TSTP Solution File: GEO011-5 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : GEO011-5 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n031.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 11:08:52 EDT 2023
% Result : Unsatisfiable 3.15s 1.68s
% Output : Refutation 3.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 26
% Syntax : Number of formulae : 44 ( 15 unt; 9 typ; 0 def)
% Number of atoms : 77 ( 6 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 396 ( 42 ~; 42 |; 0 &; 312 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-5 aty)
% Number of variables : 102 ( 0 ^; 102 !; 0 ?; 102 :)
% Comments :
%------------------------------------------------------------------------------
thf(colinear_type,type,
colinear: $i > $i > $i > $o ).
thf(lower_dimension_point_1_type,type,
lower_dimension_point_1: $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(equal_distance_type,type,
equal_distance: $i > $i > $o ).
thf(distance_type,type,
distance: $i > $i > $i ).
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(7,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equal_distance @ ( distance @ A @ B ) @ ( distance @ C @ D ) )
| ~ ( equal_distance @ ( distance @ B @ E ) @ ( distance @ D @ F ) )
| ~ ( equal_distance @ ( distance @ A @ G ) @ ( distance @ C @ H ) )
| ~ ( equal_distance @ ( distance @ B @ G ) @ ( distance @ D @ H ) )
| ~ ( between @ A @ B @ E )
| ~ ( between @ C @ D @ F )
| ( A = B )
| ( equal_distance @ ( distance @ E @ G ) @ ( distance @ F @ H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).
thf(28,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equal_distance @ ( distance @ A @ B ) @ ( distance @ C @ D ) )
| ~ ( equal_distance @ ( distance @ B @ E ) @ ( distance @ D @ F ) )
| ~ ( equal_distance @ ( distance @ A @ G ) @ ( distance @ C @ H ) )
| ~ ( equal_distance @ ( distance @ B @ G ) @ ( distance @ D @ H ) )
| ~ ( between @ A @ B @ E )
| ~ ( between @ C @ D @ F )
| ( A = B )
| ( equal_distance @ ( distance @ E @ G ) @ ( distance @ F @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity1) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(3,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equal_distance @ ( distance @ A @ B ) @ ( distance @ C @ D ) )
| ~ ( equal_distance @ ( distance @ A @ B ) @ ( distance @ E @ F ) )
| ( equal_distance @ ( distance @ C @ D ) @ ( distance @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).
thf(22,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( equal_distance @ ( distance @ A @ B ) @ ( distance @ C @ D ) )
| ~ ( equal_distance @ ( distance @ A @ B ) @ ( distance @ E @ F ) )
| ( equal_distance @ ( distance @ C @ D ) @ ( distance @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity2) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(12,axiom,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).
thf(39,plain,
~ ( between @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(10,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(35,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)],[10]) ).
thf(1,negated_conjecture,
colinear @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_lower_dimension_points_not_colinear) ).
thf(18,plain,
colinear @ lower_dimension_point_1 @ lower_dimension_point_2 @ lower_dimension_point_3,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( between @ A @ B @ A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).
thf(31,plain,
! [B: $i,A: $i] :
( ~ ( between @ A @ B @ A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',colinearity3) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( between @ A @ B @ C )
| ( colinear @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(6,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(26,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)],[6]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( equal_distance @ ( distance @ A @ B ) @ ( distance @ C @ C ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).
thf(19,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( equal_distance @ ( distance @ A @ B ) @ ( distance @ C @ C ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,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(47,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)],[16]) ).
thf(4,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( equal_distance @ ( distance @ A @ ( extension @ B @ A @ C @ D ) ) @ ( distance @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( equal_distance @ ( distance @ A @ ( extension @ B @ A @ C @ D ) ) @ ( distance @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(11,axiom,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).
thf(37,plain,
~ ( between @ lower_dimension_point_2 @ lower_dimension_point_3 @ lower_dimension_point_1 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(5,axiom,
! [B: $i,A: $i] : ( equal_distance @ ( distance @ A @ B ) @ ( distance @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).
thf(25,plain,
! [B: $i,A: $i] : ( equal_distance @ ( distance @ A @ B ) @ ( distance @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(9,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(34,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)],[9]) ).
thf(15,axiom,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).
thf(45,plain,
~ ( between @ lower_dimension_point_3 @ lower_dimension_point_1 @ lower_dimension_point_2 ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(51,plain,
$false,
inference(e,[status(thm)],[28,41,22,49,39,35,18,31,43,26,19,47,24,37,25,34,45]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO011-5 : TPTP v8.1.2. Released v1.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n031.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 04:21:41 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.91/0.83 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.20/0.96 % [INFO] Parsing done (125ms).
% 1.20/0.97 % [INFO] Running in sequential loop mode.
% 1.70/1.16 % [INFO] eprover registered as external prover.
% 1.70/1.16 % [INFO] cvc4 registered as external prover.
% 1.70/1.17 % [INFO] Scanning for conjecture ...
% 1.70/1.22 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 1.86/1.25 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.01/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 2.01/1.28 % [INFO] Type checking passed.
% 2.01/1.28 % [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 ...
% 3.15/1.67 % External prover 'e' found a proof!
% 3.15/1.67 % [INFO] Killing All external provers ...
% 3.15/1.67 % Time passed: 1160ms (effective reasoning time: 704ms)
% 3.15/1.67 % 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)>
% 3.15/1.68 % Axioms used in derivation (16): lower_dimension1, inner_pasch2, reflexivity_for_equidistance, lower_dimension2, identity_for_betweeness, colinearity4, outer_five_segment, colinearity1, segment_construction2, lower_dimension3, inner_pasch1, segment_construction1, identity_for_equidistance, colinearity2, transitivity_for_equidistance, colinearity3
% 3.15/1.68 % No. of inferences in proof: 35
% 3.15/1.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1160 ms resp. 704 ms w/o parsing
% 3.50/1.78 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.50/1.78 % [INFO] Killing All external provers ...
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