%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO058-3 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:17:44 AM UTC 2026
% Result : Unsatisfiable 1.02s 0.44s
% Output : CNFRefutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 37
% Syntax : Number of formulae : 350 ( 212 unt; 0 typ; 0 def)
% Number of atoms : 2175 ( 684 equ; 0 cnn)
% Maximal formula atoms : 8 ( 6 avg)
% Number of connectives : 5436 ( 487 ~; 759 |; 0 &;4190 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-6 aty)
% Number of variables : 1506 ( 0 ^;1506 !; 0 ?;1506 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_between,type,
between: $i > $i > $i > $o ).
thf(tp_continuous,type,
continuous: $i > $i > $i > $i > $i > $i > $i ).
thf(tp_equidistant,type,
equidistant: $i > $i > $i > $i > $o ).
thf(tp_euclid1,type,
euclid1: $i > $i > $i > $i > $i > $i ).
thf(tp_euclid2,type,
euclid2: $i > $i > $i > $i > $i > $i ).
thf(tp_extension,type,
extension: $i > $i > $i > $i > $i ).
thf(tp_inner_pasch,type,
inner_pasch: $i > $i > $i > $i > $i > $i ).
thf(tp_lower_dimension_point_1,type,
lower_dimension_point_1: $i ).
thf(tp_lower_dimension_point_2,type,
lower_dimension_point_2: $i ).
thf(tp_lower_dimension_point_3,type,
lower_dimension_point_3: $i ).
thf(tp_reflection,type,
reflection: $i > $i > $i ).
thf(tp_u,type,
u: $i ).
thf(tp_v,type,
v: $i ).
thf(1,axiom,
! [U: $i] :
( U
= ( reflection @ U @ U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).
thf(2,axiom,
! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_1) ).
thf(3,axiom,
! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
thf(4,axiom,
! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).
thf(5,axiom,
! [Y: $i,U: $i,V: $i,W: $i,X: $i] :
( ( Y
!= ( extension @ U @ V @ W @ X ) )
| ( between @ U @ V @ Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b0) ).
thf(6,axiom,
! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
thf(7,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(8,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(9,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(10,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(11,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(12,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(13,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(14,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(15,axiom,
! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
thf(16,axiom,
! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
thf(17,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(18,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(19,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(20,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(21,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(22,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(23,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(24,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(25,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(26,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(27,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(28,axiom,
! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(29,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(30,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(31,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(32,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(33,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(34,axiom,
! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(35,axiom,
( v
= ( reflection @ u @ v ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_equals_reflection) ).
thf(36,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(37,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[36]) ).
thf(38,negated_conjecture,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_u_equals_v) ).
thf(39,plain,
$false = $false,
inference(unfold_def,[status(thm)],[37]) ).
thf(40,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(41,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(42,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[3]) ).
thf(43,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(44,plain,
( ( ! [Y: $i,U: $i,V: $i,W: $i,X: $i] :
( ( Y
!= ( extension @ U @ V @ W @ X ) )
| ( between @ U @ V @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(45,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(46,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)],[7]) ).
thf(47,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)],[8]) ).
thf(48,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)],[9]) ).
thf(49,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)],[10]) ).
thf(50,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)],[11]) ).
thf(51,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)],[12]) ).
thf(52,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)],[13]) ).
thf(53,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)],[14]) ).
thf(54,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(55,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(56,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)],[17]) ).
thf(57,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)],[18]) ).
thf(58,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)],[19]) ).
thf(59,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)],[20]) ).
thf(60,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)],[21]) ).
thf(61,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)],[22]) ).
thf(62,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(63,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[24]) ).
thf(64,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[25]) ).
thf(65,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)],[26]) ).
thf(66,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)],[27]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[28]) ).
thf(68,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)],[29]) ).
thf(69,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[30]) ).
thf(70,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[31]) ).
thf(71,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[32]) ).
thf(72,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)],[33]) ).
thf(73,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[34]) ).
thf(74,plain,
( ( v
= ( reflection @ u @ v ) )
= $true ),
inference(unfold_def,[status(thm)],[35]) ).
thf(75,plain,
( ( u != v )
= $true ),
inference(unfold_def,[status(thm)],[38]) ).
thf(76,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[39]) ).
thf(77,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(78,plain,
( ( ! [Y: $i,U: $i,V: $i] :
( ! [W: $i,X: $i] :
( Y
!= ( extension @ U @ V @ W @ X ) )
| ( between @ U @ V @ Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(79,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)],[46]) ).
thf(80,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)],[56]) ).
thf(81,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)],[57]) ).
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(extcnf_combined,[status(esa)],[58]) ).
thf(83,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)],[59]) ).
thf(84,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)],[60]) ).
thf(85,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)],[61]) ).
thf(86,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)],[65]) ).
thf(87,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)],[66]) ).
thf(88,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)],[68]) ).
thf(89,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[71]) ).
thf(90,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)],[72]) ).
thf(91,plain,
( ( u != v )
= $true ),
inference(extcnf_combined,[status(esa)],[75]) ).
thf(92,plain,
( ( u != v )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(93,plain,
( ( v
= ( reflection @ u @ v ) )
= $true ),
inference(copy,[status(thm)],[74]) ).
thf(94,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(copy,[status(thm)],[73]) ).
thf(95,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)],[90]) ).
thf(96,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(97,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[70]) ).
thf(98,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[69]) ).
thf(99,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)],[88]) ).
thf(100,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[67]) ).
thf(101,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)],[87]) ).
thf(102,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)],[86]) ).
thf(103,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[64]) ).
thf(104,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(copy,[status(thm)],[63]) ).
thf(105,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(copy,[status(thm)],[62]) ).
thf(106,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)],[85]) ).
thf(107,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)],[84]) ).
thf(108,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)],[83]) ).
thf(109,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)],[82]) ).
thf(110,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)],[81]) ).
thf(111,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)],[80]) ).
thf(112,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[55]) ).
thf(113,plain,
( ( ! [U: $i,V: $i] : ( equidistant @ U @ V @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[54]) ).
thf(114,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(115,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ W @ X ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(116,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ U @ V @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[51]) ).
thf(117,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ V @ U @ X @ W ) ) )
= $true ),
inference(copy,[status(thm)],[50]) ).
thf(118,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ W @ X @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[49]) ).
thf(119,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[48]) ).
thf(120,plain,
( ( ! [U: $i,V: $i,W: $i,X: $i] :
( ~ ( equidistant @ U @ V @ W @ X )
| ( equidistant @ X @ W @ V @ U ) ) )
= $true ),
inference(copy,[status(thm)],[47]) ).
thf(121,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)],[79]) ).
thf(122,plain,
( ( ! [V: $i,U: $i,W: $i] :
( V
= ( extension @ U @ V @ W @ W ) ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(123,plain,
( ( ! [Y: $i,U: $i,V: $i] :
( ! [W: $i,X: $i] :
( Y
!= ( extension @ U @ V @ W @ X ) )
| ( between @ U @ V @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[78]) ).
thf(124,plain,
( ( ! [U: $i,V: $i] : ( between @ U @ V @ ( reflection @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(125,plain,
( ( ! [V: $i,U: $i] : ( equidistant @ V @ ( reflection @ U @ V ) @ U @ V ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(126,plain,
( ( ! [U: $i,V: $i] :
( ( U != V )
| ( V
= ( reflection @ U @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[77]) ).
thf(127,plain,
( ( ! [U: $i] :
( U
= ( reflection @ U @ U ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(128,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[76]) ).
thf(129,plain,
( ( u = v )
= $false ),
inference(extcnf_not_pos,[status(thm)],[92]) ).
thf(130,plain,
! [SV1: $i] :
( ( ! [SY124: $i] : ( equidistant @ SV1 @ SY124 @ SY124 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(131,plain,
! [SV2: $i] :
( ( ! [SY125: $i,SY126: $i,SY127: $i] :
( ~ ( equidistant @ SV2 @ SY125 @ SY126 @ SY127 )
| ! [SY128: $i,SY129: $i] :
( ~ ( equidistant @ SV2 @ SY125 @ SY128 @ SY129 )
| ( equidistant @ SY126 @ SY127 @ SY128 @ SY129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(132,plain,
! [SV3: $i] :
( ( ! [SY130: $i] :
( ! [SY131: $i] :
~ ( equidistant @ SV3 @ SY130 @ SY131 @ SY131 )
| ( SV3 = SY130 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(133,plain,
! [SV4: $i] :
( ( ! [SY132: $i,SY133: $i,SY134: $i] : ( between @ SV4 @ SY132 @ ( extension @ SV4 @ SY132 @ SY133 @ SY134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(134,plain,
! [SV5: $i] :
( ( ! [SY135: $i,SY136: $i,SY137: $i] : ( equidistant @ SV5 @ ( extension @ SY135 @ SV5 @ SY136 @ SY137 ) @ SY136 @ SY137 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(135,plain,
! [SV6: $i] :
( ( ! [SY138: $i,SY139: $i,SY140: $i,SY141: $i,SY142: $i] :
( ~ ( equidistant @ SV6 @ SY138 @ SY139 @ SY140 )
| ~ ( equidistant @ SY138 @ SY141 @ SY140 @ SY142 )
| ! [SY143: $i,SY144: $i] :
( ~ ( equidistant @ SV6 @ SY143 @ SY139 @ SY144 )
| ~ ( equidistant @ SY138 @ SY143 @ SY140 @ SY144 )
| ~ ( between @ SV6 @ SY138 @ SY141 )
| ~ ( between @ SY139 @ SY140 @ SY142 )
| ( SV6 = SY138 )
| ( equidistant @ SY141 @ SY143 @ SY142 @ SY144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(136,plain,
! [SV7: $i] :
( ( ! [SY145: $i] :
( ~ ( between @ SV7 @ SY145 @ SV7 )
| ( SV7 = SY145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(137,plain,
! [SV8: $i] :
( ( ! [SY146: $i,SY147: $i] :
( ~ ( between @ SV8 @ SY146 @ SY147 )
| ! [SY148: $i,SY149: $i] :
( ~ ( between @ SY148 @ SY149 @ SY147 )
| ( between @ SY146 @ ( inner_pasch @ SV8 @ SY146 @ SY147 @ SY149 @ SY148 ) @ SY148 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(138,plain,
! [SV9: $i] :
( ( ! [SY150: $i,SY151: $i] :
( ~ ( between @ SV9 @ SY150 @ SY151 )
| ! [SY152: $i,SY153: $i] :
( ~ ( between @ SY152 @ SY153 @ SY151 )
| ( between @ SY153 @ ( inner_pasch @ SV9 @ SY150 @ SY151 @ SY153 @ SY152 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(139,plain,
( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[103]) ).
thf(140,plain,
( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[104]) ).
thf(141,plain,
( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[105]) ).
thf(142,plain,
! [SV10: $i] :
( ( ! [SY154: $i,SY155: $i] :
( ~ ( equidistant @ SV10 @ SY154 @ SV10 @ SY155 )
| ! [SY156: $i] :
( ~ ( equidistant @ SY156 @ SY154 @ SY156 @ SY155 )
| ! [SY157: $i] :
( ~ ( equidistant @ SY157 @ SY154 @ SY157 @ SY155 )
| ( between @ SV10 @ SY156 @ SY157 )
| ( between @ SY156 @ SY157 @ SV10 )
| ( SY154 = SY155 )
| ( between @ SY157 @ SV10 @ SY156 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(143,plain,
! [SV11: $i] :
( ( ! [SY158: $i,SY159: $i] :
( ~ ( between @ SV11 @ SY158 @ SY159 )
| ! [SY160: $i,SY161: $i] :
( ~ ( between @ SY160 @ SY158 @ SY161 )
| ( SV11 = SY158 )
| ( between @ SV11 @ SY160 @ ( euclid1 @ SV11 @ SY160 @ SY158 @ SY161 @ SY159 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(144,plain,
! [SV12: $i] :
( ( ! [SY162: $i,SY163: $i] :
( ~ ( between @ SV12 @ SY162 @ SY163 )
| ! [SY164: $i,SY165: $i] :
( ~ ( between @ SY164 @ SY162 @ SY165 )
| ( SV12 = SY162 )
| ( between @ SV12 @ SY165 @ ( euclid2 @ SV12 @ SY164 @ SY162 @ SY165 @ SY163 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[108]) ).
thf(145,plain,
! [SV13: $i] :
( ( ! [SY166: $i,SY167: $i] :
( ~ ( between @ SV13 @ SY166 @ SY167 )
| ! [SY168: $i,SY169: $i] :
( ~ ( between @ SY168 @ SY166 @ SY169 )
| ( SV13 = SY166 )
| ( between @ ( euclid1 @ SV13 @ SY168 @ SY166 @ SY169 @ SY167 ) @ SY167 @ ( euclid2 @ SV13 @ SY168 @ SY166 @ SY169 @ SY167 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(146,plain,
! [SV14: $i] :
( ( ! [SY170: $i,SY171: $i,SY172: $i] :
( ~ ( equidistant @ SV14 @ SY170 @ SV14 @ SY171 )
| ! [SY173: $i] :
( ~ ( equidistant @ SV14 @ SY172 @ SV14 @ SY173 )
| ~ ( between @ SV14 @ SY170 @ SY172 )
| ! [SY174: $i] :
( ~ ( between @ SY170 @ SY174 @ SY172 )
| ( between @ SY171 @ ( continuous @ SV14 @ SY170 @ SY171 @ SY174 @ SY172 @ SY173 ) @ SY173 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(147,plain,
! [SV15: $i] :
( ( ! [SY175: $i,SY176: $i,SY177: $i] :
( ~ ( equidistant @ SV15 @ SY175 @ SV15 @ SY176 )
| ! [SY178: $i] :
( ~ ( equidistant @ SV15 @ SY177 @ SV15 @ SY178 )
| ~ ( between @ SV15 @ SY175 @ SY177 )
| ! [SY179: $i] :
( ~ ( between @ SY175 @ SY179 @ SY177 )
| ( equidistant @ SV15 @ SY179 @ SV15 @ ( continuous @ SV15 @ SY175 @ SY176 @ SY179 @ SY177 @ SY178 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(148,plain,
! [SV16: $i] :
( ( ! [SY180: $i] :
( ( reflection @ SV16 @ SY180 )
= ( extension @ SV16 @ SY180 @ SV16 @ SY180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(149,plain,
! [SV17: $i] :
( ( ! [SY181: $i] : ( equidistant @ SV17 @ SY181 @ SV17 @ SY181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(150,plain,
! [SV18: $i] :
( ( ! [SY182: $i,SY183: $i,SY184: $i] :
( ~ ( equidistant @ SV18 @ SY182 @ SY183 @ SY184 )
| ( equidistant @ SY183 @ SY184 @ SV18 @ SY182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(151,plain,
! [SV19: $i] :
( ( ! [SY185: $i,SY186: $i,SY187: $i] :
( ~ ( equidistant @ SV19 @ SY185 @ SY186 @ SY187 )
| ( equidistant @ SY185 @ SV19 @ SY186 @ SY187 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(152,plain,
! [SV20: $i] :
( ( ! [SY188: $i,SY189: $i,SY190: $i] :
( ~ ( equidistant @ SV20 @ SY188 @ SY189 @ SY190 )
| ( equidistant @ SV20 @ SY188 @ SY190 @ SY189 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(153,plain,
! [SV21: $i] :
( ( ! [SY191: $i,SY192: $i,SY193: $i] :
( ~ ( equidistant @ SV21 @ SY191 @ SY192 @ SY193 )
| ( equidistant @ SY191 @ SV21 @ SY193 @ SY192 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(154,plain,
! [SV22: $i] :
( ( ! [SY194: $i,SY195: $i,SY196: $i] :
( ~ ( equidistant @ SV22 @ SY194 @ SY195 @ SY196 )
| ( equidistant @ SY195 @ SY196 @ SY194 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(155,plain,
! [SV23: $i] :
( ( ! [SY197: $i,SY198: $i,SY199: $i] :
( ~ ( equidistant @ SV23 @ SY197 @ SY198 @ SY199 )
| ( equidistant @ SY199 @ SY198 @ SV23 @ SY197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(156,plain,
! [SV24: $i] :
( ( ! [SY200: $i,SY201: $i,SY202: $i] :
( ~ ( equidistant @ SV24 @ SY200 @ SY201 @ SY202 )
| ( equidistant @ SY202 @ SY201 @ SY200 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(157,plain,
! [SV25: $i] :
( ( ! [SY203: $i,SY204: $i,SY205: $i] :
( ~ ( equidistant @ SV25 @ SY203 @ SY204 @ SY205 )
| ! [SY206: $i,SY207: $i] :
( ~ ( equidistant @ SY204 @ SY205 @ SY206 @ SY207 )
| ( equidistant @ SV25 @ SY203 @ SY206 @ SY207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(158,plain,
! [SV26: $i] :
( ( ! [SY208: $i,SY209: $i] :
( SV26
= ( extension @ SY208 @ SV26 @ SY209 @ SY209 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(159,plain,
! [SV27: $i] :
( ( ! [SY210: $i,SY211: $i] :
( ! [SY212: $i,SY213: $i] :
( SV27
!= ( extension @ SY210 @ SY211 @ SY212 @ SY213 ) )
| ( between @ SY210 @ SY211 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(160,plain,
! [SV28: $i] :
( ( ! [SY214: $i] : ( between @ SV28 @ SY214 @ ( reflection @ SV28 @ SY214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[124]) ).
thf(161,plain,
! [SV29: $i] :
( ( ! [SY215: $i] : ( equidistant @ SV29 @ ( reflection @ SY215 @ SV29 ) @ SY215 @ SV29 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[125]) ).
thf(162,plain,
! [SV30: $i] :
( ( ! [SY216: $i] :
( ( SV30 != SY216 )
| ( SY216
= ( reflection @ SV30 @ SY216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[126]) ).
thf(163,plain,
! [SV31: $i] :
( ( SV31
= ( reflection @ SV31 @ SV31 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[127]) ).
thf(164,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[128]) ).
thf(165,plain,
! [SV32: $i,SV1: $i] :
( ( equidistant @ SV1 @ SV32 @ SV32 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(166,plain,
! [SV33: $i,SV2: $i] :
( ( ! [SY217: $i,SY218: $i] :
( ~ ( equidistant @ SV2 @ SV33 @ SY217 @ SY218 )
| ! [SY219: $i,SY220: $i] :
( ~ ( equidistant @ SV2 @ SV33 @ SY219 @ SY220 )
| ( equidistant @ SY217 @ SY218 @ SY219 @ SY220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(167,plain,
! [SV34: $i,SV3: $i] :
( ( ! [SY221: $i] :
~ ( equidistant @ SV3 @ SV34 @ SY221 @ SY221 )
| ( SV3 = SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(168,plain,
! [SV35: $i,SV4: $i] :
( ( ! [SY222: $i,SY223: $i] : ( between @ SV4 @ SV35 @ ( extension @ SV4 @ SV35 @ SY222 @ SY223 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(169,plain,
! [SV36: $i,SV5: $i] :
( ( ! [SY224: $i,SY225: $i] : ( equidistant @ SV5 @ ( extension @ SV36 @ SV5 @ SY224 @ SY225 ) @ SY224 @ SY225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(170,plain,
! [SV37: $i,SV6: $i] :
( ( ! [SY226: $i,SY227: $i,SY228: $i,SY229: $i] :
( ~ ( equidistant @ SV6 @ SV37 @ SY226 @ SY227 )
| ~ ( equidistant @ SV37 @ SY228 @ SY227 @ SY229 )
| ! [SY230: $i,SY231: $i] :
( ~ ( equidistant @ SV6 @ SY230 @ SY226 @ SY231 )
| ~ ( equidistant @ SV37 @ SY230 @ SY227 @ SY231 )
| ~ ( between @ SV6 @ SV37 @ SY228 )
| ~ ( between @ SY226 @ SY227 @ SY229 )
| ( SV6 = SV37 )
| ( equidistant @ SY228 @ SY230 @ SY229 @ SY231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[135]) ).
thf(171,plain,
! [SV38: $i,SV7: $i] :
( ( ~ ( between @ SV7 @ SV38 @ SV7 )
| ( SV7 = SV38 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(172,plain,
! [SV39: $i,SV8: $i] :
( ( ! [SY232: $i] :
( ~ ( between @ SV8 @ SV39 @ SY232 )
| ! [SY233: $i,SY234: $i] :
( ~ ( between @ SY233 @ SY234 @ SY232 )
| ( between @ SV39 @ ( inner_pasch @ SV8 @ SV39 @ SY232 @ SY234 @ SY233 ) @ SY233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(173,plain,
! [SV40: $i,SV9: $i] :
( ( ! [SY235: $i] :
( ~ ( between @ SV9 @ SV40 @ SY235 )
| ! [SY236: $i,SY237: $i] :
( ~ ( between @ SY236 @ SY237 @ SY235 )
| ( between @ SY237 @ ( inner_pasch @ SV9 @ SV40 @ SY235 @ SY237 @ SY236 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(174,plain,
! [SV41: $i,SV10: $i] :
( ( ! [SY238: $i] :
( ~ ( equidistant @ SV10 @ SV41 @ SV10 @ SY238 )
| ! [SY239: $i] :
( ~ ( equidistant @ SY239 @ SV41 @ SY239 @ SY238 )
| ! [SY240: $i] :
( ~ ( equidistant @ SY240 @ SV41 @ SY240 @ SY238 )
| ( between @ SV10 @ SY239 @ SY240 )
| ( between @ SY239 @ SY240 @ SV10 )
| ( SV41 = SY238 )
| ( between @ SY240 @ SV10 @ SY239 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[142]) ).
thf(175,plain,
! [SV42: $i,SV11: $i] :
( ( ! [SY241: $i] :
( ~ ( between @ SV11 @ SV42 @ SY241 )
| ! [SY242: $i,SY243: $i] :
( ~ ( between @ SY242 @ SV42 @ SY243 )
| ( SV11 = SV42 )
| ( between @ SV11 @ SY242 @ ( euclid1 @ SV11 @ SY242 @ SV42 @ SY243 @ SY241 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(176,plain,
! [SV43: $i,SV12: $i] :
( ( ! [SY244: $i] :
( ~ ( between @ SV12 @ SV43 @ SY244 )
| ! [SY245: $i,SY246: $i] :
( ~ ( between @ SY245 @ SV43 @ SY246 )
| ( SV12 = SV43 )
| ( between @ SV12 @ SY246 @ ( euclid2 @ SV12 @ SY245 @ SV43 @ SY246 @ SY244 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[144]) ).
thf(177,plain,
! [SV44: $i,SV13: $i] :
( ( ! [SY247: $i] :
( ~ ( between @ SV13 @ SV44 @ SY247 )
| ! [SY248: $i,SY249: $i] :
( ~ ( between @ SY248 @ SV44 @ SY249 )
| ( SV13 = SV44 )
| ( between @ ( euclid1 @ SV13 @ SY248 @ SV44 @ SY249 @ SY247 ) @ SY247 @ ( euclid2 @ SV13 @ SY248 @ SV44 @ SY249 @ SY247 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[145]) ).
thf(178,plain,
! [SV45: $i,SV14: $i] :
( ( ! [SY250: $i,SY251: $i] :
( ~ ( equidistant @ SV14 @ SV45 @ SV14 @ SY250 )
| ! [SY252: $i] :
( ~ ( equidistant @ SV14 @ SY251 @ SV14 @ SY252 )
| ~ ( between @ SV14 @ SV45 @ SY251 )
| ! [SY253: $i] :
( ~ ( between @ SV45 @ SY253 @ SY251 )
| ( between @ SY250 @ ( continuous @ SV14 @ SV45 @ SY250 @ SY253 @ SY251 @ SY252 ) @ SY252 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[146]) ).
thf(179,plain,
! [SV46: $i,SV15: $i] :
( ( ! [SY254: $i,SY255: $i] :
( ~ ( equidistant @ SV15 @ SV46 @ SV15 @ SY254 )
| ! [SY256: $i] :
( ~ ( equidistant @ SV15 @ SY255 @ SV15 @ SY256 )
| ~ ( between @ SV15 @ SV46 @ SY255 )
| ! [SY257: $i] :
( ~ ( between @ SV46 @ SY257 @ SY255 )
| ( equidistant @ SV15 @ SY257 @ SV15 @ ( continuous @ SV15 @ SV46 @ SY254 @ SY257 @ SY255 @ SY256 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[147]) ).
thf(180,plain,
! [SV47: $i,SV16: $i] :
( ( ( reflection @ SV16 @ SV47 )
= ( extension @ SV16 @ SV47 @ SV16 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(181,plain,
! [SV48: $i,SV17: $i] :
( ( equidistant @ SV17 @ SV48 @ SV17 @ SV48 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(182,plain,
! [SV49: $i,SV18: $i] :
( ( ! [SY258: $i,SY259: $i] :
( ~ ( equidistant @ SV18 @ SV49 @ SY258 @ SY259 )
| ( equidistant @ SY258 @ SY259 @ SV18 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(183,plain,
! [SV50: $i,SV19: $i] :
( ( ! [SY260: $i,SY261: $i] :
( ~ ( equidistant @ SV19 @ SV50 @ SY260 @ SY261 )
| ( equidistant @ SV50 @ SV19 @ SY260 @ SY261 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(184,plain,
! [SV51: $i,SV20: $i] :
( ( ! [SY262: $i,SY263: $i] :
( ~ ( equidistant @ SV20 @ SV51 @ SY262 @ SY263 )
| ( equidistant @ SV20 @ SV51 @ SY263 @ SY262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(185,plain,
! [SV52: $i,SV21: $i] :
( ( ! [SY264: $i,SY265: $i] :
( ~ ( equidistant @ SV21 @ SV52 @ SY264 @ SY265 )
| ( equidistant @ SV52 @ SV21 @ SY265 @ SY264 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(186,plain,
! [SV53: $i,SV22: $i] :
( ( ! [SY266: $i,SY267: $i] :
( ~ ( equidistant @ SV22 @ SV53 @ SY266 @ SY267 )
| ( equidistant @ SY266 @ SY267 @ SV53 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(187,plain,
! [SV54: $i,SV23: $i] :
( ( ! [SY268: $i,SY269: $i] :
( ~ ( equidistant @ SV23 @ SV54 @ SY268 @ SY269 )
| ( equidistant @ SY269 @ SY268 @ SV23 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[155]) ).
thf(188,plain,
! [SV55: $i,SV24: $i] :
( ( ! [SY270: $i,SY271: $i] :
( ~ ( equidistant @ SV24 @ SV55 @ SY270 @ SY271 )
| ( equidistant @ SY271 @ SY270 @ SV55 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[156]) ).
thf(189,plain,
! [SV56: $i,SV25: $i] :
( ( ! [SY272: $i,SY273: $i] :
( ~ ( equidistant @ SV25 @ SV56 @ SY272 @ SY273 )
| ! [SY274: $i,SY275: $i] :
( ~ ( equidistant @ SY272 @ SY273 @ SY274 @ SY275 )
| ( equidistant @ SV25 @ SV56 @ SY274 @ SY275 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(190,plain,
! [SV57: $i,SV26: $i] :
( ( ! [SY276: $i] :
( SV26
= ( extension @ SV57 @ SV26 @ SY276 @ SY276 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[158]) ).
thf(191,plain,
! [SV58: $i,SV27: $i] :
( ( ! [SY277: $i] :
( ! [SY278: $i,SY279: $i] :
( SV27
!= ( extension @ SV58 @ SY277 @ SY278 @ SY279 ) )
| ( between @ SV58 @ SY277 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(192,plain,
! [SV59: $i,SV28: $i] :
( ( between @ SV28 @ SV59 @ ( reflection @ SV28 @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(193,plain,
! [SV60: $i,SV29: $i] :
( ( equidistant @ SV29 @ ( reflection @ SV60 @ SV29 ) @ SV60 @ SV29 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(194,plain,
! [SV61: $i,SV30: $i] :
( ( ( SV30 != SV61 )
| ( SV61
= ( reflection @ SV30 @ SV61 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(195,plain,
! [SV62: $i,SV33: $i,SV2: $i] :
( ( ! [SY280: $i] :
( ~ ( equidistant @ SV2 @ SV33 @ SV62 @ SY280 )
| ! [SY281: $i,SY282: $i] :
( ~ ( equidistant @ SV2 @ SV33 @ SY281 @ SY282 )
| ( equidistant @ SV62 @ SY280 @ SY281 @ SY282 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(196,plain,
! [SV34: $i,SV3: $i] :
( ( ( ! [SY221: $i] :
~ ( equidistant @ SV3 @ SV34 @ SY221 @ SY221 ) )
= $true )
| ( ( SV3 = SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[167]) ).
thf(197,plain,
! [SV63: $i,SV35: $i,SV4: $i] :
( ( ! [SY283: $i] : ( between @ SV4 @ SV35 @ ( extension @ SV4 @ SV35 @ SV63 @ SY283 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[168]) ).
thf(198,plain,
! [SV64: $i,SV36: $i,SV5: $i] :
( ( ! [SY284: $i] : ( equidistant @ SV5 @ ( extension @ SV36 @ SV5 @ SV64 @ SY284 ) @ SV64 @ SY284 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[169]) ).
thf(199,plain,
! [SV65: $i,SV37: $i,SV6: $i] :
( ( ! [SY285: $i,SY286: $i,SY287: $i] :
( ~ ( equidistant @ SV6 @ SV37 @ SV65 @ SY285 )
| ~ ( equidistant @ SV37 @ SY286 @ SY285 @ SY287 )
| ! [SY288: $i,SY289: $i] :
( ~ ( equidistant @ SV6 @ SY288 @ SV65 @ SY289 )
| ~ ( equidistant @ SV37 @ SY288 @ SY285 @ SY289 )
| ~ ( between @ SV6 @ SV37 @ SY286 )
| ~ ( between @ SV65 @ SY285 @ SY287 )
| ( SV6 = SV37 )
| ( equidistant @ SY286 @ SY288 @ SY287 @ SY289 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[170]) ).
thf(200,plain,
! [SV38: $i,SV7: $i] :
( ( ( ~ ( between @ SV7 @ SV38 @ SV7 ) )
= $true )
| ( ( SV7 = SV38 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(201,plain,
! [SV66: $i,SV39: $i,SV8: $i] :
( ( ~ ( between @ SV8 @ SV39 @ SV66 )
| ! [SY290: $i,SY291: $i] :
( ~ ( between @ SY290 @ SY291 @ SV66 )
| ( between @ SV39 @ ( inner_pasch @ SV8 @ SV39 @ SV66 @ SY291 @ SY290 ) @ SY290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[172]) ).
thf(202,plain,
! [SV67: $i,SV40: $i,SV9: $i] :
( ( ~ ( between @ SV9 @ SV40 @ SV67 )
| ! [SY292: $i,SY293: $i] :
( ~ ( between @ SY292 @ SY293 @ SV67 )
| ( between @ SY293 @ ( inner_pasch @ SV9 @ SV40 @ SV67 @ SY293 @ SY292 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(203,plain,
! [SV68: $i,SV41: $i,SV10: $i] :
( ( ~ ( equidistant @ SV10 @ SV41 @ SV10 @ SV68 )
| ! [SY294: $i] :
( ~ ( equidistant @ SY294 @ SV41 @ SY294 @ SV68 )
| ! [SY295: $i] :
( ~ ( equidistant @ SY295 @ SV41 @ SY295 @ SV68 )
| ( between @ SV10 @ SY294 @ SY295 )
| ( between @ SY294 @ SY295 @ SV10 )
| ( SV41 = SV68 )
| ( between @ SY295 @ SV10 @ SY294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[174]) ).
thf(204,plain,
! [SV69: $i,SV42: $i,SV11: $i] :
( ( ~ ( between @ SV11 @ SV42 @ SV69 )
| ! [SY296: $i,SY297: $i] :
( ~ ( between @ SY296 @ SV42 @ SY297 )
| ( SV11 = SV42 )
| ( between @ SV11 @ SY296 @ ( euclid1 @ SV11 @ SY296 @ SV42 @ SY297 @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[175]) ).
thf(205,plain,
! [SV70: $i,SV43: $i,SV12: $i] :
( ( ~ ( between @ SV12 @ SV43 @ SV70 )
| ! [SY298: $i,SY299: $i] :
( ~ ( between @ SY298 @ SV43 @ SY299 )
| ( SV12 = SV43 )
| ( between @ SV12 @ SY299 @ ( euclid2 @ SV12 @ SY298 @ SV43 @ SY299 @ SV70 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[176]) ).
thf(206,plain,
! [SV71: $i,SV44: $i,SV13: $i] :
( ( ~ ( between @ SV13 @ SV44 @ SV71 )
| ! [SY300: $i,SY301: $i] :
( ~ ( between @ SY300 @ SV44 @ SY301 )
| ( SV13 = SV44 )
| ( between @ ( euclid1 @ SV13 @ SY300 @ SV44 @ SY301 @ SV71 ) @ SV71 @ ( euclid2 @ SV13 @ SY300 @ SV44 @ SY301 @ SV71 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[177]) ).
thf(207,plain,
! [SV72: $i,SV45: $i,SV14: $i] :
( ( ! [SY302: $i] :
( ~ ( equidistant @ SV14 @ SV45 @ SV14 @ SV72 )
| ! [SY303: $i] :
( ~ ( equidistant @ SV14 @ SY302 @ SV14 @ SY303 )
| ~ ( between @ SV14 @ SV45 @ SY302 )
| ! [SY304: $i] :
( ~ ( between @ SV45 @ SY304 @ SY302 )
| ( between @ SV72 @ ( continuous @ SV14 @ SV45 @ SV72 @ SY304 @ SY302 @ SY303 ) @ SY303 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[178]) ).
thf(208,plain,
! [SV73: $i,SV46: $i,SV15: $i] :
( ( ! [SY305: $i] :
( ~ ( equidistant @ SV15 @ SV46 @ SV15 @ SV73 )
| ! [SY306: $i] :
( ~ ( equidistant @ SV15 @ SY305 @ SV15 @ SY306 )
| ~ ( between @ SV15 @ SV46 @ SY305 )
| ! [SY307: $i] :
( ~ ( between @ SV46 @ SY307 @ SY305 )
| ( equidistant @ SV15 @ SY307 @ SV15 @ ( continuous @ SV15 @ SV46 @ SV73 @ SY307 @ SY305 @ SY306 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[179]) ).
thf(209,plain,
! [SV74: $i,SV49: $i,SV18: $i] :
( ( ! [SY308: $i] :
( ~ ( equidistant @ SV18 @ SV49 @ SV74 @ SY308 )
| ( equidistant @ SV74 @ SY308 @ SV18 @ SV49 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[182]) ).
thf(210,plain,
! [SV75: $i,SV50: $i,SV19: $i] :
( ( ! [SY309: $i] :
( ~ ( equidistant @ SV19 @ SV50 @ SV75 @ SY309 )
| ( equidistant @ SV50 @ SV19 @ SV75 @ SY309 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[183]) ).
thf(211,plain,
! [SV76: $i,SV51: $i,SV20: $i] :
( ( ! [SY310: $i] :
( ~ ( equidistant @ SV20 @ SV51 @ SV76 @ SY310 )
| ( equidistant @ SV20 @ SV51 @ SY310 @ SV76 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[184]) ).
thf(212,plain,
! [SV77: $i,SV52: $i,SV21: $i] :
( ( ! [SY311: $i] :
( ~ ( equidistant @ SV21 @ SV52 @ SV77 @ SY311 )
| ( equidistant @ SV52 @ SV21 @ SY311 @ SV77 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[185]) ).
thf(213,plain,
! [SV78: $i,SV53: $i,SV22: $i] :
( ( ! [SY312: $i] :
( ~ ( equidistant @ SV22 @ SV53 @ SV78 @ SY312 )
| ( equidistant @ SV78 @ SY312 @ SV53 @ SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[186]) ).
thf(214,plain,
! [SV79: $i,SV54: $i,SV23: $i] :
( ( ! [SY313: $i] :
( ~ ( equidistant @ SV23 @ SV54 @ SV79 @ SY313 )
| ( equidistant @ SY313 @ SV79 @ SV23 @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[187]) ).
thf(215,plain,
! [SV80: $i,SV55: $i,SV24: $i] :
( ( ! [SY314: $i] :
( ~ ( equidistant @ SV24 @ SV55 @ SV80 @ SY314 )
| ( equidistant @ SY314 @ SV80 @ SV55 @ SV24 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[188]) ).
thf(216,plain,
! [SV81: $i,SV56: $i,SV25: $i] :
( ( ! [SY315: $i] :
( ~ ( equidistant @ SV25 @ SV56 @ SV81 @ SY315 )
| ! [SY316: $i,SY317: $i] :
( ~ ( equidistant @ SV81 @ SY315 @ SY316 @ SY317 )
| ( equidistant @ SV25 @ SV56 @ SY316 @ SY317 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[189]) ).
thf(217,plain,
! [SV82: $i,SV57: $i,SV26: $i] :
( ( SV26
= ( extension @ SV57 @ SV26 @ SV82 @ SV82 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[190]) ).
thf(218,plain,
! [SV83: $i,SV58: $i,SV27: $i] :
( ( ! [SY318: $i,SY319: $i] :
( SV27
!= ( extension @ SV58 @ SV83 @ SY318 @ SY319 ) )
| ( between @ SV58 @ SV83 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[191]) ).
thf(219,plain,
! [SV61: $i,SV30: $i] :
( ( ( SV30 != SV61 )
= $true )
| ( ( SV61
= ( reflection @ SV30 @ SV61 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(220,plain,
! [SV84: $i,SV62: $i,SV33: $i,SV2: $i] :
( ( ~ ( equidistant @ SV2 @ SV33 @ SV62 @ SV84 )
| ! [SY320: $i,SY321: $i] :
( ~ ( equidistant @ SV2 @ SV33 @ SY320 @ SY321 )
| ( equidistant @ SV62 @ SV84 @ SY320 @ SY321 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[195]) ).
thf(221,plain,
! [SV85: $i,SV34: $i,SV3: $i] :
( ( ( ~ ( equidistant @ SV3 @ SV34 @ SV85 @ SV85 ) )
= $true )
| ( ( SV3 = SV34 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[196]) ).
thf(222,plain,
! [SV86: $i,SV63: $i,SV35: $i,SV4: $i] :
( ( between @ SV4 @ SV35 @ ( extension @ SV4 @ SV35 @ SV63 @ SV86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[197]) ).
thf(223,plain,
! [SV87: $i,SV64: $i,SV36: $i,SV5: $i] :
( ( equidistant @ SV5 @ ( extension @ SV36 @ SV5 @ SV64 @ SV87 ) @ SV64 @ SV87 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(224,plain,
! [SV88: $i,SV65: $i,SV37: $i,SV6: $i] :
( ( ! [SY322: $i,SY323: $i] :
( ~ ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
| ~ ( equidistant @ SV37 @ SY322 @ SV88 @ SY323 )
| ! [SY324: $i,SY325: $i] :
( ~ ( equidistant @ SV6 @ SY324 @ SV65 @ SY325 )
| ~ ( equidistant @ SV37 @ SY324 @ SV88 @ SY325 )
| ~ ( between @ SV6 @ SV37 @ SY322 )
| ~ ( between @ SV65 @ SV88 @ SY323 )
| ( SV6 = SV37 )
| ( equidistant @ SY322 @ SY324 @ SY323 @ SY325 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[199]) ).
thf(225,plain,
! [SV38: $i,SV7: $i] :
( ( ( between @ SV7 @ SV38 @ SV7 )
= $false )
| ( ( SV7 = SV38 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[200]) ).
thf(226,plain,
! [SV66: $i,SV39: $i,SV8: $i] :
( ( ( ~ ( between @ SV8 @ SV39 @ SV66 ) )
= $true )
| ( ( ! [SY290: $i,SY291: $i] :
( ~ ( between @ SY290 @ SY291 @ SV66 )
| ( between @ SV39 @ ( inner_pasch @ SV8 @ SV39 @ SV66 @ SY291 @ SY290 ) @ SY290 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[201]) ).
thf(227,plain,
! [SV67: $i,SV40: $i,SV9: $i] :
( ( ( ~ ( between @ SV9 @ SV40 @ SV67 ) )
= $true )
| ( ( ! [SY292: $i,SY293: $i] :
( ~ ( between @ SY292 @ SY293 @ SV67 )
| ( between @ SY293 @ ( inner_pasch @ SV9 @ SV40 @ SV67 @ SY293 @ SY292 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[202]) ).
thf(228,plain,
! [SV68: $i,SV41: $i,SV10: $i] :
( ( ( ~ ( equidistant @ SV10 @ SV41 @ SV10 @ SV68 ) )
= $true )
| ( ( ! [SY294: $i] :
( ~ ( equidistant @ SY294 @ SV41 @ SY294 @ SV68 )
| ! [SY295: $i] :
( ~ ( equidistant @ SY295 @ SV41 @ SY295 @ SV68 )
| ( between @ SV10 @ SY294 @ SY295 )
| ( between @ SY294 @ SY295 @ SV10 )
| ( SV41 = SV68 )
| ( between @ SY295 @ SV10 @ SY294 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[203]) ).
thf(229,plain,
! [SV69: $i,SV42: $i,SV11: $i] :
( ( ( ~ ( between @ SV11 @ SV42 @ SV69 ) )
= $true )
| ( ( ! [SY296: $i,SY297: $i] :
( ~ ( between @ SY296 @ SV42 @ SY297 )
| ( SV11 = SV42 )
| ( between @ SV11 @ SY296 @ ( euclid1 @ SV11 @ SY296 @ SV42 @ SY297 @ SV69 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[204]) ).
thf(230,plain,
! [SV70: $i,SV43: $i,SV12: $i] :
( ( ( ~ ( between @ SV12 @ SV43 @ SV70 ) )
= $true )
| ( ( ! [SY298: $i,SY299: $i] :
( ~ ( between @ SY298 @ SV43 @ SY299 )
| ( SV12 = SV43 )
| ( between @ SV12 @ SY299 @ ( euclid2 @ SV12 @ SY298 @ SV43 @ SY299 @ SV70 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(231,plain,
! [SV71: $i,SV44: $i,SV13: $i] :
( ( ( ~ ( between @ SV13 @ SV44 @ SV71 ) )
= $true )
| ( ( ! [SY300: $i,SY301: $i] :
( ~ ( between @ SY300 @ SV44 @ SY301 )
| ( SV13 = SV44 )
| ( between @ ( euclid1 @ SV13 @ SY300 @ SV44 @ SY301 @ SV71 ) @ SV71 @ ( euclid2 @ SV13 @ SY300 @ SV44 @ SY301 @ SV71 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(232,plain,
! [SV89: $i,SV72: $i,SV45: $i,SV14: $i] :
( ( ~ ( equidistant @ SV14 @ SV45 @ SV14 @ SV72 )
| ! [SY326: $i] :
( ~ ( equidistant @ SV14 @ SV89 @ SV14 @ SY326 )
| ~ ( between @ SV14 @ SV45 @ SV89 )
| ! [SY327: $i] :
( ~ ( between @ SV45 @ SY327 @ SV89 )
| ( between @ SV72 @ ( continuous @ SV14 @ SV45 @ SV72 @ SY327 @ SV89 @ SY326 ) @ SY326 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(233,plain,
! [SV90: $i,SV73: $i,SV46: $i,SV15: $i] :
( ( ~ ( equidistant @ SV15 @ SV46 @ SV15 @ SV73 )
| ! [SY328: $i] :
( ~ ( equidistant @ SV15 @ SV90 @ SV15 @ SY328 )
| ~ ( between @ SV15 @ SV46 @ SV90 )
| ! [SY329: $i] :
( ~ ( between @ SV46 @ SY329 @ SV90 )
| ( equidistant @ SV15 @ SY329 @ SV15 @ ( continuous @ SV15 @ SV46 @ SV73 @ SY329 @ SV90 @ SY328 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(234,plain,
! [SV91: $i,SV74: $i,SV49: $i,SV18: $i] :
( ( ~ ( equidistant @ SV18 @ SV49 @ SV74 @ SV91 )
| ( equidistant @ SV74 @ SV91 @ SV18 @ SV49 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[209]) ).
thf(235,plain,
! [SV92: $i,SV75: $i,SV50: $i,SV19: $i] :
( ( ~ ( equidistant @ SV19 @ SV50 @ SV75 @ SV92 )
| ( equidistant @ SV50 @ SV19 @ SV75 @ SV92 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[210]) ).
thf(236,plain,
! [SV93: $i,SV76: $i,SV51: $i,SV20: $i] :
( ( ~ ( equidistant @ SV20 @ SV51 @ SV76 @ SV93 )
| ( equidistant @ SV20 @ SV51 @ SV93 @ SV76 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[211]) ).
thf(237,plain,
! [SV94: $i,SV77: $i,SV52: $i,SV21: $i] :
( ( ~ ( equidistant @ SV21 @ SV52 @ SV77 @ SV94 )
| ( equidistant @ SV52 @ SV21 @ SV94 @ SV77 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[212]) ).
thf(238,plain,
! [SV95: $i,SV78: $i,SV53: $i,SV22: $i] :
( ( ~ ( equidistant @ SV22 @ SV53 @ SV78 @ SV95 )
| ( equidistant @ SV78 @ SV95 @ SV53 @ SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[213]) ).
thf(239,plain,
! [SV96: $i,SV79: $i,SV54: $i,SV23: $i] :
( ( ~ ( equidistant @ SV23 @ SV54 @ SV79 @ SV96 )
| ( equidistant @ SV96 @ SV79 @ SV23 @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[214]) ).
thf(240,plain,
! [SV97: $i,SV80: $i,SV55: $i,SV24: $i] :
( ( ~ ( equidistant @ SV24 @ SV55 @ SV80 @ SV97 )
| ( equidistant @ SV97 @ SV80 @ SV55 @ SV24 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[215]) ).
thf(241,plain,
! [SV98: $i,SV81: $i,SV56: $i,SV25: $i] :
( ( ~ ( equidistant @ SV25 @ SV56 @ SV81 @ SV98 )
| ! [SY330: $i,SY331: $i] :
( ~ ( equidistant @ SV81 @ SV98 @ SY330 @ SY331 )
| ( equidistant @ SV25 @ SV56 @ SY330 @ SY331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[216]) ).
thf(242,plain,
! [SV83: $i,SV58: $i,SV27: $i] :
( ( ( ! [SY318: $i,SY319: $i] :
( SV27
!= ( extension @ SV58 @ SV83 @ SY318 @ SY319 ) ) )
= $true )
| ( ( between @ SV58 @ SV83 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(243,plain,
! [SV61: $i,SV30: $i] :
( ( ( SV30 = SV61 )
= $false )
| ( ( SV61
= ( reflection @ SV30 @ SV61 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(244,plain,
! [SV84: $i,SV62: $i,SV33: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV33 @ SV62 @ SV84 ) )
= $true )
| ( ( ! [SY320: $i,SY321: $i] :
( ~ ( equidistant @ SV2 @ SV33 @ SY320 @ SY321 )
| ( equidistant @ SV62 @ SV84 @ SY320 @ SY321 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[220]) ).
thf(245,plain,
! [SV85: $i,SV34: $i,SV3: $i] :
( ( ( equidistant @ SV3 @ SV34 @ SV85 @ SV85 )
= $false )
| ( ( SV3 = SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(246,plain,
! [SV99: $i,SV88: $i,SV65: $i,SV37: $i,SV6: $i] :
( ( ! [SY332: $i] :
( ~ ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
| ~ ( equidistant @ SV37 @ SV99 @ SV88 @ SY332 )
| ! [SY333: $i,SY334: $i] :
( ~ ( equidistant @ SV6 @ SY333 @ SV65 @ SY334 )
| ~ ( equidistant @ SV37 @ SY333 @ SV88 @ SY334 )
| ~ ( between @ SV6 @ SV37 @ SV99 )
| ~ ( between @ SV65 @ SV88 @ SY332 )
| ( SV6 = SV37 )
| ( equidistant @ SV99 @ SY333 @ SY332 @ SY334 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[224]) ).
thf(247,plain,
! [SV66: $i,SV39: $i,SV8: $i] :
( ( ( between @ SV8 @ SV39 @ SV66 )
= $false )
| ( ( ! [SY290: $i,SY291: $i] :
( ~ ( between @ SY290 @ SY291 @ SV66 )
| ( between @ SV39 @ ( inner_pasch @ SV8 @ SV39 @ SV66 @ SY291 @ SY290 ) @ SY290 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[226]) ).
thf(248,plain,
! [SV67: $i,SV40: $i,SV9: $i] :
( ( ( between @ SV9 @ SV40 @ SV67 )
= $false )
| ( ( ! [SY292: $i,SY293: $i] :
( ~ ( between @ SY292 @ SY293 @ SV67 )
| ( between @ SY293 @ ( inner_pasch @ SV9 @ SV40 @ SV67 @ SY293 @ SY292 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(249,plain,
! [SV68: $i,SV41: $i,SV10: $i] :
( ( ( equidistant @ SV10 @ SV41 @ SV10 @ SV68 )
= $false )
| ( ( ! [SY294: $i] :
( ~ ( equidistant @ SY294 @ SV41 @ SY294 @ SV68 )
| ! [SY295: $i] :
( ~ ( equidistant @ SY295 @ SV41 @ SY295 @ SV68 )
| ( between @ SV10 @ SY294 @ SY295 )
| ( between @ SY294 @ SY295 @ SV10 )
| ( SV41 = SV68 )
| ( between @ SY295 @ SV10 @ SY294 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[228]) ).
thf(250,plain,
! [SV69: $i,SV42: $i,SV11: $i] :
( ( ( between @ SV11 @ SV42 @ SV69 )
= $false )
| ( ( ! [SY296: $i,SY297: $i] :
( ~ ( between @ SY296 @ SV42 @ SY297 )
| ( SV11 = SV42 )
| ( between @ SV11 @ SY296 @ ( euclid1 @ SV11 @ SY296 @ SV42 @ SY297 @ SV69 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(251,plain,
! [SV70: $i,SV43: $i,SV12: $i] :
( ( ( between @ SV12 @ SV43 @ SV70 )
= $false )
| ( ( ! [SY298: $i,SY299: $i] :
( ~ ( between @ SY298 @ SV43 @ SY299 )
| ( SV12 = SV43 )
| ( between @ SV12 @ SY299 @ ( euclid2 @ SV12 @ SY298 @ SV43 @ SY299 @ SV70 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[230]) ).
thf(252,plain,
! [SV71: $i,SV44: $i,SV13: $i] :
( ( ( between @ SV13 @ SV44 @ SV71 )
= $false )
| ( ( ! [SY300: $i,SY301: $i] :
( ~ ( between @ SY300 @ SV44 @ SY301 )
| ( SV13 = SV44 )
| ( between @ ( euclid1 @ SV13 @ SY300 @ SV44 @ SY301 @ SV71 ) @ SV71 @ ( euclid2 @ SV13 @ SY300 @ SV44 @ SY301 @ SV71 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[231]) ).
thf(253,plain,
! [SV89: $i,SV72: $i,SV45: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV45 @ SV14 @ SV72 ) )
= $true )
| ( ( ! [SY326: $i] :
( ~ ( equidistant @ SV14 @ SV89 @ SV14 @ SY326 )
| ~ ( between @ SV14 @ SV45 @ SV89 )
| ! [SY327: $i] :
( ~ ( between @ SV45 @ SY327 @ SV89 )
| ( between @ SV72 @ ( continuous @ SV14 @ SV45 @ SV72 @ SY327 @ SV89 @ SY326 ) @ SY326 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[232]) ).
thf(254,plain,
! [SV90: $i,SV73: $i,SV46: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV46 @ SV15 @ SV73 ) )
= $true )
| ( ( ! [SY328: $i] :
( ~ ( equidistant @ SV15 @ SV90 @ SV15 @ SY328 )
| ~ ( between @ SV15 @ SV46 @ SV90 )
| ! [SY329: $i] :
( ~ ( between @ SV46 @ SY329 @ SV90 )
| ( equidistant @ SV15 @ SY329 @ SV15 @ ( continuous @ SV15 @ SV46 @ SV73 @ SY329 @ SV90 @ SY328 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[233]) ).
thf(255,plain,
! [SV91: $i,SV74: $i,SV49: $i,SV18: $i] :
( ( ( ~ ( equidistant @ SV18 @ SV49 @ SV74 @ SV91 ) )
= $true )
| ( ( equidistant @ SV74 @ SV91 @ SV18 @ SV49 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[234]) ).
thf(256,plain,
! [SV92: $i,SV75: $i,SV50: $i,SV19: $i] :
( ( ( ~ ( equidistant @ SV19 @ SV50 @ SV75 @ SV92 ) )
= $true )
| ( ( equidistant @ SV50 @ SV19 @ SV75 @ SV92 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[235]) ).
thf(257,plain,
! [SV93: $i,SV76: $i,SV51: $i,SV20: $i] :
( ( ( ~ ( equidistant @ SV20 @ SV51 @ SV76 @ SV93 ) )
= $true )
| ( ( equidistant @ SV20 @ SV51 @ SV93 @ SV76 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[236]) ).
thf(258,plain,
! [SV94: $i,SV77: $i,SV52: $i,SV21: $i] :
( ( ( ~ ( equidistant @ SV21 @ SV52 @ SV77 @ SV94 ) )
= $true )
| ( ( equidistant @ SV52 @ SV21 @ SV94 @ SV77 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[237]) ).
thf(259,plain,
! [SV95: $i,SV78: $i,SV53: $i,SV22: $i] :
( ( ( ~ ( equidistant @ SV22 @ SV53 @ SV78 @ SV95 ) )
= $true )
| ( ( equidistant @ SV78 @ SV95 @ SV53 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[238]) ).
thf(260,plain,
! [SV96: $i,SV79: $i,SV54: $i,SV23: $i] :
( ( ( ~ ( equidistant @ SV23 @ SV54 @ SV79 @ SV96 ) )
= $true )
| ( ( equidistant @ SV96 @ SV79 @ SV23 @ SV54 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[239]) ).
thf(261,plain,
! [SV97: $i,SV80: $i,SV55: $i,SV24: $i] :
( ( ( ~ ( equidistant @ SV24 @ SV55 @ SV80 @ SV97 ) )
= $true )
| ( ( equidistant @ SV97 @ SV80 @ SV55 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[240]) ).
thf(262,plain,
! [SV98: $i,SV81: $i,SV56: $i,SV25: $i] :
( ( ( ~ ( equidistant @ SV25 @ SV56 @ SV81 @ SV98 ) )
= $true )
| ( ( ! [SY330: $i,SY331: $i] :
( ~ ( equidistant @ SV81 @ SV98 @ SY330 @ SY331 )
| ( equidistant @ SV25 @ SV56 @ SY330 @ SY331 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[241]) ).
thf(263,plain,
! [SV100: $i,SV83: $i,SV58: $i,SV27: $i] :
( ( ( ! [SY335: $i] :
( SV27
!= ( extension @ SV58 @ SV83 @ SV100 @ SY335 ) ) )
= $true )
| ( ( between @ SV58 @ SV83 @ SV27 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[242]) ).
thf(264,plain,
! [SV84: $i,SV62: $i,SV33: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV33 @ SV62 @ SV84 )
= $false )
| ( ( ! [SY320: $i,SY321: $i] :
( ~ ( equidistant @ SV2 @ SV33 @ SY320 @ SY321 )
| ( equidistant @ SV62 @ SV84 @ SY320 @ SY321 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[244]) ).
thf(265,plain,
! [SV101: $i,SV99: $i,SV88: $i,SV65: $i,SV37: $i,SV6: $i] :
( ( ~ ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
| ~ ( equidistant @ SV37 @ SV99 @ SV88 @ SV101 )
| ! [SY336: $i,SY337: $i] :
( ~ ( equidistant @ SV6 @ SY336 @ SV65 @ SY337 )
| ~ ( equidistant @ SV37 @ SY336 @ SV88 @ SY337 )
| ~ ( between @ SV6 @ SV37 @ SV99 )
| ~ ( between @ SV65 @ SV88 @ SV101 )
| ( SV6 = SV37 )
| ( equidistant @ SV99 @ SY336 @ SV101 @ SY337 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[246]) ).
thf(266,plain,
! [SV8: $i,SV39: $i,SV66: $i,SV102: $i] :
( ( ( ! [SY338: $i] :
( ~ ( between @ SV102 @ SY338 @ SV66 )
| ( between @ SV39 @ ( inner_pasch @ SV8 @ SV39 @ SV66 @ SY338 @ SV102 ) @ SV102 ) ) )
= $true )
| ( ( between @ SV8 @ SV39 @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[247]) ).
thf(267,plain,
! [SV40: $i,SV9: $i,SV67: $i,SV103: $i] :
( ( ( ! [SY339: $i] :
( ~ ( between @ SV103 @ SY339 @ SV67 )
| ( between @ SY339 @ ( inner_pasch @ SV9 @ SV40 @ SV67 @ SY339 @ SV103 ) @ SV9 ) ) )
= $true )
| ( ( between @ SV9 @ SV40 @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[248]) ).
thf(268,plain,
! [SV10: $i,SV68: $i,SV41: $i,SV104: $i] :
( ( ( ~ ( equidistant @ SV104 @ SV41 @ SV104 @ SV68 )
| ! [SY340: $i] :
( ~ ( equidistant @ SY340 @ SV41 @ SY340 @ SV68 )
| ( between @ SV10 @ SV104 @ SY340 )
| ( between @ SV104 @ SY340 @ SV10 )
| ( SV41 = SV68 )
| ( between @ SY340 @ SV10 @ SV104 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV41 @ SV10 @ SV68 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[249]) ).
thf(269,plain,
! [SV69: $i,SV11: $i,SV42: $i,SV105: $i] :
( ( ( ! [SY341: $i] :
( ~ ( between @ SV105 @ SV42 @ SY341 )
| ( SV11 = SV42 )
| ( between @ SV11 @ SV105 @ ( euclid1 @ SV11 @ SV105 @ SV42 @ SY341 @ SV69 ) ) ) )
= $true )
| ( ( between @ SV11 @ SV42 @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[250]) ).
thf(270,plain,
! [SV70: $i,SV12: $i,SV43: $i,SV106: $i] :
( ( ( ! [SY342: $i] :
( ~ ( between @ SV106 @ SV43 @ SY342 )
| ( SV12 = SV43 )
| ( between @ SV12 @ SY342 @ ( euclid2 @ SV12 @ SV106 @ SV43 @ SY342 @ SV70 ) ) ) )
= $true )
| ( ( between @ SV12 @ SV43 @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[251]) ).
thf(271,plain,
! [SV71: $i,SV13: $i,SV44: $i,SV107: $i] :
( ( ( ! [SY343: $i] :
( ~ ( between @ SV107 @ SV44 @ SY343 )
| ( SV13 = SV44 )
| ( between @ ( euclid1 @ SV13 @ SV107 @ SV44 @ SY343 @ SV71 ) @ SV71 @ ( euclid2 @ SV13 @ SV107 @ SV44 @ SY343 @ SV71 ) ) ) )
= $true )
| ( ( between @ SV13 @ SV44 @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[252]) ).
thf(272,plain,
! [SV89: $i,SV72: $i,SV45: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV45 @ SV14 @ SV72 )
= $false )
| ( ( ! [SY326: $i] :
( ~ ( equidistant @ SV14 @ SV89 @ SV14 @ SY326 )
| ~ ( between @ SV14 @ SV45 @ SV89 )
| ! [SY327: $i] :
( ~ ( between @ SV45 @ SY327 @ SV89 )
| ( between @ SV72 @ ( continuous @ SV14 @ SV45 @ SV72 @ SY327 @ SV89 @ SY326 ) @ SY326 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[253]) ).
thf(273,plain,
! [SV90: $i,SV73: $i,SV46: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV46 @ SV15 @ SV73 )
= $false )
| ( ( ! [SY328: $i] :
( ~ ( equidistant @ SV15 @ SV90 @ SV15 @ SY328 )
| ~ ( between @ SV15 @ SV46 @ SV90 )
| ! [SY329: $i] :
( ~ ( between @ SV46 @ SY329 @ SV90 )
| ( equidistant @ SV15 @ SY329 @ SV15 @ ( continuous @ SV15 @ SV46 @ SV73 @ SY329 @ SV90 @ SY328 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[254]) ).
thf(274,plain,
! [SV91: $i,SV74: $i,SV49: $i,SV18: $i] :
( ( ( equidistant @ SV18 @ SV49 @ SV74 @ SV91 )
= $false )
| ( ( equidistant @ SV74 @ SV91 @ SV18 @ SV49 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[255]) ).
thf(275,plain,
! [SV92: $i,SV75: $i,SV50: $i,SV19: $i] :
( ( ( equidistant @ SV19 @ SV50 @ SV75 @ SV92 )
= $false )
| ( ( equidistant @ SV50 @ SV19 @ SV75 @ SV92 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[256]) ).
thf(276,plain,
! [SV93: $i,SV76: $i,SV51: $i,SV20: $i] :
( ( ( equidistant @ SV20 @ SV51 @ SV76 @ SV93 )
= $false )
| ( ( equidistant @ SV20 @ SV51 @ SV93 @ SV76 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[257]) ).
thf(277,plain,
! [SV94: $i,SV77: $i,SV52: $i,SV21: $i] :
( ( ( equidistant @ SV21 @ SV52 @ SV77 @ SV94 )
= $false )
| ( ( equidistant @ SV52 @ SV21 @ SV94 @ SV77 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[258]) ).
thf(278,plain,
! [SV95: $i,SV78: $i,SV53: $i,SV22: $i] :
( ( ( equidistant @ SV22 @ SV53 @ SV78 @ SV95 )
= $false )
| ( ( equidistant @ SV78 @ SV95 @ SV53 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[259]) ).
thf(279,plain,
! [SV96: $i,SV79: $i,SV54: $i,SV23: $i] :
( ( ( equidistant @ SV23 @ SV54 @ SV79 @ SV96 )
= $false )
| ( ( equidistant @ SV96 @ SV79 @ SV23 @ SV54 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[260]) ).
thf(280,plain,
! [SV97: $i,SV80: $i,SV55: $i,SV24: $i] :
( ( ( equidistant @ SV24 @ SV55 @ SV80 @ SV97 )
= $false )
| ( ( equidistant @ SV97 @ SV80 @ SV55 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[261]) ).
thf(281,plain,
! [SV98: $i,SV81: $i,SV56: $i,SV25: $i] :
( ( ( equidistant @ SV25 @ SV56 @ SV81 @ SV98 )
= $false )
| ( ( ! [SY330: $i,SY331: $i] :
( ~ ( equidistant @ SV81 @ SV98 @ SY330 @ SY331 )
| ( equidistant @ SV25 @ SV56 @ SY330 @ SY331 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[262]) ).
thf(282,plain,
! [SV108: $i,SV100: $i,SV83: $i,SV58: $i,SV27: $i] :
( ( ( SV27
!= ( extension @ SV58 @ SV83 @ SV100 @ SV108 ) )
= $true )
| ( ( between @ SV58 @ SV83 @ SV27 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[263]) ).
thf(283,plain,
! [SV84: $i,SV62: $i,SV109: $i,SV33: $i,SV2: $i] :
( ( ( ! [SY344: $i] :
( ~ ( equidistant @ SV2 @ SV33 @ SV109 @ SY344 )
| ( equidistant @ SV62 @ SV84 @ SV109 @ SY344 ) ) )
= $true )
| ( ( equidistant @ SV2 @ SV33 @ SV62 @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[264]) ).
thf(284,plain,
! [SV101: $i,SV99: $i,SV88: $i,SV65: $i,SV37: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 ) )
= $true )
| ( ( ~ ( equidistant @ SV37 @ SV99 @ SV88 @ SV101 )
| ! [SY336: $i,SY337: $i] :
( ~ ( equidistant @ SV6 @ SY336 @ SV65 @ SY337 )
| ~ ( equidistant @ SV37 @ SY336 @ SV88 @ SY337 )
| ~ ( between @ SV6 @ SV37 @ SV99 )
| ~ ( between @ SV65 @ SV88 @ SV101 )
| ( SV6 = SV37 )
| ( equidistant @ SV99 @ SY336 @ SV101 @ SY337 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[265]) ).
thf(285,plain,
! [SV8: $i,SV39: $i,SV66: $i,SV110: $i,SV102: $i] :
( ( ( ~ ( between @ SV102 @ SV110 @ SV66 )
| ( between @ SV39 @ ( inner_pasch @ SV8 @ SV39 @ SV66 @ SV110 @ SV102 ) @ SV102 ) )
= $true )
| ( ( between @ SV8 @ SV39 @ SV66 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[266]) ).
thf(286,plain,
! [SV40: $i,SV9: $i,SV67: $i,SV111: $i,SV103: $i] :
( ( ( ~ ( between @ SV103 @ SV111 @ SV67 )
| ( between @ SV111 @ ( inner_pasch @ SV9 @ SV40 @ SV67 @ SV111 @ SV103 ) @ SV9 ) )
= $true )
| ( ( between @ SV9 @ SV40 @ SV67 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[267]) ).
thf(287,plain,
! [SV10: $i,SV68: $i,SV41: $i,SV104: $i] :
( ( ( ~ ( equidistant @ SV104 @ SV41 @ SV104 @ SV68 ) )
= $true )
| ( ( ! [SY340: $i] :
( ~ ( equidistant @ SY340 @ SV41 @ SY340 @ SV68 )
| ( between @ SV10 @ SV104 @ SY340 )
| ( between @ SV104 @ SY340 @ SV10 )
| ( SV41 = SV68 )
| ( between @ SY340 @ SV10 @ SV104 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV41 @ SV10 @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[268]) ).
thf(288,plain,
! [SV69: $i,SV11: $i,SV112: $i,SV42: $i,SV105: $i] :
( ( ( ~ ( between @ SV105 @ SV42 @ SV112 )
| ( SV11 = SV42 )
| ( between @ SV11 @ SV105 @ ( euclid1 @ SV11 @ SV105 @ SV42 @ SV112 @ SV69 ) ) )
= $true )
| ( ( between @ SV11 @ SV42 @ SV69 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[269]) ).
thf(289,plain,
! [SV70: $i,SV12: $i,SV113: $i,SV43: $i,SV106: $i] :
( ( ( ~ ( between @ SV106 @ SV43 @ SV113 )
| ( SV12 = SV43 )
| ( between @ SV12 @ SV113 @ ( euclid2 @ SV12 @ SV106 @ SV43 @ SV113 @ SV70 ) ) )
= $true )
| ( ( between @ SV12 @ SV43 @ SV70 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[270]) ).
thf(290,plain,
! [SV71: $i,SV13: $i,SV114: $i,SV44: $i,SV107: $i] :
( ( ( ~ ( between @ SV107 @ SV44 @ SV114 )
| ( SV13 = SV44 )
| ( between @ ( euclid1 @ SV13 @ SV107 @ SV44 @ SV114 @ SV71 ) @ SV71 @ ( euclid2 @ SV13 @ SV107 @ SV44 @ SV114 @ SV71 ) ) )
= $true )
| ( ( between @ SV13 @ SV44 @ SV71 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[271]) ).
thf(291,plain,
! [SV72: $i,SV45: $i,SV115: $i,SV89: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV89 @ SV14 @ SV115 )
| ~ ( between @ SV14 @ SV45 @ SV89 )
| ! [SY345: $i] :
( ~ ( between @ SV45 @ SY345 @ SV89 )
| ( between @ SV72 @ ( continuous @ SV14 @ SV45 @ SV72 @ SY345 @ SV89 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV45 @ SV14 @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[272]) ).
thf(292,plain,
! [SV73: $i,SV46: $i,SV116: $i,SV90: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV90 @ SV15 @ SV116 )
| ~ ( between @ SV15 @ SV46 @ SV90 )
| ! [SY346: $i] :
( ~ ( between @ SV46 @ SY346 @ SV90 )
| ( equidistant @ SV15 @ SY346 @ SV15 @ ( continuous @ SV15 @ SV46 @ SV73 @ SY346 @ SV90 @ SV116 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV46 @ SV15 @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[273]) ).
thf(293,plain,
! [SV56: $i,SV25: $i,SV117: $i,SV98: $i,SV81: $i] :
( ( ( ! [SY347: $i] :
( ~ ( equidistant @ SV81 @ SV98 @ SV117 @ SY347 )
| ( equidistant @ SV25 @ SV56 @ SV117 @ SY347 ) ) )
= $true )
| ( ( equidistant @ SV25 @ SV56 @ SV81 @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[281]) ).
thf(294,plain,
! [SV108: $i,SV100: $i,SV83: $i,SV58: $i,SV27: $i] :
( ( ( SV27
= ( extension @ SV58 @ SV83 @ SV100 @ SV108 ) )
= $false )
| ( ( between @ SV58 @ SV83 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[282]) ).
thf(295,plain,
! [SV84: $i,SV62: $i,SV118: $i,SV109: $i,SV33: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV33 @ SV109 @ SV118 )
| ( equidistant @ SV62 @ SV84 @ SV109 @ SV118 ) )
= $true )
| ( ( equidistant @ SV2 @ SV33 @ SV62 @ SV84 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[283]) ).
thf(296,plain,
! [SV101: $i,SV99: $i,SV88: $i,SV65: $i,SV37: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
= $false )
| ( ( ~ ( equidistant @ SV37 @ SV99 @ SV88 @ SV101 )
| ! [SY336: $i,SY337: $i] :
( ~ ( equidistant @ SV6 @ SY336 @ SV65 @ SY337 )
| ~ ( equidistant @ SV37 @ SY336 @ SV88 @ SY337 )
| ~ ( between @ SV6 @ SV37 @ SV99 )
| ~ ( between @ SV65 @ SV88 @ SV101 )
| ( SV6 = SV37 )
| ( equidistant @ SV99 @ SY336 @ SV101 @ SY337 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[284]) ).
thf(297,plain,
! [SV8: $i,SV39: $i,SV66: $i,SV110: $i,SV102: $i] :
( ( ( ~ ( between @ SV102 @ SV110 @ SV66 ) )
= $true )
| ( ( between @ SV39 @ ( inner_pasch @ SV8 @ SV39 @ SV66 @ SV110 @ SV102 ) @ SV102 )
= $true )
| ( ( between @ SV8 @ SV39 @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[285]) ).
thf(298,plain,
! [SV40: $i,SV9: $i,SV67: $i,SV111: $i,SV103: $i] :
( ( ( ~ ( between @ SV103 @ SV111 @ SV67 ) )
= $true )
| ( ( between @ SV111 @ ( inner_pasch @ SV9 @ SV40 @ SV67 @ SV111 @ SV103 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV40 @ SV67 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[286]) ).
thf(299,plain,
! [SV10: $i,SV68: $i,SV41: $i,SV104: $i] :
( ( ( equidistant @ SV104 @ SV41 @ SV104 @ SV68 )
= $false )
| ( ( ! [SY340: $i] :
( ~ ( equidistant @ SY340 @ SV41 @ SY340 @ SV68 )
| ( between @ SV10 @ SV104 @ SY340 )
| ( between @ SV104 @ SY340 @ SV10 )
| ( SV41 = SV68 )
| ( between @ SY340 @ SV10 @ SV104 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV41 @ SV10 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[287]) ).
thf(300,plain,
! [SV69: $i,SV11: $i,SV112: $i,SV42: $i,SV105: $i] :
( ( ( ~ ( between @ SV105 @ SV42 @ SV112 ) )
= $true )
| ( ( ( SV11 = SV42 )
| ( between @ SV11 @ SV105 @ ( euclid1 @ SV11 @ SV105 @ SV42 @ SV112 @ SV69 ) ) )
= $true )
| ( ( between @ SV11 @ SV42 @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[288]) ).
thf(301,plain,
! [SV70: $i,SV12: $i,SV113: $i,SV43: $i,SV106: $i] :
( ( ( ~ ( between @ SV106 @ SV43 @ SV113 ) )
= $true )
| ( ( ( SV12 = SV43 )
| ( between @ SV12 @ SV113 @ ( euclid2 @ SV12 @ SV106 @ SV43 @ SV113 @ SV70 ) ) )
= $true )
| ( ( between @ SV12 @ SV43 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[289]) ).
thf(302,plain,
! [SV71: $i,SV13: $i,SV114: $i,SV44: $i,SV107: $i] :
( ( ( ~ ( between @ SV107 @ SV44 @ SV114 ) )
= $true )
| ( ( ( SV13 = SV44 )
| ( between @ ( euclid1 @ SV13 @ SV107 @ SV44 @ SV114 @ SV71 ) @ SV71 @ ( euclid2 @ SV13 @ SV107 @ SV44 @ SV114 @ SV71 ) ) )
= $true )
| ( ( between @ SV13 @ SV44 @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[290]) ).
thf(303,plain,
! [SV72: $i,SV45: $i,SV115: $i,SV89: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV89 @ SV14 @ SV115 ) )
= $true )
| ( ( ~ ( between @ SV14 @ SV45 @ SV89 )
| ! [SY345: $i] :
( ~ ( between @ SV45 @ SY345 @ SV89 )
| ( between @ SV72 @ ( continuous @ SV14 @ SV45 @ SV72 @ SY345 @ SV89 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV45 @ SV14 @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[291]) ).
thf(304,plain,
! [SV73: $i,SV46: $i,SV116: $i,SV90: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV90 @ SV15 @ SV116 ) )
= $true )
| ( ( ~ ( between @ SV15 @ SV46 @ SV90 )
| ! [SY346: $i] :
( ~ ( between @ SV46 @ SY346 @ SV90 )
| ( equidistant @ SV15 @ SY346 @ SV15 @ ( continuous @ SV15 @ SV46 @ SV73 @ SY346 @ SV90 @ SV116 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV46 @ SV15 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[292]) ).
thf(305,plain,
! [SV56: $i,SV25: $i,SV119: $i,SV117: $i,SV98: $i,SV81: $i] :
( ( ( ~ ( equidistant @ SV81 @ SV98 @ SV117 @ SV119 )
| ( equidistant @ SV25 @ SV56 @ SV117 @ SV119 ) )
= $true )
| ( ( equidistant @ SV25 @ SV56 @ SV81 @ SV98 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[293]) ).
thf(306,plain,
! [SV84: $i,SV62: $i,SV118: $i,SV109: $i,SV33: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV33 @ SV109 @ SV118 ) )
= $true )
| ( ( equidistant @ SV62 @ SV84 @ SV109 @ SV118 )
= $true )
| ( ( equidistant @ SV2 @ SV33 @ SV62 @ SV84 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[295]) ).
thf(307,plain,
! [SV65: $i,SV6: $i,SV101: $i,SV88: $i,SV99: $i,SV37: $i] :
( ( ( ~ ( equidistant @ SV37 @ SV99 @ SV88 @ SV101 ) )
= $true )
| ( ( ! [SY336: $i,SY337: $i] :
( ~ ( equidistant @ SV6 @ SY336 @ SV65 @ SY337 )
| ~ ( equidistant @ SV37 @ SY336 @ SV88 @ SY337 )
| ~ ( between @ SV6 @ SV37 @ SV99 )
| ~ ( between @ SV65 @ SV88 @ SV101 )
| ( SV6 = SV37 )
| ( equidistant @ SV99 @ SY336 @ SV101 @ SY337 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[296]) ).
thf(308,plain,
! [SV8: $i,SV39: $i,SV66: $i,SV110: $i,SV102: $i] :
( ( ( between @ SV102 @ SV110 @ SV66 )
= $false )
| ( ( between @ SV39 @ ( inner_pasch @ SV8 @ SV39 @ SV66 @ SV110 @ SV102 ) @ SV102 )
= $true )
| ( ( between @ SV8 @ SV39 @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[297]) ).
thf(309,plain,
! [SV40: $i,SV9: $i,SV67: $i,SV111: $i,SV103: $i] :
( ( ( between @ SV103 @ SV111 @ SV67 )
= $false )
| ( ( between @ SV111 @ ( inner_pasch @ SV9 @ SV40 @ SV67 @ SV111 @ SV103 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV40 @ SV67 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[298]) ).
thf(310,plain,
! [SV104: $i,SV10: $i,SV68: $i,SV41: $i,SV120: $i] :
( ( ( ~ ( equidistant @ SV120 @ SV41 @ SV120 @ SV68 )
| ( between @ SV10 @ SV104 @ SV120 )
| ( between @ SV104 @ SV120 @ SV10 )
| ( SV41 = SV68 )
| ( between @ SV120 @ SV10 @ SV104 ) )
= $true )
| ( ( equidistant @ SV104 @ SV41 @ SV104 @ SV68 )
= $false )
| ( ( equidistant @ SV10 @ SV41 @ SV10 @ SV68 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[299]) ).
thf(311,plain,
! [SV69: $i,SV11: $i,SV112: $i,SV42: $i,SV105: $i] :
( ( ( between @ SV105 @ SV42 @ SV112 )
= $false )
| ( ( ( SV11 = SV42 )
| ( between @ SV11 @ SV105 @ ( euclid1 @ SV11 @ SV105 @ SV42 @ SV112 @ SV69 ) ) )
= $true )
| ( ( between @ SV11 @ SV42 @ SV69 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[300]) ).
thf(312,plain,
! [SV70: $i,SV12: $i,SV113: $i,SV43: $i,SV106: $i] :
( ( ( between @ SV106 @ SV43 @ SV113 )
= $false )
| ( ( ( SV12 = SV43 )
| ( between @ SV12 @ SV113 @ ( euclid2 @ SV12 @ SV106 @ SV43 @ SV113 @ SV70 ) ) )
= $true )
| ( ( between @ SV12 @ SV43 @ SV70 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[301]) ).
thf(313,plain,
! [SV71: $i,SV13: $i,SV114: $i,SV44: $i,SV107: $i] :
( ( ( between @ SV107 @ SV44 @ SV114 )
= $false )
| ( ( ( SV13 = SV44 )
| ( between @ ( euclid1 @ SV13 @ SV107 @ SV44 @ SV114 @ SV71 ) @ SV71 @ ( euclid2 @ SV13 @ SV107 @ SV44 @ SV114 @ SV71 ) ) )
= $true )
| ( ( between @ SV13 @ SV44 @ SV71 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[302]) ).
thf(314,plain,
! [SV72: $i,SV45: $i,SV115: $i,SV89: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV89 @ SV14 @ SV115 )
= $false )
| ( ( ~ ( between @ SV14 @ SV45 @ SV89 )
| ! [SY345: $i] :
( ~ ( between @ SV45 @ SY345 @ SV89 )
| ( between @ SV72 @ ( continuous @ SV14 @ SV45 @ SV72 @ SY345 @ SV89 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV45 @ SV14 @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[303]) ).
thf(315,plain,
! [SV73: $i,SV46: $i,SV116: $i,SV90: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV90 @ SV15 @ SV116 )
= $false )
| ( ( ~ ( between @ SV15 @ SV46 @ SV90 )
| ! [SY346: $i] :
( ~ ( between @ SV46 @ SY346 @ SV90 )
| ( equidistant @ SV15 @ SY346 @ SV15 @ ( continuous @ SV15 @ SV46 @ SV73 @ SY346 @ SV90 @ SV116 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV46 @ SV15 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[304]) ).
thf(316,plain,
! [SV56: $i,SV25: $i,SV119: $i,SV117: $i,SV98: $i,SV81: $i] :
( ( ( ~ ( equidistant @ SV81 @ SV98 @ SV117 @ SV119 ) )
= $true )
| ( ( equidistant @ SV25 @ SV56 @ SV117 @ SV119 )
= $true )
| ( ( equidistant @ SV25 @ SV56 @ SV81 @ SV98 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[305]) ).
thf(317,plain,
! [SV84: $i,SV62: $i,SV118: $i,SV109: $i,SV33: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV33 @ SV109 @ SV118 )
= $false )
| ( ( equidistant @ SV62 @ SV84 @ SV109 @ SV118 )
= $true )
| ( ( equidistant @ SV2 @ SV33 @ SV62 @ SV84 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[306]) ).
thf(318,plain,
! [SV65: $i,SV6: $i,SV101: $i,SV88: $i,SV99: $i,SV37: $i] :
( ( ( equidistant @ SV37 @ SV99 @ SV88 @ SV101 )
= $false )
| ( ( ! [SY336: $i,SY337: $i] :
( ~ ( equidistant @ SV6 @ SY336 @ SV65 @ SY337 )
| ~ ( equidistant @ SV37 @ SY336 @ SV88 @ SY337 )
| ~ ( between @ SV6 @ SV37 @ SV99 )
| ~ ( between @ SV65 @ SV88 @ SV101 )
| ( SV6 = SV37 )
| ( equidistant @ SV99 @ SY336 @ SV101 @ SY337 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[307]) ).
thf(319,plain,
! [SV104: $i,SV10: $i,SV68: $i,SV41: $i,SV120: $i] :
( ( ( ~ ( equidistant @ SV120 @ SV41 @ SV120 @ SV68 ) )
= $true )
| ( ( ( between @ SV10 @ SV104 @ SV120 )
| ( between @ SV104 @ SV120 @ SV10 )
| ( SV41 = SV68 )
| ( between @ SV120 @ SV10 @ SV104 ) )
= $true )
| ( ( equidistant @ SV104 @ SV41 @ SV104 @ SV68 )
= $false )
| ( ( equidistant @ SV10 @ SV41 @ SV10 @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[310]) ).
thf(320,plain,
! [SV69: $i,SV112: $i,SV105: $i,SV42: $i,SV11: $i] :
( ( ( SV11 = SV42 )
= $true )
| ( ( between @ SV11 @ SV105 @ ( euclid1 @ SV11 @ SV105 @ SV42 @ SV112 @ SV69 ) )
= $true )
| ( ( between @ SV105 @ SV42 @ SV112 )
= $false )
| ( ( between @ SV11 @ SV42 @ SV69 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[311]) ).
thf(321,plain,
! [SV70: $i,SV106: $i,SV113: $i,SV43: $i,SV12: $i] :
( ( ( SV12 = SV43 )
= $true )
| ( ( between @ SV12 @ SV113 @ ( euclid2 @ SV12 @ SV106 @ SV43 @ SV113 @ SV70 ) )
= $true )
| ( ( between @ SV106 @ SV43 @ SV113 )
= $false )
| ( ( between @ SV12 @ SV43 @ SV70 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[312]) ).
thf(322,plain,
! [SV71: $i,SV114: $i,SV107: $i,SV44: $i,SV13: $i] :
( ( ( SV13 = SV44 )
= $true )
| ( ( between @ ( euclid1 @ SV13 @ SV107 @ SV44 @ SV114 @ SV71 ) @ SV71 @ ( euclid2 @ SV13 @ SV107 @ SV44 @ SV114 @ SV71 ) )
= $true )
| ( ( between @ SV107 @ SV44 @ SV114 )
= $false )
| ( ( between @ SV13 @ SV44 @ SV71 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[313]) ).
thf(323,plain,
! [SV115: $i,SV72: $i,SV89: $i,SV45: $i,SV14: $i] :
( ( ( ~ ( between @ SV14 @ SV45 @ SV89 ) )
= $true )
| ( ( ! [SY345: $i] :
( ~ ( between @ SV45 @ SY345 @ SV89 )
| ( between @ SV72 @ ( continuous @ SV14 @ SV45 @ SV72 @ SY345 @ SV89 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV89 @ SV14 @ SV115 )
= $false )
| ( ( equidistant @ SV14 @ SV45 @ SV14 @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[314]) ).
thf(324,plain,
! [SV116: $i,SV73: $i,SV90: $i,SV46: $i,SV15: $i] :
( ( ( ~ ( between @ SV15 @ SV46 @ SV90 ) )
= $true )
| ( ( ! [SY346: $i] :
( ~ ( between @ SV46 @ SY346 @ SV90 )
| ( equidistant @ SV15 @ SY346 @ SV15 @ ( continuous @ SV15 @ SV46 @ SV73 @ SY346 @ SV90 @ SV116 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV90 @ SV15 @ SV116 )
= $false )
| ( ( equidistant @ SV15 @ SV46 @ SV15 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[315]) ).
thf(325,plain,
! [SV56: $i,SV25: $i,SV119: $i,SV117: $i,SV98: $i,SV81: $i] :
( ( ( equidistant @ SV81 @ SV98 @ SV117 @ SV119 )
= $false )
| ( ( equidistant @ SV25 @ SV56 @ SV117 @ SV119 )
= $true )
| ( ( equidistant @ SV25 @ SV56 @ SV81 @ SV98 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[316]) ).
thf(326,plain,
! [SV101: $i,SV99: $i,SV88: $i,SV37: $i,SV65: $i,SV121: $i,SV6: $i] :
( ( ( ! [SY348: $i] :
( ~ ( equidistant @ SV6 @ SV121 @ SV65 @ SY348 )
| ~ ( equidistant @ SV37 @ SV121 @ SV88 @ SY348 )
| ~ ( between @ SV6 @ SV37 @ SV99 )
| ~ ( between @ SV65 @ SV88 @ SV101 )
| ( SV6 = SV37 )
| ( equidistant @ SV99 @ SV121 @ SV101 @ SY348 ) ) )
= $true )
| ( ( equidistant @ SV37 @ SV99 @ SV88 @ SV101 )
= $false )
| ( ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[318]) ).
thf(327,plain,
! [SV104: $i,SV10: $i,SV68: $i,SV41: $i,SV120: $i] :
( ( ( equidistant @ SV120 @ SV41 @ SV120 @ SV68 )
= $false )
| ( ( ( between @ SV10 @ SV104 @ SV120 )
| ( between @ SV104 @ SV120 @ SV10 )
| ( SV41 = SV68 )
| ( between @ SV120 @ SV10 @ SV104 ) )
= $true )
| ( ( equidistant @ SV104 @ SV41 @ SV104 @ SV68 )
= $false )
| ( ( equidistant @ SV10 @ SV41 @ SV10 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[319]) ).
thf(328,plain,
! [SV115: $i,SV72: $i,SV89: $i,SV45: $i,SV14: $i] :
( ( ( between @ SV14 @ SV45 @ SV89 )
= $false )
| ( ( ! [SY345: $i] :
( ~ ( between @ SV45 @ SY345 @ SV89 )
| ( between @ SV72 @ ( continuous @ SV14 @ SV45 @ SV72 @ SY345 @ SV89 @ SV115 ) @ SV115 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV89 @ SV14 @ SV115 )
= $false )
| ( ( equidistant @ SV14 @ SV45 @ SV14 @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[323]) ).
thf(329,plain,
! [SV116: $i,SV73: $i,SV90: $i,SV46: $i,SV15: $i] :
( ( ( between @ SV15 @ SV46 @ SV90 )
= $false )
| ( ( ! [SY346: $i] :
( ~ ( between @ SV46 @ SY346 @ SV90 )
| ( equidistant @ SV15 @ SY346 @ SV15 @ ( continuous @ SV15 @ SV46 @ SV73 @ SY346 @ SV90 @ SV116 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV90 @ SV15 @ SV116 )
= $false )
| ( ( equidistant @ SV15 @ SV46 @ SV15 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[324]) ).
thf(330,plain,
! [SV101: $i,SV99: $i,SV88: $i,SV37: $i,SV122: $i,SV65: $i,SV121: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV121 @ SV65 @ SV122 )
| ~ ( equidistant @ SV37 @ SV121 @ SV88 @ SV122 )
| ~ ( between @ SV6 @ SV37 @ SV99 )
| ~ ( between @ SV65 @ SV88 @ SV101 )
| ( SV6 = SV37 )
| ( equidistant @ SV99 @ SV121 @ SV101 @ SV122 ) )
= $true )
| ( ( equidistant @ SV37 @ SV99 @ SV88 @ SV101 )
= $false )
| ( ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(331,plain,
! [SV68: $i,SV41: $i,SV120: $i,SV104: $i,SV10: $i] :
( ( ( between @ SV10 @ SV104 @ SV120 )
= $true )
| ( ( ( between @ SV104 @ SV120 @ SV10 )
| ( SV41 = SV68 )
| ( between @ SV120 @ SV10 @ SV104 ) )
= $true )
| ( ( equidistant @ SV120 @ SV41 @ SV120 @ SV68 )
= $false )
| ( ( equidistant @ SV104 @ SV41 @ SV104 @ SV68 )
= $false )
| ( ( equidistant @ SV10 @ SV41 @ SV10 @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[327]) ).
thf(332,plain,
! [SV115: $i,SV14: $i,SV72: $i,SV89: $i,SV123: $i,SV45: $i] :
( ( ( ~ ( between @ SV45 @ SV123 @ SV89 )
| ( between @ SV72 @ ( continuous @ SV14 @ SV45 @ SV72 @ SV123 @ SV89 @ SV115 ) @ SV115 ) )
= $true )
| ( ( between @ SV14 @ SV45 @ SV89 )
= $false )
| ( ( equidistant @ SV14 @ SV89 @ SV14 @ SV115 )
= $false )
| ( ( equidistant @ SV14 @ SV45 @ SV14 @ SV72 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(333,plain,
! [SV116: $i,SV73: $i,SV15: $i,SV90: $i,SV124: $i,SV46: $i] :
( ( ( ~ ( between @ SV46 @ SV124 @ SV90 )
| ( equidistant @ SV15 @ SV124 @ SV15 @ ( continuous @ SV15 @ SV46 @ SV73 @ SV124 @ SV90 @ SV116 ) ) )
= $true )
| ( ( between @ SV15 @ SV46 @ SV90 )
= $false )
| ( ( equidistant @ SV15 @ SV90 @ SV15 @ SV116 )
= $false )
| ( ( equidistant @ SV15 @ SV46 @ SV15 @ SV73 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[329]) ).
thf(334,plain,
! [SV101: $i,SV99: $i,SV88: $i,SV37: $i,SV122: $i,SV65: $i,SV121: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV121 @ SV65 @ SV122 ) )
= $true )
| ( ( ~ ( equidistant @ SV37 @ SV121 @ SV88 @ SV122 )
| ~ ( between @ SV6 @ SV37 @ SV99 )
| ~ ( between @ SV65 @ SV88 @ SV101 )
| ( SV6 = SV37 )
| ( equidistant @ SV99 @ SV121 @ SV101 @ SV122 ) )
= $true )
| ( ( equidistant @ SV37 @ SV99 @ SV88 @ SV101 )
= $false )
| ( ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[330]) ).
thf(335,plain,
! [SV68: $i,SV41: $i,SV10: $i,SV120: $i,SV104: $i] :
( ( ( between @ SV104 @ SV120 @ SV10 )
= $true )
| ( ( ( SV41 = SV68 )
| ( between @ SV120 @ SV10 @ SV104 ) )
= $true )
| ( ( between @ SV10 @ SV104 @ SV120 )
= $true )
| ( ( equidistant @ SV120 @ SV41 @ SV120 @ SV68 )
= $false )
| ( ( equidistant @ SV104 @ SV41 @ SV104 @ SV68 )
= $false )
| ( ( equidistant @ SV10 @ SV41 @ SV10 @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[331]) ).
thf(336,plain,
! [SV115: $i,SV14: $i,SV72: $i,SV89: $i,SV123: $i,SV45: $i] :
( ( ( ~ ( between @ SV45 @ SV123 @ SV89 ) )
= $true )
| ( ( between @ SV72 @ ( continuous @ SV14 @ SV45 @ SV72 @ SV123 @ SV89 @ SV115 ) @ SV115 )
= $true )
| ( ( between @ SV14 @ SV45 @ SV89 )
= $false )
| ( ( equidistant @ SV14 @ SV89 @ SV14 @ SV115 )
= $false )
| ( ( equidistant @ SV14 @ SV45 @ SV14 @ SV72 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[332]) ).
thf(337,plain,
! [SV116: $i,SV73: $i,SV15: $i,SV90: $i,SV124: $i,SV46: $i] :
( ( ( ~ ( between @ SV46 @ SV124 @ SV90 ) )
= $true )
| ( ( equidistant @ SV15 @ SV124 @ SV15 @ ( continuous @ SV15 @ SV46 @ SV73 @ SV124 @ SV90 @ SV116 ) )
= $true )
| ( ( between @ SV15 @ SV46 @ SV90 )
= $false )
| ( ( equidistant @ SV15 @ SV90 @ SV15 @ SV116 )
= $false )
| ( ( equidistant @ SV15 @ SV46 @ SV15 @ SV73 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[333]) ).
thf(338,plain,
! [SV101: $i,SV99: $i,SV88: $i,SV37: $i,SV122: $i,SV65: $i,SV121: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV121 @ SV65 @ SV122 )
= $false )
| ( ( ~ ( equidistant @ SV37 @ SV121 @ SV88 @ SV122 )
| ~ ( between @ SV6 @ SV37 @ SV99 )
| ~ ( between @ SV65 @ SV88 @ SV101 )
| ( SV6 = SV37 )
| ( equidistant @ SV99 @ SV121 @ SV101 @ SV122 ) )
= $true )
| ( ( equidistant @ SV37 @ SV99 @ SV88 @ SV101 )
= $false )
| ( ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[334]) ).
thf(339,plain,
! [SV104: $i,SV10: $i,SV120: $i,SV68: $i,SV41: $i] :
( ( ( SV41 = SV68 )
= $true )
| ( ( between @ SV120 @ SV10 @ SV104 )
= $true )
| ( ( between @ SV104 @ SV120 @ SV10 )
= $true )
| ( ( between @ SV10 @ SV104 @ SV120 )
= $true )
| ( ( equidistant @ SV120 @ SV41 @ SV120 @ SV68 )
= $false )
| ( ( equidistant @ SV104 @ SV41 @ SV104 @ SV68 )
= $false )
| ( ( equidistant @ SV10 @ SV41 @ SV10 @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[335]) ).
thf(340,plain,
! [SV115: $i,SV14: $i,SV72: $i,SV89: $i,SV123: $i,SV45: $i] :
( ( ( between @ SV45 @ SV123 @ SV89 )
= $false )
| ( ( between @ SV72 @ ( continuous @ SV14 @ SV45 @ SV72 @ SV123 @ SV89 @ SV115 ) @ SV115 )
= $true )
| ( ( between @ SV14 @ SV45 @ SV89 )
= $false )
| ( ( equidistant @ SV14 @ SV89 @ SV14 @ SV115 )
= $false )
| ( ( equidistant @ SV14 @ SV45 @ SV14 @ SV72 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[336]) ).
thf(341,plain,
! [SV116: $i,SV73: $i,SV15: $i,SV90: $i,SV124: $i,SV46: $i] :
( ( ( between @ SV46 @ SV124 @ SV90 )
= $false )
| ( ( equidistant @ SV15 @ SV124 @ SV15 @ ( continuous @ SV15 @ SV46 @ SV73 @ SV124 @ SV90 @ SV116 ) )
= $true )
| ( ( between @ SV15 @ SV46 @ SV90 )
= $false )
| ( ( equidistant @ SV15 @ SV90 @ SV15 @ SV116 )
= $false )
| ( ( equidistant @ SV15 @ SV46 @ SV15 @ SV73 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[337]) ).
thf(342,plain,
! [SV101: $i,SV65: $i,SV99: $i,SV6: $i,SV122: $i,SV88: $i,SV121: $i,SV37: $i] :
( ( ( ~ ( equidistant @ SV37 @ SV121 @ SV88 @ SV122 ) )
= $true )
| ( ( ~ ( between @ SV6 @ SV37 @ SV99 )
| ~ ( between @ SV65 @ SV88 @ SV101 )
| ( SV6 = SV37 )
| ( equidistant @ SV99 @ SV121 @ SV101 @ SV122 ) )
= $true )
| ( ( equidistant @ SV6 @ SV121 @ SV65 @ SV122 )
= $false )
| ( ( equidistant @ SV37 @ SV99 @ SV88 @ SV101 )
= $false )
| ( ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[338]) ).
thf(343,plain,
! [SV101: $i,SV65: $i,SV99: $i,SV6: $i,SV122: $i,SV88: $i,SV121: $i,SV37: $i] :
( ( ( equidistant @ SV37 @ SV121 @ SV88 @ SV122 )
= $false )
| ( ( ~ ( between @ SV6 @ SV37 @ SV99 )
| ~ ( between @ SV65 @ SV88 @ SV101 )
| ( SV6 = SV37 )
| ( equidistant @ SV99 @ SV121 @ SV101 @ SV122 ) )
= $true )
| ( ( equidistant @ SV6 @ SV121 @ SV65 @ SV122 )
= $false )
| ( ( equidistant @ SV37 @ SV99 @ SV88 @ SV101 )
= $false )
| ( ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[342]) ).
thf(344,plain,
! [SV122: $i,SV121: $i,SV101: $i,SV88: $i,SV65: $i,SV99: $i,SV37: $i,SV6: $i] :
( ( ( ~ ( between @ SV6 @ SV37 @ SV99 ) )
= $true )
| ( ( ~ ( between @ SV65 @ SV88 @ SV101 )
| ( SV6 = SV37 )
| ( equidistant @ SV99 @ SV121 @ SV101 @ SV122 ) )
= $true )
| ( ( equidistant @ SV37 @ SV121 @ SV88 @ SV122 )
= $false )
| ( ( equidistant @ SV6 @ SV121 @ SV65 @ SV122 )
= $false )
| ( ( equidistant @ SV37 @ SV99 @ SV88 @ SV101 )
= $false )
| ( ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[343]) ).
thf(345,plain,
! [SV122: $i,SV121: $i,SV101: $i,SV88: $i,SV65: $i,SV99: $i,SV37: $i,SV6: $i] :
( ( ( between @ SV6 @ SV37 @ SV99 )
= $false )
| ( ( ~ ( between @ SV65 @ SV88 @ SV101 )
| ( SV6 = SV37 )
| ( equidistant @ SV99 @ SV121 @ SV101 @ SV122 ) )
= $true )
| ( ( equidistant @ SV37 @ SV121 @ SV88 @ SV122 )
= $false )
| ( ( equidistant @ SV6 @ SV121 @ SV65 @ SV122 )
= $false )
| ( ( equidistant @ SV37 @ SV99 @ SV88 @ SV101 )
= $false )
| ( ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[344]) ).
thf(346,plain,
! [SV122: $i,SV121: $i,SV99: $i,SV37: $i,SV6: $i,SV101: $i,SV88: $i,SV65: $i] :
( ( ( ~ ( between @ SV65 @ SV88 @ SV101 ) )
= $true )
| ( ( ( SV6 = SV37 )
| ( equidistant @ SV99 @ SV121 @ SV101 @ SV122 ) )
= $true )
| ( ( between @ SV6 @ SV37 @ SV99 )
= $false )
| ( ( equidistant @ SV37 @ SV121 @ SV88 @ SV122 )
= $false )
| ( ( equidistant @ SV6 @ SV121 @ SV65 @ SV122 )
= $false )
| ( ( equidistant @ SV37 @ SV99 @ SV88 @ SV101 )
= $false )
| ( ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[345]) ).
thf(347,plain,
! [SV122: $i,SV121: $i,SV99: $i,SV37: $i,SV6: $i,SV101: $i,SV88: $i,SV65: $i] :
( ( ( between @ SV65 @ SV88 @ SV101 )
= $false )
| ( ( ( SV6 = SV37 )
| ( equidistant @ SV99 @ SV121 @ SV101 @ SV122 ) )
= $true )
| ( ( between @ SV6 @ SV37 @ SV99 )
= $false )
| ( ( equidistant @ SV37 @ SV121 @ SV88 @ SV122 )
= $false )
| ( ( equidistant @ SV6 @ SV121 @ SV65 @ SV122 )
= $false )
| ( ( equidistant @ SV37 @ SV99 @ SV88 @ SV101 )
= $false )
| ( ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[346]) ).
thf(348,plain,
! [SV88: $i,SV65: $i,SV122: $i,SV101: $i,SV121: $i,SV99: $i,SV37: $i,SV6: $i] :
( ( ( SV6 = SV37 )
= $true )
| ( ( equidistant @ SV99 @ SV121 @ SV101 @ SV122 )
= $true )
| ( ( between @ SV65 @ SV88 @ SV101 )
= $false )
| ( ( between @ SV6 @ SV37 @ SV99 )
= $false )
| ( ( equidistant @ SV37 @ SV121 @ SV88 @ SV122 )
= $false )
| ( ( equidistant @ SV6 @ SV121 @ SV65 @ SV122 )
= $false )
| ( ( equidistant @ SV37 @ SV99 @ SV88 @ SV101 )
= $false )
| ( ( equidistant @ SV6 @ SV37 @ SV65 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[347]) ).
thf(349,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[93,348,341,340,339,325,322,321,320,317,309,308,294,280,279,278,277,276,275,274,245,243,225,223,222,217,193,192,181,180,165,164,163,141,140,139,129]) ).
thf(350,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[349]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO058-3 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.12/0.18 % Computer : n013.cluster.edu
% 0.12/0.18 % Model : x86_64 x86_64
% 0.12/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.18 % Memory : 8046.5625MB
% 0.12/0.18 % OS : Linux 6.8.0-71-generic
% 0.12/0.18 % CPULimit : 300
% 0.12/0.18 % WCLimit : 300
% 0.12/0.18 % DateTime : Tue Oct 6 10:00:06 UTC 2026
% 0.12/0.18 % CPUTime :
% 0.12/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.02/0.44
% 1.02/0.44 No.of.Axioms: 36
% 1.02/0.44
% 1.02/0.44 Length.of.Defs: 0
% 1.02/0.44
% 1.02/0.44 Contains.Choice.Funs: false
% 1.02/0.44 ..............
% 1.02/0.44
% 1.02/0.44 ********************************
% 1.02/0.44 * All subproblems solved! *
% 1.02/0.44 ********************************
% 1.02/0.44 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:36,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:349,loop_count:0,foatp_calls:1,translation:fof_full)
% 1.02/0.44
% 1.02/0.44 %**** Beginning of derivation protocol ****
% 1.02/0.44 % SZS output start CNFRefutation
% See solution above
% 1.02/0.44
% 1.02/0.44 %**** End of derivation protocol ****
% 1.02/0.44 %**** no. of clauses in derivation: 350 ****
% 1.02/0.44 %**** clause counter: 349 ****
% 1.02/0.44
% 1.02/0.44 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:36,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:5,ordering:none,proof_output:1,protocol_output:false,clause_count:349,loop_count:0,foatp_calls:1,translation:fof_full)
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