TSTP Solution File: GEO172+2 by Leo-III-SAT---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III-SAT---1.7.12
% Problem  : GEO172+2 : TPTP v8.2.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n002.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 20:06:02 EDT 2024

% Result   : Theorem 123.59s 22.43s
% Output   : Refutation 123.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   62 (  13 unt;   8 typ;   0 def)
%            Number of atoms       :  168 (  10 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives :  508 (  48   ~;  70   |;   8   &; 366   @)
%                                         (   0 <=>;  16  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   12 (   7 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   10 (  10   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   11 (   8 usr;   5 con; 0-2 aty)
%            Number of variables   :   97 (   0   ^  96   !;   1   ?;  97   :)

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

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

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

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

thf(distinct_lines_type,type,
    distinct_lines: $i > $i > $o ).

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

thf(sk2_type,type,
    sk2: $i ).

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

thf(1,conjecture,
    ! [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/sandbox/benchmark/theBenchmark.p',con) ).

thf(2,negated_conjecture,
    ~ ! [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(neg_conjecture,[status(cth)],[1]) ).

thf(15,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)],[2]) ).

thf(16,plain,
    distinct_points @ sk3 @ ( intersection_point @ sk1 @ sk2 ),
    inference(cnf,[status(esa)],[15]) ).

thf(6,axiom,
    ! [A: $i,B: $i,C: $i] :
      ( ( distinct_points @ A @ B )
     => ( ( distinct_points @ A @ C )
        | ( distinct_points @ B @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart4) ).

thf(29,plain,
    ! [A: $i,B: $i,C: $i] :
      ( ( distinct_points @ A @ B )
     => ( ( distinct_points @ A @ C )
        | ( distinct_points @ B @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(30,plain,
    ! [A: $i,B: $i] :
      ( ( distinct_points @ A @ B )
     => ! [C: $i] :
          ( ( distinct_points @ A @ C )
          | ( distinct_points @ B @ C ) ) ),
    inference(miniscope,[status(thm)],[29]) ).

thf(31,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( distinct_points @ A @ B )
      | ( distinct_points @ A @ C )
      | ( distinct_points @ B @ C ) ),
    inference(cnf,[status(esa)],[30]) ).

thf(63,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( distinct_points @ A @ C )
      | ( distinct_points @ B @ C )
      | ( ( distinct_points @ sk3 @ ( intersection_point @ sk1 @ sk2 ) )
       != ( distinct_points @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[16,31]) ).

thf(64,plain,
    ! [A: $i] :
      ( ( distinct_points @ sk3 @ A )
      | ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ A ) ),
    inference(pattern_uni,[status(thm)],[63:[bind(A,$thf( sk3 )),bind(B,$thf( intersection_point @ sk1 @ sk2 )),bind(C,$thf( C ))]]) ).

thf(71,plain,
    ! [A: $i] :
      ( ( distinct_points @ sk3 @ A )
      | ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ A ) ),
    inference(simp,[status(thm)],[64]) ).

thf(78,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( distinct_points @ sk3 @ A )
      | ( distinct_points @ B @ D )
      | ( distinct_points @ C @ D )
      | ( ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ A )
       != ( distinct_points @ B @ C ) ) ),
    inference(paramod_ordered,[status(thm)],[71,31]) ).

thf(79,plain,
    ! [B: $i,A: $i] :
      ( ( distinct_points @ sk3 @ A )
      | ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ B )
      | ( distinct_points @ A @ B ) ),
    inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( A )),bind(B,$thf( intersection_point @ sk1 @ sk2 )),bind(C,$thf( A )),bind(D,$thf( D ))]]) ).

thf(84,plain,
    ! [B: $i,A: $i] :
      ( ( distinct_points @ sk3 @ A )
      | ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ B )
      | ( distinct_points @ A @ B ) ),
    inference(simp,[status(thm)],[79]) ).

thf(150,plain,
    ! [B: $i,A: $i] :
      ( ( distinct_points @ sk3 @ A )
      | ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ B )
      | ( ( distinct_points @ A @ B )
       != ( distinct_points @ sk3 @ A ) )
      | ~ $true ),
    inference(eqfactor_ordered,[status(thm)],[84]) ).

thf(152,plain,
    ( ( distinct_points @ sk3 @ sk3 )
    | ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ sk3 ) ),
    inference(pattern_uni,[status(thm)],[150:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 ))]]) ).

thf(3,axiom,
    ! [A: $i] :
      ~ ( distinct_points @ A @ A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).

thf(20,plain,
    ! [A: $i] :
      ~ ( distinct_points @ A @ A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(21,plain,
    ~ ? [A: $i] : ( distinct_points @ A @ A ),
    inference(miniscope,[status(thm)],[20]) ).

thf(22,plain,
    ! [A: $i] :
      ~ ( distinct_points @ A @ A ),
    inference(cnf,[status(esa)],[21]) ).

thf(165,plain,
    ( $false
    | ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ sk3 ) ),
    inference(rewrite,[status(thm)],[152,22]) ).

thf(166,plain,
    distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ sk3,
    inference(simp,[status(thm)],[165]) ).

thf(19,plain,
    convergent_lines @ sk1 @ sk2,
    inference(cnf,[status(esa)],[15]) ).

thf(14,axiom,
    ! [A: $i,B: $i] :
      ( ( convergent_lines @ A @ B )
     => ( distinct_lines @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).

thf(54,plain,
    ! [A: $i,B: $i] :
      ( ( convergent_lines @ A @ B )
     => ( distinct_lines @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(55,plain,
    ! [B: $i,A: $i] :
      ( ~ ( convergent_lines @ A @ B )
      | ( distinct_lines @ A @ B ) ),
    inference(cnf,[status(esa)],[54]) ).

thf(90,plain,
    ! [B: $i,A: $i] :
      ( ( distinct_lines @ A @ B )
      | ( ( convergent_lines @ sk1 @ sk2 )
       != ( convergent_lines @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[19,55]) ).

thf(91,plain,
    distinct_lines @ sk1 @ sk2,
    inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(11,axiom,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( distinct_points @ A @ B )
        & ( distinct_lines @ C @ D ) )
     => ( ( apart_point_and_line @ A @ C )
        | ( apart_point_and_line @ A @ D )
        | ( apart_point_and_line @ B @ C )
        | ( apart_point_and_line @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cu1) ).

thf(46,plain,
    ! [A: $i,B: $i,C: $i,D: $i] :
      ( ( ( distinct_points @ A @ B )
        & ( distinct_lines @ C @ D ) )
     => ( ( apart_point_and_line @ A @ C )
        | ( apart_point_and_line @ A @ D )
        | ( apart_point_and_line @ B @ C )
        | ( apart_point_and_line @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(47,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( distinct_points @ A @ B )
      | ~ ( distinct_lines @ C @ D )
      | ( apart_point_and_line @ A @ C )
      | ( apart_point_and_line @ A @ D )
      | ( apart_point_and_line @ B @ C )
      | ( apart_point_and_line @ B @ D ) ),
    inference(cnf,[status(esa)],[46]) ).

thf(758,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( distinct_points @ A @ B )
      | ( apart_point_and_line @ A @ C )
      | ( apart_point_and_line @ A @ D )
      | ( apart_point_and_line @ B @ C )
      | ( apart_point_and_line @ B @ D )
      | ( ( distinct_lines @ sk1 @ sk2 )
       != ( distinct_lines @ C @ D ) ) ),
    inference(paramod_ordered,[status(thm)],[91,47]) ).

thf(759,plain,
    ! [B: $i,A: $i] :
      ( ~ ( distinct_points @ A @ B )
      | ( apart_point_and_line @ A @ sk1 )
      | ( apart_point_and_line @ A @ sk2 )
      | ( apart_point_and_line @ B @ sk1 )
      | ( apart_point_and_line @ B @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[758:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 )),bind(D,$thf( sk2 ))]]) ).

thf(48121,plain,
    ! [B: $i,A: $i] :
      ( ( apart_point_and_line @ A @ sk1 )
      | ( apart_point_and_line @ A @ sk2 )
      | ( apart_point_and_line @ B @ sk1 )
      | ( apart_point_and_line @ B @ sk2 )
      | ( ( distinct_points @ ( intersection_point @ sk1 @ sk2 ) @ sk3 )
       != ( distinct_points @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[166,759]) ).

thf(48122,plain,
    ( ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 )
    | ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk2 )
    | ( apart_point_and_line @ sk3 @ sk1 )
    | ( apart_point_and_line @ sk3 @ sk2 ) ),
    inference(pattern_uni,[status(thm)],[48121:[bind(A,$thf( intersection_point @ sk1 @ sk2 )),bind(B,$thf( sk3 ))]]) ).

thf(17,plain,
    ~ ( apart_point_and_line @ sk3 @ sk2 ),
    inference(cnf,[status(esa)],[15]) ).

thf(18,plain,
    ~ ( apart_point_and_line @ sk3 @ sk1 ),
    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/sandbox/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(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(666,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( apart_point_and_line @ C @ A )
      | ( distinct_points @ C @ ( intersection_point @ A @ B ) )
      | ( ( convergent_lines @ sk1 @ sk2 )
       != ( convergent_lines @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[19,45]) ).

thf(667,plain,
    ! [A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk1 )
      | ( distinct_points @ A @ ( intersection_point @ sk1 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[666:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(682,plain,
    ! [A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk1 )
      | ( distinct_points @ A @ ( intersection_point @ sk1 @ sk2 ) ) ),
    inference(simp,[status(thm)],[667]) ).

thf(1098,plain,
    ! [B: $i,A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk1 )
      | ( ( distinct_points @ A @ ( intersection_point @ sk1 @ sk2 ) )
       != ( distinct_points @ B @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[682,22]) ).

thf(1099,plain,
    ~ ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk1 ),
    inference(pattern_uni,[status(thm)],[1098:[bind(A,$thf( intersection_point @ sk1 @ sk2 )),bind(B,$thf( intersection_point @ sk1 @ sk2 ))]]) ).

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(517,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( apart_point_and_line @ C @ B )
      | ( distinct_points @ C @ ( intersection_point @ A @ B ) )
      | ( ( convergent_lines @ sk1 @ sk2 )
       != ( convergent_lines @ A @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[19,44]) ).

thf(518,plain,
    ! [A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk2 )
      | ( distinct_points @ A @ ( intersection_point @ sk1 @ sk2 ) ) ),
    inference(pattern_uni,[status(thm)],[517:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).

thf(522,plain,
    ! [A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk2 )
      | ( distinct_points @ A @ ( intersection_point @ sk1 @ sk2 ) ) ),
    inference(simp,[status(thm)],[518]) ).

thf(622,plain,
    ! [B: $i,A: $i] :
      ( ~ ( apart_point_and_line @ A @ sk2 )
      | ( ( distinct_points @ A @ ( intersection_point @ sk1 @ sk2 ) )
       != ( distinct_points @ B @ B ) ) ),
    inference(paramod_ordered,[status(thm)],[522,22]) ).

thf(623,plain,
    ~ ( apart_point_and_line @ ( intersection_point @ sk1 @ sk2 ) @ sk2 ),
    inference(pattern_uni,[status(thm)],[622:[bind(A,$thf( intersection_point @ sk1 @ sk2 )),bind(B,$thf( intersection_point @ sk1 @ sk2 ))]]) ).

thf(48333,plain,
    ( $false
    | $false
    | $false
    | $false ),
    inference(rewrite,[status(thm)],[48122,17,18,1099,623]) ).

thf(48334,plain,
    $false,
    inference(simp,[status(thm)],[48333]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : GEO172+2 : TPTP v8.2.0. Released v3.3.0.
% 0.00/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n002.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 14:21:08 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.93/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.34/1.08  % [INFO] 	 Parsing done (168ms). 
% 1.34/1.10  % [INFO] 	 Running in sequential loop mode. 
% 1.80/1.43  % [INFO] 	 nitpick registered as external prover. 
% 1.80/1.44  % [INFO] 	 Scanning for conjecture ... 
% 2.04/1.52  % [INFO] 	 Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ... 
% 2.08/1.56  % [INFO] 	 Axiom selection finished. Selected 12 axioms (removed 0 axioms). 
% 2.08/1.59  % [INFO] 	 Problem is first-order (TPTP FOF). 
% 2.08/1.59  % [INFO] 	 Type checking passed. 
% 2.08/1.60  % [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 ... 
% 123.59/22.42  % [INFO] 	 Killing All external provers ... 
% 123.59/22.42  % Time passed: 21961ms (effective reasoning time: 21321ms)
% 123.59/22.42  % 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)>
% 123.59/22.43  % Axioms used in derivation (5): con2, ceq3, apart4, apart1, cu1
% 123.59/22.43  % No. of inferences in proof: 54
% 123.59/22.43  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21961 ms resp. 21321 ms w/o parsing
% 123.64/22.46  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 123.64/22.46  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------