TSTP Solution File: GEO039-3 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO039-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.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 11:09:02 EDT 2023
% Result : Unsatisfiable 3.64s 1.90s
% Output : Refutation 4.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 62
% Syntax : Number of formulae : 110 ( 39 unt; 15 typ; 0 def)
% Number of atoms : 221 ( 50 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1042 ( 112 ~; 126 |; 0 &; 804 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 8 con; 0-6 aty)
% Number of variables : 310 ( 0 ^; 310 !; 0 ?; 310 :)
% Comments :
%------------------------------------------------------------------------------
thf(between_type,type,
between: $i > $i > $i > $o ).
thf(v_type,type,
v: $i ).
thf(w_type,type,
w: $i ).
thf(x_type,type,
x: $i ).
thf(equidistant_type,type,
equidistant: $i > $i > $i > $i > $o ).
thf(reflection_type,type,
reflection: $i > $i > $i ).
thf(extension_type,type,
extension: $i > $i > $i > $i > $i ).
thf(u_type,type,
u: $i ).
thf(continuous_type,type,
continuous: $i > $i > $i > $i > $i > $i > $i ).
thf(inner_pasch_type,type,
inner_pasch: $i > $i > $i > $i > $i > $i ).
thf(lower_dimension_point_2_type,type,
lower_dimension_point_2: $i ).
thf(lower_dimension_point_3_type,type,
lower_dimension_point_3: $i ).
thf(lower_dimension_point_1_type,type,
lower_dimension_point_1: $i ).
thf(euclid2_type,type,
euclid2: $i > $i > $i > $i > $i > $i ).
thf(euclid1_type,type,
euclid1: $i > $i > $i > $i > $i > $i ).
thf(44,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(138,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)],[44]) ).
thf(35,axiom,
between @ u @ w @ x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',w_between_u_and_x) ).
thf(115,plain,
between @ u @ w @ x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(46,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(142,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)],[46]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
thf(52,plain,
! [B: $i,A: $i] : ( equidistant @ A @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(6,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(57,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)],[6]) ).
thf(31,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(106,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)],[31]) ).
thf(28,axiom,
! [B: $i,A: $i] : ( between @ A @ B @ ( reflection @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).
thf(102,plain,
! [B: $i,A: $i] : ( between @ A @ B @ ( reflection @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(4,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(53,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)],[4]) ).
thf(41,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(129,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)],[41]) ).
thf(13,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ B @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(73,plain,
! [B: $i,A: $i] : ( equidistant @ A @ B @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(9,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(64,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)],[9]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( A
!= ( reflection @ B @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( A
!= ( reflection @ B @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1,negated_conjecture,
~ ( between @ v @ w @ x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_corollary) ).
thf(48,plain,
~ ( between @ v @ w @ x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(2,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(50,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)],[2]) ).
thf(30,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(104,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)],[30]) ).
thf(47,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(146,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)],[47]) ).
thf(42,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(132,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)],[42]) ).
thf(21,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(89,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)],[21]) ).
thf(36,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(116,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)],[36]) ).
thf(14,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(74,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)],[14]) ).
thf(22,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(92,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)],[22]) ).
thf(25,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
thf(97,plain,
! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(39,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(124,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)],[39]) ).
thf(16,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(77,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)],[16]) ).
thf(24,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(96,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)],[24]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( reflection @ A @ B )
= ( extension @ A @ B @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( reflection @ A @ B )
= ( extension @ A @ B @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(20,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(86,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)],[20]) ).
thf(34,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(113,plain,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(15,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ ( reflection @ B @ A ) @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
thf(76,plain,
! [B: $i,A: $i] : ( equidistant @ A @ ( reflection @ B @ A ) @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(26,axiom,
u = x,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',u_is_x) ).
thf(98,plain,
u = x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(29,axiom,
! [B: $i,A: $i] : ( between @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
thf(103,plain,
! [B: $i,A: $i] : ( between @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( A
= ( reflection @ ( reflection @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).
thf(66,plain,
! [B: $i,A: $i] :
( A
= ( reflection @ ( reflection @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ~ ( between @ A @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(108,plain,
! [B: $i,A: $i] :
( ~ ( between @ A @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(43,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(135,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)],[43]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( extension @ B @ A @ C @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
thf(80,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( extension @ B @ A @ C @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(5,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(55,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)],[5]) ).
thf(45,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(139,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)],[45]) ).
thf(37,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(119,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)],[37]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( B
= ( reflection @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_1) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( B
= ( reflection @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(40,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(126,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)],[40]) ).
thf(17,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ ( reflection @ ( reflection @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).
thf(79,plain,
! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ ( reflection @ ( reflection @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(23,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(94,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)],[23]) ).
thf(11,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(68,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(8,axiom,
! [A: $i] :
( A
= ( reflection @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).
thf(62,plain,
! [A: $i] :
( A
= ( reflection @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(33,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(111,plain,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(38,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(122,plain,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(27,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(100,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)],[27]) ).
thf(148,plain,
$false,
inference(e,[status(thm)],[138,115,142,52,57,106,102,53,129,73,64,59,48,50,104,146,132,89,116,74,92,97,124,77,96,71,86,113,76,98,103,66,108,135,80,55,139,119,82,126,79,94,68,62,111,122,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12 % Problem : GEO039-3 : TPTP v8.1.2. Released v1.0.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n012.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Fri May 19 04:15:02 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.89/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.16/1.00 % [INFO] Parsing done (144ms).
% 1.16/1.01 % [INFO] Running in sequential loop mode.
% 1.78/1.21 % [INFO] eprover registered as external prover.
% 1.78/1.21 % [INFO] cvc4 registered as external prover.
% 1.78/1.21 % [INFO] Scanning for conjecture ...
% 1.91/1.27 % [INFO] Found a conjecture and 46 axioms. Running axiom selection ...
% 2.13/1.31 % [INFO] Axiom selection finished. Selected 46 axioms (removed 0 axioms).
% 2.13/1.36 % [INFO] Problem is propositional (TPTP CNF).
% 2.13/1.36 % [INFO] Type checking passed.
% 2.13/1.37 % [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 ...
% 3.64/1.90 % External prover 'e' found a proof!
% 3.64/1.90 % [INFO] Killing All external provers ...
% 3.64/1.90 % Time passed: 1376ms (effective reasoning time: 885ms)
% 3.64/1.90 % 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)>
% 3.64/1.90 % Axioms used in derivation (46): continuity1, w_between_u_and_x, d3, reflexivity_for_equidistance, reflection, r2_2, identity_for_betweeness, r5, outer_five_segment, d8, euclid3, d5, lower_dimension1, d4_4, continuity2, r2_1, d4_5, transitivity_for_equidistance, e1, d9, r6, inner_pasch2, lower_dimension2, t3, r3_2, b0, upper_dimension, u_is_x, euclid1, d7, d10_2, r4, segment_construction2, d2, d10_3, d4_2, d4_1, lower_dimension3, inner_pasch1, r3_1, segment_construction1, euclid2, d10_1, d1, identity_for_equidistance, d4_3
% 3.64/1.90 % No. of inferences in proof: 95
% 3.64/1.90 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1376 ms resp. 885 ms w/o parsing
% 4.06/1.95 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.06/1.95 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------