%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : GEO003-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 10:17:27 AM UTC 2026
% Result : Unsatisfiable 0.87s 0.39s
% Output : CNFRefutation 0.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 22
% Syntax : Number of formulae : 233 ( 140 unt; 0 typ; 0 def)
% Number of atoms : 1707 ( 502 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 4474 ( 424 ~; 686 |; 0 &;3364 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-6 aty)
% Number of variables : 1074 ( 0 ^;1074 !; 0 ?;1074 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_a,type,
a: $i ).
thf(tp_b,type,
b: $i ).
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_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_outer_pasch,type,
outer_pasch: $i > $i > $i > $i > $i > $i ).
thf(1,axiom,
! [V: $i,X: $i,X1: $i,Z: $i,Z1: $i,Y: $i] :
( ~ ( equidistant @ V @ X @ V @ X1 )
| ~ ( equidistant @ V @ Z @ V @ Z1 )
| ~ ( between @ V @ X @ Z )
| ~ ( between @ X @ Y @ Z )
| ( between @ X1 @ ( continuous @ X @ Y @ Z @ X1 @ Z1 @ V ) @ Z1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity2) ).
thf(2,axiom,
! [V: $i,X: $i,X1: $i,Z: $i,Z1: $i,Y: $i] :
( ~ ( equidistant @ V @ X @ V @ X1 )
| ~ ( equidistant @ V @ Z @ V @ Z1 )
| ~ ( between @ V @ X @ Z )
| ~ ( between @ X @ Y @ Z )
| ( equidistant @ V @ Y @ V @ ( continuous @ X @ Y @ Z @ X1 @ Z1 @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity1) ).
thf(3,axiom,
! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ W @ X @ V )
| ~ ( equidistant @ Y @ W @ Y @ V )
| ~ ( equidistant @ Z @ W @ Z @ V )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y )
| ( W = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_dimension) ).
thf(4,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
thf(5,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).
thf(6,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).
thf(7,axiom,
! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
thf(8,axiom,
! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
thf(9,axiom,
! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i,V: $i,V1: $i] :
( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
| ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
| ~ ( equidistant @ X @ V @ X1 @ V1 )
| ~ ( equidistant @ Y @ V @ Y1 @ V1 )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equidistant @ Z @ V @ Z1 @ V1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).
thf(10,axiom,
! [X: $i,V: $i,W: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ V @ W )
| ~ ( between @ Y @ V @ Z )
| ( X = V )
| ( between @ ( euclid1 @ W @ X @ Y @ Z @ V ) @ W @ ( euclid2 @ W @ X @ Y @ Z @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid3) ).
thf(11,axiom,
! [X: $i,V: $i,W: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ V @ W )
| ~ ( between @ Y @ V @ Z )
| ( X = V )
| ( between @ X @ Y @ ( euclid2 @ W @ X @ Y @ Z @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid2) ).
thf(12,axiom,
! [X: $i,V: $i,W: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ V @ W )
| ~ ( between @ Y @ V @ Z )
| ( X = V )
| ( between @ X @ Z @ ( euclid1 @ W @ X @ Y @ Z @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid1) ).
thf(13,axiom,
! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ W @ V )
| ~ ( between @ Y @ V @ Z )
| ( between @ Z @ W @ ( outer_pasch @ W @ X @ Y @ Z @ V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_pasch2) ).
thf(14,axiom,
! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ W @ V )
| ~ ( between @ Y @ V @ Z )
| ( between @ X @ ( outer_pasch @ W @ X @ Y @ Z @ V ) @ Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_pasch1) ).
thf(15,axiom,
! [X: $i,Y: $i,Z: $i,V: $i,V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
thf(16,axiom,
! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(17,axiom,
! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(18,axiom,
! [X: $i,Y: $i,Z: $i,V: $i] :
( ~ ( between @ X @ Y @ Z )
| ~ ( between @ X @ Y @ V )
| ( X = Y )
| ( between @ X @ Z @ V )
| ( between @ X @ V @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectivity_for_betweeness) ).
thf(19,axiom,
! [X: $i,Y: $i,V: $i,Z: $i] :
( ~ ( between @ X @ Y @ V )
| ~ ( between @ Y @ Z @ V )
| ( between @ X @ Y @ Z ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_betweeness) ).
thf(20,axiom,
! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(21,conjecture,
$false,
file('no conjecture given, we try to refute the axioms',dummy_conjecture) ).
thf(22,negated_conjecture,
$false = $false,
inference(negate_conjecture,[status(cth)],[21]) ).
thf(23,negated_conjecture,
~ ( between @ a @ b @ b ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_between_a_and_b) ).
thf(24,plain,
$false = $false,
inference(unfold_def,[status(thm)],[22]) ).
thf(25,plain,
( ( ! [V: $i,X: $i,X1: $i,Z: $i,Z1: $i,Y: $i] :
( ~ ( equidistant @ V @ X @ V @ X1 )
| ~ ( equidistant @ V @ Z @ V @ Z1 )
| ~ ( between @ V @ X @ Z )
| ~ ( between @ X @ Y @ Z )
| ( between @ X1 @ ( continuous @ X @ Y @ Z @ X1 @ Z1 @ V ) @ Z1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(26,plain,
( ( ! [V: $i,X: $i,X1: $i,Z: $i,Z1: $i,Y: $i] :
( ~ ( equidistant @ V @ X @ V @ X1 )
| ~ ( equidistant @ V @ Z @ V @ Z1 )
| ~ ( between @ V @ X @ Z )
| ~ ( between @ X @ Y @ Z )
| ( equidistant @ V @ Y @ V @ ( continuous @ X @ Y @ Z @ X1 @ Z1 @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[2]) ).
thf(27,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)],[3]) ).
thf(28,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[4]) ).
thf(29,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[5]) ).
thf(30,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(31,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[7]) ).
thf(32,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(33,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)],[9]) ).
thf(34,plain,
( ( ! [X: $i,V: $i,W: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ V @ W )
| ~ ( between @ Y @ V @ Z )
| ( X = V )
| ( between @ ( euclid1 @ W @ X @ Y @ Z @ V ) @ W @ ( euclid2 @ W @ X @ Y @ Z @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(35,plain,
( ( ! [X: $i,V: $i,W: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ V @ W )
| ~ ( between @ Y @ V @ Z )
| ( X = V )
| ( between @ X @ Y @ ( euclid2 @ W @ X @ Y @ Z @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[11]) ).
thf(36,plain,
( ( ! [X: $i,V: $i,W: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ V @ W )
| ~ ( between @ Y @ V @ Z )
| ( X = V )
| ( between @ X @ Z @ ( euclid1 @ W @ X @ Y @ Z @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[12]) ).
thf(37,plain,
( ( ! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ W @ V )
| ~ ( between @ Y @ V @ Z )
| ( between @ Z @ W @ ( outer_pasch @ W @ X @ Y @ Z @ V ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(38,plain,
( ( ! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ W @ V )
| ~ ( between @ Y @ V @ Z )
| ( between @ X @ ( outer_pasch @ W @ X @ Y @ Z @ V ) @ Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[14]) ).
thf(39,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)],[15]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(42,plain,
( ( ! [X: $i,Y: $i,Z: $i,V: $i] :
( ~ ( between @ X @ Y @ Z )
| ~ ( between @ X @ Y @ V )
| ( X = Y )
| ( between @ X @ Z @ V )
| ( between @ X @ V @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[18]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i,V: $i,Z: $i] :
( ~ ( between @ X @ Y @ V )
| ~ ( between @ Y @ Z @ V )
| ( between @ X @ Y @ Z ) ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(44,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(45,plain,
( ( ~ ( between @ a @ b @ b ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(46,plain,
( ( ~ $false ) = $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(47,plain,
( ( ~ ( between @ a @ b @ b ) )
= $true ),
inference(copy,[status(thm)],[45]) ).
thf(48,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(49,plain,
( ( ! [X: $i,Y: $i,V: $i,Z: $i] :
( ~ ( between @ X @ Y @ V )
| ~ ( between @ Y @ Z @ V )
| ( between @ X @ Y @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(50,plain,
( ( ! [X: $i,Y: $i,Z: $i,V: $i] :
( ~ ( between @ X @ Y @ Z )
| ~ ( between @ X @ Y @ V )
| ( X = Y )
| ( between @ X @ Z @ V )
| ( between @ X @ V @ Z ) ) )
= $true ),
inference(copy,[status(thm)],[42]) ).
thf(51,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(copy,[status(thm)],[41]) ).
thf(52,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(53,plain,
( ( ! [X: $i,Y: $i,Z: $i,V: $i,V2: $i,W: $i] :
( ~ ( equidistant @ X @ Y @ Z @ V )
| ~ ( equidistant @ X @ Y @ V2 @ W )
| ( equidistant @ Z @ V @ V2 @ W ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(54,plain,
( ( ! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ W @ V )
| ~ ( between @ Y @ V @ Z )
| ( between @ X @ ( outer_pasch @ W @ X @ Y @ Z @ V ) @ Y ) ) )
= $true ),
inference(copy,[status(thm)],[38]) ).
thf(55,plain,
( ( ! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ W @ V )
| ~ ( between @ Y @ V @ Z )
| ( between @ Z @ W @ ( outer_pasch @ W @ X @ Y @ Z @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(56,plain,
( ( ! [X: $i,V: $i,W: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ V @ W )
| ~ ( between @ Y @ V @ Z )
| ( X = V )
| ( between @ X @ Z @ ( euclid1 @ W @ X @ Y @ Z @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[36]) ).
thf(57,plain,
( ( ! [X: $i,V: $i,W: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ V @ W )
| ~ ( between @ Y @ V @ Z )
| ( X = V )
| ( between @ X @ Y @ ( euclid2 @ W @ X @ Y @ Z @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[35]) ).
thf(58,plain,
( ( ! [X: $i,V: $i,W: $i,Y: $i,Z: $i] :
( ~ ( between @ X @ V @ W )
| ~ ( between @ Y @ V @ Z )
| ( X = V )
| ( between @ ( euclid1 @ W @ X @ Y @ Z @ V ) @ W @ ( euclid2 @ W @ X @ Y @ Z @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(59,plain,
( ( ! [X: $i,Y: $i,X1: $i,Y1: $i,Z: $i,Z1: $i,V: $i,V1: $i] :
( ~ ( equidistant @ X @ Y @ X1 @ Y1 )
| ~ ( equidistant @ Y @ Z @ Y1 @ Z1 )
| ~ ( equidistant @ X @ V @ X1 @ V1 )
| ~ ( equidistant @ Y @ V @ Y1 @ V1 )
| ~ ( between @ X @ Y @ Z )
| ~ ( between @ X1 @ Y1 @ Z1 )
| ( X = Y )
| ( equidistant @ Z @ V @ Z1 @ V1 ) ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(60,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(61,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[31]) ).
thf(62,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[30]) ).
thf(63,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(copy,[status(thm)],[29]) ).
thf(64,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(copy,[status(thm)],[28]) ).
thf(65,plain,
( ( ! [X: $i,W: $i,V: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ W @ X @ V )
| ~ ( equidistant @ Y @ W @ Y @ V )
| ~ ( equidistant @ Z @ W @ Z @ V )
| ( between @ X @ Y @ Z )
| ( between @ Y @ Z @ X )
| ( between @ Z @ X @ Y )
| ( W = V ) ) )
= $true ),
inference(copy,[status(thm)],[27]) ).
thf(66,plain,
( ( ! [V: $i,X: $i,X1: $i,Z: $i,Z1: $i,Y: $i] :
( ~ ( equidistant @ V @ X @ V @ X1 )
| ~ ( equidistant @ V @ Z @ V @ Z1 )
| ~ ( between @ V @ X @ Z )
| ~ ( between @ X @ Y @ Z )
| ( equidistant @ V @ Y @ V @ ( continuous @ X @ Y @ Z @ X1 @ Z1 @ V ) ) ) )
= $true ),
inference(copy,[status(thm)],[26]) ).
thf(67,plain,
( ( ! [V: $i,X: $i,X1: $i,Z: $i,Z1: $i,Y: $i] :
( ~ ( equidistant @ V @ X @ V @ X1 )
| ~ ( equidistant @ V @ Z @ V @ Z1 )
| ~ ( between @ V @ X @ Z )
| ~ ( between @ X @ Y @ Z )
| ( between @ X1 @ ( continuous @ X @ Y @ Z @ X1 @ Z1 @ V ) @ Z1 ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(68,plain,
( ( ~ $false ) = $true ),
inference(copy,[status(thm)],[46]) ).
thf(69,plain,
( ( between @ a @ b @ b )
= $false ),
inference(extcnf_not_pos,[status(thm)],[47]) ).
thf(70,plain,
! [SV1: $i] :
( ( ! [SY79: $i] :
( ~ ( between @ SV1 @ SY79 @ SV1 )
| ( SV1 = SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[48]) ).
thf(71,plain,
! [SV2: $i] :
( ( ! [SY80: $i,SY81: $i,SY82: $i] :
( ~ ( between @ SV2 @ SY80 @ SY81 )
| ~ ( between @ SY80 @ SY82 @ SY81 )
| ( between @ SV2 @ SY80 @ SY82 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[49]) ).
thf(72,plain,
! [SV3: $i] :
( ( ! [SY83: $i,SY84: $i,SY85: $i] :
( ~ ( between @ SV3 @ SY83 @ SY84 )
| ~ ( between @ SV3 @ SY83 @ SY85 )
| ( SV3 = SY83 )
| ( between @ SV3 @ SY84 @ SY85 )
| ( between @ SV3 @ SY85 @ SY84 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[50]) ).
thf(73,plain,
! [SV4: $i] :
( ( ! [SY86: $i] : ( equidistant @ SV4 @ SY86 @ SY86 @ SV4 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[51]) ).
thf(74,plain,
! [SV5: $i] :
( ( ! [SY87: $i,SY88: $i] :
( ~ ( equidistant @ SV5 @ SY87 @ SY88 @ SY88 )
| ( SV5 = SY87 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[52]) ).
thf(75,plain,
! [SV6: $i] :
( ( ! [SY89: $i,SY90: $i,SY91: $i,SY92: $i,SY93: $i] :
( ~ ( equidistant @ SV6 @ SY89 @ SY90 @ SY91 )
| ~ ( equidistant @ SV6 @ SY89 @ SY92 @ SY93 )
| ( equidistant @ SY90 @ SY91 @ SY92 @ SY93 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[53]) ).
thf(76,plain,
! [SV7: $i] :
( ( ! [SY94: $i,SY95: $i,SY96: $i,SY97: $i] :
( ~ ( between @ SV7 @ SY94 @ SY95 )
| ~ ( between @ SY96 @ SY95 @ SY97 )
| ( between @ SV7 @ ( outer_pasch @ SY94 @ SV7 @ SY96 @ SY97 @ SY95 ) @ SY96 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[54]) ).
thf(77,plain,
! [SV8: $i] :
( ( ! [SY98: $i,SY99: $i,SY100: $i,SY101: $i] :
( ~ ( between @ SV8 @ SY98 @ SY99 )
| ~ ( between @ SY100 @ SY99 @ SY101 )
| ( between @ SY101 @ SY98 @ ( outer_pasch @ SY98 @ SV8 @ SY100 @ SY101 @ SY99 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[55]) ).
thf(78,plain,
! [SV9: $i] :
( ( ! [SY102: $i,SY103: $i,SY104: $i,SY105: $i] :
( ~ ( between @ SV9 @ SY102 @ SY103 )
| ~ ( between @ SY104 @ SY102 @ SY105 )
| ( SV9 = SY102 )
| ( between @ SV9 @ SY105 @ ( euclid1 @ SY103 @ SV9 @ SY104 @ SY105 @ SY102 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[56]) ).
thf(79,plain,
! [SV10: $i] :
( ( ! [SY106: $i,SY107: $i,SY108: $i,SY109: $i] :
( ~ ( between @ SV10 @ SY106 @ SY107 )
| ~ ( between @ SY108 @ SY106 @ SY109 )
| ( SV10 = SY106 )
| ( between @ SV10 @ SY108 @ ( euclid2 @ SY107 @ SV10 @ SY108 @ SY109 @ SY106 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[57]) ).
thf(80,plain,
! [SV11: $i] :
( ( ! [SY110: $i,SY111: $i,SY112: $i,SY113: $i] :
( ~ ( between @ SV11 @ SY110 @ SY111 )
| ~ ( between @ SY112 @ SY110 @ SY113 )
| ( SV11 = SY110 )
| ( between @ ( euclid1 @ SY111 @ SV11 @ SY112 @ SY113 @ SY110 ) @ SY111 @ ( euclid2 @ SY111 @ SV11 @ SY112 @ SY113 @ SY110 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[58]) ).
thf(81,plain,
! [SV12: $i] :
( ( ! [SY114: $i,SY115: $i,SY116: $i,SY117: $i,SY118: $i,SY119: $i,SY120: $i] :
( ~ ( equidistant @ SV12 @ SY114 @ SY115 @ SY116 )
| ~ ( equidistant @ SY114 @ SY117 @ SY116 @ SY118 )
| ~ ( equidistant @ SV12 @ SY119 @ SY115 @ SY120 )
| ~ ( equidistant @ SY114 @ SY119 @ SY116 @ SY120 )
| ~ ( between @ SV12 @ SY114 @ SY117 )
| ~ ( between @ SY115 @ SY116 @ SY118 )
| ( SV12 = SY114 )
| ( equidistant @ SY117 @ SY119 @ SY118 @ SY120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[59]) ).
thf(82,plain,
! [SV13: $i] :
( ( ! [SY121: $i,SY122: $i,SY123: $i] : ( between @ SV13 @ SY121 @ ( extension @ SV13 @ SY121 @ SY122 @ SY123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[60]) ).
thf(83,plain,
! [SV14: $i] :
( ( ! [SY124: $i,SY125: $i,SY126: $i] : ( equidistant @ SV14 @ ( extension @ SY124 @ SV14 @ SY125 @ SY126 ) @ SY125 @ SY126 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(84,plain,
( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[62]) ).
thf(85,plain,
( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[63]) ).
thf(86,plain,
( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[64]) ).
thf(87,plain,
! [SV15: $i] :
( ( ! [SY127: $i,SY128: $i,SY129: $i,SY130: $i] :
( ~ ( equidistant @ SV15 @ SY127 @ SV15 @ SY128 )
| ~ ( equidistant @ SY129 @ SY127 @ SY129 @ SY128 )
| ~ ( equidistant @ SY130 @ SY127 @ SY130 @ SY128 )
| ( between @ SV15 @ SY129 @ SY130 )
| ( between @ SY129 @ SY130 @ SV15 )
| ( between @ SY130 @ SV15 @ SY129 )
| ( SY127 = SY128 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(88,plain,
! [SV16: $i] :
( ( ! [SY131: $i,SY132: $i,SY133: $i,SY134: $i,SY135: $i] :
( ~ ( equidistant @ SV16 @ SY131 @ SV16 @ SY132 )
| ~ ( equidistant @ SV16 @ SY133 @ SV16 @ SY134 )
| ~ ( between @ SV16 @ SY131 @ SY133 )
| ~ ( between @ SY131 @ SY135 @ SY133 )
| ( equidistant @ SV16 @ SY135 @ SV16 @ ( continuous @ SY131 @ SY135 @ SY133 @ SY132 @ SY134 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(89,plain,
! [SV17: $i] :
( ( ! [SY136: $i,SY137: $i,SY138: $i,SY139: $i,SY140: $i] :
( ~ ( equidistant @ SV17 @ SY136 @ SV17 @ SY137 )
| ~ ( equidistant @ SV17 @ SY138 @ SV17 @ SY139 )
| ~ ( between @ SV17 @ SY136 @ SY138 )
| ~ ( between @ SY136 @ SY140 @ SY138 )
| ( between @ SY137 @ ( continuous @ SY136 @ SY140 @ SY138 @ SY137 @ SY139 @ SV17 ) @ SY139 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(90,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[68]) ).
thf(91,plain,
! [SV18: $i,SV1: $i] :
( ( ~ ( between @ SV1 @ SV18 @ SV1 )
| ( SV1 = SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[70]) ).
thf(92,plain,
! [SV19: $i,SV2: $i] :
( ( ! [SY141: $i,SY142: $i] :
( ~ ( between @ SV2 @ SV19 @ SY141 )
| ~ ( between @ SV19 @ SY142 @ SY141 )
| ( between @ SV2 @ SV19 @ SY142 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[71]) ).
thf(93,plain,
! [SV20: $i,SV3: $i] :
( ( ! [SY143: $i,SY144: $i] :
( ~ ( between @ SV3 @ SV20 @ SY143 )
| ~ ( between @ SV3 @ SV20 @ SY144 )
| ( SV3 = SV20 )
| ( between @ SV3 @ SY143 @ SY144 )
| ( between @ SV3 @ SY144 @ SY143 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[72]) ).
thf(94,plain,
! [SV21: $i,SV4: $i] :
( ( equidistant @ SV4 @ SV21 @ SV21 @ SV4 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(95,plain,
! [SV22: $i,SV5: $i] :
( ( ! [SY145: $i] :
( ~ ( equidistant @ SV5 @ SV22 @ SY145 @ SY145 )
| ( SV5 = SV22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(96,plain,
! [SV23: $i,SV6: $i] :
( ( ! [SY146: $i,SY147: $i,SY148: $i,SY149: $i] :
( ~ ( equidistant @ SV6 @ SV23 @ SY146 @ SY147 )
| ~ ( equidistant @ SV6 @ SV23 @ SY148 @ SY149 )
| ( equidistant @ SY146 @ SY147 @ SY148 @ SY149 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(97,plain,
! [SV24: $i,SV7: $i] :
( ( ! [SY150: $i,SY151: $i,SY152: $i] :
( ~ ( between @ SV7 @ SV24 @ SY150 )
| ~ ( between @ SY151 @ SY150 @ SY152 )
| ( between @ SV7 @ ( outer_pasch @ SV24 @ SV7 @ SY151 @ SY152 @ SY150 ) @ SY151 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(98,plain,
! [SV25: $i,SV8: $i] :
( ( ! [SY153: $i,SY154: $i,SY155: $i] :
( ~ ( between @ SV8 @ SV25 @ SY153 )
| ~ ( between @ SY154 @ SY153 @ SY155 )
| ( between @ SY155 @ SV25 @ ( outer_pasch @ SV25 @ SV8 @ SY154 @ SY155 @ SY153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(99,plain,
! [SV26: $i,SV9: $i] :
( ( ! [SY156: $i,SY157: $i,SY158: $i] :
( ~ ( between @ SV9 @ SV26 @ SY156 )
| ~ ( between @ SY157 @ SV26 @ SY158 )
| ( SV9 = SV26 )
| ( between @ SV9 @ SY158 @ ( euclid1 @ SY156 @ SV9 @ SY157 @ SY158 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(100,plain,
! [SV27: $i,SV10: $i] :
( ( ! [SY159: $i,SY160: $i,SY161: $i] :
( ~ ( between @ SV10 @ SV27 @ SY159 )
| ~ ( between @ SY160 @ SV27 @ SY161 )
| ( SV10 = SV27 )
| ( between @ SV10 @ SY160 @ ( euclid2 @ SY159 @ SV10 @ SY160 @ SY161 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(101,plain,
! [SV28: $i,SV11: $i] :
( ( ! [SY162: $i,SY163: $i,SY164: $i] :
( ~ ( between @ SV11 @ SV28 @ SY162 )
| ~ ( between @ SY163 @ SV28 @ SY164 )
| ( SV11 = SV28 )
| ( between @ ( euclid1 @ SY162 @ SV11 @ SY163 @ SY164 @ SV28 ) @ SY162 @ ( euclid2 @ SY162 @ SV11 @ SY163 @ SY164 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[80]) ).
thf(102,plain,
! [SV29: $i,SV12: $i] :
( ( ! [SY165: $i,SY166: $i,SY167: $i,SY168: $i,SY169: $i,SY170: $i] :
( ~ ( equidistant @ SV12 @ SV29 @ SY165 @ SY166 )
| ~ ( equidistant @ SV29 @ SY167 @ SY166 @ SY168 )
| ~ ( equidistant @ SV12 @ SY169 @ SY165 @ SY170 )
| ~ ( equidistant @ SV29 @ SY169 @ SY166 @ SY170 )
| ~ ( between @ SV12 @ SV29 @ SY167 )
| ~ ( between @ SY165 @ SY166 @ SY168 )
| ( SV12 = SV29 )
| ( equidistant @ SY167 @ SY169 @ SY168 @ SY170 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[81]) ).
thf(103,plain,
! [SV30: $i,SV13: $i] :
( ( ! [SY171: $i,SY172: $i] : ( between @ SV13 @ SV30 @ ( extension @ SV13 @ SV30 @ SY171 @ SY172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(104,plain,
! [SV31: $i,SV14: $i] :
( ( ! [SY173: $i,SY174: $i] : ( equidistant @ SV14 @ ( extension @ SV31 @ SV14 @ SY173 @ SY174 ) @ SY173 @ SY174 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(105,plain,
! [SV32: $i,SV15: $i] :
( ( ! [SY175: $i,SY176: $i,SY177: $i] :
( ~ ( equidistant @ SV15 @ SV32 @ SV15 @ SY175 )
| ~ ( equidistant @ SY176 @ SV32 @ SY176 @ SY175 )
| ~ ( equidistant @ SY177 @ SV32 @ SY177 @ SY175 )
| ( between @ SV15 @ SY176 @ SY177 )
| ( between @ SY176 @ SY177 @ SV15 )
| ( between @ SY177 @ SV15 @ SY176 )
| ( SV32 = SY175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(106,plain,
! [SV33: $i,SV16: $i] :
( ( ! [SY178: $i,SY179: $i,SY180: $i,SY181: $i] :
( ~ ( equidistant @ SV16 @ SV33 @ SV16 @ SY178 )
| ~ ( equidistant @ SV16 @ SY179 @ SV16 @ SY180 )
| ~ ( between @ SV16 @ SV33 @ SY179 )
| ~ ( between @ SV33 @ SY181 @ SY179 )
| ( equidistant @ SV16 @ SY181 @ SV16 @ ( continuous @ SV33 @ SY181 @ SY179 @ SY178 @ SY180 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(107,plain,
! [SV34: $i,SV17: $i] :
( ( ! [SY182: $i,SY183: $i,SY184: $i,SY185: $i] :
( ~ ( equidistant @ SV17 @ SV34 @ SV17 @ SY182 )
| ~ ( equidistant @ SV17 @ SY183 @ SV17 @ SY184 )
| ~ ( between @ SV17 @ SV34 @ SY183 )
| ~ ( between @ SV34 @ SY185 @ SY183 )
| ( between @ SY182 @ ( continuous @ SV34 @ SY185 @ SY183 @ SY182 @ SY184 @ SV17 ) @ SY184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(108,plain,
! [SV18: $i,SV1: $i] :
( ( ( ~ ( between @ SV1 @ SV18 @ SV1 ) )
= $true )
| ( ( SV1 = SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[91]) ).
thf(109,plain,
! [SV35: $i,SV19: $i,SV2: $i] :
( ( ! [SY186: $i] :
( ~ ( between @ SV2 @ SV19 @ SV35 )
| ~ ( between @ SV19 @ SY186 @ SV35 )
| ( between @ SV2 @ SV19 @ SY186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[92]) ).
thf(110,plain,
! [SV36: $i,SV20: $i,SV3: $i] :
( ( ! [SY187: $i] :
( ~ ( between @ SV3 @ SV20 @ SV36 )
| ~ ( between @ SV3 @ SV20 @ SY187 )
| ( SV3 = SV20 )
| ( between @ SV3 @ SV36 @ SY187 )
| ( between @ SV3 @ SY187 @ SV36 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[93]) ).
thf(111,plain,
! [SV37: $i,SV22: $i,SV5: $i] :
( ( ~ ( equidistant @ SV5 @ SV22 @ SV37 @ SV37 )
| ( SV5 = SV22 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(112,plain,
! [SV38: $i,SV23: $i,SV6: $i] :
( ( ! [SY188: $i,SY189: $i,SY190: $i] :
( ~ ( equidistant @ SV6 @ SV23 @ SV38 @ SY188 )
| ~ ( equidistant @ SV6 @ SV23 @ SY189 @ SY190 )
| ( equidistant @ SV38 @ SY188 @ SY189 @ SY190 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(113,plain,
! [SV39: $i,SV24: $i,SV7: $i] :
( ( ! [SY191: $i,SY192: $i] :
( ~ ( between @ SV7 @ SV24 @ SV39 )
| ~ ( between @ SY191 @ SV39 @ SY192 )
| ( between @ SV7 @ ( outer_pasch @ SV24 @ SV7 @ SY191 @ SY192 @ SV39 ) @ SY191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(114,plain,
! [SV40: $i,SV25: $i,SV8: $i] :
( ( ! [SY193: $i,SY194: $i] :
( ~ ( between @ SV8 @ SV25 @ SV40 )
| ~ ( between @ SY193 @ SV40 @ SY194 )
| ( between @ SY194 @ SV25 @ ( outer_pasch @ SV25 @ SV8 @ SY193 @ SY194 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(115,plain,
! [SV41: $i,SV26: $i,SV9: $i] :
( ( ! [SY195: $i,SY196: $i] :
( ~ ( between @ SV9 @ SV26 @ SV41 )
| ~ ( between @ SY195 @ SV26 @ SY196 )
| ( SV9 = SV26 )
| ( between @ SV9 @ SY196 @ ( euclid1 @ SV41 @ SV9 @ SY195 @ SY196 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(116,plain,
! [SV42: $i,SV27: $i,SV10: $i] :
( ( ! [SY197: $i,SY198: $i] :
( ~ ( between @ SV10 @ SV27 @ SV42 )
| ~ ( between @ SY197 @ SV27 @ SY198 )
| ( SV10 = SV27 )
| ( between @ SV10 @ SY197 @ ( euclid2 @ SV42 @ SV10 @ SY197 @ SY198 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(117,plain,
! [SV43: $i,SV28: $i,SV11: $i] :
( ( ! [SY199: $i,SY200: $i] :
( ~ ( between @ SV11 @ SV28 @ SV43 )
| ~ ( between @ SY199 @ SV28 @ SY200 )
| ( SV11 = SV28 )
| ( between @ ( euclid1 @ SV43 @ SV11 @ SY199 @ SY200 @ SV28 ) @ SV43 @ ( euclid2 @ SV43 @ SV11 @ SY199 @ SY200 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[101]) ).
thf(118,plain,
! [SV44: $i,SV29: $i,SV12: $i] :
( ( ! [SY201: $i,SY202: $i,SY203: $i,SY204: $i,SY205: $i] :
( ~ ( equidistant @ SV12 @ SV29 @ SV44 @ SY201 )
| ~ ( equidistant @ SV29 @ SY202 @ SY201 @ SY203 )
| ~ ( equidistant @ SV12 @ SY204 @ SV44 @ SY205 )
| ~ ( equidistant @ SV29 @ SY204 @ SY201 @ SY205 )
| ~ ( between @ SV12 @ SV29 @ SY202 )
| ~ ( between @ SV44 @ SY201 @ SY203 )
| ( SV12 = SV29 )
| ( equidistant @ SY202 @ SY204 @ SY203 @ SY205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[102]) ).
thf(119,plain,
! [SV45: $i,SV30: $i,SV13: $i] :
( ( ! [SY206: $i] : ( between @ SV13 @ SV30 @ ( extension @ SV13 @ SV30 @ SV45 @ SY206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(120,plain,
! [SV46: $i,SV31: $i,SV14: $i] :
( ( ! [SY207: $i] : ( equidistant @ SV14 @ ( extension @ SV31 @ SV14 @ SV46 @ SY207 ) @ SV46 @ SY207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[104]) ).
thf(121,plain,
! [SV47: $i,SV32: $i,SV15: $i] :
( ( ! [SY208: $i,SY209: $i] :
( ~ ( equidistant @ SV15 @ SV32 @ SV15 @ SV47 )
| ~ ( equidistant @ SY208 @ SV32 @ SY208 @ SV47 )
| ~ ( equidistant @ SY209 @ SV32 @ SY209 @ SV47 )
| ( between @ SV15 @ SY208 @ SY209 )
| ( between @ SY208 @ SY209 @ SV15 )
| ( between @ SY209 @ SV15 @ SY208 )
| ( SV32 = SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(122,plain,
! [SV48: $i,SV33: $i,SV16: $i] :
( ( ! [SY210: $i,SY211: $i,SY212: $i] :
( ~ ( equidistant @ SV16 @ SV33 @ SV16 @ SV48 )
| ~ ( equidistant @ SV16 @ SY210 @ SV16 @ SY211 )
| ~ ( between @ SV16 @ SV33 @ SY210 )
| ~ ( between @ SV33 @ SY212 @ SY210 )
| ( equidistant @ SV16 @ SY212 @ SV16 @ ( continuous @ SV33 @ SY212 @ SY210 @ SV48 @ SY211 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(123,plain,
! [SV49: $i,SV34: $i,SV17: $i] :
( ( ! [SY213: $i,SY214: $i,SY215: $i] :
( ~ ( equidistant @ SV17 @ SV34 @ SV17 @ SV49 )
| ~ ( equidistant @ SV17 @ SY213 @ SV17 @ SY214 )
| ~ ( between @ SV17 @ SV34 @ SY213 )
| ~ ( between @ SV34 @ SY215 @ SY213 )
| ( between @ SV49 @ ( continuous @ SV34 @ SY215 @ SY213 @ SV49 @ SY214 @ SV17 ) @ SY214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(124,plain,
! [SV18: $i,SV1: $i] :
( ( ( between @ SV1 @ SV18 @ SV1 )
= $false )
| ( ( SV1 = SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[108]) ).
thf(125,plain,
! [SV50: $i,SV35: $i,SV19: $i,SV2: $i] :
( ( ~ ( between @ SV2 @ SV19 @ SV35 )
| ~ ( between @ SV19 @ SV50 @ SV35 )
| ( between @ SV2 @ SV19 @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(126,plain,
! [SV51: $i,SV36: $i,SV20: $i,SV3: $i] :
( ( ~ ( between @ SV3 @ SV20 @ SV36 )
| ~ ( between @ SV3 @ SV20 @ SV51 )
| ( SV3 = SV20 )
| ( between @ SV3 @ SV36 @ SV51 )
| ( between @ SV3 @ SV51 @ SV36 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(127,plain,
! [SV37: $i,SV22: $i,SV5: $i] :
( ( ( ~ ( equidistant @ SV5 @ SV22 @ SV37 @ SV37 ) )
= $true )
| ( ( SV5 = SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[111]) ).
thf(128,plain,
! [SV52: $i,SV38: $i,SV23: $i,SV6: $i] :
( ( ! [SY216: $i,SY217: $i] :
( ~ ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
| ~ ( equidistant @ SV6 @ SV23 @ SY216 @ SY217 )
| ( equidistant @ SV38 @ SV52 @ SY216 @ SY217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(129,plain,
! [SV53: $i,SV39: $i,SV24: $i,SV7: $i] :
( ( ! [SY218: $i] :
( ~ ( between @ SV7 @ SV24 @ SV39 )
| ~ ( between @ SV53 @ SV39 @ SY218 )
| ( between @ SV7 @ ( outer_pasch @ SV24 @ SV7 @ SV53 @ SY218 @ SV39 ) @ SV53 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(130,plain,
! [SV54: $i,SV40: $i,SV25: $i,SV8: $i] :
( ( ! [SY219: $i] :
( ~ ( between @ SV8 @ SV25 @ SV40 )
| ~ ( between @ SV54 @ SV40 @ SY219 )
| ( between @ SY219 @ SV25 @ ( outer_pasch @ SV25 @ SV8 @ SV54 @ SY219 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(131,plain,
! [SV55: $i,SV41: $i,SV26: $i,SV9: $i] :
( ( ! [SY220: $i] :
( ~ ( between @ SV9 @ SV26 @ SV41 )
| ~ ( between @ SV55 @ SV26 @ SY220 )
| ( SV9 = SV26 )
| ( between @ SV9 @ SY220 @ ( euclid1 @ SV41 @ SV9 @ SV55 @ SY220 @ SV26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(132,plain,
! [SV56: $i,SV42: $i,SV27: $i,SV10: $i] :
( ( ! [SY221: $i] :
( ~ ( between @ SV10 @ SV27 @ SV42 )
| ~ ( between @ SV56 @ SV27 @ SY221 )
| ( SV10 = SV27 )
| ( between @ SV10 @ SV56 @ ( euclid2 @ SV42 @ SV10 @ SV56 @ SY221 @ SV27 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(133,plain,
! [SV57: $i,SV43: $i,SV28: $i,SV11: $i] :
( ( ! [SY222: $i] :
( ~ ( between @ SV11 @ SV28 @ SV43 )
| ~ ( between @ SV57 @ SV28 @ SY222 )
| ( SV11 = SV28 )
| ( between @ ( euclid1 @ SV43 @ SV11 @ SV57 @ SY222 @ SV28 ) @ SV43 @ ( euclid2 @ SV43 @ SV11 @ SV57 @ SY222 @ SV28 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[117]) ).
thf(134,plain,
! [SV58: $i,SV44: $i,SV29: $i,SV12: $i] :
( ( ! [SY223: $i,SY224: $i,SY225: $i,SY226: $i] :
( ~ ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
| ~ ( equidistant @ SV29 @ SY223 @ SV58 @ SY224 )
| ~ ( equidistant @ SV12 @ SY225 @ SV44 @ SY226 )
| ~ ( equidistant @ SV29 @ SY225 @ SV58 @ SY226 )
| ~ ( between @ SV12 @ SV29 @ SY223 )
| ~ ( between @ SV44 @ SV58 @ SY224 )
| ( SV12 = SV29 )
| ( equidistant @ SY223 @ SY225 @ SY224 @ SY226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(135,plain,
! [SV59: $i,SV45: $i,SV30: $i,SV13: $i] :
( ( between @ SV13 @ SV30 @ ( extension @ SV13 @ SV30 @ SV45 @ SV59 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(136,plain,
! [SV60: $i,SV46: $i,SV31: $i,SV14: $i] :
( ( equidistant @ SV14 @ ( extension @ SV31 @ SV14 @ SV46 @ SV60 ) @ SV46 @ SV60 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(137,plain,
! [SV61: $i,SV47: $i,SV32: $i,SV15: $i] :
( ( ! [SY227: $i] :
( ~ ( equidistant @ SV15 @ SV32 @ SV15 @ SV47 )
| ~ ( equidistant @ SV61 @ SV32 @ SV61 @ SV47 )
| ~ ( equidistant @ SY227 @ SV32 @ SY227 @ SV47 )
| ( between @ SV15 @ SV61 @ SY227 )
| ( between @ SV61 @ SY227 @ SV15 )
| ( between @ SY227 @ SV15 @ SV61 )
| ( SV32 = SV47 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(138,plain,
! [SV62: $i,SV48: $i,SV33: $i,SV16: $i] :
( ( ! [SY228: $i,SY229: $i] :
( ~ ( equidistant @ SV16 @ SV33 @ SV16 @ SV48 )
| ~ ( equidistant @ SV16 @ SV62 @ SV16 @ SY228 )
| ~ ( between @ SV16 @ SV33 @ SV62 )
| ~ ( between @ SV33 @ SY229 @ SV62 )
| ( equidistant @ SV16 @ SY229 @ SV16 @ ( continuous @ SV33 @ SY229 @ SV62 @ SV48 @ SY228 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(139,plain,
! [SV63: $i,SV49: $i,SV34: $i,SV17: $i] :
( ( ! [SY230: $i,SY231: $i] :
( ~ ( equidistant @ SV17 @ SV34 @ SV17 @ SV49 )
| ~ ( equidistant @ SV17 @ SV63 @ SV17 @ SY230 )
| ~ ( between @ SV17 @ SV34 @ SV63 )
| ~ ( between @ SV34 @ SY231 @ SV63 )
| ( between @ SV49 @ ( continuous @ SV34 @ SY231 @ SV63 @ SV49 @ SY230 @ SV17 ) @ SY230 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[123]) ).
thf(140,plain,
! [SV50: $i,SV35: $i,SV19: $i,SV2: $i] :
( ( ( ~ ( between @ SV2 @ SV19 @ SV35 ) )
= $true )
| ( ( ~ ( between @ SV19 @ SV50 @ SV35 )
| ( between @ SV2 @ SV19 @ SV50 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(141,plain,
! [SV51: $i,SV36: $i,SV20: $i,SV3: $i] :
( ( ( ~ ( between @ SV3 @ SV20 @ SV36 ) )
= $true )
| ( ( ~ ( between @ SV3 @ SV20 @ SV51 )
| ( SV3 = SV20 )
| ( between @ SV3 @ SV36 @ SV51 )
| ( between @ SV3 @ SV51 @ SV36 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(142,plain,
! [SV37: $i,SV22: $i,SV5: $i] :
( ( ( equidistant @ SV5 @ SV22 @ SV37 @ SV37 )
= $false )
| ( ( SV5 = SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[127]) ).
thf(143,plain,
! [SV64: $i,SV52: $i,SV38: $i,SV23: $i,SV6: $i] :
( ( ! [SY232: $i] :
( ~ ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
| ~ ( equidistant @ SV6 @ SV23 @ SV64 @ SY232 )
| ( equidistant @ SV38 @ SV52 @ SV64 @ SY232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[128]) ).
thf(144,plain,
! [SV65: $i,SV53: $i,SV39: $i,SV24: $i,SV7: $i] :
( ( ~ ( between @ SV7 @ SV24 @ SV39 )
| ~ ( between @ SV53 @ SV39 @ SV65 )
| ( between @ SV7 @ ( outer_pasch @ SV24 @ SV7 @ SV53 @ SV65 @ SV39 ) @ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[129]) ).
thf(145,plain,
! [SV66: $i,SV54: $i,SV40: $i,SV25: $i,SV8: $i] :
( ( ~ ( between @ SV8 @ SV25 @ SV40 )
| ~ ( between @ SV54 @ SV40 @ SV66 )
| ( between @ SV66 @ SV25 @ ( outer_pasch @ SV25 @ SV8 @ SV54 @ SV66 @ SV40 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(146,plain,
! [SV67: $i,SV55: $i,SV41: $i,SV26: $i,SV9: $i] :
( ( ~ ( between @ SV9 @ SV26 @ SV41 )
| ~ ( between @ SV55 @ SV26 @ SV67 )
| ( SV9 = SV26 )
| ( between @ SV9 @ SV67 @ ( euclid1 @ SV41 @ SV9 @ SV55 @ SV67 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(147,plain,
! [SV68: $i,SV56: $i,SV42: $i,SV27: $i,SV10: $i] :
( ( ~ ( between @ SV10 @ SV27 @ SV42 )
| ~ ( between @ SV56 @ SV27 @ SV68 )
| ( SV10 = SV27 )
| ( between @ SV10 @ SV56 @ ( euclid2 @ SV42 @ SV10 @ SV56 @ SV68 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[132]) ).
thf(148,plain,
! [SV69: $i,SV57: $i,SV43: $i,SV28: $i,SV11: $i] :
( ( ~ ( between @ SV11 @ SV28 @ SV43 )
| ~ ( between @ SV57 @ SV28 @ SV69 )
| ( SV11 = SV28 )
| ( between @ ( euclid1 @ SV43 @ SV11 @ SV57 @ SV69 @ SV28 ) @ SV43 @ ( euclid2 @ SV43 @ SV11 @ SV57 @ SV69 @ SV28 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[133]) ).
thf(149,plain,
! [SV70: $i,SV58: $i,SV44: $i,SV29: $i,SV12: $i] :
( ( ! [SY233: $i,SY234: $i,SY235: $i] :
( ~ ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
| ~ ( equidistant @ SV29 @ SV70 @ SV58 @ SY233 )
| ~ ( equidistant @ SV12 @ SY234 @ SV44 @ SY235 )
| ~ ( equidistant @ SV29 @ SY234 @ SV58 @ SY235 )
| ~ ( between @ SV12 @ SV29 @ SV70 )
| ~ ( between @ SV44 @ SV58 @ SY233 )
| ( SV12 = SV29 )
| ( equidistant @ SV70 @ SY234 @ SY233 @ SY235 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[134]) ).
thf(150,plain,
! [SV71: $i,SV61: $i,SV47: $i,SV32: $i,SV15: $i] :
( ( ~ ( equidistant @ SV15 @ SV32 @ SV15 @ SV47 )
| ~ ( equidistant @ SV61 @ SV32 @ SV61 @ SV47 )
| ~ ( equidistant @ SV71 @ SV32 @ SV71 @ SV47 )
| ( between @ SV15 @ SV61 @ SV71 )
| ( between @ SV61 @ SV71 @ SV15 )
| ( between @ SV71 @ SV15 @ SV61 )
| ( SV32 = SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[137]) ).
thf(151,plain,
! [SV72: $i,SV62: $i,SV48: $i,SV33: $i,SV16: $i] :
( ( ! [SY236: $i] :
( ~ ( equidistant @ SV16 @ SV33 @ SV16 @ SV48 )
| ~ ( equidistant @ SV16 @ SV62 @ SV16 @ SV72 )
| ~ ( between @ SV16 @ SV33 @ SV62 )
| ~ ( between @ SV33 @ SY236 @ SV62 )
| ( equidistant @ SV16 @ SY236 @ SV16 @ ( continuous @ SV33 @ SY236 @ SV62 @ SV48 @ SV72 @ SV16 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[138]) ).
thf(152,plain,
! [SV73: $i,SV63: $i,SV49: $i,SV34: $i,SV17: $i] :
( ( ! [SY237: $i] :
( ~ ( equidistant @ SV17 @ SV34 @ SV17 @ SV49 )
| ~ ( equidistant @ SV17 @ SV63 @ SV17 @ SV73 )
| ~ ( between @ SV17 @ SV34 @ SV63 )
| ~ ( between @ SV34 @ SY237 @ SV63 )
| ( between @ SV49 @ ( continuous @ SV34 @ SY237 @ SV63 @ SV49 @ SV73 @ SV17 ) @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[139]) ).
thf(153,plain,
! [SV50: $i,SV35: $i,SV19: $i,SV2: $i] :
( ( ( between @ SV2 @ SV19 @ SV35 )
= $false )
| ( ( ~ ( between @ SV19 @ SV50 @ SV35 )
| ( between @ SV2 @ SV19 @ SV50 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(154,plain,
! [SV51: $i,SV36: $i,SV20: $i,SV3: $i] :
( ( ( between @ SV3 @ SV20 @ SV36 )
= $false )
| ( ( ~ ( between @ SV3 @ SV20 @ SV51 )
| ( SV3 = SV20 )
| ( between @ SV3 @ SV36 @ SV51 )
| ( between @ SV3 @ SV51 @ SV36 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(155,plain,
! [SV74: $i,SV64: $i,SV52: $i,SV38: $i,SV23: $i,SV6: $i] :
( ( ~ ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
| ~ ( equidistant @ SV6 @ SV23 @ SV64 @ SV74 )
| ( equidistant @ SV38 @ SV52 @ SV64 @ SV74 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[143]) ).
thf(156,plain,
! [SV65: $i,SV53: $i,SV39: $i,SV24: $i,SV7: $i] :
( ( ( ~ ( between @ SV7 @ SV24 @ SV39 ) )
= $true )
| ( ( ~ ( between @ SV53 @ SV39 @ SV65 )
| ( between @ SV7 @ ( outer_pasch @ SV24 @ SV7 @ SV53 @ SV65 @ SV39 ) @ SV53 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(157,plain,
! [SV66: $i,SV54: $i,SV40: $i,SV25: $i,SV8: $i] :
( ( ( ~ ( between @ SV8 @ SV25 @ SV40 ) )
= $true )
| ( ( ~ ( between @ SV54 @ SV40 @ SV66 )
| ( between @ SV66 @ SV25 @ ( outer_pasch @ SV25 @ SV8 @ SV54 @ SV66 @ SV40 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(158,plain,
! [SV67: $i,SV55: $i,SV41: $i,SV26: $i,SV9: $i] :
( ( ( ~ ( between @ SV9 @ SV26 @ SV41 ) )
= $true )
| ( ( ~ ( between @ SV55 @ SV26 @ SV67 )
| ( SV9 = SV26 )
| ( between @ SV9 @ SV67 @ ( euclid1 @ SV41 @ SV9 @ SV55 @ SV67 @ SV26 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[146]) ).
thf(159,plain,
! [SV68: $i,SV56: $i,SV42: $i,SV27: $i,SV10: $i] :
( ( ( ~ ( between @ SV10 @ SV27 @ SV42 ) )
= $true )
| ( ( ~ ( between @ SV56 @ SV27 @ SV68 )
| ( SV10 = SV27 )
| ( between @ SV10 @ SV56 @ ( euclid2 @ SV42 @ SV10 @ SV56 @ SV68 @ SV27 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[147]) ).
thf(160,plain,
! [SV69: $i,SV57: $i,SV43: $i,SV28: $i,SV11: $i] :
( ( ( ~ ( between @ SV11 @ SV28 @ SV43 ) )
= $true )
| ( ( ~ ( between @ SV57 @ SV28 @ SV69 )
| ( SV11 = SV28 )
| ( between @ ( euclid1 @ SV43 @ SV11 @ SV57 @ SV69 @ SV28 ) @ SV43 @ ( euclid2 @ SV43 @ SV11 @ SV57 @ SV69 @ SV28 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[148]) ).
thf(161,plain,
! [SV75: $i,SV70: $i,SV58: $i,SV44: $i,SV29: $i,SV12: $i] :
( ( ! [SY238: $i,SY239: $i] :
( ~ ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
| ~ ( equidistant @ SV29 @ SV70 @ SV58 @ SV75 )
| ~ ( equidistant @ SV12 @ SY238 @ SV44 @ SY239 )
| ~ ( equidistant @ SV29 @ SY238 @ SV58 @ SY239 )
| ~ ( between @ SV12 @ SV29 @ SV70 )
| ~ ( between @ SV44 @ SV58 @ SV75 )
| ( SV12 = SV29 )
| ( equidistant @ SV70 @ SY238 @ SV75 @ SY239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(162,plain,
! [SV71: $i,SV61: $i,SV47: $i,SV32: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV32 @ SV15 @ SV47 ) )
= $true )
| ( ( ~ ( equidistant @ SV61 @ SV32 @ SV61 @ SV47 )
| ~ ( equidistant @ SV71 @ SV32 @ SV71 @ SV47 )
| ( between @ SV15 @ SV61 @ SV71 )
| ( between @ SV61 @ SV71 @ SV15 )
| ( between @ SV71 @ SV15 @ SV61 )
| ( SV32 = SV47 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[150]) ).
thf(163,plain,
! [SV76: $i,SV72: $i,SV62: $i,SV48: $i,SV33: $i,SV16: $i] :
( ( ~ ( equidistant @ SV16 @ SV33 @ SV16 @ SV48 )
| ~ ( equidistant @ SV16 @ SV62 @ SV16 @ SV72 )
| ~ ( between @ SV16 @ SV33 @ SV62 )
| ~ ( between @ SV33 @ SV76 @ SV62 )
| ( equidistant @ SV16 @ SV76 @ SV16 @ ( continuous @ SV33 @ SV76 @ SV62 @ SV48 @ SV72 @ SV16 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(164,plain,
! [SV77: $i,SV73: $i,SV63: $i,SV49: $i,SV34: $i,SV17: $i] :
( ( ~ ( equidistant @ SV17 @ SV34 @ SV17 @ SV49 )
| ~ ( equidistant @ SV17 @ SV63 @ SV17 @ SV73 )
| ~ ( between @ SV17 @ SV34 @ SV63 )
| ~ ( between @ SV34 @ SV77 @ SV63 )
| ( between @ SV49 @ ( continuous @ SV34 @ SV77 @ SV63 @ SV49 @ SV73 @ SV17 ) @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(165,plain,
! [SV2: $i,SV35: $i,SV50: $i,SV19: $i] :
( ( ( ~ ( between @ SV19 @ SV50 @ SV35 ) )
= $true )
| ( ( between @ SV2 @ SV19 @ SV50 )
= $true )
| ( ( between @ SV2 @ SV19 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[153]) ).
thf(166,plain,
! [SV36: $i,SV51: $i,SV20: $i,SV3: $i] :
( ( ( ~ ( between @ SV3 @ SV20 @ SV51 ) )
= $true )
| ( ( ( SV3 = SV20 )
| ( between @ SV3 @ SV36 @ SV51 )
| ( between @ SV3 @ SV51 @ SV36 ) )
= $true )
| ( ( between @ SV3 @ SV20 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[154]) ).
thf(167,plain,
! [SV74: $i,SV64: $i,SV52: $i,SV38: $i,SV23: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 ) )
= $true )
| ( ( ~ ( equidistant @ SV6 @ SV23 @ SV64 @ SV74 )
| ( equidistant @ SV38 @ SV52 @ SV64 @ SV74 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[155]) ).
thf(168,plain,
! [SV65: $i,SV53: $i,SV39: $i,SV24: $i,SV7: $i] :
( ( ( between @ SV7 @ SV24 @ SV39 )
= $false )
| ( ( ~ ( between @ SV53 @ SV39 @ SV65 )
| ( between @ SV7 @ ( outer_pasch @ SV24 @ SV7 @ SV53 @ SV65 @ SV39 ) @ SV53 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(169,plain,
! [SV66: $i,SV54: $i,SV40: $i,SV25: $i,SV8: $i] :
( ( ( between @ SV8 @ SV25 @ SV40 )
= $false )
| ( ( ~ ( between @ SV54 @ SV40 @ SV66 )
| ( between @ SV66 @ SV25 @ ( outer_pasch @ SV25 @ SV8 @ SV54 @ SV66 @ SV40 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[157]) ).
thf(170,plain,
! [SV67: $i,SV55: $i,SV41: $i,SV26: $i,SV9: $i] :
( ( ( between @ SV9 @ SV26 @ SV41 )
= $false )
| ( ( ~ ( between @ SV55 @ SV26 @ SV67 )
| ( SV9 = SV26 )
| ( between @ SV9 @ SV67 @ ( euclid1 @ SV41 @ SV9 @ SV55 @ SV67 @ SV26 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[158]) ).
thf(171,plain,
! [SV68: $i,SV56: $i,SV42: $i,SV27: $i,SV10: $i] :
( ( ( between @ SV10 @ SV27 @ SV42 )
= $false )
| ( ( ~ ( between @ SV56 @ SV27 @ SV68 )
| ( SV10 = SV27 )
| ( between @ SV10 @ SV56 @ ( euclid2 @ SV42 @ SV10 @ SV56 @ SV68 @ SV27 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[159]) ).
thf(172,plain,
! [SV69: $i,SV57: $i,SV43: $i,SV28: $i,SV11: $i] :
( ( ( between @ SV11 @ SV28 @ SV43 )
= $false )
| ( ( ~ ( between @ SV57 @ SV28 @ SV69 )
| ( SV11 = SV28 )
| ( between @ ( euclid1 @ SV43 @ SV11 @ SV57 @ SV69 @ SV28 ) @ SV43 @ ( euclid2 @ SV43 @ SV11 @ SV57 @ SV69 @ SV28 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[160]) ).
thf(173,plain,
! [SV78: $i,SV75: $i,SV70: $i,SV58: $i,SV44: $i,SV29: $i,SV12: $i] :
( ( ! [SY240: $i] :
( ~ ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
| ~ ( equidistant @ SV29 @ SV70 @ SV58 @ SV75 )
| ~ ( equidistant @ SV12 @ SV78 @ SV44 @ SY240 )
| ~ ( equidistant @ SV29 @ SV78 @ SV58 @ SY240 )
| ~ ( between @ SV12 @ SV29 @ SV70 )
| ~ ( between @ SV44 @ SV58 @ SV75 )
| ( SV12 = SV29 )
| ( equidistant @ SV70 @ SV78 @ SV75 @ SY240 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[161]) ).
thf(174,plain,
! [SV71: $i,SV61: $i,SV47: $i,SV32: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV47 )
= $false )
| ( ( ~ ( equidistant @ SV61 @ SV32 @ SV61 @ SV47 )
| ~ ( equidistant @ SV71 @ SV32 @ SV71 @ SV47 )
| ( between @ SV15 @ SV61 @ SV71 )
| ( between @ SV61 @ SV71 @ SV15 )
| ( between @ SV71 @ SV15 @ SV61 )
| ( SV32 = SV47 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[162]) ).
thf(175,plain,
! [SV76: $i,SV72: $i,SV62: $i,SV48: $i,SV33: $i,SV16: $i] :
( ( ( ~ ( equidistant @ SV16 @ SV33 @ SV16 @ SV48 ) )
= $true )
| ( ( ~ ( equidistant @ SV16 @ SV62 @ SV16 @ SV72 )
| ~ ( between @ SV16 @ SV33 @ SV62 )
| ~ ( between @ SV33 @ SV76 @ SV62 )
| ( equidistant @ SV16 @ SV76 @ SV16 @ ( continuous @ SV33 @ SV76 @ SV62 @ SV48 @ SV72 @ SV16 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[163]) ).
thf(176,plain,
! [SV77: $i,SV73: $i,SV63: $i,SV49: $i,SV34: $i,SV17: $i] :
( ( ( ~ ( equidistant @ SV17 @ SV34 @ SV17 @ SV49 ) )
= $true )
| ( ( ~ ( equidistant @ SV17 @ SV63 @ SV17 @ SV73 )
| ~ ( between @ SV17 @ SV34 @ SV63 )
| ~ ( between @ SV34 @ SV77 @ SV63 )
| ( between @ SV49 @ ( continuous @ SV34 @ SV77 @ SV63 @ SV49 @ SV73 @ SV17 ) @ SV73 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[164]) ).
thf(177,plain,
! [SV2: $i,SV35: $i,SV50: $i,SV19: $i] :
( ( ( between @ SV19 @ SV50 @ SV35 )
= $false )
| ( ( between @ SV2 @ SV19 @ SV50 )
= $true )
| ( ( between @ SV2 @ SV19 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[165]) ).
thf(178,plain,
! [SV36: $i,SV51: $i,SV20: $i,SV3: $i] :
( ( ( between @ SV3 @ SV20 @ SV51 )
= $false )
| ( ( ( SV3 = SV20 )
| ( between @ SV3 @ SV36 @ SV51 )
| ( between @ SV3 @ SV51 @ SV36 ) )
= $true )
| ( ( between @ SV3 @ SV20 @ SV36 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[166]) ).
thf(179,plain,
! [SV74: $i,SV64: $i,SV52: $i,SV38: $i,SV23: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
= $false )
| ( ( ~ ( equidistant @ SV6 @ SV23 @ SV64 @ SV74 )
| ( equidistant @ SV38 @ SV52 @ SV64 @ SV74 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[167]) ).
thf(180,plain,
! [SV24: $i,SV7: $i,SV65: $i,SV39: $i,SV53: $i] :
( ( ( ~ ( between @ SV53 @ SV39 @ SV65 ) )
= $true )
| ( ( between @ SV7 @ ( outer_pasch @ SV24 @ SV7 @ SV53 @ SV65 @ SV39 ) @ SV53 )
= $true )
| ( ( between @ SV7 @ SV24 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[168]) ).
thf(181,plain,
! [SV8: $i,SV25: $i,SV66: $i,SV40: $i,SV54: $i] :
( ( ( ~ ( between @ SV54 @ SV40 @ SV66 ) )
= $true )
| ( ( between @ SV66 @ SV25 @ ( outer_pasch @ SV25 @ SV8 @ SV54 @ SV66 @ SV40 ) )
= $true )
| ( ( between @ SV8 @ SV25 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(182,plain,
! [SV41: $i,SV9: $i,SV67: $i,SV26: $i,SV55: $i] :
( ( ( ~ ( between @ SV55 @ SV26 @ SV67 ) )
= $true )
| ( ( ( SV9 = SV26 )
| ( between @ SV9 @ SV67 @ ( euclid1 @ SV41 @ SV9 @ SV55 @ SV67 @ SV26 ) ) )
= $true )
| ( ( between @ SV9 @ SV26 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(183,plain,
! [SV42: $i,SV10: $i,SV68: $i,SV27: $i,SV56: $i] :
( ( ( ~ ( between @ SV56 @ SV27 @ SV68 ) )
= $true )
| ( ( ( SV10 = SV27 )
| ( between @ SV10 @ SV56 @ ( euclid2 @ SV42 @ SV10 @ SV56 @ SV68 @ SV27 ) ) )
= $true )
| ( ( between @ SV10 @ SV27 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[171]) ).
thf(184,plain,
! [SV43: $i,SV11: $i,SV69: $i,SV28: $i,SV57: $i] :
( ( ( ~ ( between @ SV57 @ SV28 @ SV69 ) )
= $true )
| ( ( ( SV11 = SV28 )
| ( between @ ( euclid1 @ SV43 @ SV11 @ SV57 @ SV69 @ SV28 ) @ SV43 @ ( euclid2 @ SV43 @ SV11 @ SV57 @ SV69 @ SV28 ) ) )
= $true )
| ( ( between @ SV11 @ SV28 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(185,plain,
! [SV79: $i,SV78: $i,SV75: $i,SV70: $i,SV58: $i,SV44: $i,SV29: $i,SV12: $i] :
( ( ~ ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
| ~ ( equidistant @ SV29 @ SV70 @ SV58 @ SV75 )
| ~ ( equidistant @ SV12 @ SV78 @ SV44 @ SV79 )
| ~ ( equidistant @ SV29 @ SV78 @ SV58 @ SV79 )
| ~ ( between @ SV12 @ SV29 @ SV70 )
| ~ ( between @ SV44 @ SV58 @ SV75 )
| ( SV12 = SV29 )
| ( equidistant @ SV70 @ SV78 @ SV75 @ SV79 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[173]) ).
thf(186,plain,
! [SV15: $i,SV71: $i,SV47: $i,SV32: $i,SV61: $i] :
( ( ( ~ ( equidistant @ SV61 @ SV32 @ SV61 @ SV47 ) )
= $true )
| ( ( ~ ( equidistant @ SV71 @ SV32 @ SV71 @ SV47 )
| ( between @ SV15 @ SV61 @ SV71 )
| ( between @ SV61 @ SV71 @ SV15 )
| ( between @ SV71 @ SV15 @ SV61 )
| ( SV32 = SV47 ) )
= $true )
| ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(187,plain,
! [SV76: $i,SV72: $i,SV62: $i,SV48: $i,SV33: $i,SV16: $i] :
( ( ( equidistant @ SV16 @ SV33 @ SV16 @ SV48 )
= $false )
| ( ( ~ ( equidistant @ SV16 @ SV62 @ SV16 @ SV72 )
| ~ ( between @ SV16 @ SV33 @ SV62 )
| ~ ( between @ SV33 @ SV76 @ SV62 )
| ( equidistant @ SV16 @ SV76 @ SV16 @ ( continuous @ SV33 @ SV76 @ SV62 @ SV48 @ SV72 @ SV16 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[175]) ).
thf(188,plain,
! [SV77: $i,SV73: $i,SV63: $i,SV49: $i,SV34: $i,SV17: $i] :
( ( ( equidistant @ SV17 @ SV34 @ SV17 @ SV49 )
= $false )
| ( ( ~ ( equidistant @ SV17 @ SV63 @ SV17 @ SV73 )
| ~ ( between @ SV17 @ SV34 @ SV63 )
| ~ ( between @ SV34 @ SV77 @ SV63 )
| ( between @ SV49 @ ( continuous @ SV34 @ SV77 @ SV63 @ SV49 @ SV73 @ SV17 ) @ SV73 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[176]) ).
thf(189,plain,
! [SV51: $i,SV36: $i,SV20: $i,SV3: $i] :
( ( ( SV3 = SV20 )
= $true )
| ( ( ( between @ SV3 @ SV36 @ SV51 )
| ( between @ SV3 @ SV51 @ SV36 ) )
= $true )
| ( ( between @ SV3 @ SV20 @ SV51 )
= $false )
| ( ( between @ SV3 @ SV20 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(190,plain,
! [SV52: $i,SV38: $i,SV74: $i,SV64: $i,SV23: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV23 @ SV64 @ SV74 ) )
= $true )
| ( ( equidistant @ SV38 @ SV52 @ SV64 @ SV74 )
= $true )
| ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[179]) ).
thf(191,plain,
! [SV24: $i,SV7: $i,SV65: $i,SV39: $i,SV53: $i] :
( ( ( between @ SV53 @ SV39 @ SV65 )
= $false )
| ( ( between @ SV7 @ ( outer_pasch @ SV24 @ SV7 @ SV53 @ SV65 @ SV39 ) @ SV53 )
= $true )
| ( ( between @ SV7 @ SV24 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(192,plain,
! [SV8: $i,SV25: $i,SV66: $i,SV40: $i,SV54: $i] :
( ( ( between @ SV54 @ SV40 @ SV66 )
= $false )
| ( ( between @ SV66 @ SV25 @ ( outer_pasch @ SV25 @ SV8 @ SV54 @ SV66 @ SV40 ) )
= $true )
| ( ( between @ SV8 @ SV25 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[181]) ).
thf(193,plain,
! [SV41: $i,SV9: $i,SV67: $i,SV26: $i,SV55: $i] :
( ( ( between @ SV55 @ SV26 @ SV67 )
= $false )
| ( ( ( SV9 = SV26 )
| ( between @ SV9 @ SV67 @ ( euclid1 @ SV41 @ SV9 @ SV55 @ SV67 @ SV26 ) ) )
= $true )
| ( ( between @ SV9 @ SV26 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(194,plain,
! [SV42: $i,SV10: $i,SV68: $i,SV27: $i,SV56: $i] :
( ( ( between @ SV56 @ SV27 @ SV68 )
= $false )
| ( ( ( SV10 = SV27 )
| ( between @ SV10 @ SV56 @ ( euclid2 @ SV42 @ SV10 @ SV56 @ SV68 @ SV27 ) ) )
= $true )
| ( ( between @ SV10 @ SV27 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(195,plain,
! [SV43: $i,SV11: $i,SV69: $i,SV28: $i,SV57: $i] :
( ( ( between @ SV57 @ SV28 @ SV69 )
= $false )
| ( ( ( SV11 = SV28 )
| ( between @ ( euclid1 @ SV43 @ SV11 @ SV57 @ SV69 @ SV28 ) @ SV43 @ ( euclid2 @ SV43 @ SV11 @ SV57 @ SV69 @ SV28 ) ) )
= $true )
| ( ( between @ SV11 @ SV28 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(196,plain,
! [SV79: $i,SV78: $i,SV75: $i,SV70: $i,SV58: $i,SV44: $i,SV29: $i,SV12: $i] :
( ( ( ~ ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 ) )
= $true )
| ( ( ~ ( equidistant @ SV29 @ SV70 @ SV58 @ SV75 )
| ~ ( equidistant @ SV12 @ SV78 @ SV44 @ SV79 )
| ~ ( equidistant @ SV29 @ SV78 @ SV58 @ SV79 )
| ~ ( between @ SV12 @ SV29 @ SV70 )
| ~ ( between @ SV44 @ SV58 @ SV75 )
| ( SV12 = SV29 )
| ( equidistant @ SV70 @ SV78 @ SV75 @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[185]) ).
thf(197,plain,
! [SV15: $i,SV71: $i,SV47: $i,SV32: $i,SV61: $i] :
( ( ( equidistant @ SV61 @ SV32 @ SV61 @ SV47 )
= $false )
| ( ( ~ ( equidistant @ SV71 @ SV32 @ SV71 @ SV47 )
| ( between @ SV15 @ SV61 @ SV71 )
| ( between @ SV61 @ SV71 @ SV15 )
| ( between @ SV71 @ SV15 @ SV61 )
| ( SV32 = SV47 ) )
= $true )
| ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(198,plain,
! [SV48: $i,SV76: $i,SV33: $i,SV72: $i,SV62: $i,SV16: $i] :
( ( ( ~ ( equidistant @ SV16 @ SV62 @ SV16 @ SV72 ) )
= $true )
| ( ( ~ ( between @ SV16 @ SV33 @ SV62 )
| ~ ( between @ SV33 @ SV76 @ SV62 )
| ( equidistant @ SV16 @ SV76 @ SV16 @ ( continuous @ SV33 @ SV76 @ SV62 @ SV48 @ SV72 @ SV16 ) ) )
= $true )
| ( ( equidistant @ SV16 @ SV33 @ SV16 @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[187]) ).
thf(199,plain,
! [SV49: $i,SV77: $i,SV34: $i,SV73: $i,SV63: $i,SV17: $i] :
( ( ( ~ ( equidistant @ SV17 @ SV63 @ SV17 @ SV73 ) )
= $true )
| ( ( ~ ( between @ SV17 @ SV34 @ SV63 )
| ~ ( between @ SV34 @ SV77 @ SV63 )
| ( between @ SV49 @ ( continuous @ SV34 @ SV77 @ SV63 @ SV49 @ SV73 @ SV17 ) @ SV73 ) )
= $true )
| ( ( equidistant @ SV17 @ SV34 @ SV17 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[188]) ).
thf(200,plain,
! [SV20: $i,SV51: $i,SV36: $i,SV3: $i] :
( ( ( between @ SV3 @ SV36 @ SV51 )
= $true )
| ( ( between @ SV3 @ SV51 @ SV36 )
= $true )
| ( ( SV3 = SV20 )
= $true )
| ( ( between @ SV3 @ SV20 @ SV51 )
= $false )
| ( ( between @ SV3 @ SV20 @ SV36 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[189]) ).
thf(201,plain,
! [SV52: $i,SV38: $i,SV74: $i,SV64: $i,SV23: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV23 @ SV64 @ SV74 )
= $false )
| ( ( equidistant @ SV38 @ SV52 @ SV64 @ SV74 )
= $true )
| ( ( equidistant @ SV6 @ SV23 @ SV38 @ SV52 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[190]) ).
thf(202,plain,
! [SV55: $i,SV41: $i,SV67: $i,SV26: $i,SV9: $i] :
( ( ( SV9 = SV26 )
= $true )
| ( ( between @ SV9 @ SV67 @ ( euclid1 @ SV41 @ SV9 @ SV55 @ SV67 @ SV26 ) )
= $true )
| ( ( between @ SV55 @ SV26 @ SV67 )
= $false )
| ( ( between @ SV9 @ SV26 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(203,plain,
! [SV68: $i,SV42: $i,SV56: $i,SV27: $i,SV10: $i] :
( ( ( SV10 = SV27 )
= $true )
| ( ( between @ SV10 @ SV56 @ ( euclid2 @ SV42 @ SV10 @ SV56 @ SV68 @ SV27 ) )
= $true )
| ( ( between @ SV56 @ SV27 @ SV68 )
= $false )
| ( ( between @ SV10 @ SV27 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(204,plain,
! [SV69: $i,SV57: $i,SV43: $i,SV28: $i,SV11: $i] :
( ( ( SV11 = SV28 )
= $true )
| ( ( between @ ( euclid1 @ SV43 @ SV11 @ SV57 @ SV69 @ SV28 ) @ SV43 @ ( euclid2 @ SV43 @ SV11 @ SV57 @ SV69 @ SV28 ) )
= $true )
| ( ( between @ SV57 @ SV28 @ SV69 )
= $false )
| ( ( between @ SV11 @ SV28 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(205,plain,
! [SV79: $i,SV78: $i,SV75: $i,SV70: $i,SV58: $i,SV44: $i,SV29: $i,SV12: $i] :
( ( ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
= $false )
| ( ( ~ ( equidistant @ SV29 @ SV70 @ SV58 @ SV75 )
| ~ ( equidistant @ SV12 @ SV78 @ SV44 @ SV79 )
| ~ ( equidistant @ SV29 @ SV78 @ SV58 @ SV79 )
| ~ ( between @ SV12 @ SV29 @ SV70 )
| ~ ( between @ SV44 @ SV58 @ SV75 )
| ( SV12 = SV29 )
| ( equidistant @ SV70 @ SV78 @ SV75 @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[196]) ).
thf(206,plain,
! [SV61: $i,SV15: $i,SV47: $i,SV32: $i,SV71: $i] :
( ( ( ~ ( equidistant @ SV71 @ SV32 @ SV71 @ SV47 ) )
= $true )
| ( ( ( between @ SV15 @ SV61 @ SV71 )
| ( between @ SV61 @ SV71 @ SV15 )
| ( between @ SV71 @ SV15 @ SV61 )
| ( SV32 = SV47 ) )
= $true )
| ( ( equidistant @ SV61 @ SV32 @ SV61 @ SV47 )
= $false )
| ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[197]) ).
thf(207,plain,
! [SV48: $i,SV76: $i,SV33: $i,SV72: $i,SV62: $i,SV16: $i] :
( ( ( equidistant @ SV16 @ SV62 @ SV16 @ SV72 )
= $false )
| ( ( ~ ( between @ SV16 @ SV33 @ SV62 )
| ~ ( between @ SV33 @ SV76 @ SV62 )
| ( equidistant @ SV16 @ SV76 @ SV16 @ ( continuous @ SV33 @ SV76 @ SV62 @ SV48 @ SV72 @ SV16 ) ) )
= $true )
| ( ( equidistant @ SV16 @ SV33 @ SV16 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[198]) ).
thf(208,plain,
! [SV49: $i,SV77: $i,SV34: $i,SV73: $i,SV63: $i,SV17: $i] :
( ( ( equidistant @ SV17 @ SV63 @ SV17 @ SV73 )
= $false )
| ( ( ~ ( between @ SV17 @ SV34 @ SV63 )
| ~ ( between @ SV34 @ SV77 @ SV63 )
| ( between @ SV49 @ ( continuous @ SV34 @ SV77 @ SV63 @ SV49 @ SV73 @ SV17 ) @ SV73 ) )
= $true )
| ( ( equidistant @ SV17 @ SV34 @ SV17 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(209,plain,
! [SV79: $i,SV44: $i,SV78: $i,SV12: $i,SV75: $i,SV58: $i,SV70: $i,SV29: $i] :
( ( ( ~ ( equidistant @ SV29 @ SV70 @ SV58 @ SV75 ) )
= $true )
| ( ( ~ ( equidistant @ SV12 @ SV78 @ SV44 @ SV79 )
| ~ ( equidistant @ SV29 @ SV78 @ SV58 @ SV79 )
| ~ ( between @ SV12 @ SV29 @ SV70 )
| ~ ( between @ SV44 @ SV58 @ SV75 )
| ( SV12 = SV29 )
| ( equidistant @ SV70 @ SV78 @ SV75 @ SV79 ) )
= $true )
| ( ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[205]) ).
thf(210,plain,
! [SV61: $i,SV15: $i,SV47: $i,SV32: $i,SV71: $i] :
( ( ( equidistant @ SV71 @ SV32 @ SV71 @ SV47 )
= $false )
| ( ( ( between @ SV15 @ SV61 @ SV71 )
| ( between @ SV61 @ SV71 @ SV15 )
| ( between @ SV71 @ SV15 @ SV61 )
| ( SV32 = SV47 ) )
= $true )
| ( ( equidistant @ SV61 @ SV32 @ SV61 @ SV47 )
= $false )
| ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[206]) ).
thf(211,plain,
! [SV72: $i,SV48: $i,SV76: $i,SV62: $i,SV33: $i,SV16: $i] :
( ( ( ~ ( between @ SV16 @ SV33 @ SV62 ) )
= $true )
| ( ( ~ ( between @ SV33 @ SV76 @ SV62 )
| ( equidistant @ SV16 @ SV76 @ SV16 @ ( continuous @ SV33 @ SV76 @ SV62 @ SV48 @ SV72 @ SV16 ) ) )
= $true )
| ( ( equidistant @ SV16 @ SV62 @ SV16 @ SV72 )
= $false )
| ( ( equidistant @ SV16 @ SV33 @ SV16 @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[207]) ).
thf(212,plain,
! [SV73: $i,SV49: $i,SV77: $i,SV63: $i,SV34: $i,SV17: $i] :
( ( ( ~ ( between @ SV17 @ SV34 @ SV63 ) )
= $true )
| ( ( ~ ( between @ SV34 @ SV77 @ SV63 )
| ( between @ SV49 @ ( continuous @ SV34 @ SV77 @ SV63 @ SV49 @ SV73 @ SV17 ) @ SV73 ) )
= $true )
| ( ( equidistant @ SV17 @ SV63 @ SV17 @ SV73 )
= $false )
| ( ( equidistant @ SV17 @ SV34 @ SV17 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[208]) ).
thf(213,plain,
! [SV79: $i,SV44: $i,SV78: $i,SV12: $i,SV75: $i,SV58: $i,SV70: $i,SV29: $i] :
( ( ( equidistant @ SV29 @ SV70 @ SV58 @ SV75 )
= $false )
| ( ( ~ ( equidistant @ SV12 @ SV78 @ SV44 @ SV79 )
| ~ ( equidistant @ SV29 @ SV78 @ SV58 @ SV79 )
| ~ ( between @ SV12 @ SV29 @ SV70 )
| ~ ( between @ SV44 @ SV58 @ SV75 )
| ( SV12 = SV29 )
| ( equidistant @ SV70 @ SV78 @ SV75 @ SV79 ) )
= $true )
| ( ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[209]) ).
thf(214,plain,
! [SV47: $i,SV32: $i,SV71: $i,SV61: $i,SV15: $i] :
( ( ( between @ SV15 @ SV61 @ SV71 )
= $true )
| ( ( ( between @ SV61 @ SV71 @ SV15 )
| ( between @ SV71 @ SV15 @ SV61 )
| ( SV32 = SV47 ) )
= $true )
| ( ( equidistant @ SV71 @ SV32 @ SV71 @ SV47 )
= $false )
| ( ( equidistant @ SV61 @ SV32 @ SV61 @ SV47 )
= $false )
| ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(215,plain,
! [SV72: $i,SV48: $i,SV76: $i,SV62: $i,SV33: $i,SV16: $i] :
( ( ( between @ SV16 @ SV33 @ SV62 )
= $false )
| ( ( ~ ( between @ SV33 @ SV76 @ SV62 )
| ( equidistant @ SV16 @ SV76 @ SV16 @ ( continuous @ SV33 @ SV76 @ SV62 @ SV48 @ SV72 @ SV16 ) ) )
= $true )
| ( ( equidistant @ SV16 @ SV62 @ SV16 @ SV72 )
= $false )
| ( ( equidistant @ SV16 @ SV33 @ SV16 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[211]) ).
thf(216,plain,
! [SV73: $i,SV49: $i,SV77: $i,SV63: $i,SV34: $i,SV17: $i] :
( ( ( between @ SV17 @ SV34 @ SV63 )
= $false )
| ( ( ~ ( between @ SV34 @ SV77 @ SV63 )
| ( between @ SV49 @ ( continuous @ SV34 @ SV77 @ SV63 @ SV49 @ SV73 @ SV17 ) @ SV73 ) )
= $true )
| ( ( equidistant @ SV17 @ SV63 @ SV17 @ SV73 )
= $false )
| ( ( equidistant @ SV17 @ SV34 @ SV17 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[212]) ).
thf(217,plain,
! [SV75: $i,SV70: $i,SV58: $i,SV29: $i,SV79: $i,SV44: $i,SV78: $i,SV12: $i] :
( ( ( ~ ( equidistant @ SV12 @ SV78 @ SV44 @ SV79 ) )
= $true )
| ( ( ~ ( equidistant @ SV29 @ SV78 @ SV58 @ SV79 )
| ~ ( between @ SV12 @ SV29 @ SV70 )
| ~ ( between @ SV44 @ SV58 @ SV75 )
| ( SV12 = SV29 )
| ( equidistant @ SV70 @ SV78 @ SV75 @ SV79 ) )
= $true )
| ( ( equidistant @ SV29 @ SV70 @ SV58 @ SV75 )
= $false )
| ( ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[213]) ).
thf(218,plain,
! [SV47: $i,SV32: $i,SV15: $i,SV71: $i,SV61: $i] :
( ( ( between @ SV61 @ SV71 @ SV15 )
= $true )
| ( ( ( between @ SV71 @ SV15 @ SV61 )
| ( SV32 = SV47 ) )
= $true )
| ( ( between @ SV15 @ SV61 @ SV71 )
= $true )
| ( ( equidistant @ SV71 @ SV32 @ SV71 @ SV47 )
= $false )
| ( ( equidistant @ SV61 @ SV32 @ SV61 @ SV47 )
= $false )
| ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(219,plain,
! [SV72: $i,SV48: $i,SV16: $i,SV62: $i,SV76: $i,SV33: $i] :
( ( ( ~ ( between @ SV33 @ SV76 @ SV62 ) )
= $true )
| ( ( equidistant @ SV16 @ SV76 @ SV16 @ ( continuous @ SV33 @ SV76 @ SV62 @ SV48 @ SV72 @ SV16 ) )
= $true )
| ( ( between @ SV16 @ SV33 @ SV62 )
= $false )
| ( ( equidistant @ SV16 @ SV62 @ SV16 @ SV72 )
= $false )
| ( ( equidistant @ SV16 @ SV33 @ SV16 @ SV48 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[215]) ).
thf(220,plain,
! [SV17: $i,SV73: $i,SV49: $i,SV63: $i,SV77: $i,SV34: $i] :
( ( ( ~ ( between @ SV34 @ SV77 @ SV63 ) )
= $true )
| ( ( between @ SV49 @ ( continuous @ SV34 @ SV77 @ SV63 @ SV49 @ SV73 @ SV17 ) @ SV73 )
= $true )
| ( ( between @ SV17 @ SV34 @ SV63 )
= $false )
| ( ( equidistant @ SV17 @ SV63 @ SV17 @ SV73 )
= $false )
| ( ( equidistant @ SV17 @ SV34 @ SV17 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[216]) ).
thf(221,plain,
! [SV75: $i,SV70: $i,SV58: $i,SV29: $i,SV79: $i,SV44: $i,SV78: $i,SV12: $i] :
( ( ( equidistant @ SV12 @ SV78 @ SV44 @ SV79 )
= $false )
| ( ( ~ ( equidistant @ SV29 @ SV78 @ SV58 @ SV79 )
| ~ ( between @ SV12 @ SV29 @ SV70 )
| ~ ( between @ SV44 @ SV58 @ SV75 )
| ( SV12 = SV29 )
| ( equidistant @ SV70 @ SV78 @ SV75 @ SV79 ) )
= $true )
| ( ( equidistant @ SV29 @ SV70 @ SV58 @ SV75 )
= $false )
| ( ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[217]) ).
thf(222,plain,
! [SV47: $i,SV32: $i,SV61: $i,SV15: $i,SV71: $i] :
( ( ( between @ SV71 @ SV15 @ SV61 )
= $true )
| ( ( SV32 = SV47 )
= $true )
| ( ( between @ SV61 @ SV71 @ SV15 )
= $true )
| ( ( between @ SV15 @ SV61 @ SV71 )
= $true )
| ( ( equidistant @ SV71 @ SV32 @ SV71 @ SV47 )
= $false )
| ( ( equidistant @ SV61 @ SV32 @ SV61 @ SV47 )
= $false )
| ( ( equidistant @ SV15 @ SV32 @ SV15 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[218]) ).
thf(223,plain,
! [SV72: $i,SV48: $i,SV16: $i,SV62: $i,SV76: $i,SV33: $i] :
( ( ( between @ SV33 @ SV76 @ SV62 )
= $false )
| ( ( equidistant @ SV16 @ SV76 @ SV16 @ ( continuous @ SV33 @ SV76 @ SV62 @ SV48 @ SV72 @ SV16 ) )
= $true )
| ( ( between @ SV16 @ SV33 @ SV62 )
= $false )
| ( ( equidistant @ SV16 @ SV62 @ SV16 @ SV72 )
= $false )
| ( ( equidistant @ SV16 @ SV33 @ SV16 @ SV48 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[219]) ).
thf(224,plain,
! [SV17: $i,SV73: $i,SV49: $i,SV63: $i,SV77: $i,SV34: $i] :
( ( ( between @ SV34 @ SV77 @ SV63 )
= $false )
| ( ( between @ SV49 @ ( continuous @ SV34 @ SV77 @ SV63 @ SV49 @ SV73 @ SV17 ) @ SV73 )
= $true )
| ( ( between @ SV17 @ SV34 @ SV63 )
= $false )
| ( ( equidistant @ SV17 @ SV63 @ SV17 @ SV73 )
= $false )
| ( ( equidistant @ SV17 @ SV34 @ SV17 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[220]) ).
thf(225,plain,
! [SV75: $i,SV44: $i,SV70: $i,SV12: $i,SV79: $i,SV58: $i,SV78: $i,SV29: $i] :
( ( ( ~ ( equidistant @ SV29 @ SV78 @ SV58 @ SV79 ) )
= $true )
| ( ( ~ ( between @ SV12 @ SV29 @ SV70 )
| ~ ( between @ SV44 @ SV58 @ SV75 )
| ( SV12 = SV29 )
| ( equidistant @ SV70 @ SV78 @ SV75 @ SV79 ) )
= $true )
| ( ( equidistant @ SV12 @ SV78 @ SV44 @ SV79 )
= $false )
| ( ( equidistant @ SV29 @ SV70 @ SV58 @ SV75 )
= $false )
| ( ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[221]) ).
thf(226,plain,
! [SV75: $i,SV44: $i,SV70: $i,SV12: $i,SV79: $i,SV58: $i,SV78: $i,SV29: $i] :
( ( ( equidistant @ SV29 @ SV78 @ SV58 @ SV79 )
= $false )
| ( ( ~ ( between @ SV12 @ SV29 @ SV70 )
| ~ ( between @ SV44 @ SV58 @ SV75 )
| ( SV12 = SV29 )
| ( equidistant @ SV70 @ SV78 @ SV75 @ SV79 ) )
= $true )
| ( ( equidistant @ SV12 @ SV78 @ SV44 @ SV79 )
= $false )
| ( ( equidistant @ SV29 @ SV70 @ SV58 @ SV75 )
= $false )
| ( ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(227,plain,
! [SV79: $i,SV78: $i,SV75: $i,SV58: $i,SV44: $i,SV70: $i,SV29: $i,SV12: $i] :
( ( ( ~ ( between @ SV12 @ SV29 @ SV70 ) )
= $true )
| ( ( ~ ( between @ SV44 @ SV58 @ SV75 )
| ( SV12 = SV29 )
| ( equidistant @ SV70 @ SV78 @ SV75 @ SV79 ) )
= $true )
| ( ( equidistant @ SV29 @ SV78 @ SV58 @ SV79 )
= $false )
| ( ( equidistant @ SV12 @ SV78 @ SV44 @ SV79 )
= $false )
| ( ( equidistant @ SV29 @ SV70 @ SV58 @ SV75 )
= $false )
| ( ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(228,plain,
! [SV79: $i,SV78: $i,SV75: $i,SV58: $i,SV44: $i,SV70: $i,SV29: $i,SV12: $i] :
( ( ( between @ SV12 @ SV29 @ SV70 )
= $false )
| ( ( ~ ( between @ SV44 @ SV58 @ SV75 )
| ( SV12 = SV29 )
| ( equidistant @ SV70 @ SV78 @ SV75 @ SV79 ) )
= $true )
| ( ( equidistant @ SV29 @ SV78 @ SV58 @ SV79 )
= $false )
| ( ( equidistant @ SV12 @ SV78 @ SV44 @ SV79 )
= $false )
| ( ( equidistant @ SV29 @ SV70 @ SV58 @ SV75 )
= $false )
| ( ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[227]) ).
thf(229,plain,
! [SV79: $i,SV78: $i,SV70: $i,SV29: $i,SV12: $i,SV75: $i,SV58: $i,SV44: $i] :
( ( ( ~ ( between @ SV44 @ SV58 @ SV75 ) )
= $true )
| ( ( ( SV12 = SV29 )
| ( equidistant @ SV70 @ SV78 @ SV75 @ SV79 ) )
= $true )
| ( ( between @ SV12 @ SV29 @ SV70 )
= $false )
| ( ( equidistant @ SV29 @ SV78 @ SV58 @ SV79 )
= $false )
| ( ( equidistant @ SV12 @ SV78 @ SV44 @ SV79 )
= $false )
| ( ( equidistant @ SV29 @ SV70 @ SV58 @ SV75 )
= $false )
| ( ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[228]) ).
thf(230,plain,
! [SV79: $i,SV78: $i,SV70: $i,SV29: $i,SV12: $i,SV75: $i,SV58: $i,SV44: $i] :
( ( ( between @ SV44 @ SV58 @ SV75 )
= $false )
| ( ( ( SV12 = SV29 )
| ( equidistant @ SV70 @ SV78 @ SV75 @ SV79 ) )
= $true )
| ( ( between @ SV12 @ SV29 @ SV70 )
= $false )
| ( ( equidistant @ SV29 @ SV78 @ SV58 @ SV79 )
= $false )
| ( ( equidistant @ SV12 @ SV78 @ SV44 @ SV79 )
= $false )
| ( ( equidistant @ SV29 @ SV70 @ SV58 @ SV75 )
= $false )
| ( ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[229]) ).
thf(231,plain,
! [SV58: $i,SV44: $i,SV79: $i,SV75: $i,SV78: $i,SV70: $i,SV29: $i,SV12: $i] :
( ( ( SV12 = SV29 )
= $true )
| ( ( equidistant @ SV70 @ SV78 @ SV75 @ SV79 )
= $true )
| ( ( between @ SV44 @ SV58 @ SV75 )
= $false )
| ( ( between @ SV12 @ SV29 @ SV70 )
= $false )
| ( ( equidistant @ SV29 @ SV78 @ SV58 @ SV79 )
= $false )
| ( ( equidistant @ SV12 @ SV78 @ SV44 @ SV79 )
= $false )
| ( ( equidistant @ SV29 @ SV70 @ SV58 @ SV75 )
= $false )
| ( ( equidistant @ SV12 @ SV29 @ SV44 @ SV58 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[230]) ).
thf(232,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[69,231,224,223,222,204,203,202,201,200,192,191,177,142,136,135,124,94,90,86,85,84]) ).
thf(233,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO003-1 : TPTP v9.3.1. Bugfixed v2.5.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.22 % Computer : n009.cluster.edu
% 0.09/0.22 % Model : x86_64 x86_64
% 0.09/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.22 % Memory : 8046.5625MB
% 0.09/0.22 % OS : Linux 6.8.0-71-generic
% 0.09/0.22 % CPULimit : 300
% 0.09/0.22 % WCLimit : 300
% 0.09/0.22 % DateTime : Tue Oct 6 10:01:02 UTC 2026
% 0.09/0.23 % CPUTime :
% 0.09/0.23 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.87/0.39
% 0.87/0.39 No.of.Axioms: 21
% 0.87/0.39
% 0.87/0.39 Length.of.Defs: 0
% 0.87/0.39
% 0.87/0.39 Contains.Choice.Funs: false
% 0.87/0.39 ........
% 0.87/0.39
% 0.87/0.39 ********************************
% 0.87/0.39 * All subproblems solved! *
% 0.87/0.39 ********************************
% 0.87/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:21,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:232,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.87/0.39
% 0.87/0.39 %**** Beginning of derivation protocol ****
% 0.87/0.39 % SZS output start CNFRefutation
% See solution above
% 0.87/0.39
% 0.87/0.39 %**** End of derivation protocol ****
% 0.87/0.39 %**** no. of clauses in derivation: 233 ****
% 0.87/0.39 %**** clause counter: 232 ****
% 0.87/0.39
% 0.87/0.39 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:21,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:false,expand_extuni:false,foatp:e,atp_timeout:299,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:232,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------