%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO063-3 : 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 : n018.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 07:12:13 AM UTC 2026
% Result : Unsatisfiable 7.36s 3.87s
% Output : Refutation 8.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 76
% Syntax : Number of formulae : 153 ( 55 unt; 0 typ; 0 def)
% Number of atoms : 397 ( 86 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1884 ( 226 ~; 244 |; 0 &;1414 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 10 con; 0-6 aty)
% Number of variables : 530 ( 0 ^; 530 !; 0 ?; 530 :)
% Comments :
%------------------------------------------------------------------------------
thf(insertion_decl,type,
insertion: $i > $i > $i > $i > $i ).
thf(u_decl,type,
u: $i ).
thf(v_decl,type,
v: $i ).
thf(w_decl,type,
w: $i ).
thf(x_decl,type,
x: $i ).
thf(y_decl,type,
y: $i ).
thf(z_decl,type,
z: $i ).
thf(reflection_decl,type,
reflection: $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(extension_decl,type,
extension: $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(33,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(153,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)],[33]) ).
thf(48,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(189,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)],[48]) ).
thf(36,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_3) ).
thf(160,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(41,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(173,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(23,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(128,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)],[23]) ).
thf(71,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(236,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)],[71]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A
!= ( A @ ( B @ reflection ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A
!= ( A @ ( B @ reflection ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(50,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(194,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)],[50]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(150,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(29,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(143,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)],[29]) ).
thf(40,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(170,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)],[40]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
thf(115,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(54,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(202,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)],[54]) ).
thf(46,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(184,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)],[46]) ).
thf(15,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(110,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)],[15]) ).
thf(13,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ reflection ) @ reflection ) @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).
thf(106,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ reflection ) @ reflection ) @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(72,axiom,
z @ ( y @ ( x @ ( w @ equidistant ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_to_x_equals_y_to_z) ).
thf(238,plain,
z @ ( y @ ( x @ ( w @ equidistant ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(21,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(121,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)],[21]) ).
thf(63,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(221,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)],[63]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ reflection ) @ reflection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).
thf(89,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ reflection ) @ reflection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(25,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_1) ).
thf(133,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(69,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(233,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)],[69]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( C @ ( A @ ( B @ extension ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
thf(117,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( C @ ( A @ ( B @ extension ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ reflection ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_1) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ reflection ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(62,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
thf(220,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(11,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(102,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)],[11]) ).
thf(66,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
thf(229,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(9,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(97,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)],[9]) ).
thf(64,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(224,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)],[64]) ).
thf(34,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(156,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)],[34]) ).
thf(28,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(141,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)],[28]) ).
thf(22,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(124,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)],[22]) ).
thf(1,negated_conjecture,
( ( x @ ( w @ ( v @ ( u @ insertion ) ) ) )
!= ( z @ ( y @ ( v @ ( u @ insertion ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_equality_of_insertions) ).
thf(77,plain,
( ( x @ ( w @ ( v @ ( u @ insertion ) ) ) )
!= ( z @ ( y @ ( v @ ( u @ insertion ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(58,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(212,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)],[58]) ).
thf(8,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
thf(96,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(38,axiom,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(166,plain,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(31,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(148,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)],[31]) ).
thf(44,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(180,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)],[44]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ reflection ) )
= ( B @ ( A @ ( B @ ( A @ extension ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ reflection ) )
= ( B @ ( A @ ( B @ ( A @ extension ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(49,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(191,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)],[49]) ).
thf(55,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(204,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)],[55]) ).
thf(47,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(187,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)],[47]) ).
thf(16,axiom,
! [B: $i,A: $i] : ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).
thf(113,plain,
! [B: $i,A: $i] : ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(67,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(230,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)],[67]) ).
thf(76,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(245,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)],[76]) ).
thf(59,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( B @ reflection ) @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
thf(213,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( B @ reflection ) @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(6,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(91,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)],[6]) ).
thf(74,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(240,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)],[74]) ).
thf(52,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(198,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)],[52]) ).
thf(68,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(231,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)],[68]) ).
thf(10,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(99,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)],[10]) ).
thf(61,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(218,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)],[61]) ).
thf(12,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(104,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)],[12]) ).
thf(35,axiom,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(158,plain,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(17,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
thf(114,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(27,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(139,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)],[27]) ).
thf(20,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(119,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)],[20]) ).
thf(70,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(235,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)],[70]) ).
thf(56,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_2) ).
thf(207,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(60,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(214,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)],[60]) ).
thf(39,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(168,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)],[39]) ).
thf(30,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(146,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)],[30]) ).
thf(45,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(183,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(57,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(210,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)],[57]) ).
thf(14,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(107,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)],[14]) ).
thf(26,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(136,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)],[26]) ).
thf(51,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(195,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)],[51]) ).
thf(7,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(94,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)],[7]) ).
thf(73,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(239,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)],[73]) ).
thf(75,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(242,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)],[75]) ).
thf(24,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(131,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)],[24]) ).
thf(43,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(178,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)],[43]) ).
thf(37,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(163,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)],[37]) ).
thf(53,axiom,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(200,plain,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(65,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(227,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)],[65]) ).
thf(3,axiom,
! [A: $i] :
( A
= ( A @ ( A @ reflection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).
thf(83,plain,
! [A: $i] :
( A
= ( A @ ( A @ reflection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(247,plain,
$false,
inference(e,[status(thm)],[153,189,160,173,128,236,80,194,150,143,170,115,202,184,110,106,238,121,221,89,133,233,117,85,220,102,229,97,224,156,141,124,77,212,96,166,148,180,176,191,204,187,113,230,245,213,91,240,198,231,99,218,104,158,114,139,119,235,207,214,168,146,183,210,107,136,195,94,239,242,131,178,163,200,227,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO063-3 : TPTP v9.3.1. Bugfixed v1.2.1.
% 0.00/0.11 % 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
% 0.22/0.69 % Computer : n018.cluster.edu
% 0.22/0.69 % Model : x86_64 x86_64
% 0.22/0.69 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/0.69 % Memory : 8046.5625MB
% 0.22/0.69 % OS : Linux 6.8.0-71-generic
% 0.22/0.69 % CPULimit : 300
% 0.22/0.69 % WCLimit : 300
% 0.22/0.69 % DateTime : Fri Sep 25 12:39:50 UTC 2026
% 0.22/0.69 % CPUTime :
% 0.22/0.70 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
% 1.39/1.52 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.39/1.90 % [INFO] Parsing done (372ms).
% 2.39/1.92 % [INFO] Running in sequential loop mode.
% 3.48/2.50 % [INFO] eprover registered as external prover.
% 3.48/2.51 % [INFO] Scanning for conjecture ...
% 3.68/2.66 % [INFO] Found a conjecture (or negated_conjecture) and 75 axioms. Running axiom selection ...
% 3.86/2.77 % [INFO] Axiom selection finished. Selected 75 axioms (removed 0 axioms).
% 4.13/2.85 % [INFO] Problem is propositional (TPTP CNF).
% 4.13/2.87 % [INFO] Type checking passed.
% 4.13/2.87 % [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 ...
% 7.36/3.87 % External prover 'e' found a proof!
% 7.36/3.87 % [INFO] Killing All external provers ...
% 7.36/3.87 % Time passed: 2980ms (effective reasoning time: 1936ms)
% 7.36/3.87 % Axioms used in derivation (75): e3_2, b7, d3, reflexivity_for_equidistance, outer_five_segment, i2_1, d8, euclid3, d5, i2_3, continuity1, e2_2, lower_dimension1, d4_4, b2, continuity2, b10, b3, r2_1, d4_5, transitivity_for_equidistance, e1, w_to_x_equals_y_to_z, d9, r6, inner_pasch2, b4, lower_dimension2, t3, b1, d13, reflection, r2_2, b8, d12, identity_for_betweeness, r5, i3, r3_2, b0, upper_dimension, t2, b5, d15, euclid1, d7, d10_2, r4, e2_3, segment_construction2, d2, d10_3, e3_1, d4_2, d4_1, lower_dimension3, t6_2, b9, b6, inner_pasch1, e3_3, r3_1, segment_construction1, d14, euclid2, d10_1, e2_1, d1, t1, d11, identity_for_equidistance, d4_3, t6_1, insertion, i2_2
% 7.36/3.87 % No. of inferences in proof: 153
% 7.36/3.87 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2980 ms resp. 1936 ms w/o parsing
% 8.37/4.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.37/4.06 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------