TSTP Solution File: GEO038-3 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GEO038-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:06:21 EDT 2022
% Result : Unsatisfiable 0.57s 0.77s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 46
% Syntax : Number of formulae : 326 ( 181 unt; 15 typ; 0 def)
% Number of atoms : 2039 ( 604 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 5231 ( 469 ~; 740 |; 0 &;4022 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 18 ( 15 usr; 10 con; 0-6 aty)
% Number of variables : 1401 ( 0 ^1401 !; 0 ?;1401 :)
% 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(tp_x,type,
x: $i ).
thf(tp_y,type,
y: $i ).
thf(1,axiom,
! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
thf(2,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(3,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(4,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(5,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(6,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(7,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(8,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(9,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(10,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
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 )
| ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).
thf(12,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(13,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(14,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(15,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(16,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(17,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(18,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(19,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(20,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(21,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(22,axiom,
! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(23,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(24,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(25,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(26,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(27,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(28,axiom,
! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(29,axiom,
( y
= ( extension @ u @ v @ w @ x ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',y_is_extension) ).
thf(30,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(31,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[30]) ).
thf(32,negated_conjecture,
~ ( between @ u @ v @ y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary) ).
thf(33,plain,
$false = $false,
inference(unfold_def,[status(thm)],[31]) ).
thf(34,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(35,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)],[2]) ).
thf(36,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)],[3]) ).
thf(37,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)],[4]) ).
thf(38,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)],[5]) ).
thf(39,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)],[6]) ).
thf(40,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)],[7]) ).
thf(41,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)],[8]) ).
thf(42,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)],[9]) ).
thf(43,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(44,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)],[11]) ).
thf(45,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)],[12]) ).
thf(46,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)],[13]) ).
thf(47,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)],[14]) ).
thf(48,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)],[15]) ).
thf(49,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)],[16]) ).
thf(50,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(51,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(52,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(53,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)],[20]) ).
thf(54,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)],[21]) ).
thf(55,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(56,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)],[23]) ).
thf(57,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(58,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[26]) ).
thf(60,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)],[27]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(62,plain,
( ( y
= ( extension @ u @ v @ w @ x ) )
= $true ),
inference(unfold_def,[status(thm)],[29]) ).
thf(63,plain,
( ( ~ ( between @ u @ v @ y ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(64,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[33]) ).
thf(65,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ! [Y: $i,Z: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ( equidistant @ U @ V @ Y @ Z ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(66,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ! [X1: $i] :
( ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(67,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ! [X1: $i] :
( ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(68,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(69,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(70,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(71,plain,
( ( ! [X: $i,W: $i,V: $i] :
( ~ ( equidistant @ X @ W @ X @ V )
| ! [Y: $i] :
( ~ ( equidistant @ Y @ W @ Y @ V )
| ! [Z: $i] :
( ~ ( equidistant @ Z @ W @ Z @ V )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( W = V )
| ( between @ Z @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(72,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [Y: $i,X: $i] :
( ~ ( between @ Y @ X @ W )
| ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[53]) ).
thf(73,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [Y: $i,X: $i] :
( ~ ( between @ Y @ X @ W )
| ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(74,plain,
( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i] :
( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
| ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
| ! [V: $i,V1: $i] :
( ~ ( equidistant @ X @ V @ X1 @ V1 )
| ~ ( equidistant @ Y @ V @ Y1 @ V1 )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equidistant @ Z @ V @ Z1 @ V1 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(75,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(76,plain,
( ( ! [X: $i,Y: $i,Z: $i,V: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ! [V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(77,plain,
( ( ~ ( between @ u @ v @ y ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(78,plain,
( ( y
= ( extension @ u @ v @ w @ x ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(79,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(80,plain,
( ( ! [X: $i,Y: $i,Z: $i,V: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ! [V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ) ) )
= $true ),
inference(copy,[status(thm)],[76]) ).
thf(81,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[75]) ).
thf(82,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(83,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[57]) ).
thf(84,plain,
( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i] :
( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
| ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
| ! [V: $i,V1: $i] :
( ~ ( equidistant @ X @ V @ X1 @ V1 )
| ~ ( equidistant @ Y @ V @ Y1 @ V1 )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equidistant @ Z @ V @ Z1 @ V1 ) ) ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(85,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(86,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [Y: $i,X: $i] :
( ~ ( between @ Y @ X @ W )
| ( between @ V @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ Y ) ) ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(87,plain,
( ( ! [U: $i,V: $i,W: $i] :
( ~ ( between @ U @ V @ W )
| ! [Y: $i,X: $i] :
( ~ ( between @ Y @ X @ W )
| ( between @ X @ ( inner_pasch @ U @ V @ W @ X @ Y ) @ U ) ) ) )
= $true ),
inference(copy,[status(thm)],[72]) ).
thf(88,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(89,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(90,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(91,plain,
( ( ! [X: $i,W: $i,V: $i] :
( ~ ( equidistant @ X @ W @ X @ V )
| ! [Y: $i] :
( ~ ( equidistant @ Y @ W @ Y @ V )
| ! [Z: $i] :
( ~ ( equidistant @ Z @ W @ Z @ V )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( W = V )
| ( between @ Z @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[71]) ).
thf(92,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(93,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ X @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(94,plain,
( ( ! [U: $i,W: $i,Y: $i] :
( ~ ( between @ U @ W @ Y )
| ! [V: $i,X: $i] :
( ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ ( euclid1 @ U @ V @ W @ X @ Y ) @ Y @ ( euclid2 @ U @ V @ W @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[68]) ).
thf(95,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ! [X1: $i] :
( ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( between @ V1 @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) @ X1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(96,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i] :
( ~ ( equidistant @ U @ V @ U @ V1 )
| ! [X1: $i] :
( ~ ( equidistant @ U @ X @ U @ X1 )
| ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( equidistant @ U @ W @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[66]) ).
thf(97,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(98,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(99,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(100,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(101,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(102,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(103,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(104,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(105,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ! [Y: $i,Z: $i] :
( ~ ( equidistant @ W @ X @ Y @ Z )
| ( equidistant @ U @ V @ Y @ Z ) ) ) )
= $true ),
inference(copy,[status(thm)],[65]) ).
thf(106,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(107,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(108,plain,
( ( between @ u @ v @ y )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(109,plain,
! [SV1: $i] :
( ( ! [SY110: $i] : ( equidistant @ SV1 @ SY110 @ SY110 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(110,plain,
! [SV2: $i] :
( ( ! [SY111: $i,SY112: $i,SY113: $i] :
( ~ ( equidistant @ SV2 @ SY111 @ SY112 @ SY113 )
| ! [SY114: $i,SY115: $i] :
( ~ ( equidistant @ SV2 @ SY111 @ SY114 @ SY115 )
| ( equidistant @ SY112 @ SY113 @ SY114 @ SY115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(111,plain,
! [SV3: $i] :
( ( ! [SY116: $i] :
( ! [SY117: $i] :
~ ( equidistant @ SV3 @ SY116 @ SY117 @ SY117 )
| ( SV3 = SY116 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(112,plain,
! [SV4: $i] :
( ( ! [SY118: $i,SY119: $i,SY120: $i] : ( between @ SV4 @ SY118 @ ( extension @ SV4 @ SY118 @ SY119 @ SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(113,plain,
! [SV5: $i] :
( ( ! [SY121: $i,SY122: $i,SY123: $i] : ( equidistant @ SV5 @ ( extension @ SY121 @ SV5 @ SY122 @ SY123 ) @ SY122 @ SY123 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(114,plain,
! [SV6: $i] :
( ( ! [SY124: $i,SY125: $i,SY126: $i,SY127: $i,SY128: $i] :
( ~ ( equidistant @ SV6 @ SY124 @ SY125 @ SY126 )
| ~ ( equidistant @ SY124 @ SY127 @ SY126 @ SY128 )
| ! [SY129: $i,SY130: $i] :
( ~ ( equidistant @ SV6 @ SY129 @ SY125 @ SY130 )
| ~ ( equidistant @ SY124 @ SY129 @ SY126 @ SY130 )
| ~ ( between @ SV6 @ SY124 @ SY127 )
| ~ ( between @ SY125 @ SY126 @ SY128 )
| ( SV6 = SY124 )
| ( equidistant @ SY127 @ SY129 @ SY128 @ SY130 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(115,plain,
! [SV7: $i] :
( ( ! [SY131: $i] :
( ~ ( between @ SV7 @ SY131 @ SV7 )
| ( SV7 = SY131 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(116,plain,
! [SV8: $i] :
( ( ! [SY132: $i,SY133: $i] :
( ~ ( between @ SV8 @ SY132 @ SY133 )
| ! [SY134: $i,SY135: $i] :
( ~ ( between @ SY134 @ SY135 @ SY133 )
| ( between @ SY132 @ ( inner_pasch @ SV8 @ SY132 @ SY133 @ SY135 @ SY134 ) @ SY134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(117,plain,
! [SV9: $i] :
( ( ! [SY136: $i,SY137: $i] :
( ~ ( between @ SV9 @ SY136 @ SY137 )
| ! [SY138: $i,SY139: $i] :
( ~ ( between @ SY138 @ SY139 @ SY137 )
| ( between @ SY139 @ ( inner_pasch @ SV9 @ SY136 @ SY137 @ SY139 @ SY138 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(118,plain,
( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[88]) ).
thf(119,plain,
( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[89]) ).
thf(120,plain,
( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[90]) ).
thf(121,plain,
! [SV10: $i] :
( ( ! [SY140: $i,SY141: $i] :
( ~ ( equidistant @ SV10 @ SY140 @ SV10 @ SY141 )
| ! [SY142: $i] :
( ~ ( equidistant @ SY142 @ SY140 @ SY142 @ SY141 )
| ! [SY143: $i] :
( ~ ( equidistant @ SY143 @ SY140 @ SY143 @ SY141 )
| ( between @ SV10 @ SY142 @ SY143 )
| ( between @ SY142 @ SY143 @ SV10 )
| ( SY140 = SY141 )
| ( between @ SY143 @ SV10 @ SY142 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(122,plain,
! [SV11: $i] :
( ( ! [SY144: $i,SY145: $i] :
( ~ ( between @ SV11 @ SY144 @ SY145 )
| ! [SY146: $i,SY147: $i] :
( ~ ( between @ SY146 @ SY144 @ SY147 )
| ( SV11 = SY144 )
| ( between @ SV11 @ SY146 @ ( euclid1 @ SV11 @ SY146 @ SY144 @ SY147 @ SY145 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(123,plain,
! [SV12: $i] :
( ( ! [SY148: $i,SY149: $i] :
( ~ ( between @ SV12 @ SY148 @ SY149 )
| ! [SY150: $i,SY151: $i] :
( ~ ( between @ SY150 @ SY148 @ SY151 )
| ( SV12 = SY148 )
| ( between @ SV12 @ SY151 @ ( euclid2 @ SV12 @ SY150 @ SY148 @ SY151 @ SY149 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(124,plain,
! [SV13: $i] :
( ( ! [SY152: $i,SY153: $i] :
( ~ ( between @ SV13 @ SY152 @ SY153 )
| ! [SY154: $i,SY155: $i] :
( ~ ( between @ SY154 @ SY152 @ SY155 )
| ( SV13 = SY152 )
| ( between @ ( euclid1 @ SV13 @ SY154 @ SY152 @ SY155 @ SY153 ) @ SY153 @ ( euclid2 @ SV13 @ SY154 @ SY152 @ SY155 @ SY153 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(125,plain,
! [SV14: $i] :
( ( ! [SY156: $i,SY157: $i,SY158: $i] :
( ~ ( equidistant @ SV14 @ SY156 @ SV14 @ SY157 )
| ! [SY159: $i] :
( ~ ( equidistant @ SV14 @ SY158 @ SV14 @ SY159 )
| ~ ( between @ SV14 @ SY156 @ SY158 )
| ! [SY160: $i] :
( ~ ( between @ SY156 @ SY160 @ SY158 )
| ( between @ SY157 @ ( continuous @ SV14 @ SY156 @ SY157 @ SY160 @ SY158 @ SY159 ) @ SY159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(126,plain,
! [SV15: $i] :
( ( ! [SY161: $i,SY162: $i,SY163: $i] :
( ~ ( equidistant @ SV15 @ SY161 @ SV15 @ SY162 )
| ! [SY164: $i] :
( ~ ( equidistant @ SV15 @ SY163 @ SV15 @ SY164 )
| ~ ( between @ SV15 @ SY161 @ SY163 )
| ! [SY165: $i] :
( ~ ( between @ SY161 @ SY165 @ SY163 )
| ( equidistant @ SV15 @ SY165 @ SV15 @ ( continuous @ SV15 @ SY161 @ SY162 @ SY165 @ SY163 @ SY164 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(127,plain,
! [SV16: $i] :
( ( ! [SY166: $i] : ( equidistant @ SV16 @ SY166 @ SV16 @ SY166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(128,plain,
! [SV17: $i] :
( ( ! [SY167: $i,SY168: $i,SY169: $i] :
( ~ ( equidistant @ SV17 @ SY167 @ SY168 @ SY169 )
| ( equidistant @ SY168 @ SY169 @ SV17 @ SY167 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(129,plain,
! [SV18: $i] :
( ( ! [SY170: $i,SY171: $i,SY172: $i] :
( ~ ( equidistant @ SV18 @ SY170 @ SY171 @ SY172 )
| ( equidistant @ SY170 @ SV18 @ SY171 @ SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(130,plain,
! [SV19: $i] :
( ( ! [SY173: $i,SY174: $i,SY175: $i] :
( ~ ( equidistant @ SV19 @ SY173 @ SY174 @ SY175 )
| ( equidistant @ SV19 @ SY173 @ SY175 @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(131,plain,
! [SV20: $i] :
( ( ! [SY176: $i,SY177: $i,SY178: $i] :
( ~ ( equidistant @ SV20 @ SY176 @ SY177 @ SY178 )
| ( equidistant @ SY176 @ SV20 @ SY178 @ SY177 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(132,plain,
! [SV21: $i] :
( ( ! [SY179: $i,SY180: $i,SY181: $i] :
( ~ ( equidistant @ SV21 @ SY179 @ SY180 @ SY181 )
| ( equidistant @ SY180 @ SY181 @ SY179 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(133,plain,
! [SV22: $i] :
( ( ! [SY182: $i,SY183: $i,SY184: $i] :
( ~ ( equidistant @ SV22 @ SY182 @ SY183 @ SY184 )
| ( equidistant @ SY184 @ SY183 @ SV22 @ SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(134,plain,
! [SV23: $i] :
( ( ! [SY185: $i,SY186: $i,SY187: $i] :
( ~ ( equidistant @ SV23 @ SY185 @ SY186 @ SY187 )
| ( equidistant @ SY187 @ SY186 @ SY185 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(135,plain,
! [SV24: $i] :
( ( ! [SY188: $i,SY189: $i,SY190: $i] :
( ~ ( equidistant @ SV24 @ SY188 @ SY189 @ SY190 )
| ! [SY191: $i,SY192: $i] :
( ~ ( equidistant @ SY189 @ SY190 @ SY191 @ SY192 )
| ( equidistant @ SV24 @ SY188 @ SY191 @ SY192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(136,plain,
! [SV25: $i] :
( ( ! [SY193: $i,SY194: $i] :
( SV25
= ( extension @ SY193 @ SV25 @ SY194 @ SY194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(137,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[107]) ).
thf(138,plain,
! [SV26: $i,SV1: $i] :
( ( equidistant @ SV1 @ SV26 @ SV26 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(139,plain,
! [SV27: $i,SV2: $i] :
( ( ! [SY195: $i,SY196: $i] :
( ~ ( equidistant @ SV2 @ SV27 @ SY195 @ SY196 )
| ! [SY197: $i,SY198: $i] :
( ~ ( equidistant @ SV2 @ SV27 @ SY197 @ SY198 )
| ( equidistant @ SY195 @ SY196 @ SY197 @ SY198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(140,plain,
! [SV28: $i,SV3: $i] :
( ( ! [SY199: $i] :
~ ( equidistant @ SV3 @ SV28 @ SY199 @ SY199 )
| ( SV3 = SV28 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(141,plain,
! [SV29: $i,SV4: $i] :
( ( ! [SY200: $i,SY201: $i] : ( between @ SV4 @ SV29 @ ( extension @ SV4 @ SV29 @ SY200 @ SY201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(142,plain,
! [SV30: $i,SV5: $i] :
( ( ! [SY202: $i,SY203: $i] : ( equidistant @ SV5 @ ( extension @ SV30 @ SV5 @ SY202 @ SY203 ) @ SY202 @ SY203 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(143,plain,
! [SV31: $i,SV6: $i] :
( ( ! [SY204: $i,SY205: $i,SY206: $i,SY207: $i] :
( ~ ( equidistant @ SV6 @ SV31 @ SY204 @ SY205 )
| ~ ( equidistant @ SV31 @ SY206 @ SY205 @ SY207 )
| ! [SY208: $i,SY209: $i] :
( ~ ( equidistant @ SV6 @ SY208 @ SY204 @ SY209 )
| ~ ( equidistant @ SV31 @ SY208 @ SY205 @ SY209 )
| ~ ( between @ SV6 @ SV31 @ SY206 )
| ~ ( between @ SY204 @ SY205 @ SY207 )
| ( SV6 = SV31 )
| ( equidistant @ SY206 @ SY208 @ SY207 @ SY209 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(144,plain,
! [SV32: $i,SV7: $i] :
( ( ~ ( between @ SV7 @ SV32 @ SV7 )
| ( SV7 = SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(145,plain,
! [SV33: $i,SV8: $i] :
( ( ! [SY210: $i] :
( ~ ( between @ SV8 @ SV33 @ SY210 )
| ! [SY211: $i,SY212: $i] :
( ~ ( between @ SY211 @ SY212 @ SY210 )
| ( between @ SV33 @ ( inner_pasch @ SV8 @ SV33 @ SY210 @ SY212 @ SY211 ) @ SY211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(146,plain,
! [SV34: $i,SV9: $i] :
( ( ! [SY213: $i] :
( ~ ( between @ SV9 @ SV34 @ SY213 )
| ! [SY214: $i,SY215: $i] :
( ~ ( between @ SY214 @ SY215 @ SY213 )
| ( between @ SY215 @ ( inner_pasch @ SV9 @ SV34 @ SY213 @ SY215 @ SY214 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(147,plain,
! [SV35: $i,SV10: $i] :
( ( ! [SY216: $i] :
( ~ ( equidistant @ SV10 @ SV35 @ SV10 @ SY216 )
| ! [SY217: $i] :
( ~ ( equidistant @ SY217 @ SV35 @ SY217 @ SY216 )
| ! [SY218: $i] :
( ~ ( equidistant @ SY218 @ SV35 @ SY218 @ SY216 )
| ( between @ SV10 @ SY217 @ SY218 )
| ( between @ SY217 @ SY218 @ SV10 )
| ( SV35 = SY216 )
| ( between @ SY218 @ SV10 @ SY217 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(148,plain,
! [SV36: $i,SV11: $i] :
( ( ! [SY219: $i] :
( ~ ( between @ SV11 @ SV36 @ SY219 )
| ! [SY220: $i,SY221: $i] :
( ~ ( between @ SY220 @ SV36 @ SY221 )
| ( SV11 = SV36 )
| ( between @ SV11 @ SY220 @ ( euclid1 @ SV11 @ SY220 @ SV36 @ SY221 @ SY219 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(149,plain,
! [SV37: $i,SV12: $i] :
( ( ! [SY222: $i] :
( ~ ( between @ SV12 @ SV37 @ SY222 )
| ! [SY223: $i,SY224: $i] :
( ~ ( between @ SY223 @ SV37 @ SY224 )
| ( SV12 = SV37 )
| ( between @ SV12 @ SY224 @ ( euclid2 @ SV12 @ SY223 @ SV37 @ SY224 @ SY222 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(150,plain,
! [SV38: $i,SV13: $i] :
( ( ! [SY225: $i] :
( ~ ( between @ SV13 @ SV38 @ SY225 )
| ! [SY226: $i,SY227: $i] :
( ~ ( between @ SY226 @ SV38 @ SY227 )
| ( SV13 = SV38 )
| ( between @ ( euclid1 @ SV13 @ SY226 @ SV38 @ SY227 @ SY225 ) @ SY225 @ ( euclid2 @ SV13 @ SY226 @ SV38 @ SY227 @ SY225 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(151,plain,
! [SV39: $i,SV14: $i] :
( ( ! [SY228: $i,SY229: $i] :
( ~ ( equidistant @ SV14 @ SV39 @ SV14 @ SY228 )
| ! [SY230: $i] :
( ~ ( equidistant @ SV14 @ SY229 @ SV14 @ SY230 )
| ~ ( between @ SV14 @ SV39 @ SY229 )
| ! [SY231: $i] :
( ~ ( between @ SV39 @ SY231 @ SY229 )
| ( between @ SY228 @ ( continuous @ SV14 @ SV39 @ SY228 @ SY231 @ SY229 @ SY230 ) @ SY230 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(152,plain,
! [SV40: $i,SV15: $i] :
( ( ! [SY232: $i,SY233: $i] :
( ~ ( equidistant @ SV15 @ SV40 @ SV15 @ SY232 )
| ! [SY234: $i] :
( ~ ( equidistant @ SV15 @ SY233 @ SV15 @ SY234 )
| ~ ( between @ SV15 @ SV40 @ SY233 )
| ! [SY235: $i] :
( ~ ( between @ SV40 @ SY235 @ SY233 )
| ( equidistant @ SV15 @ SY235 @ SV15 @ ( continuous @ SV15 @ SV40 @ SY232 @ SY235 @ SY233 @ SY234 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(153,plain,
! [SV41: $i,SV16: $i] :
( ( equidistant @ SV16 @ SV41 @ SV16 @ SV41 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(154,plain,
! [SV42: $i,SV17: $i] :
( ( ! [SY236: $i,SY237: $i] :
( ~ ( equidistant @ SV17 @ SV42 @ SY236 @ SY237 )
| ( equidistant @ SY236 @ SY237 @ SV17 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(155,plain,
! [SV43: $i,SV18: $i] :
( ( ! [SY238: $i,SY239: $i] :
( ~ ( equidistant @ SV18 @ SV43 @ SY238 @ SY239 )
| ( equidistant @ SV43 @ SV18 @ SY238 @ SY239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(156,plain,
! [SV44: $i,SV19: $i] :
( ( ! [SY240: $i,SY241: $i] :
( ~ ( equidistant @ SV19 @ SV44 @ SY240 @ SY241 )
| ( equidistant @ SV19 @ SV44 @ SY241 @ SY240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(157,plain,
! [SV45: $i,SV20: $i] :
( ( ! [SY242: $i,SY243: $i] :
( ~ ( equidistant @ SV20 @ SV45 @ SY242 @ SY243 )
| ( equidistant @ SV45 @ SV20 @ SY243 @ SY242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(158,plain,
! [SV46: $i,SV21: $i] :
( ( ! [SY244: $i,SY245: $i] :
( ~ ( equidistant @ SV21 @ SV46 @ SY244 @ SY245 )
| ( equidistant @ SY244 @ SY245 @ SV46 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(159,plain,
! [SV47: $i,SV22: $i] :
( ( ! [SY246: $i,SY247: $i] :
( ~ ( equidistant @ SV22 @ SV47 @ SY246 @ SY247 )
| ( equidistant @ SY247 @ SY246 @ SV22 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(160,plain,
! [SV48: $i,SV23: $i] :
( ( ! [SY248: $i,SY249: $i] :
( ~ ( equidistant @ SV23 @ SV48 @ SY248 @ SY249 )
| ( equidistant @ SY249 @ SY248 @ SV48 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(161,plain,
! [SV49: $i,SV24: $i] :
( ( ! [SY250: $i,SY251: $i] :
( ~ ( equidistant @ SV24 @ SV49 @ SY250 @ SY251 )
| ! [SY252: $i,SY253: $i] :
( ~ ( equidistant @ SY250 @ SY251 @ SY252 @ SY253 )
| ( equidistant @ SV24 @ SV49 @ SY252 @ SY253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(162,plain,
! [SV50: $i,SV25: $i] :
( ( ! [SY254: $i] :
( SV25
= ( extension @ SV50 @ SV25 @ SY254 @ SY254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(163,plain,
! [SV51: $i,SV27: $i,SV2: $i] :
( ( ! [SY255: $i] :
( ~ ( equidistant @ SV2 @ SV27 @ SV51 @ SY255 )
| ! [SY256: $i,SY257: $i] :
( ~ ( equidistant @ SV2 @ SV27 @ SY256 @ SY257 )
| ( equidistant @ SV51 @ SY255 @ SY256 @ SY257 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(164,plain,
! [SV28: $i,SV3: $i] :
( ( ( ! [SY199: $i] :
~ ( equidistant @ SV3 @ SV28 @ SY199 @ SY199 ) )
= $true )
| ( ( SV3 = SV28 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(165,plain,
! [SV52: $i,SV29: $i,SV4: $i] :
( ( ! [SY258: $i] : ( between @ SV4 @ SV29 @ ( extension @ SV4 @ SV29 @ SV52 @ SY258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[141]) ).
thf(166,plain,
! [SV53: $i,SV30: $i,SV5: $i] :
( ( ! [SY259: $i] : ( equidistant @ SV5 @ ( extension @ SV30 @ SV5 @ SV53 @ SY259 ) @ SV53 @ SY259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(167,plain,
! [SV54: $i,SV31: $i,SV6: $i] :
( ( ! [SY260: $i,SY261: $i,SY262: $i] :
( ~ ( equidistant @ SV6 @ SV31 @ SV54 @ SY260 )
| ~ ( equidistant @ SV31 @ SY261 @ SY260 @ SY262 )
| ! [SY263: $i,SY264: $i] :
( ~ ( equidistant @ SV6 @ SY263 @ SV54 @ SY264 )
| ~ ( equidistant @ SV31 @ SY263 @ SY260 @ SY264 )
| ~ ( between @ SV6 @ SV31 @ SY261 )
| ~ ( between @ SV54 @ SY260 @ SY262 )
| ( SV6 = SV31 )
| ( equidistant @ SY261 @ SY263 @ SY262 @ SY264 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(168,plain,
! [SV32: $i,SV7: $i] :
( ( ( ~ ( between @ SV7 @ SV32 @ SV7 ) )
= $true )
| ( ( SV7 = SV32 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(169,plain,
! [SV55: $i,SV33: $i,SV8: $i] :
( ( ~ ( between @ SV8 @ SV33 @ SV55 )
| ! [SY265: $i,SY266: $i] :
( ~ ( between @ SY265 @ SY266 @ SV55 )
| ( between @ SV33 @ ( inner_pasch @ SV8 @ SV33 @ SV55 @ SY266 @ SY265 ) @ SY265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(170,plain,
! [SV56: $i,SV34: $i,SV9: $i] :
( ( ~ ( between @ SV9 @ SV34 @ SV56 )
| ! [SY267: $i,SY268: $i] :
( ~ ( between @ SY267 @ SY268 @ SV56 )
| ( between @ SY268 @ ( inner_pasch @ SV9 @ SV34 @ SV56 @ SY268 @ SY267 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(171,plain,
! [SV57: $i,SV35: $i,SV10: $i] :
( ( ~ ( equidistant @ SV10 @ SV35 @ SV10 @ SV57 )
| ! [SY269: $i] :
( ~ ( equidistant @ SY269 @ SV35 @ SY269 @ SV57 )
| ! [SY270: $i] :
( ~ ( equidistant @ SY270 @ SV35 @ SY270 @ SV57 )
| ( between @ SV10 @ SY269 @ SY270 )
| ( between @ SY269 @ SY270 @ SV10 )
| ( SV35 = SV57 )
| ( between @ SY270 @ SV10 @ SY269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(172,plain,
! [SV58: $i,SV36: $i,SV11: $i] :
( ( ~ ( between @ SV11 @ SV36 @ SV58 )
| ! [SY271: $i,SY272: $i] :
( ~ ( between @ SY271 @ SV36 @ SY272 )
| ( SV11 = SV36 )
| ( between @ SV11 @ SY271 @ ( euclid1 @ SV11 @ SY271 @ SV36 @ SY272 @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(173,plain,
! [SV59: $i,SV37: $i,SV12: $i] :
( ( ~ ( between @ SV12 @ SV37 @ SV59 )
| ! [SY273: $i,SY274: $i] :
( ~ ( between @ SY273 @ SV37 @ SY274 )
| ( SV12 = SV37 )
| ( between @ SV12 @ SY274 @ ( euclid2 @ SV12 @ SY273 @ SV37 @ SY274 @ SV59 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(174,plain,
! [SV60: $i,SV38: $i,SV13: $i] :
( ( ~ ( between @ SV13 @ SV38 @ SV60 )
| ! [SY275: $i,SY276: $i] :
( ~ ( between @ SY275 @ SV38 @ SY276 )
| ( SV13 = SV38 )
| ( between @ ( euclid1 @ SV13 @ SY275 @ SV38 @ SY276 @ SV60 ) @ SV60 @ ( euclid2 @ SV13 @ SY275 @ SV38 @ SY276 @ SV60 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(175,plain,
! [SV61: $i,SV39: $i,SV14: $i] :
( ( ! [SY277: $i] :
( ~ ( equidistant @ SV14 @ SV39 @ SV14 @ SV61 )
| ! [SY278: $i] :
( ~ ( equidistant @ SV14 @ SY277 @ SV14 @ SY278 )
| ~ ( between @ SV14 @ SV39 @ SY277 )
| ! [SY279: $i] :
( ~ ( between @ SV39 @ SY279 @ SY277 )
| ( between @ SV61 @ ( continuous @ SV14 @ SV39 @ SV61 @ SY279 @ SY277 @ SY278 ) @ SY278 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(176,plain,
! [SV62: $i,SV40: $i,SV15: $i] :
( ( ! [SY280: $i] :
( ~ ( equidistant @ SV15 @ SV40 @ SV15 @ SV62 )
| ! [SY281: $i] :
( ~ ( equidistant @ SV15 @ SY280 @ SV15 @ SY281 )
| ~ ( between @ SV15 @ SV40 @ SY280 )
| ! [SY282: $i] :
( ~ ( between @ SV40 @ SY282 @ SY280 )
| ( equidistant @ SV15 @ SY282 @ SV15 @ ( continuous @ SV15 @ SV40 @ SV62 @ SY282 @ SY280 @ SY281 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(177,plain,
! [SV63: $i,SV42: $i,SV17: $i] :
( ( ! [SY283: $i] :
( ~ ( equidistant @ SV17 @ SV42 @ SV63 @ SY283 )
| ( equidistant @ SV63 @ SY283 @ SV17 @ SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(178,plain,
! [SV64: $i,SV43: $i,SV18: $i] :
( ( ! [SY284: $i] :
( ~ ( equidistant @ SV18 @ SV43 @ SV64 @ SY284 )
| ( equidistant @ SV43 @ SV18 @ SV64 @ SY284 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(179,plain,
! [SV65: $i,SV44: $i,SV19: $i] :
( ( ! [SY285: $i] :
( ~ ( equidistant @ SV19 @ SV44 @ SV65 @ SY285 )
| ( equidistant @ SV19 @ SV44 @ SY285 @ SV65 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(180,plain,
! [SV66: $i,SV45: $i,SV20: $i] :
( ( ! [SY286: $i] :
( ~ ( equidistant @ SV20 @ SV45 @ SV66 @ SY286 )
| ( equidistant @ SV45 @ SV20 @ SY286 @ SV66 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(181,plain,
! [SV67: $i,SV46: $i,SV21: $i] :
( ( ! [SY287: $i] :
( ~ ( equidistant @ SV21 @ SV46 @ SV67 @ SY287 )
| ( equidistant @ SV67 @ SY287 @ SV46 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(182,plain,
! [SV68: $i,SV47: $i,SV22: $i] :
( ( ! [SY288: $i] :
( ~ ( equidistant @ SV22 @ SV47 @ SV68 @ SY288 )
| ( equidistant @ SY288 @ SV68 @ SV22 @ SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(183,plain,
! [SV69: $i,SV48: $i,SV23: $i] :
( ( ! [SY289: $i] :
( ~ ( equidistant @ SV23 @ SV48 @ SV69 @ SY289 )
| ( equidistant @ SY289 @ SV69 @ SV48 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(184,plain,
! [SV70: $i,SV49: $i,SV24: $i] :
( ( ! [SY290: $i] :
( ~ ( equidistant @ SV24 @ SV49 @ SV70 @ SY290 )
| ! [SY291: $i,SY292: $i] :
( ~ ( equidistant @ SV70 @ SY290 @ SY291 @ SY292 )
| ( equidistant @ SV24 @ SV49 @ SY291 @ SY292 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(185,plain,
! [SV71: $i,SV50: $i,SV25: $i] :
( ( SV25
= ( extension @ SV50 @ SV25 @ SV71 @ SV71 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(186,plain,
! [SV72: $i,SV51: $i,SV27: $i,SV2: $i] :
( ( ~ ( equidistant @ SV2 @ SV27 @ SV51 @ SV72 )
| ! [SY293: $i,SY294: $i] :
( ~ ( equidistant @ SV2 @ SV27 @ SY293 @ SY294 )
| ( equidistant @ SV51 @ SV72 @ SY293 @ SY294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(187,plain,
! [SV73: $i,SV28: $i,SV3: $i] :
( ( ( ~ ( equidistant @ SV3 @ SV28 @ SV73 @ SV73 ) )
= $true )
| ( ( SV3 = SV28 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(188,plain,
! [SV74: $i,SV52: $i,SV29: $i,SV4: $i] :
( ( between @ SV4 @ SV29 @ ( extension @ SV4 @ SV29 @ SV52 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(189,plain,
! [SV75: $i,SV53: $i,SV30: $i,SV5: $i] :
( ( equidistant @ SV5 @ ( extension @ SV30 @ SV5 @ SV53 @ SV75 ) @ SV53 @ SV75 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(190,plain,
! [SV76: $i,SV54: $i,SV31: $i,SV6: $i] :
( ( ! [SY295: $i,SY296: $i] :
( ~ ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
| ~ ( equidistant @ SV31 @ SY295 @ SV76 @ SY296 )
| ! [SY297: $i,SY298: $i] :
( ~ ( equidistant @ SV6 @ SY297 @ SV54 @ SY298 )
| ~ ( equidistant @ SV31 @ SY297 @ SV76 @ SY298 )
| ~ ( between @ SV6 @ SV31 @ SY295 )
| ~ ( between @ SV54 @ SV76 @ SY296 )
| ( SV6 = SV31 )
| ( equidistant @ SY295 @ SY297 @ SY296 @ SY298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(191,plain,
! [SV32: $i,SV7: $i] :
( ( ( between @ SV7 @ SV32 @ SV7 )
= $false )
| ( ( SV7 = SV32 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(192,plain,
! [SV55: $i,SV33: $i,SV8: $i] :
( ( ( ~ ( between @ SV8 @ SV33 @ SV55 ) )
= $true )
| ( ( ! [SY265: $i,SY266: $i] :
( ~ ( between @ SY265 @ SY266 @ SV55 )
| ( between @ SV33 @ ( inner_pasch @ SV8 @ SV33 @ SV55 @ SY266 @ SY265 ) @ SY265 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(193,plain,
! [SV56: $i,SV34: $i,SV9: $i] :
( ( ( ~ ( between @ SV9 @ SV34 @ SV56 ) )
= $true )
| ( ( ! [SY267: $i,SY268: $i] :
( ~ ( between @ SY267 @ SY268 @ SV56 )
| ( between @ SY268 @ ( inner_pasch @ SV9 @ SV34 @ SV56 @ SY268 @ SY267 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(194,plain,
! [SV57: $i,SV35: $i,SV10: $i] :
( ( ( ~ ( equidistant @ SV10 @ SV35 @ SV10 @ SV57 ) )
= $true )
| ( ( ! [SY269: $i] :
( ~ ( equidistant @ SY269 @ SV35 @ SY269 @ SV57 )
| ! [SY270: $i] :
( ~ ( equidistant @ SY270 @ SV35 @ SY270 @ SV57 )
| ( between @ SV10 @ SY269 @ SY270 )
| ( between @ SY269 @ SY270 @ SV10 )
| ( SV35 = SV57 )
| ( between @ SY270 @ SV10 @ SY269 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(195,plain,
! [SV58: $i,SV36: $i,SV11: $i] :
( ( ( ~ ( between @ SV11 @ SV36 @ SV58 ) )
= $true )
| ( ( ! [SY271: $i,SY272: $i] :
( ~ ( between @ SY271 @ SV36 @ SY272 )
| ( SV11 = SV36 )
| ( between @ SV11 @ SY271 @ ( euclid1 @ SV11 @ SY271 @ SV36 @ SY272 @ SV58 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(196,plain,
! [SV59: $i,SV37: $i,SV12: $i] :
( ( ( ~ ( between @ SV12 @ SV37 @ SV59 ) )
= $true )
| ( ( ! [SY273: $i,SY274: $i] :
( ~ ( between @ SY273 @ SV37 @ SY274 )
| ( SV12 = SV37 )
| ( between @ SV12 @ SY274 @ ( euclid2 @ SV12 @ SY273 @ SV37 @ SY274 @ SV59 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(197,plain,
! [SV60: $i,SV38: $i,SV13: $i] :
( ( ( ~ ( between @ SV13 @ SV38 @ SV60 ) )
= $true )
| ( ( ! [SY275: $i,SY276: $i] :
( ~ ( between @ SY275 @ SV38 @ SY276 )
| ( SV13 = SV38 )
| ( between @ ( euclid1 @ SV13 @ SY275 @ SV38 @ SY276 @ SV60 ) @ SV60 @ ( euclid2 @ SV13 @ SY275 @ SV38 @ SY276 @ SV60 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(198,plain,
! [SV77: $i,SV61: $i,SV39: $i,SV14: $i] :
( ( ~ ( equidistant @ SV14 @ SV39 @ SV14 @ SV61 )
| ! [SY299: $i] :
( ~ ( equidistant @ SV14 @ SV77 @ SV14 @ SY299 )
| ~ ( between @ SV14 @ SV39 @ SV77 )
| ! [SY300: $i] :
( ~ ( between @ SV39 @ SY300 @ SV77 )
| ( between @ SV61 @ ( continuous @ SV14 @ SV39 @ SV61 @ SY300 @ SV77 @ SY299 ) @ SY299 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(199,plain,
! [SV78: $i,SV62: $i,SV40: $i,SV15: $i] :
( ( ~ ( equidistant @ SV15 @ SV40 @ SV15 @ SV62 )
| ! [SY301: $i] :
( ~ ( equidistant @ SV15 @ SV78 @ SV15 @ SY301 )
| ~ ( between @ SV15 @ SV40 @ SV78 )
| ! [SY302: $i] :
( ~ ( between @ SV40 @ SY302 @ SV78 )
| ( equidistant @ SV15 @ SY302 @ SV15 @ ( continuous @ SV15 @ SV40 @ SV62 @ SY302 @ SV78 @ SY301 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(200,plain,
! [SV79: $i,SV63: $i,SV42: $i,SV17: $i] :
( ( ~ ( equidistant @ SV17 @ SV42 @ SV63 @ SV79 )
| ( equidistant @ SV63 @ SV79 @ SV17 @ SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(201,plain,
! [SV80: $i,SV64: $i,SV43: $i,SV18: $i] :
( ( ~ ( equidistant @ SV18 @ SV43 @ SV64 @ SV80 )
| ( equidistant @ SV43 @ SV18 @ SV64 @ SV80 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(202,plain,
! [SV81: $i,SV65: $i,SV44: $i,SV19: $i] :
( ( ~ ( equidistant @ SV19 @ SV44 @ SV65 @ SV81 )
| ( equidistant @ SV19 @ SV44 @ SV81 @ SV65 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(203,plain,
! [SV82: $i,SV66: $i,SV45: $i,SV20: $i] :
( ( ~ ( equidistant @ SV20 @ SV45 @ SV66 @ SV82 )
| ( equidistant @ SV45 @ SV20 @ SV82 @ SV66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(204,plain,
! [SV83: $i,SV67: $i,SV46: $i,SV21: $i] :
( ( ~ ( equidistant @ SV21 @ SV46 @ SV67 @ SV83 )
| ( equidistant @ SV67 @ SV83 @ SV46 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(205,plain,
! [SV84: $i,SV68: $i,SV47: $i,SV22: $i] :
( ( ~ ( equidistant @ SV22 @ SV47 @ SV68 @ SV84 )
| ( equidistant @ SV84 @ SV68 @ SV22 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(206,plain,
! [SV85: $i,SV69: $i,SV48: $i,SV23: $i] :
( ( ~ ( equidistant @ SV23 @ SV48 @ SV69 @ SV85 )
| ( equidistant @ SV85 @ SV69 @ SV48 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(207,plain,
! [SV86: $i,SV70: $i,SV49: $i,SV24: $i] :
( ( ~ ( equidistant @ SV24 @ SV49 @ SV70 @ SV86 )
| ! [SY303: $i,SY304: $i] :
( ~ ( equidistant @ SV70 @ SV86 @ SY303 @ SY304 )
| ( equidistant @ SV24 @ SV49 @ SY303 @ SY304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(208,plain,
! [SV72: $i,SV51: $i,SV27: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV27 @ SV51 @ SV72 ) )
= $true )
| ( ( ! [SY293: $i,SY294: $i] :
( ~ ( equidistant @ SV2 @ SV27 @ SY293 @ SY294 )
| ( equidistant @ SV51 @ SV72 @ SY293 @ SY294 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[186]) ).
thf(209,plain,
! [SV73: $i,SV28: $i,SV3: $i] :
( ( ( equidistant @ SV3 @ SV28 @ SV73 @ SV73 )
= $false )
| ( ( SV3 = SV28 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(210,plain,
! [SV87: $i,SV76: $i,SV54: $i,SV31: $i,SV6: $i] :
( ( ! [SY305: $i] :
( ~ ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
| ~ ( equidistant @ SV31 @ SV87 @ SV76 @ SY305 )
| ! [SY306: $i,SY307: $i] :
( ~ ( equidistant @ SV6 @ SY306 @ SV54 @ SY307 )
| ~ ( equidistant @ SV31 @ SY306 @ SV76 @ SY307 )
| ~ ( between @ SV6 @ SV31 @ SV87 )
| ~ ( between @ SV54 @ SV76 @ SY305 )
| ( SV6 = SV31 )
| ( equidistant @ SV87 @ SY306 @ SY305 @ SY307 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(211,plain,
! [SV55: $i,SV33: $i,SV8: $i] :
( ( ( between @ SV8 @ SV33 @ SV55 )
= $false )
| ( ( ! [SY265: $i,SY266: $i] :
( ~ ( between @ SY265 @ SY266 @ SV55 )
| ( between @ SV33 @ ( inner_pasch @ SV8 @ SV33 @ SV55 @ SY266 @ SY265 ) @ SY265 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(212,plain,
! [SV56: $i,SV34: $i,SV9: $i] :
( ( ( between @ SV9 @ SV34 @ SV56 )
= $false )
| ( ( ! [SY267: $i,SY268: $i] :
( ~ ( between @ SY267 @ SY268 @ SV56 )
| ( between @ SY268 @ ( inner_pasch @ SV9 @ SV34 @ SV56 @ SY268 @ SY267 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[193]) ).
thf(213,plain,
! [SV57: $i,SV35: $i,SV10: $i] :
( ( ( equidistant @ SV10 @ SV35 @ SV10 @ SV57 )
= $false )
| ( ( ! [SY269: $i] :
( ~ ( equidistant @ SY269 @ SV35 @ SY269 @ SV57 )
| ! [SY270: $i] :
( ~ ( equidistant @ SY270 @ SV35 @ SY270 @ SV57 )
| ( between @ SV10 @ SY269 @ SY270 )
| ( between @ SY269 @ SY270 @ SV10 )
| ( SV35 = SV57 )
| ( between @ SY270 @ SV10 @ SY269 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[194]) ).
thf(214,plain,
! [SV58: $i,SV36: $i,SV11: $i] :
( ( ( between @ SV11 @ SV36 @ SV58 )
= $false )
| ( ( ! [SY271: $i,SY272: $i] :
( ~ ( between @ SY271 @ SV36 @ SY272 )
| ( SV11 = SV36 )
| ( between @ SV11 @ SY271 @ ( euclid1 @ SV11 @ SY271 @ SV36 @ SY272 @ SV58 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(215,plain,
! [SV59: $i,SV37: $i,SV12: $i] :
( ( ( between @ SV12 @ SV37 @ SV59 )
= $false )
| ( ( ! [SY273: $i,SY274: $i] :
( ~ ( between @ SY273 @ SV37 @ SY274 )
| ( SV12 = SV37 )
| ( between @ SV12 @ SY274 @ ( euclid2 @ SV12 @ SY273 @ SV37 @ SY274 @ SV59 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(216,plain,
! [SV60: $i,SV38: $i,SV13: $i] :
( ( ( between @ SV13 @ SV38 @ SV60 )
= $false )
| ( ( ! [SY275: $i,SY276: $i] :
( ~ ( between @ SY275 @ SV38 @ SY276 )
| ( SV13 = SV38 )
| ( between @ ( euclid1 @ SV13 @ SY275 @ SV38 @ SY276 @ SV60 ) @ SV60 @ ( euclid2 @ SV13 @ SY275 @ SV38 @ SY276 @ SV60 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[197]) ).
thf(217,plain,
! [SV77: $i,SV61: $i,SV39: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV39 @ SV14 @ SV61 ) )
= $true )
| ( ( ! [SY299: $i] :
( ~ ( equidistant @ SV14 @ SV77 @ SV14 @ SY299 )
| ~ ( between @ SV14 @ SV39 @ SV77 )
| ! [SY300: $i] :
( ~ ( between @ SV39 @ SY300 @ SV77 )
| ( between @ SV61 @ ( continuous @ SV14 @ SV39 @ SV61 @ SY300 @ SV77 @ SY299 ) @ SY299 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(218,plain,
! [SV78: $i,SV62: $i,SV40: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV40 @ SV15 @ SV62 ) )
= $true )
| ( ( ! [SY301: $i] :
( ~ ( equidistant @ SV15 @ SV78 @ SV15 @ SY301 )
| ~ ( between @ SV15 @ SV40 @ SV78 )
| ! [SY302: $i] :
( ~ ( between @ SV40 @ SY302 @ SV78 )
| ( equidistant @ SV15 @ SY302 @ SV15 @ ( continuous @ SV15 @ SV40 @ SV62 @ SY302 @ SV78 @ SY301 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(219,plain,
! [SV79: $i,SV63: $i,SV42: $i,SV17: $i] :
( ( ( ~ ( equidistant @ SV17 @ SV42 @ SV63 @ SV79 ) )
= $true )
| ( ( equidistant @ SV63 @ SV79 @ SV17 @ SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(220,plain,
! [SV80: $i,SV64: $i,SV43: $i,SV18: $i] :
( ( ( ~ ( equidistant @ SV18 @ SV43 @ SV64 @ SV80 ) )
= $true )
| ( ( equidistant @ SV43 @ SV18 @ SV64 @ SV80 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(221,plain,
! [SV81: $i,SV65: $i,SV44: $i,SV19: $i] :
( ( ( ~ ( equidistant @ SV19 @ SV44 @ SV65 @ SV81 ) )
= $true )
| ( ( equidistant @ SV19 @ SV44 @ SV81 @ SV65 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(222,plain,
! [SV82: $i,SV66: $i,SV45: $i,SV20: $i] :
( ( ( ~ ( equidistant @ SV20 @ SV45 @ SV66 @ SV82 ) )
= $true )
| ( ( equidistant @ SV45 @ SV20 @ SV82 @ SV66 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(223,plain,
! [SV83: $i,SV67: $i,SV46: $i,SV21: $i] :
( ( ( ~ ( equidistant @ SV21 @ SV46 @ SV67 @ SV83 ) )
= $true )
| ( ( equidistant @ SV67 @ SV83 @ SV46 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(224,plain,
! [SV84: $i,SV68: $i,SV47: $i,SV22: $i] :
( ( ( ~ ( equidistant @ SV22 @ SV47 @ SV68 @ SV84 ) )
= $true )
| ( ( equidistant @ SV84 @ SV68 @ SV22 @ SV47 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(225,plain,
! [SV85: $i,SV69: $i,SV48: $i,SV23: $i] :
( ( ( ~ ( equidistant @ SV23 @ SV48 @ SV69 @ SV85 ) )
= $true )
| ( ( equidistant @ SV85 @ SV69 @ SV48 @ SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(226,plain,
! [SV86: $i,SV70: $i,SV49: $i,SV24: $i] :
( ( ( ~ ( equidistant @ SV24 @ SV49 @ SV70 @ SV86 ) )
= $true )
| ( ( ! [SY303: $i,SY304: $i] :
( ~ ( equidistant @ SV70 @ SV86 @ SY303 @ SY304 )
| ( equidistant @ SV24 @ SV49 @ SY303 @ SY304 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(227,plain,
! [SV72: $i,SV51: $i,SV27: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV27 @ SV51 @ SV72 )
= $false )
| ( ( ! [SY293: $i,SY294: $i] :
( ~ ( equidistant @ SV2 @ SV27 @ SY293 @ SY294 )
| ( equidistant @ SV51 @ SV72 @ SY293 @ SY294 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(228,plain,
! [SV88: $i,SV87: $i,SV76: $i,SV54: $i,SV31: $i,SV6: $i] :
( ( ~ ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
| ~ ( equidistant @ SV31 @ SV87 @ SV76 @ SV88 )
| ! [SY308: $i,SY309: $i] :
( ~ ( equidistant @ SV6 @ SY308 @ SV54 @ SY309 )
| ~ ( equidistant @ SV31 @ SY308 @ SV76 @ SY309 )
| ~ ( between @ SV6 @ SV31 @ SV87 )
| ~ ( between @ SV54 @ SV76 @ SV88 )
| ( SV6 = SV31 )
| ( equidistant @ SV87 @ SY308 @ SV88 @ SY309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(229,plain,
! [SV8: $i,SV33: $i,SV55: $i,SV89: $i] :
( ( ( ! [SY310: $i] :
( ~ ( between @ SV89 @ SY310 @ SV55 )
| ( between @ SV33 @ ( inner_pasch @ SV8 @ SV33 @ SV55 @ SY310 @ SV89 ) @ SV89 ) ) )
= $true )
| ( ( between @ SV8 @ SV33 @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(230,plain,
! [SV34: $i,SV9: $i,SV56: $i,SV90: $i] :
( ( ( ! [SY311: $i] :
( ~ ( between @ SV90 @ SY311 @ SV56 )
| ( between @ SY311 @ ( inner_pasch @ SV9 @ SV34 @ SV56 @ SY311 @ SV90 ) @ SV9 ) ) )
= $true )
| ( ( between @ SV9 @ SV34 @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(231,plain,
! [SV10: $i,SV57: $i,SV35: $i,SV91: $i] :
( ( ( ~ ( equidistant @ SV91 @ SV35 @ SV91 @ SV57 )
| ! [SY312: $i] :
( ~ ( equidistant @ SY312 @ SV35 @ SY312 @ SV57 )
| ( between @ SV10 @ SV91 @ SY312 )
| ( between @ SV91 @ SY312 @ SV10 )
| ( SV35 = SV57 )
| ( between @ SY312 @ SV10 @ SV91 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV35 @ SV10 @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(232,plain,
! [SV58: $i,SV11: $i,SV36: $i,SV92: $i] :
( ( ( ! [SY313: $i] :
( ~ ( between @ SV92 @ SV36 @ SY313 )
| ( SV11 = SV36 )
| ( between @ SV11 @ SV92 @ ( euclid1 @ SV11 @ SV92 @ SV36 @ SY313 @ SV58 ) ) ) )
= $true )
| ( ( between @ SV11 @ SV36 @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(233,plain,
! [SV59: $i,SV12: $i,SV37: $i,SV93: $i] :
( ( ( ! [SY314: $i] :
( ~ ( between @ SV93 @ SV37 @ SY314 )
| ( SV12 = SV37 )
| ( between @ SV12 @ SY314 @ ( euclid2 @ SV12 @ SV93 @ SV37 @ SY314 @ SV59 ) ) ) )
= $true )
| ( ( between @ SV12 @ SV37 @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(234,plain,
! [SV60: $i,SV13: $i,SV38: $i,SV94: $i] :
( ( ( ! [SY315: $i] :
( ~ ( between @ SV94 @ SV38 @ SY315 )
| ( SV13 = SV38 )
| ( between @ ( euclid1 @ SV13 @ SV94 @ SV38 @ SY315 @ SV60 ) @ SV60 @ ( euclid2 @ SV13 @ SV94 @ SV38 @ SY315 @ SV60 ) ) ) )
= $true )
| ( ( between @ SV13 @ SV38 @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(235,plain,
! [SV77: $i,SV61: $i,SV39: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV39 @ SV14 @ SV61 )
= $false )
| ( ( ! [SY299: $i] :
( ~ ( equidistant @ SV14 @ SV77 @ SV14 @ SY299 )
| ~ ( between @ SV14 @ SV39 @ SV77 )
| ! [SY300: $i] :
( ~ ( between @ SV39 @ SY300 @ SV77 )
| ( between @ SV61 @ ( continuous @ SV14 @ SV39 @ SV61 @ SY300 @ SV77 @ SY299 ) @ SY299 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(236,plain,
! [SV78: $i,SV62: $i,SV40: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV40 @ SV15 @ SV62 )
= $false )
| ( ( ! [SY301: $i] :
( ~ ( equidistant @ SV15 @ SV78 @ SV15 @ SY301 )
| ~ ( between @ SV15 @ SV40 @ SV78 )
| ! [SY302: $i] :
( ~ ( between @ SV40 @ SY302 @ SV78 )
| ( equidistant @ SV15 @ SY302 @ SV15 @ ( continuous @ SV15 @ SV40 @ SV62 @ SY302 @ SV78 @ SY301 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[218]) ).
thf(237,plain,
! [SV79: $i,SV63: $i,SV42: $i,SV17: $i] :
( ( ( equidistant @ SV17 @ SV42 @ SV63 @ SV79 )
= $false )
| ( ( equidistant @ SV63 @ SV79 @ SV17 @ SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(238,plain,
! [SV80: $i,SV64: $i,SV43: $i,SV18: $i] :
( ( ( equidistant @ SV18 @ SV43 @ SV64 @ SV80 )
= $false )
| ( ( equidistant @ SV43 @ SV18 @ SV64 @ SV80 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(239,plain,
! [SV81: $i,SV65: $i,SV44: $i,SV19: $i] :
( ( ( equidistant @ SV19 @ SV44 @ SV65 @ SV81 )
= $false )
| ( ( equidistant @ SV19 @ SV44 @ SV81 @ SV65 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(240,plain,
! [SV82: $i,SV66: $i,SV45: $i,SV20: $i] :
( ( ( equidistant @ SV20 @ SV45 @ SV66 @ SV82 )
= $false )
| ( ( equidistant @ SV45 @ SV20 @ SV82 @ SV66 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[222]) ).
thf(241,plain,
! [SV83: $i,SV67: $i,SV46: $i,SV21: $i] :
( ( ( equidistant @ SV21 @ SV46 @ SV67 @ SV83 )
= $false )
| ( ( equidistant @ SV67 @ SV83 @ SV46 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(242,plain,
! [SV84: $i,SV68: $i,SV47: $i,SV22: $i] :
( ( ( equidistant @ SV22 @ SV47 @ SV68 @ SV84 )
= $false )
| ( ( equidistant @ SV84 @ SV68 @ SV22 @ SV47 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[224]) ).
thf(243,plain,
! [SV85: $i,SV69: $i,SV48: $i,SV23: $i] :
( ( ( equidistant @ SV23 @ SV48 @ SV69 @ SV85 )
= $false )
| ( ( equidistant @ SV85 @ SV69 @ SV48 @ SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(244,plain,
! [SV86: $i,SV70: $i,SV49: $i,SV24: $i] :
( ( ( equidistant @ SV24 @ SV49 @ SV70 @ SV86 )
= $false )
| ( ( ! [SY303: $i,SY304: $i] :
( ~ ( equidistant @ SV70 @ SV86 @ SY303 @ SY304 )
| ( equidistant @ SV24 @ SV49 @ SY303 @ SY304 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(245,plain,
! [SV72: $i,SV51: $i,SV95: $i,SV27: $i,SV2: $i] :
( ( ( ! [SY316: $i] :
( ~ ( equidistant @ SV2 @ SV27 @ SV95 @ SY316 )
| ( equidistant @ SV51 @ SV72 @ SV95 @ SY316 ) ) )
= $true )
| ( ( equidistant @ SV2 @ SV27 @ SV51 @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[227]) ).
thf(246,plain,
! [SV88: $i,SV87: $i,SV76: $i,SV54: $i,SV31: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 ) )
= $true )
| ( ( ~ ( equidistant @ SV31 @ SV87 @ SV76 @ SV88 )
| ! [SY308: $i,SY309: $i] :
( ~ ( equidistant @ SV6 @ SY308 @ SV54 @ SY309 )
| ~ ( equidistant @ SV31 @ SY308 @ SV76 @ SY309 )
| ~ ( between @ SV6 @ SV31 @ SV87 )
| ~ ( between @ SV54 @ SV76 @ SV88 )
| ( SV6 = SV31 )
| ( equidistant @ SV87 @ SY308 @ SV88 @ SY309 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(247,plain,
! [SV8: $i,SV33: $i,SV55: $i,SV96: $i,SV89: $i] :
( ( ( ~ ( between @ SV89 @ SV96 @ SV55 )
| ( between @ SV33 @ ( inner_pasch @ SV8 @ SV33 @ SV55 @ SV96 @ SV89 ) @ SV89 ) )
= $true )
| ( ( between @ SV8 @ SV33 @ SV55 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(248,plain,
! [SV34: $i,SV9: $i,SV56: $i,SV97: $i,SV90: $i] :
( ( ( ~ ( between @ SV90 @ SV97 @ SV56 )
| ( between @ SV97 @ ( inner_pasch @ SV9 @ SV34 @ SV56 @ SV97 @ SV90 ) @ SV9 ) )
= $true )
| ( ( between @ SV9 @ SV34 @ SV56 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[230]) ).
thf(249,plain,
! [SV10: $i,SV57: $i,SV35: $i,SV91: $i] :
( ( ( ~ ( equidistant @ SV91 @ SV35 @ SV91 @ SV57 ) )
= $true )
| ( ( ! [SY312: $i] :
( ~ ( equidistant @ SY312 @ SV35 @ SY312 @ SV57 )
| ( between @ SV10 @ SV91 @ SY312 )
| ( between @ SV91 @ SY312 @ SV10 )
| ( SV35 = SV57 )
| ( between @ SY312 @ SV10 @ SV91 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV35 @ SV10 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[231]) ).
thf(250,plain,
! [SV58: $i,SV11: $i,SV98: $i,SV36: $i,SV92: $i] :
( ( ( ~ ( between @ SV92 @ SV36 @ SV98 )
| ( SV11 = SV36 )
| ( between @ SV11 @ SV92 @ ( euclid1 @ SV11 @ SV92 @ SV36 @ SV98 @ SV58 ) ) )
= $true )
| ( ( between @ SV11 @ SV36 @ SV58 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(251,plain,
! [SV59: $i,SV12: $i,SV99: $i,SV37: $i,SV93: $i] :
( ( ( ~ ( between @ SV93 @ SV37 @ SV99 )
| ( SV12 = SV37 )
| ( between @ SV12 @ SV99 @ ( euclid2 @ SV12 @ SV93 @ SV37 @ SV99 @ SV59 ) ) )
= $true )
| ( ( between @ SV12 @ SV37 @ SV59 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[233]) ).
thf(252,plain,
! [SV60: $i,SV13: $i,SV100: $i,SV38: $i,SV94: $i] :
( ( ( ~ ( between @ SV94 @ SV38 @ SV100 )
| ( SV13 = SV38 )
| ( between @ ( euclid1 @ SV13 @ SV94 @ SV38 @ SV100 @ SV60 ) @ SV60 @ ( euclid2 @ SV13 @ SV94 @ SV38 @ SV100 @ SV60 ) ) )
= $true )
| ( ( between @ SV13 @ SV38 @ SV60 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[234]) ).
thf(253,plain,
! [SV61: $i,SV39: $i,SV101: $i,SV77: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV77 @ SV14 @ SV101 )
| ~ ( between @ SV14 @ SV39 @ SV77 )
| ! [SY317: $i] :
( ~ ( between @ SV39 @ SY317 @ SV77 )
| ( between @ SV61 @ ( continuous @ SV14 @ SV39 @ SV61 @ SY317 @ SV77 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV39 @ SV14 @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[235]) ).
thf(254,plain,
! [SV62: $i,SV40: $i,SV102: $i,SV78: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV78 @ SV15 @ SV102 )
| ~ ( between @ SV15 @ SV40 @ SV78 )
| ! [SY318: $i] :
( ~ ( between @ SV40 @ SY318 @ SV78 )
| ( equidistant @ SV15 @ SY318 @ SV15 @ ( continuous @ SV15 @ SV40 @ SV62 @ SY318 @ SV78 @ SV102 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV40 @ SV15 @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[236]) ).
thf(255,plain,
! [SV49: $i,SV24: $i,SV103: $i,SV86: $i,SV70: $i] :
( ( ( ! [SY319: $i] :
( ~ ( equidistant @ SV70 @ SV86 @ SV103 @ SY319 )
| ( equidistant @ SV24 @ SV49 @ SV103 @ SY319 ) ) )
= $true )
| ( ( equidistant @ SV24 @ SV49 @ SV70 @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[244]) ).
thf(256,plain,
! [SV72: $i,SV51: $i,SV104: $i,SV95: $i,SV27: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV27 @ SV95 @ SV104 )
| ( equidistant @ SV51 @ SV72 @ SV95 @ SV104 ) )
= $true )
| ( ( equidistant @ SV2 @ SV27 @ SV51 @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[245]) ).
thf(257,plain,
! [SV88: $i,SV87: $i,SV76: $i,SV54: $i,SV31: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
= $false )
| ( ( ~ ( equidistant @ SV31 @ SV87 @ SV76 @ SV88 )
| ! [SY308: $i,SY309: $i] :
( ~ ( equidistant @ SV6 @ SY308 @ SV54 @ SY309 )
| ~ ( equidistant @ SV31 @ SY308 @ SV76 @ SY309 )
| ~ ( between @ SV6 @ SV31 @ SV87 )
| ~ ( between @ SV54 @ SV76 @ SV88 )
| ( SV6 = SV31 )
| ( equidistant @ SV87 @ SY308 @ SV88 @ SY309 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[246]) ).
thf(258,plain,
! [SV8: $i,SV33: $i,SV55: $i,SV96: $i,SV89: $i] :
( ( ( ~ ( between @ SV89 @ SV96 @ SV55 ) )
= $true )
| ( ( between @ SV33 @ ( inner_pasch @ SV8 @ SV33 @ SV55 @ SV96 @ SV89 ) @ SV89 )
= $true )
| ( ( between @ SV8 @ SV33 @ SV55 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[247]) ).
thf(259,plain,
! [SV34: $i,SV9: $i,SV56: $i,SV97: $i,SV90: $i] :
( ( ( ~ ( between @ SV90 @ SV97 @ SV56 ) )
= $true )
| ( ( between @ SV97 @ ( inner_pasch @ SV9 @ SV34 @ SV56 @ SV97 @ SV90 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV34 @ SV56 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(260,plain,
! [SV10: $i,SV57: $i,SV35: $i,SV91: $i] :
( ( ( equidistant @ SV91 @ SV35 @ SV91 @ SV57 )
= $false )
| ( ( ! [SY312: $i] :
( ~ ( equidistant @ SY312 @ SV35 @ SY312 @ SV57 )
| ( between @ SV10 @ SV91 @ SY312 )
| ( between @ SV91 @ SY312 @ SV10 )
| ( SV35 = SV57 )
| ( between @ SY312 @ SV10 @ SV91 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV35 @ SV10 @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(261,plain,
! [SV58: $i,SV11: $i,SV98: $i,SV36: $i,SV92: $i] :
( ( ( ~ ( between @ SV92 @ SV36 @ SV98 ) )
= $true )
| ( ( ( SV11 = SV36 )
| ( between @ SV11 @ SV92 @ ( euclid1 @ SV11 @ SV92 @ SV36 @ SV98 @ SV58 ) ) )
= $true )
| ( ( between @ SV11 @ SV36 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(262,plain,
! [SV59: $i,SV12: $i,SV99: $i,SV37: $i,SV93: $i] :
( ( ( ~ ( between @ SV93 @ SV37 @ SV99 ) )
= $true )
| ( ( ( SV12 = SV37 )
| ( between @ SV12 @ SV99 @ ( euclid2 @ SV12 @ SV93 @ SV37 @ SV99 @ SV59 ) ) )
= $true )
| ( ( between @ SV12 @ SV37 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[251]) ).
thf(263,plain,
! [SV60: $i,SV13: $i,SV100: $i,SV38: $i,SV94: $i] :
( ( ( ~ ( between @ SV94 @ SV38 @ SV100 ) )
= $true )
| ( ( ( SV13 = SV38 )
| ( between @ ( euclid1 @ SV13 @ SV94 @ SV38 @ SV100 @ SV60 ) @ SV60 @ ( euclid2 @ SV13 @ SV94 @ SV38 @ SV100 @ SV60 ) ) )
= $true )
| ( ( between @ SV13 @ SV38 @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[252]) ).
thf(264,plain,
! [SV61: $i,SV39: $i,SV101: $i,SV77: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV77 @ SV14 @ SV101 ) )
= $true )
| ( ( ~ ( between @ SV14 @ SV39 @ SV77 )
| ! [SY317: $i] :
( ~ ( between @ SV39 @ SY317 @ SV77 )
| ( between @ SV61 @ ( continuous @ SV14 @ SV39 @ SV61 @ SY317 @ SV77 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV39 @ SV14 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[253]) ).
thf(265,plain,
! [SV62: $i,SV40: $i,SV102: $i,SV78: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV78 @ SV15 @ SV102 ) )
= $true )
| ( ( ~ ( between @ SV15 @ SV40 @ SV78 )
| ! [SY318: $i] :
( ~ ( between @ SV40 @ SY318 @ SV78 )
| ( equidistant @ SV15 @ SY318 @ SV15 @ ( continuous @ SV15 @ SV40 @ SV62 @ SY318 @ SV78 @ SV102 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV40 @ SV15 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[254]) ).
thf(266,plain,
! [SV49: $i,SV24: $i,SV105: $i,SV103: $i,SV86: $i,SV70: $i] :
( ( ( ~ ( equidistant @ SV70 @ SV86 @ SV103 @ SV105 )
| ( equidistant @ SV24 @ SV49 @ SV103 @ SV105 ) )
= $true )
| ( ( equidistant @ SV24 @ SV49 @ SV70 @ SV86 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[255]) ).
thf(267,plain,
! [SV72: $i,SV51: $i,SV104: $i,SV95: $i,SV27: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV27 @ SV95 @ SV104 ) )
= $true )
| ( ( equidistant @ SV51 @ SV72 @ SV95 @ SV104 )
= $true )
| ( ( equidistant @ SV2 @ SV27 @ SV51 @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[256]) ).
thf(268,plain,
! [SV54: $i,SV6: $i,SV88: $i,SV76: $i,SV87: $i,SV31: $i] :
( ( ( ~ ( equidistant @ SV31 @ SV87 @ SV76 @ SV88 ) )
= $true )
| ( ( ! [SY308: $i,SY309: $i] :
( ~ ( equidistant @ SV6 @ SY308 @ SV54 @ SY309 )
| ~ ( equidistant @ SV31 @ SY308 @ SV76 @ SY309 )
| ~ ( between @ SV6 @ SV31 @ SV87 )
| ~ ( between @ SV54 @ SV76 @ SV88 )
| ( SV6 = SV31 )
| ( equidistant @ SV87 @ SY308 @ SV88 @ SY309 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[257]) ).
thf(269,plain,
! [SV8: $i,SV33: $i,SV55: $i,SV96: $i,SV89: $i] :
( ( ( between @ SV89 @ SV96 @ SV55 )
= $false )
| ( ( between @ SV33 @ ( inner_pasch @ SV8 @ SV33 @ SV55 @ SV96 @ SV89 ) @ SV89 )
= $true )
| ( ( between @ SV8 @ SV33 @ SV55 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(270,plain,
! [SV34: $i,SV9: $i,SV56: $i,SV97: $i,SV90: $i] :
( ( ( between @ SV90 @ SV97 @ SV56 )
= $false )
| ( ( between @ SV97 @ ( inner_pasch @ SV9 @ SV34 @ SV56 @ SV97 @ SV90 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV34 @ SV56 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(271,plain,
! [SV91: $i,SV10: $i,SV57: $i,SV35: $i,SV106: $i] :
( ( ( ~ ( equidistant @ SV106 @ SV35 @ SV106 @ SV57 )
| ( between @ SV10 @ SV91 @ SV106 )
| ( between @ SV91 @ SV106 @ SV10 )
| ( SV35 = SV57 )
| ( between @ SV106 @ SV10 @ SV91 ) )
= $true )
| ( ( equidistant @ SV91 @ SV35 @ SV91 @ SV57 )
= $false )
| ( ( equidistant @ SV10 @ SV35 @ SV10 @ SV57 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[260]) ).
thf(272,plain,
! [SV58: $i,SV11: $i,SV98: $i,SV36: $i,SV92: $i] :
( ( ( between @ SV92 @ SV36 @ SV98 )
= $false )
| ( ( ( SV11 = SV36 )
| ( between @ SV11 @ SV92 @ ( euclid1 @ SV11 @ SV92 @ SV36 @ SV98 @ SV58 ) ) )
= $true )
| ( ( between @ SV11 @ SV36 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(273,plain,
! [SV59: $i,SV12: $i,SV99: $i,SV37: $i,SV93: $i] :
( ( ( between @ SV93 @ SV37 @ SV99 )
= $false )
| ( ( ( SV12 = SV37 )
| ( between @ SV12 @ SV99 @ ( euclid2 @ SV12 @ SV93 @ SV37 @ SV99 @ SV59 ) ) )
= $true )
| ( ( between @ SV12 @ SV37 @ SV59 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(274,plain,
! [SV60: $i,SV13: $i,SV100: $i,SV38: $i,SV94: $i] :
( ( ( between @ SV94 @ SV38 @ SV100 )
= $false )
| ( ( ( SV13 = SV38 )
| ( between @ ( euclid1 @ SV13 @ SV94 @ SV38 @ SV100 @ SV60 ) @ SV60 @ ( euclid2 @ SV13 @ SV94 @ SV38 @ SV100 @ SV60 ) ) )
= $true )
| ( ( between @ SV13 @ SV38 @ SV60 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[263]) ).
thf(275,plain,
! [SV61: $i,SV39: $i,SV101: $i,SV77: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV77 @ SV14 @ SV101 )
= $false )
| ( ( ~ ( between @ SV14 @ SV39 @ SV77 )
| ! [SY317: $i] :
( ~ ( between @ SV39 @ SY317 @ SV77 )
| ( between @ SV61 @ ( continuous @ SV14 @ SV39 @ SV61 @ SY317 @ SV77 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV39 @ SV14 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[264]) ).
thf(276,plain,
! [SV62: $i,SV40: $i,SV102: $i,SV78: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV78 @ SV15 @ SV102 )
= $false )
| ( ( ~ ( between @ SV15 @ SV40 @ SV78 )
| ! [SY318: $i] :
( ~ ( between @ SV40 @ SY318 @ SV78 )
| ( equidistant @ SV15 @ SY318 @ SV15 @ ( continuous @ SV15 @ SV40 @ SV62 @ SY318 @ SV78 @ SV102 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV40 @ SV15 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[265]) ).
thf(277,plain,
! [SV49: $i,SV24: $i,SV105: $i,SV103: $i,SV86: $i,SV70: $i] :
( ( ( ~ ( equidistant @ SV70 @ SV86 @ SV103 @ SV105 ) )
= $true )
| ( ( equidistant @ SV24 @ SV49 @ SV103 @ SV105 )
= $true )
| ( ( equidistant @ SV24 @ SV49 @ SV70 @ SV86 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[266]) ).
thf(278,plain,
! [SV72: $i,SV51: $i,SV104: $i,SV95: $i,SV27: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV27 @ SV95 @ SV104 )
= $false )
| ( ( equidistant @ SV51 @ SV72 @ SV95 @ SV104 )
= $true )
| ( ( equidistant @ SV2 @ SV27 @ SV51 @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[267]) ).
thf(279,plain,
! [SV54: $i,SV6: $i,SV88: $i,SV76: $i,SV87: $i,SV31: $i] :
( ( ( equidistant @ SV31 @ SV87 @ SV76 @ SV88 )
= $false )
| ( ( ! [SY308: $i,SY309: $i] :
( ~ ( equidistant @ SV6 @ SY308 @ SV54 @ SY309 )
| ~ ( equidistant @ SV31 @ SY308 @ SV76 @ SY309 )
| ~ ( between @ SV6 @ SV31 @ SV87 )
| ~ ( between @ SV54 @ SV76 @ SV88 )
| ( SV6 = SV31 )
| ( equidistant @ SV87 @ SY308 @ SV88 @ SY309 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[268]) ).
thf(280,plain,
! [SV91: $i,SV10: $i,SV57: $i,SV35: $i,SV106: $i] :
( ( ( ~ ( equidistant @ SV106 @ SV35 @ SV106 @ SV57 ) )
= $true )
| ( ( ( between @ SV10 @ SV91 @ SV106 )
| ( between @ SV91 @ SV106 @ SV10 )
| ( SV35 = SV57 )
| ( between @ SV106 @ SV10 @ SV91 ) )
= $true )
| ( ( equidistant @ SV91 @ SV35 @ SV91 @ SV57 )
= $false )
| ( ( equidistant @ SV10 @ SV35 @ SV10 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[271]) ).
thf(281,plain,
! [SV58: $i,SV98: $i,SV92: $i,SV36: $i,SV11: $i] :
( ( ( SV11 = SV36 )
= $true )
| ( ( between @ SV11 @ SV92 @ ( euclid1 @ SV11 @ SV92 @ SV36 @ SV98 @ SV58 ) )
= $true )
| ( ( between @ SV92 @ SV36 @ SV98 )
= $false )
| ( ( between @ SV11 @ SV36 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[272]) ).
thf(282,plain,
! [SV59: $i,SV93: $i,SV99: $i,SV37: $i,SV12: $i] :
( ( ( SV12 = SV37 )
= $true )
| ( ( between @ SV12 @ SV99 @ ( euclid2 @ SV12 @ SV93 @ SV37 @ SV99 @ SV59 ) )
= $true )
| ( ( between @ SV93 @ SV37 @ SV99 )
= $false )
| ( ( between @ SV12 @ SV37 @ SV59 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[273]) ).
thf(283,plain,
! [SV60: $i,SV100: $i,SV94: $i,SV38: $i,SV13: $i] :
( ( ( SV13 = SV38 )
= $true )
| ( ( between @ ( euclid1 @ SV13 @ SV94 @ SV38 @ SV100 @ SV60 ) @ SV60 @ ( euclid2 @ SV13 @ SV94 @ SV38 @ SV100 @ SV60 ) )
= $true )
| ( ( between @ SV94 @ SV38 @ SV100 )
= $false )
| ( ( between @ SV13 @ SV38 @ SV60 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[274]) ).
thf(284,plain,
! [SV101: $i,SV61: $i,SV77: $i,SV39: $i,SV14: $i] :
( ( ( ~ ( between @ SV14 @ SV39 @ SV77 ) )
= $true )
| ( ( ! [SY317: $i] :
( ~ ( between @ SV39 @ SY317 @ SV77 )
| ( between @ SV61 @ ( continuous @ SV14 @ SV39 @ SV61 @ SY317 @ SV77 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV77 @ SV14 @ SV101 )
= $false )
| ( ( equidistant @ SV14 @ SV39 @ SV14 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[275]) ).
thf(285,plain,
! [SV102: $i,SV62: $i,SV78: $i,SV40: $i,SV15: $i] :
( ( ( ~ ( between @ SV15 @ SV40 @ SV78 ) )
= $true )
| ( ( ! [SY318: $i] :
( ~ ( between @ SV40 @ SY318 @ SV78 )
| ( equidistant @ SV15 @ SY318 @ SV15 @ ( continuous @ SV15 @ SV40 @ SV62 @ SY318 @ SV78 @ SV102 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV78 @ SV15 @ SV102 )
= $false )
| ( ( equidistant @ SV15 @ SV40 @ SV15 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[276]) ).
thf(286,plain,
! [SV49: $i,SV24: $i,SV105: $i,SV103: $i,SV86: $i,SV70: $i] :
( ( ( equidistant @ SV70 @ SV86 @ SV103 @ SV105 )
= $false )
| ( ( equidistant @ SV24 @ SV49 @ SV103 @ SV105 )
= $true )
| ( ( equidistant @ SV24 @ SV49 @ SV70 @ SV86 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[277]) ).
thf(287,plain,
! [SV88: $i,SV87: $i,SV76: $i,SV31: $i,SV54: $i,SV107: $i,SV6: $i] :
( ( ( ! [SY320: $i] :
( ~ ( equidistant @ SV6 @ SV107 @ SV54 @ SY320 )
| ~ ( equidistant @ SV31 @ SV107 @ SV76 @ SY320 )
| ~ ( between @ SV6 @ SV31 @ SV87 )
| ~ ( between @ SV54 @ SV76 @ SV88 )
| ( SV6 = SV31 )
| ( equidistant @ SV87 @ SV107 @ SV88 @ SY320 ) ) )
= $true )
| ( ( equidistant @ SV31 @ SV87 @ SV76 @ SV88 )
= $false )
| ( ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[279]) ).
thf(288,plain,
! [SV91: $i,SV10: $i,SV57: $i,SV35: $i,SV106: $i] :
( ( ( equidistant @ SV106 @ SV35 @ SV106 @ SV57 )
= $false )
| ( ( ( between @ SV10 @ SV91 @ SV106 )
| ( between @ SV91 @ SV106 @ SV10 )
| ( SV35 = SV57 )
| ( between @ SV106 @ SV10 @ SV91 ) )
= $true )
| ( ( equidistant @ SV91 @ SV35 @ SV91 @ SV57 )
= $false )
| ( ( equidistant @ SV10 @ SV35 @ SV10 @ SV57 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[280]) ).
thf(289,plain,
! [SV101: $i,SV61: $i,SV77: $i,SV39: $i,SV14: $i] :
( ( ( between @ SV14 @ SV39 @ SV77 )
= $false )
| ( ( ! [SY317: $i] :
( ~ ( between @ SV39 @ SY317 @ SV77 )
| ( between @ SV61 @ ( continuous @ SV14 @ SV39 @ SV61 @ SY317 @ SV77 @ SV101 ) @ SV101 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV77 @ SV14 @ SV101 )
= $false )
| ( ( equidistant @ SV14 @ SV39 @ SV14 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(290,plain,
! [SV102: $i,SV62: $i,SV78: $i,SV40: $i,SV15: $i] :
( ( ( between @ SV15 @ SV40 @ SV78 )
= $false )
| ( ( ! [SY318: $i] :
( ~ ( between @ SV40 @ SY318 @ SV78 )
| ( equidistant @ SV15 @ SY318 @ SV15 @ ( continuous @ SV15 @ SV40 @ SV62 @ SY318 @ SV78 @ SV102 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV78 @ SV15 @ SV102 )
= $false )
| ( ( equidistant @ SV15 @ SV40 @ SV15 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[285]) ).
thf(291,plain,
! [SV88: $i,SV87: $i,SV76: $i,SV31: $i,SV108: $i,SV54: $i,SV107: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV107 @ SV54 @ SV108 )
| ~ ( equidistant @ SV31 @ SV107 @ SV76 @ SV108 )
| ~ ( between @ SV6 @ SV31 @ SV87 )
| ~ ( between @ SV54 @ SV76 @ SV88 )
| ( SV6 = SV31 )
| ( equidistant @ SV87 @ SV107 @ SV88 @ SV108 ) )
= $true )
| ( ( equidistant @ SV31 @ SV87 @ SV76 @ SV88 )
= $false )
| ( ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[287]) ).
thf(292,plain,
! [SV57: $i,SV35: $i,SV106: $i,SV91: $i,SV10: $i] :
( ( ( between @ SV10 @ SV91 @ SV106 )
= $true )
| ( ( ( between @ SV91 @ SV106 @ SV10 )
| ( SV35 = SV57 )
| ( between @ SV106 @ SV10 @ SV91 ) )
= $true )
| ( ( equidistant @ SV106 @ SV35 @ SV106 @ SV57 )
= $false )
| ( ( equidistant @ SV91 @ SV35 @ SV91 @ SV57 )
= $false )
| ( ( equidistant @ SV10 @ SV35 @ SV10 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(293,plain,
! [SV101: $i,SV14: $i,SV61: $i,SV77: $i,SV109: $i,SV39: $i] :
( ( ( ~ ( between @ SV39 @ SV109 @ SV77 )
| ( between @ SV61 @ ( continuous @ SV14 @ SV39 @ SV61 @ SV109 @ SV77 @ SV101 ) @ SV101 ) )
= $true )
| ( ( between @ SV14 @ SV39 @ SV77 )
= $false )
| ( ( equidistant @ SV14 @ SV77 @ SV14 @ SV101 )
= $false )
| ( ( equidistant @ SV14 @ SV39 @ SV14 @ SV61 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[289]) ).
thf(294,plain,
! [SV102: $i,SV62: $i,SV15: $i,SV78: $i,SV110: $i,SV40: $i] :
( ( ( ~ ( between @ SV40 @ SV110 @ SV78 )
| ( equidistant @ SV15 @ SV110 @ SV15 @ ( continuous @ SV15 @ SV40 @ SV62 @ SV110 @ SV78 @ SV102 ) ) )
= $true )
| ( ( between @ SV15 @ SV40 @ SV78 )
= $false )
| ( ( equidistant @ SV15 @ SV78 @ SV15 @ SV102 )
= $false )
| ( ( equidistant @ SV15 @ SV40 @ SV15 @ SV62 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[290]) ).
thf(295,plain,
! [SV88: $i,SV87: $i,SV76: $i,SV31: $i,SV108: $i,SV54: $i,SV107: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV107 @ SV54 @ SV108 ) )
= $true )
| ( ( ~ ( equidistant @ SV31 @ SV107 @ SV76 @ SV108 )
| ~ ( between @ SV6 @ SV31 @ SV87 )
| ~ ( between @ SV54 @ SV76 @ SV88 )
| ( SV6 = SV31 )
| ( equidistant @ SV87 @ SV107 @ SV88 @ SV108 ) )
= $true )
| ( ( equidistant @ SV31 @ SV87 @ SV76 @ SV88 )
= $false )
| ( ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(296,plain,
! [SV57: $i,SV35: $i,SV10: $i,SV106: $i,SV91: $i] :
( ( ( between @ SV91 @ SV106 @ SV10 )
= $true )
| ( ( ( SV35 = SV57 )
| ( between @ SV106 @ SV10 @ SV91 ) )
= $true )
| ( ( between @ SV10 @ SV91 @ SV106 )
= $true )
| ( ( equidistant @ SV106 @ SV35 @ SV106 @ SV57 )
= $false )
| ( ( equidistant @ SV91 @ SV35 @ SV91 @ SV57 )
= $false )
| ( ( equidistant @ SV10 @ SV35 @ SV10 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(297,plain,
! [SV101: $i,SV14: $i,SV61: $i,SV77: $i,SV109: $i,SV39: $i] :
( ( ( ~ ( between @ SV39 @ SV109 @ SV77 ) )
= $true )
| ( ( between @ SV61 @ ( continuous @ SV14 @ SV39 @ SV61 @ SV109 @ SV77 @ SV101 ) @ SV101 )
= $true )
| ( ( between @ SV14 @ SV39 @ SV77 )
= $false )
| ( ( equidistant @ SV14 @ SV77 @ SV14 @ SV101 )
= $false )
| ( ( equidistant @ SV14 @ SV39 @ SV14 @ SV61 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[293]) ).
thf(298,plain,
! [SV102: $i,SV62: $i,SV15: $i,SV78: $i,SV110: $i,SV40: $i] :
( ( ( ~ ( between @ SV40 @ SV110 @ SV78 ) )
= $true )
| ( ( equidistant @ SV15 @ SV110 @ SV15 @ ( continuous @ SV15 @ SV40 @ SV62 @ SV110 @ SV78 @ SV102 ) )
= $true )
| ( ( between @ SV15 @ SV40 @ SV78 )
= $false )
| ( ( equidistant @ SV15 @ SV78 @ SV15 @ SV102 )
= $false )
| ( ( equidistant @ SV15 @ SV40 @ SV15 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[294]) ).
thf(299,plain,
! [SV88: $i,SV87: $i,SV76: $i,SV31: $i,SV108: $i,SV54: $i,SV107: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV107 @ SV54 @ SV108 )
= $false )
| ( ( ~ ( equidistant @ SV31 @ SV107 @ SV76 @ SV108 )
| ~ ( between @ SV6 @ SV31 @ SV87 )
| ~ ( between @ SV54 @ SV76 @ SV88 )
| ( SV6 = SV31 )
| ( equidistant @ SV87 @ SV107 @ SV88 @ SV108 ) )
= $true )
| ( ( equidistant @ SV31 @ SV87 @ SV76 @ SV88 )
= $false )
| ( ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[295]) ).
thf(300,plain,
! [SV91: $i,SV10: $i,SV106: $i,SV57: $i,SV35: $i] :
( ( ( SV35 = SV57 )
= $true )
| ( ( between @ SV106 @ SV10 @ SV91 )
= $true )
| ( ( between @ SV91 @ SV106 @ SV10 )
= $true )
| ( ( between @ SV10 @ SV91 @ SV106 )
= $true )
| ( ( equidistant @ SV106 @ SV35 @ SV106 @ SV57 )
= $false )
| ( ( equidistant @ SV91 @ SV35 @ SV91 @ SV57 )
= $false )
| ( ( equidistant @ SV10 @ SV35 @ SV10 @ SV57 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(301,plain,
! [SV101: $i,SV14: $i,SV61: $i,SV77: $i,SV109: $i,SV39: $i] :
( ( ( between @ SV39 @ SV109 @ SV77 )
= $false )
| ( ( between @ SV61 @ ( continuous @ SV14 @ SV39 @ SV61 @ SV109 @ SV77 @ SV101 ) @ SV101 )
= $true )
| ( ( between @ SV14 @ SV39 @ SV77 )
= $false )
| ( ( equidistant @ SV14 @ SV77 @ SV14 @ SV101 )
= $false )
| ( ( equidistant @ SV14 @ SV39 @ SV14 @ SV61 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(302,plain,
! [SV102: $i,SV62: $i,SV15: $i,SV78: $i,SV110: $i,SV40: $i] :
( ( ( between @ SV40 @ SV110 @ SV78 )
= $false )
| ( ( equidistant @ SV15 @ SV110 @ SV15 @ ( continuous @ SV15 @ SV40 @ SV62 @ SV110 @ SV78 @ SV102 ) )
= $true )
| ( ( between @ SV15 @ SV40 @ SV78 )
= $false )
| ( ( equidistant @ SV15 @ SV78 @ SV15 @ SV102 )
= $false )
| ( ( equidistant @ SV15 @ SV40 @ SV15 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(303,plain,
! [SV88: $i,SV54: $i,SV87: $i,SV6: $i,SV108: $i,SV76: $i,SV107: $i,SV31: $i] :
( ( ( ~ ( equidistant @ SV31 @ SV107 @ SV76 @ SV108 ) )
= $true )
| ( ( ~ ( between @ SV6 @ SV31 @ SV87 )
| ~ ( between @ SV54 @ SV76 @ SV88 )
| ( SV6 = SV31 )
| ( equidistant @ SV87 @ SV107 @ SV88 @ SV108 ) )
= $true )
| ( ( equidistant @ SV6 @ SV107 @ SV54 @ SV108 )
= $false )
| ( ( equidistant @ SV31 @ SV87 @ SV76 @ SV88 )
= $false )
| ( ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[299]) ).
thf(304,plain,
! [SV88: $i,SV54: $i,SV87: $i,SV6: $i,SV108: $i,SV76: $i,SV107: $i,SV31: $i] :
( ( ( equidistant @ SV31 @ SV107 @ SV76 @ SV108 )
= $false )
| ( ( ~ ( between @ SV6 @ SV31 @ SV87 )
| ~ ( between @ SV54 @ SV76 @ SV88 )
| ( SV6 = SV31 )
| ( equidistant @ SV87 @ SV107 @ SV88 @ SV108 ) )
= $true )
| ( ( equidistant @ SV6 @ SV107 @ SV54 @ SV108 )
= $false )
| ( ( equidistant @ SV31 @ SV87 @ SV76 @ SV88 )
= $false )
| ( ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(305,plain,
! [SV108: $i,SV107: $i,SV88: $i,SV76: $i,SV54: $i,SV87: $i,SV31: $i,SV6: $i] :
( ( ( ~ ( between @ SV6 @ SV31 @ SV87 ) )
= $true )
| ( ( ~ ( between @ SV54 @ SV76 @ SV88 )
| ( SV6 = SV31 )
| ( equidistant @ SV87 @ SV107 @ SV88 @ SV108 ) )
= $true )
| ( ( equidistant @ SV31 @ SV107 @ SV76 @ SV108 )
= $false )
| ( ( equidistant @ SV6 @ SV107 @ SV54 @ SV108 )
= $false )
| ( ( equidistant @ SV31 @ SV87 @ SV76 @ SV88 )
= $false )
| ( ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[304]) ).
thf(306,plain,
! [SV108: $i,SV107: $i,SV88: $i,SV76: $i,SV54: $i,SV87: $i,SV31: $i,SV6: $i] :
( ( ( between @ SV6 @ SV31 @ SV87 )
= $false )
| ( ( ~ ( between @ SV54 @ SV76 @ SV88 )
| ( SV6 = SV31 )
| ( equidistant @ SV87 @ SV107 @ SV88 @ SV108 ) )
= $true )
| ( ( equidistant @ SV31 @ SV107 @ SV76 @ SV108 )
= $false )
| ( ( equidistant @ SV6 @ SV107 @ SV54 @ SV108 )
= $false )
| ( ( equidistant @ SV31 @ SV87 @ SV76 @ SV88 )
= $false )
| ( ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[305]) ).
thf(307,plain,
! [SV108: $i,SV107: $i,SV87: $i,SV31: $i,SV6: $i,SV88: $i,SV76: $i,SV54: $i] :
( ( ( ~ ( between @ SV54 @ SV76 @ SV88 ) )
= $true )
| ( ( ( SV6 = SV31 )
| ( equidistant @ SV87 @ SV107 @ SV88 @ SV108 ) )
= $true )
| ( ( between @ SV6 @ SV31 @ SV87 )
= $false )
| ( ( equidistant @ SV31 @ SV107 @ SV76 @ SV108 )
= $false )
| ( ( equidistant @ SV6 @ SV107 @ SV54 @ SV108 )
= $false )
| ( ( equidistant @ SV31 @ SV87 @ SV76 @ SV88 )
= $false )
| ( ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[306]) ).
thf(308,plain,
! [SV108: $i,SV107: $i,SV87: $i,SV31: $i,SV6: $i,SV88: $i,SV76: $i,SV54: $i] :
( ( ( between @ SV54 @ SV76 @ SV88 )
= $false )
| ( ( ( SV6 = SV31 )
| ( equidistant @ SV87 @ SV107 @ SV88 @ SV108 ) )
= $true )
| ( ( between @ SV6 @ SV31 @ SV87 )
= $false )
| ( ( equidistant @ SV31 @ SV107 @ SV76 @ SV108 )
= $false )
| ( ( equidistant @ SV6 @ SV107 @ SV54 @ SV108 )
= $false )
| ( ( equidistant @ SV31 @ SV87 @ SV76 @ SV88 )
= $false )
| ( ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(309,plain,
! [SV76: $i,SV54: $i,SV108: $i,SV88: $i,SV107: $i,SV87: $i,SV31: $i,SV6: $i] :
( ( ( SV6 = SV31 )
= $true )
| ( ( equidistant @ SV87 @ SV107 @ SV88 @ SV108 )
= $true )
| ( ( between @ SV54 @ SV76 @ SV88 )
= $false )
| ( ( between @ SV6 @ SV31 @ SV87 )
= $false )
| ( ( equidistant @ SV31 @ SV107 @ SV76 @ SV108 )
= $false )
| ( ( equidistant @ SV6 @ SV107 @ SV54 @ SV108 )
= $false )
| ( ( equidistant @ SV31 @ SV87 @ SV76 @ SV88 )
= $false )
| ( ( equidistant @ SV6 @ SV31 @ SV54 @ SV76 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[308]) ).
thf(310,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[78,309,302,301,300,286,283,282,281,278,270,269,243,242,241,240,239,238,237,209,191,189,188,185,153,138,137,120,119,118,108]) ).
thf(311,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[310]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO038-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n020.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Fri Jun 17 23:43:34 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.20/0.43
% 0.20/0.43 No.of.Axioms: 30
% 0.20/0.43
% 0.20/0.43 Length.of.Defs: 0
% 0.20/0.43
% 0.20/0.43 Contains.Choice.Funs: false
% 0.20/0.46 .
% 0.20/0.51 (rf:0,axioms:30,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:32,loop_count:0,foatp_calls:0,translation:fof_full).....................
% 0.57/0.77
% 0.57/0.77 ********************************
% 0.57/0.77 * All subproblems solved! *
% 0.57/0.77 ********************************
% 0.57/0.77 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:30,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:310,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.57/0.80
% 0.57/0.80 %**** Beginning of derivation protocol ****
% 0.57/0.80 % SZS output start CNFRefutation
% See solution above
% 0.57/0.80
% 0.57/0.80 %**** End of derivation protocol ****
% 0.57/0.80 %**** no. of clauses in derivation: 311 ****
% 0.57/0.80 %**** clause counter: 310 ****
% 0.57/0.80
% 0.57/0.80 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:30,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:310,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------