV147 @ SY443 ) ) )
= $true )
| ( ( equidistant @ SV2 @ SV47 @ SV90 @ SV119 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(392,plain,
! [SV138: $i,SV136: $i,SV123: $i,SV93: $i,SV51: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 ) )
= $true )
| ( ( ~ ( equidistant @ SV51 @ SV136 @ SV123 @ SV138 )
| ! [SY435: $i,SY436: $i] :
( ~ ( equidistant @ SV6 @ SY435 @ SV93 @ SY436 )
| ~ ( equidistant @ SV51 @ SY435 @ SV123 @ SY436 )
| ~ ( between @ SV6 @ SV51 @ SV136 )
| ~ ( between @ SV93 @ SV123 @ SV138 )
| ( SV6 = SV51 )
| ( equidistant @ SV136 @ SY435 @ SV138 @ SY436 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(393,plain,
! [SV8: $i,SV53: $i,SV94: $i,SV148: $i,SV139: $i] :
( ( ( ~ ( between @ SV139 @ SV148 @ SV94 )
| ( between @ SV53 @ ( inner_pasch @ SV8 @ SV53 @ SV94 @ SV148 @ SV139 ) @ SV139 ) )
= $true )
| ( ( between @ SV8 @ SV53 @ SV94 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(394,plain,
! [SV54: $i,SV9: $i,SV95: $i,SV149: $i,SV140: $i] :
( ( ( ~ ( between @ SV140 @ SV149 @ SV95 )
| ( between @ SV149 @ ( inner_pasch @ SV9 @ SV54 @ SV95 @ SV149 @ SV140 ) @ SV9 ) )
= $true )
| ( ( between @ SV9 @ SV54 @ SV95 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(395,plain,
! [SV10: $i,SV96: $i,SV55: $i,SV141: $i] :
( ( ( ~ ( equidistant @ SV141 @ SV55 @ SV141 @ SV96 ) )
= $true )
| ( ( ! [SY439: $i] :
( ~ ( equidistant @ SY439 @ SV55 @ SY439 @ SV96 )
| ( between @ SV10 @ SV141 @ SY439 )
| ( between @ SV141 @ SY439 @ SV10 )
| ( SV55 = SV96 )
| ( between @ SY439 @ SV10 @ SV141 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV55 @ SV10 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(396,plain,
! [SV97: $i,SV11: $i,SV150: $i,SV56: $i,SV142: $i] :
( ( ( ~ ( between @ SV142 @ SV56 @ SV150 )
| ( SV11 = SV56 )
| ( between @ SV11 @ SV142 @ ( euclid1 @ SV11 @ SV142 @ SV56 @ SV150 @ SV97 ) ) )
= $true )
| ( ( between @ SV11 @ SV56 @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(397,plain,
! [SV98: $i,SV12: $i,SV151: $i,SV57: $i,SV143: $i] :
( ( ( ~ ( between @ SV143 @ SV57 @ SV151 )
| ( SV12 = SV57 )
| ( between @ SV12 @ SV151 @ ( euclid2 @ SV12 @ SV143 @ SV57 @ SV151 @ SV98 ) ) )
= $true )
| ( ( between @ SV12 @ SV57 @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(398,plain,
! [SV99: $i,SV13: $i,SV152: $i,SV58: $i,SV144: $i] :
( ( ( ~ ( between @ SV144 @ SV58 @ SV152 )
| ( SV13 = SV58 )
| ( between @ ( euclid1 @ SV13 @ SV144 @ SV58 @ SV152 @ SV99 ) @ SV99 @ ( euclid2 @ SV13 @ SV144 @ SV58 @ SV152 @ SV99 ) ) )
= $true )
| ( ( between @ SV13 @ SV58 @ SV99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(399,plain,
! [SV100: $i,SV59: $i,SV153: $i,SV124: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV124 @ SV14 @ SV153 )
| ~ ( between @ SV14 @ SV59 @ SV124 )
| ! [SY444: $i] :
( ~ ( between @ SV59 @ SY444 @ SV124 )
| ( between @ SV100 @ ( continuous @ SV14 @ SV59 @ SV100 @ SY444 @ SV124 @ SV153 ) @ SV153 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV59 @ SV14 @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(400,plain,
! [SV101: $i,SV60: $i,SV154: $i,SV125: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV125 @ SV15 @ SV154 )
| ~ ( between @ SV15 @ SV60 @ SV125 )
| ! [SY445: $i] :
( ~ ( between @ SV60 @ SY445 @ SV125 )
| ( equidistant @ SV15 @ SY445 @ SV15 @ ( continuous @ SV15 @ SV60 @ SV101 @ SY445 @ SV125 @ SV154 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV60 @ SV15 @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(401,plain,
! [SV70: $i,SV25: $i,SV155: $i,SV133: $i,SV109: $i] :
( ( ( ! [SY446: $i] :
( ~ ( equidistant @ SV109 @ SV133 @ SV155 @ SY446 )
| ( equidistant @ SV25 @ SV70 @ SV155 @ SY446 ) ) )
= $true )
| ( ( equidistant @ SV25 @ SV70 @ SV109 @ SV133 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(402,plain,
! [SV145: $i,SV137: $i,SV111: $i,SV72: $i,SV27: $i] :
( ( ( SV27
= ( extension @ SV72 @ SV111 @ SV137 @ SV145 ) )
= $false )
| ( ( between @ SV72 @ SV111 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(403,plain,
! [SV112: $i,SV34: $i,SV134: $i,SV156: $i,SV78: $i] :
( ( ( ! [SY447: $i] :
( ~ ( equidistant @ SV78 @ SV156 @ SV134 @ SY447 )
| ~ ( between @ SV34 @ SV78 @ SV156 )
| ~ ( between @ SV112 @ SV134 @ SY447 )
| ( equidistant @ SV34 @ SV156 @ SV112 @ SY447 ) ) )
= $true )
| ( ( equidistant @ SV34 @ SV78 @ SV112 @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(404,plain,
! [SV113: $i,SV146: $i,SV79: $i,SV35: $i] :
( ( ( ~ ( between @ SV35 @ SV79 @ SV146 ) )
= $true )
| ( ( ~ ( equidistant @ SV79 @ SV113 @ SV79 @ SV146 )
| ( SV35 = SV79 )
| ( SV113 = SV146 ) )
= $true )
| ( ( between @ SV35 @ SV79 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(405,plain,
! [SV135: $i,SV115: $i,SV81: $i,SV37: $i,SV157: $i] :
( ( ( ! [SY448: $i] :
( ( ( extension @ SV157 @ SY448 @ SV37 @ SV81 )
= ( extension @ SV157 @ SY448 @ SV115 @ SV135 ) )
| ( SV157 = SY448 ) ) )
= $true )
| ( ( equidistant @ SV37 @ SV81 @ SV115 @ SV135 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(406,plain,
! [SV86: $i,SV116: $i,SV42: $i] :
( ( ( SV42 = SV116 )
= $false )
| ( ( ! [SY414: $i] : ( between @ SY414 @ SV86 @ SV116 ) )
= $true )
| ( ( between @ SV42 @ SV86 @ SV116 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[389]) ).
thf(407,plain,
! [SV118: $i,SV45: $i,SV89: $i] :
( ( ( between @ SV89 @ SV45 @ SV118 )
= $false )
| ( ( SV45 = SV89 )
= $true )
| ( ( between @ SV45 @ SV89 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[390]) ).
thf(408,plain,
! [SV119: $i,SV90: $i,SV158: $i,SV147: $i,SV47: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV47 @ SV147 @ SV158 )
| ( equidistant @ SV90 @ SV119 @ SV147 @ SV158 ) )
= $true )
| ( ( equidistant @ SV2 @ SV47 @ SV90 @ SV119 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(409,plain,
! [SV138: $i,SV136: $i,SV123: $i,SV93: $i,SV51: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
= $false )
| ( ( ~ ( equidistant @ SV51 @ SV136 @ SV123 @ SV138 )
| ! [SY435: $i,SY436: $i] :
( ~ ( equidistant @ SV6 @ SY435 @ SV93 @ SY436 )
| ~ ( equidistant @ SV51 @ SY435 @ SV123 @ SY436 )
| ~ ( between @ SV6 @ SV51 @ SV136 )
| ~ ( between @ SV93 @ SV123 @ SV138 )
| ( SV6 = SV51 )
| ( equidistant @ SV136 @ SY435 @ SV138 @ SY436 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[392]) ).
thf(410,plain,
! [SV8: $i,SV53: $i,SV94: $i,SV148: $i,SV139: $i] :
( ( ( ~ ( between @ SV139 @ SV148 @ SV94 ) )
= $true )
| ( ( between @ SV53 @ ( inner_pasch @ SV8 @ SV53 @ SV94 @ SV148 @ SV139 ) @ SV139 )
= $true )
| ( ( between @ SV8 @ SV53 @ SV94 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(411,plain,
! [SV54: $i,SV9: $i,SV95: $i,SV149: $i,SV140: $i] :
( ( ( ~ ( between @ SV140 @ SV149 @ SV95 ) )
= $true )
| ( ( between @ SV149 @ ( inner_pasch @ SV9 @ SV54 @ SV95 @ SV149 @ SV140 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV54 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(412,plain,
! [SV10: $i,SV96: $i,SV55: $i,SV141: $i] :
( ( ( equidistant @ SV141 @ SV55 @ SV141 @ SV96 )
= $false )
| ( ( ! [SY439: $i] :
( ~ ( equidistant @ SY439 @ SV55 @ SY439 @ SV96 )
| ( between @ SV10 @ SV141 @ SY439 )
| ( between @ SV141 @ SY439 @ SV10 )
| ( SV55 = SV96 )
| ( between @ SY439 @ SV10 @ SV141 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV55 @ SV10 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[395]) ).
thf(413,plain,
! [SV97: $i,SV11: $i,SV150: $i,SV56: $i,SV142: $i] :
( ( ( ~ ( between @ SV142 @ SV56 @ SV150 ) )
= $true )
| ( ( ( SV11 = SV56 )
| ( between @ SV11 @ SV142 @ ( euclid1 @ SV11 @ SV142 @ SV56 @ SV150 @ SV97 ) ) )
= $true )
| ( ( between @ SV11 @ SV56 @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(414,plain,
! [SV98: $i,SV12: $i,SV151: $i,SV57: $i,SV143: $i] :
( ( ( ~ ( between @ SV143 @ SV57 @ SV151 ) )
= $true )
| ( ( ( SV12 = SV57 )
| ( between @ SV12 @ SV151 @ ( euclid2 @ SV12 @ SV143 @ SV57 @ SV151 @ SV98 ) ) )
= $true )
| ( ( between @ SV12 @ SV57 @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(415,plain,
! [SV99: $i,SV13: $i,SV152: $i,SV58: $i,SV144: $i] :
( ( ( ~ ( between @ SV144 @ SV58 @ SV152 ) )
= $true )
| ( ( ( SV13 = SV58 )
| ( between @ ( euclid1 @ SV13 @ SV144 @ SV58 @ SV152 @ SV99 ) @ SV99 @ ( euclid2 @ SV13 @ SV144 @ SV58 @ SV152 @ SV99 ) ) )
= $true )
| ( ( between @ SV13 @ SV58 @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(416,plain,
! [SV100: $i,SV59: $i,SV153: $i,SV124: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV124 @ SV14 @ SV153 ) )
= $true )
| ( ( ~ ( between @ SV14 @ SV59 @ SV124 )
| ! [SY444: $i] :
( ~ ( between @ SV59 @ SY444 @ SV124 )
| ( between @ SV100 @ ( continuous @ SV14 @ SV59 @ SV100 @ SY444 @ SV124 @ SV153 ) @ SV153 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV59 @ SV14 @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(417,plain,
! [SV101: $i,SV60: $i,SV154: $i,SV125: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV125 @ SV15 @ SV154 ) )
= $true )
| ( ( ~ ( between @ SV15 @ SV60 @ SV125 )
| ! [SY445: $i] :
( ~ ( between @ SV60 @ SY445 @ SV125 )
| ( equidistant @ SV15 @ SY445 @ SV15 @ ( continuous @ SV15 @ SV60 @ SV101 @ SY445 @ SV125 @ SV154 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV60 @ SV15 @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(418,plain,
! [SV70: $i,SV25: $i,SV159: $i,SV155: $i,SV133: $i,SV109: $i] :
( ( ( ~ ( equidistant @ SV109 @ SV133 @ SV155 @ SV159 )
| ( equidistant @ SV25 @ SV70 @ SV155 @ SV159 ) )
= $true )
| ( ( equidistant @ SV25 @ SV70 @ SV109 @ SV133 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[401]) ).
thf(419,plain,
! [SV112: $i,SV34: $i,SV160: $i,SV134: $i,SV156: $i,SV78: $i] :
( ( ( ~ ( equidistant @ SV78 @ SV156 @ SV134 @ SV160 )
| ~ ( between @ SV34 @ SV78 @ SV156 )
| ~ ( between @ SV112 @ SV134 @ SV160 )
| ( equidistant @ SV34 @ SV156 @ SV112 @ SV160 ) )
= $true )
| ( ( equidistant @ SV34 @ SV78 @ SV112 @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[403]) ).
thf(420,plain,
! [SV113: $i,SV146: $i,SV79: $i,SV35: $i] :
( ( ( between @ SV35 @ SV79 @ SV146 )
= $false )
| ( ( ~ ( equidistant @ SV79 @ SV113 @ SV79 @ SV146 )
| ( SV35 = SV79 )
| ( SV113 = SV146 ) )
= $true )
| ( ( between @ SV35 @ SV79 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(421,plain,
! [SV135: $i,SV115: $i,SV81: $i,SV37: $i,SV161: $i,SV157: $i] :
( ( ( ( ( extension @ SV157 @ SV161 @ SV37 @ SV81 )
= ( extension @ SV157 @ SV161 @ SV115 @ SV135 ) )
| ( SV157 = SV161 ) )
= $true )
| ( ( equidistant @ SV37 @ SV81 @ SV115 @ SV135 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(422,plain,
! [SV42: $i,SV116: $i,SV86: $i,SV162: $i] :
( ( ( between @ SV162 @ SV86 @ SV116 )
= $true )
| ( ( SV42 = SV116 )
= $false )
| ( ( between @ SV42 @ SV86 @ SV116 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[406]) ).
thf(423,plain,
! [SV119: $i,SV90: $i,SV158: $i,SV147: $i,SV47: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV47 @ SV147 @ SV158 ) )
= $true )
| ( ( equidistant @ SV90 @ SV119 @ SV147 @ SV158 )
= $true )
| ( ( equidistant @ SV2 @ SV47 @ SV90 @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[408]) ).
thf(424,plain,
! [SV93: $i,SV6: $i,SV138: $i,SV123: $i,SV136: $i,SV51: $i] :
( ( ( ~ ( equidistant @ SV51 @ SV136 @ SV123 @ SV138 ) )
= $true )
| ( ( ! [SY435: $i,SY436: $i] :
( ~ ( equidistant @ SV6 @ SY435 @ SV93 @ SY436 )
| ~ ( equidistant @ SV51 @ SY435 @ SV123 @ SY436 )
| ~ ( between @ SV6 @ SV51 @ SV136 )
| ~ ( between @ SV93 @ SV123 @ SV138 )
| ( SV6 = SV51 )
| ( equidistant @ SV136 @ SY435 @ SV138 @ SY436 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[409]) ).
thf(425,plain,
! [SV8: $i,SV53: $i,SV94: $i,SV148: $i,SV139: $i] :
( ( ( between @ SV139 @ SV148 @ SV94 )
= $false )
| ( ( between @ SV53 @ ( inner_pasch @ SV8 @ SV53 @ SV94 @ SV148 @ SV139 ) @ SV139 )
= $true )
| ( ( between @ SV8 @ SV53 @ SV94 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(426,plain,
! [SV54: $i,SV9: $i,SV95: $i,SV149: $i,SV140: $i] :
( ( ( between @ SV140 @ SV149 @ SV95 )
= $false )
| ( ( between @ SV149 @ ( inner_pasch @ SV9 @ SV54 @ SV95 @ SV149 @ SV140 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV54 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(427,plain,
! [SV141: $i,SV10: $i,SV96: $i,SV55: $i,SV163: $i] :
( ( ( ~ ( equidistant @ SV163 @ SV55 @ SV163 @ SV96 )
| ( between @ SV10 @ SV141 @ SV163 )
| ( between @ SV141 @ SV163 @ SV10 )
| ( SV55 = SV96 )
| ( between @ SV163 @ SV10 @ SV141 ) )
= $true )
| ( ( equidistant @ SV141 @ SV55 @ SV141 @ SV96 )
= $false )
| ( ( equidistant @ SV10 @ SV55 @ SV10 @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[412]) ).
thf(428,plain,
! [SV97: $i,SV11: $i,SV150: $i,SV56: $i,SV142: $i] :
( ( ( between @ SV142 @ SV56 @ SV150 )
= $false )
| ( ( ( SV11 = SV56 )
| ( between @ SV11 @ SV142 @ ( euclid1 @ SV11 @ SV142 @ SV56 @ SV150 @ SV97 ) ) )
= $true )
| ( ( between @ SV11 @ SV56 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(429,plain,
! [SV98: $i,SV12: $i,SV151: $i,SV57: $i,SV143: $i] :
( ( ( between @ SV143 @ SV57 @ SV151 )
= $false )
| ( ( ( SV12 = SV57 )
| ( between @ SV12 @ SV151 @ ( euclid2 @ SV12 @ SV143 @ SV57 @ SV151 @ SV98 ) ) )
= $true )
| ( ( between @ SV12 @ SV57 @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(430,plain,
! [SV99: $i,SV13: $i,SV152: $i,SV58: $i,SV144: $i] :
( ( ( between @ SV144 @ SV58 @ SV152 )
= $false )
| ( ( ( SV13 = SV58 )
| ( between @ ( euclid1 @ SV13 @ SV144 @ SV58 @ SV152 @ SV99 ) @ SV99 @ ( euclid2 @ SV13 @ SV144 @ SV58 @ SV152 @ SV99 ) ) )
= $true )
| ( ( between @ SV13 @ SV58 @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(431,plain,
! [SV100: $i,SV59: $i,SV153: $i,SV124: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV124 @ SV14 @ SV153 )
= $false )
| ( ( ~ ( between @ SV14 @ SV59 @ SV124 )
| ! [SY444: $i] :
( ~ ( between @ SV59 @ SY444 @ SV124 )
| ( between @ SV100 @ ( continuous @ SV14 @ SV59 @ SV100 @ SY444 @ SV124 @ SV153 ) @ SV153 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV59 @ SV14 @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(432,plain,
! [SV101: $i,SV60: $i,SV154: $i,SV125: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV125 @ SV15 @ SV154 )
= $false )
| ( ( ~ ( between @ SV15 @ SV60 @ SV125 )
| ! [SY445: $i] :
( ~ ( between @ SV60 @ SY445 @ SV125 )
| ( equidistant @ SV15 @ SY445 @ SV15 @ ( continuous @ SV15 @ SV60 @ SV101 @ SY445 @ SV125 @ SV154 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV60 @ SV15 @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(433,plain,
! [SV70: $i,SV25: $i,SV159: $i,SV155: $i,SV133: $i,SV109: $i] :
( ( ( ~ ( equidistant @ SV109 @ SV133 @ SV155 @ SV159 ) )
= $true )
| ( ( equidistant @ SV25 @ SV70 @ SV155 @ SV159 )
= $true )
| ( ( equidistant @ SV25 @ SV70 @ SV109 @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(434,plain,
! [SV112: $i,SV34: $i,SV160: $i,SV134: $i,SV156: $i,SV78: $i] :
( ( ( ~ ( equidistant @ SV78 @ SV156 @ SV134 @ SV160 ) )
= $true )
| ( ( ~ ( between @ SV34 @ SV78 @ SV156 )
| ~ ( between @ SV112 @ SV134 @ SV160 )
| ( equidistant @ SV34 @ SV156 @ SV112 @ SV160 ) )
= $true )
| ( ( equidistant @ SV34 @ SV78 @ SV112 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(435,plain,
! [SV35: $i,SV146: $i,SV113: $i,SV79: $i] :
( ( ( ~ ( equidistant @ SV79 @ SV113 @ SV79 @ SV146 ) )
= $true )
| ( ( ( SV35 = SV79 )
| ( SV113 = SV146 ) )
= $true )
| ( ( between @ SV35 @ SV79 @ SV146 )
= $false )
| ( ( between @ SV35 @ SV79 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(436,plain,
! [SV135: $i,SV115: $i,SV81: $i,SV37: $i,SV161: $i,SV157: $i] :
( ( ( ( extension @ SV157 @ SV161 @ SV37 @ SV81 )
= ( extension @ SV157 @ SV161 @ SV115 @ SV135 ) )
= $true )
| ( ( SV157 = SV161 )
= $true )
| ( ( equidistant @ SV37 @ SV81 @ SV115 @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(437,plain,
! [SV119: $i,SV90: $i,SV158: $i,SV147: $i,SV47: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV47 @ SV147 @ SV158 )
= $false )
| ( ( equidistant @ SV90 @ SV119 @ SV147 @ SV158 )
= $true )
| ( ( equidistant @ SV2 @ SV47 @ SV90 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[423]) ).
thf(438,plain,
! [SV93: $i,SV6: $i,SV138: $i,SV123: $i,SV136: $i,SV51: $i] :
( ( ( equidistant @ SV51 @ SV136 @ SV123 @ SV138 )
= $false )
| ( ( ! [SY435: $i,SY436: $i] :
( ~ ( equidistant @ SV6 @ SY435 @ SV93 @ SY436 )
| ~ ( equidistant @ SV51 @ SY435 @ SV123 @ SY436 )
| ~ ( between @ SV6 @ SV51 @ SV136 )
| ~ ( between @ SV93 @ SV123 @ SV138 )
| ( SV6 = SV51 )
| ( equidistant @ SV136 @ SY435 @ SV138 @ SY436 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(439,plain,
! [SV141: $i,SV10: $i,SV96: $i,SV55: $i,SV163: $i] :
( ( ( ~ ( equidistant @ SV163 @ SV55 @ SV163 @ SV96 ) )
= $true )
| ( ( ( between @ SV10 @ SV141 @ SV163 )
| ( between @ SV141 @ SV163 @ SV10 )
| ( SV55 = SV96 )
| ( between @ SV163 @ SV10 @ SV141 ) )
= $true )
| ( ( equidistant @ SV141 @ SV55 @ SV141 @ SV96 )
= $false )
| ( ( equidistant @ SV10 @ SV55 @ SV10 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(440,plain,
! [SV97: $i,SV150: $i,SV142: $i,SV56: $i,SV11: $i] :
( ( ( SV11 = SV56 )
= $true )
| ( ( between @ SV11 @ SV142 @ ( euclid1 @ SV11 @ SV142 @ SV56 @ SV150 @ SV97 ) )
= $true )
| ( ( between @ SV142 @ SV56 @ SV150 )
= $false )
| ( ( between @ SV11 @ SV56 @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[428]) ).
thf(441,plain,
! [SV98: $i,SV143: $i,SV151: $i,SV57: $i,SV12: $i] :
( ( ( SV12 = SV57 )
= $true )
| ( ( between @ SV12 @ SV151 @ ( euclid2 @ SV12 @ SV143 @ SV57 @ SV151 @ SV98 ) )
= $true )
| ( ( between @ SV143 @ SV57 @ SV151 )
= $false )
| ( ( between @ SV12 @ SV57 @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(442,plain,
! [SV99: $i,SV152: $i,SV144: $i,SV58: $i,SV13: $i] :
( ( ( SV13 = SV58 )
= $true )
| ( ( between @ ( euclid1 @ SV13 @ SV144 @ SV58 @ SV152 @ SV99 ) @ SV99 @ ( euclid2 @ SV13 @ SV144 @ SV58 @ SV152 @ SV99 ) )
= $true )
| ( ( between @ SV144 @ SV58 @ SV152 )
= $false )
| ( ( between @ SV13 @ SV58 @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(443,plain,
! [SV153: $i,SV100: $i,SV124: $i,SV59: $i,SV14: $i] :
( ( ( ~ ( between @ SV14 @ SV59 @ SV124 ) )
= $true )
| ( ( ! [SY444: $i] :
( ~ ( between @ SV59 @ SY444 @ SV124 )
| ( between @ SV100 @ ( continuous @ SV14 @ SV59 @ SV100 @ SY444 @ SV124 @ SV153 ) @ SV153 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV124 @ SV14 @ SV153 )
= $false )
| ( ( equidistant @ SV14 @ SV59 @ SV14 @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(444,plain,
! [SV154: $i,SV101: $i,SV125: $i,SV60: $i,SV15: $i] :
( ( ( ~ ( between @ SV15 @ SV60 @ SV125 ) )
= $true )
| ( ( ! [SY445: $i] :
( ~ ( between @ SV60 @ SY445 @ SV125 )
| ( equidistant @ SV15 @ SY445 @ SV15 @ ( continuous @ SV15 @ SV60 @ SV101 @ SY445 @ SV125 @ SV154 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV125 @ SV15 @ SV154 )
= $false )
| ( ( equidistant @ SV15 @ SV60 @ SV15 @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[432]) ).
thf(445,plain,
! [SV70: $i,SV25: $i,SV159: $i,SV155: $i,SV133: $i,SV109: $i] :
( ( ( equidistant @ SV109 @ SV133 @ SV155 @ SV159 )
= $false )
| ( ( equidistant @ SV25 @ SV70 @ SV155 @ SV159 )
= $true )
| ( ( equidistant @ SV25 @ SV70 @ SV109 @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(446,plain,
! [SV112: $i,SV34: $i,SV160: $i,SV134: $i,SV156: $i,SV78: $i] :
( ( ( equidistant @ SV78 @ SV156 @ SV134 @ SV160 )
= $false )
| ( ( ~ ( between @ SV34 @ SV78 @ SV156 )
| ~ ( between @ SV112 @ SV134 @ SV160 )
| ( equidistant @ SV34 @ SV156 @ SV112 @ SV160 ) )
= $true )
| ( ( equidistant @ SV34 @ SV78 @ SV112 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(447,plain,
! [SV35: $i,SV146: $i,SV113: $i,SV79: $i] :
( ( ( equidistant @ SV79 @ SV113 @ SV79 @ SV146 )
= $false )
| ( ( ( SV35 = SV79 )
| ( SV113 = SV146 ) )
= $true )
| ( ( between @ SV35 @ SV79 @ SV146 )
= $false )
| ( ( between @ SV35 @ SV79 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(448,plain,
! [SV138: $i,SV136: $i,SV123: $i,SV51: $i,SV93: $i,SV164: $i,SV6: $i] :
( ( ( ! [SY449: $i] :
( ~ ( equidistant @ SV6 @ SV164 @ SV93 @ SY449 )
| ~ ( equidistant @ SV51 @ SV164 @ SV123 @ SY449 )
| ~ ( between @ SV6 @ SV51 @ SV136 )
| ~ ( between @ SV93 @ SV123 @ SV138 )
| ( SV6 = SV51 )
| ( equidistant @ SV136 @ SV164 @ SV138 @ SY449 ) ) )
= $true )
| ( ( equidistant @ SV51 @ SV136 @ SV123 @ SV138 )
= $false )
| ( ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(449,plain,
! [SV141: $i,SV10: $i,SV96: $i,SV55: $i,SV163: $i] :
( ( ( equidistant @ SV163 @ SV55 @ SV163 @ SV96 )
= $false )
| ( ( ( between @ SV10 @ SV141 @ SV163 )
| ( between @ SV141 @ SV163 @ SV10 )
| ( SV55 = SV96 )
| ( between @ SV163 @ SV10 @ SV141 ) )
= $true )
| ( ( equidistant @ SV141 @ SV55 @ SV141 @ SV96 )
= $false )
| ( ( equidistant @ SV10 @ SV55 @ SV10 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(450,plain,
! [SV153: $i,SV100: $i,SV124: $i,SV59: $i,SV14: $i] :
( ( ( between @ SV14 @ SV59 @ SV124 )
= $false )
| ( ( ! [SY444: $i] :
( ~ ( between @ SV59 @ SY444 @ SV124 )
| ( between @ SV100 @ ( continuous @ SV14 @ SV59 @ SV100 @ SY444 @ SV124 @ SV153 ) @ SV153 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV124 @ SV14 @ SV153 )
= $false )
| ( ( equidistant @ SV14 @ SV59 @ SV14 @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(451,plain,
! [SV154: $i,SV101: $i,SV125: $i,SV60: $i,SV15: $i] :
( ( ( between @ SV15 @ SV60 @ SV125 )
= $false )
| ( ( ! [SY445: $i] :
( ~ ( between @ SV60 @ SY445 @ SV125 )
| ( equidistant @ SV15 @ SY445 @ SV15 @ ( continuous @ SV15 @ SV60 @ SV101 @ SY445 @ SV125 @ SV154 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV125 @ SV15 @ SV154 )
= $false )
| ( ( equidistant @ SV15 @ SV60 @ SV15 @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(452,plain,
! [SV160: $i,SV134: $i,SV112: $i,SV156: $i,SV78: $i,SV34: $i] :
( ( ( ~ ( between @ SV34 @ SV78 @ SV156 ) )
= $true )
| ( ( ~ ( between @ SV112 @ SV134 @ SV160 )
| ( equidistant @ SV34 @ SV156 @ SV112 @ SV160 ) )
= $true )
| ( ( equidistant @ SV78 @ SV156 @ SV134 @ SV160 )
= $false )
| ( ( equidistant @ SV34 @ SV78 @ SV112 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[446]) ).
thf(453,plain,
! [SV146: $i,SV113: $i,SV79: $i,SV35: $i] :
( ( ( SV35 = SV79 )
= $true )
| ( ( SV113 = SV146 )
= $true )
| ( ( equidistant @ SV79 @ SV113 @ SV79 @ SV146 )
= $false )
| ( ( between @ SV35 @ SV79 @ SV146 )
= $false )
| ( ( between @ SV35 @ SV79 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[447]) ).
thf(454,plain,
! [SV138: $i,SV136: $i,SV123: $i,SV51: $i,SV165: $i,SV93: $i,SV164: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV164 @ SV93 @ SV165 )
| ~ ( equidistant @ SV51 @ SV164 @ SV123 @ SV165 )
| ~ ( between @ SV6 @ SV51 @ SV136 )
| ~ ( between @ SV93 @ SV123 @ SV138 )
| ( SV6 = SV51 )
| ( equidistant @ SV136 @ SV164 @ SV138 @ SV165 ) )
= $true )
| ( ( equidistant @ SV51 @ SV136 @ SV123 @ SV138 )
= $false )
| ( ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(455,plain,
! [SV96: $i,SV55: $i,SV163: $i,SV141: $i,SV10: $i] :
( ( ( between @ SV10 @ SV141 @ SV163 )
= $true )
| ( ( ( between @ SV141 @ SV163 @ SV10 )
| ( SV55 = SV96 )
| ( between @ SV163 @ SV10 @ SV141 ) )
= $true )
| ( ( equidistant @ SV163 @ SV55 @ SV163 @ SV96 )
= $false )
| ( ( equidistant @ SV141 @ SV55 @ SV141 @ SV96 )
= $false )
| ( ( equidistant @ SV10 @ SV55 @ SV10 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(456,plain,
! [SV153: $i,SV14: $i,SV100: $i,SV124: $i,SV166: $i,SV59: $i] :
( ( ( ~ ( between @ SV59 @ SV166 @ SV124 )
| ( between @ SV100 @ ( continuous @ SV14 @ SV59 @ SV100 @ SV166 @ SV124 @ SV153 ) @ SV153 ) )
= $true )
| ( ( between @ SV14 @ SV59 @ SV124 )
= $false )
| ( ( equidistant @ SV14 @ SV124 @ SV14 @ SV153 )
= $false )
| ( ( equidistant @ SV14 @ SV59 @ SV14 @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(457,plain,
! [SV154: $i,SV101: $i,SV15: $i,SV125: $i,SV167: $i,SV60: $i] :
( ( ( ~ ( between @ SV60 @ SV167 @ SV125 )
| ( equidistant @ SV15 @ SV167 @ SV15 @ ( continuous @ SV15 @ SV60 @ SV101 @ SV167 @ SV125 @ SV154 ) ) )
= $true )
| ( ( between @ SV15 @ SV60 @ SV125 )
= $false )
| ( ( equidistant @ SV15 @ SV125 @ SV15 @ SV154 )
= $false )
| ( ( equidistant @ SV15 @ SV60 @ SV15 @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(458,plain,
! [SV160: $i,SV134: $i,SV112: $i,SV156: $i,SV78: $i,SV34: $i] :
( ( ( between @ SV34 @ SV78 @ SV156 )
= $false )
| ( ( ~ ( between @ SV112 @ SV134 @ SV160 )
| ( equidistant @ SV34 @ SV156 @ SV112 @ SV160 ) )
= $true )
| ( ( equidistant @ SV78 @ SV156 @ SV134 @ SV160 )
= $false )
| ( ( equidistant @ SV34 @ SV78 @ SV112 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[452]) ).
thf(459,plain,
! [SV138: $i,SV136: $i,SV123: $i,SV51: $i,SV165: $i,SV93: $i,SV164: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV164 @ SV93 @ SV165 ) )
= $true )
| ( ( ~ ( equidistant @ SV51 @ SV164 @ SV123 @ SV165 )
| ~ ( between @ SV6 @ SV51 @ SV136 )
| ~ ( between @ SV93 @ SV123 @ SV138 )
| ( SV6 = SV51 )
| ( equidistant @ SV136 @ SV164 @ SV138 @ SV165 ) )
= $true )
| ( ( equidistant @ SV51 @ SV136 @ SV123 @ SV138 )
= $false )
| ( ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(460,plain,
! [SV96: $i,SV55: $i,SV10: $i,SV163: $i,SV141: $i] :
( ( ( between @ SV141 @ SV163 @ SV10 )
= $true )
| ( ( ( SV55 = SV96 )
| ( between @ SV163 @ SV10 @ SV141 ) )
= $true )
| ( ( between @ SV10 @ SV141 @ SV163 )
= $true )
| ( ( equidistant @ SV163 @ SV55 @ SV163 @ SV96 )
= $false )
| ( ( equidistant @ SV141 @ SV55 @ SV141 @ SV96 )
= $false )
| ( ( equidistant @ SV10 @ SV55 @ SV10 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(461,plain,
! [SV153: $i,SV14: $i,SV100: $i,SV124: $i,SV166: $i,SV59: $i] :
( ( ( ~ ( between @ SV59 @ SV166 @ SV124 ) )
= $true )
| ( ( between @ SV100 @ ( continuous @ SV14 @ SV59 @ SV100 @ SV166 @ SV124 @ SV153 ) @ SV153 )
= $true )
| ( ( between @ SV14 @ SV59 @ SV124 )
= $false )
| ( ( equidistant @ SV14 @ SV124 @ SV14 @ SV153 )
= $false )
| ( ( equidistant @ SV14 @ SV59 @ SV14 @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[456]) ).
thf(462,plain,
! [SV154: $i,SV101: $i,SV15: $i,SV125: $i,SV167: $i,SV60: $i] :
( ( ( ~ ( between @ SV60 @ SV167 @ SV125 ) )
= $true )
| ( ( equidistant @ SV15 @ SV167 @ SV15 @ ( continuous @ SV15 @ SV60 @ SV101 @ SV167 @ SV125 @ SV154 ) )
= $true )
| ( ( between @ SV15 @ SV60 @ SV125 )
= $false )
| ( ( equidistant @ SV15 @ SV125 @ SV15 @ SV154 )
= $false )
| ( ( equidistant @ SV15 @ SV60 @ SV15 @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(463,plain,
! [SV78: $i,SV156: $i,SV34: $i,SV160: $i,SV134: $i,SV112: $i] :
( ( ( ~ ( between @ SV112 @ SV134 @ SV160 ) )
= $true )
| ( ( equidistant @ SV34 @ SV156 @ SV112 @ SV160 )
= $true )
| ( ( between @ SV34 @ SV78 @ SV156 )
= $false )
| ( ( equidistant @ SV78 @ SV156 @ SV134 @ SV160 )
= $false )
| ( ( equidistant @ SV34 @ SV78 @ SV112 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(464,plain,
! [SV138: $i,SV136: $i,SV123: $i,SV51: $i,SV165: $i,SV93: $i,SV164: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV164 @ SV93 @ SV165 )
= $false )
| ( ( ~ ( equidistant @ SV51 @ SV164 @ SV123 @ SV165 )
| ~ ( between @ SV6 @ SV51 @ SV136 )
| ~ ( between @ SV93 @ SV123 @ SV138 )
| ( SV6 = SV51 )
| ( equidistant @ SV136 @ SV164 @ SV138 @ SV165 ) )
= $true )
| ( ( equidistant @ SV51 @ SV136 @ SV123 @ SV138 )
= $false )
| ( ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(465,plain,
! [SV141: $i,SV10: $i,SV163: $i,SV96: $i,SV55: $i] :
( ( ( SV55 = SV96 )
= $true )
| ( ( between @ SV163 @ SV10 @ SV141 )
= $true )
| ( ( between @ SV141 @ SV163 @ SV10 )
= $true )
| ( ( between @ SV10 @ SV141 @ SV163 )
= $true )
| ( ( equidistant @ SV163 @ SV55 @ SV163 @ SV96 )
= $false )
| ( ( equidistant @ SV141 @ SV55 @ SV141 @ SV96 )
= $false )
| ( ( equidistant @ SV10 @ SV55 @ SV10 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(466,plain,
! [SV153: $i,SV14: $i,SV100: $i,SV124: $i,SV166: $i,SV59: $i] :
( ( ( between @ SV59 @ SV166 @ SV124 )
= $false )
| ( ( between @ SV100 @ ( continuous @ SV14 @ SV59 @ SV100 @ SV166 @ SV124 @ SV153 ) @ SV153 )
= $true )
| ( ( between @ SV14 @ SV59 @ SV124 )
= $false )
| ( ( equidistant @ SV14 @ SV124 @ SV14 @ SV153 )
= $false )
| ( ( equidistant @ SV14 @ SV59 @ SV14 @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(467,plain,
! [SV154: $i,SV101: $i,SV15: $i,SV125: $i,SV167: $i,SV60: $i] :
( ( ( between @ SV60 @ SV167 @ SV125 )
= $false )
| ( ( equidistant @ SV15 @ SV167 @ SV15 @ ( continuous @ SV15 @ SV60 @ SV101 @ SV167 @ SV125 @ SV154 ) )
= $true )
| ( ( between @ SV15 @ SV60 @ SV125 )
= $false )
| ( ( equidistant @ SV15 @ SV125 @ SV15 @ SV154 )
= $false )
| ( ( equidistant @ SV15 @ SV60 @ SV15 @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(468,plain,
! [SV78: $i,SV156: $i,SV34: $i,SV160: $i,SV134: $i,SV112: $i] :
( ( ( between @ SV112 @ SV134 @ SV160 )
= $false )
| ( ( equidistant @ SV34 @ SV156 @ SV112 @ SV160 )
= $true )
| ( ( between @ SV34 @ SV78 @ SV156 )
= $false )
| ( ( equidistant @ SV78 @ SV156 @ SV134 @ SV160 )
= $false )
| ( ( equidistant @ SV34 @ SV78 @ SV112 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(469,plain,
! [SV138: $i,SV93: $i,SV136: $i,SV6: $i,SV165: $i,SV123: $i,SV164: $i,SV51: $i] :
( ( ( ~ ( equidistant @ SV51 @ SV164 @ SV123 @ SV165 ) )
= $true )
| ( ( ~ ( between @ SV6 @ SV51 @ SV136 )
| ~ ( between @ SV93 @ SV123 @ SV138 )
| ( SV6 = SV51 )
| ( equidistant @ SV136 @ SV164 @ SV138 @ SV165 ) )
= $true )
| ( ( equidistant @ SV6 @ SV164 @ SV93 @ SV165 )
= $false )
| ( ( equidistant @ SV51 @ SV136 @ SV123 @ SV138 )
= $false )
| ( ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[464]) ).
thf(470,plain,
! [SV138: $i,SV93: $i,SV136: $i,SV6: $i,SV165: $i,SV123: $i,SV164: $i,SV51: $i] :
( ( ( equidistant @ SV51 @ SV164 @ SV123 @ SV165 )
= $false )
| ( ( ~ ( between @ SV6 @ SV51 @ SV136 )
| ~ ( between @ SV93 @ SV123 @ SV138 )
| ( SV6 = SV51 )
| ( equidistant @ SV136 @ SV164 @ SV138 @ SV165 ) )
= $true )
| ( ( equidistant @ SV6 @ SV164 @ SV93 @ SV165 )
= $false )
| ( ( equidistant @ SV51 @ SV136 @ SV123 @ SV138 )
= $false )
| ( ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(471,plain,
! [SV165: $i,SV164: $i,SV138: $i,SV123: $i,SV93: $i,SV136: $i,SV51: $i,SV6: $i] :
( ( ( ~ ( between @ SV6 @ SV51 @ SV136 ) )
= $true )
| ( ( ~ ( between @ SV93 @ SV123 @ SV138 )
| ( SV6 = SV51 )
| ( equidistant @ SV136 @ SV164 @ SV138 @ SV165 ) )
= $true )
| ( ( equidistant @ SV51 @ SV164 @ SV123 @ SV165 )
= $false )
| ( ( equidistant @ SV6 @ SV164 @ SV93 @ SV165 )
= $false )
| ( ( equidistant @ SV51 @ SV136 @ SV123 @ SV138 )
= $false )
| ( ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(472,plain,
! [SV165: $i,SV164: $i,SV138: $i,SV123: $i,SV93: $i,SV136: $i,SV51: $i,SV6: $i] :
( ( ( between @ SV6 @ SV51 @ SV136 )
= $false )
| ( ( ~ ( between @ SV93 @ SV123 @ SV138 )
| ( SV6 = SV51 )
| ( equidistant @ SV136 @ SV164 @ SV138 @ SV165 ) )
= $true )
| ( ( equidistant @ SV51 @ SV164 @ SV123 @ SV165 )
= $false )
| ( ( equidistant @ SV6 @ SV164 @ SV93 @ SV165 )
= $false )
| ( ( equidistant @ SV51 @ SV136 @ SV123 @ SV138 )
= $false )
| ( ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(473,plain,
! [SV165: $i,SV164: $i,SV136: $i,SV51: $i,SV6: $i,SV138: $i,SV123: $i,SV93: $i] :
( ( ( ~ ( between @ SV93 @ SV123 @ SV138 ) )
= $true )
| ( ( ( SV6 = SV51 )
| ( equidistant @ SV136 @ SV164 @ SV138 @ SV165 ) )
= $true )
| ( ( between @ SV6 @ SV51 @ SV136 )
= $false )
| ( ( equidistant @ SV51 @ SV164 @ SV123 @ SV165 )
= $false )
| ( ( equidistant @ SV6 @ SV164 @ SV93 @ SV165 )
= $false )
| ( ( equidistant @ SV51 @ SV136 @ SV123 @ SV138 )
= $false )
| ( ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(474,plain,
! [SV165: $i,SV164: $i,SV136: $i,SV51: $i,SV6: $i,SV138: $i,SV123: $i,SV93: $i] :
( ( ( between @ SV93 @ SV123 @ SV138 )
= $false )
| ( ( ( SV6 = SV51 )
| ( equidistant @ SV136 @ SV164 @ SV138 @ SV165 ) )
= $true )
| ( ( between @ SV6 @ SV51 @ SV136 )
= $false )
| ( ( equidistant @ SV51 @ SV164 @ SV123 @ SV165 )
= $false )
| ( ( equidistant @ SV6 @ SV164 @ SV93 @ SV165 )
= $false )
| ( ( equidistant @ SV51 @ SV136 @ SV123 @ SV138 )
= $false )
| ( ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(475,plain,
! [SV123: $i,SV93: $i,SV165: $i,SV138: $i,SV164: $i,SV136: $i,SV51: $i,SV6: $i] :
( ( ( SV6 = SV51 )
= $true )
| ( ( equidistant @ SV136 @ SV164 @ SV138 @ SV165 )
= $true )
| ( ( between @ SV93 @ SV123 @ SV138 )
= $false )
| ( ( between @ SV6 @ SV51 @ SV136 )
= $false )
| ( ( equidistant @ SV51 @ SV164 @ SV123 @ SV165 )
= $false )
| ( ( equidistant @ SV6 @ SV164 @ SV93 @ SV165 )
= $false )
| ( ( equidistant @ SV51 @ SV136 @ SV123 @ SV138 )
= $false )
| ( ( equidistant @ SV6 @ SV51 @ SV93 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(476,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[128,475,468,467,466,465,453,445,442,441,440,437,436,426,425,422,407,402,387,382,381,380,379,378,377,376,364,340,331,330,312,310,309,303,295,271,268,267,266,260,257,256,245,244,229,228,213,191,190,189,179,129]) ).
thf(477,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[476]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO041-3 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.17 % Computer : n020.cluster.edu
% 0.10/0.17 % Model : x86_64 x86_64
% 0.10/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.17 % Memory : 8046.5625MB
% 0.10/0.17 % OS : Linux 6.8.0-71-generic
% 0.10/0.17 % CPULimit : 300
% 0.10/0.17 % WCLimit : 300
% 0.10/0.17 % DateTime : Tue Oct 6 10:01:24 UTC 2026
% 0.10/0.18 % CPUTime :
% 0.10/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.86/0.52
% 1.86/0.52 No.of.Axioms: 51
% 1.86/0.52
% 1.86/0.52 Length.of.Defs: 0
% 1.86/0.52
% 1.86/0.52 Contains.Choice.Funs: false
% 1.86/0.52 ...................
% 1.86/0.52
% 1.86/0.52 ********************************
% 1.86/0.52 * All subproblems solved! *
% 1.86/0.52 ********************************
% 1.86/0.52 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:51,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:476,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.86/0.52
% 1.86/0.52 %**** Beginning of derivation protocol ****
% 1.86/0.52 % SZS output start CNFRefutation
% See solution above
% 1.86/0.53
% 1.86/0.53 %**** End of derivation protocol ****
% 1.86/0.53 %**** no. of clauses in derivation: 477 ****
% 1.86/0.53 %**** clause counter: 476 ****
% 1.86/0.53
% 1.86/0.53 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:51,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:476,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------