%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO035-3 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n005.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 10:17:37 AM UTC 2026
% Result : Unsatisfiable 0.48s 0.32s
% Output : CNFRefutation 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 29
% Syntax : Number of formulae : 291 ( 184 unt; 0 typ; 0 def)
% Number of atoms : 1884 ( 546 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 4965 ( 467 ~; 701 |; 0 &;3797 @)
% ( 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 : 16 ( 13 usr; 8 con; 0-6 aty)
% Number of variables : 1318 ( 0 ^;1318 !; 0 ?;1318 :)
% 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_u,type,
u: $i ).
thf(tp_v,type,
v: $i ).
thf(tp_w,type,
w: $i ).
thf(1,axiom,
! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ~ ( equidistant @ W @ X @ Y @ Z )
| ( equidistant @ U @ V @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5) ).
thf(2,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_5) ).
thf(3,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_4) ).
thf(4,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_3) ).
thf(5,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_2) ).
thf(6,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_1) ).
thf(7,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3) ).
thf(8,axiom,
! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
thf(9,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
thf(10,axiom,
! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity2) ).
thf(11,axiom,
! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity1) ).
thf(12,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid3) ).
thf(13,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid2) ).
thf(14,axiom,
! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid1) ).
thf(15,axiom,
! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ W @ X @ V )
| ~ ( equidistant @ Y @ W @ Y @ V )
| ~ ( equidistant @ Z @ W @ Z @ V )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y )
| ( W = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_dimension) ).
thf(16,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
thf(17,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).
thf(18,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).
thf(19,axiom,
! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ Y @ X @ W )
| ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch2) ).
thf(20,axiom,
! [U: $i,V: $i,W: $i,Y: $i,X: $i] :
( ~ ( between @ U @ V @ W )
| ~ ( between @ Y @ X @ W )
| ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inner_pasch1) ).
thf(21,axiom,
! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(22,axiom,
! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i,V: $i,V1: $i] :
( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
| ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
| ~ ( equidistant @ X @ V @ X1 @ V1 )
| ~ ( equidistant @ Y @ V @ Y1 @ V1 )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equidistant @ Z @ V @ Z1 @ V1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).
thf(23,axiom,
! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
thf(24,axiom,
! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
thf(25,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(26,axiom,
! [X: $i,Y: $i,Z: $i,V: $i,V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
thf(27,axiom,
! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(28,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(29,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[28]) ).
thf(30,negated_conjecture,
( v
!= ( extension @ u @ v @ w @ w ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_null_extension) ).
thf(31,plain,
$false = $false,
inference(unfold_def,[status(thm)],[29]) ).
thf(32,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)],[1]) ).
thf(33,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)],[2]) ).
thf(34,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)],[3]) ).
thf(35,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)],[4]) ).
thf(36,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)],[5]) ).
thf(37,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)],[6]) ).
thf(38,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)],[7]) ).
thf(39,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)],[8]) ).
thf(40,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(41,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)],[10]) ).
thf(42,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)],[11]) ).
thf(43,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)],[12]) ).
thf(44,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)],[13]) ).
thf(45,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)],[14]) ).
thf(46,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)],[15]) ).
thf(47,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(48,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(49,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(50,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)],[19]) ).
thf(51,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)],[20]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(53,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)],[22]) ).
thf(54,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(57,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)],[26]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[27]) ).
thf(59,plain,
( ( v
!= ( extension @ u @ v @ w @ w ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(60,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[31]) ).
thf(61,plain,
( ( v
!= ( extension @ u @ v @ w @ w ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(62,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(63,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)],[57]) ).
thf(64,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(65,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(66,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(67,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)],[53]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(69,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)],[51]) ).
thf(70,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)],[50]) ).
thf(71,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(72,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(73,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(74,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)],[46]) ).
thf(75,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)],[45]) ).
thf(76,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)],[44]) ).
thf(77,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)],[43]) ).
thf(78,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)],[42]) ).
thf(79,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)],[41]) ).
thf(80,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(81,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(82,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(83,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(84,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(85,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(86,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(87,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(88,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ~ ( equidistant @ W @ X @ Y @ Z )
| ( equidistant @ U @ V @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(89,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[60]) ).
thf(90,plain,
( ( v
!= ( extension @ u @ v @ w @ w ) )
= $true ),
inference(unfold_def,[status(thm)],[61]) ).
thf(91,plain,
! [SV1: $i] :
( ( ! [SY107: $i] : ( equidistant @ SV1 @ SY107 @ SY107 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(92,plain,
! [SV2: $i] :
( ( ! [SY108: $i,SY109: $i,SY110: $i,SY111: $i,SY112: $i] :
( ~ ( equidistant @ SV2 @ SY108 @ SY109 @ SY110 )
| ~ ( equidistant @ SV2 @ SY108 @ SY111 @ SY112 )
| ( equidistant @ SY109 @ SY110 @ SY111 @ SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(93,plain,
! [SV3: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ~ ( equidistant @ SV3 @ SY113 @ SY114 @ SY114 )
| ( SV3 = SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(94,plain,
! [SV4: $i] :
( ( ! [SY115: $i,SY116: $i,SY117: $i] : ( between @ SV4 @ SY115 @ ( extension @ SV4 @ SY115 @ SY116 @ SY117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(95,plain,
! [SV5: $i] :
( ( ! [SY118: $i,SY119: $i,SY120: $i] : ( equidistant @ SV5 @ ( extension @ SY118 @ SV5 @ SY119 @ SY120 ) @ SY119 @ SY120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(96,plain,
! [SV6: $i] :
( ( ! [SY121: $i,SY122: $i,SY123: $i,SY124: $i,SY125: $i,SY126: $i,SY127: $i] :
( ~ ( equidistant @ SV6 @ SY121 @ SY122 @ SY123 )
| ~ ( equidistant @ SY121 @ SY124 @ SY123 @ SY125 )
| ~ ( equidistant @ SV6 @ SY126 @ SY122 @ SY127 )
| ~ ( equidistant @ SY121 @ SY126 @ SY123 @ SY127 )
| ~ ( between @ SV6 @ SY121 @ SY124 )
| ~ ( between @ SY122 @ SY123 @ SY125 )
| ( SV6 = SY121 )
| ( equidistant @ SY124 @ SY126 @ SY125 @ SY127 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(97,plain,
! [SV7: $i] :
( ( ! [SY128: $i] :
( ~ ( between @ SV7 @ SY128 @ SV7 )
| ( SV7 = SY128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(98,plain,
! [SV8: $i] :
( ( ! [SY129: $i,SY130: $i,SY131: $i,SY132: $i] :
( ~ ( between @ SV8 @ SY129 @ SY130 )
| ~ ( between @ SY131 @ SY132 @ SY130 )
| ( between @ SY129 @ ( inner_pasch @ SV8 @ SY129 @ SY130 @ SY132 @ SY131 ) @ SY131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(99,plain,
! [SV9: $i] :
( ( ! [SY133: $i,SY134: $i,SY135: $i,SY136: $i] :
( ~ ( between @ SV9 @ SY133 @ SY134 )
| ~ ( between @ SY135 @ SY136 @ SY134 )
| ( between @ SY136 @ ( inner_pasch @ SV9 @ SY133 @ SY134 @ SY136 @ SY135 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(100,plain,
( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(101,plain,
( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(102,plain,
( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[73]) ).
thf(103,plain,
! [SV10: $i] :
( ( ! [SY137: $i,SY138: $i,SY139: $i,SY140: $i] :
( ~ ( equidistant @ SV10 @ SY137 @ SV10 @ SY138 )
| ~ ( equidistant @ SY139 @ SY137 @ SY139 @ SY138 )
| ~ ( equidistant @ SY140 @ SY137 @ SY140 @ SY138 )
| ( between @ SV10 @ SY139 @ SY140 )
| ( between @ SY139 @ SY140 @ SV10 )
| ( between @ SY140 @ SV10 @ SY139 )
| ( SY137 = SY138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(104,plain,
! [SV11: $i] :
( ( ! [SY141: $i,SY142: $i,SY143: $i,SY144: $i] :
( ~ ( between @ SV11 @ SY141 @ SY142 )
| ~ ( between @ SY143 @ SY141 @ SY144 )
| ( SV11 = SY141 )
| ( between @ SV11 @ SY143 @ ( euclid1 @ SV11 @ SY143 @ SY141 @ SY144 @ SY142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(105,plain,
! [SV12: $i] :
( ( ! [SY145: $i,SY146: $i,SY147: $i,SY148: $i] :
( ~ ( between @ SV12 @ SY145 @ SY146 )
| ~ ( between @ SY147 @ SY145 @ SY148 )
| ( SV12 = SY145 )
| ( between @ SV12 @ SY148 @ ( euclid2 @ SV12 @ SY147 @ SY145 @ SY148 @ SY146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(106,plain,
! [SV13: $i] :
( ( ! [SY149: $i,SY150: $i,SY151: $i,SY152: $i] :
( ~ ( between @ SV13 @ SY149 @ SY150 )
| ~ ( between @ SY151 @ SY149 @ SY152 )
| ( SV13 = SY149 )
| ( between @ ( euclid1 @ SV13 @ SY151 @ SY149 @ SY152 @ SY150 ) @ SY150 @ ( euclid2 @ SV13 @ SY151 @ SY149 @ SY152 @ SY150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(107,plain,
! [SV14: $i] :
( ( ! [SY153: $i,SY154: $i,SY155: $i,SY156: $i,SY157: $i] :
( ~ ( equidistant @ SV14 @ SY153 @ SV14 @ SY154 )
| ~ ( equidistant @ SV14 @ SY155 @ SV14 @ SY156 )
| ~ ( between @ SV14 @ SY153 @ SY155 )
| ~ ( between @ SY153 @ SY157 @ SY155 )
| ( between @ SY154 @ ( continuous @ SV14 @ SY153 @ SY154 @ SY157 @ SY155 @ SY156 ) @ SY156 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(108,plain,
! [SV15: $i] :
( ( ! [SY158: $i,SY159: $i,SY160: $i,SY161: $i,SY162: $i] :
( ~ ( equidistant @ SV15 @ SY158 @ SV15 @ SY159 )
| ~ ( equidistant @ SV15 @ SY160 @ SV15 @ SY161 )
| ~ ( between @ SV15 @ SY158 @ SY160 )
| ~ ( between @ SY158 @ SY162 @ SY160 )
| ( equidistant @ SV15 @ SY162 @ SV15 @ ( continuous @ SV15 @ SY158 @ SY159 @ SY162 @ SY160 @ SY161 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(109,plain,
! [SV16: $i] :
( ( ! [SY163: $i] : ( equidistant @ SV16 @ SY163 @ SV16 @ SY163 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(110,plain,
! [SV17: $i] :
( ( ! [SY164: $i,SY165: $i,SY166: $i] :
( ~ ( equidistant @ SV17 @ SY164 @ SY165 @ SY166 )
| ( equidistant @ SY165 @ SY166 @ SV17 @ SY164 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(111,plain,
! [SV18: $i] :
( ( ! [SY167: $i,SY168: $i,SY169: $i] :
( ~ ( equidistant @ SV18 @ SY167 @ SY168 @ SY169 )
| ( equidistant @ SY167 @ SV18 @ SY168 @ SY169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(112,plain,
! [SV19: $i] :
( ( ! [SY170: $i,SY171: $i,SY172: $i] :
( ~ ( equidistant @ SV19 @ SY170 @ SY171 @ SY172 )
| ( equidistant @ SV19 @ SY170 @ SY172 @ SY171 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(113,plain,
! [SV20: $i] :
( ( ! [SY173: $i,SY174: $i,SY175: $i] :
( ~ ( equidistant @ SV20 @ SY173 @ SY174 @ SY175 )
| ( equidistant @ SY173 @ SV20 @ SY175 @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(114,plain,
! [SV21: $i] :
( ( ! [SY176: $i,SY177: $i,SY178: $i] :
( ~ ( equidistant @ SV21 @ SY176 @ SY177 @ SY178 )
| ( equidistant @ SY177 @ SY178 @ SY176 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(115,plain,
! [SV22: $i] :
( ( ! [SY179: $i,SY180: $i,SY181: $i] :
( ~ ( equidistant @ SV22 @ SY179 @ SY180 @ SY181 )
| ( equidistant @ SY181 @ SY180 @ SV22 @ SY179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(116,plain,
! [SV23: $i] :
( ( ! [SY182: $i,SY183: $i,SY184: $i] :
( ~ ( equidistant @ SV23 @ SY182 @ SY183 @ SY184 )
| ( equidistant @ SY184 @ SY183 @ SY182 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(117,plain,
! [SV24: $i] :
( ( ! [SY185: $i,SY186: $i,SY187: $i,SY188: $i,SY189: $i] :
( ~ ( equidistant @ SV24 @ SY185 @ SY186 @ SY187 )
| ~ ( equidistant @ SY186 @ SY187 @ SY188 @ SY189 )
| ( equidistant @ SV24 @ SY185 @ SY188 @ SY189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(118,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(119,plain,
( ( v
= ( extension @ u @ v @ w @ w ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(120,plain,
! [SV25: $i,SV1: $i] :
( ( equidistant @ SV1 @ SV25 @ SV25 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(121,plain,
! [SV26: $i,SV2: $i] :
( ( ! [SY190: $i,SY191: $i,SY192: $i,SY193: $i] :
( ~ ( equidistant @ SV2 @ SV26 @ SY190 @ SY191 )
| ~ ( equidistant @ SV2 @ SV26 @ SY192 @ SY193 )
| ( equidistant @ SY190 @ SY191 @ SY192 @ SY193 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(122,plain,
! [SV27: $i,SV3: $i] :
( ( ! [SY194: $i] :
( ~ ( equidistant @ SV3 @ SV27 @ SY194 @ SY194 )
| ( SV3 = SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(123,plain,
! [SV28: $i,SV4: $i] :
( ( ! [SY195: $i,SY196: $i] : ( between @ SV4 @ SV28 @ ( extension @ SV4 @ SV28 @ SY195 @ SY196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(124,plain,
! [SV29: $i,SV5: $i] :
( ( ! [SY197: $i,SY198: $i] : ( equidistant @ SV5 @ ( extension @ SV29 @ SV5 @ SY197 @ SY198 ) @ SY197 @ SY198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(125,plain,
! [SV30: $i,SV6: $i] :
( ( ! [SY199: $i,SY200: $i,SY201: $i,SY202: $i,SY203: $i,SY204: $i] :
( ~ ( equidistant @ SV6 @ SV30 @ SY199 @ SY200 )
| ~ ( equidistant @ SV30 @ SY201 @ SY200 @ SY202 )
| ~ ( equidistant @ SV6 @ SY203 @ SY199 @ SY204 )
| ~ ( equidistant @ SV30 @ SY203 @ SY200 @ SY204 )
| ~ ( between @ SV6 @ SV30 @ SY201 )
| ~ ( between @ SY199 @ SY200 @ SY202 )
| ( SV6 = SV30 )
| ( equidistant @ SY201 @ SY203 @ SY202 @ SY204 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(126,plain,
! [SV31: $i,SV7: $i] :
( ( ~ ( between @ SV7 @ SV31 @ SV7 )
| ( SV7 = SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(127,plain,
! [SV32: $i,SV8: $i] :
( ( ! [SY205: $i,SY206: $i,SY207: $i] :
( ~ ( between @ SV8 @ SV32 @ SY205 )
| ~ ( between @ SY206 @ SY207 @ SY205 )
| ( between @ SV32 @ ( inner_pasch @ SV8 @ SV32 @ SY205 @ SY207 @ SY206 ) @ SY206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(128,plain,
! [SV33: $i,SV9: $i] :
( ( ! [SY208: $i,SY209: $i,SY210: $i] :
( ~ ( between @ SV9 @ SV33 @ SY208 )
| ~ ( between @ SY209 @ SY210 @ SY208 )
| ( between @ SY210 @ ( inner_pasch @ SV9 @ SV33 @ SY208 @ SY210 @ SY209 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(129,plain,
! [SV34: $i,SV10: $i] :
( ( ! [SY211: $i,SY212: $i,SY213: $i] :
( ~ ( equidistant @ SV10 @ SV34 @ SV10 @ SY211 )
| ~ ( equidistant @ SY212 @ SV34 @ SY212 @ SY211 )
| ~ ( equidistant @ SY213 @ SV34 @ SY213 @ SY211 )
| ( between @ SV10 @ SY212 @ SY213 )
| ( between @ SY212 @ SY213 @ SV10 )
| ( between @ SY213 @ SV10 @ SY212 )
| ( SV34 = SY211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(130,plain,
! [SV35: $i,SV11: $i] :
( ( ! [SY214: $i,SY215: $i,SY216: $i] :
( ~ ( between @ SV11 @ SV35 @ SY214 )
| ~ ( between @ SY215 @ SV35 @ SY216 )
| ( SV11 = SV35 )
| ( between @ SV11 @ SY215 @ ( euclid1 @ SV11 @ SY215 @ SV35 @ SY216 @ SY214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(131,plain,
! [SV36: $i,SV12: $i] :
( ( ! [SY217: $i,SY218: $i,SY219: $i] :
( ~ ( between @ SV12 @ SV36 @ SY217 )
| ~ ( between @ SY218 @ SV36 @ SY219 )
| ( SV12 = SV36 )
| ( between @ SV12 @ SY219 @ ( euclid2 @ SV12 @ SY218 @ SV36 @ SY219 @ SY217 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(132,plain,
! [SV37: $i,SV13: $i] :
( ( ! [SY220: $i,SY221: $i,SY222: $i] :
( ~ ( between @ SV13 @ SV37 @ SY220 )
| ~ ( between @ SY221 @ SV37 @ SY222 )
| ( SV13 = SV37 )
| ( between @ ( euclid1 @ SV13 @ SY221 @ SV37 @ SY222 @ SY220 ) @ SY220 @ ( euclid2 @ SV13 @ SY221 @ SV37 @ SY222 @ SY220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(133,plain,
! [SV38: $i,SV14: $i] :
( ( ! [SY223: $i,SY224: $i,SY225: $i,SY226: $i] :
( ~ ( equidistant @ SV14 @ SV38 @ SV14 @ SY223 )
| ~ ( equidistant @ SV14 @ SY224 @ SV14 @ SY225 )
| ~ ( between @ SV14 @ SV38 @ SY224 )
| ~ ( between @ SV38 @ SY226 @ SY224 )
| ( between @ SY223 @ ( continuous @ SV14 @ SV38 @ SY223 @ SY226 @ SY224 @ SY225 ) @ SY225 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(134,plain,
! [SV39: $i,SV15: $i] :
( ( ! [SY227: $i,SY228: $i,SY229: $i,SY230: $i] :
( ~ ( equidistant @ SV15 @ SV39 @ SV15 @ SY227 )
| ~ ( equidistant @ SV15 @ SY228 @ SV15 @ SY229 )
| ~ ( between @ SV15 @ SV39 @ SY228 )
| ~ ( between @ SV39 @ SY230 @ SY228 )
| ( equidistant @ SV15 @ SY230 @ SV15 @ ( continuous @ SV15 @ SV39 @ SY227 @ SY230 @ SY228 @ SY229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(135,plain,
! [SV40: $i,SV16: $i] :
( ( equidistant @ SV16 @ SV40 @ SV16 @ SV40 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(136,plain,
! [SV41: $i,SV17: $i] :
( ( ! [SY231: $i,SY232: $i] :
( ~ ( equidistant @ SV17 @ SV41 @ SY231 @ SY232 )
| ( equidistant @ SY231 @ SY232 @ SV17 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(137,plain,
! [SV42: $i,SV18: $i] :
( ( ! [SY233: $i,SY234: $i] :
( ~ ( equidistant @ SV18 @ SV42 @ SY233 @ SY234 )
| ( equidistant @ SV42 @ SV18 @ SY233 @ SY234 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(138,plain,
! [SV43: $i,SV19: $i] :
( ( ! [SY235: $i,SY236: $i] :
( ~ ( equidistant @ SV19 @ SV43 @ SY235 @ SY236 )
| ( equidistant @ SV19 @ SV43 @ SY236 @ SY235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(139,plain,
! [SV44: $i,SV20: $i] :
( ( ! [SY237: $i,SY238: $i] :
( ~ ( equidistant @ SV20 @ SV44 @ SY237 @ SY238 )
| ( equidistant @ SV44 @ SV20 @ SY238 @ SY237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(140,plain,
! [SV45: $i,SV21: $i] :
( ( ! [SY239: $i,SY240: $i] :
( ~ ( equidistant @ SV21 @ SV45 @ SY239 @ SY240 )
| ( equidistant @ SY239 @ SY240 @ SV45 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(141,plain,
! [SV46: $i,SV22: $i] :
( ( ! [SY241: $i,SY242: $i] :
( ~ ( equidistant @ SV22 @ SV46 @ SY241 @ SY242 )
| ( equidistant @ SY242 @ SY241 @ SV22 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(142,plain,
! [SV47: $i,SV23: $i] :
( ( ! [SY243: $i,SY244: $i] :
( ~ ( equidistant @ SV23 @ SV47 @ SY243 @ SY244 )
| ( equidistant @ SY244 @ SY243 @ SV47 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(143,plain,
! [SV48: $i,SV24: $i] :
( ( ! [SY245: $i,SY246: $i,SY247: $i,SY248: $i] :
( ~ ( equidistant @ SV24 @ SV48 @ SY245 @ SY246 )
| ~ ( equidistant @ SY245 @ SY246 @ SY247 @ SY248 )
| ( equidistant @ SV24 @ SV48 @ SY247 @ SY248 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(144,plain,
! [SV49: $i,SV26: $i,SV2: $i] :
( ( ! [SY249: $i,SY250: $i,SY251: $i] :
( ~ ( equidistant @ SV2 @ SV26 @ SV49 @ SY249 )
| ~ ( equidistant @ SV2 @ SV26 @ SY250 @ SY251 )
| ( equidistant @ SV49 @ SY249 @ SY250 @ SY251 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(145,plain,
! [SV50: $i,SV27: $i,SV3: $i] :
( ( ~ ( equidistant @ SV3 @ SV27 @ SV50 @ SV50 )
| ( SV3 = SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(146,plain,
! [SV51: $i,SV28: $i,SV4: $i] :
( ( ! [SY252: $i] : ( between @ SV4 @ SV28 @ ( extension @ SV4 @ SV28 @ SV51 @ SY252 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(147,plain,
! [SV52: $i,SV29: $i,SV5: $i] :
( ( ! [SY253: $i] : ( equidistant @ SV5 @ ( extension @ SV29 @ SV5 @ SV52 @ SY253 ) @ SV52 @ SY253 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(148,plain,
! [SV53: $i,SV30: $i,SV6: $i] :
( ( ! [SY254: $i,SY255: $i,SY256: $i,SY257: $i,SY258: $i] :
( ~ ( equidistant @ SV6 @ SV30 @ SV53 @ SY254 )
| ~ ( equidistant @ SV30 @ SY255 @ SY254 @ SY256 )
| ~ ( equidistant @ SV6 @ SY257 @ SV53 @ SY258 )
| ~ ( equidistant @ SV30 @ SY257 @ SY254 @ SY258 )
| ~ ( between @ SV6 @ SV30 @ SY255 )
| ~ ( between @ SV53 @ SY254 @ SY256 )
| ( SV6 = SV30 )
| ( equidistant @ SY255 @ SY257 @ SY256 @ SY258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(149,plain,
! [SV31: $i,SV7: $i] :
( ( ( ~ ( between @ SV7 @ SV31 @ SV7 ) )
= $true )
| ( ( SV7 = SV31 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(150,plain,
! [SV54: $i,SV32: $i,SV8: $i] :
( ( ! [SY259: $i,SY260: $i] :
( ~ ( between @ SV8 @ SV32 @ SV54 )
| ~ ( between @ SY259 @ SY260 @ SV54 )
| ( between @ SV32 @ ( inner_pasch @ SV8 @ SV32 @ SV54 @ SY260 @ SY259 ) @ SY259 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(151,plain,
! [SV55: $i,SV33: $i,SV9: $i] :
( ( ! [SY261: $i,SY262: $i] :
( ~ ( between @ SV9 @ SV33 @ SV55 )
| ~ ( between @ SY261 @ SY262 @ SV55 )
| ( between @ SY262 @ ( inner_pasch @ SV9 @ SV33 @ SV55 @ SY262 @ SY261 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(152,plain,
! [SV56: $i,SV34: $i,SV10: $i] :
( ( ! [SY263: $i,SY264: $i] :
( ~ ( equidistant @ SV10 @ SV34 @ SV10 @ SV56 )
| ~ ( equidistant @ SY263 @ SV34 @ SY263 @ SV56 )
| ~ ( equidistant @ SY264 @ SV34 @ SY264 @ SV56 )
| ( between @ SV10 @ SY263 @ SY264 )
| ( between @ SY263 @ SY264 @ SV10 )
| ( between @ SY264 @ SV10 @ SY263 )
| ( SV34 = SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(153,plain,
! [SV57: $i,SV35: $i,SV11: $i] :
( ( ! [SY265: $i,SY266: $i] :
( ~ ( between @ SV11 @ SV35 @ SV57 )
| ~ ( between @ SY265 @ SV35 @ SY266 )
| ( SV11 = SV35 )
| ( between @ SV11 @ SY265 @ ( euclid1 @ SV11 @ SY265 @ SV35 @ SY266 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(154,plain,
! [SV58: $i,SV36: $i,SV12: $i] :
( ( ! [SY267: $i,SY268: $i] :
( ~ ( between @ SV12 @ SV36 @ SV58 )
| ~ ( between @ SY267 @ SV36 @ SY268 )
| ( SV12 = SV36 )
| ( between @ SV12 @ SY268 @ ( euclid2 @ SV12 @ SY267 @ SV36 @ SY268 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(155,plain,
! [SV59: $i,SV37: $i,SV13: $i] :
( ( ! [SY269: $i,SY270: $i] :
( ~ ( between @ SV13 @ SV37 @ SV59 )
| ~ ( between @ SY269 @ SV37 @ SY270 )
| ( SV13 = SV37 )
| ( between @ ( euclid1 @ SV13 @ SY269 @ SV37 @ SY270 @ SV59 ) @ SV59 @ ( euclid2 @ SV13 @ SY269 @ SV37 @ SY270 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(156,plain,
! [SV60: $i,SV38: $i,SV14: $i] :
( ( ! [SY271: $i,SY272: $i,SY273: $i] :
( ~ ( equidistant @ SV14 @ SV38 @ SV14 @ SV60 )
| ~ ( equidistant @ SV14 @ SY271 @ SV14 @ SY272 )
| ~ ( between @ SV14 @ SV38 @ SY271 )
| ~ ( between @ SV38 @ SY273 @ SY271 )
| ( between @ SV60 @ ( continuous @ SV14 @ SV38 @ SV60 @ SY273 @ SY271 @ SY272 ) @ SY272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(157,plain,
! [SV61: $i,SV39: $i,SV15: $i] :
( ( ! [SY274: $i,SY275: $i,SY276: $i] :
( ~ ( equidistant @ SV15 @ SV39 @ SV15 @ SV61 )
| ~ ( equidistant @ SV15 @ SY274 @ SV15 @ SY275 )
| ~ ( between @ SV15 @ SV39 @ SY274 )
| ~ ( between @ SV39 @ SY276 @ SY274 )
| ( equidistant @ SV15 @ SY276 @ SV15 @ ( continuous @ SV15 @ SV39 @ SV61 @ SY276 @ SY274 @ SY275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(158,plain,
! [SV62: $i,SV41: $i,SV17: $i] :
( ( ! [SY277: $i] :
( ~ ( equidistant @ SV17 @ SV41 @ SV62 @ SY277 )
| ( equidistant @ SV62 @ SY277 @ SV17 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(159,plain,
! [SV63: $i,SV42: $i,SV18: $i] :
( ( ! [SY278: $i] :
( ~ ( equidistant @ SV18 @ SV42 @ SV63 @ SY278 )
| ( equidistant @ SV42 @ SV18 @ SV63 @ SY278 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(160,plain,
! [SV64: $i,SV43: $i,SV19: $i] :
( ( ! [SY279: $i] :
( ~ ( equidistant @ SV19 @ SV43 @ SV64 @ SY279 )
| ( equidistant @ SV19 @ SV43 @ SY279 @ SV64 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(161,plain,
! [SV65: $i,SV44: $i,SV20: $i] :
( ( ! [SY280: $i] :
( ~ ( equidistant @ SV20 @ SV44 @ SV65 @ SY280 )
| ( equidistant @ SV44 @ SV20 @ SY280 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(162,plain,
! [SV66: $i,SV45: $i,SV21: $i] :
( ( ! [SY281: $i] :
( ~ ( equidistant @ SV21 @ SV45 @ SV66 @ SY281 )
| ( equidistant @ SV66 @ SY281 @ SV45 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[140]) ).
thf(163,plain,
! [SV67: $i,SV46: $i,SV22: $i] :
( ( ! [SY282: $i] :
( ~ ( equidistant @ SV22 @ SV46 @ SV67 @ SY282 )
| ( equidistant @ SY282 @ SV67 @ SV22 @ SV46 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(164,plain,
! [SV68: $i,SV47: $i,SV23: $i] :
( ( ! [SY283: $i] :
( ~ ( equidistant @ SV23 @ SV47 @ SV68 @ SY283 )
| ( equidistant @ SY283 @ SV68 @ SV47 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(165,plain,
! [SV69: $i,SV48: $i,SV24: $i] :
( ( ! [SY284: $i,SY285: $i,SY286: $i] :
( ~ ( equidistant @ SV24 @ SV48 @ SV69 @ SY284 )
| ~ ( equidistant @ SV69 @ SY284 @ SY285 @ SY286 )
| ( equidistant @ SV24 @ SV48 @ SY285 @ SY286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(166,plain,
! [SV70: $i,SV49: $i,SV26: $i,SV2: $i] :
( ( ! [SY287: $i,SY288: $i] :
( ~ ( equidistant @ SV2 @ SV26 @ SV49 @ SV70 )
| ~ ( equidistant @ SV2 @ SV26 @ SY287 @ SY288 )
| ( equidistant @ SV49 @ SV70 @ SY287 @ SY288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(167,plain,
! [SV50: $i,SV27: $i,SV3: $i] :
( ( ( ~ ( equidistant @ SV3 @ SV27 @ SV50 @ SV50 ) )
= $true )
| ( ( SV3 = SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(168,plain,
! [SV71: $i,SV51: $i,SV28: $i,SV4: $i] :
( ( between @ SV4 @ SV28 @ ( extension @ SV4 @ SV28 @ SV51 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(169,plain,
! [SV72: $i,SV52: $i,SV29: $i,SV5: $i] :
( ( equidistant @ SV5 @ ( extension @ SV29 @ SV5 @ SV52 @ SV72 ) @ SV52 @ SV72 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(170,plain,
! [SV73: $i,SV53: $i,SV30: $i,SV6: $i] :
( ( ! [SY289: $i,SY290: $i,SY291: $i,SY292: $i] :
( ~ ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
| ~ ( equidistant @ SV30 @ SY289 @ SV73 @ SY290 )
| ~ ( equidistant @ SV6 @ SY291 @ SV53 @ SY292 )
| ~ ( equidistant @ SV30 @ SY291 @ SV73 @ SY292 )
| ~ ( between @ SV6 @ SV30 @ SY289 )
| ~ ( between @ SV53 @ SV73 @ SY290 )
| ( SV6 = SV30 )
| ( equidistant @ SY289 @ SY291 @ SY290 @ SY292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(171,plain,
! [SV31: $i,SV7: $i] :
( ( ( between @ SV7 @ SV31 @ SV7 )
= $false )
| ( ( SV7 = SV31 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(172,plain,
! [SV74: $i,SV54: $i,SV32: $i,SV8: $i] :
( ( ! [SY293: $i] :
( ~ ( between @ SV8 @ SV32 @ SV54 )
| ~ ( between @ SV74 @ SY293 @ SV54 )
| ( between @ SV32 @ ( inner_pasch @ SV8 @ SV32 @ SV54 @ SY293 @ SV74 ) @ SV74 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(173,plain,
! [SV75: $i,SV55: $i,SV33: $i,SV9: $i] :
( ( ! [SY294: $i] :
( ~ ( between @ SV9 @ SV33 @ SV55 )
| ~ ( between @ SV75 @ SY294 @ SV55 )
| ( between @ SY294 @ ( inner_pasch @ SV9 @ SV33 @ SV55 @ SY294 @ SV75 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(174,plain,
! [SV76: $i,SV56: $i,SV34: $i,SV10: $i] :
( ( ! [SY295: $i] :
( ~ ( equidistant @ SV10 @ SV34 @ SV10 @ SV56 )
| ~ ( equidistant @ SV76 @ SV34 @ SV76 @ SV56 )
| ~ ( equidistant @ SY295 @ SV34 @ SY295 @ SV56 )
| ( between @ SV10 @ SV76 @ SY295 )
| ( between @ SV76 @ SY295 @ SV10 )
| ( between @ SY295 @ SV10 @ SV76 )
| ( SV34 = SV56 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(175,plain,
! [SV77: $i,SV57: $i,SV35: $i,SV11: $i] :
( ( ! [SY296: $i] :
( ~ ( between @ SV11 @ SV35 @ SV57 )
| ~ ( between @ SV77 @ SV35 @ SY296 )
| ( SV11 = SV35 )
| ( between @ SV11 @ SV77 @ ( euclid1 @ SV11 @ SV77 @ SV35 @ SY296 @ SV57 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(176,plain,
! [SV78: $i,SV58: $i,SV36: $i,SV12: $i] :
( ( ! [SY297: $i] :
( ~ ( between @ SV12 @ SV36 @ SV58 )
| ~ ( between @ SV78 @ SV36 @ SY297 )
| ( SV12 = SV36 )
| ( between @ SV12 @ SY297 @ ( euclid2 @ SV12 @ SV78 @ SV36 @ SY297 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(177,plain,
! [SV79: $i,SV59: $i,SV37: $i,SV13: $i] :
( ( ! [SY298: $i] :
( ~ ( between @ SV13 @ SV37 @ SV59 )
| ~ ( between @ SV79 @ SV37 @ SY298 )
| ( SV13 = SV37 )
| ( between @ ( euclid1 @ SV13 @ SV79 @ SV37 @ SY298 @ SV59 ) @ SV59 @ ( euclid2 @ SV13 @ SV79 @ SV37 @ SY298 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(178,plain,
! [SV80: $i,SV60: $i,SV38: $i,SV14: $i] :
( ( ! [SY299: $i,SY300: $i] :
( ~ ( equidistant @ SV14 @ SV38 @ SV14 @ SV60 )
| ~ ( equidistant @ SV14 @ SV80 @ SV14 @ SY299 )
| ~ ( between @ SV14 @ SV38 @ SV80 )
| ~ ( between @ SV38 @ SY300 @ SV80 )
| ( between @ SV60 @ ( continuous @ SV14 @ SV38 @ SV60 @ SY300 @ SV80 @ SY299 ) @ SY299 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(179,plain,
! [SV81: $i,SV61: $i,SV39: $i,SV15: $i] :
( ( ! [SY301: $i,SY302: $i] :
( ~ ( equidistant @ SV15 @ SV39 @ SV15 @ SV61 )
| ~ ( equidistant @ SV15 @ SV81 @ SV15 @ SY301 )
| ~ ( between @ SV15 @ SV39 @ SV81 )
| ~ ( between @ SV39 @ SY302 @ SV81 )
| ( equidistant @ SV15 @ SY302 @ SV15 @ ( continuous @ SV15 @ SV39 @ SV61 @ SY302 @ SV81 @ SY301 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(180,plain,
! [SV82: $i,SV62: $i,SV41: $i,SV17: $i] :
( ( ~ ( equidistant @ SV17 @ SV41 @ SV62 @ SV82 )
| ( equidistant @ SV62 @ SV82 @ SV17 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(181,plain,
! [SV83: $i,SV63: $i,SV42: $i,SV18: $i] :
( ( ~ ( equidistant @ SV18 @ SV42 @ SV63 @ SV83 )
| ( equidistant @ SV42 @ SV18 @ SV63 @ SV83 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(182,plain,
! [SV84: $i,SV64: $i,SV43: $i,SV19: $i] :
( ( ~ ( equidistant @ SV19 @ SV43 @ SV64 @ SV84 )
| ( equidistant @ SV19 @ SV43 @ SV84 @ SV64 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(183,plain,
! [SV85: $i,SV65: $i,SV44: $i,SV20: $i] :
( ( ~ ( equidistant @ SV20 @ SV44 @ SV65 @ SV85 )
| ( equidistant @ SV44 @ SV20 @ SV85 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(184,plain,
! [SV86: $i,SV66: $i,SV45: $i,SV21: $i] :
( ( ~ ( equidistant @ SV21 @ SV45 @ SV66 @ SV86 )
| ( equidistant @ SV66 @ SV86 @ SV45 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(185,plain,
! [SV87: $i,SV67: $i,SV46: $i,SV22: $i] :
( ( ~ ( equidistant @ SV22 @ SV46 @ SV67 @ SV87 )
| ( equidistant @ SV87 @ SV67 @ SV22 @ SV46 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(186,plain,
! [SV88: $i,SV68: $i,SV47: $i,SV23: $i] :
( ( ~ ( equidistant @ SV23 @ SV47 @ SV68 @ SV88 )
| ( equidistant @ SV88 @ SV68 @ SV47 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(187,plain,
! [SV89: $i,SV69: $i,SV48: $i,SV24: $i] :
( ( ! [SY303: $i,SY304: $i] :
( ~ ( equidistant @ SV24 @ SV48 @ SV69 @ SV89 )
| ~ ( equidistant @ SV69 @ SV89 @ SY303 @ SY304 )
| ( equidistant @ SV24 @ SV48 @ SY303 @ SY304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(188,plain,
! [SV90: $i,SV70: $i,SV49: $i,SV26: $i,SV2: $i] :
( ( ! [SY305: $i] :
( ~ ( equidistant @ SV2 @ SV26 @ SV49 @ SV70 )
| ~ ( equidistant @ SV2 @ SV26 @ SV90 @ SY305 )
| ( equidistant @ SV49 @ SV70 @ SV90 @ SY305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(189,plain,
! [SV50: $i,SV27: $i,SV3: $i] :
( ( ( equidistant @ SV3 @ SV27 @ SV50 @ SV50 )
= $false )
| ( ( SV3 = SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(190,plain,
! [SV91: $i,SV73: $i,SV53: $i,SV30: $i,SV6: $i] :
( ( ! [SY306: $i,SY307: $i,SY308: $i] :
( ~ ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
| ~ ( equidistant @ SV30 @ SV91 @ SV73 @ SY306 )
| ~ ( equidistant @ SV6 @ SY307 @ SV53 @ SY308 )
| ~ ( equidistant @ SV30 @ SY307 @ SV73 @ SY308 )
| ~ ( between @ SV6 @ SV30 @ SV91 )
| ~ ( between @ SV53 @ SV73 @ SY306 )
| ( SV6 = SV30 )
| ( equidistant @ SV91 @ SY307 @ SY306 @ SY308 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(191,plain,
! [SV92: $i,SV74: $i,SV54: $i,SV32: $i,SV8: $i] :
( ( ~ ( between @ SV8 @ SV32 @ SV54 )
| ~ ( between @ SV74 @ SV92 @ SV54 )
| ( between @ SV32 @ ( inner_pasch @ SV8 @ SV32 @ SV54 @ SV92 @ SV74 ) @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(192,plain,
! [SV93: $i,SV75: $i,SV55: $i,SV33: $i,SV9: $i] :
( ( ~ ( between @ SV9 @ SV33 @ SV55 )
| ~ ( between @ SV75 @ SV93 @ SV55 )
| ( between @ SV93 @ ( inner_pasch @ SV9 @ SV33 @ SV55 @ SV93 @ SV75 ) @ SV9 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(193,plain,
! [SV94: $i,SV76: $i,SV56: $i,SV34: $i,SV10: $i] :
( ( ~ ( equidistant @ SV10 @ SV34 @ SV10 @ SV56 )
| ~ ( equidistant @ SV76 @ SV34 @ SV76 @ SV56 )
| ~ ( equidistant @ SV94 @ SV34 @ SV94 @ SV56 )
| ( between @ SV10 @ SV76 @ SV94 )
| ( between @ SV76 @ SV94 @ SV10 )
| ( between @ SV94 @ SV10 @ SV76 )
| ( SV34 = SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(194,plain,
! [SV95: $i,SV77: $i,SV57: $i,SV35: $i,SV11: $i] :
( ( ~ ( between @ SV11 @ SV35 @ SV57 )
| ~ ( between @ SV77 @ SV35 @ SV95 )
| ( SV11 = SV35 )
| ( between @ SV11 @ SV77 @ ( euclid1 @ SV11 @ SV77 @ SV35 @ SV95 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(195,plain,
! [SV96: $i,SV78: $i,SV58: $i,SV36: $i,SV12: $i] :
( ( ~ ( between @ SV12 @ SV36 @ SV58 )
| ~ ( between @ SV78 @ SV36 @ SV96 )
| ( SV12 = SV36 )
| ( between @ SV12 @ SV96 @ ( euclid2 @ SV12 @ SV78 @ SV36 @ SV96 @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(196,plain,
! [SV97: $i,SV79: $i,SV59: $i,SV37: $i,SV13: $i] :
( ( ~ ( between @ SV13 @ SV37 @ SV59 )
| ~ ( between @ SV79 @ SV37 @ SV97 )
| ( SV13 = SV37 )
| ( between @ ( euclid1 @ SV13 @ SV79 @ SV37 @ SV97 @ SV59 ) @ SV59 @ ( euclid2 @ SV13 @ SV79 @ SV37 @ SV97 @ SV59 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(197,plain,
! [SV98: $i,SV80: $i,SV60: $i,SV38: $i,SV14: $i] :
( ( ! [SY309: $i] :
( ~ ( equidistant @ SV14 @ SV38 @ SV14 @ SV60 )
| ~ ( equidistant @ SV14 @ SV80 @ SV14 @ SV98 )
| ~ ( between @ SV14 @ SV38 @ SV80 )
| ~ ( between @ SV38 @ SY309 @ SV80 )
| ( between @ SV60 @ ( continuous @ SV14 @ SV38 @ SV60 @ SY309 @ SV80 @ SV98 ) @ SV98 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(198,plain,
! [SV99: $i,SV81: $i,SV61: $i,SV39: $i,SV15: $i] :
( ( ! [SY310: $i] :
( ~ ( equidistant @ SV15 @ SV39 @ SV15 @ SV61 )
| ~ ( equidistant @ SV15 @ SV81 @ SV15 @ SV99 )
| ~ ( between @ SV15 @ SV39 @ SV81 )
| ~ ( between @ SV39 @ SY310 @ SV81 )
| ( equidistant @ SV15 @ SY310 @ SV15 @ ( continuous @ SV15 @ SV39 @ SV61 @ SY310 @ SV81 @ SV99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(199,plain,
! [SV82: $i,SV62: $i,SV41: $i,SV17: $i] :
( ( ( ~ ( equidistant @ SV17 @ SV41 @ SV62 @ SV82 ) )
= $true )
| ( ( equidistant @ SV62 @ SV82 @ SV17 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[180]) ).
thf(200,plain,
! [SV83: $i,SV63: $i,SV42: $i,SV18: $i] :
( ( ( ~ ( equidistant @ SV18 @ SV42 @ SV63 @ SV83 ) )
= $true )
| ( ( equidistant @ SV42 @ SV18 @ SV63 @ SV83 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(201,plain,
! [SV84: $i,SV64: $i,SV43: $i,SV19: $i] :
( ( ( ~ ( equidistant @ SV19 @ SV43 @ SV64 @ SV84 ) )
= $true )
| ( ( equidistant @ SV19 @ SV43 @ SV84 @ SV64 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[182]) ).
thf(202,plain,
! [SV85: $i,SV65: $i,SV44: $i,SV20: $i] :
( ( ( ~ ( equidistant @ SV20 @ SV44 @ SV65 @ SV85 ) )
= $true )
| ( ( equidistant @ SV44 @ SV20 @ SV85 @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[183]) ).
thf(203,plain,
! [SV86: $i,SV66: $i,SV45: $i,SV21: $i] :
( ( ( ~ ( equidistant @ SV21 @ SV45 @ SV66 @ SV86 ) )
= $true )
| ( ( equidistant @ SV66 @ SV86 @ SV45 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(204,plain,
! [SV87: $i,SV67: $i,SV46: $i,SV22: $i] :
( ( ( ~ ( equidistant @ SV22 @ SV46 @ SV67 @ SV87 ) )
= $true )
| ( ( equidistant @ SV87 @ SV67 @ SV22 @ SV46 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(205,plain,
! [SV88: $i,SV68: $i,SV47: $i,SV23: $i] :
( ( ( ~ ( equidistant @ SV23 @ SV47 @ SV68 @ SV88 ) )
= $true )
| ( ( equidistant @ SV88 @ SV68 @ SV47 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(206,plain,
! [SV100: $i,SV89: $i,SV69: $i,SV48: $i,SV24: $i] :
( ( ! [SY311: $i] :
( ~ ( equidistant @ SV24 @ SV48 @ SV69 @ SV89 )
| ~ ( equidistant @ SV69 @ SV89 @ SV100 @ SY311 )
| ( equidistant @ SV24 @ SV48 @ SV100 @ SY311 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(207,plain,
! [SV101: $i,SV90: $i,SV70: $i,SV49: $i,SV26: $i,SV2: $i] :
( ( ~ ( equidistant @ SV2 @ SV26 @ SV49 @ SV70 )
| ~ ( equidistant @ SV2 @ SV26 @ SV90 @ SV101 )
| ( equidistant @ SV49 @ SV70 @ SV90 @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(208,plain,
! [SV102: $i,SV91: $i,SV73: $i,SV53: $i,SV30: $i,SV6: $i] :
( ( ! [SY312: $i,SY313: $i] :
( ~ ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
| ~ ( equidistant @ SV30 @ SV91 @ SV73 @ SV102 )
| ~ ( equidistant @ SV6 @ SY312 @ SV53 @ SY313 )
| ~ ( equidistant @ SV30 @ SY312 @ SV73 @ SY313 )
| ~ ( between @ SV6 @ SV30 @ SV91 )
| ~ ( between @ SV53 @ SV73 @ SV102 )
| ( SV6 = SV30 )
| ( equidistant @ SV91 @ SY312 @ SV102 @ SY313 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(209,plain,
! [SV92: $i,SV74: $i,SV54: $i,SV32: $i,SV8: $i] :
( ( ( ~ ( between @ SV8 @ SV32 @ SV54 ) )
= $true )
| ( ( ~ ( between @ SV74 @ SV92 @ SV54 )
| ( between @ SV32 @ ( inner_pasch @ SV8 @ SV32 @ SV54 @ SV92 @ SV74 ) @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(210,plain,
! [SV93: $i,SV75: $i,SV55: $i,SV33: $i,SV9: $i] :
( ( ( ~ ( between @ SV9 @ SV33 @ SV55 ) )
= $true )
| ( ( ~ ( between @ SV75 @ SV93 @ SV55 )
| ( between @ SV93 @ ( inner_pasch @ SV9 @ SV33 @ SV55 @ SV93 @ SV75 ) @ SV9 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(211,plain,
! [SV94: $i,SV76: $i,SV56: $i,SV34: $i,SV10: $i] :
( ( ( ~ ( equidistant @ SV10 @ SV34 @ SV10 @ SV56 ) )
= $true )
| ( ( ~ ( equidistant @ SV76 @ SV34 @ SV76 @ SV56 )
| ~ ( equidistant @ SV94 @ SV34 @ SV94 @ SV56 )
| ( between @ SV10 @ SV76 @ SV94 )
| ( between @ SV76 @ SV94 @ SV10 )
| ( between @ SV94 @ SV10 @ SV76 )
| ( SV34 = SV56 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(212,plain,
! [SV95: $i,SV77: $i,SV57: $i,SV35: $i,SV11: $i] :
( ( ( ~ ( between @ SV11 @ SV35 @ SV57 ) )
= $true )
| ( ( ~ ( between @ SV77 @ SV35 @ SV95 )
| ( SV11 = SV35 )
| ( between @ SV11 @ SV77 @ ( euclid1 @ SV11 @ SV77 @ SV35 @ SV95 @ SV57 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(213,plain,
! [SV96: $i,SV78: $i,SV58: $i,SV36: $i,SV12: $i] :
( ( ( ~ ( between @ SV12 @ SV36 @ SV58 ) )
= $true )
| ( ( ~ ( between @ SV78 @ SV36 @ SV96 )
| ( SV12 = SV36 )
| ( between @ SV12 @ SV96 @ ( euclid2 @ SV12 @ SV78 @ SV36 @ SV96 @ SV58 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(214,plain,
! [SV97: $i,SV79: $i,SV59: $i,SV37: $i,SV13: $i] :
( ( ( ~ ( between @ SV13 @ SV37 @ SV59 ) )
= $true )
| ( ( ~ ( between @ SV79 @ SV37 @ SV97 )
| ( SV13 = SV37 )
| ( between @ ( euclid1 @ SV13 @ SV79 @ SV37 @ SV97 @ SV59 ) @ SV59 @ ( euclid2 @ SV13 @ SV79 @ SV37 @ SV97 @ SV59 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(215,plain,
! [SV103: $i,SV98: $i,SV80: $i,SV60: $i,SV38: $i,SV14: $i] :
( ( ~ ( equidistant @ SV14 @ SV38 @ SV14 @ SV60 )
| ~ ( equidistant @ SV14 @ SV80 @ SV14 @ SV98 )
| ~ ( between @ SV14 @ SV38 @ SV80 )
| ~ ( between @ SV38 @ SV103 @ SV80 )
| ( between @ SV60 @ ( continuous @ SV14 @ SV38 @ SV60 @ SV103 @ SV80 @ SV98 ) @ SV98 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(216,plain,
! [SV104: $i,SV99: $i,SV81: $i,SV61: $i,SV39: $i,SV15: $i] :
( ( ~ ( equidistant @ SV15 @ SV39 @ SV15 @ SV61 )
| ~ ( equidistant @ SV15 @ SV81 @ SV15 @ SV99 )
| ~ ( between @ SV15 @ SV39 @ SV81 )
| ~ ( between @ SV39 @ SV104 @ SV81 )
| ( equidistant @ SV15 @ SV104 @ SV15 @ ( continuous @ SV15 @ SV39 @ SV61 @ SV104 @ SV81 @ SV99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(217,plain,
! [SV82: $i,SV62: $i,SV41: $i,SV17: $i] :
( ( ( equidistant @ SV17 @ SV41 @ SV62 @ SV82 )
= $false )
| ( ( equidistant @ SV62 @ SV82 @ SV17 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(218,plain,
! [SV83: $i,SV63: $i,SV42: $i,SV18: $i] :
( ( ( equidistant @ SV18 @ SV42 @ SV63 @ SV83 )
= $false )
| ( ( equidistant @ SV42 @ SV18 @ SV63 @ SV83 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(219,plain,
! [SV84: $i,SV64: $i,SV43: $i,SV19: $i] :
( ( ( equidistant @ SV19 @ SV43 @ SV64 @ SV84 )
= $false )
| ( ( equidistant @ SV19 @ SV43 @ SV84 @ SV64 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[201]) ).
thf(220,plain,
! [SV85: $i,SV65: $i,SV44: $i,SV20: $i] :
( ( ( equidistant @ SV20 @ SV44 @ SV65 @ SV85 )
= $false )
| ( ( equidistant @ SV44 @ SV20 @ SV85 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[202]) ).
thf(221,plain,
! [SV86: $i,SV66: $i,SV45: $i,SV21: $i] :
( ( ( equidistant @ SV21 @ SV45 @ SV66 @ SV86 )
= $false )
| ( ( equidistant @ SV66 @ SV86 @ SV45 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(222,plain,
! [SV87: $i,SV67: $i,SV46: $i,SV22: $i] :
( ( ( equidistant @ SV22 @ SV46 @ SV67 @ SV87 )
= $false )
| ( ( equidistant @ SV87 @ SV67 @ SV22 @ SV46 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(223,plain,
! [SV88: $i,SV68: $i,SV47: $i,SV23: $i] :
( ( ( equidistant @ SV23 @ SV47 @ SV68 @ SV88 )
= $false )
| ( ( equidistant @ SV88 @ SV68 @ SV47 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[205]) ).
thf(224,plain,
! [SV105: $i,SV100: $i,SV89: $i,SV69: $i,SV48: $i,SV24: $i] :
( ( ~ ( equidistant @ SV24 @ SV48 @ SV69 @ SV89 )
| ~ ( equidistant @ SV69 @ SV89 @ SV100 @ SV105 )
| ( equidistant @ SV24 @ SV48 @ SV100 @ SV105 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[206]) ).
thf(225,plain,
! [SV101: $i,SV90: $i,SV70: $i,SV49: $i,SV26: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV26 @ SV49 @ SV70 ) )
= $true )
| ( ( ~ ( equidistant @ SV2 @ SV26 @ SV90 @ SV101 )
| ( equidistant @ SV49 @ SV70 @ SV90 @ SV101 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(226,plain,
! [SV106: $i,SV102: $i,SV91: $i,SV73: $i,SV53: $i,SV30: $i,SV6: $i] :
( ( ! [SY314: $i] :
( ~ ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
| ~ ( equidistant @ SV30 @ SV91 @ SV73 @ SV102 )
| ~ ( equidistant @ SV6 @ SV106 @ SV53 @ SY314 )
| ~ ( equidistant @ SV30 @ SV106 @ SV73 @ SY314 )
| ~ ( between @ SV6 @ SV30 @ SV91 )
| ~ ( between @ SV53 @ SV73 @ SV102 )
| ( SV6 = SV30 )
| ( equidistant @ SV91 @ SV106 @ SV102 @ SY314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(227,plain,
! [SV92: $i,SV74: $i,SV54: $i,SV32: $i,SV8: $i] :
( ( ( between @ SV8 @ SV32 @ SV54 )
= $false )
| ( ( ~ ( between @ SV74 @ SV92 @ SV54 )
| ( between @ SV32 @ ( inner_pasch @ SV8 @ SV32 @ SV54 @ SV92 @ SV74 ) @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(228,plain,
! [SV93: $i,SV75: $i,SV55: $i,SV33: $i,SV9: $i] :
( ( ( between @ SV9 @ SV33 @ SV55 )
= $false )
| ( ( ~ ( between @ SV75 @ SV93 @ SV55 )
| ( between @ SV93 @ ( inner_pasch @ SV9 @ SV33 @ SV55 @ SV93 @ SV75 ) @ SV9 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(229,plain,
! [SV94: $i,SV76: $i,SV56: $i,SV34: $i,SV10: $i] :
( ( ( equidistant @ SV10 @ SV34 @ SV10 @ SV56 )
= $false )
| ( ( ~ ( equidistant @ SV76 @ SV34 @ SV76 @ SV56 )
| ~ ( equidistant @ SV94 @ SV34 @ SV94 @ SV56 )
| ( between @ SV10 @ SV76 @ SV94 )
| ( between @ SV76 @ SV94 @ SV10 )
| ( between @ SV94 @ SV10 @ SV76 )
| ( SV34 = SV56 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(230,plain,
! [SV95: $i,SV77: $i,SV57: $i,SV35: $i,SV11: $i] :
( ( ( between @ SV11 @ SV35 @ SV57 )
= $false )
| ( ( ~ ( between @ SV77 @ SV35 @ SV95 )
| ( SV11 = SV35 )
| ( between @ SV11 @ SV77 @ ( euclid1 @ SV11 @ SV77 @ SV35 @ SV95 @ SV57 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(231,plain,
! [SV96: $i,SV78: $i,SV58: $i,SV36: $i,SV12: $i] :
( ( ( between @ SV12 @ SV36 @ SV58 )
= $false )
| ( ( ~ ( between @ SV78 @ SV36 @ SV96 )
| ( SV12 = SV36 )
| ( between @ SV12 @ SV96 @ ( euclid2 @ SV12 @ SV78 @ SV36 @ SV96 @ SV58 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(232,plain,
! [SV97: $i,SV79: $i,SV59: $i,SV37: $i,SV13: $i] :
( ( ( between @ SV13 @ SV37 @ SV59 )
= $false )
| ( ( ~ ( between @ SV79 @ SV37 @ SV97 )
| ( SV13 = SV37 )
| ( between @ ( euclid1 @ SV13 @ SV79 @ SV37 @ SV97 @ SV59 ) @ SV59 @ ( euclid2 @ SV13 @ SV79 @ SV37 @ SV97 @ SV59 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[214]) ).
thf(233,plain,
! [SV103: $i,SV98: $i,SV80: $i,SV60: $i,SV38: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV38 @ SV14 @ SV60 ) )
= $true )
| ( ( ~ ( equidistant @ SV14 @ SV80 @ SV14 @ SV98 )
| ~ ( between @ SV14 @ SV38 @ SV80 )
| ~ ( between @ SV38 @ SV103 @ SV80 )
| ( between @ SV60 @ ( continuous @ SV14 @ SV38 @ SV60 @ SV103 @ SV80 @ SV98 ) @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(234,plain,
! [SV104: $i,SV99: $i,SV81: $i,SV61: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV39 @ SV15 @ SV61 ) )
= $true )
| ( ( ~ ( equidistant @ SV15 @ SV81 @ SV15 @ SV99 )
| ~ ( between @ SV15 @ SV39 @ SV81 )
| ~ ( between @ SV39 @ SV104 @ SV81 )
| ( equidistant @ SV15 @ SV104 @ SV15 @ ( continuous @ SV15 @ SV39 @ SV61 @ SV104 @ SV81 @ SV99 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(235,plain,
! [SV105: $i,SV100: $i,SV89: $i,SV69: $i,SV48: $i,SV24: $i] :
( ( ( ~ ( equidistant @ SV24 @ SV48 @ SV69 @ SV89 ) )
= $true )
| ( ( ~ ( equidistant @ SV69 @ SV89 @ SV100 @ SV105 )
| ( equidistant @ SV24 @ SV48 @ SV100 @ SV105 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(236,plain,
! [SV101: $i,SV90: $i,SV70: $i,SV49: $i,SV26: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV26 @ SV49 @ SV70 )
= $false )
| ( ( ~ ( equidistant @ SV2 @ SV26 @ SV90 @ SV101 )
| ( equidistant @ SV49 @ SV70 @ SV90 @ SV101 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(237,plain,
! [SV107: $i,SV106: $i,SV102: $i,SV91: $i,SV73: $i,SV53: $i,SV30: $i,SV6: $i] :
( ( ~ ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
| ~ ( equidistant @ SV30 @ SV91 @ SV73 @ SV102 )
| ~ ( equidistant @ SV6 @ SV106 @ SV53 @ SV107 )
| ~ ( equidistant @ SV30 @ SV106 @ SV73 @ SV107 )
| ~ ( between @ SV6 @ SV30 @ SV91 )
| ~ ( between @ SV53 @ SV73 @ SV102 )
| ( SV6 = SV30 )
| ( equidistant @ SV91 @ SV106 @ SV102 @ SV107 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[226]) ).
thf(238,plain,
! [SV8: $i,SV32: $i,SV54: $i,SV92: $i,SV74: $i] :
( ( ( ~ ( between @ SV74 @ SV92 @ SV54 ) )
= $true )
| ( ( between @ SV32 @ ( inner_pasch @ SV8 @ SV32 @ SV54 @ SV92 @ SV74 ) @ SV74 )
= $true )
| ( ( between @ SV8 @ SV32 @ SV54 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[227]) ).
thf(239,plain,
! [SV33: $i,SV9: $i,SV55: $i,SV93: $i,SV75: $i] :
( ( ( ~ ( between @ SV75 @ SV93 @ SV55 ) )
= $true )
| ( ( between @ SV93 @ ( inner_pasch @ SV9 @ SV33 @ SV55 @ SV93 @ SV75 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV33 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(240,plain,
! [SV10: $i,SV94: $i,SV56: $i,SV34: $i,SV76: $i] :
( ( ( ~ ( equidistant @ SV76 @ SV34 @ SV76 @ SV56 ) )
= $true )
| ( ( ~ ( equidistant @ SV94 @ SV34 @ SV94 @ SV56 )
| ( between @ SV10 @ SV76 @ SV94 )
| ( between @ SV76 @ SV94 @ SV10 )
| ( between @ SV94 @ SV10 @ SV76 )
| ( SV34 = SV56 ) )
= $true )
| ( ( equidistant @ SV10 @ SV34 @ SV10 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[229]) ).
thf(241,plain,
! [SV57: $i,SV11: $i,SV95: $i,SV35: $i,SV77: $i] :
( ( ( ~ ( between @ SV77 @ SV35 @ SV95 ) )
= $true )
| ( ( ( SV11 = SV35 )
| ( between @ SV11 @ SV77 @ ( euclid1 @ SV11 @ SV77 @ SV35 @ SV95 @ SV57 ) ) )
= $true )
| ( ( between @ SV11 @ SV35 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(242,plain,
! [SV58: $i,SV12: $i,SV96: $i,SV36: $i,SV78: $i] :
( ( ( ~ ( between @ SV78 @ SV36 @ SV96 ) )
= $true )
| ( ( ( SV12 = SV36 )
| ( between @ SV12 @ SV96 @ ( euclid2 @ SV12 @ SV78 @ SV36 @ SV96 @ SV58 ) ) )
= $true )
| ( ( between @ SV12 @ SV36 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(243,plain,
! [SV59: $i,SV13: $i,SV97: $i,SV37: $i,SV79: $i] :
( ( ( ~ ( between @ SV79 @ SV37 @ SV97 ) )
= $true )
| ( ( ( SV13 = SV37 )
| ( between @ ( euclid1 @ SV13 @ SV79 @ SV37 @ SV97 @ SV59 ) @ SV59 @ ( euclid2 @ SV13 @ SV79 @ SV37 @ SV97 @ SV59 ) ) )
= $true )
| ( ( between @ SV13 @ SV37 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(244,plain,
! [SV103: $i,SV98: $i,SV80: $i,SV60: $i,SV38: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV38 @ SV14 @ SV60 )
= $false )
| ( ( ~ ( equidistant @ SV14 @ SV80 @ SV14 @ SV98 )
| ~ ( between @ SV14 @ SV38 @ SV80 )
| ~ ( between @ SV38 @ SV103 @ SV80 )
| ( between @ SV60 @ ( continuous @ SV14 @ SV38 @ SV60 @ SV103 @ SV80 @ SV98 ) @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[233]) ).
thf(245,plain,
! [SV104: $i,SV99: $i,SV81: $i,SV61: $i,SV39: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV39 @ SV15 @ SV61 )
= $false )
| ( ( ~ ( equidistant @ SV15 @ SV81 @ SV15 @ SV99 )
| ~ ( between @ SV15 @ SV39 @ SV81 )
| ~ ( between @ SV39 @ SV104 @ SV81 )
| ( equidistant @ SV15 @ SV104 @ SV15 @ ( continuous @ SV15 @ SV39 @ SV61 @ SV104 @ SV81 @ SV99 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[234]) ).
thf(246,plain,
! [SV105: $i,SV100: $i,SV89: $i,SV69: $i,SV48: $i,SV24: $i] :
( ( ( equidistant @ SV24 @ SV48 @ SV69 @ SV89 )
= $false )
| ( ( ~ ( equidistant @ SV69 @ SV89 @ SV100 @ SV105 )
| ( equidistant @ SV24 @ SV48 @ SV100 @ SV105 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[235]) ).
thf(247,plain,
! [SV70: $i,SV49: $i,SV101: $i,SV90: $i,SV26: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV26 @ SV90 @ SV101 ) )
= $true )
| ( ( equidistant @ SV49 @ SV70 @ SV90 @ SV101 )
= $true )
| ( ( equidistant @ SV2 @ SV26 @ SV49 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(248,plain,
! [SV107: $i,SV106: $i,SV102: $i,SV91: $i,SV73: $i,SV53: $i,SV30: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 ) )
= $true )
| ( ( ~ ( equidistant @ SV30 @ SV91 @ SV73 @ SV102 )
| ~ ( equidistant @ SV6 @ SV106 @ SV53 @ SV107 )
| ~ ( equidistant @ SV30 @ SV106 @ SV73 @ SV107 )
| ~ ( between @ SV6 @ SV30 @ SV91 )
| ~ ( between @ SV53 @ SV73 @ SV102 )
| ( SV6 = SV30 )
| ( equidistant @ SV91 @ SV106 @ SV102 @ SV107 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(249,plain,
! [SV8: $i,SV32: $i,SV54: $i,SV92: $i,SV74: $i] :
( ( ( between @ SV74 @ SV92 @ SV54 )
= $false )
| ( ( between @ SV32 @ ( inner_pasch @ SV8 @ SV32 @ SV54 @ SV92 @ SV74 ) @ SV74 )
= $true )
| ( ( between @ SV8 @ SV32 @ SV54 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[238]) ).
thf(250,plain,
! [SV33: $i,SV9: $i,SV55: $i,SV93: $i,SV75: $i] :
( ( ( between @ SV75 @ SV93 @ SV55 )
= $false )
| ( ( between @ SV93 @ ( inner_pasch @ SV9 @ SV33 @ SV55 @ SV93 @ SV75 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV33 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(251,plain,
! [SV10: $i,SV94: $i,SV56: $i,SV34: $i,SV76: $i] :
( ( ( equidistant @ SV76 @ SV34 @ SV76 @ SV56 )
= $false )
| ( ( ~ ( equidistant @ SV94 @ SV34 @ SV94 @ SV56 )
| ( between @ SV10 @ SV76 @ SV94 )
| ( between @ SV76 @ SV94 @ SV10 )
| ( between @ SV94 @ SV10 @ SV76 )
| ( SV34 = SV56 ) )
= $true )
| ( ( equidistant @ SV10 @ SV34 @ SV10 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(252,plain,
! [SV57: $i,SV11: $i,SV95: $i,SV35: $i,SV77: $i] :
( ( ( between @ SV77 @ SV35 @ SV95 )
= $false )
| ( ( ( SV11 = SV35 )
| ( between @ SV11 @ SV77 @ ( euclid1 @ SV11 @ SV77 @ SV35 @ SV95 @ SV57 ) ) )
= $true )
| ( ( between @ SV11 @ SV35 @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[241]) ).
thf(253,plain,
! [SV58: $i,SV12: $i,SV96: $i,SV36: $i,SV78: $i] :
( ( ( between @ SV78 @ SV36 @ SV96 )
= $false )
| ( ( ( SV12 = SV36 )
| ( between @ SV12 @ SV96 @ ( euclid2 @ SV12 @ SV78 @ SV36 @ SV96 @ SV58 ) ) )
= $true )
| ( ( between @ SV12 @ SV36 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[242]) ).
thf(254,plain,
! [SV59: $i,SV13: $i,SV97: $i,SV37: $i,SV79: $i] :
( ( ( between @ SV79 @ SV37 @ SV97 )
= $false )
| ( ( ( SV13 = SV37 )
| ( between @ ( euclid1 @ SV13 @ SV79 @ SV37 @ SV97 @ SV59 ) @ SV59 @ ( euclid2 @ SV13 @ SV79 @ SV37 @ SV97 @ SV59 ) ) )
= $true )
| ( ( between @ SV13 @ SV37 @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[243]) ).
thf(255,plain,
! [SV60: $i,SV103: $i,SV38: $i,SV98: $i,SV80: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV80 @ SV14 @ SV98 ) )
= $true )
| ( ( ~ ( between @ SV14 @ SV38 @ SV80 )
| ~ ( between @ SV38 @ SV103 @ SV80 )
| ( between @ SV60 @ ( continuous @ SV14 @ SV38 @ SV60 @ SV103 @ SV80 @ SV98 ) @ SV98 ) )
= $true )
| ( ( equidistant @ SV14 @ SV38 @ SV14 @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[244]) ).
thf(256,plain,
! [SV61: $i,SV104: $i,SV39: $i,SV99: $i,SV81: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV81 @ SV15 @ SV99 ) )
= $true )
| ( ( ~ ( between @ SV15 @ SV39 @ SV81 )
| ~ ( between @ SV39 @ SV104 @ SV81 )
| ( equidistant @ SV15 @ SV104 @ SV15 @ ( continuous @ SV15 @ SV39 @ SV61 @ SV104 @ SV81 @ SV99 ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV39 @ SV15 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[245]) ).
thf(257,plain,
! [SV48: $i,SV24: $i,SV105: $i,SV100: $i,SV89: $i,SV69: $i] :
( ( ( ~ ( equidistant @ SV69 @ SV89 @ SV100 @ SV105 ) )
= $true )
| ( ( equidistant @ SV24 @ SV48 @ SV100 @ SV105 )
= $true )
| ( ( equidistant @ SV24 @ SV48 @ SV69 @ SV89 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(258,plain,
! [SV70: $i,SV49: $i,SV101: $i,SV90: $i,SV26: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV26 @ SV90 @ SV101 )
= $false )
| ( ( equidistant @ SV49 @ SV70 @ SV90 @ SV101 )
= $true )
| ( ( equidistant @ SV2 @ SV26 @ SV49 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(259,plain,
! [SV107: $i,SV106: $i,SV102: $i,SV91: $i,SV73: $i,SV53: $i,SV30: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
= $false )
| ( ( ~ ( equidistant @ SV30 @ SV91 @ SV73 @ SV102 )
| ~ ( equidistant @ SV6 @ SV106 @ SV53 @ SV107 )
| ~ ( equidistant @ SV30 @ SV106 @ SV73 @ SV107 )
| ~ ( between @ SV6 @ SV30 @ SV91 )
| ~ ( between @ SV53 @ SV73 @ SV102 )
| ( SV6 = SV30 )
| ( equidistant @ SV91 @ SV106 @ SV102 @ SV107 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[248]) ).
thf(260,plain,
! [SV76: $i,SV10: $i,SV56: $i,SV34: $i,SV94: $i] :
( ( ( ~ ( equidistant @ SV94 @ SV34 @ SV94 @ SV56 ) )
= $true )
| ( ( ( between @ SV10 @ SV76 @ SV94 )
| ( between @ SV76 @ SV94 @ SV10 )
| ( between @ SV94 @ SV10 @ SV76 )
| ( SV34 = SV56 ) )
= $true )
| ( ( equidistant @ SV76 @ SV34 @ SV76 @ SV56 )
= $false )
| ( ( equidistant @ SV10 @ SV34 @ SV10 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(261,plain,
! [SV57: $i,SV95: $i,SV77: $i,SV35: $i,SV11: $i] :
( ( ( SV11 = SV35 )
= $true )
| ( ( between @ SV11 @ SV77 @ ( euclid1 @ SV11 @ SV77 @ SV35 @ SV95 @ SV57 ) )
= $true )
| ( ( between @ SV77 @ SV35 @ SV95 )
= $false )
| ( ( between @ SV11 @ SV35 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(262,plain,
! [SV58: $i,SV78: $i,SV96: $i,SV36: $i,SV12: $i] :
( ( ( SV12 = SV36 )
= $true )
| ( ( between @ SV12 @ SV96 @ ( euclid2 @ SV12 @ SV78 @ SV36 @ SV96 @ SV58 ) )
= $true )
| ( ( between @ SV78 @ SV36 @ SV96 )
= $false )
| ( ( between @ SV12 @ SV36 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(263,plain,
! [SV59: $i,SV97: $i,SV79: $i,SV37: $i,SV13: $i] :
( ( ( SV13 = SV37 )
= $true )
| ( ( between @ ( euclid1 @ SV13 @ SV79 @ SV37 @ SV97 @ SV59 ) @ SV59 @ ( euclid2 @ SV13 @ SV79 @ SV37 @ SV97 @ SV59 ) )
= $true )
| ( ( between @ SV79 @ SV37 @ SV97 )
= $false )
| ( ( between @ SV13 @ SV37 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(264,plain,
! [SV60: $i,SV103: $i,SV38: $i,SV98: $i,SV80: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV80 @ SV14 @ SV98 )
= $false )
| ( ( ~ ( between @ SV14 @ SV38 @ SV80 )
| ~ ( between @ SV38 @ SV103 @ SV80 )
| ( between @ SV60 @ ( continuous @ SV14 @ SV38 @ SV60 @ SV103 @ SV80 @ SV98 ) @ SV98 ) )
= $true )
| ( ( equidistant @ SV14 @ SV38 @ SV14 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(265,plain,
! [SV61: $i,SV104: $i,SV39: $i,SV99: $i,SV81: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV81 @ SV15 @ SV99 )
= $false )
| ( ( ~ ( between @ SV15 @ SV39 @ SV81 )
| ~ ( between @ SV39 @ SV104 @ SV81 )
| ( equidistant @ SV15 @ SV104 @ SV15 @ ( continuous @ SV15 @ SV39 @ SV61 @ SV104 @ SV81 @ SV99 ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV39 @ SV15 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(266,plain,
! [SV48: $i,SV24: $i,SV105: $i,SV100: $i,SV89: $i,SV69: $i] :
( ( ( equidistant @ SV69 @ SV89 @ SV100 @ SV105 )
= $false )
| ( ( equidistant @ SV24 @ SV48 @ SV100 @ SV105 )
= $true )
| ( ( equidistant @ SV24 @ SV48 @ SV69 @ SV89 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(267,plain,
! [SV107: $i,SV53: $i,SV106: $i,SV6: $i,SV102: $i,SV73: $i,SV91: $i,SV30: $i] :
( ( ( ~ ( equidistant @ SV30 @ SV91 @ SV73 @ SV102 ) )
= $true )
| ( ( ~ ( equidistant @ SV6 @ SV106 @ SV53 @ SV107 )
| ~ ( equidistant @ SV30 @ SV106 @ SV73 @ SV107 )
| ~ ( between @ SV6 @ SV30 @ SV91 )
| ~ ( between @ SV53 @ SV73 @ SV102 )
| ( SV6 = SV30 )
| ( equidistant @ SV91 @ SV106 @ SV102 @ SV107 ) )
= $true )
| ( ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[259]) ).
thf(268,plain,
! [SV76: $i,SV10: $i,SV56: $i,SV34: $i,SV94: $i] :
( ( ( equidistant @ SV94 @ SV34 @ SV94 @ SV56 )
= $false )
| ( ( ( between @ SV10 @ SV76 @ SV94 )
| ( between @ SV76 @ SV94 @ SV10 )
| ( between @ SV94 @ SV10 @ SV76 )
| ( SV34 = SV56 ) )
= $true )
| ( ( equidistant @ SV76 @ SV34 @ SV76 @ SV56 )
= $false )
| ( ( equidistant @ SV10 @ SV34 @ SV10 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(269,plain,
! [SV98: $i,SV60: $i,SV103: $i,SV80: $i,SV38: $i,SV14: $i] :
( ( ( ~ ( between @ SV14 @ SV38 @ SV80 ) )
= $true )
| ( ( ~ ( between @ SV38 @ SV103 @ SV80 )
| ( between @ SV60 @ ( continuous @ SV14 @ SV38 @ SV60 @ SV103 @ SV80 @ SV98 ) @ SV98 ) )
= $true )
| ( ( equidistant @ SV14 @ SV80 @ SV14 @ SV98 )
= $false )
| ( ( equidistant @ SV14 @ SV38 @ SV14 @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[264]) ).
thf(270,plain,
! [SV99: $i,SV61: $i,SV104: $i,SV81: $i,SV39: $i,SV15: $i] :
( ( ( ~ ( between @ SV15 @ SV39 @ SV81 ) )
= $true )
| ( ( ~ ( between @ SV39 @ SV104 @ SV81 )
| ( equidistant @ SV15 @ SV104 @ SV15 @ ( continuous @ SV15 @ SV39 @ SV61 @ SV104 @ SV81 @ SV99 ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV81 @ SV15 @ SV99 )
= $false )
| ( ( equidistant @ SV15 @ SV39 @ SV15 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(271,plain,
! [SV107: $i,SV53: $i,SV106: $i,SV6: $i,SV102: $i,SV73: $i,SV91: $i,SV30: $i] :
( ( ( equidistant @ SV30 @ SV91 @ SV73 @ SV102 )
= $false )
| ( ( ~ ( equidistant @ SV6 @ SV106 @ SV53 @ SV107 )
| ~ ( equidistant @ SV30 @ SV106 @ SV73 @ SV107 )
| ~ ( between @ SV6 @ SV30 @ SV91 )
| ~ ( between @ SV53 @ SV73 @ SV102 )
| ( SV6 = SV30 )
| ( equidistant @ SV91 @ SV106 @ SV102 @ SV107 ) )
= $true )
| ( ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(272,plain,
! [SV56: $i,SV34: $i,SV94: $i,SV76: $i,SV10: $i] :
( ( ( between @ SV10 @ SV76 @ SV94 )
= $true )
| ( ( ( between @ SV76 @ SV94 @ SV10 )
| ( between @ SV94 @ SV10 @ SV76 )
| ( SV34 = SV56 ) )
= $true )
| ( ( equidistant @ SV94 @ SV34 @ SV94 @ SV56 )
= $false )
| ( ( equidistant @ SV76 @ SV34 @ SV76 @ SV56 )
= $false )
| ( ( equidistant @ SV10 @ SV34 @ SV10 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(273,plain,
! [SV98: $i,SV60: $i,SV103: $i,SV80: $i,SV38: $i,SV14: $i] :
( ( ( between @ SV14 @ SV38 @ SV80 )
= $false )
| ( ( ~ ( between @ SV38 @ SV103 @ SV80 )
| ( between @ SV60 @ ( continuous @ SV14 @ SV38 @ SV60 @ SV103 @ SV80 @ SV98 ) @ SV98 ) )
= $true )
| ( ( equidistant @ SV14 @ SV80 @ SV14 @ SV98 )
= $false )
| ( ( equidistant @ SV14 @ SV38 @ SV14 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[269]) ).
thf(274,plain,
! [SV99: $i,SV61: $i,SV104: $i,SV81: $i,SV39: $i,SV15: $i] :
( ( ( between @ SV15 @ SV39 @ SV81 )
= $false )
| ( ( ~ ( between @ SV39 @ SV104 @ SV81 )
| ( equidistant @ SV15 @ SV104 @ SV15 @ ( continuous @ SV15 @ SV39 @ SV61 @ SV104 @ SV81 @ SV99 ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV81 @ SV15 @ SV99 )
= $false )
| ( ( equidistant @ SV15 @ SV39 @ SV15 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[270]) ).
thf(275,plain,
! [SV102: $i,SV91: $i,SV73: $i,SV30: $i,SV107: $i,SV53: $i,SV106: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV106 @ SV53 @ SV107 ) )
= $true )
| ( ( ~ ( equidistant @ SV30 @ SV106 @ SV73 @ SV107 )
| ~ ( between @ SV6 @ SV30 @ SV91 )
| ~ ( between @ SV53 @ SV73 @ SV102 )
| ( SV6 = SV30 )
| ( equidistant @ SV91 @ SV106 @ SV102 @ SV107 ) )
= $true )
| ( ( equidistant @ SV30 @ SV91 @ SV73 @ SV102 )
= $false )
| ( ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(276,plain,
! [SV56: $i,SV34: $i,SV10: $i,SV94: $i,SV76: $i] :
( ( ( between @ SV76 @ SV94 @ SV10 )
= $true )
| ( ( ( between @ SV94 @ SV10 @ SV76 )
| ( SV34 = SV56 ) )
= $true )
| ( ( between @ SV10 @ SV76 @ SV94 )
= $true )
| ( ( equidistant @ SV94 @ SV34 @ SV94 @ SV56 )
= $false )
| ( ( equidistant @ SV76 @ SV34 @ SV76 @ SV56 )
= $false )
| ( ( equidistant @ SV10 @ SV34 @ SV10 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(277,plain,
! [SV98: $i,SV14: $i,SV60: $i,SV80: $i,SV103: $i,SV38: $i] :
( ( ( ~ ( between @ SV38 @ SV103 @ SV80 ) )
= $true )
| ( ( between @ SV60 @ ( continuous @ SV14 @ SV38 @ SV60 @ SV103 @ SV80 @ SV98 ) @ SV98 )
= $true )
| ( ( between @ SV14 @ SV38 @ SV80 )
= $false )
| ( ( equidistant @ SV14 @ SV80 @ SV14 @ SV98 )
= $false )
| ( ( equidistant @ SV14 @ SV38 @ SV14 @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(278,plain,
! [SV99: $i,SV61: $i,SV15: $i,SV81: $i,SV104: $i,SV39: $i] :
( ( ( ~ ( between @ SV39 @ SV104 @ SV81 ) )
= $true )
| ( ( equidistant @ SV15 @ SV104 @ SV15 @ ( continuous @ SV15 @ SV39 @ SV61 @ SV104 @ SV81 @ SV99 ) )
= $true )
| ( ( between @ SV15 @ SV39 @ SV81 )
= $false )
| ( ( equidistant @ SV15 @ SV81 @ SV15 @ SV99 )
= $false )
| ( ( equidistant @ SV15 @ SV39 @ SV15 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(279,plain,
! [SV102: $i,SV91: $i,SV73: $i,SV30: $i,SV107: $i,SV53: $i,SV106: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV106 @ SV53 @ SV107 )
= $false )
| ( ( ~ ( equidistant @ SV30 @ SV106 @ SV73 @ SV107 )
| ~ ( between @ SV6 @ SV30 @ SV91 )
| ~ ( between @ SV53 @ SV73 @ SV102 )
| ( SV6 = SV30 )
| ( equidistant @ SV91 @ SV106 @ SV102 @ SV107 ) )
= $true )
| ( ( equidistant @ SV30 @ SV91 @ SV73 @ SV102 )
= $false )
| ( ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[275]) ).
thf(280,plain,
! [SV56: $i,SV34: $i,SV76: $i,SV10: $i,SV94: $i] :
( ( ( between @ SV94 @ SV10 @ SV76 )
= $true )
| ( ( SV34 = SV56 )
= $true )
| ( ( between @ SV76 @ SV94 @ SV10 )
= $true )
| ( ( between @ SV10 @ SV76 @ SV94 )
= $true )
| ( ( equidistant @ SV94 @ SV34 @ SV94 @ SV56 )
= $false )
| ( ( equidistant @ SV76 @ SV34 @ SV76 @ SV56 )
= $false )
| ( ( equidistant @ SV10 @ SV34 @ SV10 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(281,plain,
! [SV98: $i,SV14: $i,SV60: $i,SV80: $i,SV103: $i,SV38: $i] :
( ( ( between @ SV38 @ SV103 @ SV80 )
= $false )
| ( ( between @ SV60 @ ( continuous @ SV14 @ SV38 @ SV60 @ SV103 @ SV80 @ SV98 ) @ SV98 )
= $true )
| ( ( between @ SV14 @ SV38 @ SV80 )
= $false )
| ( ( equidistant @ SV14 @ SV80 @ SV14 @ SV98 )
= $false )
| ( ( equidistant @ SV14 @ SV38 @ SV14 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(282,plain,
! [SV99: $i,SV61: $i,SV15: $i,SV81: $i,SV104: $i,SV39: $i] :
( ( ( between @ SV39 @ SV104 @ SV81 )
= $false )
| ( ( equidistant @ SV15 @ SV104 @ SV15 @ ( continuous @ SV15 @ SV39 @ SV61 @ SV104 @ SV81 @ SV99 ) )
= $true )
| ( ( between @ SV15 @ SV39 @ SV81 )
= $false )
| ( ( equidistant @ SV15 @ SV81 @ SV15 @ SV99 )
= $false )
| ( ( equidistant @ SV15 @ SV39 @ SV15 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[278]) ).
thf(283,plain,
! [SV102: $i,SV53: $i,SV91: $i,SV6: $i,SV107: $i,SV73: $i,SV106: $i,SV30: $i] :
( ( ( ~ ( equidistant @ SV30 @ SV106 @ SV73 @ SV107 ) )
= $true )
| ( ( ~ ( between @ SV6 @ SV30 @ SV91 )
| ~ ( between @ SV53 @ SV73 @ SV102 )
| ( SV6 = SV30 )
| ( equidistant @ SV91 @ SV106 @ SV102 @ SV107 ) )
= $true )
| ( ( equidistant @ SV6 @ SV106 @ SV53 @ SV107 )
= $false )
| ( ( equidistant @ SV30 @ SV91 @ SV73 @ SV102 )
= $false )
| ( ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[279]) ).
thf(284,plain,
! [SV102: $i,SV53: $i,SV91: $i,SV6: $i,SV107: $i,SV73: $i,SV106: $i,SV30: $i] :
( ( ( equidistant @ SV30 @ SV106 @ SV73 @ SV107 )
= $false )
| ( ( ~ ( between @ SV6 @ SV30 @ SV91 )
| ~ ( between @ SV53 @ SV73 @ SV102 )
| ( SV6 = SV30 )
| ( equidistant @ SV91 @ SV106 @ SV102 @ SV107 ) )
= $true )
| ( ( equidistant @ SV6 @ SV106 @ SV53 @ SV107 )
= $false )
| ( ( equidistant @ SV30 @ SV91 @ SV73 @ SV102 )
= $false )
| ( ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[283]) ).
thf(285,plain,
! [SV107: $i,SV106: $i,SV102: $i,SV73: $i,SV53: $i,SV91: $i,SV30: $i,SV6: $i] :
( ( ( ~ ( between @ SV6 @ SV30 @ SV91 ) )
= $true )
| ( ( ~ ( between @ SV53 @ SV73 @ SV102 )
| ( SV6 = SV30 )
| ( equidistant @ SV91 @ SV106 @ SV102 @ SV107 ) )
= $true )
| ( ( equidistant @ SV30 @ SV106 @ SV73 @ SV107 )
= $false )
| ( ( equidistant @ SV6 @ SV106 @ SV53 @ SV107 )
= $false )
| ( ( equidistant @ SV30 @ SV91 @ SV73 @ SV102 )
= $false )
| ( ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[284]) ).
thf(286,plain,
! [SV107: $i,SV106: $i,SV102: $i,SV73: $i,SV53: $i,SV91: $i,SV30: $i,SV6: $i] :
( ( ( between @ SV6 @ SV30 @ SV91 )
= $false )
| ( ( ~ ( between @ SV53 @ SV73 @ SV102 )
| ( SV6 = SV30 )
| ( equidistant @ SV91 @ SV106 @ SV102 @ SV107 ) )
= $true )
| ( ( equidistant @ SV30 @ SV106 @ SV73 @ SV107 )
= $false )
| ( ( equidistant @ SV6 @ SV106 @ SV53 @ SV107 )
= $false )
| ( ( equidistant @ SV30 @ SV91 @ SV73 @ SV102 )
= $false )
| ( ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(287,plain,
! [SV107: $i,SV106: $i,SV91: $i,SV30: $i,SV6: $i,SV102: $i,SV73: $i,SV53: $i] :
( ( ( ~ ( between @ SV53 @ SV73 @ SV102 ) )
= $true )
| ( ( ( SV6 = SV30 )
| ( equidistant @ SV91 @ SV106 @ SV102 @ SV107 ) )
= $true )
| ( ( between @ SV6 @ SV30 @ SV91 )
= $false )
| ( ( equidistant @ SV30 @ SV106 @ SV73 @ SV107 )
= $false )
| ( ( equidistant @ SV6 @ SV106 @ SV53 @ SV107 )
= $false )
| ( ( equidistant @ SV30 @ SV91 @ SV73 @ SV102 )
= $false )
| ( ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(288,plain,
! [SV107: $i,SV106: $i,SV91: $i,SV30: $i,SV6: $i,SV102: $i,SV73: $i,SV53: $i] :
( ( ( between @ SV53 @ SV73 @ SV102 )
= $false )
| ( ( ( SV6 = SV30 )
| ( equidistant @ SV91 @ SV106 @ SV102 @ SV107 ) )
= $true )
| ( ( between @ SV6 @ SV30 @ SV91 )
= $false )
| ( ( equidistant @ SV30 @ SV106 @ SV73 @ SV107 )
= $false )
| ( ( equidistant @ SV6 @ SV106 @ SV53 @ SV107 )
= $false )
| ( ( equidistant @ SV30 @ SV91 @ SV73 @ SV102 )
= $false )
| ( ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(289,plain,
! [SV73: $i,SV53: $i,SV107: $i,SV102: $i,SV106: $i,SV91: $i,SV30: $i,SV6: $i] :
( ( ( SV6 = SV30 )
= $true )
| ( ( equidistant @ SV91 @ SV106 @ SV102 @ SV107 )
= $true )
| ( ( between @ SV53 @ SV73 @ SV102 )
= $false )
| ( ( between @ SV6 @ SV30 @ SV91 )
= $false )
| ( ( equidistant @ SV30 @ SV106 @ SV73 @ SV107 )
= $false )
| ( ( equidistant @ SV6 @ SV106 @ SV53 @ SV107 )
= $false )
| ( ( equidistant @ SV30 @ SV91 @ SV73 @ SV102 )
= $false )
| ( ( equidistant @ SV6 @ SV30 @ SV53 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(290,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[100,289,282,281,280,266,263,262,261,258,250,249,223,222,221,220,219,218,217,189,171,169,168,135,120,119,118,102,101]) ).
thf(291,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[290]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO035-3 : 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/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n005.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 10:00:17 UTC 2026
% 0.07/0.19 % CPUTime :
% 0.07/0.19 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.32
% 0.48/0.32 No.of.Axioms: 28
% 0.48/0.32
% 0.48/0.32 Length.of.Defs: 0
% 0.48/0.32
% 0.48/0.32 Contains.Choice.Funs: false
% 0.48/0.32 .........
% 0.48/0.32
% 0.48/0.32 ********************************
% 0.48/0.32 * All subproblems solved! *
% 0.48/0.32 ********************************
% 0.48/0.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:28,ps:3,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:290,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.48/0.32
% 0.48/0.32 %**** Beginning of derivation protocol ****
% 0.48/0.32 % SZS output start CNFRefutation
% See solution above
% 0.48/0.32
% 0.48/0.32 %**** End of derivation protocol ****
% 0.48/0.32 %**** no. of clauses in derivation: 291 ****
% 0.48/0.32 %**** clause counter: 290 ****
% 0.48/0.32
% 0.48/0.32 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:28,ps:3,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:290,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------