TSTP Solution File: SYO664-1 by SnakeForV---1.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : SnakeForV---1.0
% Problem  : SYO664-1 : TPTP v8.1.0. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s

% Computer : n025.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 19:48:53 EDT 2022

% Result   : Unsatisfiable 0.20s 0.52s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   22
% Syntax   : Number of formulae    :  105 (   3 unt;   0 def)
%            Number of atoms       :  519 (   0 equ)
%            Maximal formula atoms :   15 (   4 avg)
%            Number of connectives :  846 ( 432   ~; 402   |;   0   &)
%                                         (  12 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   20 (   6 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of predicates  :   16 (  15 usr;  13 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-1 aty)
%            Number of variables   :   84 (  84   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f179,plain,
    $false,
    inference(avatar_sat_refutation,[],[f23,f32,f38,f55,f89,f97,f101,f107,f117,f146,f156,f163,f171,f178]) ).

fof(f178,plain,
    ( ~ spl0_3
    | ~ spl0_7
    | ~ spl0_11
    | ~ spl0_12 ),
    inference(avatar_contradiction_clause,[],[f177]) ).

fof(f177,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_7
    | ~ spl0_11
    | ~ spl0_12 ),
    inference(subsumption_resolution,[],[f176,f54]) ).

fof(f54,plain,
    ( 'E'(s('0'),f(suc(suc(z))))
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f52]) ).

fof(f52,plain,
    ( spl0_7
  <=> 'E'(s('0'),f(suc(suc(z)))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f176,plain,
    ( ~ 'E'(s('0'),f(suc(suc(z))))
    | ~ spl0_3
    | ~ spl0_7
    | ~ spl0_11
    | ~ spl0_12 ),
    inference(subsumption_resolution,[],[f175,f31]) ).

fof(f31,plain,
    ( 'E'(s('0'),f(suc(z)))
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f29]) ).

fof(f29,plain,
    ( spl0_3
  <=> 'E'(s('0'),f(suc(z))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f175,plain,
    ( ~ 'E'(s('0'),f(suc(z)))
    | ~ 'E'(s('0'),f(suc(suc(z))))
    | ~ spl0_3
    | ~ spl0_7
    | ~ spl0_11
    | ~ spl0_12 ),
    inference(resolution,[],[f174,f88]) ).

fof(f88,plain,
    ( iLEQ(suc(suc(z)),suc(suc(z)))
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f86]) ).

fof(f86,plain,
    ( spl0_12
  <=> iLEQ(suc(suc(z)),suc(suc(z))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f174,plain,
    ( ! [X0] :
        ( ~ iLEQ(suc(X0),suc(suc(z)))
        | ~ 'E'(s('0'),f(X0))
        | ~ 'E'(s('0'),f(suc(X0))) )
    | ~ spl0_3
    | ~ spl0_7
    | ~ spl0_11
    | ~ spl0_12 ),
    inference(subsumption_resolution,[],[f173,f31]) ).

fof(f173,plain,
    ( ! [X0] :
        ( ~ iLEQ(suc(X0),suc(suc(z)))
        | ~ 'E'(s('0'),f(suc(z)))
        | ~ 'E'(s('0'),f(X0))
        | ~ 'E'(s('0'),f(suc(X0))) )
    | ~ spl0_7
    | ~ spl0_11
    | ~ spl0_12 ),
    inference(subsumption_resolution,[],[f172,f54]) ).

fof(f172,plain,
    ( ! [X0] :
        ( ~ iLEQ(suc(X0),suc(suc(z)))
        | ~ 'E'(s('0'),f(suc(X0)))
        | ~ 'E'(s('0'),f(suc(suc(z))))
        | ~ 'E'(s('0'),f(suc(z)))
        | ~ 'E'(s('0'),f(X0)) )
    | ~ spl0_11
    | ~ spl0_12 ),
    inference(resolution,[],[f83,f88]) ).

fof(f83,plain,
    ( ! [X3,X1] :
        ( ~ iLEQ(suc(X1),suc(suc(z)))
        | ~ 'E'(s('0'),f(X1))
        | ~ 'E'(s('0'),f(suc(X3)))
        | ~ 'E'(s('0'),f(X3))
        | ~ 'E'(s('0'),f(suc(X1)))
        | ~ iLEQ(suc(X3),suc(X1)) )
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f82]) ).

fof(f82,plain,
    ( spl0_11
  <=> ! [X1,X3] :
        ( ~ 'E'(s('0'),f(X1))
        | ~ 'E'(s('0'),f(X3))
        | ~ 'E'(s('0'),f(suc(X1)))
        | ~ iLEQ(suc(X1),suc(suc(z)))
        | ~ 'E'(s('0'),f(suc(X3)))
        | ~ iLEQ(suc(X3),suc(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f171,plain,
    ( spl0_11
    | spl0_10
    | ~ spl0_3
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f170,f52,f29,f79,f82]) ).

fof(f79,plain,
    ( spl0_10
  <=> ! [X2,X0] :
        ( ~ iLEQ(suc(X2),suc(X0))
        | ~ 'E'(s('0'),f(X2))
        | ~ 'E'(s('0'),f(X0))
        | ~ iLEQ(suc(suc(z)),suc(X2))
        | ~ 'E'(s('0'),f(suc(X0)))
        | ~ 'E'(s('0'),f(suc(X2))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f170,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ 'E'(s('0'),f(suc(X2)))
        | ~ 'E'(s('0'),f(suc(X0)))
        | ~ iLEQ(suc(X1),suc(suc(z)))
        | ~ iLEQ(suc(suc(z)),suc(X2))
        | ~ 'E'(s('0'),f(X1))
        | ~ 'E'(s('0'),f(X3))
        | ~ 'E'(s('0'),f(X2))
        | ~ 'E'(s('0'),f(suc(X3)))
        | ~ iLEQ(suc(X3),suc(X1))
        | ~ 'E'(s('0'),f(X0))
        | ~ iLEQ(suc(X2),suc(X0))
        | ~ 'E'(s('0'),f(suc(X1))) )
    | ~ spl0_3
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f168,f31]) ).

fof(f168,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ 'E'(s('0'),f(X0))
        | ~ 'E'(s('0'),f(suc(X3)))
        | ~ iLEQ(suc(suc(z)),suc(X2))
        | ~ 'E'(s('0'),f(X3))
        | ~ 'E'(s('0'),f(X2))
        | ~ 'E'(s('0'),f(suc(X1)))
        | ~ 'E'(s('0'),f(X1))
        | ~ 'E'(s('0'),f(suc(X2)))
        | ~ iLEQ(suc(X3),suc(X1))
        | ~ iLEQ(suc(X2),suc(X0))
        | ~ iLEQ(suc(X1),suc(suc(z)))
        | ~ 'E'(s('0'),f(suc(z)))
        | ~ 'E'(s('0'),f(suc(X0))) )
    | ~ spl0_7 ),
    inference(resolution,[],[f54,f1]) ).

fof(f1,axiom,
    ! [X2,X3,X0,X1,X4] :
      ( ~ 'E'(s('0'),f(suc(X4)))
      | ~ 'E'(s('0'),f(X1))
      | ~ 'E'(s('0'),f(suc(X2)))
      | ~ 'E'(s('0'),f(suc(X0)))
      | ~ 'E'(s('0'),f(X3))
      | ~ iLEQ(suc(X4),suc(X0))
      | ~ iLEQ(suc(X0),suc(X1))
      | ~ 'E'(s('0'),f(X2))
      | ~ 'E'(s('0'),f(suc(X3)))
      | ~ 'E'(s('0'),f(suc(X1)))
      | ~ 'E'(s('0'),f(X4))
      | ~ iLEQ(suc(X2),suc(X4))
      | ~ 'E'(s('0'),f(X0))
      | ~ iLEQ(suc(X3),suc(X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_37) ).

fof(f163,plain,
    ( ~ spl0_2
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(avatar_contradiction_clause,[],[f162]) ).

fof(f162,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(subsumption_resolution,[],[f161,f49]) ).

fof(f49,plain,
    ( iLEQ(suc(z),suc(z))
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f40,f22]) ).

fof(f22,plain,
    ( 'E'(s('0'),f(z))
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f20]) ).

fof(f20,plain,
    ( spl0_2
  <=> 'E'(s('0'),f(z)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f40,plain,
    ( ~ 'E'(s('0'),f(z))
    | iLEQ(suc(z),suc(z))
    | ~ spl0_3 ),
    inference(resolution,[],[f31,f9]) ).

fof(f9,axiom,
    ! [X3] :
      ( ~ 'E'(s('0'),f(suc(X3)))
      | ~ 'E'(s('0'),f(X3))
      | iLEQ(suc(X3),suc(X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_50) ).

fof(f161,plain,
    ( ~ iLEQ(suc(z),suc(z))
    | ~ spl0_2
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(subsumption_resolution,[],[f160,f22]) ).

fof(f160,plain,
    ( ~ 'E'(s('0'),f(z))
    | ~ iLEQ(suc(z),suc(z))
    | ~ spl0_2
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(resolution,[],[f159,f31]) ).

fof(f159,plain,
    ( ! [X0] :
        ( ~ 'E'(s('0'),f(suc(X0)))
        | ~ iLEQ(suc(z),suc(X0))
        | ~ 'E'(s('0'),f(X0)) )
    | ~ spl0_2
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(subsumption_resolution,[],[f158,f22]) ).

fof(f158,plain,
    ( ! [X0] :
        ( ~ 'E'(s('0'),f(suc(X0)))
        | ~ iLEQ(suc(z),suc(X0))
        | ~ 'E'(s('0'),f(z))
        | ~ 'E'(s('0'),f(X0)) )
    | ~ spl0_2
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(subsumption_resolution,[],[f157,f49]) ).

fof(f157,plain,
    ( ! [X0] :
        ( ~ iLEQ(suc(z),suc(z))
        | ~ 'E'(s('0'),f(X0))
        | ~ iLEQ(suc(z),suc(X0))
        | ~ 'E'(s('0'),f(suc(X0)))
        | ~ 'E'(s('0'),f(z)) )
    | ~ spl0_3
    | ~ spl0_6 ),
    inference(resolution,[],[f47,f31]) ).

fof(f47,plain,
    ( ! [X2,X0] :
        ( ~ 'E'(s('0'),f(suc(X2)))
        | ~ iLEQ(suc(X2),suc(X0))
        | ~ iLEQ(suc(z),suc(X2))
        | ~ 'E'(s('0'),f(X0))
        | ~ 'E'(s('0'),f(suc(X0)))
        | ~ 'E'(s('0'),f(X2)) )
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f46]) ).

fof(f46,plain,
    ( spl0_6
  <=> ! [X2,X0] :
        ( ~ iLEQ(suc(z),suc(X2))
        | ~ iLEQ(suc(X2),suc(X0))
        | ~ 'E'(s('0'),f(X0))
        | ~ 'E'(s('0'),f(suc(X0)))
        | ~ 'E'(s('0'),f(suc(X2)))
        | ~ 'E'(s('0'),f(X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f156,plain,
    ( ~ spl0_2
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(avatar_contradiction_clause,[],[f155]) ).

fof(f155,plain,
    ( $false
    | ~ spl0_2
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(subsumption_resolution,[],[f154,f49]) ).

fof(f154,plain,
    ( ~ iLEQ(suc(z),suc(z))
    | ~ spl0_2
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(subsumption_resolution,[],[f153,f22]) ).

fof(f153,plain,
    ( ~ 'E'(s('0'),f(z))
    | ~ iLEQ(suc(z),suc(z))
    | ~ spl0_2
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(duplicate_literal_removal,[],[f152]) ).

fof(f152,plain,
    ( ~ 'E'(s('0'),f(z))
    | ~ iLEQ(suc(z),suc(z))
    | ~ iLEQ(suc(z),suc(z))
    | ~ spl0_2
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(resolution,[],[f138,f31]) ).

fof(f138,plain,
    ( ! [X1] :
        ( ~ 'E'(s('0'),f(suc(X1)))
        | ~ 'E'(s('0'),f(X1))
        | ~ iLEQ(suc(z),suc(X1))
        | ~ iLEQ(suc(X1),suc(z)) )
    | ~ spl0_2
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(subsumption_resolution,[],[f137,f22]) ).

fof(f137,plain,
    ( ! [X1] :
        ( ~ iLEQ(suc(z),suc(X1))
        | ~ 'E'(s('0'),f(z))
        | ~ 'E'(s('0'),f(X1))
        | ~ iLEQ(suc(X1),suc(z))
        | ~ 'E'(s('0'),f(suc(X1))) )
    | ~ spl0_3
    | ~ spl0_5 ),
    inference(resolution,[],[f44,f31]) ).

fof(f44,plain,
    ( ! [X3,X1] :
        ( ~ 'E'(s('0'),f(suc(X3)))
        | ~ 'E'(s('0'),f(X3))
        | ~ 'E'(s('0'),f(suc(X1)))
        | ~ iLEQ(suc(X1),suc(z))
        | ~ iLEQ(suc(X3),suc(X1))
        | ~ 'E'(s('0'),f(X1)) )
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f43]) ).

fof(f43,plain,
    ( spl0_5
  <=> ! [X1,X3] :
        ( ~ 'E'(s('0'),f(suc(X3)))
        | ~ iLEQ(suc(X1),suc(z))
        | ~ 'E'(s('0'),f(X3))
        | ~ iLEQ(suc(X3),suc(X1))
        | ~ 'E'(s('0'),f(X1))
        | ~ 'E'(s('0'),f(suc(X1))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f146,plain,
    ( ~ spl0_3
    | ~ spl0_7
    | ~ spl0_10 ),
    inference(avatar_contradiction_clause,[],[f145]) ).

fof(f145,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_7
    | ~ spl0_10 ),
    inference(subsumption_resolution,[],[f144,f31]) ).

fof(f144,plain,
    ( ~ 'E'(s('0'),f(suc(z)))
    | ~ spl0_3
    | ~ spl0_7
    | ~ spl0_10 ),
    inference(subsumption_resolution,[],[f143,f54]) ).

fof(f143,plain,
    ( ~ 'E'(s('0'),f(suc(suc(z))))
    | ~ 'E'(s('0'),f(suc(z)))
    | ~ spl0_3
    | ~ spl0_7
    | ~ spl0_10 ),
    inference(resolution,[],[f142,f76]) ).

fof(f76,plain,
    ( iLEQ(suc(suc(z)),suc(suc(z)))
    | ~ spl0_3
    | ~ spl0_7 ),
    inference(subsumption_resolution,[],[f75,f31]) ).

fof(f75,plain,
    ( iLEQ(suc(suc(z)),suc(suc(z)))
    | ~ 'E'(s('0'),f(suc(z)))
    | ~ spl0_7 ),
    inference(resolution,[],[f54,f9]) ).

fof(f142,plain,
    ( ! [X0] :
        ( ~ iLEQ(suc(suc(z)),suc(X0))
        | ~ 'E'(s('0'),f(X0))
        | ~ 'E'(s('0'),f(suc(X0))) )
    | ~ spl0_3
    | ~ spl0_7
    | ~ spl0_10 ),
    inference(subsumption_resolution,[],[f141,f31]) ).

fof(f141,plain,
    ( ! [X0] :
        ( ~ 'E'(s('0'),f(suc(X0)))
        | ~ 'E'(s('0'),f(X0))
        | ~ iLEQ(suc(suc(z)),suc(X0))
        | ~ 'E'(s('0'),f(suc(z))) )
    | ~ spl0_3
    | ~ spl0_7
    | ~ spl0_10 ),
    inference(subsumption_resolution,[],[f140,f54]) ).

fof(f140,plain,
    ( ! [X0] :
        ( ~ 'E'(s('0'),f(suc(suc(z))))
        | ~ 'E'(s('0'),f(suc(X0)))
        | ~ 'E'(s('0'),f(suc(z)))
        | ~ 'E'(s('0'),f(X0))
        | ~ iLEQ(suc(suc(z)),suc(X0)) )
    | ~ spl0_3
    | ~ spl0_7
    | ~ spl0_10 ),
    inference(resolution,[],[f80,f76]) ).

fof(f80,plain,
    ( ! [X2,X0] :
        ( ~ iLEQ(suc(suc(z)),suc(X2))
        | ~ 'E'(s('0'),f(X2))
        | ~ 'E'(s('0'),f(suc(X2)))
        | ~ 'E'(s('0'),f(suc(X0)))
        | ~ 'E'(s('0'),f(X0))
        | ~ iLEQ(suc(X2),suc(X0)) )
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f79]) ).

fof(f117,plain,
    ( spl0_5
    | spl0_6
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(avatar_split_clause,[],[f116,f29,f20,f46,f43]) ).

fof(f116,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ iLEQ(suc(X2),suc(X0))
        | ~ 'E'(s('0'),f(X0))
        | ~ iLEQ(suc(X1),suc(z))
        | ~ iLEQ(suc(z),suc(X2))
        | ~ iLEQ(suc(X3),suc(X1))
        | ~ 'E'(s('0'),f(suc(X2)))
        | ~ 'E'(s('0'),f(X2))
        | ~ 'E'(s('0'),f(suc(X3)))
        | ~ 'E'(s('0'),f(suc(X1)))
        | ~ 'E'(s('0'),f(X3))
        | ~ 'E'(s('0'),f(suc(X0)))
        | ~ 'E'(s('0'),f(X1)) )
    | ~ spl0_2
    | ~ spl0_3 ),
    inference(subsumption_resolution,[],[f113,f22]) ).

fof(f113,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ 'E'(s('0'),f(suc(X0)))
        | ~ iLEQ(suc(X3),suc(X1))
        | ~ iLEQ(suc(z),suc(X2))
        | ~ 'E'(s('0'),f(X1))
        | ~ 'E'(s('0'),f(suc(X1)))
        | ~ iLEQ(suc(X2),suc(X0))
        | ~ 'E'(s('0'),f(suc(X3)))
        | ~ 'E'(s('0'),f(z))
        | ~ iLEQ(suc(X1),suc(z))
        | ~ 'E'(s('0'),f(X0))
        | ~ 'E'(s('0'),f(X3))
        | ~ 'E'(s('0'),f(suc(X2)))
        | ~ 'E'(s('0'),f(X2)) )
    | ~ spl0_3 ),
    inference(resolution,[],[f31,f1]) ).

fof(f107,plain,
    ( ~ spl0_1
    | ~ spl0_4
    | ~ spl0_9 ),
    inference(avatar_contradiction_clause,[],[f106]) ).

fof(f106,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_9 ),
    inference(subsumption_resolution,[],[f105,f18]) ).

fof(f18,plain,
    ( 'E'('0',f(z))
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f16]) ).

fof(f16,plain,
    ( spl0_1
  <=> 'E'('0',f(z)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f105,plain,
    ( ~ 'E'('0',f(z))
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_9 ),
    inference(subsumption_resolution,[],[f104,f37]) ).

fof(f37,plain,
    ( 'E'('0',f(suc(z)))
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f35]) ).

fof(f35,plain,
    ( spl0_4
  <=> 'E'('0',f(suc(z))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f104,plain,
    ( ~ 'E'('0',f(suc(z)))
    | ~ 'E'('0',f(z))
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_9 ),
    inference(subsumption_resolution,[],[f103,f57]) ).

fof(f57,plain,
    ( iLEQ(suc(z),suc(z))
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(subsumption_resolution,[],[f56,f18]) ).

fof(f56,plain,
    ( iLEQ(suc(z),suc(z))
    | ~ 'E'('0',f(z))
    | ~ spl0_4 ),
    inference(resolution,[],[f37,f6]) ).

fof(f6,axiom,
    ! [X8] :
      ( ~ 'E'('0',f(suc(X8)))
      | iLEQ(suc(X8),suc(X8))
      | ~ 'E'('0',f(X8)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_6) ).

fof(f103,plain,
    ( ~ iLEQ(suc(z),suc(z))
    | ~ 'E'('0',f(z))
    | ~ 'E'('0',f(suc(z)))
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_9 ),
    inference(duplicate_literal_removal,[],[f102]) ).

fof(f102,plain,
    ( ~ 'E'('0',f(z))
    | ~ 'E'('0',f(suc(z)))
    | ~ 'E'('0',f(z))
    | ~ iLEQ(suc(z),suc(z))
    | ~ 'E'('0',f(suc(z)))
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_9 ),
    inference(resolution,[],[f67,f57]) ).

fof(f67,plain,
    ( ! [X2,X1] :
        ( ~ iLEQ(suc(X2),suc(X1))
        | ~ 'E'('0',f(suc(X1)))
        | ~ 'E'('0',f(X2))
        | ~ 'E'('0',f(X1))
        | ~ iLEQ(suc(X1),suc(z))
        | ~ 'E'('0',f(suc(X2))) )
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f66]) ).

fof(f66,plain,
    ( spl0_9
  <=> ! [X2,X1] :
        ( ~ 'E'('0',f(suc(X1)))
        | ~ 'E'('0',f(X2))
        | ~ iLEQ(suc(X2),suc(X1))
        | ~ 'E'('0',f(suc(X2)))
        | ~ 'E'('0',f(X1))
        | ~ iLEQ(suc(X1),suc(z)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f101,plain,
    ( ~ spl0_1
    | ~ spl0_4
    | ~ spl0_8 ),
    inference(avatar_contradiction_clause,[],[f100]) ).

fof(f100,plain,
    ( $false
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_8 ),
    inference(subsumption_resolution,[],[f99,f37]) ).

fof(f99,plain,
    ( ~ 'E'('0',f(suc(z)))
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_8 ),
    inference(subsumption_resolution,[],[f98,f18]) ).

fof(f98,plain,
    ( ~ 'E'('0',f(z))
    | ~ 'E'('0',f(suc(z)))
    | ~ spl0_1
    | ~ spl0_4
    | ~ spl0_8 ),
    inference(resolution,[],[f64,f57]) ).

fof(f64,plain,
    ( ! [X0] :
        ( ~ iLEQ(suc(z),suc(X0))
        | ~ 'E'('0',f(X0))
        | ~ 'E'('0',f(suc(X0))) )
    | ~ spl0_8 ),
    inference(avatar_component_clause,[],[f63]) ).

fof(f63,plain,
    ( spl0_8
  <=> ! [X0] :
        ( ~ 'E'('0',f(suc(X0)))
        | ~ iLEQ(suc(z),suc(X0))
        | ~ 'E'('0',f(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f97,plain,
    ( spl0_8
    | spl0_9
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(avatar_split_clause,[],[f96,f35,f16,f66,f63]) ).

fof(f96,plain,
    ( ! [X2,X0,X1] :
        ( ~ iLEQ(suc(X1),suc(z))
        | ~ 'E'('0',f(X2))
        | ~ iLEQ(suc(X2),suc(X1))
        | ~ 'E'('0',f(X0))
        | ~ iLEQ(suc(z),suc(X0))
        | ~ 'E'('0',f(suc(X2)))
        | ~ 'E'('0',f(suc(X1)))
        | ~ 'E'('0',f(X1))
        | ~ 'E'('0',f(suc(X0))) )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(subsumption_resolution,[],[f95,f18]) ).

fof(f95,plain,
    ( ! [X2,X0,X1] :
        ( ~ 'E'('0',f(X1))
        | ~ 'E'('0',f(suc(X2)))
        | ~ iLEQ(suc(z),suc(X0))
        | ~ 'E'('0',f(z))
        | ~ 'E'('0',f(X0))
        | ~ 'E'('0',f(suc(X1)))
        | ~ iLEQ(suc(X1),suc(z))
        | ~ iLEQ(suc(X2),suc(X1))
        | ~ 'E'('0',f(X2))
        | ~ 'E'('0',f(suc(X0))) )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(subsumption_resolution,[],[f94,f37]) ).

fof(f94,plain,
    ( ! [X2,X0,X1] :
        ( ~ 'E'('0',f(suc(z)))
        | ~ iLEQ(suc(X1),suc(z))
        | ~ 'E'('0',f(suc(X1)))
        | ~ iLEQ(suc(z),suc(X0))
        | ~ 'E'('0',f(suc(X0)))
        | ~ 'E'('0',f(X0))
        | ~ 'E'('0',f(X2))
        | ~ 'E'('0',f(z))
        | ~ iLEQ(suc(X2),suc(X1))
        | ~ 'E'('0',f(X1))
        | ~ 'E'('0',f(suc(X2))) )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(duplicate_literal_removal,[],[f93]) ).

fof(f93,plain,
    ( ! [X2,X0,X1] :
        ( ~ 'E'('0',f(suc(X0)))
        | ~ 'E'('0',f(z))
        | ~ 'E'('0',f(X0))
        | ~ iLEQ(suc(z),suc(X0))
        | ~ 'E'('0',f(X2))
        | ~ iLEQ(suc(X2),suc(X1))
        | ~ 'E'('0',f(suc(X1)))
        | ~ 'E'('0',f(z))
        | ~ 'E'('0',f(suc(z)))
        | ~ 'E'('0',f(suc(z)))
        | ~ 'E'('0',f(X1))
        | ~ iLEQ(suc(X1),suc(z))
        | ~ 'E'('0',f(suc(X2))) )
    | ~ spl0_1
    | ~ spl0_4 ),
    inference(resolution,[],[f57,f4]) ).

fof(f4,axiom,
    ! [X10,X8,X6,X9,X7] :
      ( ~ iLEQ(suc(X9),suc(X6))
      | ~ 'E'('0',f(suc(X6)))
      | ~ 'E'('0',f(X9))
      | ~ 'E'('0',f(X10))
      | ~ iLEQ(suc(X7),suc(X9))
      | ~ 'E'('0',f(X6))
      | ~ 'E'('0',f(X8))
      | ~ 'E'('0',f(X7))
      | ~ 'E'('0',f(suc(X8)))
      | ~ 'E'('0',f(suc(X7)))
      | ~ 'E'('0',f(suc(X10)))
      | ~ iLEQ(suc(X6),suc(X10))
      | ~ iLEQ(suc(X8),suc(X7))
      | ~ 'E'('0',f(suc(X9))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_66) ).

fof(f89,plain,
    ( ~ spl0_3
    | spl0_12
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f75,f52,f86,f29]) ).

fof(f55,plain,
    ( spl0_7
    | spl0_4 ),
    inference(avatar_split_clause,[],[f50,f35,f52]) ).

fof(f50,plain,
    ( 'E'('0',f(suc(z)))
    | 'E'(s('0'),f(suc(suc(z)))) ),
    inference(resolution,[],[f26,f2]) ).

fof(f2,axiom,
    ~ 'LE'(f(z),'0'),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_70) ).

fof(f26,plain,
    ! [X1] :
      ( 'LE'(f(X1),'0')
      | 'E'('0',f(suc(X1)))
      | 'E'(s('0'),f(suc(suc(X1)))) ),
    inference(resolution,[],[f24,f7]) ).

fof(f7,axiom,
    ! [X12] :
      ( ~ 'LE'(f(suc(X12)),s('0'))
      | 'LE'(f(X12),'0')
      | 'E'('0',f(suc(X12))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_117) ).

fof(f24,plain,
    ! [X5] :
      ( 'LE'(f(X5),s('0'))
      | 'E'(s('0'),f(suc(X5))) ),
    inference(subsumption_resolution,[],[f10,f5]) ).

fof(f5,axiom,
    ! [X11] : 'LE'(f(X11),s(s('0'))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_58) ).

fof(f10,axiom,
    ! [X5] :
      ( 'LE'(f(X5),s('0'))
      | 'E'(s('0'),f(suc(X5)))
      | ~ 'LE'(f(suc(X5)),s(s('0'))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_83) ).

fof(f38,plain,
    ( spl0_4
    | spl0_3 ),
    inference(avatar_split_clause,[],[f33,f29,f35]) ).

fof(f33,plain,
    ( 'E'(s('0'),f(suc(z)))
    | 'E'('0',f(suc(z))) ),
    inference(resolution,[],[f13,f2]) ).

fof(f13,plain,
    ! [X1] :
      ( 'LE'(f(X1),'0')
      | 'E'(s('0'),f(suc(X1)))
      | 'E'('0',f(suc(X1))) ),
    inference(resolution,[],[f11,f7]) ).

fof(f11,plain,
    ! [X5] :
      ( 'LE'(f(X5),s('0'))
      | 'E'(s('0'),f(X5)) ),
    inference(subsumption_resolution,[],[f3,f5]) ).

fof(f3,axiom,
    ! [X5] :
      ( 'E'(s('0'),f(X5))
      | ~ 'LE'(f(X5),s(s('0')))
      | 'LE'(f(X5),s('0')) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_20) ).

fof(f32,plain,
    ( spl0_3
    | spl0_1 ),
    inference(avatar_split_clause,[],[f27,f16,f29]) ).

fof(f27,plain,
    ( 'E'('0',f(z))
    | 'E'(s('0'),f(suc(z))) ),
    inference(resolution,[],[f25,f2]) ).

fof(f25,plain,
    ! [X0] :
      ( 'LE'(f(X0),'0')
      | 'E'('0',f(X0))
      | 'E'(s('0'),f(suc(X0))) ),
    inference(resolution,[],[f24,f8]) ).

fof(f8,axiom,
    ! [X12] :
      ( ~ 'LE'(f(X12),s('0'))
      | 'E'('0',f(X12))
      | 'LE'(f(X12),'0') ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clause_94) ).

fof(f23,plain,
    ( spl0_1
    | spl0_2 ),
    inference(avatar_split_clause,[],[f14,f20,f16]) ).

fof(f14,plain,
    ( 'E'(s('0'),f(z))
    | 'E'('0',f(z)) ),
    inference(resolution,[],[f12,f2]) ).

fof(f12,plain,
    ! [X0] :
      ( 'LE'(f(X0),'0')
      | 'E'(s('0'),f(X0))
      | 'E'('0',f(X0)) ),
    inference(resolution,[],[f11,f8]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SYO664-1 : TPTP v8.1.0. Released v7.3.0.
% 0.11/0.13  % Command    : vampire --input_syntax tptp --proof tptp --output_axiom_names on --mode portfolio --schedule snake_tptp_uns --cores 0 -t %d %s
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit   : 300
% 0.13/0.34  % WCLimit    : 300
% 0.13/0.34  % DateTime   : Tue Aug 30 23:20:00 EDT 2022
% 0.13/0.34  % CPUTime    : 
% 0.20/0.50  % (29169)lrs+1011_1:1_atotf=0.0306256:ep=RST:mep=off:nm=0:sos=all:i=3:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/3Mi)
% 0.20/0.50  % (29185)dis+10_1:1_add=large:alpa=false:anc=none:fd=off:lcm=reverse:nwc=5.0:sd=2:sgt=20:ss=included:i=46:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/46Mi)
% 0.20/0.50  % (29170)lrs+1010_1:1_bd=off:fd=off:fde=none:ins=3:sac=on:sos=on:spb=goal:to=lpo:i=51:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/51Mi)
% 0.20/0.50  % (29170)Refutation not found, incomplete strategy% (29170)------------------------------
% 0.20/0.50  % (29170)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.50  % (29170)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.50  % (29170)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.50  
% 0.20/0.50  % (29170)Memory used [KB]: 5756
% 0.20/0.50  % (29170)Time elapsed: 0.003 s
% 0.20/0.50  % (29170)Instructions burned: 1 (million)
% 0.20/0.50  % (29170)------------------------------
% 0.20/0.50  % (29170)------------------------------
% 0.20/0.51  % (29177)lrs+1_1:1_aac=none:add=large:anc=all_dependent:cond=fast:ep=RST:fsr=off:lma=on:nm=2:sos=on:sp=reverse_arity:stl=30:uhcvi=on:urr=on:i=2:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/2Mi)
% 0.20/0.51  % (29177)Refutation not found, incomplete strategy% (29177)------------------------------
% 0.20/0.51  % (29177)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (29177)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (29177)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.51  
% 0.20/0.51  % (29177)Memory used [KB]: 5756
% 0.20/0.51  % (29177)Time elapsed: 0.003 s
% 0.20/0.51  % (29177)Instructions burned: 1 (million)
% 0.20/0.51  % (29177)------------------------------
% 0.20/0.51  % (29177)------------------------------
% 0.20/0.51  % (29169)Refutation not found, incomplete strategy% (29169)------------------------------
% 0.20/0.51  % (29169)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (29169)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (29169)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.51  
% 0.20/0.51  % (29169)Memory used [KB]: 5756
% 0.20/0.51  % (29169)Time elapsed: 0.003 s
% 0.20/0.51  % (29169)Instructions burned: 1 (million)
% 0.20/0.51  % (29169)------------------------------
% 0.20/0.51  % (29169)------------------------------
% 0.20/0.51  % (29162)dis+21_1:1_av=off:fd=off:lcm=predicate:sos=on:spb=goal:urr=ec_only:i=42:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/42Mi)
% 0.20/0.51  % (29162)Refutation not found, incomplete strategy% (29162)------------------------------
% 0.20/0.51  % (29162)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (29162)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (29162)Termination reason: Refutation not found, incomplete strategy
% 0.20/0.51  
% 0.20/0.51  % (29162)Memory used [KB]: 1279
% 0.20/0.51  % (29162)Time elapsed: 0.001 s
% 0.20/0.51  % (29162)------------------------------
% 0.20/0.51  % (29162)------------------------------
% 0.20/0.51  % (29181)lrs+10_1:7_av=off:awrs=converge:awrsf=40:br=off:bsd=on:cond=on:drc=off:nwc=3.0:plsq=on:plsqc=1:s2a=on:s2agt=16:to=lpo:urr=on:i=6:si=on:rawr=on:rtra=on_0 on theBenchmark for (2999ds/6Mi)
% 0.20/0.51  % (29185)First to succeed.
% 0.20/0.51  % (29181)Instruction limit reached!
% 0.20/0.51  % (29181)------------------------------
% 0.20/0.51  % (29181)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.51  % (29181)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.51  % (29181)Termination reason: Unknown
% 0.20/0.51  % (29181)Termination phase: Saturation
% 0.20/0.51  
% 0.20/0.51  % (29181)Memory used [KB]: 1407
% 0.20/0.51  % (29181)Time elapsed: 0.004 s
% 0.20/0.51  % (29181)Instructions burned: 6 (million)
% 0.20/0.51  % (29181)------------------------------
% 0.20/0.51  % (29181)------------------------------
% 0.20/0.52  % (29185)Refutation found. Thanks to Tanya!
% 0.20/0.52  % SZS status Unsatisfiable for theBenchmark
% 0.20/0.52  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.52  % (29185)------------------------------
% 0.20/0.52  % (29185)Version: Vampire 4.7 (commit 807e37dd9 on 2022-08-23 09:55:27 +0200)
% 0.20/0.52  % (29185)Linked with Z3 4.8.13.0 f03d756e086f81f2596157241e0decfb1c982299 z3-4.8.4-5390-gf03d756e0
% 0.20/0.52  % (29185)Termination reason: Refutation
% 0.20/0.52  
% 0.20/0.52  % (29185)Memory used [KB]: 6012
% 0.20/0.52  % (29185)Time elapsed: 0.114 s
% 0.20/0.52  % (29185)Instructions burned: 8 (million)
% 0.20/0.52  % (29185)------------------------------
% 0.20/0.52  % (29185)------------------------------
% 0.20/0.52  % (29160)Success in time 0.166 s
%------------------------------------------------------------------------------