TSTP Solution File: SYO040_8 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SYO040_8 : TPTP v8.2.0. Released v8.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n027.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 : Tue May 21 09:10:04 EDT 2024

% Result   : Theorem 0.12s 0.38s
% Output   : Refutation 0.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   44
% Syntax   : Number of formulae    :  243 (  10 unt;   8 typ;   0 def)
%            Number of atoms       : 1002 ( 158 equ)
%            Maximal formula atoms :    5 (   4 avg)
%            Number of connectives :  728 ( 328   ~; 361   |;   6   &)
%                                         (  33 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   4 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of FOOLs       :  389 ( 369 fml;  20 var)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    2 (   2   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   38 (  35 usr;  36 prp; 0-2 aty)
%            Number of functors    :    1 (   1 usr;   0 con; 1-1 aty)
%            Number of variables   :   10 (  10   !;   0   ?;  10   :)

% Comments : 
%------------------------------------------------------------------------------
tff(func_def_0,type,
    h: $o > $i ).

tff(func_def_3,type,
    bG0: $o ).

tff(func_def_4,type,
    bG1: $o ).

tff(func_def_5,type,
    bG2: $o ).

tff(func_def_6,type,
    bG3: $o ).

tff(func_def_7,type,
    bG4: $o ).

tff(func_def_8,type,
    bG5: $o ).

tff(pred_def_1,type,
    f: $o > $o ).

tff(f778,plain,
    $false,
    inference(avatar_sat_refutation,[],[f36,f41,f50,f55,f64,f73,f82,f91,f95,f120,f129,f136,f139,f142,f148,f154,f156,f161,f165,f167,f172,f177,f181,f188,f192,f202,f204,f216,f217,f219,f229,f248,f354,f360,f368,f376,f381,f395,f412,f423,f434,f451,f456,f459,f473,f487,f517,f522,f560,f567,f580,f586,f588,f613,f647,f657,f658,f679,f726,f735,f777]) ).

tff(f777,plain,
    ( ~ spl6_16
    | spl6_10
    | ~ spl6_21 ),
    inference(avatar_split_clause,[],[f240,f174,f75,f126]) ).

tff(f126,plain,
    ( spl6_16
  <=> f($false) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_16])]) ).

tff(f75,plain,
    ( spl6_10
  <=> f(bG1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).

tff(f174,plain,
    ( spl6_21
  <=> ( $false = bG1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_21])]) ).

tff(f240,plain,
    ( ~ f($false)
    | spl6_10
    | ~ spl6_21 ),
    inference(superposition,[],[f77,f176]) ).

tff(f176,plain,
    ( ( $false = bG1 )
    | ~ spl6_21 ),
    inference(avatar_component_clause,[],[f174]) ).

tff(f77,plain,
    ( ~ f(bG1)
    | spl6_10 ),
    inference(avatar_component_clause,[],[f75]) ).

tff(f735,plain,
    ( ~ spl6_9
    | spl6_27 ),
    inference(avatar_contradiction_clause,[],[f734]) ).

tff(f734,plain,
    ( $false
    | ~ spl6_9
    | spl6_27 ),
    inference(trivial_inequality_removal,[],[f727]) ).

tff(f727,plain,
    ( ( h($true) != h($true) )
    | ~ spl6_9
    | spl6_27 ),
    inference(superposition,[],[f559,f72]) ).

tff(f72,plain,
    ( ( $true = bG3 )
    | ~ spl6_9 ),
    inference(avatar_component_clause,[],[f70]) ).

tff(f70,plain,
    ( spl6_9
  <=> ( $true = bG3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).

tff(f559,plain,
    ( ( h(bG3) != h($true) )
    | spl6_27 ),
    inference(avatar_component_clause,[],[f557]) ).

tff(f557,plain,
    ( spl6_27
  <=> ( h(bG3) = h($true) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_27])]) ).

tff(f726,plain,
    ( ~ spl6_7
    | spl6_18
    | ~ spl6_4 ),
    inference(avatar_split_clause,[],[f195,f47,f145,f61]) ).

tff(f61,plain,
    ( spl6_7
  <=> ( $true = bG5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).

tff(f145,plain,
    ( spl6_18
  <=> f($true) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_18])]) ).

tff(f47,plain,
    ( spl6_4
  <=> ( $true = bG4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).

tff(f195,plain,
    ( f($true)
    | ( $true != bG5 )
    | ~ spl6_4 ),
    inference(forward_demodulation,[],[f20,f49]) ).

tff(f49,plain,
    ( ( $true = bG4 )
    | ~ spl6_4 ),
    inference(avatar_component_clause,[],[f47]) ).

tff(f20,plain,
    ( f(bG4)
    | ( $true != bG5 ) ),
    inference(cnf_transformation,[],[f13]) ).

tff(f13,plain,
    ( ( f(bG4)
      | ( $true != bG5 ) )
    & ( ( $true = bG5 )
      | ~ f(bG4) ) ),
    inference(nnf_transformation,[],[f10]) ).

tff(f10,plain,
    ( f(bG4)
  <=> ( $true = bG5 ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG5])]) ).

tff(f679,plain,
    ( spl6_18
    | ~ spl6_4
    | ~ spl6_7 ),
    inference(avatar_split_clause,[],[f667,f61,f47,f145]) ).

tff(f667,plain,
    ( f($true)
    | ~ spl6_4
    | ~ spl6_7 ),
    inference(trivial_inequality_removal,[],[f666]) ).

tff(f666,plain,
    ( ( $true != $true )
    | f($true)
    | ~ spl6_4
    | ~ spl6_7 ),
    inference(forward_demodulation,[],[f651,f63]) ).

tff(f63,plain,
    ( ( $true = bG5 )
    | ~ spl6_7 ),
    inference(avatar_component_clause,[],[f61]) ).

tff(f651,plain,
    ( f($true)
    | ( $true != bG5 )
    | ~ spl6_4 ),
    inference(forward_demodulation,[],[f20,f49]) ).

tff(f658,plain,
    ( ~ spl6_18
    | spl6_10
    | ~ spl6_13 ),
    inference(avatar_split_clause,[],[f479,f88,f75,f145]) ).

tff(f88,plain,
    ( spl6_13
  <=> ( $true = bG1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_13])]) ).

tff(f479,plain,
    ( ~ f($true)
    | spl6_10
    | ~ spl6_13 ),
    inference(forward_demodulation,[],[f77,f90]) ).

tff(f90,plain,
    ( ( $true = bG1 )
    | ~ spl6_13 ),
    inference(avatar_component_clause,[],[f88]) ).

tff(f657,plain,
    ( spl6_19
    | ~ spl6_25
    | ~ spl6_26 ),
    inference(avatar_split_clause,[],[f566,f453,f352,f151]) ).

tff(f151,plain,
    ( spl6_19
  <=> ( $false = bG3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_19])]) ).

tff(f352,plain,
    ( spl6_25
  <=> ! [X0: $o] :
        ( ( h($false) != h((X0)) )
        | ( $false = (X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_25])]) ).

tff(f453,plain,
    ( spl6_26
  <=> ( h(bG3) = h($false) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_26])]) ).

tff(f566,plain,
    ( ( $false = bG3 )
    | ~ spl6_25
    | ~ spl6_26 ),
    inference(trivial_inequality_removal,[],[f565]) ).

tff(f565,plain,
    ( ( h($false) != h($false) )
    | ( $false = bG3 )
    | ~ spl6_25
    | ~ spl6_26 ),
    inference(superposition,[],[f353,f454]) ).

tff(f454,plain,
    ( ( h(bG3) = h($false) )
    | ~ spl6_26 ),
    inference(avatar_component_clause,[],[f453]) ).

tff(f353,plain,
    ( ! [X0: $o] :
        ( ( h($false) != h((X0)) )
        | ( $false = (X0) ) )
    | ~ spl6_25 ),
    inference(avatar_component_clause,[],[f352]) ).

tff(f647,plain,
    ( ~ spl6_4
    | ~ spl6_14
    | ~ spl6_17 ),
    inference(avatar_contradiction_clause,[],[f646]) ).

tff(f646,plain,
    ( $false
    | ~ spl6_4
    | ~ spl6_14
    | ~ spl6_17 ),
    inference(trivial_inequality_removal,[],[f645]) ).

tff(f645,plain,
    ( ( $true = $false )
    | ~ spl6_4
    | ~ spl6_14
    | ~ spl6_17 ),
    inference(forward_demodulation,[],[f49,f571]) ).

tff(f571,plain,
    ( ( $false = bG4 )
    | ~ spl6_14
    | ~ spl6_17 ),
    inference(trivial_inequality_removal,[],[f232]) ).

tff(f232,plain,
    ( ( $true = $false )
    | ( $false = bG4 )
    | ~ spl6_14
    | ~ spl6_17 ),
    inference(superposition,[],[f135,f94]) ).

tff(f94,plain,
    ( ! [X0: $o] :
        ( ( $true = (X0) )
        | ( $false = (X0) ) )
    | ~ spl6_14 ),
    inference(avatar_component_clause,[],[f93]) ).

tff(f93,plain,
    ( spl6_14
  <=> ! [X0: $o] :
        ( ( $true = (X0) )
        | ( $false = (X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_14])]) ).

tff(f135,plain,
    ( ( $false = bG4 )
    | ~ spl6_17 ),
    inference(avatar_component_clause,[],[f133]) ).

tff(f133,plain,
    ( spl6_17
  <=> ( $false = bG4 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_17])]) ).

tff(f613,plain,
    ( spl6_16
    | ~ spl6_12
    | ~ spl6_14
    | ~ spl6_23 ),
    inference(avatar_split_clause,[],[f587,f226,f93,f84,f126]) ).

tff(f84,plain,
    ( spl6_12
  <=> f(bG0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_12])]) ).

tff(f226,plain,
    ( spl6_23
  <=> ( $false = bG0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_23])]) ).

tff(f587,plain,
    ( f($false)
    | ~ spl6_12
    | ~ spl6_14
    | ~ spl6_23 ),
    inference(forward_demodulation,[],[f85,f574]) ).

tff(f574,plain,
    ( ( $false = bG0 )
    | ~ spl6_14
    | ~ spl6_23 ),
    inference(trivial_inequality_removal,[],[f242]) ).

tff(f242,plain,
    ( ( $true = $false )
    | ( $false = bG0 )
    | ~ spl6_14
    | ~ spl6_23 ),
    inference(superposition,[],[f228,f94]) ).

tff(f228,plain,
    ( ( $false = bG0 )
    | ~ spl6_23 ),
    inference(avatar_component_clause,[],[f226]) ).

tff(f85,plain,
    ( f(bG0)
    | ~ spl6_12 ),
    inference(avatar_component_clause,[],[f84]) ).

tff(f588,plain,
    ( spl6_18
    | ~ spl6_10
    | ~ spl6_13 ),
    inference(avatar_split_clause,[],[f504,f88,f75,f145]) ).

tff(f504,plain,
    ( f($true)
    | ~ spl6_10
    | ~ spl6_13 ),
    inference(forward_demodulation,[],[f76,f90]) ).

tff(f76,plain,
    ( f(bG1)
    | ~ spl6_10 ),
    inference(avatar_component_clause,[],[f75]) ).

tff(f586,plain,
    ( spl6_12
    | ~ spl6_13 ),
    inference(avatar_split_clause,[],[f213,f88,f84]) ).

tff(f213,plain,
    ( f(bG0)
    | ~ spl6_13 ),
    inference(trivial_inequality_removal,[],[f212]) ).

tff(f212,plain,
    ( ( $true != $true )
    | f(bG0)
    | ~ spl6_13 ),
    inference(forward_demodulation,[],[f28,f90]) ).

tff(f28,plain,
    ( f(bG0)
    | ( $true != bG1 ) ),
    inference(cnf_transformation,[],[f17]) ).

tff(f17,plain,
    ( ( f(bG0)
      | ( $true != bG1 ) )
    & ( ( $true = bG1 )
      | ~ f(bG0) ) ),
    inference(nnf_transformation,[],[f6]) ).

tff(f6,plain,
    ( f(bG0)
  <=> ( $true = bG1 ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG1])]) ).

tff(f580,plain,
    ( ~ spl6_3
    | ~ spl6_23 ),
    inference(avatar_split_clause,[],[f577,f226,f43]) ).

tff(f43,plain,
    ( spl6_3
  <=> x ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).

tff(f577,plain,
    ( ~ x
    | ~ spl6_23 ),
    inference(trivial_inequality_removal,[],[f499]) ).

tff(f499,plain,
    ( ( $true = $false )
    | ~ x
    | ~ spl6_23 ),
    inference(forward_demodulation,[],[f29,f228]) ).

tff(f29,plain,
    ( ( $true = bG0 )
    | ~ x ),
    inference(cnf_transformation,[],[f18]) ).

tff(f18,plain,
    ( ( x
      | ( $true != bG0 ) )
    & ( ( $true = bG0 )
      | ~ x ) ),
    inference(nnf_transformation,[],[f5]) ).

tff(f5,plain,
    ( x
  <=> ( $true = bG0 ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG0])]) ).

tff(f567,plain,
    ( ~ spl6_18
    | spl6_8
    | ~ spl6_11
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f511,f93,f79,f66,f145]) ).

tff(f66,plain,
    ( spl6_8
  <=> f(bG2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).

tff(f79,plain,
    ( spl6_11
  <=> ( $true = bG2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_11])]) ).

tff(f511,plain,
    ( ~ f($true)
    | spl6_8
    | ~ spl6_11
    | ~ spl6_14 ),
    inference(trivial_inequality_removal,[],[f510]) ).

tff(f510,plain,
    ( ( $true = $false )
    | ~ f($true)
    | spl6_8
    | ~ spl6_11
    | ~ spl6_14 ),
    inference(forward_demodulation,[],[f186,f81]) ).

tff(f81,plain,
    ( ( $true = bG2 )
    | ~ spl6_11 ),
    inference(avatar_component_clause,[],[f79]) ).

tff(f186,plain,
    ( ~ f($true)
    | ( $false = bG2 )
    | spl6_8
    | ~ spl6_14 ),
    inference(superposition,[],[f68,f94]) ).

tff(f68,plain,
    ( ~ f(bG2)
    | spl6_8 ),
    inference(avatar_component_clause,[],[f66]) ).

tff(f560,plain,
    ( spl6_15
    | ~ spl6_27
    | spl6_1
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f108,f93,f33,f557,f117]) ).

tff(f117,plain,
    ( spl6_15
  <=> ( $false = bG5 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_15])]) ).

tff(f33,plain,
    ( spl6_1
  <=> ( h(bG3) = h(bG5) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).

tff(f108,plain,
    ( ( h(bG3) != h($true) )
    | ( $false = bG5 )
    | spl6_1
    | ~ spl6_14 ),
    inference(superposition,[],[f35,f94]) ).

tff(f35,plain,
    ( ( h(bG3) != h(bG5) )
    | spl6_1 ),
    inference(avatar_component_clause,[],[f33]) ).

tff(f522,plain,
    ( spl6_6
    | ~ spl6_7 ),
    inference(avatar_split_clause,[],[f209,f61,f57]) ).

tff(f57,plain,
    ( spl6_6
  <=> f(bG4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).

tff(f209,plain,
    ( f(bG4)
    | ~ spl6_7 ),
    inference(trivial_inequality_removal,[],[f208]) ).

tff(f208,plain,
    ( ( $true != $true )
    | f(bG4)
    | ~ spl6_7 ),
    inference(forward_demodulation,[],[f20,f63]) ).

tff(f517,plain,
    ( ~ spl6_5
    | ~ spl6_23 ),
    inference(avatar_contradiction_clause,[],[f516]) ).

tff(f516,plain,
    ( $false
    | ~ spl6_5
    | ~ spl6_23 ),
    inference(trivial_inequality_removal,[],[f515]) ).

tff(f515,plain,
    ( ( $true = $false )
    | ~ spl6_5
    | ~ spl6_23 ),
    inference(forward_demodulation,[],[f53,f228]) ).

tff(f53,plain,
    ( ( $true = bG0 )
    | ~ spl6_5 ),
    inference(avatar_component_clause,[],[f52]) ).

tff(f52,plain,
    ( spl6_5
  <=> ( $true = bG0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).

tff(f487,plain,
    ( ~ spl6_16
    | spl6_6
    | ~ spl6_17 ),
    inference(avatar_split_clause,[],[f388,f133,f57,f126]) ).

tff(f388,plain,
    ( ~ f($false)
    | spl6_6
    | ~ spl6_17 ),
    inference(forward_demodulation,[],[f59,f135]) ).

tff(f59,plain,
    ( ~ f(bG4)
    | spl6_6 ),
    inference(avatar_component_clause,[],[f57]) ).

tff(f473,plain,
    ( ~ spl6_13
    | ~ spl6_21 ),
    inference(avatar_contradiction_clause,[],[f472]) ).

tff(f472,plain,
    ( $false
    | ~ spl6_13
    | ~ spl6_21 ),
    inference(trivial_inequality_removal,[],[f471]) ).

tff(f471,plain,
    ( ( $true = $false )
    | ~ spl6_13
    | ~ spl6_21 ),
    inference(forward_demodulation,[],[f90,f176]) ).

tff(f459,plain,
    ( ~ spl6_14
    | ~ spl6_19
    | spl6_26 ),
    inference(avatar_contradiction_clause,[],[f458]) ).

tff(f458,plain,
    ( $false
    | ~ spl6_14
    | ~ spl6_19
    | spl6_26 ),
    inference(trivial_inequality_removal,[],[f457]) ).

tff(f457,plain,
    ( ( h($false) != h($false) )
    | ~ spl6_14
    | ~ spl6_19
    | spl6_26 ),
    inference(forward_demodulation,[],[f455,f438]) ).

tff(f438,plain,
    ( ( $false = bG3 )
    | ~ spl6_14
    | ~ spl6_19 ),
    inference(trivial_inequality_removal,[],[f234]) ).

tff(f234,plain,
    ( ( $true = $false )
    | ( $false = bG3 )
    | ~ spl6_14
    | ~ spl6_19 ),
    inference(superposition,[],[f153,f94]) ).

tff(f153,plain,
    ( ( $false = bG3 )
    | ~ spl6_19 ),
    inference(avatar_component_clause,[],[f151]) ).

tff(f455,plain,
    ( ( h(bG3) != h($false) )
    | spl6_26 ),
    inference(avatar_component_clause,[],[f453]) ).

tff(f456,plain,
    ( ~ spl6_26
    | spl6_1
    | ~ spl6_15 ),
    inference(avatar_split_clause,[],[f399,f117,f33,f453]) ).

tff(f399,plain,
    ( ( h(bG3) != h($false) )
    | spl6_1
    | ~ spl6_15 ),
    inference(superposition,[],[f35,f119]) ).

tff(f119,plain,
    ( ( $false = bG5 )
    | ~ spl6_15 ),
    inference(avatar_component_clause,[],[f117]) ).

tff(f451,plain,
    ( ~ spl6_9
    | spl6_8 ),
    inference(avatar_split_clause,[],[f24,f66,f70]) ).

tff(f24,plain,
    ( f(bG2)
    | ( $true != bG3 ) ),
    inference(cnf_transformation,[],[f15]) ).

tff(f15,plain,
    ( ( f(bG2)
      | ( $true != bG3 ) )
    & ( ( $true = bG3 )
      | ~ f(bG2) ) ),
    inference(nnf_transformation,[],[f8]) ).

tff(f8,plain,
    ( f(bG2)
  <=> ( $true = bG3 ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG3])]) ).

tff(f434,plain,
    ( spl6_16
    | ~ spl6_10
    | ~ spl6_21 ),
    inference(avatar_split_clause,[],[f424,f174,f75,f126]) ).

tff(f424,plain,
    ( f($false)
    | ~ spl6_10
    | ~ spl6_21 ),
    inference(forward_demodulation,[],[f76,f176]) ).

tff(f423,plain,
    ( ~ spl6_11
    | ~ spl6_20 ),
    inference(avatar_contradiction_clause,[],[f422]) ).

tff(f422,plain,
    ( $false
    | ~ spl6_11
    | ~ spl6_20 ),
    inference(trivial_inequality_removal,[],[f421]) ).

tff(f421,plain,
    ( ( $true = $false )
    | ~ spl6_11
    | ~ spl6_20 ),
    inference(forward_demodulation,[],[f81,f160]) ).

tff(f160,plain,
    ( ( $false = bG2 )
    | ~ spl6_20 ),
    inference(avatar_component_clause,[],[f158]) ).

tff(f158,plain,
    ( spl6_20
  <=> ( $false = bG2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_20])]) ).

tff(f412,plain,
    ( ~ spl6_16
    | spl6_12
    | ~ spl6_23 ),
    inference(avatar_split_clause,[],[f243,f226,f84,f126]) ).

tff(f243,plain,
    ( ~ f($false)
    | spl6_12
    | ~ spl6_23 ),
    inference(superposition,[],[f86,f228]) ).

tff(f86,plain,
    ( ~ f(bG0)
    | spl6_12 ),
    inference(avatar_component_clause,[],[f84]) ).

tff(f395,plain,
    ( spl6_15
    | spl6_1
    | ~ spl6_9
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f378,f93,f70,f33,f117]) ).

tff(f378,plain,
    ( ( $false = bG5 )
    | spl6_1
    | ~ spl6_9
    | ~ spl6_14 ),
    inference(trivial_inequality_removal,[],[f377]) ).

tff(f377,plain,
    ( ( h($true) != h($true) )
    | ( $false = bG5 )
    | spl6_1
    | ~ spl6_9
    | ~ spl6_14 ),
    inference(forward_demodulation,[],[f108,f72]) ).

tff(f381,plain,
    ( spl6_1
    | ~ spl6_7
    | ~ spl6_9 ),
    inference(avatar_contradiction_clause,[],[f380]) ).

tff(f380,plain,
    ( $false
    | spl6_1
    | ~ spl6_7
    | ~ spl6_9 ),
    inference(trivial_inequality_removal,[],[f379]) ).

tff(f379,plain,
    ( ( h($true) != h($true) )
    | spl6_1
    | ~ spl6_7
    | ~ spl6_9 ),
    inference(forward_demodulation,[],[f123,f72]) ).

tff(f123,plain,
    ( ( h(bG3) != h($true) )
    | spl6_1
    | ~ spl6_7 ),
    inference(superposition,[],[f35,f63]) ).

tff(f376,plain,
    ( spl6_1
    | ~ spl6_7
    | ~ spl6_9 ),
    inference(avatar_contradiction_clause,[],[f375]) ).

tff(f375,plain,
    ( $false
    | spl6_1
    | ~ spl6_7
    | ~ spl6_9 ),
    inference(trivial_inequality_removal,[],[f374]) ).

tff(f374,plain,
    ( ( h($true) != h($true) )
    | spl6_1
    | ~ spl6_7
    | ~ spl6_9 ),
    inference(forward_demodulation,[],[f196,f72]) ).

tff(f196,plain,
    ( ( h(bG3) != h($true) )
    | spl6_1
    | ~ spl6_7 ),
    inference(superposition,[],[f35,f63]) ).

tff(f368,plain,
    ( ~ spl6_9
    | ~ spl6_19 ),
    inference(avatar_contradiction_clause,[],[f367]) ).

tff(f367,plain,
    ( $false
    | ~ spl6_9
    | ~ spl6_19 ),
    inference(trivial_inequality_removal,[],[f366]) ).

tff(f366,plain,
    ( ( $true = $false )
    | ~ spl6_9
    | ~ spl6_19 ),
    inference(forward_demodulation,[],[f72,f153]) ).

tff(f360,plain,
    ( ~ spl6_16
    | spl6_8
    | ~ spl6_20 ),
    inference(avatar_split_clause,[],[f237,f158,f66,f126]) ).

tff(f237,plain,
    ( ~ f($false)
    | spl6_8
    | ~ spl6_20 ),
    inference(superposition,[],[f68,f160]) ).

tff(f354,plain,
    ( spl6_25
    | ~ spl6_14
    | spl6_22 ),
    inference(avatar_split_clause,[],[f203,f199,f93,f352]) ).

tff(f199,plain,
    ( spl6_22
  <=> ( h($true) = h($false) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_22])]) ).

tff(f203,plain,
    ( ! [X0: $o] :
        ( ( h($false) != h((X0)) )
        | ( $false = (X0) ) )
    | ~ spl6_14
    | spl6_22 ),
    inference(superposition,[],[f201,f94]) ).

tff(f201,plain,
    ( ( h($true) != h($false) )
    | spl6_22 ),
    inference(avatar_component_clause,[],[f199]) ).

tff(f248,plain,
    ( spl6_24
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f96,f93,f246]) ).

tff(f246,plain,
    ( spl6_24
  <=> ! [X0: $o,X1: $o] :
        ( ( (X0) = (X1) )
        | ( $false = (X1) )
        | ( $false = (X0) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_24])]) ).

tff(f96,plain,
    ( ! [X0: $o,X1: $o] :
        ( ( (X0) = (X1) )
        | ( $false = (X1) )
        | ( $false = (X0) ) )
    | ~ spl6_14 ),
    inference(superposition,[],[f94,f94]) ).

tff(f229,plain,
    ( spl6_23
    | spl6_5
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f115,f93,f52,f226]) ).

tff(f115,plain,
    ( ( $false = bG0 )
    | spl6_5
    | ~ spl6_14 ),
    inference(trivial_inequality_removal,[],[f99]) ).

tff(f99,plain,
    ( ( $true != $true )
    | ( $false = bG0 )
    | spl6_5
    | ~ spl6_14 ),
    inference(superposition,[],[f54,f94]) ).

tff(f54,plain,
    ( ( $true != bG0 )
    | spl6_5 ),
    inference(avatar_component_clause,[],[f52]) ).

tff(f219,plain,
    ( spl6_12
    | ~ spl6_13 ),
    inference(avatar_split_clause,[],[f213,f88,f84]) ).

tff(f217,plain,
    ( spl6_6
    | ~ spl6_7 ),
    inference(avatar_split_clause,[],[f209,f61,f57]) ).

tff(f216,plain,
    ( ~ spl6_3
    | spl6_5
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f141,f93,f52,f43]) ).

tff(f141,plain,
    ( ~ x
    | spl6_5
    | ~ spl6_14 ),
    inference(trivial_inequality_removal,[],[f140]) ).

tff(f140,plain,
    ( ( $true = $false )
    | ~ x
    | spl6_5
    | ~ spl6_14 ),
    inference(forward_demodulation,[],[f29,f115]) ).

tff(f204,plain,
    ( ~ spl6_18
    | ~ spl6_5
    | spl6_12 ),
    inference(avatar_split_clause,[],[f143,f84,f52,f145]) ).

tff(f143,plain,
    ( ~ f($true)
    | ~ spl6_5
    | spl6_12 ),
    inference(superposition,[],[f86,f53]) ).

tff(f202,plain,
    ( ~ spl6_22
    | spl6_1
    | ~ spl6_7
    | spl6_9
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f124,f93,f70,f61,f33,f199]) ).

tff(f124,plain,
    ( ( h($true) != h($false) )
    | spl6_1
    | ~ spl6_7
    | spl6_9
    | ~ spl6_14 ),
    inference(forward_demodulation,[],[f123,f112]) ).

tff(f112,plain,
    ( ( $false = bG3 )
    | spl6_9
    | ~ spl6_14 ),
    inference(trivial_inequality_removal,[],[f104]) ).

tff(f104,plain,
    ( ( $true != $true )
    | ( $false = bG3 )
    | spl6_9
    | ~ spl6_14 ),
    inference(superposition,[],[f71,f94]) ).

tff(f71,plain,
    ( ( $true != bG3 )
    | spl6_9 ),
    inference(avatar_component_clause,[],[f70]) ).

tff(f192,plain,
    ( ~ spl6_7
    | ~ spl6_15 ),
    inference(avatar_contradiction_clause,[],[f191]) ).

tff(f191,plain,
    ( $false
    | ~ spl6_7
    | ~ spl6_15 ),
    inference(trivial_inequality_removal,[],[f190]) ).

tff(f190,plain,
    ( ( $true = $false )
    | ~ spl6_7
    | ~ spl6_15 ),
    inference(forward_demodulation,[],[f63,f119]) ).

tff(f188,plain,
    ( ~ spl6_13
    | spl6_18
    | ~ spl6_5 ),
    inference(avatar_split_clause,[],[f180,f52,f145,f88]) ).

tff(f180,plain,
    ( f($true)
    | ( $true != bG1 )
    | ~ spl6_5 ),
    inference(forward_demodulation,[],[f28,f53]) ).

tff(f181,plain,
    ( spl6_10
    | ~ spl6_11 ),
    inference(avatar_split_clause,[],[f179,f79,f75]) ).

tff(f179,plain,
    ( f(bG1)
    | ~ spl6_11 ),
    inference(trivial_inequality_removal,[],[f178]) ).

tff(f178,plain,
    ( ( $true != $true )
    | f(bG1)
    | ~ spl6_11 ),
    inference(forward_demodulation,[],[f26,f81]) ).

tff(f26,plain,
    ( f(bG1)
    | ( $true != bG2 ) ),
    inference(cnf_transformation,[],[f16]) ).

tff(f16,plain,
    ( ( f(bG1)
      | ( $true != bG2 ) )
    & ( ( $true = bG2 )
      | ~ f(bG1) ) ),
    inference(nnf_transformation,[],[f7]) ).

tff(f7,plain,
    ( f(bG1)
  <=> ( $true = bG2 ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG2])]) ).

tff(f177,plain,
    ( spl6_21
    | spl6_13
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f114,f93,f88,f174]) ).

tff(f114,plain,
    ( ( $false = bG1 )
    | spl6_13
    | ~ spl6_14 ),
    inference(trivial_inequality_removal,[],[f100]) ).

tff(f100,plain,
    ( ( $true != $true )
    | ( $false = bG1 )
    | spl6_13
    | ~ spl6_14 ),
    inference(superposition,[],[f89,f94]) ).

tff(f89,plain,
    ( ( $true != bG1 )
    | spl6_13 ),
    inference(avatar_component_clause,[],[f88]) ).

tff(f172,plain,
    ( ~ spl6_9
    | spl6_18
    | ~ spl6_11 ),
    inference(avatar_split_clause,[],[f169,f79,f145,f70]) ).

tff(f169,plain,
    ( f($true)
    | ( $true != bG3 )
    | ~ spl6_11 ),
    inference(forward_demodulation,[],[f24,f81]) ).

tff(f167,plain,
    ( spl6_18
    | ~ spl6_8
    | ~ spl6_11 ),
    inference(avatar_split_clause,[],[f166,f79,f66,f145]) ).

tff(f166,plain,
    ( f($true)
    | ~ spl6_8
    | ~ spl6_11 ),
    inference(forward_demodulation,[],[f67,f81]) ).

tff(f67,plain,
    ( f(bG2)
    | ~ spl6_8 ),
    inference(avatar_component_clause,[],[f66]) ).

tff(f165,plain,
    ( spl6_8
    | ~ spl6_9 ),
    inference(avatar_split_clause,[],[f163,f70,f66]) ).

tff(f163,plain,
    ( f(bG2)
    | ~ spl6_9 ),
    inference(trivial_inequality_removal,[],[f162]) ).

tff(f162,plain,
    ( ( $true != $true )
    | f(bG2)
    | ~ spl6_9 ),
    inference(forward_demodulation,[],[f24,f72]) ).

tff(f161,plain,
    ( spl6_20
    | spl6_11
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f113,f93,f79,f158]) ).

tff(f113,plain,
    ( ( $false = bG2 )
    | spl6_11
    | ~ spl6_14 ),
    inference(trivial_inequality_removal,[],[f102]) ).

tff(f102,plain,
    ( ( $true != $true )
    | ( $false = bG2 )
    | spl6_11
    | ~ spl6_14 ),
    inference(superposition,[],[f80,f94]) ).

tff(f80,plain,
    ( ( $true != bG2 )
    | spl6_11 ),
    inference(avatar_component_clause,[],[f79]) ).

tff(f156,plain,
    ( ~ spl6_9
    | spl6_16
    | spl6_11
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f155,f93,f79,f126,f70]) ).

tff(f155,plain,
    ( f($false)
    | ( $true != bG3 )
    | spl6_11
    | ~ spl6_14 ),
    inference(forward_demodulation,[],[f24,f113]) ).

tff(f154,plain,
    ( spl6_19
    | spl6_9
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f112,f93,f70,f151]) ).

tff(f148,plain,
    ( ~ spl6_18
    | ~ spl6_4
    | spl6_6 ),
    inference(avatar_split_clause,[],[f138,f57,f47,f145]) ).

tff(f138,plain,
    ( ~ f($true)
    | ~ spl6_4
    | spl6_6 ),
    inference(superposition,[],[f59,f49]) ).

tff(f142,plain,
    ( ~ spl6_3
    | spl6_5
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f141,f93,f52,f43]) ).

tff(f139,plain,
    ( ~ spl6_4
    | spl6_3 ),
    inference(avatar_split_clause,[],[f22,f43,f47]) ).

tff(f22,plain,
    ( x
    | ( $true != bG4 ) ),
    inference(cnf_transformation,[],[f14]) ).

tff(f14,plain,
    ( ( x
      | ( $true != bG4 ) )
    & ( ( $true = bG4 )
      | ~ x ) ),
    inference(nnf_transformation,[],[f9]) ).

tff(f9,plain,
    ( x
  <=> ( $true = bG4 ) ),
    introduced(fool_formula_definition,[new_symbols(definition,[bG4])]) ).

tff(f136,plain,
    ( spl6_17
    | spl6_4
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f111,f93,f47,f133]) ).

tff(f111,plain,
    ( ( $false = bG4 )
    | spl6_4
    | ~ spl6_14 ),
    inference(trivial_inequality_removal,[],[f106]) ).

tff(f106,plain,
    ( ( $true != $true )
    | ( $false = bG4 )
    | spl6_4
    | ~ spl6_14 ),
    inference(superposition,[],[f48,f94]) ).

tff(f48,plain,
    ( ( $true != bG4 )
    | spl6_4 ),
    inference(avatar_component_clause,[],[f47]) ).

tff(f129,plain,
    ( ~ spl6_7
    | spl6_16
    | spl6_4
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f122,f93,f47,f126,f61]) ).

tff(f122,plain,
    ( f($false)
    | ( $true != bG5 )
    | spl6_4
    | ~ spl6_14 ),
    inference(forward_demodulation,[],[f20,f111]) ).

tff(f120,plain,
    ( spl6_15
    | spl6_7
    | ~ spl6_14 ),
    inference(avatar_split_clause,[],[f110,f93,f61,f117]) ).

tff(f110,plain,
    ( ( $false = bG5 )
    | spl6_7
    | ~ spl6_14 ),
    inference(trivial_inequality_removal,[],[f107]) ).

tff(f107,plain,
    ( ( $true != $true )
    | ( $false = bG5 )
    | spl6_7
    | ~ spl6_14 ),
    inference(superposition,[],[f62,f94]) ).

tff(f62,plain,
    ( ( $true != bG5 )
    | spl6_7 ),
    inference(avatar_component_clause,[],[f61]) ).

tff(f95,plain,
    spl6_14,
    inference(avatar_split_clause,[],[f4,f93]) ).

tff(f4,plain,
    ! [X0: $o] :
      ( ( $true = (X0) )
      | ( $false = (X0) ) ),
    introduced(fool_axiom,[]) ).

tff(f91,plain,
    ( ~ spl6_12
    | spl6_13 ),
    inference(avatar_split_clause,[],[f27,f88,f84]) ).

tff(f27,plain,
    ( ( $true = bG1 )
    | ~ f(bG0) ),
    inference(cnf_transformation,[],[f17]) ).

tff(f82,plain,
    ( ~ spl6_10
    | spl6_11 ),
    inference(avatar_split_clause,[],[f25,f79,f75]) ).

tff(f25,plain,
    ( ( $true = bG2 )
    | ~ f(bG1) ),
    inference(cnf_transformation,[],[f16]) ).

tff(f73,plain,
    ( ~ spl6_8
    | spl6_9 ),
    inference(avatar_split_clause,[],[f23,f70,f66]) ).

tff(f23,plain,
    ( ( $true = bG3 )
    | ~ f(bG2) ),
    inference(cnf_transformation,[],[f15]) ).

tff(f64,plain,
    ( ~ spl6_6
    | spl6_7 ),
    inference(avatar_split_clause,[],[f19,f61,f57]) ).

tff(f19,plain,
    ( ( $true = bG5 )
    | ~ f(bG4) ),
    inference(cnf_transformation,[],[f13]) ).

tff(f55,plain,
    ( ~ spl6_5
    | spl6_3 ),
    inference(avatar_split_clause,[],[f30,f43,f52]) ).

tff(f30,plain,
    ( x
    | ( $true != bG0 ) ),
    inference(cnf_transformation,[],[f18]) ).

tff(f50,plain,
    ( ~ spl6_3
    | spl6_4 ),
    inference(avatar_split_clause,[],[f21,f47,f43]) ).

tff(f21,plain,
    ( ( $true = bG4 )
    | ~ x ),
    inference(cnf_transformation,[],[f14]) ).

tff(f41,plain,
    ~ spl6_2,
    inference(avatar_split_clause,[],[f3,f38]) ).

tff(f38,plain,
    ( spl6_2
  <=> ( $true = $false ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).

tff(f3,plain,
    $true != $false,
    introduced(fool_axiom,[]) ).

tff(f36,plain,
    ~ spl6_1,
    inference(avatar_split_clause,[],[f31,f33]) ).

tff(f31,plain,
    h(bG3) != h(bG5),
    inference(cnf_transformation,[],[f12]) ).

tff(f12,plain,
    h(bG3) != h(bG5),
    inference(flattening,[],[f11]) ).

tff(f11,plain,
    ( ~ h(bG3) = h(bG5) ),
    inference(fool_elimination,[],[f2,f10,f9,f8,f7,f6,f5]) ).

tff(f2,negated_conjecture,
    ( ~ h(f(f(f(x)))) = h(f(x)) ),
    inference(negated_conjecture,[],[f1]) ).

tff(f1,conjecture,
    h(f(f(f(x)))) = h(f(x)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',2) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11  % Problem    : SYO040_8 : TPTP v8.2.0. Released v8.0.0.
% 0.10/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.12/0.34  % Computer : n027.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Mon May 20 10:38:08 EDT 2024
% 0.12/0.34  % CPUTime    : 
% 0.12/0.34  % (18742)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.36  % (18747)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)
% 0.12/0.36  % (18745)WARNING: value z3 for option sas not known
% 0.12/0.36  % (18748)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  % (18749)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)
% 0.12/0.36  % (18746)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.36  % (18744)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.36  % (18743)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.36  % (18745)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.36  Detected minimum model sizes of [1,1]
% 0.12/0.36  Detected maximum model sizes of [max,8]
% 0.12/0.36  TRYING [1,1]
% 0.12/0.36  TRYING [1,2]
% 0.12/0.36  TRYING [1]
% 0.12/0.36  TRYING [2,2]
% 0.12/0.36  TRYING [2]
% 0.12/0.36  TRYING [3,2]
% 0.12/0.36  TRYING [3]
% 0.12/0.36  TRYING [2,3]
% 0.12/0.36  TRYING [3,3]
% 0.12/0.36  TRYING [2,4]
% 0.12/0.36  TRYING [4]
% 0.12/0.36  TRYING [3,4]
% 0.12/0.36  TRYING [2,5]
% 0.12/0.36  TRYING [4,2]
% 0.12/0.36  TRYING [3,5]
% 0.12/0.36  TRYING [5]
% 0.12/0.36  TRYING [2,6]
% 0.12/0.36  TRYING [4,3]
% 0.12/0.37  TRYING [3,6]
% 0.12/0.37  TRYING [2,7]
% 0.12/0.37  TRYING [4,4]
% 0.12/0.37  TRYING [3,7]
% 0.12/0.37  TRYING [6]
% 0.12/0.37  TRYING [2,8]
% 0.12/0.37  TRYING [4,5]
% 0.12/0.37  TRYING [3,8]
% 0.12/0.37  TRYING [4,6]
% 0.12/0.37  TRYING [4,7]
% 0.12/0.37  TRYING [4,8]
% 0.12/0.37  Cannot enumerate next child to try in an incomplete setup
% 0.12/0.37  % (18746)Refutation not found, incomplete strategy% (18746)------------------------------
% 0.12/0.37  % (18746)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.37  % (18746)Termination reason: Refutation not found, incomplete strategy
% 0.12/0.37  
% 0.12/0.37  % (18746)Memory used [KB]: 737
% 0.12/0.37  % (18746)Time elapsed: 0.016 s
% 0.12/0.37  % (18746)Instructions burned: 25 (million)
% 0.12/0.37  TRYING [7]
% 0.12/0.37  % (18746)------------------------------
% 0.12/0.37  % (18746)------------------------------
% 0.12/0.37  % (18747)First to succeed.
% 0.12/0.38  % (18747)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-18742"
% 0.12/0.38  % (18747)Refutation found. Thanks to Tanya!
% 0.12/0.38  % SZS status Theorem for theBenchmark
% 0.12/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.12/0.38  % (18747)------------------------------
% 0.12/0.38  % (18747)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.12/0.38  % (18747)Termination reason: Refutation
% 0.12/0.38  
% 0.12/0.38  % (18747)Memory used [KB]: 904
% 0.12/0.38  % (18747)Time elapsed: 0.022 s
% 0.12/0.38  % (18747)Instructions burned: 33 (million)
% 0.12/0.38  % (18742)Success in time 0.036 s
%------------------------------------------------------------------------------