TSTP Solution File: GEO067-2 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : GEO067-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.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 : Tue May 7 07:40:52 EDT 2024
% Result : Unsatisfiable 3.93s 2.07s
% Output : Refutation 4.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 38
% Syntax : Number of formulae : 63 ( 13 unt; 14 typ; 0 def)
% Number of atoms : 149 ( 16 equ; 0 cnn)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 724 ( 90 ~; 100 |; 0 &; 534 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 35 ( 35 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 7 con; 0-6 aty)
% Number of variables : 166 ( 0 ^ 166 !; 0 ?; 166 :)
% Comments :
%------------------------------------------------------------------------------
thf(colinear_type,type,
colinear: $i > $i > $i > $o ).
thf(x_type,type,
x: $i ).
thf(y_type,type,
y: $i ).
thf(z_type,type,
z: $i ).
thf(equidistant_type,type,
equidistant: $i > $i > $i > $i > $o ).
thf(extension_type,type,
extension: $i > $i > $i > $i > $i ).
thf(between_type,type,
between: $i > $i > $i > $o ).
thf(inner_pasch_type,type,
inner_pasch: $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(euclid1_type,type,
euclid1: $i > $i > $i > $i > $i > $i ).
thf(euclid2_type,type,
euclid2: $i > $i > $i > $i > $i > $i ).
thf(20,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(69,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)],[20]) ).
thf(14,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ B @ E @ D @ F )
| ~ ( equidistant @ A @ G @ C @ H )
| ~ ( equidistant @ B @ G @ D @ H )
| ~ ( between @ A @ B @ E )
| ~ ( between @ C @ D @ F )
| ( A = B )
| ( equidistant @ E @ G @ F @ H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).
thf(52,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ D )
| ~ ( equidistant @ B @ E @ D @ F )
| ~ ( equidistant @ A @ G @ C @ H )
| ~ ( equidistant @ B @ G @ D @ H )
| ~ ( between @ A @ B @ E )
| ~ ( between @ C @ D @ F )
| ( A = B )
| ( equidistant @ E @ G @ F @ H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity1) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(17,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(60,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)],[17]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity3) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( between @ A @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox/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(4,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(32,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equidistant @ A @ B @ C @ C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(10,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox/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(19,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(66,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)],[19]) ).
thf(5,axiom,
! [B: $i,A: $i] : ( equidistant @ A @ B @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(35,plain,
! [B: $i,A: $i] : ( equidistant @ A @ B @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(13,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(50,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)],[13]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( colinear @ A @ B @ C )
| ( between @ A @ B @ C )
| ( between @ B @ C @ A )
| ( between @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity4) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( colinear @ A @ B @ C )
| ( between @ A @ B @ C )
| ( between @ B @ C @ A )
| ( between @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(7,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(37,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)],[7]) ).
thf(1,negated_conjecture,
( ~ ( colinear @ x @ x @ y )
| ~ ( colinear @ x @ y @ x )
| ~ ( colinear @ y @ x @ x )
| ( x = y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_1) ).
thf(25,plain,
( ~ ( colinear @ x @ x @ y )
| ~ ( colinear @ x @ y @ x )
| ~ ( colinear @ y @ x @ x )
| ( x = y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox/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 @ B @ E )
| ( A = B )
| ( between @ A @ D @ ( euclid1 @ A @ D @ B @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid1) ).
thf(57,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)],[16]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity2) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
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 @ A @ B @ C @ F @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity1) ).
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 @ A @ B @ C @ F @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(12,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
thf(48,plain,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(18,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(63,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)],[18]) ).
thf(2,negated_conjecture,
( ~ ( colinear @ x @ x @ y )
| ~ ( colinear @ x @ y @ x )
| ~ ( colinear @ y @ x @ x )
| ~ ( colinear @ x @ z @ y ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',part_2) ).
thf(26,plain,
( ~ ( colinear @ x @ x @ y )
| ~ ( colinear @ x @ y @ x )
| ~ ( colinear @ y @ x @ x )
| ~ ( colinear @ x @ z @ y ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,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(55,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)],[15]) ).
thf(6,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(36,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)],[6]) ).
thf(3,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(30,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)],[3]) ).
thf(78,plain,
$false,
inference(e,[status(thm)],[69,52,74,60,70,41,32,44,66,35,50,72,37,25,46,57,76,39,48,63,26,55,36,30]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO067-2 : TPTP v8.1.2. Released v1.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n003.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 : Mon May 6 17:23:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.08/0.96 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.38/1.11 % [INFO] Parsing done (152ms).
% 1.38/1.12 % [INFO] Running in sequential loop mode.
% 2.08/1.39 % [INFO] eprover registered as external prover.
% 2.08/1.39 % [INFO] cvc4 registered as external prover.
% 2.08/1.40 % [INFO] Scanning for conjecture ...
% 2.28/1.46 % [INFO] Found a conjecture and 22 axioms. Running axiom selection ...
% 2.31/1.51 % [INFO] Axiom selection finished. Selected 22 axioms (removed 0 axioms).
% 2.57/1.55 % [INFO] Problem is propositional (TPTP CNF).
% 2.57/1.56 % [INFO] Type checking passed.
% 2.57/1.56 % [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 ...
% 3.93/2.07 % External prover 'e' found a proof!
% 3.93/2.07 % [INFO] Killing All external provers ...
% 3.93/2.07 % Time passed: 1530ms (effective reasoning time: 945ms)
% 3.93/2.07 % 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)>
% 3.93/2.07 % Axioms used in derivation (22): euclid3, continuity1, lower_dimension1, continuity2, inner_pasch2, reflexivity_for_equidistance, lower_dimension2, identity_for_betweeness, colinearity4, outer_five_segment, upper_dimension, segment_construction2, lower_dimension3, inner_pasch1, identity_for_equidistance, colinearity2, transitivity_for_equidistance, colinearity3, euclid1, colinearity1, segment_construction1, euclid2
% 3.93/2.07 % No. of inferences in proof: 49
% 3.93/2.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1530 ms resp. 945 ms w/o parsing
% 4.16/2.18 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.16/2.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------