TSTP Solution File: GEO048-3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GEO048-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:06:30 EDT 2022
% Result : Unsatisfiable 0.75s 1.02s
% Output : CNFRefutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 86
% Syntax : Number of formulae : 640 ( 381 unt; 17 typ; 0 def)
% Number of atoms : 3714 (1289 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 8447 ( 819 ~;1261 |; 0 &;6367 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 11 con; 0-6 aty)
% Number of variables : 2403 ( 0 ^2403 !; 0 ?;2403 :)
% 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_u1,type,
u1: $i ).
thf(tp_v,type,
v: $i ).
thf(tp_v1,type,
v1: $i ).
thf(tp_w,type,
w: $i ).
thf(tp_x,type,
x: $i ).
thf(1,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_3) ).
thf(2,axiom,
! [V: $i,U: $i,X: $i,W: $i] : ( equidistant @ V @ ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ X @ ( extension @ W @ X @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_2) ).
thf(3,axiom,
! [V: $i,U: $i] :
( V
!= ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e3_1) ).
thf(4,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_3) ).
thf(5,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_2) ).
thf(6,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e2_1) ).
thf(7,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ X )
| ( between @ U @ V @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b9) ).
thf(8,axiom,
! [U: $i,V: $i,X: $i,W: $i] :
( ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b8) ).
thf(9,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ V @ X )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b7) ).
thf(10,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b6) ).
thf(11,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ X )
| ( between @ V @ W @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b5) ).
thf(12,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ V @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b4) ).
thf(13,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( U = V )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_2) ).
thf(14,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_1) ).
thf(15,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b3) ).
thf(16,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
thf(17,axiom,
! [U: $i,V: $i] : ( between @ U @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2) ).
thf(18,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
thf(19,axiom,
! [U: $i,W: $i,X: $i,V: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ( between @ V @ W @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b1) ).
thf(20,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3) ).
thf(21,axiom,
! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r6) ).
thf(22,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r5) ).
thf(23,axiom,
! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_3) ).
thf(24,axiom,
! [W: $i,X: $i,Y: $i,Z: $i,U: $i,V: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ( ( extension @ U @ V @ W @ X )
= ( extension @ U @ V @ Y @ Z ) )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_2) ).
thf(25,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( U = V )
| ( W
= ( extension @ U @ V @ V @ W ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_1) ).
thf(26,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ V @ X )
| ~ ( equidistant @ V @ W @ V @ X )
| ( U = V )
| ( W = X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9) ).
thf(27,axiom,
! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ U @ W @ U1 @ W1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d8) ).
thf(28,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7) ).
thf(29,axiom,
! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).
thf(30,axiom,
! [U: $i] :
( U
= ( reflection @ U @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3_2) ).
thf(31,axiom,
! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3_1) ).
thf(32,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_2) ).
thf(33,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_1) ).
thf(34,axiom,
! [Y: $i,U: $i,V: $i,W: $i,X: $i] :
( ( Y
!= ( extension @ U @ V @ W @ X ) )
| ( between @ U @ V @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b0) ).
thf(35,axiom,
! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e1) ).
thf(36,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ~ ( equidistant @ W @ X @ Y @ Z )
| ( equidistant @ U @ V @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5) ).
thf(37,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_5) ).
thf(38,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_4) ).
thf(39,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_3) ).
thf(40,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_2) ).
thf(41,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_1) ).
thf(42,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3) ).
thf(43,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
thf(44,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
thf(45,axiom,
! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflection) ).
thf(46,axiom,
! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity2) ).
thf(47,axiom,
! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity1) ).
thf(48,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid3) ).
thf(49,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid2) ).
thf(50,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid1) ).
thf(51,axiom,
! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ W @ X @ V )
| ~ ( equidistant @ Y @ W @ Y @ V )
| ~ ( equidistant @ Z @ W @ Z @ V )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y )
| ( W = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_dimension) ).
thf(52,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
thf(53,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).
thf(54,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).
thf(55,axiom,
! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ Y @ X @ W )
| ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch2) ).
thf(56,axiom,
! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ Y @ X @ W )
| ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch1) ).
thf(57,axiom,
! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(58,axiom,
! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i,V: $i,V1: $i] :
( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
| ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
| ~ ( equidistant @ X @ V @ X1 @ V1 )
| ~ ( equidistant @ Y @ V @ Y1 @ V1 )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equidistant @ Z @ V @ Z1 @ V1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).
thf(59,axiom,
! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
thf(60,axiom,
! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
thf(61,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(62,axiom,
! [X: $i,Y: $i,Z: $i,V: $i,V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
thf(63,axiom,
! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(64,axiom,
between @ u @ x @ u1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',x_between_u_and_u1) ).
thf(65,axiom,
between @ u1 @ v1 @ w,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v1_between_u1_and_w) ).
thf(66,axiom,
between @ u @ v @ w,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
thf(67,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(68,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[67]) ).
thf(69,negated_conjecture,
~ ( between @ v @ ( inner_pasch @ v1 @ ( inner_pasch @ u @ x @ u1 @ v1 @ w ) @ u @ v @ w ) @ v1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_conclusion2) ).
thf(70,negated_conjecture,
~ ( between @ x @ ( inner_pasch @ v1 @ ( inner_pasch @ u @ x @ u1 @ v1 @ w ) @ u @ v @ w ) @ w ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_conclusion1) ).
thf(71,plain,
$false = $false,
inference(unfold_def,[status(thm)],[68]) ).
thf(72,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(73,plain,
( ( ! [V: $i,U: $i,X: $i,W: $i] : ( equidistant @ V @ ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ X @ ( extension @ W @ X @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(74,plain,
( ( ! [V: $i,U: $i] :
( V
!= ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(75,plain,
( ( ( lower_dimension_point_1 != lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(76,plain,
( ( ( lower_dimension_point_2 != lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(77,plain,
( ( ( lower_dimension_point_1 != lower_dimension_point_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(78,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ X )
| ( between @ U @ V @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(79,plain,
( ( ! [U: $i,V: $i,X: $i,W: $i] :
( ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(80,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ V @ X )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(81,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(82,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ X )
| ( between @ V @ W @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(83,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ V @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(84,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( U = V )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(85,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(86,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(87,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(88,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(89,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(90,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)],[19]) ).
thf(91,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(92,plain,
( ( ! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(93,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(94,plain,
( ( ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(95,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)],[24]) ).
thf(96,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)],[25]) ).
thf(97,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)],[26]) ).
thf(98,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)],[27]) ).
thf(99,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(100,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(101,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(102,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(103,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(104,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(105,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)],[34]) ).
thf(106,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(107,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)],[36]) ).
thf(108,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)],[37]) ).
thf(109,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)],[38]) ).
thf(110,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)],[39]) ).
thf(111,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)],[40]) ).
thf(112,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)],[41]) ).
thf(113,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)],[42]) ).
thf(114,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)],[43]) ).
thf(115,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(116,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(117,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)],[46]) ).
thf(118,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)],[47]) ).
thf(119,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)],[48]) ).
thf(120,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)],[49]) ).
thf(121,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)],[50]) ).
thf(122,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)],[51]) ).
thf(123,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(124,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(125,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(126,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)],[55]) ).
thf(127,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)],[56]) ).
thf(128,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(129,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)],[58]) ).
thf(130,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[59]) ).
thf(131,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(132,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(133,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)],[62]) ).
thf(134,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[63]) ).
thf(135,plain,
( ( between @ u @ x @ u1 )
= $true ),
inference(unfold_def,[status(thm)],[64]) ).
thf(136,plain,
( ( between @ u1 @ v1 @ w )
= $true ),
inference(unfold_def,[status(thm)],[65]) ).
thf(137,plain,
( ( between @ u @ v @ w )
= $true ),
inference(unfold_def,[status(thm)],[66]) ).
thf(138,plain,
( ( ~ ( between @ v @ ( inner_pasch @ v1 @ ( inner_pasch @ u @ x @ u1 @ v1 @ w ) @ u @ v @ w ) @ v1 ) )
= $true ),
inference(unfold_def,[status(thm)],[69]) ).
thf(139,plain,
( ( ~ ( between @ x @ ( inner_pasch @ v1 @ ( inner_pasch @ u @ x @ u1 @ v1 @ w ) @ u @ v @ w ) @ w ) )
= $true ),
inference(unfold_def,[status(thm)],[70]) ).
thf(140,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[71]) ).
thf(141,plain,
( ( ! [V: $i,U: $i] :
( V
!= ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(142,plain,
( ( ( lower_dimension_point_1 != lower_dimension_point_3 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(143,plain,
( ( ( lower_dimension_point_2 != lower_dimension_point_3 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[76]) ).
thf(144,plain,
( ( ( lower_dimension_point_1 != lower_dimension_point_2 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(145,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ U @ W @ X )
| ( between @ U @ V @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(146,plain,
( ( ! [U: $i,V: $i,X: $i] :
( ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(147,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ V @ W @ X )
| ( V = W )
| ( between @ U @ V @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(148,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ V @ W @ X )
| ( V = W )
| ( between @ U @ W @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(149,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ U @ W @ X )
| ( between @ V @ W @ X ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(150,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
~ ( between @ V @ W @ X )
| ( between @ U @ V @ W ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[83]) ).
thf(151,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)],[90]) ).
thf(152,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)],[95]) ).
thf(153,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)],[97]) ).
thf(154,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)],[98]) ).
thf(155,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[100]) ).
thf(156,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[102]) ).
thf(157,plain,
( ( ! [Y: $i,U: $i,V: $i] :
( ! [W: $i,X: $i] :
( Y
!= ( extension @ U @ V @ W @ X ) )
| ( between @ U @ V @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(158,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)],[107]) ).
thf(159,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)],[117]) ).
thf(160,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)],[118]) ).
thf(161,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)],[119]) ).
thf(162,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)],[120]) ).
thf(163,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)],[121]) ).
thf(164,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)],[122]) ).
thf(165,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)],[126]) ).
thf(166,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)],[127]) ).
thf(167,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)],[129]) ).
thf(168,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[132]) ).
thf(169,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)],[133]) ).
thf(170,plain,
( ( ~ ( between @ x @ ( inner_pasch @ v1 @ ( inner_pasch @ u @ x @ u1 @ v1 @ w ) @ u @ v @ w ) @ w ) )
= $true ),
inference(copy,[status(thm)],[139]) ).
thf(171,plain,
( ( ~ ( between @ v @ ( inner_pasch @ v1 @ ( inner_pasch @ u @ x @ u1 @ v1 @ w ) @ u @ v @ w ) @ v1 ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(172,plain,
( ( between @ u @ v @ w )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(173,plain,
( ( between @ u1 @ v1 @ w )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(174,plain,
( ( between @ u @ x @ u1 )
= $true ),
inference(copy,[status(thm)],[135]) ).
thf(175,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(176,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)],[169]) ).
thf(177,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[168]) ).
thf(178,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[131]) ).
thf(179,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(180,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)],[167]) ).
thf(181,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(182,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)],[166]) ).
thf(183,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)],[165]) ).
thf(184,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[125]) ).
thf(185,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(186,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(copy,[status(thm)],[123]) ).
thf(187,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)],[164]) ).
thf(188,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)],[163]) ).
thf(189,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)],[162]) ).
thf(190,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)],[161]) ).
thf(191,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)],[160]) ).
thf(192,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)],[159]) ).
thf(193,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[116]) ).
thf(194,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(195,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[114]) ).
thf(196,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(197,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(198,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(199,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[110]) ).
thf(200,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(201,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(202,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)],[158]) ).
thf(203,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(204,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)],[157]) ).
thf(205,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(206,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(207,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(208,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(209,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(210,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[99]) ).
thf(211,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)],[154]) ).
thf(212,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)],[153]) ).
thf(213,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( U = V )
| ( W
= ( extension @ U @ V @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(214,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)],[152]) ).
thf(215,plain,
( ( ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(216,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(217,plain,
( ( ! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(218,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(219,plain,
( ( ! [U: $i,W: $i,X: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ! [V: $i] : ( between @ V @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[151]) ).
thf(220,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(221,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(222,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(223,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(224,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(225,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( U = V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(226,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
~ ( between @ V @ W @ X )
| ( between @ U @ V @ W ) ) )
= $true ),
inference(copy,[status(thm)],[150]) ).
thf(227,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ U @ W @ X )
| ( between @ V @ W @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[149]) ).
thf(228,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ V @ W @ X )
| ( V = W )
| ( between @ U @ W @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[148]) ).
thf(229,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ V @ W @ X )
| ( V = W )
| ( between @ U @ V @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[147]) ).
thf(230,plain,
( ( ! [U: $i,V: $i,X: $i] :
( ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[146]) ).
thf(231,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [X: $i] :
( ~ ( between @ U @ W @ X )
| ( between @ U @ V @ X ) ) ) )
= $true ),
inference(copy,[status(thm)],[145]) ).
thf(232,plain,
( ( ( lower_dimension_point_1 != lower_dimension_point_2 ) )
= $true ),
inference(copy,[status(thm)],[144]) ).
thf(233,plain,
( ( ( lower_dimension_point_2 != lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(234,plain,
( ( ( lower_dimension_point_1 != lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[142]) ).
thf(235,plain,
( ( ! [V: $i,U: $i] :
( V
!= ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(236,plain,
( ( ! [V: $i,U: $i,X: $i,W: $i] : ( equidistant @ V @ ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ X @ ( extension @ W @ X @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(237,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( extension @ U @ V @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(238,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[140]) ).
thf(239,plain,
( ( between @ x @ ( inner_pasch @ v1 @ ( inner_pasch @ u @ x @ u1 @ v1 @ w ) @ u @ v @ w ) @ w )
= $false ),
inference(extcnf_not_pos,[status(thm)],[170]) ).
thf(240,plain,
( ( between @ v @ ( inner_pasch @ v1 @ ( inner_pasch @ u @ x @ u1 @ v1 @ w ) @ u @ v @ w ) @ v1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(241,plain,
! [SV1: $i] :
( ( ! [SY208: $i] : ( equidistant @ SV1 @ SY208 @ SY208 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(242,plain,
! [SV2: $i] :
( ( ! [SY209: $i,SY210: $i,SY211: $i] :
( ~ ( equidistant @ SV2 @ SY209 @ SY210 @ SY211 )
| ! [SY212: $i,SY213: $i] :
( ~ ( equidistant @ SV2 @ SY209 @ SY212 @ SY213 )
| ( equidistant @ SY210 @ SY211 @ SY212 @ SY213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(243,plain,
! [SV3: $i] :
( ( ! [SY214: $i] :
( ! [SY215: $i] :
~ ( equidistant @ SV3 @ SY214 @ SY215 @ SY215 )
| ( SV3 = SY214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(244,plain,
! [SV4: $i] :
( ( ! [SY216: $i,SY217: $i,SY218: $i] : ( between @ SV4 @ SY216 @ ( extension @ SV4 @ SY216 @ SY217 @ SY218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(245,plain,
! [SV5: $i] :
( ( ! [SY219: $i,SY220: $i,SY221: $i] : ( equidistant @ SV5 @ ( extension @ SY219 @ SV5 @ SY220 @ SY221 ) @ SY220 @ SY221 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(246,plain,
! [SV6: $i] :
( ( ! [SY222: $i,SY223: $i,SY224: $i,SY225: $i,SY226: $i] :
( ~ ( equidistant @ SV6 @ SY222 @ SY223 @ SY224 )
| ~ ( equidistant @ SY222 @ SY225 @ SY224 @ SY226 )
| ! [SY227: $i,SY228: $i] :
( ~ ( equidistant @ SV6 @ SY227 @ SY223 @ SY228 )
| ~ ( equidistant @ SY222 @ SY227 @ SY224 @ SY228 )
| ~ ( between @ SV6 @ SY222 @ SY225 )
| ~ ( between @ SY223 @ SY224 @ SY226 )
| ( SV6 = SY222 )
| ( equidistant @ SY225 @ SY227 @ SY226 @ SY228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(247,plain,
! [SV7: $i] :
( ( ! [SY229: $i] :
( ~ ( between @ SV7 @ SY229 @ SV7 )
| ( SV7 = SY229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(248,plain,
! [SV8: $i] :
( ( ! [SY230: $i,SY231: $i] :
( ~ ( between @ SV8 @ SY230 @ SY231 )
| ! [SY232: $i,SY233: $i] :
( ~ ( between @ SY232 @ SY233 @ SY231 )
| ( between @ SY230 @ ( inner_pasch @ SV8 @ SY230 @ SY231 @ SY233 @ SY232 ) @ SY232 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(249,plain,
! [SV9: $i] :
( ( ! [SY234: $i,SY235: $i] :
( ~ ( between @ SV9 @ SY234 @ SY235 )
| ! [SY236: $i,SY237: $i] :
( ~ ( between @ SY236 @ SY237 @ SY235 )
| ( between @ SY237 @ ( inner_pasch @ SV9 @ SY234 @ SY235 @ SY237 @ SY236 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(250,plain,
( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(251,plain,
( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(252,plain,
( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(253,plain,
! [SV10: $i] :
( ( ! [SY238: $i,SY239: $i] :
( ~ ( equidistant @ SV10 @ SY238 @ SV10 @ SY239 )
| ! [SY240: $i] :
( ~ ( equidistant @ SY240 @ SY238 @ SY240 @ SY239 )
| ! [SY241: $i] :
( ~ ( equidistant @ SY241 @ SY238 @ SY241 @ SY239 )
| ( between @ SV10 @ SY240 @ SY241 )
| ( between @ SY240 @ SY241 @ SV10 )
| ( SY238 = SY239 )
| ( between @ SY241 @ SV10 @ SY240 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(254,plain,
! [SV11: $i] :
( ( ! [SY242: $i,SY243: $i] :
( ~ ( between @ SV11 @ SY242 @ SY243 )
| ! [SY244: $i,SY245: $i] :
( ~ ( between @ SY244 @ SY242 @ SY245 )
| ( SV11 = SY242 )
| ( between @ SV11 @ SY244 @ ( euclid1 @ SV11 @ SY244 @ SY242 @ SY245 @ SY243 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(255,plain,
! [SV12: $i] :
( ( ! [SY246: $i,SY247: $i] :
( ~ ( between @ SV12 @ SY246 @ SY247 )
| ! [SY248: $i,SY249: $i] :
( ~ ( between @ SY248 @ SY246 @ SY249 )
| ( SV12 = SY246 )
| ( between @ SV12 @ SY249 @ ( euclid2 @ SV12 @ SY248 @ SY246 @ SY249 @ SY247 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(256,plain,
! [SV13: $i] :
( ( ! [SY250: $i,SY251: $i] :
( ~ ( between @ SV13 @ SY250 @ SY251 )
| ! [SY252: $i,SY253: $i] :
( ~ ( between @ SY252 @ SY250 @ SY253 )
| ( SV13 = SY250 )
| ( between @ ( euclid1 @ SV13 @ SY252 @ SY250 @ SY253 @ SY251 ) @ SY251 @ ( euclid2 @ SV13 @ SY252 @ SY250 @ SY253 @ SY251 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(257,plain,
! [SV14: $i] :
( ( ! [SY254: $i,SY255: $i,SY256: $i] :
( ~ ( equidistant @ SV14 @ SY254 @ SV14 @ SY255 )
| ! [SY257: $i] :
( ~ ( equidistant @ SV14 @ SY256 @ SV14 @ SY257 )
| ~ ( between @ SV14 @ SY254 @ SY256 )
| ! [SY258: $i] :
( ~ ( between @ SY254 @ SY258 @ SY256 )
| ( between @ SY255 @ ( continuous @ SV14 @ SY254 @ SY255 @ SY258 @ SY256 @ SY257 ) @ SY257 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(258,plain,
! [SV15: $i] :
( ( ! [SY259: $i,SY260: $i,SY261: $i] :
( ~ ( equidistant @ SV15 @ SY259 @ SV15 @ SY260 )
| ! [SY262: $i] :
( ~ ( equidistant @ SV15 @ SY261 @ SV15 @ SY262 )
| ~ ( between @ SV15 @ SY259 @ SY261 )
| ! [SY263: $i] :
( ~ ( between @ SY259 @ SY263 @ SY261 )
| ( equidistant @ SV15 @ SY263 @ SV15 @ ( continuous @ SV15 @ SY259 @ SY260 @ SY263 @ SY261 @ SY262 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(259,plain,
! [SV16: $i] :
( ( ! [SY264: $i] :
( ( reflection @ SV16 @ SY264 )
= ( extension @ SV16 @ SY264 @ SV16 @ SY264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(260,plain,
! [SV17: $i] :
( ( ! [SY265: $i] : ( equidistant @ SV17 @ SY265 @ SV17 @ SY265 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(261,plain,
! [SV18: $i] :
( ( ! [SY266: $i,SY267: $i,SY268: $i] :
( ~ ( equidistant @ SV18 @ SY266 @ SY267 @ SY268 )
| ( equidistant @ SY267 @ SY268 @ SV18 @ SY266 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(262,plain,
! [SV19: $i] :
( ( ! [SY269: $i,SY270: $i,SY271: $i] :
( ~ ( equidistant @ SV19 @ SY269 @ SY270 @ SY271 )
| ( equidistant @ SY269 @ SV19 @ SY270 @ SY271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(263,plain,
! [SV20: $i] :
( ( ! [SY272: $i,SY273: $i,SY274: $i] :
( ~ ( equidistant @ SV20 @ SY272 @ SY273 @ SY274 )
| ( equidistant @ SV20 @ SY272 @ SY274 @ SY273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(264,plain,
! [SV21: $i] :
( ( ! [SY275: $i,SY276: $i,SY277: $i] :
( ~ ( equidistant @ SV21 @ SY275 @ SY276 @ SY277 )
| ( equidistant @ SY275 @ SV21 @ SY277 @ SY276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(265,plain,
! [SV22: $i] :
( ( ! [SY278: $i,SY279: $i,SY280: $i] :
( ~ ( equidistant @ SV22 @ SY278 @ SY279 @ SY280 )
| ( equidistant @ SY279 @ SY280 @ SY278 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(266,plain,
! [SV23: $i] :
( ( ! [SY281: $i,SY282: $i,SY283: $i] :
( ~ ( equidistant @ SV23 @ SY281 @ SY282 @ SY283 )
| ( equidistant @ SY283 @ SY282 @ SV23 @ SY281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(267,plain,
! [SV24: $i] :
( ( ! [SY284: $i,SY285: $i,SY286: $i] :
( ~ ( equidistant @ SV24 @ SY284 @ SY285 @ SY286 )
| ( equidistant @ SY286 @ SY285 @ SY284 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(268,plain,
! [SV25: $i] :
( ( ! [SY287: $i,SY288: $i,SY289: $i] :
( ~ ( equidistant @ SV25 @ SY287 @ SY288 @ SY289 )
| ! [SY290: $i,SY291: $i] :
( ~ ( equidistant @ SY288 @ SY289 @ SY290 @ SY291 )
| ( equidistant @ SV25 @ SY287 @ SY290 @ SY291 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(269,plain,
! [SV26: $i] :
( ( ! [SY292: $i,SY293: $i] :
( SV26
= ( extension @ SY292 @ SV26 @ SY293 @ SY293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[203]) ).
thf(270,plain,
! [SV27: $i] :
( ( ! [SY294: $i,SY295: $i] :
( ! [SY296: $i,SY297: $i] :
( SV27
!= ( extension @ SY294 @ SY295 @ SY296 @ SY297 ) )
| ( between @ SY294 @ SY295 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(271,plain,
! [SV28: $i] :
( ( ! [SY298: $i] : ( between @ SV28 @ SY298 @ ( reflection @ SV28 @ SY298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(272,plain,
! [SV29: $i] :
( ( ! [SY299: $i] : ( equidistant @ SV29 @ ( reflection @ SY299 @ SV29 ) @ SY299 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(273,plain,
! [SV30: $i] :
( ( ! [SY300: $i] :
( ( SV30 != SY300 )
| ( SY300
= ( reflection @ SV30 @ SY300 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(274,plain,
! [SV31: $i] :
( ( SV31
= ( reflection @ SV31 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(275,plain,
! [SV32: $i] :
( ( ! [SY301: $i] :
( ( SV32
!= ( reflection @ SY301 @ SV32 ) )
| ( SY301 = SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(276,plain,
! [SV33: $i] :
( ( ! [SY302: $i] : ( equidistant @ SV33 @ SV33 @ SY302 @ SY302 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(277,plain,
! [SV34: $i] :
( ( ! [SY303: $i,SY304: $i,SY305: $i] :
( ~ ( equidistant @ SV34 @ SY303 @ SY304 @ SY305 )
| ! [SY306: $i,SY307: $i] :
( ~ ( equidistant @ SY303 @ SY306 @ SY305 @ SY307 )
| ~ ( between @ SV34 @ SY303 @ SY306 )
| ~ ( between @ SY304 @ SY305 @ SY307 )
| ( equidistant @ SV34 @ SY306 @ SY304 @ SY307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(278,plain,
! [SV35: $i] :
( ( ! [SY308: $i,SY309: $i] :
( ~ ( between @ SV35 @ SY308 @ SY309 )
| ! [SY310: $i] :
( ~ ( between @ SV35 @ SY308 @ SY310 )
| ~ ( equidistant @ SY308 @ SY309 @ SY308 @ SY310 )
| ( SV35 = SY308 )
| ( SY309 = SY310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(279,plain,
! [SV36: $i] :
( ( ! [SY311: $i,SY312: $i] :
( ~ ( between @ SV36 @ SY311 @ SY312 )
| ( SV36 = SY311 )
| ( SY312
= ( extension @ SV36 @ SY311 @ SY311 @ SY312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(280,plain,
! [SV37: $i] :
( ( ! [SY313: $i,SY314: $i,SY315: $i] :
( ~ ( equidistant @ SV37 @ SY313 @ SY314 @ SY315 )
| ! [SY316: $i,SY317: $i] :
( ( ( extension @ SY316 @ SY317 @ SV37 @ SY313 )
= ( extension @ SY316 @ SY317 @ SY314 @ SY315 ) )
| ( SY316 = SY317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(281,plain,
! [SV38: $i] :
( ( ! [SY318: $i] :
( ( ( extension @ SV38 @ SY318 @ SV38 @ SY318 )
= ( extension @ SV38 @ SY318 @ SY318 @ SV38 ) )
| ( SV38 = SY318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(282,plain,
! [SV39: $i] :
( ( ! [SY319: $i] : ( equidistant @ SV39 @ SY319 @ SV39 @ ( reflection @ ( reflection @ SY319 @ SV39 ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(283,plain,
! [SV40: $i] :
( ( ! [SY320: $i] :
( SV40
= ( reflection @ ( reflection @ SV40 @ SY320 ) @ SY320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(284,plain,
! [SV41: $i] :
( ( ! [SY321: $i] : ( between @ SV41 @ SY321 @ SY321 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(285,plain,
! [SV42: $i] :
( ( ! [SY322: $i,SY323: $i] :
( ~ ( between @ SV42 @ SY322 @ SY323 )
| ( SV42 != SY323 )
| ! [V: $i] : ( between @ V @ SY322 @ SY323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(286,plain,
! [SV43: $i] :
( ( ! [SY325: $i,SY326: $i] :
( ~ ( between @ SV43 @ SY325 @ SY326 )
| ( between @ SY326 @ SY325 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(287,plain,
! [SV44: $i] :
( ( ! [SY327: $i] : ( between @ SV44 @ SV44 @ SY327 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(288,plain,
! [SV45: $i] :
( ( ! [SY328: $i,SY329: $i] :
( ~ ( between @ SV45 @ SY328 @ SY329 )
| ~ ( between @ SY328 @ SV45 @ SY329 )
| ( SV45 = SY328 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(289,plain,
! [SV46: $i] :
( ( ! [SY330: $i,SY331: $i] :
( ~ ( between @ SV46 @ SY330 @ SY331 )
| ~ ( between @ SV46 @ SY331 @ SY330 )
| ( SY330 = SY331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(290,plain,
! [SV47: $i] :
( ( ! [SY332: $i,SY333: $i] :
( ~ ( between @ SV47 @ SY332 @ SY333 )
| ~ ( between @ SY332 @ SV47 @ SY333 )
| ( SV47 = SY332 )
| ( SY332 = SY333 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(291,plain,
! [SV48: $i] :
( ( ! [SY334: $i,SY335: $i] :
( ~ ( between @ SV48 @ SY334 @ SY335 )
| ~ ( between @ SV48 @ SY335 @ SY334 )
| ( SV48 = SY334 )
| ( SY334 = SY335 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(292,plain,
! [SV49: $i] :
( ( ! [SY336: $i,SY337: $i] :
( ~ ( between @ SV49 @ SY336 @ SY337 )
| ! [X: $i] :
~ ( between @ SY336 @ SY337 @ X )
| ( between @ SV49 @ SY336 @ SY337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(293,plain,
! [SV50: $i] :
( ( ! [SY339: $i,SY340: $i] :
( ~ ( between @ SV50 @ SY339 @ SY340 )
| ! [SY341: $i] :
( ~ ( between @ SV50 @ SY340 @ SY341 )
| ( between @ SY339 @ SY340 @ SY341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(294,plain,
! [SV51: $i] :
( ( ! [SY342: $i,SY343: $i] :
( ~ ( between @ SV51 @ SY342 @ SY343 )
| ! [SY344: $i] :
( ~ ( between @ SY342 @ SY343 @ SY344 )
| ( SY342 = SY343 )
| ( between @ SV51 @ SY343 @ SY344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(295,plain,
! [SV52: $i] :
( ( ! [SY345: $i,SY346: $i] :
( ~ ( between @ SV52 @ SY345 @ SY346 )
| ! [SY347: $i] :
( ~ ( between @ SY345 @ SY346 @ SY347 )
| ( SY345 = SY346 )
| ( between @ SV52 @ SY345 @ SY347 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(296,plain,
! [SV53: $i] :
( ( ! [SY348: $i,SY349: $i] :
( ~ ( between @ SV53 @ SY348 @ SY349 )
| ! [SY350: $i] :
( ~ ( between @ SY348 @ SY350 @ SY349 )
| ( between @ SV53 @ SY350 @ SY349 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(297,plain,
! [SV54: $i] :
( ( ! [SY351: $i,SY352: $i] :
( ~ ( between @ SV54 @ SY351 @ SY352 )
| ! [SY353: $i] :
( ~ ( between @ SV54 @ SY352 @ SY353 )
| ( between @ SV54 @ SY351 @ SY353 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(298,plain,
( ( lower_dimension_point_1 = lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[232]) ).
thf(299,plain,
( ( lower_dimension_point_2 = lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(300,plain,
( ( lower_dimension_point_1 = lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(301,plain,
! [SV55: $i] :
( ( ! [SY354: $i] :
( SV55
!= ( extension @ SY354 @ SV55 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(302,plain,
! [SV56: $i] :
( ( ! [SY355: $i,SY356: $i,SY357: $i] : ( equidistant @ SV56 @ ( extension @ SY355 @ SV56 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SY356 @ ( extension @ SY357 @ SY356 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(303,plain,
! [SV57: $i] :
( ( ! [SY358: $i] : ( between @ SV57 @ SY358 @ ( extension @ SV57 @ SY358 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(304,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(305,plain,
! [SV58: $i,SV1: $i] :
( ( equidistant @ SV1 @ SV58 @ SV58 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(306,plain,
! [SV59: $i,SV2: $i] :
( ( ! [SY359: $i,SY360: $i] :
( ~ ( equidistant @ SV2 @ SV59 @ SY359 @ SY360 )
| ! [SY361: $i,SY362: $i] :
( ~ ( equidistant @ SV2 @ SV59 @ SY361 @ SY362 )
| ( equidistant @ SY359 @ SY360 @ SY361 @ SY362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(307,plain,
! [SV60: $i,SV3: $i] :
( ( ! [SY363: $i] :
~ ( equidistant @ SV3 @ SV60 @ SY363 @ SY363 )
| ( SV3 = SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(308,plain,
! [SV61: $i,SV4: $i] :
( ( ! [SY364: $i,SY365: $i] : ( between @ SV4 @ SV61 @ ( extension @ SV4 @ SV61 @ SY364 @ SY365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(309,plain,
! [SV62: $i,SV5: $i] :
( ( ! [SY366: $i,SY367: $i] : ( equidistant @ SV5 @ ( extension @ SV62 @ SV5 @ SY366 @ SY367 ) @ SY366 @ SY367 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(310,plain,
! [SV63: $i,SV6: $i] :
( ( ! [SY368: $i,SY369: $i,SY370: $i,SY371: $i] :
( ~ ( equidistant @ SV6 @ SV63 @ SY368 @ SY369 )
| ~ ( equidistant @ SV63 @ SY370 @ SY369 @ SY371 )
| ! [SY372: $i,SY373: $i] :
( ~ ( equidistant @ SV6 @ SY372 @ SY368 @ SY373 )
| ~ ( equidistant @ SV63 @ SY372 @ SY369 @ SY373 )
| ~ ( between @ SV6 @ SV63 @ SY370 )
| ~ ( between @ SY368 @ SY369 @ SY371 )
| ( SV6 = SV63 )
| ( equidistant @ SY370 @ SY372 @ SY371 @ SY373 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(311,plain,
! [SV64: $i,SV7: $i] :
( ( ~ ( between @ SV7 @ SV64 @ SV7 )
| ( SV7 = SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(312,plain,
! [SV65: $i,SV8: $i] :
( ( ! [SY374: $i] :
( ~ ( between @ SV8 @ SV65 @ SY374 )
| ! [SY375: $i,SY376: $i] :
( ~ ( between @ SY375 @ SY376 @ SY374 )
| ( between @ SV65 @ ( inner_pasch @ SV8 @ SV65 @ SY374 @ SY376 @ SY375 ) @ SY375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(313,plain,
! [SV66: $i,SV9: $i] :
( ( ! [SY377: $i] :
( ~ ( between @ SV9 @ SV66 @ SY377 )
| ! [SY378: $i,SY379: $i] :
( ~ ( between @ SY378 @ SY379 @ SY377 )
| ( between @ SY379 @ ( inner_pasch @ SV9 @ SV66 @ SY377 @ SY379 @ SY378 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(314,plain,
! [SV67: $i,SV10: $i] :
( ( ! [SY380: $i] :
( ~ ( equidistant @ SV10 @ SV67 @ SV10 @ SY380 )
| ! [SY381: $i] :
( ~ ( equidistant @ SY381 @ SV67 @ SY381 @ SY380 )
| ! [SY382: $i] :
( ~ ( equidistant @ SY382 @ SV67 @ SY382 @ SY380 )
| ( between @ SV10 @ SY381 @ SY382 )
| ( between @ SY381 @ SY382 @ SV10 )
| ( SV67 = SY380 )
| ( between @ SY382 @ SV10 @ SY381 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(315,plain,
! [SV68: $i,SV11: $i] :
( ( ! [SY383: $i] :
( ~ ( between @ SV11 @ SV68 @ SY383 )
| ! [SY384: $i,SY385: $i] :
( ~ ( between @ SY384 @ SV68 @ SY385 )
| ( SV11 = SV68 )
| ( between @ SV11 @ SY384 @ ( euclid1 @ SV11 @ SY384 @ SV68 @ SY385 @ SY383 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(316,plain,
! [SV69: $i,SV12: $i] :
( ( ! [SY386: $i] :
( ~ ( between @ SV12 @ SV69 @ SY386 )
| ! [SY387: $i,SY388: $i] :
( ~ ( between @ SY387 @ SV69 @ SY388 )
| ( SV12 = SV69 )
| ( between @ SV12 @ SY388 @ ( euclid2 @ SV12 @ SY387 @ SV69 @ SY388 @ SY386 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(317,plain,
! [SV70: $i,SV13: $i] :
( ( ! [SY389: $i] :
( ~ ( between @ SV13 @ SV70 @ SY389 )
| ! [SY390: $i,SY391: $i] :
( ~ ( between @ SY390 @ SV70 @ SY391 )
| ( SV13 = SV70 )
| ( between @ ( euclid1 @ SV13 @ SY390 @ SV70 @ SY391 @ SY389 ) @ SY389 @ ( euclid2 @ SV13 @ SY390 @ SV70 @ SY391 @ SY389 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(318,plain,
! [SV71: $i,SV14: $i] :
( ( ! [SY392: $i,SY393: $i] :
( ~ ( equidistant @ SV14 @ SV71 @ SV14 @ SY392 )
| ! [SY394: $i] :
( ~ ( equidistant @ SV14 @ SY393 @ SV14 @ SY394 )
| ~ ( between @ SV14 @ SV71 @ SY393 )
| ! [SY395: $i] :
( ~ ( between @ SV71 @ SY395 @ SY393 )
| ( between @ SY392 @ ( continuous @ SV14 @ SV71 @ SY392 @ SY395 @ SY393 @ SY394 ) @ SY394 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(319,plain,
! [SV72: $i,SV15: $i] :
( ( ! [SY396: $i,SY397: $i] :
( ~ ( equidistant @ SV15 @ SV72 @ SV15 @ SY396 )
| ! [SY398: $i] :
( ~ ( equidistant @ SV15 @ SY397 @ SV15 @ SY398 )
| ~ ( between @ SV15 @ SV72 @ SY397 )
| ! [SY399: $i] :
( ~ ( between @ SV72 @ SY399 @ SY397 )
| ( equidistant @ SV15 @ SY399 @ SV15 @ ( continuous @ SV15 @ SV72 @ SY396 @ SY399 @ SY397 @ SY398 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(320,plain,
! [SV73: $i,SV16: $i] :
( ( ( reflection @ SV16 @ SV73 )
= ( extension @ SV16 @ SV73 @ SV16 @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[259]) ).
thf(321,plain,
! [SV74: $i,SV17: $i] :
( ( equidistant @ SV17 @ SV74 @ SV17 @ SV74 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(322,plain,
! [SV75: $i,SV18: $i] :
( ( ! [SY400: $i,SY401: $i] :
( ~ ( equidistant @ SV18 @ SV75 @ SY400 @ SY401 )
| ( equidistant @ SY400 @ SY401 @ SV18 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(323,plain,
! [SV76: $i,SV19: $i] :
( ( ! [SY402: $i,SY403: $i] :
( ~ ( equidistant @ SV19 @ SV76 @ SY402 @ SY403 )
| ( equidistant @ SV76 @ SV19 @ SY402 @ SY403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(324,plain,
! [SV77: $i,SV20: $i] :
( ( ! [SY404: $i,SY405: $i] :
( ~ ( equidistant @ SV20 @ SV77 @ SY404 @ SY405 )
| ( equidistant @ SV20 @ SV77 @ SY405 @ SY404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(325,plain,
! [SV78: $i,SV21: $i] :
( ( ! [SY406: $i,SY407: $i] :
( ~ ( equidistant @ SV21 @ SV78 @ SY406 @ SY407 )
| ( equidistant @ SV78 @ SV21 @ SY407 @ SY406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(326,plain,
! [SV79: $i,SV22: $i] :
( ( ! [SY408: $i,SY409: $i] :
( ~ ( equidistant @ SV22 @ SV79 @ SY408 @ SY409 )
| ( equidistant @ SY408 @ SY409 @ SV79 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(327,plain,
! [SV80: $i,SV23: $i] :
( ( ! [SY410: $i,SY411: $i] :
( ~ ( equidistant @ SV23 @ SV80 @ SY410 @ SY411 )
| ( equidistant @ SY411 @ SY410 @ SV23 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(328,plain,
! [SV81: $i,SV24: $i] :
( ( ! [SY412: $i,SY413: $i] :
( ~ ( equidistant @ SV24 @ SV81 @ SY412 @ SY413 )
| ( equidistant @ SY413 @ SY412 @ SV81 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(329,plain,
! [SV82: $i,SV25: $i] :
( ( ! [SY414: $i,SY415: $i] :
( ~ ( equidistant @ SV25 @ SV82 @ SY414 @ SY415 )
| ! [SY416: $i,SY417: $i] :
( ~ ( equidistant @ SY414 @ SY415 @ SY416 @ SY417 )
| ( equidistant @ SV25 @ SV82 @ SY416 @ SY417 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(330,plain,
! [SV83: $i,SV26: $i] :
( ( ! [SY418: $i] :
( SV26
= ( extension @ SV83 @ SV26 @ SY418 @ SY418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(331,plain,
! [SV84: $i,SV27: $i] :
( ( ! [SY419: $i] :
( ! [SY420: $i,SY421: $i] :
( SV27
!= ( extension @ SV84 @ SY419 @ SY420 @ SY421 ) )
| ( between @ SV84 @ SY419 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(332,plain,
! [SV85: $i,SV28: $i] :
( ( between @ SV28 @ SV85 @ ( reflection @ SV28 @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(333,plain,
! [SV86: $i,SV29: $i] :
( ( equidistant @ SV29 @ ( reflection @ SV86 @ SV29 ) @ SV86 @ SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(334,plain,
! [SV87: $i,SV30: $i] :
( ( ( SV30 != SV87 )
| ( SV87
= ( reflection @ SV30 @ SV87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(335,plain,
! [SV88: $i,SV32: $i] :
( ( ( SV32
!= ( reflection @ SV88 @ SV32 ) )
| ( SV88 = SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[275]) ).
thf(336,plain,
! [SV89: $i,SV33: $i] :
( ( equidistant @ SV33 @ SV33 @ SV89 @ SV89 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(337,plain,
! [SV90: $i,SV34: $i] :
( ( ! [SY422: $i,SY423: $i] :
( ~ ( equidistant @ SV34 @ SV90 @ SY422 @ SY423 )
| ! [SY424: $i,SY425: $i] :
( ~ ( equidistant @ SV90 @ SY424 @ SY423 @ SY425 )
| ~ ( between @ SV34 @ SV90 @ SY424 )
| ~ ( between @ SY422 @ SY423 @ SY425 )
| ( equidistant @ SV34 @ SY424 @ SY422 @ SY425 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(338,plain,
! [SV91: $i,SV35: $i] :
( ( ! [SY426: $i] :
( ~ ( between @ SV35 @ SV91 @ SY426 )
| ! [SY427: $i] :
( ~ ( between @ SV35 @ SV91 @ SY427 )
| ~ ( equidistant @ SV91 @ SY426 @ SV91 @ SY427 )
| ( SV35 = SV91 )
| ( SY426 = SY427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(339,plain,
! [SV92: $i,SV36: $i] :
( ( ! [SY428: $i] :
( ~ ( between @ SV36 @ SV92 @ SY428 )
| ( SV36 = SV92 )
| ( SY428
= ( extension @ SV36 @ SV92 @ SV92 @ SY428 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(340,plain,
! [SV93: $i,SV37: $i] :
( ( ! [SY429: $i,SY430: $i] :
( ~ ( equidistant @ SV37 @ SV93 @ SY429 @ SY430 )
| ! [SY431: $i,SY432: $i] :
( ( ( extension @ SY431 @ SY432 @ SV37 @ SV93 )
= ( extension @ SY431 @ SY432 @ SY429 @ SY430 ) )
| ( SY431 = SY432 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(341,plain,
! [SV94: $i,SV38: $i] :
( ( ( ( extension @ SV38 @ SV94 @ SV38 @ SV94 )
= ( extension @ SV38 @ SV94 @ SV94 @ SV38 ) )
| ( SV38 = SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(342,plain,
! [SV95: $i,SV39: $i] :
( ( equidistant @ SV39 @ SV95 @ SV39 @ ( reflection @ ( reflection @ SV95 @ SV39 ) @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(343,plain,
! [SV96: $i,SV40: $i] :
( ( SV40
= ( reflection @ ( reflection @ SV40 @ SV96 ) @ SV96 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(344,plain,
! [SV97: $i,SV41: $i] :
( ( between @ SV41 @ SV97 @ SV97 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(345,plain,
! [SV98: $i,SV42: $i] :
( ( ! [SY433: $i] :
( ~ ( between @ SV42 @ SV98 @ SY433 )
| ( SV42 != SY433 )
| ! [SY434: $i] : ( between @ SY434 @ SV98 @ SY433 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(346,plain,
! [SV99: $i,SV43: $i] :
( ( ! [SY435: $i] :
( ~ ( between @ SV43 @ SV99 @ SY435 )
| ( between @ SY435 @ SV99 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(347,plain,
! [SV100: $i,SV44: $i] :
( ( between @ SV44 @ SV44 @ SV100 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(348,plain,
! [SV101: $i,SV45: $i] :
( ( ! [SY436: $i] :
( ~ ( between @ SV45 @ SV101 @ SY436 )
| ~ ( between @ SV101 @ SV45 @ SY436 )
| ( SV45 = SV101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(349,plain,
! [SV102: $i,SV46: $i] :
( ( ! [SY437: $i] :
( ~ ( between @ SV46 @ SV102 @ SY437 )
| ~ ( between @ SV46 @ SY437 @ SV102 )
| ( SV102 = SY437 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(350,plain,
! [SV103: $i,SV47: $i] :
( ( ! [SY438: $i] :
( ~ ( between @ SV47 @ SV103 @ SY438 )
| ~ ( between @ SV103 @ SV47 @ SY438 )
| ( SV47 = SV103 )
| ( SV103 = SY438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(351,plain,
! [SV104: $i,SV48: $i] :
( ( ! [SY439: $i] :
( ~ ( between @ SV48 @ SV104 @ SY439 )
| ~ ( between @ SV48 @ SY439 @ SV104 )
| ( SV48 = SV104 )
| ( SV104 = SY439 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(352,plain,
! [SV105: $i,SV49: $i] :
( ( ! [SY440: $i] :
( ~ ( between @ SV49 @ SV105 @ SY440 )
| ! [SY441: $i] :
~ ( between @ SV105 @ SY440 @ SY441 )
| ( between @ SV49 @ SV105 @ SY440 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(353,plain,
! [SV106: $i,SV50: $i] :
( ( ! [SY442: $i] :
( ~ ( between @ SV50 @ SV106 @ SY442 )
| ! [SY443: $i] :
( ~ ( between @ SV50 @ SY442 @ SY443 )
| ( between @ SV106 @ SY442 @ SY443 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(354,plain,
! [SV107: $i,SV51: $i] :
( ( ! [SY444: $i] :
( ~ ( between @ SV51 @ SV107 @ SY444 )
| ! [SY445: $i] :
( ~ ( between @ SV107 @ SY444 @ SY445 )
| ( SV107 = SY444 )
| ( between @ SV51 @ SY444 @ SY445 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(355,plain,
! [SV108: $i,SV52: $i] :
( ( ! [SY446: $i] :
( ~ ( between @ SV52 @ SV108 @ SY446 )
| ! [SY447: $i] :
( ~ ( between @ SV108 @ SY446 @ SY447 )
| ( SV108 = SY446 )
| ( between @ SV52 @ SV108 @ SY447 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(356,plain,
! [SV109: $i,SV53: $i] :
( ( ! [SY448: $i] :
( ~ ( between @ SV53 @ SV109 @ SY448 )
| ! [SY449: $i] :
( ~ ( between @ SV109 @ SY449 @ SY448 )
| ( between @ SV53 @ SY449 @ SY448 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[296]) ).
thf(357,plain,
! [SV110: $i,SV54: $i] :
( ( ! [SY450: $i] :
( ~ ( between @ SV54 @ SV110 @ SY450 )
| ! [SY451: $i] :
( ~ ( between @ SV54 @ SY450 @ SY451 )
| ( between @ SV54 @ SV110 @ SY451 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[297]) ).
thf(358,plain,
! [SV111: $i,SV55: $i] :
( ( ( SV55
!= ( extension @ SV111 @ SV55 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(359,plain,
! [SV112: $i,SV56: $i] :
( ( ! [SY452: $i,SY453: $i] : ( equidistant @ SV56 @ ( extension @ SV112 @ SV56 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SY452 @ ( extension @ SY453 @ SY452 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(360,plain,
! [SV113: $i,SV57: $i] :
( ( between @ SV57 @ SV113 @ ( extension @ SV57 @ SV113 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(361,plain,
! [SV114: $i,SV59: $i,SV2: $i] :
( ( ! [SY454: $i] :
( ~ ( equidistant @ SV2 @ SV59 @ SV114 @ SY454 )
| ! [SY455: $i,SY456: $i] :
( ~ ( equidistant @ SV2 @ SV59 @ SY455 @ SY456 )
| ( equidistant @ SV114 @ SY454 @ SY455 @ SY456 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(362,plain,
! [SV60: $i,SV3: $i] :
( ( ( ! [SY363: $i] :
~ ( equidistant @ SV3 @ SV60 @ SY363 @ SY363 ) )
= $true )
| ( ( SV3 = SV60 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[307]) ).
thf(363,plain,
! [SV115: $i,SV61: $i,SV4: $i] :
( ( ! [SY457: $i] : ( between @ SV4 @ SV61 @ ( extension @ SV4 @ SV61 @ SV115 @ SY457 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(364,plain,
! [SV116: $i,SV62: $i,SV5: $i] :
( ( ! [SY458: $i] : ( equidistant @ SV5 @ ( extension @ SV62 @ SV5 @ SV116 @ SY458 ) @ SV116 @ SY458 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(365,plain,
! [SV117: $i,SV63: $i,SV6: $i] :
( ( ! [SY459: $i,SY460: $i,SY461: $i] :
( ~ ( equidistant @ SV6 @ SV63 @ SV117 @ SY459 )
| ~ ( equidistant @ SV63 @ SY460 @ SY459 @ SY461 )
| ! [SY462: $i,SY463: $i] :
( ~ ( equidistant @ SV6 @ SY462 @ SV117 @ SY463 )
| ~ ( equidistant @ SV63 @ SY462 @ SY459 @ SY463 )
| ~ ( between @ SV6 @ SV63 @ SY460 )
| ~ ( between @ SV117 @ SY459 @ SY461 )
| ( SV6 = SV63 )
| ( equidistant @ SY460 @ SY462 @ SY461 @ SY463 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(366,plain,
! [SV64: $i,SV7: $i] :
( ( ( ~ ( between @ SV7 @ SV64 @ SV7 ) )
= $true )
| ( ( SV7 = SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(367,plain,
! [SV118: $i,SV65: $i,SV8: $i] :
( ( ~ ( between @ SV8 @ SV65 @ SV118 )
| ! [SY464: $i,SY465: $i] :
( ~ ( between @ SY464 @ SY465 @ SV118 )
| ( between @ SV65 @ ( inner_pasch @ SV8 @ SV65 @ SV118 @ SY465 @ SY464 ) @ SY464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(368,plain,
! [SV119: $i,SV66: $i,SV9: $i] :
( ( ~ ( between @ SV9 @ SV66 @ SV119 )
| ! [SY466: $i,SY467: $i] :
( ~ ( between @ SY466 @ SY467 @ SV119 )
| ( between @ SY467 @ ( inner_pasch @ SV9 @ SV66 @ SV119 @ SY467 @ SY466 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(369,plain,
! [SV120: $i,SV67: $i,SV10: $i] :
( ( ~ ( equidistant @ SV10 @ SV67 @ SV10 @ SV120 )
| ! [SY468: $i] :
( ~ ( equidistant @ SY468 @ SV67 @ SY468 @ SV120 )
| ! [SY469: $i] :
( ~ ( equidistant @ SY469 @ SV67 @ SY469 @ SV120 )
| ( between @ SV10 @ SY468 @ SY469 )
| ( between @ SY468 @ SY469 @ SV10 )
| ( SV67 = SV120 )
| ( between @ SY469 @ SV10 @ SY468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(370,plain,
! [SV121: $i,SV68: $i,SV11: $i] :
( ( ~ ( between @ SV11 @ SV68 @ SV121 )
| ! [SY470: $i,SY471: $i] :
( ~ ( between @ SY470 @ SV68 @ SY471 )
| ( SV11 = SV68 )
| ( between @ SV11 @ SY470 @ ( euclid1 @ SV11 @ SY470 @ SV68 @ SY471 @ SV121 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(371,plain,
! [SV122: $i,SV69: $i,SV12: $i] :
( ( ~ ( between @ SV12 @ SV69 @ SV122 )
| ! [SY472: $i,SY473: $i] :
( ~ ( between @ SY472 @ SV69 @ SY473 )
| ( SV12 = SV69 )
| ( between @ SV12 @ SY473 @ ( euclid2 @ SV12 @ SY472 @ SV69 @ SY473 @ SV122 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[316]) ).
thf(372,plain,
! [SV123: $i,SV70: $i,SV13: $i] :
( ( ~ ( between @ SV13 @ SV70 @ SV123 )
| ! [SY474: $i,SY475: $i] :
( ~ ( between @ SY474 @ SV70 @ SY475 )
| ( SV13 = SV70 )
| ( between @ ( euclid1 @ SV13 @ SY474 @ SV70 @ SY475 @ SV123 ) @ SV123 @ ( euclid2 @ SV13 @ SY474 @ SV70 @ SY475 @ SV123 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[317]) ).
thf(373,plain,
! [SV124: $i,SV71: $i,SV14: $i] :
( ( ! [SY476: $i] :
( ~ ( equidistant @ SV14 @ SV71 @ SV14 @ SV124 )
| ! [SY477: $i] :
( ~ ( equidistant @ SV14 @ SY476 @ SV14 @ SY477 )
| ~ ( between @ SV14 @ SV71 @ SY476 )
| ! [SY478: $i] :
( ~ ( between @ SV71 @ SY478 @ SY476 )
| ( between @ SV124 @ ( continuous @ SV14 @ SV71 @ SV124 @ SY478 @ SY476 @ SY477 ) @ SY477 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(374,plain,
! [SV125: $i,SV72: $i,SV15: $i] :
( ( ! [SY479: $i] :
( ~ ( equidistant @ SV15 @ SV72 @ SV15 @ SV125 )
| ! [SY480: $i] :
( ~ ( equidistant @ SV15 @ SY479 @ SV15 @ SY480 )
| ~ ( between @ SV15 @ SV72 @ SY479 )
| ! [SY481: $i] :
( ~ ( between @ SV72 @ SY481 @ SY479 )
| ( equidistant @ SV15 @ SY481 @ SV15 @ ( continuous @ SV15 @ SV72 @ SV125 @ SY481 @ SY479 @ SY480 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(375,plain,
! [SV126: $i,SV75: $i,SV18: $i] :
( ( ! [SY482: $i] :
( ~ ( equidistant @ SV18 @ SV75 @ SV126 @ SY482 )
| ( equidistant @ SV126 @ SY482 @ SV18 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(376,plain,
! [SV127: $i,SV76: $i,SV19: $i] :
( ( ! [SY483: $i] :
( ~ ( equidistant @ SV19 @ SV76 @ SV127 @ SY483 )
| ( equidistant @ SV76 @ SV19 @ SV127 @ SY483 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(377,plain,
! [SV128: $i,SV77: $i,SV20: $i] :
( ( ! [SY484: $i] :
( ~ ( equidistant @ SV20 @ SV77 @ SV128 @ SY484 )
| ( equidistant @ SV20 @ SV77 @ SY484 @ SV128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(378,plain,
! [SV129: $i,SV78: $i,SV21: $i] :
( ( ! [SY485: $i] :
( ~ ( equidistant @ SV21 @ SV78 @ SV129 @ SY485 )
| ( equidistant @ SV78 @ SV21 @ SY485 @ SV129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(379,plain,
! [SV130: $i,SV79: $i,SV22: $i] :
( ( ! [SY486: $i] :
( ~ ( equidistant @ SV22 @ SV79 @ SV130 @ SY486 )
| ( equidistant @ SV130 @ SY486 @ SV79 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(380,plain,
! [SV131: $i,SV80: $i,SV23: $i] :
( ( ! [SY487: $i] :
( ~ ( equidistant @ SV23 @ SV80 @ SV131 @ SY487 )
| ( equidistant @ SY487 @ SV131 @ SV23 @ SV80 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(381,plain,
! [SV132: $i,SV81: $i,SV24: $i] :
( ( ! [SY488: $i] :
( ~ ( equidistant @ SV24 @ SV81 @ SV132 @ SY488 )
| ( equidistant @ SY488 @ SV132 @ SV81 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(382,plain,
! [SV133: $i,SV82: $i,SV25: $i] :
( ( ! [SY489: $i] :
( ~ ( equidistant @ SV25 @ SV82 @ SV133 @ SY489 )
| ! [SY490: $i,SY491: $i] :
( ~ ( equidistant @ SV133 @ SY489 @ SY490 @ SY491 )
| ( equidistant @ SV25 @ SV82 @ SY490 @ SY491 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(383,plain,
! [SV134: $i,SV83: $i,SV26: $i] :
( ( SV26
= ( extension @ SV83 @ SV26 @ SV134 @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(384,plain,
! [SV135: $i,SV84: $i,SV27: $i] :
( ( ! [SY492: $i,SY493: $i] :
( SV27
!= ( extension @ SV84 @ SV135 @ SY492 @ SY493 ) )
| ( between @ SV84 @ SV135 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(385,plain,
! [SV87: $i,SV30: $i] :
( ( ( ( SV30 != SV87 ) )
= $true )
| ( ( SV87
= ( reflection @ SV30 @ SV87 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[334]) ).
thf(386,plain,
! [SV88: $i,SV32: $i] :
( ( ( ( SV32
!= ( reflection @ SV88 @ SV32 ) ) )
= $true )
| ( ( SV88 = SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(387,plain,
! [SV136: $i,SV90: $i,SV34: $i] :
( ( ! [SY494: $i] :
( ~ ( equidistant @ SV34 @ SV90 @ SV136 @ SY494 )
| ! [SY495: $i,SY496: $i] :
( ~ ( equidistant @ SV90 @ SY495 @ SY494 @ SY496 )
| ~ ( between @ SV34 @ SV90 @ SY495 )
| ~ ( between @ SV136 @ SY494 @ SY496 )
| ( equidistant @ SV34 @ SY495 @ SV136 @ SY496 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(388,plain,
! [SV137: $i,SV91: $i,SV35: $i] :
( ( ~ ( between @ SV35 @ SV91 @ SV137 )
| ! [SY497: $i] :
( ~ ( between @ SV35 @ SV91 @ SY497 )
| ~ ( equidistant @ SV91 @ SV137 @ SV91 @ SY497 )
| ( SV35 = SV91 )
| ( SV137 = SY497 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[338]) ).
thf(389,plain,
! [SV138: $i,SV92: $i,SV36: $i] :
( ( ~ ( between @ SV36 @ SV92 @ SV138 )
| ( SV36 = SV92 )
| ( SV138
= ( extension @ SV36 @ SV92 @ SV92 @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(390,plain,
! [SV139: $i,SV93: $i,SV37: $i] :
( ( ! [SY498: $i] :
( ~ ( equidistant @ SV37 @ SV93 @ SV139 @ SY498 )
| ! [SY499: $i,SY500: $i] :
( ( ( extension @ SY499 @ SY500 @ SV37 @ SV93 )
= ( extension @ SY499 @ SY500 @ SV139 @ SY498 ) )
| ( SY499 = SY500 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(391,plain,
! [SV94: $i,SV38: $i] :
( ( ( ( extension @ SV38 @ SV94 @ SV38 @ SV94 )
= ( extension @ SV38 @ SV94 @ SV94 @ SV38 ) )
= $true )
| ( ( SV38 = SV94 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(392,plain,
! [SV140: $i,SV98: $i,SV42: $i] :
( ( ~ ( between @ SV42 @ SV98 @ SV140 )
| ( SV42 != SV140 )
| ! [SY501: $i] : ( between @ SY501 @ SV98 @ SV140 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(393,plain,
! [SV141: $i,SV99: $i,SV43: $i] :
( ( ~ ( between @ SV43 @ SV99 @ SV141 )
| ( between @ SV141 @ SV99 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(394,plain,
! [SV142: $i,SV101: $i,SV45: $i] :
( ( ~ ( between @ SV45 @ SV101 @ SV142 )
| ~ ( between @ SV101 @ SV45 @ SV142 )
| ( SV45 = SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(395,plain,
! [SV143: $i,SV102: $i,SV46: $i] :
( ( ~ ( between @ SV46 @ SV102 @ SV143 )
| ~ ( between @ SV46 @ SV143 @ SV102 )
| ( SV102 = SV143 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(396,plain,
! [SV144: $i,SV103: $i,SV47: $i] :
( ( ~ ( between @ SV47 @ SV103 @ SV144 )
| ~ ( between @ SV103 @ SV47 @ SV144 )
| ( SV47 = SV103 )
| ( SV103 = SV144 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(397,plain,
! [SV145: $i,SV104: $i,SV48: $i] :
( ( ~ ( between @ SV48 @ SV104 @ SV145 )
| ~ ( between @ SV48 @ SV145 @ SV104 )
| ( SV48 = SV104 )
| ( SV104 = SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(398,plain,
! [SV146: $i,SV105: $i,SV49: $i] :
( ( ~ ( between @ SV49 @ SV105 @ SV146 )
| ! [SY502: $i] :
~ ( between @ SV105 @ SV146 @ SY502 )
| ( between @ SV49 @ SV105 @ SV146 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(399,plain,
! [SV147: $i,SV106: $i,SV50: $i] :
( ( ~ ( between @ SV50 @ SV106 @ SV147 )
| ! [SY503: $i] :
( ~ ( between @ SV50 @ SV147 @ SY503 )
| ( between @ SV106 @ SV147 @ SY503 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[353]) ).
thf(400,plain,
! [SV148: $i,SV107: $i,SV51: $i] :
( ( ~ ( between @ SV51 @ SV107 @ SV148 )
| ! [SY504: $i] :
( ~ ( between @ SV107 @ SV148 @ SY504 )
| ( SV107 = SV148 )
| ( between @ SV51 @ SV148 @ SY504 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(401,plain,
! [SV149: $i,SV108: $i,SV52: $i] :
( ( ~ ( between @ SV52 @ SV108 @ SV149 )
| ! [SY505: $i] :
( ~ ( between @ SV108 @ SV149 @ SY505 )
| ( SV108 = SV149 )
| ( between @ SV52 @ SV108 @ SY505 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(402,plain,
! [SV150: $i,SV109: $i,SV53: $i] :
( ( ~ ( between @ SV53 @ SV109 @ SV150 )
| ! [SY506: $i] :
( ~ ( between @ SV109 @ SY506 @ SV150 )
| ( between @ SV53 @ SY506 @ SV150 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(403,plain,
! [SV151: $i,SV110: $i,SV54: $i] :
( ( ~ ( between @ SV54 @ SV110 @ SV151 )
| ! [SY507: $i] :
( ~ ( between @ SV54 @ SV151 @ SY507 )
| ( between @ SV54 @ SV110 @ SY507 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(404,plain,
! [SV111: $i,SV55: $i] :
( ( SV55
= ( extension @ SV111 @ SV55 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(405,plain,
! [SV152: $i,SV112: $i,SV56: $i] :
( ( ! [SY508: $i] : ( equidistant @ SV56 @ ( extension @ SV112 @ SV56 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV152 @ ( extension @ SY508 @ SV152 @ lower_dimension_point_1 @ lower_dimension_point_2 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(406,plain,
! [SV153: $i,SV114: $i,SV59: $i,SV2: $i] :
( ( ~ ( equidistant @ SV2 @ SV59 @ SV114 @ SV153 )
| ! [SY509: $i,SY510: $i] :
( ~ ( equidistant @ SV2 @ SV59 @ SY509 @ SY510 )
| ( equidistant @ SV114 @ SV153 @ SY509 @ SY510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(407,plain,
! [SV154: $i,SV60: $i,SV3: $i] :
( ( ( ~ ( equidistant @ SV3 @ SV60 @ SV154 @ SV154 ) )
= $true )
| ( ( SV3 = SV60 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(408,plain,
! [SV155: $i,SV115: $i,SV61: $i,SV4: $i] :
( ( between @ SV4 @ SV61 @ ( extension @ SV4 @ SV61 @ SV115 @ SV155 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(409,plain,
! [SV156: $i,SV116: $i,SV62: $i,SV5: $i] :
( ( equidistant @ SV5 @ ( extension @ SV62 @ SV5 @ SV116 @ SV156 ) @ SV116 @ SV156 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(410,plain,
! [SV157: $i,SV117: $i,SV63: $i,SV6: $i] :
( ( ! [SY511: $i,SY512: $i] :
( ~ ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
| ~ ( equidistant @ SV63 @ SY511 @ SV157 @ SY512 )
| ! [SY513: $i,SY514: $i] :
( ~ ( equidistant @ SV6 @ SY513 @ SV117 @ SY514 )
| ~ ( equidistant @ SV63 @ SY513 @ SV157 @ SY514 )
| ~ ( between @ SV6 @ SV63 @ SY511 )
| ~ ( between @ SV117 @ SV157 @ SY512 )
| ( SV6 = SV63 )
| ( equidistant @ SY511 @ SY513 @ SY512 @ SY514 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(411,plain,
! [SV64: $i,SV7: $i] :
( ( ( between @ SV7 @ SV64 @ SV7 )
= $false )
| ( ( SV7 = SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(412,plain,
! [SV118: $i,SV65: $i,SV8: $i] :
( ( ( ~ ( between @ SV8 @ SV65 @ SV118 ) )
= $true )
| ( ( ! [SY464: $i,SY465: $i] :
( ~ ( between @ SY464 @ SY465 @ SV118 )
| ( between @ SV65 @ ( inner_pasch @ SV8 @ SV65 @ SV118 @ SY465 @ SY464 ) @ SY464 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(413,plain,
! [SV119: $i,SV66: $i,SV9: $i] :
( ( ( ~ ( between @ SV9 @ SV66 @ SV119 ) )
= $true )
| ( ( ! [SY466: $i,SY467: $i] :
( ~ ( between @ SY466 @ SY467 @ SV119 )
| ( between @ SY467 @ ( inner_pasch @ SV9 @ SV66 @ SV119 @ SY467 @ SY466 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(414,plain,
! [SV120: $i,SV67: $i,SV10: $i] :
( ( ( ~ ( equidistant @ SV10 @ SV67 @ SV10 @ SV120 ) )
= $true )
| ( ( ! [SY468: $i] :
( ~ ( equidistant @ SY468 @ SV67 @ SY468 @ SV120 )
| ! [SY469: $i] :
( ~ ( equidistant @ SY469 @ SV67 @ SY469 @ SV120 )
| ( between @ SV10 @ SY468 @ SY469 )
| ( between @ SY468 @ SY469 @ SV10 )
| ( SV67 = SV120 )
| ( between @ SY469 @ SV10 @ SY468 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(415,plain,
! [SV121: $i,SV68: $i,SV11: $i] :
( ( ( ~ ( between @ SV11 @ SV68 @ SV121 ) )
= $true )
| ( ( ! [SY470: $i,SY471: $i] :
( ~ ( between @ SY470 @ SV68 @ SY471 )
| ( SV11 = SV68 )
| ( between @ SV11 @ SY470 @ ( euclid1 @ SV11 @ SY470 @ SV68 @ SY471 @ SV121 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(416,plain,
! [SV122: $i,SV69: $i,SV12: $i] :
( ( ( ~ ( between @ SV12 @ SV69 @ SV122 ) )
= $true )
| ( ( ! [SY472: $i,SY473: $i] :
( ~ ( between @ SY472 @ SV69 @ SY473 )
| ( SV12 = SV69 )
| ( between @ SV12 @ SY473 @ ( euclid2 @ SV12 @ SY472 @ SV69 @ SY473 @ SV122 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(417,plain,
! [SV123: $i,SV70: $i,SV13: $i] :
( ( ( ~ ( between @ SV13 @ SV70 @ SV123 ) )
= $true )
| ( ( ! [SY474: $i,SY475: $i] :
( ~ ( between @ SY474 @ SV70 @ SY475 )
| ( SV13 = SV70 )
| ( between @ ( euclid1 @ SV13 @ SY474 @ SV70 @ SY475 @ SV123 ) @ SV123 @ ( euclid2 @ SV13 @ SY474 @ SV70 @ SY475 @ SV123 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[372]) ).
thf(418,plain,
! [SV158: $i,SV124: $i,SV71: $i,SV14: $i] :
( ( ~ ( equidistant @ SV14 @ SV71 @ SV14 @ SV124 )
| ! [SY515: $i] :
( ~ ( equidistant @ SV14 @ SV158 @ SV14 @ SY515 )
| ~ ( between @ SV14 @ SV71 @ SV158 )
| ! [SY516: $i] :
( ~ ( between @ SV71 @ SY516 @ SV158 )
| ( between @ SV124 @ ( continuous @ SV14 @ SV71 @ SV124 @ SY516 @ SV158 @ SY515 ) @ SY515 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(419,plain,
! [SV159: $i,SV125: $i,SV72: $i,SV15: $i] :
( ( ~ ( equidistant @ SV15 @ SV72 @ SV15 @ SV125 )
| ! [SY517: $i] :
( ~ ( equidistant @ SV15 @ SV159 @ SV15 @ SY517 )
| ~ ( between @ SV15 @ SV72 @ SV159 )
| ! [SY518: $i] :
( ~ ( between @ SV72 @ SY518 @ SV159 )
| ( equidistant @ SV15 @ SY518 @ SV15 @ ( continuous @ SV15 @ SV72 @ SV125 @ SY518 @ SV159 @ SY517 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(420,plain,
! [SV160: $i,SV126: $i,SV75: $i,SV18: $i] :
( ( ~ ( equidistant @ SV18 @ SV75 @ SV126 @ SV160 )
| ( equidistant @ SV126 @ SV160 @ SV18 @ SV75 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(421,plain,
! [SV161: $i,SV127: $i,SV76: $i,SV19: $i] :
( ( ~ ( equidistant @ SV19 @ SV76 @ SV127 @ SV161 )
| ( equidistant @ SV76 @ SV19 @ SV127 @ SV161 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(422,plain,
! [SV162: $i,SV128: $i,SV77: $i,SV20: $i] :
( ( ~ ( equidistant @ SV20 @ SV77 @ SV128 @ SV162 )
| ( equidistant @ SV20 @ SV77 @ SV162 @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(423,plain,
! [SV163: $i,SV129: $i,SV78: $i,SV21: $i] :
( ( ~ ( equidistant @ SV21 @ SV78 @ SV129 @ SV163 )
| ( equidistant @ SV78 @ SV21 @ SV163 @ SV129 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(424,plain,
! [SV164: $i,SV130: $i,SV79: $i,SV22: $i] :
( ( ~ ( equidistant @ SV22 @ SV79 @ SV130 @ SV164 )
| ( equidistant @ SV130 @ SV164 @ SV79 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(425,plain,
! [SV165: $i,SV131: $i,SV80: $i,SV23: $i] :
( ( ~ ( equidistant @ SV23 @ SV80 @ SV131 @ SV165 )
| ( equidistant @ SV165 @ SV131 @ SV23 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(426,plain,
! [SV166: $i,SV132: $i,SV81: $i,SV24: $i] :
( ( ~ ( equidistant @ SV24 @ SV81 @ SV132 @ SV166 )
| ( equidistant @ SV166 @ SV132 @ SV81 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(427,plain,
! [SV167: $i,SV133: $i,SV82: $i,SV25: $i] :
( ( ~ ( equidistant @ SV25 @ SV82 @ SV133 @ SV167 )
| ! [SY519: $i,SY520: $i] :
( ~ ( equidistant @ SV133 @ SV167 @ SY519 @ SY520 )
| ( equidistant @ SV25 @ SV82 @ SY519 @ SY520 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(428,plain,
! [SV135: $i,SV84: $i,SV27: $i] :
( ( ( ! [SY492: $i,SY493: $i] :
( SV27
!= ( extension @ SV84 @ SV135 @ SY492 @ SY493 ) ) )
= $true )
| ( ( between @ SV84 @ SV135 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(429,plain,
! [SV87: $i,SV30: $i] :
( ( ( SV30 = SV87 )
= $false )
| ( ( SV87
= ( reflection @ SV30 @ SV87 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(430,plain,
! [SV88: $i,SV32: $i] :
( ( ( SV32
= ( reflection @ SV88 @ SV32 ) )
= $false )
| ( ( SV88 = SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(431,plain,
! [SV168: $i,SV136: $i,SV90: $i,SV34: $i] :
( ( ~ ( equidistant @ SV34 @ SV90 @ SV136 @ SV168 )
| ! [SY521: $i,SY522: $i] :
( ~ ( equidistant @ SV90 @ SY521 @ SV168 @ SY522 )
| ~ ( between @ SV34 @ SV90 @ SY521 )
| ~ ( between @ SV136 @ SV168 @ SY522 )
| ( equidistant @ SV34 @ SY521 @ SV136 @ SY522 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(432,plain,
! [SV137: $i,SV91: $i,SV35: $i] :
( ( ( ~ ( between @ SV35 @ SV91 @ SV137 ) )
= $true )
| ( ( ! [SY497: $i] :
( ~ ( between @ SV35 @ SV91 @ SY497 )
| ~ ( equidistant @ SV91 @ SV137 @ SV91 @ SY497 )
| ( SV35 = SV91 )
| ( SV137 = SY497 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[388]) ).
thf(433,plain,
! [SV138: $i,SV92: $i,SV36: $i] :
( ( ( ~ ( between @ SV36 @ SV92 @ SV138 ) )
= $true )
| ( ( ( SV36 = SV92 )
| ( SV138
= ( extension @ SV36 @ SV92 @ SV92 @ SV138 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(434,plain,
! [SV169: $i,SV139: $i,SV93: $i,SV37: $i] :
( ( ~ ( equidistant @ SV37 @ SV93 @ SV139 @ SV169 )
| ! [SY523: $i,SY524: $i] :
( ( ( extension @ SY523 @ SY524 @ SV37 @ SV93 )
= ( extension @ SY523 @ SY524 @ SV139 @ SV169 ) )
| ( SY523 = SY524 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(435,plain,
! [SV140: $i,SV98: $i,SV42: $i] :
( ( ( ~ ( between @ SV42 @ SV98 @ SV140 ) )
= $true )
| ( ( ( SV42 != SV140 )
| ! [SY501: $i] : ( between @ SY501 @ SV98 @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[392]) ).
thf(436,plain,
! [SV141: $i,SV99: $i,SV43: $i] :
( ( ( ~ ( between @ SV43 @ SV99 @ SV141 ) )
= $true )
| ( ( between @ SV141 @ SV99 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[393]) ).
thf(437,plain,
! [SV142: $i,SV101: $i,SV45: $i] :
( ( ( ~ ( between @ SV45 @ SV101 @ SV142 ) )
= $true )
| ( ( ~ ( between @ SV101 @ SV45 @ SV142 )
| ( SV45 = SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[394]) ).
thf(438,plain,
! [SV143: $i,SV102: $i,SV46: $i] :
( ( ( ~ ( between @ SV46 @ SV102 @ SV143 ) )
= $true )
| ( ( ~ ( between @ SV46 @ SV143 @ SV102 )
| ( SV102 = SV143 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[395]) ).
thf(439,plain,
! [SV144: $i,SV103: $i,SV47: $i] :
( ( ( ~ ( between @ SV47 @ SV103 @ SV144 ) )
= $true )
| ( ( ~ ( between @ SV103 @ SV47 @ SV144 )
| ( SV47 = SV103 )
| ( SV103 = SV144 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[396]) ).
thf(440,plain,
! [SV145: $i,SV104: $i,SV48: $i] :
( ( ( ~ ( between @ SV48 @ SV104 @ SV145 ) )
= $true )
| ( ( ~ ( between @ SV48 @ SV145 @ SV104 )
| ( SV48 = SV104 )
| ( SV104 = SV145 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[397]) ).
thf(441,plain,
! [SV146: $i,SV105: $i,SV49: $i] :
( ( ( ~ ( between @ SV49 @ SV105 @ SV146 ) )
= $true )
| ( ( ! [SY502: $i] :
~ ( between @ SV105 @ SV146 @ SY502 )
| ( between @ SV49 @ SV105 @ SV146 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[398]) ).
thf(442,plain,
! [SV147: $i,SV106: $i,SV50: $i] :
( ( ( ~ ( between @ SV50 @ SV106 @ SV147 ) )
= $true )
| ( ( ! [SY503: $i] :
( ~ ( between @ SV50 @ SV147 @ SY503 )
| ( between @ SV106 @ SV147 @ SY503 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[399]) ).
thf(443,plain,
! [SV148: $i,SV107: $i,SV51: $i] :
( ( ( ~ ( between @ SV51 @ SV107 @ SV148 ) )
= $true )
| ( ( ! [SY504: $i] :
( ~ ( between @ SV107 @ SV148 @ SY504 )
| ( SV107 = SV148 )
| ( between @ SV51 @ SV148 @ SY504 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[400]) ).
thf(444,plain,
! [SV149: $i,SV108: $i,SV52: $i] :
( ( ( ~ ( between @ SV52 @ SV108 @ SV149 ) )
= $true )
| ( ( ! [SY505: $i] :
( ~ ( between @ SV108 @ SV149 @ SY505 )
| ( SV108 = SV149 )
| ( between @ SV52 @ SV108 @ SY505 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[401]) ).
thf(445,plain,
! [SV150: $i,SV109: $i,SV53: $i] :
( ( ( ~ ( between @ SV53 @ SV109 @ SV150 ) )
= $true )
| ( ( ! [SY506: $i] :
( ~ ( between @ SV109 @ SY506 @ SV150 )
| ( between @ SV53 @ SY506 @ SV150 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[402]) ).
thf(446,plain,
! [SV151: $i,SV110: $i,SV54: $i] :
( ( ( ~ ( between @ SV54 @ SV110 @ SV151 ) )
= $true )
| ( ( ! [SY507: $i] :
( ~ ( between @ SV54 @ SV151 @ SY507 )
| ( between @ SV54 @ SV110 @ SY507 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[403]) ).
thf(447,plain,
! [SV170: $i,SV152: $i,SV112: $i,SV56: $i] :
( ( equidistant @ SV56 @ ( extension @ SV112 @ SV56 @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ SV152 @ ( extension @ SV170 @ SV152 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[405]) ).
thf(448,plain,
! [SV153: $i,SV114: $i,SV59: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV59 @ SV114 @ SV153 ) )
= $true )
| ( ( ! [SY509: $i,SY510: $i] :
( ~ ( equidistant @ SV2 @ SV59 @ SY509 @ SY510 )
| ( equidistant @ SV114 @ SV153 @ SY509 @ SY510 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[406]) ).
thf(449,plain,
! [SV154: $i,SV60: $i,SV3: $i] :
( ( ( equidistant @ SV3 @ SV60 @ SV154 @ SV154 )
= $false )
| ( ( SV3 = SV60 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[407]) ).
thf(450,plain,
! [SV171: $i,SV157: $i,SV117: $i,SV63: $i,SV6: $i] :
( ( ! [SY525: $i] :
( ~ ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
| ~ ( equidistant @ SV63 @ SV171 @ SV157 @ SY525 )
| ! [SY526: $i,SY527: $i] :
( ~ ( equidistant @ SV6 @ SY526 @ SV117 @ SY527 )
| ~ ( equidistant @ SV63 @ SY526 @ SV157 @ SY527 )
| ~ ( between @ SV6 @ SV63 @ SV171 )
| ~ ( between @ SV117 @ SV157 @ SY525 )
| ( SV6 = SV63 )
| ( equidistant @ SV171 @ SY526 @ SY525 @ SY527 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[410]) ).
thf(451,plain,
! [SV118: $i,SV65: $i,SV8: $i] :
( ( ( between @ SV8 @ SV65 @ SV118 )
= $false )
| ( ( ! [SY464: $i,SY465: $i] :
( ~ ( between @ SY464 @ SY465 @ SV118 )
| ( between @ SV65 @ ( inner_pasch @ SV8 @ SV65 @ SV118 @ SY465 @ SY464 ) @ SY464 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(452,plain,
! [SV119: $i,SV66: $i,SV9: $i] :
( ( ( between @ SV9 @ SV66 @ SV119 )
= $false )
| ( ( ! [SY466: $i,SY467: $i] :
( ~ ( between @ SY466 @ SY467 @ SV119 )
| ( between @ SY467 @ ( inner_pasch @ SV9 @ SV66 @ SV119 @ SY467 @ SY466 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[413]) ).
thf(453,plain,
! [SV120: $i,SV67: $i,SV10: $i] :
( ( ( equidistant @ SV10 @ SV67 @ SV10 @ SV120 )
= $false )
| ( ( ! [SY468: $i] :
( ~ ( equidistant @ SY468 @ SV67 @ SY468 @ SV120 )
| ! [SY469: $i] :
( ~ ( equidistant @ SY469 @ SV67 @ SY469 @ SV120 )
| ( between @ SV10 @ SY468 @ SY469 )
| ( between @ SY468 @ SY469 @ SV10 )
| ( SV67 = SV120 )
| ( between @ SY469 @ SV10 @ SY468 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[414]) ).
thf(454,plain,
! [SV121: $i,SV68: $i,SV11: $i] :
( ( ( between @ SV11 @ SV68 @ SV121 )
= $false )
| ( ( ! [SY470: $i,SY471: $i] :
( ~ ( between @ SY470 @ SV68 @ SY471 )
| ( SV11 = SV68 )
| ( between @ SV11 @ SY470 @ ( euclid1 @ SV11 @ SY470 @ SV68 @ SY471 @ SV121 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(455,plain,
! [SV122: $i,SV69: $i,SV12: $i] :
( ( ( between @ SV12 @ SV69 @ SV122 )
= $false )
| ( ( ! [SY472: $i,SY473: $i] :
( ~ ( between @ SY472 @ SV69 @ SY473 )
| ( SV12 = SV69 )
| ( between @ SV12 @ SY473 @ ( euclid2 @ SV12 @ SY472 @ SV69 @ SY473 @ SV122 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[416]) ).
thf(456,plain,
! [SV123: $i,SV70: $i,SV13: $i] :
( ( ( between @ SV13 @ SV70 @ SV123 )
= $false )
| ( ( ! [SY474: $i,SY475: $i] :
( ~ ( between @ SY474 @ SV70 @ SY475 )
| ( SV13 = SV70 )
| ( between @ ( euclid1 @ SV13 @ SY474 @ SV70 @ SY475 @ SV123 ) @ SV123 @ ( euclid2 @ SV13 @ SY474 @ SV70 @ SY475 @ SV123 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[417]) ).
thf(457,plain,
! [SV158: $i,SV124: $i,SV71: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV71 @ SV14 @ SV124 ) )
= $true )
| ( ( ! [SY515: $i] :
( ~ ( equidistant @ SV14 @ SV158 @ SV14 @ SY515 )
| ~ ( between @ SV14 @ SV71 @ SV158 )
| ! [SY516: $i] :
( ~ ( between @ SV71 @ SY516 @ SV158 )
| ( between @ SV124 @ ( continuous @ SV14 @ SV71 @ SV124 @ SY516 @ SV158 @ SY515 ) @ SY515 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(458,plain,
! [SV159: $i,SV125: $i,SV72: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV72 @ SV15 @ SV125 ) )
= $true )
| ( ( ! [SY517: $i] :
( ~ ( equidistant @ SV15 @ SV159 @ SV15 @ SY517 )
| ~ ( between @ SV15 @ SV72 @ SV159 )
| ! [SY518: $i] :
( ~ ( between @ SV72 @ SY518 @ SV159 )
| ( equidistant @ SV15 @ SY518 @ SV15 @ ( continuous @ SV15 @ SV72 @ SV125 @ SY518 @ SV159 @ SY517 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(459,plain,
! [SV160: $i,SV126: $i,SV75: $i,SV18: $i] :
( ( ( ~ ( equidistant @ SV18 @ SV75 @ SV126 @ SV160 ) )
= $true )
| ( ( equidistant @ SV126 @ SV160 @ SV18 @ SV75 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(460,plain,
! [SV161: $i,SV127: $i,SV76: $i,SV19: $i] :
( ( ( ~ ( equidistant @ SV19 @ SV76 @ SV127 @ SV161 ) )
= $true )
| ( ( equidistant @ SV76 @ SV19 @ SV127 @ SV161 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[421]) ).
thf(461,plain,
! [SV162: $i,SV128: $i,SV77: $i,SV20: $i] :
( ( ( ~ ( equidistant @ SV20 @ SV77 @ SV128 @ SV162 ) )
= $true )
| ( ( equidistant @ SV20 @ SV77 @ SV162 @ SV128 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(462,plain,
! [SV163: $i,SV129: $i,SV78: $i,SV21: $i] :
( ( ( ~ ( equidistant @ SV21 @ SV78 @ SV129 @ SV163 ) )
= $true )
| ( ( equidistant @ SV78 @ SV21 @ SV163 @ SV129 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[423]) ).
thf(463,plain,
! [SV164: $i,SV130: $i,SV79: $i,SV22: $i] :
( ( ( ~ ( equidistant @ SV22 @ SV79 @ SV130 @ SV164 ) )
= $true )
| ( ( equidistant @ SV130 @ SV164 @ SV79 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[424]) ).
thf(464,plain,
! [SV165: $i,SV131: $i,SV80: $i,SV23: $i] :
( ( ( ~ ( equidistant @ SV23 @ SV80 @ SV131 @ SV165 ) )
= $true )
| ( ( equidistant @ SV165 @ SV131 @ SV23 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(465,plain,
! [SV166: $i,SV132: $i,SV81: $i,SV24: $i] :
( ( ( ~ ( equidistant @ SV24 @ SV81 @ SV132 @ SV166 ) )
= $true )
| ( ( equidistant @ SV166 @ SV132 @ SV81 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[426]) ).
thf(466,plain,
! [SV167: $i,SV133: $i,SV82: $i,SV25: $i] :
( ( ( ~ ( equidistant @ SV25 @ SV82 @ SV133 @ SV167 ) )
= $true )
| ( ( ! [SY519: $i,SY520: $i] :
( ~ ( equidistant @ SV133 @ SV167 @ SY519 @ SY520 )
| ( equidistant @ SV25 @ SV82 @ SY519 @ SY520 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[427]) ).
thf(467,plain,
! [SV172: $i,SV135: $i,SV84: $i,SV27: $i] :
( ( ( ! [SY528: $i] :
( SV27
!= ( extension @ SV84 @ SV135 @ SV172 @ SY528 ) ) )
= $true )
| ( ( between @ SV84 @ SV135 @ SV27 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(468,plain,
! [SV168: $i,SV136: $i,SV90: $i,SV34: $i] :
( ( ( ~ ( equidistant @ SV34 @ SV90 @ SV136 @ SV168 ) )
= $true )
| ( ( ! [SY521: $i,SY522: $i] :
( ~ ( equidistant @ SV90 @ SY521 @ SV168 @ SY522 )
| ~ ( between @ SV34 @ SV90 @ SY521 )
| ~ ( between @ SV136 @ SV168 @ SY522 )
| ( equidistant @ SV34 @ SY521 @ SV136 @ SY522 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[431]) ).
thf(469,plain,
! [SV137: $i,SV91: $i,SV35: $i] :
( ( ( between @ SV35 @ SV91 @ SV137 )
= $false )
| ( ( ! [SY497: $i] :
( ~ ( between @ SV35 @ SV91 @ SY497 )
| ~ ( equidistant @ SV91 @ SV137 @ SV91 @ SY497 )
| ( SV35 = SV91 )
| ( SV137 = SY497 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(470,plain,
! [SV138: $i,SV92: $i,SV36: $i] :
( ( ( between @ SV36 @ SV92 @ SV138 )
= $false )
| ( ( ( SV36 = SV92 )
| ( SV138
= ( extension @ SV36 @ SV92 @ SV92 @ SV138 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[433]) ).
thf(471,plain,
! [SV169: $i,SV139: $i,SV93: $i,SV37: $i] :
( ( ( ~ ( equidistant @ SV37 @ SV93 @ SV139 @ SV169 ) )
= $true )
| ( ( ! [SY523: $i,SY524: $i] :
( ( ( extension @ SY523 @ SY524 @ SV37 @ SV93 )
= ( extension @ SY523 @ SY524 @ SV139 @ SV169 ) )
| ( SY523 = SY524 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[434]) ).
thf(472,plain,
! [SV140: $i,SV98: $i,SV42: $i] :
( ( ( between @ SV42 @ SV98 @ SV140 )
= $false )
| ( ( ( SV42 != SV140 )
| ! [SY501: $i] : ( between @ SY501 @ SV98 @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(473,plain,
! [SV141: $i,SV99: $i,SV43: $i] :
( ( ( between @ SV43 @ SV99 @ SV141 )
= $false )
| ( ( between @ SV141 @ SV99 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(474,plain,
! [SV142: $i,SV101: $i,SV45: $i] :
( ( ( between @ SV45 @ SV101 @ SV142 )
= $false )
| ( ( ~ ( between @ SV101 @ SV45 @ SV142 )
| ( SV45 = SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(475,plain,
! [SV143: $i,SV102: $i,SV46: $i] :
( ( ( between @ SV46 @ SV102 @ SV143 )
= $false )
| ( ( ~ ( between @ SV46 @ SV143 @ SV102 )
| ( SV102 = SV143 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(476,plain,
! [SV144: $i,SV103: $i,SV47: $i] :
( ( ( between @ SV47 @ SV103 @ SV144 )
= $false )
| ( ( ~ ( between @ SV103 @ SV47 @ SV144 )
| ( SV47 = SV103 )
| ( SV103 = SV144 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(477,plain,
! [SV145: $i,SV104: $i,SV48: $i] :
( ( ( between @ SV48 @ SV104 @ SV145 )
= $false )
| ( ( ~ ( between @ SV48 @ SV145 @ SV104 )
| ( SV48 = SV104 )
| ( SV104 = SV145 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[440]) ).
thf(478,plain,
! [SV146: $i,SV105: $i,SV49: $i] :
( ( ( between @ SV49 @ SV105 @ SV146 )
= $false )
| ( ( ! [SY502: $i] :
~ ( between @ SV105 @ SV146 @ SY502 )
| ( between @ SV49 @ SV105 @ SV146 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[441]) ).
thf(479,plain,
! [SV147: $i,SV106: $i,SV50: $i] :
( ( ( between @ SV50 @ SV106 @ SV147 )
= $false )
| ( ( ! [SY503: $i] :
( ~ ( between @ SV50 @ SV147 @ SY503 )
| ( between @ SV106 @ SV147 @ SY503 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[442]) ).
thf(480,plain,
! [SV148: $i,SV107: $i,SV51: $i] :
( ( ( between @ SV51 @ SV107 @ SV148 )
= $false )
| ( ( ! [SY504: $i] :
( ~ ( between @ SV107 @ SV148 @ SY504 )
| ( SV107 = SV148 )
| ( between @ SV51 @ SV148 @ SY504 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[443]) ).
thf(481,plain,
! [SV149: $i,SV108: $i,SV52: $i] :
( ( ( between @ SV52 @ SV108 @ SV149 )
= $false )
| ( ( ! [SY505: $i] :
( ~ ( between @ SV108 @ SV149 @ SY505 )
| ( SV108 = SV149 )
| ( between @ SV52 @ SV108 @ SY505 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(482,plain,
! [SV150: $i,SV109: $i,SV53: $i] :
( ( ( between @ SV53 @ SV109 @ SV150 )
= $false )
| ( ( ! [SY506: $i] :
( ~ ( between @ SV109 @ SY506 @ SV150 )
| ( between @ SV53 @ SY506 @ SV150 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(483,plain,
! [SV151: $i,SV110: $i,SV54: $i] :
( ( ( between @ SV54 @ SV110 @ SV151 )
= $false )
| ( ( ! [SY507: $i] :
( ~ ( between @ SV54 @ SV151 @ SY507 )
| ( between @ SV54 @ SV110 @ SY507 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(484,plain,
! [SV153: $i,SV114: $i,SV59: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV59 @ SV114 @ SV153 )
= $false )
| ( ( ! [SY509: $i,SY510: $i] :
( ~ ( equidistant @ SV2 @ SV59 @ SY509 @ SY510 )
| ( equidistant @ SV114 @ SV153 @ SY509 @ SY510 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(485,plain,
! [SV173: $i,SV171: $i,SV157: $i,SV117: $i,SV63: $i,SV6: $i] :
( ( ~ ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
| ~ ( equidistant @ SV63 @ SV171 @ SV157 @ SV173 )
| ! [SY529: $i,SY530: $i] :
( ~ ( equidistant @ SV6 @ SY529 @ SV117 @ SY530 )
| ~ ( equidistant @ SV63 @ SY529 @ SV157 @ SY530 )
| ~ ( between @ SV6 @ SV63 @ SV171 )
| ~ ( between @ SV117 @ SV157 @ SV173 )
| ( SV6 = SV63 )
| ( equidistant @ SV171 @ SY529 @ SV173 @ SY530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(486,plain,
! [SV8: $i,SV65: $i,SV118: $i,SV174: $i] :
( ( ( ! [SY531: $i] :
( ~ ( between @ SV174 @ SY531 @ SV118 )
| ( between @ SV65 @ ( inner_pasch @ SV8 @ SV65 @ SV118 @ SY531 @ SV174 ) @ SV174 ) ) )
= $true )
| ( ( between @ SV8 @ SV65 @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(487,plain,
! [SV66: $i,SV9: $i,SV119: $i,SV175: $i] :
( ( ( ! [SY532: $i] :
( ~ ( between @ SV175 @ SY532 @ SV119 )
| ( between @ SY532 @ ( inner_pasch @ SV9 @ SV66 @ SV119 @ SY532 @ SV175 ) @ SV9 ) ) )
= $true )
| ( ( between @ SV9 @ SV66 @ SV119 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(488,plain,
! [SV10: $i,SV120: $i,SV67: $i,SV176: $i] :
( ( ( ~ ( equidistant @ SV176 @ SV67 @ SV176 @ SV120 )
| ! [SY533: $i] :
( ~ ( equidistant @ SY533 @ SV67 @ SY533 @ SV120 )
| ( between @ SV10 @ SV176 @ SY533 )
| ( between @ SV176 @ SY533 @ SV10 )
| ( SV67 = SV120 )
| ( between @ SY533 @ SV10 @ SV176 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV67 @ SV10 @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(489,plain,
! [SV121: $i,SV11: $i,SV68: $i,SV177: $i] :
( ( ( ! [SY534: $i] :
( ~ ( between @ SV177 @ SV68 @ SY534 )
| ( SV11 = SV68 )
| ( between @ SV11 @ SV177 @ ( euclid1 @ SV11 @ SV177 @ SV68 @ SY534 @ SV121 ) ) ) )
= $true )
| ( ( between @ SV11 @ SV68 @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(490,plain,
! [SV122: $i,SV12: $i,SV69: $i,SV178: $i] :
( ( ( ! [SY535: $i] :
( ~ ( between @ SV178 @ SV69 @ SY535 )
| ( SV12 = SV69 )
| ( between @ SV12 @ SY535 @ ( euclid2 @ SV12 @ SV178 @ SV69 @ SY535 @ SV122 ) ) ) )
= $true )
| ( ( between @ SV12 @ SV69 @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(491,plain,
! [SV123: $i,SV13: $i,SV70: $i,SV179: $i] :
( ( ( ! [SY536: $i] :
( ~ ( between @ SV179 @ SV70 @ SY536 )
| ( SV13 = SV70 )
| ( between @ ( euclid1 @ SV13 @ SV179 @ SV70 @ SY536 @ SV123 ) @ SV123 @ ( euclid2 @ SV13 @ SV179 @ SV70 @ SY536 @ SV123 ) ) ) )
= $true )
| ( ( between @ SV13 @ SV70 @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(492,plain,
! [SV158: $i,SV124: $i,SV71: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV71 @ SV14 @ SV124 )
= $false )
| ( ( ! [SY515: $i] :
( ~ ( equidistant @ SV14 @ SV158 @ SV14 @ SY515 )
| ~ ( between @ SV14 @ SV71 @ SV158 )
| ! [SY516: $i] :
( ~ ( between @ SV71 @ SY516 @ SV158 )
| ( between @ SV124 @ ( continuous @ SV14 @ SV71 @ SV124 @ SY516 @ SV158 @ SY515 ) @ SY515 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[457]) ).
thf(493,plain,
! [SV159: $i,SV125: $i,SV72: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV72 @ SV15 @ SV125 )
= $false )
| ( ( ! [SY517: $i] :
( ~ ( equidistant @ SV15 @ SV159 @ SV15 @ SY517 )
| ~ ( between @ SV15 @ SV72 @ SV159 )
| ! [SY518: $i] :
( ~ ( between @ SV72 @ SY518 @ SV159 )
| ( equidistant @ SV15 @ SY518 @ SV15 @ ( continuous @ SV15 @ SV72 @ SV125 @ SY518 @ SV159 @ SY517 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[458]) ).
thf(494,plain,
! [SV160: $i,SV126: $i,SV75: $i,SV18: $i] :
( ( ( equidistant @ SV18 @ SV75 @ SV126 @ SV160 )
= $false )
| ( ( equidistant @ SV126 @ SV160 @ SV18 @ SV75 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[459]) ).
thf(495,plain,
! [SV161: $i,SV127: $i,SV76: $i,SV19: $i] :
( ( ( equidistant @ SV19 @ SV76 @ SV127 @ SV161 )
= $false )
| ( ( equidistant @ SV76 @ SV19 @ SV127 @ SV161 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(496,plain,
! [SV162: $i,SV128: $i,SV77: $i,SV20: $i] :
( ( ( equidistant @ SV20 @ SV77 @ SV128 @ SV162 )
= $false )
| ( ( equidistant @ SV20 @ SV77 @ SV162 @ SV128 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[461]) ).
thf(497,plain,
! [SV163: $i,SV129: $i,SV78: $i,SV21: $i] :
( ( ( equidistant @ SV21 @ SV78 @ SV129 @ SV163 )
= $false )
| ( ( equidistant @ SV78 @ SV21 @ SV163 @ SV129 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[462]) ).
thf(498,plain,
! [SV164: $i,SV130: $i,SV79: $i,SV22: $i] :
( ( ( equidistant @ SV22 @ SV79 @ SV130 @ SV164 )
= $false )
| ( ( equidistant @ SV130 @ SV164 @ SV79 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[463]) ).
thf(499,plain,
! [SV165: $i,SV131: $i,SV80: $i,SV23: $i] :
( ( ( equidistant @ SV23 @ SV80 @ SV131 @ SV165 )
= $false )
| ( ( equidistant @ SV165 @ SV131 @ SV23 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(500,plain,
! [SV166: $i,SV132: $i,SV81: $i,SV24: $i] :
( ( ( equidistant @ SV24 @ SV81 @ SV132 @ SV166 )
= $false )
| ( ( equidistant @ SV166 @ SV132 @ SV81 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(501,plain,
! [SV167: $i,SV133: $i,SV82: $i,SV25: $i] :
( ( ( equidistant @ SV25 @ SV82 @ SV133 @ SV167 )
= $false )
| ( ( ! [SY519: $i,SY520: $i] :
( ~ ( equidistant @ SV133 @ SV167 @ SY519 @ SY520 )
| ( equidistant @ SV25 @ SV82 @ SY519 @ SY520 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[466]) ).
thf(502,plain,
! [SV180: $i,SV172: $i,SV135: $i,SV84: $i,SV27: $i] :
( ( ( ( SV27
!= ( extension @ SV84 @ SV135 @ SV172 @ SV180 ) ) )
= $true )
| ( ( between @ SV84 @ SV135 @ SV27 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(503,plain,
! [SV168: $i,SV136: $i,SV90: $i,SV34: $i] :
( ( ( equidistant @ SV34 @ SV90 @ SV136 @ SV168 )
= $false )
| ( ( ! [SY521: $i,SY522: $i] :
( ~ ( equidistant @ SV90 @ SY521 @ SV168 @ SY522 )
| ~ ( between @ SV34 @ SV90 @ SY521 )
| ~ ( between @ SV136 @ SV168 @ SY522 )
| ( equidistant @ SV34 @ SY521 @ SV136 @ SY522 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[468]) ).
thf(504,plain,
! [SV137: $i,SV181: $i,SV91: $i,SV35: $i] :
( ( ( ~ ( between @ SV35 @ SV91 @ SV181 )
| ~ ( equidistant @ SV91 @ SV137 @ SV91 @ SV181 )
| ( SV35 = SV91 )
| ( SV137 = SV181 ) )
= $true )
| ( ( between @ SV35 @ SV91 @ SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(505,plain,
! [SV138: $i,SV92: $i,SV36: $i] :
( ( ( SV36 = SV92 )
= $true )
| ( ( SV138
= ( extension @ SV36 @ SV92 @ SV92 @ SV138 ) )
= $true )
| ( ( between @ SV36 @ SV92 @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(506,plain,
! [SV169: $i,SV139: $i,SV93: $i,SV37: $i] :
( ( ( equidistant @ SV37 @ SV93 @ SV139 @ SV169 )
= $false )
| ( ( ! [SY523: $i,SY524: $i] :
( ( ( extension @ SY523 @ SY524 @ SV37 @ SV93 )
= ( extension @ SY523 @ SY524 @ SV139 @ SV169 ) )
| ( SY523 = SY524 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[471]) ).
thf(507,plain,
! [SV98: $i,SV140: $i,SV42: $i] :
( ( ( ( SV42 != SV140 ) )
= $true )
| ( ( ! [SY501: $i] : ( between @ SY501 @ SV98 @ SV140 ) )
= $true )
| ( ( between @ SV42 @ SV98 @ SV140 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[472]) ).
thf(508,plain,
! [SV142: $i,SV45: $i,SV101: $i] :
( ( ( ~ ( between @ SV101 @ SV45 @ SV142 ) )
= $true )
| ( ( SV45 = SV101 )
= $true )
| ( ( between @ SV45 @ SV101 @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[474]) ).
thf(509,plain,
! [SV102: $i,SV143: $i,SV46: $i] :
( ( ( ~ ( between @ SV46 @ SV143 @ SV102 ) )
= $true )
| ( ( SV102 = SV143 )
= $true )
| ( ( between @ SV46 @ SV102 @ SV143 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(510,plain,
! [SV144: $i,SV47: $i,SV103: $i] :
( ( ( ~ ( between @ SV103 @ SV47 @ SV144 ) )
= $true )
| ( ( ( SV47 = SV103 )
| ( SV103 = SV144 ) )
= $true )
| ( ( between @ SV47 @ SV103 @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(511,plain,
! [SV104: $i,SV145: $i,SV48: $i] :
( ( ( ~ ( between @ SV48 @ SV145 @ SV104 ) )
= $true )
| ( ( ( SV48 = SV104 )
| ( SV104 = SV145 ) )
= $true )
| ( ( between @ SV48 @ SV104 @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(512,plain,
! [SV49: $i,SV146: $i,SV105: $i] :
( ( ( ! [SY502: $i] :
~ ( between @ SV105 @ SV146 @ SY502 ) )
= $true )
| ( ( between @ SV49 @ SV105 @ SV146 )
= $true )
| ( ( between @ SV49 @ SV105 @ SV146 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(513,plain,
! [SV106: $i,SV182: $i,SV147: $i,SV50: $i] :
( ( ( ~ ( between @ SV50 @ SV147 @ SV182 )
| ( between @ SV106 @ SV147 @ SV182 ) )
= $true )
| ( ( between @ SV50 @ SV106 @ SV147 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(514,plain,
! [SV51: $i,SV183: $i,SV148: $i,SV107: $i] :
( ( ( ~ ( between @ SV107 @ SV148 @ SV183 )
| ( SV107 = SV148 )
| ( between @ SV51 @ SV148 @ SV183 ) )
= $true )
| ( ( between @ SV51 @ SV107 @ SV148 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(515,plain,
! [SV52: $i,SV184: $i,SV149: $i,SV108: $i] :
( ( ( ~ ( between @ SV108 @ SV149 @ SV184 )
| ( SV108 = SV149 )
| ( between @ SV52 @ SV108 @ SV184 ) )
= $true )
| ( ( between @ SV52 @ SV108 @ SV149 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(516,plain,
! [SV53: $i,SV150: $i,SV185: $i,SV109: $i] :
( ( ( ~ ( between @ SV109 @ SV185 @ SV150 )
| ( between @ SV53 @ SV185 @ SV150 ) )
= $true )
| ( ( between @ SV53 @ SV109 @ SV150 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(517,plain,
! [SV110: $i,SV186: $i,SV151: $i,SV54: $i] :
( ( ( ~ ( between @ SV54 @ SV151 @ SV186 )
| ( between @ SV54 @ SV110 @ SV186 ) )
= $true )
| ( ( between @ SV54 @ SV110 @ SV151 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(518,plain,
! [SV153: $i,SV114: $i,SV187: $i,SV59: $i,SV2: $i] :
( ( ( ! [SY537: $i] :
( ~ ( equidistant @ SV2 @ SV59 @ SV187 @ SY537 )
| ( equidistant @ SV114 @ SV153 @ SV187 @ SY537 ) ) )
= $true )
| ( ( equidistant @ SV2 @ SV59 @ SV114 @ SV153 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(519,plain,
! [SV173: $i,SV171: $i,SV157: $i,SV117: $i,SV63: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 ) )
= $true )
| ( ( ~ ( equidistant @ SV63 @ SV171 @ SV157 @ SV173 )
| ! [SY529: $i,SY530: $i] :
( ~ ( equidistant @ SV6 @ SY529 @ SV117 @ SY530 )
| ~ ( equidistant @ SV63 @ SY529 @ SV157 @ SY530 )
| ~ ( between @ SV6 @ SV63 @ SV171 )
| ~ ( between @ SV117 @ SV157 @ SV173 )
| ( SV6 = SV63 )
| ( equidistant @ SV171 @ SY529 @ SV173 @ SY530 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(520,plain,
! [SV8: $i,SV65: $i,SV118: $i,SV188: $i,SV174: $i] :
( ( ( ~ ( between @ SV174 @ SV188 @ SV118 )
| ( between @ SV65 @ ( inner_pasch @ SV8 @ SV65 @ SV118 @ SV188 @ SV174 ) @ SV174 ) )
= $true )
| ( ( between @ SV8 @ SV65 @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(521,plain,
! [SV66: $i,SV9: $i,SV119: $i,SV189: $i,SV175: $i] :
( ( ( ~ ( between @ SV175 @ SV189 @ SV119 )
| ( between @ SV189 @ ( inner_pasch @ SV9 @ SV66 @ SV119 @ SV189 @ SV175 ) @ SV9 ) )
= $true )
| ( ( between @ SV9 @ SV66 @ SV119 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(522,plain,
! [SV10: $i,SV120: $i,SV67: $i,SV176: $i] :
( ( ( ~ ( equidistant @ SV176 @ SV67 @ SV176 @ SV120 ) )
= $true )
| ( ( ! [SY533: $i] :
( ~ ( equidistant @ SY533 @ SV67 @ SY533 @ SV120 )
| ( between @ SV10 @ SV176 @ SY533 )
| ( between @ SV176 @ SY533 @ SV10 )
| ( SV67 = SV120 )
| ( between @ SY533 @ SV10 @ SV176 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV67 @ SV10 @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(523,plain,
! [SV121: $i,SV11: $i,SV190: $i,SV68: $i,SV177: $i] :
( ( ( ~ ( between @ SV177 @ SV68 @ SV190 )
| ( SV11 = SV68 )
| ( between @ SV11 @ SV177 @ ( euclid1 @ SV11 @ SV177 @ SV68 @ SV190 @ SV121 ) ) )
= $true )
| ( ( between @ SV11 @ SV68 @ SV121 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(524,plain,
! [SV122: $i,SV12: $i,SV191: $i,SV69: $i,SV178: $i] :
( ( ( ~ ( between @ SV178 @ SV69 @ SV191 )
| ( SV12 = SV69 )
| ( between @ SV12 @ SV191 @ ( euclid2 @ SV12 @ SV178 @ SV69 @ SV191 @ SV122 ) ) )
= $true )
| ( ( between @ SV12 @ SV69 @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(525,plain,
! [SV123: $i,SV13: $i,SV192: $i,SV70: $i,SV179: $i] :
( ( ( ~ ( between @ SV179 @ SV70 @ SV192 )
| ( SV13 = SV70 )
| ( between @ ( euclid1 @ SV13 @ SV179 @ SV70 @ SV192 @ SV123 ) @ SV123 @ ( euclid2 @ SV13 @ SV179 @ SV70 @ SV192 @ SV123 ) ) )
= $true )
| ( ( between @ SV13 @ SV70 @ SV123 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(526,plain,
! [SV124: $i,SV71: $i,SV193: $i,SV158: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV158 @ SV14 @ SV193 )
| ~ ( between @ SV14 @ SV71 @ SV158 )
| ! [SY538: $i] :
( ~ ( between @ SV71 @ SY538 @ SV158 )
| ( between @ SV124 @ ( continuous @ SV14 @ SV71 @ SV124 @ SY538 @ SV158 @ SV193 ) @ SV193 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV71 @ SV14 @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(527,plain,
! [SV125: $i,SV72: $i,SV194: $i,SV159: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV159 @ SV15 @ SV194 )
| ~ ( between @ SV15 @ SV72 @ SV159 )
| ! [SY539: $i] :
( ~ ( between @ SV72 @ SY539 @ SV159 )
| ( equidistant @ SV15 @ SY539 @ SV15 @ ( continuous @ SV15 @ SV72 @ SV125 @ SY539 @ SV159 @ SV194 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV72 @ SV15 @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(528,plain,
! [SV82: $i,SV25: $i,SV195: $i,SV167: $i,SV133: $i] :
( ( ( ! [SY540: $i] :
( ~ ( equidistant @ SV133 @ SV167 @ SV195 @ SY540 )
| ( equidistant @ SV25 @ SV82 @ SV195 @ SY540 ) ) )
= $true )
| ( ( equidistant @ SV25 @ SV82 @ SV133 @ SV167 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(529,plain,
! [SV180: $i,SV172: $i,SV135: $i,SV84: $i,SV27: $i] :
( ( ( SV27
= ( extension @ SV84 @ SV135 @ SV172 @ SV180 ) )
= $false )
| ( ( between @ SV84 @ SV135 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[502]) ).
thf(530,plain,
! [SV136: $i,SV34: $i,SV168: $i,SV196: $i,SV90: $i] :
( ( ( ! [SY541: $i] :
( ~ ( equidistant @ SV90 @ SV196 @ SV168 @ SY541 )
| ~ ( between @ SV34 @ SV90 @ SV196 )
| ~ ( between @ SV136 @ SV168 @ SY541 )
| ( equidistant @ SV34 @ SV196 @ SV136 @ SY541 ) ) )
= $true )
| ( ( equidistant @ SV34 @ SV90 @ SV136 @ SV168 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(531,plain,
! [SV137: $i,SV181: $i,SV91: $i,SV35: $i] :
( ( ( ~ ( between @ SV35 @ SV91 @ SV181 ) )
= $true )
| ( ( ~ ( equidistant @ SV91 @ SV137 @ SV91 @ SV181 )
| ( SV35 = SV91 )
| ( SV137 = SV181 ) )
= $true )
| ( ( between @ SV35 @ SV91 @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(532,plain,
! [SV169: $i,SV139: $i,SV93: $i,SV37: $i,SV197: $i] :
( ( ( ! [SY542: $i] :
( ( ( extension @ SV197 @ SY542 @ SV37 @ SV93 )
= ( extension @ SV197 @ SY542 @ SV139 @ SV169 ) )
| ( SV197 = SY542 ) ) )
= $true )
| ( ( equidistant @ SV37 @ SV93 @ SV139 @ SV169 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(533,plain,
! [SV98: $i,SV140: $i,SV42: $i] :
( ( ( SV42 = SV140 )
= $false )
| ( ( ! [SY501: $i] : ( between @ SY501 @ SV98 @ SV140 ) )
= $true )
| ( ( between @ SV42 @ SV98 @ SV140 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(534,plain,
! [SV142: $i,SV45: $i,SV101: $i] :
( ( ( between @ SV101 @ SV45 @ SV142 )
= $false )
| ( ( SV45 = SV101 )
= $true )
| ( ( between @ SV45 @ SV101 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[508]) ).
thf(535,plain,
! [SV102: $i,SV143: $i,SV46: $i] :
( ( ( between @ SV46 @ SV143 @ SV102 )
= $false )
| ( ( SV102 = SV143 )
= $true )
| ( ( between @ SV46 @ SV102 @ SV143 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[509]) ).
thf(536,plain,
! [SV144: $i,SV47: $i,SV103: $i] :
( ( ( between @ SV103 @ SV47 @ SV144 )
= $false )
| ( ( ( SV47 = SV103 )
| ( SV103 = SV144 ) )
= $true )
| ( ( between @ SV47 @ SV103 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[510]) ).
thf(537,plain,
! [SV104: $i,SV145: $i,SV48: $i] :
( ( ( between @ SV48 @ SV145 @ SV104 )
= $false )
| ( ( ( SV48 = SV104 )
| ( SV104 = SV145 ) )
= $true )
| ( ( between @ SV48 @ SV104 @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[511]) ).
thf(538,plain,
! [SV49: $i,SV198: $i,SV146: $i,SV105: $i] :
( ( ( ~ ( between @ SV105 @ SV146 @ SV198 ) )
= $true )
| ( ( between @ SV49 @ SV105 @ SV146 )
= $true )
| ( ( between @ SV49 @ SV105 @ SV146 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(539,plain,
! [SV106: $i,SV182: $i,SV147: $i,SV50: $i] :
( ( ( ~ ( between @ SV50 @ SV147 @ SV182 ) )
= $true )
| ( ( between @ SV106 @ SV147 @ SV182 )
= $true )
| ( ( between @ SV50 @ SV106 @ SV147 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[513]) ).
thf(540,plain,
! [SV51: $i,SV183: $i,SV148: $i,SV107: $i] :
( ( ( ~ ( between @ SV107 @ SV148 @ SV183 ) )
= $true )
| ( ( ( SV107 = SV148 )
| ( between @ SV51 @ SV148 @ SV183 ) )
= $true )
| ( ( between @ SV51 @ SV107 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[514]) ).
thf(541,plain,
! [SV52: $i,SV184: $i,SV149: $i,SV108: $i] :
( ( ( ~ ( between @ SV108 @ SV149 @ SV184 ) )
= $true )
| ( ( ( SV108 = SV149 )
| ( between @ SV52 @ SV108 @ SV184 ) )
= $true )
| ( ( between @ SV52 @ SV108 @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[515]) ).
thf(542,plain,
! [SV53: $i,SV150: $i,SV185: $i,SV109: $i] :
( ( ( ~ ( between @ SV109 @ SV185 @ SV150 ) )
= $true )
| ( ( between @ SV53 @ SV185 @ SV150 )
= $true )
| ( ( between @ SV53 @ SV109 @ SV150 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[516]) ).
thf(543,plain,
! [SV110: $i,SV186: $i,SV151: $i,SV54: $i] :
( ( ( ~ ( between @ SV54 @ SV151 @ SV186 ) )
= $true )
| ( ( between @ SV54 @ SV110 @ SV186 )
= $true )
| ( ( between @ SV54 @ SV110 @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(544,plain,
! [SV153: $i,SV114: $i,SV199: $i,SV187: $i,SV59: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV59 @ SV187 @ SV199 )
| ( equidistant @ SV114 @ SV153 @ SV187 @ SV199 ) )
= $true )
| ( ( equidistant @ SV2 @ SV59 @ SV114 @ SV153 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(545,plain,
! [SV173: $i,SV171: $i,SV157: $i,SV117: $i,SV63: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
= $false )
| ( ( ~ ( equidistant @ SV63 @ SV171 @ SV157 @ SV173 )
| ! [SY529: $i,SY530: $i] :
( ~ ( equidistant @ SV6 @ SY529 @ SV117 @ SY530 )
| ~ ( equidistant @ SV63 @ SY529 @ SV157 @ SY530 )
| ~ ( between @ SV6 @ SV63 @ SV171 )
| ~ ( between @ SV117 @ SV157 @ SV173 )
| ( SV6 = SV63 )
| ( equidistant @ SV171 @ SY529 @ SV173 @ SY530 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[519]) ).
thf(546,plain,
! [SV8: $i,SV65: $i,SV118: $i,SV188: $i,SV174: $i] :
( ( ( ~ ( between @ SV174 @ SV188 @ SV118 ) )
= $true )
| ( ( between @ SV65 @ ( inner_pasch @ SV8 @ SV65 @ SV118 @ SV188 @ SV174 ) @ SV174 )
= $true )
| ( ( between @ SV8 @ SV65 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(547,plain,
! [SV66: $i,SV9: $i,SV119: $i,SV189: $i,SV175: $i] :
( ( ( ~ ( between @ SV175 @ SV189 @ SV119 ) )
= $true )
| ( ( between @ SV189 @ ( inner_pasch @ SV9 @ SV66 @ SV119 @ SV189 @ SV175 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV66 @ SV119 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[521]) ).
thf(548,plain,
! [SV10: $i,SV120: $i,SV67: $i,SV176: $i] :
( ( ( equidistant @ SV176 @ SV67 @ SV176 @ SV120 )
= $false )
| ( ( ! [SY533: $i] :
( ~ ( equidistant @ SY533 @ SV67 @ SY533 @ SV120 )
| ( between @ SV10 @ SV176 @ SY533 )
| ( between @ SV176 @ SY533 @ SV10 )
| ( SV67 = SV120 )
| ( between @ SY533 @ SV10 @ SV176 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV67 @ SV10 @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[522]) ).
thf(549,plain,
! [SV121: $i,SV11: $i,SV190: $i,SV68: $i,SV177: $i] :
( ( ( ~ ( between @ SV177 @ SV68 @ SV190 ) )
= $true )
| ( ( ( SV11 = SV68 )
| ( between @ SV11 @ SV177 @ ( euclid1 @ SV11 @ SV177 @ SV68 @ SV190 @ SV121 ) ) )
= $true )
| ( ( between @ SV11 @ SV68 @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[523]) ).
thf(550,plain,
! [SV122: $i,SV12: $i,SV191: $i,SV69: $i,SV178: $i] :
( ( ( ~ ( between @ SV178 @ SV69 @ SV191 ) )
= $true )
| ( ( ( SV12 = SV69 )
| ( between @ SV12 @ SV191 @ ( euclid2 @ SV12 @ SV178 @ SV69 @ SV191 @ SV122 ) ) )
= $true )
| ( ( between @ SV12 @ SV69 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[524]) ).
thf(551,plain,
! [SV123: $i,SV13: $i,SV192: $i,SV70: $i,SV179: $i] :
( ( ( ~ ( between @ SV179 @ SV70 @ SV192 ) )
= $true )
| ( ( ( SV13 = SV70 )
| ( between @ ( euclid1 @ SV13 @ SV179 @ SV70 @ SV192 @ SV123 ) @ SV123 @ ( euclid2 @ SV13 @ SV179 @ SV70 @ SV192 @ SV123 ) ) )
= $true )
| ( ( between @ SV13 @ SV70 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[525]) ).
thf(552,plain,
! [SV124: $i,SV71: $i,SV193: $i,SV158: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV158 @ SV14 @ SV193 ) )
= $true )
| ( ( ~ ( between @ SV14 @ SV71 @ SV158 )
| ! [SY538: $i] :
( ~ ( between @ SV71 @ SY538 @ SV158 )
| ( between @ SV124 @ ( continuous @ SV14 @ SV71 @ SV124 @ SY538 @ SV158 @ SV193 ) @ SV193 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV71 @ SV14 @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[526]) ).
thf(553,plain,
! [SV125: $i,SV72: $i,SV194: $i,SV159: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV159 @ SV15 @ SV194 ) )
= $true )
| ( ( ~ ( between @ SV15 @ SV72 @ SV159 )
| ! [SY539: $i] :
( ~ ( between @ SV72 @ SY539 @ SV159 )
| ( equidistant @ SV15 @ SY539 @ SV15 @ ( continuous @ SV15 @ SV72 @ SV125 @ SY539 @ SV159 @ SV194 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV72 @ SV15 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(554,plain,
! [SV82: $i,SV25: $i,SV200: $i,SV195: $i,SV167: $i,SV133: $i] :
( ( ( ~ ( equidistant @ SV133 @ SV167 @ SV195 @ SV200 )
| ( equidistant @ SV25 @ SV82 @ SV195 @ SV200 ) )
= $true )
| ( ( equidistant @ SV25 @ SV82 @ SV133 @ SV167 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(555,plain,
! [SV136: $i,SV34: $i,SV201: $i,SV168: $i,SV196: $i,SV90: $i] :
( ( ( ~ ( equidistant @ SV90 @ SV196 @ SV168 @ SV201 )
| ~ ( between @ SV34 @ SV90 @ SV196 )
| ~ ( between @ SV136 @ SV168 @ SV201 )
| ( equidistant @ SV34 @ SV196 @ SV136 @ SV201 ) )
= $true )
| ( ( equidistant @ SV34 @ SV90 @ SV136 @ SV168 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(556,plain,
! [SV137: $i,SV181: $i,SV91: $i,SV35: $i] :
( ( ( between @ SV35 @ SV91 @ SV181 )
= $false )
| ( ( ~ ( equidistant @ SV91 @ SV137 @ SV91 @ SV181 )
| ( SV35 = SV91 )
| ( SV137 = SV181 ) )
= $true )
| ( ( between @ SV35 @ SV91 @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[531]) ).
thf(557,plain,
! [SV169: $i,SV139: $i,SV93: $i,SV37: $i,SV202: $i,SV197: $i] :
( ( ( ( ( extension @ SV197 @ SV202 @ SV37 @ SV93 )
= ( extension @ SV197 @ SV202 @ SV139 @ SV169 ) )
| ( SV197 = SV202 ) )
= $true )
| ( ( equidistant @ SV37 @ SV93 @ SV139 @ SV169 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(558,plain,
! [SV42: $i,SV140: $i,SV98: $i,SV203: $i] :
( ( ( between @ SV203 @ SV98 @ SV140 )
= $true )
| ( ( SV42 = SV140 )
= $false )
| ( ( between @ SV42 @ SV98 @ SV140 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(559,plain,
! [SV144: $i,SV103: $i,SV47: $i] :
( ( ( SV47 = SV103 )
= $true )
| ( ( SV103 = SV144 )
= $true )
| ( ( between @ SV103 @ SV47 @ SV144 )
= $false )
| ( ( between @ SV47 @ SV103 @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[536]) ).
thf(560,plain,
! [SV145: $i,SV104: $i,SV48: $i] :
( ( ( SV48 = SV104 )
= $true )
| ( ( SV104 = SV145 )
= $true )
| ( ( between @ SV48 @ SV145 @ SV104 )
= $false )
| ( ( between @ SV48 @ SV104 @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[537]) ).
thf(561,plain,
! [SV49: $i,SV198: $i,SV146: $i,SV105: $i] :
( ( ( between @ SV105 @ SV146 @ SV198 )
= $false )
| ( ( between @ SV49 @ SV105 @ SV146 )
= $true )
| ( ( between @ SV49 @ SV105 @ SV146 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[538]) ).
thf(562,plain,
! [SV106: $i,SV182: $i,SV147: $i,SV50: $i] :
( ( ( between @ SV50 @ SV147 @ SV182 )
= $false )
| ( ( between @ SV106 @ SV147 @ SV182 )
= $true )
| ( ( between @ SV50 @ SV106 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[539]) ).
thf(563,plain,
! [SV51: $i,SV183: $i,SV148: $i,SV107: $i] :
( ( ( between @ SV107 @ SV148 @ SV183 )
= $false )
| ( ( ( SV107 = SV148 )
| ( between @ SV51 @ SV148 @ SV183 ) )
= $true )
| ( ( between @ SV51 @ SV107 @ SV148 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[540]) ).
thf(564,plain,
! [SV52: $i,SV184: $i,SV149: $i,SV108: $i] :
( ( ( between @ SV108 @ SV149 @ SV184 )
= $false )
| ( ( ( SV108 = SV149 )
| ( between @ SV52 @ SV108 @ SV184 ) )
= $true )
| ( ( between @ SV52 @ SV108 @ SV149 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[541]) ).
thf(565,plain,
! [SV53: $i,SV150: $i,SV185: $i,SV109: $i] :
( ( ( between @ SV109 @ SV185 @ SV150 )
= $false )
| ( ( between @ SV53 @ SV185 @ SV150 )
= $true )
| ( ( between @ SV53 @ SV109 @ SV150 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(566,plain,
! [SV110: $i,SV186: $i,SV151: $i,SV54: $i] :
( ( ( between @ SV54 @ SV151 @ SV186 )
= $false )
| ( ( between @ SV54 @ SV110 @ SV186 )
= $true )
| ( ( between @ SV54 @ SV110 @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[543]) ).
thf(567,plain,
! [SV153: $i,SV114: $i,SV199: $i,SV187: $i,SV59: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV59 @ SV187 @ SV199 ) )
= $true )
| ( ( equidistant @ SV114 @ SV153 @ SV187 @ SV199 )
= $true )
| ( ( equidistant @ SV2 @ SV59 @ SV114 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[544]) ).
thf(568,plain,
! [SV117: $i,SV6: $i,SV173: $i,SV157: $i,SV171: $i,SV63: $i] :
( ( ( ~ ( equidistant @ SV63 @ SV171 @ SV157 @ SV173 ) )
= $true )
| ( ( ! [SY529: $i,SY530: $i] :
( ~ ( equidistant @ SV6 @ SY529 @ SV117 @ SY530 )
| ~ ( equidistant @ SV63 @ SY529 @ SV157 @ SY530 )
| ~ ( between @ SV6 @ SV63 @ SV171 )
| ~ ( between @ SV117 @ SV157 @ SV173 )
| ( SV6 = SV63 )
| ( equidistant @ SV171 @ SY529 @ SV173 @ SY530 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(569,plain,
! [SV8: $i,SV65: $i,SV118: $i,SV188: $i,SV174: $i] :
( ( ( between @ SV174 @ SV188 @ SV118 )
= $false )
| ( ( between @ SV65 @ ( inner_pasch @ SV8 @ SV65 @ SV118 @ SV188 @ SV174 ) @ SV174 )
= $true )
| ( ( between @ SV8 @ SV65 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(570,plain,
! [SV66: $i,SV9: $i,SV119: $i,SV189: $i,SV175: $i] :
( ( ( between @ SV175 @ SV189 @ SV119 )
= $false )
| ( ( between @ SV189 @ ( inner_pasch @ SV9 @ SV66 @ SV119 @ SV189 @ SV175 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV66 @ SV119 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[547]) ).
thf(571,plain,
! [SV176: $i,SV10: $i,SV120: $i,SV67: $i,SV204: $i] :
( ( ( ~ ( equidistant @ SV204 @ SV67 @ SV204 @ SV120 )
| ( between @ SV10 @ SV176 @ SV204 )
| ( between @ SV176 @ SV204 @ SV10 )
| ( SV67 = SV120 )
| ( between @ SV204 @ SV10 @ SV176 ) )
= $true )
| ( ( equidistant @ SV176 @ SV67 @ SV176 @ SV120 )
= $false )
| ( ( equidistant @ SV10 @ SV67 @ SV10 @ SV120 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(572,plain,
! [SV121: $i,SV11: $i,SV190: $i,SV68: $i,SV177: $i] :
( ( ( between @ SV177 @ SV68 @ SV190 )
= $false )
| ( ( ( SV11 = SV68 )
| ( between @ SV11 @ SV177 @ ( euclid1 @ SV11 @ SV177 @ SV68 @ SV190 @ SV121 ) ) )
= $true )
| ( ( between @ SV11 @ SV68 @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[549]) ).
thf(573,plain,
! [SV122: $i,SV12: $i,SV191: $i,SV69: $i,SV178: $i] :
( ( ( between @ SV178 @ SV69 @ SV191 )
= $false )
| ( ( ( SV12 = SV69 )
| ( between @ SV12 @ SV191 @ ( euclid2 @ SV12 @ SV178 @ SV69 @ SV191 @ SV122 ) ) )
= $true )
| ( ( between @ SV12 @ SV69 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[550]) ).
thf(574,plain,
! [SV123: $i,SV13: $i,SV192: $i,SV70: $i,SV179: $i] :
( ( ( between @ SV179 @ SV70 @ SV192 )
= $false )
| ( ( ( SV13 = SV70 )
| ( between @ ( euclid1 @ SV13 @ SV179 @ SV70 @ SV192 @ SV123 ) @ SV123 @ ( euclid2 @ SV13 @ SV179 @ SV70 @ SV192 @ SV123 ) ) )
= $true )
| ( ( between @ SV13 @ SV70 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[551]) ).
thf(575,plain,
! [SV124: $i,SV71: $i,SV193: $i,SV158: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV158 @ SV14 @ SV193 )
= $false )
| ( ( ~ ( between @ SV14 @ SV71 @ SV158 )
| ! [SY538: $i] :
( ~ ( between @ SV71 @ SY538 @ SV158 )
| ( between @ SV124 @ ( continuous @ SV14 @ SV71 @ SV124 @ SY538 @ SV158 @ SV193 ) @ SV193 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV71 @ SV14 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[552]) ).
thf(576,plain,
! [SV125: $i,SV72: $i,SV194: $i,SV159: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV159 @ SV15 @ SV194 )
= $false )
| ( ( ~ ( between @ SV15 @ SV72 @ SV159 )
| ! [SY539: $i] :
( ~ ( between @ SV72 @ SY539 @ SV159 )
| ( equidistant @ SV15 @ SY539 @ SV15 @ ( continuous @ SV15 @ SV72 @ SV125 @ SY539 @ SV159 @ SV194 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV72 @ SV15 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[553]) ).
thf(577,plain,
! [SV82: $i,SV25: $i,SV200: $i,SV195: $i,SV167: $i,SV133: $i] :
( ( ( ~ ( equidistant @ SV133 @ SV167 @ SV195 @ SV200 ) )
= $true )
| ( ( equidistant @ SV25 @ SV82 @ SV195 @ SV200 )
= $true )
| ( ( equidistant @ SV25 @ SV82 @ SV133 @ SV167 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[554]) ).
thf(578,plain,
! [SV136: $i,SV34: $i,SV201: $i,SV168: $i,SV196: $i,SV90: $i] :
( ( ( ~ ( equidistant @ SV90 @ SV196 @ SV168 @ SV201 ) )
= $true )
| ( ( ~ ( between @ SV34 @ SV90 @ SV196 )
| ~ ( between @ SV136 @ SV168 @ SV201 )
| ( equidistant @ SV34 @ SV196 @ SV136 @ SV201 ) )
= $true )
| ( ( equidistant @ SV34 @ SV90 @ SV136 @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[555]) ).
thf(579,plain,
! [SV35: $i,SV181: $i,SV137: $i,SV91: $i] :
( ( ( ~ ( equidistant @ SV91 @ SV137 @ SV91 @ SV181 ) )
= $true )
| ( ( ( SV35 = SV91 )
| ( SV137 = SV181 ) )
= $true )
| ( ( between @ SV35 @ SV91 @ SV181 )
= $false )
| ( ( between @ SV35 @ SV91 @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[556]) ).
thf(580,plain,
! [SV169: $i,SV139: $i,SV93: $i,SV37: $i,SV202: $i,SV197: $i] :
( ( ( ( extension @ SV197 @ SV202 @ SV37 @ SV93 )
= ( extension @ SV197 @ SV202 @ SV139 @ SV169 ) )
= $true )
| ( ( SV197 = SV202 )
= $true )
| ( ( equidistant @ SV37 @ SV93 @ SV139 @ SV169 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[557]) ).
thf(581,plain,
! [SV183: $i,SV51: $i,SV148: $i,SV107: $i] :
( ( ( SV107 = SV148 )
= $true )
| ( ( between @ SV51 @ SV148 @ SV183 )
= $true )
| ( ( between @ SV107 @ SV148 @ SV183 )
= $false )
| ( ( between @ SV51 @ SV107 @ SV148 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[563]) ).
thf(582,plain,
! [SV184: $i,SV52: $i,SV149: $i,SV108: $i] :
( ( ( SV108 = SV149 )
= $true )
| ( ( between @ SV52 @ SV108 @ SV184 )
= $true )
| ( ( between @ SV108 @ SV149 @ SV184 )
= $false )
| ( ( between @ SV52 @ SV108 @ SV149 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[564]) ).
thf(583,plain,
! [SV153: $i,SV114: $i,SV199: $i,SV187: $i,SV59: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV59 @ SV187 @ SV199 )
= $false )
| ( ( equidistant @ SV114 @ SV153 @ SV187 @ SV199 )
= $true )
| ( ( equidistant @ SV2 @ SV59 @ SV114 @ SV153 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[567]) ).
thf(584,plain,
! [SV117: $i,SV6: $i,SV173: $i,SV157: $i,SV171: $i,SV63: $i] :
( ( ( equidistant @ SV63 @ SV171 @ SV157 @ SV173 )
= $false )
| ( ( ! [SY529: $i,SY530: $i] :
( ~ ( equidistant @ SV6 @ SY529 @ SV117 @ SY530 )
| ~ ( equidistant @ SV63 @ SY529 @ SV157 @ SY530 )
| ~ ( between @ SV6 @ SV63 @ SV171 )
| ~ ( between @ SV117 @ SV157 @ SV173 )
| ( SV6 = SV63 )
| ( equidistant @ SV171 @ SY529 @ SV173 @ SY530 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[568]) ).
thf(585,plain,
! [SV176: $i,SV10: $i,SV120: $i,SV67: $i,SV204: $i] :
( ( ( ~ ( equidistant @ SV204 @ SV67 @ SV204 @ SV120 ) )
= $true )
| ( ( ( between @ SV10 @ SV176 @ SV204 )
| ( between @ SV176 @ SV204 @ SV10 )
| ( SV67 = SV120 )
| ( between @ SV204 @ SV10 @ SV176 ) )
= $true )
| ( ( equidistant @ SV176 @ SV67 @ SV176 @ SV120 )
= $false )
| ( ( equidistant @ SV10 @ SV67 @ SV10 @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[571]) ).
thf(586,plain,
! [SV121: $i,SV190: $i,SV177: $i,SV68: $i,SV11: $i] :
( ( ( SV11 = SV68 )
= $true )
| ( ( between @ SV11 @ SV177 @ ( euclid1 @ SV11 @ SV177 @ SV68 @ SV190 @ SV121 ) )
= $true )
| ( ( between @ SV177 @ SV68 @ SV190 )
= $false )
| ( ( between @ SV11 @ SV68 @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[572]) ).
thf(587,plain,
! [SV122: $i,SV178: $i,SV191: $i,SV69: $i,SV12: $i] :
( ( ( SV12 = SV69 )
= $true )
| ( ( between @ SV12 @ SV191 @ ( euclid2 @ SV12 @ SV178 @ SV69 @ SV191 @ SV122 ) )
= $true )
| ( ( between @ SV178 @ SV69 @ SV191 )
= $false )
| ( ( between @ SV12 @ SV69 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(588,plain,
! [SV123: $i,SV192: $i,SV179: $i,SV70: $i,SV13: $i] :
( ( ( SV13 = SV70 )
= $true )
| ( ( between @ ( euclid1 @ SV13 @ SV179 @ SV70 @ SV192 @ SV123 ) @ SV123 @ ( euclid2 @ SV13 @ SV179 @ SV70 @ SV192 @ SV123 ) )
= $true )
| ( ( between @ SV179 @ SV70 @ SV192 )
= $false )
| ( ( between @ SV13 @ SV70 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[574]) ).
thf(589,plain,
! [SV193: $i,SV124: $i,SV158: $i,SV71: $i,SV14: $i] :
( ( ( ~ ( between @ SV14 @ SV71 @ SV158 ) )
= $true )
| ( ( ! [SY538: $i] :
( ~ ( between @ SV71 @ SY538 @ SV158 )
| ( between @ SV124 @ ( continuous @ SV14 @ SV71 @ SV124 @ SY538 @ SV158 @ SV193 ) @ SV193 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV158 @ SV14 @ SV193 )
= $false )
| ( ( equidistant @ SV14 @ SV71 @ SV14 @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[575]) ).
thf(590,plain,
! [SV194: $i,SV125: $i,SV159: $i,SV72: $i,SV15: $i] :
( ( ( ~ ( between @ SV15 @ SV72 @ SV159 ) )
= $true )
| ( ( ! [SY539: $i] :
( ~ ( between @ SV72 @ SY539 @ SV159 )
| ( equidistant @ SV15 @ SY539 @ SV15 @ ( continuous @ SV15 @ SV72 @ SV125 @ SY539 @ SV159 @ SV194 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV159 @ SV15 @ SV194 )
= $false )
| ( ( equidistant @ SV15 @ SV72 @ SV15 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[576]) ).
thf(591,plain,
! [SV82: $i,SV25: $i,SV200: $i,SV195: $i,SV167: $i,SV133: $i] :
( ( ( equidistant @ SV133 @ SV167 @ SV195 @ SV200 )
= $false )
| ( ( equidistant @ SV25 @ SV82 @ SV195 @ SV200 )
= $true )
| ( ( equidistant @ SV25 @ SV82 @ SV133 @ SV167 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[577]) ).
thf(592,plain,
! [SV136: $i,SV34: $i,SV201: $i,SV168: $i,SV196: $i,SV90: $i] :
( ( ( equidistant @ SV90 @ SV196 @ SV168 @ SV201 )
= $false )
| ( ( ~ ( between @ SV34 @ SV90 @ SV196 )
| ~ ( between @ SV136 @ SV168 @ SV201 )
| ( equidistant @ SV34 @ SV196 @ SV136 @ SV201 ) )
= $true )
| ( ( equidistant @ SV34 @ SV90 @ SV136 @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[578]) ).
thf(593,plain,
! [SV35: $i,SV181: $i,SV137: $i,SV91: $i] :
( ( ( equidistant @ SV91 @ SV137 @ SV91 @ SV181 )
= $false )
| ( ( ( SV35 = SV91 )
| ( SV137 = SV181 ) )
= $true )
| ( ( between @ SV35 @ SV91 @ SV181 )
= $false )
| ( ( between @ SV35 @ SV91 @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[579]) ).
thf(594,plain,
! [SV173: $i,SV171: $i,SV157: $i,SV63: $i,SV117: $i,SV205: $i,SV6: $i] :
( ( ( ! [SY543: $i] :
( ~ ( equidistant @ SV6 @ SV205 @ SV117 @ SY543 )
| ~ ( equidistant @ SV63 @ SV205 @ SV157 @ SY543 )
| ~ ( between @ SV6 @ SV63 @ SV171 )
| ~ ( between @ SV117 @ SV157 @ SV173 )
| ( SV6 = SV63 )
| ( equidistant @ SV171 @ SV205 @ SV173 @ SY543 ) ) )
= $true )
| ( ( equidistant @ SV63 @ SV171 @ SV157 @ SV173 )
= $false )
| ( ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(595,plain,
! [SV176: $i,SV10: $i,SV120: $i,SV67: $i,SV204: $i] :
( ( ( equidistant @ SV204 @ SV67 @ SV204 @ SV120 )
= $false )
| ( ( ( between @ SV10 @ SV176 @ SV204 )
| ( between @ SV176 @ SV204 @ SV10 )
| ( SV67 = SV120 )
| ( between @ SV204 @ SV10 @ SV176 ) )
= $true )
| ( ( equidistant @ SV176 @ SV67 @ SV176 @ SV120 )
= $false )
| ( ( equidistant @ SV10 @ SV67 @ SV10 @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[585]) ).
thf(596,plain,
! [SV193: $i,SV124: $i,SV158: $i,SV71: $i,SV14: $i] :
( ( ( between @ SV14 @ SV71 @ SV158 )
= $false )
| ( ( ! [SY538: $i] :
( ~ ( between @ SV71 @ SY538 @ SV158 )
| ( between @ SV124 @ ( continuous @ SV14 @ SV71 @ SV124 @ SY538 @ SV158 @ SV193 ) @ SV193 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV158 @ SV14 @ SV193 )
= $false )
| ( ( equidistant @ SV14 @ SV71 @ SV14 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[589]) ).
thf(597,plain,
! [SV194: $i,SV125: $i,SV159: $i,SV72: $i,SV15: $i] :
( ( ( between @ SV15 @ SV72 @ SV159 )
= $false )
| ( ( ! [SY539: $i] :
( ~ ( between @ SV72 @ SY539 @ SV159 )
| ( equidistant @ SV15 @ SY539 @ SV15 @ ( continuous @ SV15 @ SV72 @ SV125 @ SY539 @ SV159 @ SV194 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV159 @ SV15 @ SV194 )
= $false )
| ( ( equidistant @ SV15 @ SV72 @ SV15 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[590]) ).
thf(598,plain,
! [SV201: $i,SV168: $i,SV136: $i,SV196: $i,SV90: $i,SV34: $i] :
( ( ( ~ ( between @ SV34 @ SV90 @ SV196 ) )
= $true )
| ( ( ~ ( between @ SV136 @ SV168 @ SV201 )
| ( equidistant @ SV34 @ SV196 @ SV136 @ SV201 ) )
= $true )
| ( ( equidistant @ SV90 @ SV196 @ SV168 @ SV201 )
= $false )
| ( ( equidistant @ SV34 @ SV90 @ SV136 @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(599,plain,
! [SV181: $i,SV137: $i,SV91: $i,SV35: $i] :
( ( ( SV35 = SV91 )
= $true )
| ( ( SV137 = SV181 )
= $true )
| ( ( equidistant @ SV91 @ SV137 @ SV91 @ SV181 )
= $false )
| ( ( between @ SV35 @ SV91 @ SV181 )
= $false )
| ( ( between @ SV35 @ SV91 @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(600,plain,
! [SV173: $i,SV171: $i,SV157: $i,SV63: $i,SV206: $i,SV117: $i,SV205: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV205 @ SV117 @ SV206 )
| ~ ( equidistant @ SV63 @ SV205 @ SV157 @ SV206 )
| ~ ( between @ SV6 @ SV63 @ SV171 )
| ~ ( between @ SV117 @ SV157 @ SV173 )
| ( SV6 = SV63 )
| ( equidistant @ SV171 @ SV205 @ SV173 @ SV206 ) )
= $true )
| ( ( equidistant @ SV63 @ SV171 @ SV157 @ SV173 )
= $false )
| ( ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(601,plain,
! [SV120: $i,SV67: $i,SV204: $i,SV176: $i,SV10: $i] :
( ( ( between @ SV10 @ SV176 @ SV204 )
= $true )
| ( ( ( between @ SV176 @ SV204 @ SV10 )
| ( SV67 = SV120 )
| ( between @ SV204 @ SV10 @ SV176 ) )
= $true )
| ( ( equidistant @ SV204 @ SV67 @ SV204 @ SV120 )
= $false )
| ( ( equidistant @ SV176 @ SV67 @ SV176 @ SV120 )
= $false )
| ( ( equidistant @ SV10 @ SV67 @ SV10 @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(602,plain,
! [SV193: $i,SV14: $i,SV124: $i,SV158: $i,SV207: $i,SV71: $i] :
( ( ( ~ ( between @ SV71 @ SV207 @ SV158 )
| ( between @ SV124 @ ( continuous @ SV14 @ SV71 @ SV124 @ SV207 @ SV158 @ SV193 ) @ SV193 ) )
= $true )
| ( ( between @ SV14 @ SV71 @ SV158 )
= $false )
| ( ( equidistant @ SV14 @ SV158 @ SV14 @ SV193 )
= $false )
| ( ( equidistant @ SV14 @ SV71 @ SV14 @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(603,plain,
! [SV194: $i,SV125: $i,SV15: $i,SV159: $i,SV208: $i,SV72: $i] :
( ( ( ~ ( between @ SV72 @ SV208 @ SV159 )
| ( equidistant @ SV15 @ SV208 @ SV15 @ ( continuous @ SV15 @ SV72 @ SV125 @ SV208 @ SV159 @ SV194 ) ) )
= $true )
| ( ( between @ SV15 @ SV72 @ SV159 )
= $false )
| ( ( equidistant @ SV15 @ SV159 @ SV15 @ SV194 )
= $false )
| ( ( equidistant @ SV15 @ SV72 @ SV15 @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(604,plain,
! [SV201: $i,SV168: $i,SV136: $i,SV196: $i,SV90: $i,SV34: $i] :
( ( ( between @ SV34 @ SV90 @ SV196 )
= $false )
| ( ( ~ ( between @ SV136 @ SV168 @ SV201 )
| ( equidistant @ SV34 @ SV196 @ SV136 @ SV201 ) )
= $true )
| ( ( equidistant @ SV90 @ SV196 @ SV168 @ SV201 )
= $false )
| ( ( equidistant @ SV34 @ SV90 @ SV136 @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[598]) ).
thf(605,plain,
! [SV173: $i,SV171: $i,SV157: $i,SV63: $i,SV206: $i,SV117: $i,SV205: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV205 @ SV117 @ SV206 ) )
= $true )
| ( ( ~ ( equidistant @ SV63 @ SV205 @ SV157 @ SV206 )
| ~ ( between @ SV6 @ SV63 @ SV171 )
| ~ ( between @ SV117 @ SV157 @ SV173 )
| ( SV6 = SV63 )
| ( equidistant @ SV171 @ SV205 @ SV173 @ SV206 ) )
= $true )
| ( ( equidistant @ SV63 @ SV171 @ SV157 @ SV173 )
= $false )
| ( ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[600]) ).
thf(606,plain,
! [SV120: $i,SV67: $i,SV10: $i,SV204: $i,SV176: $i] :
( ( ( between @ SV176 @ SV204 @ SV10 )
= $true )
| ( ( ( SV67 = SV120 )
| ( between @ SV204 @ SV10 @ SV176 ) )
= $true )
| ( ( between @ SV10 @ SV176 @ SV204 )
= $true )
| ( ( equidistant @ SV204 @ SV67 @ SV204 @ SV120 )
= $false )
| ( ( equidistant @ SV176 @ SV67 @ SV176 @ SV120 )
= $false )
| ( ( equidistant @ SV10 @ SV67 @ SV10 @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[601]) ).
thf(607,plain,
! [SV193: $i,SV14: $i,SV124: $i,SV158: $i,SV207: $i,SV71: $i] :
( ( ( ~ ( between @ SV71 @ SV207 @ SV158 ) )
= $true )
| ( ( between @ SV124 @ ( continuous @ SV14 @ SV71 @ SV124 @ SV207 @ SV158 @ SV193 ) @ SV193 )
= $true )
| ( ( between @ SV14 @ SV71 @ SV158 )
= $false )
| ( ( equidistant @ SV14 @ SV158 @ SV14 @ SV193 )
= $false )
| ( ( equidistant @ SV14 @ SV71 @ SV14 @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[602]) ).
thf(608,plain,
! [SV194: $i,SV125: $i,SV15: $i,SV159: $i,SV208: $i,SV72: $i] :
( ( ( ~ ( between @ SV72 @ SV208 @ SV159 ) )
= $true )
| ( ( equidistant @ SV15 @ SV208 @ SV15 @ ( continuous @ SV15 @ SV72 @ SV125 @ SV208 @ SV159 @ SV194 ) )
= $true )
| ( ( between @ SV15 @ SV72 @ SV159 )
= $false )
| ( ( equidistant @ SV15 @ SV159 @ SV15 @ SV194 )
= $false )
| ( ( equidistant @ SV15 @ SV72 @ SV15 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[603]) ).
thf(609,plain,
! [SV90: $i,SV196: $i,SV34: $i,SV201: $i,SV168: $i,SV136: $i] :
( ( ( ~ ( between @ SV136 @ SV168 @ SV201 ) )
= $true )
| ( ( equidistant @ SV34 @ SV196 @ SV136 @ SV201 )
= $true )
| ( ( between @ SV34 @ SV90 @ SV196 )
= $false )
| ( ( equidistant @ SV90 @ SV196 @ SV168 @ SV201 )
= $false )
| ( ( equidistant @ SV34 @ SV90 @ SV136 @ SV168 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[604]) ).
thf(610,plain,
! [SV173: $i,SV171: $i,SV157: $i,SV63: $i,SV206: $i,SV117: $i,SV205: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV205 @ SV117 @ SV206 )
= $false )
| ( ( ~ ( equidistant @ SV63 @ SV205 @ SV157 @ SV206 )
| ~ ( between @ SV6 @ SV63 @ SV171 )
| ~ ( between @ SV117 @ SV157 @ SV173 )
| ( SV6 = SV63 )
| ( equidistant @ SV171 @ SV205 @ SV173 @ SV206 ) )
= $true )
| ( ( equidistant @ SV63 @ SV171 @ SV157 @ SV173 )
= $false )
| ( ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[605]) ).
thf(611,plain,
! [SV176: $i,SV10: $i,SV204: $i,SV120: $i,SV67: $i] :
( ( ( SV67 = SV120 )
= $true )
| ( ( between @ SV204 @ SV10 @ SV176 )
= $true )
| ( ( between @ SV176 @ SV204 @ SV10 )
= $true )
| ( ( between @ SV10 @ SV176 @ SV204 )
= $true )
| ( ( equidistant @ SV204 @ SV67 @ SV204 @ SV120 )
= $false )
| ( ( equidistant @ SV176 @ SV67 @ SV176 @ SV120 )
= $false )
| ( ( equidistant @ SV10 @ SV67 @ SV10 @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[606]) ).
thf(612,plain,
! [SV193: $i,SV14: $i,SV124: $i,SV158: $i,SV207: $i,SV71: $i] :
( ( ( between @ SV71 @ SV207 @ SV158 )
= $false )
| ( ( between @ SV124 @ ( continuous @ SV14 @ SV71 @ SV124 @ SV207 @ SV158 @ SV193 ) @ SV193 )
= $true )
| ( ( between @ SV14 @ SV71 @ SV158 )
= $false )
| ( ( equidistant @ SV14 @ SV158 @ SV14 @ SV193 )
= $false )
| ( ( equidistant @ SV14 @ SV71 @ SV14 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[607]) ).
thf(613,plain,
! [SV194: $i,SV125: $i,SV15: $i,SV159: $i,SV208: $i,SV72: $i] :
( ( ( between @ SV72 @ SV208 @ SV159 )
= $false )
| ( ( equidistant @ SV15 @ SV208 @ SV15 @ ( continuous @ SV15 @ SV72 @ SV125 @ SV208 @ SV159 @ SV194 ) )
= $true )
| ( ( between @ SV15 @ SV72 @ SV159 )
= $false )
| ( ( equidistant @ SV15 @ SV159 @ SV15 @ SV194 )
= $false )
| ( ( equidistant @ SV15 @ SV72 @ SV15 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[608]) ).
thf(614,plain,
! [SV90: $i,SV196: $i,SV34: $i,SV201: $i,SV168: $i,SV136: $i] :
( ( ( between @ SV136 @ SV168 @ SV201 )
= $false )
| ( ( equidistant @ SV34 @ SV196 @ SV136 @ SV201 )
= $true )
| ( ( between @ SV34 @ SV90 @ SV196 )
= $false )
| ( ( equidistant @ SV90 @ SV196 @ SV168 @ SV201 )
= $false )
| ( ( equidistant @ SV34 @ SV90 @ SV136 @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[609]) ).
thf(615,plain,
! [SV173: $i,SV117: $i,SV171: $i,SV6: $i,SV206: $i,SV157: $i,SV205: $i,SV63: $i] :
( ( ( ~ ( equidistant @ SV63 @ SV205 @ SV157 @ SV206 ) )
= $true )
| ( ( ~ ( between @ SV6 @ SV63 @ SV171 )
| ~ ( between @ SV117 @ SV157 @ SV173 )
| ( SV6 = SV63 )
| ( equidistant @ SV171 @ SV205 @ SV173 @ SV206 ) )
= $true )
| ( ( equidistant @ SV6 @ SV205 @ SV117 @ SV206 )
= $false )
| ( ( equidistant @ SV63 @ SV171 @ SV157 @ SV173 )
= $false )
| ( ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[610]) ).
thf(616,plain,
! [SV173: $i,SV117: $i,SV171: $i,SV6: $i,SV206: $i,SV157: $i,SV205: $i,SV63: $i] :
( ( ( equidistant @ SV63 @ SV205 @ SV157 @ SV206 )
= $false )
| ( ( ~ ( between @ SV6 @ SV63 @ SV171 )
| ~ ( between @ SV117 @ SV157 @ SV173 )
| ( SV6 = SV63 )
| ( equidistant @ SV171 @ SV205 @ SV173 @ SV206 ) )
= $true )
| ( ( equidistant @ SV6 @ SV205 @ SV117 @ SV206 )
= $false )
| ( ( equidistant @ SV63 @ SV171 @ SV157 @ SV173 )
= $false )
| ( ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[615]) ).
thf(617,plain,
! [SV206: $i,SV205: $i,SV173: $i,SV157: $i,SV117: $i,SV171: $i,SV63: $i,SV6: $i] :
( ( ( ~ ( between @ SV6 @ SV63 @ SV171 ) )
= $true )
| ( ( ~ ( between @ SV117 @ SV157 @ SV173 )
| ( SV6 = SV63 )
| ( equidistant @ SV171 @ SV205 @ SV173 @ SV206 ) )
= $true )
| ( ( equidistant @ SV63 @ SV205 @ SV157 @ SV206 )
= $false )
| ( ( equidistant @ SV6 @ SV205 @ SV117 @ SV206 )
= $false )
| ( ( equidistant @ SV63 @ SV171 @ SV157 @ SV173 )
= $false )
| ( ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[616]) ).
thf(618,plain,
! [SV206: $i,SV205: $i,SV173: $i,SV157: $i,SV117: $i,SV171: $i,SV63: $i,SV6: $i] :
( ( ( between @ SV6 @ SV63 @ SV171 )
= $false )
| ( ( ~ ( between @ SV117 @ SV157 @ SV173 )
| ( SV6 = SV63 )
| ( equidistant @ SV171 @ SV205 @ SV173 @ SV206 ) )
= $true )
| ( ( equidistant @ SV63 @ SV205 @ SV157 @ SV206 )
= $false )
| ( ( equidistant @ SV6 @ SV205 @ SV117 @ SV206 )
= $false )
| ( ( equidistant @ SV63 @ SV171 @ SV157 @ SV173 )
= $false )
| ( ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[617]) ).
thf(619,plain,
! [SV206: $i,SV205: $i,SV171: $i,SV63: $i,SV6: $i,SV173: $i,SV157: $i,SV117: $i] :
( ( ( ~ ( between @ SV117 @ SV157 @ SV173 ) )
= $true )
| ( ( ( SV6 = SV63 )
| ( equidistant @ SV171 @ SV205 @ SV173 @ SV206 ) )
= $true )
| ( ( between @ SV6 @ SV63 @ SV171 )
= $false )
| ( ( equidistant @ SV63 @ SV205 @ SV157 @ SV206 )
= $false )
| ( ( equidistant @ SV6 @ SV205 @ SV117 @ SV206 )
= $false )
| ( ( equidistant @ SV63 @ SV171 @ SV157 @ SV173 )
= $false )
| ( ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[618]) ).
thf(620,plain,
! [SV206: $i,SV205: $i,SV171: $i,SV63: $i,SV6: $i,SV173: $i,SV157: $i,SV117: $i] :
( ( ( between @ SV117 @ SV157 @ SV173 )
= $false )
| ( ( ( SV6 = SV63 )
| ( equidistant @ SV171 @ SV205 @ SV173 @ SV206 ) )
= $true )
| ( ( between @ SV6 @ SV63 @ SV171 )
= $false )
| ( ( equidistant @ SV63 @ SV205 @ SV157 @ SV206 )
= $false )
| ( ( equidistant @ SV6 @ SV205 @ SV117 @ SV206 )
= $false )
| ( ( equidistant @ SV63 @ SV171 @ SV157 @ SV173 )
= $false )
| ( ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[619]) ).
thf(621,plain,
! [SV157: $i,SV117: $i,SV206: $i,SV173: $i,SV205: $i,SV171: $i,SV63: $i,SV6: $i] :
( ( ( SV6 = SV63 )
= $true )
| ( ( equidistant @ SV171 @ SV205 @ SV173 @ SV206 )
= $true )
| ( ( between @ SV117 @ SV157 @ SV173 )
= $false )
| ( ( between @ SV6 @ SV63 @ SV171 )
= $false )
| ( ( equidistant @ SV63 @ SV205 @ SV157 @ SV206 )
= $false )
| ( ( equidistant @ SV6 @ SV205 @ SV117 @ SV206 )
= $false )
| ( ( equidistant @ SV63 @ SV171 @ SV157 @ SV173 )
= $false )
| ( ( equidistant @ SV6 @ SV63 @ SV117 @ SV157 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(622,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[172,621,614,613,612,611,599,591,588,587,586,583,582,581,580,570,569,566,565,562,561,560,559,558,535,534,529,505,500,499,498,497,496,495,494,473,449,447,430,429,411,409,408,404,391,383,360,347,344,343,342,336,333,332,321,320,305,304,300,299,298,274,252,251,250,240,239,174,173]) ).
thf(623,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[622]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : GEO048-3 : TPTP v8.1.0. Released v1.0.0.
% 0.08/0.15 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.16/0.36 % Computer : n010.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 600
% 0.16/0.37 % DateTime : Sat Jun 18 01:23:38 EDT 2022
% 0.16/0.37 % CPUTime :
% 0.23/0.48 .
% 0.23/0.49
% 0.23/0.49 No.of.Axioms: 68
% 0.23/0.49
% 0.23/0.49 Length.of.Defs: 0
% 0.23/0.49
% 0.23/0.49 Contains.Choice.Funs: false
% 0.23/0.52 .
% 0.23/0.57 (rf:0,axioms:68,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:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:70,loop_count:0,foatp_calls:0,translation:fof_full).......................................
% 0.75/1.02
% 0.75/1.02 ********************************
% 0.75/1.02 * All subproblems solved! *
% 0.75/1.02 ********************************
% 0.75/1.02 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:68,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:622,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.93/1.12
% 0.93/1.12 %**** Beginning of derivation protocol ****
% 0.93/1.12 % SZS output start CNFRefutation
% See solution above
% 0.93/1.12
% 0.93/1.12 %**** End of derivation protocol ****
% 0.93/1.12 %**** no. of clauses in derivation: 623 ****
% 0.93/1.12 %**** clause counter: 622 ****
% 0.93/1.12
% 0.93/1.12 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:68,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:10,ordering:none,proof_output:1,protocol_output:false,clause_count:622,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------