TSTP Solution File: GEO172+2 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : GEO172+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_sat --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 16:12:05 EDT 2022

% Result   : Theorem 0.20s 0.56s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   41 (   9 unt;   0 def)
%            Number of atoms       :  139 (   0 equ)
%            Maximal formula atoms :    8 (   3 avg)
%            Number of connectives :  170 (  72   ~;  58   |;  29   &)
%                                         (   0 <=>;  11  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    5 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :    4 (   4 usr;   3 con; 0-2 aty)
%            Number of variables   :   82 (  70   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f136,plain,
    $false,
    inference(resolution,[],[f135,f54]) ).

fof(f54,plain,
    convergent_lines(sK1,sK0),
    inference(cnf_transformation,[],[f43]) ).

fof(f43,plain,
    ( convergent_lines(sK1,sK0)
    & distinct_points(sK2,intersection_point(sK1,sK0))
    & ~ apart_point_and_line(sK2,sK0)
    & ~ apart_point_and_line(sK2,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f41,f42]) ).

fof(f42,plain,
    ( ? [X0,X1,X2] :
        ( convergent_lines(X1,X0)
        & distinct_points(X2,intersection_point(X1,X0))
        & ~ apart_point_and_line(X2,X0)
        & ~ apart_point_and_line(X2,X1) )
   => ( convergent_lines(sK1,sK0)
      & distinct_points(sK2,intersection_point(sK1,sK0))
      & ~ apart_point_and_line(sK2,sK0)
      & ~ apart_point_and_line(sK2,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f41,plain,
    ? [X0,X1,X2] :
      ( convergent_lines(X1,X0)
      & distinct_points(X2,intersection_point(X1,X0))
      & ~ apart_point_and_line(X2,X0)
      & ~ apart_point_and_line(X2,X1) ),
    inference(rectify,[],[f35]) ).

fof(f35,plain,
    ? [X0,X2,X1] :
      ( convergent_lines(X2,X0)
      & distinct_points(X1,intersection_point(X2,X0))
      & ~ apart_point_and_line(X1,X0)
      & ~ apart_point_and_line(X1,X2) ),
    inference(flattening,[],[f34]) ).

fof(f34,plain,
    ? [X1,X0,X2] :
      ( distinct_points(X1,intersection_point(X2,X0))
      & ~ apart_point_and_line(X1,X2)
      & convergent_lines(X2,X0)
      & ~ apart_point_and_line(X1,X0) ),
    inference(ennf_transformation,[],[f16]) ).

fof(f16,plain,
    ~ ! [X1,X0,X2] :
        ( ( ~ apart_point_and_line(X1,X2)
          & convergent_lines(X2,X0)
          & ~ apart_point_and_line(X1,X0) )
       => ~ distinct_points(X1,intersection_point(X2,X0)) ),
    inference(rectify,[],[f14]) ).

fof(f14,negated_conjecture,
    ~ ! [X1,X2,X0] :
        ( ( ~ apart_point_and_line(X2,X1)
          & ~ apart_point_and_line(X2,X0)
          & convergent_lines(X0,X1) )
       => ~ distinct_points(X2,intersection_point(X0,X1)) ),
    inference(negated_conjecture,[],[f13]) ).

fof(f13,conjecture,
    ! [X1,X2,X0] :
      ( ( ~ apart_point_and_line(X2,X1)
        & ~ apart_point_and_line(X2,X0)
        & convergent_lines(X0,X1) )
     => ~ distinct_points(X2,intersection_point(X0,X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(f135,plain,
    ~ convergent_lines(sK1,sK0),
    inference(resolution,[],[f131,f50]) ).

fof(f50,plain,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f31]) ).

fof(f31,plain,
    ! [X0,X1] :
      ( ~ convergent_lines(X0,X1)
      | distinct_lines(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

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

fof(f131,plain,
    ~ distinct_lines(sK1,sK0),
    inference(resolution,[],[f122,f54]) ).

fof(f122,plain,
    ( ~ convergent_lines(sK1,sK0)
    | ~ distinct_lines(sK1,sK0) ),
    inference(resolution,[],[f121,f53]) ).

fof(f53,plain,
    distinct_points(sK2,intersection_point(sK1,sK0)),
    inference(cnf_transformation,[],[f43]) ).

fof(f121,plain,
    ( ~ distinct_points(sK2,intersection_point(sK1,sK0))
    | ~ distinct_lines(sK1,sK0)
    | ~ convergent_lines(sK1,sK0) ),
    inference(duplicate_literal_removal,[],[f120]) ).

fof(f120,plain,
    ( ~ convergent_lines(sK1,sK0)
    | ~ distinct_points(sK2,intersection_point(sK1,sK0))
    | ~ convergent_lines(sK1,sK0)
    | ~ distinct_lines(sK1,sK0) ),
    inference(resolution,[],[f87,f72]) ).

fof(f72,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
      | ~ convergent_lines(X0,X1) ),
    inference(resolution,[],[f48,f61]) ).

fof(f61,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(f48,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,intersection_point(X0,X1))
      | ~ apart_point_and_line(X2,X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( ~ convergent_lines(X0,X1)
      | ( ~ apart_point_and_line(X2,X0)
        & ~ apart_point_and_line(X2,X1) )
      | distinct_points(X2,intersection_point(X0,X1)) ),
    inference(rectify,[],[f37]) ).

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

fof(f36,plain,
    ! [X0,X1,X2] :
      ( distinct_points(X0,intersection_point(X2,X1))
      | ( ~ apart_point_and_line(X0,X2)
        & ~ apart_point_and_line(X0,X1) )
      | ~ convergent_lines(X2,X1) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X0,X1,X2] :
      ( convergent_lines(X2,X1)
     => ( ( apart_point_and_line(X0,X1)
          | apart_point_and_line(X0,X2) )
       => distinct_points(X0,intersection_point(X2,X1)) ) ),
    inference(rectify,[],[f8]) ).

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

fof(f87,plain,
    ! [X1] :
      ( apart_point_and_line(intersection_point(sK1,X1),sK0)
      | ~ distinct_lines(sK1,sK0)
      | ~ convergent_lines(sK1,X1)
      | ~ distinct_points(sK2,intersection_point(sK1,X1)) ),
    inference(resolution,[],[f82,f73]) ).

fof(f73,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X0)
      | ~ convergent_lines(X0,X1) ),
    inference(resolution,[],[f49,f61]) ).

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

fof(f82,plain,
    ! [X1] :
      ( apart_point_and_line(X1,sK1)
      | ~ distinct_points(sK2,X1)
      | apart_point_and_line(X1,sK0)
      | ~ distinct_lines(sK1,sK0) ),
    inference(resolution,[],[f76,f52]) ).

fof(f52,plain,
    ~ apart_point_and_line(sK2,sK0),
    inference(cnf_transformation,[],[f43]) ).

fof(f76,plain,
    ! [X0,X1] :
      ( apart_point_and_line(sK2,X0)
      | apart_point_and_line(X1,sK1)
      | apart_point_and_line(X1,X0)
      | ~ distinct_lines(sK1,X0)
      | ~ distinct_points(sK2,X1) ),
    inference(resolution,[],[f62,f51]) ).

fof(f51,plain,
    ~ apart_point_and_line(sK2,sK1),
    inference(cnf_transformation,[],[f43]) ).

fof(f62,plain,
    ! [X2,X3,X0,X1] :
      ( apart_point_and_line(X0,X1)
      | apart_point_and_line(X0,X2)
      | ~ distinct_points(X0,X3)
      | ~ distinct_lines(X1,X2)
      | apart_point_and_line(X3,X2)
      | apart_point_and_line(X3,X1) ),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1,X2,X3] :
      ( ~ distinct_points(X0,X3)
      | apart_point_and_line(X3,X1)
      | apart_point_and_line(X3,X2)
      | ~ distinct_lines(X1,X2)
      | apart_point_and_line(X0,X1)
      | apart_point_and_line(X0,X2) ),
    inference(rectify,[],[f39]) ).

fof(f39,plain,
    ! [X0,X2,X1,X3] :
      ( ~ distinct_points(X0,X3)
      | apart_point_and_line(X3,X2)
      | apart_point_and_line(X3,X1)
      | ~ distinct_lines(X2,X1)
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f38]) ).

fof(f38,plain,
    ! [X3,X2,X0,X1] :
      ( apart_point_and_line(X3,X2)
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X3,X1)
      | apart_point_and_line(X0,X1)
      | ~ distinct_lines(X2,X1)
      | ~ distinct_points(X0,X3) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X3,X2,X0,X1] :
      ( ( distinct_lines(X2,X1)
        & distinct_points(X0,X3) )
     => ( apart_point_and_line(X3,X2)
        | apart_point_and_line(X0,X2)
        | apart_point_and_line(X3,X1)
        | apart_point_and_line(X0,X1) ) ),
    inference(rectify,[],[f9]) ).

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

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : GEO172+2 : TPTP v8.1.0. Released v3.3.0.
% 0.04/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --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 20:47:50 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.53  % (21165)ott-1_1:6_av=off:cond=on:fsr=off:nwc=3.0:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.53  % (21156)fmb+10_1:1_bce=on:fmbsr=1.5:nm=4:skr=on:i=191324:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/191324Mi)
% 0.20/0.55  % (21164)dis+2_1:64_add=large:bce=on:bd=off:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.55  TRYING [1]
% 0.20/0.55  TRYING [2]
% 0.20/0.55  TRYING [3]
% 0.20/0.55  TRYING [4]
% 0.20/0.56  % (21166)ott+2_1:1_fsr=off:gsp=on:i=50:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/50Mi)
% 0.20/0.56  TRYING [5]
% 0.20/0.56  % (21165)First to succeed.
% 0.20/0.56  % (21172)dis+34_1:32_abs=on:add=off:bsr=on:gsp=on:sp=weighted_frequency:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.56  % (21169)ott+10_1:5_bd=off:tgt=full:i=99:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/99Mi)
% 0.20/0.56  % (21165)Refutation found. Thanks to Tanya!
% 0.20/0.56  % SZS status Theorem for theBenchmark
% 0.20/0.56  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.56  % (21165)------------------------------
% 0.20/0.56  % (21165)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.56  % (21165)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.56  % (21165)Termination reason: Refutation
% 0.20/0.56  
% 0.20/0.56  % (21165)Memory used [KB]: 895
% 0.20/0.56  % (21165)Time elapsed: 0.133 s
% 0.20/0.56  % (21165)Instructions burned: 3 (million)
% 0.20/0.56  % (21165)------------------------------
% 0.20/0.56  % (21165)------------------------------
% 0.20/0.56  % (21155)Success in time 0.21 s
%------------------------------------------------------------------------------