TSTP Solution File: GEO044-3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO044-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 11:09:04 EDT 2023
% Result : Unsatisfiable 4.07s 1.94s
% Output : Refutation 4.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 72
% Syntax : Number of formulae : 130 ( 43 unt; 15 typ; 0 def)
% Number of atoms : 275 ( 64 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1228 ( 144 ~; 160 |; 0 &; 924 @)
% ( 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 : 368 ( 0 ^; 368 !; 0 ?; 368 :)
% Comments :
%------------------------------------------------------------------------------
thf(between_type,type,
between: $i > $i > $i > $o ).
thf(u_type,type,
u: $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(v_type,type,
v: $i ).
thf(continuous_type,type,
continuous: $i > $i > $i > $i > $i > $i > $i ).
thf(euclid1_type,type,
euclid1: $i > $i > $i > $i > $i > $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_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(7,axiom,
! [B: $i,A: $i] :
( ( A
!= ( reflection @ B @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r4) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( A
!= ( reflection @ B @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(55,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
!= ( extension @ B @ C @ D @ E ) )
| ( between @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b0) ).
thf(174,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)],[55]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(39,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/sandbox/benchmark/theBenchmark.p',inner_pasch2) ).
thf(137,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)],[39]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( ( extension @ A @ B @ A @ B )
= ( extension @ A @ B @ B @ A ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_3) ).
thf(96,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(38,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/sandbox/benchmark/theBenchmark.p',euclid3) ).
thf(134,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)],[38]) ).
thf(26,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/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).
thf(108,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)],[26]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ C @ D )
| ( between @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b5) ).
thf(130,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)],[36]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( A != C )
| ( between @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b1) ).
thf(123,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)],[34]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ C @ D @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d2) ).
thf(63,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(25,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1) ).
thf(107,plain,
! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( between @ A @ B @ ( extension @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).
thf(170,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)],[53]) ).
thf(31,axiom,
between @ u @ v @ w,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_between_u_and_w) ).
thf(120,plain,
between @ u @ v @ w,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( equidistant @ A @ ( extension @ B @ A @ C @ D ) @ C @ D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
thf(106,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(32,axiom,
! [B: $i,A: $i] : ( between @ A @ B @ ( reflection @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_1) ).
thf(121,plain,
! [B: $i,A: $i] : ( between @ A @ B @ ( reflection @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
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/sandbox/benchmark/theBenchmark.p',d5) ).
thf(84,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(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ C @ D )
| ( between @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b4) ).
thf(132,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)],[37]) ).
thf(17,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ ( reflection @ ( reflection @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r5) ).
thf(89,plain,
! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ ( reflection @ ( reflection @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ A @ C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b2) ).
thf(116,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)],[29]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ D @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_4) ).
thf(74,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(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_1) ).
thf(60,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(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ C @ D @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_3) ).
thf(102,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(19,axiom,
! [B: $i,A: $i] :
( ( A != B )
| ( B
= ( reflection @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3_1) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( B
= ( reflection @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3) ).
thf(65,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(47,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/sandbox/benchmark/theBenchmark.p',inner_pasch1) ).
thf(156,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)],[47]) ).
thf(52,axiom,
! [B: $i,A: $i] : ( between @ A @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2) ).
thf(169,plain,
! [B: $i,A: $i] : ( between @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ~ ( between @ A @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(141,plain,
! [B: $i,A: $i] :
( ~ ( between @ A @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ C @ B )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b3) ).
thf(166,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)],[51]) ).
thf(44,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/sandbox/benchmark/theBenchmark.p',d9) ).
thf(148,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)],[44]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( between @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( between @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(42,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).
thf(144,plain,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',d8) ).
thf(181,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)],[57]) ).
thf(15,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ ( reflection @ B @ A ) @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r2_2) ).
thf(86,plain,
! [B: $i,A: $i] : ( equidistant @ A @ ( reflection @ B @ A ) @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( reflection @ A @ B )
= ( extension @ A @ B @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflection) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( reflection @ A @ B )
= ( extension @ A @ B @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( A
= ( reflection @ ( reflection @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r6) ).
thf(76,plain,
! [B: $i,A: $i] :
( A
= ( reflection @ ( reflection @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
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/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
thf(67,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(35,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/sandbox/benchmark/theBenchmark.p',upper_dimension) ).
thf(127,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)],[35]) ).
thf(46,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
thf(154,plain,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(8,axiom,
! [A: $i] :
( A
= ( reflection @ A @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',r3_2) ).
thf(72,plain,
! [A: $i] :
( A
= ( reflection @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
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/sandbox/benchmark/theBenchmark.p',d10_2) ).
thf(99,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(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ B @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_2) ).
thf(87,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(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ( equidistant @ D @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d4_5) ).
thf(104,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(48,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ A @ C @ B )
| ( A = B )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_2) ).
thf(158,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)],[48]) ).
thf(28,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/sandbox/benchmark/theBenchmark.p',continuity2) ).
thf(114,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)],[28]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( A = B )
| ( C
= ( extension @ A @ B @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d10_1) ).
thf(171,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)],[54]) ).
thf(40,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/sandbox/benchmark/theBenchmark.p',continuity1) ).
thf(139,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)],[40]) ).
thf(30,axiom,
between @ v @ w @ x,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',w_between_v_and_x) ).
thf(119,plain,
between @ v @ w @ x,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(1,negated_conjecture,
~ ( between @ u @ w @ x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_w_between_u_and_x) ).
thf(58,plain,
~ ( between @ u @ w @ x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(45,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/sandbox/benchmark/theBenchmark.p',euclid2) ).
thf(151,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)],[45]) ).
thf(43,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).
thf(146,plain,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(50,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/sandbox/benchmark/theBenchmark.p',euclid1) ).
thf(163,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)],[50]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ A @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d7) ).
thf(62,plain,
! [B: $i,A: $i] : ( equidistant @ A @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ A @ C )
| ( A = B )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_1) ).
thf(178,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)],[56]) ).
thf(33,axiom,
! [B: $i,A: $i] : ( between @ A @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3) ).
thf(122,plain,
! [B: $i,A: $i] : ( between @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(13,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ B @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(83,plain,
! [B: $i,A: $i] : ( equidistant @ A @ B @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( extension @ B @ A @ C @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',e1) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( extension @ B @ A @ C @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(27,axiom,
v != w,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',v_not_w) ).
thf(111,plain,
v != w,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(183,plain,
$false,
inference(e,[status(thm)],[69,174,78,137,96,134,108,130,123,63,107,170,120,106,121,84,132,89,116,74,60,102,92,65,156,169,141,166,148,161,144,181,86,81,76,67,127,154,72,99,87,104,158,114,171,139,119,58,151,146,163,62,178,122,83,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO044-3 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 19 04:29:22 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.92/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.37/0.98 % [INFO] Parsing done (138ms).
% 1.37/0.98 % [INFO] Running in sequential loop mode.
% 1.78/1.18 % [INFO] eprover registered as external prover.
% 1.78/1.18 % [INFO] cvc4 registered as external prover.
% 1.78/1.19 % [INFO] Scanning for conjecture ...
% 1.96/1.25 % [INFO] Found a conjecture and 56 axioms. Running axiom selection ...
% 2.00/1.29 % [INFO] Axiom selection finished. Selected 56 axioms (removed 0 axioms).
% 2.23/1.34 % [INFO] Problem is propositional (TPTP CNF).
% 2.23/1.35 % [INFO] Type checking passed.
% 2.23/1.35 % [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 ...
% 4.07/1.93 % External prover 'e' found a proof!
% 4.07/1.93 % [INFO] Killing All external provers ...
% 4.07/1.93 % Time passed: 1412ms (effective reasoning time: 946ms)
% 4.07/1.93 % 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)>
% 4.07/1.94 % Axioms used in derivation (56): continuity1, d3, reflexivity_for_equidistance, r2_2, identity_for_betweeness, r5, t6_2, d8, euclid3, d5, lower_dimension1, d4_4, b2, continuity2, b3, r2_1, d4_5, transitivity_for_equidistance, e1, d9, r6, inner_pasch2, b4, v_not_w, lower_dimension2, t3, reflection, b1, outer_five_segment, w_between_v_and_x, r3_2, b0, upper_dimension, t2, b5, 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, t1, identity_for_equidistance, d4_3, v_between_u_and_w, t6_1
% 4.07/1.94 % No. of inferences in proof: 115
% 4.07/1.94 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1412 ms resp. 946 ms w/o parsing
% 4.29/1.99 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.29/1.99 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------