TSTP Solution File: GEO006-3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GEO006-3 : 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 : n032.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 05:05:55 EDT 2022
% Result : Unsatisfiable 0.60s 0.80s
% Output : CNFRefutation 0.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 69
% Syntax : Number of formulae : 512 ( 304 unt; 14 typ; 0 def)
% Number of atoms : 2999 (1035 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 7010 ( 661 ~;1025 |; 0 &;5324 @)
% ( 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 : 17 ( 14 usr; 8 con; 0-6 aty)
% Number of variables : 1989 ( 0 ^1989 !; 0 ?;1989 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_between,type,
between: $i > $i > $i > $o ).
thf(tp_c,type,
c: $i ).
thf(tp_continuous,type,
continuous: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_d,type,
d: $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(1,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(2,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(3,axiom,
! [U: $i,V: $i] : ( between @ U @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
thf(4,axiom,
! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
thf(5,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(6,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
thf(7,axiom,
! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).
thf(8,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).
thf(9,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(10,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(11,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(12,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(13,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(14,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
thf(15,axiom,
! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
thf(16,axiom,
! [U: $i] :
( U
= ( reflection @ U @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).
thf(17,axiom,
! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_1) ).
thf(18,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
thf(19,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).
thf(20,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(21,axiom,
! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
thf(22,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(23,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(24,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(25,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(26,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(27,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(28,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(29,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(30,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
thf(31,axiom,
! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
thf(32,axiom,
! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).
thf(33,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(34,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(35,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(36,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(37,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(38,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(39,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(40,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(41,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(42,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(43,axiom,
! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(44,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(45,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(46,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(47,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(48,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(49,axiom,
! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(50,axiom,
between @ a @ c @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_between_a_and_d) ).
thf(51,axiom,
c != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_not_d) ).
thf(52,axiom,
a != d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_d) ).
thf(53,axiom,
a != c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_c) ).
thf(54,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(55,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[54]) ).
thf(56,negated_conjecture,
( ( between @ c @ a @ d )
| ( between @ a @ d @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_not_between_others) ).
thf(57,plain,
$false = $false,
inference(unfold_def,[status(thm)],[55]) ).
thf(58,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(59,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(60,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(61,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(62,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)],[5]) ).
thf(63,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(64,plain,
( ( ! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(65,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(66,plain,
( ( ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(67,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)],[10]) ).
thf(68,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)],[11]) ).
thf(69,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)],[12]) ).
thf(70,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)],[13]) ).
thf(71,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(72,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(73,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(74,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(75,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(76,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(77,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)],[20]) ).
thf(78,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(79,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)],[22]) ).
thf(80,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)],[23]) ).
thf(81,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)],[24]) ).
thf(82,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)],[25]) ).
thf(83,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)],[26]) ).
thf(84,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)],[27]) ).
thf(85,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)],[28]) ).
thf(86,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)],[29]) ).
thf(87,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(88,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(89,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)],[32]) ).
thf(90,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)],[33]) ).
thf(91,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)],[34]) ).
thf(92,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)],[35]) ).
thf(93,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)],[36]) ).
thf(94,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)],[37]) ).
thf(95,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(96,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(97,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(98,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)],[41]) ).
thf(99,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)],[42]) ).
thf(100,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(101,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)],[44]) ).
thf(102,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[45]) ).
thf(103,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[46]) ).
thf(104,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[47]) ).
thf(105,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)],[48]) ).
thf(106,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[49]) ).
thf(107,plain,
( ( between @ a @ c @ d )
= $true ),
inference(unfold_def,[status(thm)],[50]) ).
thf(108,plain,
( ( ( c != d ) )
= $true ),
inference(unfold_def,[status(thm)],[51]) ).
thf(109,plain,
( ( ( a != d ) )
= $true ),
inference(unfold_def,[status(thm)],[52]) ).
thf(110,plain,
( ( ( a != c ) )
= $true ),
inference(unfold_def,[status(thm)],[53]) ).
thf(111,plain,
( ( ( between @ c @ a @ d )
| ( between @ a @ d @ c ) )
= $true ),
inference(unfold_def,[status(thm)],[56]) ).
thf(112,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[57]) ).
thf(113,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)],[62]) ).
thf(114,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)],[67]) ).
thf(115,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)],[69]) ).
thf(116,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)],[70]) ).
thf(117,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(118,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(119,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)],[77]) ).
thf(120,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)],[79]) ).
thf(121,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)],[89]) ).
thf(122,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)],[90]) ).
thf(123,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)],[91]) ).
thf(124,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)],[92]) ).
thf(125,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)],[93]) ).
thf(126,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)],[94]) ).
thf(127,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)],[98]) ).
thf(128,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)],[99]) ).
thf(129,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)],[101]) ).
thf(130,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(131,plain,
( ( ! [X: $i,Y: $i,Z: $i,V: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ! [V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(132,plain,
( ( ( c != d ) )
= $true ),
inference(extcnf_combined,[status(esa)],[108]) ).
thf(133,plain,
( ( ( a != d ) )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(134,plain,
( ( ( a != c ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(135,plain,
( ( ( between @ c @ a @ d )
| ( between @ a @ d @ c ) )
= $true ),
inference(copy,[status(thm)],[111]) ).
thf(136,plain,
( ( ( a != c ) )
= $true ),
inference(copy,[status(thm)],[134]) ).
thf(137,plain,
( ( ( a != d ) )
= $true ),
inference(copy,[status(thm)],[133]) ).
thf(138,plain,
( ( ( c != d ) )
= $true ),
inference(copy,[status(thm)],[132]) ).
thf(139,plain,
( ( between @ a @ c @ d )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(140,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(copy,[status(thm)],[106]) ).
thf(141,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)],[131]) ).
thf(142,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[130]) ).
thf(143,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(144,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[102]) ).
thf(145,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)],[129]) ).
thf(146,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(147,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)],[128]) ).
thf(148,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)],[127]) ).
thf(149,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[97]) ).
thf(150,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(copy,[status(thm)],[96]) ).
thf(151,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(copy,[status(thm)],[95]) ).
thf(152,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)],[126]) ).
thf(153,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)],[125]) ).
thf(154,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)],[124]) ).
thf(155,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)],[123]) ).
thf(156,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)],[122]) ).
thf(157,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)],[121]) ).
thf(158,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[88]) ).
thf(159,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[87]) ).
thf(160,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[86]) ).
thf(161,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(162,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(163,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(164,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(165,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(166,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(167,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)],[120]) ).
thf(168,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(169,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)],[119]) ).
thf(170,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(171,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(172,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[118]) ).
thf(173,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(174,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(175,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(176,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)],[116]) ).
thf(177,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)],[115]) ).
thf(178,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( U = V )
| ( W
= ( extension @ U @ V @ V @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(179,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)],[114]) ).
thf(180,plain,
( ( ! [U: $i,V: $i] :
( ( ( extension @ U @ V @ U @ V )
= ( extension @ U @ V @ V @ U ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(181,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ U @ V @ ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(182,plain,
( ( ! [U: $i,V: $i] :
( U
= ( reflection @ ( reflection @ U @ V ) @ V ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(183,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(184,plain,
( ( ! [U: $i,W: $i,X: $i] :
( ~ ( between @ U @ W @ X )
| ( U != X )
| ! [V: $i] : ( between @ V @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[113]) ).
thf(185,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ( between @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(186,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(187,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ V @ U @ W )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(188,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ U @ W @ V )
| ( V = W ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(189,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(190,plain,
( ( ( between @ c @ a @ d )
= $true )
| ( ( between @ a @ d @ c )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[135]) ).
thf(191,plain,
( ( a = c )
= $false ),
inference(extcnf_not_pos,[status(thm)],[136]) ).
thf(192,plain,
( ( a = d )
= $false ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(193,plain,
( ( c = d )
= $false ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(194,plain,
! [SV1: $i] :
( ( ! [SY170: $i] : ( equidistant @ SV1 @ SY170 @ SY170 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(195,plain,
! [SV2: $i] :
( ( ! [SY171: $i,SY172: $i,SY173: $i] :
( ~ ( equidistant @ SV2 @ SY171 @ SY172 @ SY173 )
| ! [SY174: $i,SY175: $i] :
( ~ ( equidistant @ SV2 @ SY171 @ SY174 @ SY175 )
| ( equidistant @ SY172 @ SY173 @ SY174 @ SY175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(196,plain,
! [SV3: $i] :
( ( ! [SY176: $i] :
( ! [SY177: $i] :
~ ( equidistant @ SV3 @ SY176 @ SY177 @ SY177 )
| ( SV3 = SY176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(197,plain,
! [SV4: $i] :
( ( ! [SY178: $i,SY179: $i,SY180: $i] : ( between @ SV4 @ SY178 @ ( extension @ SV4 @ SY178 @ SY179 @ SY180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(198,plain,
! [SV5: $i] :
( ( ! [SY181: $i,SY182: $i,SY183: $i] : ( equidistant @ SV5 @ ( extension @ SY181 @ SV5 @ SY182 @ SY183 ) @ SY182 @ SY183 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(199,plain,
! [SV6: $i] :
( ( ! [SY184: $i,SY185: $i,SY186: $i,SY187: $i,SY188: $i] :
( ~ ( equidistant @ SV6 @ SY184 @ SY185 @ SY186 )
| ~ ( equidistant @ SY184 @ SY187 @ SY186 @ SY188 )
| ! [SY189: $i,SY190: $i] :
( ~ ( equidistant @ SV6 @ SY189 @ SY185 @ SY190 )
| ~ ( equidistant @ SY184 @ SY189 @ SY186 @ SY190 )
| ~ ( between @ SV6 @ SY184 @ SY187 )
| ~ ( between @ SY185 @ SY186 @ SY188 )
| ( SV6 = SY184 )
| ( equidistant @ SY187 @ SY189 @ SY188 @ SY190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(200,plain,
! [SV7: $i] :
( ( ! [SY191: $i] :
( ~ ( between @ SV7 @ SY191 @ SV7 )
| ( SV7 = SY191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(201,plain,
! [SV8: $i] :
( ( ! [SY192: $i,SY193: $i] :
( ~ ( between @ SV8 @ SY192 @ SY193 )
| ! [SY194: $i,SY195: $i] :
( ~ ( between @ SY194 @ SY195 @ SY193 )
| ( between @ SY192 @ ( inner_pasch @ SV8 @ SY192 @ SY193 @ SY195 @ SY194 ) @ SY194 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(202,plain,
! [SV9: $i] :
( ( ! [SY196: $i,SY197: $i] :
( ~ ( between @ SV9 @ SY196 @ SY197 )
| ! [SY198: $i,SY199: $i] :
( ~ ( between @ SY198 @ SY199 @ SY197 )
| ( between @ SY199 @ ( inner_pasch @ SV9 @ SY196 @ SY197 @ SY199 @ SY198 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(203,plain,
( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(204,plain,
( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[150]) ).
thf(205,plain,
( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(206,plain,
! [SV10: $i] :
( ( ! [SY200: $i,SY201: $i] :
( ~ ( equidistant @ SV10 @ SY200 @ SV10 @ SY201 )
| ! [SY202: $i] :
( ~ ( equidistant @ SY202 @ SY200 @ SY202 @ SY201 )
| ! [SY203: $i] :
( ~ ( equidistant @ SY203 @ SY200 @ SY203 @ SY201 )
| ( between @ SV10 @ SY202 @ SY203 )
| ( between @ SY202 @ SY203 @ SV10 )
| ( SY200 = SY201 )
| ( between @ SY203 @ SV10 @ SY202 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(207,plain,
! [SV11: $i] :
( ( ! [SY204: $i,SY205: $i] :
( ~ ( between @ SV11 @ SY204 @ SY205 )
| ! [SY206: $i,SY207: $i] :
( ~ ( between @ SY206 @ SY204 @ SY207 )
| ( SV11 = SY204 )
| ( between @ SV11 @ SY206 @ ( euclid1 @ SV11 @ SY206 @ SY204 @ SY207 @ SY205 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(208,plain,
! [SV12: $i] :
( ( ! [SY208: $i,SY209: $i] :
( ~ ( between @ SV12 @ SY208 @ SY209 )
| ! [SY210: $i,SY211: $i] :
( ~ ( between @ SY210 @ SY208 @ SY211 )
| ( SV12 = SY208 )
| ( between @ SV12 @ SY211 @ ( euclid2 @ SV12 @ SY210 @ SY208 @ SY211 @ SY209 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(209,plain,
! [SV13: $i] :
( ( ! [SY212: $i,SY213: $i] :
( ~ ( between @ SV13 @ SY212 @ SY213 )
| ! [SY214: $i,SY215: $i] :
( ~ ( between @ SY214 @ SY212 @ SY215 )
| ( SV13 = SY212 )
| ( between @ ( euclid1 @ SV13 @ SY214 @ SY212 @ SY215 @ SY213 ) @ SY213 @ ( euclid2 @ SV13 @ SY214 @ SY212 @ SY215 @ SY213 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(210,plain,
! [SV14: $i] :
( ( ! [SY216: $i,SY217: $i,SY218: $i] :
( ~ ( equidistant @ SV14 @ SY216 @ SV14 @ SY217 )
| ! [SY219: $i] :
( ~ ( equidistant @ SV14 @ SY218 @ SV14 @ SY219 )
| ~ ( between @ SV14 @ SY216 @ SY218 )
| ! [SY220: $i] :
( ~ ( between @ SY216 @ SY220 @ SY218 )
| ( between @ SY217 @ ( continuous @ SV14 @ SY216 @ SY217 @ SY220 @ SY218 @ SY219 ) @ SY219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(211,plain,
! [SV15: $i] :
( ( ! [SY221: $i,SY222: $i,SY223: $i] :
( ~ ( equidistant @ SV15 @ SY221 @ SV15 @ SY222 )
| ! [SY224: $i] :
( ~ ( equidistant @ SV15 @ SY223 @ SV15 @ SY224 )
| ~ ( between @ SV15 @ SY221 @ SY223 )
| ! [SY225: $i] :
( ~ ( between @ SY221 @ SY225 @ SY223 )
| ( equidistant @ SV15 @ SY225 @ SV15 @ ( continuous @ SV15 @ SY221 @ SY222 @ SY225 @ SY223 @ SY224 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(212,plain,
! [SV16: $i] :
( ( ! [SY226: $i] :
( ( reflection @ SV16 @ SY226 )
= ( extension @ SV16 @ SY226 @ SV16 @ SY226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(213,plain,
! [SV17: $i] :
( ( ! [SY227: $i] : ( equidistant @ SV17 @ SY227 @ SV17 @ SY227 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(214,plain,
! [SV18: $i] :
( ( ! [SY228: $i,SY229: $i,SY230: $i] :
( ~ ( equidistant @ SV18 @ SY228 @ SY229 @ SY230 )
| ( equidistant @ SY229 @ SY230 @ SV18 @ SY228 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(215,plain,
! [SV19: $i] :
( ( ! [SY231: $i,SY232: $i,SY233: $i] :
( ~ ( equidistant @ SV19 @ SY231 @ SY232 @ SY233 )
| ( equidistant @ SY231 @ SV19 @ SY232 @ SY233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(216,plain,
! [SV20: $i] :
( ( ! [SY234: $i,SY235: $i,SY236: $i] :
( ~ ( equidistant @ SV20 @ SY234 @ SY235 @ SY236 )
| ( equidistant @ SV20 @ SY234 @ SY236 @ SY235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(217,plain,
! [SV21: $i] :
( ( ! [SY237: $i,SY238: $i,SY239: $i] :
( ~ ( equidistant @ SV21 @ SY237 @ SY238 @ SY239 )
| ( equidistant @ SY237 @ SV21 @ SY239 @ SY238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(218,plain,
! [SV22: $i] :
( ( ! [SY240: $i,SY241: $i,SY242: $i] :
( ~ ( equidistant @ SV22 @ SY240 @ SY241 @ SY242 )
| ( equidistant @ SY241 @ SY242 @ SY240 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(219,plain,
! [SV23: $i] :
( ( ! [SY243: $i,SY244: $i,SY245: $i] :
( ~ ( equidistant @ SV23 @ SY243 @ SY244 @ SY245 )
| ( equidistant @ SY245 @ SY244 @ SV23 @ SY243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(220,plain,
! [SV24: $i] :
( ( ! [SY246: $i,SY247: $i,SY248: $i] :
( ~ ( equidistant @ SV24 @ SY246 @ SY247 @ SY248 )
| ( equidistant @ SY248 @ SY247 @ SY246 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(221,plain,
! [SV25: $i] :
( ( ! [SY249: $i,SY250: $i,SY251: $i] :
( ~ ( equidistant @ SV25 @ SY249 @ SY250 @ SY251 )
| ! [SY252: $i,SY253: $i] :
( ~ ( equidistant @ SY250 @ SY251 @ SY252 @ SY253 )
| ( equidistant @ SV25 @ SY249 @ SY252 @ SY253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(222,plain,
! [SV26: $i] :
( ( ! [SY254: $i,SY255: $i] :
( SV26
= ( extension @ SY254 @ SV26 @ SY255 @ SY255 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(223,plain,
! [SV27: $i] :
( ( ! [SY256: $i,SY257: $i] :
( ! [SY258: $i,SY259: $i] :
( SV27
!= ( extension @ SY256 @ SY257 @ SY258 @ SY259 ) )
| ( between @ SY256 @ SY257 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(224,plain,
! [SV28: $i] :
( ( ! [SY260: $i] : ( between @ SV28 @ SY260 @ ( reflection @ SV28 @ SY260 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(225,plain,
! [SV29: $i] :
( ( ! [SY261: $i] : ( equidistant @ SV29 @ ( reflection @ SY261 @ SV29 ) @ SY261 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(226,plain,
! [SV30: $i] :
( ( ! [SY262: $i] :
( ( SV30 != SY262 )
| ( SY262
= ( reflection @ SV30 @ SY262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(227,plain,
! [SV31: $i] :
( ( SV31
= ( reflection @ SV31 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(228,plain,
! [SV32: $i] :
( ( ! [SY263: $i] :
( ( SV32
!= ( reflection @ SY263 @ SV32 ) )
| ( SY263 = SV32 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(229,plain,
! [SV33: $i] :
( ( ! [SY264: $i] : ( equidistant @ SV33 @ SV33 @ SY264 @ SY264 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(230,plain,
! [SV34: $i] :
( ( ! [SY265: $i,SY266: $i,SY267: $i] :
( ~ ( equidistant @ SV34 @ SY265 @ SY266 @ SY267 )
| ! [SY268: $i,SY269: $i] :
( ~ ( equidistant @ SY265 @ SY268 @ SY267 @ SY269 )
| ~ ( between @ SV34 @ SY265 @ SY268 )
| ~ ( between @ SY266 @ SY267 @ SY269 )
| ( equidistant @ SV34 @ SY268 @ SY266 @ SY269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(231,plain,
! [SV35: $i] :
( ( ! [SY270: $i,SY271: $i] :
( ~ ( between @ SV35 @ SY270 @ SY271 )
| ! [SY272: $i] :
( ~ ( between @ SV35 @ SY270 @ SY272 )
| ~ ( equidistant @ SY270 @ SY271 @ SY270 @ SY272 )
| ( SV35 = SY270 )
| ( SY271 = SY272 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(232,plain,
! [SV36: $i] :
( ( ! [SY273: $i,SY274: $i] :
( ~ ( between @ SV36 @ SY273 @ SY274 )
| ( SV36 = SY273 )
| ( SY274
= ( extension @ SV36 @ SY273 @ SY273 @ SY274 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(233,plain,
! [SV37: $i] :
( ( ! [SY275: $i,SY276: $i,SY277: $i] :
( ~ ( equidistant @ SV37 @ SY275 @ SY276 @ SY277 )
| ! [SY278: $i,SY279: $i] :
( ( ( extension @ SY278 @ SY279 @ SV37 @ SY275 )
= ( extension @ SY278 @ SY279 @ SY276 @ SY277 ) )
| ( SY278 = SY279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(234,plain,
! [SV38: $i] :
( ( ! [SY280: $i] :
( ( ( extension @ SV38 @ SY280 @ SV38 @ SY280 )
= ( extension @ SV38 @ SY280 @ SY280 @ SV38 ) )
| ( SV38 = SY280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(235,plain,
! [SV39: $i] :
( ( ! [SY281: $i] : ( equidistant @ SV39 @ SY281 @ SV39 @ ( reflection @ ( reflection @ SY281 @ SV39 ) @ SV39 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(236,plain,
! [SV40: $i] :
( ( ! [SY282: $i] :
( SV40
= ( reflection @ ( reflection @ SV40 @ SY282 ) @ SY282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(237,plain,
! [SV41: $i] :
( ( ! [SY283: $i] : ( between @ SV41 @ SY283 @ SY283 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(238,plain,
! [SV42: $i] :
( ( ! [SY284: $i,SY285: $i] :
( ~ ( between @ SV42 @ SY284 @ SY285 )
| ( SV42 != SY285 )
| ! [V: $i] : ( between @ V @ SY284 @ SY285 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(239,plain,
! [SV43: $i] :
( ( ! [SY287: $i,SY288: $i] :
( ~ ( between @ SV43 @ SY287 @ SY288 )
| ( between @ SY288 @ SY287 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(240,plain,
! [SV44: $i] :
( ( ! [SY289: $i] : ( between @ SV44 @ SV44 @ SY289 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(241,plain,
! [SV45: $i] :
( ( ! [SY290: $i,SY291: $i] :
( ~ ( between @ SV45 @ SY290 @ SY291 )
| ~ ( between @ SY290 @ SV45 @ SY291 )
| ( SV45 = SY290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(242,plain,
! [SV46: $i] :
( ( ! [SY292: $i,SY293: $i] :
( ~ ( between @ SV46 @ SY292 @ SY293 )
| ~ ( between @ SV46 @ SY293 @ SY292 )
| ( SY292 = SY293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(243,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[189]) ).
thf(244,plain,
! [SV47: $i,SV1: $i] :
( ( equidistant @ SV1 @ SV47 @ SV47 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(245,plain,
! [SV48: $i,SV2: $i] :
( ( ! [SY294: $i,SY295: $i] :
( ~ ( equidistant @ SV2 @ SV48 @ SY294 @ SY295 )
| ! [SY296: $i,SY297: $i] :
( ~ ( equidistant @ SV2 @ SV48 @ SY296 @ SY297 )
| ( equidistant @ SY294 @ SY295 @ SY296 @ SY297 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(246,plain,
! [SV49: $i,SV3: $i] :
( ( ! [SY298: $i] :
~ ( equidistant @ SV3 @ SV49 @ SY298 @ SY298 )
| ( SV3 = SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(247,plain,
! [SV50: $i,SV4: $i] :
( ( ! [SY299: $i,SY300: $i] : ( between @ SV4 @ SV50 @ ( extension @ SV4 @ SV50 @ SY299 @ SY300 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(248,plain,
! [SV51: $i,SV5: $i] :
( ( ! [SY301: $i,SY302: $i] : ( equidistant @ SV5 @ ( extension @ SV51 @ SV5 @ SY301 @ SY302 ) @ SY301 @ SY302 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(249,plain,
! [SV52: $i,SV6: $i] :
( ( ! [SY303: $i,SY304: $i,SY305: $i,SY306: $i] :
( ~ ( equidistant @ SV6 @ SV52 @ SY303 @ SY304 )
| ~ ( equidistant @ SV52 @ SY305 @ SY304 @ SY306 )
| ! [SY307: $i,SY308: $i] :
( ~ ( equidistant @ SV6 @ SY307 @ SY303 @ SY308 )
| ~ ( equidistant @ SV52 @ SY307 @ SY304 @ SY308 )
| ~ ( between @ SV6 @ SV52 @ SY305 )
| ~ ( between @ SY303 @ SY304 @ SY306 )
| ( SV6 = SV52 )
| ( equidistant @ SY305 @ SY307 @ SY306 @ SY308 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(250,plain,
! [SV53: $i,SV7: $i] :
( ( ~ ( between @ SV7 @ SV53 @ SV7 )
| ( SV7 = SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[200]) ).
thf(251,plain,
! [SV54: $i,SV8: $i] :
( ( ! [SY309: $i] :
( ~ ( between @ SV8 @ SV54 @ SY309 )
| ! [SY310: $i,SY311: $i] :
( ~ ( between @ SY310 @ SY311 @ SY309 )
| ( between @ SV54 @ ( inner_pasch @ SV8 @ SV54 @ SY309 @ SY311 @ SY310 ) @ SY310 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(252,plain,
! [SV55: $i,SV9: $i] :
( ( ! [SY312: $i] :
( ~ ( between @ SV9 @ SV55 @ SY312 )
| ! [SY313: $i,SY314: $i] :
( ~ ( between @ SY313 @ SY314 @ SY312 )
| ( between @ SY314 @ ( inner_pasch @ SV9 @ SV55 @ SY312 @ SY314 @ SY313 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(253,plain,
! [SV56: $i,SV10: $i] :
( ( ! [SY315: $i] :
( ~ ( equidistant @ SV10 @ SV56 @ SV10 @ SY315 )
| ! [SY316: $i] :
( ~ ( equidistant @ SY316 @ SV56 @ SY316 @ SY315 )
| ! [SY317: $i] :
( ~ ( equidistant @ SY317 @ SV56 @ SY317 @ SY315 )
| ( between @ SV10 @ SY316 @ SY317 )
| ( between @ SY316 @ SY317 @ SV10 )
| ( SV56 = SY315 )
| ( between @ SY317 @ SV10 @ SY316 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(254,plain,
! [SV57: $i,SV11: $i] :
( ( ! [SY318: $i] :
( ~ ( between @ SV11 @ SV57 @ SY318 )
| ! [SY319: $i,SY320: $i] :
( ~ ( between @ SY319 @ SV57 @ SY320 )
| ( SV11 = SV57 )
| ( between @ SV11 @ SY319 @ ( euclid1 @ SV11 @ SY319 @ SV57 @ SY320 @ SY318 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(255,plain,
! [SV58: $i,SV12: $i] :
( ( ! [SY321: $i] :
( ~ ( between @ SV12 @ SV58 @ SY321 )
| ! [SY322: $i,SY323: $i] :
( ~ ( between @ SY322 @ SV58 @ SY323 )
| ( SV12 = SV58 )
| ( between @ SV12 @ SY323 @ ( euclid2 @ SV12 @ SY322 @ SV58 @ SY323 @ SY321 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(256,plain,
! [SV59: $i,SV13: $i] :
( ( ! [SY324: $i] :
( ~ ( between @ SV13 @ SV59 @ SY324 )
| ! [SY325: $i,SY326: $i] :
( ~ ( between @ SY325 @ SV59 @ SY326 )
| ( SV13 = SV59 )
| ( between @ ( euclid1 @ SV13 @ SY325 @ SV59 @ SY326 @ SY324 ) @ SY324 @ ( euclid2 @ SV13 @ SY325 @ SV59 @ SY326 @ SY324 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(257,plain,
! [SV60: $i,SV14: $i] :
( ( ! [SY327: $i,SY328: $i] :
( ~ ( equidistant @ SV14 @ SV60 @ SV14 @ SY327 )
| ! [SY329: $i] :
( ~ ( equidistant @ SV14 @ SY328 @ SV14 @ SY329 )
| ~ ( between @ SV14 @ SV60 @ SY328 )
| ! [SY330: $i] :
( ~ ( between @ SV60 @ SY330 @ SY328 )
| ( between @ SY327 @ ( continuous @ SV14 @ SV60 @ SY327 @ SY330 @ SY328 @ SY329 ) @ SY329 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(258,plain,
! [SV61: $i,SV15: $i] :
( ( ! [SY331: $i,SY332: $i] :
( ~ ( equidistant @ SV15 @ SV61 @ SV15 @ SY331 )
| ! [SY333: $i] :
( ~ ( equidistant @ SV15 @ SY332 @ SV15 @ SY333 )
| ~ ( between @ SV15 @ SV61 @ SY332 )
| ! [SY334: $i] :
( ~ ( between @ SV61 @ SY334 @ SY332 )
| ( equidistant @ SV15 @ SY334 @ SV15 @ ( continuous @ SV15 @ SV61 @ SY331 @ SY334 @ SY332 @ SY333 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(259,plain,
! [SV62: $i,SV16: $i] :
( ( ( reflection @ SV16 @ SV62 )
= ( extension @ SV16 @ SV62 @ SV16 @ SV62 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(260,plain,
! [SV63: $i,SV17: $i] :
( ( equidistant @ SV17 @ SV63 @ SV17 @ SV63 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(261,plain,
! [SV64: $i,SV18: $i] :
( ( ! [SY335: $i,SY336: $i] :
( ~ ( equidistant @ SV18 @ SV64 @ SY335 @ SY336 )
| ( equidistant @ SY335 @ SY336 @ SV18 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(262,plain,
! [SV65: $i,SV19: $i] :
( ( ! [SY337: $i,SY338: $i] :
( ~ ( equidistant @ SV19 @ SV65 @ SY337 @ SY338 )
| ( equidistant @ SV65 @ SV19 @ SY337 @ SY338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(263,plain,
! [SV66: $i,SV20: $i] :
( ( ! [SY339: $i,SY340: $i] :
( ~ ( equidistant @ SV20 @ SV66 @ SY339 @ SY340 )
| ( equidistant @ SV20 @ SV66 @ SY340 @ SY339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(264,plain,
! [SV67: $i,SV21: $i] :
( ( ! [SY341: $i,SY342: $i] :
( ~ ( equidistant @ SV21 @ SV67 @ SY341 @ SY342 )
| ( equidistant @ SV67 @ SV21 @ SY342 @ SY341 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(265,plain,
! [SV68: $i,SV22: $i] :
( ( ! [SY343: $i,SY344: $i] :
( ~ ( equidistant @ SV22 @ SV68 @ SY343 @ SY344 )
| ( equidistant @ SY343 @ SY344 @ SV68 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(266,plain,
! [SV69: $i,SV23: $i] :
( ( ! [SY345: $i,SY346: $i] :
( ~ ( equidistant @ SV23 @ SV69 @ SY345 @ SY346 )
| ( equidistant @ SY346 @ SY345 @ SV23 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(267,plain,
! [SV70: $i,SV24: $i] :
( ( ! [SY347: $i,SY348: $i] :
( ~ ( equidistant @ SV24 @ SV70 @ SY347 @ SY348 )
| ( equidistant @ SY348 @ SY347 @ SV70 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(268,plain,
! [SV71: $i,SV25: $i] :
( ( ! [SY349: $i,SY350: $i] :
( ~ ( equidistant @ SV25 @ SV71 @ SY349 @ SY350 )
| ! [SY351: $i,SY352: $i] :
( ~ ( equidistant @ SY349 @ SY350 @ SY351 @ SY352 )
| ( equidistant @ SV25 @ SV71 @ SY351 @ SY352 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(269,plain,
! [SV72: $i,SV26: $i] :
( ( ! [SY353: $i] :
( SV26
= ( extension @ SV72 @ SV26 @ SY353 @ SY353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(270,plain,
! [SV73: $i,SV27: $i] :
( ( ! [SY354: $i] :
( ! [SY355: $i,SY356: $i] :
( SV27
!= ( extension @ SV73 @ SY354 @ SY355 @ SY356 ) )
| ( between @ SV73 @ SY354 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(271,plain,
! [SV74: $i,SV28: $i] :
( ( between @ SV28 @ SV74 @ ( reflection @ SV28 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(272,plain,
! [SV75: $i,SV29: $i] :
( ( equidistant @ SV29 @ ( reflection @ SV75 @ SV29 ) @ SV75 @ SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[225]) ).
thf(273,plain,
! [SV76: $i,SV30: $i] :
( ( ( SV30 != SV76 )
| ( SV76
= ( reflection @ SV30 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(274,plain,
! [SV77: $i,SV32: $i] :
( ( ( SV32
!= ( reflection @ SV77 @ SV32 ) )
| ( SV77 = SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(275,plain,
! [SV78: $i,SV33: $i] :
( ( equidistant @ SV33 @ SV33 @ SV78 @ SV78 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(276,plain,
! [SV79: $i,SV34: $i] :
( ( ! [SY357: $i,SY358: $i] :
( ~ ( equidistant @ SV34 @ SV79 @ SY357 @ SY358 )
| ! [SY359: $i,SY360: $i] :
( ~ ( equidistant @ SV79 @ SY359 @ SY358 @ SY360 )
| ~ ( between @ SV34 @ SV79 @ SY359 )
| ~ ( between @ SY357 @ SY358 @ SY360 )
| ( equidistant @ SV34 @ SY359 @ SY357 @ SY360 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(277,plain,
! [SV80: $i,SV35: $i] :
( ( ! [SY361: $i] :
( ~ ( between @ SV35 @ SV80 @ SY361 )
| ! [SY362: $i] :
( ~ ( between @ SV35 @ SV80 @ SY362 )
| ~ ( equidistant @ SV80 @ SY361 @ SV80 @ SY362 )
| ( SV35 = SV80 )
| ( SY361 = SY362 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(278,plain,
! [SV81: $i,SV36: $i] :
( ( ! [SY363: $i] :
( ~ ( between @ SV36 @ SV81 @ SY363 )
| ( SV36 = SV81 )
| ( SY363
= ( extension @ SV36 @ SV81 @ SV81 @ SY363 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(279,plain,
! [SV82: $i,SV37: $i] :
( ( ! [SY364: $i,SY365: $i] :
( ~ ( equidistant @ SV37 @ SV82 @ SY364 @ SY365 )
| ! [SY366: $i,SY367: $i] :
( ( ( extension @ SY366 @ SY367 @ SV37 @ SV82 )
= ( extension @ SY366 @ SY367 @ SY364 @ SY365 ) )
| ( SY366 = SY367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(280,plain,
! [SV83: $i,SV38: $i] :
( ( ( ( extension @ SV38 @ SV83 @ SV38 @ SV83 )
= ( extension @ SV38 @ SV83 @ SV83 @ SV38 ) )
| ( SV38 = SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(281,plain,
! [SV84: $i,SV39: $i] :
( ( equidistant @ SV39 @ SV84 @ SV39 @ ( reflection @ ( reflection @ SV84 @ SV39 ) @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(282,plain,
! [SV85: $i,SV40: $i] :
( ( SV40
= ( reflection @ ( reflection @ SV40 @ SV85 ) @ SV85 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(283,plain,
! [SV86: $i,SV41: $i] :
( ( between @ SV41 @ SV86 @ SV86 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(284,plain,
! [SV87: $i,SV42: $i] :
( ( ! [SY368: $i] :
( ~ ( between @ SV42 @ SV87 @ SY368 )
| ( SV42 != SY368 )
| ! [SY369: $i] : ( between @ SY369 @ SV87 @ SY368 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(285,plain,
! [SV88: $i,SV43: $i] :
( ( ! [SY370: $i] :
( ~ ( between @ SV43 @ SV88 @ SY370 )
| ( between @ SY370 @ SV88 @ SV43 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(286,plain,
! [SV89: $i,SV44: $i] :
( ( between @ SV44 @ SV44 @ SV89 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(287,plain,
! [SV90: $i,SV45: $i] :
( ( ! [SY371: $i] :
( ~ ( between @ SV45 @ SV90 @ SY371 )
| ~ ( between @ SV90 @ SV45 @ SY371 )
| ( SV45 = SV90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(288,plain,
! [SV91: $i,SV46: $i] :
( ( ! [SY372: $i] :
( ~ ( between @ SV46 @ SV91 @ SY372 )
| ~ ( between @ SV46 @ SY372 @ SV91 )
| ( SV91 = SY372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(289,plain,
! [SV92: $i,SV48: $i,SV2: $i] :
( ( ! [SY373: $i] :
( ~ ( equidistant @ SV2 @ SV48 @ SV92 @ SY373 )
| ! [SY374: $i,SY375: $i] :
( ~ ( equidistant @ SV2 @ SV48 @ SY374 @ SY375 )
| ( equidistant @ SV92 @ SY373 @ SY374 @ SY375 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(290,plain,
! [SV49: $i,SV3: $i] :
( ( ( ! [SY298: $i] :
~ ( equidistant @ SV3 @ SV49 @ SY298 @ SY298 ) )
= $true )
| ( ( SV3 = SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(291,plain,
! [SV93: $i,SV50: $i,SV4: $i] :
( ( ! [SY376: $i] : ( between @ SV4 @ SV50 @ ( extension @ SV4 @ SV50 @ SV93 @ SY376 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(292,plain,
! [SV94: $i,SV51: $i,SV5: $i] :
( ( ! [SY377: $i] : ( equidistant @ SV5 @ ( extension @ SV51 @ SV5 @ SV94 @ SY377 ) @ SV94 @ SY377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(293,plain,
! [SV95: $i,SV52: $i,SV6: $i] :
( ( ! [SY378: $i,SY379: $i,SY380: $i] :
( ~ ( equidistant @ SV6 @ SV52 @ SV95 @ SY378 )
| ~ ( equidistant @ SV52 @ SY379 @ SY378 @ SY380 )
| ! [SY381: $i,SY382: $i] :
( ~ ( equidistant @ SV6 @ SY381 @ SV95 @ SY382 )
| ~ ( equidistant @ SV52 @ SY381 @ SY378 @ SY382 )
| ~ ( between @ SV6 @ SV52 @ SY379 )
| ~ ( between @ SV95 @ SY378 @ SY380 )
| ( SV6 = SV52 )
| ( equidistant @ SY379 @ SY381 @ SY380 @ SY382 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(294,plain,
! [SV53: $i,SV7: $i] :
( ( ( ~ ( between @ SV7 @ SV53 @ SV7 ) )
= $true )
| ( ( SV7 = SV53 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(295,plain,
! [SV96: $i,SV54: $i,SV8: $i] :
( ( ~ ( between @ SV8 @ SV54 @ SV96 )
| ! [SY383: $i,SY384: $i] :
( ~ ( between @ SY383 @ SY384 @ SV96 )
| ( between @ SV54 @ ( inner_pasch @ SV8 @ SV54 @ SV96 @ SY384 @ SY383 ) @ SY383 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(296,plain,
! [SV97: $i,SV55: $i,SV9: $i] :
( ( ~ ( between @ SV9 @ SV55 @ SV97 )
| ! [SY385: $i,SY386: $i] :
( ~ ( between @ SY385 @ SY386 @ SV97 )
| ( between @ SY386 @ ( inner_pasch @ SV9 @ SV55 @ SV97 @ SY386 @ SY385 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(297,plain,
! [SV98: $i,SV56: $i,SV10: $i] :
( ( ~ ( equidistant @ SV10 @ SV56 @ SV10 @ SV98 )
| ! [SY387: $i] :
( ~ ( equidistant @ SY387 @ SV56 @ SY387 @ SV98 )
| ! [SY388: $i] :
( ~ ( equidistant @ SY388 @ SV56 @ SY388 @ SV98 )
| ( between @ SV10 @ SY387 @ SY388 )
| ( between @ SY387 @ SY388 @ SV10 )
| ( SV56 = SV98 )
| ( between @ SY388 @ SV10 @ SY387 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(298,plain,
! [SV99: $i,SV57: $i,SV11: $i] :
( ( ~ ( between @ SV11 @ SV57 @ SV99 )
| ! [SY389: $i,SY390: $i] :
( ~ ( between @ SY389 @ SV57 @ SY390 )
| ( SV11 = SV57 )
| ( between @ SV11 @ SY389 @ ( euclid1 @ SV11 @ SY389 @ SV57 @ SY390 @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[254]) ).
thf(299,plain,
! [SV100: $i,SV58: $i,SV12: $i] :
( ( ~ ( between @ SV12 @ SV58 @ SV100 )
| ! [SY391: $i,SY392: $i] :
( ~ ( between @ SY391 @ SV58 @ SY392 )
| ( SV12 = SV58 )
| ( between @ SV12 @ SY392 @ ( euclid2 @ SV12 @ SY391 @ SV58 @ SY392 @ SV100 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(300,plain,
! [SV101: $i,SV59: $i,SV13: $i] :
( ( ~ ( between @ SV13 @ SV59 @ SV101 )
| ! [SY393: $i,SY394: $i] :
( ~ ( between @ SY393 @ SV59 @ SY394 )
| ( SV13 = SV59 )
| ( between @ ( euclid1 @ SV13 @ SY393 @ SV59 @ SY394 @ SV101 ) @ SV101 @ ( euclid2 @ SV13 @ SY393 @ SV59 @ SY394 @ SV101 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[256]) ).
thf(301,plain,
! [SV102: $i,SV60: $i,SV14: $i] :
( ( ! [SY395: $i] :
( ~ ( equidistant @ SV14 @ SV60 @ SV14 @ SV102 )
| ! [SY396: $i] :
( ~ ( equidistant @ SV14 @ SY395 @ SV14 @ SY396 )
| ~ ( between @ SV14 @ SV60 @ SY395 )
| ! [SY397: $i] :
( ~ ( between @ SV60 @ SY397 @ SY395 )
| ( between @ SV102 @ ( continuous @ SV14 @ SV60 @ SV102 @ SY397 @ SY395 @ SY396 ) @ SY396 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[257]) ).
thf(302,plain,
! [SV103: $i,SV61: $i,SV15: $i] :
( ( ! [SY398: $i] :
( ~ ( equidistant @ SV15 @ SV61 @ SV15 @ SV103 )
| ! [SY399: $i] :
( ~ ( equidistant @ SV15 @ SY398 @ SV15 @ SY399 )
| ~ ( between @ SV15 @ SV61 @ SY398 )
| ! [SY400: $i] :
( ~ ( between @ SV61 @ SY400 @ SY398 )
| ( equidistant @ SV15 @ SY400 @ SV15 @ ( continuous @ SV15 @ SV61 @ SV103 @ SY400 @ SY398 @ SY399 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[258]) ).
thf(303,plain,
! [SV104: $i,SV64: $i,SV18: $i] :
( ( ! [SY401: $i] :
( ~ ( equidistant @ SV18 @ SV64 @ SV104 @ SY401 )
| ( equidistant @ SV104 @ SY401 @ SV18 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[261]) ).
thf(304,plain,
! [SV105: $i,SV65: $i,SV19: $i] :
( ( ! [SY402: $i] :
( ~ ( equidistant @ SV19 @ SV65 @ SV105 @ SY402 )
| ( equidistant @ SV65 @ SV19 @ SV105 @ SY402 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(305,plain,
! [SV106: $i,SV66: $i,SV20: $i] :
( ( ! [SY403: $i] :
( ~ ( equidistant @ SV20 @ SV66 @ SV106 @ SY403 )
| ( equidistant @ SV20 @ SV66 @ SY403 @ SV106 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(306,plain,
! [SV107: $i,SV67: $i,SV21: $i] :
( ( ! [SY404: $i] :
( ~ ( equidistant @ SV21 @ SV67 @ SV107 @ SY404 )
| ( equidistant @ SV67 @ SV21 @ SY404 @ SV107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(307,plain,
! [SV108: $i,SV68: $i,SV22: $i] :
( ( ! [SY405: $i] :
( ~ ( equidistant @ SV22 @ SV68 @ SV108 @ SY405 )
| ( equidistant @ SV108 @ SY405 @ SV68 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[265]) ).
thf(308,plain,
! [SV109: $i,SV69: $i,SV23: $i] :
( ( ! [SY406: $i] :
( ~ ( equidistant @ SV23 @ SV69 @ SV109 @ SY406 )
| ( equidistant @ SY406 @ SV109 @ SV23 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(309,plain,
! [SV110: $i,SV70: $i,SV24: $i] :
( ( ! [SY407: $i] :
( ~ ( equidistant @ SV24 @ SV70 @ SV110 @ SY407 )
| ( equidistant @ SY407 @ SV110 @ SV70 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(310,plain,
! [SV111: $i,SV71: $i,SV25: $i] :
( ( ! [SY408: $i] :
( ~ ( equidistant @ SV25 @ SV71 @ SV111 @ SY408 )
| ! [SY409: $i,SY410: $i] :
( ~ ( equidistant @ SV111 @ SY408 @ SY409 @ SY410 )
| ( equidistant @ SV25 @ SV71 @ SY409 @ SY410 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[268]) ).
thf(311,plain,
! [SV112: $i,SV72: $i,SV26: $i] :
( ( SV26
= ( extension @ SV72 @ SV26 @ SV112 @ SV112 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(312,plain,
! [SV113: $i,SV73: $i,SV27: $i] :
( ( ! [SY411: $i,SY412: $i] :
( SV27
!= ( extension @ SV73 @ SV113 @ SY411 @ SY412 ) )
| ( between @ SV73 @ SV113 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(313,plain,
! [SV76: $i,SV30: $i] :
( ( ( ( SV30 != SV76 ) )
= $true )
| ( ( SV76
= ( reflection @ SV30 @ SV76 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(314,plain,
! [SV77: $i,SV32: $i] :
( ( ( ( SV32
!= ( reflection @ SV77 @ SV32 ) ) )
= $true )
| ( ( SV77 = SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(315,plain,
! [SV114: $i,SV79: $i,SV34: $i] :
( ( ! [SY413: $i] :
( ~ ( equidistant @ SV34 @ SV79 @ SV114 @ SY413 )
| ! [SY414: $i,SY415: $i] :
( ~ ( equidistant @ SV79 @ SY414 @ SY413 @ SY415 )
| ~ ( between @ SV34 @ SV79 @ SY414 )
| ~ ( between @ SV114 @ SY413 @ SY415 )
| ( equidistant @ SV34 @ SY414 @ SV114 @ SY415 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[276]) ).
thf(316,plain,
! [SV115: $i,SV80: $i,SV35: $i] :
( ( ~ ( between @ SV35 @ SV80 @ SV115 )
| ! [SY416: $i] :
( ~ ( between @ SV35 @ SV80 @ SY416 )
| ~ ( equidistant @ SV80 @ SV115 @ SV80 @ SY416 )
| ( SV35 = SV80 )
| ( SV115 = SY416 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[277]) ).
thf(317,plain,
! [SV116: $i,SV81: $i,SV36: $i] :
( ( ~ ( between @ SV36 @ SV81 @ SV116 )
| ( SV36 = SV81 )
| ( SV116
= ( extension @ SV36 @ SV81 @ SV81 @ SV116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[278]) ).
thf(318,plain,
! [SV117: $i,SV82: $i,SV37: $i] :
( ( ! [SY417: $i] :
( ~ ( equidistant @ SV37 @ SV82 @ SV117 @ SY417 )
| ! [SY418: $i,SY419: $i] :
( ( ( extension @ SY418 @ SY419 @ SV37 @ SV82 )
= ( extension @ SY418 @ SY419 @ SV117 @ SY417 ) )
| ( SY418 = SY419 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(319,plain,
! [SV83: $i,SV38: $i] :
( ( ( ( extension @ SV38 @ SV83 @ SV38 @ SV83 )
= ( extension @ SV38 @ SV83 @ SV83 @ SV38 ) )
= $true )
| ( ( SV38 = SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[280]) ).
thf(320,plain,
! [SV118: $i,SV87: $i,SV42: $i] :
( ( ~ ( between @ SV42 @ SV87 @ SV118 )
| ( SV42 != SV118 )
| ! [SY420: $i] : ( between @ SY420 @ SV87 @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[284]) ).
thf(321,plain,
! [SV119: $i,SV88: $i,SV43: $i] :
( ( ~ ( between @ SV43 @ SV88 @ SV119 )
| ( between @ SV119 @ SV88 @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[285]) ).
thf(322,plain,
! [SV120: $i,SV90: $i,SV45: $i] :
( ( ~ ( between @ SV45 @ SV90 @ SV120 )
| ~ ( between @ SV90 @ SV45 @ SV120 )
| ( SV45 = SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(323,plain,
! [SV121: $i,SV91: $i,SV46: $i] :
( ( ~ ( between @ SV46 @ SV91 @ SV121 )
| ~ ( between @ SV46 @ SV121 @ SV91 )
| ( SV91 = SV121 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[288]) ).
thf(324,plain,
! [SV122: $i,SV92: $i,SV48: $i,SV2: $i] :
( ( ~ ( equidistant @ SV2 @ SV48 @ SV92 @ SV122 )
| ! [SY421: $i,SY422: $i] :
( ~ ( equidistant @ SV2 @ SV48 @ SY421 @ SY422 )
| ( equidistant @ SV92 @ SV122 @ SY421 @ SY422 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(325,plain,
! [SV123: $i,SV49: $i,SV3: $i] :
( ( ( ~ ( equidistant @ SV3 @ SV49 @ SV123 @ SV123 ) )
= $true )
| ( ( SV3 = SV49 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(326,plain,
! [SV124: $i,SV93: $i,SV50: $i,SV4: $i] :
( ( between @ SV4 @ SV50 @ ( extension @ SV4 @ SV50 @ SV93 @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[291]) ).
thf(327,plain,
! [SV125: $i,SV94: $i,SV51: $i,SV5: $i] :
( ( equidistant @ SV5 @ ( extension @ SV51 @ SV5 @ SV94 @ SV125 ) @ SV94 @ SV125 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[292]) ).
thf(328,plain,
! [SV126: $i,SV95: $i,SV52: $i,SV6: $i] :
( ( ! [SY423: $i,SY424: $i] :
( ~ ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
| ~ ( equidistant @ SV52 @ SY423 @ SV126 @ SY424 )
| ! [SY425: $i,SY426: $i] :
( ~ ( equidistant @ SV6 @ SY425 @ SV95 @ SY426 )
| ~ ( equidistant @ SV52 @ SY425 @ SV126 @ SY426 )
| ~ ( between @ SV6 @ SV52 @ SY423 )
| ~ ( between @ SV95 @ SV126 @ SY424 )
| ( SV6 = SV52 )
| ( equidistant @ SY423 @ SY425 @ SY424 @ SY426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(329,plain,
! [SV53: $i,SV7: $i] :
( ( ( between @ SV7 @ SV53 @ SV7 )
= $false )
| ( ( SV7 = SV53 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[294]) ).
thf(330,plain,
! [SV96: $i,SV54: $i,SV8: $i] :
( ( ( ~ ( between @ SV8 @ SV54 @ SV96 ) )
= $true )
| ( ( ! [SY383: $i,SY384: $i] :
( ~ ( between @ SY383 @ SY384 @ SV96 )
| ( between @ SV54 @ ( inner_pasch @ SV8 @ SV54 @ SV96 @ SY384 @ SY383 ) @ SY383 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(331,plain,
! [SV97: $i,SV55: $i,SV9: $i] :
( ( ( ~ ( between @ SV9 @ SV55 @ SV97 ) )
= $true )
| ( ( ! [SY385: $i,SY386: $i] :
( ~ ( between @ SY385 @ SY386 @ SV97 )
| ( between @ SY386 @ ( inner_pasch @ SV9 @ SV55 @ SV97 @ SY386 @ SY385 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(332,plain,
! [SV98: $i,SV56: $i,SV10: $i] :
( ( ( ~ ( equidistant @ SV10 @ SV56 @ SV10 @ SV98 ) )
= $true )
| ( ( ! [SY387: $i] :
( ~ ( equidistant @ SY387 @ SV56 @ SY387 @ SV98 )
| ! [SY388: $i] :
( ~ ( equidistant @ SY388 @ SV56 @ SY388 @ SV98 )
| ( between @ SV10 @ SY387 @ SY388 )
| ( between @ SY387 @ SY388 @ SV10 )
| ( SV56 = SV98 )
| ( between @ SY388 @ SV10 @ SY387 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(333,plain,
! [SV99: $i,SV57: $i,SV11: $i] :
( ( ( ~ ( between @ SV11 @ SV57 @ SV99 ) )
= $true )
| ( ( ! [SY389: $i,SY390: $i] :
( ~ ( between @ SY389 @ SV57 @ SY390 )
| ( SV11 = SV57 )
| ( between @ SV11 @ SY389 @ ( euclid1 @ SV11 @ SY389 @ SV57 @ SY390 @ SV99 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(334,plain,
! [SV100: $i,SV58: $i,SV12: $i] :
( ( ( ~ ( between @ SV12 @ SV58 @ SV100 ) )
= $true )
| ( ( ! [SY391: $i,SY392: $i] :
( ~ ( between @ SY391 @ SV58 @ SY392 )
| ( SV12 = SV58 )
| ( between @ SV12 @ SY392 @ ( euclid2 @ SV12 @ SY391 @ SV58 @ SY392 @ SV100 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(335,plain,
! [SV101: $i,SV59: $i,SV13: $i] :
( ( ( ~ ( between @ SV13 @ SV59 @ SV101 ) )
= $true )
| ( ( ! [SY393: $i,SY394: $i] :
( ~ ( between @ SY393 @ SV59 @ SY394 )
| ( SV13 = SV59 )
| ( between @ ( euclid1 @ SV13 @ SY393 @ SV59 @ SY394 @ SV101 ) @ SV101 @ ( euclid2 @ SV13 @ SY393 @ SV59 @ SY394 @ SV101 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[300]) ).
thf(336,plain,
! [SV127: $i,SV102: $i,SV60: $i,SV14: $i] :
( ( ~ ( equidistant @ SV14 @ SV60 @ SV14 @ SV102 )
| ! [SY427: $i] :
( ~ ( equidistant @ SV14 @ SV127 @ SV14 @ SY427 )
| ~ ( between @ SV14 @ SV60 @ SV127 )
| ! [SY428: $i] :
( ~ ( between @ SV60 @ SY428 @ SV127 )
| ( between @ SV102 @ ( continuous @ SV14 @ SV60 @ SV102 @ SY428 @ SV127 @ SY427 ) @ SY427 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[301]) ).
thf(337,plain,
! [SV128: $i,SV103: $i,SV61: $i,SV15: $i] :
( ( ~ ( equidistant @ SV15 @ SV61 @ SV15 @ SV103 )
| ! [SY429: $i] :
( ~ ( equidistant @ SV15 @ SV128 @ SV15 @ SY429 )
| ~ ( between @ SV15 @ SV61 @ SV128 )
| ! [SY430: $i] :
( ~ ( between @ SV61 @ SY430 @ SV128 )
| ( equidistant @ SV15 @ SY430 @ SV15 @ ( continuous @ SV15 @ SV61 @ SV103 @ SY430 @ SV128 @ SY429 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[302]) ).
thf(338,plain,
! [SV129: $i,SV104: $i,SV64: $i,SV18: $i] :
( ( ~ ( equidistant @ SV18 @ SV64 @ SV104 @ SV129 )
| ( equidistant @ SV104 @ SV129 @ SV18 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(339,plain,
! [SV130: $i,SV105: $i,SV65: $i,SV19: $i] :
( ( ~ ( equidistant @ SV19 @ SV65 @ SV105 @ SV130 )
| ( equidistant @ SV65 @ SV19 @ SV105 @ SV130 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(340,plain,
! [SV131: $i,SV106: $i,SV66: $i,SV20: $i] :
( ( ~ ( equidistant @ SV20 @ SV66 @ SV106 @ SV131 )
| ( equidistant @ SV20 @ SV66 @ SV131 @ SV106 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(341,plain,
! [SV132: $i,SV107: $i,SV67: $i,SV21: $i] :
( ( ~ ( equidistant @ SV21 @ SV67 @ SV107 @ SV132 )
| ( equidistant @ SV67 @ SV21 @ SV132 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[306]) ).
thf(342,plain,
! [SV133: $i,SV108: $i,SV68: $i,SV22: $i] :
( ( ~ ( equidistant @ SV22 @ SV68 @ SV108 @ SV133 )
| ( equidistant @ SV108 @ SV133 @ SV68 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(343,plain,
! [SV134: $i,SV109: $i,SV69: $i,SV23: $i] :
( ( ~ ( equidistant @ SV23 @ SV69 @ SV109 @ SV134 )
| ( equidistant @ SV134 @ SV109 @ SV23 @ SV69 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(344,plain,
! [SV135: $i,SV110: $i,SV70: $i,SV24: $i] :
( ( ~ ( equidistant @ SV24 @ SV70 @ SV110 @ SV135 )
| ( equidistant @ SV135 @ SV110 @ SV70 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[309]) ).
thf(345,plain,
! [SV136: $i,SV111: $i,SV71: $i,SV25: $i] :
( ( ~ ( equidistant @ SV25 @ SV71 @ SV111 @ SV136 )
| ! [SY431: $i,SY432: $i] :
( ~ ( equidistant @ SV111 @ SV136 @ SY431 @ SY432 )
| ( equidistant @ SV25 @ SV71 @ SY431 @ SY432 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[310]) ).
thf(346,plain,
! [SV113: $i,SV73: $i,SV27: $i] :
( ( ( ! [SY411: $i,SY412: $i] :
( SV27
!= ( extension @ SV73 @ SV113 @ SY411 @ SY412 ) ) )
= $true )
| ( ( between @ SV73 @ SV113 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(347,plain,
! [SV76: $i,SV30: $i] :
( ( ( SV30 = SV76 )
= $false )
| ( ( SV76
= ( reflection @ SV30 @ SV76 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[313]) ).
thf(348,plain,
! [SV77: $i,SV32: $i] :
( ( ( SV32
= ( reflection @ SV77 @ SV32 ) )
= $false )
| ( ( SV77 = SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[314]) ).
thf(349,plain,
! [SV137: $i,SV114: $i,SV79: $i,SV34: $i] :
( ( ~ ( equidistant @ SV34 @ SV79 @ SV114 @ SV137 )
| ! [SY433: $i,SY434: $i] :
( ~ ( equidistant @ SV79 @ SY433 @ SV137 @ SY434 )
| ~ ( between @ SV34 @ SV79 @ SY433 )
| ~ ( between @ SV114 @ SV137 @ SY434 )
| ( equidistant @ SV34 @ SY433 @ SV114 @ SY434 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(350,plain,
! [SV115: $i,SV80: $i,SV35: $i] :
( ( ( ~ ( between @ SV35 @ SV80 @ SV115 ) )
= $true )
| ( ( ! [SY416: $i] :
( ~ ( between @ SV35 @ SV80 @ SY416 )
| ~ ( equidistant @ SV80 @ SV115 @ SV80 @ SY416 )
| ( SV35 = SV80 )
| ( SV115 = SY416 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[316]) ).
thf(351,plain,
! [SV116: $i,SV81: $i,SV36: $i] :
( ( ( ~ ( between @ SV36 @ SV81 @ SV116 ) )
= $true )
| ( ( ( SV36 = SV81 )
| ( SV116
= ( extension @ SV36 @ SV81 @ SV81 @ SV116 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[317]) ).
thf(352,plain,
! [SV138: $i,SV117: $i,SV82: $i,SV37: $i] :
( ( ~ ( equidistant @ SV37 @ SV82 @ SV117 @ SV138 )
| ! [SY435: $i,SY436: $i] :
( ( ( extension @ SY435 @ SY436 @ SV37 @ SV82 )
= ( extension @ SY435 @ SY436 @ SV117 @ SV138 ) )
| ( SY435 = SY436 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(353,plain,
! [SV118: $i,SV87: $i,SV42: $i] :
( ( ( ~ ( between @ SV42 @ SV87 @ SV118 ) )
= $true )
| ( ( ( SV42 != SV118 )
| ! [SY420: $i] : ( between @ SY420 @ SV87 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(354,plain,
! [SV119: $i,SV88: $i,SV43: $i] :
( ( ( ~ ( between @ SV43 @ SV88 @ SV119 ) )
= $true )
| ( ( between @ SV119 @ SV88 @ SV43 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(355,plain,
! [SV120: $i,SV90: $i,SV45: $i] :
( ( ( ~ ( between @ SV45 @ SV90 @ SV120 ) )
= $true )
| ( ( ~ ( between @ SV90 @ SV45 @ SV120 )
| ( SV45 = SV90 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(356,plain,
! [SV121: $i,SV91: $i,SV46: $i] :
( ( ( ~ ( between @ SV46 @ SV91 @ SV121 ) )
= $true )
| ( ( ~ ( between @ SV46 @ SV121 @ SV91 )
| ( SV91 = SV121 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[323]) ).
thf(357,plain,
! [SV122: $i,SV92: $i,SV48: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV48 @ SV92 @ SV122 ) )
= $true )
| ( ( ! [SY421: $i,SY422: $i] :
( ~ ( equidistant @ SV2 @ SV48 @ SY421 @ SY422 )
| ( equidistant @ SV92 @ SV122 @ SY421 @ SY422 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[324]) ).
thf(358,plain,
! [SV123: $i,SV49: $i,SV3: $i] :
( ( ( equidistant @ SV3 @ SV49 @ SV123 @ SV123 )
= $false )
| ( ( SV3 = SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(359,plain,
! [SV139: $i,SV126: $i,SV95: $i,SV52: $i,SV6: $i] :
( ( ! [SY437: $i] :
( ~ ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
| ~ ( equidistant @ SV52 @ SV139 @ SV126 @ SY437 )
| ! [SY438: $i,SY439: $i] :
( ~ ( equidistant @ SV6 @ SY438 @ SV95 @ SY439 )
| ~ ( equidistant @ SV52 @ SY438 @ SV126 @ SY439 )
| ~ ( between @ SV6 @ SV52 @ SV139 )
| ~ ( between @ SV95 @ SV126 @ SY437 )
| ( SV6 = SV52 )
| ( equidistant @ SV139 @ SY438 @ SY437 @ SY439 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(360,plain,
! [SV96: $i,SV54: $i,SV8: $i] :
( ( ( between @ SV8 @ SV54 @ SV96 )
= $false )
| ( ( ! [SY383: $i,SY384: $i] :
( ~ ( between @ SY383 @ SY384 @ SV96 )
| ( between @ SV54 @ ( inner_pasch @ SV8 @ SV54 @ SV96 @ SY384 @ SY383 ) @ SY383 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[330]) ).
thf(361,plain,
! [SV97: $i,SV55: $i,SV9: $i] :
( ( ( between @ SV9 @ SV55 @ SV97 )
= $false )
| ( ( ! [SY385: $i,SY386: $i] :
( ~ ( between @ SY385 @ SY386 @ SV97 )
| ( between @ SY386 @ ( inner_pasch @ SV9 @ SV55 @ SV97 @ SY386 @ SY385 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[331]) ).
thf(362,plain,
! [SV98: $i,SV56: $i,SV10: $i] :
( ( ( equidistant @ SV10 @ SV56 @ SV10 @ SV98 )
= $false )
| ( ( ! [SY387: $i] :
( ~ ( equidistant @ SY387 @ SV56 @ SY387 @ SV98 )
| ! [SY388: $i] :
( ~ ( equidistant @ SY388 @ SV56 @ SY388 @ SV98 )
| ( between @ SV10 @ SY387 @ SY388 )
| ( between @ SY387 @ SY388 @ SV10 )
| ( SV56 = SV98 )
| ( between @ SY388 @ SV10 @ SY387 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[332]) ).
thf(363,plain,
! [SV99: $i,SV57: $i,SV11: $i] :
( ( ( between @ SV11 @ SV57 @ SV99 )
= $false )
| ( ( ! [SY389: $i,SY390: $i] :
( ~ ( between @ SY389 @ SV57 @ SY390 )
| ( SV11 = SV57 )
| ( between @ SV11 @ SY389 @ ( euclid1 @ SV11 @ SY389 @ SV57 @ SY390 @ SV99 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[333]) ).
thf(364,plain,
! [SV100: $i,SV58: $i,SV12: $i] :
( ( ( between @ SV12 @ SV58 @ SV100 )
= $false )
| ( ( ! [SY391: $i,SY392: $i] :
( ~ ( between @ SY391 @ SV58 @ SY392 )
| ( SV12 = SV58 )
| ( between @ SV12 @ SY392 @ ( euclid2 @ SV12 @ SY391 @ SV58 @ SY392 @ SV100 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(365,plain,
! [SV101: $i,SV59: $i,SV13: $i] :
( ( ( between @ SV13 @ SV59 @ SV101 )
= $false )
| ( ( ! [SY393: $i,SY394: $i] :
( ~ ( between @ SY393 @ SV59 @ SY394 )
| ( SV13 = SV59 )
| ( between @ ( euclid1 @ SV13 @ SY393 @ SV59 @ SY394 @ SV101 ) @ SV101 @ ( euclid2 @ SV13 @ SY393 @ SV59 @ SY394 @ SV101 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(366,plain,
! [SV127: $i,SV102: $i,SV60: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV60 @ SV14 @ SV102 ) )
= $true )
| ( ( ! [SY427: $i] :
( ~ ( equidistant @ SV14 @ SV127 @ SV14 @ SY427 )
| ~ ( between @ SV14 @ SV60 @ SV127 )
| ! [SY428: $i] :
( ~ ( between @ SV60 @ SY428 @ SV127 )
| ( between @ SV102 @ ( continuous @ SV14 @ SV60 @ SV102 @ SY428 @ SV127 @ SY427 ) @ SY427 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(367,plain,
! [SV128: $i,SV103: $i,SV61: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV61 @ SV15 @ SV103 ) )
= $true )
| ( ( ! [SY429: $i] :
( ~ ( equidistant @ SV15 @ SV128 @ SV15 @ SY429 )
| ~ ( between @ SV15 @ SV61 @ SV128 )
| ! [SY430: $i] :
( ~ ( between @ SV61 @ SY430 @ SV128 )
| ( equidistant @ SV15 @ SY430 @ SV15 @ ( continuous @ SV15 @ SV61 @ SV103 @ SY430 @ SV128 @ SY429 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[337]) ).
thf(368,plain,
! [SV129: $i,SV104: $i,SV64: $i,SV18: $i] :
( ( ( ~ ( equidistant @ SV18 @ SV64 @ SV104 @ SV129 ) )
= $true )
| ( ( equidistant @ SV104 @ SV129 @ SV18 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(369,plain,
! [SV130: $i,SV105: $i,SV65: $i,SV19: $i] :
( ( ( ~ ( equidistant @ SV19 @ SV65 @ SV105 @ SV130 ) )
= $true )
| ( ( equidistant @ SV65 @ SV19 @ SV105 @ SV130 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(370,plain,
! [SV131: $i,SV106: $i,SV66: $i,SV20: $i] :
( ( ( ~ ( equidistant @ SV20 @ SV66 @ SV106 @ SV131 ) )
= $true )
| ( ( equidistant @ SV20 @ SV66 @ SV131 @ SV106 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(371,plain,
! [SV132: $i,SV107: $i,SV67: $i,SV21: $i] :
( ( ( ~ ( equidistant @ SV21 @ SV67 @ SV107 @ SV132 ) )
= $true )
| ( ( equidistant @ SV67 @ SV21 @ SV132 @ SV107 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(372,plain,
! [SV133: $i,SV108: $i,SV68: $i,SV22: $i] :
( ( ( ~ ( equidistant @ SV22 @ SV68 @ SV108 @ SV133 ) )
= $true )
| ( ( equidistant @ SV108 @ SV133 @ SV68 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(373,plain,
! [SV134: $i,SV109: $i,SV69: $i,SV23: $i] :
( ( ( ~ ( equidistant @ SV23 @ SV69 @ SV109 @ SV134 ) )
= $true )
| ( ( equidistant @ SV134 @ SV109 @ SV23 @ SV69 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(374,plain,
! [SV135: $i,SV110: $i,SV70: $i,SV24: $i] :
( ( ( ~ ( equidistant @ SV24 @ SV70 @ SV110 @ SV135 ) )
= $true )
| ( ( equidistant @ SV135 @ SV110 @ SV70 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(375,plain,
! [SV136: $i,SV111: $i,SV71: $i,SV25: $i] :
( ( ( ~ ( equidistant @ SV25 @ SV71 @ SV111 @ SV136 ) )
= $true )
| ( ( ! [SY431: $i,SY432: $i] :
( ~ ( equidistant @ SV111 @ SV136 @ SY431 @ SY432 )
| ( equidistant @ SV25 @ SV71 @ SY431 @ SY432 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(376,plain,
! [SV140: $i,SV113: $i,SV73: $i,SV27: $i] :
( ( ( ! [SY440: $i] :
( SV27
!= ( extension @ SV73 @ SV113 @ SV140 @ SY440 ) ) )
= $true )
| ( ( between @ SV73 @ SV113 @ SV27 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(377,plain,
! [SV137: $i,SV114: $i,SV79: $i,SV34: $i] :
( ( ( ~ ( equidistant @ SV34 @ SV79 @ SV114 @ SV137 ) )
= $true )
| ( ( ! [SY433: $i,SY434: $i] :
( ~ ( equidistant @ SV79 @ SY433 @ SV137 @ SY434 )
| ~ ( between @ SV34 @ SV79 @ SY433 )
| ~ ( between @ SV114 @ SV137 @ SY434 )
| ( equidistant @ SV34 @ SY433 @ SV114 @ SY434 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[349]) ).
thf(378,plain,
! [SV115: $i,SV80: $i,SV35: $i] :
( ( ( between @ SV35 @ SV80 @ SV115 )
= $false )
| ( ( ! [SY416: $i] :
( ~ ( between @ SV35 @ SV80 @ SY416 )
| ~ ( equidistant @ SV80 @ SV115 @ SV80 @ SY416 )
| ( SV35 = SV80 )
| ( SV115 = SY416 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[350]) ).
thf(379,plain,
! [SV116: $i,SV81: $i,SV36: $i] :
( ( ( between @ SV36 @ SV81 @ SV116 )
= $false )
| ( ( ( SV36 = SV81 )
| ( SV116
= ( extension @ SV36 @ SV81 @ SV81 @ SV116 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(380,plain,
! [SV138: $i,SV117: $i,SV82: $i,SV37: $i] :
( ( ( ~ ( equidistant @ SV37 @ SV82 @ SV117 @ SV138 ) )
= $true )
| ( ( ! [SY435: $i,SY436: $i] :
( ( ( extension @ SY435 @ SY436 @ SV37 @ SV82 )
= ( extension @ SY435 @ SY436 @ SV117 @ SV138 ) )
| ( SY435 = SY436 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(381,plain,
! [SV118: $i,SV87: $i,SV42: $i] :
( ( ( between @ SV42 @ SV87 @ SV118 )
= $false )
| ( ( ( SV42 != SV118 )
| ! [SY420: $i] : ( between @ SY420 @ SV87 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(382,plain,
! [SV119: $i,SV88: $i,SV43: $i] :
( ( ( between @ SV43 @ SV88 @ SV119 )
= $false )
| ( ( between @ SV119 @ SV88 @ SV43 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[354]) ).
thf(383,plain,
! [SV120: $i,SV90: $i,SV45: $i] :
( ( ( between @ SV45 @ SV90 @ SV120 )
= $false )
| ( ( ~ ( between @ SV90 @ SV45 @ SV120 )
| ( SV45 = SV90 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(384,plain,
! [SV121: $i,SV91: $i,SV46: $i] :
( ( ( between @ SV46 @ SV91 @ SV121 )
= $false )
| ( ( ~ ( between @ SV46 @ SV121 @ SV91 )
| ( SV91 = SV121 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[356]) ).
thf(385,plain,
! [SV122: $i,SV92: $i,SV48: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV48 @ SV92 @ SV122 )
= $false )
| ( ( ! [SY421: $i,SY422: $i] :
( ~ ( equidistant @ SV2 @ SV48 @ SY421 @ SY422 )
| ( equidistant @ SV92 @ SV122 @ SY421 @ SY422 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[357]) ).
thf(386,plain,
! [SV141: $i,SV139: $i,SV126: $i,SV95: $i,SV52: $i,SV6: $i] :
( ( ~ ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
| ~ ( equidistant @ SV52 @ SV139 @ SV126 @ SV141 )
| ! [SY441: $i,SY442: $i] :
( ~ ( equidistant @ SV6 @ SY441 @ SV95 @ SY442 )
| ~ ( equidistant @ SV52 @ SY441 @ SV126 @ SY442 )
| ~ ( between @ SV6 @ SV52 @ SV139 )
| ~ ( between @ SV95 @ SV126 @ SV141 )
| ( SV6 = SV52 )
| ( equidistant @ SV139 @ SY441 @ SV141 @ SY442 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(387,plain,
! [SV8: $i,SV54: $i,SV96: $i,SV142: $i] :
( ( ( ! [SY443: $i] :
( ~ ( between @ SV142 @ SY443 @ SV96 )
| ( between @ SV54 @ ( inner_pasch @ SV8 @ SV54 @ SV96 @ SY443 @ SV142 ) @ SV142 ) ) )
= $true )
| ( ( between @ SV8 @ SV54 @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(388,plain,
! [SV55: $i,SV9: $i,SV97: $i,SV143: $i] :
( ( ( ! [SY444: $i] :
( ~ ( between @ SV143 @ SY444 @ SV97 )
| ( between @ SY444 @ ( inner_pasch @ SV9 @ SV55 @ SV97 @ SY444 @ SV143 ) @ SV9 ) ) )
= $true )
| ( ( between @ SV9 @ SV55 @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(389,plain,
! [SV10: $i,SV98: $i,SV56: $i,SV144: $i] :
( ( ( ~ ( equidistant @ SV144 @ SV56 @ SV144 @ SV98 )
| ! [SY445: $i] :
( ~ ( equidistant @ SY445 @ SV56 @ SY445 @ SV98 )
| ( between @ SV10 @ SV144 @ SY445 )
| ( between @ SV144 @ SY445 @ SV10 )
| ( SV56 = SV98 )
| ( between @ SY445 @ SV10 @ SV144 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV56 @ SV10 @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(390,plain,
! [SV99: $i,SV11: $i,SV57: $i,SV145: $i] :
( ( ( ! [SY446: $i] :
( ~ ( between @ SV145 @ SV57 @ SY446 )
| ( SV11 = SV57 )
| ( between @ SV11 @ SV145 @ ( euclid1 @ SV11 @ SV145 @ SV57 @ SY446 @ SV99 ) ) ) )
= $true )
| ( ( between @ SV11 @ SV57 @ SV99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(391,plain,
! [SV100: $i,SV12: $i,SV58: $i,SV146: $i] :
( ( ( ! [SY447: $i] :
( ~ ( between @ SV146 @ SV58 @ SY447 )
| ( SV12 = SV58 )
| ( between @ SV12 @ SY447 @ ( euclid2 @ SV12 @ SV146 @ SV58 @ SY447 @ SV100 ) ) ) )
= $true )
| ( ( between @ SV12 @ SV58 @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[364]) ).
thf(392,plain,
! [SV101: $i,SV13: $i,SV59: $i,SV147: $i] :
( ( ( ! [SY448: $i] :
( ~ ( between @ SV147 @ SV59 @ SY448 )
| ( SV13 = SV59 )
| ( between @ ( euclid1 @ SV13 @ SV147 @ SV59 @ SY448 @ SV101 ) @ SV101 @ ( euclid2 @ SV13 @ SV147 @ SV59 @ SY448 @ SV101 ) ) ) )
= $true )
| ( ( between @ SV13 @ SV59 @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(393,plain,
! [SV127: $i,SV102: $i,SV60: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV60 @ SV14 @ SV102 )
= $false )
| ( ( ! [SY427: $i] :
( ~ ( equidistant @ SV14 @ SV127 @ SV14 @ SY427 )
| ~ ( between @ SV14 @ SV60 @ SV127 )
| ! [SY428: $i] :
( ~ ( between @ SV60 @ SY428 @ SV127 )
| ( between @ SV102 @ ( continuous @ SV14 @ SV60 @ SV102 @ SY428 @ SV127 @ SY427 ) @ SY427 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[366]) ).
thf(394,plain,
! [SV128: $i,SV103: $i,SV61: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV61 @ SV15 @ SV103 )
= $false )
| ( ( ! [SY429: $i] :
( ~ ( equidistant @ SV15 @ SV128 @ SV15 @ SY429 )
| ~ ( between @ SV15 @ SV61 @ SV128 )
| ! [SY430: $i] :
( ~ ( between @ SV61 @ SY430 @ SV128 )
| ( equidistant @ SV15 @ SY430 @ SV15 @ ( continuous @ SV15 @ SV61 @ SV103 @ SY430 @ SV128 @ SY429 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[367]) ).
thf(395,plain,
! [SV129: $i,SV104: $i,SV64: $i,SV18: $i] :
( ( ( equidistant @ SV18 @ SV64 @ SV104 @ SV129 )
= $false )
| ( ( equidistant @ SV104 @ SV129 @ SV18 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[368]) ).
thf(396,plain,
! [SV130: $i,SV105: $i,SV65: $i,SV19: $i] :
( ( ( equidistant @ SV19 @ SV65 @ SV105 @ SV130 )
= $false )
| ( ( equidistant @ SV65 @ SV19 @ SV105 @ SV130 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[369]) ).
thf(397,plain,
! [SV131: $i,SV106: $i,SV66: $i,SV20: $i] :
( ( ( equidistant @ SV20 @ SV66 @ SV106 @ SV131 )
= $false )
| ( ( equidistant @ SV20 @ SV66 @ SV131 @ SV106 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[370]) ).
thf(398,plain,
! [SV132: $i,SV107: $i,SV67: $i,SV21: $i] :
( ( ( equidistant @ SV21 @ SV67 @ SV107 @ SV132 )
= $false )
| ( ( equidistant @ SV67 @ SV21 @ SV132 @ SV107 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[371]) ).
thf(399,plain,
! [SV133: $i,SV108: $i,SV68: $i,SV22: $i] :
( ( ( equidistant @ SV22 @ SV68 @ SV108 @ SV133 )
= $false )
| ( ( equidistant @ SV108 @ SV133 @ SV68 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[372]) ).
thf(400,plain,
! [SV134: $i,SV109: $i,SV69: $i,SV23: $i] :
( ( ( equidistant @ SV23 @ SV69 @ SV109 @ SV134 )
= $false )
| ( ( equidistant @ SV134 @ SV109 @ SV23 @ SV69 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[373]) ).
thf(401,plain,
! [SV135: $i,SV110: $i,SV70: $i,SV24: $i] :
( ( ( equidistant @ SV24 @ SV70 @ SV110 @ SV135 )
= $false )
| ( ( equidistant @ SV135 @ SV110 @ SV70 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[374]) ).
thf(402,plain,
! [SV136: $i,SV111: $i,SV71: $i,SV25: $i] :
( ( ( equidistant @ SV25 @ SV71 @ SV111 @ SV136 )
= $false )
| ( ( ! [SY431: $i,SY432: $i] :
( ~ ( equidistant @ SV111 @ SV136 @ SY431 @ SY432 )
| ( equidistant @ SV25 @ SV71 @ SY431 @ SY432 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[375]) ).
thf(403,plain,
! [SV148: $i,SV140: $i,SV113: $i,SV73: $i,SV27: $i] :
( ( ( ( SV27
!= ( extension @ SV73 @ SV113 @ SV140 @ SV148 ) ) )
= $true )
| ( ( between @ SV73 @ SV113 @ SV27 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(404,plain,
! [SV137: $i,SV114: $i,SV79: $i,SV34: $i] :
( ( ( equidistant @ SV34 @ SV79 @ SV114 @ SV137 )
= $false )
| ( ( ! [SY433: $i,SY434: $i] :
( ~ ( equidistant @ SV79 @ SY433 @ SV137 @ SY434 )
| ~ ( between @ SV34 @ SV79 @ SY433 )
| ~ ( between @ SV114 @ SV137 @ SY434 )
| ( equidistant @ SV34 @ SY433 @ SV114 @ SY434 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[377]) ).
thf(405,plain,
! [SV115: $i,SV149: $i,SV80: $i,SV35: $i] :
( ( ( ~ ( between @ SV35 @ SV80 @ SV149 )
| ~ ( equidistant @ SV80 @ SV115 @ SV80 @ SV149 )
| ( SV35 = SV80 )
| ( SV115 = SV149 ) )
= $true )
| ( ( between @ SV35 @ SV80 @ SV115 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(406,plain,
! [SV116: $i,SV81: $i,SV36: $i] :
( ( ( SV36 = SV81 )
= $true )
| ( ( SV116
= ( extension @ SV36 @ SV81 @ SV81 @ SV116 ) )
= $true )
| ( ( between @ SV36 @ SV81 @ SV116 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[379]) ).
thf(407,plain,
! [SV138: $i,SV117: $i,SV82: $i,SV37: $i] :
( ( ( equidistant @ SV37 @ SV82 @ SV117 @ SV138 )
= $false )
| ( ( ! [SY435: $i,SY436: $i] :
( ( ( extension @ SY435 @ SY436 @ SV37 @ SV82 )
= ( extension @ SY435 @ SY436 @ SV117 @ SV138 ) )
| ( SY435 = SY436 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[380]) ).
thf(408,plain,
! [SV87: $i,SV118: $i,SV42: $i] :
( ( ( ( SV42 != SV118 ) )
= $true )
| ( ( ! [SY420: $i] : ( between @ SY420 @ SV87 @ SV118 ) )
= $true )
| ( ( between @ SV42 @ SV87 @ SV118 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[381]) ).
thf(409,plain,
! [SV120: $i,SV45: $i,SV90: $i] :
( ( ( ~ ( between @ SV90 @ SV45 @ SV120 ) )
= $true )
| ( ( SV45 = SV90 )
= $true )
| ( ( between @ SV45 @ SV90 @ SV120 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[383]) ).
thf(410,plain,
! [SV91: $i,SV121: $i,SV46: $i] :
( ( ( ~ ( between @ SV46 @ SV121 @ SV91 ) )
= $true )
| ( ( SV91 = SV121 )
= $true )
| ( ( between @ SV46 @ SV91 @ SV121 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[384]) ).
thf(411,plain,
! [SV122: $i,SV92: $i,SV150: $i,SV48: $i,SV2: $i] :
( ( ( ! [SY449: $i] :
( ~ ( equidistant @ SV2 @ SV48 @ SV150 @ SY449 )
| ( equidistant @ SV92 @ SV122 @ SV150 @ SY449 ) ) )
= $true )
| ( ( equidistant @ SV2 @ SV48 @ SV92 @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(412,plain,
! [SV141: $i,SV139: $i,SV126: $i,SV95: $i,SV52: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 ) )
= $true )
| ( ( ~ ( equidistant @ SV52 @ SV139 @ SV126 @ SV141 )
| ! [SY441: $i,SY442: $i] :
( ~ ( equidistant @ SV6 @ SY441 @ SV95 @ SY442 )
| ~ ( equidistant @ SV52 @ SY441 @ SV126 @ SY442 )
| ~ ( between @ SV6 @ SV52 @ SV139 )
| ~ ( between @ SV95 @ SV126 @ SV141 )
| ( SV6 = SV52 )
| ( equidistant @ SV139 @ SY441 @ SV141 @ SY442 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[386]) ).
thf(413,plain,
! [SV8: $i,SV54: $i,SV96: $i,SV151: $i,SV142: $i] :
( ( ( ~ ( between @ SV142 @ SV151 @ SV96 )
| ( between @ SV54 @ ( inner_pasch @ SV8 @ SV54 @ SV96 @ SV151 @ SV142 ) @ SV142 ) )
= $true )
| ( ( between @ SV8 @ SV54 @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[387]) ).
thf(414,plain,
! [SV55: $i,SV9: $i,SV97: $i,SV152: $i,SV143: $i] :
( ( ( ~ ( between @ SV143 @ SV152 @ SV97 )
| ( between @ SV152 @ ( inner_pasch @ SV9 @ SV55 @ SV97 @ SV152 @ SV143 ) @ SV9 ) )
= $true )
| ( ( between @ SV9 @ SV55 @ SV97 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(415,plain,
! [SV10: $i,SV98: $i,SV56: $i,SV144: $i] :
( ( ( ~ ( equidistant @ SV144 @ SV56 @ SV144 @ SV98 ) )
= $true )
| ( ( ! [SY445: $i] :
( ~ ( equidistant @ SY445 @ SV56 @ SY445 @ SV98 )
| ( between @ SV10 @ SV144 @ SY445 )
| ( between @ SV144 @ SY445 @ SV10 )
| ( SV56 = SV98 )
| ( between @ SY445 @ SV10 @ SV144 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV56 @ SV10 @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[389]) ).
thf(416,plain,
! [SV99: $i,SV11: $i,SV153: $i,SV57: $i,SV145: $i] :
( ( ( ~ ( between @ SV145 @ SV57 @ SV153 )
| ( SV11 = SV57 )
| ( between @ SV11 @ SV145 @ ( euclid1 @ SV11 @ SV145 @ SV57 @ SV153 @ SV99 ) ) )
= $true )
| ( ( between @ SV11 @ SV57 @ SV99 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[390]) ).
thf(417,plain,
! [SV100: $i,SV12: $i,SV154: $i,SV58: $i,SV146: $i] :
( ( ( ~ ( between @ SV146 @ SV58 @ SV154 )
| ( SV12 = SV58 )
| ( between @ SV12 @ SV154 @ ( euclid2 @ SV12 @ SV146 @ SV58 @ SV154 @ SV100 ) ) )
= $true )
| ( ( between @ SV12 @ SV58 @ SV100 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[391]) ).
thf(418,plain,
! [SV101: $i,SV13: $i,SV155: $i,SV59: $i,SV147: $i] :
( ( ( ~ ( between @ SV147 @ SV59 @ SV155 )
| ( SV13 = SV59 )
| ( between @ ( euclid1 @ SV13 @ SV147 @ SV59 @ SV155 @ SV101 ) @ SV101 @ ( euclid2 @ SV13 @ SV147 @ SV59 @ SV155 @ SV101 ) ) )
= $true )
| ( ( between @ SV13 @ SV59 @ SV101 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[392]) ).
thf(419,plain,
! [SV102: $i,SV60: $i,SV156: $i,SV127: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV127 @ SV14 @ SV156 )
| ~ ( between @ SV14 @ SV60 @ SV127 )
| ! [SY450: $i] :
( ~ ( between @ SV60 @ SY450 @ SV127 )
| ( between @ SV102 @ ( continuous @ SV14 @ SV60 @ SV102 @ SY450 @ SV127 @ SV156 ) @ SV156 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV60 @ SV14 @ SV102 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[393]) ).
thf(420,plain,
! [SV103: $i,SV61: $i,SV157: $i,SV128: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV128 @ SV15 @ SV157 )
| ~ ( between @ SV15 @ SV61 @ SV128 )
| ! [SY451: $i] :
( ~ ( between @ SV61 @ SY451 @ SV128 )
| ( equidistant @ SV15 @ SY451 @ SV15 @ ( continuous @ SV15 @ SV61 @ SV103 @ SY451 @ SV128 @ SV157 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV61 @ SV15 @ SV103 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[394]) ).
thf(421,plain,
! [SV71: $i,SV25: $i,SV158: $i,SV136: $i,SV111: $i] :
( ( ( ! [SY452: $i] :
( ~ ( equidistant @ SV111 @ SV136 @ SV158 @ SY452 )
| ( equidistant @ SV25 @ SV71 @ SV158 @ SY452 ) ) )
= $true )
| ( ( equidistant @ SV25 @ SV71 @ SV111 @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(422,plain,
! [SV148: $i,SV140: $i,SV113: $i,SV73: $i,SV27: $i] :
( ( ( SV27
= ( extension @ SV73 @ SV113 @ SV140 @ SV148 ) )
= $false )
| ( ( between @ SV73 @ SV113 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[403]) ).
thf(423,plain,
! [SV114: $i,SV34: $i,SV137: $i,SV159: $i,SV79: $i] :
( ( ( ! [SY453: $i] :
( ~ ( equidistant @ SV79 @ SV159 @ SV137 @ SY453 )
| ~ ( between @ SV34 @ SV79 @ SV159 )
| ~ ( between @ SV114 @ SV137 @ SY453 )
| ( equidistant @ SV34 @ SV159 @ SV114 @ SY453 ) ) )
= $true )
| ( ( equidistant @ SV34 @ SV79 @ SV114 @ SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[404]) ).
thf(424,plain,
! [SV115: $i,SV149: $i,SV80: $i,SV35: $i] :
( ( ( ~ ( between @ SV35 @ SV80 @ SV149 ) )
= $true )
| ( ( ~ ( equidistant @ SV80 @ SV115 @ SV80 @ SV149 )
| ( SV35 = SV80 )
| ( SV115 = SV149 ) )
= $true )
| ( ( between @ SV35 @ SV80 @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[405]) ).
thf(425,plain,
! [SV138: $i,SV117: $i,SV82: $i,SV37: $i,SV160: $i] :
( ( ( ! [SY454: $i] :
( ( ( extension @ SV160 @ SY454 @ SV37 @ SV82 )
= ( extension @ SV160 @ SY454 @ SV117 @ SV138 ) )
| ( SV160 = SY454 ) ) )
= $true )
| ( ( equidistant @ SV37 @ SV82 @ SV117 @ SV138 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[407]) ).
thf(426,plain,
! [SV87: $i,SV118: $i,SV42: $i] :
( ( ( SV42 = SV118 )
= $false )
| ( ( ! [SY420: $i] : ( between @ SY420 @ SV87 @ SV118 ) )
= $true )
| ( ( between @ SV42 @ SV87 @ SV118 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[408]) ).
thf(427,plain,
! [SV120: $i,SV45: $i,SV90: $i] :
( ( ( between @ SV90 @ SV45 @ SV120 )
= $false )
| ( ( SV45 = SV90 )
= $true )
| ( ( between @ SV45 @ SV90 @ SV120 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[409]) ).
thf(428,plain,
! [SV91: $i,SV121: $i,SV46: $i] :
( ( ( between @ SV46 @ SV121 @ SV91 )
= $false )
| ( ( SV91 = SV121 )
= $true )
| ( ( between @ SV46 @ SV91 @ SV121 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[410]) ).
thf(429,plain,
! [SV122: $i,SV92: $i,SV161: $i,SV150: $i,SV48: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV48 @ SV150 @ SV161 )
| ( equidistant @ SV92 @ SV122 @ SV150 @ SV161 ) )
= $true )
| ( ( equidistant @ SV2 @ SV48 @ SV92 @ SV122 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[411]) ).
thf(430,plain,
! [SV141: $i,SV139: $i,SV126: $i,SV95: $i,SV52: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
= $false )
| ( ( ~ ( equidistant @ SV52 @ SV139 @ SV126 @ SV141 )
| ! [SY441: $i,SY442: $i] :
( ~ ( equidistant @ SV6 @ SY441 @ SV95 @ SY442 )
| ~ ( equidistant @ SV52 @ SY441 @ SV126 @ SY442 )
| ~ ( between @ SV6 @ SV52 @ SV139 )
| ~ ( between @ SV95 @ SV126 @ SV141 )
| ( SV6 = SV52 )
| ( equidistant @ SV139 @ SY441 @ SV141 @ SY442 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[412]) ).
thf(431,plain,
! [SV8: $i,SV54: $i,SV96: $i,SV151: $i,SV142: $i] :
( ( ( ~ ( between @ SV142 @ SV151 @ SV96 ) )
= $true )
| ( ( between @ SV54 @ ( inner_pasch @ SV8 @ SV54 @ SV96 @ SV151 @ SV142 ) @ SV142 )
= $true )
| ( ( between @ SV8 @ SV54 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[413]) ).
thf(432,plain,
! [SV55: $i,SV9: $i,SV97: $i,SV152: $i,SV143: $i] :
( ( ( ~ ( between @ SV143 @ SV152 @ SV97 ) )
= $true )
| ( ( between @ SV152 @ ( inner_pasch @ SV9 @ SV55 @ SV97 @ SV152 @ SV143 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV55 @ SV97 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[414]) ).
thf(433,plain,
! [SV10: $i,SV98: $i,SV56: $i,SV144: $i] :
( ( ( equidistant @ SV144 @ SV56 @ SV144 @ SV98 )
= $false )
| ( ( ! [SY445: $i] :
( ~ ( equidistant @ SY445 @ SV56 @ SY445 @ SV98 )
| ( between @ SV10 @ SV144 @ SY445 )
| ( between @ SV144 @ SY445 @ SV10 )
| ( SV56 = SV98 )
| ( between @ SY445 @ SV10 @ SV144 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV56 @ SV10 @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[415]) ).
thf(434,plain,
! [SV99: $i,SV11: $i,SV153: $i,SV57: $i,SV145: $i] :
( ( ( ~ ( between @ SV145 @ SV57 @ SV153 ) )
= $true )
| ( ( ( SV11 = SV57 )
| ( between @ SV11 @ SV145 @ ( euclid1 @ SV11 @ SV145 @ SV57 @ SV153 @ SV99 ) ) )
= $true )
| ( ( between @ SV11 @ SV57 @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[416]) ).
thf(435,plain,
! [SV100: $i,SV12: $i,SV154: $i,SV58: $i,SV146: $i] :
( ( ( ~ ( between @ SV146 @ SV58 @ SV154 ) )
= $true )
| ( ( ( SV12 = SV58 )
| ( between @ SV12 @ SV154 @ ( euclid2 @ SV12 @ SV146 @ SV58 @ SV154 @ SV100 ) ) )
= $true )
| ( ( between @ SV12 @ SV58 @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[417]) ).
thf(436,plain,
! [SV101: $i,SV13: $i,SV155: $i,SV59: $i,SV147: $i] :
( ( ( ~ ( between @ SV147 @ SV59 @ SV155 ) )
= $true )
| ( ( ( SV13 = SV59 )
| ( between @ ( euclid1 @ SV13 @ SV147 @ SV59 @ SV155 @ SV101 ) @ SV101 @ ( euclid2 @ SV13 @ SV147 @ SV59 @ SV155 @ SV101 ) ) )
= $true )
| ( ( between @ SV13 @ SV59 @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[418]) ).
thf(437,plain,
! [SV102: $i,SV60: $i,SV156: $i,SV127: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV127 @ SV14 @ SV156 ) )
= $true )
| ( ( ~ ( between @ SV14 @ SV60 @ SV127 )
| ! [SY450: $i] :
( ~ ( between @ SV60 @ SY450 @ SV127 )
| ( between @ SV102 @ ( continuous @ SV14 @ SV60 @ SV102 @ SY450 @ SV127 @ SV156 ) @ SV156 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV60 @ SV14 @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[419]) ).
thf(438,plain,
! [SV103: $i,SV61: $i,SV157: $i,SV128: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV128 @ SV15 @ SV157 ) )
= $true )
| ( ( ~ ( between @ SV15 @ SV61 @ SV128 )
| ! [SY451: $i] :
( ~ ( between @ SV61 @ SY451 @ SV128 )
| ( equidistant @ SV15 @ SY451 @ SV15 @ ( continuous @ SV15 @ SV61 @ SV103 @ SY451 @ SV128 @ SV157 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV61 @ SV15 @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[420]) ).
thf(439,plain,
! [SV71: $i,SV25: $i,SV162: $i,SV158: $i,SV136: $i,SV111: $i] :
( ( ( ~ ( equidistant @ SV111 @ SV136 @ SV158 @ SV162 )
| ( equidistant @ SV25 @ SV71 @ SV158 @ SV162 ) )
= $true )
| ( ( equidistant @ SV25 @ SV71 @ SV111 @ SV136 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(440,plain,
! [SV114: $i,SV34: $i,SV163: $i,SV137: $i,SV159: $i,SV79: $i] :
( ( ( ~ ( equidistant @ SV79 @ SV159 @ SV137 @ SV163 )
| ~ ( between @ SV34 @ SV79 @ SV159 )
| ~ ( between @ SV114 @ SV137 @ SV163 )
| ( equidistant @ SV34 @ SV159 @ SV114 @ SV163 ) )
= $true )
| ( ( equidistant @ SV34 @ SV79 @ SV114 @ SV137 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(441,plain,
! [SV115: $i,SV149: $i,SV80: $i,SV35: $i] :
( ( ( between @ SV35 @ SV80 @ SV149 )
= $false )
| ( ( ~ ( equidistant @ SV80 @ SV115 @ SV80 @ SV149 )
| ( SV35 = SV80 )
| ( SV115 = SV149 ) )
= $true )
| ( ( between @ SV35 @ SV80 @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[424]) ).
thf(442,plain,
! [SV138: $i,SV117: $i,SV82: $i,SV37: $i,SV164: $i,SV160: $i] :
( ( ( ( ( extension @ SV160 @ SV164 @ SV37 @ SV82 )
= ( extension @ SV160 @ SV164 @ SV117 @ SV138 ) )
| ( SV160 = SV164 ) )
= $true )
| ( ( equidistant @ SV37 @ SV82 @ SV117 @ SV138 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(443,plain,
! [SV42: $i,SV118: $i,SV87: $i,SV165: $i] :
( ( ( between @ SV165 @ SV87 @ SV118 )
= $true )
| ( ( SV42 = SV118 )
= $false )
| ( ( between @ SV42 @ SV87 @ SV118 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(444,plain,
! [SV122: $i,SV92: $i,SV161: $i,SV150: $i,SV48: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV48 @ SV150 @ SV161 ) )
= $true )
| ( ( equidistant @ SV92 @ SV122 @ SV150 @ SV161 )
= $true )
| ( ( equidistant @ SV2 @ SV48 @ SV92 @ SV122 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[429]) ).
thf(445,plain,
! [SV95: $i,SV6: $i,SV141: $i,SV126: $i,SV139: $i,SV52: $i] :
( ( ( ~ ( equidistant @ SV52 @ SV139 @ SV126 @ SV141 ) )
= $true )
| ( ( ! [SY441: $i,SY442: $i] :
( ~ ( equidistant @ SV6 @ SY441 @ SV95 @ SY442 )
| ~ ( equidistant @ SV52 @ SY441 @ SV126 @ SY442 )
| ~ ( between @ SV6 @ SV52 @ SV139 )
| ~ ( between @ SV95 @ SV126 @ SV141 )
| ( SV6 = SV52 )
| ( equidistant @ SV139 @ SY441 @ SV141 @ SY442 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[430]) ).
thf(446,plain,
! [SV8: $i,SV54: $i,SV96: $i,SV151: $i,SV142: $i] :
( ( ( between @ SV142 @ SV151 @ SV96 )
= $false )
| ( ( between @ SV54 @ ( inner_pasch @ SV8 @ SV54 @ SV96 @ SV151 @ SV142 ) @ SV142 )
= $true )
| ( ( between @ SV8 @ SV54 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[431]) ).
thf(447,plain,
! [SV55: $i,SV9: $i,SV97: $i,SV152: $i,SV143: $i] :
( ( ( between @ SV143 @ SV152 @ SV97 )
= $false )
| ( ( between @ SV152 @ ( inner_pasch @ SV9 @ SV55 @ SV97 @ SV152 @ SV143 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV55 @ SV97 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[432]) ).
thf(448,plain,
! [SV144: $i,SV10: $i,SV98: $i,SV56: $i,SV166: $i] :
( ( ( ~ ( equidistant @ SV166 @ SV56 @ SV166 @ SV98 )
| ( between @ SV10 @ SV144 @ SV166 )
| ( between @ SV144 @ SV166 @ SV10 )
| ( SV56 = SV98 )
| ( between @ SV166 @ SV10 @ SV144 ) )
= $true )
| ( ( equidistant @ SV144 @ SV56 @ SV144 @ SV98 )
= $false )
| ( ( equidistant @ SV10 @ SV56 @ SV10 @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(449,plain,
! [SV99: $i,SV11: $i,SV153: $i,SV57: $i,SV145: $i] :
( ( ( between @ SV145 @ SV57 @ SV153 )
= $false )
| ( ( ( SV11 = SV57 )
| ( between @ SV11 @ SV145 @ ( euclid1 @ SV11 @ SV145 @ SV57 @ SV153 @ SV99 ) ) )
= $true )
| ( ( between @ SV11 @ SV57 @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[434]) ).
thf(450,plain,
! [SV100: $i,SV12: $i,SV154: $i,SV58: $i,SV146: $i] :
( ( ( between @ SV146 @ SV58 @ SV154 )
= $false )
| ( ( ( SV12 = SV58 )
| ( between @ SV12 @ SV154 @ ( euclid2 @ SV12 @ SV146 @ SV58 @ SV154 @ SV100 ) ) )
= $true )
| ( ( between @ SV12 @ SV58 @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[435]) ).
thf(451,plain,
! [SV101: $i,SV13: $i,SV155: $i,SV59: $i,SV147: $i] :
( ( ( between @ SV147 @ SV59 @ SV155 )
= $false )
| ( ( ( SV13 = SV59 )
| ( between @ ( euclid1 @ SV13 @ SV147 @ SV59 @ SV155 @ SV101 ) @ SV101 @ ( euclid2 @ SV13 @ SV147 @ SV59 @ SV155 @ SV101 ) ) )
= $true )
| ( ( between @ SV13 @ SV59 @ SV101 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[436]) ).
thf(452,plain,
! [SV102: $i,SV60: $i,SV156: $i,SV127: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV127 @ SV14 @ SV156 )
= $false )
| ( ( ~ ( between @ SV14 @ SV60 @ SV127 )
| ! [SY450: $i] :
( ~ ( between @ SV60 @ SY450 @ SV127 )
| ( between @ SV102 @ ( continuous @ SV14 @ SV60 @ SV102 @ SY450 @ SV127 @ SV156 ) @ SV156 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV60 @ SV14 @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[437]) ).
thf(453,plain,
! [SV103: $i,SV61: $i,SV157: $i,SV128: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV128 @ SV15 @ SV157 )
= $false )
| ( ( ~ ( between @ SV15 @ SV61 @ SV128 )
| ! [SY451: $i] :
( ~ ( between @ SV61 @ SY451 @ SV128 )
| ( equidistant @ SV15 @ SY451 @ SV15 @ ( continuous @ SV15 @ SV61 @ SV103 @ SY451 @ SV128 @ SV157 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV61 @ SV15 @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[438]) ).
thf(454,plain,
! [SV71: $i,SV25: $i,SV162: $i,SV158: $i,SV136: $i,SV111: $i] :
( ( ( ~ ( equidistant @ SV111 @ SV136 @ SV158 @ SV162 ) )
= $true )
| ( ( equidistant @ SV25 @ SV71 @ SV158 @ SV162 )
= $true )
| ( ( equidistant @ SV25 @ SV71 @ SV111 @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[439]) ).
thf(455,plain,
! [SV114: $i,SV34: $i,SV163: $i,SV137: $i,SV159: $i,SV79: $i] :
( ( ( ~ ( equidistant @ SV79 @ SV159 @ SV137 @ SV163 ) )
= $true )
| ( ( ~ ( between @ SV34 @ SV79 @ SV159 )
| ~ ( between @ SV114 @ SV137 @ SV163 )
| ( equidistant @ SV34 @ SV159 @ SV114 @ SV163 ) )
= $true )
| ( ( equidistant @ SV34 @ SV79 @ SV114 @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[440]) ).
thf(456,plain,
! [SV35: $i,SV149: $i,SV115: $i,SV80: $i] :
( ( ( ~ ( equidistant @ SV80 @ SV115 @ SV80 @ SV149 ) )
= $true )
| ( ( ( SV35 = SV80 )
| ( SV115 = SV149 ) )
= $true )
| ( ( between @ SV35 @ SV80 @ SV149 )
= $false )
| ( ( between @ SV35 @ SV80 @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[441]) ).
thf(457,plain,
! [SV138: $i,SV117: $i,SV82: $i,SV37: $i,SV164: $i,SV160: $i] :
( ( ( ( extension @ SV160 @ SV164 @ SV37 @ SV82 )
= ( extension @ SV160 @ SV164 @ SV117 @ SV138 ) )
= $true )
| ( ( SV160 = SV164 )
= $true )
| ( ( equidistant @ SV37 @ SV82 @ SV117 @ SV138 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[442]) ).
thf(458,plain,
! [SV122: $i,SV92: $i,SV161: $i,SV150: $i,SV48: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV48 @ SV150 @ SV161 )
= $false )
| ( ( equidistant @ SV92 @ SV122 @ SV150 @ SV161 )
= $true )
| ( ( equidistant @ SV2 @ SV48 @ SV92 @ SV122 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[444]) ).
thf(459,plain,
! [SV95: $i,SV6: $i,SV141: $i,SV126: $i,SV139: $i,SV52: $i] :
( ( ( equidistant @ SV52 @ SV139 @ SV126 @ SV141 )
= $false )
| ( ( ! [SY441: $i,SY442: $i] :
( ~ ( equidistant @ SV6 @ SY441 @ SV95 @ SY442 )
| ~ ( equidistant @ SV52 @ SY441 @ SV126 @ SY442 )
| ~ ( between @ SV6 @ SV52 @ SV139 )
| ~ ( between @ SV95 @ SV126 @ SV141 )
| ( SV6 = SV52 )
| ( equidistant @ SV139 @ SY441 @ SV141 @ SY442 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[445]) ).
thf(460,plain,
! [SV144: $i,SV10: $i,SV98: $i,SV56: $i,SV166: $i] :
( ( ( ~ ( equidistant @ SV166 @ SV56 @ SV166 @ SV98 ) )
= $true )
| ( ( ( between @ SV10 @ SV144 @ SV166 )
| ( between @ SV144 @ SV166 @ SV10 )
| ( SV56 = SV98 )
| ( between @ SV166 @ SV10 @ SV144 ) )
= $true )
| ( ( equidistant @ SV144 @ SV56 @ SV144 @ SV98 )
= $false )
| ( ( equidistant @ SV10 @ SV56 @ SV10 @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(461,plain,
! [SV99: $i,SV153: $i,SV145: $i,SV57: $i,SV11: $i] :
( ( ( SV11 = SV57 )
= $true )
| ( ( between @ SV11 @ SV145 @ ( euclid1 @ SV11 @ SV145 @ SV57 @ SV153 @ SV99 ) )
= $true )
| ( ( between @ SV145 @ SV57 @ SV153 )
= $false )
| ( ( between @ SV11 @ SV57 @ SV99 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[449]) ).
thf(462,plain,
! [SV100: $i,SV146: $i,SV154: $i,SV58: $i,SV12: $i] :
( ( ( SV12 = SV58 )
= $true )
| ( ( between @ SV12 @ SV154 @ ( euclid2 @ SV12 @ SV146 @ SV58 @ SV154 @ SV100 ) )
= $true )
| ( ( between @ SV146 @ SV58 @ SV154 )
= $false )
| ( ( between @ SV12 @ SV58 @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[450]) ).
thf(463,plain,
! [SV101: $i,SV155: $i,SV147: $i,SV59: $i,SV13: $i] :
( ( ( SV13 = SV59 )
= $true )
| ( ( between @ ( euclid1 @ SV13 @ SV147 @ SV59 @ SV155 @ SV101 ) @ SV101 @ ( euclid2 @ SV13 @ SV147 @ SV59 @ SV155 @ SV101 ) )
= $true )
| ( ( between @ SV147 @ SV59 @ SV155 )
= $false )
| ( ( between @ SV13 @ SV59 @ SV101 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[451]) ).
thf(464,plain,
! [SV156: $i,SV102: $i,SV127: $i,SV60: $i,SV14: $i] :
( ( ( ~ ( between @ SV14 @ SV60 @ SV127 ) )
= $true )
| ( ( ! [SY450: $i] :
( ~ ( between @ SV60 @ SY450 @ SV127 )
| ( between @ SV102 @ ( continuous @ SV14 @ SV60 @ SV102 @ SY450 @ SV127 @ SV156 ) @ SV156 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV127 @ SV14 @ SV156 )
= $false )
| ( ( equidistant @ SV14 @ SV60 @ SV14 @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[452]) ).
thf(465,plain,
! [SV157: $i,SV103: $i,SV128: $i,SV61: $i,SV15: $i] :
( ( ( ~ ( between @ SV15 @ SV61 @ SV128 ) )
= $true )
| ( ( ! [SY451: $i] :
( ~ ( between @ SV61 @ SY451 @ SV128 )
| ( equidistant @ SV15 @ SY451 @ SV15 @ ( continuous @ SV15 @ SV61 @ SV103 @ SY451 @ SV128 @ SV157 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV128 @ SV15 @ SV157 )
= $false )
| ( ( equidistant @ SV15 @ SV61 @ SV15 @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[453]) ).
thf(466,plain,
! [SV71: $i,SV25: $i,SV162: $i,SV158: $i,SV136: $i,SV111: $i] :
( ( ( equidistant @ SV111 @ SV136 @ SV158 @ SV162 )
= $false )
| ( ( equidistant @ SV25 @ SV71 @ SV158 @ SV162 )
= $true )
| ( ( equidistant @ SV25 @ SV71 @ SV111 @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[454]) ).
thf(467,plain,
! [SV114: $i,SV34: $i,SV163: $i,SV137: $i,SV159: $i,SV79: $i] :
( ( ( equidistant @ SV79 @ SV159 @ SV137 @ SV163 )
= $false )
| ( ( ~ ( between @ SV34 @ SV79 @ SV159 )
| ~ ( between @ SV114 @ SV137 @ SV163 )
| ( equidistant @ SV34 @ SV159 @ SV114 @ SV163 ) )
= $true )
| ( ( equidistant @ SV34 @ SV79 @ SV114 @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[455]) ).
thf(468,plain,
! [SV35: $i,SV149: $i,SV115: $i,SV80: $i] :
( ( ( equidistant @ SV80 @ SV115 @ SV80 @ SV149 )
= $false )
| ( ( ( SV35 = SV80 )
| ( SV115 = SV149 ) )
= $true )
| ( ( between @ SV35 @ SV80 @ SV149 )
= $false )
| ( ( between @ SV35 @ SV80 @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[456]) ).
thf(469,plain,
! [SV141: $i,SV139: $i,SV126: $i,SV52: $i,SV95: $i,SV167: $i,SV6: $i] :
( ( ( ! [SY455: $i] :
( ~ ( equidistant @ SV6 @ SV167 @ SV95 @ SY455 )
| ~ ( equidistant @ SV52 @ SV167 @ SV126 @ SY455 )
| ~ ( between @ SV6 @ SV52 @ SV139 )
| ~ ( between @ SV95 @ SV126 @ SV141 )
| ( SV6 = SV52 )
| ( equidistant @ SV139 @ SV167 @ SV141 @ SY455 ) ) )
= $true )
| ( ( equidistant @ SV52 @ SV139 @ SV126 @ SV141 )
= $false )
| ( ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(470,plain,
! [SV144: $i,SV10: $i,SV98: $i,SV56: $i,SV166: $i] :
( ( ( equidistant @ SV166 @ SV56 @ SV166 @ SV98 )
= $false )
| ( ( ( between @ SV10 @ SV144 @ SV166 )
| ( between @ SV144 @ SV166 @ SV10 )
| ( SV56 = SV98 )
| ( between @ SV166 @ SV10 @ SV144 ) )
= $true )
| ( ( equidistant @ SV144 @ SV56 @ SV144 @ SV98 )
= $false )
| ( ( equidistant @ SV10 @ SV56 @ SV10 @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[460]) ).
thf(471,plain,
! [SV156: $i,SV102: $i,SV127: $i,SV60: $i,SV14: $i] :
( ( ( between @ SV14 @ SV60 @ SV127 )
= $false )
| ( ( ! [SY450: $i] :
( ~ ( between @ SV60 @ SY450 @ SV127 )
| ( between @ SV102 @ ( continuous @ SV14 @ SV60 @ SV102 @ SY450 @ SV127 @ SV156 ) @ SV156 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV127 @ SV14 @ SV156 )
= $false )
| ( ( equidistant @ SV14 @ SV60 @ SV14 @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[464]) ).
thf(472,plain,
! [SV157: $i,SV103: $i,SV128: $i,SV61: $i,SV15: $i] :
( ( ( between @ SV15 @ SV61 @ SV128 )
= $false )
| ( ( ! [SY451: $i] :
( ~ ( between @ SV61 @ SY451 @ SV128 )
| ( equidistant @ SV15 @ SY451 @ SV15 @ ( continuous @ SV15 @ SV61 @ SV103 @ SY451 @ SV128 @ SV157 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV128 @ SV15 @ SV157 )
= $false )
| ( ( equidistant @ SV15 @ SV61 @ SV15 @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[465]) ).
thf(473,plain,
! [SV163: $i,SV137: $i,SV114: $i,SV159: $i,SV79: $i,SV34: $i] :
( ( ( ~ ( between @ SV34 @ SV79 @ SV159 ) )
= $true )
| ( ( ~ ( between @ SV114 @ SV137 @ SV163 )
| ( equidistant @ SV34 @ SV159 @ SV114 @ SV163 ) )
= $true )
| ( ( equidistant @ SV79 @ SV159 @ SV137 @ SV163 )
= $false )
| ( ( equidistant @ SV34 @ SV79 @ SV114 @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[467]) ).
thf(474,plain,
! [SV149: $i,SV115: $i,SV80: $i,SV35: $i] :
( ( ( SV35 = SV80 )
= $true )
| ( ( SV115 = SV149 )
= $true )
| ( ( equidistant @ SV80 @ SV115 @ SV80 @ SV149 )
= $false )
| ( ( between @ SV35 @ SV80 @ SV149 )
= $false )
| ( ( between @ SV35 @ SV80 @ SV115 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[468]) ).
thf(475,plain,
! [SV141: $i,SV139: $i,SV126: $i,SV52: $i,SV168: $i,SV95: $i,SV167: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV167 @ SV95 @ SV168 )
| ~ ( equidistant @ SV52 @ SV167 @ SV126 @ SV168 )
| ~ ( between @ SV6 @ SV52 @ SV139 )
| ~ ( between @ SV95 @ SV126 @ SV141 )
| ( SV6 = SV52 )
| ( equidistant @ SV139 @ SV167 @ SV141 @ SV168 ) )
= $true )
| ( ( equidistant @ SV52 @ SV139 @ SV126 @ SV141 )
= $false )
| ( ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(476,plain,
! [SV98: $i,SV56: $i,SV166: $i,SV144: $i,SV10: $i] :
( ( ( between @ SV10 @ SV144 @ SV166 )
= $true )
| ( ( ( between @ SV144 @ SV166 @ SV10 )
| ( SV56 = SV98 )
| ( between @ SV166 @ SV10 @ SV144 ) )
= $true )
| ( ( equidistant @ SV166 @ SV56 @ SV166 @ SV98 )
= $false )
| ( ( equidistant @ SV144 @ SV56 @ SV144 @ SV98 )
= $false )
| ( ( equidistant @ SV10 @ SV56 @ SV10 @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[470]) ).
thf(477,plain,
! [SV156: $i,SV14: $i,SV102: $i,SV127: $i,SV169: $i,SV60: $i] :
( ( ( ~ ( between @ SV60 @ SV169 @ SV127 )
| ( between @ SV102 @ ( continuous @ SV14 @ SV60 @ SV102 @ SV169 @ SV127 @ SV156 ) @ SV156 ) )
= $true )
| ( ( between @ SV14 @ SV60 @ SV127 )
= $false )
| ( ( equidistant @ SV14 @ SV127 @ SV14 @ SV156 )
= $false )
| ( ( equidistant @ SV14 @ SV60 @ SV14 @ SV102 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(478,plain,
! [SV157: $i,SV103: $i,SV15: $i,SV128: $i,SV170: $i,SV61: $i] :
( ( ( ~ ( between @ SV61 @ SV170 @ SV128 )
| ( equidistant @ SV15 @ SV170 @ SV15 @ ( continuous @ SV15 @ SV61 @ SV103 @ SV170 @ SV128 @ SV157 ) ) )
= $true )
| ( ( between @ SV15 @ SV61 @ SV128 )
= $false )
| ( ( equidistant @ SV15 @ SV128 @ SV15 @ SV157 )
= $false )
| ( ( equidistant @ SV15 @ SV61 @ SV15 @ SV103 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(479,plain,
! [SV163: $i,SV137: $i,SV114: $i,SV159: $i,SV79: $i,SV34: $i] :
( ( ( between @ SV34 @ SV79 @ SV159 )
= $false )
| ( ( ~ ( between @ SV114 @ SV137 @ SV163 )
| ( equidistant @ SV34 @ SV159 @ SV114 @ SV163 ) )
= $true )
| ( ( equidistant @ SV79 @ SV159 @ SV137 @ SV163 )
= $false )
| ( ( equidistant @ SV34 @ SV79 @ SV114 @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(480,plain,
! [SV141: $i,SV139: $i,SV126: $i,SV52: $i,SV168: $i,SV95: $i,SV167: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV167 @ SV95 @ SV168 ) )
= $true )
| ( ( ~ ( equidistant @ SV52 @ SV167 @ SV126 @ SV168 )
| ~ ( between @ SV6 @ SV52 @ SV139 )
| ~ ( between @ SV95 @ SV126 @ SV141 )
| ( SV6 = SV52 )
| ( equidistant @ SV139 @ SV167 @ SV141 @ SV168 ) )
= $true )
| ( ( equidistant @ SV52 @ SV139 @ SV126 @ SV141 )
= $false )
| ( ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[475]) ).
thf(481,plain,
! [SV98: $i,SV56: $i,SV10: $i,SV166: $i,SV144: $i] :
( ( ( between @ SV144 @ SV166 @ SV10 )
= $true )
| ( ( ( SV56 = SV98 )
| ( between @ SV166 @ SV10 @ SV144 ) )
= $true )
| ( ( between @ SV10 @ SV144 @ SV166 )
= $true )
| ( ( equidistant @ SV166 @ SV56 @ SV166 @ SV98 )
= $false )
| ( ( equidistant @ SV144 @ SV56 @ SV144 @ SV98 )
= $false )
| ( ( equidistant @ SV10 @ SV56 @ SV10 @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[476]) ).
thf(482,plain,
! [SV156: $i,SV14: $i,SV102: $i,SV127: $i,SV169: $i,SV60: $i] :
( ( ( ~ ( between @ SV60 @ SV169 @ SV127 ) )
= $true )
| ( ( between @ SV102 @ ( continuous @ SV14 @ SV60 @ SV102 @ SV169 @ SV127 @ SV156 ) @ SV156 )
= $true )
| ( ( between @ SV14 @ SV60 @ SV127 )
= $false )
| ( ( equidistant @ SV14 @ SV127 @ SV14 @ SV156 )
= $false )
| ( ( equidistant @ SV14 @ SV60 @ SV14 @ SV102 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[477]) ).
thf(483,plain,
! [SV157: $i,SV103: $i,SV15: $i,SV128: $i,SV170: $i,SV61: $i] :
( ( ( ~ ( between @ SV61 @ SV170 @ SV128 ) )
= $true )
| ( ( equidistant @ SV15 @ SV170 @ SV15 @ ( continuous @ SV15 @ SV61 @ SV103 @ SV170 @ SV128 @ SV157 ) )
= $true )
| ( ( between @ SV15 @ SV61 @ SV128 )
= $false )
| ( ( equidistant @ SV15 @ SV128 @ SV15 @ SV157 )
= $false )
| ( ( equidistant @ SV15 @ SV61 @ SV15 @ SV103 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[478]) ).
thf(484,plain,
! [SV79: $i,SV159: $i,SV34: $i,SV163: $i,SV137: $i,SV114: $i] :
( ( ( ~ ( between @ SV114 @ SV137 @ SV163 ) )
= $true )
| ( ( equidistant @ SV34 @ SV159 @ SV114 @ SV163 )
= $true )
| ( ( between @ SV34 @ SV79 @ SV159 )
= $false )
| ( ( equidistant @ SV79 @ SV159 @ SV137 @ SV163 )
= $false )
| ( ( equidistant @ SV34 @ SV79 @ SV114 @ SV137 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[479]) ).
thf(485,plain,
! [SV141: $i,SV139: $i,SV126: $i,SV52: $i,SV168: $i,SV95: $i,SV167: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV167 @ SV95 @ SV168 )
= $false )
| ( ( ~ ( equidistant @ SV52 @ SV167 @ SV126 @ SV168 )
| ~ ( between @ SV6 @ SV52 @ SV139 )
| ~ ( between @ SV95 @ SV126 @ SV141 )
| ( SV6 = SV52 )
| ( equidistant @ SV139 @ SV167 @ SV141 @ SV168 ) )
= $true )
| ( ( equidistant @ SV52 @ SV139 @ SV126 @ SV141 )
= $false )
| ( ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[480]) ).
thf(486,plain,
! [SV144: $i,SV10: $i,SV166: $i,SV98: $i,SV56: $i] :
( ( ( SV56 = SV98 )
= $true )
| ( ( between @ SV166 @ SV10 @ SV144 )
= $true )
| ( ( between @ SV144 @ SV166 @ SV10 )
= $true )
| ( ( between @ SV10 @ SV144 @ SV166 )
= $true )
| ( ( equidistant @ SV166 @ SV56 @ SV166 @ SV98 )
= $false )
| ( ( equidistant @ SV144 @ SV56 @ SV144 @ SV98 )
= $false )
| ( ( equidistant @ SV10 @ SV56 @ SV10 @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[481]) ).
thf(487,plain,
! [SV156: $i,SV14: $i,SV102: $i,SV127: $i,SV169: $i,SV60: $i] :
( ( ( between @ SV60 @ SV169 @ SV127 )
= $false )
| ( ( between @ SV102 @ ( continuous @ SV14 @ SV60 @ SV102 @ SV169 @ SV127 @ SV156 ) @ SV156 )
= $true )
| ( ( between @ SV14 @ SV60 @ SV127 )
= $false )
| ( ( equidistant @ SV14 @ SV127 @ SV14 @ SV156 )
= $false )
| ( ( equidistant @ SV14 @ SV60 @ SV14 @ SV102 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[482]) ).
thf(488,plain,
! [SV157: $i,SV103: $i,SV15: $i,SV128: $i,SV170: $i,SV61: $i] :
( ( ( between @ SV61 @ SV170 @ SV128 )
= $false )
| ( ( equidistant @ SV15 @ SV170 @ SV15 @ ( continuous @ SV15 @ SV61 @ SV103 @ SV170 @ SV128 @ SV157 ) )
= $true )
| ( ( between @ SV15 @ SV61 @ SV128 )
= $false )
| ( ( equidistant @ SV15 @ SV128 @ SV15 @ SV157 )
= $false )
| ( ( equidistant @ SV15 @ SV61 @ SV15 @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[483]) ).
thf(489,plain,
! [SV79: $i,SV159: $i,SV34: $i,SV163: $i,SV137: $i,SV114: $i] :
( ( ( between @ SV114 @ SV137 @ SV163 )
= $false )
| ( ( equidistant @ SV34 @ SV159 @ SV114 @ SV163 )
= $true )
| ( ( between @ SV34 @ SV79 @ SV159 )
= $false )
| ( ( equidistant @ SV79 @ SV159 @ SV137 @ SV163 )
= $false )
| ( ( equidistant @ SV34 @ SV79 @ SV114 @ SV137 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(490,plain,
! [SV141: $i,SV95: $i,SV139: $i,SV6: $i,SV168: $i,SV126: $i,SV167: $i,SV52: $i] :
( ( ( ~ ( equidistant @ SV52 @ SV167 @ SV126 @ SV168 ) )
= $true )
| ( ( ~ ( between @ SV6 @ SV52 @ SV139 )
| ~ ( between @ SV95 @ SV126 @ SV141 )
| ( SV6 = SV52 )
| ( equidistant @ SV139 @ SV167 @ SV141 @ SV168 ) )
= $true )
| ( ( equidistant @ SV6 @ SV167 @ SV95 @ SV168 )
= $false )
| ( ( equidistant @ SV52 @ SV139 @ SV126 @ SV141 )
= $false )
| ( ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[485]) ).
thf(491,plain,
! [SV141: $i,SV95: $i,SV139: $i,SV6: $i,SV168: $i,SV126: $i,SV167: $i,SV52: $i] :
( ( ( equidistant @ SV52 @ SV167 @ SV126 @ SV168 )
= $false )
| ( ( ~ ( between @ SV6 @ SV52 @ SV139 )
| ~ ( between @ SV95 @ SV126 @ SV141 )
| ( SV6 = SV52 )
| ( equidistant @ SV139 @ SV167 @ SV141 @ SV168 ) )
= $true )
| ( ( equidistant @ SV6 @ SV167 @ SV95 @ SV168 )
= $false )
| ( ( equidistant @ SV52 @ SV139 @ SV126 @ SV141 )
= $false )
| ( ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[490]) ).
thf(492,plain,
! [SV168: $i,SV167: $i,SV141: $i,SV126: $i,SV95: $i,SV139: $i,SV52: $i,SV6: $i] :
( ( ( ~ ( between @ SV6 @ SV52 @ SV139 ) )
= $true )
| ( ( ~ ( between @ SV95 @ SV126 @ SV141 )
| ( SV6 = SV52 )
| ( equidistant @ SV139 @ SV167 @ SV141 @ SV168 ) )
= $true )
| ( ( equidistant @ SV52 @ SV167 @ SV126 @ SV168 )
= $false )
| ( ( equidistant @ SV6 @ SV167 @ SV95 @ SV168 )
= $false )
| ( ( equidistant @ SV52 @ SV139 @ SV126 @ SV141 )
= $false )
| ( ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[491]) ).
thf(493,plain,
! [SV168: $i,SV167: $i,SV141: $i,SV126: $i,SV95: $i,SV139: $i,SV52: $i,SV6: $i] :
( ( ( between @ SV6 @ SV52 @ SV139 )
= $false )
| ( ( ~ ( between @ SV95 @ SV126 @ SV141 )
| ( SV6 = SV52 )
| ( equidistant @ SV139 @ SV167 @ SV141 @ SV168 ) )
= $true )
| ( ( equidistant @ SV52 @ SV167 @ SV126 @ SV168 )
= $false )
| ( ( equidistant @ SV6 @ SV167 @ SV95 @ SV168 )
= $false )
| ( ( equidistant @ SV52 @ SV139 @ SV126 @ SV141 )
= $false )
| ( ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[492]) ).
thf(494,plain,
! [SV168: $i,SV167: $i,SV139: $i,SV52: $i,SV6: $i,SV141: $i,SV126: $i,SV95: $i] :
( ( ( ~ ( between @ SV95 @ SV126 @ SV141 ) )
= $true )
| ( ( ( SV6 = SV52 )
| ( equidistant @ SV139 @ SV167 @ SV141 @ SV168 ) )
= $true )
| ( ( between @ SV6 @ SV52 @ SV139 )
= $false )
| ( ( equidistant @ SV52 @ SV167 @ SV126 @ SV168 )
= $false )
| ( ( equidistant @ SV6 @ SV167 @ SV95 @ SV168 )
= $false )
| ( ( equidistant @ SV52 @ SV139 @ SV126 @ SV141 )
= $false )
| ( ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[493]) ).
thf(495,plain,
! [SV168: $i,SV167: $i,SV139: $i,SV52: $i,SV6: $i,SV141: $i,SV126: $i,SV95: $i] :
( ( ( between @ SV95 @ SV126 @ SV141 )
= $false )
| ( ( ( SV6 = SV52 )
| ( equidistant @ SV139 @ SV167 @ SV141 @ SV168 ) )
= $true )
| ( ( between @ SV6 @ SV52 @ SV139 )
= $false )
| ( ( equidistant @ SV52 @ SV167 @ SV126 @ SV168 )
= $false )
| ( ( equidistant @ SV6 @ SV167 @ SV95 @ SV168 )
= $false )
| ( ( equidistant @ SV52 @ SV139 @ SV126 @ SV141 )
= $false )
| ( ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[494]) ).
thf(496,plain,
! [SV126: $i,SV95: $i,SV168: $i,SV141: $i,SV167: $i,SV139: $i,SV52: $i,SV6: $i] :
( ( ( SV6 = SV52 )
= $true )
| ( ( equidistant @ SV139 @ SV167 @ SV141 @ SV168 )
= $true )
| ( ( between @ SV95 @ SV126 @ SV141 )
= $false )
| ( ( between @ SV6 @ SV52 @ SV139 )
= $false )
| ( ( equidistant @ SV52 @ SV167 @ SV126 @ SV168 )
= $false )
| ( ( equidistant @ SV6 @ SV167 @ SV95 @ SV168 )
= $false )
| ( ( equidistant @ SV52 @ SV139 @ SV126 @ SV141 )
= $false )
| ( ( equidistant @ SV6 @ SV52 @ SV95 @ SV126 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[495]) ).
thf(497,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[139,496,489,488,487,486,474,466,463,462,461,458,457,447,446,443,428,427,422,406,401,400,399,398,397,396,395,382,358,348,347,329,327,326,319,311,286,283,282,281,275,272,271,260,259,244,243,227,205,204,203,193,192,191,190]) ).
thf(498,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[497]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : GEO006-3 : TPTP v8.1.0. Released v1.0.0.
% 0.00/0.10 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.10/0.29 % Computer : n032.cluster.edu
% 0.10/0.29 % Model : x86_64 x86_64
% 0.10/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.29 % Memory : 8042.1875MB
% 0.10/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.29 % CPULimit : 300
% 0.10/0.29 % WCLimit : 600
% 0.10/0.29 % DateTime : Sat Jun 18 14:37:02 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.14/0.38 .
% 0.14/0.39
% 0.14/0.39 No.of.Axioms: 54
% 0.14/0.39
% 0.14/0.39 Length.of.Defs: 0
% 0.14/0.39
% 0.14/0.39 Contains.Choice.Funs: false
% 0.14/0.45 .
% 0.14/0.46 (rf:0,axioms:54,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:56,loop_count:0,foatp_calls:0,translation:fof_full)................................
% 0.60/0.80
% 0.60/0.80 ********************************
% 0.60/0.80 * All subproblems solved! *
% 0.60/0.80 ********************************
% 0.60/0.80 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:54,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:497,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.71/0.91
% 0.71/0.91 %**** Beginning of derivation protocol ****
% 0.71/0.91 % SZS output start CNFRefutation
% See solution above
% 0.71/0.91
% 0.71/0.91 %**** End of derivation protocol ****
% 0.71/0.91 %**** no. of clauses in derivation: 498 ****
% 0.71/0.91 %**** clause counter: 497 ****
% 0.71/0.91
% 0.71/0.91 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:54,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:497,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------