TSTP Solution File: GEO003-1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO003-1 : TPTP v8.2.0. Bugfixed v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -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 : Mon May 20 20:11:55 EDT 2024

% Result   : Unsatisfiable 0.20s 0.36s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   50
% Syntax   : Number of formulae    :  102 (  29 unt;   0 def)
%            Number of atoms       :  298 (  23 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  352 ( 156   ~; 167   |;   0   &)
%                                         (  29 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   6 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   33 (  31 usr;  30 prp; 0-4 aty)
%            Number of functors    :   10 (  10 usr;   5 con; 0-6 aty)
%            Number of variables   :  270 ( 270   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f196,plain,
    $false,
    inference(avatar_sat_refutation,[],[f26,f31,f36,f41,f45,f49,f53,f57,f62,f67,f72,f78,f82,f86,f93,f100,f104,f112,f120,f126,f132,f139,f146,f150,f157,f163,f171,f181,f185,f195]) ).

fof(f195,plain,
    ( spl0_1
    | ~ spl0_24 ),
    inference(avatar_contradiction_clause,[],[f194]) ).

fof(f194,plain,
    ( $false
    | spl0_1
    | ~ spl0_24 ),
    inference(resolution,[],[f149,f25]) ).

fof(f25,plain,
    ( ~ between(a,b,b)
    | spl0_1 ),
    inference(avatar_component_clause,[],[f23]) ).

fof(f23,plain,
    ( spl0_1
  <=> between(a,b,b) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f149,plain,
    ( ! [X0,X1] : between(X0,X1,X1)
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f148]) ).

fof(f148,plain,
    ( spl0_24
  <=> ! [X0,X1] : between(X0,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f185,plain,
    ( spl0_29
    | ~ spl0_10
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f89,f84,f65,f183]) ).

fof(f183,plain,
    ( spl0_29
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X4,X1)
        | ~ between(X5,X2,outer_pasch(X4,X3,X0,X2,X1))
        | between(X5,X2,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f65,plain,
    ( spl0_10
  <=> ! [X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X1,X3,X2)
        | between(X0,X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f84,plain,
    ( spl0_14
  <=> ! [X3,X0,X5,X2,X1] :
        ( ~ between(X0,X5,X2)
        | ~ between(X1,X2,X3)
        | between(X3,X5,outer_pasch(X5,X0,X1,X3,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f89,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X4,X1)
        | ~ between(X5,X2,outer_pasch(X4,X3,X0,X2,X1))
        | between(X5,X2,X4) )
    | ~ spl0_10
    | ~ spl0_14 ),
    inference(resolution,[],[f85,f66]) ).

fof(f66,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ between(X1,X3,X2)
        | ~ between(X0,X1,X2)
        | between(X0,X1,X3) )
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f65]) ).

fof(f85,plain,
    ( ! [X2,X3,X0,X1,X5] :
        ( between(X3,X5,outer_pasch(X5,X0,X1,X3,X2))
        | ~ between(X1,X2,X3)
        | ~ between(X0,X5,X2) )
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f84]) ).

fof(f181,plain,
    ( spl0_28
    | ~ spl0_10
    | ~ spl0_12 ),
    inference(avatar_split_clause,[],[f88,f76,f65,f179]) ).

fof(f179,plain,
    ( spl0_28
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X4,X1)
        | ~ between(X5,X3,X0)
        | between(X5,X3,outer_pasch(X4,X3,X0,X2,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f76,plain,
    ( spl0_12
  <=> ! [X3,X0,X5,X2,X1] :
        ( ~ between(X0,X5,X2)
        | ~ between(X1,X2,X3)
        | between(X0,outer_pasch(X5,X0,X1,X3,X2),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f88,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X4,X1)
        | ~ between(X5,X3,X0)
        | between(X5,X3,outer_pasch(X4,X3,X0,X2,X1)) )
    | ~ spl0_10
    | ~ spl0_12 ),
    inference(resolution,[],[f77,f66]) ).

fof(f77,plain,
    ( ! [X2,X3,X0,X1,X5] :
        ( between(X0,outer_pasch(X5,X0,X1,X3,X2),X1)
        | ~ between(X1,X2,X3)
        | ~ between(X0,X5,X2) )
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f76]) ).

fof(f171,plain,
    ( spl0_27
    | ~ spl0_6
    | ~ spl0_12 ),
    inference(avatar_split_clause,[],[f87,f76,f47,f169]) ).

fof(f169,plain,
    ( spl0_27
  <=> ! [X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X0,X3,X1)
        | outer_pasch(X3,X0,X0,X2,X1) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f47,plain,
    ( spl0_6
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ between(X0,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f87,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X0,X3,X1)
        | outer_pasch(X3,X0,X0,X2,X1) = X0 )
    | ~ spl0_6
    | ~ spl0_12 ),
    inference(resolution,[],[f77,f48]) ).

fof(f48,plain,
    ( ! [X0,X1] :
        ( ~ between(X0,X1,X0)
        | X0 = X1 )
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f47]) ).

fof(f163,plain,
    ( spl0_26
    | ~ spl0_9
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f74,f70,f60,f161]) ).

fof(f161,plain,
    ( spl0_26
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5)
        | equidistant(X4,X5,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f60,plain,
    ( spl0_9
  <=> ! [X0,X5,X2,X1] : equidistant(X1,extension(X0,X1,X5,X2),X5,X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f70,plain,
    ( spl0_11
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ equidistant(X0,X1,X3,X2)
        | ~ equidistant(X0,X1,X4,X5)
        | equidistant(X3,X2,X4,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f74,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5)
        | equidistant(X4,X5,X2,X3) )
    | ~ spl0_9
    | ~ spl0_11 ),
    inference(resolution,[],[f71,f61]) ).

fof(f61,plain,
    ( ! [X2,X0,X1,X5] : equidistant(X1,extension(X0,X1,X5,X2),X5,X2)
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f71,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ equidistant(X0,X1,X4,X5)
        | ~ equidistant(X0,X1,X3,X2)
        | equidistant(X3,X2,X4,X5) )
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f70]) ).

fof(f157,plain,
    ( spl0_25
    | ~ spl0_8
    | ~ spl0_10 ),
    inference(avatar_split_clause,[],[f68,f65,f55,f155]) ).

fof(f155,plain,
    ( spl0_25
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ between(X0,X1,extension(X1,X2,X3,X4))
        | between(X0,X1,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f55,plain,
    ( spl0_8
  <=> ! [X0,X5,X2,X1] : between(X0,X1,extension(X0,X1,X5,X2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f68,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( ~ between(X0,X1,extension(X1,X2,X3,X4))
        | between(X0,X1,X2) )
    | ~ spl0_8
    | ~ spl0_10 ),
    inference(resolution,[],[f66,f56]) ).

fof(f56,plain,
    ( ! [X2,X0,X1,X5] : between(X0,X1,extension(X0,X1,X5,X2))
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f150,plain,
    ( spl0_24
    | ~ spl0_8
    | ~ spl0_13 ),
    inference(avatar_split_clause,[],[f114,f80,f55,f148]) ).

fof(f80,plain,
    ( spl0_13
  <=> ! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f114,plain,
    ( ! [X0,X1] : between(X0,X1,X1)
    | ~ spl0_8
    | ~ spl0_13 ),
    inference(superposition,[],[f56,f81]) ).

fof(f81,plain,
    ( ! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f80]) ).

fof(f146,plain,
    ( spl0_23
    | ~ spl0_5
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f73,f70,f43,f144]) ).

fof(f144,plain,
    ( spl0_23
  <=> ! [X0,X3,X2,X1] :
        ( ~ equidistant(X0,X1,X2,X3)
        | equidistant(X2,X3,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f43,plain,
    ( spl0_5
  <=> ! [X0,X1] : equidistant(X0,X1,X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f73,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ equidistant(X0,X1,X2,X3)
        | equidistant(X2,X3,X1,X0) )
    | ~ spl0_5
    | ~ spl0_11 ),
    inference(resolution,[],[f71,f44]) ).

fof(f44,plain,
    ( ! [X0,X1] : equidistant(X0,X1,X1,X0)
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f43]) ).

fof(f139,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f12,f137]) ).

fof(f137,plain,
    ( spl0_22
  <=> ! [X2,X3,X9,X0,X8,X6,X1,X7] :
        ( X0 = X1
        | ~ between(X6,X7,X8)
        | ~ between(X0,X1,X3)
        | ~ equidistant(X1,X2,X7,X9)
        | ~ equidistant(X0,X2,X6,X9)
        | ~ equidistant(X1,X3,X7,X8)
        | ~ equidistant(X0,X1,X6,X7)
        | equidistant(X3,X2,X8,X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f12,axiom,
    ! [X2,X3,X0,X1,X8,X6,X9,X7] :
      ( X0 = X1
      | ~ between(X6,X7,X8)
      | ~ between(X0,X1,X3)
      | ~ equidistant(X1,X2,X7,X9)
      | ~ equidistant(X0,X2,X6,X9)
      | ~ equidistant(X1,X3,X7,X8)
      | ~ equidistant(X0,X1,X6,X7)
      | equidistant(X3,X2,X8,X9) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_five_segment) ).

fof(f132,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f18,f130]) ).

fof(f130,plain,
    ( spl0_21
  <=> ! [X3,X0,X5,X2,X1] :
        ( X2 = X5
        | between(X3,X0,X1)
        | between(X1,X3,X0)
        | between(X0,X1,X3)
        | ~ equidistant(X3,X5,X3,X2)
        | ~ equidistant(X1,X5,X1,X2)
        | ~ equidistant(X0,X5,X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f18,axiom,
    ! [X2,X3,X0,X1,X5] :
      ( X2 = X5
      | between(X3,X0,X1)
      | between(X1,X3,X0)
      | between(X0,X1,X3)
      | ~ equidistant(X3,X5,X3,X2)
      | ~ equidistant(X1,X5,X1,X2)
      | ~ equidistant(X0,X5,X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',upper_dimension) ).

fof(f126,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f19,f124]) ).

fof(f124,plain,
    ( spl0_20
  <=> ! [X6,X0,X8,X3,X2,X1] :
        ( ~ between(X0,X1,X3)
        | ~ between(X2,X0,X3)
        | ~ equidistant(X2,X3,X2,X8)
        | ~ equidistant(X2,X0,X2,X6)
        | equidistant(X2,X1,X2,continuous(X0,X1,X3,X6,X8,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f19,axiom,
    ! [X2,X3,X0,X1,X8,X6] :
      ( ~ between(X0,X1,X3)
      | ~ between(X2,X0,X3)
      | ~ equidistant(X2,X3,X2,X8)
      | ~ equidistant(X2,X0,X2,X6)
      | equidistant(X2,X1,X2,continuous(X0,X1,X3,X6,X8,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity1) ).

fof(f120,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f20,f118]) ).

fof(f118,plain,
    ( spl0_19
  <=> ! [X6,X0,X8,X3,X2,X1] :
        ( ~ between(X0,X1,X3)
        | ~ between(X2,X0,X3)
        | ~ equidistant(X2,X3,X2,X8)
        | ~ equidistant(X2,X0,X2,X6)
        | between(X6,continuous(X0,X1,X3,X6,X8,X2),X8) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f20,axiom,
    ! [X2,X3,X0,X1,X8,X6] :
      ( ~ between(X0,X1,X3)
      | ~ between(X2,X0,X3)
      | ~ equidistant(X2,X3,X2,X8)
      | ~ equidistant(X2,X0,X2,X6)
      | between(X6,continuous(X0,X1,X3,X6,X8,X2),X8) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',continuity2) ).

fof(f112,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f11,f110]) ).

fof(f110,plain,
    ( spl0_18
  <=> ! [X5,X0,X3,X2,X1] :
        ( X0 = X2
        | ~ between(X1,X2,X3)
        | ~ between(X0,X2,X5)
        | between(euclid1(X5,X0,X1,X3,X2),X5,euclid2(X5,X0,X1,X3,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f11,axiom,
    ! [X2,X3,X0,X1,X5] :
      ( X0 = X2
      | ~ between(X1,X2,X3)
      | ~ between(X0,X2,X5)
      | between(euclid1(X5,X0,X1,X3,X2),X5,euclid2(X5,X0,X1,X3,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid3) ).

fof(f104,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f10,f102]) ).

fof(f102,plain,
    ( spl0_17
  <=> ! [X5,X0,X3,X2,X1] :
        ( X0 = X2
        | ~ between(X1,X2,X3)
        | ~ between(X0,X2,X5)
        | between(X0,X1,euclid2(X5,X0,X1,X3,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f10,axiom,
    ! [X2,X3,X0,X1,X5] :
      ( X0 = X2
      | ~ between(X1,X2,X3)
      | ~ between(X0,X2,X5)
      | between(X0,X1,euclid2(X5,X0,X1,X3,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid2) ).

fof(f100,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f9,f98]) ).

fof(f98,plain,
    ( spl0_16
  <=> ! [X5,X0,X3,X2,X1] :
        ( X0 = X2
        | ~ between(X1,X2,X3)
        | ~ between(X0,X2,X5)
        | between(X0,X3,euclid1(X5,X0,X1,X3,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f9,axiom,
    ! [X2,X3,X0,X1,X5] :
      ( X0 = X2
      | ~ between(X1,X2,X3)
      | ~ between(X0,X2,X5)
      | between(X0,X3,euclid1(X5,X0,X1,X3,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',euclid1) ).

fof(f93,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f3,f91]) ).

fof(f91,plain,
    ( spl0_15
  <=> ! [X0,X3,X2,X1] :
        ( X0 = X1
        | ~ between(X0,X1,X3)
        | ~ between(X0,X1,X2)
        | between(X0,X2,X3)
        | between(X0,X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f3,axiom,
    ! [X2,X3,X0,X1] :
      ( X0 = X1
      | ~ between(X0,X1,X3)
      | ~ between(X0,X1,X2)
      | between(X0,X2,X3)
      | between(X0,X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',connectivity_for_betweeness) ).

fof(f86,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f8,f84]) ).

fof(f8,axiom,
    ! [X2,X3,X0,X1,X5] :
      ( ~ between(X0,X5,X2)
      | ~ between(X1,X2,X3)
      | between(X3,X5,outer_pasch(X5,X0,X1,X3,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_pasch2) ).

fof(f82,plain,
    ( spl0_13
    | ~ spl0_7
    | ~ spl0_9 ),
    inference(avatar_split_clause,[],[f63,f60,f51,f80]) ).

fof(f51,plain,
    ( spl0_7
  <=> ! [X0,X1,X3] :
        ( X0 = X1
        | ~ equidistant(X0,X1,X3,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f63,plain,
    ( ! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0
    | ~ spl0_7
    | ~ spl0_9 ),
    inference(resolution,[],[f61,f52]) ).

fof(f52,plain,
    ( ! [X3,X0,X1] :
        ( ~ equidistant(X0,X1,X3,X3)
        | X0 = X1 )
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f51]) ).

fof(f78,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f7,f76]) ).

fof(f7,axiom,
    ! [X2,X3,X0,X1,X5] :
      ( ~ between(X0,X5,X2)
      | ~ between(X1,X2,X3)
      | between(X0,outer_pasch(X5,X0,X1,X3,X2),X1) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',outer_pasch1) ).

fof(f72,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f6,f70]) ).

fof(f6,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ equidistant(X0,X1,X3,X2)
      | ~ equidistant(X0,X1,X4,X5)
      | equidistant(X3,X2,X4,X5) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_equidistance) ).

fof(f67,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f2,f65]) ).

fof(f2,axiom,
    ! [X2,X3,X0,X1] :
      ( ~ between(X0,X1,X2)
      | ~ between(X1,X3,X2)
      | between(X0,X1,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity_for_betweeness) ).

fof(f62,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f14,f60]) ).

fof(f14,axiom,
    ! [X2,X0,X1,X5] : equidistant(X1,extension(X0,X1,X5,X2),X5,X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction2) ).

fof(f57,plain,
    spl0_8,
    inference(avatar_split_clause,[],[f13,f55]) ).

fof(f13,axiom,
    ! [X2,X0,X1,X5] : between(X0,X1,extension(X0,X1,X5,X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',segment_construction1) ).

fof(f53,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f5,f51]) ).

fof(f5,axiom,
    ! [X3,X0,X1] :
      ( X0 = X1
      | ~ equidistant(X0,X1,X3,X3) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_equidistance) ).

fof(f49,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f1,f47]) ).

fof(f1,axiom,
    ! [X0,X1] :
      ( X0 = X1
      | ~ between(X0,X1,X0) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',identity_for_betweeness) ).

fof(f45,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f4,f43]) ).

fof(f4,axiom,
    ! [X0,X1] : equidistant(X0,X1,X1,X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).

fof(f41,plain,
    ~ spl0_4,
    inference(avatar_split_clause,[],[f17,f38]) ).

fof(f38,plain,
    ( spl0_4
  <=> between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f17,axiom,
    ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension3) ).

fof(f36,plain,
    ~ spl0_3,
    inference(avatar_split_clause,[],[f16,f33]) ).

fof(f33,plain,
    ( spl0_3
  <=> between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f16,axiom,
    ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension2) ).

fof(f31,plain,
    ~ spl0_2,
    inference(avatar_split_clause,[],[f15,f28]) ).

fof(f28,plain,
    ( spl0_2
  <=> between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f15,axiom,
    ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',lower_dimension1) ).

fof(f26,plain,
    ~ spl0_1,
    inference(avatar_split_clause,[],[f21,f23]) ).

fof(f21,axiom,
    ~ between(a,b,b),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_b_between_a_and_b) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12  % Problem    : GEO003-1 : TPTP v8.2.0. Bugfixed v2.5.0.
% 0.02/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34  % Computer : n017.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Sun May 19 13:42:23 EDT 2024
% 0.14/0.34  % CPUTime    : 
% 0.14/0.34  % (26648)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.35  % (26653)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.20/0.36  % (26653)First to succeed.
% 0.20/0.36  % (26651)WARNING: value z3 for option sas not known
% 0.20/0.36  % (26653)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-26648"
% 0.20/0.36  % (26653)Refutation found. Thanks to Tanya!
% 0.20/0.36  % SZS status Unsatisfiable for theBenchmark
% 0.20/0.36  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.36  % (26653)------------------------------
% 0.20/0.36  % (26653)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.36  % (26653)Termination reason: Refutation
% 0.20/0.36  
% 0.20/0.36  % (26653)Memory used [KB]: 940
% 0.20/0.36  % (26653)Time elapsed: 0.006 s
% 0.20/0.36  % (26653)Instructions burned: 13 (million)
% 0.20/0.36  % (26648)Success in time 0.016 s
%------------------------------------------------------------------------------