TSTP Solution File: GEO185+2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : GEO185+2 : TPTP v8.2.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n024.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 : Mon May 20 20:06:08 EDT 2024

% Result   : Theorem 12.09s 3.46s
% Output   : Refutation 12.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    9
% Syntax   : Number of formulae    :   32 (   6 unt;   7 typ;   0 def)
%            Number of atoms       :   72 (   4 equ;   0 cnn)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  233 (  26   ~;  21   |;   9   &; 168   @)
%                                         (   0 <=>;   9  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   8   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :    9 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   39 (   0   ^  39   !;   0   ?;  39   :)

% Comments : 
%------------------------------------------------------------------------------
thf(distinct_points_type,type,
    distinct_points: $i > $i > $o ).

thf(convergent_lines_type,type,
    convergent_lines: $i > $i > $o ).

thf(intersection_point_type,type,
    intersection_point: $i > $i > $i ).

thf(apart_point_and_line_type,type,
    apart_point_and_line: $i > $i > $o ).

thf(sk1_type,type,
    sk1: $i ).

thf(sk3_type,type,
    sk3: $i ).

thf(sk4_type,type,
    sk4: $i ).

thf(1,conjecture,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( distinct_points @ A @ B )
        & ( convergent_lines @ C @ D )
        & ~ ( distinct_points @ A @ ( intersection_point @ C @ D ) ) )
     => ( ~ ( apart_point_and_line @ A @ C )
        & ~ ( apart_point_and_line @ A @ D ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).

thf(2,negated_conjecture,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( ( ( distinct_points @ A @ B )
          & ( convergent_lines @ C @ D )
          & ~ ( distinct_points @ A @ ( intersection_point @ C @ D ) ) )
       => ( ~ ( apart_point_and_line @ A @ C )
          & ~ ( apart_point_and_line @ A @ D ) ) ),
    inference(neg_conjecture,[status(cth)],[1]) ).

thf(15,plain,
    ~ ! [A: $i,B: $i,C: $i,D: $i] :
        ( ( ( distinct_points @ A @ B )
          & ( convergent_lines @ C @ D )
          & ~ ( distinct_points @ A @ ( intersection_point @ C @ D ) ) )
       => ( ~ ( apart_point_and_line @ A @ C )
          & ~ ( apart_point_and_line @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(16,plain,
    ( ( apart_point_and_line @ sk1 @ sk3 )
    | ( apart_point_and_line @ sk1 @ sk4 ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(18,plain,
    convergent_lines @ sk3 @ sk4,
    inference(cnf,[status(esa)],[15]) ).

thf(10,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( convergent_lines @ A @ B )
     => ( ( ( apart_point_and_line @ C @ A )
          | ( apart_point_and_line @ C @ B ) )
       => ( distinct_points @ C @ ( intersection_point @ A @ B ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con2) ).

thf(42,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( convergent_lines @ A @ B )
     => ( ( ( apart_point_and_line @ C @ A )
          | ( apart_point_and_line @ C @ B ) )
       => ( distinct_points @ C @ ( intersection_point @ A @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(43,plain,
    ! [A: $i,B: $i] :
      ( ( convergent_lines @ A @ B )
     => ! [C: $i] :
          ( ( ( apart_point_and_line @ C @ A )
            | ( apart_point_and_line @ C @ B ) )
         => ( distinct_points @ C @ ( intersection_point @ A @ B ) ) ) ),
    inference(miniscope,[status(thm)],[42]) ).

thf(44,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( convergent_lines @ A @ B )
      | ~ ( apart_point_and_line @ C @ B )
      | ( distinct_points @ C @ ( intersection_point @ A @ B ) ) ),
    inference(cnf,[status(esa)],[43]) ).

thf(187,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( apart_point_and_line @ C @ B )
      | ( distinct_points @ C @ ( intersection_point @ A @ B ) )
      | ( ( convergent_lines @ sk3 @ sk4 )
       != ( convergent_lines @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[18,44]) ).

thf(188,plain,
    ! [A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk4 )
      | ( distinct_points @ A @ ( intersection_point @ sk3 @ sk4 ) ) ),
    inference(pattern_uni,[status(thm)],[187:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(198,plain,
    ! [A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk4 )
      | ( distinct_points @ A @ ( intersection_point @ sk3 @ sk4 ) ) ),
    inference(simp,[status(thm)],[188]) ).

thf(1224,plain,
    ! [A: $i] :
      ( ( apart_point_and_line @ sk1 @ sk3 )
      | ( distinct_points @ A @ ( intersection_point @ sk3 @ sk4 ) )
      | ( ( apart_point_and_line @ sk1 @ sk4 )
       != ( apart_point_and_line @ A @ sk4 ) ) ),
    inference(paramod_ordered,[status(thm)],[16,198]) ).

thf(1225,plain,
    ( ( apart_point_and_line @ sk1 @ sk3 )
    | ( distinct_points @ sk1 @ ( intersection_point @ sk3 @ sk4 ) ) ),
    inference(pattern_uni,[status(thm)],[1224:[bind(A,$thf( sk1 ))]]) ).

thf(17,plain,
    ~ ( distinct_points @ sk1 @ ( intersection_point @ sk3 @ sk4 ) ),
    inference(cnf,[status(esa)],[15]) ).

thf(1231,plain,
    ( ( apart_point_and_line @ sk1 @ sk3 )
    | $false ),
    inference(rewrite,[status(thm)],[1225,17]) ).

thf(1232,plain,
    apart_point_and_line @ sk1 @ sk3,
    inference(simp,[status(thm)],[1231]) ).

thf(45,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( convergent_lines @ A @ B )
      | ~ ( apart_point_and_line @ C @ A )
      | ( distinct_points @ C @ ( intersection_point @ A @ B ) ) ),
    inference(cnf,[status(esa)],[43]) ).

thf(397,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( apart_point_and_line @ C @ A )
      | ( distinct_points @ C @ ( intersection_point @ A @ B ) )
      | ( ( convergent_lines @ sk3 @ sk4 )
       != ( convergent_lines @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[18,45]) ).

thf(398,plain,
    ! [A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk3 )
      | ( distinct_points @ A @ ( intersection_point @ sk3 @ sk4 ) ) ),
    inference(pattern_uni,[status(thm)],[397:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 ))]]) ).

thf(414,plain,
    ! [A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk3 )
      | ( distinct_points @ A @ ( intersection_point @ sk3 @ sk4 ) ) ),
    inference(simp,[status(thm)],[398]) ).

thf(1702,plain,
    ! [A: $i] :
      ( ( distinct_points @ A @ ( intersection_point @ sk3 @ sk4 ) )
      | ( ( apart_point_and_line @ sk1 @ sk3 )
       != ( apart_point_and_line @ A @ sk3 ) ) ),
    inference(paramod_ordered,[status(thm)],[1232,414]) ).

thf(1703,plain,
    distinct_points @ sk1 @ ( intersection_point @ sk3 @ sk4 ),
    inference(pattern_uni,[status(thm)],[1702:[bind(A,$thf( sk1 ))]]) ).

thf(1709,plain,
    $false,
    inference(rewrite,[status(thm)],[1703,17]) ).

thf(1710,plain,
    $false,
    inference(simp,[status(thm)],[1709]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09  % Problem  : GEO185+2 : TPTP v8.2.0. Released v3.3.0.
% 0.05/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n024.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sun May 19 15:38:23 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 1.00/0.96  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.28/1.14  % [INFO] 	 Parsing done (180ms). 
% 1.45/1.16  % [INFO] 	 Running in sequential loop mode. 
% 1.81/1.43  % [INFO] 	 nitpick registered as external prover. 
% 1.81/1.44  % [INFO] 	 Scanning for conjecture ... 
% 2.06/1.50  % [INFO] 	 Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ... 
% 2.06/1.53  % [INFO] 	 Axiom selection finished. Selected 12 axioms (removed 0 axioms). 
% 2.28/1.55  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.28/1.55  % [INFO] 	 Type checking passed. 
% 2.28/1.56  % [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 ... 
% 12.09/3.43  % [INFO] 	 Killing All external provers ... 
% 12.09/3.44  % Time passed: 2966ms (effective reasoning time: 2277ms)
% 12.09/3.45  % 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)>
% 12.09/3.46  % Axioms used in derivation (1): con2
% 12.09/3.46  % No. of inferences in proof: 25
% 12.09/3.46  % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2966 ms resp. 2277 ms w/o parsing
% 12.20/3.48  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.20/3.48  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------