TSTP Solution File: GEO058-2 by LEO-II---1.7.0
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- Process Solution
%------------------------------------------------------------------------------
% File : LEO-II---1.7.0
% Problem : GEO058-2 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Sat Jul 16 05:06:37 EDT 2022
% Result : Unsatisfiable 0.51s 0.76s
% Output : CNFRefutation 0.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 35
% Syntax : Number of formulae : 242 ( 127 unt; 13 typ; 0 def)
% Number of atoms : 1676 ( 513 equ; 0 cnn)
% Maximal formula atoms : 8 ( 7 avg)
% Number of connectives : 4359 ( 392 ~; 649 |; 0 &;3318 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 7 con; 0-6 aty)
% Number of variables : 1047 ( 0 ^1047 !; 0 ?;1047 :)
% 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,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
thf(2,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(3,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(4,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(5,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(6,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(7,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(8,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(9,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(10,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(11,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(12,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(13,axiom,
! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(14,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(15,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(16,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(17,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(18,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(19,axiom,
! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(20,axiom,
( v
= ( reflection @ u @ v ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_equals_reflection) ).
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,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_u_equals_v) ).
thf(24,plain,
$false = $false,
inference(unfold_def,[status(thm)],[22]) ).
thf(25,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[1]) ).
thf(26,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)],[2]) ).
thf(27,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)],[3]) ).
thf(28,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)],[4]) ).
thf(29,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)],[5]) ).
thf(30,plain,
( ( ! [U: $i,W: $i,Y: $i,V: $i,X: $i] :
( ~ ( between @ U @ W @ Y )
| ~ ( between @ V @ W @ X )
| ( U = W )
| ( between @ U @ V @ ( euclid1 @ U @ V @ W @ X @ Y ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[6]) ).
thf(31,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)],[7]) ).
thf(32,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(unfold_def,[status(thm)],[8]) ).
thf(33,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(unfold_def,[status(thm)],[9]) ).
thf(34,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(unfold_def,[status(thm)],[10]) ).
thf(35,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)],[11]) ).
thf(36,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)],[12]) ).
thf(37,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[13]) ).
thf(38,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)],[14]) ).
thf(39,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(unfold_def,[status(thm)],[15]) ).
thf(40,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(unfold_def,[status(thm)],[16]) ).
thf(41,plain,
( ( ! [X: $i,Y: $i,Z: $i] :
( ~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(unfold_def,[status(thm)],[17]) ).
thf(42,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)],[18]) ).
thf(43,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(unfold_def,[status(thm)],[19]) ).
thf(44,plain,
( ( v
= ( reflection @ u @ v ) )
= $true ),
inference(unfold_def,[status(thm)],[20]) ).
thf(45,plain,
( ( ( u != v ) )
= $true ),
inference(unfold_def,[status(thm)],[23]) ).
thf(46,plain,
( ( ~ $false )
= $true ),
inference(polarity_switch,[status(thm)],[24]) ).
thf(47,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)],[26]) ).
thf(48,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)],[27]) ).
thf(49,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)],[28]) ).
thf(50,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)],[29]) ).
thf(51,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)],[30]) ).
thf(52,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)],[31]) ).
thf(53,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)],[35]) ).
thf(54,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)],[36]) ).
thf(55,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)],[38]) ).
thf(56,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(57,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)],[42]) ).
thf(58,plain,
( ( ( u != v ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(59,plain,
( ( ( u != v ) )
= $true ),
inference(copy,[status(thm)],[58]) ).
thf(60,plain,
( ( v
= ( reflection @ u @ v ) )
= $true ),
inference(copy,[status(thm)],[44]) ).
thf(61,plain,
( ( ! [X: $i,Y: $i] : ( equidistant @ X @ Y @ Y @ X ) )
= $true ),
inference(copy,[status(thm)],[43]) ).
thf(62,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)],[57]) ).
thf(63,plain,
( ( ! [X: $i,Y: $i] :
( ! [Z: $i] :
~ ( equidistant @ X @ Y @ Z @ Z )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[56]) ).
thf(64,plain,
( ( ! [X: $i,Y: $i,W: $i,V: $i] : ( between @ X @ Y @ ( extension @ X @ Y @ W @ V ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(65,plain,
( ( ! [Y: $i,X: $i,W: $i,V: $i] : ( equidistant @ Y @ ( extension @ X @ Y @ W @ V ) @ W @ V ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(66,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)],[55]) ).
thf(67,plain,
( ( ! [X: $i,Y: $i] :
( ~ ( between @ X @ Y @ X )
| ( X = Y ) ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(68,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)],[54]) ).
thf(69,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)],[53]) ).
thf(70,plain,
( ( ~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ) )
= $true ),
inference(copy,[status(thm)],[34]) ).
thf(71,plain,
( ( ~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(72,plain,
( ( ~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(73,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)],[52]) ).
thf(74,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)],[51]) ).
thf(75,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)],[50]) ).
thf(76,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)],[49]) ).
thf(77,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)],[48]) ).
thf(78,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)],[47]) ).
thf(79,plain,
( ( ! [U: $i,V: $i] :
( ( reflection @ U @ V )
= ( extension @ U @ V @ U @ V ) ) )
= $true ),
inference(copy,[status(thm)],[25]) ).
thf(80,plain,
( ( ~ $false )
= $true ),
inference(copy,[status(thm)],[46]) ).
thf(81,plain,
( ( u = v )
= $false ),
inference(extcnf_not_pos,[status(thm)],[59]) ).
thf(82,plain,
! [SV1: $i] :
( ( ! [SY73: $i] : ( equidistant @ SV1 @ SY73 @ SY73 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[61]) ).
thf(83,plain,
! [SV2: $i] :
( ( ! [SY74: $i,SY75: $i,SY76: $i] :
( ~ ( equidistant @ SV2 @ SY74 @ SY75 @ SY76 )
| ! [SY77: $i,SY78: $i] :
( ~ ( equidistant @ SV2 @ SY74 @ SY77 @ SY78 )
| ( equidistant @ SY75 @ SY76 @ SY77 @ SY78 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[62]) ).
thf(84,plain,
! [SV3: $i] :
( ( ! [SY79: $i] :
( ! [SY80: $i] :
~ ( equidistant @ SV3 @ SY79 @ SY80 @ SY80 )
| ( SV3 = SY79 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[63]) ).
thf(85,plain,
! [SV4: $i] :
( ( ! [SY81: $i,SY82: $i,SY83: $i] : ( between @ SV4 @ SY81 @ ( extension @ SV4 @ SY81 @ SY82 @ SY83 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[64]) ).
thf(86,plain,
! [SV5: $i] :
( ( ! [SY84: $i,SY85: $i,SY86: $i] : ( equidistant @ SV5 @ ( extension @ SY84 @ SV5 @ SY85 @ SY86 ) @ SY85 @ SY86 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[65]) ).
thf(87,plain,
! [SV6: $i] :
( ( ! [SY87: $i,SY88: $i,SY89: $i,SY90: $i,SY91: $i] :
( ~ ( equidistant @ SV6 @ SY87 @ SY88 @ SY89 )
| ~ ( equidistant @ SY87 @ SY90 @ SY89 @ SY91 )
| ! [SY92: $i,SY93: $i] :
( ~ ( equidistant @ SV6 @ SY92 @ SY88 @ SY93 )
| ~ ( equidistant @ SY87 @ SY92 @ SY89 @ SY93 )
| ~ ( between @ SV6 @ SY87 @ SY90 )
| ~ ( between @ SY88 @ SY89 @ SY91 )
| ( SV6 = SY87 )
| ( equidistant @ SY90 @ SY92 @ SY91 @ SY93 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[66]) ).
thf(88,plain,
! [SV7: $i] :
( ( ! [SY94: $i] :
( ~ ( between @ SV7 @ SY94 @ SV7 )
| ( SV7 = SY94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[67]) ).
thf(89,plain,
! [SV8: $i] :
( ( ! [SY95: $i,SY96: $i] :
( ~ ( between @ SV8 @ SY95 @ SY96 )
| ! [SY97: $i,SY98: $i] :
( ~ ( between @ SY97 @ SY98 @ SY96 )
| ( between @ SY95 @ ( inner_pasch @ SV8 @ SY95 @ SY96 @ SY98 @ SY97 ) @ SY97 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[68]) ).
thf(90,plain,
! [SV9: $i] :
( ( ! [SY99: $i,SY100: $i] :
( ~ ( between @ SV9 @ SY99 @ SY100 )
| ! [SY101: $i,SY102: $i] :
( ~ ( between @ SY101 @ SY102 @ SY100 )
| ( between @ SY102 @ ( inner_pasch @ SV9 @ SY99 @ SY100 @ SY102 @ SY101 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[69]) ).
thf(91,plain,
( ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[70]) ).
thf(92,plain,
( ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[71]) ).
thf(93,plain,
( ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[72]) ).
thf(94,plain,
! [SV10: $i] :
( ( ! [SY103: $i,SY104: $i] :
( ~ ( equidistant @ SV10 @ SY103 @ SV10 @ SY104 )
| ! [SY105: $i] :
( ~ ( equidistant @ SY105 @ SY103 @ SY105 @ SY104 )
| ! [SY106: $i] :
( ~ ( equidistant @ SY106 @ SY103 @ SY106 @ SY104 )
| ( between @ SV10 @ SY105 @ SY106 )
| ( between @ SY105 @ SY106 @ SV10 )
| ( SY103 = SY104 )
| ( between @ SY106 @ SV10 @ SY105 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[73]) ).
thf(95,plain,
! [SV11: $i] :
( ( ! [SY107: $i,SY108: $i] :
( ~ ( between @ SV11 @ SY107 @ SY108 )
| ! [SY109: $i,SY110: $i] :
( ~ ( between @ SY109 @ SY107 @ SY110 )
| ( SV11 = SY107 )
| ( between @ SV11 @ SY109 @ ( euclid1 @ SV11 @ SY109 @ SY107 @ SY110 @ SY108 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[74]) ).
thf(96,plain,
! [SV12: $i] :
( ( ! [SY111: $i,SY112: $i] :
( ~ ( between @ SV12 @ SY111 @ SY112 )
| ! [SY113: $i,SY114: $i] :
( ~ ( between @ SY113 @ SY111 @ SY114 )
| ( SV12 = SY111 )
| ( between @ SV12 @ SY114 @ ( euclid2 @ SV12 @ SY113 @ SY111 @ SY114 @ SY112 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[75]) ).
thf(97,plain,
! [SV13: $i] :
( ( ! [SY115: $i,SY116: $i] :
( ~ ( between @ SV13 @ SY115 @ SY116 )
| ! [SY117: $i,SY118: $i] :
( ~ ( between @ SY117 @ SY115 @ SY118 )
| ( SV13 = SY115 )
| ( between @ ( euclid1 @ SV13 @ SY117 @ SY115 @ SY118 @ SY116 ) @ SY116 @ ( euclid2 @ SV13 @ SY117 @ SY115 @ SY118 @ SY116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[76]) ).
thf(98,plain,
! [SV14: $i] :
( ( ! [SY119: $i,SY120: $i,SY121: $i] :
( ~ ( equidistant @ SV14 @ SY119 @ SV14 @ SY120 )
| ! [SY122: $i] :
( ~ ( equidistant @ SV14 @ SY121 @ SV14 @ SY122 )
| ~ ( between @ SV14 @ SY119 @ SY121 )
| ! [SY123: $i] :
( ~ ( between @ SY119 @ SY123 @ SY121 )
| ( between @ SY120 @ ( continuous @ SV14 @ SY119 @ SY120 @ SY123 @ SY121 @ SY122 ) @ SY122 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[77]) ).
thf(99,plain,
! [SV15: $i] :
( ( ! [SY124: $i,SY125: $i,SY126: $i] :
( ~ ( equidistant @ SV15 @ SY124 @ SV15 @ SY125 )
| ! [SY127: $i] :
( ~ ( equidistant @ SV15 @ SY126 @ SV15 @ SY127 )
| ~ ( between @ SV15 @ SY124 @ SY126 )
| ! [SY128: $i] :
( ~ ( between @ SY124 @ SY128 @ SY126 )
| ( equidistant @ SV15 @ SY128 @ SV15 @ ( continuous @ SV15 @ SY124 @ SY125 @ SY128 @ SY126 @ SY127 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[78]) ).
thf(100,plain,
! [SV16: $i] :
( ( ! [SY129: $i] :
( ( reflection @ SV16 @ SY129 )
= ( extension @ SV16 @ SY129 @ SV16 @ SY129 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[79]) ).
thf(101,plain,
$false = $false,
inference(extcnf_not_pos,[status(thm)],[80]) ).
thf(102,plain,
! [SV17: $i,SV1: $i] :
( ( equidistant @ SV1 @ SV17 @ SV17 @ SV1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[82]) ).
thf(103,plain,
! [SV18: $i,SV2: $i] :
( ( ! [SY130: $i,SY131: $i] :
( ~ ( equidistant @ SV2 @ SV18 @ SY130 @ SY131 )
| ! [SY132: $i,SY133: $i] :
( ~ ( equidistant @ SV2 @ SV18 @ SY132 @ SY133 )
| ( equidistant @ SY130 @ SY131 @ SY132 @ SY133 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[83]) ).
thf(104,plain,
! [SV19: $i,SV3: $i] :
( ( ! [SY134: $i] :
~ ( equidistant @ SV3 @ SV19 @ SY134 @ SY134 )
| ( SV3 = SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[84]) ).
thf(105,plain,
! [SV20: $i,SV4: $i] :
( ( ! [SY135: $i,SY136: $i] : ( between @ SV4 @ SV20 @ ( extension @ SV4 @ SV20 @ SY135 @ SY136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[85]) ).
thf(106,plain,
! [SV21: $i,SV5: $i] :
( ( ! [SY137: $i,SY138: $i] : ( equidistant @ SV5 @ ( extension @ SV21 @ SV5 @ SY137 @ SY138 ) @ SY137 @ SY138 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[86]) ).
thf(107,plain,
! [SV22: $i,SV6: $i] :
( ( ! [SY139: $i,SY140: $i,SY141: $i,SY142: $i] :
( ~ ( equidistant @ SV6 @ SV22 @ SY139 @ SY140 )
| ~ ( equidistant @ SV22 @ SY141 @ SY140 @ SY142 )
| ! [SY143: $i,SY144: $i] :
( ~ ( equidistant @ SV6 @ SY143 @ SY139 @ SY144 )
| ~ ( equidistant @ SV22 @ SY143 @ SY140 @ SY144 )
| ~ ( between @ SV6 @ SV22 @ SY141 )
| ~ ( between @ SY139 @ SY140 @ SY142 )
| ( SV6 = SV22 )
| ( equidistant @ SY141 @ SY143 @ SY142 @ SY144 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[87]) ).
thf(108,plain,
! [SV23: $i,SV7: $i] :
( ( ~ ( between @ SV7 @ SV23 @ SV7 )
| ( SV7 = SV23 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[88]) ).
thf(109,plain,
! [SV24: $i,SV8: $i] :
( ( ! [SY145: $i] :
( ~ ( between @ SV8 @ SV24 @ SY145 )
| ! [SY146: $i,SY147: $i] :
( ~ ( between @ SY146 @ SY147 @ SY145 )
| ( between @ SV24 @ ( inner_pasch @ SV8 @ SV24 @ SY145 @ SY147 @ SY146 ) @ SY146 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[89]) ).
thf(110,plain,
! [SV25: $i,SV9: $i] :
( ( ! [SY148: $i] :
( ~ ( between @ SV9 @ SV25 @ SY148 )
| ! [SY149: $i,SY150: $i] :
( ~ ( between @ SY149 @ SY150 @ SY148 )
| ( between @ SY150 @ ( inner_pasch @ SV9 @ SV25 @ SY148 @ SY150 @ SY149 ) @ SV9 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[90]) ).
thf(111,plain,
! [SV26: $i,SV10: $i] :
( ( ! [SY151: $i] :
( ~ ( equidistant @ SV10 @ SV26 @ SV10 @ SY151 )
| ! [SY152: $i] :
( ~ ( equidistant @ SY152 @ SV26 @ SY152 @ SY151 )
| ! [SY153: $i] :
( ~ ( equidistant @ SY153 @ SV26 @ SY153 @ SY151 )
| ( between @ SV10 @ SY152 @ SY153 )
| ( between @ SY152 @ SY153 @ SV10 )
| ( SV26 = SY151 )
| ( between @ SY153 @ SV10 @ SY152 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[94]) ).
thf(112,plain,
! [SV27: $i,SV11: $i] :
( ( ! [SY154: $i] :
( ~ ( between @ SV11 @ SV27 @ SY154 )
| ! [SY155: $i,SY156: $i] :
( ~ ( between @ SY155 @ SV27 @ SY156 )
| ( SV11 = SV27 )
| ( between @ SV11 @ SY155 @ ( euclid1 @ SV11 @ SY155 @ SV27 @ SY156 @ SY154 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[95]) ).
thf(113,plain,
! [SV28: $i,SV12: $i] :
( ( ! [SY157: $i] :
( ~ ( between @ SV12 @ SV28 @ SY157 )
| ! [SY158: $i,SY159: $i] :
( ~ ( between @ SY158 @ SV28 @ SY159 )
| ( SV12 = SV28 )
| ( between @ SV12 @ SY159 @ ( euclid2 @ SV12 @ SY158 @ SV28 @ SY159 @ SY157 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[96]) ).
thf(114,plain,
! [SV29: $i,SV13: $i] :
( ( ! [SY160: $i] :
( ~ ( between @ SV13 @ SV29 @ SY160 )
| ! [SY161: $i,SY162: $i] :
( ~ ( between @ SY161 @ SV29 @ SY162 )
| ( SV13 = SV29 )
| ( between @ ( euclid1 @ SV13 @ SY161 @ SV29 @ SY162 @ SY160 ) @ SY160 @ ( euclid2 @ SV13 @ SY161 @ SV29 @ SY162 @ SY160 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[97]) ).
thf(115,plain,
! [SV30: $i,SV14: $i] :
( ( ! [SY163: $i,SY164: $i] :
( ~ ( equidistant @ SV14 @ SV30 @ SV14 @ SY163 )
| ! [SY165: $i] :
( ~ ( equidistant @ SV14 @ SY164 @ SV14 @ SY165 )
| ~ ( between @ SV14 @ SV30 @ SY164 )
| ! [SY166: $i] :
( ~ ( between @ SV30 @ SY166 @ SY164 )
| ( between @ SY163 @ ( continuous @ SV14 @ SV30 @ SY163 @ SY166 @ SY164 @ SY165 ) @ SY165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[98]) ).
thf(116,plain,
! [SV31: $i,SV15: $i] :
( ( ! [SY167: $i,SY168: $i] :
( ~ ( equidistant @ SV15 @ SV31 @ SV15 @ SY167 )
| ! [SY169: $i] :
( ~ ( equidistant @ SV15 @ SY168 @ SV15 @ SY169 )
| ~ ( between @ SV15 @ SV31 @ SY168 )
| ! [SY170: $i] :
( ~ ( between @ SV31 @ SY170 @ SY168 )
| ( equidistant @ SV15 @ SY170 @ SV15 @ ( continuous @ SV15 @ SV31 @ SY167 @ SY170 @ SY168 @ SY169 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[99]) ).
thf(117,plain,
! [SV32: $i,SV16: $i] :
( ( ( reflection @ SV16 @ SV32 )
= ( extension @ SV16 @ SV32 @ SV16 @ SV32 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[100]) ).
thf(118,plain,
! [SV33: $i,SV18: $i,SV2: $i] :
( ( ! [SY171: $i] :
( ~ ( equidistant @ SV2 @ SV18 @ SV33 @ SY171 )
| ! [SY172: $i,SY173: $i] :
( ~ ( equidistant @ SV2 @ SV18 @ SY172 @ SY173 )
| ( equidistant @ SV33 @ SY171 @ SY172 @ SY173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[103]) ).
thf(119,plain,
! [SV19: $i,SV3: $i] :
( ( ( ! [SY134: $i] :
~ ( equidistant @ SV3 @ SV19 @ SY134 @ SY134 ) )
= $true )
| ( ( SV3 = SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[104]) ).
thf(120,plain,
! [SV34: $i,SV20: $i,SV4: $i] :
( ( ! [SY174: $i] : ( between @ SV4 @ SV20 @ ( extension @ SV4 @ SV20 @ SV34 @ SY174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[105]) ).
thf(121,plain,
! [SV35: $i,SV21: $i,SV5: $i] :
( ( ! [SY175: $i] : ( equidistant @ SV5 @ ( extension @ SV21 @ SV5 @ SV35 @ SY175 ) @ SV35 @ SY175 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[106]) ).
thf(122,plain,
! [SV36: $i,SV22: $i,SV6: $i] :
( ( ! [SY176: $i,SY177: $i,SY178: $i] :
( ~ ( equidistant @ SV6 @ SV22 @ SV36 @ SY176 )
| ~ ( equidistant @ SV22 @ SY177 @ SY176 @ SY178 )
| ! [SY179: $i,SY180: $i] :
( ~ ( equidistant @ SV6 @ SY179 @ SV36 @ SY180 )
| ~ ( equidistant @ SV22 @ SY179 @ SY176 @ SY180 )
| ~ ( between @ SV6 @ SV22 @ SY177 )
| ~ ( between @ SV36 @ SY176 @ SY178 )
| ( SV6 = SV22 )
| ( equidistant @ SY177 @ SY179 @ SY178 @ SY180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[107]) ).
thf(123,plain,
! [SV23: $i,SV7: $i] :
( ( ( ~ ( between @ SV7 @ SV23 @ SV7 ) )
= $true )
| ( ( SV7 = SV23 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[108]) ).
thf(124,plain,
! [SV37: $i,SV24: $i,SV8: $i] :
( ( ~ ( between @ SV8 @ SV24 @ SV37 )
| ! [SY181: $i,SY182: $i] :
( ~ ( between @ SY181 @ SY182 @ SV37 )
| ( between @ SV24 @ ( inner_pasch @ SV8 @ SV24 @ SV37 @ SY182 @ SY181 ) @ SY181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[109]) ).
thf(125,plain,
! [SV38: $i,SV25: $i,SV9: $i] :
( ( ~ ( between @ SV9 @ SV25 @ SV38 )
| ! [SY183: $i,SY184: $i] :
( ~ ( between @ SY183 @ SY184 @ SV38 )
| ( between @ SY184 @ ( inner_pasch @ SV9 @ SV25 @ SV38 @ SY184 @ SY183 ) @ SV9 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[110]) ).
thf(126,plain,
! [SV39: $i,SV26: $i,SV10: $i] :
( ( ~ ( equidistant @ SV10 @ SV26 @ SV10 @ SV39 )
| ! [SY185: $i] :
( ~ ( equidistant @ SY185 @ SV26 @ SY185 @ SV39 )
| ! [SY186: $i] :
( ~ ( equidistant @ SY186 @ SV26 @ SY186 @ SV39 )
| ( between @ SV10 @ SY185 @ SY186 )
| ( between @ SY185 @ SY186 @ SV10 )
| ( SV26 = SV39 )
| ( between @ SY186 @ SV10 @ SY185 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[111]) ).
thf(127,plain,
! [SV40: $i,SV27: $i,SV11: $i] :
( ( ~ ( between @ SV11 @ SV27 @ SV40 )
| ! [SY187: $i,SY188: $i] :
( ~ ( between @ SY187 @ SV27 @ SY188 )
| ( SV11 = SV27 )
| ( between @ SV11 @ SY187 @ ( euclid1 @ SV11 @ SY187 @ SV27 @ SY188 @ SV40 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[112]) ).
thf(128,plain,
! [SV41: $i,SV28: $i,SV12: $i] :
( ( ~ ( between @ SV12 @ SV28 @ SV41 )
| ! [SY189: $i,SY190: $i] :
( ~ ( between @ SY189 @ SV28 @ SY190 )
| ( SV12 = SV28 )
| ( between @ SV12 @ SY190 @ ( euclid2 @ SV12 @ SY189 @ SV28 @ SY190 @ SV41 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[113]) ).
thf(129,plain,
! [SV42: $i,SV29: $i,SV13: $i] :
( ( ~ ( between @ SV13 @ SV29 @ SV42 )
| ! [SY191: $i,SY192: $i] :
( ~ ( between @ SY191 @ SV29 @ SY192 )
| ( SV13 = SV29 )
| ( between @ ( euclid1 @ SV13 @ SY191 @ SV29 @ SY192 @ SV42 ) @ SV42 @ ( euclid2 @ SV13 @ SY191 @ SV29 @ SY192 @ SV42 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[114]) ).
thf(130,plain,
! [SV43: $i,SV30: $i,SV14: $i] :
( ( ! [SY193: $i] :
( ~ ( equidistant @ SV14 @ SV30 @ SV14 @ SV43 )
| ! [SY194: $i] :
( ~ ( equidistant @ SV14 @ SY193 @ SV14 @ SY194 )
| ~ ( between @ SV14 @ SV30 @ SY193 )
| ! [SY195: $i] :
( ~ ( between @ SV30 @ SY195 @ SY193 )
| ( between @ SV43 @ ( continuous @ SV14 @ SV30 @ SV43 @ SY195 @ SY193 @ SY194 ) @ SY194 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[115]) ).
thf(131,plain,
! [SV44: $i,SV31: $i,SV15: $i] :
( ( ! [SY196: $i] :
( ~ ( equidistant @ SV15 @ SV31 @ SV15 @ SV44 )
| ! [SY197: $i] :
( ~ ( equidistant @ SV15 @ SY196 @ SV15 @ SY197 )
| ~ ( between @ SV15 @ SV31 @ SY196 )
| ! [SY198: $i] :
( ~ ( between @ SV31 @ SY198 @ SY196 )
| ( equidistant @ SV15 @ SY198 @ SV15 @ ( continuous @ SV15 @ SV31 @ SV44 @ SY198 @ SY196 @ SY197 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[116]) ).
thf(132,plain,
! [SV45: $i,SV33: $i,SV18: $i,SV2: $i] :
( ( ~ ( equidistant @ SV2 @ SV18 @ SV33 @ SV45 )
| ! [SY199: $i,SY200: $i] :
( ~ ( equidistant @ SV2 @ SV18 @ SY199 @ SY200 )
| ( equidistant @ SV33 @ SV45 @ SY199 @ SY200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[118]) ).
thf(133,plain,
! [SV46: $i,SV19: $i,SV3: $i] :
( ( ( ~ ( equidistant @ SV3 @ SV19 @ SV46 @ SV46 ) )
= $true )
| ( ( SV3 = SV19 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[119]) ).
thf(134,plain,
! [SV47: $i,SV34: $i,SV20: $i,SV4: $i] :
( ( between @ SV4 @ SV20 @ ( extension @ SV4 @ SV20 @ SV34 @ SV47 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[120]) ).
thf(135,plain,
! [SV48: $i,SV35: $i,SV21: $i,SV5: $i] :
( ( equidistant @ SV5 @ ( extension @ SV21 @ SV5 @ SV35 @ SV48 ) @ SV35 @ SV48 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[121]) ).
thf(136,plain,
! [SV49: $i,SV36: $i,SV22: $i,SV6: $i] :
( ( ! [SY201: $i,SY202: $i] :
( ~ ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
| ~ ( equidistant @ SV22 @ SY201 @ SV49 @ SY202 )
| ! [SY203: $i,SY204: $i] :
( ~ ( equidistant @ SV6 @ SY203 @ SV36 @ SY204 )
| ~ ( equidistant @ SV22 @ SY203 @ SV49 @ SY204 )
| ~ ( between @ SV6 @ SV22 @ SY201 )
| ~ ( between @ SV36 @ SV49 @ SY202 )
| ( SV6 = SV22 )
| ( equidistant @ SY201 @ SY203 @ SY202 @ SY204 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[122]) ).
thf(137,plain,
! [SV23: $i,SV7: $i] :
( ( ( between @ SV7 @ SV23 @ SV7 )
= $false )
| ( ( SV7 = SV23 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[123]) ).
thf(138,plain,
! [SV37: $i,SV24: $i,SV8: $i] :
( ( ( ~ ( between @ SV8 @ SV24 @ SV37 ) )
= $true )
| ( ( ! [SY181: $i,SY182: $i] :
( ~ ( between @ SY181 @ SY182 @ SV37 )
| ( between @ SV24 @ ( inner_pasch @ SV8 @ SV24 @ SV37 @ SY182 @ SY181 ) @ SY181 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[124]) ).
thf(139,plain,
! [SV38: $i,SV25: $i,SV9: $i] :
( ( ( ~ ( between @ SV9 @ SV25 @ SV38 ) )
= $true )
| ( ( ! [SY183: $i,SY184: $i] :
( ~ ( between @ SY183 @ SY184 @ SV38 )
| ( between @ SY184 @ ( inner_pasch @ SV9 @ SV25 @ SV38 @ SY184 @ SY183 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[125]) ).
thf(140,plain,
! [SV39: $i,SV26: $i,SV10: $i] :
( ( ( ~ ( equidistant @ SV10 @ SV26 @ SV10 @ SV39 ) )
= $true )
| ( ( ! [SY185: $i] :
( ~ ( equidistant @ SY185 @ SV26 @ SY185 @ SV39 )
| ! [SY186: $i] :
( ~ ( equidistant @ SY186 @ SV26 @ SY186 @ SV39 )
| ( between @ SV10 @ SY185 @ SY186 )
| ( between @ SY185 @ SY186 @ SV10 )
| ( SV26 = SV39 )
| ( between @ SY186 @ SV10 @ SY185 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[126]) ).
thf(141,plain,
! [SV40: $i,SV27: $i,SV11: $i] :
( ( ( ~ ( between @ SV11 @ SV27 @ SV40 ) )
= $true )
| ( ( ! [SY187: $i,SY188: $i] :
( ~ ( between @ SY187 @ SV27 @ SY188 )
| ( SV11 = SV27 )
| ( between @ SV11 @ SY187 @ ( euclid1 @ SV11 @ SY187 @ SV27 @ SY188 @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[127]) ).
thf(142,plain,
! [SV41: $i,SV28: $i,SV12: $i] :
( ( ( ~ ( between @ SV12 @ SV28 @ SV41 ) )
= $true )
| ( ( ! [SY189: $i,SY190: $i] :
( ~ ( between @ SY189 @ SV28 @ SY190 )
| ( SV12 = SV28 )
| ( between @ SV12 @ SY190 @ ( euclid2 @ SV12 @ SY189 @ SV28 @ SY190 @ SV41 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[128]) ).
thf(143,plain,
! [SV42: $i,SV29: $i,SV13: $i] :
( ( ( ~ ( between @ SV13 @ SV29 @ SV42 ) )
= $true )
| ( ( ! [SY191: $i,SY192: $i] :
( ~ ( between @ SY191 @ SV29 @ SY192 )
| ( SV13 = SV29 )
| ( between @ ( euclid1 @ SV13 @ SY191 @ SV29 @ SY192 @ SV42 ) @ SV42 @ ( euclid2 @ SV13 @ SY191 @ SV29 @ SY192 @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[129]) ).
thf(144,plain,
! [SV50: $i,SV43: $i,SV30: $i,SV14: $i] :
( ( ~ ( equidistant @ SV14 @ SV30 @ SV14 @ SV43 )
| ! [SY205: $i] :
( ~ ( equidistant @ SV14 @ SV50 @ SV14 @ SY205 )
| ~ ( between @ SV14 @ SV30 @ SV50 )
| ! [SY206: $i] :
( ~ ( between @ SV30 @ SY206 @ SV50 )
| ( between @ SV43 @ ( continuous @ SV14 @ SV30 @ SV43 @ SY206 @ SV50 @ SY205 ) @ SY205 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[130]) ).
thf(145,plain,
! [SV51: $i,SV44: $i,SV31: $i,SV15: $i] :
( ( ~ ( equidistant @ SV15 @ SV31 @ SV15 @ SV44 )
| ! [SY207: $i] :
( ~ ( equidistant @ SV15 @ SV51 @ SV15 @ SY207 )
| ~ ( between @ SV15 @ SV31 @ SV51 )
| ! [SY208: $i] :
( ~ ( between @ SV31 @ SY208 @ SV51 )
| ( equidistant @ SV15 @ SY208 @ SV15 @ ( continuous @ SV15 @ SV31 @ SV44 @ SY208 @ SV51 @ SY207 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[131]) ).
thf(146,plain,
! [SV45: $i,SV33: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV18 @ SV33 @ SV45 ) )
= $true )
| ( ( ! [SY199: $i,SY200: $i] :
( ~ ( equidistant @ SV2 @ SV18 @ SY199 @ SY200 )
| ( equidistant @ SV33 @ SV45 @ SY199 @ SY200 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[132]) ).
thf(147,plain,
! [SV46: $i,SV19: $i,SV3: $i] :
( ( ( equidistant @ SV3 @ SV19 @ SV46 @ SV46 )
= $false )
| ( ( SV3 = SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[133]) ).
thf(148,plain,
! [SV52: $i,SV49: $i,SV36: $i,SV22: $i,SV6: $i] :
( ( ! [SY209: $i] :
( ~ ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
| ~ ( equidistant @ SV22 @ SV52 @ SV49 @ SY209 )
| ! [SY210: $i,SY211: $i] :
( ~ ( equidistant @ SV6 @ SY210 @ SV36 @ SY211 )
| ~ ( equidistant @ SV22 @ SY210 @ SV49 @ SY211 )
| ~ ( between @ SV6 @ SV22 @ SV52 )
| ~ ( between @ SV36 @ SV49 @ SY209 )
| ( SV6 = SV22 )
| ( equidistant @ SV52 @ SY210 @ SY209 @ SY211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[136]) ).
thf(149,plain,
! [SV37: $i,SV24: $i,SV8: $i] :
( ( ( between @ SV8 @ SV24 @ SV37 )
= $false )
| ( ( ! [SY181: $i,SY182: $i] :
( ~ ( between @ SY181 @ SY182 @ SV37 )
| ( between @ SV24 @ ( inner_pasch @ SV8 @ SV24 @ SV37 @ SY182 @ SY181 ) @ SY181 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[138]) ).
thf(150,plain,
! [SV38: $i,SV25: $i,SV9: $i] :
( ( ( between @ SV9 @ SV25 @ SV38 )
= $false )
| ( ( ! [SY183: $i,SY184: $i] :
( ~ ( between @ SY183 @ SY184 @ SV38 )
| ( between @ SY184 @ ( inner_pasch @ SV9 @ SV25 @ SV38 @ SY184 @ SY183 ) @ SV9 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[139]) ).
thf(151,plain,
! [SV39: $i,SV26: $i,SV10: $i] :
( ( ( equidistant @ SV10 @ SV26 @ SV10 @ SV39 )
= $false )
| ( ( ! [SY185: $i] :
( ~ ( equidistant @ SY185 @ SV26 @ SY185 @ SV39 )
| ! [SY186: $i] :
( ~ ( equidistant @ SY186 @ SV26 @ SY186 @ SV39 )
| ( between @ SV10 @ SY185 @ SY186 )
| ( between @ SY185 @ SY186 @ SV10 )
| ( SV26 = SV39 )
| ( between @ SY186 @ SV10 @ SY185 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[140]) ).
thf(152,plain,
! [SV40: $i,SV27: $i,SV11: $i] :
( ( ( between @ SV11 @ SV27 @ SV40 )
= $false )
| ( ( ! [SY187: $i,SY188: $i] :
( ~ ( between @ SY187 @ SV27 @ SY188 )
| ( SV11 = SV27 )
| ( between @ SV11 @ SY187 @ ( euclid1 @ SV11 @ SY187 @ SV27 @ SY188 @ SV40 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[141]) ).
thf(153,plain,
! [SV41: $i,SV28: $i,SV12: $i] :
( ( ( between @ SV12 @ SV28 @ SV41 )
= $false )
| ( ( ! [SY189: $i,SY190: $i] :
( ~ ( between @ SY189 @ SV28 @ SY190 )
| ( SV12 = SV28 )
| ( between @ SV12 @ SY190 @ ( euclid2 @ SV12 @ SY189 @ SV28 @ SY190 @ SV41 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[142]) ).
thf(154,plain,
! [SV42: $i,SV29: $i,SV13: $i] :
( ( ( between @ SV13 @ SV29 @ SV42 )
= $false )
| ( ( ! [SY191: $i,SY192: $i] :
( ~ ( between @ SY191 @ SV29 @ SY192 )
| ( SV13 = SV29 )
| ( between @ ( euclid1 @ SV13 @ SY191 @ SV29 @ SY192 @ SV42 ) @ SV42 @ ( euclid2 @ SV13 @ SY191 @ SV29 @ SY192 @ SV42 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[143]) ).
thf(155,plain,
! [SV50: $i,SV43: $i,SV30: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV30 @ SV14 @ SV43 ) )
= $true )
| ( ( ! [SY205: $i] :
( ~ ( equidistant @ SV14 @ SV50 @ SV14 @ SY205 )
| ~ ( between @ SV14 @ SV30 @ SV50 )
| ! [SY206: $i] :
( ~ ( between @ SV30 @ SY206 @ SV50 )
| ( between @ SV43 @ ( continuous @ SV14 @ SV30 @ SV43 @ SY206 @ SV50 @ SY205 ) @ SY205 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[144]) ).
thf(156,plain,
! [SV51: $i,SV44: $i,SV31: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV31 @ SV15 @ SV44 ) )
= $true )
| ( ( ! [SY207: $i] :
( ~ ( equidistant @ SV15 @ SV51 @ SV15 @ SY207 )
| ~ ( between @ SV15 @ SV31 @ SV51 )
| ! [SY208: $i] :
( ~ ( between @ SV31 @ SY208 @ SV51 )
| ( equidistant @ SV15 @ SY208 @ SV15 @ ( continuous @ SV15 @ SV31 @ SV44 @ SY208 @ SV51 @ SY207 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[145]) ).
thf(157,plain,
! [SV45: $i,SV33: $i,SV18: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV18 @ SV33 @ SV45 )
= $false )
| ( ( ! [SY199: $i,SY200: $i] :
( ~ ( equidistant @ SV2 @ SV18 @ SY199 @ SY200 )
| ( equidistant @ SV33 @ SV45 @ SY199 @ SY200 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[146]) ).
thf(158,plain,
! [SV53: $i,SV52: $i,SV49: $i,SV36: $i,SV22: $i,SV6: $i] :
( ( ~ ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
| ~ ( equidistant @ SV22 @ SV52 @ SV49 @ SV53 )
| ! [SY212: $i,SY213: $i] :
( ~ ( equidistant @ SV6 @ SY212 @ SV36 @ SY213 )
| ~ ( equidistant @ SV22 @ SY212 @ SV49 @ SY213 )
| ~ ( between @ SV6 @ SV22 @ SV52 )
| ~ ( between @ SV36 @ SV49 @ SV53 )
| ( SV6 = SV22 )
| ( equidistant @ SV52 @ SY212 @ SV53 @ SY213 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[148]) ).
thf(159,plain,
! [SV8: $i,SV24: $i,SV37: $i,SV54: $i] :
( ( ( ! [SY214: $i] :
( ~ ( between @ SV54 @ SY214 @ SV37 )
| ( between @ SV24 @ ( inner_pasch @ SV8 @ SV24 @ SV37 @ SY214 @ SV54 ) @ SV54 ) ) )
= $true )
| ( ( between @ SV8 @ SV24 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[149]) ).
thf(160,plain,
! [SV25: $i,SV9: $i,SV38: $i,SV55: $i] :
( ( ( ! [SY215: $i] :
( ~ ( between @ SV55 @ SY215 @ SV38 )
| ( between @ SY215 @ ( inner_pasch @ SV9 @ SV25 @ SV38 @ SY215 @ SV55 ) @ SV9 ) ) )
= $true )
| ( ( between @ SV9 @ SV25 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[150]) ).
thf(161,plain,
! [SV10: $i,SV39: $i,SV26: $i,SV56: $i] :
( ( ( ~ ( equidistant @ SV56 @ SV26 @ SV56 @ SV39 )
| ! [SY216: $i] :
( ~ ( equidistant @ SY216 @ SV26 @ SY216 @ SV39 )
| ( between @ SV10 @ SV56 @ SY216 )
| ( between @ SV56 @ SY216 @ SV10 )
| ( SV26 = SV39 )
| ( between @ SY216 @ SV10 @ SV56 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV26 @ SV10 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[151]) ).
thf(162,plain,
! [SV40: $i,SV11: $i,SV27: $i,SV57: $i] :
( ( ( ! [SY217: $i] :
( ~ ( between @ SV57 @ SV27 @ SY217 )
| ( SV11 = SV27 )
| ( between @ SV11 @ SV57 @ ( euclid1 @ SV11 @ SV57 @ SV27 @ SY217 @ SV40 ) ) ) )
= $true )
| ( ( between @ SV11 @ SV27 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[152]) ).
thf(163,plain,
! [SV41: $i,SV12: $i,SV28: $i,SV58: $i] :
( ( ( ! [SY218: $i] :
( ~ ( between @ SV58 @ SV28 @ SY218 )
| ( SV12 = SV28 )
| ( between @ SV12 @ SY218 @ ( euclid2 @ SV12 @ SV58 @ SV28 @ SY218 @ SV41 ) ) ) )
= $true )
| ( ( between @ SV12 @ SV28 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[153]) ).
thf(164,plain,
! [SV42: $i,SV13: $i,SV29: $i,SV59: $i] :
( ( ( ! [SY219: $i] :
( ~ ( between @ SV59 @ SV29 @ SY219 )
| ( SV13 = SV29 )
| ( between @ ( euclid1 @ SV13 @ SV59 @ SV29 @ SY219 @ SV42 ) @ SV42 @ ( euclid2 @ SV13 @ SV59 @ SV29 @ SY219 @ SV42 ) ) ) )
= $true )
| ( ( between @ SV13 @ SV29 @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[154]) ).
thf(165,plain,
! [SV50: $i,SV43: $i,SV30: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV30 @ SV14 @ SV43 )
= $false )
| ( ( ! [SY205: $i] :
( ~ ( equidistant @ SV14 @ SV50 @ SV14 @ SY205 )
| ~ ( between @ SV14 @ SV30 @ SV50 )
| ! [SY206: $i] :
( ~ ( between @ SV30 @ SY206 @ SV50 )
| ( between @ SV43 @ ( continuous @ SV14 @ SV30 @ SV43 @ SY206 @ SV50 @ SY205 ) @ SY205 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[155]) ).
thf(166,plain,
! [SV51: $i,SV44: $i,SV31: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV31 @ SV15 @ SV44 )
= $false )
| ( ( ! [SY207: $i] :
( ~ ( equidistant @ SV15 @ SV51 @ SV15 @ SY207 )
| ~ ( between @ SV15 @ SV31 @ SV51 )
| ! [SY208: $i] :
( ~ ( between @ SV31 @ SY208 @ SV51 )
| ( equidistant @ SV15 @ SY208 @ SV15 @ ( continuous @ SV15 @ SV31 @ SV44 @ SY208 @ SV51 @ SY207 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[156]) ).
thf(167,plain,
! [SV45: $i,SV33: $i,SV60: $i,SV18: $i,SV2: $i] :
( ( ( ! [SY220: $i] :
( ~ ( equidistant @ SV2 @ SV18 @ SV60 @ SY220 )
| ( equidistant @ SV33 @ SV45 @ SV60 @ SY220 ) ) )
= $true )
| ( ( equidistant @ SV2 @ SV18 @ SV33 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[157]) ).
thf(168,plain,
! [SV53: $i,SV52: $i,SV49: $i,SV36: $i,SV22: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 ) )
= $true )
| ( ( ~ ( equidistant @ SV22 @ SV52 @ SV49 @ SV53 )
| ! [SY212: $i,SY213: $i] :
( ~ ( equidistant @ SV6 @ SY212 @ SV36 @ SY213 )
| ~ ( equidistant @ SV22 @ SY212 @ SV49 @ SY213 )
| ~ ( between @ SV6 @ SV22 @ SV52 )
| ~ ( between @ SV36 @ SV49 @ SV53 )
| ( SV6 = SV22 )
| ( equidistant @ SV52 @ SY212 @ SV53 @ SY213 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[158]) ).
thf(169,plain,
! [SV8: $i,SV24: $i,SV37: $i,SV61: $i,SV54: $i] :
( ( ( ~ ( between @ SV54 @ SV61 @ SV37 )
| ( between @ SV24 @ ( inner_pasch @ SV8 @ SV24 @ SV37 @ SV61 @ SV54 ) @ SV54 ) )
= $true )
| ( ( between @ SV8 @ SV24 @ SV37 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[159]) ).
thf(170,plain,
! [SV25: $i,SV9: $i,SV38: $i,SV62: $i,SV55: $i] :
( ( ( ~ ( between @ SV55 @ SV62 @ SV38 )
| ( between @ SV62 @ ( inner_pasch @ SV9 @ SV25 @ SV38 @ SV62 @ SV55 ) @ SV9 ) )
= $true )
| ( ( between @ SV9 @ SV25 @ SV38 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[160]) ).
thf(171,plain,
! [SV10: $i,SV39: $i,SV26: $i,SV56: $i] :
( ( ( ~ ( equidistant @ SV56 @ SV26 @ SV56 @ SV39 ) )
= $true )
| ( ( ! [SY216: $i] :
( ~ ( equidistant @ SY216 @ SV26 @ SY216 @ SV39 )
| ( between @ SV10 @ SV56 @ SY216 )
| ( between @ SV56 @ SY216 @ SV10 )
| ( SV26 = SV39 )
| ( between @ SY216 @ SV10 @ SV56 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV26 @ SV10 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[161]) ).
thf(172,plain,
! [SV40: $i,SV11: $i,SV63: $i,SV27: $i,SV57: $i] :
( ( ( ~ ( between @ SV57 @ SV27 @ SV63 )
| ( SV11 = SV27 )
| ( between @ SV11 @ SV57 @ ( euclid1 @ SV11 @ SV57 @ SV27 @ SV63 @ SV40 ) ) )
= $true )
| ( ( between @ SV11 @ SV27 @ SV40 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[162]) ).
thf(173,plain,
! [SV41: $i,SV12: $i,SV64: $i,SV28: $i,SV58: $i] :
( ( ( ~ ( between @ SV58 @ SV28 @ SV64 )
| ( SV12 = SV28 )
| ( between @ SV12 @ SV64 @ ( euclid2 @ SV12 @ SV58 @ SV28 @ SV64 @ SV41 ) ) )
= $true )
| ( ( between @ SV12 @ SV28 @ SV41 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[163]) ).
thf(174,plain,
! [SV42: $i,SV13: $i,SV65: $i,SV29: $i,SV59: $i] :
( ( ( ~ ( between @ SV59 @ SV29 @ SV65 )
| ( SV13 = SV29 )
| ( between @ ( euclid1 @ SV13 @ SV59 @ SV29 @ SV65 @ SV42 ) @ SV42 @ ( euclid2 @ SV13 @ SV59 @ SV29 @ SV65 @ SV42 ) ) )
= $true )
| ( ( between @ SV13 @ SV29 @ SV42 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[164]) ).
thf(175,plain,
! [SV43: $i,SV30: $i,SV66: $i,SV50: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV50 @ SV14 @ SV66 )
| ~ ( between @ SV14 @ SV30 @ SV50 )
| ! [SY221: $i] :
( ~ ( between @ SV30 @ SY221 @ SV50 )
| ( between @ SV43 @ ( continuous @ SV14 @ SV30 @ SV43 @ SY221 @ SV50 @ SV66 ) @ SV66 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV30 @ SV14 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[165]) ).
thf(176,plain,
! [SV44: $i,SV31: $i,SV67: $i,SV51: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV51 @ SV15 @ SV67 )
| ~ ( between @ SV15 @ SV31 @ SV51 )
| ! [SY222: $i] :
( ~ ( between @ SV31 @ SY222 @ SV51 )
| ( equidistant @ SV15 @ SY222 @ SV15 @ ( continuous @ SV15 @ SV31 @ SV44 @ SY222 @ SV51 @ SV67 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV31 @ SV15 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[166]) ).
thf(177,plain,
! [SV45: $i,SV33: $i,SV68: $i,SV60: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV18 @ SV60 @ SV68 )
| ( equidistant @ SV33 @ SV45 @ SV60 @ SV68 ) )
= $true )
| ( ( equidistant @ SV2 @ SV18 @ SV33 @ SV45 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[167]) ).
thf(178,plain,
! [SV53: $i,SV52: $i,SV49: $i,SV36: $i,SV22: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
= $false )
| ( ( ~ ( equidistant @ SV22 @ SV52 @ SV49 @ SV53 )
| ! [SY212: $i,SY213: $i] :
( ~ ( equidistant @ SV6 @ SY212 @ SV36 @ SY213 )
| ~ ( equidistant @ SV22 @ SY212 @ SV49 @ SY213 )
| ~ ( between @ SV6 @ SV22 @ SV52 )
| ~ ( between @ SV36 @ SV49 @ SV53 )
| ( SV6 = SV22 )
| ( equidistant @ SV52 @ SY212 @ SV53 @ SY213 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[168]) ).
thf(179,plain,
! [SV8: $i,SV24: $i,SV37: $i,SV61: $i,SV54: $i] :
( ( ( ~ ( between @ SV54 @ SV61 @ SV37 ) )
= $true )
| ( ( between @ SV24 @ ( inner_pasch @ SV8 @ SV24 @ SV37 @ SV61 @ SV54 ) @ SV54 )
= $true )
| ( ( between @ SV8 @ SV24 @ SV37 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[169]) ).
thf(180,plain,
! [SV25: $i,SV9: $i,SV38: $i,SV62: $i,SV55: $i] :
( ( ( ~ ( between @ SV55 @ SV62 @ SV38 ) )
= $true )
| ( ( between @ SV62 @ ( inner_pasch @ SV9 @ SV25 @ SV38 @ SV62 @ SV55 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV25 @ SV38 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[170]) ).
thf(181,plain,
! [SV10: $i,SV39: $i,SV26: $i,SV56: $i] :
( ( ( equidistant @ SV56 @ SV26 @ SV56 @ SV39 )
= $false )
| ( ( ! [SY216: $i] :
( ~ ( equidistant @ SY216 @ SV26 @ SY216 @ SV39 )
| ( between @ SV10 @ SV56 @ SY216 )
| ( between @ SV56 @ SY216 @ SV10 )
| ( SV26 = SV39 )
| ( between @ SY216 @ SV10 @ SV56 ) ) )
= $true )
| ( ( equidistant @ SV10 @ SV26 @ SV10 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[171]) ).
thf(182,plain,
! [SV40: $i,SV11: $i,SV63: $i,SV27: $i,SV57: $i] :
( ( ( ~ ( between @ SV57 @ SV27 @ SV63 ) )
= $true )
| ( ( ( SV11 = SV27 )
| ( between @ SV11 @ SV57 @ ( euclid1 @ SV11 @ SV57 @ SV27 @ SV63 @ SV40 ) ) )
= $true )
| ( ( between @ SV11 @ SV27 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[172]) ).
thf(183,plain,
! [SV41: $i,SV12: $i,SV64: $i,SV28: $i,SV58: $i] :
( ( ( ~ ( between @ SV58 @ SV28 @ SV64 ) )
= $true )
| ( ( ( SV12 = SV28 )
| ( between @ SV12 @ SV64 @ ( euclid2 @ SV12 @ SV58 @ SV28 @ SV64 @ SV41 ) ) )
= $true )
| ( ( between @ SV12 @ SV28 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[173]) ).
thf(184,plain,
! [SV42: $i,SV13: $i,SV65: $i,SV29: $i,SV59: $i] :
( ( ( ~ ( between @ SV59 @ SV29 @ SV65 ) )
= $true )
| ( ( ( SV13 = SV29 )
| ( between @ ( euclid1 @ SV13 @ SV59 @ SV29 @ SV65 @ SV42 ) @ SV42 @ ( euclid2 @ SV13 @ SV59 @ SV29 @ SV65 @ SV42 ) ) )
= $true )
| ( ( between @ SV13 @ SV29 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[174]) ).
thf(185,plain,
! [SV43: $i,SV30: $i,SV66: $i,SV50: $i,SV14: $i] :
( ( ( ~ ( equidistant @ SV14 @ SV50 @ SV14 @ SV66 ) )
= $true )
| ( ( ~ ( between @ SV14 @ SV30 @ SV50 )
| ! [SY221: $i] :
( ~ ( between @ SV30 @ SY221 @ SV50 )
| ( between @ SV43 @ ( continuous @ SV14 @ SV30 @ SV43 @ SY221 @ SV50 @ SV66 ) @ SV66 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV30 @ SV14 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[175]) ).
thf(186,plain,
! [SV44: $i,SV31: $i,SV67: $i,SV51: $i,SV15: $i] :
( ( ( ~ ( equidistant @ SV15 @ SV51 @ SV15 @ SV67 ) )
= $true )
| ( ( ~ ( between @ SV15 @ SV31 @ SV51 )
| ! [SY222: $i] :
( ~ ( between @ SV31 @ SY222 @ SV51 )
| ( equidistant @ SV15 @ SY222 @ SV15 @ ( continuous @ SV15 @ SV31 @ SV44 @ SY222 @ SV51 @ SV67 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV31 @ SV15 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[176]) ).
thf(187,plain,
! [SV45: $i,SV33: $i,SV68: $i,SV60: $i,SV18: $i,SV2: $i] :
( ( ( ~ ( equidistant @ SV2 @ SV18 @ SV60 @ SV68 ) )
= $true )
| ( ( equidistant @ SV33 @ SV45 @ SV60 @ SV68 )
= $true )
| ( ( equidistant @ SV2 @ SV18 @ SV33 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[177]) ).
thf(188,plain,
! [SV36: $i,SV6: $i,SV53: $i,SV49: $i,SV52: $i,SV22: $i] :
( ( ( ~ ( equidistant @ SV22 @ SV52 @ SV49 @ SV53 ) )
= $true )
| ( ( ! [SY212: $i,SY213: $i] :
( ~ ( equidistant @ SV6 @ SY212 @ SV36 @ SY213 )
| ~ ( equidistant @ SV22 @ SY212 @ SV49 @ SY213 )
| ~ ( between @ SV6 @ SV22 @ SV52 )
| ~ ( between @ SV36 @ SV49 @ SV53 )
| ( SV6 = SV22 )
| ( equidistant @ SV52 @ SY212 @ SV53 @ SY213 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[178]) ).
thf(189,plain,
! [SV8: $i,SV24: $i,SV37: $i,SV61: $i,SV54: $i] :
( ( ( between @ SV54 @ SV61 @ SV37 )
= $false )
| ( ( between @ SV24 @ ( inner_pasch @ SV8 @ SV24 @ SV37 @ SV61 @ SV54 ) @ SV54 )
= $true )
| ( ( between @ SV8 @ SV24 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[179]) ).
thf(190,plain,
! [SV25: $i,SV9: $i,SV38: $i,SV62: $i,SV55: $i] :
( ( ( between @ SV55 @ SV62 @ SV38 )
= $false )
| ( ( between @ SV62 @ ( inner_pasch @ SV9 @ SV25 @ SV38 @ SV62 @ SV55 ) @ SV9 )
= $true )
| ( ( between @ SV9 @ SV25 @ SV38 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[180]) ).
thf(191,plain,
! [SV56: $i,SV10: $i,SV39: $i,SV26: $i,SV69: $i] :
( ( ( ~ ( equidistant @ SV69 @ SV26 @ SV69 @ SV39 )
| ( between @ SV10 @ SV56 @ SV69 )
| ( between @ SV56 @ SV69 @ SV10 )
| ( SV26 = SV39 )
| ( between @ SV69 @ SV10 @ SV56 ) )
= $true )
| ( ( equidistant @ SV56 @ SV26 @ SV56 @ SV39 )
= $false )
| ( ( equidistant @ SV10 @ SV26 @ SV10 @ SV39 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[181]) ).
thf(192,plain,
! [SV40: $i,SV11: $i,SV63: $i,SV27: $i,SV57: $i] :
( ( ( between @ SV57 @ SV27 @ SV63 )
= $false )
| ( ( ( SV11 = SV27 )
| ( between @ SV11 @ SV57 @ ( euclid1 @ SV11 @ SV57 @ SV27 @ SV63 @ SV40 ) ) )
= $true )
| ( ( between @ SV11 @ SV27 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[182]) ).
thf(193,plain,
! [SV41: $i,SV12: $i,SV64: $i,SV28: $i,SV58: $i] :
( ( ( between @ SV58 @ SV28 @ SV64 )
= $false )
| ( ( ( SV12 = SV28 )
| ( between @ SV12 @ SV64 @ ( euclid2 @ SV12 @ SV58 @ SV28 @ SV64 @ SV41 ) ) )
= $true )
| ( ( between @ SV12 @ SV28 @ SV41 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[183]) ).
thf(194,plain,
! [SV42: $i,SV13: $i,SV65: $i,SV29: $i,SV59: $i] :
( ( ( between @ SV59 @ SV29 @ SV65 )
= $false )
| ( ( ( SV13 = SV29 )
| ( between @ ( euclid1 @ SV13 @ SV59 @ SV29 @ SV65 @ SV42 ) @ SV42 @ ( euclid2 @ SV13 @ SV59 @ SV29 @ SV65 @ SV42 ) ) )
= $true )
| ( ( between @ SV13 @ SV29 @ SV42 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[184]) ).
thf(195,plain,
! [SV43: $i,SV30: $i,SV66: $i,SV50: $i,SV14: $i] :
( ( ( equidistant @ SV14 @ SV50 @ SV14 @ SV66 )
= $false )
| ( ( ~ ( between @ SV14 @ SV30 @ SV50 )
| ! [SY221: $i] :
( ~ ( between @ SV30 @ SY221 @ SV50 )
| ( between @ SV43 @ ( continuous @ SV14 @ SV30 @ SV43 @ SY221 @ SV50 @ SV66 ) @ SV66 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV30 @ SV14 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[185]) ).
thf(196,plain,
! [SV44: $i,SV31: $i,SV67: $i,SV51: $i,SV15: $i] :
( ( ( equidistant @ SV15 @ SV51 @ SV15 @ SV67 )
= $false )
| ( ( ~ ( between @ SV15 @ SV31 @ SV51 )
| ! [SY222: $i] :
( ~ ( between @ SV31 @ SY222 @ SV51 )
| ( equidistant @ SV15 @ SY222 @ SV15 @ ( continuous @ SV15 @ SV31 @ SV44 @ SY222 @ SV51 @ SV67 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV31 @ SV15 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[186]) ).
thf(197,plain,
! [SV45: $i,SV33: $i,SV68: $i,SV60: $i,SV18: $i,SV2: $i] :
( ( ( equidistant @ SV2 @ SV18 @ SV60 @ SV68 )
= $false )
| ( ( equidistant @ SV33 @ SV45 @ SV60 @ SV68 )
= $true )
| ( ( equidistant @ SV2 @ SV18 @ SV33 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[187]) ).
thf(198,plain,
! [SV36: $i,SV6: $i,SV53: $i,SV49: $i,SV52: $i,SV22: $i] :
( ( ( equidistant @ SV22 @ SV52 @ SV49 @ SV53 )
= $false )
| ( ( ! [SY212: $i,SY213: $i] :
( ~ ( equidistant @ SV6 @ SY212 @ SV36 @ SY213 )
| ~ ( equidistant @ SV22 @ SY212 @ SV49 @ SY213 )
| ~ ( between @ SV6 @ SV22 @ SV52 )
| ~ ( between @ SV36 @ SV49 @ SV53 )
| ( SV6 = SV22 )
| ( equidistant @ SV52 @ SY212 @ SV53 @ SY213 ) ) )
= $true )
| ( ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[188]) ).
thf(199,plain,
! [SV56: $i,SV10: $i,SV39: $i,SV26: $i,SV69: $i] :
( ( ( ~ ( equidistant @ SV69 @ SV26 @ SV69 @ SV39 ) )
= $true )
| ( ( ( between @ SV10 @ SV56 @ SV69 )
| ( between @ SV56 @ SV69 @ SV10 )
| ( SV26 = SV39 )
| ( between @ SV69 @ SV10 @ SV56 ) )
= $true )
| ( ( equidistant @ SV56 @ SV26 @ SV56 @ SV39 )
= $false )
| ( ( equidistant @ SV10 @ SV26 @ SV10 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[191]) ).
thf(200,plain,
! [SV40: $i,SV63: $i,SV57: $i,SV27: $i,SV11: $i] :
( ( ( SV11 = SV27 )
= $true )
| ( ( between @ SV11 @ SV57 @ ( euclid1 @ SV11 @ SV57 @ SV27 @ SV63 @ SV40 ) )
= $true )
| ( ( between @ SV57 @ SV27 @ SV63 )
= $false )
| ( ( between @ SV11 @ SV27 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[192]) ).
thf(201,plain,
! [SV41: $i,SV58: $i,SV64: $i,SV28: $i,SV12: $i] :
( ( ( SV12 = SV28 )
= $true )
| ( ( between @ SV12 @ SV64 @ ( euclid2 @ SV12 @ SV58 @ SV28 @ SV64 @ SV41 ) )
= $true )
| ( ( between @ SV58 @ SV28 @ SV64 )
= $false )
| ( ( between @ SV12 @ SV28 @ SV41 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[193]) ).
thf(202,plain,
! [SV42: $i,SV65: $i,SV59: $i,SV29: $i,SV13: $i] :
( ( ( SV13 = SV29 )
= $true )
| ( ( between @ ( euclid1 @ SV13 @ SV59 @ SV29 @ SV65 @ SV42 ) @ SV42 @ ( euclid2 @ SV13 @ SV59 @ SV29 @ SV65 @ SV42 ) )
= $true )
| ( ( between @ SV59 @ SV29 @ SV65 )
= $false )
| ( ( between @ SV13 @ SV29 @ SV42 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[194]) ).
thf(203,plain,
! [SV66: $i,SV43: $i,SV50: $i,SV30: $i,SV14: $i] :
( ( ( ~ ( between @ SV14 @ SV30 @ SV50 ) )
= $true )
| ( ( ! [SY221: $i] :
( ~ ( between @ SV30 @ SY221 @ SV50 )
| ( between @ SV43 @ ( continuous @ SV14 @ SV30 @ SV43 @ SY221 @ SV50 @ SV66 ) @ SV66 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV50 @ SV14 @ SV66 )
= $false )
| ( ( equidistant @ SV14 @ SV30 @ SV14 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[195]) ).
thf(204,plain,
! [SV67: $i,SV44: $i,SV51: $i,SV31: $i,SV15: $i] :
( ( ( ~ ( between @ SV15 @ SV31 @ SV51 ) )
= $true )
| ( ( ! [SY222: $i] :
( ~ ( between @ SV31 @ SY222 @ SV51 )
| ( equidistant @ SV15 @ SY222 @ SV15 @ ( continuous @ SV15 @ SV31 @ SV44 @ SY222 @ SV51 @ SV67 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV51 @ SV15 @ SV67 )
= $false )
| ( ( equidistant @ SV15 @ SV31 @ SV15 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[196]) ).
thf(205,plain,
! [SV53: $i,SV52: $i,SV49: $i,SV22: $i,SV36: $i,SV70: $i,SV6: $i] :
( ( ( ! [SY223: $i] :
( ~ ( equidistant @ SV6 @ SV70 @ SV36 @ SY223 )
| ~ ( equidistant @ SV22 @ SV70 @ SV49 @ SY223 )
| ~ ( between @ SV6 @ SV22 @ SV52 )
| ~ ( between @ SV36 @ SV49 @ SV53 )
| ( SV6 = SV22 )
| ( equidistant @ SV52 @ SV70 @ SV53 @ SY223 ) ) )
= $true )
| ( ( equidistant @ SV22 @ SV52 @ SV49 @ SV53 )
= $false )
| ( ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[198]) ).
thf(206,plain,
! [SV56: $i,SV10: $i,SV39: $i,SV26: $i,SV69: $i] :
( ( ( equidistant @ SV69 @ SV26 @ SV69 @ SV39 )
= $false )
| ( ( ( between @ SV10 @ SV56 @ SV69 )
| ( between @ SV56 @ SV69 @ SV10 )
| ( SV26 = SV39 )
| ( between @ SV69 @ SV10 @ SV56 ) )
= $true )
| ( ( equidistant @ SV56 @ SV26 @ SV56 @ SV39 )
= $false )
| ( ( equidistant @ SV10 @ SV26 @ SV10 @ SV39 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[199]) ).
thf(207,plain,
! [SV66: $i,SV43: $i,SV50: $i,SV30: $i,SV14: $i] :
( ( ( between @ SV14 @ SV30 @ SV50 )
= $false )
| ( ( ! [SY221: $i] :
( ~ ( between @ SV30 @ SY221 @ SV50 )
| ( between @ SV43 @ ( continuous @ SV14 @ SV30 @ SV43 @ SY221 @ SV50 @ SV66 ) @ SV66 ) ) )
= $true )
| ( ( equidistant @ SV14 @ SV50 @ SV14 @ SV66 )
= $false )
| ( ( equidistant @ SV14 @ SV30 @ SV14 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[203]) ).
thf(208,plain,
! [SV67: $i,SV44: $i,SV51: $i,SV31: $i,SV15: $i] :
( ( ( between @ SV15 @ SV31 @ SV51 )
= $false )
| ( ( ! [SY222: $i] :
( ~ ( between @ SV31 @ SY222 @ SV51 )
| ( equidistant @ SV15 @ SY222 @ SV15 @ ( continuous @ SV15 @ SV31 @ SV44 @ SY222 @ SV51 @ SV67 ) ) ) )
= $true )
| ( ( equidistant @ SV15 @ SV51 @ SV15 @ SV67 )
= $false )
| ( ( equidistant @ SV15 @ SV31 @ SV15 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[204]) ).
thf(209,plain,
! [SV53: $i,SV52: $i,SV49: $i,SV22: $i,SV71: $i,SV36: $i,SV70: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV70 @ SV36 @ SV71 )
| ~ ( equidistant @ SV22 @ SV70 @ SV49 @ SV71 )
| ~ ( between @ SV6 @ SV22 @ SV52 )
| ~ ( between @ SV36 @ SV49 @ SV53 )
| ( SV6 = SV22 )
| ( equidistant @ SV52 @ SV70 @ SV53 @ SV71 ) )
= $true )
| ( ( equidistant @ SV22 @ SV52 @ SV49 @ SV53 )
= $false )
| ( ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[205]) ).
thf(210,plain,
! [SV39: $i,SV26: $i,SV69: $i,SV56: $i,SV10: $i] :
( ( ( between @ SV10 @ SV56 @ SV69 )
= $true )
| ( ( ( between @ SV56 @ SV69 @ SV10 )
| ( SV26 = SV39 )
| ( between @ SV69 @ SV10 @ SV56 ) )
= $true )
| ( ( equidistant @ SV69 @ SV26 @ SV69 @ SV39 )
= $false )
| ( ( equidistant @ SV56 @ SV26 @ SV56 @ SV39 )
= $false )
| ( ( equidistant @ SV10 @ SV26 @ SV10 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[206]) ).
thf(211,plain,
! [SV66: $i,SV14: $i,SV43: $i,SV50: $i,SV72: $i,SV30: $i] :
( ( ( ~ ( between @ SV30 @ SV72 @ SV50 )
| ( between @ SV43 @ ( continuous @ SV14 @ SV30 @ SV43 @ SV72 @ SV50 @ SV66 ) @ SV66 ) )
= $true )
| ( ( between @ SV14 @ SV30 @ SV50 )
= $false )
| ( ( equidistant @ SV14 @ SV50 @ SV14 @ SV66 )
= $false )
| ( ( equidistant @ SV14 @ SV30 @ SV14 @ SV43 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[207]) ).
thf(212,plain,
! [SV67: $i,SV44: $i,SV15: $i,SV51: $i,SV73: $i,SV31: $i] :
( ( ( ~ ( between @ SV31 @ SV73 @ SV51 )
| ( equidistant @ SV15 @ SV73 @ SV15 @ ( continuous @ SV15 @ SV31 @ SV44 @ SV73 @ SV51 @ SV67 ) ) )
= $true )
| ( ( between @ SV15 @ SV31 @ SV51 )
= $false )
| ( ( equidistant @ SV15 @ SV51 @ SV15 @ SV67 )
= $false )
| ( ( equidistant @ SV15 @ SV31 @ SV15 @ SV44 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[208]) ).
thf(213,plain,
! [SV53: $i,SV52: $i,SV49: $i,SV22: $i,SV71: $i,SV36: $i,SV70: $i,SV6: $i] :
( ( ( ~ ( equidistant @ SV6 @ SV70 @ SV36 @ SV71 ) )
= $true )
| ( ( ~ ( equidistant @ SV22 @ SV70 @ SV49 @ SV71 )
| ~ ( between @ SV6 @ SV22 @ SV52 )
| ~ ( between @ SV36 @ SV49 @ SV53 )
| ( SV6 = SV22 )
| ( equidistant @ SV52 @ SV70 @ SV53 @ SV71 ) )
= $true )
| ( ( equidistant @ SV22 @ SV52 @ SV49 @ SV53 )
= $false )
| ( ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[209]) ).
thf(214,plain,
! [SV39: $i,SV26: $i,SV10: $i,SV69: $i,SV56: $i] :
( ( ( between @ SV56 @ SV69 @ SV10 )
= $true )
| ( ( ( SV26 = SV39 )
| ( between @ SV69 @ SV10 @ SV56 ) )
= $true )
| ( ( between @ SV10 @ SV56 @ SV69 )
= $true )
| ( ( equidistant @ SV69 @ SV26 @ SV69 @ SV39 )
= $false )
| ( ( equidistant @ SV56 @ SV26 @ SV56 @ SV39 )
= $false )
| ( ( equidistant @ SV10 @ SV26 @ SV10 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[210]) ).
thf(215,plain,
! [SV66: $i,SV14: $i,SV43: $i,SV50: $i,SV72: $i,SV30: $i] :
( ( ( ~ ( between @ SV30 @ SV72 @ SV50 ) )
= $true )
| ( ( between @ SV43 @ ( continuous @ SV14 @ SV30 @ SV43 @ SV72 @ SV50 @ SV66 ) @ SV66 )
= $true )
| ( ( between @ SV14 @ SV30 @ SV50 )
= $false )
| ( ( equidistant @ SV14 @ SV50 @ SV14 @ SV66 )
= $false )
| ( ( equidistant @ SV14 @ SV30 @ SV14 @ SV43 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[211]) ).
thf(216,plain,
! [SV67: $i,SV44: $i,SV15: $i,SV51: $i,SV73: $i,SV31: $i] :
( ( ( ~ ( between @ SV31 @ SV73 @ SV51 ) )
= $true )
| ( ( equidistant @ SV15 @ SV73 @ SV15 @ ( continuous @ SV15 @ SV31 @ SV44 @ SV73 @ SV51 @ SV67 ) )
= $true )
| ( ( between @ SV15 @ SV31 @ SV51 )
= $false )
| ( ( equidistant @ SV15 @ SV51 @ SV15 @ SV67 )
= $false )
| ( ( equidistant @ SV15 @ SV31 @ SV15 @ SV44 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[212]) ).
thf(217,plain,
! [SV53: $i,SV52: $i,SV49: $i,SV22: $i,SV71: $i,SV36: $i,SV70: $i,SV6: $i] :
( ( ( equidistant @ SV6 @ SV70 @ SV36 @ SV71 )
= $false )
| ( ( ~ ( equidistant @ SV22 @ SV70 @ SV49 @ SV71 )
| ~ ( between @ SV6 @ SV22 @ SV52 )
| ~ ( between @ SV36 @ SV49 @ SV53 )
| ( SV6 = SV22 )
| ( equidistant @ SV52 @ SV70 @ SV53 @ SV71 ) )
= $true )
| ( ( equidistant @ SV22 @ SV52 @ SV49 @ SV53 )
= $false )
| ( ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[213]) ).
thf(218,plain,
! [SV56: $i,SV10: $i,SV69: $i,SV39: $i,SV26: $i] :
( ( ( SV26 = SV39 )
= $true )
| ( ( between @ SV69 @ SV10 @ SV56 )
= $true )
| ( ( between @ SV56 @ SV69 @ SV10 )
= $true )
| ( ( between @ SV10 @ SV56 @ SV69 )
= $true )
| ( ( equidistant @ SV69 @ SV26 @ SV69 @ SV39 )
= $false )
| ( ( equidistant @ SV56 @ SV26 @ SV56 @ SV39 )
= $false )
| ( ( equidistant @ SV10 @ SV26 @ SV10 @ SV39 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[214]) ).
thf(219,plain,
! [SV66: $i,SV14: $i,SV43: $i,SV50: $i,SV72: $i,SV30: $i] :
( ( ( between @ SV30 @ SV72 @ SV50 )
= $false )
| ( ( between @ SV43 @ ( continuous @ SV14 @ SV30 @ SV43 @ SV72 @ SV50 @ SV66 ) @ SV66 )
= $true )
| ( ( between @ SV14 @ SV30 @ SV50 )
= $false )
| ( ( equidistant @ SV14 @ SV50 @ SV14 @ SV66 )
= $false )
| ( ( equidistant @ SV14 @ SV30 @ SV14 @ SV43 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[215]) ).
thf(220,plain,
! [SV67: $i,SV44: $i,SV15: $i,SV51: $i,SV73: $i,SV31: $i] :
( ( ( between @ SV31 @ SV73 @ SV51 )
= $false )
| ( ( equidistant @ SV15 @ SV73 @ SV15 @ ( continuous @ SV15 @ SV31 @ SV44 @ SV73 @ SV51 @ SV67 ) )
= $true )
| ( ( between @ SV15 @ SV31 @ SV51 )
= $false )
| ( ( equidistant @ SV15 @ SV51 @ SV15 @ SV67 )
= $false )
| ( ( equidistant @ SV15 @ SV31 @ SV15 @ SV44 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[216]) ).
thf(221,plain,
! [SV53: $i,SV36: $i,SV52: $i,SV6: $i,SV71: $i,SV49: $i,SV70: $i,SV22: $i] :
( ( ( ~ ( equidistant @ SV22 @ SV70 @ SV49 @ SV71 ) )
= $true )
| ( ( ~ ( between @ SV6 @ SV22 @ SV52 )
| ~ ( between @ SV36 @ SV49 @ SV53 )
| ( SV6 = SV22 )
| ( equidistant @ SV52 @ SV70 @ SV53 @ SV71 ) )
= $true )
| ( ( equidistant @ SV6 @ SV70 @ SV36 @ SV71 )
= $false )
| ( ( equidistant @ SV22 @ SV52 @ SV49 @ SV53 )
= $false )
| ( ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[217]) ).
thf(222,plain,
! [SV53: $i,SV36: $i,SV52: $i,SV6: $i,SV71: $i,SV49: $i,SV70: $i,SV22: $i] :
( ( ( equidistant @ SV22 @ SV70 @ SV49 @ SV71 )
= $false )
| ( ( ~ ( between @ SV6 @ SV22 @ SV52 )
| ~ ( between @ SV36 @ SV49 @ SV53 )
| ( SV6 = SV22 )
| ( equidistant @ SV52 @ SV70 @ SV53 @ SV71 ) )
= $true )
| ( ( equidistant @ SV6 @ SV70 @ SV36 @ SV71 )
= $false )
| ( ( equidistant @ SV22 @ SV52 @ SV49 @ SV53 )
= $false )
| ( ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[221]) ).
thf(223,plain,
! [SV71: $i,SV70: $i,SV53: $i,SV49: $i,SV36: $i,SV52: $i,SV22: $i,SV6: $i] :
( ( ( ~ ( between @ SV6 @ SV22 @ SV52 ) )
= $true )
| ( ( ~ ( between @ SV36 @ SV49 @ SV53 )
| ( SV6 = SV22 )
| ( equidistant @ SV52 @ SV70 @ SV53 @ SV71 ) )
= $true )
| ( ( equidistant @ SV22 @ SV70 @ SV49 @ SV71 )
= $false )
| ( ( equidistant @ SV6 @ SV70 @ SV36 @ SV71 )
= $false )
| ( ( equidistant @ SV22 @ SV52 @ SV49 @ SV53 )
= $false )
| ( ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[222]) ).
thf(224,plain,
! [SV71: $i,SV70: $i,SV53: $i,SV49: $i,SV36: $i,SV52: $i,SV22: $i,SV6: $i] :
( ( ( between @ SV6 @ SV22 @ SV52 )
= $false )
| ( ( ~ ( between @ SV36 @ SV49 @ SV53 )
| ( SV6 = SV22 )
| ( equidistant @ SV52 @ SV70 @ SV53 @ SV71 ) )
= $true )
| ( ( equidistant @ SV22 @ SV70 @ SV49 @ SV71 )
= $false )
| ( ( equidistant @ SV6 @ SV70 @ SV36 @ SV71 )
= $false )
| ( ( equidistant @ SV22 @ SV52 @ SV49 @ SV53 )
= $false )
| ( ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[223]) ).
thf(225,plain,
! [SV71: $i,SV70: $i,SV52: $i,SV22: $i,SV6: $i,SV53: $i,SV49: $i,SV36: $i] :
( ( ( ~ ( between @ SV36 @ SV49 @ SV53 ) )
= $true )
| ( ( ( SV6 = SV22 )
| ( equidistant @ SV52 @ SV70 @ SV53 @ SV71 ) )
= $true )
| ( ( between @ SV6 @ SV22 @ SV52 )
= $false )
| ( ( equidistant @ SV22 @ SV70 @ SV49 @ SV71 )
= $false )
| ( ( equidistant @ SV6 @ SV70 @ SV36 @ SV71 )
= $false )
| ( ( equidistant @ SV22 @ SV52 @ SV49 @ SV53 )
= $false )
| ( ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[224]) ).
thf(226,plain,
! [SV71: $i,SV70: $i,SV52: $i,SV22: $i,SV6: $i,SV53: $i,SV49: $i,SV36: $i] :
( ( ( between @ SV36 @ SV49 @ SV53 )
= $false )
| ( ( ( SV6 = SV22 )
| ( equidistant @ SV52 @ SV70 @ SV53 @ SV71 ) )
= $true )
| ( ( between @ SV6 @ SV22 @ SV52 )
= $false )
| ( ( equidistant @ SV22 @ SV70 @ SV49 @ SV71 )
= $false )
| ( ( equidistant @ SV6 @ SV70 @ SV36 @ SV71 )
= $false )
| ( ( equidistant @ SV22 @ SV52 @ SV49 @ SV53 )
= $false )
| ( ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[225]) ).
thf(227,plain,
! [SV49: $i,SV36: $i,SV71: $i,SV53: $i,SV70: $i,SV52: $i,SV22: $i,SV6: $i] :
( ( ( SV6 = SV22 )
= $true )
| ( ( equidistant @ SV52 @ SV70 @ SV53 @ SV71 )
= $true )
| ( ( between @ SV36 @ SV49 @ SV53 )
= $false )
| ( ( between @ SV6 @ SV22 @ SV52 )
= $false )
| ( ( equidistant @ SV22 @ SV70 @ SV49 @ SV71 )
= $false )
| ( ( equidistant @ SV6 @ SV70 @ SV36 @ SV71 )
= $false )
| ( ( equidistant @ SV22 @ SV52 @ SV49 @ SV53 )
= $false )
| ( ( equidistant @ SV6 @ SV22 @ SV36 @ SV49 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[226]) ).
thf(228,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[60,227,220,219,218,202,201,200,197,190,189,147,137,135,134,117,102,101,93,92,91,81]) ).
thf(229,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[228]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO058-2 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : leo --timeout %d --proofoutput 1 --foatp e --atp e=./eprover %s
% 0.13/0.34 % Computer : n006.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 14:58:40 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.20/0.42
% 0.20/0.42 No.of.Axioms: 21
% 0.20/0.42
% 0.20/0.42 Length.of.Defs: 0
% 0.20/0.42
% 0.20/0.42 Contains.Choice.Funs: false
% 0.20/0.49 (rf:0,axioms:21,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:600,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:23,loop_count:0,foatp_calls:0,translation:fof_full).................
% 0.51/0.76
% 0.51/0.76 ********************************
% 0.51/0.76 * All subproblems solved! *
% 0.51/0.76 ********************************
% 0.51/0.76 % SZS status Unsatisfiable for /export/starexec/sandbox2/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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:228,loop_count:0,foatp_calls:1,translation:fof_full)
% 0.60/0.77
% 0.60/0.77 %**** Beginning of derivation protocol ****
% 0.60/0.77 % SZS output start CNFRefutation
% See solution above
% 0.60/0.77
% 0.60/0.77 %**** End of derivation protocol ****
% 0.60/0.77 %**** no. of clauses in derivation: 229 ****
% 0.60/0.77 %**** clause counter: 228 ****
% 0.60/0.77
% 0.60/0.77 % SZS status Unsatisfiable for /export/starexec/sandbox2/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:true,expand_extuni:false,foatp:e,atp_timeout:74,atp_calls_frequency:10,ordering:none,proof_output:1,protocol_output:false,clause_count:228,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------