TSTP Solution File: GEO185+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO185+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n010.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 : Sun May  5 05:15:55 EDT 2024

% Result   : Theorem 0.13s 0.35s
% Output   : Refutation 0.13s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :    5
% Syntax   : Number of formulae    :   28 (   5 unt;   0 def)
%            Number of atoms       :   83 (   0 equ)
%            Maximal formula atoms :   10 (   2 avg)
%            Number of connectives :   87 (  32   ~;  24   |;  24   &)
%                                         (   0 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :    4 (   3 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   4 con; 0-2 aty)
%            Number of variables   :   52 (  40   !;  12   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f622,plain,
    $false,
    inference(subsumption_resolution,[],[f580,f43]) ).

fof(f43,plain,
    ~ distinct_points(sK0,intersection_point(sK2,sK3)),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ( ( apart_point_and_line(sK0,sK3)
      | apart_point_and_line(sK0,sK2) )
    & ~ distinct_points(sK0,intersection_point(sK2,sK3))
    & convergent_lines(sK2,sK3)
    & distinct_points(sK0,sK1) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f20,f39]) ).

fof(f39,plain,
    ( ? [X0,X1,X2,X3] :
        ( ( apart_point_and_line(X0,X3)
          | apart_point_and_line(X0,X2) )
        & ~ distinct_points(X0,intersection_point(X2,X3))
        & convergent_lines(X2,X3)
        & distinct_points(X0,X1) )
   => ( ( apart_point_and_line(sK0,sK3)
        | apart_point_and_line(sK0,sK2) )
      & ~ distinct_points(sK0,intersection_point(sK2,sK3))
      & convergent_lines(sK2,sK3)
      & distinct_points(sK0,sK1) ) ),
    introduced(choice_axiom,[]) ).

fof(f20,plain,
    ? [X0,X1,X2,X3] :
      ( ( apart_point_and_line(X0,X3)
        | apart_point_and_line(X0,X2) )
      & ~ distinct_points(X0,intersection_point(X2,X3))
      & convergent_lines(X2,X3)
      & distinct_points(X0,X1) ),
    inference(flattening,[],[f19]) ).

fof(f19,plain,
    ? [X0,X1,X2,X3] :
      ( ( apart_point_and_line(X0,X3)
        | apart_point_and_line(X0,X2) )
      & ~ distinct_points(X0,intersection_point(X2,X3))
      & convergent_lines(X2,X3)
      & distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,plain,
    ~ ! [X0,X1,X2,X3] :
        ( ( ~ distinct_points(X0,intersection_point(X2,X3))
          & convergent_lines(X2,X3)
          & distinct_points(X0,X1) )
       => ( ~ apart_point_and_line(X0,X3)
          & ~ apart_point_and_line(X0,X2) ) ),
    inference(rectify,[],[f16]) ).

fof(f16,negated_conjecture,
    ~ ! [X0,X1,X3,X4] :
        ( ( ~ distinct_points(X0,intersection_point(X3,X4))
          & convergent_lines(X3,X4)
          & distinct_points(X0,X1) )
       => ( ~ apart_point_and_line(X0,X4)
          & ~ apart_point_and_line(X0,X3) ) ),
    inference(negated_conjecture,[],[f15]) ).

fof(f15,conjecture,
    ! [X0,X1,X3,X4] :
      ( ( ~ distinct_points(X0,intersection_point(X3,X4))
        & convergent_lines(X3,X4)
        & distinct_points(X0,X1) )
     => ( ~ apart_point_and_line(X0,X4)
        & ~ apart_point_and_line(X0,X3) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(f580,plain,
    distinct_points(sK0,intersection_point(sK2,sK3)),
    inference(resolution,[],[f508,f42]) ).

fof(f42,plain,
    convergent_lines(sK2,sK3),
    inference(cnf_transformation,[],[f40]) ).

fof(f508,plain,
    ! [X0] :
      ( ~ convergent_lines(sK2,X0)
      | distinct_points(sK0,intersection_point(sK2,X0)) ),
    inference(resolution,[],[f505,f49]) ).

fof(f49,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X0)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f22]) ).

fof(f22,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X0)
      | ~ convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
     => ~ apart_point_and_line(intersection_point(X0,X1),X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci3) ).

fof(f505,plain,
    ! [X0] :
      ( apart_point_and_line(X0,sK2)
      | distinct_points(sK0,X0) ),
    inference(resolution,[],[f480,f57]) ).

fof(f57,plain,
    ! [X2,X0,X1] :
      ( ~ apart_point_and_line(X0,X1)
      | distinct_points(X0,X2)
      | apart_point_and_line(X2,X1) ),
    inference(cnf_transformation,[],[f36]) ).

fof(f36,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X2,X1)
      | distinct_points(X0,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(flattening,[],[f35]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X2,X1)
      | distinct_points(X0,X2)
      | ~ apart_point_and_line(X0,X1) ),
    inference(ennf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1,X2] :
      ( apart_point_and_line(X0,X1)
     => ( apart_point_and_line(X2,X1)
        | distinct_points(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq1) ).

fof(f480,plain,
    apart_point_and_line(sK0,sK2),
    inference(subsumption_resolution,[],[f428,f43]) ).

fof(f428,plain,
    ( distinct_points(sK0,intersection_point(sK2,sK3))
    | apart_point_and_line(sK0,sK2) ),
    inference(resolution,[],[f422,f42]) ).

fof(f422,plain,
    ! [X0] :
      ( ~ convergent_lines(X0,sK3)
      | distinct_points(sK0,intersection_point(X0,sK3))
      | apart_point_and_line(sK0,sK2) ),
    inference(resolution,[],[f417,f48]) ).

fof(f48,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
      | ~ convergent_lines(X0,X1) ),
    inference(cnf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(intersection_point(X0,X1),X1)
      | ~ convergent_lines(X0,X1) ),
    inference(ennf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] :
      ( convergent_lines(X0,X1)
     => ~ apart_point_and_line(intersection_point(X0,X1),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ci4) ).

fof(f417,plain,
    ! [X0] :
      ( apart_point_and_line(X0,sK3)
      | apart_point_and_line(sK0,sK2)
      | distinct_points(sK0,X0) ),
    inference(resolution,[],[f57,f44]) ).

fof(f44,plain,
    ( apart_point_and_line(sK0,sK3)
    | apart_point_and_line(sK0,sK2) ),
    inference(cnf_transformation,[],[f40]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem    : GEO185+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.13/0.33  % Computer : n010.cluster.edu
% 0.13/0.33  % Model    : x86_64 x86_64
% 0.13/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33  % Memory   : 8042.1875MB
% 0.13/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33  % CPULimit   : 300
% 0.13/0.33  % WCLimit    : 300
% 0.13/0.33  % DateTime   : Fri May  3 22:06:08 EDT 2024
% 0.13/0.33  % CPUTime    : 
% 0.13/0.33  % (31122)Running in auto input_syntax mode. Trying TPTP
% 0.13/0.35  % (31127)dis+1_20_av=off:lcm=predicate:nm=2:nwc=2.0_396 on theBenchmark for (396ds/0Mi)
% 0.13/0.35  % (31123)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.35  % (31125)dis-2_2:3_amm=sco:anc=none:bce=on:fsr=off:gsp=on:nm=16:nwc=1.2:nicw=on:sac=on:sp=weighted_frequency_476 on theBenchmark for (476ds/0Mi)
% 0.13/0.35  % (31124)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3_569 on theBenchmark for (569ds/0Mi)
% 0.13/0.35  % (31126)fmb+10_1_bce=on:fmbas=expand:fmbksg=on:fmbsr=1.3:gsp=on:nm=4_470 on theBenchmark for (470ds/0Mi)
% 0.13/0.35  % (31128)dis+11_4:5_nm=4_216 on theBenchmark for (216ds/0Mi)
% 0.13/0.35  % (31129)fmb+10_1_fmbas=off:fmbsr=1.3:nm=2:si=on:rtra=on:rawr=on:rp=on:fmbksg=on_1451 on theBenchmark for (1451ds/0Mi)
% 0.13/0.35  TRYING [1]
% 0.13/0.35  TRYING [2]
% 0.13/0.35  TRYING [1,1]
% 0.13/0.35  TRYING [1]
% 0.13/0.35  TRYING [3]
% 0.13/0.35  TRYING [1,2]
% 0.13/0.35  TRYING [1,1]
% 0.13/0.35  TRYING [2]
% 0.13/0.35  % (31127)First to succeed.
% 0.13/0.35  TRYING [1,2]
% 0.13/0.35  TRYING [2,2]
% 0.13/0.35  TRYING [2,2]
% 0.13/0.35  TRYING [3]
% 0.13/0.35  % (31127)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-31122"
% 0.13/0.35  TRYING [2,3]
% 0.13/0.35  TRYING [2,3]
% 0.13/0.35  TRYING [4]
% 0.13/0.35  % (31125)Also succeeded, but the first one will report.
% 0.13/0.35  % (31127)Refutation found. Thanks to Tanya!
% 0.13/0.35  % SZS status Theorem for theBenchmark
% 0.13/0.35  % SZS output start Proof for theBenchmark
% See solution above
% 0.13/0.35  % (31127)------------------------------
% 0.13/0.35  % (31127)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.13/0.35  % (31127)Termination reason: Refutation
% 0.13/0.35  
% 0.13/0.35  % (31127)Memory used [KB]: 902
% 0.13/0.35  % (31127)Time elapsed: 0.009 s
% 0.13/0.35  % (31127)Instructions burned: 26 (million)
% 0.13/0.35  % (31122)Success in time 0.02 s
%------------------------------------------------------------------------------