TSTP Solution File: GEO011-5 by Leo-III---1.7.7

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%------------------------------------------------------------------------------
% 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 ... 
%------------------------------------------------------------------------------