TSTP Solution File: GEO011-4 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GEO011-4 : 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 : n024.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 05:06:02 EDT 2022
% Result : Unsatisfiable 0.60s 0.77s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 36
% Syntax : Number of formulae : 265 ( 137 unt; 12 typ; 0 def)
% Number of atoms : 1824 ( 535 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 5338 ( 416 ~; 703 |; 0 &;4219 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 5 con; 0-6 aty)
% Number of variables : 1139 ( 0 ^1139 !; 0 ?;1139 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_between,type,
between: $i > $i > $i > $o ).
thf(tp_colinear,type,
colinear: $i > $i > $i > $o ).
thf(tp_continuous,type,
continuous: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_distance,type,
distance: $i > $i > $i ).
thf(tp_equal_distance,type,
equal_distance: $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(1,axiom,
! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equal_distance @ ( distance @ U @ V ) @ ( distance @ U @ V1 ) )
| ~ ( equal_distance @ ( distance @ U @ X ) @ ( distance @ U @ X1 ) )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( equal_distance @ ( distance @ U @ W ) @ ( distance @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).
thf(2,axiom,
! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equal_distance @ ( distance @ U @ V ) @ ( distance @ U @ V1 ) )
| ~ ( equal_distance @ ( distance @ U @ X ) @ ( distance @ 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(3,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(4,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(5,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(6,axiom,
! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( equal_distance @ ( distance @ X @ W ) @ ( distance @ X @ V ) )
| ~ ( equal_distance @ ( distance @ Y @ W ) @ ( distance @ Y @ V ) )
| ~ ( equal_distance @ ( distance @ Z @ W ) @ ( distance @ 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(7,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(8,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(9,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(10,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(11,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(12,axiom,
! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(13,axiom,
! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i,V: $i,V1: $i] :
( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ X1 @ Y1 ) )
| ~ ( equal_distance @ ( distance @ Y @ Z ) @ ( distance @ Y1 @ Z1 ) )
| ~ ( equal_distance @ ( distance @ X @ V ) @ ( distance @ X1 @ V1 ) )
| ~ ( equal_distance @ ( distance @ Y @ V ) @ ( distance @ Y1 @ V1 ) )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equal_distance @ ( distance @ Z @ V ) @ ( distance @ Z1 @ V1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_five_segment) ).
thf(14,axiom,
! [Y: $i,X: $i,W: $i,V: $i] : ( equal_distance @ ( distance @ Y @ ( extension @ X @ Y @ W @ V ) ) @ ( distance @ W @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).
thf(15,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(16,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Z @ Z ) )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(17,axiom,
! [X: $i,Y: $i,Z: $i,V: $i,V2: $i,W: $i] :
( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Z @ V ) )
| ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ V2 @ W ) )
| ( equal_distance @ ( distance @ Z @ V ) @ ( distance @ V2 @ W ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
thf(18,axiom,
! [X: $i,Y: $i] : ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Y @ X ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(19,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( colinear @ X @ Y @ Z )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity4) ).
thf(20,axiom,
! [Z: $i,X: $i,Y: $i] :
( ~ ( between @ Z @ X @ Y )
| ( colinear @ X @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity3) ).
thf(21,axiom,
! [Y: $i,Z: $i,X: $i] :
( ~ ( between @ Y @ Z @ X )
| ( colinear @ X @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity2) ).
thf(22,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ Y @ Z )
| ( colinear @ X @ Y @ Z ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity1) ).
thf(23,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(24,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[23]) ).
thf(25,negated_conjecture,
colinear @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_lower_dimension_points_not_colinear) ).
thf(26,plain,
$false = $false,
inference(unfold_def,[status(thm)],[24]) ).
thf(27,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equal_distance @ ( distance @ U @ V ) @ ( distance @ U @ V1 ) )
| ~ ( equal_distance @ ( distance @ U @ X ) @ ( distance @ U @ X1 ) )
| ~ ( between @ U @ V @ X )
| ~ ( between @ V @ W @ X )
| ( equal_distance @ ( distance @ U @ W ) @ ( distance @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(28,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i,X1: $i,W: $i] :
( ~ ( equal_distance @ ( distance @ U @ V ) @ ( distance @ U @ V1 ) )
| ~ ( equal_distance @ ( distance @ U @ X ) @ ( distance @ 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)],[2]) ).
thf(29,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)],[3]) ).
thf(30,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)],[4]) ).
thf(31,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)],[5]) ).
thf(32,plain,
( ( ! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( equal_distance @ ( distance @ X @ W ) @ ( distance @ X @ V ) )
| ~ ( equal_distance @ ( distance @ Y @ W ) @ ( distance @ Y @ V ) )
| ~ ( equal_distance @ ( distance @ Z @ W ) @ ( distance @ Z @ V ) )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y )
| ( W = V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(33,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(34,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(35,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(36,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)],[10]) ).
thf(37,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)],[11]) ).
thf(38,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(39,plain,
( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i,V: $i,V1: $i] :
( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ X1 @ Y1 ) )
| ~ ( equal_distance @ ( distance @ Y @ Z ) @ ( distance @ Y1 @ Z1 ) )
| ~ ( equal_distance @ ( distance @ X @ V ) @ ( distance @ X1 @ V1 ) )
| ~ ( equal_distance @ ( distance @ Y @ V ) @ ( distance @ Y1 @ V1 ) )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equal_distance @ ( distance @ Z @ V ) @ ( distance @ Z1 @ V1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(40,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equal_distance @ ( distance @ Y @ ( extension @ X @ Y @ W @ V ) ) @ ( distance @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Z @ Z ) )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i,Z: $i,V: $i,V2: $i,W: $i] :
( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Z @ V ) )
| ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ V2 @ W ) )
| ( equal_distance @ ( distance @ Z @ V ) @ ( distance @ V2 @ W ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(44,plain,
( ( ! [X: $i,Y: $i] : ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Y @ X ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(45,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( colinear @ X @ Y @ Z )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(46,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( between @ Z @ X @ Y )
| ( colinear @ X @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(47,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ~ ( between @ Y @ Z @ X )
| ( colinear @ X @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[21]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ Y @ Z )
| ( colinear @ X @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[22]) ).
thf(49,plain,
( ( colinear @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(50,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[26]) ).
thf(51,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i] :
( ~ ( equal_distance @ ( distance @ U @ V ) @ ( distance @ U @ V1 ) )
| ! [X1: $i] :
( ~ ( equal_distance @ ( distance @ U @ X ) @ ( distance @ U @ X1 ) )
| ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( equal_distance @ ( distance @ U @ W ) @ ( distance @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(52,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i] :
( ~ ( equal_distance @ ( distance @ U @ V ) @ ( distance @ U @ V1 ) )
| ! [X1: $i] :
( ~ ( equal_distance @ ( distance @ U @ X ) @ ( distance @ 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)],[28]) ).
thf(53,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)],[29]) ).
thf(54,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)],[30]) ).
thf(55,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)],[31]) ).
thf(56,plain,
( ( ! [X: $i,W: $i,V: $i] :
( ~ ( equal_distance @ ( distance @ X @ W ) @ ( distance @ X @ V ) )
| ! [Y: $i] :
( ~ ( equal_distance @ ( distance @ Y @ W ) @ ( distance @ Y @ V ) )
| ! [Z: $i] :
( ~ ( equal_distance @ ( distance @ Z @ W ) @ ( distance @ Z @ V ) )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( W = V )
| ( between @ Z @ X @ Y ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[32]) ).
thf(57,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)],[36]) ).
thf(58,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)],[37]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i] :
( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ X1 @ Y1 ) )
| ~ ( equal_distance @ ( distance @ Y @ Z ) @ ( distance @ Y1 @ Z1 ) )
| ! [V: $i,V1: $i] :
( ~ ( equal_distance @ ( distance @ X @ V ) @ ( distance @ X1 @ V1 ) )
| ~ ( equal_distance @ ( distance @ Y @ V ) @ ( distance @ Y1 @ V1 ) )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equal_distance @ ( distance @ Z @ V ) @ ( distance @ Z1 @ V1 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[39]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Z @ Z ) )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i,Z: $i,V: $i] :
( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Z @ V ) )
| ! [V2: $i,W: $i] :
( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ V2 @ W ) )
| ( equal_distance @ ( distance @ Z @ V ) @ ( distance @ V2 @ W ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(62,plain,
( ( colinear @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ Y @ Z )
| ( colinear @ X @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(64,plain,
( ( ! [Y: $i,Z: $i,X: $i] :
( ~ ( between @ Y @ Z @ X )
| ( colinear @ X @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(65,plain,
( ( ! [Z: $i,X: $i,Y: $i] :
( ~ ( between @ Z @ X @ Y )
| ( colinear @ X @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(66,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( colinear @ X @ Y @ Z )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i] : ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Y @ X ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(68,plain,
( ( ! [X: $i,Y: $i,Z: $i,V: $i] :
( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Z @ V ) )
| ! [V2: $i,W: $i] :
( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ V2 @ W ) )
| ( equal_distance @ ( distance @ Z @ V ) @ ( distance @ V2 @ W ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[61]) ).
thf(69,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ Z @ Z ) )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[60]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(71,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equal_distance @ ( distance @ Y @ ( extension @ X @ Y @ W @ V ) ) @ ( distance @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(72,plain,
( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i] :
( ~ ( equal_distance @ ( distance @ X @ Y ) @ ( distance @ X1 @ Y1 ) )
| ~ ( equal_distance @ ( distance @ Y @ Z ) @ ( distance @ Y1 @ Z1 ) )
| ! [V: $i,V1: $i] :
( ~ ( equal_distance @ ( distance @ X @ V ) @ ( distance @ X1 @ V1 ) )
| ~ ( equal_distance @ ( distance @ Y @ V ) @ ( distance @ Y1 @ V1 ) )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equal_distance @ ( distance @ Z @ V ) @ ( distance @ Z1 @ V1 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[59]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(74,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)],[58]) ).
thf(75,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)],[57]) ).
thf(76,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(77,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(78,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(79,plain,
( ( ! [X: $i,W: $i,V: $i] :
( ~ ( equal_distance @ ( distance @ X @ W ) @ ( distance @ X @ V ) )
| ! [Y: $i] :
( ~ ( equal_distance @ ( distance @ Y @ W ) @ ( distance @ Y @ V ) )
| ! [Z: $i] :
( ~ ( equal_distance @ ( distance @ Z @ W ) @ ( distance @ Z @ V ) )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( W = V )
| ( between @ Z @ X @ Y ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(80,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)],[55]) ).
thf(81,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)],[54]) ).
thf(82,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)],[53]) ).
thf(83,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i] :
( ~ ( equal_distance @ ( distance @ U @ V ) @ ( distance @ U @ V1 ) )
| ! [X1: $i] :
( ~ ( equal_distance @ ( distance @ U @ X ) @ ( distance @ 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)],[52]) ).
thf(84,plain,
( ( ! [U: $i,V: $i,V1: $i,X: $i] :
( ~ ( equal_distance @ ( distance @ U @ V ) @ ( distance @ U @ V1 ) )
| ! [X1: $i] :
( ~ ( equal_distance @ ( distance @ U @ X ) @ ( distance @ U @ X1 ) )
| ~ ( between @ U @ V @ X )
| ! [W: $i] :
( ~ ( between @ V @ W @ X )
| ( equal_distance @ ( distance @ U @ W ) @ ( distance @ U @ ( continuous @ U @ V @ V1 @ W @ X @ X1 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(85,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(86,plain,
! [SV1: $i] :
( ( ! [SY83: $i,SY84: $i] :
( ~ ( between @ SV1 @ SY83 @ SY84 )
| ( colinear @ SV1 @ SY83 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(87,plain,
! [SV2: $i] :
( ( ! [SY85: $i,SY86: $i] :
( ~ ( between @ SV2 @ SY85 @ SY86 )
| ( colinear @ SY86 @ SV2 @ SY85 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(88,plain,
! [SV3: $i] :
( ( ! [SY87: $i,SY88: $i] :
( ~ ( between @ SV3 @ SY87 @ SY88 )
| ( colinear @ SY87 @ SY88 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(89,plain,
! [SV4: $i] :
( ( ! [SY89: $i,SY90: $i] :
( ~ ( colinear @ SV4 @ SY89 @ SY90 )
| ( between @ SV4 @ SY89 @ SY90 )
| ( between @ SY89 @ SY90 @ SV4 )
| ( between @ SY90 @ SV4 @ SY89 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(90,plain,
! [SV5: $i] :
( ( ! [SY91: $i] : ( equal_distance @ ( distance @ SV5 @ SY91 ) @ ( distance @ SY91 @ SV5 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(91,plain,
! [SV6: $i] :
( ( ! [SY92: $i,SY93: $i,SY94: $i] :
( ~ ( equal_distance @ ( distance @ SV6 @ SY92 ) @ ( distance @ SY93 @ SY94 ) )
| ! [SY95: $i,SY96: $i] :
( ~ ( equal_distance @ ( distance @ SV6 @ SY92 ) @ ( distance @ SY95 @ SY96 ) )
| ( equal_distance @ ( distance @ SY93 @ SY94 ) @ ( distance @ SY95 @ SY96 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(92,plain,
! [SV7: $i] :
( ( ! [SY97: $i] :
( ! [SY98: $i] :
~ ( equal_distance @ ( distance @ SV7 @ SY97 ) @ ( distance @ SY98 @ SY98 ) )
| ( SV7 = SY97 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(93,plain,
! [SV8: $i] :
( ( ! [SY99: $i,SY100: $i,SY101: $i] : ( between @ SV8 @ SY99 @ ( extension @ SV8 @ SY99 @ SY100 @ SY101 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(94,plain,
! [SV9: $i] :
( ( ! [SY102: $i,SY103: $i,SY104: $i] : ( equal_distance @ ( distance @ SV9 @ ( extension @ SY102 @ SV9 @ SY103 @ SY104 ) ) @ ( distance @ SY103 @ SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(95,plain,
! [SV10: $i] :
( ( ! [SY105: $i,SY106: $i,SY107: $i,SY108: $i,SY109: $i] :
( ~ ( equal_distance @ ( distance @ SV10 @ SY105 ) @ ( distance @ SY106 @ SY107 ) )
| ~ ( equal_distance @ ( distance @ SY105 @ SY108 ) @ ( distance @ SY107 @ SY109 ) )
| ! [SY110: $i,SY111: $i] :
( ~ ( equal_distance @ ( distance @ SV10 @ SY110 ) @ ( distance @ SY106 @ SY111 ) )
| ~ ( equal_distance @ ( distance @ SY105 @ SY110 ) @ ( distance @ SY107 @ SY111 ) )
| ~ ( between @ SV10 @ SY105 @ SY108 )
| ~ ( between @ SY106 @ SY107 @ SY109 )
| ( SV10 = SY105 )
| ( equal_distance @ ( distance @ SY108 @ SY110 ) @ ( distance @ SY109 @ SY111 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(96,plain,
! [SV11: $i] :
( ( ! [SY112: $i] :
( ~ ( between @ SV11 @ SY112 @ SV11 )
| ( SV11 = SY112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(97,plain,
! [SV12: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ~ ( between @ SV12 @ SY113 @ SY114 )
| ! [SY115: $i,SY116: $i] :
( ~ ( between @ SY115 @ SY116 @ SY114 )
| ( between @ SY113 @ ( inner_pasch @ SV12 @ SY113 @ SY114 @ SY116 @ SY115 ) @ SY115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(98,plain,
! [SV13: $i] :
( ( ! [SY117: $i,SY118: $i] :
( ~ ( between @ SV13 @ SY117 @ SY118 )
| ! [SY119: $i,SY120: $i] :
( ~ ( between @ SY119 @ SY120 @ SY118 )
| ( between @ SY120 @ ( inner_pasch @ SV13 @ SY117 @ SY118 @ SY120 @ SY119 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(99,plain,
( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[76]) ).
thf(100,plain,
( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[77]) ).
thf(101,plain,
( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[78]) ).
thf(102,plain,
! [SV14: $i] :
( ( ! [SY121: $i,SY122: $i] :
( ~ ( equal_distance @ ( distance @ SV14 @ SY121 ) @ ( distance @ SV14 @ SY122 ) )
| ! [SY123: $i] :
( ~ ( equal_distance @ ( distance @ SY123 @ SY121 ) @ ( distance @ SY123 @ SY122 ) )
| ! [SY124: $i] :
( ~ ( equal_distance @ ( distance @ SY124 @ SY121 ) @ ( distance @ SY124 @ SY122 ) )
| ( between @ SV14 @ SY123 @ SY124 )
| ( between @ SY123 @ SY124 @ SV14 )
| ( SY121 = SY122 )
| ( between @ SY124 @ SV14 @ SY123 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(103,plain,
! [SV15: $i] :
( ( ! [SY125: $i,SY126: $i] :
( ~ ( between @ SV15 @ SY125 @ SY126 )
| ! [SY127: $i,SY128: $i] :
( ~ ( between @ SY127 @ SY125 @ SY128 )
| ( SV15 = SY125 )
| ( between @ SV15 @ SY127 @ ( euclid1 @ SV15 @ SY127 @ SY125 @ SY128 @ SY126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(104,plain,
! [SV16: $i] :
( ( ! [SY129: $i,SY130: $i] :
( ~ ( between @ SV16 @ SY129 @ SY130 )
| ! [SY131: $i,SY132: $i] :
( ~ ( between @ SY131 @ SY129 @ SY132 )
| ( SV16 = SY129 )
| ( between @ SV16 @ SY132 @ ( euclid2 @ SV16 @ SY131 @ SY129 @ SY132 @ SY130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(105,plain,
! [SV17: $i] :
( ( ! [SY133: $i,SY134: $i] :
( ~ ( between @ SV17 @ SY133 @ SY134 )
| ! [SY135: $i,SY136: $i] :
( ~ ( between @ SY135 @ SY133 @ SY136 )
| ( SV17 = SY133 )
| ( between @ ( euclid1 @ SV17 @ SY135 @ SY133 @ SY136 @ SY134 ) @ SY134 @ ( euclid2 @ SV17 @ SY135 @ SY133 @ SY136 @ SY134 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(106,plain,
! [SV18: $i] :
( ( ! [SY137: $i,SY138: $i,SY139: $i] :
( ~ ( equal_distance @ ( distance @ SV18 @ SY137 ) @ ( distance @ SV18 @ SY138 ) )
| ! [SY140: $i] :
( ~ ( equal_distance @ ( distance @ SV18 @ SY139 ) @ ( distance @ SV18 @ SY140 ) )
| ~ ( between @ SV18 @ SY137 @ SY139 )
| ! [SY141: $i] :
( ~ ( between @ SY137 @ SY141 @ SY139 )
| ( between @ SY138 @ ( continuous @ SV18 @ SY137 @ SY138 @ SY141 @ SY139 @ SY140 ) @ SY140 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(107,plain,
! [SV19: $i] :
( ( ! [SY142: $i,SY143: $i,SY144: $i] :
( ~ ( equal_distance @ ( distance @ SV19 @ SY142 ) @ ( distance @ SV19 @ SY143 ) )
| ! [SY145: $i] :
( ~ ( equal_distance @ ( distance @ SV19 @ SY144 ) @ ( distance @ SV19 @ SY145 ) )
| ~ ( between @ SV19 @ SY142 @ SY144 )
| ! [SY146: $i] :
( ~ ( between @ SY142 @ SY146 @ SY144 )
| ( equal_distance @ ( distance @ SV19 @ SY146 ) @ ( distance @ SV19 @ ( continuous @ SV19 @ SY142 @ SY143 @ SY146 @ SY144 @ SY145 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(108,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[85]) ).
thf(109,plain,
! [SV20: $i,SV1: $i] :
( ( ! [SY147: $i] :
( ~ ( between @ SV1 @ SV20 @ SY147 )
| ( colinear @ SV1 @ SV20 @ SY147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(110,plain,
! [SV21: $i,SV2: $i] :
( ( ! [SY148: $i] :
( ~ ( between @ SV2 @ SV21 @ SY148 )
| ( colinear @ SY148 @ SV2 @ SV21 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(111,plain,
! [SV22: $i,SV3: $i] :
( ( ! [SY149: $i] :
( ~ ( between @ SV3 @ SV22 @ SY149 )
| ( colinear @ SV22 @ SY149 @ SV3 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(112,plain,
! [SV23: $i,SV4: $i] :
( ( ! [SY150: $i] :
( ~ ( colinear @ SV4 @ SV23 @ SY150 )
| ( between @ SV4 @ SV23 @ SY150 )
| ( between @ SV23 @ SY150 @ SV4 )
| ( between @ SY150 @ SV4 @ SV23 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(113,plain,
! [SV24: $i,SV5: $i] :
( ( equal_distance @ ( distance @ SV5 @ SV24 ) @ ( distance @ SV24 @ SV5 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(114,plain,
! [SV25: $i,SV6: $i] :
( ( ! [SY151: $i,SY152: $i] :
( ~ ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SY151 @ SY152 ) )
| ! [SY153: $i,SY154: $i] :
( ~ ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SY153 @ SY154 ) )
| ( equal_distance @ ( distance @ SY151 @ SY152 ) @ ( distance @ SY153 @ SY154 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[91]) ).
thf(115,plain,
! [SV26: $i,SV7: $i] :
( ( ! [SY155: $i] :
~ ( equal_distance @ ( distance @ SV7 @ SV26 ) @ ( distance @ SY155 @ SY155 ) )
| ( SV7 = SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(116,plain,
! [SV27: $i,SV8: $i] :
( ( ! [SY156: $i,SY157: $i] : ( between @ SV8 @ SV27 @ ( extension @ SV8 @ SV27 @ SY156 @ SY157 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(117,plain,
! [SV28: $i,SV9: $i] :
( ( ! [SY158: $i,SY159: $i] : ( equal_distance @ ( distance @ SV9 @ ( extension @ SV28 @ SV9 @ SY158 @ SY159 ) ) @ ( distance @ SY158 @ SY159 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(118,plain,
! [SV29: $i,SV10: $i] :
( ( ! [SY160: $i,SY161: $i,SY162: $i,SY163: $i] :
( ~ ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SY160 @ SY161 ) )
| ~ ( equal_distance @ ( distance @ SV29 @ SY162 ) @ ( distance @ SY161 @ SY163 ) )
| ! [SY164: $i,SY165: $i] :
( ~ ( equal_distance @ ( distance @ SV10 @ SY164 ) @ ( distance @ SY160 @ SY165 ) )
| ~ ( equal_distance @ ( distance @ SV29 @ SY164 ) @ ( distance @ SY161 @ SY165 ) )
| ~ ( between @ SV10 @ SV29 @ SY162 )
| ~ ( between @ SY160 @ SY161 @ SY163 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SY162 @ SY164 ) @ ( distance @ SY163 @ SY165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(119,plain,
! [SV30: $i,SV11: $i] :
( ( ~ ( between @ SV11 @ SV30 @ SV11 )
| ( SV11 = SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(120,plain,
! [SV31: $i,SV12: $i] :
( ( ! [SY166: $i] :
( ~ ( between @ SV12 @ SV31 @ SY166 )
| ! [SY167: $i,SY168: $i] :
( ~ ( between @ SY167 @ SY168 @ SY166 )
| ( between @ SV31 @ ( inner_pasch @ SV12 @ SV31 @ SY166 @ SY168 @ SY167 ) @ SY167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(121,plain,
! [SV32: $i,SV13: $i] :
( ( ! [SY169: $i] :
( ~ ( between @ SV13 @ SV32 @ SY169 )
| ! [SY170: $i,SY171: $i] :
( ~ ( between @ SY170 @ SY171 @ SY169 )
| ( between @ SY171 @ ( inner_pasch @ SV13 @ SV32 @ SY169 @ SY171 @ SY170 ) @ SV13 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(122,plain,
! [SV33: $i,SV14: $i] :
( ( ! [SY172: $i] :
( ~ ( equal_distance @ ( distance @ SV14 @ SV33 ) @ ( distance @ SV14 @ SY172 ) )
| ! [SY173: $i] :
( ~ ( equal_distance @ ( distance @ SY173 @ SV33 ) @ ( distance @ SY173 @ SY172 ) )
| ! [SY174: $i] :
( ~ ( equal_distance @ ( distance @ SY174 @ SV33 ) @ ( distance @ SY174 @ SY172 ) )
| ( between @ SV14 @ SY173 @ SY174 )
| ( between @ SY173 @ SY174 @ SV14 )
| ( SV33 = SY172 )
| ( between @ SY174 @ SV14 @ SY173 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(123,plain,
! [SV34: $i,SV15: $i] :
( ( ! [SY175: $i] :
( ~ ( between @ SV15 @ SV34 @ SY175 )
| ! [SY176: $i,SY177: $i] :
( ~ ( between @ SY176 @ SV34 @ SY177 )
| ( SV15 = SV34 )
| ( between @ SV15 @ SY176 @ ( euclid1 @ SV15 @ SY176 @ SV34 @ SY177 @ SY175 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(124,plain,
! [SV35: $i,SV16: $i] :
( ( ! [SY178: $i] :
( ~ ( between @ SV16 @ SV35 @ SY178 )
| ! [SY179: $i,SY180: $i] :
( ~ ( between @ SY179 @ SV35 @ SY180 )
| ( SV16 = SV35 )
| ( between @ SV16 @ SY180 @ ( euclid2 @ SV16 @ SY179 @ SV35 @ SY180 @ SY178 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(125,plain,
! [SV36: $i,SV17: $i] :
( ( ! [SY181: $i] :
( ~ ( between @ SV17 @ SV36 @ SY181 )
| ! [SY182: $i,SY183: $i] :
( ~ ( between @ SY182 @ SV36 @ SY183 )
| ( SV17 = SV36 )
| ( between @ ( euclid1 @ SV17 @ SY182 @ SV36 @ SY183 @ SY181 ) @ SY181 @ ( euclid2 @ SV17 @ SY182 @ SV36 @ SY183 @ SY181 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(126,plain,
! [SV37: $i,SV18: $i] :
( ( ! [SY184: $i,SY185: $i] :
( ~ ( equal_distance @ ( distance @ SV18 @ SV37 ) @ ( distance @ SV18 @ SY184 ) )
| ! [SY186: $i] :
( ~ ( equal_distance @ ( distance @ SV18 @ SY185 ) @ ( distance @ SV18 @ SY186 ) )
| ~ ( between @ SV18 @ SV37 @ SY185 )
| ! [SY187: $i] :
( ~ ( between @ SV37 @ SY187 @ SY185 )
| ( between @ SY184 @ ( continuous @ SV18 @ SV37 @ SY184 @ SY187 @ SY185 @ SY186 ) @ SY186 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(127,plain,
! [SV38: $i,SV19: $i] :
( ( ! [SY188: $i,SY189: $i] :
( ~ ( equal_distance @ ( distance @ SV19 @ SV38 ) @ ( distance @ SV19 @ SY188 ) )
| ! [SY190: $i] :
( ~ ( equal_distance @ ( distance @ SV19 @ SY189 ) @ ( distance @ SV19 @ SY190 ) )
| ~ ( between @ SV19 @ SV38 @ SY189 )
| ! [SY191: $i] :
( ~ ( between @ SV38 @ SY191 @ SY189 )
| ( equal_distance @ ( distance @ SV19 @ SY191 ) @ ( distance @ SV19 @ ( continuous @ SV19 @ SV38 @ SY188 @ SY191 @ SY189 @ SY190 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(128,plain,
! [SV39: $i,SV20: $i,SV1: $i] :
( ( ~ ( between @ SV1 @ SV20 @ SV39 )
| ( colinear @ SV1 @ SV20 @ SV39 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(129,plain,
! [SV40: $i,SV21: $i,SV2: $i] :
( ( ~ ( between @ SV2 @ SV21 @ SV40 )
| ( colinear @ SV40 @ SV2 @ SV21 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(130,plain,
! [SV41: $i,SV22: $i,SV3: $i] :
( ( ~ ( between @ SV3 @ SV22 @ SV41 )
| ( colinear @ SV22 @ SV41 @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(131,plain,
! [SV42: $i,SV23: $i,SV4: $i] :
( ( ~ ( colinear @ SV4 @ SV23 @ SV42 )
| ( between @ SV4 @ SV23 @ SV42 )
| ( between @ SV23 @ SV42 @ SV4 )
| ( between @ SV42 @ SV4 @ SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(132,plain,
! [SV43: $i,SV25: $i,SV6: $i] :
( ( ! [SY192: $i] :
( ~ ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SV43 @ SY192 ) )
| ! [SY193: $i,SY194: $i] :
( ~ ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SY193 @ SY194 ) )
| ( equal_distance @ ( distance @ SV43 @ SY192 ) @ ( distance @ SY193 @ SY194 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(133,plain,
! [SV26: $i,SV7: $i] :
( ( ( ! [SY155: $i] :
~ ( equal_distance @ ( distance @ SV7 @ SV26 ) @ ( distance @ SY155 @ SY155 ) ) )
= $true )
| ( ( SV7 = SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[115]) ).
thf(134,plain,
! [SV44: $i,SV27: $i,SV8: $i] :
( ( ! [SY195: $i] : ( between @ SV8 @ SV27 @ ( extension @ SV8 @ SV27 @ SV44 @ SY195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(135,plain,
! [SV45: $i,SV28: $i,SV9: $i] :
( ( ! [SY196: $i] : ( equal_distance @ ( distance @ SV9 @ ( extension @ SV28 @ SV9 @ SV45 @ SY196 ) ) @ ( distance @ SV45 @ SY196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(136,plain,
! [SV46: $i,SV29: $i,SV10: $i] :
( ( ! [SY197: $i,SY198: $i,SY199: $i] :
( ~ ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SY197 ) )
| ~ ( equal_distance @ ( distance @ SV29 @ SY198 ) @ ( distance @ SY197 @ SY199 ) )
| ! [SY200: $i,SY201: $i] :
( ~ ( equal_distance @ ( distance @ SV10 @ SY200 ) @ ( distance @ SV46 @ SY201 ) )
| ~ ( equal_distance @ ( distance @ SV29 @ SY200 ) @ ( distance @ SY197 @ SY201 ) )
| ~ ( between @ SV10 @ SV29 @ SY198 )
| ~ ( between @ SV46 @ SY197 @ SY199 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SY198 @ SY200 ) @ ( distance @ SY199 @ SY201 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(137,plain,
! [SV30: $i,SV11: $i] :
( ( ( ~ ( between @ SV11 @ SV30 @ SV11 ) )
= $true )
| ( ( SV11 = SV30 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[119]) ).
thf(138,plain,
! [SV47: $i,SV31: $i,SV12: $i] :
( ( ~ ( between @ SV12 @ SV31 @ SV47 )
| ! [SY202: $i,SY203: $i] :
( ~ ( between @ SY202 @ SY203 @ SV47 )
| ( between @ SV31 @ ( inner_pasch @ SV12 @ SV31 @ SV47 @ SY203 @ SY202 ) @ SY202 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(139,plain,
! [SV48: $i,SV32: $i,SV13: $i] :
( ( ~ ( between @ SV13 @ SV32 @ SV48 )
| ! [SY204: $i,SY205: $i] :
( ~ ( between @ SY204 @ SY205 @ SV48 )
| ( between @ SY205 @ ( inner_pasch @ SV13 @ SV32 @ SV48 @ SY205 @ SY204 ) @ SV13 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(140,plain,
! [SV49: $i,SV33: $i,SV14: $i] :
( ( ~ ( equal_distance @ ( distance @ SV14 @ SV33 ) @ ( distance @ SV14 @ SV49 ) )
| ! [SY206: $i] :
( ~ ( equal_distance @ ( distance @ SY206 @ SV33 ) @ ( distance @ SY206 @ SV49 ) )
| ! [SY207: $i] :
( ~ ( equal_distance @ ( distance @ SY207 @ SV33 ) @ ( distance @ SY207 @ SV49 ) )
| ( between @ SV14 @ SY206 @ SY207 )
| ( between @ SY206 @ SY207 @ SV14 )
| ( SV33 = SV49 )
| ( between @ SY207 @ SV14 @ SY206 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(141,plain,
! [SV50: $i,SV34: $i,SV15: $i] :
( ( ~ ( between @ SV15 @ SV34 @ SV50 )
| ! [SY208: $i,SY209: $i] :
( ~ ( between @ SY208 @ SV34 @ SY209 )
| ( SV15 = SV34 )
| ( between @ SV15 @ SY208 @ ( euclid1 @ SV15 @ SY208 @ SV34 @ SY209 @ SV50 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(142,plain,
! [SV51: $i,SV35: $i,SV16: $i] :
( ( ~ ( between @ SV16 @ SV35 @ SV51 )
| ! [SY210: $i,SY211: $i] :
( ~ ( between @ SY210 @ SV35 @ SY211 )
| ( SV16 = SV35 )
| ( between @ SV16 @ SY211 @ ( euclid2 @ SV16 @ SY210 @ SV35 @ SY211 @ SV51 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(143,plain,
! [SV52: $i,SV36: $i,SV17: $i] :
( ( ~ ( between @ SV17 @ SV36 @ SV52 )
| ! [SY212: $i,SY213: $i] :
( ~ ( between @ SY212 @ SV36 @ SY213 )
| ( SV17 = SV36 )
| ( between @ ( euclid1 @ SV17 @ SY212 @ SV36 @ SY213 @ SV52 ) @ SV52 @ ( euclid2 @ SV17 @ SY212 @ SV36 @ SY213 @ SV52 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(144,plain,
! [SV53: $i,SV37: $i,SV18: $i] :
( ( ! [SY214: $i] :
( ~ ( equal_distance @ ( distance @ SV18 @ SV37 ) @ ( distance @ SV18 @ SV53 ) )
| ! [SY215: $i] :
( ~ ( equal_distance @ ( distance @ SV18 @ SY214 ) @ ( distance @ SV18 @ SY215 ) )
| ~ ( between @ SV18 @ SV37 @ SY214 )
| ! [SY216: $i] :
( ~ ( between @ SV37 @ SY216 @ SY214 )
| ( between @ SV53 @ ( continuous @ SV18 @ SV37 @ SV53 @ SY216 @ SY214 @ SY215 ) @ SY215 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(145,plain,
! [SV54: $i,SV38: $i,SV19: $i] :
( ( ! [SY217: $i] :
( ~ ( equal_distance @ ( distance @ SV19 @ SV38 ) @ ( distance @ SV19 @ SV54 ) )
| ! [SY218: $i] :
( ~ ( equal_distance @ ( distance @ SV19 @ SY217 ) @ ( distance @ SV19 @ SY218 ) )
| ~ ( between @ SV19 @ SV38 @ SY217 )
| ! [SY219: $i] :
( ~ ( between @ SV38 @ SY219 @ SY217 )
| ( equal_distance @ ( distance @ SV19 @ SY219 ) @ ( distance @ SV19 @ ( continuous @ SV19 @ SV38 @ SV54 @ SY219 @ SY217 @ SY218 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(146,plain,
! [SV39: $i,SV20: $i,SV1: $i] :
( ( ( ~ ( between @ SV1 @ SV20 @ SV39 ) )
= $true )
| ( ( colinear @ SV1 @ SV20 @ SV39 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(147,plain,
! [SV40: $i,SV21: $i,SV2: $i] :
( ( ( ~ ( between @ SV2 @ SV21 @ SV40 ) )
= $true )
| ( ( colinear @ SV40 @ SV2 @ SV21 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(148,plain,
! [SV41: $i,SV22: $i,SV3: $i] :
( ( ( ~ ( between @ SV3 @ SV22 @ SV41 ) )
= $true )
| ( ( colinear @ SV22 @ SV41 @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[130]) ).
thf(149,plain,
! [SV42: $i,SV23: $i,SV4: $i] :
( ( ( ~ ( colinear @ SV4 @ SV23 @ SV42 ) )
= $true )
| ( ( ( between @ SV4 @ SV23 @ SV42 )
| ( between @ SV23 @ SV42 @ SV4 )
| ( between @ SV42 @ SV4 @ SV23 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[131]) ).
thf(150,plain,
! [SV55: $i,SV43: $i,SV25: $i,SV6: $i] :
( ( ~ ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SV43 @ SV55 ) )
| ! [SY220: $i,SY221: $i] :
( ~ ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SY220 @ SY221 ) )
| ( equal_distance @ ( distance @ SV43 @ SV55 ) @ ( distance @ SY220 @ SY221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(151,plain,
! [SV56: $i,SV26: $i,SV7: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV7 @ SV26 ) @ ( distance @ SV56 @ SV56 ) ) )
= $true )
| ( ( SV7 = SV26 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(152,plain,
! [SV57: $i,SV44: $i,SV27: $i,SV8: $i] :
( ( between @ SV8 @ SV27 @ ( extension @ SV8 @ SV27 @ SV44 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(153,plain,
! [SV58: $i,SV45: $i,SV28: $i,SV9: $i] :
( ( equal_distance @ ( distance @ SV9 @ ( extension @ SV28 @ SV9 @ SV45 @ SV58 ) ) @ ( distance @ SV45 @ SV58 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(154,plain,
! [SV59: $i,SV46: $i,SV29: $i,SV10: $i] :
( ( ! [SY222: $i,SY223: $i] :
( ~ ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
| ~ ( equal_distance @ ( distance @ SV29 @ SY222 ) @ ( distance @ SV59 @ SY223 ) )
| ! [SY224: $i,SY225: $i] :
( ~ ( equal_distance @ ( distance @ SV10 @ SY224 ) @ ( distance @ SV46 @ SY225 ) )
| ~ ( equal_distance @ ( distance @ SV29 @ SY224 ) @ ( distance @ SV59 @ SY225 ) )
| ~ ( between @ SV10 @ SV29 @ SY222 )
| ~ ( between @ SV46 @ SV59 @ SY223 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SY222 @ SY224 ) @ ( distance @ SY223 @ SY225 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(155,plain,
! [SV30: $i,SV11: $i] :
( ( ( between @ SV11 @ SV30 @ SV11 )
= $false )
| ( ( SV11 = SV30 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[137]) ).
thf(156,plain,
! [SV47: $i,SV31: $i,SV12: $i] :
( ( ( ~ ( between @ SV12 @ SV31 @ SV47 ) )
= $true )
| ( ( ! [SY202: $i,SY203: $i] :
( ~ ( between @ SY202 @ SY203 @ SV47 )
| ( between @ SV31 @ ( inner_pasch @ SV12 @ SV31 @ SV47 @ SY203 @ SY202 ) @ SY202 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[138]) ).
thf(157,plain,
! [SV48: $i,SV32: $i,SV13: $i] :
( ( ( ~ ( between @ SV13 @ SV32 @ SV48 ) )
= $true )
| ( ( ! [SY204: $i,SY205: $i] :
( ~ ( between @ SY204 @ SY205 @ SV48 )
| ( between @ SY205 @ ( inner_pasch @ SV13 @ SV32 @ SV48 @ SY205 @ SY204 ) @ SV13 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[139]) ).
thf(158,plain,
! [SV49: $i,SV33: $i,SV14: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV14 @ SV33 ) @ ( distance @ SV14 @ SV49 ) ) )
= $true )
| ( ( ! [SY206: $i] :
( ~ ( equal_distance @ ( distance @ SY206 @ SV33 ) @ ( distance @ SY206 @ SV49 ) )
| ! [SY207: $i] :
( ~ ( equal_distance @ ( distance @ SY207 @ SV33 ) @ ( distance @ SY207 @ SV49 ) )
| ( between @ SV14 @ SY206 @ SY207 )
| ( between @ SY206 @ SY207 @ SV14 )
| ( SV33 = SV49 )
| ( between @ SY207 @ SV14 @ SY206 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[140]) ).
thf(159,plain,
! [SV50: $i,SV34: $i,SV15: $i] :
( ( ( ~ ( between @ SV15 @ SV34 @ SV50 ) )
= $true )
| ( ( ! [SY208: $i,SY209: $i] :
( ~ ( between @ SY208 @ SV34 @ SY209 )
| ( SV15 = SV34 )
| ( between @ SV15 @ SY208 @ ( euclid1 @ SV15 @ SY208 @ SV34 @ SY209 @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[141]) ).
thf(160,plain,
! [SV51: $i,SV35: $i,SV16: $i] :
( ( ( ~ ( between @ SV16 @ SV35 @ SV51 ) )
= $true )
| ( ( ! [SY210: $i,SY211: $i] :
( ~ ( between @ SY210 @ SV35 @ SY211 )
| ( SV16 = SV35 )
| ( between @ SV16 @ SY211 @ ( euclid2 @ SV16 @ SY210 @ SV35 @ SY211 @ SV51 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[142]) ).
thf(161,plain,
! [SV52: $i,SV36: $i,SV17: $i] :
( ( ( ~ ( between @ SV17 @ SV36 @ SV52 ) )
= $true )
| ( ( ! [SY212: $i,SY213: $i] :
( ~ ( between @ SY212 @ SV36 @ SY213 )
| ( SV17 = SV36 )
| ( between @ ( euclid1 @ SV17 @ SY212 @ SV36 @ SY213 @ SV52 ) @ SV52 @ ( euclid2 @ SV17 @ SY212 @ SV36 @ SY213 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[143]) ).
thf(162,plain,
! [SV60: $i,SV53: $i,SV37: $i,SV18: $i] :
( ( ~ ( equal_distance @ ( distance @ SV18 @ SV37 ) @ ( distance @ SV18 @ SV53 ) )
| ! [SY226: $i] :
( ~ ( equal_distance @ ( distance @ SV18 @ SV60 ) @ ( distance @ SV18 @ SY226 ) )
| ~ ( between @ SV18 @ SV37 @ SV60 )
| ! [SY227: $i] :
( ~ ( between @ SV37 @ SY227 @ SV60 )
| ( between @ SV53 @ ( continuous @ SV18 @ SV37 @ SV53 @ SY227 @ SV60 @ SY226 ) @ SY226 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(163,plain,
! [SV61: $i,SV54: $i,SV38: $i,SV19: $i] :
( ( ~ ( equal_distance @ ( distance @ SV19 @ SV38 ) @ ( distance @ SV19 @ SV54 ) )
| ! [SY228: $i] :
( ~ ( equal_distance @ ( distance @ SV19 @ SV61 ) @ ( distance @ SV19 @ SY228 ) )
| ~ ( between @ SV19 @ SV38 @ SV61 )
| ! [SY229: $i] :
( ~ ( between @ SV38 @ SY229 @ SV61 )
| ( equal_distance @ ( distance @ SV19 @ SY229 ) @ ( distance @ SV19 @ ( continuous @ SV19 @ SV38 @ SV54 @ SY229 @ SV61 @ SY228 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(164,plain,
! [SV39: $i,SV20: $i,SV1: $i] :
( ( ( between @ SV1 @ SV20 @ SV39 )
= $false )
| ( ( colinear @ SV1 @ SV20 @ SV39 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(165,plain,
! [SV40: $i,SV21: $i,SV2: $i] :
( ( ( between @ SV2 @ SV21 @ SV40 )
= $false )
| ( ( colinear @ SV40 @ SV2 @ SV21 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[147]) ).
thf(166,plain,
! [SV41: $i,SV22: $i,SV3: $i] :
( ( ( between @ SV3 @ SV22 @ SV41 )
= $false )
| ( ( colinear @ SV22 @ SV41 @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[148]) ).
thf(167,plain,
! [SV42: $i,SV23: $i,SV4: $i] :
( ( ( colinear @ SV4 @ SV23 @ SV42 )
= $false )
| ( ( ( between @ SV4 @ SV23 @ SV42 )
| ( between @ SV23 @ SV42 @ SV4 )
| ( between @ SV42 @ SV4 @ SV23 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[149]) ).
thf(168,plain,
! [SV55: $i,SV43: $i,SV25: $i,SV6: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SV43 @ SV55 ) ) )
= $true )
| ( ( ! [SY220: $i,SY221: $i] :
( ~ ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SY220 @ SY221 ) )
| ( equal_distance @ ( distance @ SV43 @ SV55 ) @ ( distance @ SY220 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(169,plain,
! [SV56: $i,SV26: $i,SV7: $i] :
( ( ( equal_distance @ ( distance @ SV7 @ SV26 ) @ ( distance @ SV56 @ SV56 ) )
= $false )
| ( ( SV7 = SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[151]) ).
thf(170,plain,
! [SV62: $i,SV59: $i,SV46: $i,SV29: $i,SV10: $i] :
( ( ! [SY230: $i] :
( ~ ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
| ~ ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SY230 ) )
| ! [SY231: $i,SY232: $i] :
( ~ ( equal_distance @ ( distance @ SV10 @ SY231 ) @ ( distance @ SV46 @ SY232 ) )
| ~ ( equal_distance @ ( distance @ SV29 @ SY231 ) @ ( distance @ SV59 @ SY232 ) )
| ~ ( between @ SV10 @ SV29 @ SV62 )
| ~ ( between @ SV46 @ SV59 @ SY230 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SV62 @ SY231 ) @ ( distance @ SY230 @ SY232 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(171,plain,
! [SV47: $i,SV31: $i,SV12: $i] :
( ( ( between @ SV12 @ SV31 @ SV47 )
= $false )
| ( ( ! [SY202: $i,SY203: $i] :
( ~ ( between @ SY202 @ SY203 @ SV47 )
| ( between @ SV31 @ ( inner_pasch @ SV12 @ SV31 @ SV47 @ SY203 @ SY202 ) @ SY202 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(172,plain,
! [SV48: $i,SV32: $i,SV13: $i] :
( ( ( between @ SV13 @ SV32 @ SV48 )
= $false )
| ( ( ! [SY204: $i,SY205: $i] :
( ~ ( between @ SY204 @ SY205 @ SV48 )
| ( between @ SY205 @ ( inner_pasch @ SV13 @ SV32 @ SV48 @ SY205 @ SY204 ) @ SV13 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(173,plain,
! [SV49: $i,SV33: $i,SV14: $i] :
( ( ( equal_distance @ ( distance @ SV14 @ SV33 ) @ ( distance @ SV14 @ SV49 ) )
= $false )
| ( ( ! [SY206: $i] :
( ~ ( equal_distance @ ( distance @ SY206 @ SV33 ) @ ( distance @ SY206 @ SV49 ) )
| ! [SY207: $i] :
( ~ ( equal_distance @ ( distance @ SY207 @ SV33 ) @ ( distance @ SY207 @ SV49 ) )
| ( between @ SV14 @ SY206 @ SY207 )
| ( between @ SY206 @ SY207 @ SV14 )
| ( SV33 = SV49 )
| ( between @ SY207 @ SV14 @ SY206 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(174,plain,
! [SV50: $i,SV34: $i,SV15: $i] :
( ( ( between @ SV15 @ SV34 @ SV50 )
= $false )
| ( ( ! [SY208: $i,SY209: $i] :
( ~ ( between @ SY208 @ SV34 @ SY209 )
| ( SV15 = SV34 )
| ( between @ SV15 @ SY208 @ ( euclid1 @ SV15 @ SY208 @ SV34 @ SY209 @ SV50 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(175,plain,
! [SV51: $i,SV35: $i,SV16: $i] :
( ( ( between @ SV16 @ SV35 @ SV51 )
= $false )
| ( ( ! [SY210: $i,SY211: $i] :
( ~ ( between @ SY210 @ SV35 @ SY211 )
| ( SV16 = SV35 )
| ( between @ SV16 @ SY211 @ ( euclid2 @ SV16 @ SY210 @ SV35 @ SY211 @ SV51 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(176,plain,
! [SV52: $i,SV36: $i,SV17: $i] :
( ( ( between @ SV17 @ SV36 @ SV52 )
= $false )
| ( ( ! [SY212: $i,SY213: $i] :
( ~ ( between @ SY212 @ SV36 @ SY213 )
| ( SV17 = SV36 )
| ( between @ ( euclid1 @ SV17 @ SY212 @ SV36 @ SY213 @ SV52 ) @ SV52 @ ( euclid2 @ SV17 @ SY212 @ SV36 @ SY213 @ SV52 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[161]) ).
thf(177,plain,
! [SV60: $i,SV53: $i,SV37: $i,SV18: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV18 @ SV37 ) @ ( distance @ SV18 @ SV53 ) ) )
= $true )
| ( ( ! [SY226: $i] :
( ~ ( equal_distance @ ( distance @ SV18 @ SV60 ) @ ( distance @ SV18 @ SY226 ) )
| ~ ( between @ SV18 @ SV37 @ SV60 )
| ! [SY227: $i] :
( ~ ( between @ SV37 @ SY227 @ SV60 )
| ( between @ SV53 @ ( continuous @ SV18 @ SV37 @ SV53 @ SY227 @ SV60 @ SY226 ) @ SY226 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[162]) ).
thf(178,plain,
! [SV61: $i,SV54: $i,SV38: $i,SV19: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV19 @ SV38 ) @ ( distance @ SV19 @ SV54 ) ) )
= $true )
| ( ( ! [SY228: $i] :
( ~ ( equal_distance @ ( distance @ SV19 @ SV61 ) @ ( distance @ SV19 @ SY228 ) )
| ~ ( between @ SV19 @ SV38 @ SV61 )
| ! [SY229: $i] :
( ~ ( between @ SV38 @ SY229 @ SV61 )
| ( equal_distance @ ( distance @ SV19 @ SY229 ) @ ( distance @ SV19 @ ( continuous @ SV19 @ SV38 @ SV54 @ SY229 @ SV61 @ SY228 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(179,plain,
! [SV42: $i,SV23: $i,SV4: $i] :
( ( ( between @ SV4 @ SV23 @ SV42 )
= $true )
| ( ( ( between @ SV23 @ SV42 @ SV4 )
| ( between @ SV42 @ SV4 @ SV23 ) )
= $true )
| ( ( colinear @ SV4 @ SV23 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(180,plain,
! [SV55: $i,SV43: $i,SV25: $i,SV6: $i] :
( ( ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SV43 @ SV55 ) )
= $false )
| ( ( ! [SY220: $i,SY221: $i] :
( ~ ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SY220 @ SY221 ) )
| ( equal_distance @ ( distance @ SV43 @ SV55 ) @ ( distance @ SY220 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(181,plain,
! [SV63: $i,SV62: $i,SV59: $i,SV46: $i,SV29: $i,SV10: $i] :
( ( ~ ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
| ~ ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SV63 ) )
| ! [SY233: $i,SY234: $i] :
( ~ ( equal_distance @ ( distance @ SV10 @ SY233 ) @ ( distance @ SV46 @ SY234 ) )
| ~ ( equal_distance @ ( distance @ SV29 @ SY233 ) @ ( distance @ SV59 @ SY234 ) )
| ~ ( between @ SV10 @ SV29 @ SV62 )
| ~ ( between @ SV46 @ SV59 @ SV63 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SV62 @ SY233 ) @ ( distance @ SV63 @ SY234 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(182,plain,
! [SV12: $i,SV31: $i,SV47: $i,SV64: $i] :
( ( ( ! [SY235: $i] :
( ~ ( between @ SV64 @ SY235 @ SV47 )
| ( between @ SV31 @ ( inner_pasch @ SV12 @ SV31 @ SV47 @ SY235 @ SV64 ) @ SV64 ) ) )
= $true )
| ( ( between @ SV12 @ SV31 @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[171]) ).
thf(183,plain,
! [SV32: $i,SV13: $i,SV48: $i,SV65: $i] :
( ( ( ! [SY236: $i] :
( ~ ( between @ SV65 @ SY236 @ SV48 )
| ( between @ SY236 @ ( inner_pasch @ SV13 @ SV32 @ SV48 @ SY236 @ SV65 ) @ SV13 ) ) )
= $true )
| ( ( between @ SV13 @ SV32 @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(184,plain,
! [SV14: $i,SV49: $i,SV33: $i,SV66: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV66 @ SV33 ) @ ( distance @ SV66 @ SV49 ) )
| ! [SY237: $i] :
( ~ ( equal_distance @ ( distance @ SY237 @ SV33 ) @ ( distance @ SY237 @ SV49 ) )
| ( between @ SV14 @ SV66 @ SY237 )
| ( between @ SV66 @ SY237 @ SV14 )
| ( SV33 = SV49 )
| ( between @ SY237 @ SV14 @ SV66 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV14 @ SV33 ) @ ( distance @ SV14 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(185,plain,
! [SV50: $i,SV15: $i,SV34: $i,SV67: $i] :
( ( ( ! [SY238: $i] :
( ~ ( between @ SV67 @ SV34 @ SY238 )
| ( SV15 = SV34 )
| ( between @ SV15 @ SV67 @ ( euclid1 @ SV15 @ SV67 @ SV34 @ SY238 @ SV50 ) ) ) )
= $true )
| ( ( between @ SV15 @ SV34 @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(186,plain,
! [SV51: $i,SV16: $i,SV35: $i,SV68: $i] :
( ( ( ! [SY239: $i] :
( ~ ( between @ SV68 @ SV35 @ SY239 )
| ( SV16 = SV35 )
| ( between @ SV16 @ SY239 @ ( euclid2 @ SV16 @ SV68 @ SV35 @ SY239 @ SV51 ) ) ) )
= $true )
| ( ( between @ SV16 @ SV35 @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(187,plain,
! [SV52: $i,SV17: $i,SV36: $i,SV69: $i] :
( ( ( ! [SY240: $i] :
( ~ ( between @ SV69 @ SV36 @ SY240 )
| ( SV17 = SV36 )
| ( between @ ( euclid1 @ SV17 @ SV69 @ SV36 @ SY240 @ SV52 ) @ SV52 @ ( euclid2 @ SV17 @ SV69 @ SV36 @ SY240 @ SV52 ) ) ) )
= $true )
| ( ( between @ SV17 @ SV36 @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(188,plain,
! [SV60: $i,SV53: $i,SV37: $i,SV18: $i] :
( ( ( equal_distance @ ( distance @ SV18 @ SV37 ) @ ( distance @ SV18 @ SV53 ) )
= $false )
| ( ( ! [SY226: $i] :
( ~ ( equal_distance @ ( distance @ SV18 @ SV60 ) @ ( distance @ SV18 @ SY226 ) )
| ~ ( between @ SV18 @ SV37 @ SV60 )
| ! [SY227: $i] :
( ~ ( between @ SV37 @ SY227 @ SV60 )
| ( between @ SV53 @ ( continuous @ SV18 @ SV37 @ SV53 @ SY227 @ SV60 @ SY226 ) @ SY226 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[177]) ).
thf(189,plain,
! [SV61: $i,SV54: $i,SV38: $i,SV19: $i] :
( ( ( equal_distance @ ( distance @ SV19 @ SV38 ) @ ( distance @ SV19 @ SV54 ) )
= $false )
| ( ( ! [SY228: $i] :
( ~ ( equal_distance @ ( distance @ SV19 @ SV61 ) @ ( distance @ SV19 @ SY228 ) )
| ~ ( between @ SV19 @ SV38 @ SV61 )
| ! [SY229: $i] :
( ~ ( between @ SV38 @ SY229 @ SV61 )
| ( equal_distance @ ( distance @ SV19 @ SY229 ) @ ( distance @ SV19 @ ( continuous @ SV19 @ SV38 @ SV54 @ SY229 @ SV61 @ SY228 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[178]) ).
thf(190,plain,
! [SV4: $i,SV42: $i,SV23: $i] :
( ( ( between @ SV23 @ SV42 @ SV4 )
= $true )
| ( ( between @ SV42 @ SV4 @ SV23 )
= $true )
| ( ( between @ SV4 @ SV23 @ SV42 )
= $true )
| ( ( colinear @ SV4 @ SV23 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(191,plain,
! [SV55: $i,SV43: $i,SV70: $i,SV25: $i,SV6: $i] :
( ( ( ! [SY241: $i] :
( ~ ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SV70 @ SY241 ) )
| ( equal_distance @ ( distance @ SV43 @ SV55 ) @ ( distance @ SV70 @ SY241 ) ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SV43 @ SV55 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[180]) ).
thf(192,plain,
! [SV63: $i,SV62: $i,SV59: $i,SV46: $i,SV29: $i,SV10: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) ) )
= $true )
| ( ( ~ ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SV63 ) )
| ! [SY233: $i,SY234: $i] :
( ~ ( equal_distance @ ( distance @ SV10 @ SY233 ) @ ( distance @ SV46 @ SY234 ) )
| ~ ( equal_distance @ ( distance @ SV29 @ SY233 ) @ ( distance @ SV59 @ SY234 ) )
| ~ ( between @ SV10 @ SV29 @ SV62 )
| ~ ( between @ SV46 @ SV59 @ SV63 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SV62 @ SY233 ) @ ( distance @ SV63 @ SY234 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[181]) ).
thf(193,plain,
! [SV12: $i,SV31: $i,SV47: $i,SV71: $i,SV64: $i] :
( ( ( ~ ( between @ SV64 @ SV71 @ SV47 )
| ( between @ SV31 @ ( inner_pasch @ SV12 @ SV31 @ SV47 @ SV71 @ SV64 ) @ SV64 ) )
= $true )
| ( ( between @ SV12 @ SV31 @ SV47 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(194,plain,
! [SV32: $i,SV13: $i,SV48: $i,SV72: $i,SV65: $i] :
( ( ( ~ ( between @ SV65 @ SV72 @ SV48 )
| ( between @ SV72 @ ( inner_pasch @ SV13 @ SV32 @ SV48 @ SV72 @ SV65 ) @ SV13 ) )
= $true )
| ( ( between @ SV13 @ SV32 @ SV48 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(195,plain,
! [SV14: $i,SV49: $i,SV33: $i,SV66: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV66 @ SV33 ) @ ( distance @ SV66 @ SV49 ) ) )
= $true )
| ( ( ! [SY237: $i] :
( ~ ( equal_distance @ ( distance @ SY237 @ SV33 ) @ ( distance @ SY237 @ SV49 ) )
| ( between @ SV14 @ SV66 @ SY237 )
| ( between @ SV66 @ SY237 @ SV14 )
| ( SV33 = SV49 )
| ( between @ SY237 @ SV14 @ SV66 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV14 @ SV33 ) @ ( distance @ SV14 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[184]) ).
thf(196,plain,
! [SV50: $i,SV15: $i,SV73: $i,SV34: $i,SV67: $i] :
( ( ( ~ ( between @ SV67 @ SV34 @ SV73 )
| ( SV15 = SV34 )
| ( between @ SV15 @ SV67 @ ( euclid1 @ SV15 @ SV67 @ SV34 @ SV73 @ SV50 ) ) )
= $true )
| ( ( between @ SV15 @ SV34 @ SV50 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(197,plain,
! [SV51: $i,SV16: $i,SV74: $i,SV35: $i,SV68: $i] :
( ( ( ~ ( between @ SV68 @ SV35 @ SV74 )
| ( SV16 = SV35 )
| ( between @ SV16 @ SV74 @ ( euclid2 @ SV16 @ SV68 @ SV35 @ SV74 @ SV51 ) ) )
= $true )
| ( ( between @ SV16 @ SV35 @ SV51 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(198,plain,
! [SV52: $i,SV17: $i,SV75: $i,SV36: $i,SV69: $i] :
( ( ( ~ ( between @ SV69 @ SV36 @ SV75 )
| ( SV17 = SV36 )
| ( between @ ( euclid1 @ SV17 @ SV69 @ SV36 @ SV75 @ SV52 ) @ SV52 @ ( euclid2 @ SV17 @ SV69 @ SV36 @ SV75 @ SV52 ) ) )
= $true )
| ( ( between @ SV17 @ SV36 @ SV52 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(199,plain,
! [SV53: $i,SV37: $i,SV76: $i,SV60: $i,SV18: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV18 @ SV60 ) @ ( distance @ SV18 @ SV76 ) )
| ~ ( between @ SV18 @ SV37 @ SV60 )
| ! [SY242: $i] :
( ~ ( between @ SV37 @ SY242 @ SV60 )
| ( between @ SV53 @ ( continuous @ SV18 @ SV37 @ SV53 @ SY242 @ SV60 @ SV76 ) @ SV76 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV18 @ SV37 ) @ ( distance @ SV18 @ SV53 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(200,plain,
! [SV54: $i,SV38: $i,SV77: $i,SV61: $i,SV19: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV19 @ SV61 ) @ ( distance @ SV19 @ SV77 ) )
| ~ ( between @ SV19 @ SV38 @ SV61 )
| ! [SY243: $i] :
( ~ ( between @ SV38 @ SY243 @ SV61 )
| ( equal_distance @ ( distance @ SV19 @ SY243 ) @ ( distance @ SV19 @ ( continuous @ SV19 @ SV38 @ SV54 @ SY243 @ SV61 @ SV77 ) ) ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV19 @ SV38 ) @ ( distance @ SV19 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(201,plain,
! [SV55: $i,SV43: $i,SV78: $i,SV70: $i,SV25: $i,SV6: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SV70 @ SV78 ) )
| ( equal_distance @ ( distance @ SV43 @ SV55 ) @ ( distance @ SV70 @ SV78 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SV43 @ SV55 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(202,plain,
! [SV63: $i,SV62: $i,SV59: $i,SV46: $i,SV29: $i,SV10: $i] :
( ( ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
= $false )
| ( ( ~ ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SV63 ) )
| ! [SY233: $i,SY234: $i] :
( ~ ( equal_distance @ ( distance @ SV10 @ SY233 ) @ ( distance @ SV46 @ SY234 ) )
| ~ ( equal_distance @ ( distance @ SV29 @ SY233 ) @ ( distance @ SV59 @ SY234 ) )
| ~ ( between @ SV10 @ SV29 @ SV62 )
| ~ ( between @ SV46 @ SV59 @ SV63 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SV62 @ SY233 ) @ ( distance @ SV63 @ SY234 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[192]) ).
thf(203,plain,
! [SV12: $i,SV31: $i,SV47: $i,SV71: $i,SV64: $i] :
( ( ( ~ ( between @ SV64 @ SV71 @ SV47 ) )
= $true )
| ( ( between @ SV31 @ ( inner_pasch @ SV12 @ SV31 @ SV47 @ SV71 @ SV64 ) @ SV64 )
= $true )
| ( ( between @ SV12 @ SV31 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(204,plain,
! [SV32: $i,SV13: $i,SV48: $i,SV72: $i,SV65: $i] :
( ( ( ~ ( between @ SV65 @ SV72 @ SV48 ) )
= $true )
| ( ( between @ SV72 @ ( inner_pasch @ SV13 @ SV32 @ SV48 @ SV72 @ SV65 ) @ SV13 )
= $true )
| ( ( between @ SV13 @ SV32 @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(205,plain,
! [SV14: $i,SV49: $i,SV33: $i,SV66: $i] :
( ( ( equal_distance @ ( distance @ SV66 @ SV33 ) @ ( distance @ SV66 @ SV49 ) )
= $false )
| ( ( ! [SY237: $i] :
( ~ ( equal_distance @ ( distance @ SY237 @ SV33 ) @ ( distance @ SY237 @ SV49 ) )
| ( between @ SV14 @ SV66 @ SY237 )
| ( between @ SV66 @ SY237 @ SV14 )
| ( SV33 = SV49 )
| ( between @ SY237 @ SV14 @ SV66 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV14 @ SV33 ) @ ( distance @ SV14 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[195]) ).
thf(206,plain,
! [SV50: $i,SV15: $i,SV73: $i,SV34: $i,SV67: $i] :
( ( ( ~ ( between @ SV67 @ SV34 @ SV73 ) )
= $true )
| ( ( ( SV15 = SV34 )
| ( between @ SV15 @ SV67 @ ( euclid1 @ SV15 @ SV67 @ SV34 @ SV73 @ SV50 ) ) )
= $true )
| ( ( between @ SV15 @ SV34 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(207,plain,
! [SV51: $i,SV16: $i,SV74: $i,SV35: $i,SV68: $i] :
( ( ( ~ ( between @ SV68 @ SV35 @ SV74 ) )
= $true )
| ( ( ( SV16 = SV35 )
| ( between @ SV16 @ SV74 @ ( euclid2 @ SV16 @ SV68 @ SV35 @ SV74 @ SV51 ) ) )
= $true )
| ( ( between @ SV16 @ SV35 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(208,plain,
! [SV52: $i,SV17: $i,SV75: $i,SV36: $i,SV69: $i] :
( ( ( ~ ( between @ SV69 @ SV36 @ SV75 ) )
= $true )
| ( ( ( SV17 = SV36 )
| ( between @ ( euclid1 @ SV17 @ SV69 @ SV36 @ SV75 @ SV52 ) @ SV52 @ ( euclid2 @ SV17 @ SV69 @ SV36 @ SV75 @ SV52 ) ) )
= $true )
| ( ( between @ SV17 @ SV36 @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[198]) ).
thf(209,plain,
! [SV53: $i,SV37: $i,SV76: $i,SV60: $i,SV18: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV18 @ SV60 ) @ ( distance @ SV18 @ SV76 ) ) )
= $true )
| ( ( ~ ( between @ SV18 @ SV37 @ SV60 )
| ! [SY242: $i] :
( ~ ( between @ SV37 @ SY242 @ SV60 )
| ( between @ SV53 @ ( continuous @ SV18 @ SV37 @ SV53 @ SY242 @ SV60 @ SV76 ) @ SV76 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV18 @ SV37 ) @ ( distance @ SV18 @ SV53 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[199]) ).
thf(210,plain,
! [SV54: $i,SV38: $i,SV77: $i,SV61: $i,SV19: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV19 @ SV61 ) @ ( distance @ SV19 @ SV77 ) ) )
= $true )
| ( ( ~ ( between @ SV19 @ SV38 @ SV61 )
| ! [SY243: $i] :
( ~ ( between @ SV38 @ SY243 @ SV61 )
| ( equal_distance @ ( distance @ SV19 @ SY243 ) @ ( distance @ SV19 @ ( continuous @ SV19 @ SV38 @ SV54 @ SY243 @ SV61 @ SV77 ) ) ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV19 @ SV38 ) @ ( distance @ SV19 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[200]) ).
thf(211,plain,
! [SV55: $i,SV43: $i,SV78: $i,SV70: $i,SV25: $i,SV6: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SV70 @ SV78 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV43 @ SV55 ) @ ( distance @ SV70 @ SV78 ) )
= $true )
| ( ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SV43 @ SV55 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(212,plain,
! [SV46: $i,SV10: $i,SV63: $i,SV59: $i,SV62: $i,SV29: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SV63 ) ) )
= $true )
| ( ( ! [SY233: $i,SY234: $i] :
( ~ ( equal_distance @ ( distance @ SV10 @ SY233 ) @ ( distance @ SV46 @ SY234 ) )
| ~ ( equal_distance @ ( distance @ SV29 @ SY233 ) @ ( distance @ SV59 @ SY234 ) )
| ~ ( between @ SV10 @ SV29 @ SV62 )
| ~ ( between @ SV46 @ SV59 @ SV63 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SV62 @ SY233 ) @ ( distance @ SV63 @ SY234 ) ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(213,plain,
! [SV12: $i,SV31: $i,SV47: $i,SV71: $i,SV64: $i] :
( ( ( between @ SV64 @ SV71 @ SV47 )
= $false )
| ( ( between @ SV31 @ ( inner_pasch @ SV12 @ SV31 @ SV47 @ SV71 @ SV64 ) @ SV64 )
= $true )
| ( ( between @ SV12 @ SV31 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(214,plain,
! [SV32: $i,SV13: $i,SV48: $i,SV72: $i,SV65: $i] :
( ( ( between @ SV65 @ SV72 @ SV48 )
= $false )
| ( ( between @ SV72 @ ( inner_pasch @ SV13 @ SV32 @ SV48 @ SV72 @ SV65 ) @ SV13 )
= $true )
| ( ( between @ SV13 @ SV32 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(215,plain,
! [SV66: $i,SV14: $i,SV49: $i,SV33: $i,SV79: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV79 @ SV33 ) @ ( distance @ SV79 @ SV49 ) )
| ( between @ SV14 @ SV66 @ SV79 )
| ( between @ SV66 @ SV79 @ SV14 )
| ( SV33 = SV49 )
| ( between @ SV79 @ SV14 @ SV66 ) )
= $true )
| ( ( equal_distance @ ( distance @ SV66 @ SV33 ) @ ( distance @ SV66 @ SV49 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV14 @ SV33 ) @ ( distance @ SV14 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(216,plain,
! [SV50: $i,SV15: $i,SV73: $i,SV34: $i,SV67: $i] :
( ( ( between @ SV67 @ SV34 @ SV73 )
= $false )
| ( ( ( SV15 = SV34 )
| ( between @ SV15 @ SV67 @ ( euclid1 @ SV15 @ SV67 @ SV34 @ SV73 @ SV50 ) ) )
= $true )
| ( ( between @ SV15 @ SV34 @ SV50 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(217,plain,
! [SV51: $i,SV16: $i,SV74: $i,SV35: $i,SV68: $i] :
( ( ( between @ SV68 @ SV35 @ SV74 )
= $false )
| ( ( ( SV16 = SV35 )
| ( between @ SV16 @ SV74 @ ( euclid2 @ SV16 @ SV68 @ SV35 @ SV74 @ SV51 ) ) )
= $true )
| ( ( between @ SV16 @ SV35 @ SV51 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[207]) ).
thf(218,plain,
! [SV52: $i,SV17: $i,SV75: $i,SV36: $i,SV69: $i] :
( ( ( between @ SV69 @ SV36 @ SV75 )
= $false )
| ( ( ( SV17 = SV36 )
| ( between @ ( euclid1 @ SV17 @ SV69 @ SV36 @ SV75 @ SV52 ) @ SV52 @ ( euclid2 @ SV17 @ SV69 @ SV36 @ SV75 @ SV52 ) ) )
= $true )
| ( ( between @ SV17 @ SV36 @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[208]) ).
thf(219,plain,
! [SV53: $i,SV37: $i,SV76: $i,SV60: $i,SV18: $i] :
( ( ( equal_distance @ ( distance @ SV18 @ SV60 ) @ ( distance @ SV18 @ SV76 ) )
= $false )
| ( ( ~ ( between @ SV18 @ SV37 @ SV60 )
| ! [SY242: $i] :
( ~ ( between @ SV37 @ SY242 @ SV60 )
| ( between @ SV53 @ ( continuous @ SV18 @ SV37 @ SV53 @ SY242 @ SV60 @ SV76 ) @ SV76 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV18 @ SV37 ) @ ( distance @ SV18 @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(220,plain,
! [SV54: $i,SV38: $i,SV77: $i,SV61: $i,SV19: $i] :
( ( ( equal_distance @ ( distance @ SV19 @ SV61 ) @ ( distance @ SV19 @ SV77 ) )
= $false )
| ( ( ~ ( between @ SV19 @ SV38 @ SV61 )
| ! [SY243: $i] :
( ~ ( between @ SV38 @ SY243 @ SV61 )
| ( equal_distance @ ( distance @ SV19 @ SY243 ) @ ( distance @ SV19 @ ( continuous @ SV19 @ SV38 @ SV54 @ SY243 @ SV61 @ SV77 ) ) ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV19 @ SV38 ) @ ( distance @ SV19 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[210]) ).
thf(221,plain,
! [SV55: $i,SV43: $i,SV78: $i,SV70: $i,SV25: $i,SV6: $i] :
( ( ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SV70 @ SV78 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV43 @ SV55 ) @ ( distance @ SV70 @ SV78 ) )
= $true )
| ( ( equal_distance @ ( distance @ SV6 @ SV25 ) @ ( distance @ SV43 @ SV55 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(222,plain,
! [SV46: $i,SV10: $i,SV63: $i,SV59: $i,SV62: $i,SV29: $i] :
( ( ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SV63 ) )
= $false )
| ( ( ! [SY233: $i,SY234: $i] :
( ~ ( equal_distance @ ( distance @ SV10 @ SY233 ) @ ( distance @ SV46 @ SY234 ) )
| ~ ( equal_distance @ ( distance @ SV29 @ SY233 ) @ ( distance @ SV59 @ SY234 ) )
| ~ ( between @ SV10 @ SV29 @ SV62 )
| ~ ( between @ SV46 @ SV59 @ SV63 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SV62 @ SY233 ) @ ( distance @ SV63 @ SY234 ) ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(223,plain,
! [SV66: $i,SV14: $i,SV49: $i,SV33: $i,SV79: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV79 @ SV33 ) @ ( distance @ SV79 @ SV49 ) ) )
= $true )
| ( ( ( between @ SV14 @ SV66 @ SV79 )
| ( between @ SV66 @ SV79 @ SV14 )
| ( SV33 = SV49 )
| ( between @ SV79 @ SV14 @ SV66 ) )
= $true )
| ( ( equal_distance @ ( distance @ SV66 @ SV33 ) @ ( distance @ SV66 @ SV49 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV14 @ SV33 ) @ ( distance @ SV14 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(224,plain,
! [SV50: $i,SV73: $i,SV67: $i,SV34: $i,SV15: $i] :
( ( ( SV15 = SV34 )
= $true )
| ( ( between @ SV15 @ SV67 @ ( euclid1 @ SV15 @ SV67 @ SV34 @ SV73 @ SV50 ) )
= $true )
| ( ( between @ SV67 @ SV34 @ SV73 )
= $false )
| ( ( between @ SV15 @ SV34 @ SV50 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(225,plain,
! [SV51: $i,SV68: $i,SV74: $i,SV35: $i,SV16: $i] :
( ( ( SV16 = SV35 )
= $true )
| ( ( between @ SV16 @ SV74 @ ( euclid2 @ SV16 @ SV68 @ SV35 @ SV74 @ SV51 ) )
= $true )
| ( ( between @ SV68 @ SV35 @ SV74 )
= $false )
| ( ( between @ SV16 @ SV35 @ SV51 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(226,plain,
! [SV52: $i,SV75: $i,SV69: $i,SV36: $i,SV17: $i] :
( ( ( SV17 = SV36 )
= $true )
| ( ( between @ ( euclid1 @ SV17 @ SV69 @ SV36 @ SV75 @ SV52 ) @ SV52 @ ( euclid2 @ SV17 @ SV69 @ SV36 @ SV75 @ SV52 ) )
= $true )
| ( ( between @ SV69 @ SV36 @ SV75 )
= $false )
| ( ( between @ SV17 @ SV36 @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(227,plain,
! [SV76: $i,SV53: $i,SV60: $i,SV37: $i,SV18: $i] :
( ( ( ~ ( between @ SV18 @ SV37 @ SV60 ) )
= $true )
| ( ( ! [SY242: $i] :
( ~ ( between @ SV37 @ SY242 @ SV60 )
| ( between @ SV53 @ ( continuous @ SV18 @ SV37 @ SV53 @ SY242 @ SV60 @ SV76 ) @ SV76 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV18 @ SV60 ) @ ( distance @ SV18 @ SV76 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV18 @ SV37 ) @ ( distance @ SV18 @ SV53 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[219]) ).
thf(228,plain,
! [SV77: $i,SV54: $i,SV61: $i,SV38: $i,SV19: $i] :
( ( ( ~ ( between @ SV19 @ SV38 @ SV61 ) )
= $true )
| ( ( ! [SY243: $i] :
( ~ ( between @ SV38 @ SY243 @ SV61 )
| ( equal_distance @ ( distance @ SV19 @ SY243 ) @ ( distance @ SV19 @ ( continuous @ SV19 @ SV38 @ SV54 @ SY243 @ SV61 @ SV77 ) ) ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV19 @ SV61 ) @ ( distance @ SV19 @ SV77 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV19 @ SV38 ) @ ( distance @ SV19 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(229,plain,
! [SV63: $i,SV62: $i,SV59: $i,SV29: $i,SV46: $i,SV80: $i,SV10: $i] :
( ( ( ! [SY244: $i] :
( ~ ( equal_distance @ ( distance @ SV10 @ SV80 ) @ ( distance @ SV46 @ SY244 ) )
| ~ ( equal_distance @ ( distance @ SV29 @ SV80 ) @ ( distance @ SV59 @ SY244 ) )
| ~ ( between @ SV10 @ SV29 @ SV62 )
| ~ ( between @ SV46 @ SV59 @ SV63 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SV62 @ SV80 ) @ ( distance @ SV63 @ SY244 ) ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SV63 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[222]) ).
thf(230,plain,
! [SV66: $i,SV14: $i,SV49: $i,SV33: $i,SV79: $i] :
( ( ( equal_distance @ ( distance @ SV79 @ SV33 ) @ ( distance @ SV79 @ SV49 ) )
= $false )
| ( ( ( between @ SV14 @ SV66 @ SV79 )
| ( between @ SV66 @ SV79 @ SV14 )
| ( SV33 = SV49 )
| ( between @ SV79 @ SV14 @ SV66 ) )
= $true )
| ( ( equal_distance @ ( distance @ SV66 @ SV33 ) @ ( distance @ SV66 @ SV49 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV14 @ SV33 ) @ ( distance @ SV14 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(231,plain,
! [SV76: $i,SV53: $i,SV60: $i,SV37: $i,SV18: $i] :
( ( ( between @ SV18 @ SV37 @ SV60 )
= $false )
| ( ( ! [SY242: $i] :
( ~ ( between @ SV37 @ SY242 @ SV60 )
| ( between @ SV53 @ ( continuous @ SV18 @ SV37 @ SV53 @ SY242 @ SV60 @ SV76 ) @ SV76 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV18 @ SV60 ) @ ( distance @ SV18 @ SV76 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV18 @ SV37 ) @ ( distance @ SV18 @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(232,plain,
! [SV77: $i,SV54: $i,SV61: $i,SV38: $i,SV19: $i] :
( ( ( between @ SV19 @ SV38 @ SV61 )
= $false )
| ( ( ! [SY243: $i] :
( ~ ( between @ SV38 @ SY243 @ SV61 )
| ( equal_distance @ ( distance @ SV19 @ SY243 ) @ ( distance @ SV19 @ ( continuous @ SV19 @ SV38 @ SV54 @ SY243 @ SV61 @ SV77 ) ) ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV19 @ SV61 ) @ ( distance @ SV19 @ SV77 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV19 @ SV38 ) @ ( distance @ SV19 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(233,plain,
! [SV63: $i,SV62: $i,SV59: $i,SV29: $i,SV81: $i,SV46: $i,SV80: $i,SV10: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV10 @ SV80 ) @ ( distance @ SV46 @ SV81 ) )
| ~ ( equal_distance @ ( distance @ SV29 @ SV80 ) @ ( distance @ SV59 @ SV81 ) )
| ~ ( between @ SV10 @ SV29 @ SV62 )
| ~ ( between @ SV46 @ SV59 @ SV63 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SV62 @ SV80 ) @ ( distance @ SV63 @ SV81 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SV63 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[229]) ).
thf(234,plain,
! [SV49: $i,SV33: $i,SV79: $i,SV66: $i,SV14: $i] :
( ( ( between @ SV14 @ SV66 @ SV79 )
= $true )
| ( ( ( between @ SV66 @ SV79 @ SV14 )
| ( SV33 = SV49 )
| ( between @ SV79 @ SV14 @ SV66 ) )
= $true )
| ( ( equal_distance @ ( distance @ SV79 @ SV33 ) @ ( distance @ SV79 @ SV49 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV66 @ SV33 ) @ ( distance @ SV66 @ SV49 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV14 @ SV33 ) @ ( distance @ SV14 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(235,plain,
! [SV76: $i,SV18: $i,SV53: $i,SV60: $i,SV82: $i,SV37: $i] :
( ( ( ~ ( between @ SV37 @ SV82 @ SV60 )
| ( between @ SV53 @ ( continuous @ SV18 @ SV37 @ SV53 @ SV82 @ SV60 @ SV76 ) @ SV76 ) )
= $true )
| ( ( between @ SV18 @ SV37 @ SV60 )
= $false )
| ( ( equal_distance @ ( distance @ SV18 @ SV60 ) @ ( distance @ SV18 @ SV76 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV18 @ SV37 ) @ ( distance @ SV18 @ SV53 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[231]) ).
thf(236,plain,
! [SV77: $i,SV54: $i,SV19: $i,SV61: $i,SV83: $i,SV38: $i] :
( ( ( ~ ( between @ SV38 @ SV83 @ SV61 )
| ( equal_distance @ ( distance @ SV19 @ SV83 ) @ ( distance @ SV19 @ ( continuous @ SV19 @ SV38 @ SV54 @ SV83 @ SV61 @ SV77 ) ) ) )
= $true )
| ( ( between @ SV19 @ SV38 @ SV61 )
= $false )
| ( ( equal_distance @ ( distance @ SV19 @ SV61 ) @ ( distance @ SV19 @ SV77 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV19 @ SV38 ) @ ( distance @ SV19 @ SV54 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[232]) ).
thf(237,plain,
! [SV63: $i,SV62: $i,SV59: $i,SV29: $i,SV81: $i,SV46: $i,SV80: $i,SV10: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV10 @ SV80 ) @ ( distance @ SV46 @ SV81 ) ) )
= $true )
| ( ( ~ ( equal_distance @ ( distance @ SV29 @ SV80 ) @ ( distance @ SV59 @ SV81 ) )
| ~ ( between @ SV10 @ SV29 @ SV62 )
| ~ ( between @ SV46 @ SV59 @ SV63 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SV62 @ SV80 ) @ ( distance @ SV63 @ SV81 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SV63 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(238,plain,
! [SV49: $i,SV33: $i,SV14: $i,SV79: $i,SV66: $i] :
( ( ( between @ SV66 @ SV79 @ SV14 )
= $true )
| ( ( ( SV33 = SV49 )
| ( between @ SV79 @ SV14 @ SV66 ) )
= $true )
| ( ( between @ SV14 @ SV66 @ SV79 )
= $true )
| ( ( equal_distance @ ( distance @ SV79 @ SV33 ) @ ( distance @ SV79 @ SV49 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV66 @ SV33 ) @ ( distance @ SV66 @ SV49 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV14 @ SV33 ) @ ( distance @ SV14 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(239,plain,
! [SV76: $i,SV18: $i,SV53: $i,SV60: $i,SV82: $i,SV37: $i] :
( ( ( ~ ( between @ SV37 @ SV82 @ SV60 ) )
= $true )
| ( ( between @ SV53 @ ( continuous @ SV18 @ SV37 @ SV53 @ SV82 @ SV60 @ SV76 ) @ SV76 )
= $true )
| ( ( between @ SV18 @ SV37 @ SV60 )
= $false )
| ( ( equal_distance @ ( distance @ SV18 @ SV60 ) @ ( distance @ SV18 @ SV76 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV18 @ SV37 ) @ ( distance @ SV18 @ SV53 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(240,plain,
! [SV77: $i,SV54: $i,SV19: $i,SV61: $i,SV83: $i,SV38: $i] :
( ( ( ~ ( between @ SV38 @ SV83 @ SV61 ) )
= $true )
| ( ( equal_distance @ ( distance @ SV19 @ SV83 ) @ ( distance @ SV19 @ ( continuous @ SV19 @ SV38 @ SV54 @ SV83 @ SV61 @ SV77 ) ) )
= $true )
| ( ( between @ SV19 @ SV38 @ SV61 )
= $false )
| ( ( equal_distance @ ( distance @ SV19 @ SV61 ) @ ( distance @ SV19 @ SV77 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV19 @ SV38 ) @ ( distance @ SV19 @ SV54 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(241,plain,
! [SV63: $i,SV62: $i,SV59: $i,SV29: $i,SV81: $i,SV46: $i,SV80: $i,SV10: $i] :
( ( ( equal_distance @ ( distance @ SV10 @ SV80 ) @ ( distance @ SV46 @ SV81 ) )
= $false )
| ( ( ~ ( equal_distance @ ( distance @ SV29 @ SV80 ) @ ( distance @ SV59 @ SV81 ) )
| ~ ( between @ SV10 @ SV29 @ SV62 )
| ~ ( between @ SV46 @ SV59 @ SV63 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SV62 @ SV80 ) @ ( distance @ SV63 @ SV81 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SV63 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[237]) ).
thf(242,plain,
! [SV66: $i,SV14: $i,SV79: $i,SV49: $i,SV33: $i] :
( ( ( SV33 = SV49 )
= $true )
| ( ( between @ SV79 @ SV14 @ SV66 )
= $true )
| ( ( between @ SV66 @ SV79 @ SV14 )
= $true )
| ( ( between @ SV14 @ SV66 @ SV79 )
= $true )
| ( ( equal_distance @ ( distance @ SV79 @ SV33 ) @ ( distance @ SV79 @ SV49 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV66 @ SV33 ) @ ( distance @ SV66 @ SV49 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV14 @ SV33 ) @ ( distance @ SV14 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(243,plain,
! [SV76: $i,SV18: $i,SV53: $i,SV60: $i,SV82: $i,SV37: $i] :
( ( ( between @ SV37 @ SV82 @ SV60 )
= $false )
| ( ( between @ SV53 @ ( continuous @ SV18 @ SV37 @ SV53 @ SV82 @ SV60 @ SV76 ) @ SV76 )
= $true )
| ( ( between @ SV18 @ SV37 @ SV60 )
= $false )
| ( ( equal_distance @ ( distance @ SV18 @ SV60 ) @ ( distance @ SV18 @ SV76 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV18 @ SV37 ) @ ( distance @ SV18 @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[239]) ).
thf(244,plain,
! [SV77: $i,SV54: $i,SV19: $i,SV61: $i,SV83: $i,SV38: $i] :
( ( ( between @ SV38 @ SV83 @ SV61 )
= $false )
| ( ( equal_distance @ ( distance @ SV19 @ SV83 ) @ ( distance @ SV19 @ ( continuous @ SV19 @ SV38 @ SV54 @ SV83 @ SV61 @ SV77 ) ) )
= $true )
| ( ( between @ SV19 @ SV38 @ SV61 )
= $false )
| ( ( equal_distance @ ( distance @ SV19 @ SV61 ) @ ( distance @ SV19 @ SV77 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV19 @ SV38 ) @ ( distance @ SV19 @ SV54 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[240]) ).
thf(245,plain,
! [SV63: $i,SV46: $i,SV62: $i,SV10: $i,SV81: $i,SV59: $i,SV80: $i,SV29: $i] :
( ( ( ~ ( equal_distance @ ( distance @ SV29 @ SV80 ) @ ( distance @ SV59 @ SV81 ) ) )
= $true )
| ( ( ~ ( between @ SV10 @ SV29 @ SV62 )
| ~ ( between @ SV46 @ SV59 @ SV63 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SV62 @ SV80 ) @ ( distance @ SV63 @ SV81 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV10 @ SV80 ) @ ( distance @ SV46 @ SV81 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SV63 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(246,plain,
! [SV63: $i,SV46: $i,SV62: $i,SV10: $i,SV81: $i,SV59: $i,SV80: $i,SV29: $i] :
( ( ( equal_distance @ ( distance @ SV29 @ SV80 ) @ ( distance @ SV59 @ SV81 ) )
= $false )
| ( ( ~ ( between @ SV10 @ SV29 @ SV62 )
| ~ ( between @ SV46 @ SV59 @ SV63 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SV62 @ SV80 ) @ ( distance @ SV63 @ SV81 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV10 @ SV80 ) @ ( distance @ SV46 @ SV81 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SV63 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[245]) ).
thf(247,plain,
! [SV81: $i,SV80: $i,SV63: $i,SV59: $i,SV46: $i,SV62: $i,SV29: $i,SV10: $i] :
( ( ( ~ ( between @ SV10 @ SV29 @ SV62 ) )
= $true )
| ( ( ~ ( between @ SV46 @ SV59 @ SV63 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SV62 @ SV80 ) @ ( distance @ SV63 @ SV81 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV29 @ SV80 ) @ ( distance @ SV59 @ SV81 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV10 @ SV80 ) @ ( distance @ SV46 @ SV81 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SV63 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[246]) ).
thf(248,plain,
! [SV81: $i,SV80: $i,SV63: $i,SV59: $i,SV46: $i,SV62: $i,SV29: $i,SV10: $i] :
( ( ( between @ SV10 @ SV29 @ SV62 )
= $false )
| ( ( ~ ( between @ SV46 @ SV59 @ SV63 )
| ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SV62 @ SV80 ) @ ( distance @ SV63 @ SV81 ) ) )
= $true )
| ( ( equal_distance @ ( distance @ SV29 @ SV80 ) @ ( distance @ SV59 @ SV81 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV10 @ SV80 ) @ ( distance @ SV46 @ SV81 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SV63 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[247]) ).
thf(249,plain,
! [SV81: $i,SV80: $i,SV62: $i,SV29: $i,SV10: $i,SV63: $i,SV59: $i,SV46: $i] :
( ( ( ~ ( between @ SV46 @ SV59 @ SV63 ) )
= $true )
| ( ( ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SV62 @ SV80 ) @ ( distance @ SV63 @ SV81 ) ) )
= $true )
| ( ( between @ SV10 @ SV29 @ SV62 )
= $false )
| ( ( equal_distance @ ( distance @ SV29 @ SV80 ) @ ( distance @ SV59 @ SV81 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV10 @ SV80 ) @ ( distance @ SV46 @ SV81 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SV63 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[248]) ).
thf(250,plain,
! [SV81: $i,SV80: $i,SV62: $i,SV29: $i,SV10: $i,SV63: $i,SV59: $i,SV46: $i] :
( ( ( between @ SV46 @ SV59 @ SV63 )
= $false )
| ( ( ( SV10 = SV29 )
| ( equal_distance @ ( distance @ SV62 @ SV80 ) @ ( distance @ SV63 @ SV81 ) ) )
= $true )
| ( ( between @ SV10 @ SV29 @ SV62 )
= $false )
| ( ( equal_distance @ ( distance @ SV29 @ SV80 ) @ ( distance @ SV59 @ SV81 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV10 @ SV80 ) @ ( distance @ SV46 @ SV81 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SV63 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[249]) ).
thf(251,plain,
! [SV59: $i,SV46: $i,SV81: $i,SV63: $i,SV80: $i,SV62: $i,SV29: $i,SV10: $i] :
( ( ( SV10 = SV29 )
= $true )
| ( ( equal_distance @ ( distance @ SV62 @ SV80 ) @ ( distance @ SV63 @ SV81 ) )
= $true )
| ( ( between @ SV46 @ SV59 @ SV63 )
= $false )
| ( ( between @ SV10 @ SV29 @ SV62 )
= $false )
| ( ( equal_distance @ ( distance @ SV29 @ SV80 ) @ ( distance @ SV59 @ SV81 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV10 @ SV80 ) @ ( distance @ SV46 @ SV81 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV29 @ SV62 ) @ ( distance @ SV59 @ SV63 ) )
= $false )
| ( ( equal_distance @ ( distance @ SV10 @ SV29 ) @ ( distance @ SV46 @ SV59 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[250]) ).
thf(252,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[62,251,244,243,242,226,225,224,221,214,213,190,169,166,165,164,155,153,152,113,108,101,100,99]) ).
thf(253,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[252]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO011-4 : 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 : n024.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 15:10:03 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.19/0.44
% 0.19/0.44 No.of.Axioms: 23
% 0.19/0.44
% 0.19/0.44 Length.of.Defs: 0
% 0.19/0.44
% 0.19/0.44 Contains.Choice.Funs: false
% 0.19/0.51 (rf:0,axioms:23,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:25,loop_count:0,foatp_calls:0,translation:fof_full)...................
% 0.60/0.77
% 0.60/0.77 ********************************
% 0.60/0.77 * All subproblems solved! *
% 0.60/0.77 ********************************
% 0.60/0.77 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:23,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:252,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.60/0.79
% 0.60/0.79 %**** Beginning of derivation protocol ****
% 0.60/0.79 % SZS output start CNFRefutation
% See solution above
% 0.60/0.79
% 0.60/0.79 %**** End of derivation protocol ****
% 0.60/0.79 %**** no. of clauses in derivation: 253 ****
% 0.60/0.79 %**** clause counter: 252 ****
% 0.60/0.79
% 0.60/0.79 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:23,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:252,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------