TSTP Solution File: GEO201+2 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : GEO201+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n017.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 : Wed Aug 31 16:09:10 EDT 2022

% Result   : Theorem 0.21s 0.49s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   43 (  14 unt;   0 def)
%            Number of atoms       :  115 (   0 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  112 (  40   ~;  49   |;  10   &)
%                                         (   0 <=>;  13  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    3 (   3 usr;   2 con; 0-2 aty)
%            Number of variables   :   84 (  78   !;   6   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f123,plain,
    $false,
    inference(subsumption_resolution,[],[f114,f82]) ).

fof(f82,plain,
    ~ apart_point_and_line(intersection_point(sK1,sK0),sK1),
    inference(unit_resulting_resolution,[],[f50,f63,f51]) ).

fof(f51,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,intersection_point(X1,X0))
      | ~ convergent_lines(X1,X0)
      | ~ apart_point_and_line(X2,X1) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,plain,
    ! [X0,X1,X2] :
      ( ( ~ apart_point_and_line(X2,X0)
        & ~ apart_point_and_line(X2,X1) )
      | ~ convergent_lines(X1,X0)
      | distinct_points(X2,intersection_point(X1,X0)) ),
    inference(rectify,[],[f37]) ).

fof(f37,plain,
    ! [X2,X1,X0] :
      ( ( ~ apart_point_and_line(X0,X2)
        & ~ apart_point_and_line(X0,X1) )
      | ~ convergent_lines(X1,X2)
      | distinct_points(X0,intersection_point(X1,X2)) ),
    inference(flattening,[],[f36]) ).

fof(f36,plain,
    ! [X1,X0,X2] :
      ( distinct_points(X0,intersection_point(X1,X2))
      | ( ~ apart_point_and_line(X0,X2)
        & ~ apart_point_and_line(X0,X1) )
      | ~ convergent_lines(X1,X2) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X1,X0,X2] :
      ( convergent_lines(X1,X2)
     => ( ( apart_point_and_line(X0,X2)
          | apart_point_and_line(X0,X1) )
       => distinct_points(X0,intersection_point(X1,X2)) ) ),
    inference(rectify,[],[f8]) ).

fof(f8,axiom,
    ! [X2,X0,X1] :
      ( convergent_lines(X0,X1)
     => ( ( apart_point_and_line(X2,X1)
          | apart_point_and_line(X2,X0) )
       => distinct_points(X2,intersection_point(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con2) ).

fof(f63,plain,
    convergent_lines(sK1,sK0),
    inference(unit_resulting_resolution,[],[f58,f55,f60]) ).

fof(f60,plain,
    ! [X2,X0,X1] :
      ( convergent_lines(X0,X1)
      | ~ convergent_lines(X0,X2)
      | convergent_lines(X2,X1) ),
    inference(cnf_transformation,[],[f27]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X0,X1)
      | ~ convergent_lines(X0,X2)
      | convergent_lines(X2,X1) ),
    inference(flattening,[],[f26]) ).

fof(f26,plain,
    ! [X2,X0,X1] :
      ( convergent_lines(X0,X1)
      | convergent_lines(X2,X1)
      | ~ convergent_lines(X0,X2) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X2,X0,X1] :
      ( convergent_lines(X0,X2)
     => ( convergent_lines(X0,X1)
        | convergent_lines(X2,X1) ) ),
    inference(rectify,[],[f6]) ).

fof(f6,axiom,
    ! [X0,X2,X1] :
      ( convergent_lines(X0,X1)
     => ( convergent_lines(X1,X2)
        | convergent_lines(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart6) ).

fof(f55,plain,
    convergent_lines(sK0,sK1),
    inference(cnf_transformation,[],[f44]) ).

fof(f44,plain,
    ( convergent_lines(sK0,sK1)
    & distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f42,f43]) ).

fof(f43,plain,
    ( ? [X0,X1] :
        ( convergent_lines(X0,X1)
        & distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) )
   => ( convergent_lines(sK0,sK1)
      & distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)) ) ),
    introduced(choice_axiom,[]) ).

fof(f42,plain,
    ? [X0,X1] :
      ( convergent_lines(X0,X1)
      & distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
    inference(rectify,[],[f31]) ).

fof(f31,plain,
    ? [X1,X0] :
      ( convergent_lines(X1,X0)
      & distinct_points(intersection_point(X1,X0),intersection_point(X0,X1)) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ~ ! [X0,X1] :
        ( convergent_lines(X1,X0)
       => ~ distinct_points(intersection_point(X1,X0),intersection_point(X0,X1)) ),
    inference(rectify,[],[f14]) ).

fof(f14,negated_conjecture,
    ~ ! [X1,X0] :
        ( convergent_lines(X0,X1)
       => ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
    inference(negated_conjecture,[],[f13]) ).

fof(f13,conjecture,
    ! [X1,X0] :
      ( convergent_lines(X0,X1)
     => ~ distinct_points(intersection_point(X0,X1),intersection_point(X1,X0)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(f58,plain,
    ! [X0] : ~ convergent_lines(X0,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : ~ convergent_lines(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart3) ).

fof(f50,plain,
    ! [X0] : ~ distinct_points(X0,X0),
    inference(cnf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0] : ~ distinct_points(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart1) ).

fof(f114,plain,
    apart_point_and_line(intersection_point(sK1,sK0),sK1),
    inference(unit_resulting_resolution,[],[f61,f64,f65,f54,f81,f49]) ).

fof(f49,plain,
    ! [X2,X3,X0,X1] :
      ( apart_point_and_line(X2,X1)
      | apart_point_and_line(X3,X0)
      | ~ distinct_lines(X0,X1)
      | apart_point_and_line(X2,X0)
      | apart_point_and_line(X3,X1)
      | ~ distinct_points(X2,X3) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1,X2,X3] :
      ( apart_point_and_line(X2,X0)
      | apart_point_and_line(X3,X1)
      | apart_point_and_line(X2,X1)
      | apart_point_and_line(X3,X0)
      | ~ distinct_points(X2,X3)
      | ~ distinct_lines(X0,X1) ),
    inference(rectify,[],[f33]) ).

fof(f33,plain,
    ! [X1,X2,X3,X0] :
      ( apart_point_and_line(X3,X1)
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X3,X2)
      | apart_point_and_line(X0,X1)
      | ~ distinct_points(X3,X0)
      | ~ distinct_lines(X1,X2) ),
    inference(flattening,[],[f32]) ).

fof(f32,plain,
    ! [X2,X1,X3,X0] :
      ( apart_point_and_line(X3,X2)
      | apart_point_and_line(X0,X1)
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X3,X1)
      | ~ distinct_lines(X1,X2)
      | ~ distinct_points(X3,X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ! [X2,X1,X3,X0] :
      ( ( distinct_lines(X1,X2)
        & distinct_points(X3,X0) )
     => ( apart_point_and_line(X3,X2)
        | apart_point_and_line(X0,X1)
        | apart_point_and_line(X0,X2)
        | apart_point_and_line(X3,X1) ) ),
    inference(rectify,[],[f9]) ).

fof(f9,axiom,
    ! [X1,X3,X4,X0] :
      ( ( distinct_lines(X3,X4)
        & distinct_points(X0,X1) )
     => ( apart_point_and_line(X0,X4)
        | apart_point_and_line(X1,X3)
        | apart_point_and_line(X0,X3)
        | apart_point_and_line(X1,X4) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cu1) ).

fof(f81,plain,
    ~ apart_point_and_line(intersection_point(sK1,sK0),sK0),
    inference(unit_resulting_resolution,[],[f50,f63,f52]) ).

fof(f52,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,intersection_point(X1,X0))
      | ~ convergent_lines(X1,X0)
      | ~ apart_point_and_line(X2,X0) ),
    inference(cnf_transformation,[],[f41]) ).

fof(f54,plain,
    distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
    inference(cnf_transformation,[],[f44]) ).

fof(f65,plain,
    ~ apart_point_and_line(intersection_point(sK0,sK1),sK0),
    inference(unit_resulting_resolution,[],[f50,f55,f51]) ).

fof(f64,plain,
    ~ apart_point_and_line(intersection_point(sK0,sK1),sK1),
    inference(unit_resulting_resolution,[],[f50,f55,f52]) ).

fof(f61,plain,
    distinct_lines(sK0,sK1),
    inference(unit_resulting_resolution,[],[f55,f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( distinct_lines(X1,X0)
      | ~ convergent_lines(X1,X0) ),
    inference(cnf_transformation,[],[f39]) ).

fof(f39,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X1,X0)
      | distinct_lines(X1,X0) ),
    inference(rectify,[],[f28]) ).

fof(f28,plain,
    ! [X1,X0] :
      ( ~ convergent_lines(X0,X1)
      | distinct_lines(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
     => distinct_lines(X0,X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq3) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : GEO201+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n017.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Mon Aug 29 20:59:50 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.21/0.47  % (3739)lrs+2_1:1_lcm=reverse:lma=on:sos=all:spb=goal_then_units:ss=included:urr=on:i=39:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/39Mi)
% 0.21/0.48  % (3755)dis+10_1:1_av=off:sos=on:sp=reverse_arity:ss=included:st=2.0:to=lpo:urr=ec_only:i=45:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/45Mi)
% 0.21/0.49  % (3739)First to succeed.
% 0.21/0.49  % (3739)Refutation found. Thanks to Tanya!
% 0.21/0.49  % SZS status Theorem for theBenchmark
% 0.21/0.49  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.49  % (3739)------------------------------
% 0.21/0.49  % (3739)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.21/0.49  % (3739)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.21/0.49  % (3739)Termination reason: Refutation
% 0.21/0.49  
% 0.21/0.49  % (3739)Memory used [KB]: 5884
% 0.21/0.49  % (3739)Time elapsed: 0.077 s
% 0.21/0.49  % (3739)Instructions burned: 4 (million)
% 0.21/0.49  % (3739)------------------------------
% 0.21/0.49  % (3739)------------------------------
% 0.21/0.49  % (3731)Success in time 0.138 s
%------------------------------------------------------------------------------