TSTP Solution File: GEO187+2 by SnakeForV-SAT---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV-SAT---1.0
% Problem  : GEO187+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 : n018.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 16:12:10 EDT 2022

% Result   : Theorem 0.20s 0.50s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :    8
% Syntax   : Number of formulae    :   58 (  10 unt;   0 def)
%            Number of atoms       :  206 (   0 equ)
%            Maximal formula atoms :   12 (   3 avg)
%            Number of connectives :  242 (  94   ~;  91   |;  43   &)
%                                         (   0 <=>;  14  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   6 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   :  121 ( 105   !;  16   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f178,plain,
    $false,
    inference(resolution,[],[f174,f59]) ).

fof(f59,plain,
    distinct_points(sK0,sK3),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ( distinct_points(sK0,sK3)
    & ( apart_point_and_line(sK2,line_connecting(sK0,sK3))
      | apart_point_and_line(sK1,line_connecting(sK0,sK3)) )
    & ~ apart_point_and_line(sK3,line_connecting(sK1,sK2))
    & ~ apart_point_and_line(sK0,line_connecting(sK1,sK2))
    & distinct_points(sK1,sK2) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f44,f45]) ).

fof(f45,plain,
    ( ? [X0,X1,X2,X3] :
        ( distinct_points(X0,X3)
        & ( apart_point_and_line(X2,line_connecting(X0,X3))
          | apart_point_and_line(X1,line_connecting(X0,X3)) )
        & ~ apart_point_and_line(X3,line_connecting(X1,X2))
        & ~ apart_point_and_line(X0,line_connecting(X1,X2))
        & distinct_points(X1,X2) )
   => ( distinct_points(sK0,sK3)
      & ( apart_point_and_line(sK2,line_connecting(sK0,sK3))
        | apart_point_and_line(sK1,line_connecting(sK0,sK3)) )
      & ~ apart_point_and_line(sK3,line_connecting(sK1,sK2))
      & ~ apart_point_and_line(sK0,line_connecting(sK1,sK2))
      & distinct_points(sK1,sK2) ) ),
    introduced(choice_axiom,[]) ).

fof(f44,plain,
    ? [X0,X1,X2,X3] :
      ( distinct_points(X0,X3)
      & ( apart_point_and_line(X2,line_connecting(X0,X3))
        | apart_point_and_line(X1,line_connecting(X0,X3)) )
      & ~ apart_point_and_line(X3,line_connecting(X1,X2))
      & ~ apart_point_and_line(X0,line_connecting(X1,X2))
      & distinct_points(X1,X2) ),
    inference(rectify,[],[f37]) ).

fof(f37,plain,
    ? [X3,X2,X0,X1] :
      ( distinct_points(X3,X1)
      & ( apart_point_and_line(X0,line_connecting(X3,X1))
        | apart_point_and_line(X2,line_connecting(X3,X1)) )
      & ~ apart_point_and_line(X1,line_connecting(X2,X0))
      & ~ apart_point_and_line(X3,line_connecting(X2,X0))
      & distinct_points(X2,X0) ),
    inference(flattening,[],[f36]) ).

fof(f36,plain,
    ? [X1,X2,X0,X3] :
      ( ( apart_point_and_line(X0,line_connecting(X3,X1))
        | apart_point_and_line(X2,line_connecting(X3,X1)) )
      & distinct_points(X3,X1)
      & ~ apart_point_and_line(X1,line_connecting(X2,X0))
      & ~ apart_point_and_line(X3,line_connecting(X2,X0))
      & distinct_points(X2,X0) ),
    inference(ennf_transformation,[],[f19]) ).

fof(f19,plain,
    ~ ! [X1,X2,X0,X3] :
        ( ( distinct_points(X3,X1)
          & ~ apart_point_and_line(X1,line_connecting(X2,X0))
          & ~ apart_point_and_line(X3,line_connecting(X2,X0))
          & distinct_points(X2,X0) )
       => ( ~ apart_point_and_line(X0,line_connecting(X3,X1))
          & ~ apart_point_and_line(X2,line_connecting(X3,X1)) ) ),
    inference(rectify,[],[f14]) ).

fof(f14,negated_conjecture,
    ~ ! [X4,X1,X3,X0] :
        ( ( distinct_points(X3,X4)
          & distinct_points(X0,X1)
          & ~ apart_point_and_line(X0,line_connecting(X3,X4))
          & ~ apart_point_and_line(X1,line_connecting(X3,X4)) )
       => ( ~ apart_point_and_line(X3,line_connecting(X0,X1))
          & ~ apart_point_and_line(X4,line_connecting(X0,X1)) ) ),
    inference(negated_conjecture,[],[f13]) ).

fof(f13,conjecture,
    ! [X4,X1,X3,X0] :
      ( ( distinct_points(X3,X4)
        & distinct_points(X0,X1)
        & ~ apart_point_and_line(X0,line_connecting(X3,X4))
        & ~ apart_point_and_line(X1,line_connecting(X3,X4)) )
     => ( ~ apart_point_and_line(X3,line_connecting(X0,X1))
        & ~ apart_point_and_line(X4,line_connecting(X0,X1)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con) ).

fof(f174,plain,
    ~ distinct_points(sK0,sK3),
    inference(resolution,[],[f169,f55]) ).

fof(f55,plain,
    distinct_points(sK1,sK2),
    inference(cnf_transformation,[],[f46]) ).

fof(f169,plain,
    ( ~ distinct_points(sK1,sK2)
    | ~ distinct_points(sK0,sK3) ),
    inference(duplicate_literal_removal,[],[f168]) ).

fof(f168,plain,
    ( ~ distinct_points(sK0,sK3)
    | ~ distinct_points(sK0,sK3)
    | ~ distinct_points(sK1,sK2)
    | ~ distinct_points(sK1,sK2) ),
    inference(resolution,[],[f152,f149]) ).

fof(f149,plain,
    ( ~ apart_point_and_line(sK1,line_connecting(sK0,sK3))
    | ~ distinct_points(sK0,sK3)
    | ~ distinct_points(sK1,sK2) ),
    inference(resolution,[],[f124,f87]) ).

fof(f87,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(X0,line_connecting(X0,X1))
      | ~ distinct_points(X0,X1) ),
    inference(resolution,[],[f67,f68]) ).

fof(f68,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(f67,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,X1)
      | ~ apart_point_and_line(X2,line_connecting(X1,X0))
      | ~ distinct_points(X1,X0) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ( distinct_points(X2,X1)
        & distinct_points(X2,X0) )
      | ~ distinct_points(X1,X0)
      | ~ apart_point_and_line(X2,line_connecting(X1,X0)) ),
    inference(rectify,[],[f35]) ).

fof(f35,plain,
    ! [X1,X2,X0] :
      ( ( distinct_points(X0,X2)
        & distinct_points(X0,X1) )
      | ~ distinct_points(X2,X1)
      | ~ apart_point_and_line(X0,line_connecting(X2,X1)) ),
    inference(flattening,[],[f34]) ).

fof(f34,plain,
    ! [X2,X0,X1] :
      ( ( distinct_points(X0,X2)
        & distinct_points(X0,X1) )
      | ~ apart_point_and_line(X0,line_connecting(X2,X1))
      | ~ distinct_points(X2,X1) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,X1)
     => ( apart_point_and_line(X0,line_connecting(X2,X1))
       => ( distinct_points(X0,X2)
          & distinct_points(X0,X1) ) ) ),
    inference(rectify,[],[f7]) ).

fof(f7,axiom,
    ! [X2,X1,X0] :
      ( distinct_points(X0,X1)
     => ( apart_point_and_line(X2,line_connecting(X0,X1))
       => ( distinct_points(X2,X0)
          & distinct_points(X2,X1) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',con1) ).

fof(f124,plain,
    ! [X0] :
      ( apart_point_and_line(X0,line_connecting(sK1,sK2))
      | ~ apart_point_and_line(X0,line_connecting(sK0,sK3))
      | ~ distinct_points(sK0,sK3) ),
    inference(resolution,[],[f121,f60]) ).

fof(f60,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X2,X0)
      | ~ apart_point_and_line(X1,X2)
      | apart_point_and_line(X1,X0) ),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,plain,
    ! [X0,X1,X2] :
      ( distinct_lines(X2,X0)
      | ~ apart_point_and_line(X1,X2)
      | apart_point_and_line(X1,X0) ),
    inference(flattening,[],[f39]) ).

fof(f39,plain,
    ! [X2,X1,X0] :
      ( apart_point_and_line(X1,X0)
      | distinct_lines(X2,X0)
      | ~ apart_point_and_line(X1,X2) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,plain,
    ! [X2,X1,X0] :
      ( apart_point_and_line(X1,X2)
     => ( apart_point_and_line(X1,X0)
        | distinct_lines(X2,X0) ) ),
    inference(rectify,[],[f11]) ).

fof(f11,axiom,
    ! [X2,X0,X1] :
      ( apart_point_and_line(X0,X1)
     => ( apart_point_and_line(X0,X2)
        | distinct_lines(X1,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ceq2) ).

fof(f121,plain,
    ( ~ distinct_lines(line_connecting(sK0,sK3),line_connecting(sK1,sK2))
    | ~ distinct_points(sK0,sK3) ),
    inference(resolution,[],[f119,f71]) ).

fof(f71,plain,
    ! [X0,X1] :
      ( distinct_lines(X0,X1)
      | ~ distinct_lines(X1,X0) ),
    inference(resolution,[],[f53,f63]) ).

fof(f63,plain,
    ! [X0] : ~ distinct_lines(X0,X0),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0] : ~ distinct_lines(X0,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart2) ).

fof(f53,plain,
    ! [X2,X0,X1] :
      ( distinct_lines(X2,X1)
      | distinct_lines(X0,X1)
      | ~ distinct_lines(X2,X0) ),
    inference(cnf_transformation,[],[f42]) ).

fof(f42,plain,
    ! [X0,X1,X2] :
      ( distinct_lines(X0,X1)
      | distinct_lines(X2,X1)
      | ~ distinct_lines(X2,X0) ),
    inference(rectify,[],[f27]) ).

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

fof(f26,plain,
    ! [X1,X2,X0] :
      ( distinct_lines(X2,X0)
      | distinct_lines(X1,X0)
      | ~ distinct_lines(X1,X2) ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,plain,
    ! [X1,X2,X0] :
      ( distinct_lines(X1,X2)
     => ( distinct_lines(X2,X0)
        | distinct_lines(X1,X0) ) ),
    inference(rectify,[],[f5]) ).

fof(f5,axiom,
    ! [X2,X0,X1] :
      ( distinct_lines(X0,X1)
     => ( distinct_lines(X1,X2)
        | distinct_lines(X0,X2) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',apart5) ).

fof(f119,plain,
    ( ~ distinct_lines(line_connecting(sK1,sK2),line_connecting(sK0,sK3))
    | ~ distinct_points(sK0,sK3) ),
    inference(duplicate_literal_removal,[],[f118]) ).

fof(f118,plain,
    ( ~ distinct_points(sK0,sK3)
    | ~ distinct_points(sK0,sK3)
    | ~ distinct_points(sK0,sK3)
    | ~ distinct_lines(line_connecting(sK1,sK2),line_connecting(sK0,sK3)) ),
    inference(resolution,[],[f110,f87]) ).

fof(f110,plain,
    ! [X0] :
      ( apart_point_and_line(sK0,line_connecting(X0,sK3))
      | ~ distinct_lines(line_connecting(sK1,sK2),line_connecting(X0,sK3))
      | ~ distinct_points(sK0,sK3)
      | ~ distinct_points(X0,sK3) ),
    inference(resolution,[],[f102,f85]) ).

fof(f85,plain,
    ! [X0,X1] :
      ( ~ apart_point_and_line(X0,line_connecting(X1,X0))
      | ~ distinct_points(X1,X0) ),
    inference(resolution,[],[f66,f68]) ).

fof(f66,plain,
    ! [X2,X0,X1] :
      ( distinct_points(X2,X0)
      | ~ apart_point_and_line(X2,line_connecting(X1,X0))
      | ~ distinct_points(X1,X0) ),
    inference(cnf_transformation,[],[f49]) ).

fof(f102,plain,
    ! [X0] :
      ( apart_point_and_line(sK3,X0)
      | ~ distinct_lines(line_connecting(sK1,sK2),X0)
      | apart_point_and_line(sK0,X0)
      | ~ distinct_points(sK0,sK3) ),
    inference(resolution,[],[f90,f56]) ).

fof(f56,plain,
    ~ apart_point_and_line(sK0,line_connecting(sK1,sK2)),
    inference(cnf_transformation,[],[f46]) ).

fof(f90,plain,
    ! [X2,X3] :
      ( apart_point_and_line(X3,line_connecting(sK1,sK2))
      | ~ distinct_lines(line_connecting(sK1,sK2),X2)
      | apart_point_and_line(X3,X2)
      | apart_point_and_line(sK3,X2)
      | ~ distinct_points(X3,sK3) ),
    inference(resolution,[],[f64,f57]) ).

fof(f57,plain,
    ~ apart_point_and_line(sK3,line_connecting(sK1,sK2)),
    inference(cnf_transformation,[],[f46]) ).

fof(f64,plain,
    ! [X2,X3,X0,X1] :
      ( apart_point_and_line(X3,X2)
      | apart_point_and_line(X3,X1)
      | apart_point_and_line(X0,X1)
      | ~ distinct_points(X0,X3)
      | apart_point_and_line(X0,X2)
      | ~ distinct_lines(X2,X1) ),
    inference(cnf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0,X1,X2,X3] :
      ( apart_point_and_line(X3,X1)
      | apart_point_and_line(X0,X2)
      | apart_point_and_line(X3,X2)
      | ~ distinct_points(X0,X3)
      | ~ distinct_lines(X2,X1)
      | apart_point_and_line(X0,X1) ),
    inference(rectify,[],[f33]) ).

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

fof(f32,plain,
    ! [X2,X3,X0,X1] :
      ( apart_point_and_line(X1,X2)
      | apart_point_and_line(X0,X3)
      | apart_point_and_line(X1,X3)
      | apart_point_and_line(X0,X2)
      | ~ distinct_lines(X3,X2)
      | ~ distinct_points(X0,X1) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,plain,
    ! [X2,X3,X0,X1] :
      ( ( distinct_lines(X3,X2)
        & distinct_points(X0,X1) )
     => ( apart_point_and_line(X1,X2)
        | apart_point_and_line(X0,X3)
        | apart_point_and_line(X1,X3)
        | apart_point_and_line(X0,X2) ) ),
    inference(rectify,[],[f9]) ).

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

fof(f152,plain,
    ( apart_point_and_line(sK1,line_connecting(sK0,sK3))
    | ~ distinct_points(sK1,sK2)
    | ~ distinct_points(sK0,sK3) ),
    inference(resolution,[],[f148,f58]) ).

fof(f58,plain,
    ( apart_point_and_line(sK2,line_connecting(sK0,sK3))
    | apart_point_and_line(sK1,line_connecting(sK0,sK3)) ),
    inference(cnf_transformation,[],[f46]) ).

fof(f148,plain,
    ( ~ apart_point_and_line(sK2,line_connecting(sK0,sK3))
    | ~ distinct_points(sK1,sK2)
    | ~ distinct_points(sK0,sK3) ),
    inference(resolution,[],[f124,f85]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : GEO187+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_sat --cores 0 -t %d %s
% 0.13/0.35  % Computer : n018.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon Aug 29 21:30:09 EDT 2022
% 0.13/0.35  % CPUTime    : 
% 0.20/0.48  % (20397)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)
% 0.20/0.48  % (20405)fmb+10_1:1_bce=on:i=59:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/59Mi)
% 0.20/0.49  TRYING [1]
% 0.20/0.49  TRYING [2]
% 0.20/0.49  TRYING [3]
% 0.20/0.49  % (20397)First to succeed.
% 0.20/0.49  TRYING [4]
% 0.20/0.50  TRYING [5]
% 0.20/0.50  % (20397)Refutation found. Thanks to Tanya!
% 0.20/0.50  % SZS status Theorem for theBenchmark
% 0.20/0.50  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.50  % (20397)------------------------------
% 0.20/0.50  % (20397)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (20397)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (20397)Termination reason: Refutation
% 0.20/0.50  
% 0.20/0.50  % (20397)Memory used [KB]: 1023
% 0.20/0.50  % (20397)Time elapsed: 0.080 s
% 0.20/0.50  % (20397)Instructions burned: 6 (million)
% 0.20/0.50  % (20397)------------------------------
% 0.20/0.50  % (20397)------------------------------
% 0.20/0.50  % (20387)Success in time 0.145 s
%------------------------------------------------------------------------------