TSTP Solution File: GEO045-3 by LEO-II---1.7.0
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%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GEO045-3 : 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 : n004.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 05:06:27 EDT 2022
% Result : Unsatisfiable 0.68s 0.98s
% Output : CNFRefutation 0.83s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 74
% Syntax : Number of formulae : 565 ( 327 unt; 15 typ; 0 def)
% Number of atoms : 3380 (1172 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 7705 ( 745 ~;1174 |; 0 &;5786 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 9 con; 0-6 aty)
% Number of variables : 2203 ( 0 ^2203 !; 0 ?;2203 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_between,type,
between: $i > $i > $i > $o ).
thf(tp_continuous,type,
continuous: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_equidistant,type,
equidistant: $i > $i > $i > $i > $o ).
thf(tp_euclid1,type,
euclid1: $i > $i > $i > $i > $i > $i ).
thf(tp_euclid2,type,
euclid2: $i > $i > $i > $i > $i > $i ).
thf(tp_extension,type,
extension: $i > $i > $i > $i > $i ).
thf(tp_inner_pasch,type,
inner_pasch: $i > $i > $i > $i > $i > $i ).
thf(tp_lower_dimension_point_1,type,
lower_dimension_point_1: $i ).
thf(tp_lower_dimension_point_2,type,
lower_dimension_point_2: $i ).
thf(tp_lower_dimension_point_3,type,
lower_dimension_point_3: $i ).
thf(tp_reflection,type,
reflection: $i > $i > $i ).
thf(tp_u,type,
u: $i ).
thf(tp_v,type,
v: $i ).
thf(tp_w,type,
w: $i ).
thf(tp_x,type,
x: $i ).
thf(1,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ W @ X )
| ( V = W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b6) ).
thf(2,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ X )
| ( between @ V @ W @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b5) ).
thf(3,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ W @ X )
| ( between @ U @ V @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b4) ).
thf(4,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( U = V )
| ( V = W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_2) ).
thf(5,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V )
| ( V = W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_1) ).
thf(6,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b3) ).
thf(7,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).
thf(8,axiom,
! [U: $i,V: $i] : ( between @ U @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
thf(9,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
thf(10,axiom,
! [U: $i,W: $i,X: $i,V: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ( between @ V @ W @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).
thf(11,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
thf(12,axiom,
! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).
thf(13,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).
thf(14,axiom,
! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_3) ).
thf(15,axiom,
! [W: $i,X: $i,Y: $i,Z: $i,U: $i,V: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ( ( extension @ U @ V @ W @ X )
= ( extension @ U @ V @ Y @ Z ) )
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_2) ).
thf(16,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( U = V )
| ( W
= ( extension @ U @ V @ V @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_1) ).
thf(17,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ V @ X )
| ~ ( equidistant @ V @ W @ V @ X )
| ( U = V )
| ( W = X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9) ).
thf(18,axiom,
! [U: $i,V: $i,U1: $i,V1: $i,W: $i,W1: $i] :
( ~ ( equidistant @ U @ V @ U1 @ V1 )
| ~ ( equidistant @ V @ W @ V1 @ W1 )
| ~ ( between @ U @ V @ W )
| ~ ( between @ U1 @ V1 @ W1 )
| ( equidistant @ U @ W @ U1 @ W1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8) ).
thf(19,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
thf(20,axiom,
! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
thf(21,axiom,
! [U: $i] :
( U
= ( reflection @ U @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).
thf(22,axiom,
! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_1) ).
thf(23,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
thf(24,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).
thf(25,axiom,
! [Y: $i,U: $i,V: $i,W: $i,X: $i] :
( ( Y
!= ( extension @ U @ V @ W @ X ) )
| ( between @ U @ V @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b0) ).
thf(26,axiom,
! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
thf(27,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ~ ( equidistant @ W @ X @ Y @ Z )
| ( equidistant @ U @ V @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5) ).
thf(28,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_5) ).
thf(29,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_4) ).
thf(30,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_3) ).
thf(31,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_2) ).
thf(32,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_1) ).
thf(33,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3) ).
thf(34,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
thf(35,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
thf(36,axiom,
! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
thf(37,axiom,
! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).
thf(38,axiom,
! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity1) ).
thf(39,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid3) ).
thf(40,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid2) ).
thf(41,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid1) ).
thf(42,axiom,
! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ W @ X @ V )
| ~ ( equidistant @ Y @ W @ Y @ V )
| ~ ( equidistant @ Z @ W @ Z @ V )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y )
| ( W = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_dimension) ).
thf(43,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(44,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(45,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(46,axiom,
! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ Y @ X @ W )
| ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch2) ).
thf(47,axiom,
! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ Y @ X @ W )
| ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch1) ).
thf(48,axiom,
! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(49,axiom,
! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i,V: $i,V1: $i] :
( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
| ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
| ~ ( equidistant @ X @ V @ X1 @ V1 )
| ~ ( equidistant @ Y @ V @ Y1 @ V1 )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equidistant @ Z @ V @ Z1 @ V1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_five_segment) ).
thf(50,axiom,
! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).
thf(51,axiom,
! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).
thf(52,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(53,axiom,
! [X: $i,Y: $i,Z: $i,V: $i,V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
thf(54,axiom,
! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(55,axiom,
v != w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_not_w) ).
thf(56,axiom,
between @ v @ w @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_between_v_and_x) ).
thf(57,axiom,
between @ u @ v @ w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
thf(58,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(59,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[58]) ).
thf(60,negated_conjecture,
~ ( between @ u @ v @ x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_v_between_u_and_x) ).
thf(61,plain,
$false = $false,
inference(unfold_def,[status(thm)],[59]) ).
thf(62,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)],[1]) ).
thf(63,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)],[2]) ).
thf(64,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)],[3]) ).
thf(65,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)],[4]) ).
thf(66,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)],[5]) ).
thf(67,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(68,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(69,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(70,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(71,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)],[10]) ).
thf(72,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(73,plain,
( ( ! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(74,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(75,plain,
( ( ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(76,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)],[15]) ).
thf(77,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)],[16]) ).
thf(78,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)],[17]) ).
thf(79,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)],[18]) ).
thf(80,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(81,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(82,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(83,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(84,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(85,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(86,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)],[25]) ).
thf(87,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(88,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)],[27]) ).
thf(89,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)],[28]) ).
thf(90,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)],[29]) ).
thf(91,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)],[30]) ).
thf(92,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)],[31]) ).
thf(93,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)],[32]) ).
thf(94,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)],[33]) ).
thf(95,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)],[34]) ).
thf(96,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(97,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(98,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)],[37]) ).
thf(99,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)],[38]) ).
thf(100,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)],[39]) ).
thf(101,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)],[40]) ).
thf(102,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)],[41]) ).
thf(103,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)],[42]) ).
thf(104,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(105,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[44]) ).
thf(106,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(107,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)],[46]) ).
thf(108,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)],[47]) ).
thf(109,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[48]) ).
thf(110,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)],[49]) ).
thf(111,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(112,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(113,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(114,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)],[53]) ).
thf(115,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[54]) ).
thf(116,plain,
( ( ( v != w ) )
= $true ),
inference(unfold_def,[status(thm)],[55]) ).
thf(117,plain,
( ( between @ v @ w @ x )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(118,plain,
( ( between @ u @ v @ w )
= $true ),
inference(unfold_def,[status(thm)],[57]) ).
thf(119,plain,
( ( ~ ( between @ u @ v @ x ) )
= $true ),
inference(unfold_def,[status(thm)],[60]) ).
thf(120,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[61]) ).
thf(121,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)],[62]) ).
thf(122,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)],[63]) ).
thf(123,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)],[64]) ).
thf(124,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)],[71]) ).
thf(125,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)],[76]) ).
thf(126,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)],[78]) ).
thf(127,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)],[79]) ).
thf(128,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(129,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[83]) ).
thf(130,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)],[86]) ).
thf(131,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)],[88]) ).
thf(132,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)],[98]) ).
thf(133,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)],[99]) ).
thf(134,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)],[100]) ).
thf(135,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)],[101]) ).
thf(136,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)],[102]) ).
thf(137,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)],[103]) ).
thf(138,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [Y: $i,X: $i] :
( ~ ( between @ Y @ X @ W )
| ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[107]) ).
thf(139,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)],[108]) ).
thf(140,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)],[110]) ).
thf(141,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[113]) ).
thf(142,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)],[114]) ).
thf(143,plain,
( ( ( v != w ) )
= $true ),
inference(extcnf_combined,[status(esa)],[116]) ).
thf(144,plain,
( ( ~ ( between @ u @ v @ x ) )
= $true ),
inference(copy,[status(thm)],[119]) ).
thf(145,plain,
( ( between @ u @ v @ w )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(146,plain,
( ( between @ v @ w @ x )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(147,plain,
( ( ( v != w ) )
= $true ),
inference(copy,[status(thm)],[143]) ).
thf(148,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(copy,[status(thm)],[115]) ).
thf(149,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)],[142]) ).
thf(150,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[141]) ).
thf(151,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(152,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(153,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)],[140]) ).
thf(154,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[109]) ).
thf(155,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)],[139]) ).
thf(156,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)],[138]) ).
thf(157,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(158,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(copy,[status(thm)],[105]) ).
thf(159,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(copy,[status(thm)],[104]) ).
thf(160,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)],[137]) ).
thf(161,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)],[136]) ).
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(copy,[status(thm)],[135]) ).
thf(163,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)],[134]) ).
thf(164,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)],[133]) ).
thf(165,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)],[132]) ).
thf(166,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(167,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(168,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(169,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[94]) ).
thf(170,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[93]) ).
thf(171,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[92]) ).
thf(172,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(173,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[90]) ).
thf(174,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(175,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)],[131]) ).
thf(176,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(177,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)],[130]) ).
thf(178,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(179,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(180,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(181,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(182,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[128]) ).
thf(183,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(184,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)],[127]) ).
thf(185,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)],[126]) ).
thf(186,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( U = V )
| ( W
= ( extension @ U @ V @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(187,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)],[125]) ).
thf(188,plain,
( ( ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(189,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(190,plain,
( ( ! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(191,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(192,plain,
( ( ! [U: $i,W: $i,X: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ! [V: $i] : ( between @ V @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[124]) ).
thf(193,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(194,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(195,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(196,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(197,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(198,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( U = V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(199,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)],[123]) ).
thf(200,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)],[122]) ).
thf(201,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)],[121]) ).
thf(202,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(203,plain,
( ( between @ u @ v @ x )
= $false ),
inference(extcnf_not_pos,[status(thm)],[144]) ).
thf(204,plain,
( ( v = w )
= $false ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(205,plain,
! [SV1: $i] :
( ( ! [SY188: $i] : ( equidistant @ SV1 @ SY188 @ SY188 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(206,plain,
! [SV2: $i] :
( ( ! [SY189: $i,SY190: $i,SY191: $i] :
( ~ ( equidistant @ SV2 @ SY189 @ SY190 @ SY191 )
| ! [SY192: $i,SY193: $i] :
( ~ ( equidistant @ SV2 @ SY189 @ SY192 @ SY193 )
| ( equidistant @ SY190 @ SY191 @ SY192 @ SY193 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(207,plain,
! [SV3: $i] :
( ( ! [SY194: $i] :
( ! [SY195: $i] :
~ ( equidistant @ SV3 @ SY194 @ SY195 @ SY195 )
| ( SV3 = SY194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(208,plain,
! [SV4: $i] :
( ( ! [SY196: $i,SY197: $i,SY198: $i] : ( between @ SV4 @ SY196 @ ( extension @ SV4 @ SY196 @ SY197 @ SY198 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(209,plain,
! [SV5: $i] :
( ( ! [SY199: $i,SY200: $i,SY201: $i] : ( equidistant @ SV5 @ ( extension @ SY199 @ SV5 @ SY200 @ SY201 ) @ SY200 @ SY201 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(210,plain,
! [SV6: $i] :
( ( ! [SY202: $i,SY203: $i,SY204: $i,SY205: $i,SY206: $i] :
( ~ ( equidistant @ SV6 @ SY202 @ SY203 @ SY204 )
| ~ ( equidistant @ SY202 @ SY205 @ SY204 @ SY206 )
| ! [SY207: $i,SY208: $i] :
( ~ ( equidistant @ SV6 @ SY207 @ SY203 @ SY208 )
| ~ ( equidistant @ SY202 @ SY207 @ SY204 @ SY208 )
| ~ ( between @ SV6 @ SY202 @ SY205 )
| ~ ( between @ SY203 @ SY204 @ SY206 )
| ( SV6 = SY202 )
| ( equidistant @ SY205 @ SY207 @ SY206 @ SY208 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(211,plain,
! [SV7: $i] :
( ( ! [SY209: $i] :
( ~ ( between @ SV7 @ SY209 @ SV7 )
| ( SV7 = SY209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(212,plain,
! [SV8: $i] :
( ( ! [SY210: $i,SY211: $i] :
( ~ ( between @ SV8 @ SY210 @ SY211 )
| ! [SY212: $i,SY213: $i] :
( ~ ( between @ SY212 @ SY213 @ SY211 )
| ( between @ SY210 @ ( inner_pasch @ SV8 @ SY210 @ SY211 @ SY213 @ SY212 ) @ SY212 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(213,plain,
! [SV9: $i] :
( ( ! [SY214: $i,SY215: $i] :
( ~ ( between @ SV9 @ SY214 @ SY215 )
| ! [SY216: $i,SY217: $i] :
( ~ ( between @ SY216 @ SY217 @ SY215 )
| ( between @ SY217 @ ( inner_pasch @ SV9 @ SY214 @ SY215 @ SY217 @ SY216 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(214,plain,
( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(215,plain,
( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(216,plain,
( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(217,plain,
! [SV10: $i] :
( ( ! [SY218: $i,SY219: $i] :
( ~ ( equidistant @ SV10 @ SY218 @ SV10 @ SY219 )
| ! [SY220: $i] :
( ~ ( equidistant @ SY220 @ SY218 @ SY220 @ SY219 )
| ! [SY221: $i] :
( ~ ( equidistant @ SY221 @ SY218 @ SY221 @ SY219 )
| ( between @ SV10 @ SY220 @ SY221 )
| ( between @ SY220 @ SY221 @ SV10 )
| ( SY218 = SY219 )
| ( between @ SY221 @ SV10 @ SY220 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(218,plain,
! [SV11: $i] :
( ( ! [SY222: $i,SY223: $i] :
( ~ ( between @ SV11 @ SY222 @ SY223 )
| ! [SY224: $i,SY225: $i] :
( ~ ( between @ SY224 @ SY222 @ SY225 )
| ( SV11 = SY222 )
| ( between @ SV11 @ SY224 @ ( euclid1 @ SV11 @ SY224 @ SY222 @ SY225 @ SY223 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(219,plain,
! [SV12: $i] :
( ( ! [SY226: $i,SY227: $i] :
( ~ ( between @ SV12 @ SY226 @ SY227 )
| ! [SY228: $i,SY229: $i] :
( ~ ( between @ SY228 @ SY226 @ SY229 )
| ( SV12 = SY226 )
| ( between @ SV12 @ SY229 @ ( euclid2 @ SV12 @ SY228 @ SY226 @ SY229 @ SY227 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(220,plain,
! [SV13: $i] :
( ( ! [SY230: $i,SY231: $i] :
( ~ ( between @ SV13 @ SY230 @ SY231 )
| ! [SY232: $i,SY233: $i] :
( ~ ( between @ SY232 @ SY230 @ SY233 )
| ( SV13 = SY230 )
| ( between @ ( euclid1 @ SV13 @ SY232 @ SY230 @ SY233 @ SY231 ) @ SY231 @ ( euclid2 @ SV13 @ SY232 @ SY230 @ SY233 @ SY231 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(221,plain,
! [SV14: $i] :
( ( ! [SY234: $i,SY235: $i,SY236: $i] :
( ~ ( equidistant @ SV14 @ SY234 @ SV14 @ SY235 )
| ! [SY237: $i] :
( ~ ( equidistant @ SV14 @ SY236 @ SV14 @ SY237 )
| ~ ( between @ SV14 @ SY234 @ SY236 )
| ! [SY238: $i] :
( ~ ( between @ SY234 @ SY238 @ SY236 )
| ( between @ SY235 @ ( continuous @ SV14 @ SY234 @ SY235 @ SY238 @ SY236 @ SY237 ) @ SY237 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(222,plain,
! [SV15: $i] :
( ( ! [SY239: $i,SY240: $i,SY241: $i] :
( ~ ( equidistant @ SV15 @ SY239 @ SV15 @ SY240 )
| ! [SY242: $i] :
( ~ ( equidistant @ SV15 @ SY241 @ SV15 @ SY242 )
| ~ ( between @ SV15 @ SY239 @ SY241 )
| ! [SY243: $i] :
( ~ ( between @ SY239 @ SY243 @ SY241 )
| ( equidistant @ SV15 @ SY243 @ SV15 @ ( continuous @ SV15 @ SY239 @ SY240 @ SY243 @ SY241 @ SY242 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(223,plain,
! [SV16: $i] :
( ( ! [SY244: $i] :
( ( reflection @ SV16 @ SY244 )
= ( extension @ SV16 @ SY244 @ SV16 @ SY244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(224,plain,
! [SV17: $i] :
( ( ! [SY245: $i] : ( equidistant @ SV17 @ SY245 @ SV17 @ SY245 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(225,plain,
! [SV18: $i] :
( ( ! [SY246: $i,SY247: $i,SY248: $i] :
( ~ ( equidistant @ SV18 @ SY246 @ SY247 @ SY248 )
| ( equidistant @ SY247 @ SY248 @ SV18 @ SY246 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(226,plain,
! [SV19: $i] :
( ( ! [SY249: $i,SY250: $i,SY251: $i] :
( ~ ( equidistant @ SV19 @ SY249 @ SY250 @ SY251 )
| ( equidistant @ SY249 @ SV19 @ SY250 @ SY251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(227,plain,
! [SV20: $i] :
( ( ! [SY252: $i,SY253: $i,SY254: $i] :
( ~ ( equidistant @ SV20 @ SY252 @ SY253 @ SY254 )
| ( equidistant @ SV20 @ SY252 @ SY254 @ SY253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(228,plain,
! [SV21: $i] :
( ( ! [SY255: $i,SY256: $i,SY257: $i] :
( ~ ( equidistant @ SV21 @ SY255 @ SY256 @ SY257 )
| ( equidistant @ SY255 @ SV21 @ SY257 @ SY256 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(229,plain,
! [SV22: $i] :
( ( ! [SY258: $i,SY259: $i,SY260: $i] :
( ~ ( equidistant @ SV22 @ SY258 @ SY259 @ SY260 )
| ( equidistant @ SY259 @ SY260 @ SY258 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(230,plain,
! [SV23: $i] :
( ( ! [SY261: $i,SY262: $i,SY263: $i] :
( ~ ( equidistant @ SV23 @ SY261 @ SY262 @ SY263 )
| ( equidistant @ SY263 @ SY262 @ SV23 @ SY261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(231,plain,
! [SV24: $i] :
( ( ! [SY264: $i,SY265: $i,SY266: $i] :
( ~ ( equidistant @ SV24 @ SY264 @ SY265 @ SY266 )
| ( equidistant @ SY266 @ SY265 @ SY264 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(232,plain,
! [SV25: $i] :
( ( ! [SY267: $i,SY268: $i,SY269: $i] :
( ~ ( equidistant @ SV25 @ SY267 @ SY268 @ SY269 )
| ! [SY270: $i,SY271: $i] :
( ~ ( equidistant @ SY268 @ SY269 @ SY270 @ SY271 )
| ( equidistant @ SV25 @ SY267 @ SY270 @ SY271 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(233,plain,
! [SV26: $i] :
( ( ! [SY272: $i,SY273: $i] :
( SV26
= ( extension @ SY272 @ SV26 @ SY273 @ SY273 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(234,plain,
! [SV27: $i] :
( ( ! [SY274: $i,SY275: $i] :
( ! [SY276: $i,SY277: $i] :
( SV27
!= ( extension @ SY274 @ SY275 @ SY276 @ SY277 ) )
| ( between @ SY274 @ SY275 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(235,plain,
! [SV28: $i] :
( ( ! [SY278: $i] : ( between @ SV28 @ SY278 @ ( reflection @ SV28 @ SY278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(236,plain,
! [SV29: $i] :
( ( ! [SY279: $i] : ( equidistant @ SV29 @ ( reflection @ SY279 @ SV29 ) @ SY279 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(237,plain,
! [SV30: $i] :
( ( ! [SY280: $i] :
( ( SV30 != SY280 )
| ( SY280
= ( reflection @ SV30 @ SY280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(238,plain,
! [SV31: $i] :
( ( SV31
= ( reflection @ SV31 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(239,plain,
! [SV32: $i] :
( ( ! [SY281: $i] :
( ( SV32
!= ( reflection @ SY281 @ SV32 ) )
| ( SY281 = SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(240,plain,
! [SV33: $i] :
( ( ! [SY282: $i] : ( equidistant @ SV33 @ SV33 @ SY282 @ SY282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(241,plain,
! [SV34: $i] :
( ( ! [SY283: $i,SY284: $i,SY285: $i] :
( ~ ( equidistant @ SV34 @ SY283 @ SY284 @ SY285 )
| ! [SY286: $i,SY287: $i] :
( ~ ( equidistant @ SY283 @ SY286 @ SY285 @ SY287 )
| ~ ( between @ SV34 @ SY283 @ SY286 )
| ~ ( between @ SY284 @ SY285 @ SY287 )
| ( equidistant @ SV34 @ SY286 @ SY284 @ SY287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(242,plain,
! [SV35: $i] :
( ( ! [SY288: $i,SY289: $i] :
( ~ ( between @ SV35 @ SY288 @ SY289 )
| ! [SY290: $i] :
( ~ ( between @ SV35 @ SY288 @ SY290 )
| ~ ( equidistant @ SY288 @ SY289 @ SY288 @ SY290 )
| ( SV35 = SY288 )
| ( SY289 = SY290 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(243,plain,
! [SV36: $i] :
( ( ! [SY291: $i,SY292: $i] :
( ~ ( between @ SV36 @ SY291 @ SY292 )
| ( SV36 = SY291 )
| ( SY292
= ( extension @ SV36 @ SY291 @ SY291 @ SY292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(244,plain,
! [SV37: $i] :
( ( ! [SY293: $i,SY294: $i,SY295: $i] :
( ~ ( equidistant @ SV37 @ SY293 @ SY294 @ SY295 )
| ! [SY296: $i,SY297: $i] :
( ( ( extension @ SY296 @ SY297 @ SV37 @ SY293 )
= ( extension @ SY296 @ SY297 @ SY294 @ SY295 ) )
| ( SY296 = SY297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(245,plain,
! [SV38: $i] :
( ( ! [SY298: $i] :
( ( ( extension @ SV38 @ SY298 @ SV38 @ SY298 )
= ( extension @ SV38 @ SY298 @ SY298 @ SV38 ) )
| ( SV38 = SY298 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(246,plain,
! [SV39: $i] :
( ( ! [SY299: $i] : ( equidistant @ SV39 @ SY299 @ SV39 @ ( reflection @ ( reflection @ SY299 @ SV39 ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(247,plain,
! [SV40: $i] :
( ( ! [SY300: $i] :
( SV40
= ( reflection @ ( reflection @ SV40 @ SY300 ) @ SY300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(248,plain,
! [SV41: $i] :
( ( ! [SY301: $i] : ( between @ SV41 @ SY301 @ SY301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(249,plain,
! [SV42: $i] :
( ( ! [SY302: $i,SY303: $i] :
( ~ ( between @ SV42 @ SY302 @ SY303 )
| ( SV42 != SY303 )
| ! [V: $i] : ( between @ V @ SY302 @ SY303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(250,plain,
! [SV43: $i] :
( ( ! [SY305: $i,SY306: $i] :
( ~ ( between @ SV43 @ SY305 @ SY306 )
| ( between @ SY306 @ SY305 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(251,plain,
! [SV44: $i] :
( ( ! [SY307: $i] : ( between @ SV44 @ SV44 @ SY307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(252,plain,
! [SV45: $i] :
( ( ! [SY308: $i,SY309: $i] :
( ~ ( between @ SV45 @ SY308 @ SY309 )
| ~ ( between @ SY308 @ SV45 @ SY309 )
| ( SV45 = SY308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(253,plain,
! [SV46: $i] :
( ( ! [SY310: $i,SY311: $i] :
( ~ ( between @ SV46 @ SY310 @ SY311 )
| ~ ( between @ SV46 @ SY311 @ SY310 )
| ( SY310 = SY311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(254,plain,
! [SV47: $i] :
( ( ! [SY312: $i,SY313: $i] :
( ~ ( between @ SV47 @ SY312 @ SY313 )
| ~ ( between @ SY312 @ SV47 @ SY313 )
| ( SV47 = SY312 )
| ( SY312 = SY313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(255,plain,
! [SV48: $i] :
( ( ! [SY314: $i,SY315: $i] :
( ~ ( between @ SV48 @ SY314 @ SY315 )
| ~ ( between @ SV48 @ SY315 @ SY314 )
| ( SV48 = SY314 )
| ( SY314 = SY315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(256,plain,
! [SV49: $i] :
( ( ! [SY316: $i,SY317: $i] :
( ~ ( between @ SV49 @ SY316 @ SY317 )
| ! [X: $i] :
~ ( between @ SY316 @ SY317 @ X )
| ( between @ SV49 @ SY316 @ SY317 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(257,plain,
! [SV50: $i] :
( ( ! [SY319: $i,SY320: $i] :
( ~ ( between @ SV50 @ SY319 @ SY320 )
| ! [SY321: $i] :
( ~ ( between @ SV50 @ SY320 @ SY321 )
| ( between @ SY319 @ SY320 @ SY321 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(258,plain,
! [SV51: $i] :
( ( ! [SY322: $i,SY323: $i] :
( ~ ( between @ SV51 @ SY322 @ SY323 )
| ! [SY324: $i] :
( ~ ( between @ SY322 @ SY323 @ SY324 )
| ( SY322 = SY323 )
| ( between @ SV51 @ SY323 @ SY324 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(259,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(260,plain,
! [SV52: $i,SV1: $i] :
( ( equidistant @ SV1 @ SV52 @ SV52 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(261,plain,
! [SV53: $i,SV2: $i] :
( ( ! [SY325: $i,SY326: $i] :
( ~ ( equidistant @ SV2 @ SV53 @ SY325 @ SY326 )
| ! [SY327: $i,SY328: $i] :
( ~ ( equidistant @ SV2 @ SV53 @ SY327 @ SY328 )
| ( equidistant @ SY325 @ SY326 @ SY327 @ SY328 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(262,plain,
! [SV54: $i,SV3: $i] :
( ( ! [SY329: $i] :
~ ( equidistant @ SV3 @ SV54 @ SY329 @ SY329 )
| ( SV3 = SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(263,plain,
! [SV55: $i,SV4: $i] :
( ( ! [SY330: $i,SY331: $i] : ( between @ SV4 @ SV55 @ ( extension @ SV4 @ SV55 @ SY330 @ SY331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(264,plain,
! [SV56: $i,SV5: $i] :
( ( ! [SY332: $i,SY333: $i] : ( equidistant @ SV5 @ ( extension @ SV56 @ SV5 @ SY332 @ SY333 ) @ SY332 @ SY333 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(265,plain,
! [SV57: $i,SV6: $i] :
( ( ! [SY334: $i,SY335: $i,SY336: $i,SY337: $i] :
( ~ ( equidistant @ SV6 @ SV57 @ SY334 @ SY335 )
| ~ ( equidistant @ SV57 @ SY336 @ SY335 @ SY337 )
| ! [SY338: $i,SY339: $i] :
( ~ ( equidistant @ SV6 @ SY338 @ SY334 @ SY339 )
| ~ ( equidistant @ SV57 @ SY338 @ SY335 @ SY339 )
| ~ ( between @ SV6 @ SV57 @ SY336 )
| ~ ( between @ SY334 @ SY335 @ SY337 )
| ( SV6 = SV57 )
| ( equidistant @ SY336 @ SY338 @ SY337 @ SY339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(266,plain,
! [SV58: $i,SV7: $i] :
( ( ~ ( between @ SV7 @ SV58 @ SV7 )
| ( SV7 = SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(267,plain,
! [SV59: $i,SV8: $i] :
( ( ! [SY340: $i] :
( ~ ( between @ SV8 @ SV59 @ SY340 )
| ! [SY341: $i,SY342: $i] :
( ~ ( between @ SY341 @ SY342 @ SY340 )
| ( between @ SV59 @ ( inner_pasch @ SV8 @ SV59 @ SY340 @ SY342 @ SY341 ) @ SY341 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(268,plain,
! [SV60: $i,SV9: $i] :
( ( ! [SY343: $i] :
( ~ ( between @ SV9 @ SV60 @ SY343 )
| ! [SY344: $i,SY345: $i] :
( ~ ( between @ SY344 @ SY345 @ SY343 )
| ( between @ SY345 @ ( inner_pasch @ SV9 @ SV60 @ SY343 @ SY345 @ SY344 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(269,plain,
! [SV61: $i,SV10: $i] :
( ( ! [SY346: $i] :
( ~ ( equidistant @ SV10 @ SV61 @ SV10 @ SY346 )
| ! [SY347: $i] :
( ~ ( equidistant @ SY347 @ SV61 @ SY347 @ SY346 )
| ! [SY348: $i] :
( ~ ( equidistant @ SY348 @ SV61 @ SY348 @ SY346 )
| ( between @ SV10 @ SY347 @ SY348 )
| ( between @ SY347 @ SY348 @ SV10 )
| ( SV61 = SY346 )
| ( between @ SY348 @ SV10 @ SY347 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(270,plain,
! [SV62: $i,SV11: $i] :
( ( ! [SY349: $i] :
( ~ ( between @ SV11 @ SV62 @ SY349 )
| ! [SY350: $i,SY351: $i] :
( ~ ( between @ SY350 @ SV62 @ SY351 )
| ( SV11 = SV62 )
| ( between @ SV11 @ SY350 @ ( euclid1 @ SV11 @ SY350 @ SV62 @ SY351 @ SY349 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(271,plain,
! [SV63: $i,SV12: $i] :
( ( ! [SY352: $i] :
( ~ ( between @ SV12 @ SV63 @ SY352 )
| ! [SY353: $i,SY354: $i] :
( ~ ( between @ SY353 @ SV63 @ SY354 )
| ( SV12 = SV63 )
| ( between @ SV12 @ SY354 @ ( euclid2 @ SV12 @ SY353 @ SV63 @ SY354 @ SY352 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(272,plain,
! [SV64: $i,SV13: $i] :
( ( ! [SY355: $i] :
( ~ ( between @ SV13 @ SV64 @ SY355 )
| ! [SY356: $i,SY357: $i] :
( ~ ( between @ SY356 @ SV64 @ SY357 )
| ( SV13 = SV64 )
| ( between @ ( euclid1 @ SV13 @ SY356 @ SV64 @ SY357 @ SY355 ) @ SY355 @ ( euclid2 @ SV13 @ SY356 @ SV64 @ SY357 @ SY355 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(273,plain,
! [SV65: $i,SV14: $i] :
( ( ! [SY358: $i,SY359: $i] :
( ~ ( equidistant @ SV14 @ SV65 @ SV14 @ SY358 )
| ! [SY360: $i] :
( ~ ( equidistant @ SV14 @ SY359 @ SV14 @ SY360 )
| ~ ( between @ SV14 @ SV65 @ SY359 )
| ! [SY361: $i] :
( ~ ( between @ SV65 @ SY361 @ SY359 )
| ( between @ SY358 @ ( continuous @ SV14 @ SV65 @ SY358 @ SY361 @ SY359 @ SY360 ) @ SY360 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(274,plain,
! [SV66: $i,SV15: $i] :
( ( ! [SY362: $i,SY363: $i] :
( ~ ( equidistant @ SV15 @ SV66 @ SV15 @ SY362 )
| ! [SY364: $i] :
( ~ ( equidistant @ SV15 @ SY363 @ SV15 @ SY364 )
| ~ ( between @ SV15 @ SV66 @ SY363 )
| ! [SY365: $i] :
( ~ ( between @ SV66 @ SY365 @ SY363 )
| ( equidistant @ SV15 @ SY365 @ SV15 @ ( continuous @ SV15 @ SV66 @ SY362 @ SY365 @ SY363 @ SY364 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(275,plain,
! [SV67: $i,SV16: $i] :
( ( ( reflection @ SV16 @ SV67 )
= ( extension @ SV16 @ SV67 @ SV16 @ SV67 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(276,plain,
! [SV68: $i,SV17: $i] :
( ( equidistant @ SV17 @ SV68 @ SV17 @ SV68 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(277,plain,
! [SV69: $i,SV18: $i] :
( ( ! [SY366: $i,SY367: $i] :
( ~ ( equidistant @ SV18 @ SV69 @ SY366 @ SY367 )
| ( equidistant @ SY366 @ SY367 @ SV18 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(278,plain,
! [SV70: $i,SV19: $i] :
( ( ! [SY368: $i,SY369: $i] :
( ~ ( equidistant @ SV19 @ SV70 @ SY368 @ SY369 )
| ( equidistant @ SV70 @ SV19 @ SY368 @ SY369 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(279,plain,
! [SV71: $i,SV20: $i] :
( ( ! [SY370: $i,SY371: $i] :
( ~ ( equidistant @ SV20 @ SV71 @ SY370 @ SY371 )
| ( equidistant @ SV20 @ SV71 @ SY371 @ SY370 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(280,plain,
! [SV72: $i,SV21: $i] :
( ( ! [SY372: $i,SY373: $i] :
( ~ ( equidistant @ SV21 @ SV72 @ SY372 @ SY373 )
| ( equidistant @ SV72 @ SV21 @ SY373 @ SY372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(281,plain,
! [SV73: $i,SV22: $i] :
( ( ! [SY374: $i,SY375: $i] :
( ~ ( equidistant @ SV22 @ SV73 @ SY374 @ SY375 )
| ( equidistant @ SY374 @ SY375 @ SV73 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(282,plain,
! [SV74: $i,SV23: $i] :
( ( ! [SY376: $i,SY377: $i] :
( ~ ( equidistant @ SV23 @ SV74 @ SY376 @ SY377 )
| ( equidistant @ SY377 @ SY376 @ SV23 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(283,plain,
! [SV75: $i,SV24: $i] :
( ( ! [SY378: $i,SY379: $i] :
( ~ ( equidistant @ SV24 @ SV75 @ SY378 @ SY379 )
| ( equidistant @ SY379 @ SY378 @ SV75 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(284,plain,
! [SV76: $i,SV25: $i] :
( ( ! [SY380: $i,SY381: $i] :
( ~ ( equidistant @ SV25 @ SV76 @ SY380 @ SY381 )
| ! [SY382: $i,SY383: $i] :
( ~ ( equidistant @ SY380 @ SY381 @ SY382 @ SY383 )
| ( equidistant @ SV25 @ SV76 @ SY382 @ SY383 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(285,plain,
! [SV77: $i,SV26: $i] :
( ( ! [SY384: $i] :
( SV26
= ( extension @ SV77 @ SV26 @ SY384 @ SY384 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(286,plain,
! [SV78: $i,SV27: $i] :
( ( ! [SY385: $i] :
( ! [SY386: $i,SY387: $i] :
( SV27
!= ( extension @ SV78 @ SY385 @ SY386 @ SY387 ) )
| ( between @ SV78 @ SY385 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(287,plain,
! [SV79: $i,SV28: $i] :
( ( between @ SV28 @ SV79 @ ( reflection @ SV28 @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(288,plain,
! [SV80: $i,SV29: $i] :
( ( equidistant @ SV29 @ ( reflection @ SV80 @ SV29 ) @ SV80 @ SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(289,plain,
! [SV81: $i,SV30: $i] :
( ( ( SV30 != SV81 )
| ( SV81
= ( reflection @ SV30 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(290,plain,
! [SV82: $i,SV32: $i] :
( ( ( SV32
!= ( reflection @ SV82 @ SV32 ) )
| ( SV82 = SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(291,plain,
! [SV83: $i,SV33: $i] :
( ( equidistant @ SV33 @ SV33 @ SV83 @ SV83 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(292,plain,
! [SV84: $i,SV34: $i] :
( ( ! [SY388: $i,SY389: $i] :
( ~ ( equidistant @ SV34 @ SV84 @ SY388 @ SY389 )
| ! [SY390: $i,SY391: $i] :
( ~ ( equidistant @ SV84 @ SY390 @ SY389 @ SY391 )
| ~ ( between @ SV34 @ SV84 @ SY390 )
| ~ ( between @ SY388 @ SY389 @ SY391 )
| ( equidistant @ SV34 @ SY390 @ SY388 @ SY391 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(293,plain,
! [SV85: $i,SV35: $i] :
( ( ! [SY392: $i] :
( ~ ( between @ SV35 @ SV85 @ SY392 )
| ! [SY393: $i] :
( ~ ( between @ SV35 @ SV85 @ SY393 )
| ~ ( equidistant @ SV85 @ SY392 @ SV85 @ SY393 )
| ( SV35 = SV85 )
| ( SY392 = SY393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(294,plain,
! [SV86: $i,SV36: $i] :
( ( ! [SY394: $i] :
( ~ ( between @ SV36 @ SV86 @ SY394 )
| ( SV36 = SV86 )
| ( SY394
= ( extension @ SV36 @ SV86 @ SV86 @ SY394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[243]) ).
thf(295,plain,
! [SV87: $i,SV37: $i] :
( ( ! [SY395: $i,SY396: $i] :
( ~ ( equidistant @ SV37 @ SV87 @ SY395 @ SY396 )
| ! [SY397: $i,SY398: $i] :
( ( ( extension @ SY397 @ SY398 @ SV37 @ SV87 )
= ( extension @ SY397 @ SY398 @ SY395 @ SY396 ) )
| ( SY397 = SY398 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(296,plain,
! [SV88: $i,SV38: $i] :
( ( ( ( extension @ SV38 @ SV88 @ SV38 @ SV88 )
= ( extension @ SV38 @ SV88 @ SV88 @ SV38 ) )
| ( SV38 = SV88 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(297,plain,
! [SV89: $i,SV39: $i] :
( ( equidistant @ SV39 @ SV89 @ SV39 @ ( reflection @ ( reflection @ SV89 @ SV39 ) @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(298,plain,
! [SV90: $i,SV40: $i] :
( ( SV40
= ( reflection @ ( reflection @ SV40 @ SV90 ) @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(299,plain,
! [SV91: $i,SV41: $i] :
( ( between @ SV41 @ SV91 @ SV91 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(300,plain,
! [SV92: $i,SV42: $i] :
( ( ! [SY399: $i] :
( ~ ( between @ SV42 @ SV92 @ SY399 )
| ( SV42 != SY399 )
| ! [SY400: $i] : ( between @ SY400 @ SV92 @ SY399 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(301,plain,
! [SV93: $i,SV43: $i] :
( ( ! [SY401: $i] :
( ~ ( between @ SV43 @ SV93 @ SY401 )
| ( between @ SY401 @ SV93 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(302,plain,
! [SV94: $i,SV44: $i] :
( ( between @ SV44 @ SV44 @ SV94 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(303,plain,
! [SV95: $i,SV45: $i] :
( ( ! [SY402: $i] :
( ~ ( between @ SV45 @ SV95 @ SY402 )
| ~ ( between @ SV95 @ SV45 @ SY402 )
| ( SV45 = SV95 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(304,plain,
! [SV96: $i,SV46: $i] :
( ( ! [SY403: $i] :
( ~ ( between @ SV46 @ SV96 @ SY403 )
| ~ ( between @ SV46 @ SY403 @ SV96 )
| ( SV96 = SY403 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(305,plain,
! [SV97: $i,SV47: $i] :
( ( ! [SY404: $i] :
( ~ ( between @ SV47 @ SV97 @ SY404 )
| ~ ( between @ SV97 @ SV47 @ SY404 )
| ( SV47 = SV97 )
| ( SV97 = SY404 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(306,plain,
! [SV98: $i,SV48: $i] :
( ( ! [SY405: $i] :
( ~ ( between @ SV48 @ SV98 @ SY405 )
| ~ ( between @ SV48 @ SY405 @ SV98 )
| ( SV48 = SV98 )
| ( SV98 = SY405 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(307,plain,
! [SV99: $i,SV49: $i] :
( ( ! [SY406: $i] :
( ~ ( between @ SV49 @ SV99 @ SY406 )
| ! [SY407: $i] :
~ ( between @ SV99 @ SY406 @ SY407 )
| ( between @ SV49 @ SV99 @ SY406 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(308,plain,
! [SV100: $i,SV50: $i] :
( ( ! [SY408: $i] :
( ~ ( between @ SV50 @ SV100 @ SY408 )
| ! [SY409: $i] :
( ~ ( between @ SV50 @ SY408 @ SY409 )
| ( between @ SV100 @ SY408 @ SY409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(309,plain,
! [SV101: $i,SV51: $i] :
( ( ! [SY410: $i] :
( ~ ( between @ SV51 @ SV101 @ SY410 )
| ! [SY411: $i] :
( ~ ( between @ SV101 @ SY410 @ SY411 )
| ( SV101 = SY410 )
| ( between @ SV51 @ SY410 @ SY411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(310,plain,
! [SV102: $i,SV53: $i,SV2: $i] :
( ( ! [SY412: $i] :
( ~ ( equidistant @ SV2 @ SV53 @ SV102 @ SY412 )
| ! [SY413: $i,SY414: $i] :
( ~ ( equidistant @ SV2 @ SV53 @ SY413 @ SY414 )
| ( equidistant @ SV102 @ SY412 @ SY413 @ SY414 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(311,plain,
! [SV54: $i,SV3: $i] :
( ( ( ! [SY329: $i] :
~ ( equidistant @ SV3 @ SV54 @ SY329 @ SY329 ) )
= $true )
| ( ( SV3 = SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[262]) ).
thf(312,plain,
! [SV103: $i,SV55: $i,SV4: $i] :
( ( ! [SY415: $i] : ( between @ SV4 @ SV55 @ ( extension @ SV4 @ SV55 @ SV103 @ SY415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(313,plain,
! [SV104: $i,SV56: $i,SV5: $i] :
( ( ! [SY416: $i] : ( equidistant @ SV5 @ ( extension @ SV56 @ SV5 @ SV104 @ SY416 ) @ SV104 @ SY416 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(314,plain,
! [SV105: $i,SV57: $i,SV6: $i] :
( ( ! [SY417: $i,SY418: $i,SY419: $i] :
( ~ ( equidistant @ SV6 @ SV57 @ SV105 @ SY417 )
| ~ ( equidistant @ SV57 @ SY418 @ SY417 @ SY419 )
| ! [SY420: $i,SY421: $i] :
( ~ ( equidistant @ SV6 @ SY420 @ SV105 @ SY421 )
| ~ ( equidistant @ SV57 @ SY420 @ SY417 @ SY421 )
| ~ ( between @ SV6 @ SV57 @ SY418 )
| ~ ( between @ SV105 @ SY417 @ SY419 )
| ( SV6 = SV57 )
| ( equidistant @ SY418 @ SY420 @ SY419 @ SY421 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(315,plain,
! [SV58: $i,SV7: $i] :
( ( ( ~ ( between @ SV7 @ SV58 @ SV7 ) )
= $true )
| ( ( SV7 = SV58 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(316,plain,
! [SV106: $i,SV59: $i,SV8: $i] :
( ( ~ ( between @ SV8 @ SV59 @ SV106 )
| ! [SY422: $i,SY423: $i] :
( ~ ( between @ SY422 @ SY423 @ SV106 )
| ( between @ SV59 @ ( inner_pasch @ SV8 @ SV59 @ SV106 @ SY423 @ SY422 ) @ SY422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(317,plain,
! [SV107: $i,SV60: $i,SV9: $i] :
( ( ~ ( between @ SV9 @ SV60 @ SV107 )
| ! [SY424: $i,SY425: $i] :
( ~ ( between @ SY424 @ SY425 @ SV107 )
| ( between @ SY425 @ ( inner_pasch @ SV9 @ SV60 @ SV107 @ SY425 @ SY424 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(318,plain,
! [SV108: $i,SV61: $i,SV10: $i] :
( ( ~ ( equidistant @ SV10 @ SV61 @ SV10 @ SV108 )
| ! [SY426: $i] :
( ~ ( equidistant @ SY426 @ SV61 @ SY426 @ SV108 )
| ! [SY427: $i] :
( ~ ( equidistant @ SY427 @ SV61 @ SY427 @ SV108 )
| ( between @ SV10 @ SY426 @ SY427 )
| ( between @ SY426 @ SY427 @ SV10 )
| ( SV61 = SV108 )
| ( between @ SY427 @ SV10 @ SY426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(319,plain,
! [SV109: $i,SV62: $i,SV11: $i] :
( ( ~ ( between @ SV11 @ SV62 @ SV109 )
| ! [SY428: $i,SY429: $i] :
( ~ ( between @ SY428 @ SV62 @ SY429 )
| ( SV11 = SV62 )
| ( between @ SV11 @ SY428 @ ( euclid1 @ SV11 @ SY428 @ SV62 @ SY429 @ SV109 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(320,plain,
! [SV110: $i,SV63: $i,SV12: $i] :
( ( ~ ( between @ SV12 @ SV63 @ SV110 )
| ! [SY430: $i,SY431: $i] :
( ~ ( between @ SY430 @ SV63 @ SY431 )
| ( SV12 = SV63 )
| ( between @ SV12 @ SY431 @ ( euclid2 @ SV12 @ SY430 @ SV63 @ SY431 @ SV110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(321,plain,
! [SV111: $i,SV64: $i,SV13: $i] :
( ( ~ ( between @ SV13 @ SV64 @ SV111 )
| ! [SY432: $i,SY433: $i] :
( ~ ( between @ SY432 @ SV64 @ SY433 )
| ( SV13 = SV64 )
| ( between @ ( euclid1 @ SV13 @ SY432 @ SV64 @ SY433 @ SV111 ) @ SV111 @ ( euclid2 @ SV13 @ SY432 @ SV64 @ SY433 @ SV111 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(322,plain,
! [SV112: $i,SV65: $i,SV14: $i] :
( ( ! [SY434: $i] :
( ~ ( equidistant @ SV14 @ SV65 @ SV14 @ SV112 )
| ! [SY435: $i] :
( ~ ( equidistant @ SV14 @ SY434 @ SV14 @ SY435 )
| ~ ( between @ SV14 @ SV65 @ SY434 )
| ! [SY436: $i] :
( ~ ( between @ SV65 @ SY436 @ SY434 )
| ( between @ SV112 @ ( continuous @ SV14 @ SV65 @ SV112 @ SY436 @ SY434 @ SY435 ) @ SY435 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(323,plain,
! [SV113: $i,SV66: $i,SV15: $i] :
( ( ! [SY437: $i] :
( ~ ( equidistant @ SV15 @ SV66 @ SV15 @ SV113 )
| ! [SY438: $i] :
( ~ ( equidistant @ SV15 @ SY437 @ SV15 @ SY438 )
| ~ ( between @ SV15 @ SV66 @ SY437 )
| ! [SY439: $i] :
( ~ ( between @ SV66 @ SY439 @ SY437 )
| ( equidistant @ SV15 @ SY439 @ SV15 @ ( continuous @ SV15 @ SV66 @ SV113 @ SY439 @ SY437 @ SY438 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(324,plain,
! [SV114: $i,SV69: $i,SV18: $i] :
( ( ! [SY440: $i] :
( ~ ( equidistant @ SV18 @ SV69 @ SV114 @ SY440 )
| ( equidistant @ SV114 @ SY440 @ SV18 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(325,plain,
! [SV115: $i,SV70: $i,SV19: $i] :
( ( ! [SY441: $i] :
( ~ ( equidistant @ SV19 @ SV70 @ SV115 @ SY441 )
| ( equidistant @ SV70 @ SV19 @ SV115 @ SY441 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(326,plain,
! [SV116: $i,SV71: $i,SV20: $i] :
( ( ! [SY442: $i] :
( ~ ( equidistant @ SV20 @ SV71 @ SV116 @ SY442 )
| ( equidistant @ SV20 @ SV71 @ SY442 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(327,plain,
! [SV117: $i,SV72: $i,SV21: $i] :
( ( ! [SY443: $i] :
( ~ ( equidistant @ SV21 @ SV72 @ SV117 @ SY443 )
| ( equidistant @ SV72 @ SV21 @ SY443 @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[280]) ).
thf(328,plain,
! [SV118: $i,SV73: $i,SV22: $i] :
( ( ! [SY444: $i] :
( ~ ( equidistant @ SV22 @ SV73 @ SV118 @ SY444 )
| ( equidistant @ SV118 @ SY444 @ SV73 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(329,plain,
! [SV119: $i,SV74: $i,SV23: $i] :
( ( ! [SY445: $i] :
( ~ ( equidistant @ SV23 @ SV74 @ SV119 @ SY445 )
| ( equidistant @ SY445 @ SV119 @ SV23 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[282]) ).
thf(330,plain,
! [SV120: $i,SV75: $i,SV24: $i] :
( ( ! [SY446: $i] :
( ~ ( equidistant @ SV24 @ SV75 @ SV120 @ SY446 )
| ( equidistant @ SY446 @ SV120 @ SV75 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(331,plain,
! [SV121: $i,SV76: $i,SV25: $i] :
( ( ! [SY447: $i] :
( ~ ( equidistant @ SV25 @ SV76 @ SV121 @ SY447 )
| ! [SY448: $i,SY449: $i] :
( ~ ( equidistant @ SV121 @ SY447 @ SY448 @ SY449 )
| ( equidistant @ SV25 @ SV76 @ SY448 @ SY449 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(332,plain,
! [SV122: $i,SV77: $i,SV26: $i] :
( ( SV26
= ( extension @ SV77 @ SV26 @ SV122 @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(333,plain,
! [SV123: $i,SV78: $i,SV27: $i] :
( ( ! [SY450: $i,SY451: $i] :
( SV27
!= ( extension @ SV78 @ SV123 @ SY450 @ SY451 ) )
| ( between @ SV78 @ SV123 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[286]) ).
thf(334,plain,
! [SV81: $i,SV30: $i] :
( ( ( ( SV30 != SV81 ) )
= $true )
| ( ( SV81
= ( reflection @ SV30 @ SV81 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(335,plain,
! [SV82: $i,SV32: $i] :
( ( ( ( SV32
!= ( reflection @ SV82 @ SV32 ) ) )
= $true )
| ( ( SV82 = SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(336,plain,
! [SV124: $i,SV84: $i,SV34: $i] :
( ( ! [SY452: $i] :
( ~ ( equidistant @ SV34 @ SV84 @ SV124 @ SY452 )
| ! [SY453: $i,SY454: $i] :
( ~ ( equidistant @ SV84 @ SY453 @ SY452 @ SY454 )
| ~ ( between @ SV34 @ SV84 @ SY453 )
| ~ ( between @ SV124 @ SY452 @ SY454 )
| ( equidistant @ SV34 @ SY453 @ SV124 @ SY454 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(337,plain,
! [SV125: $i,SV85: $i,SV35: $i] :
( ( ~ ( between @ SV35 @ SV85 @ SV125 )
| ! [SY455: $i] :
( ~ ( between @ SV35 @ SV85 @ SY455 )
| ~ ( equidistant @ SV85 @ SV125 @ SV85 @ SY455 )
| ( SV35 = SV85 )
| ( SV125 = SY455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(338,plain,
! [SV126: $i,SV86: $i,SV36: $i] :
( ( ~ ( between @ SV36 @ SV86 @ SV126 )
| ( SV36 = SV86 )
| ( SV126
= ( extension @ SV36 @ SV86 @ SV86 @ SV126 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[294]) ).
thf(339,plain,
! [SV127: $i,SV87: $i,SV37: $i] :
( ( ! [SY456: $i] :
( ~ ( equidistant @ SV37 @ SV87 @ SV127 @ SY456 )
| ! [SY457: $i,SY458: $i] :
( ( ( extension @ SY457 @ SY458 @ SV37 @ SV87 )
= ( extension @ SY457 @ SY458 @ SV127 @ SY456 ) )
| ( SY457 = SY458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[295]) ).
thf(340,plain,
! [SV88: $i,SV38: $i] :
( ( ( ( extension @ SV38 @ SV88 @ SV38 @ SV88 )
= ( extension @ SV38 @ SV88 @ SV88 @ SV38 ) )
= $true )
| ( ( SV38 = SV88 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(341,plain,
! [SV128: $i,SV92: $i,SV42: $i] :
( ( ~ ( between @ SV42 @ SV92 @ SV128 )
| ( SV42 != SV128 )
| ! [SY459: $i] : ( between @ SY459 @ SV92 @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[300]) ).
thf(342,plain,
! [SV129: $i,SV93: $i,SV43: $i] :
( ( ~ ( between @ SV43 @ SV93 @ SV129 )
| ( between @ SV129 @ SV93 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(343,plain,
! [SV130: $i,SV95: $i,SV45: $i] :
( ( ~ ( between @ SV45 @ SV95 @ SV130 )
| ~ ( between @ SV95 @ SV45 @ SV130 )
| ( SV45 = SV95 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(344,plain,
! [SV131: $i,SV96: $i,SV46: $i] :
( ( ~ ( between @ SV46 @ SV96 @ SV131 )
| ~ ( between @ SV46 @ SV131 @ SV96 )
| ( SV96 = SV131 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(345,plain,
! [SV132: $i,SV97: $i,SV47: $i] :
( ( ~ ( between @ SV47 @ SV97 @ SV132 )
| ~ ( between @ SV97 @ SV47 @ SV132 )
| ( SV47 = SV97 )
| ( SV97 = SV132 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(346,plain,
! [SV133: $i,SV98: $i,SV48: $i] :
( ( ~ ( between @ SV48 @ SV98 @ SV133 )
| ~ ( between @ SV48 @ SV133 @ SV98 )
| ( SV48 = SV98 )
| ( SV98 = SV133 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(347,plain,
! [SV134: $i,SV99: $i,SV49: $i] :
( ( ~ ( between @ SV49 @ SV99 @ SV134 )
| ! [SY460: $i] :
~ ( between @ SV99 @ SV134 @ SY460 )
| ( between @ SV49 @ SV99 @ SV134 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(348,plain,
! [SV135: $i,SV100: $i,SV50: $i] :
( ( ~ ( between @ SV50 @ SV100 @ SV135 )
| ! [SY461: $i] :
( ~ ( between @ SV50 @ SV135 @ SY461 )
| ( between @ SV100 @ SV135 @ SY461 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(349,plain,
! [SV136: $i,SV101: $i,SV51: $i] :
( ( ~ ( between @ SV51 @ SV101 @ SV136 )
| ! [SY462: $i] :
( ~ ( between @ SV101 @ SV136 @ SY462 )
| ( SV101 = SV136 )
| ( between @ SV51 @ SV136 @ SY462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(350,plain,
! [SV137: $i,SV102: $i,SV53: $i,SV2: $i] :
( ( ~ ( equidistant @ SV2 @ SV53 @ SV102 @ SV137 )
| ! [SY463: $i,SY464: $i] :
( ~ ( equidistant @ SV2 @ SV53 @ SY463 @ SY464 )
| ( equidistant @ SV102 @ SV137 @ SY463 @ SY464 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(351,plain,
! [SV138: $i,SV54: $i,SV3: $i] :
( ( ( ~ ( equidistant @ SV3 @ SV54 @ SV138 @ SV138 ) )
= $true )
| ( ( SV3 = SV54 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[311]) ).
thf(352,plain,
! [SV139: $i,SV103: $i,SV55: $i,SV4: $i] :
( ( between @ SV4 @ SV55 @ ( extension @ SV4 @ SV55 @ SV103 @ SV139 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[312]) ).
thf(353,plain,
! [SV140: $i,SV104: $i,SV56: $i,SV5: $i] :
( ( equidistant @ SV5 @ ( extension @ SV56 @ SV5 @ SV104 @ SV140 ) @ SV104 @ SV140 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(354,plain,
! [SV141: $i,SV105: $i,SV57: $i,SV6: $i] :
( ( ! [SY465: $i,SY466: $i] :
( ~ ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
| ~ ( equidistant @ SV57 @ SY465 @ SV141 @ SY466 )
| ! [SY467: $i,SY468: $i] :
( ~ ( equidistant @ SV6 @ SY467 @ SV105 @ SY468 )
| ~ ( equidistant @ SV57 @ SY467 @ SV141 @ SY468 )
| ~ ( between @ SV6 @ SV57 @ SY465 )
| ~ ( between @ SV105 @ SV141 @ SY466 )
| ( SV6 = SV57 )
| ( equidistant @ SY465 @ SY467 @ SY466 @ SY468 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(355,plain,
! [SV58: $i,SV7: $i] :
( ( ( between @ SV7 @ SV58 @ SV7 )
= $false )
| ( ( SV7 = SV58 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(356,plain,
! [SV106: $i,SV59: $i,SV8: $i] :
( ( ( ~ ( between @ SV8 @ SV59 @ SV106 ) )
= $true )
| ( ( ! [SY422: $i,SY423: $i] :
( ~ ( between @ SY422 @ SY423 @ SV106 )
| ( between @ SV59 @ ( inner_pasch @ SV8 @ SV59 @ SV106 @ SY423 @ SY422 ) @ SY422 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(357,plain,
! [SV107: $i,SV60: $i,SV9: $i] :
( ( ( ~ ( between @ SV9 @ SV60 @ SV107 ) )
= $true )
| ( ( ! [SY424: $i,SY425: $i] :
( ~ ( between @ SY424 @ SY425 @ SV107 )
| ( between @ SY425 @ ( inner_pasch @ SV9 @ SV60 @ SV107 @ SY425 @ SY424 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(358,plain,
! [SV108: $i,SV61: $i,SV10: $i] :
( ( ( ~ ( equidistant @ SV10 @ SV61 @ SV10 @ SV108 ) )
= $true )
| ( ( ! [SY426: $i] :
( ~ ( equidistant @ SY426 @ SV61 @ SY426 @ SV108 )
| ! [SY427: $i] :
( ~ ( equidistant @ SY427 @ SV61 @ SY427 @ SV108 )
| ( between @ SV10 @ SY426 @ SY427 )
| ( between @ SY426 @ SY427 @ SV10 )
| ( SV61 = SV108 )
| ( between @ SY427 @ SV10 @ SY426 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[318]) ).
thf(359,plain,
! [SV109: $i,SV62: $i,SV11: $i] :
( ( ( ~ ( between @ SV11 @ SV62 @ SV109 ) )
= $true )
| ( ( ! [SY428: $i,SY429: $i] :
( ~ ( between @ SY428 @ SV62 @ SY429 )
| ( SV11 = SV62 )
| ( between @ SV11 @ SY428 @ ( euclid1 @ SV11 @ SY428 @ SV62 @ SY429 @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(360,plain,
! [SV110: $i,SV63: $i,SV12: $i] :
( ( ( ~ ( between @ SV12 @ SV63 @ SV110 ) )
= $true )
| ( ( ! [SY430: $i,SY431: $i] :
( ~ ( between @ SY430 @ SV63 @ SY431 )
| ( SV12 = SV63 )
| ( between @ SV12 @ SY431 @ ( euclid2 @ SV12 @ SY430 @ SV63 @ SY431 @ SV110 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(361,plain,
! [SV111: $i,SV64: $i,SV13: $i] :
( ( ( ~ ( between @ SV13 @ SV64 @ SV111 ) )
= $true )
| ( ( ! [SY432: $i,SY433: $i] :
( ~ ( between @ SY432 @ SV64 @ SY433 )
| ( SV13 = SV64 )
| ( between @ ( euclid1 @ SV13 @ SY432 @ SV64 @ SY433 @ SV111 ) @ SV111 @ ( euclid2 @ SV13 @ SY432 @ SV64 @ SY433 @ SV111 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(362,plain,
! [SV142: $i,SV112: $i,SV65: $i,SV14: $i] :
( ( ~ ( equidistant @ SV14 @ SV65 @ SV14 @ SV112 )
| ! [SY469: $i] :
( ~ ( equidistant @ SV14 @ SV142 @ SV14 @ SY469 )
| ~ ( between @ SV14 @ SV65 @ SV142 )
| ! [SY470: $i] :
( ~ ( between @ SV65 @ SY470 @ SV142 )
| ( between @ SV112 @ ( continuous @ SV14 @ SV65 @ SV112 @ SY470 @ SV142 @ SY469 ) @ SY469 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(363,plain,
! [SV143: $i,SV113: $i,SV66: $i,SV15: $i] :
( ( ~ ( equidistant @ SV15 @ SV66 @ SV15 @ SV113 )
| ! [SY471: $i] :
( ~ ( equidistant @ SV15 @ SV143 @ SV15 @ SY471 )
| ~ ( between @ SV15 @ SV66 @ SV143 )
| ! [SY472: $i] :
( ~ ( between @ SV66 @ SY472 @ SV143 )
| ( equidistant @ SV15 @ SY472 @ SV15 @ ( continuous @ SV15 @ SV66 @ SV113 @ SY472 @ SV143 @ SY471 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(364,plain,
! [SV144: $i,SV114: $i,SV69: $i,SV18: $i] :
( ( ~ ( equidistant @ SV18 @ SV69 @ SV114 @ SV144 )
| ( equidistant @ SV114 @ SV144 @ SV18 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(365,plain,
! [SV145: $i,SV115: $i,SV70: $i,SV19: $i] :
( ( ~ ( equidistant @ SV19 @ SV70 @ SV115 @ SV145 )
| ( equidistant @ SV70 @ SV19 @ SV115 @ SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(366,plain,
! [SV146: $i,SV116: $i,SV71: $i,SV20: $i] :
( ( ~ ( equidistant @ SV20 @ SV71 @ SV116 @ SV146 )
| ( equidistant @ SV20 @ SV71 @ SV146 @ SV116 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(367,plain,
! [SV147: $i,SV117: $i,SV72: $i,SV21: $i] :
( ( ~ ( equidistant @ SV21 @ SV72 @ SV117 @ SV147 )
| ( equidistant @ SV72 @ SV21 @ SV147 @ SV117 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(368,plain,
! [SV148: $i,SV118: $i,SV73: $i,SV22: $i] :
( ( ~ ( equidistant @ SV22 @ SV73 @ SV118 @ SV148 )
| ( equidistant @ SV118 @ SV148 @ SV73 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(369,plain,
! [SV149: $i,SV119: $i,SV74: $i,SV23: $i] :
( ( ~ ( equidistant @ SV23 @ SV74 @ SV119 @ SV149 )
| ( equidistant @ SV149 @ SV119 @ SV23 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(370,plain,
! [SV150: $i,SV120: $i,SV75: $i,SV24: $i] :
( ( ~ ( equidistant @ SV24 @ SV75 @ SV120 @ SV150 )
| ( equidistant @ SV150 @ SV120 @ SV75 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[330]) ).
thf(371,plain,
! [SV151: $i,SV121: $i,SV76: $i,SV25: $i] :
( ( ~ ( equidistant @ SV25 @ SV76 @ SV121 @ SV151 )
| ! [SY473: $i,SY474: $i] :
( ~ ( equidistant @ SV121 @ SV151 @ SY473 @ SY474 )
| ( equidistant @ SV25 @ SV76 @ SY473 @ SY474 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(372,plain,
! [SV123: $i,SV78: $i,SV27: $i] :
( ( ( ! [SY450: $i,SY451: $i] :
( SV27
!= ( extension @ SV78 @ SV123 @ SY450 @ SY451 ) ) )
= $true )
| ( ( between @ SV78 @ SV123 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(373,plain,
! [SV81: $i,SV30: $i] :
( ( ( SV30 = SV81 )
= $false )
| ( ( SV81
= ( reflection @ SV30 @ SV81 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(374,plain,
! [SV82: $i,SV32: $i] :
( ( ( SV32
= ( reflection @ SV82 @ SV32 ) )
= $false )
| ( ( SV82 = SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(375,plain,
! [SV152: $i,SV124: $i,SV84: $i,SV34: $i] :
( ( ~ ( equidistant @ SV34 @ SV84 @ SV124 @ SV152 )
| ! [SY475: $i,SY476: $i] :
( ~ ( equidistant @ SV84 @ SY475 @ SV152 @ SY476 )
| ~ ( between @ SV34 @ SV84 @ SY475 )
| ~ ( between @ SV124 @ SV152 @ SY476 )
| ( equidistant @ SV34 @ SY475 @ SV124 @ SY476 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(376,plain,
! [SV125: $i,SV85: $i,SV35: $i] :
( ( ( ~ ( between @ SV35 @ SV85 @ SV125 ) )
= $true )
| ( ( ! [SY455: $i] :
( ~ ( between @ SV35 @ SV85 @ SY455 )
| ~ ( equidistant @ SV85 @ SV125 @ SV85 @ SY455 )
| ( SV35 = SV85 )
| ( SV125 = SY455 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(377,plain,
! [SV126: $i,SV86: $i,SV36: $i] :
( ( ( ~ ( between @ SV36 @ SV86 @ SV126 ) )
= $true )
| ( ( ( SV36 = SV86 )
| ( SV126
= ( extension @ SV36 @ SV86 @ SV86 @ SV126 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(378,plain,
! [SV153: $i,SV127: $i,SV87: $i,SV37: $i] :
( ( ~ ( equidistant @ SV37 @ SV87 @ SV127 @ SV153 )
| ! [SY477: $i,SY478: $i] :
( ( ( extension @ SY477 @ SY478 @ SV37 @ SV87 )
= ( extension @ SY477 @ SY478 @ SV127 @ SV153 ) )
| ( SY477 = SY478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(379,plain,
! [SV128: $i,SV92: $i,SV42: $i] :
( ( ( ~ ( between @ SV42 @ SV92 @ SV128 ) )
= $true )
| ( ( ( SV42 != SV128 )
| ! [SY459: $i] : ( between @ SY459 @ SV92 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(380,plain,
! [SV129: $i,SV93: $i,SV43: $i] :
( ( ( ~ ( between @ SV43 @ SV93 @ SV129 ) )
= $true )
| ( ( between @ SV129 @ SV93 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(381,plain,
! [SV130: $i,SV95: $i,SV45: $i] :
( ( ( ~ ( between @ SV45 @ SV95 @ SV130 ) )
= $true )
| ( ( ~ ( between @ SV95 @ SV45 @ SV130 )
| ( SV45 = SV95 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(382,plain,
! [SV131: $i,SV96: $i,SV46: $i] :
( ( ( ~ ( between @ SV46 @ SV96 @ SV131 ) )
= $true )
| ( ( ~ ( between @ SV46 @ SV131 @ SV96 )
| ( SV96 = SV131 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(383,plain,
! [SV132: $i,SV97: $i,SV47: $i] :
( ( ( ~ ( between @ SV47 @ SV97 @ SV132 ) )
= $true )
| ( ( ~ ( between @ SV97 @ SV47 @ SV132 )
| ( SV47 = SV97 )
| ( SV97 = SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(384,plain,
! [SV133: $i,SV98: $i,SV48: $i] :
( ( ( ~ ( between @ SV48 @ SV98 @ SV133 ) )
= $true )
| ( ( ~ ( between @ SV48 @ SV133 @ SV98 )
| ( SV48 = SV98 )
| ( SV98 = SV133 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[346]) ).
thf(385,plain,
! [SV134: $i,SV99: $i,SV49: $i] :
( ( ( ~ ( between @ SV49 @ SV99 @ SV134 ) )
= $true )
| ( ( ! [SY460: $i] :
~ ( between @ SV99 @ SV134 @ SY460 )
| ( between @ SV49 @ SV99 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(386,plain,
! [SV135: $i,SV100: $i,SV50: $i] :
( ( ( ~ ( between @ SV50 @ SV100 @ SV135 ) )
= $true )
| ( ( ! [SY461: $i] :
( ~ ( between @ SV50 @ SV135 @ SY461 )
| ( between @ SV100 @ SV135 @ SY461 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[348]) ).
thf(387,plain,
! [SV136: $i,SV101: $i,SV51: $i] :
( ( ( ~ ( between @ SV51 @ SV101 @ SV136 ) )
= $true )
| ( ( ! [SY462: $i] :
( ~ ( between @ SV101 @ SV136 @ SY462 )
| ( SV101 = SV136 )
| ( between @ SV51 @ SV136 @ SY462 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(388,plain,
! [SV137: $i,SV102: $i,SV53: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV53 @ SV102 @ SV137 ) )
= $true )
| ( ( ! [SY463: $i,SY464: $i] :
( ~ ( equidistant @ SV2 @ SV53 @ SY463 @ SY464 )
| ( equidistant @ SV102 @ SV137 @ SY463 @ SY464 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[350]) ).
thf(389,plain,
! [SV138: $i,SV54: $i,SV3: $i] :
( ( ( equidistant @ SV3 @ SV54 @ SV138 @ SV138 )
= $false )
| ( ( SV3 = SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(390,plain,
! [SV154: $i,SV141: $i,SV105: $i,SV57: $i,SV6: $i] :
( ( ! [SY479: $i] :
( ~ ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
| ~ ( equidistant @ SV57 @ SV154 @ SV141 @ SY479 )
| ! [SY480: $i,SY481: $i] :
( ~ ( equidistant @ SV6 @ SY480 @ SV105 @ SY481 )
| ~ ( equidistant @ SV57 @ SY480 @ SV141 @ SY481 )
| ~ ( between @ SV6 @ SV57 @ SV154 )
| ~ ( between @ SV105 @ SV141 @ SY479 )
| ( SV6 = SV57 )
| ( equidistant @ SV154 @ SY480 @ SY479 @ SY481 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(391,plain,
! [SV106: $i,SV59: $i,SV8: $i] :
( ( ( between @ SV8 @ SV59 @ SV106 )
= $false )
| ( ( ! [SY422: $i,SY423: $i] :
( ~ ( between @ SY422 @ SY423 @ SV106 )
| ( between @ SV59 @ ( inner_pasch @ SV8 @ SV59 @ SV106 @ SY423 @ SY422 ) @ SY422 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(392,plain,
! [SV107: $i,SV60: $i,SV9: $i] :
( ( ( between @ SV9 @ SV60 @ SV107 )
= $false )
| ( ( ! [SY424: $i,SY425: $i] :
( ~ ( between @ SY424 @ SY425 @ SV107 )
| ( between @ SY425 @ ( inner_pasch @ SV9 @ SV60 @ SV107 @ SY425 @ SY424 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(393,plain,
! [SV108: $i,SV61: $i,SV10: $i] :
( ( ( equidistant @ SV10 @ SV61 @ SV10 @ SV108 )
= $false )
| ( ( ! [SY426: $i] :
( ~ ( equidistant @ SY426 @ SV61 @ SY426 @ SV108 )
| ! [SY427: $i] :
( ~ ( equidistant @ SY427 @ SV61 @ SY427 @ SV108 )
| ( between @ SV10 @ SY426 @ SY427 )
| ( between @ SY426 @ SY427 @ SV10 )
| ( SV61 = SV108 )
| ( between @ SY427 @ SV10 @ SY426 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[358]) ).
thf(394,plain,
! [SV109: $i,SV62: $i,SV11: $i] :
( ( ( between @ SV11 @ SV62 @ SV109 )
= $false )
| ( ( ! [SY428: $i,SY429: $i] :
( ~ ( between @ SY428 @ SV62 @ SY429 )
| ( SV11 = SV62 )
| ( between @ SV11 @ SY428 @ ( euclid1 @ SV11 @ SY428 @ SV62 @ SY429 @ SV109 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[359]) ).
thf(395,plain,
! [SV110: $i,SV63: $i,SV12: $i] :
( ( ( between @ SV12 @ SV63 @ SV110 )
= $false )
| ( ( ! [SY430: $i,SY431: $i] :
( ~ ( between @ SY430 @ SV63 @ SY431 )
| ( SV12 = SV63 )
| ( between @ SV12 @ SY431 @ ( euclid2 @ SV12 @ SY430 @ SV63 @ SY431 @ SV110 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[360]) ).
thf(396,plain,
! [SV111: $i,SV64: $i,SV13: $i] :
( ( ( between @ SV13 @ SV64 @ SV111 )
= $false )
| ( ( ! [SY432: $i,SY433: $i] :
( ~ ( between @ SY432 @ SV64 @ SY433 )
| ( SV13 = SV64 )
| ( between @ ( euclid1 @ SV13 @ SY432 @ SV64 @ SY433 @ SV111 ) @ SV111 @ ( euclid2 @ SV13 @ SY432 @ SV64 @ SY433 @ SV111 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[361]) ).
thf(397,plain,
! [SV142: $i,SV112: $i,SV65: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV65 @ SV14 @ SV112 ) )
= $true )
| ( ( ! [SY469: $i] :
( ~ ( equidistant @ SV14 @ SV142 @ SV14 @ SY469 )
| ~ ( between @ SV14 @ SV65 @ SV142 )
| ! [SY470: $i] :
( ~ ( between @ SV65 @ SY470 @ SV142 )
| ( between @ SV112 @ ( continuous @ SV14 @ SV65 @ SV112 @ SY470 @ SV142 @ SY469 ) @ SY469 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[362]) ).
thf(398,plain,
! [SV143: $i,SV113: $i,SV66: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV66 @ SV15 @ SV113 ) )
= $true )
| ( ( ! [SY471: $i] :
( ~ ( equidistant @ SV15 @ SV143 @ SV15 @ SY471 )
| ~ ( between @ SV15 @ SV66 @ SV143 )
| ! [SY472: $i] :
( ~ ( between @ SV66 @ SY472 @ SV143 )
| ( equidistant @ SV15 @ SY472 @ SV15 @ ( continuous @ SV15 @ SV66 @ SV113 @ SY472 @ SV143 @ SY471 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[363]) ).
thf(399,plain,
! [SV144: $i,SV114: $i,SV69: $i,SV18: $i] :
( ( ( ~ ( equidistant @ SV18 @ SV69 @ SV114 @ SV144 ) )
= $true )
| ( ( equidistant @ SV114 @ SV144 @ SV18 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[364]) ).
thf(400,plain,
! [SV145: $i,SV115: $i,SV70: $i,SV19: $i] :
( ( ( ~ ( equidistant @ SV19 @ SV70 @ SV115 @ SV145 ) )
= $true )
| ( ( equidistant @ SV70 @ SV19 @ SV115 @ SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[365]) ).
thf(401,plain,
! [SV146: $i,SV116: $i,SV71: $i,SV20: $i] :
( ( ( ~ ( equidistant @ SV20 @ SV71 @ SV116 @ SV146 ) )
= $true )
| ( ( equidistant @ SV20 @ SV71 @ SV146 @ SV116 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[366]) ).
thf(402,plain,
! [SV147: $i,SV117: $i,SV72: $i,SV21: $i] :
( ( ( ~ ( equidistant @ SV21 @ SV72 @ SV117 @ SV147 ) )
= $true )
| ( ( equidistant @ SV72 @ SV21 @ SV147 @ SV117 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[367]) ).
thf(403,plain,
! [SV148: $i,SV118: $i,SV73: $i,SV22: $i] :
( ( ( ~ ( equidistant @ SV22 @ SV73 @ SV118 @ SV148 ) )
= $true )
| ( ( equidistant @ SV118 @ SV148 @ SV73 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[368]) ).
thf(404,plain,
! [SV149: $i,SV119: $i,SV74: $i,SV23: $i] :
( ( ( ~ ( equidistant @ SV23 @ SV74 @ SV119 @ SV149 ) )
= $true )
| ( ( equidistant @ SV149 @ SV119 @ SV23 @ SV74 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[369]) ).
thf(405,plain,
! [SV150: $i,SV120: $i,SV75: $i,SV24: $i] :
( ( ( ~ ( equidistant @ SV24 @ SV75 @ SV120 @ SV150 ) )
= $true )
| ( ( equidistant @ SV150 @ SV120 @ SV75 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[370]) ).
thf(406,plain,
! [SV151: $i,SV121: $i,SV76: $i,SV25: $i] :
( ( ( ~ ( equidistant @ SV25 @ SV76 @ SV121 @ SV151 ) )
= $true )
| ( ( ! [SY473: $i,SY474: $i] :
( ~ ( equidistant @ SV121 @ SV151 @ SY473 @ SY474 )
| ( equidistant @ SV25 @ SV76 @ SY473 @ SY474 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[371]) ).
thf(407,plain,
! [SV155: $i,SV123: $i,SV78: $i,SV27: $i] :
( ( ( ! [SY482: $i] :
( SV27
!= ( extension @ SV78 @ SV123 @ SV155 @ SY482 ) ) )
= $true )
| ( ( between @ SV78 @ SV123 @ SV27 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(408,plain,
! [SV152: $i,SV124: $i,SV84: $i,SV34: $i] :
( ( ( ~ ( equidistant @ SV34 @ SV84 @ SV124 @ SV152 ) )
= $true )
| ( ( ! [SY475: $i,SY476: $i] :
( ~ ( equidistant @ SV84 @ SY475 @ SV152 @ SY476 )
| ~ ( between @ SV34 @ SV84 @ SY475 )
| ~ ( between @ SV124 @ SV152 @ SY476 )
| ( equidistant @ SV34 @ SY475 @ SV124 @ SY476 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[375]) ).
thf(409,plain,
! [SV125: $i,SV85: $i,SV35: $i] :
( ( ( between @ SV35 @ SV85 @ SV125 )
= $false )
| ( ( ! [SY455: $i] :
( ~ ( between @ SV35 @ SV85 @ SY455 )
| ~ ( equidistant @ SV85 @ SV125 @ SV85 @ SY455 )
| ( SV35 = SV85 )
| ( SV125 = SY455 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[376]) ).
thf(410,plain,
! [SV126: $i,SV86: $i,SV36: $i] :
( ( ( between @ SV36 @ SV86 @ SV126 )
= $false )
| ( ( ( SV36 = SV86 )
| ( SV126
= ( extension @ SV36 @ SV86 @ SV86 @ SV126 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(411,plain,
! [SV153: $i,SV127: $i,SV87: $i,SV37: $i] :
( ( ( ~ ( equidistant @ SV37 @ SV87 @ SV127 @ SV153 ) )
= $true )
| ( ( ! [SY477: $i,SY478: $i] :
( ( ( extension @ SY477 @ SY478 @ SV37 @ SV87 )
= ( extension @ SY477 @ SY478 @ SV127 @ SV153 ) )
| ( SY477 = SY478 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[378]) ).
thf(412,plain,
! [SV128: $i,SV92: $i,SV42: $i] :
( ( ( between @ SV42 @ SV92 @ SV128 )
= $false )
| ( ( ( SV42 != SV128 )
| ! [SY459: $i] : ( between @ SY459 @ SV92 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[379]) ).
thf(413,plain,
! [SV129: $i,SV93: $i,SV43: $i] :
( ( ( between @ SV43 @ SV93 @ SV129 )
= $false )
| ( ( between @ SV129 @ SV93 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(414,plain,
! [SV130: $i,SV95: $i,SV45: $i] :
( ( ( between @ SV45 @ SV95 @ SV130 )
= $false )
| ( ( ~ ( between @ SV95 @ SV45 @ SV130 )
| ( SV45 = SV95 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[381]) ).
thf(415,plain,
! [SV131: $i,SV96: $i,SV46: $i] :
( ( ( between @ SV46 @ SV96 @ SV131 )
= $false )
| ( ( ~ ( between @ SV46 @ SV131 @ SV96 )
| ( SV96 = SV131 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[382]) ).
thf(416,plain,
! [SV132: $i,SV97: $i,SV47: $i] :
( ( ( between @ SV47 @ SV97 @ SV132 )
= $false )
| ( ( ~ ( between @ SV97 @ SV47 @ SV132 )
| ( SV47 = SV97 )
| ( SV97 = SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[383]) ).
thf(417,plain,
! [SV133: $i,SV98: $i,SV48: $i] :
( ( ( between @ SV48 @ SV98 @ SV133 )
= $false )
| ( ( ~ ( between @ SV48 @ SV133 @ SV98 )
| ( SV48 = SV98 )
| ( SV98 = SV133 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[384]) ).
thf(418,plain,
! [SV134: $i,SV99: $i,SV49: $i] :
( ( ( between @ SV49 @ SV99 @ SV134 )
= $false )
| ( ( ! [SY460: $i] :
~ ( between @ SV99 @ SV134 @ SY460 )
| ( between @ SV49 @ SV99 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[385]) ).
thf(419,plain,
! [SV135: $i,SV100: $i,SV50: $i] :
( ( ( between @ SV50 @ SV100 @ SV135 )
= $false )
| ( ( ! [SY461: $i] :
( ~ ( between @ SV50 @ SV135 @ SY461 )
| ( between @ SV100 @ SV135 @ SY461 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[386]) ).
thf(420,plain,
! [SV136: $i,SV101: $i,SV51: $i] :
( ( ( between @ SV51 @ SV101 @ SV136 )
= $false )
| ( ( ! [SY462: $i] :
( ~ ( between @ SV101 @ SV136 @ SY462 )
| ( SV101 = SV136 )
| ( between @ SV51 @ SV136 @ SY462 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[387]) ).
thf(421,plain,
! [SV137: $i,SV102: $i,SV53: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV53 @ SV102 @ SV137 )
= $false )
| ( ( ! [SY463: $i,SY464: $i] :
( ~ ( equidistant @ SV2 @ SV53 @ SY463 @ SY464 )
| ( equidistant @ SV102 @ SV137 @ SY463 @ SY464 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[388]) ).
thf(422,plain,
! [SV156: $i,SV154: $i,SV141: $i,SV105: $i,SV57: $i,SV6: $i] :
( ( ~ ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
| ~ ( equidistant @ SV57 @ SV154 @ SV141 @ SV156 )
| ! [SY483: $i,SY484: $i] :
( ~ ( equidistant @ SV6 @ SY483 @ SV105 @ SY484 )
| ~ ( equidistant @ SV57 @ SY483 @ SV141 @ SY484 )
| ~ ( between @ SV6 @ SV57 @ SV154 )
| ~ ( between @ SV105 @ SV141 @ SV156 )
| ( SV6 = SV57 )
| ( equidistant @ SV154 @ SY483 @ SV156 @ SY484 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(423,plain,
! [SV8: $i,SV59: $i,SV106: $i,SV157: $i] :
( ( ( ! [SY485: $i] :
( ~ ( between @ SV157 @ SY485 @ SV106 )
| ( between @ SV59 @ ( inner_pasch @ SV8 @ SV59 @ SV106 @ SY485 @ SV157 ) @ SV157 ) ) )
= $true )
| ( ( between @ SV8 @ SV59 @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(424,plain,
! [SV60: $i,SV9: $i,SV107: $i,SV158: $i] :
( ( ( ! [SY486: $i] :
( ~ ( between @ SV158 @ SY486 @ SV107 )
| ( between @ SY486 @ ( inner_pasch @ SV9 @ SV60 @ SV107 @ SY486 @ SV158 ) @ SV9 ) ) )
= $true )
| ( ( between @ SV9 @ SV60 @ SV107 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(425,plain,
! [SV10: $i,SV108: $i,SV61: $i,SV159: $i] :
( ( ( ~ ( equidistant @ SV159 @ SV61 @ SV159 @ SV108 )
| ! [SY487: $i] :
( ~ ( equidistant @ SY487 @ SV61 @ SY487 @ SV108 )
| ( between @ SV10 @ SV159 @ SY487 )
| ( between @ SV159 @ SY487 @ SV10 )
| ( SV61 = SV108 )
| ( between @ SY487 @ SV10 @ SV159 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV61 @ SV10 @ SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(426,plain,
! [SV109: $i,SV11: $i,SV62: $i,SV160: $i] :
( ( ( ! [SY488: $i] :
( ~ ( between @ SV160 @ SV62 @ SY488 )
| ( SV11 = SV62 )
| ( between @ SV11 @ SV160 @ ( euclid1 @ SV11 @ SV160 @ SV62 @ SY488 @ SV109 ) ) ) )
= $true )
| ( ( between @ SV11 @ SV62 @ SV109 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(427,plain,
! [SV110: $i,SV12: $i,SV63: $i,SV161: $i] :
( ( ( ! [SY489: $i] :
( ~ ( between @ SV161 @ SV63 @ SY489 )
| ( SV12 = SV63 )
| ( between @ SV12 @ SY489 @ ( euclid2 @ SV12 @ SV161 @ SV63 @ SY489 @ SV110 ) ) ) )
= $true )
| ( ( between @ SV12 @ SV63 @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(428,plain,
! [SV111: $i,SV13: $i,SV64: $i,SV162: $i] :
( ( ( ! [SY490: $i] :
( ~ ( between @ SV162 @ SV64 @ SY490 )
| ( SV13 = SV64 )
| ( between @ ( euclid1 @ SV13 @ SV162 @ SV64 @ SY490 @ SV111 ) @ SV111 @ ( euclid2 @ SV13 @ SV162 @ SV64 @ SY490 @ SV111 ) ) ) )
= $true )
| ( ( between @ SV13 @ SV64 @ SV111 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(429,plain,
! [SV142: $i,SV112: $i,SV65: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV65 @ SV14 @ SV112 )
= $false )
| ( ( ! [SY469: $i] :
( ~ ( equidistant @ SV14 @ SV142 @ SV14 @ SY469 )
| ~ ( between @ SV14 @ SV65 @ SV142 )
| ! [SY470: $i] :
( ~ ( between @ SV65 @ SY470 @ SV142 )
| ( between @ SV112 @ ( continuous @ SV14 @ SV65 @ SV112 @ SY470 @ SV142 @ SY469 ) @ SY469 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[397]) ).
thf(430,plain,
! [SV143: $i,SV113: $i,SV66: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV66 @ SV15 @ SV113 )
= $false )
| ( ( ! [SY471: $i] :
( ~ ( equidistant @ SV15 @ SV143 @ SV15 @ SY471 )
| ~ ( between @ SV15 @ SV66 @ SV143 )
| ! [SY472: $i] :
( ~ ( between @ SV66 @ SY472 @ SV143 )
| ( equidistant @ SV15 @ SY472 @ SV15 @ ( continuous @ SV15 @ SV66 @ SV113 @ SY472 @ SV143 @ SY471 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[398]) ).
thf(431,plain,
! [SV144: $i,SV114: $i,SV69: $i,SV18: $i] :
( ( ( equidistant @ SV18 @ SV69 @ SV114 @ SV144 )
= $false )
| ( ( equidistant @ SV114 @ SV144 @ SV18 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[399]) ).
thf(432,plain,
! [SV145: $i,SV115: $i,SV70: $i,SV19: $i] :
( ( ( equidistant @ SV19 @ SV70 @ SV115 @ SV145 )
= $false )
| ( ( equidistant @ SV70 @ SV19 @ SV115 @ SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[400]) ).
thf(433,plain,
! [SV146: $i,SV116: $i,SV71: $i,SV20: $i] :
( ( ( equidistant @ SV20 @ SV71 @ SV116 @ SV146 )
= $false )
| ( ( equidistant @ SV20 @ SV71 @ SV146 @ SV116 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[401]) ).
thf(434,plain,
! [SV147: $i,SV117: $i,SV72: $i,SV21: $i] :
( ( ( equidistant @ SV21 @ SV72 @ SV117 @ SV147 )
= $false )
| ( ( equidistant @ SV72 @ SV21 @ SV147 @ SV117 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[402]) ).
thf(435,plain,
! [SV148: $i,SV118: $i,SV73: $i,SV22: $i] :
( ( ( equidistant @ SV22 @ SV73 @ SV118 @ SV148 )
= $false )
| ( ( equidistant @ SV118 @ SV148 @ SV73 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(436,plain,
! [SV149: $i,SV119: $i,SV74: $i,SV23: $i] :
( ( ( equidistant @ SV23 @ SV74 @ SV119 @ SV149 )
= $false )
| ( ( equidistant @ SV149 @ SV119 @ SV23 @ SV74 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[404]) ).
thf(437,plain,
! [SV150: $i,SV120: $i,SV75: $i,SV24: $i] :
( ( ( equidistant @ SV24 @ SV75 @ SV120 @ SV150 )
= $false )
| ( ( equidistant @ SV150 @ SV120 @ SV75 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[405]) ).
thf(438,plain,
! [SV151: $i,SV121: $i,SV76: $i,SV25: $i] :
( ( ( equidistant @ SV25 @ SV76 @ SV121 @ SV151 )
= $false )
| ( ( ! [SY473: $i,SY474: $i] :
( ~ ( equidistant @ SV121 @ SV151 @ SY473 @ SY474 )
| ( equidistant @ SV25 @ SV76 @ SY473 @ SY474 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[406]) ).
thf(439,plain,
! [SV163: $i,SV155: $i,SV123: $i,SV78: $i,SV27: $i] :
( ( ( ( SV27
!= ( extension @ SV78 @ SV123 @ SV155 @ SV163 ) ) )
= $true )
| ( ( between @ SV78 @ SV123 @ SV27 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(440,plain,
! [SV152: $i,SV124: $i,SV84: $i,SV34: $i] :
( ( ( equidistant @ SV34 @ SV84 @ SV124 @ SV152 )
= $false )
| ( ( ! [SY475: $i,SY476: $i] :
( ~ ( equidistant @ SV84 @ SY475 @ SV152 @ SY476 )
| ~ ( between @ SV34 @ SV84 @ SY475 )
| ~ ( between @ SV124 @ SV152 @ SY476 )
| ( equidistant @ SV34 @ SY475 @ SV124 @ SY476 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(441,plain,
! [SV125: $i,SV164: $i,SV85: $i,SV35: $i] :
( ( ( ~ ( between @ SV35 @ SV85 @ SV164 )
| ~ ( equidistant @ SV85 @ SV125 @ SV85 @ SV164 )
| ( SV35 = SV85 )
| ( SV125 = SV164 ) )
= $true )
| ( ( between @ SV35 @ SV85 @ SV125 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[409]) ).
thf(442,plain,
! [SV126: $i,SV86: $i,SV36: $i] :
( ( ( SV36 = SV86 )
= $true )
| ( ( SV126
= ( extension @ SV36 @ SV86 @ SV86 @ SV126 ) )
= $true )
| ( ( between @ SV36 @ SV86 @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[410]) ).
thf(443,plain,
! [SV153: $i,SV127: $i,SV87: $i,SV37: $i] :
( ( ( equidistant @ SV37 @ SV87 @ SV127 @ SV153 )
= $false )
| ( ( ! [SY477: $i,SY478: $i] :
( ( ( extension @ SY477 @ SY478 @ SV37 @ SV87 )
= ( extension @ SY477 @ SY478 @ SV127 @ SV153 ) )
| ( SY477 = SY478 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[411]) ).
thf(444,plain,
! [SV92: $i,SV128: $i,SV42: $i] :
( ( ( ( SV42 != SV128 ) )
= $true )
| ( ( ! [SY459: $i] : ( between @ SY459 @ SV92 @ SV128 ) )
= $true )
| ( ( between @ SV42 @ SV92 @ SV128 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[412]) ).
thf(445,plain,
! [SV130: $i,SV45: $i,SV95: $i] :
( ( ( ~ ( between @ SV95 @ SV45 @ SV130 ) )
= $true )
| ( ( SV45 = SV95 )
= $true )
| ( ( between @ SV45 @ SV95 @ SV130 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(446,plain,
! [SV96: $i,SV131: $i,SV46: $i] :
( ( ( ~ ( between @ SV46 @ SV131 @ SV96 ) )
= $true )
| ( ( SV96 = SV131 )
= $true )
| ( ( between @ SV46 @ SV96 @ SV131 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[415]) ).
thf(447,plain,
! [SV132: $i,SV47: $i,SV97: $i] :
( ( ( ~ ( between @ SV97 @ SV47 @ SV132 ) )
= $true )
| ( ( ( SV47 = SV97 )
| ( SV97 = SV132 ) )
= $true )
| ( ( between @ SV47 @ SV97 @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(448,plain,
! [SV98: $i,SV133: $i,SV48: $i] :
( ( ( ~ ( between @ SV48 @ SV133 @ SV98 ) )
= $true )
| ( ( ( SV48 = SV98 )
| ( SV98 = SV133 ) )
= $true )
| ( ( between @ SV48 @ SV98 @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(449,plain,
! [SV49: $i,SV134: $i,SV99: $i] :
( ( ( ! [SY460: $i] :
~ ( between @ SV99 @ SV134 @ SY460 ) )
= $true )
| ( ( between @ SV49 @ SV99 @ SV134 )
= $true )
| ( ( between @ SV49 @ SV99 @ SV134 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(450,plain,
! [SV100: $i,SV165: $i,SV135: $i,SV50: $i] :
( ( ( ~ ( between @ SV50 @ SV135 @ SV165 )
| ( between @ SV100 @ SV135 @ SV165 ) )
= $true )
| ( ( between @ SV50 @ SV100 @ SV135 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(451,plain,
! [SV51: $i,SV166: $i,SV136: $i,SV101: $i] :
( ( ( ~ ( between @ SV101 @ SV136 @ SV166 )
| ( SV101 = SV136 )
| ( between @ SV51 @ SV136 @ SV166 ) )
= $true )
| ( ( between @ SV51 @ SV101 @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(452,plain,
! [SV137: $i,SV102: $i,SV167: $i,SV53: $i,SV2: $i] :
( ( ( ! [SY491: $i] :
( ~ ( equidistant @ SV2 @ SV53 @ SV167 @ SY491 )
| ( equidistant @ SV102 @ SV137 @ SV167 @ SY491 ) ) )
= $true )
| ( ( equidistant @ SV2 @ SV53 @ SV102 @ SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(453,plain,
! [SV156: $i,SV154: $i,SV141: $i,SV105: $i,SV57: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 ) )
= $true )
| ( ( ~ ( equidistant @ SV57 @ SV154 @ SV141 @ SV156 )
| ! [SY483: $i,SY484: $i] :
( ~ ( equidistant @ SV6 @ SY483 @ SV105 @ SY484 )
| ~ ( equidistant @ SV57 @ SY483 @ SV141 @ SY484 )
| ~ ( between @ SV6 @ SV57 @ SV154 )
| ~ ( between @ SV105 @ SV141 @ SV156 )
| ( SV6 = SV57 )
| ( equidistant @ SV154 @ SY483 @ SV156 @ SY484 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[422]) ).
thf(454,plain,
! [SV8: $i,SV59: $i,SV106: $i,SV168: $i,SV157: $i] :
( ( ( ~ ( between @ SV157 @ SV168 @ SV106 )
| ( between @ SV59 @ ( inner_pasch @ SV8 @ SV59 @ SV106 @ SV168 @ SV157 ) @ SV157 ) )
= $true )
| ( ( between @ SV8 @ SV59 @ SV106 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(455,plain,
! [SV60: $i,SV9: $i,SV107: $i,SV169: $i,SV158: $i] :
( ( ( ~ ( between @ SV158 @ SV169 @ SV107 )
| ( between @ SV169 @ ( inner_pasch @ SV9 @ SV60 @ SV107 @ SV169 @ SV158 ) @ SV9 ) )
= $true )
| ( ( between @ SV9 @ SV60 @ SV107 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[424]) ).
thf(456,plain,
! [SV10: $i,SV108: $i,SV61: $i,SV159: $i] :
( ( ( ~ ( equidistant @ SV159 @ SV61 @ SV159 @ SV108 ) )
= $true )
| ( ( ! [SY487: $i] :
( ~ ( equidistant @ SY487 @ SV61 @ SY487 @ SV108 )
| ( between @ SV10 @ SV159 @ SY487 )
| ( between @ SV159 @ SY487 @ SV10 )
| ( SV61 = SV108 )
| ( between @ SY487 @ SV10 @ SV159 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV61 @ SV10 @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[425]) ).
thf(457,plain,
! [SV109: $i,SV11: $i,SV170: $i,SV62: $i,SV160: $i] :
( ( ( ~ ( between @ SV160 @ SV62 @ SV170 )
| ( SV11 = SV62 )
| ( between @ SV11 @ SV160 @ ( euclid1 @ SV11 @ SV160 @ SV62 @ SV170 @ SV109 ) ) )
= $true )
| ( ( between @ SV11 @ SV62 @ SV109 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(458,plain,
! [SV110: $i,SV12: $i,SV171: $i,SV63: $i,SV161: $i] :
( ( ( ~ ( between @ SV161 @ SV63 @ SV171 )
| ( SV12 = SV63 )
| ( between @ SV12 @ SV171 @ ( euclid2 @ SV12 @ SV161 @ SV63 @ SV171 @ SV110 ) ) )
= $true )
| ( ( between @ SV12 @ SV63 @ SV110 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(459,plain,
! [SV111: $i,SV13: $i,SV172: $i,SV64: $i,SV162: $i] :
( ( ( ~ ( between @ SV162 @ SV64 @ SV172 )
| ( SV13 = SV64 )
| ( between @ ( euclid1 @ SV13 @ SV162 @ SV64 @ SV172 @ SV111 ) @ SV111 @ ( euclid2 @ SV13 @ SV162 @ SV64 @ SV172 @ SV111 ) ) )
= $true )
| ( ( between @ SV13 @ SV64 @ SV111 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(460,plain,
! [SV112: $i,SV65: $i,SV173: $i,SV142: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV142 @ SV14 @ SV173 )
| ~ ( between @ SV14 @ SV65 @ SV142 )
| ! [SY492: $i] :
( ~ ( between @ SV65 @ SY492 @ SV142 )
| ( between @ SV112 @ ( continuous @ SV14 @ SV65 @ SV112 @ SY492 @ SV142 @ SV173 ) @ SV173 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV65 @ SV14 @ SV112 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(461,plain,
! [SV113: $i,SV66: $i,SV174: $i,SV143: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV143 @ SV15 @ SV174 )
| ~ ( between @ SV15 @ SV66 @ SV143 )
| ! [SY493: $i] :
( ~ ( between @ SV66 @ SY493 @ SV143 )
| ( equidistant @ SV15 @ SY493 @ SV15 @ ( continuous @ SV15 @ SV66 @ SV113 @ SY493 @ SV143 @ SV174 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV66 @ SV15 @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(462,plain,
! [SV76: $i,SV25: $i,SV175: $i,SV151: $i,SV121: $i] :
( ( ( ! [SY494: $i] :
( ~ ( equidistant @ SV121 @ SV151 @ SV175 @ SY494 )
| ( equidistant @ SV25 @ SV76 @ SV175 @ SY494 ) ) )
= $true )
| ( ( equidistant @ SV25 @ SV76 @ SV121 @ SV151 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(463,plain,
! [SV163: $i,SV155: $i,SV123: $i,SV78: $i,SV27: $i] :
( ( ( SV27
= ( extension @ SV78 @ SV123 @ SV155 @ SV163 ) )
= $false )
| ( ( between @ SV78 @ SV123 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[439]) ).
thf(464,plain,
! [SV124: $i,SV34: $i,SV152: $i,SV176: $i,SV84: $i] :
( ( ( ! [SY495: $i] :
( ~ ( equidistant @ SV84 @ SV176 @ SV152 @ SY495 )
| ~ ( between @ SV34 @ SV84 @ SV176 )
| ~ ( between @ SV124 @ SV152 @ SY495 )
| ( equidistant @ SV34 @ SV176 @ SV124 @ SY495 ) ) )
= $true )
| ( ( equidistant @ SV34 @ SV84 @ SV124 @ SV152 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(465,plain,
! [SV125: $i,SV164: $i,SV85: $i,SV35: $i] :
( ( ( ~ ( between @ SV35 @ SV85 @ SV164 ) )
= $true )
| ( ( ~ ( equidistant @ SV85 @ SV125 @ SV85 @ SV164 )
| ( SV35 = SV85 )
| ( SV125 = SV164 ) )
= $true )
| ( ( between @ SV35 @ SV85 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(466,plain,
! [SV153: $i,SV127: $i,SV87: $i,SV37: $i,SV177: $i] :
( ( ( ! [SY496: $i] :
( ( ( extension @ SV177 @ SY496 @ SV37 @ SV87 )
= ( extension @ SV177 @ SY496 @ SV127 @ SV153 ) )
| ( SV177 = SY496 ) ) )
= $true )
| ( ( equidistant @ SV37 @ SV87 @ SV127 @ SV153 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(467,plain,
! [SV92: $i,SV128: $i,SV42: $i] :
( ( ( SV42 = SV128 )
= $false )
| ( ( ! [SY459: $i] : ( between @ SY459 @ SV92 @ SV128 ) )
= $true )
| ( ( between @ SV42 @ SV92 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(468,plain,
! [SV130: $i,SV45: $i,SV95: $i] :
( ( ( between @ SV95 @ SV45 @ SV130 )
= $false )
| ( ( SV45 = SV95 )
= $true )
| ( ( between @ SV45 @ SV95 @ SV130 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(469,plain,
! [SV96: $i,SV131: $i,SV46: $i] :
( ( ( between @ SV46 @ SV131 @ SV96 )
= $false )
| ( ( SV96 = SV131 )
= $true )
| ( ( between @ SV46 @ SV96 @ SV131 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[446]) ).
thf(470,plain,
! [SV132: $i,SV47: $i,SV97: $i] :
( ( ( between @ SV97 @ SV47 @ SV132 )
= $false )
| ( ( ( SV47 = SV97 )
| ( SV97 = SV132 ) )
= $true )
| ( ( between @ SV47 @ SV97 @ SV132 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[447]) ).
thf(471,plain,
! [SV98: $i,SV133: $i,SV48: $i] :
( ( ( between @ SV48 @ SV133 @ SV98 )
= $false )
| ( ( ( SV48 = SV98 )
| ( SV98 = SV133 ) )
= $true )
| ( ( between @ SV48 @ SV98 @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[448]) ).
thf(472,plain,
! [SV49: $i,SV178: $i,SV134: $i,SV99: $i] :
( ( ( ~ ( between @ SV99 @ SV134 @ SV178 ) )
= $true )
| ( ( between @ SV49 @ SV99 @ SV134 )
= $true )
| ( ( between @ SV49 @ SV99 @ SV134 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(473,plain,
! [SV100: $i,SV165: $i,SV135: $i,SV50: $i] :
( ( ( ~ ( between @ SV50 @ SV135 @ SV165 ) )
= $true )
| ( ( between @ SV100 @ SV135 @ SV165 )
= $true )
| ( ( between @ SV50 @ SV100 @ SV135 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(474,plain,
! [SV51: $i,SV166: $i,SV136: $i,SV101: $i] :
( ( ( ~ ( between @ SV101 @ SV136 @ SV166 ) )
= $true )
| ( ( ( SV101 = SV136 )
| ( between @ SV51 @ SV136 @ SV166 ) )
= $true )
| ( ( between @ SV51 @ SV101 @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(475,plain,
! [SV137: $i,SV102: $i,SV179: $i,SV167: $i,SV53: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV53 @ SV167 @ SV179 )
| ( equidistant @ SV102 @ SV137 @ SV167 @ SV179 ) )
= $true )
| ( ( equidistant @ SV2 @ SV53 @ SV102 @ SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(476,plain,
! [SV156: $i,SV154: $i,SV141: $i,SV105: $i,SV57: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
= $false )
| ( ( ~ ( equidistant @ SV57 @ SV154 @ SV141 @ SV156 )
| ! [SY483: $i,SY484: $i] :
( ~ ( equidistant @ SV6 @ SY483 @ SV105 @ SY484 )
| ~ ( equidistant @ SV57 @ SY483 @ SV141 @ SY484 )
| ~ ( between @ SV6 @ SV57 @ SV154 )
| ~ ( between @ SV105 @ SV141 @ SV156 )
| ( SV6 = SV57 )
| ( equidistant @ SV154 @ SY483 @ SV156 @ SY484 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[453]) ).
thf(477,plain,
! [SV8: $i,SV59: $i,SV106: $i,SV168: $i,SV157: $i] :
( ( ( ~ ( between @ SV157 @ SV168 @ SV106 ) )
= $true )
| ( ( between @ SV59 @ ( inner_pasch @ SV8 @ SV59 @ SV106 @ SV168 @ SV157 ) @ SV157 )
= $true )
| ( ( between @ SV8 @ SV59 @ SV106 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[454]) ).
thf(478,plain,
! [SV60: $i,SV9: $i,SV107: $i,SV169: $i,SV158: $i] :
( ( ( ~ ( between @ SV158 @ SV169 @ SV107 ) )
= $true )
| ( ( between @ SV169 @ ( inner_pasch @ SV9 @ SV60 @ SV107 @ SV169 @ SV158 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV60 @ SV107 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[455]) ).
thf(479,plain,
! [SV10: $i,SV108: $i,SV61: $i,SV159: $i] :
( ( ( equidistant @ SV159 @ SV61 @ SV159 @ SV108 )
= $false )
| ( ( ! [SY487: $i] :
( ~ ( equidistant @ SY487 @ SV61 @ SY487 @ SV108 )
| ( between @ SV10 @ SV159 @ SY487 )
| ( between @ SV159 @ SY487 @ SV10 )
| ( SV61 = SV108 )
| ( between @ SY487 @ SV10 @ SV159 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV61 @ SV10 @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(480,plain,
! [SV109: $i,SV11: $i,SV170: $i,SV62: $i,SV160: $i] :
( ( ( ~ ( between @ SV160 @ SV62 @ SV170 ) )
= $true )
| ( ( ( SV11 = SV62 )
| ( between @ SV11 @ SV160 @ ( euclid1 @ SV11 @ SV160 @ SV62 @ SV170 @ SV109 ) ) )
= $true )
| ( ( between @ SV11 @ SV62 @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[457]) ).
thf(481,plain,
! [SV110: $i,SV12: $i,SV171: $i,SV63: $i,SV161: $i] :
( ( ( ~ ( between @ SV161 @ SV63 @ SV171 ) )
= $true )
| ( ( ( SV12 = SV63 )
| ( between @ SV12 @ SV171 @ ( euclid2 @ SV12 @ SV161 @ SV63 @ SV171 @ SV110 ) ) )
= $true )
| ( ( between @ SV12 @ SV63 @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[458]) ).
thf(482,plain,
! [SV111: $i,SV13: $i,SV172: $i,SV64: $i,SV162: $i] :
( ( ( ~ ( between @ SV162 @ SV64 @ SV172 ) )
= $true )
| ( ( ( SV13 = SV64 )
| ( between @ ( euclid1 @ SV13 @ SV162 @ SV64 @ SV172 @ SV111 ) @ SV111 @ ( euclid2 @ SV13 @ SV162 @ SV64 @ SV172 @ SV111 ) ) )
= $true )
| ( ( between @ SV13 @ SV64 @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[459]) ).
thf(483,plain,
! [SV112: $i,SV65: $i,SV173: $i,SV142: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV142 @ SV14 @ SV173 ) )
= $true )
| ( ( ~ ( between @ SV14 @ SV65 @ SV142 )
| ! [SY492: $i] :
( ~ ( between @ SV65 @ SY492 @ SV142 )
| ( between @ SV112 @ ( continuous @ SV14 @ SV65 @ SV112 @ SY492 @ SV142 @ SV173 ) @ SV173 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV65 @ SV14 @ SV112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[460]) ).
thf(484,plain,
! [SV113: $i,SV66: $i,SV174: $i,SV143: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV143 @ SV15 @ SV174 ) )
= $true )
| ( ( ~ ( between @ SV15 @ SV66 @ SV143 )
| ! [SY493: $i] :
( ~ ( between @ SV66 @ SY493 @ SV143 )
| ( equidistant @ SV15 @ SY493 @ SV15 @ ( continuous @ SV15 @ SV66 @ SV113 @ SY493 @ SV143 @ SV174 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV66 @ SV15 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[461]) ).
thf(485,plain,
! [SV76: $i,SV25: $i,SV180: $i,SV175: $i,SV151: $i,SV121: $i] :
( ( ( ~ ( equidistant @ SV121 @ SV151 @ SV175 @ SV180 )
| ( equidistant @ SV25 @ SV76 @ SV175 @ SV180 ) )
= $true )
| ( ( equidistant @ SV25 @ SV76 @ SV121 @ SV151 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(486,plain,
! [SV124: $i,SV34: $i,SV181: $i,SV152: $i,SV176: $i,SV84: $i] :
( ( ( ~ ( equidistant @ SV84 @ SV176 @ SV152 @ SV181 )
| ~ ( between @ SV34 @ SV84 @ SV176 )
| ~ ( between @ SV124 @ SV152 @ SV181 )
| ( equidistant @ SV34 @ SV176 @ SV124 @ SV181 ) )
= $true )
| ( ( equidistant @ SV34 @ SV84 @ SV124 @ SV152 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(487,plain,
! [SV125: $i,SV164: $i,SV85: $i,SV35: $i] :
( ( ( between @ SV35 @ SV85 @ SV164 )
= $false )
| ( ( ~ ( equidistant @ SV85 @ SV125 @ SV85 @ SV164 )
| ( SV35 = SV85 )
| ( SV125 = SV164 ) )
= $true )
| ( ( between @ SV35 @ SV85 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(488,plain,
! [SV153: $i,SV127: $i,SV87: $i,SV37: $i,SV182: $i,SV177: $i] :
( ( ( ( ( extension @ SV177 @ SV182 @ SV37 @ SV87 )
= ( extension @ SV177 @ SV182 @ SV127 @ SV153 ) )
| ( SV177 = SV182 ) )
= $true )
| ( ( equidistant @ SV37 @ SV87 @ SV127 @ SV153 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(489,plain,
! [SV42: $i,SV128: $i,SV92: $i,SV183: $i] :
( ( ( between @ SV183 @ SV92 @ SV128 )
= $true )
| ( ( SV42 = SV128 )
= $false )
| ( ( between @ SV42 @ SV92 @ SV128 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(490,plain,
! [SV132: $i,SV97: $i,SV47: $i] :
( ( ( SV47 = SV97 )
= $true )
| ( ( SV97 = SV132 )
= $true )
| ( ( between @ SV97 @ SV47 @ SV132 )
= $false )
| ( ( between @ SV47 @ SV97 @ SV132 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(491,plain,
! [SV133: $i,SV98: $i,SV48: $i] :
( ( ( SV48 = SV98 )
= $true )
| ( ( SV98 = SV133 )
= $true )
| ( ( between @ SV48 @ SV133 @ SV98 )
= $false )
| ( ( between @ SV48 @ SV98 @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[471]) ).
thf(492,plain,
! [SV49: $i,SV178: $i,SV134: $i,SV99: $i] :
( ( ( between @ SV99 @ SV134 @ SV178 )
= $false )
| ( ( between @ SV49 @ SV99 @ SV134 )
= $true )
| ( ( between @ SV49 @ SV99 @ SV134 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[472]) ).
thf(493,plain,
! [SV100: $i,SV165: $i,SV135: $i,SV50: $i] :
( ( ( between @ SV50 @ SV135 @ SV165 )
= $false )
| ( ( between @ SV100 @ SV135 @ SV165 )
= $true )
| ( ( between @ SV50 @ SV100 @ SV135 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(494,plain,
! [SV51: $i,SV166: $i,SV136: $i,SV101: $i] :
( ( ( between @ SV101 @ SV136 @ SV166 )
= $false )
| ( ( ( SV101 = SV136 )
| ( between @ SV51 @ SV136 @ SV166 ) )
= $true )
| ( ( between @ SV51 @ SV101 @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[474]) ).
thf(495,plain,
! [SV137: $i,SV102: $i,SV179: $i,SV167: $i,SV53: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV53 @ SV167 @ SV179 ) )
= $true )
| ( ( equidistant @ SV102 @ SV137 @ SV167 @ SV179 )
= $true )
| ( ( equidistant @ SV2 @ SV53 @ SV102 @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(496,plain,
! [SV105: $i,SV6: $i,SV156: $i,SV141: $i,SV154: $i,SV57: $i] :
( ( ( ~ ( equidistant @ SV57 @ SV154 @ SV141 @ SV156 ) )
= $true )
| ( ( ! [SY483: $i,SY484: $i] :
( ~ ( equidistant @ SV6 @ SY483 @ SV105 @ SY484 )
| ~ ( equidistant @ SV57 @ SY483 @ SV141 @ SY484 )
| ~ ( between @ SV6 @ SV57 @ SV154 )
| ~ ( between @ SV105 @ SV141 @ SV156 )
| ( SV6 = SV57 )
| ( equidistant @ SV154 @ SY483 @ SV156 @ SY484 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(497,plain,
! [SV8: $i,SV59: $i,SV106: $i,SV168: $i,SV157: $i] :
( ( ( between @ SV157 @ SV168 @ SV106 )
= $false )
| ( ( between @ SV59 @ ( inner_pasch @ SV8 @ SV59 @ SV106 @ SV168 @ SV157 ) @ SV157 )
= $true )
| ( ( between @ SV8 @ SV59 @ SV106 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[477]) ).
thf(498,plain,
! [SV60: $i,SV9: $i,SV107: $i,SV169: $i,SV158: $i] :
( ( ( between @ SV158 @ SV169 @ SV107 )
= $false )
| ( ( between @ SV169 @ ( inner_pasch @ SV9 @ SV60 @ SV107 @ SV169 @ SV158 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV60 @ SV107 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[478]) ).
thf(499,plain,
! [SV159: $i,SV10: $i,SV108: $i,SV61: $i,SV184: $i] :
( ( ( ~ ( equidistant @ SV184 @ SV61 @ SV184 @ SV108 )
| ( between @ SV10 @ SV159 @ SV184 )
| ( between @ SV159 @ SV184 @ SV10 )
| ( SV61 = SV108 )
| ( between @ SV184 @ SV10 @ SV159 ) )
= $true )
| ( ( equidistant @ SV159 @ SV61 @ SV159 @ SV108 )
= $false )
| ( ( equidistant @ SV10 @ SV61 @ SV10 @ SV108 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(500,plain,
! [SV109: $i,SV11: $i,SV170: $i,SV62: $i,SV160: $i] :
( ( ( between @ SV160 @ SV62 @ SV170 )
= $false )
| ( ( ( SV11 = SV62 )
| ( between @ SV11 @ SV160 @ ( euclid1 @ SV11 @ SV160 @ SV62 @ SV170 @ SV109 ) ) )
= $true )
| ( ( between @ SV11 @ SV62 @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(501,plain,
! [SV110: $i,SV12: $i,SV171: $i,SV63: $i,SV161: $i] :
( ( ( between @ SV161 @ SV63 @ SV171 )
= $false )
| ( ( ( SV12 = SV63 )
| ( between @ SV12 @ SV171 @ ( euclid2 @ SV12 @ SV161 @ SV63 @ SV171 @ SV110 ) ) )
= $true )
| ( ( between @ SV12 @ SV63 @ SV110 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[481]) ).
thf(502,plain,
! [SV111: $i,SV13: $i,SV172: $i,SV64: $i,SV162: $i] :
( ( ( between @ SV162 @ SV64 @ SV172 )
= $false )
| ( ( ( SV13 = SV64 )
| ( between @ ( euclid1 @ SV13 @ SV162 @ SV64 @ SV172 @ SV111 ) @ SV111 @ ( euclid2 @ SV13 @ SV162 @ SV64 @ SV172 @ SV111 ) ) )
= $true )
| ( ( between @ SV13 @ SV64 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(503,plain,
! [SV112: $i,SV65: $i,SV173: $i,SV142: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV142 @ SV14 @ SV173 )
= $false )
| ( ( ~ ( between @ SV14 @ SV65 @ SV142 )
| ! [SY492: $i] :
( ~ ( between @ SV65 @ SY492 @ SV142 )
| ( between @ SV112 @ ( continuous @ SV14 @ SV65 @ SV112 @ SY492 @ SV142 @ SV173 ) @ SV173 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV65 @ SV14 @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(504,plain,
! [SV113: $i,SV66: $i,SV174: $i,SV143: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV143 @ SV15 @ SV174 )
= $false )
| ( ( ~ ( between @ SV15 @ SV66 @ SV143 )
| ! [SY493: $i] :
( ~ ( between @ SV66 @ SY493 @ SV143 )
| ( equidistant @ SV15 @ SY493 @ SV15 @ ( continuous @ SV15 @ SV66 @ SV113 @ SY493 @ SV143 @ SV174 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV66 @ SV15 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(505,plain,
! [SV76: $i,SV25: $i,SV180: $i,SV175: $i,SV151: $i,SV121: $i] :
( ( ( ~ ( equidistant @ SV121 @ SV151 @ SV175 @ SV180 ) )
= $true )
| ( ( equidistant @ SV25 @ SV76 @ SV175 @ SV180 )
= $true )
| ( ( equidistant @ SV25 @ SV76 @ SV121 @ SV151 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(506,plain,
! [SV124: $i,SV34: $i,SV181: $i,SV152: $i,SV176: $i,SV84: $i] :
( ( ( ~ ( equidistant @ SV84 @ SV176 @ SV152 @ SV181 ) )
= $true )
| ( ( ~ ( between @ SV34 @ SV84 @ SV176 )
| ~ ( between @ SV124 @ SV152 @ SV181 )
| ( equidistant @ SV34 @ SV176 @ SV124 @ SV181 ) )
= $true )
| ( ( equidistant @ SV34 @ SV84 @ SV124 @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[486]) ).
thf(507,plain,
! [SV35: $i,SV164: $i,SV125: $i,SV85: $i] :
( ( ( ~ ( equidistant @ SV85 @ SV125 @ SV85 @ SV164 ) )
= $true )
| ( ( ( SV35 = SV85 )
| ( SV125 = SV164 ) )
= $true )
| ( ( between @ SV35 @ SV85 @ SV164 )
= $false )
| ( ( between @ SV35 @ SV85 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[487]) ).
thf(508,plain,
! [SV153: $i,SV127: $i,SV87: $i,SV37: $i,SV182: $i,SV177: $i] :
( ( ( ( extension @ SV177 @ SV182 @ SV37 @ SV87 )
= ( extension @ SV177 @ SV182 @ SV127 @ SV153 ) )
= $true )
| ( ( SV177 = SV182 )
= $true )
| ( ( equidistant @ SV37 @ SV87 @ SV127 @ SV153 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[488]) ).
thf(509,plain,
! [SV166: $i,SV51: $i,SV136: $i,SV101: $i] :
( ( ( SV101 = SV136 )
= $true )
| ( ( between @ SV51 @ SV136 @ SV166 )
= $true )
| ( ( between @ SV101 @ SV136 @ SV166 )
= $false )
| ( ( between @ SV51 @ SV101 @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[494]) ).
thf(510,plain,
! [SV137: $i,SV102: $i,SV179: $i,SV167: $i,SV53: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV53 @ SV167 @ SV179 )
= $false )
| ( ( equidistant @ SV102 @ SV137 @ SV167 @ SV179 )
= $true )
| ( ( equidistant @ SV2 @ SV53 @ SV102 @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[495]) ).
thf(511,plain,
! [SV105: $i,SV6: $i,SV156: $i,SV141: $i,SV154: $i,SV57: $i] :
( ( ( equidistant @ SV57 @ SV154 @ SV141 @ SV156 )
= $false )
| ( ( ! [SY483: $i,SY484: $i] :
( ~ ( equidistant @ SV6 @ SY483 @ SV105 @ SY484 )
| ~ ( equidistant @ SV57 @ SY483 @ SV141 @ SY484 )
| ~ ( between @ SV6 @ SV57 @ SV154 )
| ~ ( between @ SV105 @ SV141 @ SV156 )
| ( SV6 = SV57 )
| ( equidistant @ SV154 @ SY483 @ SV156 @ SY484 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(512,plain,
! [SV159: $i,SV10: $i,SV108: $i,SV61: $i,SV184: $i] :
( ( ( ~ ( equidistant @ SV184 @ SV61 @ SV184 @ SV108 ) )
= $true )
| ( ( ( between @ SV10 @ SV159 @ SV184 )
| ( between @ SV159 @ SV184 @ SV10 )
| ( SV61 = SV108 )
| ( between @ SV184 @ SV10 @ SV159 ) )
= $true )
| ( ( equidistant @ SV159 @ SV61 @ SV159 @ SV108 )
= $false )
| ( ( equidistant @ SV10 @ SV61 @ SV10 @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[499]) ).
thf(513,plain,
! [SV109: $i,SV170: $i,SV160: $i,SV62: $i,SV11: $i] :
( ( ( SV11 = SV62 )
= $true )
| ( ( between @ SV11 @ SV160 @ ( euclid1 @ SV11 @ SV160 @ SV62 @ SV170 @ SV109 ) )
= $true )
| ( ( between @ SV160 @ SV62 @ SV170 )
= $false )
| ( ( between @ SV11 @ SV62 @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[500]) ).
thf(514,plain,
! [SV110: $i,SV161: $i,SV171: $i,SV63: $i,SV12: $i] :
( ( ( SV12 = SV63 )
= $true )
| ( ( between @ SV12 @ SV171 @ ( euclid2 @ SV12 @ SV161 @ SV63 @ SV171 @ SV110 ) )
= $true )
| ( ( between @ SV161 @ SV63 @ SV171 )
= $false )
| ( ( between @ SV12 @ SV63 @ SV110 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[501]) ).
thf(515,plain,
! [SV111: $i,SV172: $i,SV162: $i,SV64: $i,SV13: $i] :
( ( ( SV13 = SV64 )
= $true )
| ( ( between @ ( euclid1 @ SV13 @ SV162 @ SV64 @ SV172 @ SV111 ) @ SV111 @ ( euclid2 @ SV13 @ SV162 @ SV64 @ SV172 @ SV111 ) )
= $true )
| ( ( between @ SV162 @ SV64 @ SV172 )
= $false )
| ( ( between @ SV13 @ SV64 @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[502]) ).
thf(516,plain,
! [SV173: $i,SV112: $i,SV142: $i,SV65: $i,SV14: $i] :
( ( ( ~ ( between @ SV14 @ SV65 @ SV142 ) )
= $true )
| ( ( ! [SY492: $i] :
( ~ ( between @ SV65 @ SY492 @ SV142 )
| ( between @ SV112 @ ( continuous @ SV14 @ SV65 @ SV112 @ SY492 @ SV142 @ SV173 ) @ SV173 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV142 @ SV14 @ SV173 )
= $false )
| ( ( equidistant @ SV14 @ SV65 @ SV14 @ SV112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[503]) ).
thf(517,plain,
! [SV174: $i,SV113: $i,SV143: $i,SV66: $i,SV15: $i] :
( ( ( ~ ( between @ SV15 @ SV66 @ SV143 ) )
= $true )
| ( ( ! [SY493: $i] :
( ~ ( between @ SV66 @ SY493 @ SV143 )
| ( equidistant @ SV15 @ SY493 @ SV15 @ ( continuous @ SV15 @ SV66 @ SV113 @ SY493 @ SV143 @ SV174 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV143 @ SV15 @ SV174 )
= $false )
| ( ( equidistant @ SV15 @ SV66 @ SV15 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[504]) ).
thf(518,plain,
! [SV76: $i,SV25: $i,SV180: $i,SV175: $i,SV151: $i,SV121: $i] :
( ( ( equidistant @ SV121 @ SV151 @ SV175 @ SV180 )
= $false )
| ( ( equidistant @ SV25 @ SV76 @ SV175 @ SV180 )
= $true )
| ( ( equidistant @ SV25 @ SV76 @ SV121 @ SV151 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[505]) ).
thf(519,plain,
! [SV124: $i,SV34: $i,SV181: $i,SV152: $i,SV176: $i,SV84: $i] :
( ( ( equidistant @ SV84 @ SV176 @ SV152 @ SV181 )
= $false )
| ( ( ~ ( between @ SV34 @ SV84 @ SV176 )
| ~ ( between @ SV124 @ SV152 @ SV181 )
| ( equidistant @ SV34 @ SV176 @ SV124 @ SV181 ) )
= $true )
| ( ( equidistant @ SV34 @ SV84 @ SV124 @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[506]) ).
thf(520,plain,
! [SV35: $i,SV164: $i,SV125: $i,SV85: $i] :
( ( ( equidistant @ SV85 @ SV125 @ SV85 @ SV164 )
= $false )
| ( ( ( SV35 = SV85 )
| ( SV125 = SV164 ) )
= $true )
| ( ( between @ SV35 @ SV85 @ SV164 )
= $false )
| ( ( between @ SV35 @ SV85 @ SV125 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[507]) ).
thf(521,plain,
! [SV156: $i,SV154: $i,SV141: $i,SV57: $i,SV105: $i,SV185: $i,SV6: $i] :
( ( ( ! [SY497: $i] :
( ~ ( equidistant @ SV6 @ SV185 @ SV105 @ SY497 )
| ~ ( equidistant @ SV57 @ SV185 @ SV141 @ SY497 )
| ~ ( between @ SV6 @ SV57 @ SV154 )
| ~ ( between @ SV105 @ SV141 @ SV156 )
| ( SV6 = SV57 )
| ( equidistant @ SV154 @ SV185 @ SV156 @ SY497 ) ) )
= $true )
| ( ( equidistant @ SV57 @ SV154 @ SV141 @ SV156 )
= $false )
| ( ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(522,plain,
! [SV159: $i,SV10: $i,SV108: $i,SV61: $i,SV184: $i] :
( ( ( equidistant @ SV184 @ SV61 @ SV184 @ SV108 )
= $false )
| ( ( ( between @ SV10 @ SV159 @ SV184 )
| ( between @ SV159 @ SV184 @ SV10 )
| ( SV61 = SV108 )
| ( between @ SV184 @ SV10 @ SV159 ) )
= $true )
| ( ( equidistant @ SV159 @ SV61 @ SV159 @ SV108 )
= $false )
| ( ( equidistant @ SV10 @ SV61 @ SV10 @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[512]) ).
thf(523,plain,
! [SV173: $i,SV112: $i,SV142: $i,SV65: $i,SV14: $i] :
( ( ( between @ SV14 @ SV65 @ SV142 )
= $false )
| ( ( ! [SY492: $i] :
( ~ ( between @ SV65 @ SY492 @ SV142 )
| ( between @ SV112 @ ( continuous @ SV14 @ SV65 @ SV112 @ SY492 @ SV142 @ SV173 ) @ SV173 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV142 @ SV14 @ SV173 )
= $false )
| ( ( equidistant @ SV14 @ SV65 @ SV14 @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[516]) ).
thf(524,plain,
! [SV174: $i,SV113: $i,SV143: $i,SV66: $i,SV15: $i] :
( ( ( between @ SV15 @ SV66 @ SV143 )
= $false )
| ( ( ! [SY493: $i] :
( ~ ( between @ SV66 @ SY493 @ SV143 )
| ( equidistant @ SV15 @ SY493 @ SV15 @ ( continuous @ SV15 @ SV66 @ SV113 @ SY493 @ SV143 @ SV174 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV143 @ SV15 @ SV174 )
= $false )
| ( ( equidistant @ SV15 @ SV66 @ SV15 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[517]) ).
thf(525,plain,
! [SV181: $i,SV152: $i,SV124: $i,SV176: $i,SV84: $i,SV34: $i] :
( ( ( ~ ( between @ SV34 @ SV84 @ SV176 ) )
= $true )
| ( ( ~ ( between @ SV124 @ SV152 @ SV181 )
| ( equidistant @ SV34 @ SV176 @ SV124 @ SV181 ) )
= $true )
| ( ( equidistant @ SV84 @ SV176 @ SV152 @ SV181 )
= $false )
| ( ( equidistant @ SV34 @ SV84 @ SV124 @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[519]) ).
thf(526,plain,
! [SV164: $i,SV125: $i,SV85: $i,SV35: $i] :
( ( ( SV35 = SV85 )
= $true )
| ( ( SV125 = SV164 )
= $true )
| ( ( equidistant @ SV85 @ SV125 @ SV85 @ SV164 )
= $false )
| ( ( between @ SV35 @ SV85 @ SV164 )
= $false )
| ( ( between @ SV35 @ SV85 @ SV125 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[520]) ).
thf(527,plain,
! [SV156: $i,SV154: $i,SV141: $i,SV57: $i,SV186: $i,SV105: $i,SV185: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV185 @ SV105 @ SV186 )
| ~ ( equidistant @ SV57 @ SV185 @ SV141 @ SV186 )
| ~ ( between @ SV6 @ SV57 @ SV154 )
| ~ ( between @ SV105 @ SV141 @ SV156 )
| ( SV6 = SV57 )
| ( equidistant @ SV154 @ SV185 @ SV156 @ SV186 ) )
= $true )
| ( ( equidistant @ SV57 @ SV154 @ SV141 @ SV156 )
= $false )
| ( ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(528,plain,
! [SV108: $i,SV61: $i,SV184: $i,SV159: $i,SV10: $i] :
( ( ( between @ SV10 @ SV159 @ SV184 )
= $true )
| ( ( ( between @ SV159 @ SV184 @ SV10 )
| ( SV61 = SV108 )
| ( between @ SV184 @ SV10 @ SV159 ) )
= $true )
| ( ( equidistant @ SV184 @ SV61 @ SV184 @ SV108 )
= $false )
| ( ( equidistant @ SV159 @ SV61 @ SV159 @ SV108 )
= $false )
| ( ( equidistant @ SV10 @ SV61 @ SV10 @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[522]) ).
thf(529,plain,
! [SV173: $i,SV14: $i,SV112: $i,SV142: $i,SV187: $i,SV65: $i] :
( ( ( ~ ( between @ SV65 @ SV187 @ SV142 )
| ( between @ SV112 @ ( continuous @ SV14 @ SV65 @ SV112 @ SV187 @ SV142 @ SV173 ) @ SV173 ) )
= $true )
| ( ( between @ SV14 @ SV65 @ SV142 )
= $false )
| ( ( equidistant @ SV14 @ SV142 @ SV14 @ SV173 )
= $false )
| ( ( equidistant @ SV14 @ SV65 @ SV14 @ SV112 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(530,plain,
! [SV174: $i,SV113: $i,SV15: $i,SV143: $i,SV188: $i,SV66: $i] :
( ( ( ~ ( between @ SV66 @ SV188 @ SV143 )
| ( equidistant @ SV15 @ SV188 @ SV15 @ ( continuous @ SV15 @ SV66 @ SV113 @ SV188 @ SV143 @ SV174 ) ) )
= $true )
| ( ( between @ SV15 @ SV66 @ SV143 )
= $false )
| ( ( equidistant @ SV15 @ SV143 @ SV15 @ SV174 )
= $false )
| ( ( equidistant @ SV15 @ SV66 @ SV15 @ SV113 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(531,plain,
! [SV181: $i,SV152: $i,SV124: $i,SV176: $i,SV84: $i,SV34: $i] :
( ( ( between @ SV34 @ SV84 @ SV176 )
= $false )
| ( ( ~ ( between @ SV124 @ SV152 @ SV181 )
| ( equidistant @ SV34 @ SV176 @ SV124 @ SV181 ) )
= $true )
| ( ( equidistant @ SV84 @ SV176 @ SV152 @ SV181 )
= $false )
| ( ( equidistant @ SV34 @ SV84 @ SV124 @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[525]) ).
thf(532,plain,
! [SV156: $i,SV154: $i,SV141: $i,SV57: $i,SV186: $i,SV105: $i,SV185: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV185 @ SV105 @ SV186 ) )
= $true )
| ( ( ~ ( equidistant @ SV57 @ SV185 @ SV141 @ SV186 )
| ~ ( between @ SV6 @ SV57 @ SV154 )
| ~ ( between @ SV105 @ SV141 @ SV156 )
| ( SV6 = SV57 )
| ( equidistant @ SV154 @ SV185 @ SV156 @ SV186 ) )
= $true )
| ( ( equidistant @ SV57 @ SV154 @ SV141 @ SV156 )
= $false )
| ( ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[527]) ).
thf(533,plain,
! [SV108: $i,SV61: $i,SV10: $i,SV184: $i,SV159: $i] :
( ( ( between @ SV159 @ SV184 @ SV10 )
= $true )
| ( ( ( SV61 = SV108 )
| ( between @ SV184 @ SV10 @ SV159 ) )
= $true )
| ( ( between @ SV10 @ SV159 @ SV184 )
= $true )
| ( ( equidistant @ SV184 @ SV61 @ SV184 @ SV108 )
= $false )
| ( ( equidistant @ SV159 @ SV61 @ SV159 @ SV108 )
= $false )
| ( ( equidistant @ SV10 @ SV61 @ SV10 @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[528]) ).
thf(534,plain,
! [SV173: $i,SV14: $i,SV112: $i,SV142: $i,SV187: $i,SV65: $i] :
( ( ( ~ ( between @ SV65 @ SV187 @ SV142 ) )
= $true )
| ( ( between @ SV112 @ ( continuous @ SV14 @ SV65 @ SV112 @ SV187 @ SV142 @ SV173 ) @ SV173 )
= $true )
| ( ( between @ SV14 @ SV65 @ SV142 )
= $false )
| ( ( equidistant @ SV14 @ SV142 @ SV14 @ SV173 )
= $false )
| ( ( equidistant @ SV14 @ SV65 @ SV14 @ SV112 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[529]) ).
thf(535,plain,
! [SV174: $i,SV113: $i,SV15: $i,SV143: $i,SV188: $i,SV66: $i] :
( ( ( ~ ( between @ SV66 @ SV188 @ SV143 ) )
= $true )
| ( ( equidistant @ SV15 @ SV188 @ SV15 @ ( continuous @ SV15 @ SV66 @ SV113 @ SV188 @ SV143 @ SV174 ) )
= $true )
| ( ( between @ SV15 @ SV66 @ SV143 )
= $false )
| ( ( equidistant @ SV15 @ SV143 @ SV15 @ SV174 )
= $false )
| ( ( equidistant @ SV15 @ SV66 @ SV15 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[530]) ).
thf(536,plain,
! [SV84: $i,SV176: $i,SV34: $i,SV181: $i,SV152: $i,SV124: $i] :
( ( ( ~ ( between @ SV124 @ SV152 @ SV181 ) )
= $true )
| ( ( equidistant @ SV34 @ SV176 @ SV124 @ SV181 )
= $true )
| ( ( between @ SV34 @ SV84 @ SV176 )
= $false )
| ( ( equidistant @ SV84 @ SV176 @ SV152 @ SV181 )
= $false )
| ( ( equidistant @ SV34 @ SV84 @ SV124 @ SV152 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[531]) ).
thf(537,plain,
! [SV156: $i,SV154: $i,SV141: $i,SV57: $i,SV186: $i,SV105: $i,SV185: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV185 @ SV105 @ SV186 )
= $false )
| ( ( ~ ( equidistant @ SV57 @ SV185 @ SV141 @ SV186 )
| ~ ( between @ SV6 @ SV57 @ SV154 )
| ~ ( between @ SV105 @ SV141 @ SV156 )
| ( SV6 = SV57 )
| ( equidistant @ SV154 @ SV185 @ SV156 @ SV186 ) )
= $true )
| ( ( equidistant @ SV57 @ SV154 @ SV141 @ SV156 )
= $false )
| ( ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[532]) ).
thf(538,plain,
! [SV159: $i,SV10: $i,SV184: $i,SV108: $i,SV61: $i] :
( ( ( SV61 = SV108 )
= $true )
| ( ( between @ SV184 @ SV10 @ SV159 )
= $true )
| ( ( between @ SV159 @ SV184 @ SV10 )
= $true )
| ( ( between @ SV10 @ SV159 @ SV184 )
= $true )
| ( ( equidistant @ SV184 @ SV61 @ SV184 @ SV108 )
= $false )
| ( ( equidistant @ SV159 @ SV61 @ SV159 @ SV108 )
= $false )
| ( ( equidistant @ SV10 @ SV61 @ SV10 @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[533]) ).
thf(539,plain,
! [SV173: $i,SV14: $i,SV112: $i,SV142: $i,SV187: $i,SV65: $i] :
( ( ( between @ SV65 @ SV187 @ SV142 )
= $false )
| ( ( between @ SV112 @ ( continuous @ SV14 @ SV65 @ SV112 @ SV187 @ SV142 @ SV173 ) @ SV173 )
= $true )
| ( ( between @ SV14 @ SV65 @ SV142 )
= $false )
| ( ( equidistant @ SV14 @ SV142 @ SV14 @ SV173 )
= $false )
| ( ( equidistant @ SV14 @ SV65 @ SV14 @ SV112 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[534]) ).
thf(540,plain,
! [SV174: $i,SV113: $i,SV15: $i,SV143: $i,SV188: $i,SV66: $i] :
( ( ( between @ SV66 @ SV188 @ SV143 )
= $false )
| ( ( equidistant @ SV15 @ SV188 @ SV15 @ ( continuous @ SV15 @ SV66 @ SV113 @ SV188 @ SV143 @ SV174 ) )
= $true )
| ( ( between @ SV15 @ SV66 @ SV143 )
= $false )
| ( ( equidistant @ SV15 @ SV143 @ SV15 @ SV174 )
= $false )
| ( ( equidistant @ SV15 @ SV66 @ SV15 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[535]) ).
thf(541,plain,
! [SV84: $i,SV176: $i,SV34: $i,SV181: $i,SV152: $i,SV124: $i] :
( ( ( between @ SV124 @ SV152 @ SV181 )
= $false )
| ( ( equidistant @ SV34 @ SV176 @ SV124 @ SV181 )
= $true )
| ( ( between @ SV34 @ SV84 @ SV176 )
= $false )
| ( ( equidistant @ SV84 @ SV176 @ SV152 @ SV181 )
= $false )
| ( ( equidistant @ SV34 @ SV84 @ SV124 @ SV152 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[536]) ).
thf(542,plain,
! [SV156: $i,SV105: $i,SV154: $i,SV6: $i,SV186: $i,SV141: $i,SV185: $i,SV57: $i] :
( ( ( ~ ( equidistant @ SV57 @ SV185 @ SV141 @ SV186 ) )
= $true )
| ( ( ~ ( between @ SV6 @ SV57 @ SV154 )
| ~ ( between @ SV105 @ SV141 @ SV156 )
| ( SV6 = SV57 )
| ( equidistant @ SV154 @ SV185 @ SV156 @ SV186 ) )
= $true )
| ( ( equidistant @ SV6 @ SV185 @ SV105 @ SV186 )
= $false )
| ( ( equidistant @ SV57 @ SV154 @ SV141 @ SV156 )
= $false )
| ( ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[537]) ).
thf(543,plain,
! [SV156: $i,SV105: $i,SV154: $i,SV6: $i,SV186: $i,SV141: $i,SV185: $i,SV57: $i] :
( ( ( equidistant @ SV57 @ SV185 @ SV141 @ SV186 )
= $false )
| ( ( ~ ( between @ SV6 @ SV57 @ SV154 )
| ~ ( between @ SV105 @ SV141 @ SV156 )
| ( SV6 = SV57 )
| ( equidistant @ SV154 @ SV185 @ SV156 @ SV186 ) )
= $true )
| ( ( equidistant @ SV6 @ SV185 @ SV105 @ SV186 )
= $false )
| ( ( equidistant @ SV57 @ SV154 @ SV141 @ SV156 )
= $false )
| ( ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[542]) ).
thf(544,plain,
! [SV186: $i,SV185: $i,SV156: $i,SV141: $i,SV105: $i,SV154: $i,SV57: $i,SV6: $i] :
( ( ( ~ ( between @ SV6 @ SV57 @ SV154 ) )
= $true )
| ( ( ~ ( between @ SV105 @ SV141 @ SV156 )
| ( SV6 = SV57 )
| ( equidistant @ SV154 @ SV185 @ SV156 @ SV186 ) )
= $true )
| ( ( equidistant @ SV57 @ SV185 @ SV141 @ SV186 )
= $false )
| ( ( equidistant @ SV6 @ SV185 @ SV105 @ SV186 )
= $false )
| ( ( equidistant @ SV57 @ SV154 @ SV141 @ SV156 )
= $false )
| ( ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[543]) ).
thf(545,plain,
! [SV186: $i,SV185: $i,SV156: $i,SV141: $i,SV105: $i,SV154: $i,SV57: $i,SV6: $i] :
( ( ( between @ SV6 @ SV57 @ SV154 )
= $false )
| ( ( ~ ( between @ SV105 @ SV141 @ SV156 )
| ( SV6 = SV57 )
| ( equidistant @ SV154 @ SV185 @ SV156 @ SV186 ) )
= $true )
| ( ( equidistant @ SV57 @ SV185 @ SV141 @ SV186 )
= $false )
| ( ( equidistant @ SV6 @ SV185 @ SV105 @ SV186 )
= $false )
| ( ( equidistant @ SV57 @ SV154 @ SV141 @ SV156 )
= $false )
| ( ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[544]) ).
thf(546,plain,
! [SV186: $i,SV185: $i,SV154: $i,SV57: $i,SV6: $i,SV156: $i,SV141: $i,SV105: $i] :
( ( ( ~ ( between @ SV105 @ SV141 @ SV156 ) )
= $true )
| ( ( ( SV6 = SV57 )
| ( equidistant @ SV154 @ SV185 @ SV156 @ SV186 ) )
= $true )
| ( ( between @ SV6 @ SV57 @ SV154 )
= $false )
| ( ( equidistant @ SV57 @ SV185 @ SV141 @ SV186 )
= $false )
| ( ( equidistant @ SV6 @ SV185 @ SV105 @ SV186 )
= $false )
| ( ( equidistant @ SV57 @ SV154 @ SV141 @ SV156 )
= $false )
| ( ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[545]) ).
thf(547,plain,
! [SV186: $i,SV185: $i,SV154: $i,SV57: $i,SV6: $i,SV156: $i,SV141: $i,SV105: $i] :
( ( ( between @ SV105 @ SV141 @ SV156 )
= $false )
| ( ( ( SV6 = SV57 )
| ( equidistant @ SV154 @ SV185 @ SV156 @ SV186 ) )
= $true )
| ( ( between @ SV6 @ SV57 @ SV154 )
= $false )
| ( ( equidistant @ SV57 @ SV185 @ SV141 @ SV186 )
= $false )
| ( ( equidistant @ SV6 @ SV185 @ SV105 @ SV186 )
= $false )
| ( ( equidistant @ SV57 @ SV154 @ SV141 @ SV156 )
= $false )
| ( ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[546]) ).
thf(548,plain,
! [SV141: $i,SV105: $i,SV186: $i,SV156: $i,SV185: $i,SV154: $i,SV57: $i,SV6: $i] :
( ( ( SV6 = SV57 )
= $true )
| ( ( equidistant @ SV154 @ SV185 @ SV156 @ SV186 )
= $true )
| ( ( between @ SV105 @ SV141 @ SV156 )
= $false )
| ( ( between @ SV6 @ SV57 @ SV154 )
= $false )
| ( ( equidistant @ SV57 @ SV185 @ SV141 @ SV186 )
= $false )
| ( ( equidistant @ SV6 @ SV185 @ SV105 @ SV186 )
= $false )
| ( ( equidistant @ SV57 @ SV154 @ SV141 @ SV156 )
= $false )
| ( ( equidistant @ SV6 @ SV57 @ SV105 @ SV141 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[547]) ).
thf(549,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[145,548,541,540,539,538,526,518,515,514,513,510,509,508,498,497,493,492,491,490,489,469,468,463,442,437,436,435,434,433,432,431,413,389,374,373,355,353,352,340,332,302,299,298,297,291,288,287,276,275,260,259,238,216,215,214,204,203,146]) ).
thf(550,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[549]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : GEO045-3 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.12/0.34 % Computer : n004.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 14:44:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.19/0.45 .
% 0.19/0.46
% 0.19/0.46 No.of.Axioms: 58
% 0.19/0.46
% 0.19/0.46 Length.of.Defs: 0
% 0.19/0.46
% 0.19/0.46 Contains.Choice.Funs: false
% 0.19/0.49 .
% 0.19/0.54 (rf:0,axioms:58,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:60,loop_count:0,foatp_calls:0,translation:fof_full)...................................
% 0.68/0.98
% 0.68/0.98 ********************************
% 0.68/0.98 * All subproblems solved! *
% 0.68/0.98 ********************************
% 0.68/0.98 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:58,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:549,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.83/1.07
% 0.83/1.07 %**** Beginning of derivation protocol ****
% 0.83/1.07 % SZS output start CNFRefutation
% See solution above
% 0.83/1.07
% 0.83/1.07 %**** End of derivation protocol ****
% 0.83/1.07 %**** no. of clauses in derivation: 550 ****
% 0.83/1.07 %**** clause counter: 549 ****
% 0.83/1.07
% 0.83/1.07 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:58,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:549,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------