%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO025-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:17:35 AM UTC 2026
% Result : Unsatisfiable 66.16s 11.29s
% Output : CNFRefutation 66.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 42
% Syntax : Number of formulae : 359 ( 243 unt; 0 typ; 0 def)
% Number of atoms : 2101 ( 660 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 5299 ( 490 ~; 728 |; 0 &;4081 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 11 con; 0-6 aty)
% Number of variables : 1467 ( 0 ^;1467 !; 0 ?;1467 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_between,type,
between: $i > $i > $i > $o ).
thf(tp_continuous,type,
continuous: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_equidistant,type,
equidistant: $i > $i > $i > $i > $o ).
thf(tp_euclid1,type,
euclid1: $i > $i > $i > $i > $i > $i ).
thf(tp_euclid2,type,
euclid2: $i > $i > $i > $i > $i > $i ).
thf(tp_extension,type,
extension: $i > $i > $i > $i > $i ).
thf(tp_inner_pasch,type,
inner_pasch: $i > $i > $i > $i > $i > $i ).
thf(tp_lower_dimension_point_1,type,
lower_dimension_point_1: $i ).
thf(tp_lower_dimension_point_2,type,
lower_dimension_point_2: $i ).
thf(tp_lower_dimension_point_3,type,
lower_dimension_point_3: $i ).
thf(tp_reflection,type,
reflection: $i > $i > $i ).
thf(tp_u,type,
u: $i ).
thf(tp_u1,type,
u1: $i ).
thf(tp_v,type,
v: $i ).
thf(tp_v1,type,
v1: $i ).
thf(tp_w,type,
w: $i ).
thf(tp_w1,type,
w1: $i ).
thf(1,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
thf(2,axiom,
! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
thf(3,axiom,
! [U: $i] :
( U
= ( reflection @ U @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).
thf(4,axiom,
! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_1) ).
thf(5,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
thf(6,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).
thf(7,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(8,axiom,
! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
thf(9,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(10,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(11,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(12,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(13,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(14,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(15,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(16,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(17,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
thf(18,axiom,
! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
thf(19,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(20,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(21,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(22,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(23,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(24,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(25,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(26,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(27,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(28,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(29,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(30,axiom,
! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(31,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(32,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(33,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(34,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(35,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(36,axiom,
! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(37,axiom,
between @ u1 @ v1 @ w1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v1_between_u1_and_w1) ).
thf(38,axiom,
between @ u @ v @ w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
thf(39,axiom,
equidistant @ v @ w @ v1 @ w1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_to_w_equals_v1_to_w1) ).
thf(40,axiom,
equidistant @ u @ v @ u1 @ v1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_u1_to_v1) ).
thf(41,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(42,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[41]) ).
thf(43,negated_conjecture,
~ ( equidistant @ u @ w @ u1 @ w1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equal_sums) ).
thf(44,plain,
$false = $false,
inference(unfold_def,[status(thm)],[42]) ).
thf(45,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(46,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(47,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(48,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(49,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(50,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(51,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)],[7]) ).
thf(52,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(53,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)],[9]) ).
thf(54,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)],[10]) ).
thf(55,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)],[11]) ).
thf(56,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)],[12]) ).
thf(57,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)],[13]) ).
thf(58,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)],[14]) ).
thf(59,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)],[15]) ).
thf(60,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)],[16]) ).
thf(61,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(62,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(63,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)],[19]) ).
thf(64,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)],[20]) ).
thf(65,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)],[21]) ).
thf(66,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)],[22]) ).
thf(67,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)],[23]) ).
thf(68,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)],[24]) ).
thf(69,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(70,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(71,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(72,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)],[28]) ).
thf(73,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)],[29]) ).
thf(74,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(75,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)],[31]) ).
thf(76,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(77,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[33]) ).
thf(78,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(79,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)],[35]) ).
thf(80,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[36]) ).
thf(81,plain,
( ( between @ u1 @ v1 @ w1 )
= $true ),
inference(unfold_def,[status(thm)],[37]) ).
thf(82,plain,
( ( between @ u @ v @ w )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(83,plain,
( ( equidistant @ v @ w @ v1 @ w1 )
= $true ),
inference(unfold_def,[status(thm)],[39]) ).
thf(84,plain,
( ( equidistant @ u @ v @ u1 @ v1 )
= $true ),
inference(unfold_def,[status(thm)],[40]) ).
thf(85,plain,
( ( ~ ( equidistant @ u @ w @ u1 @ w1 ) )
= $true ),
inference(unfold_def,[status(thm)],[43]) ).
thf(86,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[44]) ).
thf(87,plain,
( ( ~ ( equidistant @ u @ w @ u1 @ w1 ) )
= $true ),
inference(copy,[status(thm)],[85]) ).
thf(88,plain,
( ( equidistant @ u @ v @ u1 @ v1 )
= $true ),
inference(copy,[status(thm)],[84]) ).
thf(89,plain,
( ( equidistant @ v @ w @ v1 @ w1 )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(90,plain,
( ( between @ u @ v @ w )
= $true ),
inference(copy,[status(thm)],[82]) ).
thf(91,plain,
( ( between @ u1 @ v1 @ w1 )
= $true ),
inference(copy,[status(thm)],[81]) ).
thf(92,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(copy,[status(thm)],[80]) ).
thf(93,plain,
( ( ! [X: $i,Y: $i,Z: $i,V: $i,V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ) )
= $true ),
inference(copy,[status(thm)],[79]) ).
thf(94,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(95,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(96,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(97,plain,
( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i,V: $i,V1: $i] :
( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
| ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
| ~ ( equidistant @ X @ V @ X1 @ V1 )
| ~ ( equidistant @ Y @ V @ Y1 @ V1 )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equidistant @ Z @ V @ Z1 @ V1 ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(98,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
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(copy,[status(thm)],[73]) ).
thf(100,plain,
( ( ! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ Y @ X @ W )
| ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(101,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(102,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(103,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(104,plain,
( ( ! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ W @ X @ V )
| ~ ( equidistant @ Y @ W @ Y @ V )
| ~ ( equidistant @ Z @ W @ Z @ V )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y )
| ( W = V ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(105,plain,
( ( ! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(106,plain,
( ( ! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(107,plain,
( ( ! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(108,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(109,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(110,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(111,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(112,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(113,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(114,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(115,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(116,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(117,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(118,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(119,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ~ ( equidistant @ W @ X @ Y @ Z )
| ( equidistant @ U @ V @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(120,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(121,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)],[51]) ).
thf(122,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(123,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(124,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(125,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(126,plain,
( ( ! [V: $i,U: $i] :
( ( V
!= ( reflection @ U @ V ) )
| ( U = V ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(127,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ U @ V @ V ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(128,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[86]) ).
thf(129,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0
!= ( reflection @ SX1 @ SX0 ) )
| ( SX1 = SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[126]) ).
thf(130,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( SX1
= ( reflection @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[124]) ).
thf(131,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i,SX4: $i] :
( ( SX0
!= ( extension @ SX1 @ SX2 @ SX3 @ SX4 ) )
| ( between @ SX1 @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[121]) ).
thf(132,plain,
( ( equidistant @ u @ w @ u1 @ w1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[87]) ).
thf(133,plain,
! [SV1: $i] :
( ( ! [SY128: $i] : ( equidistant @ SV1 @ SY128 @ SY128 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(134,plain,
! [SV2: $i] :
( ( ! [SY129: $i,SY130: $i,SY131: $i,SY132: $i,SY133: $i] :
( ~ ( equidistant @ SV2 @ SY129 @ SY130 @ SY131 )
| ~ ( equidistant @ SV2 @ SY129 @ SY132 @ SY133 )
| ( equidistant @ SY130 @ SY131 @ SY132 @ SY133 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(135,plain,
! [SV3: $i] :
( ( ! [SY134: $i,SY135: $i] :
( ~ ( equidistant @ SV3 @ SY134 @ SY135 @ SY135 )
| ( SV3 = SY134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(136,plain,
! [SV4: $i] :
( ( ! [SY136: $i,SY137: $i,SY138: $i] : ( between @ SV4 @ SY136 @ ( extension @ SV4 @ SY136 @ SY137 @ SY138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(137,plain,
! [SV5: $i] :
( ( ! [SY139: $i,SY140: $i,SY141: $i] : ( equidistant @ SV5 @ ( extension @ SY139 @ SV5 @ SY140 @ SY141 ) @ SY140 @ SY141 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(138,plain,
! [SV6: $i] :
( ( ! [SY142: $i,SY143: $i,SY144: $i,SY145: $i,SY146: $i,SY147: $i,SY148: $i] :
( ~ ( equidistant @ SV6 @ SY142 @ SY143 @ SY144 )
| ~ ( equidistant @ SY142 @ SY145 @ SY144 @ SY146 )
| ~ ( equidistant @ SV6 @ SY147 @ SY143 @ SY148 )
| ~ ( equidistant @ SY142 @ SY147 @ SY144 @ SY148 )
| ~ ( between @ SV6 @ SY142 @ SY145 )
| ~ ( between @ SY143 @ SY144 @ SY146 )
| ( SV6 = SY142 )
| ( equidistant @ SY145 @ SY147 @ SY146 @ SY148 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(139,plain,
! [SV7: $i] :
( ( ! [SY149: $i] :
( ~ ( between @ SV7 @ SY149 @ SV7 )
| ( SV7 = SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(140,plain,
! [SV8: $i] :
( ( ! [SY150: $i,SY151: $i,SY152: $i,SY153: $i] :
( ~ ( between @ SV8 @ SY150 @ SY151 )
| ~ ( between @ SY152 @ SY153 @ SY151 )
| ( between @ SY150 @ ( inner_pasch @ SV8 @ SY150 @ SY151 @ SY153 @ SY152 ) @ SY152 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(141,plain,
! [SV9: $i] :
( ( ! [SY154: $i,SY155: $i,SY156: $i,SY157: $i] :
( ~ ( between @ SV9 @ SY154 @ SY155 )
| ~ ( between @ SY156 @ SY157 @ SY155 )
| ( between @ SY157 @ ( inner_pasch @ SV9 @ SY154 @ SY155 @ SY157 @ SY156 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(142,plain,
( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[101]) ).
thf(143,plain,
( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[102]) ).
thf(144,plain,
( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(145,plain,
! [SV10: $i] :
( ( ! [SY158: $i,SY159: $i,SY160: $i,SY161: $i] :
( ~ ( equidistant @ SV10 @ SY158 @ SV10 @ SY159 )
| ~ ( equidistant @ SY160 @ SY158 @ SY160 @ SY159 )
| ~ ( equidistant @ SY161 @ SY158 @ SY161 @ SY159 )
| ( between @ SV10 @ SY160 @ SY161 )
| ( between @ SY160 @ SY161 @ SV10 )
| ( between @ SY161 @ SV10 @ SY160 )
| ( SY158 = SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(146,plain,
! [SV11: $i] :
( ( ! [SY162: $i,SY163: $i,SY164: $i,SY165: $i] :
( ~ ( between @ SV11 @ SY162 @ SY163 )
| ~ ( between @ SY164 @ SY162 @ SY165 )
| ( SV11 = SY162 )
| ( between @ SV11 @ SY164 @ ( euclid1 @ SV11 @ SY164 @ SY162 @ SY165 @ SY163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(147,plain,
! [SV12: $i] :
( ( ! [SY166: $i,SY167: $i,SY168: $i,SY169: $i] :
( ~ ( between @ SV12 @ SY166 @ SY167 )
| ~ ( between @ SY168 @ SY166 @ SY169 )
| ( SV12 = SY166 )
| ( between @ SV12 @ SY169 @ ( euclid2 @ SV12 @ SY168 @ SY166 @ SY169 @ SY167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(148,plain,
! [SV13: $i] :
( ( ! [SY170: $i,SY171: $i,SY172: $i,SY173: $i] :
( ~ ( between @ SV13 @ SY170 @ SY171 )
| ~ ( between @ SY172 @ SY170 @ SY173 )
| ( SV13 = SY170 )
| ( between @ ( euclid1 @ SV13 @ SY172 @ SY170 @ SY173 @ SY171 ) @ SY171 @ ( euclid2 @ SV13 @ SY172 @ SY170 @ SY173 @ SY171 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(149,plain,
! [SV14: $i] :
( ( ! [SY174: $i,SY175: $i,SY176: $i,SY177: $i,SY178: $i] :
( ~ ( equidistant @ SV14 @ SY174 @ SV14 @ SY175 )
| ~ ( equidistant @ SV14 @ SY176 @ SV14 @ SY177 )
| ~ ( between @ SV14 @ SY174 @ SY176 )
| ~ ( between @ SY174 @ SY178 @ SY176 )
| ( between @ SY175 @ ( continuous @ SV14 @ SY174 @ SY175 @ SY178 @ SY176 @ SY177 ) @ SY177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(150,plain,
! [SV15: $i] :
( ( ! [SY179: $i,SY180: $i,SY181: $i,SY182: $i,SY183: $i] :
( ~ ( equidistant @ SV15 @ SY179 @ SV15 @ SY180 )
| ~ ( equidistant @ SV15 @ SY181 @ SV15 @ SY182 )
| ~ ( between @ SV15 @ SY179 @ SY181 )
| ~ ( between @ SY179 @ SY183 @ SY181 )
| ( equidistant @ SV15 @ SY183 @ SV15 @ ( continuous @ SV15 @ SY179 @ SY180 @ SY183 @ SY181 @ SY182 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(151,plain,
! [SV16: $i] :
( ( ! [SY184: $i] :
( ( reflection @ SV16 @ SY184 )
= ( extension @ SV16 @ SY184 @ SV16 @ SY184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(152,plain,
! [SV17: $i] :
( ( ! [SY185: $i] : ( equidistant @ SV17 @ SY185 @ SV17 @ SY185 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(153,plain,
! [SV18: $i] :
( ( ! [SY186: $i,SY187: $i,SY188: $i] :
( ~ ( equidistant @ SV18 @ SY186 @ SY187 @ SY188 )
| ( equidistant @ SY187 @ SY188 @ SV18 @ SY186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(154,plain,
! [SV19: $i] :
( ( ! [SY189: $i,SY190: $i,SY191: $i] :
( ~ ( equidistant @ SV19 @ SY189 @ SY190 @ SY191 )
| ( equidistant @ SY189 @ SV19 @ SY190 @ SY191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(155,plain,
! [SV20: $i] :
( ( ! [SY192: $i,SY193: $i,SY194: $i] :
( ~ ( equidistant @ SV20 @ SY192 @ SY193 @ SY194 )
| ( equidistant @ SV20 @ SY192 @ SY194 @ SY193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(156,plain,
! [SV21: $i] :
( ( ! [SY195: $i,SY196: $i,SY197: $i] :
( ~ ( equidistant @ SV21 @ SY195 @ SY196 @ SY197 )
| ( equidistant @ SY195 @ SV21 @ SY197 @ SY196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(157,plain,
! [SV22: $i] :
( ( ! [SY198: $i,SY199: $i,SY200: $i] :
( ~ ( equidistant @ SV22 @ SY198 @ SY199 @ SY200 )
| ( equidistant @ SY199 @ SY200 @ SY198 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(158,plain,
! [SV23: $i] :
( ( ! [SY201: $i,SY202: $i,SY203: $i] :
( ~ ( equidistant @ SV23 @ SY201 @ SY202 @ SY203 )
| ( equidistant @ SY203 @ SY202 @ SV23 @ SY201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(159,plain,
! [SV24: $i] :
( ( ! [SY204: $i,SY205: $i,SY206: $i] :
( ~ ( equidistant @ SV24 @ SY204 @ SY205 @ SY206 )
| ( equidistant @ SY206 @ SY205 @ SY204 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(160,plain,
! [SV25: $i] :
( ( ! [SY207: $i,SY208: $i,SY209: $i,SY210: $i,SY211: $i] :
( ~ ( equidistant @ SV25 @ SY207 @ SY208 @ SY209 )
| ~ ( equidistant @ SY208 @ SY209 @ SY210 @ SY211 )
| ( equidistant @ SV25 @ SY207 @ SY210 @ SY211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(161,plain,
! [SV26: $i] :
( ( ! [SY212: $i,SY213: $i] :
( SV26
= ( extension @ SY212 @ SV26 @ SY213 @ SY213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(162,plain,
! [SV27: $i] :
( ( ! [SY214: $i] : ( between @ SV27 @ SY214 @ ( reflection @ SV27 @ SY214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(163,plain,
! [SV28: $i] :
( ( ! [SY215: $i] : ( equidistant @ SV28 @ ( reflection @ SY215 @ SV28 ) @ SY215 @ SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(164,plain,
! [SV29: $i] :
( ( SV29
= ( reflection @ SV29 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(165,plain,
! [SV30: $i] :
( ( ! [SY216: $i] : ( equidistant @ SV30 @ SV30 @ SY216 @ SY216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(166,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(167,plain,
! [SV31: $i] :
( ( ! [SY217: $i] :
( ( SV31
!= ( reflection @ SY217 @ SV31 ) )
| ( SY217 = SV31 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(168,plain,
! [SV32: $i] :
( ( ! [SY218: $i] :
( ( SV32 != SY218 )
| ( SY218
= ( reflection @ SV32 @ SY218 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(169,plain,
! [SV33: $i] :
( ( ! [SY219: $i,SY220: $i,SY221: $i,SY222: $i] :
( ( SV33
!= ( extension @ SY219 @ SY220 @ SY221 @ SY222 ) )
| ( between @ SY219 @ SY220 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(170,plain,
! [SV34: $i,SV1: $i] :
( ( equidistant @ SV1 @ SV34 @ SV34 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(171,plain,
! [SV35: $i,SV2: $i] :
( ( ! [SY223: $i,SY224: $i,SY225: $i,SY226: $i] :
( ~ ( equidistant @ SV2 @ SV35 @ SY223 @ SY224 )
| ~ ( equidistant @ SV2 @ SV35 @ SY225 @ SY226 )
| ( equidistant @ SY223 @ SY224 @ SY225 @ SY226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(172,plain,
! [SV36: $i,SV3: $i] :
( ( ! [SY227: $i] :
( ~ ( equidistant @ SV3 @ SV36 @ SY227 @ SY227 )
| ( SV3 = SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(173,plain,
! [SV37: $i,SV4: $i] :
( ( ! [SY228: $i,SY229: $i] : ( between @ SV4 @ SV37 @ ( extension @ SV4 @ SV37 @ SY228 @ SY229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(174,plain,
! [SV38: $i,SV5: $i] :
( ( ! [SY230: $i,SY231: $i] : ( equidistant @ SV5 @ ( extension @ SV38 @ SV5 @ SY230 @ SY231 ) @ SY230 @ SY231 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(175,plain,
! [SV39: $i,SV6: $i] :
( ( ! [SY232: $i,SY233: $i,SY234: $i,SY235: $i,SY236: $i,SY237: $i] :
( ~ ( equidistant @ SV6 @ SV39 @ SY232 @ SY233 )
| ~ ( equidistant @ SV39 @ SY234 @ SY233 @ SY235 )
| ~ ( equidistant @ SV6 @ SY236 @ SY232 @ SY237 )
| ~ ( equidistant @ SV39 @ SY236 @ SY233 @ SY237 )
| ~ ( between @ SV6 @ SV39 @ SY234 )
| ~ ( between @ SY232 @ SY233 @ SY235 )
| ( SV6 = SV39 )
| ( equidistant @ SY234 @ SY236 @ SY235 @ SY237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(176,plain,
! [SV40: $i,SV7: $i] :
( ( ~ ( between @ SV7 @ SV40 @ SV7 )
| ( SV7 = SV40 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(177,plain,
! [SV41: $i,SV8: $i] :
( ( ! [SY238: $i,SY239: $i,SY240: $i] :
( ~ ( between @ SV8 @ SV41 @ SY238 )
| ~ ( between @ SY239 @ SY240 @ SY238 )
| ( between @ SV41 @ ( inner_pasch @ SV8 @ SV41 @ SY238 @ SY240 @ SY239 ) @ SY239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(178,plain,
! [SV42: $i,SV9: $i] :
( ( ! [SY241: $i,SY242: $i,SY243: $i] :
( ~ ( between @ SV9 @ SV42 @ SY241 )
| ~ ( between @ SY242 @ SY243 @ SY241 )
| ( between @ SY243 @ ( inner_pasch @ SV9 @ SV42 @ SY241 @ SY243 @ SY242 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(179,plain,
! [SV43: $i,SV10: $i] :
( ( ! [SY244: $i,SY245: $i,SY246: $i] :
( ~ ( equidistant @ SV10 @ SV43 @ SV10 @ SY244 )
| ~ ( equidistant @ SY245 @ SV43 @ SY245 @ SY244 )
| ~ ( equidistant @ SY246 @ SV43 @ SY246 @ SY244 )
| ( between @ SV10 @ SY245 @ SY246 )
| ( between @ SY245 @ SY246 @ SV10 )
| ( between @ SY246 @ SV10 @ SY245 )
| ( SV43 = SY244 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(180,plain,
! [SV44: $i,SV11: $i] :
( ( ! [SY247: $i,SY248: $i,SY249: $i] :
( ~ ( between @ SV11 @ SV44 @ SY247 )
| ~ ( between @ SY248 @ SV44 @ SY249 )
| ( SV11 = SV44 )
| ( between @ SV11 @ SY248 @ ( euclid1 @ SV11 @ SY248 @ SV44 @ SY249 @ SY247 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(181,plain,
! [SV45: $i,SV12: $i] :
( ( ! [SY250: $i,SY251: $i,SY252: $i] :
( ~ ( between @ SV12 @ SV45 @ SY250 )
| ~ ( between @ SY251 @ SV45 @ SY252 )
| ( SV12 = SV45 )
| ( between @ SV12 @ SY252 @ ( euclid2 @ SV12 @ SY251 @ SV45 @ SY252 @ SY250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(182,plain,
! [SV46: $i,SV13: $i] :
( ( ! [SY253: $i,SY254: $i,SY255: $i] :
( ~ ( between @ SV13 @ SV46 @ SY253 )
| ~ ( between @ SY254 @ SV46 @ SY255 )
| ( SV13 = SV46 )
| ( between @ ( euclid1 @ SV13 @ SY254 @ SV46 @ SY255 @ SY253 ) @ SY253 @ ( euclid2 @ SV13 @ SY254 @ SV46 @ SY255 @ SY253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(183,plain,
! [SV47: $i,SV14: $i] :
( ( ! [SY256: $i,SY257: $i,SY258: $i,SY259: $i] :
( ~ ( equidistant @ SV14 @ SV47 @ SV14 @ SY256 )
| ~ ( equidistant @ SV14 @ SY257 @ SV14 @ SY258 )
| ~ ( between @ SV14 @ SV47 @ SY257 )
| ~ ( between @ SV47 @ SY259 @ SY257 )
| ( between @ SY256 @ ( continuous @ SV14 @ SV47 @ SY256 @ SY259 @ SY257 @ SY258 ) @ SY258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(184,plain,
! [SV48: $i,SV15: $i] :
( ( ! [SY260: $i,SY261: $i,SY262: $i,SY263: $i] :
( ~ ( equidistant @ SV15 @ SV48 @ SV15 @ SY260 )
| ~ ( equidistant @ SV15 @ SY261 @ SV15 @ SY262 )
| ~ ( between @ SV15 @ SV48 @ SY261 )
| ~ ( between @ SV48 @ SY263 @ SY261 )
| ( equidistant @ SV15 @ SY263 @ SV15 @ ( continuous @ SV15 @ SV48 @ SY260 @ SY263 @ SY261 @ SY262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(185,plain,
! [SV49: $i,SV16: $i] :
( ( ( reflection @ SV16 @ SV49 )
= ( extension @ SV16 @ SV49 @ SV16 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(186,plain,
! [SV50: $i,SV17: $i] :
( ( equidistant @ SV17 @ SV50 @ SV17 @ SV50 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(187,plain,
! [SV51: $i,SV18: $i] :
( ( ! [SY264: $i,SY265: $i] :
( ~ ( equidistant @ SV18 @ SV51 @ SY264 @ SY265 )
| ( equidistant @ SY264 @ SY265 @ SV18 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(188,plain,
! [SV52: $i,SV19: $i] :
( ( ! [SY266: $i,SY267: $i] :
( ~ ( equidistant @ SV19 @ SV52 @ SY266 @ SY267 )
| ( equidistant @ SV52 @ SV19 @ SY266 @ SY267 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(189,plain,
! [SV53: $i,SV20: $i] :
( ( ! [SY268: $i,SY269: $i] :
( ~ ( equidistant @ SV20 @ SV53 @ SY268 @ SY269 )
| ( equidistant @ SV20 @ SV53 @ SY269 @ SY268 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(190,plain,
! [SV54: $i,SV21: $i] :
( ( ! [SY270: $i,SY271: $i] :
( ~ ( equidistant @ SV21 @ SV54 @ SY270 @ SY271 )
| ( equidistant @ SV54 @ SV21 @ SY271 @ SY270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(191,plain,
! [SV55: $i,SV22: $i] :
( ( ! [SY272: $i,SY273: $i] :
( ~ ( equidistant @ SV22 @ SV55 @ SY272 @ SY273 )
| ( equidistant @ SY272 @ SY273 @ SV55 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(192,plain,
! [SV56: $i,SV23: $i] :
( ( ! [SY274: $i,SY275: $i] :
( ~ ( equidistant @ SV23 @ SV56 @ SY274 @ SY275 )
| ( equidistant @ SY275 @ SY274 @ SV23 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(193,plain,
! [SV57: $i,SV24: $i] :
( ( ! [SY276: $i,SY277: $i] :
( ~ ( equidistant @ SV24 @ SV57 @ SY276 @ SY277 )
| ( equidistant @ SY277 @ SY276 @ SV57 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(194,plain,
! [SV58: $i,SV25: $i] :
( ( ! [SY278: $i,SY279: $i,SY280: $i,SY281: $i] :
( ~ ( equidistant @ SV25 @ SV58 @ SY278 @ SY279 )
| ~ ( equidistant @ SY278 @ SY279 @ SY280 @ SY281 )
| ( equidistant @ SV25 @ SV58 @ SY280 @ SY281 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(195,plain,
! [SV59: $i,SV26: $i] :
( ( ! [SY282: $i] :
( SV26
= ( extension @ SV59 @ SV26 @ SY282 @ SY282 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(196,plain,
! [SV60: $i,SV27: $i] :
( ( between @ SV27 @ SV60 @ ( reflection @ SV27 @ SV60 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(197,plain,
! [SV61: $i,SV28: $i] :
( ( equidistant @ SV28 @ ( reflection @ SV61 @ SV28 ) @ SV61 @ SV28 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(198,plain,
! [SV62: $i,SV30: $i] :
( ( equidistant @ SV30 @ SV30 @ SV62 @ SV62 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(199,plain,
! [SV63: $i,SV31: $i] :
( ( ( SV31
!= ( reflection @ SV63 @ SV31 ) )
| ( SV63 = SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(200,plain,
! [SV64: $i,SV32: $i] :
( ( ( SV32 != SV64 )
| ( SV64
= ( reflection @ SV32 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(201,plain,
! [SV65: $i,SV33: $i] :
( ( ! [SY283: $i,SY284: $i,SY285: $i] :
( ( SV33
!= ( extension @ SV65 @ SY283 @ SY284 @ SY285 ) )
| ( between @ SV65 @ SY283 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(202,plain,
! [SV66: $i,SV35: $i,SV2: $i] :
( ( ! [SY286: $i,SY287: $i,SY288: $i] :
( ~ ( equidistant @ SV2 @ SV35 @ SV66 @ SY286 )
| ~ ( equidistant @ SV2 @ SV35 @ SY287 @ SY288 )
| ( equidistant @ SV66 @ SY286 @ SY287 @ SY288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(203,plain,
! [SV67: $i,SV36: $i,SV3: $i] :
( ( ~ ( equidistant @ SV3 @ SV36 @ SV67 @ SV67 )
| ( SV3 = SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(204,plain,
! [SV68: $i,SV37: $i,SV4: $i] :
( ( ! [SY289: $i] : ( between @ SV4 @ SV37 @ ( extension @ SV4 @ SV37 @ SV68 @ SY289 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(205,plain,
! [SV69: $i,SV38: $i,SV5: $i] :
( ( ! [SY290: $i] : ( equidistant @ SV5 @ ( extension @ SV38 @ SV5 @ SV69 @ SY290 ) @ SV69 @ SY290 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(206,plain,
! [SV70: $i,SV39: $i,SV6: $i] :
( ( ! [SY291: $i,SY292: $i,SY293: $i,SY294: $i,SY295: $i] :
( ~ ( equidistant @ SV6 @ SV39 @ SV70 @ SY291 )
| ~ ( equidistant @ SV39 @ SY292 @ SY291 @ SY293 )
| ~ ( equidistant @ SV6 @ SY294 @ SV70 @ SY295 )
| ~ ( equidistant @ SV39 @ SY294 @ SY291 @ SY295 )
| ~ ( between @ SV6 @ SV39 @ SY292 )
| ~ ( between @ SV70 @ SY291 @ SY293 )
| ( SV6 = SV39 )
| ( equidistant @ SY292 @ SY294 @ SY293 @ SY295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(207,plain,
! [SV40: $i,SV7: $i] :
( ( ( ~ ( between @ SV7 @ SV40 @ SV7 ) )
= $true )
| ( ( SV7 = SV40 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(208,plain,
! [SV71: $i,SV41: $i,SV8: $i] :
( ( ! [SY296: $i,SY297: $i] :
( ~ ( between @ SV8 @ SV41 @ SV71 )
| ~ ( between @ SY296 @ SY297 @ SV71 )
| ( between @ SV41 @ ( inner_pasch @ SV8 @ SV41 @ SV71 @ SY297 @ SY296 ) @ SY296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(209,plain,
! [SV72: $i,SV42: $i,SV9: $i] :
( ( ! [SY298: $i,SY299: $i] :
( ~ ( between @ SV9 @ SV42 @ SV72 )
| ~ ( between @ SY298 @ SY299 @ SV72 )
| ( between @ SY299 @ ( inner_pasch @ SV9 @ SV42 @ SV72 @ SY299 @ SY298 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(210,plain,
! [SV73: $i,SV43: $i,SV10: $i] :
( ( ! [SY300: $i,SY301: $i] :
( ~ ( equidistant @ SV10 @ SV43 @ SV10 @ SV73 )
| ~ ( equidistant @ SY300 @ SV43 @ SY300 @ SV73 )
| ~ ( equidistant @ SY301 @ SV43 @ SY301 @ SV73 )
| ( between @ SV10 @ SY300 @ SY301 )
| ( between @ SY300 @ SY301 @ SV10 )
| ( between @ SY301 @ SV10 @ SY300 )
| ( SV43 = SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(211,plain,
! [SV74: $i,SV44: $i,SV11: $i] :
( ( ! [SY302: $i,SY303: $i] :
( ~ ( between @ SV11 @ SV44 @ SV74 )
| ~ ( between @ SY302 @ SV44 @ SY303 )
| ( SV11 = SV44 )
| ( between @ SV11 @ SY302 @ ( euclid1 @ SV11 @ SY302 @ SV44 @ SY303 @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(212,plain,
! [SV75: $i,SV45: $i,SV12: $i] :
( ( ! [SY304: $i,SY305: $i] :
( ~ ( between @ SV12 @ SV45 @ SV75 )
| ~ ( between @ SY304 @ SV45 @ SY305 )
| ( SV12 = SV45 )
| ( between @ SV12 @ SY305 @ ( euclid2 @ SV12 @ SY304 @ SV45 @ SY305 @ SV75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(213,plain,
! [SV76: $i,SV46: $i,SV13: $i] :
( ( ! [SY306: $i,SY307: $i] :
( ~ ( between @ SV13 @ SV46 @ SV76 )
| ~ ( between @ SY306 @ SV46 @ SY307 )
| ( SV13 = SV46 )
| ( between @ ( euclid1 @ SV13 @ SY306 @ SV46 @ SY307 @ SV76 ) @ SV76 @ ( euclid2 @ SV13 @ SY306 @ SV46 @ SY307 @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(214,plain,
! [SV77: $i,SV47: $i,SV14: $i] :
( ( ! [SY308: $i,SY309: $i,SY310: $i] :
( ~ ( equidistant @ SV14 @ SV47 @ SV14 @ SV77 )
| ~ ( equidistant @ SV14 @ SY308 @ SV14 @ SY309 )
| ~ ( between @ SV14 @ SV47 @ SY308 )
| ~ ( between @ SV47 @ SY310 @ SY308 )
| ( between @ SV77 @ ( continuous @ SV14 @ SV47 @ SV77 @ SY310 @ SY308 @ SY309 ) @ SY309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(215,plain,
! [SV78: $i,SV48: $i,SV15: $i] :
( ( ! [SY311: $i,SY312: $i,SY313: $i] :
( ~ ( equidistant @ SV15 @ SV48 @ SV15 @ SV78 )
| ~ ( equidistant @ SV15 @ SY311 @ SV15 @ SY312 )
| ~ ( between @ SV15 @ SV48 @ SY311 )
| ~ ( between @ SV48 @ SY313 @ SY311 )
| ( equidistant @ SV15 @ SY313 @ SV15 @ ( continuous @ SV15 @ SV48 @ SV78 @ SY313 @ SY311 @ SY312 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(216,plain,
! [SV79: $i,SV51: $i,SV18: $i] :
( ( ! [SY314: $i] :
( ~ ( equidistant @ SV18 @ SV51 @ SV79 @ SY314 )
| ( equidistant @ SV79 @ SY314 @ SV18 @ SV51 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(217,plain,
! [SV80: $i,SV52: $i,SV19: $i] :
( ( ! [SY315: $i] :
( ~ ( equidistant @ SV19 @ SV52 @ SV80 @ SY315 )
| ( equidistant @ SV52 @ SV19 @ SV80 @ SY315 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(218,plain,
! [SV81: $i,SV53: $i,SV20: $i] :
( ( ! [SY316: $i] :
( ~ ( equidistant @ SV20 @ SV53 @ SV81 @ SY316 )
| ( equidistant @ SV20 @ SV53 @ SY316 @ SV81 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(219,plain,
! [SV82: $i,SV54: $i,SV21: $i] :
( ( ! [SY317: $i] :
( ~ ( equidistant @ SV21 @ SV54 @ SV82 @ SY317 )
| ( equidistant @ SV54 @ SV21 @ SY317 @ SV82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(220,plain,
! [SV83: $i,SV55: $i,SV22: $i] :
( ( ! [SY318: $i] :
( ~ ( equidistant @ SV22 @ SV55 @ SV83 @ SY318 )
| ( equidistant @ SV83 @ SY318 @ SV55 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(221,plain,
! [SV84: $i,SV56: $i,SV23: $i] :
( ( ! [SY319: $i] :
( ~ ( equidistant @ SV23 @ SV56 @ SV84 @ SY319 )
| ( equidistant @ SY319 @ SV84 @ SV23 @ SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[192]) ).
thf(222,plain,
! [SV85: $i,SV57: $i,SV24: $i] :
( ( ! [SY320: $i] :
( ~ ( equidistant @ SV24 @ SV57 @ SV85 @ SY320 )
| ( equidistant @ SY320 @ SV85 @ SV57 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[193]) ).
thf(223,plain,
! [SV86: $i,SV58: $i,SV25: $i] :
( ( ! [SY321: $i,SY322: $i,SY323: $i] :
( ~ ( equidistant @ SV25 @ SV58 @ SV86 @ SY321 )
| ~ ( equidistant @ SV86 @ SY321 @ SY322 @ SY323 )
| ( equidistant @ SV25 @ SV58 @ SY322 @ SY323 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[194]) ).
thf(224,plain,
! [SV87: $i,SV59: $i,SV26: $i] :
( ( SV26
= ( extension @ SV59 @ SV26 @ SV87 @ SV87 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(225,plain,
! [SV63: $i,SV31: $i] :
( ( ( SV31
!= ( reflection @ SV63 @ SV31 ) )
= $true )
| ( ( SV63 = SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(226,plain,
! [SV64: $i,SV32: $i] :
( ( ( SV32 != SV64 )
= $true )
| ( ( SV64
= ( reflection @ SV32 @ SV64 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(227,plain,
! [SV88: $i,SV65: $i,SV33: $i] :
( ( ! [SY324: $i,SY325: $i] :
( ( SV33
!= ( extension @ SV65 @ SV88 @ SY324 @ SY325 ) )
| ( between @ SV65 @ SV88 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[201]) ).
thf(228,plain,
! [SV89: $i,SV66: $i,SV35: $i,SV2: $i] :
( ( ! [SY326: $i,SY327: $i] :
( ~ ( equidistant @ SV2 @ SV35 @ SV66 @ SV89 )
| ~ ( equidistant @ SV2 @ SV35 @ SY326 @ SY327 )
| ( equidistant @ SV66 @ SV89 @ SY326 @ SY327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[202]) ).
thf(229,plain,
! [SV67: $i,SV36: $i,SV3: $i] :
( ( ( ~ ( equidistant @ SV3 @ SV36 @ SV67 @ SV67 ) )
= $true )
| ( ( SV3 = SV36 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(230,plain,
! [SV90: $i,SV68: $i,SV37: $i,SV4: $i] :
( ( between @ SV4 @ SV37 @ ( extension @ SV4 @ SV37 @ SV68 @ SV90 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[204]) ).
thf(231,plain,
! [SV91: $i,SV69: $i,SV38: $i,SV5: $i] :
( ( equidistant @ SV5 @ ( extension @ SV38 @ SV5 @ SV69 @ SV91 ) @ SV69 @ SV91 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(232,plain,
! [SV92: $i,SV70: $i,SV39: $i,SV6: $i] :
( ( ! [SY328: $i,SY329: $i,SY330: $i,SY331: $i] :
( ~ ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
| ~ ( equidistant @ SV39 @ SY328 @ SV92 @ SY329 )
| ~ ( equidistant @ SV6 @ SY330 @ SV70 @ SY331 )
| ~ ( equidistant @ SV39 @ SY330 @ SV92 @ SY331 )
| ~ ( between @ SV6 @ SV39 @ SY328 )
| ~ ( between @ SV70 @ SV92 @ SY329 )
| ( SV6 = SV39 )
| ( equidistant @ SY328 @ SY330 @ SY329 @ SY331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(233,plain,
! [SV40: $i,SV7: $i] :
( ( ( between @ SV7 @ SV40 @ SV7 )
= $false )
| ( ( SV7 = SV40 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(234,plain,
! [SV93: $i,SV71: $i,SV41: $i,SV8: $i] :
( ( ! [SY332: $i] :
( ~ ( between @ SV8 @ SV41 @ SV71 )
| ~ ( between @ SV93 @ SY332 @ SV71 )
| ( between @ SV41 @ ( inner_pasch @ SV8 @ SV41 @ SV71 @ SY332 @ SV93 ) @ SV93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(235,plain,
! [SV94: $i,SV72: $i,SV42: $i,SV9: $i] :
( ( ! [SY333: $i] :
( ~ ( between @ SV9 @ SV42 @ SV72 )
| ~ ( between @ SV94 @ SY333 @ SV72 )
| ( between @ SY333 @ ( inner_pasch @ SV9 @ SV42 @ SV72 @ SY333 @ SV94 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(236,plain,
! [SV95: $i,SV73: $i,SV43: $i,SV10: $i] :
( ( ! [SY334: $i] :
( ~ ( equidistant @ SV10 @ SV43 @ SV10 @ SV73 )
| ~ ( equidistant @ SV95 @ SV43 @ SV95 @ SV73 )
| ~ ( equidistant @ SY334 @ SV43 @ SY334 @ SV73 )
| ( between @ SV10 @ SV95 @ SY334 )
| ( between @ SV95 @ SY334 @ SV10 )
| ( between @ SY334 @ SV10 @ SV95 )
| ( SV43 = SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(237,plain,
! [SV96: $i,SV74: $i,SV44: $i,SV11: $i] :
( ( ! [SY335: $i] :
( ~ ( between @ SV11 @ SV44 @ SV74 )
| ~ ( between @ SV96 @ SV44 @ SY335 )
| ( SV11 = SV44 )
| ( between @ SV11 @ SV96 @ ( euclid1 @ SV11 @ SV96 @ SV44 @ SY335 @ SV74 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(238,plain,
! [SV97: $i,SV75: $i,SV45: $i,SV12: $i] :
( ( ! [SY336: $i] :
( ~ ( between @ SV12 @ SV45 @ SV75 )
| ~ ( between @ SV97 @ SV45 @ SY336 )
| ( SV12 = SV45 )
| ( between @ SV12 @ SY336 @ ( euclid2 @ SV12 @ SV97 @ SV45 @ SY336 @ SV75 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(239,plain,
! [SV98: $i,SV76: $i,SV46: $i,SV13: $i] :
( ( ! [SY337: $i] :
( ~ ( between @ SV13 @ SV46 @ SV76 )
| ~ ( between @ SV98 @ SV46 @ SY337 )
| ( SV13 = SV46 )
| ( between @ ( euclid1 @ SV13 @ SV98 @ SV46 @ SY337 @ SV76 ) @ SV76 @ ( euclid2 @ SV13 @ SV98 @ SV46 @ SY337 @ SV76 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(240,plain,
! [SV99: $i,SV77: $i,SV47: $i,SV14: $i] :
( ( ! [SY338: $i,SY339: $i] :
( ~ ( equidistant @ SV14 @ SV47 @ SV14 @ SV77 )
| ~ ( equidistant @ SV14 @ SV99 @ SV14 @ SY338 )
| ~ ( between @ SV14 @ SV47 @ SV99 )
| ~ ( between @ SV47 @ SY339 @ SV99 )
| ( between @ SV77 @ ( continuous @ SV14 @ SV47 @ SV77 @ SY339 @ SV99 @ SY338 ) @ SY338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(241,plain,
! [SV100: $i,SV78: $i,SV48: $i,SV15: $i] :
( ( ! [SY340: $i,SY341: $i] :
( ~ ( equidistant @ SV15 @ SV48 @ SV15 @ SV78 )
| ~ ( equidistant @ SV15 @ SV100 @ SV15 @ SY340 )
| ~ ( between @ SV15 @ SV48 @ SV100 )
| ~ ( between @ SV48 @ SY341 @ SV100 )
| ( equidistant @ SV15 @ SY341 @ SV15 @ ( continuous @ SV15 @ SV48 @ SV78 @ SY341 @ SV100 @ SY340 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(242,plain,
! [SV101: $i,SV79: $i,SV51: $i,SV18: $i] :
( ( ~ ( equidistant @ SV18 @ SV51 @ SV79 @ SV101 )
| ( equidistant @ SV79 @ SV101 @ SV18 @ SV51 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(243,plain,
! [SV102: $i,SV80: $i,SV52: $i,SV19: $i] :
( ( ~ ( equidistant @ SV19 @ SV52 @ SV80 @ SV102 )
| ( equidistant @ SV52 @ SV19 @ SV80 @ SV102 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[217]) ).
thf(244,plain,
! [SV103: $i,SV81: $i,SV53: $i,SV20: $i] :
( ( ~ ( equidistant @ SV20 @ SV53 @ SV81 @ SV103 )
| ( equidistant @ SV20 @ SV53 @ SV103 @ SV81 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[218]) ).
thf(245,plain,
! [SV104: $i,SV82: $i,SV54: $i,SV21: $i] :
( ( ~ ( equidistant @ SV21 @ SV54 @ SV82 @ SV104 )
| ( equidistant @ SV54 @ SV21 @ SV104 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[219]) ).
thf(246,plain,
! [SV105: $i,SV83: $i,SV55: $i,SV22: $i] :
( ( ~ ( equidistant @ SV22 @ SV55 @ SV83 @ SV105 )
| ( equidistant @ SV83 @ SV105 @ SV55 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[220]) ).
thf(247,plain,
! [SV106: $i,SV84: $i,SV56: $i,SV23: $i] :
( ( ~ ( equidistant @ SV23 @ SV56 @ SV84 @ SV106 )
| ( equidistant @ SV106 @ SV84 @ SV23 @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[221]) ).
thf(248,plain,
! [SV107: $i,SV85: $i,SV57: $i,SV24: $i] :
( ( ~ ( equidistant @ SV24 @ SV57 @ SV85 @ SV107 )
| ( equidistant @ SV107 @ SV85 @ SV57 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(249,plain,
! [SV108: $i,SV86: $i,SV58: $i,SV25: $i] :
( ( ! [SY342: $i,SY343: $i] :
( ~ ( equidistant @ SV25 @ SV58 @ SV86 @ SV108 )
| ~ ( equidistant @ SV86 @ SV108 @ SY342 @ SY343 )
| ( equidistant @ SV25 @ SV58 @ SY342 @ SY343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[223]) ).
thf(250,plain,
! [SV63: $i,SV31: $i] :
( ( ( SV31
= ( reflection @ SV63 @ SV31 ) )
= $false )
| ( ( SV63 = SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(251,plain,
! [SV64: $i,SV32: $i] :
( ( ( SV32 = SV64 )
= $false )
| ( ( SV64
= ( reflection @ SV32 @ SV64 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(252,plain,
! [SV109: $i,SV88: $i,SV65: $i,SV33: $i] :
( ( ! [SY344: $i] :
( ( SV33
!= ( extension @ SV65 @ SV88 @ SV109 @ SY344 ) )
| ( between @ SV65 @ SV88 @ SV33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(253,plain,
! [SV110: $i,SV89: $i,SV66: $i,SV35: $i,SV2: $i] :
( ( ! [SY345: $i] :
( ~ ( equidistant @ SV2 @ SV35 @ SV66 @ SV89 )
| ~ ( equidistant @ SV2 @ SV35 @ SV110 @ SY345 )
| ( equidistant @ SV66 @ SV89 @ SV110 @ SY345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[228]) ).
thf(254,plain,
! [SV67: $i,SV36: $i,SV3: $i] :
( ( ( equidistant @ SV3 @ SV36 @ SV67 @ SV67 )
= $false )
| ( ( SV3 = SV36 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(255,plain,
! [SV111: $i,SV92: $i,SV70: $i,SV39: $i,SV6: $i] :
( ( ! [SY346: $i,SY347: $i,SY348: $i] :
( ~ ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
| ~ ( equidistant @ SV39 @ SV111 @ SV92 @ SY346 )
| ~ ( equidistant @ SV6 @ SY347 @ SV70 @ SY348 )
| ~ ( equidistant @ SV39 @ SY347 @ SV92 @ SY348 )
| ~ ( between @ SV6 @ SV39 @ SV111 )
| ~ ( between @ SV70 @ SV92 @ SY346 )
| ( SV6 = SV39 )
| ( equidistant @ SV111 @ SY347 @ SY346 @ SY348 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(256,plain,
! [SV112: $i,SV93: $i,SV71: $i,SV41: $i,SV8: $i] :
( ( ~ ( between @ SV8 @ SV41 @ SV71 )
| ~ ( between @ SV93 @ SV112 @ SV71 )
| ( between @ SV41 @ ( inner_pasch @ SV8 @ SV41 @ SV71 @ SV112 @ SV93 ) @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(257,plain,
! [SV113: $i,SV94: $i,SV72: $i,SV42: $i,SV9: $i] :
( ( ~ ( between @ SV9 @ SV42 @ SV72 )
| ~ ( between @ SV94 @ SV113 @ SV72 )
| ( between @ SV113 @ ( inner_pasch @ SV9 @ SV42 @ SV72 @ SV113 @ SV94 ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(258,plain,
! [SV114: $i,SV95: $i,SV73: $i,SV43: $i,SV10: $i] :
( ( ~ ( equidistant @ SV10 @ SV43 @ SV10 @ SV73 )
| ~ ( equidistant @ SV95 @ SV43 @ SV95 @ SV73 )
| ~ ( equidistant @ SV114 @ SV43 @ SV114 @ SV73 )
| ( between @ SV10 @ SV95 @ SV114 )
| ( between @ SV95 @ SV114 @ SV10 )
| ( between @ SV114 @ SV10 @ SV95 )
| ( SV43 = SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(259,plain,
! [SV115: $i,SV96: $i,SV74: $i,SV44: $i,SV11: $i] :
( ( ~ ( between @ SV11 @ SV44 @ SV74 )
| ~ ( between @ SV96 @ SV44 @ SV115 )
| ( SV11 = SV44 )
| ( between @ SV11 @ SV96 @ ( euclid1 @ SV11 @ SV96 @ SV44 @ SV115 @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[237]) ).
thf(260,plain,
! [SV116: $i,SV97: $i,SV75: $i,SV45: $i,SV12: $i] :
( ( ~ ( between @ SV12 @ SV45 @ SV75 )
| ~ ( between @ SV97 @ SV45 @ SV116 )
| ( SV12 = SV45 )
| ( between @ SV12 @ SV116 @ ( euclid2 @ SV12 @ SV97 @ SV45 @ SV116 @ SV75 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[238]) ).
thf(261,plain,
! [SV117: $i,SV98: $i,SV76: $i,SV46: $i,SV13: $i] :
( ( ~ ( between @ SV13 @ SV46 @ SV76 )
| ~ ( between @ SV98 @ SV46 @ SV117 )
| ( SV13 = SV46 )
| ( between @ ( euclid1 @ SV13 @ SV98 @ SV46 @ SV117 @ SV76 ) @ SV76 @ ( euclid2 @ SV13 @ SV98 @ SV46 @ SV117 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[239]) ).
thf(262,plain,
! [SV118: $i,SV99: $i,SV77: $i,SV47: $i,SV14: $i] :
( ( ! [SY349: $i] :
( ~ ( equidistant @ SV14 @ SV47 @ SV14 @ SV77 )
| ~ ( equidistant @ SV14 @ SV99 @ SV14 @ SV118 )
| ~ ( between @ SV14 @ SV47 @ SV99 )
| ~ ( between @ SV47 @ SY349 @ SV99 )
| ( between @ SV77 @ ( continuous @ SV14 @ SV47 @ SV77 @ SY349 @ SV99 @ SV118 ) @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[240]) ).
thf(263,plain,
! [SV119: $i,SV100: $i,SV78: $i,SV48: $i,SV15: $i] :
( ( ! [SY350: $i] :
( ~ ( equidistant @ SV15 @ SV48 @ SV15 @ SV78 )
| ~ ( equidistant @ SV15 @ SV100 @ SV15 @ SV119 )
| ~ ( between @ SV15 @ SV48 @ SV100 )
| ~ ( between @ SV48 @ SY350 @ SV100 )
| ( equidistant @ SV15 @ SY350 @ SV15 @ ( continuous @ SV15 @ SV48 @ SV78 @ SY350 @ SV100 @ SV119 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[241]) ).
thf(264,plain,
! [SV101: $i,SV79: $i,SV51: $i,SV18: $i] :
( ( ( ~ ( equidistant @ SV18 @ SV51 @ SV79 @ SV101 ) )
= $true )
| ( ( equidistant @ SV79 @ SV101 @ SV18 @ SV51 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[242]) ).
thf(265,plain,
! [SV102: $i,SV80: $i,SV52: $i,SV19: $i] :
( ( ( ~ ( equidistant @ SV19 @ SV52 @ SV80 @ SV102 ) )
= $true )
| ( ( equidistant @ SV52 @ SV19 @ SV80 @ SV102 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[243]) ).
thf(266,plain,
! [SV103: $i,SV81: $i,SV53: $i,SV20: $i] :
( ( ( ~ ( equidistant @ SV20 @ SV53 @ SV81 @ SV103 ) )
= $true )
| ( ( equidistant @ SV20 @ SV53 @ SV103 @ SV81 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(267,plain,
! [SV104: $i,SV82: $i,SV54: $i,SV21: $i] :
( ( ( ~ ( equidistant @ SV21 @ SV54 @ SV82 @ SV104 ) )
= $true )
| ( ( equidistant @ SV54 @ SV21 @ SV104 @ SV82 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(268,plain,
! [SV105: $i,SV83: $i,SV55: $i,SV22: $i] :
( ( ( ~ ( equidistant @ SV22 @ SV55 @ SV83 @ SV105 ) )
= $true )
| ( ( equidistant @ SV83 @ SV105 @ SV55 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(269,plain,
! [SV106: $i,SV84: $i,SV56: $i,SV23: $i] :
( ( ( ~ ( equidistant @ SV23 @ SV56 @ SV84 @ SV106 ) )
= $true )
| ( ( equidistant @ SV106 @ SV84 @ SV23 @ SV56 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(270,plain,
! [SV107: $i,SV85: $i,SV57: $i,SV24: $i] :
( ( ( ~ ( equidistant @ SV24 @ SV57 @ SV85 @ SV107 ) )
= $true )
| ( ( equidistant @ SV107 @ SV85 @ SV57 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(271,plain,
! [SV120: $i,SV108: $i,SV86: $i,SV58: $i,SV25: $i] :
( ( ! [SY351: $i] :
( ~ ( equidistant @ SV25 @ SV58 @ SV86 @ SV108 )
| ~ ( equidistant @ SV86 @ SV108 @ SV120 @ SY351 )
| ( equidistant @ SV25 @ SV58 @ SV120 @ SY351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(272,plain,
! [SV121: $i,SV109: $i,SV88: $i,SV65: $i,SV33: $i] :
( ( ( SV33
!= ( extension @ SV65 @ SV88 @ SV109 @ SV121 ) )
| ( between @ SV65 @ SV88 @ SV33 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(273,plain,
! [SV122: $i,SV110: $i,SV89: $i,SV66: $i,SV35: $i,SV2: $i] :
( ( ~ ( equidistant @ SV2 @ SV35 @ SV66 @ SV89 )
| ~ ( equidistant @ SV2 @ SV35 @ SV110 @ SV122 )
| ( equidistant @ SV66 @ SV89 @ SV110 @ SV122 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[253]) ).
thf(274,plain,
! [SV123: $i,SV111: $i,SV92: $i,SV70: $i,SV39: $i,SV6: $i] :
( ( ! [SY352: $i,SY353: $i] :
( ~ ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
| ~ ( equidistant @ SV39 @ SV111 @ SV92 @ SV123 )
| ~ ( equidistant @ SV6 @ SY352 @ SV70 @ SY353 )
| ~ ( equidistant @ SV39 @ SY352 @ SV92 @ SY353 )
| ~ ( between @ SV6 @ SV39 @ SV111 )
| ~ ( between @ SV70 @ SV92 @ SV123 )
| ( SV6 = SV39 )
| ( equidistant @ SV111 @ SY352 @ SV123 @ SY353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(275,plain,
! [SV112: $i,SV93: $i,SV71: $i,SV41: $i,SV8: $i] :
( ( ( ~ ( between @ SV8 @ SV41 @ SV71 ) )
= $true )
| ( ( ~ ( between @ SV93 @ SV112 @ SV71 )
| ( between @ SV41 @ ( inner_pasch @ SV8 @ SV41 @ SV71 @ SV112 @ SV93 ) @ SV93 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(276,plain,
! [SV113: $i,SV94: $i,SV72: $i,SV42: $i,SV9: $i] :
( ( ( ~ ( between @ SV9 @ SV42 @ SV72 ) )
= $true )
| ( ( ~ ( between @ SV94 @ SV113 @ SV72 )
| ( between @ SV113 @ ( inner_pasch @ SV9 @ SV42 @ SV72 @ SV113 @ SV94 ) @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(277,plain,
! [SV114: $i,SV95: $i,SV73: $i,SV43: $i,SV10: $i] :
( ( ( ~ ( equidistant @ SV10 @ SV43 @ SV10 @ SV73 ) )
= $true )
| ( ( ~ ( equidistant @ SV95 @ SV43 @ SV95 @ SV73 )
| ~ ( equidistant @ SV114 @ SV43 @ SV114 @ SV73 )
| ( between @ SV10 @ SV95 @ SV114 )
| ( between @ SV95 @ SV114 @ SV10 )
| ( between @ SV114 @ SV10 @ SV95 )
| ( SV43 = SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[258]) ).
thf(278,plain,
! [SV115: $i,SV96: $i,SV74: $i,SV44: $i,SV11: $i] :
( ( ( ~ ( between @ SV11 @ SV44 @ SV74 ) )
= $true )
| ( ( ~ ( between @ SV96 @ SV44 @ SV115 )
| ( SV11 = SV44 )
| ( between @ SV11 @ SV96 @ ( euclid1 @ SV11 @ SV96 @ SV44 @ SV115 @ SV74 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(279,plain,
! [SV116: $i,SV97: $i,SV75: $i,SV45: $i,SV12: $i] :
( ( ( ~ ( between @ SV12 @ SV45 @ SV75 ) )
= $true )
| ( ( ~ ( between @ SV97 @ SV45 @ SV116 )
| ( SV12 = SV45 )
| ( between @ SV12 @ SV116 @ ( euclid2 @ SV12 @ SV97 @ SV45 @ SV116 @ SV75 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[260]) ).
thf(280,plain,
! [SV117: $i,SV98: $i,SV76: $i,SV46: $i,SV13: $i] :
( ( ( ~ ( between @ SV13 @ SV46 @ SV76 ) )
= $true )
| ( ( ~ ( between @ SV98 @ SV46 @ SV117 )
| ( SV13 = SV46 )
| ( between @ ( euclid1 @ SV13 @ SV98 @ SV46 @ SV117 @ SV76 ) @ SV76 @ ( euclid2 @ SV13 @ SV98 @ SV46 @ SV117 @ SV76 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[261]) ).
thf(281,plain,
! [SV124: $i,SV118: $i,SV99: $i,SV77: $i,SV47: $i,SV14: $i] :
( ( ~ ( equidistant @ SV14 @ SV47 @ SV14 @ SV77 )
| ~ ( equidistant @ SV14 @ SV99 @ SV14 @ SV118 )
| ~ ( between @ SV14 @ SV47 @ SV99 )
| ~ ( between @ SV47 @ SV124 @ SV99 )
| ( between @ SV77 @ ( continuous @ SV14 @ SV47 @ SV77 @ SV124 @ SV99 @ SV118 ) @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[262]) ).
thf(282,plain,
! [SV125: $i,SV119: $i,SV100: $i,SV78: $i,SV48: $i,SV15: $i] :
( ( ~ ( equidistant @ SV15 @ SV48 @ SV15 @ SV78 )
| ~ ( equidistant @ SV15 @ SV100 @ SV15 @ SV119 )
| ~ ( between @ SV15 @ SV48 @ SV100 )
| ~ ( between @ SV48 @ SV125 @ SV100 )
| ( equidistant @ SV15 @ SV125 @ SV15 @ ( continuous @ SV15 @ SV48 @ SV78 @ SV125 @ SV100 @ SV119 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(283,plain,
! [SV101: $i,SV79: $i,SV51: $i,SV18: $i] :
( ( ( equidistant @ SV18 @ SV51 @ SV79 @ SV101 )
= $false )
| ( ( equidistant @ SV79 @ SV101 @ SV18 @ SV51 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(284,plain,
! [SV102: $i,SV80: $i,SV52: $i,SV19: $i] :
( ( ( equidistant @ SV19 @ SV52 @ SV80 @ SV102 )
= $false )
| ( ( equidistant @ SV52 @ SV19 @ SV80 @ SV102 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(285,plain,
! [SV103: $i,SV81: $i,SV53: $i,SV20: $i] :
( ( ( equidistant @ SV20 @ SV53 @ SV81 @ SV103 )
= $false )
| ( ( equidistant @ SV20 @ SV53 @ SV103 @ SV81 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[266]) ).
thf(286,plain,
! [SV104: $i,SV82: $i,SV54: $i,SV21: $i] :
( ( ( equidistant @ SV21 @ SV54 @ SV82 @ SV104 )
= $false )
| ( ( equidistant @ SV54 @ SV21 @ SV104 @ SV82 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(287,plain,
! [SV105: $i,SV83: $i,SV55: $i,SV22: $i] :
( ( ( equidistant @ SV22 @ SV55 @ SV83 @ SV105 )
= $false )
| ( ( equidistant @ SV83 @ SV105 @ SV55 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(288,plain,
! [SV106: $i,SV84: $i,SV56: $i,SV23: $i] :
( ( ( equidistant @ SV23 @ SV56 @ SV84 @ SV106 )
= $false )
| ( ( equidistant @ SV106 @ SV84 @ SV23 @ SV56 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(289,plain,
! [SV107: $i,SV85: $i,SV57: $i,SV24: $i] :
( ( ( equidistant @ SV24 @ SV57 @ SV85 @ SV107 )
= $false )
| ( ( equidistant @ SV107 @ SV85 @ SV57 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(290,plain,
! [SV126: $i,SV120: $i,SV108: $i,SV86: $i,SV58: $i,SV25: $i] :
( ( ~ ( equidistant @ SV25 @ SV58 @ SV86 @ SV108 )
| ~ ( equidistant @ SV86 @ SV108 @ SV120 @ SV126 )
| ( equidistant @ SV25 @ SV58 @ SV120 @ SV126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(291,plain,
! [SV121: $i,SV109: $i,SV88: $i,SV65: $i,SV33: $i] :
( ( ( SV33
!= ( extension @ SV65 @ SV88 @ SV109 @ SV121 ) )
= $true )
| ( ( between @ SV65 @ SV88 @ SV33 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(292,plain,
! [SV122: $i,SV110: $i,SV89: $i,SV66: $i,SV35: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV35 @ SV66 @ SV89 ) )
= $true )
| ( ( ~ ( equidistant @ SV2 @ SV35 @ SV110 @ SV122 )
| ( equidistant @ SV66 @ SV89 @ SV110 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(293,plain,
! [SV127: $i,SV123: $i,SV111: $i,SV92: $i,SV70: $i,SV39: $i,SV6: $i] :
( ( ! [SY354: $i] :
( ~ ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
| ~ ( equidistant @ SV39 @ SV111 @ SV92 @ SV123 )
| ~ ( equidistant @ SV6 @ SV127 @ SV70 @ SY354 )
| ~ ( equidistant @ SV39 @ SV127 @ SV92 @ SY354 )
| ~ ( between @ SV6 @ SV39 @ SV111 )
| ~ ( between @ SV70 @ SV92 @ SV123 )
| ( SV6 = SV39 )
| ( equidistant @ SV111 @ SV127 @ SV123 @ SY354 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[274]) ).
thf(294,plain,
! [SV112: $i,SV93: $i,SV71: $i,SV41: $i,SV8: $i] :
( ( ( between @ SV8 @ SV41 @ SV71 )
= $false )
| ( ( ~ ( between @ SV93 @ SV112 @ SV71 )
| ( between @ SV41 @ ( inner_pasch @ SV8 @ SV41 @ SV71 @ SV112 @ SV93 ) @ SV93 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(295,plain,
! [SV113: $i,SV94: $i,SV72: $i,SV42: $i,SV9: $i] :
( ( ( between @ SV9 @ SV42 @ SV72 )
= $false )
| ( ( ~ ( between @ SV94 @ SV113 @ SV72 )
| ( between @ SV113 @ ( inner_pasch @ SV9 @ SV42 @ SV72 @ SV113 @ SV94 ) @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[276]) ).
thf(296,plain,
! [SV114: $i,SV95: $i,SV73: $i,SV43: $i,SV10: $i] :
( ( ( equidistant @ SV10 @ SV43 @ SV10 @ SV73 )
= $false )
| ( ( ~ ( equidistant @ SV95 @ SV43 @ SV95 @ SV73 )
| ~ ( equidistant @ SV114 @ SV43 @ SV114 @ SV73 )
| ( between @ SV10 @ SV95 @ SV114 )
| ( between @ SV95 @ SV114 @ SV10 )
| ( between @ SV114 @ SV10 @ SV95 )
| ( SV43 = SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(297,plain,
! [SV115: $i,SV96: $i,SV74: $i,SV44: $i,SV11: $i] :
( ( ( between @ SV11 @ SV44 @ SV74 )
= $false )
| ( ( ~ ( between @ SV96 @ SV44 @ SV115 )
| ( SV11 = SV44 )
| ( between @ SV11 @ SV96 @ ( euclid1 @ SV11 @ SV96 @ SV44 @ SV115 @ SV74 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(298,plain,
! [SV116: $i,SV97: $i,SV75: $i,SV45: $i,SV12: $i] :
( ( ( between @ SV12 @ SV45 @ SV75 )
= $false )
| ( ( ~ ( between @ SV97 @ SV45 @ SV116 )
| ( SV12 = SV45 )
| ( between @ SV12 @ SV116 @ ( euclid2 @ SV12 @ SV97 @ SV45 @ SV116 @ SV75 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[279]) ).
thf(299,plain,
! [SV117: $i,SV98: $i,SV76: $i,SV46: $i,SV13: $i] :
( ( ( between @ SV13 @ SV46 @ SV76 )
= $false )
| ( ( ~ ( between @ SV98 @ SV46 @ SV117 )
| ( SV13 = SV46 )
| ( between @ ( euclid1 @ SV13 @ SV98 @ SV46 @ SV117 @ SV76 ) @ SV76 @ ( euclid2 @ SV13 @ SV98 @ SV46 @ SV117 @ SV76 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(300,plain,
! [SV124: $i,SV118: $i,SV99: $i,SV77: $i,SV47: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV47 @ SV14 @ SV77 ) )
= $true )
| ( ( ~ ( equidistant @ SV14 @ SV99 @ SV14 @ SV118 )
| ~ ( between @ SV14 @ SV47 @ SV99 )
| ~ ( between @ SV47 @ SV124 @ SV99 )
| ( between @ SV77 @ ( continuous @ SV14 @ SV47 @ SV77 @ SV124 @ SV99 @ SV118 ) @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[281]) ).
thf(301,plain,
! [SV125: $i,SV119: $i,SV100: $i,SV78: $i,SV48: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV48 @ SV15 @ SV78 ) )
= $true )
| ( ( ~ ( equidistant @ SV15 @ SV100 @ SV15 @ SV119 )
| ~ ( between @ SV15 @ SV48 @ SV100 )
| ~ ( between @ SV48 @ SV125 @ SV100 )
| ( equidistant @ SV15 @ SV125 @ SV15 @ ( continuous @ SV15 @ SV48 @ SV78 @ SV125 @ SV100 @ SV119 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[282]) ).
thf(302,plain,
! [SV126: $i,SV120: $i,SV108: $i,SV86: $i,SV58: $i,SV25: $i] :
( ( ( ~ ( equidistant @ SV25 @ SV58 @ SV86 @ SV108 ) )
= $true )
| ( ( ~ ( equidistant @ SV86 @ SV108 @ SV120 @ SV126 )
| ( equidistant @ SV25 @ SV58 @ SV120 @ SV126 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(303,plain,
! [SV121: $i,SV109: $i,SV88: $i,SV65: $i,SV33: $i] :
( ( ( SV33
= ( extension @ SV65 @ SV88 @ SV109 @ SV121 ) )
= $false )
| ( ( between @ SV65 @ SV88 @ SV33 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[291]) ).
thf(304,plain,
! [SV122: $i,SV110: $i,SV89: $i,SV66: $i,SV35: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV35 @ SV66 @ SV89 )
= $false )
| ( ( ~ ( equidistant @ SV2 @ SV35 @ SV110 @ SV122 )
| ( equidistant @ SV66 @ SV89 @ SV110 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[292]) ).
thf(305,plain,
! [SV128: $i,SV127: $i,SV123: $i,SV111: $i,SV92: $i,SV70: $i,SV39: $i,SV6: $i] :
( ( ~ ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
| ~ ( equidistant @ SV39 @ SV111 @ SV92 @ SV123 )
| ~ ( equidistant @ SV6 @ SV127 @ SV70 @ SV128 )
| ~ ( equidistant @ SV39 @ SV127 @ SV92 @ SV128 )
| ~ ( between @ SV6 @ SV39 @ SV111 )
| ~ ( between @ SV70 @ SV92 @ SV123 )
| ( SV6 = SV39 )
| ( equidistant @ SV111 @ SV127 @ SV123 @ SV128 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(306,plain,
! [SV8: $i,SV41: $i,SV71: $i,SV112: $i,SV93: $i] :
( ( ( ~ ( between @ SV93 @ SV112 @ SV71 ) )
= $true )
| ( ( between @ SV41 @ ( inner_pasch @ SV8 @ SV41 @ SV71 @ SV112 @ SV93 ) @ SV93 )
= $true )
| ( ( between @ SV8 @ SV41 @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(307,plain,
! [SV42: $i,SV9: $i,SV72: $i,SV113: $i,SV94: $i] :
( ( ( ~ ( between @ SV94 @ SV113 @ SV72 ) )
= $true )
| ( ( between @ SV113 @ ( inner_pasch @ SV9 @ SV42 @ SV72 @ SV113 @ SV94 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV42 @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(308,plain,
! [SV10: $i,SV114: $i,SV73: $i,SV43: $i,SV95: $i] :
( ( ( ~ ( equidistant @ SV95 @ SV43 @ SV95 @ SV73 ) )
= $true )
| ( ( ~ ( equidistant @ SV114 @ SV43 @ SV114 @ SV73 )
| ( between @ SV10 @ SV95 @ SV114 )
| ( between @ SV95 @ SV114 @ SV10 )
| ( between @ SV114 @ SV10 @ SV95 )
| ( SV43 = SV73 ) )
= $true )
| ( ( equidistant @ SV10 @ SV43 @ SV10 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(309,plain,
! [SV74: $i,SV11: $i,SV115: $i,SV44: $i,SV96: $i] :
( ( ( ~ ( between @ SV96 @ SV44 @ SV115 ) )
= $true )
| ( ( ( SV11 = SV44 )
| ( between @ SV11 @ SV96 @ ( euclid1 @ SV11 @ SV96 @ SV44 @ SV115 @ SV74 ) ) )
= $true )
| ( ( between @ SV11 @ SV44 @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[297]) ).
thf(310,plain,
! [SV75: $i,SV12: $i,SV116: $i,SV45: $i,SV97: $i] :
( ( ( ~ ( between @ SV97 @ SV45 @ SV116 ) )
= $true )
| ( ( ( SV12 = SV45 )
| ( between @ SV12 @ SV116 @ ( euclid2 @ SV12 @ SV97 @ SV45 @ SV116 @ SV75 ) ) )
= $true )
| ( ( between @ SV12 @ SV45 @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[298]) ).
thf(311,plain,
! [SV76: $i,SV13: $i,SV117: $i,SV46: $i,SV98: $i] :
( ( ( ~ ( between @ SV98 @ SV46 @ SV117 ) )
= $true )
| ( ( ( SV13 = SV46 )
| ( between @ ( euclid1 @ SV13 @ SV98 @ SV46 @ SV117 @ SV76 ) @ SV76 @ ( euclid2 @ SV13 @ SV98 @ SV46 @ SV117 @ SV76 ) ) )
= $true )
| ( ( between @ SV13 @ SV46 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(312,plain,
! [SV124: $i,SV118: $i,SV99: $i,SV77: $i,SV47: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV47 @ SV14 @ SV77 )
= $false )
| ( ( ~ ( equidistant @ SV14 @ SV99 @ SV14 @ SV118 )
| ~ ( between @ SV14 @ SV47 @ SV99 )
| ~ ( between @ SV47 @ SV124 @ SV99 )
| ( between @ SV77 @ ( continuous @ SV14 @ SV47 @ SV77 @ SV124 @ SV99 @ SV118 ) @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(313,plain,
! [SV125: $i,SV119: $i,SV100: $i,SV78: $i,SV48: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV48 @ SV15 @ SV78 )
= $false )
| ( ( ~ ( equidistant @ SV15 @ SV100 @ SV15 @ SV119 )
| ~ ( between @ SV15 @ SV48 @ SV100 )
| ~ ( between @ SV48 @ SV125 @ SV100 )
| ( equidistant @ SV15 @ SV125 @ SV15 @ ( continuous @ SV15 @ SV48 @ SV78 @ SV125 @ SV100 @ SV119 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(314,plain,
! [SV126: $i,SV120: $i,SV108: $i,SV86: $i,SV58: $i,SV25: $i] :
( ( ( equidistant @ SV25 @ SV58 @ SV86 @ SV108 )
= $false )
| ( ( ~ ( equidistant @ SV86 @ SV108 @ SV120 @ SV126 )
| ( equidistant @ SV25 @ SV58 @ SV120 @ SV126 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(315,plain,
! [SV89: $i,SV66: $i,SV122: $i,SV110: $i,SV35: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV35 @ SV110 @ SV122 ) )
= $true )
| ( ( equidistant @ SV66 @ SV89 @ SV110 @ SV122 )
= $true )
| ( ( equidistant @ SV2 @ SV35 @ SV66 @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(316,plain,
! [SV128: $i,SV127: $i,SV123: $i,SV111: $i,SV92: $i,SV70: $i,SV39: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 ) )
= $true )
| ( ( ~ ( equidistant @ SV39 @ SV111 @ SV92 @ SV123 )
| ~ ( equidistant @ SV6 @ SV127 @ SV70 @ SV128 )
| ~ ( equidistant @ SV39 @ SV127 @ SV92 @ SV128 )
| ~ ( between @ SV6 @ SV39 @ SV111 )
| ~ ( between @ SV70 @ SV92 @ SV123 )
| ( SV6 = SV39 )
| ( equidistant @ SV111 @ SV127 @ SV123 @ SV128 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(317,plain,
! [SV8: $i,SV41: $i,SV71: $i,SV112: $i,SV93: $i] :
( ( ( between @ SV93 @ SV112 @ SV71 )
= $false )
| ( ( between @ SV41 @ ( inner_pasch @ SV8 @ SV41 @ SV71 @ SV112 @ SV93 ) @ SV93 )
= $true )
| ( ( between @ SV8 @ SV41 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(318,plain,
! [SV42: $i,SV9: $i,SV72: $i,SV113: $i,SV94: $i] :
( ( ( between @ SV94 @ SV113 @ SV72 )
= $false )
| ( ( between @ SV113 @ ( inner_pasch @ SV9 @ SV42 @ SV72 @ SV113 @ SV94 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV42 @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(319,plain,
! [SV10: $i,SV114: $i,SV73: $i,SV43: $i,SV95: $i] :
( ( ( equidistant @ SV95 @ SV43 @ SV95 @ SV73 )
= $false )
| ( ( ~ ( equidistant @ SV114 @ SV43 @ SV114 @ SV73 )
| ( between @ SV10 @ SV95 @ SV114 )
| ( between @ SV95 @ SV114 @ SV10 )
| ( between @ SV114 @ SV10 @ SV95 )
| ( SV43 = SV73 ) )
= $true )
| ( ( equidistant @ SV10 @ SV43 @ SV10 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[308]) ).
thf(320,plain,
! [SV74: $i,SV11: $i,SV115: $i,SV44: $i,SV96: $i] :
( ( ( between @ SV96 @ SV44 @ SV115 )
= $false )
| ( ( ( SV11 = SV44 )
| ( between @ SV11 @ SV96 @ ( euclid1 @ SV11 @ SV96 @ SV44 @ SV115 @ SV74 ) ) )
= $true )
| ( ( between @ SV11 @ SV44 @ SV74 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[309]) ).
thf(321,plain,
! [SV75: $i,SV12: $i,SV116: $i,SV45: $i,SV97: $i] :
( ( ( between @ SV97 @ SV45 @ SV116 )
= $false )
| ( ( ( SV12 = SV45 )
| ( between @ SV12 @ SV116 @ ( euclid2 @ SV12 @ SV97 @ SV45 @ SV116 @ SV75 ) ) )
= $true )
| ( ( between @ SV12 @ SV45 @ SV75 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[310]) ).
thf(322,plain,
! [SV76: $i,SV13: $i,SV117: $i,SV46: $i,SV98: $i] :
( ( ( between @ SV98 @ SV46 @ SV117 )
= $false )
| ( ( ( SV13 = SV46 )
| ( between @ ( euclid1 @ SV13 @ SV98 @ SV46 @ SV117 @ SV76 ) @ SV76 @ ( euclid2 @ SV13 @ SV98 @ SV46 @ SV117 @ SV76 ) ) )
= $true )
| ( ( between @ SV13 @ SV46 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[311]) ).
thf(323,plain,
! [SV77: $i,SV124: $i,SV47: $i,SV118: $i,SV99: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV99 @ SV14 @ SV118 ) )
= $true )
| ( ( ~ ( between @ SV14 @ SV47 @ SV99 )
| ~ ( between @ SV47 @ SV124 @ SV99 )
| ( between @ SV77 @ ( continuous @ SV14 @ SV47 @ SV77 @ SV124 @ SV99 @ SV118 ) @ SV118 ) )
= $true )
| ( ( equidistant @ SV14 @ SV47 @ SV14 @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(324,plain,
! [SV78: $i,SV125: $i,SV48: $i,SV119: $i,SV100: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV100 @ SV15 @ SV119 ) )
= $true )
| ( ( ~ ( between @ SV15 @ SV48 @ SV100 )
| ~ ( between @ SV48 @ SV125 @ SV100 )
| ( equidistant @ SV15 @ SV125 @ SV15 @ ( continuous @ SV15 @ SV48 @ SV78 @ SV125 @ SV100 @ SV119 ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV48 @ SV15 @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(325,plain,
! [SV58: $i,SV25: $i,SV126: $i,SV120: $i,SV108: $i,SV86: $i] :
( ( ( ~ ( equidistant @ SV86 @ SV108 @ SV120 @ SV126 ) )
= $true )
| ( ( equidistant @ SV25 @ SV58 @ SV120 @ SV126 )
= $true )
| ( ( equidistant @ SV25 @ SV58 @ SV86 @ SV108 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(326,plain,
! [SV89: $i,SV66: $i,SV122: $i,SV110: $i,SV35: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV35 @ SV110 @ SV122 )
= $false )
| ( ( equidistant @ SV66 @ SV89 @ SV110 @ SV122 )
= $true )
| ( ( equidistant @ SV2 @ SV35 @ SV66 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[315]) ).
thf(327,plain,
! [SV128: $i,SV127: $i,SV123: $i,SV111: $i,SV92: $i,SV70: $i,SV39: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
= $false )
| ( ( ~ ( equidistant @ SV39 @ SV111 @ SV92 @ SV123 )
| ~ ( equidistant @ SV6 @ SV127 @ SV70 @ SV128 )
| ~ ( equidistant @ SV39 @ SV127 @ SV92 @ SV128 )
| ~ ( between @ SV6 @ SV39 @ SV111 )
| ~ ( between @ SV70 @ SV92 @ SV123 )
| ( SV6 = SV39 )
| ( equidistant @ SV111 @ SV127 @ SV123 @ SV128 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(328,plain,
! [SV95: $i,SV10: $i,SV73: $i,SV43: $i,SV114: $i] :
( ( ( ~ ( equidistant @ SV114 @ SV43 @ SV114 @ SV73 ) )
= $true )
| ( ( ( between @ SV10 @ SV95 @ SV114 )
| ( between @ SV95 @ SV114 @ SV10 )
| ( between @ SV114 @ SV10 @ SV95 )
| ( SV43 = SV73 ) )
= $true )
| ( ( equidistant @ SV95 @ SV43 @ SV95 @ SV73 )
= $false )
| ( ( equidistant @ SV10 @ SV43 @ SV10 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[319]) ).
thf(329,plain,
! [SV74: $i,SV115: $i,SV96: $i,SV44: $i,SV11: $i] :
( ( ( SV11 = SV44 )
= $true )
| ( ( between @ SV11 @ SV96 @ ( euclid1 @ SV11 @ SV96 @ SV44 @ SV115 @ SV74 ) )
= $true )
| ( ( between @ SV96 @ SV44 @ SV115 )
= $false )
| ( ( between @ SV11 @ SV44 @ SV74 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[320]) ).
thf(330,plain,
! [SV75: $i,SV97: $i,SV116: $i,SV45: $i,SV12: $i] :
( ( ( SV12 = SV45 )
= $true )
| ( ( between @ SV12 @ SV116 @ ( euclid2 @ SV12 @ SV97 @ SV45 @ SV116 @ SV75 ) )
= $true )
| ( ( between @ SV97 @ SV45 @ SV116 )
= $false )
| ( ( between @ SV12 @ SV45 @ SV75 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[321]) ).
thf(331,plain,
! [SV76: $i,SV117: $i,SV98: $i,SV46: $i,SV13: $i] :
( ( ( SV13 = SV46 )
= $true )
| ( ( between @ ( euclid1 @ SV13 @ SV98 @ SV46 @ SV117 @ SV76 ) @ SV76 @ ( euclid2 @ SV13 @ SV98 @ SV46 @ SV117 @ SV76 ) )
= $true )
| ( ( between @ SV98 @ SV46 @ SV117 )
= $false )
| ( ( between @ SV13 @ SV46 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[322]) ).
thf(332,plain,
! [SV77: $i,SV124: $i,SV47: $i,SV118: $i,SV99: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV99 @ SV14 @ SV118 )
= $false )
| ( ( ~ ( between @ SV14 @ SV47 @ SV99 )
| ~ ( between @ SV47 @ SV124 @ SV99 )
| ( between @ SV77 @ ( continuous @ SV14 @ SV47 @ SV77 @ SV124 @ SV99 @ SV118 ) @ SV118 ) )
= $true )
| ( ( equidistant @ SV14 @ SV47 @ SV14 @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(333,plain,
! [SV78: $i,SV125: $i,SV48: $i,SV119: $i,SV100: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV100 @ SV15 @ SV119 )
= $false )
| ( ( ~ ( between @ SV15 @ SV48 @ SV100 )
| ~ ( between @ SV48 @ SV125 @ SV100 )
| ( equidistant @ SV15 @ SV125 @ SV15 @ ( continuous @ SV15 @ SV48 @ SV78 @ SV125 @ SV100 @ SV119 ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV48 @ SV15 @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(334,plain,
! [SV58: $i,SV25: $i,SV126: $i,SV120: $i,SV108: $i,SV86: $i] :
( ( ( equidistant @ SV86 @ SV108 @ SV120 @ SV126 )
= $false )
| ( ( equidistant @ SV25 @ SV58 @ SV120 @ SV126 )
= $true )
| ( ( equidistant @ SV25 @ SV58 @ SV86 @ SV108 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[325]) ).
thf(335,plain,
! [SV128: $i,SV70: $i,SV127: $i,SV6: $i,SV123: $i,SV92: $i,SV111: $i,SV39: $i] :
( ( ( ~ ( equidistant @ SV39 @ SV111 @ SV92 @ SV123 ) )
= $true )
| ( ( ~ ( equidistant @ SV6 @ SV127 @ SV70 @ SV128 )
| ~ ( equidistant @ SV39 @ SV127 @ SV92 @ SV128 )
| ~ ( between @ SV6 @ SV39 @ SV111 )
| ~ ( between @ SV70 @ SV92 @ SV123 )
| ( SV6 = SV39 )
| ( equidistant @ SV111 @ SV127 @ SV123 @ SV128 ) )
= $true )
| ( ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(336,plain,
! [SV95: $i,SV10: $i,SV73: $i,SV43: $i,SV114: $i] :
( ( ( equidistant @ SV114 @ SV43 @ SV114 @ SV73 )
= $false )
| ( ( ( between @ SV10 @ SV95 @ SV114 )
| ( between @ SV95 @ SV114 @ SV10 )
| ( between @ SV114 @ SV10 @ SV95 )
| ( SV43 = SV73 ) )
= $true )
| ( ( equidistant @ SV95 @ SV43 @ SV95 @ SV73 )
= $false )
| ( ( equidistant @ SV10 @ SV43 @ SV10 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[328]) ).
thf(337,plain,
! [SV118: $i,SV77: $i,SV124: $i,SV99: $i,SV47: $i,SV14: $i] :
( ( ( ~ ( between @ SV14 @ SV47 @ SV99 ) )
= $true )
| ( ( ~ ( between @ SV47 @ SV124 @ SV99 )
| ( between @ SV77 @ ( continuous @ SV14 @ SV47 @ SV77 @ SV124 @ SV99 @ SV118 ) @ SV118 ) )
= $true )
| ( ( equidistant @ SV14 @ SV99 @ SV14 @ SV118 )
= $false )
| ( ( equidistant @ SV14 @ SV47 @ SV14 @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(338,plain,
! [SV119: $i,SV78: $i,SV125: $i,SV100: $i,SV48: $i,SV15: $i] :
( ( ( ~ ( between @ SV15 @ SV48 @ SV100 ) )
= $true )
| ( ( ~ ( between @ SV48 @ SV125 @ SV100 )
| ( equidistant @ SV15 @ SV125 @ SV15 @ ( continuous @ SV15 @ SV48 @ SV78 @ SV125 @ SV100 @ SV119 ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV100 @ SV15 @ SV119 )
= $false )
| ( ( equidistant @ SV15 @ SV48 @ SV15 @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(339,plain,
! [SV128: $i,SV70: $i,SV127: $i,SV6: $i,SV123: $i,SV92: $i,SV111: $i,SV39: $i] :
( ( ( equidistant @ SV39 @ SV111 @ SV92 @ SV123 )
= $false )
| ( ( ~ ( equidistant @ SV6 @ SV127 @ SV70 @ SV128 )
| ~ ( equidistant @ SV39 @ SV127 @ SV92 @ SV128 )
| ~ ( between @ SV6 @ SV39 @ SV111 )
| ~ ( between @ SV70 @ SV92 @ SV123 )
| ( SV6 = SV39 )
| ( equidistant @ SV111 @ SV127 @ SV123 @ SV128 ) )
= $true )
| ( ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[335]) ).
thf(340,plain,
! [SV73: $i,SV43: $i,SV114: $i,SV95: $i,SV10: $i] :
( ( ( between @ SV10 @ SV95 @ SV114 )
= $true )
| ( ( ( between @ SV95 @ SV114 @ SV10 )
| ( between @ SV114 @ SV10 @ SV95 )
| ( SV43 = SV73 ) )
= $true )
| ( ( equidistant @ SV114 @ SV43 @ SV114 @ SV73 )
= $false )
| ( ( equidistant @ SV95 @ SV43 @ SV95 @ SV73 )
= $false )
| ( ( equidistant @ SV10 @ SV43 @ SV10 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[336]) ).
thf(341,plain,
! [SV118: $i,SV77: $i,SV124: $i,SV99: $i,SV47: $i,SV14: $i] :
( ( ( between @ SV14 @ SV47 @ SV99 )
= $false )
| ( ( ~ ( between @ SV47 @ SV124 @ SV99 )
| ( between @ SV77 @ ( continuous @ SV14 @ SV47 @ SV77 @ SV124 @ SV99 @ SV118 ) @ SV118 ) )
= $true )
| ( ( equidistant @ SV14 @ SV99 @ SV14 @ SV118 )
= $false )
| ( ( equidistant @ SV14 @ SV47 @ SV14 @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(342,plain,
! [SV119: $i,SV78: $i,SV125: $i,SV100: $i,SV48: $i,SV15: $i] :
( ( ( between @ SV15 @ SV48 @ SV100 )
= $false )
| ( ( ~ ( between @ SV48 @ SV125 @ SV100 )
| ( equidistant @ SV15 @ SV125 @ SV15 @ ( continuous @ SV15 @ SV48 @ SV78 @ SV125 @ SV100 @ SV119 ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV100 @ SV15 @ SV119 )
= $false )
| ( ( equidistant @ SV15 @ SV48 @ SV15 @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[338]) ).
thf(343,plain,
! [SV123: $i,SV111: $i,SV92: $i,SV39: $i,SV128: $i,SV70: $i,SV127: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV127 @ SV70 @ SV128 ) )
= $true )
| ( ( ~ ( equidistant @ SV39 @ SV127 @ SV92 @ SV128 )
| ~ ( between @ SV6 @ SV39 @ SV111 )
| ~ ( between @ SV70 @ SV92 @ SV123 )
| ( SV6 = SV39 )
| ( equidistant @ SV111 @ SV127 @ SV123 @ SV128 ) )
= $true )
| ( ( equidistant @ SV39 @ SV111 @ SV92 @ SV123 )
= $false )
| ( ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[339]) ).
thf(344,plain,
! [SV73: $i,SV43: $i,SV10: $i,SV114: $i,SV95: $i] :
( ( ( between @ SV95 @ SV114 @ SV10 )
= $true )
| ( ( ( between @ SV114 @ SV10 @ SV95 )
| ( SV43 = SV73 ) )
= $true )
| ( ( between @ SV10 @ SV95 @ SV114 )
= $true )
| ( ( equidistant @ SV114 @ SV43 @ SV114 @ SV73 )
= $false )
| ( ( equidistant @ SV95 @ SV43 @ SV95 @ SV73 )
= $false )
| ( ( equidistant @ SV10 @ SV43 @ SV10 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[340]) ).
thf(345,plain,
! [SV118: $i,SV14: $i,SV77: $i,SV99: $i,SV124: $i,SV47: $i] :
( ( ( ~ ( between @ SV47 @ SV124 @ SV99 ) )
= $true )
| ( ( between @ SV77 @ ( continuous @ SV14 @ SV47 @ SV77 @ SV124 @ SV99 @ SV118 ) @ SV118 )
= $true )
| ( ( between @ SV14 @ SV47 @ SV99 )
= $false )
| ( ( equidistant @ SV14 @ SV99 @ SV14 @ SV118 )
= $false )
| ( ( equidistant @ SV14 @ SV47 @ SV14 @ SV77 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[341]) ).
thf(346,plain,
! [SV119: $i,SV78: $i,SV15: $i,SV100: $i,SV125: $i,SV48: $i] :
( ( ( ~ ( between @ SV48 @ SV125 @ SV100 ) )
= $true )
| ( ( equidistant @ SV15 @ SV125 @ SV15 @ ( continuous @ SV15 @ SV48 @ SV78 @ SV125 @ SV100 @ SV119 ) )
= $true )
| ( ( between @ SV15 @ SV48 @ SV100 )
= $false )
| ( ( equidistant @ SV15 @ SV100 @ SV15 @ SV119 )
= $false )
| ( ( equidistant @ SV15 @ SV48 @ SV15 @ SV78 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[342]) ).
thf(347,plain,
! [SV123: $i,SV111: $i,SV92: $i,SV39: $i,SV128: $i,SV70: $i,SV127: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV127 @ SV70 @ SV128 )
= $false )
| ( ( ~ ( equidistant @ SV39 @ SV127 @ SV92 @ SV128 )
| ~ ( between @ SV6 @ SV39 @ SV111 )
| ~ ( between @ SV70 @ SV92 @ SV123 )
| ( SV6 = SV39 )
| ( equidistant @ SV111 @ SV127 @ SV123 @ SV128 ) )
= $true )
| ( ( equidistant @ SV39 @ SV111 @ SV92 @ SV123 )
= $false )
| ( ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[343]) ).
thf(348,plain,
! [SV73: $i,SV43: $i,SV95: $i,SV10: $i,SV114: $i] :
( ( ( between @ SV114 @ SV10 @ SV95 )
= $true )
| ( ( SV43 = SV73 )
= $true )
| ( ( between @ SV95 @ SV114 @ SV10 )
= $true )
| ( ( between @ SV10 @ SV95 @ SV114 )
= $true )
| ( ( equidistant @ SV114 @ SV43 @ SV114 @ SV73 )
= $false )
| ( ( equidistant @ SV95 @ SV43 @ SV95 @ SV73 )
= $false )
| ( ( equidistant @ SV10 @ SV43 @ SV10 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[344]) ).
thf(349,plain,
! [SV118: $i,SV14: $i,SV77: $i,SV99: $i,SV124: $i,SV47: $i] :
( ( ( between @ SV47 @ SV124 @ SV99 )
= $false )
| ( ( between @ SV77 @ ( continuous @ SV14 @ SV47 @ SV77 @ SV124 @ SV99 @ SV118 ) @ SV118 )
= $true )
| ( ( between @ SV14 @ SV47 @ SV99 )
= $false )
| ( ( equidistant @ SV14 @ SV99 @ SV14 @ SV118 )
= $false )
| ( ( equidistant @ SV14 @ SV47 @ SV14 @ SV77 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[345]) ).
thf(350,plain,
! [SV119: $i,SV78: $i,SV15: $i,SV100: $i,SV125: $i,SV48: $i] :
( ( ( between @ SV48 @ SV125 @ SV100 )
= $false )
| ( ( equidistant @ SV15 @ SV125 @ SV15 @ ( continuous @ SV15 @ SV48 @ SV78 @ SV125 @ SV100 @ SV119 ) )
= $true )
| ( ( between @ SV15 @ SV48 @ SV100 )
= $false )
| ( ( equidistant @ SV15 @ SV100 @ SV15 @ SV119 )
= $false )
| ( ( equidistant @ SV15 @ SV48 @ SV15 @ SV78 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(351,plain,
! [SV123: $i,SV70: $i,SV111: $i,SV6: $i,SV128: $i,SV92: $i,SV127: $i,SV39: $i] :
( ( ( ~ ( equidistant @ SV39 @ SV127 @ SV92 @ SV128 ) )
= $true )
| ( ( ~ ( between @ SV6 @ SV39 @ SV111 )
| ~ ( between @ SV70 @ SV92 @ SV123 )
| ( SV6 = SV39 )
| ( equidistant @ SV111 @ SV127 @ SV123 @ SV128 ) )
= $true )
| ( ( equidistant @ SV6 @ SV127 @ SV70 @ SV128 )
= $false )
| ( ( equidistant @ SV39 @ SV111 @ SV92 @ SV123 )
= $false )
| ( ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(352,plain,
! [SV123: $i,SV70: $i,SV111: $i,SV6: $i,SV128: $i,SV92: $i,SV127: $i,SV39: $i] :
( ( ( equidistant @ SV39 @ SV127 @ SV92 @ SV128 )
= $false )
| ( ( ~ ( between @ SV6 @ SV39 @ SV111 )
| ~ ( between @ SV70 @ SV92 @ SV123 )
| ( SV6 = SV39 )
| ( equidistant @ SV111 @ SV127 @ SV123 @ SV128 ) )
= $true )
| ( ( equidistant @ SV6 @ SV127 @ SV70 @ SV128 )
= $false )
| ( ( equidistant @ SV39 @ SV111 @ SV92 @ SV123 )
= $false )
| ( ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[351]) ).
thf(353,plain,
! [SV128: $i,SV127: $i,SV123: $i,SV92: $i,SV70: $i,SV111: $i,SV39: $i,SV6: $i] :
( ( ( ~ ( between @ SV6 @ SV39 @ SV111 ) )
= $true )
| ( ( ~ ( between @ SV70 @ SV92 @ SV123 )
| ( SV6 = SV39 )
| ( equidistant @ SV111 @ SV127 @ SV123 @ SV128 ) )
= $true )
| ( ( equidistant @ SV39 @ SV127 @ SV92 @ SV128 )
= $false )
| ( ( equidistant @ SV6 @ SV127 @ SV70 @ SV128 )
= $false )
| ( ( equidistant @ SV39 @ SV111 @ SV92 @ SV123 )
= $false )
| ( ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[352]) ).
thf(354,plain,
! [SV128: $i,SV127: $i,SV123: $i,SV92: $i,SV70: $i,SV111: $i,SV39: $i,SV6: $i] :
( ( ( between @ SV6 @ SV39 @ SV111 )
= $false )
| ( ( ~ ( between @ SV70 @ SV92 @ SV123 )
| ( SV6 = SV39 )
| ( equidistant @ SV111 @ SV127 @ SV123 @ SV128 ) )
= $true )
| ( ( equidistant @ SV39 @ SV127 @ SV92 @ SV128 )
= $false )
| ( ( equidistant @ SV6 @ SV127 @ SV70 @ SV128 )
= $false )
| ( ( equidistant @ SV39 @ SV111 @ SV92 @ SV123 )
= $false )
| ( ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[353]) ).
thf(355,plain,
! [SV128: $i,SV127: $i,SV111: $i,SV39: $i,SV6: $i,SV123: $i,SV92: $i,SV70: $i] :
( ( ( ~ ( between @ SV70 @ SV92 @ SV123 ) )
= $true )
| ( ( ( SV6 = SV39 )
| ( equidistant @ SV111 @ SV127 @ SV123 @ SV128 ) )
= $true )
| ( ( between @ SV6 @ SV39 @ SV111 )
= $false )
| ( ( equidistant @ SV39 @ SV127 @ SV92 @ SV128 )
= $false )
| ( ( equidistant @ SV6 @ SV127 @ SV70 @ SV128 )
= $false )
| ( ( equidistant @ SV39 @ SV111 @ SV92 @ SV123 )
= $false )
| ( ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[354]) ).
thf(356,plain,
! [SV128: $i,SV127: $i,SV111: $i,SV39: $i,SV6: $i,SV123: $i,SV92: $i,SV70: $i] :
( ( ( between @ SV70 @ SV92 @ SV123 )
= $false )
| ( ( ( SV6 = SV39 )
| ( equidistant @ SV111 @ SV127 @ SV123 @ SV128 ) )
= $true )
| ( ( between @ SV6 @ SV39 @ SV111 )
= $false )
| ( ( equidistant @ SV39 @ SV127 @ SV92 @ SV128 )
= $false )
| ( ( equidistant @ SV6 @ SV127 @ SV70 @ SV128 )
= $false )
| ( ( equidistant @ SV39 @ SV111 @ SV92 @ SV123 )
= $false )
| ( ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[355]) ).
thf(357,plain,
! [SV92: $i,SV70: $i,SV128: $i,SV123: $i,SV127: $i,SV111: $i,SV39: $i,SV6: $i] :
( ( ( SV6 = SV39 )
= $true )
| ( ( equidistant @ SV111 @ SV127 @ SV123 @ SV128 )
= $true )
| ( ( between @ SV70 @ SV92 @ SV123 )
= $false )
| ( ( between @ SV6 @ SV39 @ SV111 )
= $false )
| ( ( equidistant @ SV39 @ SV127 @ SV92 @ SV128 )
= $false )
| ( ( equidistant @ SV6 @ SV127 @ SV70 @ SV128 )
= $false )
| ( ( equidistant @ SV39 @ SV111 @ SV92 @ SV123 )
= $false )
| ( ( equidistant @ SV6 @ SV39 @ SV70 @ SV92 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[356]) ).
thf(358,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[88,357,350,349,348,334,331,330,329,326,318,317,303,289,288,287,286,285,284,283,254,251,250,233,231,230,224,198,197,196,186,185,170,166,164,144,143,142,132,91,90,89]) ).
thf(359,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[358]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO025-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.17 % Computer : n001.cluster.edu
% 0.08/0.17 % Model : x86_64 x86_64
% 0.08/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.17 % Memory : 8046.5625MB
% 0.08/0.17 % OS : Linux 6.8.0-71-generic
% 0.08/0.17 % CPULimit : 300
% 0.08/0.17 % WCLimit : 300
% 0.08/0.17 % DateTime : Tue Oct 6 10:07:59 UTC 2026
% 0.08/0.17 % CPUTime :
% 0.08/0.17 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 66.16/11.29
% 66.16/11.29 No.of.Axioms: 41
% 66.16/11.29
% 66.16/11.29 Length.of.Defs: 0
% 66.16/11.29
% 66.16/11.29 Contains.Choice.Funs: false
% 66.16/11.29 ............
% 66.16/11.29
% 66.16/11.29 ********************************
% 66.16/11.29 * All subproblems solved! *
% 66.16/11.29 ********************************
% 66.16/11.29 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:41,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:358,loop_count:0,foatp_calls:1,translation:fof_full)
% 66.16/11.29
% 66.16/11.29 %**** Beginning of derivation protocol ****
% 66.16/11.29 % SZS output start CNFRefutation
% See solution above
% 66.16/11.29
% 66.16/11.29 %**** End of derivation protocol ****
% 66.16/11.29 %**** no. of clauses in derivation: 359 ****
% 66.16/11.29 %**** clause counter: 358 ****
% 66.16/11.29
% 66.16/11.29 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:1,axioms:41,ps:0,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:358,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------