%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO070-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n012.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 : Sun Sep 27 07:12:15 AM UTC 2026
% Result : Unsatisfiable 25.95s 5.55s
% Output : Refutation 22.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 114
% Syntax : Number of formulae : 272 ( 103 unt; 0 typ; 0 def)
% Number of atoms : 692 ( 164 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 2879 ( 387 ~; 392 |; 0 &;2100 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 10 con; 0-6 aty)
% Number of variables : 770 ( 0 ^; 770 !; 0 ?; 770 :)
% Comments :
%------------------------------------------------------------------------------
thf(colinear_decl,type,
colinear: $i > $i > $i > $o ).
thf(u_decl,type,
u: $i ).
thf(v_decl,type,
v: $i ).
thf(w_decl,type,
w: $i ).
thf(reflection_decl,type,
reflection: $i > $i > $i ).
thf(extension_decl,type,
extension: $i > $i > $i > $i > $i ).
thf(equidistant_decl,type,
equidistant: $i > $i > $i > $i > $o ).
thf(between_decl,type,
between: $i > $i > $i > $o ).
thf(continuous_decl,type,
continuous: $i > $i > $i > $i > $i > $i > $i ).
thf(insertion_decl,type,
insertion: $i > $i > $i > $i > $i ).
thf(euclid1_decl,type,
euclid1: $i > $i > $i > $i > $i > $i ).
thf(lower_dimension_point_1_decl,type,
lower_dimension_point_1: $i ).
thf(lower_dimension_point_2_decl,type,
lower_dimension_point_2: $i ).
thf(euclid2_decl,type,
euclid2: $i > $i > $i > $i > $i > $i ).
thf(inner_pasch_decl,type,
inner_pasch: $i > $i > $i > $i > $i > $i ).
thf(lower_dimension_point_3_decl,type,
lower_dimension_point_3: $i ).
thf(x_decl,type,
x: $i ).
thf(y_decl,type,
y: $i ).
thf(51,axiom,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(231,plain,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(105,axiom,
u != v,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_not_v) ).
thf(345,plain,
u != v,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(346,plain,
u != v,
inference(polarity_switch,[status(thm)],[345]) ).
thf(347,plain,
v != u,
inference(lifteq,[status(thm)],[346]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_5) ).
thf(249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( D @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(114,axiom,
w @ ( y @ ( u @ between ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',y_between_u_and_w) ).
thf(365,plain,
w @ ( y @ ( u @ between ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( C @ ( B @ ( B @ ( A @ extension ) ) ) ) )
| ( A = B )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_1) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( C @ ( B @ ( B @ ( A @ extension ) ) ) ) )
| ( A = B )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(25,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ reflection ) @ reflection ) @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).
thf(170,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ reflection ) @ reflection ) @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(1,negated_conjecture,
w @ ( v @ ( u @ colinear ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_uvw_not_colinear) ).
thf(115,plain,
w @ ( v @ ( u @ colinear ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(102,axiom,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ colinear ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11) ).
thf(338,plain,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ colinear ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(339,plain,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ colinear ) ) ),
inference(polarity_switch,[status(thm)],[338]) ).
thf(377,plain,
( ( ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ colinear ) ) )
!= ( w @ ( v @ ( u @ colinear ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[115,339]) ).
thf(378,plain,
( ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ colinear ) ) )
!= ( w @ ( v @ ( u @ colinear ) ) ) ),
inference(simp,[status(thm)],[377]) ).
thf(379,plain,
( ( lower_dimension_point_3 != w )
| ( lower_dimension_point_2 != v )
| ( lower_dimension_point_1 != u ) ),
inference(simp,[status(thm)],[378]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ reflection ) )
= ( B @ ( A @ ( B @ ( A @ extension ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
thf(118,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ reflection ) )
= ( B @ ( A @ ( B @ ( A @ extension ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( A @ extension ) ) ) )
= ( B @ ( A @ reflection ) ) ),
inference(lifteq,[status(thm)],[118]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( A
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( A @ ( B @ extension ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e3_1) ).
thf(251,plain,
! [B: $i,A: $i] :
( A
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( A @ ( B @ extension ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(252,plain,
! [B: $i,A: $i] :
( A
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( A @ ( B @ extension ) ) ) ) ),
inference(polarity_switch,[status(thm)],[251]) ).
thf(253,plain,
! [B: $i,A: $i] :
( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( A @ ( B @ extension ) ) ) )
!= A ),
inference(lifteq,[status(thm)],[252]) ).
thf(439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ ( A @ extension ) ) ) )
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( C @ ( D @ extension ) ) ) ) )
| ( ( B @ ( A @ reflection ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[119,253]) ).
thf(440,plain,
( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ reflection ) )
!= lower_dimension_point_2 ),
inference(pattern_uni,[status(thm)],[439:[bind(A,$thf( lower_dimension_point_1 )),bind(B,$thf( lower_dimension_point_2 )),bind(C,$thf( lower_dimension_point_2 )),bind(D,$thf( lower_dimension_point_1 ))]]) ).
thf(67,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_2) ).
thf(267,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(268,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(polarity_switch,[status(thm)],[267]) ).
thf(269,plain,
lower_dimension_point_3 != lower_dimension_point_2,
inference(lifteq,[status(thm)],[268]) ).
thf(39,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_1) ).
thf(202,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(45,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( E @ ( C @ ( B @ ( A @ inner_pasch ) ) ) ) @ ( E @ between ) ) )
| ~ ( C @ ( E @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch2) ).
thf(217,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( E @ ( C @ ( B @ ( A @ inner_pasch ) ) ) ) @ ( E @ between ) ) )
| ~ ( C @ ( E @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_2) ).
thf(276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( C @ ( A @ ( B @ extension ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
thf(120,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( C @ ( A @ ( B @ extension ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(58,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5) ).
thf(247,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( E @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(13,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ between ) ) )
| ( A
!= ( E @ ( D @ ( C @ ( B @ extension ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b0) ).
thf(142,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ between ) ) )
| ( A
!= ( E @ ( D @ ( C @ ( B @ extension ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity1) ).
thf(340,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(17,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
thf(153,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(27,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( F @ ( E @ insertion ) ) ) )
= ( D @ ( C @ ( F @ ( E @ insertion ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i4) ).
thf(174,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( F @ ( E @ insertion ) ) ) )
= ( D @ ( C @ ( F @ ( E @ insertion ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(77,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( A @ ( E @ ( D @ insertion ) ) ) @ ( D @ between ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i2_2) ).
thf(288,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( A @ ( E @ ( D @ insertion ) ) ) @ ( D @ between ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(95,axiom,
x != u,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_not_u) ).
thf(320,plain,
x != u,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(32,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
thf(184,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( F @ ( E @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(6,axiom,
! [A: $i] :
( A
= ( A @ ( A @ reflection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).
thf(125,plain,
! [A: $i] :
( A
= ( A @ ( A @ reflection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(36,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( D @ ( A @ ( E @ between ) ) )
| ( A @ ( E @ ( D @ between ) ) )
| ( E @ ( D @ ( A @ between ) ) )
| ~ ( C @ ( E @ ( B @ ( E @ equidistant ) ) ) )
| ~ ( C @ ( D @ ( B @ ( D @ equidistant ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_dimension) ).
thf(196,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( D @ ( A @ ( E @ between ) ) )
| ( A @ ( E @ ( D @ between ) ) )
| ( E @ ( D @ ( A @ between ) ) )
| ~ ( C @ ( E @ ( B @ ( E @ equidistant ) ) ) )
| ~ ( C @ ( D @ ( B @ ( D @ equidistant ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(19,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ continuous ) ) ) ) ) @ ( A @ ( F @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( F @ ( B @ between ) ) )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).
thf(157,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ continuous ) ) ) ) ) @ ( A @ ( F @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( F @ ( B @ between ) ) )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ between ) ) )
| ( B @ ( D @ ( A @ between ) ) )
| ( B = C )
| ~ ( C @ ( B @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7) ).
thf(189,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ between ) ) )
| ( B @ ( D @ ( A @ between ) ) )
| ( B = C )
| ~ ( C @ ( B @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_3) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(50,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_3) ).
thf(228,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_2) ).
thf(316,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(64,axiom,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(260,plain,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(261,plain,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
inference(polarity_switch,[status(thm)],[260]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3) ).
thf(164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( A = B )
| ~ ( D @ ( B @ ( C @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( A @ ( C @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11) ).
thf(179,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( A = B )
| ~ ( D @ ( B @ ( C @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( A @ ( C @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(93,axiom,
x @ ( y @ ( v @ between ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',y_between_v_and_x) ).
thf(318,plain,
x @ ( y @ ( v @ between ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(232,plain,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
inference(polarity_switch,[status(thm)],[231]) ).
thf(372,plain,
( ( ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) )
!= ( x @ ( y @ ( v @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[318,232]) ).
thf(373,plain,
( ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) )
!= ( x @ ( y @ ( v @ between ) ) ) ),
inference(simp,[status(thm)],[372]) ).
thf(376,plain,
( ( x != lower_dimension_point_3 )
| ( y != lower_dimension_point_2 )
| ( lower_dimension_point_1 != v ) ),
inference(simp,[status(thm)],[373]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(238,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(121,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ ( B @ extension ) ) ) )
= A ),
inference(lifteq,[status(thm)],[120]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( B @ colinear ) ) )
| ~ ( D @ ( B @ ( A @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_2) ).
thf(348,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( B @ colinear ) ) )
| ~ ( D @ ( B @ ( A @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_1) ).
thf(353,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(221,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(89,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ colinear ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3_1) ).
thf(312,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ colinear ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ reflection ) @ reflection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).
thf(116,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ reflection ) @ reflection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(56,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( B @ ( D @ ( A @ euclid2 ) ) ) ) @ ( E @ ( A @ between ) ) )
| ( A = B )
| ~ ( E @ ( B @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid2) ).
thf(243,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( B @ ( D @ ( A @ euclid2 ) ) ) ) @ ( E @ ( A @ between ) ) )
| ( A = B )
| ~ ( E @ ( B @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(87,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ colinear ) ) )
| ~ ( E @ ( B @ ( A @ colinear ) ) )
| ~ ( F @ ( C @ ( E @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c4) ).
thf(307,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ colinear ) ) )
| ~ ( E @ ( B @ ( A @ colinear ) ) )
| ~ ( F @ ( C @ ( E @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( B @ ( A @ ( C @ ( A @ insertion ) ) ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i3) ).
thf(292,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( B @ ( A @ ( C @ ( A @ insertion ) ) ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(52,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( B @ ( A @ ( C @ ( E @ ( D @ ( F @ ( A @ inner_pasch ) ) ) ) @ ( E @ inner_pasch ) ) ) ) @ ( B @ between ) ) )
| ( C @ ( C @ ( B @ ( A @ ( C @ ( E @ ( D @ ( F @ ( A @ inner_pasch ) ) ) ) @ ( E @ inner_pasch ) ) ) ) @ ( F @ between ) ) )
| ~ ( D @ ( F @ ( A @ between ) ) )
| ~ ( C @ ( E @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b10) ).
thf(233,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( B @ ( A @ ( C @ ( E @ ( D @ ( F @ ( A @ inner_pasch ) ) ) ) @ ( E @ inner_pasch ) ) ) ) @ ( B @ between ) ) )
| ( C @ ( C @ ( B @ ( A @ ( C @ ( E @ ( D @ ( F @ ( A @ inner_pasch ) ) ) ) @ ( E @ inner_pasch ) ) ) ) @ ( F @ between ) ) )
| ~ ( D @ ( F @ ( A @ between ) ) )
| ~ ( C @ ( E @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ reflection ) @ reflection ) )
= A ),
inference(lifteq,[status(thm)],[116]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ between ) ) )
| ( D @ ( C @ ( A @ between ) ) )
| ( A = B )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b12) ).
thf(270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ between ) ) )
| ( D @ ( C @ ( A @ between ) ) )
| ( A = B )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ colinear ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3_4) ).
thf(334,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ colinear ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ between ) ) )
| ( D @ ( C @ ( B @ between ) ) )
| ( A = B )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b13) ).
thf(302,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ between ) ) )
| ( D @ ( C @ ( B @ between ) ) )
| ( A = B )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ between ) ) )
| ( A != C )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).
thf(192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ between ) ) )
| ( A != C )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(70,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( B @ reflection ) @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
thf(275,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( B @ reflection ) @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).
thf(137,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = B )
| ( B @ ( A @ ( D @ colinear ) ) )
| ~ ( C @ ( B @ ( D @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c5_2) ).
thf(329,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = B )
| ( B @ ( A @ ( D @ colinear ) ) )
| ~ ( C @ ( B @ ( D @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(75,axiom,
! [B: $i,A: $i] : ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e3_3) ).
thf(285,plain,
! [B: $i,A: $i] : ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( B @ ( A @ extension ) ) ) @ ( B @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(48,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ between ) ) )
| ~ ( C @ ( E @ ( A @ between ) ) )
| ~ ( E @ ( D @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8) ).
thf(224,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ between ) ) )
| ~ ( C @ ( E @ ( A @ between ) ) )
| ~ ( E @ ( D @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(384,plain,
( ( ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) )
!= ( w @ ( y @ ( u @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[365,232]) ).
thf(385,plain,
( ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) )
!= ( w @ ( y @ ( u @ between ) ) ) ),
inference(simp,[status(thm)],[384]) ).
thf(388,plain,
( ( lower_dimension_point_3 != w )
| ( y != lower_dimension_point_2 )
| ( lower_dimension_point_1 != u ) ),
inference(simp,[status(thm)],[385]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ extension ) ) ) @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).
thf(141,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( C @ ( A @ ( B @ extension ) ) ) @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( D @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_4) ).
thf(212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ ( D @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(9,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = F )
| ( ( B @ ( A @ ( F @ ( E @ extension ) ) ) )
= ( D @ ( C @ ( F @ ( E @ extension ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_2) ).
thf(134,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = F )
| ( ( B @ ( A @ ( F @ ( E @ extension ) ) ) )
= ( D @ ( C @ ( F @ ( E @ extension ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_4) ).
thf(360,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( B @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b3) ).
thf(205,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( B @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_3) ).
thf(298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(23,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( A @ ( E @ ( D @ insertion ) ) ) @ ( C @ ( B @ equidistant ) ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i2_3) ).
thf(166,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( A @ ( E @ ( D @ insertion ) ) ) @ ( C @ ( B @ equidistant ) ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( D @ ( C @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b6) ).
thf(264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( D @ ( C @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A = B )
| ~ ( C @ ( A @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_1) ).
thf(279,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A = B )
| ~ ( C @ ( A @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b9) ).
thf(296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_1) ).
thf(149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(49,axiom,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(226,plain,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(227,plain,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
inference(polarity_switch,[status(thm)],[226]) ).
thf(370,plain,
( ( ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) )
!= ( x @ ( y @ ( v @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[318,227]) ).
thf(371,plain,
( ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) )
!= ( x @ ( y @ ( v @ between ) ) ) ),
inference(simp,[status(thm)],[370]) ).
thf(375,plain,
( ( x != lower_dimension_point_1 )
| ( y != lower_dimension_point_3 )
| ( lower_dimension_point_2 != v ) ),
inference(simp,[status(thm)],[371]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( A @ between ) ) )
| ( D @ ( B @ ( A @ between ) ) )
| ~ ( C @ ( D @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9) ).
thf(286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( A @ between ) ) )
| ( D @ ( B @ ( A @ between ) ) )
| ~ ( C @ ( D @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(203,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(polarity_switch,[status(thm)],[202]) ).
thf(204,plain,
lower_dimension_point_2 != lower_dimension_point_1,
inference(lifteq,[status(thm)],[203]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_5) ).
thf(313,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( A @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( A @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(46,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ continuous ) ) ) ) ) @ ( C @ between ) ) )
| ~ ( D @ ( F @ ( B @ between ) ) )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity1) ).
thf(219,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( D @ ( F @ ( C @ ( B @ ( A @ continuous ) ) ) ) ) @ ( C @ between ) ) )
| ~ ( D @ ( F @ ( B @ between ) ) )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( E @ ( A @ ( D @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(229,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(polarity_switch,[status(thm)],[228]) ).
thf(230,plain,
lower_dimension_point_3 != lower_dimension_point_1,
inference(lifteq,[status(thm)],[229]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ between ) ) )
| ( A @ ( C @ ( B @ between ) ) )
| ( C @ ( B @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity4) ).
thf(362,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ between ) ) )
| ( A @ ( C @ ( B @ between ) ) )
| ( C @ ( B @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ insertion ) ) ) )
= ( D @ ( C @ ( A @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( A @ ( B @ extension ) ) ) @ extension ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',insertion) ).
thf(208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ insertion ) ) ) )
= ( D @ ( C @ ( A @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( A @ ( B @ extension ) ) ) @ extension ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(382,plain,
( ( ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) )
!= ( w @ ( y @ ( u @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[365,227]) ).
thf(383,plain,
( ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) )
!= ( w @ ( y @ ( u @ between ) ) ) ),
inference(simp,[status(thm)],[382]) ).
thf(387,plain,
( ( lower_dimension_point_1 != w )
| ( y != lower_dimension_point_3 )
| ( lower_dimension_point_2 != u ) ),
inference(simp,[status(thm)],[383]) ).
thf(96,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_3) ).
thf(323,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(72,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
thf(278,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(86,axiom,
x @ ( v @ ( w @ ( u @ equidistant ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_w_equals_v_to_x) ).
thf(306,plain,
x @ ( v @ ( w @ ( u @ equidistant ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(55,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( D @ ( G @ ( B @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( C @ between ) ) )
| ~ ( E @ ( B @ ( A @ between ) ) )
| ~ ( H @ ( F @ ( G @ ( E @ equidistant ) ) ) )
| ~ ( H @ ( C @ ( G @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( C @ ( E @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12) ).
thf(241,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( D @ ( G @ ( B @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( C @ between ) ) )
| ~ ( E @ ( B @ ( A @ between ) ) )
| ~ ( H @ ( F @ ( G @ ( E @ equidistant ) ) ) )
| ~ ( H @ ( C @ ( G @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( C @ ( E @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
thf(162,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(368,plain,
( ( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) )
!= ( x @ ( y @ ( v @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[318,261]) ).
thf(369,plain,
( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) )
!= ( x @ ( y @ ( v @ between ) ) ) ),
inference(simp,[status(thm)],[368]) ).
thf(374,plain,
( ( x != lower_dimension_point_2 )
| ( y != lower_dimension_point_1 )
| ( lower_dimension_point_3 != v ) ),
inference(simp,[status(thm)],[369]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( D @ ( B @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b7) ).
thf(255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( D @ ( B @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(104,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( E @ ( D @ ( C @ colinear ) ) )
| ~ ( E @ ( B @ ( A @ colinear ) ) )
| ~ ( D @ ( B @ ( A @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t13) ).
thf(342,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( E @ ( D @ ( C @ colinear ) ) )
| ~ ( E @ ( B @ ( A @ colinear ) ) )
| ~ ( D @ ( B @ ( A @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ colinear ) ) )
| ~ ( D @ ( B @ ( A @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_1) ).
thf(355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D @ ( C @ ( A @ colinear ) ) )
| ~ ( D @ ( B @ ( A @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(80,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
thf(295,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ~ ( D @ ( C @ ( B @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( A @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15) ).
thf(282,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ~ ( D @ ( C @ ( B @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( A @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity2) ).
thf(327,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ ( D @ ( C @ insertion ) ) ) @ ( C @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i2_1) ).
thf(199,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ ( D @ ( C @ insertion ) ) ) @ ( C @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ reflection ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_1) ).
thf(127,plain,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ reflection ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ between ) ) )
| ~ ( C @ ( D @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b8) ).
thf(177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ between ) ) )
| ~ ( C @ ( D @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(30,axiom,
! [B: $i,A: $i] : ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).
thf(182,plain,
! [B: $i,A: $i] : ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b15) ).
thf(154,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ( A @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(380,plain,
( ( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) )
!= ( w @ ( y @ ( u @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[365,261]) ).
thf(381,plain,
( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) )
!= ( w @ ( y @ ( u @ between ) ) ) ),
inference(simp,[status(thm)],[380]) ).
thf(386,plain,
( ( lower_dimension_point_2 != w )
| ( y != lower_dimension_point_1 )
| ( lower_dimension_point_3 != u ) ),
inference(simp,[status(thm)],[381]) ).
thf(94,axiom,
u @ ( x @ ( w @ ( v @ equidistant ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_to_w_equals_x_to_u) ).
thf(319,plain,
u @ ( x @ ( w @ ( v @ equidistant ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(63,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( D @ ( G @ ( B @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( C @ between ) ) )
| ~ ( E @ ( B @ ( A @ between ) ) )
| ~ ( H @ ( F @ ( G @ ( E @ equidistant ) ) ) )
| ~ ( H @ ( C @ ( G @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14) ).
thf(258,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( D @ ( G @ ( B @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( C @ between ) ) )
| ~ ( E @ ( B @ ( A @ between ) ) )
| ~ ( H @ ( F @ ( G @ ( E @ equidistant ) ) ) )
| ~ ( H @ ( C @ ( G @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity3) ).
thf(351,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(33,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( B @ ( D @ ( A @ euclid1 ) ) ) ) @ ( D @ ( A @ between ) ) )
| ( A = B )
| ~ ( E @ ( B @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid1) ).
thf(186,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( B @ ( D @ ( A @ euclid1 ) ) ) ) @ ( D @ ( A @ between ) ) )
| ( A = B )
| ~ ( E @ ( B @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A = B )
| ~ ( B @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_2) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( A = B )
| ~ ( B @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(44,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( B @ ( D @ ( A @ euclid2 ) ) ) ) @ ( C @ ( C @ ( E @ ( B @ ( D @ ( A @ euclid1 ) ) ) ) @ between ) ) )
| ( A = B )
| ~ ( E @ ( B @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid3) ).
thf(214,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( E @ ( B @ ( D @ ( A @ euclid2 ) ) ) ) @ ( C @ ( C @ ( E @ ( B @ ( D @ ( A @ euclid1 ) ) ) ) @ between ) ) )
| ( A = B )
| ~ ( E @ ( B @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
thf(290,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( A = B )
| ~ ( D @ ( B @ ( C @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9) ).
thf(235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( A = B )
| ~ ( D @ ( B @ ( C @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( B @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(57,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(246,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(16,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ between ) ) )
| ~ ( E @ ( B @ ( A @ between ) ) )
| ~ ( F @ ( C @ ( E @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b11) ).
thf(151,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ between ) ) )
| ~ ( E @ ( B @ ( A @ between ) ) )
| ~ ( F @ ( C @ ( E @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(83,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( C @ ( E @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( C @ between ) ) )
| ~ ( E @ ( B @ ( A @ between ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8) ).
thf(300,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( C @ ( E @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( C @ between ) ) )
| ~ ( E @ ( B @ ( A @ between ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(91,axiom,
x @ ( w @ ( v @ ( u @ equidistant ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_to_v_equals_w_to_x) ).
thf(315,plain,
x @ ( w @ ( v @ ( u @ equidistant ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(14,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( F @ ( G @ ( E @ equidistant ) ) ) )
| ( A = B )
| ~ ( F @ ( D @ ( C @ between ) ) )
| ~ ( E @ ( B @ ( A @ between ) ) )
| ~ ( H @ ( D @ ( G @ ( B @ equidistant ) ) ) )
| ~ ( H @ ( C @ ( G @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_five_segment) ).
thf(146,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( H @ ( F @ ( G @ ( E @ equidistant ) ) ) )
| ( A = B )
| ~ ( F @ ( D @ ( C @ between ) ) )
| ~ ( E @ ( B @ ( A @ between ) ) )
| ~ ( H @ ( D @ ( G @ ( B @ equidistant ) ) ) )
| ~ ( H @ ( C @ ( G @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( E @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(31,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
thf(183,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(69,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( C @ ( B @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( C @ ( A @ equidistant ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( E @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13) ).
thf(273,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( C @ ( B @ equidistant ) ) ) )
| ~ ( F @ ( D @ ( C @ ( A @ equidistant ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( F @ ( E @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ between ) ) )
| ( C @ ( D @ ( B @ between ) ) )
| ~ ( C @ ( D @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b14) ).
thf(168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ between ) ) )
| ( C @ ( D @ ( B @ between ) ) )
| ~ ( C @ ( D @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(65,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( E @ ( C @ ( B @ ( A @ inner_pasch ) ) ) ) @ ( B @ between ) ) )
| ~ ( C @ ( E @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch1) ).
thf(262,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( E @ ( C @ ( B @ ( A @ inner_pasch ) ) ) ) @ ( B @ between ) ) )
| ~ ( C @ ( E @ ( D @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(85,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ colinear ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3_2) ).
thf(305,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ colinear ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b4) ).
thf(210,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ between ) ) )
| ~ ( D @ ( C @ ( B @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(126,plain,
! [A: $i] :
( ( A @ ( A @ reflection ) )
= A ),
inference(lifteq,[status(thm)],[125]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_2) ).
thf(358,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_1) ).
thf(332,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ ( B @ ( A @ extension ) ) ) )
= ( A @ ( B @ ( B @ ( A @ extension ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_3) ).
thf(131,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( B @ ( A @ ( B @ ( A @ extension ) ) ) )
= ( A @ ( B @ ( B @ ( A @ extension ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ between ) ) )
| ~ ( D @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b5) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ between ) ) )
| ~ ( D @ ( C @ ( A @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(321,plain,
x != u,
inference(polarity_switch,[status(thm)],[320]) ).
thf(322,plain,
x != u,
inference(lifteq,[status(thm)],[321]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A
!= ( A @ ( B @ reflection ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
thf(122,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A
!= ( A @ ( B @ reflection ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = B )
| ( C @ ( A @ ( D @ colinear ) ) )
| ~ ( C @ ( B @ ( D @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c5_1) ).
thf(309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = B )
| ( C @ ( A @ ( D @ colinear ) ) )
| ~ ( C @ ( B @ ( D @ colinear ) ) )
| ~ ( C @ ( B @ ( A @ colinear ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(113,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ colinear ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3_3) ).
thf(364,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ colinear ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( C @ ( D @ extension ) ) ) @ ( C @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( A @ ( B @ extension ) ) ) @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e3_2) ).
thf(254,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( C @ ( D @ extension ) ) ) @ ( C @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( A @ ( B @ extension ) ) ) @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(9037,plain,
$false,
inference(e,[status(thm)],[231,347,249,365,138,170,115,379,440,269,202,217,276,120,247,142,340,153,174,288,320,184,125,196,157,189,325,228,316,261,164,179,376,253,238,121,348,353,221,312,116,243,307,292,233,117,270,334,302,260,192,275,137,329,285,224,388,141,339,212,134,360,205,298,166,264,279,296,149,375,286,118,204,313,159,219,230,362,318,208,387,345,323,251,278,306,226,267,241,162,374,255,342,355,295,282,327,199,127,338,177,182,154,386,319,258,351,186,171,214,290,119,235,246,151,300,315,146,183,273,168,262,305,210,126,358,332,131,200,322,122,309,364,232,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO070-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.04 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.05/0.33 % Computer : n012.cluster.edu
% 0.05/0.33 % Model : x86_64 x86_64
% 0.05/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.33 % Memory : 8046.5625MB
% 0.05/0.33 % OS : Linux 6.8.0-71-generic
% 0.05/0.33 % CPULimit : 300
% 0.05/0.33 % WCLimit : 300
% 0.05/0.33 % DateTime : Fri Sep 25 12:38:35 UTC 2026
% 0.05/0.33 % CPUTime :
% 0.05/0.33 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.50/0.63 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.64/0.79 % [INFO] Parsing done (150ms).
% 0.64/0.79 % [INFO] Running in sequential loop mode.
% 1.25/0.99 % [INFO] eprover registered as external prover.
% 1.25/1.00 % [INFO] Scanning for conjecture ...
% 1.47/1.05 % [INFO] Found a conjecture (or negated_conjecture) and 113 axioms. Running axiom selection ...
% 1.47/1.10 % [INFO] Axiom selection finished. Selected 113 axioms (removed 0 axioms).
% 1.71/1.16 % [INFO] Problem is propositional (TPTP CNF).
% 1.71/1.17 % [INFO] Type checking passed.
% 1.71/1.18 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 25.95/5.54 % External prover 'e' found a proof!
% 25.95/5.54 % [INFO] Killing All external provers ...
% 25.95/5.55 % Time passed: 5137ms (effective reasoning time: 4749ms)
% 25.95/5.55 % Axioms used in derivation (113): d3, reflexivity_for_equidistance, e3_2, c2_1, c3_3, euclid3, d5, t10_4, t13, i2_3, continuity1, c4, e2_2, lower_dimension1, u_not_v, d4_4, b2, t12_1, c5_1, continuity2, b10, t9, b3, r2_1, d4_5, transitivity_for_equidistance, y_between_u_and_w, colinearity3, e1, b14, b7, t10_5, d9, r6, inner_pasch2, i4, t12_2, b4, lower_dimension2, t3, b1, d13, reflection, c5_2, r2_2, b8, u_to_w_equals_v_to_x, u_to_v_equals_w_to_x, d12, identity_for_betweeness, b11, colinearity4, r5, i3, c3_4, outer_five_segment, r3_2, b0, b15, upper_dimension, t2, t7, c2_3, b5, d15, euclid1, d7, d10_2, colinearity1, r4, e2_3, segment_construction2, x_not_u, d2, d10_3, e3_1, d4_2, i2_1, t10_1, c3_1, b12, d4_1, lower_dimension3, y_between_v_and_x, t6_2, b9, t8, t10_3, d8, b6, inner_pasch1, e3_3, r3_1, b13, c2_2, segment_construction1, d14, euclid2, d10_1, e2_1, d1, t1, d11, identity_for_equidistance, t10_2, d4_3, colinearity2, t6_1, insertion, i2_2, c3_2, v_to_w_equals_x_to_u, t11
% 25.95/5.55 % No. of inferences in proof: 272
% 25.95/5.55 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5137 ms resp. 4749 ms w/o parsing
% 22.70/5.61 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.70/5.61 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------