TSTP Solution File: GEO036-2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : GEO036-2 : TPTP v8.2.0. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n020.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 20:13:41 EDT 2024

% Result   : Unsatisfiable 0.12s 0.36s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    4
%            Number of leaves      :   57
% Syntax   : Number of formulae    :  141 (  25 unt;   0 def)
%            Number of atoms       :  391 (  32 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  446 ( 196   ~; 212   |;   0   &)
%                                         (  38 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   5 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of predicates  :   42 (  40 usr;  39 prp; 0-4 aty)
%            Number of functors    :    8 (   8 usr;   3 con; 0-6 aty)
%            Number of variables   :  238 ( 238   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f253,plain,
    $false,
    inference(avatar_sat_refutation,[],[f32,f38,f44,f49,f55,f60,f66,f70,f74,f78,f82,f87,f92,f96,f102,f106,f112,f116,f122,f126,f132,f138,f145,f152,f156,f163,f171,f175,f191,f199,f208,f213,f218,f220,f232,f237,f242,f247,f249,f252]) ).

fof(f252,plain,
    ( ~ spl0_26
    | spl0_38 ),
    inference(avatar_contradiction_clause,[],[f251]) ).

fof(f251,plain,
    ( $false
    | ~ spl0_26
    | spl0_38 ),
    inference(resolution,[],[f246,f151]) ).

fof(f151,plain,
    ( ! [X0,X1] : between(X0,X1,X1)
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f150]) ).

fof(f150,plain,
    ( spl0_26
  <=> ! [X0,X1] : between(X0,X1,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f246,plain,
    ( ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1)
    | spl0_38 ),
    inference(avatar_component_clause,[],[f244]) ).

fof(f244,plain,
    ( spl0_38
  <=> between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f249,plain,
    ( ~ spl0_26
    | spl0_37 ),
    inference(avatar_contradiction_clause,[],[f248]) ).

fof(f248,plain,
    ( $false
    | ~ spl0_26
    | spl0_37 ),
    inference(resolution,[],[f241,f151]) ).

fof(f241,plain,
    ( ~ between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_1)
    | spl0_37 ),
    inference(avatar_component_clause,[],[f239]) ).

fof(f239,plain,
    ( spl0_37
  <=> between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f247,plain,
    ( ~ spl0_38
    | ~ spl0_1
    | spl0_8 ),
    inference(avatar_split_clause,[],[f224,f57,f21,f244]) ).

fof(f21,plain,
    ( spl0_1
  <=> lower_dimension_point_1 = lower_dimension_point_2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f57,plain,
    ( spl0_8
  <=> between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f224,plain,
    ( ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_1)
    | ~ spl0_1
    | spl0_8 ),
    inference(superposition,[],[f59,f23]) ).

fof(f23,plain,
    ( lower_dimension_point_1 = lower_dimension_point_2
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f21]) ).

fof(f59,plain,
    ( ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2)
    | spl0_8 ),
    inference(avatar_component_clause,[],[f57]) ).

fof(f242,plain,
    ( ~ spl0_37
    | ~ spl0_1
    | spl0_7 ),
    inference(avatar_split_clause,[],[f223,f52,f21,f239]) ).

fof(f52,plain,
    ( spl0_7
  <=> between(lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f223,plain,
    ( ~ between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_1)
    | ~ spl0_1
    | spl0_7 ),
    inference(superposition,[],[f54,f23]) ).

fof(f54,plain,
    ( ~ between(lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_1)
    | spl0_7 ),
    inference(avatar_component_clause,[],[f52]) ).

fof(f237,plain,
    ( ~ spl0_36
    | ~ spl0_1
    | spl0_6 ),
    inference(avatar_split_clause,[],[f222,f46,f21,f234]) ).

fof(f234,plain,
    ( spl0_36
  <=> between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f46,plain,
    ( spl0_6
  <=> between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f222,plain,
    ( ~ between(lower_dimension_point_1,lower_dimension_point_3,lower_dimension_point_1)
    | ~ spl0_1
    | spl0_6 ),
    inference(superposition,[],[f48,f23]) ).

fof(f48,plain,
    ( ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1)
    | spl0_6 ),
    inference(avatar_component_clause,[],[f46]) ).

fof(f232,plain,
    ( ~ spl0_35
    | ~ spl0_1
    | spl0_4 ),
    inference(avatar_split_clause,[],[f221,f35,f21,f229]) ).

fof(f229,plain,
    ( spl0_35
  <=> between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f35,plain,
    ( spl0_4
  <=> between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f221,plain,
    ( ~ between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_3)
    | ~ spl0_1
    | spl0_4 ),
    inference(superposition,[],[f37,f23]) ).

fof(f37,plain,
    ( ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3)
    | spl0_4 ),
    inference(avatar_component_clause,[],[f35]) ).

fof(f220,plain,
    ( ~ spl0_26
    | spl0_33 ),
    inference(avatar_contradiction_clause,[],[f219]) ).

fof(f219,plain,
    ( $false
    | ~ spl0_26
    | spl0_33 ),
    inference(resolution,[],[f212,f151]) ).

fof(f212,plain,
    ( ~ between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_1)
    | spl0_33 ),
    inference(avatar_component_clause,[],[f210]) ).

fof(f210,plain,
    ( spl0_33
  <=> between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f218,plain,
    ( ~ spl0_34
    | ~ spl0_3
    | spl0_8 ),
    inference(avatar_split_clause,[],[f203,f57,f29,f215]) ).

fof(f215,plain,
    ( spl0_34
  <=> between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f29,plain,
    ( spl0_3
  <=> lower_dimension_point_1 = lower_dimension_point_3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f203,plain,
    ( ~ between(lower_dimension_point_1,lower_dimension_point_1,lower_dimension_point_2)
    | ~ spl0_3
    | spl0_8 ),
    inference(superposition,[],[f59,f31]) ).

fof(f31,plain,
    ( lower_dimension_point_1 = lower_dimension_point_3
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f29]) ).

fof(f213,plain,
    ( ~ spl0_33
    | ~ spl0_3
    | spl0_6 ),
    inference(avatar_split_clause,[],[f202,f46,f29,f210]) ).

fof(f202,plain,
    ( ~ between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_1)
    | ~ spl0_3
    | spl0_6 ),
    inference(superposition,[],[f48,f31]) ).

fof(f208,plain,
    ( ~ spl0_32
    | ~ spl0_3
    | spl0_4 ),
    inference(avatar_split_clause,[],[f201,f35,f29,f205]) ).

fof(f205,plain,
    ( spl0_32
  <=> between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f201,plain,
    ( ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_1)
    | ~ spl0_3
    | spl0_4 ),
    inference(superposition,[],[f37,f31]) ).

fof(f199,plain,
    ( spl0_5
    | ~ spl0_26 ),
    inference(avatar_contradiction_clause,[],[f195]) ).

fof(f195,plain,
    ( $false
    | spl0_5
    | ~ spl0_26 ),
    inference(resolution,[],[f151,f43]) ).

fof(f43,plain,
    ( ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2)
    | spl0_5 ),
    inference(avatar_component_clause,[],[f41]) ).

fof(f41,plain,
    ( spl0_5
  <=> between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f191,plain,
    ( spl0_31
    | ~ spl0_10
    | ~ spl0_22 ),
    inference(avatar_split_clause,[],[f127,f124,f68,f189]) ).

fof(f189,plain,
    ( spl0_31
  <=> ! [X0,X3,X2,X1] :
        ( ~ between(X0,X0,X1)
        | ~ equidistant(X0,X1,X0,X2)
        | ~ between(X0,X3,X1)
        | between(X0,continuous(X0,X0,X0,X3,X1,X2),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f68,plain,
    ( spl0_10
  <=> ! [X0,X1] : equidistant(X0,X1,X1,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f124,plain,
    ( spl0_22
  <=> ! [X6,X10,X9,X0,X5,X3] :
        ( ~ between(X3,X5,X0)
        | ~ between(X10,X3,X0)
        | ~ equidistant(X10,X0,X10,X6)
        | ~ equidistant(X10,X3,X10,X9)
        | between(X9,continuous(X10,X3,X9,X5,X0,X6),X6) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f127,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ between(X0,X0,X1)
        | ~ equidistant(X0,X1,X0,X2)
        | ~ between(X0,X3,X1)
        | between(X0,continuous(X0,X0,X0,X3,X1,X2),X2) )
    | ~ spl0_10
    | ~ spl0_22 ),
    inference(resolution,[],[f125,f69]) ).

fof(f69,plain,
    ( ! [X0,X1] : equidistant(X0,X1,X1,X0)
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f68]) ).

fof(f125,plain,
    ( ! [X3,X10,X0,X6,X9,X5] :
        ( ~ equidistant(X10,X3,X10,X9)
        | ~ between(X10,X3,X0)
        | ~ equidistant(X10,X0,X10,X6)
        | ~ between(X3,X5,X0)
        | between(X9,continuous(X10,X3,X9,X5,X0,X6),X6) )
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f124]) ).

fof(f175,plain,
    ( spl0_30
    | ~ spl0_11
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f108,f104,f72,f173]) ).

fof(f173,plain,
    ( spl0_30
  <=> ! [X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X1,X3,X2)
        | inner_pasch(X1,X3,X2,X1,X0) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f72,plain,
    ( spl0_11
  <=> ! [X0,X1] :
        ( X0 = X1
        | ~ between(X0,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f104,plain,
    ( spl0_18
  <=> ! [X10,X0,X5,X3,X1] :
        ( ~ between(X10,X3,X5)
        | ~ between(X1,X0,X5)
        | between(X0,inner_pasch(X10,X3,X5,X0,X1),X10) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f108,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X1,X3,X2)
        | inner_pasch(X1,X3,X2,X1,X0) = X1 )
    | ~ spl0_11
    | ~ spl0_18 ),
    inference(resolution,[],[f105,f73]) ).

fof(f73,plain,
    ( ! [X0,X1] :
        ( ~ between(X0,X1,X0)
        | X0 = X1 )
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f72]) ).

fof(f105,plain,
    ( ! [X3,X10,X0,X1,X5] :
        ( between(X0,inner_pasch(X10,X3,X5,X0,X1),X10)
        | ~ between(X1,X0,X5)
        | ~ between(X10,X3,X5) )
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f104]) ).

fof(f171,plain,
    ( spl0_29
    | ~ spl0_11
    | ~ spl0_17 ),
    inference(avatar_split_clause,[],[f107,f100,f72,f169]) ).

fof(f169,plain,
    ( spl0_29
  <=> ! [X0,X3,X2,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X0,X2)
        | inner_pasch(X3,X0,X2,X1,X0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f100,plain,
    ( spl0_17
  <=> ! [X10,X0,X5,X3,X1] :
        ( ~ between(X10,X3,X5)
        | ~ between(X1,X0,X5)
        | between(X3,inner_pasch(X10,X3,X5,X0,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f107,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ between(X0,X1,X2)
        | ~ between(X3,X0,X2)
        | inner_pasch(X3,X0,X2,X1,X0) = X0 )
    | ~ spl0_11
    | ~ spl0_17 ),
    inference(resolution,[],[f101,f73]) ).

fof(f101,plain,
    ( ! [X3,X10,X0,X1,X5] :
        ( between(X3,inner_pasch(X10,X3,X5,X0,X1),X1)
        | ~ between(X1,X0,X5)
        | ~ between(X10,X3,X5) )
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f100]) ).

fof(f163,plain,
    ( spl0_28
    | ~ spl0_14
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f98,f94,f85,f161]) ).

fof(f161,plain,
    ( spl0_28
  <=> ! [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_28])]) ).

fof(f85,plain,
    ( spl0_14
  <=> ! [X3,X0,X5,X1] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f94,plain,
    ( spl0_16
  <=> ! [X5,X4,X0,X3,X2,X1] :
        ( ~ equidistant(X0,X1,X2,X3)
        | ~ equidistant(X0,X1,X4,X5)
        | equidistant(X2,X3,X4,X5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f98,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ equidistant(X0,extension(X1,X0,X2,X3),X4,X5)
        | equidistant(X4,X5,X2,X3) )
    | ~ spl0_14
    | ~ spl0_16 ),
    inference(resolution,[],[f95,f86]) ).

fof(f86,plain,
    ( ! [X3,X0,X1,X5] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3)
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f85]) ).

fof(f95,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ equidistant(X0,X1,X4,X5)
        | ~ equidistant(X0,X1,X2,X3)
        | equidistant(X2,X3,X4,X5) )
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f94]) ).

fof(f156,plain,
    ( spl0_27
    | ~ spl0_10
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f97,f94,f68,f154]) ).

fof(f154,plain,
    ( spl0_27
  <=> ! [X0,X3,X2,X1] :
        ( ~ equidistant(X0,X1,X2,X3)
        | equidistant(X2,X3,X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f97,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ equidistant(X0,X1,X2,X3)
        | equidistant(X2,X3,X1,X0) )
    | ~ spl0_10
    | ~ spl0_16 ),
    inference(resolution,[],[f95,f69]) ).

fof(f152,plain,
    ( spl0_26
    | ~ spl0_13
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f118,f90,f80,f150]) ).

fof(f80,plain,
    ( spl0_13
  <=> ! [X3,X0,X5,X1] : between(X0,X1,extension(X0,X1,X5,X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f90,plain,
    ( spl0_15
  <=> ! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f118,plain,
    ( ! [X0,X1] : between(X0,X1,X1)
    | ~ spl0_13
    | ~ spl0_15 ),
    inference(superposition,[],[f81,f91]) ).

fof(f91,plain,
    ( ! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f90]) ).

fof(f81,plain,
    ( ! [X3,X0,X1,X5] : between(X0,X1,extension(X0,X1,X5,X3))
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f80]) ).

fof(f145,plain,
    spl0_25,
    inference(avatar_split_clause,[],[f6,f143]) ).

fof(f143,plain,
    ( spl0_25
  <=> ! [X2,X3,X9,X0,X8,X6,X1,X7] :
        ( X0 = X1
        | ~ between(X6,X7,X8)
        | ~ between(X0,X1,X2)
        | ~ equidistant(X1,X3,X7,X9)
        | ~ equidistant(X0,X3,X6,X9)
        | ~ equidistant(X1,X2,X7,X8)
        | ~ equidistant(X0,X1,X6,X7)
        | equidistant(X2,X3,X8,X9) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f6,axiom,
    ! [X2,X3,X0,X1,X8,X6,X9,X7] :
      ( X0 = X1
      | ~ between(X6,X7,X8)
      | ~ between(X0,X1,X2)
      | ~ equidistant(X1,X3,X7,X9)
      | ~ equidistant(X0,X3,X6,X9)
      | ~ equidistant(X1,X2,X7,X8)
      | ~ equidistant(X0,X1,X6,X7)
      | equidistant(X2,X3,X8,X9) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',outer_five_segment) ).

fof(f138,plain,
    spl0_24,
    inference(avatar_split_clause,[],[f13,f136]) ).

fof(f136,plain,
    ( spl0_24
  <=> ! [X2,X3,X0,X5,X1] :
        ( X3 = X5
        | between(X2,X0,X1)
        | between(X1,X2,X0)
        | between(X0,X1,X2)
        | ~ equidistant(X2,X5,X2,X3)
        | ~ equidistant(X1,X5,X1,X3)
        | ~ equidistant(X0,X5,X0,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f13,axiom,
    ! [X2,X3,X0,X1,X5] :
      ( X3 = X5
      | between(X2,X0,X1)
      | between(X1,X2,X0)
      | between(X0,X1,X2)
      | ~ equidistant(X2,X5,X2,X3)
      | ~ equidistant(X1,X5,X1,X3)
      | ~ equidistant(X0,X5,X0,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upper_dimension) ).

fof(f132,plain,
    spl0_23,
    inference(avatar_split_clause,[],[f18,f130]) ).

fof(f130,plain,
    ( spl0_23
  <=> ! [X6,X10,X9,X0,X5,X3] :
        ( ~ between(X3,X5,X0)
        | ~ between(X10,X3,X0)
        | ~ equidistant(X10,X0,X10,X6)
        | ~ equidistant(X10,X3,X10,X9)
        | equidistant(X10,X5,X10,continuous(X10,X3,X9,X5,X0,X6)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f18,axiom,
    ! [X3,X10,X0,X6,X9,X5] :
      ( ~ between(X3,X5,X0)
      | ~ between(X10,X3,X0)
      | ~ equidistant(X10,X0,X10,X6)
      | ~ equidistant(X10,X3,X10,X9)
      | equidistant(X10,X5,X10,continuous(X10,X3,X9,X5,X0,X6)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity2) ).

fof(f126,plain,
    spl0_22,
    inference(avatar_split_clause,[],[f17,f124]) ).

fof(f17,axiom,
    ! [X3,X10,X0,X6,X9,X5] :
      ( ~ between(X3,X5,X0)
      | ~ between(X10,X3,X0)
      | ~ equidistant(X10,X0,X10,X6)
      | ~ equidistant(X10,X3,X10,X9)
      | between(X9,continuous(X10,X3,X9,X5,X0,X6),X6) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',continuity1) ).

fof(f122,plain,
    spl0_21,
    inference(avatar_split_clause,[],[f16,f120]) ).

fof(f120,plain,
    ( spl0_21
  <=> ! [X10,X0,X5,X3,X1] :
        ( X5 = X10
        | ~ between(X3,X5,X0)
        | ~ between(X10,X5,X1)
        | between(euclid1(X10,X3,X5,X0,X1),X1,euclid2(X10,X3,X5,X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f16,axiom,
    ! [X3,X10,X0,X1,X5] :
      ( X5 = X10
      | ~ between(X3,X5,X0)
      | ~ between(X10,X5,X1)
      | between(euclid1(X10,X3,X5,X0,X1),X1,euclid2(X10,X3,X5,X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid3) ).

fof(f116,plain,
    spl0_20,
    inference(avatar_split_clause,[],[f15,f114]) ).

fof(f114,plain,
    ( spl0_20
  <=> ! [X10,X0,X5,X3,X1] :
        ( X5 = X10
        | ~ between(X3,X5,X0)
        | ~ between(X10,X5,X1)
        | between(X10,X0,euclid2(X10,X3,X5,X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f15,axiom,
    ! [X3,X10,X0,X1,X5] :
      ( X5 = X10
      | ~ between(X3,X5,X0)
      | ~ between(X10,X5,X1)
      | between(X10,X0,euclid2(X10,X3,X5,X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid2) ).

fof(f112,plain,
    spl0_19,
    inference(avatar_split_clause,[],[f14,f110]) ).

fof(f110,plain,
    ( spl0_19
  <=> ! [X10,X0,X5,X3,X1] :
        ( X5 = X10
        | ~ between(X3,X5,X0)
        | ~ between(X10,X5,X1)
        | between(X10,X3,euclid1(X10,X3,X5,X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f14,axiom,
    ! [X3,X10,X0,X1,X5] :
      ( X5 = X10
      | ~ between(X3,X5,X0)
      | ~ between(X10,X5,X1)
      | between(X10,X3,euclid1(X10,X3,X5,X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',euclid1) ).

fof(f106,plain,
    spl0_18,
    inference(avatar_split_clause,[],[f9,f104]) ).

fof(f9,axiom,
    ! [X3,X10,X0,X1,X5] :
      ( ~ between(X10,X3,X5)
      | ~ between(X1,X0,X5)
      | between(X0,inner_pasch(X10,X3,X5,X0,X1),X10) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch2) ).

fof(f102,plain,
    spl0_17,
    inference(avatar_split_clause,[],[f8,f100]) ).

fof(f8,axiom,
    ! [X3,X10,X0,X1,X5] :
      ( ~ between(X10,X3,X5)
      | ~ between(X1,X0,X5)
      | between(X3,inner_pasch(X10,X3,X5,X0,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inner_pasch1) ).

fof(f96,plain,
    spl0_16,
    inference(avatar_split_clause,[],[f2,f94]) ).

fof(f2,axiom,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ equidistant(X0,X1,X2,X3)
      | ~ equidistant(X0,X1,X4,X5)
      | equidistant(X2,X3,X4,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity_for_equidistance) ).

fof(f92,plain,
    ( spl0_15
    | ~ spl0_12
    | ~ spl0_14 ),
    inference(avatar_split_clause,[],[f88,f85,f76,f90]) ).

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

fof(f88,plain,
    ( ! [X2,X0,X1] : extension(X1,X0,X2,X2) = X0
    | ~ spl0_12
    | ~ spl0_14 ),
    inference(resolution,[],[f86,f77]) ).

fof(f77,plain,
    ( ! [X2,X0,X1] :
        ( ~ equidistant(X0,X1,X2,X2)
        | X0 = X1 )
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f76]) ).

fof(f87,plain,
    spl0_14,
    inference(avatar_split_clause,[],[f5,f85]) ).

fof(f5,axiom,
    ! [X3,X0,X1,X5] : equidistant(X1,extension(X0,X1,X5,X3),X5,X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction2) ).

fof(f82,plain,
    spl0_13,
    inference(avatar_split_clause,[],[f4,f80]) ).

fof(f4,axiom,
    ! [X3,X0,X1,X5] : between(X0,X1,extension(X0,X1,X5,X3)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',segment_construction1) ).

fof(f78,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f3,f76]) ).

fof(f3,axiom,
    ! [X2,X0,X1] :
      ( X0 = X1
      | ~ equidistant(X0,X1,X2,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_equidistance) ).

fof(f74,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f7,f72]) ).

fof(f7,axiom,
    ! [X0,X1] :
      ( X0 = X1
      | ~ between(X0,X1,X0) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity_for_betweeness) ).

fof(f70,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f1,f68]) ).

fof(f1,axiom,
    ! [X0,X1] : equidistant(X0,X1,X1,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity_for_equidistance) ).

fof(f66,plain,
    ( ~ spl0_9
    | ~ spl0_2
    | spl0_8 ),
    inference(avatar_split_clause,[],[f61,f57,f25,f63]) ).

fof(f63,plain,
    ( spl0_9
  <=> between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f25,plain,
    ( spl0_2
  <=> lower_dimension_point_2 = lower_dimension_point_3 ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f61,plain,
    ( ~ between(lower_dimension_point_2,lower_dimension_point_1,lower_dimension_point_2)
    | ~ spl0_2
    | spl0_8 ),
    inference(forward_demodulation,[],[f59,f27]) ).

fof(f27,plain,
    ( lower_dimension_point_2 = lower_dimension_point_3
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f25]) ).

fof(f60,plain,
    ~ spl0_8,
    inference(avatar_split_clause,[],[f12,f57]) ).

fof(f12,axiom,
    ~ between(lower_dimension_point_3,lower_dimension_point_1,lower_dimension_point_2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension3) ).

fof(f55,plain,
    ( ~ spl0_7
    | ~ spl0_2
    | spl0_6 ),
    inference(avatar_split_clause,[],[f50,f46,f25,f52]) ).

fof(f50,plain,
    ( ~ between(lower_dimension_point_2,lower_dimension_point_2,lower_dimension_point_1)
    | ~ spl0_2
    | spl0_6 ),
    inference(forward_demodulation,[],[f48,f27]) ).

fof(f49,plain,
    ~ spl0_6,
    inference(avatar_split_clause,[],[f11,f46]) ).

fof(f11,axiom,
    ~ between(lower_dimension_point_2,lower_dimension_point_3,lower_dimension_point_1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension2) ).

fof(f44,plain,
    ( ~ spl0_5
    | ~ spl0_2
    | spl0_4 ),
    inference(avatar_split_clause,[],[f39,f35,f25,f41]) ).

fof(f39,plain,
    ( ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_2)
    | ~ spl0_2
    | spl0_4 ),
    inference(forward_demodulation,[],[f37,f27]) ).

fof(f38,plain,
    ~ spl0_4,
    inference(avatar_split_clause,[],[f10,f35]) ).

fof(f10,axiom,
    ~ between(lower_dimension_point_1,lower_dimension_point_2,lower_dimension_point_3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lower_dimension1) ).

fof(f32,plain,
    ( spl0_1
    | spl0_2
    | spl0_3 ),
    inference(avatar_split_clause,[],[f19,f29,f25,f21]) ).

fof(f19,axiom,
    ( lower_dimension_point_1 = lower_dimension_point_3
    | lower_dimension_point_2 = lower_dimension_point_3
    | lower_dimension_point_1 = lower_dimension_point_2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_axioms_points_are_distinct) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem    : GEO036-2 : TPTP v8.2.0. Released v1.0.0.
% 0.03/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.33  % Computer : n020.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Sun May 19 14:59:38 EDT 2024
% 0.12/0.33  % CPUTime    : 
% 0.12/0.33  % (6961)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.34  % (6962)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.35  % (6966)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)
% 0.12/0.35  % (6965)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.35  TRYING [1]
% 0.12/0.35  TRYING [2]
% 0.12/0.35  % (6968)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.12/0.35  % (6966)First to succeed.
% 0.12/0.36  % (6968)Also succeeded, but the first one will report.
% 0.12/0.36  % (6967)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.12/0.36  % (6966)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-6961"
% 0.12/0.36  % (6966)Refutation found. Thanks to Tanya!
% 0.12/0.36  % SZS status Unsatisfiable for theBenchmark
% 0.12/0.36  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.36  % (6966)------------------------------
% 0.12/0.36  % (6966)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.36  % (6966)Termination reason: Refutation
% 0.12/0.36  
% 0.12/0.36  % (6966)Memory used [KB]: 948
% 0.12/0.36  % (6966)Time elapsed: 0.010 s
% 0.12/0.36  % (6966)Instructions burned: 14 (million)
% 0.12/0.36  % (6961)Success in time 0.025 s
%------------------------------------------------------------------------------