TSTP Solution File: GEO048-3 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO048-3 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 11:09:05 EDT 2023
% Result : Unsatisfiable 4.65s 2.11s
% Output : Refutation 4.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 85
% Syntax : Number of formulae : 154 ( 57 unt; 17 typ; 0 def)
% Number of atoms : 317 ( 74 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1442 ( 168 ~; 180 |; 0 &;1094 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 17 usr; 10 con; 0-6 aty)
% Number of variables : 416 ( 0 ^; 416 !; 0 ?; 416 :)
% Comments :
%------------------------------------------------------------------------------
thf(between_type,type,
between: $i > $i > $i > $o ).
thf(x_type,type,
x: $i ).
thf(inner_pasch_type,type,
inner_pasch: $i > $i > $i > $i > $i > $i ).
thf(v1_type,type,
v1: $i ).
thf(u_type,type,
u: $i ).
thf(u1_type,type,
u1: $i ).
thf(w_type,type,
w: $i ).
thf(v_type,type,
v: $i ).
thf(equidistant_type,type,
equidistant: $i > $i > $i > $i > $o ).
thf(reflection_type,type,
reflection: $i > $i > $i ).
thf(lower_dimension_point_1_type,type,
lower_dimension_point_1: $i ).
thf(lower_dimension_point_3_type,type,
lower_dimension_point_3: $i ).
thf(extension_type,type,
extension: $i > $i > $i > $i > $i ).
thf(lower_dimension_point_2_type,type,
lower_dimension_point_2: $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(1,negated_conjecture,
~ ( between @ x @ ( inner_pasch @ v1 @ ( inner_pasch @ u @ x @ u1 @ v1 @ w ) @ u @ v @ w ) @ w ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_conclusion1) ).
thf(69,plain,
~ ( between @ x @ ( inner_pasch @ v1 @ ( inner_pasch @ u @ x @ u1 @ v1 @ w ) @ u @ v @ w ) @ w ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(6,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(78,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)],[6]) ).
thf(57,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(193,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)],[57]) ).
thf(63,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(204,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)],[63]) ).
thf(26,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)],[26]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( A
= ( reflection @ ( reflection @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r6) ).
thf(95,plain,
! [B: $i,A: $i] :
( A
= ( reflection @ ( reflection @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(50,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(175,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)],[50]) ).
thf(10,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(87,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)],[10]) ).
thf(48,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(170,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)],[48]) ).
thf(68,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(217,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)],[68]) ).
thf(37,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(142,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)],[37]) ).
thf(41,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(153,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)],[41]) ).
thf(20,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ ( reflection @ B @ A ) @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_2) ).
thf(110,plain,
! [B: $i,A: $i] : ( equidistant @ A @ ( reflection @ B @ A ) @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(58,axiom,
! [B: $i,A: $i] : ( between @ A @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t2) ).
thf(196,plain,
! [B: $i,A: $i] : ( between @ A @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(67,axiom,
between @ u1 @ v1 @ w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v1_between_u1_and_w) ).
thf(216,plain,
between @ u1 @ v1 @ w,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(65,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(211,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)],[65]) ).
thf(30,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(132,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)],[30]) ).
thf(24,axiom,
lower_dimension_point_1 != lower_dimension_point_2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_1) ).
thf(116,plain,
lower_dimension_point_1 != lower_dimension_point_2,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(11,axiom,
lower_dimension_point_1 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_3) ).
thf(89,plain,
lower_dimension_point_1 != lower_dimension_point_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(31,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1) ).
thf(133,plain,
! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(16,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ B @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(102,plain,
! [B: $i,A: $i] : ( equidistant @ A @ B @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(9,axiom,
! [A: $i] :
( A
= ( reflection @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r3_2) ).
thf(85,plain,
! [A: $i] :
( A
= ( reflection @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(62,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(201,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)],[62]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ~ ( between @ A @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(160,plain,
! [B: $i,A: $i] :
( ~ ( between @ A @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(2,negated_conjecture,
~ ( between @ v @ ( inner_pasch @ v1 @ ( inner_pasch @ u @ x @ u1 @ v1 @ w ) @ u @ v @ w ) @ v1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_conclusion2) ).
thf(70,plain,
~ ( between @ v @ ( inner_pasch @ v1 @ ( inner_pasch @ u @ x @ u1 @ v1 @ w ) @ u @ v @ w ) @ v1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(46,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(165,plain,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(12,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(92,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)],[12]) ).
thf(59,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(197,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)],[59]) ).
thf(14,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(97,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(42,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(156,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)],[42]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( between @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t1) ).
thf(188,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( between @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(36,axiom,
! [B: $i,A: $i] : ( between @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3) ).
thf(141,plain,
! [B: $i,A: $i] : ( between @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(49,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(173,plain,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(29,axiom,
lower_dimension_point_2 != lower_dimension_point_3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e2_2) ).
thf(129,plain,
lower_dimension_point_2 != lower_dimension_point_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(32,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(134,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)],[32]) ).
thf(3,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(73,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)],[3]) ).
thf(28,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(128,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)],[28]) ).
thf(18,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(105,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)],[18]) ).
thf(52,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(180,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)],[52]) ).
thf(39,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(149,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)],[39]) ).
thf(22,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ ( reflection @ ( reflection @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r5) ).
thf(113,plain,
! [B: $i,A: $i] : ( equidistant @ A @ B @ A @ ( reflection @ ( reflection @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(5,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(76,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)],[5]) ).
thf(17,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(103,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)],[17]) ).
thf(35,axiom,
! [B: $i,A: $i] : ( between @ A @ B @ ( reflection @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r2_1) ).
thf(140,plain,
! [B: $i,A: $i] : ( between @ A @ B @ ( reflection @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(7,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(80,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)],[7]) ).
thf(47,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(167,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)],[47]) ).
thf(60,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(199,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)],[60]) ).
thf(51,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(177,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)],[51]) ).
thf(43,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(158,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)],[43]) ).
thf(54,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(186,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)],[54]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( A
= ( extension @ B @ A @ C @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e1) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( A
= ( extension @ B @ A @ C @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(34,axiom,
between @ u @ v @ w,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',v_between_u_and_w) ).
thf(139,plain,
between @ u @ v @ w,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ A @ B @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d7) ).
thf(75,plain,
! [B: $i,A: $i] : ( equidistant @ A @ A @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(25,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)],[25]) ).
thf(64,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(207,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)],[64]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( A
!= ( reflection @ B @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',r4) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( A
!= ( reflection @ B @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(66,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(214,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)],[66]) ).
thf(40,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(151,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)],[40]) ).
thf(38,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(146,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)],[38]) ).
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 @ D @ ( euclid1 @ A @ D @ B @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid1) ).
thf(190,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)],[56]) ).
thf(53,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(183,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)],[53]) ).
thf(19,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(107,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)],[19]) ).
thf(27,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(126,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)],[27]) ).
thf(33,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(136,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)],[33]) ).
thf(45,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(163,plain,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(61,axiom,
between @ u @ x @ u1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',x_between_u_and_u1) ).
thf(200,plain,
between @ u @ x @ u1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(21,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(111,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)],[21]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( reflection @ A @ B )
= ( extension @ A @ B @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflection) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( reflection @ A @ B )
= ( extension @ A @ B @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(220,plain,
$false,
inference(e,[status(thm)],[69,78,193,204,123,95,175,87,170,217,142,153,110,196,216,211,132,116,89,133,102,85,201,160,70,165,92,197,97,156,188,141,173,129,134,73,128,105,180,149,113,76,103,140,80,167,199,177,158,186,114,139,75,119,207,82,214,151,146,190,183,107,126,136,163,200,111,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO048-3 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n026.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Fri May 19 04:29:07 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.96/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.26/1.03 % [INFO] Parsing done (152ms).
% 1.26/1.04 % [INFO] Running in sequential loop mode.
% 1.91/1.25 % [INFO] eprover registered as external prover.
% 1.91/1.26 % [INFO] cvc4 registered as external prover.
% 1.91/1.26 % [INFO] Scanning for conjecture ...
% 1.98/1.32 % [INFO] Found a conjecture and 66 axioms. Running axiom selection ...
% 2.27/1.38 % [INFO] Axiom selection finished. Selected 66 axioms (removed 0 axioms).
% 2.27/1.43 % [INFO] Problem is propositional (TPTP CNF).
% 2.53/1.44 % [INFO] Type checking passed.
% 2.53/1.44 % [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 ...
% 4.65/2.11 % External prover 'e' found a proof!
% 4.65/2.11 % [INFO] Killing All external provers ...
% 4.65/2.11 % Time passed: 1570ms (effective reasoning time: 1069ms)
% 4.65/2.11 % 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)>
% 4.65/2.11 % Axioms used in derivation (66): e3_2, b7, d3, reflexivity_for_equidistance, r5, outer_five_segment, d8, euclid3, d5, continuity1, e2_2, lower_dimension1, d4_4, b2, continuity2, b3, r2_1, d4_5, transitivity_for_equidistance, e1, d9, r6, inner_pasch2, b4, lower_dimension2, t3, reflection, b1, r2_2, b8, x_between_u_and_u1, identity_for_betweeness, r3_2, b0, upper_dimension, t2, b5, euclid1, d7, d10_2, r4, e2_3, segment_construction2, d2, d10_3, e3_1, d4_2, d4_1, lower_dimension3, t6_2, b9, b6, inner_pasch1, e3_3, r3_1, segment_construction1, euclid2, d10_1, e2_1, d1, t1, identity_for_equidistance, d4_3, v1_between_u1_and_w, v_between_u_and_w, t6_1
% 4.65/2.11 % No. of inferences in proof: 137
% 4.65/2.11 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1570 ms resp. 1069 ms w/o parsing
% 4.92/2.17 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 4.92/2.17 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------