TSTP Solution File: GEO008-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO008-1 : TPTP v8.1.2. Bugfixed v2.5.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n022.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 11:08:50 EDT 2023
% Result : Unsatisfiable 3.91s 2.01s
% Output : Refutation 3.91s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 39
% Syntax : Number of formulae : 64 ( 21 unt; 15 typ; 0 def)
% Number of atoms : 137 ( 16 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 664 ( 78 ~; 88 |; 0 &; 498 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 15 usr; 9 con; 0-6 aty)
% Number of variables : 158 ( 0 ^; 158 !; 0 ?; 158 :)
% Comments :
%------------------------------------------------------------------------------
thf(between_type,type,
between: $i > $i > $i > $o ).
thf(a_type,type,
a: $i ).
thf(b_type,type,
b: $i ).
thf(e_type,type,
e: $i ).
thf(equidistant_type,type,
equidistant: $i > $i > $i > $i > $o ).
thf(extension_type,type,
extension: $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(continuous_type,type,
continuous: $i > $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(c_type,type,
c: $i ).
thf(d_type,type,
d: $i ).
thf(outer_pasch_type,type,
outer_pasch: $i > $i > $i > $i > $i > $i ).
thf(22,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).
thf(69,plain,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(1,negated_conjecture,
~ ( between @ a @ b @ e ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_betweenness) ).
thf(25,plain,
~ ( between @ a @ b @ e ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(14,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',connectivity_for_betweeness) ).
thf(52,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)],[14]) ).
thf(5,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(33,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)],[5]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( between @ A @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(41,plain,
! [B: $i,A: $i] :
( ~ ( between @ A @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(8,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 @ B @ F @ D @ C @ E @ A ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).
thf(39,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 @ B @ F @ D @ C @ E @ A ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(20,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 @ B @ F @ D @ C @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity1) ).
thf(66,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 @ B @ F @ D @ C @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(24,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ B @ E )
| ( A = B )
| ( between @ A @ E @ ( euclid1 @ C @ A @ D @ E @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid1) ).
thf(72,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ B @ E )
| ( A = B )
| ( between @ A @ E @ ( euclid1 @ C @ A @ D @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ C @ E )
| ( between @ A @ ( outer_pasch @ B @ A @ D @ E @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_pasch1) ).
thf(55,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ C @ E )
| ( between @ A @ ( outer_pasch @ B @ A @ D @ E @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(7,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ B @ E )
| ( A = B )
| ( between @ ( euclid1 @ C @ A @ D @ E @ B ) @ C @ ( euclid2 @ C @ A @ D @ E @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid3) ).
thf(36,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ B @ E )
| ( A = B )
| ( between @ ( euclid1 @ C @ A @ D @ E @ B ) @ C @ ( euclid2 @ C @ A @ D @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).
thf(46,plain,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(16,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ C @ E )
| ( between @ E @ B @ ( outer_pasch @ B @ A @ D @ E @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_pasch2) ).
thf(57,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ C @ E )
| ( between @ E @ B @ ( outer_pasch @ B @ A @ D @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(3,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(29,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ B @ B @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(32,plain,
! [B: $i,A: $i] : ( equidistant @ A @ B @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(6,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ D @ C )
| ( between @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_betweeness) ).
thf(34,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ B @ D @ C )
| ( between @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).
thf(44,plain,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(17,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(59,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)],[17]) ).
thf(2,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(27,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)],[2]) ).
thf(23,axiom,
between @ a @ c @ e,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',c_between_a_and_e) ).
thf(71,plain,
between @ a @ c @ e,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(13,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ B @ E )
| ( A = B )
| ( between @ A @ D @ ( euclid2 @ C @ A @ D @ E @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid2) ).
thf(49,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ~ ( between @ D @ B @ E )
| ( A = B )
| ( between @ A @ D @ ( euclid2 @ C @ A @ D @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(12,axiom,
between @ c @ b @ d,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',b_between_c_and_d) ).
thf(48,plain,
between @ c @ b @ d,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,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(63,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)],[19]) ).
thf(21,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(68,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)],[21]) ).
thf(18,axiom,
between @ a @ d @ e,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d_between_a_and_e) ).
thf(62,plain,
between @ a @ d @ e,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(129,plain,
$false,
inference(e,[status(thm)],[69,25,52,33,41,39,66,72,55,36,46,57,29,32,34,44,59,27,71,49,48,63,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO008-1 : TPTP v8.1.2. Bugfixed v2.5.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n022.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 04:02:32 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.94/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.25/0.98 % [INFO] Parsing done (124ms).
% 1.25/0.99 % [INFO] Running in sequential loop mode.
% 1.70/1.19 % [INFO] eprover registered as external prover.
% 1.70/1.19 % [INFO] cvc4 registered as external prover.
% 1.80/1.19 % [INFO] Scanning for conjecture ...
% 1.92/1.24 % [INFO] Found a conjecture and 23 axioms. Running axiom selection ...
% 1.92/1.28 % [INFO] Axiom selection finished. Selected 23 axioms (removed 0 axioms).
% 2.13/1.32 % [INFO] Problem is propositional (TPTP CNF).
% 2.13/1.32 % [INFO] Type checking passed.
% 2.13/1.32 % [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 ...
% 3.91/2.01 % External prover 'e' found a proof!
% 3.91/2.01 % [INFO] Killing All external provers ...
% 3.91/2.01 % Time passed: 1481ms (effective reasoning time: 1015ms)
% 3.91/2.01 % 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)>
% 3.91/2.01 % Axioms used in derivation (23): euclid3, continuity1, lower_dimension1, transitivity_for_equidistance, reflexivity_for_equidistance, lower_dimension2, identity_for_betweeness, outer_five_segment, upper_dimension, euclid1, segment_construction2, continuity2, b_between_c_and_d, outer_pasch1, connectivity_for_betweeness, outer_pasch2, c_between_a_and_e, lower_dimension3, d_between_a_and_e, segment_construction1, euclid2, identity_for_equidistance, transitivity_for_betweeness
% 3.91/2.01 % No. of inferences in proof: 49
% 3.91/2.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1481 ms resp. 1015 ms w/o parsing
% 3.91/2.05 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 3.91/2.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------