%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : GEO009-3 : 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 07:12:00 AM UTC 2026
% Result : Unsatisfiable 6.92s 7.30s
% Output : Refutation 6.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 83
% Syntax : Number of formulae : 232 ( 93 unt; 0 typ; 0 def)
% Number of atoms : 611 ( 168 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 2484 ( 346 ~; 323 |; 0 &;1815 @)
% ( 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 : 19 ( 16 usr; 9 con; 0-6 aty)
% Number of variables : 657 ( 0 ^; 657 !; 0 ?; 657 :)
% Comments :
%------------------------------------------------------------------------------
thf(between_decl,type,
between: $i > $i > $i > $o ).
thf(a_decl,type,
a: $i ).
thf(d_decl,type,
d: $i ).
thf(c_decl,type,
c: $i ).
thf(equidistant_decl,type,
equidistant: $i > $i > $i > $i > $o ).
thf(reflection_decl,type,
reflection: $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(insertion_decl,type,
insertion: $i > $i > $i > $i > $i ).
thf(extension_decl,type,
extension: $i > $i > $i > $i > $i ).
thf(lower_dimension_point_3_decl,type,
lower_dimension_point_3: $i ).
thf(continuous_decl,type,
continuous: $i > $i > $i > $i > $i > $i > $i ).
thf(e_decl,type,
e: $i ).
thf(euclid1_decl,type,
euclid1: $i > $i > $i > $i > $i > $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(67,axiom,
e @ ( c @ ( a @ between ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_between_a_and_e) ).
thf(231,plain,
e @ ( c @ ( a @ between ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(54,axiom,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(200,plain,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(201,plain,
~ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) ),
inference(polarity_switch,[status(thm)],[200]) ).
thf(296,plain,
( ( ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) )
!= ( e @ ( c @ ( a @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[231,201]) ).
thf(297,plain,
( ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) )
!= ( e @ ( c @ ( a @ between ) ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(301,plain,
( ( e != lower_dimension_point_1 )
| ( lower_dimension_point_3 != c )
| ( lower_dimension_point_2 != a ) ),
inference(simp,[status(thm)],[297]) ).
thf(20,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(125,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)],[20]) ).
thf(126,plain,
! [B: $i,A: $i] :
( A
!= ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( A @ ( B @ extension ) ) ) ) ),
inference(polarity_switch,[status(thm)],[125]) ).
thf(127,plain,
! [B: $i,A: $i] :
( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( A @ ( B @ extension ) ) ) )
!= A ),
inference(lifteq,[status(thm)],[126]) ).
thf(60,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(214,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)],[60]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ reflection ) ) )
| ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_1) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( B
= ( B @ ( A @ reflection ) ) )
| ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(9,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(101,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)],[9]) ).
thf(78,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
thf(258,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(1,negated_conjecture,
~ ( c @ ( d @ ( a @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_d_between_a_and_c) ).
thf(84,plain,
~ ( c @ ( d @ ( a @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(85,plain,
~ ( c @ ( d @ ( a @ between ) ) ),
inference(polarity_switch,[status(thm)],[84]) ).
thf(334,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ between ) ) )
!= ( c @ ( d @ ( a @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[258,85]) ).
thf(335,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ between ) ) )
!= ( c @ ( d @ ( a @ between ) ) ) ),
inference(simp,[status(thm)],[334]) ).
thf(342,plain,
! [B: $i,A: $i] :
( ( B != c )
| ( A != d )
| ( A != a ) ),
inference(simp,[status(thm)],[335]) ).
thf(347,plain,
d != a,
inference(simp,[status(thm)],[342]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
thf(88,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(42,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
thf(170,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(15,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(115,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(61,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(217,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)],[61]) ).
thf(17,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(120,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(55,axiom,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(202,plain,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(28,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(142,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)],[28]) ).
thf(34,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(153,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)],[34]) ).
thf(13,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(110,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)],[13]) ).
thf(6,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(93,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)],[6]) ).
thf(33,axiom,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
thf(152,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(38,axiom,
e @ ( d @ ( a @ between ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_between_a_and_e) ).
thf(163,plain,
e @ ( d @ ( a @ between ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(62,axiom,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(219,plain,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(220,plain,
~ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) ),
inference(polarity_switch,[status(thm)],[219]) ).
thf(287,plain,
( ( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) )
!= ( e @ ( d @ ( a @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[163,220]) ).
thf(288,plain,
( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) )
!= ( e @ ( d @ ( a @ between ) ) ) ),
inference(simp,[status(thm)],[287]) ).
thf(289,plain,
( ( e != lower_dimension_point_2 )
| ( lower_dimension_point_1 != d )
| ( lower_dimension_point_3 != a ) ),
inference(simp,[status(thm)],[288]) ).
thf(80,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(261,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)],[80]) ).
thf(39,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(164,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)],[39]) ).
thf(46,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(179,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)],[46]) ).
thf(59,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(211,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)],[59]) ).
thf(18,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(121,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)],[18]) ).
thf(43,axiom,
~ ( d @ ( c @ ( a @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_not_between_a_and_d) ).
thf(171,plain,
~ ( d @ ( c @ ( a @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(172,plain,
~ ( d @ ( c @ ( a @ between ) ) ),
inference(polarity_switch,[status(thm)],[171]) ).
thf(330,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ between ) ) )
!= ( d @ ( c @ ( a @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[258,172]) ).
thf(331,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( A @ between ) ) )
!= ( d @ ( c @ ( a @ between ) ) ) ),
inference(simp,[status(thm)],[330]) ).
thf(343,plain,
! [B: $i,A: $i] :
( ( B != d )
| ( A != c )
| ( A != a ) ),
inference(simp,[status(thm)],[331]) ).
thf(348,plain,
c != a,
inference(simp,[status(thm)],[343]) ).
thf(30,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(147,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)],[30]) ).
thf(272,plain,
( ( ( e @ ( d @ ( a @ between ) ) )
!= ( c @ ( d @ ( a @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[163,85]) ).
thf(273,plain,
( ( e @ ( d @ ( a @ between ) ) )
!= ( c @ ( d @ ( a @ between ) ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(277,plain,
( ( e != c )
| ( d != d )
| ( a != a ) ),
inference(simp,[status(thm)],[273]) ).
thf(280,plain,
e != c,
inference(simp,[status(thm)],[277]) ).
thf(63,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(221,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)],[63]) ).
thf(24,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(132,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)],[24]) ).
thf(4,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(89,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)],[4]) ).
thf(72,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(243,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)],[72]) ).
thf(82,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(265,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)],[82]) ).
thf(57,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(206,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)],[57]) ).
thf(74,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(248,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)],[74]) ).
thf(37,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(160,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)],[37]) ).
thf(26,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(137,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)],[26]) ).
thf(5,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(91,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)],[5]) ).
thf(92,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( B @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(cnf,[status(esa)],[91]) ).
thf(66,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(229,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)],[66]) ).
thf(76,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(252,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)],[76]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(197,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( A @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(35,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(156,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)],[35]) ).
thf(49,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(188,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)],[49]) ).
thf(41,axiom,
! [B: $i,A: $i] : ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).
thf(169,plain,
! [B: $i,A: $i] : ( B @ ( A @ reflection ) @ ( B @ ( A @ between ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(12,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_3) ).
thf(107,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(108,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(polarity_switch,[status(thm)],[107]) ).
thf(109,plain,
lower_dimension_point_3 != lower_dimension_point_1,
inference(lifteq,[status(thm)],[108]) ).
thf(51,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(193,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)],[51]) ).
thf(44,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(173,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)],[44]) ).
thf(22,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(129,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)],[22]) ).
thf(21,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( B @ reflection ) @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
thf(128,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( B @ reflection ) @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(11,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(105,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)],[11]) ).
thf(40,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(166,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)],[40]) ).
thf(31,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_2) ).
thf(148,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(45,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(176,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)],[45]) ).
thf(16,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)],[16]) ).
thf(56,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(204,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)],[56]) ).
thf(79,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(259,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)],[79]) ).
thf(90,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ ( C @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(cnf,[status(esa)],[89]) ).
thf(356,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ equidistant ) ) ) )
!= ( F @ ( E @ ( D @ ( C @ equidistant ) ) ) ) )
| ( D @ ( C @ ( F @ ( E @ equidistant ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[120,90]) ).
thf(357,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( A @ equidistant ) ) ) )
!= ( F @ ( E @ ( D @ ( C @ equidistant ) ) ) ) )
| ( D @ ( C @ ( F @ ( E @ equidistant ) ) ) ) ),
inference(simp,[status(thm)],[356]) ).
thf(358,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( A @ ( B @ equidistant ) ) ) ),
inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( B )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(2,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(86,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)],[2]) ).
thf(87,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( B @ ( A @ equidistant ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ equidistant ) ) ) ) ),
inference(cnf,[status(esa)],[86]) ).
thf(380,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ ( B @ equidistant ) ) ) )
!= ( F @ ( E @ ( D @ ( C @ equidistant ) ) ) ) )
| ( E @ ( F @ ( D @ ( C @ equidistant ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[358,87]) ).
thf(381,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( A @ ( B @ equidistant ) ) ) )
!= ( F @ ( E @ ( D @ ( C @ equidistant ) ) ) ) )
| ( E @ ( F @ ( D @ ( C @ equidistant ) ) ) ) ),
inference(simp,[status(thm)],[380]) ).
thf(382,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( A @ ( B @ equidistant ) ) ) ),
inference(pattern_uni,[status(thm)],[381:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A )),bind(E,$thf( A )),bind(F,$thf( B ))]]) ).
thf(69,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(236,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)],[69]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ reflection ) @ reflection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).
thf(113,plain,
! [B: $i,A: $i] :
( A
= ( B @ ( B @ ( A @ reflection ) @ reflection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(73,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(245,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)],[73]) ).
thf(8,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_1) ).
thf(98,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(203,plain,
~ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) ),
inference(polarity_switch,[status(thm)],[202]) ).
thf(298,plain,
( ( ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) )
!= ( e @ ( c @ ( a @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[231,203]) ).
thf(299,plain,
( ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) )
!= ( e @ ( c @ ( a @ between ) ) ) ),
inference(simp,[status(thm)],[298]) ).
thf(303,plain,
( ( e != lower_dimension_point_3 )
| ( lower_dimension_point_2 != c )
| ( lower_dimension_point_1 != a ) ),
inference(simp,[status(thm)],[299]) ).
thf(10,axiom,
! [A: $i] :
( A
= ( A @ ( A @ reflection ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).
thf(103,plain,
! [A: $i] :
( A
= ( A @ ( A @ reflection ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(274,plain,
( ( ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) )
!= ( e @ ( d @ ( a @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[163,201]) ).
thf(275,plain,
( ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ between ) ) )
!= ( e @ ( d @ ( a @ between ) ) ) ),
inference(simp,[status(thm)],[274]) ).
thf(278,plain,
( ( e != lower_dimension_point_1 )
| ( lower_dimension_point_3 != d )
| ( lower_dimension_point_2 != a ) ),
inference(simp,[status(thm)],[275]) ).
thf(64,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(223,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)],[64]) ).
thf(290,plain,
( ( ( e @ ( c @ ( a @ between ) ) )
!= ( d @ ( c @ ( a @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[231,172]) ).
thf(291,plain,
( ( e @ ( c @ ( a @ between ) ) )
!= ( d @ ( c @ ( a @ between ) ) ) ),
inference(simp,[status(thm)],[290]) ).
thf(302,plain,
( ( e != d )
| ( c != c )
| ( a != a ) ),
inference(simp,[status(thm)],[291]) ).
thf(306,plain,
e != d,
inference(simp,[status(thm)],[302]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( C @ ( A @ ( B @ extension ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
thf(135,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( C @ ( C @ ( A @ ( B @ extension ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(65,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(226,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)],[65]) ).
thf(83,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(267,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)],[83]) ).
thf(77,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(255,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)],[77]) ).
thf(58,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(209,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)],[58]) ).
thf(19,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(123,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)],[19]) ).
thf(353,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ ( A @ equidistant ) ) ) )
!= ( F @ ( E @ ( D @ ( C @ equidistant ) ) ) ) )
| ( D @ ( C @ ( F @ ( E @ equidistant ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,90]) ).
thf(354,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ ( A @ equidistant ) ) ) )
!= ( F @ ( E @ ( D @ ( C @ equidistant ) ) ) ) )
| ( D @ ( C @ ( F @ ( E @ equidistant ) ) ) ) ),
inference(simp,[status(thm)],[353]) ).
thf(355,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( B @ equidistant ) ) ) ),
inference(pattern_uni,[status(thm)],[354:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A )),bind(E,$thf( B )),bind(F,$thf( B ))]]) ).
thf(29,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(145,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)],[29]) ).
thf(149,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(polarity_switch,[status(thm)],[148]) ).
thf(150,plain,
lower_dimension_point_3 != lower_dimension_point_2,
inference(lifteq,[status(thm)],[149]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( A
!= ( A @ ( B @ reflection ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
thf(95,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( A
!= ( A @ ( B @ reflection ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(104,plain,
! [A: $i] :
( ( A @ ( A @ reflection ) )
= A ),
inference(lifteq,[status(thm)],[103]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
thf(250,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ between ) ) )
| ~ ( C @ ( B @ ( A @ between ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(36,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(158,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)],[36]) ).
thf(48,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(186,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)],[48]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ reflection ) @ reflection ) )
= A ),
inference(lifteq,[status(thm)],[113]) ).
thf(32,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(151,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)],[32]) ).
thf(292,plain,
( ( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) )
!= ( e @ ( c @ ( a @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[231,220]) ).
thf(293,plain,
( ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ ( lower_dimension_point_3 @ between ) ) )
!= ( e @ ( c @ ( a @ between ) ) ) ),
inference(simp,[status(thm)],[292]) ).
thf(300,plain,
( ( e != lower_dimension_point_2 )
| ( lower_dimension_point_1 != c )
| ( lower_dimension_point_3 != a ) ),
inference(simp,[status(thm)],[293]) ).
thf(81,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(262,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)],[81]) ).
thf(50,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(190,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)],[50]) ).
thf(47,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(183,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)],[47]) ).
thf(52,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(195,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)],[52]) ).
thf(281,plain,
( ( ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) )
!= ( e @ ( d @ ( a @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[163,203]) ).
thf(282,plain,
( ( lower_dimension_point_3 @ ( lower_dimension_point_2 @ ( lower_dimension_point_1 @ between ) ) )
!= ( e @ ( d @ ( a @ between ) ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(283,plain,
( ( e != lower_dimension_point_3 )
| ( lower_dimension_point_2 != d )
| ( lower_dimension_point_1 != a ) ),
inference(simp,[status(thm)],[282]) ).
thf(310,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ between ) ) )
!= ( d @ ( c @ ( a @ between ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[170,172]) ).
thf(311,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ between ) ) )
!= ( d @ ( c @ ( a @ between ) ) ) ),
inference(simp,[status(thm)],[310]) ).
thf(321,plain,
! [B: $i,A: $i] :
( ( B != d )
| ( B != c )
| ( A != a ) ),
inference(simp,[status(thm)],[311]) ).
thf(326,plain,
c != d,
inference(simp,[status(thm)],[321]) ).
thf(70,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(239,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)],[70]) ).
thf(71,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(242,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)],[71]) ).
thf(23,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ reflection ) @ reflection ) @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).
thf(131,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ reflection ) @ reflection ) @ ( A @ ( B @ ( A @ equidistant ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(68,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(232,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)],[68]) ).
thf(99,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(polarity_switch,[status(thm)],[98]) ).
thf(100,plain,
lower_dimension_point_2 != lower_dimension_point_1,
inference(lifteq,[status(thm)],[99]) ).
thf(966,plain,
$false,
inference(e,[status(thm)],[301,127,214,138,101,347,88,170,115,217,120,202,142,153,110,125,93,152,289,261,164,179,211,121,348,84,147,280,221,132,89,243,265,206,248,220,85,201,160,137,92,229,252,197,156,188,169,109,193,173,129,128,105,166,148,176,118,204,259,382,236,86,172,113,219,245,98,303,103,91,278,223,306,135,226,267,255,209,123,355,145,150,95,87,203,104,250,231,258,158,186,114,171,151,300,262,190,183,358,195,283,326,107,239,242,131,163,200,90,232,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO009-3 : 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
% 0.06/5.33 % Computer : n012.cluster.edu
% 0.06/5.33 % Model : x86_64 x86_64
% 0.06/5.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/5.33 % Memory : 8046.5625MB
% 0.06/5.33 % OS : Linux 6.8.0-71-generic
% 0.06/5.33 % CPULimit : 300
% 0.06/5.33 % WCLimit : 300
% 0.06/5.33 % DateTime : Fri Sep 25 12:30:41 UTC 2026
% 0.06/5.33 % CPUTime :
% 0.06/5.33 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
% 0.10/5.61 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.10/5.74 % [INFO] Parsing done (124ms).
% 0.10/5.75 % [INFO] Running in sequential loop mode.
% 0.10/5.94 % [INFO] eprover registered as external prover.
% 0.10/5.94 % [INFO] Scanning for conjecture ...
% 0.10/5.99 % [INFO] Found a conjecture (or negated_conjecture) and 82 axioms. Running axiom selection ...
% 1.43/6.04 % [INFO] Axiom selection finished. Selected 82 axioms (removed 0 axioms).
% 1.43/6.09 % [INFO] Problem is propositional (TPTP CNF).
% 1.43/6.09 % [INFO] Type checking passed.
% 1.43/6.10 % [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 ...
% 6.92/7.30 % External prover 'e' found a proof!
% 6.92/7.30 % [INFO] Killing All external provers ...
% 6.92/7.30 % Time passed: 1895ms (effective reasoning time: 1550ms)
% 6.92/7.30 % Axioms used in derivation (82): e3_2, b7, d3, reflexivity_for_equidistance, outer_five_segment, d8, euclid3, d5, i2_3, continuity1, e2_2, lower_dimension1, d4_4, b2, continuity2, b10, b3, r2_1, d4_5, transitivity_for_equidistance, e1, d9, r6, inner_pasch2, i4, b4, lower_dimension2, t3, c_not_between_a_and_d, b1, d13, reflection, r2_2, b8, d12, identity_for_betweeness, b11, r5, i3, c_between_a_and_e, r3_2, b0, upper_dimension, t2, t7, b5, d15, euclid1, d7, d10_2, r4, e2_3, segment_construction2, d2, d10_3, e3_1, d4_2, i2_1, b12, d4_1, lower_dimension3, d_between_a_and_e, t6_2, b9, b6, inner_pasch1, e3_3, r3_1, b13, segment_construction1, d14, euclid2, d10_1, e2_1, d1, t1, d11, identity_for_equidistance, d4_3, t6_1, insertion, i2_2
% 6.92/7.30 % No. of inferences in proof: 232
% 6.92/7.30 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1895 ms resp. 1550 ms w/o parsing
% 6.92/7.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 6.92/7.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------