TSTP Solution File: GEO012-3 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO012-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:08:52 EDT 2023
% Result : Unsatisfiable 5.58s 2.53s
% Output : Refutation 5.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 122
% Syntax : Number of formulae : 228 ( 65 unt; 17 typ; 0 def)
% Number of atoms : 551 ( 98 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 2500 ( 306 ~; 340 |; 0 &;1854 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 41 ( 41 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 8 con; 0-6 aty)
% Number of variables : 712 ( 0 ^; 712 !; 0 ?; 712 :)
% Comments :
%------------------------------------------------------------------------------
thf(colinear_type,type,
colinear: $i > $i > $i > $o ).
thf(a_type,type,
a: $i ).
thf(c_type,type,
c: $i ).
thf(d_type,type,
d: $i ).
thf(b_type,type,
b: $i ).
thf(reflection_type,type,
reflection: $i > $i > $i ).
thf(extension_type,type,
extension: $i > $i > $i > $i > $i ).
thf(equidistant_type,type,
equidistant: $i > $i > $i > $i > $o ).
thf(between_type,type,
between: $i > $i > $i > $o ).
thf(continuous_type,type,
continuous: $i > $i > $i > $i > $i > $i > $i ).
thf(insertion_type,type,
insertion: $i > $i > $i > $i > $i ).
thf(euclid1_type,type,
euclid1: $i > $i > $i > $i > $i > $i ).
thf(lower_dimension_point_1_type,type,
lower_dimension_point_1: $i ).
thf(lower_dimension_point_2_type,type,
lower_dimension_point_2: $i ).
thf(euclid2_type,type,
euclid2: $i > $i > $i > $i > $i > $i ).
thf(inner_pasch_type,type,
inner_pasch: $i > $i > $i > $i > $i > $i ).
thf(lower_dimension_point_3_type,type,
lower_dimension_point_3: $i ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( between @ A @ B @ ( extension @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).
thf(129,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( between @ A @ B @ ( extension @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( colinear @ A @ B @ C )
| ( between @ A @ B @ C )
| ( between @ B @ C @ A )
| ( between @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity4) ).
thf(331,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( colinear @ A @ B @ C )
| ( between @ A @ B @ C )
| ( between @ B @ C @ A )
| ( between @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(14,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ B @ E @ D @ F )
| ~ ( equidistant @ A @ G @ C @ H )
| ~ ( equidistant @ B @ G @ D @ H )
| ~ ( between @ A @ B @ E )
| ~ ( between @ C @ D @ F )
| ( A = B )
| ( equidistant @ E @ G @ F @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_five_segment) ).
thf(138,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ B @ E @ D @ F )
| ~ ( equidistant @ A @ G @ C @ H )
| ~ ( equidistant @ B @ G @ D @ H )
| ~ ( between @ A @ B @ E )
| ~ ( between @ C @ D @ F )
| ( A = B )
| ( equidistant @ E @ G @ F @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(104,axiom,
a != b,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_not_b) ).
thf(333,plain,
a != b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ C @ D )
| ( between @ A @ B @ D )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b7) ).
thf(247,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ C @ D )
| ( between @ A @ B @ D )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ C @ D )
| ( between @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b4) ).
thf(202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ C @ D )
| ( between @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(30,axiom,
! [B: $i,A: $i] : ( between @ A @ B @ ( reflection @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).
thf(174,plain,
! [B: $i,A: $i] : ( between @ A @ B @ ( reflection @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ C @ D )
| ( between @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b9) ).
thf(288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ C @ D )
| ( between @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ A @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_2) ).
thf(301,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( A != C )
| ( between @ D @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b1) ).
thf(184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( A != C )
| ( between @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( reflection @ A @ B )
= ( extension @ A @ B @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( reflection @ A @ B )
= ( extension @ A @ B @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( B
= ( insertion @ A @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i3) ).
thf(284,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( B
= ( insertion @ A @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( colinear @ A @ B @ C )
| ( colinear @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_5) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( colinear @ A @ B @ C )
| ( colinear @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(48,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ D @ E )
| ~ ( between @ A @ E @ C )
| ( between @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t8) ).
thf(216,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ D @ E )
| ~ ( between @ A @ E @ C )
| ( between @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity3) ).
thf(321,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(46,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ A @ C )
| ~ ( equidistant @ A @ D @ A @ E )
| ~ ( between @ A @ B @ D )
| ~ ( between @ B @ F @ D )
| ( between @ C @ ( continuous @ A @ B @ C @ F @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity1) ).
thf(211,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ A @ C )
| ~ ( equidistant @ A @ D @ A @ E )
| ~ ( between @ A @ B @ D )
| ~ ( between @ B @ F @ D )
| ( between @ C @ ( continuous @ A @ B @ C @ F @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(1,negated_conjecture,
( ~ ( colinear @ a @ c @ d )
| ~ ( colinear @ b @ c @ d ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_colinearity) ).
thf(106,plain,
( ~ ( colinear @ a @ c @ d )
| ~ ( colinear @ b @ c @ d ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(57,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ B @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(238,plain,
! [B: $i,A: $i] : ( equidistant @ A @ B @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(77,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( equidistant @ A @ C @ D @ E )
| ( between @ D @ ( insertion @ D @ E @ A @ B ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i2_2) ).
thf(280,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( equidistant @ A @ C @ D @ E )
| ( between @ D @ ( insertion @ D @ E @ A @ B ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ ( extension @ B @ A @ C @ D ) @ C @ D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).
thf(133,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ ( extension @ B @ A @ C @ D ) @ C @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( A
!= ( extension @ B @ A @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e3_1) ).
thf(243,plain,
! [B: $i,A: $i] :
( A
!= ( extension @ B @ A @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(69,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ E @ F )
| ~ ( equidistant @ A @ B @ D @ E )
| ~ ( equidistant @ A @ C @ D @ F )
| ( equidistant @ B @ C @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d13) ).
thf(265,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ E @ F )
| ~ ( equidistant @ A @ B @ D @ E )
| ~ ( equidistant @ A @ C @ D @ F )
| ( equidistant @ B @ C @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(44,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ B @ E )
| ( A = B )
| ( between @ ( euclid1 @ A @ D @ B @ E @ C ) @ C @ ( euclid2 @ A @ D @ B @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid3) ).
thf(206,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ B @ E )
| ( A = B )
| ( between @ ( euclid1 @ A @ D @ B @ E @ C ) @ C @ ( euclid2 @ A @ D @ B @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity2) ).
thf(307,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(83,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ B @ E @ D @ F )
| ~ ( between @ A @ B @ E )
| ~ ( between @ C @ D @ F )
| ( equidistant @ A @ E @ C @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d8) ).
thf(292,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ B @ E @ D @ F )
| ~ ( between @ A @ B @ E )
| ~ ( between @ C @ D @ F )
| ( equidistant @ A @ E @ C @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(55,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ A @ E @ C @ F )
| ~ ( equidistant @ A @ G @ C @ H )
| ~ ( equidistant @ E @ G @ F @ H )
| ~ ( between @ A @ B @ E )
| ~ ( between @ C @ D @ F )
| ( equidistant @ B @ G @ D @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d12) ).
thf(233,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ A @ E @ C @ F )
| ~ ( equidistant @ A @ G @ C @ H )
| ~ ( equidistant @ E @ G @ F @ H )
| ~ ( between @ A @ B @ E )
| ~ ( between @ C @ D @ F )
| ( equidistant @ B @ G @ D @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(6,axiom,
! [A: $i] :
( A
= ( reflection @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).
thf(117,plain,
! [A: $i] :
( A
= ( reflection @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(72,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
thf(270,plain,
! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(50,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_3) ).
thf(220,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ D @ C )
| ( between @ B @ D @ C )
| ( between @ D @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b14) ).
thf(160,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ D @ C )
| ( between @ B @ D @ C )
| ( between @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(85,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ B @ E @ D @ F )
| ~ ( equidistant @ A @ E @ C @ F )
| ~ ( colinear @ A @ B @ E )
| ( colinear @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c4) ).
thf(297,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ B @ E @ D @ F )
| ~ ( equidistant @ A @ E @ C @ F )
| ~ ( colinear @ A @ B @ E )
| ( colinear @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ C @ D )
| ( between @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b5) ).
thf(192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ C @ D )
| ( between @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(64,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(252,plain,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ C @ B )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b3) ).
thf(197,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ C @ B )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( colinear @ A @ B @ C )
| ( colinear @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_2) ).
thf(329,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( colinear @ A @ B @ C )
| ( colinear @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(96,axiom,
~ ( colinear @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t11) ).
thf(317,plain,
~ ( colinear @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3) ).
thf(156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(36,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ A @ C )
| ~ ( equidistant @ D @ B @ D @ C )
| ~ ( equidistant @ E @ B @ E @ C )
| ( between @ A @ D @ E )
| ( between @ D @ E @ A )
| ( between @ E @ A @ D )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_dimension) ).
thf(188,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ A @ C )
| ~ ( equidistant @ D @ B @ D @ C )
| ~ ( equidistant @ E @ B @ E @ C )
| ( between @ A @ D @ E )
| ( between @ D @ E @ A )
| ( between @ E @ A @ D )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ D @ C )
| ( between @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b8) ).
thf(169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ D @ C )
| ( between @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_1) ).
thf(141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ A @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ C @ D )
| ( between @ A @ C @ D )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b6) ).
thf(256,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ C @ D )
| ( between @ A @ C @ D )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(52,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ E @ C )
| ~ ( between @ A @ F @ D )
| ( between @ F @ ( inner_pasch @ E @ ( inner_pasch @ A @ F @ D @ E @ C ) @ A @ B @ C ) @ C )
| ( between @ B @ ( inner_pasch @ E @ ( inner_pasch @ A @ F @ D @ E @ C ) @ A @ B @ C ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b10) ).
thf(225,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ E @ C )
| ~ ( between @ A @ F @ D )
| ( between @ F @ ( inner_pasch @ E @ ( inner_pasch @ A @ F @ D @ E @ C ) @ A @ B @ C ) @ C )
| ( between @ B @ ( inner_pasch @ E @ ( inner_pasch @ A @ F @ D @ E @ C ) @ A @ B @ C ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(13,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( extension @ B @ C @ D @ E ) )
| ( between @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b0) ).
thf(134,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( extension @ B @ C @ D @ E ) )
| ( between @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( colinear @ A @ B @ C )
| ( colinear @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_1) ).
thf(311,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( colinear @ A @ B @ C )
| ( colinear @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(27,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( ( insertion @ E @ F @ A @ B )
= ( insertion @ E @ F @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i4) ).
thf(166,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( ( insertion @ E @ F @ A @ B )
= ( insertion @ E @ F @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(19,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ A @ C )
| ~ ( equidistant @ A @ D @ A @ E )
| ~ ( between @ A @ B @ D )
| ~ ( between @ B @ F @ D )
| ( equidistant @ A @ F @ A @ ( continuous @ A @ B @ C @ F @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).
thf(149,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ A @ C )
| ~ ( equidistant @ A @ D @ A @ E )
| ~ ( between @ A @ B @ D )
| ~ ( between @ B @ F @ D )
| ( equidistant @ A @ F @ A @ ( continuous @ A @ B @ C @ F @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(32,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ A @ B @ E @ F )
| ( equidistant @ C @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
thf(176,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ A @ B @ E @ F )
| ( equidistant @ C @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ B @ C @ ( insertion @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i2_1) ).
thf(191,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ B @ C @ ( insertion @ C @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ D @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_4) ).
thf(204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ D @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(67,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_2) ).
thf(259,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( colinear @ A @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3_4) ).
thf(313,plain,
! [C: $i,B: $i,A: $i] :
( ( A != B )
| ( colinear @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ B @ C )
| ( B = C )
| ( between @ A @ D @ B )
| ( between @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7) ).
thf(181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ B @ C )
| ( B = C )
| ( between @ A @ D @ B )
| ( between @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( equidistant @ A @ B @ A @ D )
| ~ ( equidistant @ C @ B @ C @ D )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d15) ).
thf(274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( equidistant @ A @ B @ A @ D )
| ~ ( equidistant @ C @ B @ C @ D )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(230,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_3) ).
thf(303,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ A @ C )
| ( A = B )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_1) ).
thf(271,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ A @ C )
| ( A = B )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c2_1) ).
thf(323,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ~ ( between @ A @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(213,plain,
! [B: $i,A: $i] :
( ~ ( between @ A @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(2,axiom,
! [B: $i,A: $i] :
( A
= ( reflection @ ( reflection @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).
thf(108,plain,
! [B: $i,A: $i] :
( A
= ( reflection @ ( reflection @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( A = B )
| ( C
= ( extension @ A @ B @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_1) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( A = B )
| ( C
= ( extension @ A @ B @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(76,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ D @ C )
| ( between @ A @ B @ D )
| ( between @ A @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t9) ).
thf(278,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ D @ C )
| ( between @ A @ B @ D )
| ( between @ A @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(51,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(223,plain,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(86,axiom,
! [B: $i,A: $i] : ( colinear @ A @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3_1) ).
thf(299,plain,
! [B: $i,A: $i] : ( colinear @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(70,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ ( reflection @ B @ A ) @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
thf(267,plain,
! [B: $i,A: $i] : ( equidistant @ A @ ( reflection @ B @ A ) @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ D @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_5) ).
thf(241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ D @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(25,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ ( reflection @ ( reflection @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).
thf(162,plain,
! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ ( reflection @ ( reflection @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(45,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ E @ C )
| ( between @ E @ ( inner_pasch @ A @ B @ C @ E @ D ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch2) ).
thf(209,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ E @ C )
| ( between @ E @ ( inner_pasch @ A @ B @ C @ E @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( extension @ B @ A @ C @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
thf(112,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( extension @ B @ A @ C @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( ( extension @ A @ B @ A @ B )
= ( extension @ A @ B @ B @ A ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_3) ).
thf(123,plain,
! [B: $i,A: $i] :
( ( ( extension @ A @ B @ A @ B )
= ( extension @ A @ B @ B @ A ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(39,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_1) ).
thf(194,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(17,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
thf(145,plain,
! [B: $i,A: $i] : ( equidistant @ A @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( between @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
thf(282,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( between @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( colinear @ A @ B @ C )
| ( colinear @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_4) ).
thf(327,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( colinear @ A @ B @ C )
| ( colinear @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(93,axiom,
colinear @ a @ b @ c,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abc_colinear) ).
thf(310,plain,
colinear @ a @ b @ c,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(105,axiom,
! [B: $i,A: $i] : ( colinear @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3_3) ).
thf(336,plain,
! [B: $i,A: $i] : ( colinear @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2) ).
thf(154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ C @ D @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(31,axiom,
! [B: $i,A: $i] : ( between @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
thf(175,plain,
! [B: $i,A: $i] : ( between @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(16,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ B @ E @ D @ F )
| ~ ( equidistant @ A @ E @ C @ F )
| ~ ( between @ A @ B @ E )
| ( between @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b11) ).
thf(143,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ B @ E @ D @ F )
| ~ ( equidistant @ A @ E @ C @ F )
| ~ ( between @ A @ B @ E )
| ( between @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(63,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ B @ E @ D @ F )
| ~ ( equidistant @ A @ G @ C @ H )
| ~ ( equidistant @ E @ G @ F @ H )
| ~ ( between @ A @ B @ E )
| ~ ( between @ C @ D @ F )
| ( equidistant @ B @ G @ D @ H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d14) ).
thf(250,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ B @ E @ D @ F )
| ~ ( equidistant @ A @ G @ C @ H )
| ~ ( equidistant @ E @ G @ F @ H )
| ~ ( between @ A @ B @ E )
| ~ ( between @ C @ D @ F )
| ( equidistant @ B @ G @ D @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(49,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(218,plain,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',colinearity1) ).
thf(319,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(23,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( equidistant @ A @ C @ D @ E )
| ( equidistant @ B @ C @ ( insertion @ D @ E @ A @ B ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',i2_3) ).
thf(158,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( equidistant @ A @ C @ D @ E )
| ( equidistant @ B @ C @ ( insertion @ D @ E @ A @ B ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( A
!= ( reflection @ B @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( A
!= ( reflection @ B @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( equidistant @ A @ C @ A @ D )
| ~ ( equidistant @ B @ C @ B @ D )
| ( A = B )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d11) ).
thf(171,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( equidistant @ A @ C @ A @ D )
| ~ ( equidistant @ B @ C @ B @ D )
| ( A = B )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(80,axiom,
! [B: $i,A: $i] : ( between @ A @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
thf(287,plain,
! [B: $i,A: $i] : ( between @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ C @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_3) ).
thf(290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ C @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( B
= ( reflection @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_1) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( B
= ( reflection @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(56,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ B @ E )
| ( A = B )
| ( between @ A @ E @ ( euclid2 @ A @ D @ B @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid2) ).
thf(235,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ B @ E )
| ( A = B )
| ( between @ A @ E @ ( euclid2 @ A @ D @ B @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ ( extension @ B @ A @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ C @ ( extension @ D @ C @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e3_2) ).
thf(246,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ ( extension @ B @ A @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ C @ ( extension @ D @ C @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ A @ C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b2) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ A @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(87,axiom,
colinear @ a @ b @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',abd_colinear) ).
thf(300,plain,
colinear @ a @ b @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ B @ D )
| ( A = B )
| ( between @ A @ C @ D )
| ( between @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b12) ).
thf(262,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ B @ D )
| ( A = B )
| ( between @ A @ C @ D )
| ( between @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( equidistant @ A @ B @ A @ C )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b15) ).
thf(146,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( equidistant @ A @ B @ A @ C )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( colinear @ A @ B @ C )
| ( colinear @ A @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t10_3) ).
thf(305,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( colinear @ A @ B @ C )
| ( colinear @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(58,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ C @ D @ E @ F )
| ( equidistant @ A @ B @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d5) ).
thf(239,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ C @ D @ E @ F )
| ( equidistant @ A @ B @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ B @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d4_2) ).
thf(268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ B @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ B @ D )
| ( A = B )
| ( between @ B @ C @ D )
| ( between @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b13) ).
thf(294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ B @ D )
| ( A = B )
| ( between @ B @ C @ D )
| ( between @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(9,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( ( extension @ E @ F @ A @ B )
= ( extension @ E @ F @ C @ D ) )
| ( E = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d10_2) ).
thf(126,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( ( extension @ E @ F @ A @ B )
= ( extension @ E @ F @ C @ D ) )
| ( E = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(33,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ B @ E )
| ( A = B )
| ( between @ A @ D @ ( euclid1 @ A @ D @ B @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid1) ).
thf(178,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ B @ E )
| ( A = B )
| ( between @ A @ D @ ( euclid1 @ A @ D @ B @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(75,axiom,
! [B: $i,A: $i] : ( between @ A @ B @ ( extension @ A @ B @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e3_3) ).
thf(277,plain,
! [B: $i,A: $i] : ( between @ A @ B @ ( extension @ A @ B @ lower_dimension_point_1 @ lower_dimension_point_2 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ C @ B )
| ( A = B )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t6_2) ).
thf(163,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ C @ B )
| ( A = B )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( insertion @ A @ B @ C @ D )
= ( extension @ ( extension @ B @ A @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',insertion) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( insertion @ A @ B @ C @ D )
= ( extension @ ( extension @ B @ A @ lower_dimension_point_1 @ lower_dimension_point_2 ) @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(92,axiom,
! [B: $i,A: $i] : ( colinear @ A @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c3_2) ).
thf(309,plain,
! [B: $i,A: $i] : ( colinear @ A @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(65,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ E @ C )
| ( between @ B @ ( inner_pasch @ A @ B @ C @ E @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch1) ).
thf(254,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ E @ C )
| ( between @ B @ ( inner_pasch @ A @ B @ C @ E @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ B @ D )
| ~ ( equidistant @ B @ C @ B @ D )
| ( A = B )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d9) ).
thf(227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ B @ D )
| ~ ( equidistant @ B @ C @ B @ D )
| ( A = B )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(390,plain,
$false,
inference(cvc4,[status(thm)],[129,331,138,333,247,202,174,288,301,184,110,284,325,216,321,211,106,238,280,133,243,265,206,307,292,233,117,270,220,160,297,192,252,197,329,317,156,188,169,141,256,225,134,311,166,149,176,191,204,259,313,181,274,230,303,271,323,213,108,130,278,223,299,267,241,162,209,112,123,194,145,282,327,310,336,154,175,143,250,218,319,158,114,171,287,290,119,235,246,151,300,262,146,305,239,268,294,126,178,277,163,200,309,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO012-3 : TPTP v8.1.2. Bugfixed v1.2.1.
% 0.12/0.14 % Command : run_Leo-III %s %d
% 0.14/0.34 % Computer : n008.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri May 19 04:37:55 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.94/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.39/1.06 % [INFO] Parsing done (209ms).
% 1.39/1.07 % [INFO] Running in sequential loop mode.
% 1.81/1.29 % [INFO] eprover registered as external prover.
% 1.81/1.29 % [INFO] cvc4 registered as external prover.
% 1.81/1.30 % [INFO] Scanning for conjecture ...
% 1.95/1.36 % [INFO] Found a conjecture and 104 axioms. Running axiom selection ...
% 2.08/1.42 % [INFO] Axiom selection finished. Selected 104 axioms (removed 0 axioms).
% 2.46/1.50 % [INFO] Problem is propositional (TPTP CNF).
% 2.46/1.51 % [INFO] Type checking passed.
% 2.46/1.51 % [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 ...
% 5.58/2.53 % External prover 'cvc4' found a proof!
% 5.58/2.53 % [INFO] Killing All external provers ...
% 5.58/2.53 % Time passed: 2034ms (effective reasoning time: 1456ms)
% 5.58/2.53 % Solved by 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)>
% 5.58/2.53 % Axioms used in derivation (104): d3, reflexivity_for_equidistance, e3_2, c2_1, c3_3, euclid3, d5, t10_4, i2_3, abc_colinear, continuity1, c4, e2_2, lower_dimension1, d4_4, b2, continuity2, b10, t9, b3, r2_1, d4_5, transitivity_for_equidistance, colinearity3, e1, b14, b7, t10_5, d9, r6, inner_pasch2, i4, b4, lower_dimension2, t3, b1, d13, reflection, r2_2, b8, d12, identity_for_betweeness, b11, colinearity4, r5, i3, c3_4, outer_five_segment, r3_2, b0, b15, upper_dimension, t2, t7, c2_3, b5, d15, euclid1, d7, d10_2, colinearity1, r4, abd_colinear, e2_3, segment_construction2, d2, d10_3, e3_1, d4_2, i2_1, t10_1, c3_1, b12, d4_1, lower_dimension3, a_not_b, t6_2, b9, t8, t10_3, d8, b6, inner_pasch1, e3_3, r3_1, b13, c2_2, segment_construction1, d14, euclid2, d10_1, e2_1, d1, t1, d11, identity_for_equidistance, t10_2, d4_3, colinearity2, t6_1, insertion, i2_2, c3_2, t11
% 5.58/2.53 % No. of inferences in proof: 211
% 5.58/2.53 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2034 ms resp. 1456 ms w/o parsing
% 5.58/2.59 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 5.58/2.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------