TSTP Solution File: NUM916_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : NUM916_1 : TPTP v8.1.2. Released v5.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n015.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 Apr 30 14:38:26 EDT 2024

% Result   : Theorem 0.14s 0.38s
% Output   : Refutation 0.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   47
% Syntax   : Number of formulae    :  118 (  27 unt;   2 typ;   0 def)
%            Number of atoms       :  280 (  52 equ)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives :  306 ( 142   ~; 132   |;   0   &)
%                                         (  31 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    5 (   1 avg)
%            Number arithmetic     :  410 (  74 atm; 144 fun;  28 num; 164 var)
%            Number of types       :    1 (   0 usr;   1 ari)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of predicates  :   34 (  31 usr;  32 prp; 0-2 aty)
%            Number of functors    :    6 (   2 usr;   4 con; 0-2 aty)
%            Number of variables   :  164 ( 158   !;   6   ?; 164   :)

% Comments : 
%------------------------------------------------------------------------------
tff(func_def_4,type,
    sK0: $int ).

tff(func_def_5,type,
    sK1: $int ).

tff(f452,plain,
    $false,
    inference(avatar_sat_refutation,[],[f22,f26,f30,f34,f38,f42,f48,f52,f56,f66,f70,f82,f86,f114,f137,f147,f156,f160,f164,f176,f207,f211,f230,f234,f238,f242,f247,f305,f309,f313,f449,f451]) ).

tff(f451,plain,
    ~ spl2_27,
    inference(avatar_contradiction_clause,[],[f450]) ).

tff(f450,plain,
    ( $false
    | ~ spl2_27 ),
    inference(equality_resolution,[],[f246]) ).

tff(f246,plain,
    ( ! [X0: $int] : ( sK1 != X0 )
    | ~ spl2_27 ),
    inference(avatar_component_clause,[],[f245]) ).

tff(f245,plain,
    ( spl2_27
  <=> ! [X0: $int] : ( sK1 != X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_27])]) ).

tff(f449,plain,
    ( spl2_31
    | ~ spl2_10
    | ~ spl2_11 ),
    inference(avatar_split_clause,[],[f74,f68,f64,f447]) ).

tff(f447,plain,
    ( spl2_31
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less(X1,X0)
        | ( X0 = X1 )
        | ~ $less(X2,X0)
        | $less(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_31])]) ).

tff(f64,plain,
    ( spl2_10
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,X2)
        | $less(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_10])]) ).

tff(f68,plain,
    ( spl2_11
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,X1)
        | $less(X1,X0)
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_11])]) ).

tff(f74,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( $less(X1,X0)
        | ( X0 = X1 )
        | ~ $less(X2,X0)
        | $less(X2,X1) )
    | ~ spl2_10
    | ~ spl2_11 ),
    inference(resolution,[],[f69,f65]) ).

tff(f65,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X1,X2)
        | ~ $less(X0,X1)
        | $less(X0,X2) )
    | ~ spl2_10 ),
    inference(avatar_component_clause,[],[f64]) ).

tff(f69,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less(X1,X0)
        | $less(X0,X1)
        | ( X0 = X1 ) )
    | ~ spl2_11 ),
    inference(avatar_component_clause,[],[f68]) ).

tff(f313,plain,
    ( spl2_30
    | ~ spl2_6
    | ~ spl2_14 ),
    inference(avatar_split_clause,[],[f121,f112,f40,f311]) ).

tff(f311,plain,
    ( spl2_30
  <=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_30])]) ).

tff(f40,plain,
    ( spl2_6
  <=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_6])]) ).

tff(f112,plain,
    ( spl2_14
  <=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_14])]) ).

tff(f121,plain,
    ( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) )
    | ~ spl2_6
    | ~ spl2_14 ),
    inference(superposition,[],[f113,f41]) ).

tff(f41,plain,
    ( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
    | ~ spl2_6 ),
    inference(avatar_component_clause,[],[f40]) ).

tff(f113,plain,
    ( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
    | ~ spl2_14 ),
    inference(avatar_component_clause,[],[f112]) ).

tff(f309,plain,
    ( spl2_29
    | ~ spl2_6
    | ~ spl2_14 ),
    inference(avatar_split_clause,[],[f116,f112,f40,f307]) ).

tff(f307,plain,
    ( spl2_29
  <=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_29])]) ).

tff(f116,plain,
    ( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) )
    | ~ spl2_6
    | ~ spl2_14 ),
    inference(superposition,[],[f113,f41]) ).

tff(f305,plain,
    ( spl2_28
    | ~ spl2_7
    | ~ spl2_10 ),
    inference(avatar_split_clause,[],[f71,f64,f46,f303]) ).

tff(f303,plain,
    ( spl2_28
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | $less(X0,$sum(X2,1))
        | $less(X2,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_28])]) ).

tff(f46,plain,
    ( spl2_7
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,X1)
        | $less(X1,$sum(X0,1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_7])]) ).

tff(f71,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | $less(X0,$sum(X2,1))
        | $less(X2,X1) )
    | ~ spl2_7
    | ~ spl2_10 ),
    inference(resolution,[],[f65,f47]) ).

tff(f47,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less(X1,$sum(X0,1))
        | $less(X0,X1) )
    | ~ spl2_7 ),
    inference(avatar_component_clause,[],[f46]) ).

tff(f247,plain,
    ( spl2_27
    | ~ spl2_9
    | ~ spl2_19 ),
    inference(avatar_split_clause,[],[f200,f162,f54,f245]) ).

tff(f54,plain,
    ( spl2_9
  <=> ! [X0: $int] : ( sK1 != $sum(sK0,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_9])]) ).

tff(f162,plain,
    ( spl2_19
  <=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_19])]) ).

tff(f200,plain,
    ( ! [X0: $int] : ( sK1 != X0 )
    | ~ spl2_9
    | ~ spl2_19 ),
    inference(superposition,[],[f55,f163]) ).

tff(f163,plain,
    ( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
    | ~ spl2_19 ),
    inference(avatar_component_clause,[],[f162]) ).

tff(f55,plain,
    ( ! [X0: $int] : ( sK1 != $sum(sK0,X0) )
    | ~ spl2_9 ),
    inference(avatar_component_clause,[],[f54]) ).

tff(f242,plain,
    ( spl2_26
    | ~ spl2_5
    | ~ spl2_14 ),
    inference(avatar_split_clause,[],[f120,f112,f36,f240]) ).

tff(f240,plain,
    ( spl2_26
  <=> ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_26])]) ).

tff(f36,plain,
    ( spl2_5
  <=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_5])]) ).

tff(f120,plain,
    ( ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) )
    | ~ spl2_5
    | ~ spl2_14 ),
    inference(superposition,[],[f113,f37]) ).

tff(f37,plain,
    ( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
    | ~ spl2_5 ),
    inference(avatar_component_clause,[],[f36]) ).

tff(f238,plain,
    ( spl2_25
    | ~ spl2_6
    | ~ spl2_13 ),
    inference(avatar_split_clause,[],[f105,f84,f40,f236]) ).

tff(f236,plain,
    ( spl2_25
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X2,X1),$sum(X1,X0))
        | ~ $less(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_25])]) ).

tff(f84,plain,
    ( spl2_13
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | $less($sum(X0,X2),$sum(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_13])]) ).

tff(f105,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X2,X1),$sum(X1,X0))
        | ~ $less(X2,X0) )
    | ~ spl2_6
    | ~ spl2_13 ),
    inference(superposition,[],[f85,f41]) ).

tff(f85,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X0,X2),$sum(X1,X2))
        | ~ $less(X0,X1) )
    | ~ spl2_13 ),
    inference(avatar_component_clause,[],[f84]) ).

tff(f234,plain,
    ( spl2_24
    | ~ spl2_6
    | ~ spl2_13 ),
    inference(avatar_split_clause,[],[f101,f84,f40,f232]) ).

tff(f232,plain,
    ( spl2_24
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X1,X0),$sum(X2,X1))
        | ~ $less(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_24])]) ).

tff(f101,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X1,X0),$sum(X2,X1))
        | ~ $less(X0,X2) )
    | ~ spl2_6
    | ~ spl2_13 ),
    inference(superposition,[],[f85,f41]) ).

tff(f230,plain,
    ( spl2_23
    | ~ spl2_6
    | ~ spl2_12 ),
    inference(avatar_split_clause,[],[f88,f80,f40,f228]) ).

tff(f228,plain,
    ( spl2_23
  <=> ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_23])]) ).

tff(f80,plain,
    ( spl2_12
  <=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_12])]) ).

tff(f88,plain,
    ( ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) )
    | ~ spl2_6
    | ~ spl2_12 ),
    inference(superposition,[],[f81,f41]) ).

tff(f81,plain,
    ( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) )
    | ~ spl2_12 ),
    inference(avatar_component_clause,[],[f80]) ).

tff(f211,plain,
    ( spl2_22
    | ~ spl2_5
    | ~ spl2_13 ),
    inference(avatar_split_clause,[],[f104,f84,f36,f209]) ).

tff(f209,plain,
    ( spl2_22
  <=> ! [X0: $int,X1: $int] :
        ( $less($sum(X1,$uminus(X0)),0)
        | ~ $less(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_22])]) ).

tff(f104,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less($sum(X1,$uminus(X0)),0)
        | ~ $less(X1,X0) )
    | ~ spl2_5
    | ~ spl2_13 ),
    inference(superposition,[],[f85,f37]) ).

tff(f207,plain,
    ( spl2_21
    | ~ spl2_5
    | ~ spl2_13 ),
    inference(avatar_split_clause,[],[f100,f84,f36,f205]) ).

tff(f205,plain,
    ( spl2_21
  <=> ! [X0: $int,X1: $int] :
        ( $less(0,$sum(X1,$uminus(X0)))
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_21])]) ).

tff(f100,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less(0,$sum(X1,$uminus(X0)))
        | ~ $less(X0,X1) )
    | ~ spl2_5
    | ~ spl2_13 ),
    inference(superposition,[],[f85,f37]) ).

tff(f176,plain,
    ( ~ spl2_20
    | ~ spl2_5
    | ~ spl2_9 ),
    inference(avatar_split_clause,[],[f108,f54,f36,f173]) ).

tff(f173,plain,
    ( spl2_20
  <=> ( 0 = sK1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_20])]) ).

tff(f108,plain,
    ( ( 0 != sK1 )
    | ~ spl2_5
    | ~ spl2_9 ),
    inference(superposition,[],[f55,f37]) ).

tff(f164,plain,
    ( spl2_19
    | ~ spl2_5
    | ~ spl2_14 ),
    inference(avatar_split_clause,[],[f131,f112,f36,f162]) ).

tff(f131,plain,
    ( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
    | ~ spl2_5
    | ~ spl2_14 ),
    inference(evaluation,[],[f115]) ).

tff(f115,plain,
    ( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
    | ~ spl2_5
    | ~ spl2_14 ),
    inference(superposition,[],[f113,f37]) ).

tff(f160,plain,
    ( spl2_18
    | ~ spl2_6
    | ~ spl2_8 ),
    inference(avatar_split_clause,[],[f61,f50,f40,f158]) ).

tff(f158,plain,
    ( spl2_18
  <=> ! [X0: $int,X1: $int] :
        ( ~ $less(X1,$sum(1,X0))
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_18])]) ).

tff(f50,plain,
    ( spl2_8
  <=> ! [X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,$sum(X0,1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_8])]) ).

tff(f61,plain,
    ( ! [X0: $int,X1: $int] :
        ( ~ $less(X1,$sum(1,X0))
        | ~ $less(X0,X1) )
    | ~ spl2_6
    | ~ spl2_8 ),
    inference(superposition,[],[f51,f41]) ).

tff(f51,plain,
    ( ! [X0: $int,X1: $int] :
        ( ~ $less(X1,$sum(X0,1))
        | ~ $less(X0,X1) )
    | ~ spl2_8 ),
    inference(avatar_component_clause,[],[f50]) ).

tff(f156,plain,
    ( spl2_17
    | ~ spl2_6
    | ~ spl2_7 ),
    inference(avatar_split_clause,[],[f58,f46,f40,f154]) ).

tff(f154,plain,
    ( spl2_17
  <=> ! [X0: $int,X1: $int] :
        ( $less(X1,$sum(1,X0))
        | $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_17])]) ).

tff(f58,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less(X1,$sum(1,X0))
        | $less(X0,X1) )
    | ~ spl2_6
    | ~ spl2_7 ),
    inference(superposition,[],[f47,f41]) ).

tff(f147,plain,
    ( spl2_16
    | ~ spl2_2
    | ~ spl2_7 ),
    inference(avatar_split_clause,[],[f57,f46,f24,f145]) ).

tff(f145,plain,
    ( spl2_16
  <=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_16])]) ).

tff(f24,plain,
    ( spl2_2
  <=> ! [X0: $int] : ~ $less(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_2])]) ).

tff(f57,plain,
    ( ! [X0: $int] : $less(X0,$sum(X0,1))
    | ~ spl2_2
    | ~ spl2_7 ),
    inference(resolution,[],[f47,f25]) ).

tff(f25,plain,
    ( ! [X0: $int] : ~ $less(X0,X0)
    | ~ spl2_2 ),
    inference(avatar_component_clause,[],[f24]) ).

tff(f137,plain,
    ( spl2_15
    | ~ spl2_1
    | ~ spl2_14 ),
    inference(avatar_split_clause,[],[f130,f112,f20,f135]) ).

tff(f135,plain,
    ( spl2_15
  <=> ! [X0: $int,X1: $int] : ( sK1 != $sum(X0,$sum(X1,sK0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_15])]) ).

tff(f20,plain,
    ( spl2_1
  <=> ! [X2: $int] : ( sK1 != $sum(X2,sK0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_1])]) ).

tff(f130,plain,
    ( ! [X0: $int,X1: $int] : ( sK1 != $sum(X0,$sum(X1,sK0)) )
    | ~ spl2_1
    | ~ spl2_14 ),
    inference(superposition,[],[f21,f113]) ).

tff(f21,plain,
    ( ! [X2: $int] : ( sK1 != $sum(X2,sK0) )
    | ~ spl2_1 ),
    inference(avatar_component_clause,[],[f20]) ).

tff(f114,plain,
    spl2_14,
    inference(avatar_split_clause,[],[f4,f112]) ).

tff(f4,plain,
    ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
    introduced(theory_axiom_136,[]) ).

tff(f86,plain,
    spl2_13,
    inference(avatar_split_clause,[],[f11,f84]) ).

tff(f11,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | $less($sum(X0,X2),$sum(X1,X2)) ),
    introduced(theory_axiom_145,[]) ).

tff(f82,plain,
    spl2_12,
    inference(avatar_split_clause,[],[f6,f80]) ).

tff(f6,plain,
    ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
    introduced(theory_axiom_139,[]) ).

tff(f70,plain,
    spl2_11,
    inference(avatar_split_clause,[],[f10,f68]) ).

tff(f10,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,X0)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_144,[]) ).

tff(f66,plain,
    spl2_10,
    inference(avatar_split_clause,[],[f9,f64]) ).

tff(f9,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,X2)
      | $less(X0,X2) ),
    introduced(theory_axiom_143,[]) ).

tff(f56,plain,
    ( spl2_9
    | ~ spl2_1
    | ~ spl2_6 ),
    inference(avatar_split_clause,[],[f43,f40,f20,f54]) ).

tff(f43,plain,
    ( ! [X0: $int] : ( sK1 != $sum(sK0,X0) )
    | ~ spl2_1
    | ~ spl2_6 ),
    inference(superposition,[],[f21,f41]) ).

tff(f52,plain,
    spl2_8,
    inference(avatar_split_clause,[],[f14,f50]) ).

tff(f14,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_161,[]) ).

tff(f48,plain,
    spl2_7,
    inference(avatar_split_clause,[],[f12,f46]) ).

tff(f12,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_147,[]) ).

tff(f42,plain,
    spl2_6,
    inference(avatar_split_clause,[],[f3,f40]) ).

tff(f3,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f38,plain,
    spl2_5,
    inference(avatar_split_clause,[],[f7,f36]) ).

tff(f7,plain,
    ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
    introduced(theory_axiom_140,[]) ).

tff(f34,plain,
    spl2_4,
    inference(avatar_split_clause,[],[f13,f32]) ).

tff(f32,plain,
    ( spl2_4
  <=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_4])]) ).

tff(f13,plain,
    ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
    introduced(theory_axiom_148,[]) ).

tff(f30,plain,
    spl2_3,
    inference(avatar_split_clause,[],[f5,f28]) ).

tff(f28,plain,
    ( spl2_3
  <=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl2_3])]) ).

tff(f5,plain,
    ! [X0: $int] : ( $sum(X0,0) = X0 ),
    introduced(theory_axiom_137,[]) ).

tff(f26,plain,
    spl2_2,
    inference(avatar_split_clause,[],[f8,f24]) ).

tff(f8,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_142,[]) ).

tff(f22,plain,
    spl2_1,
    inference(avatar_split_clause,[],[f18,f20]) ).

tff(f18,plain,
    ! [X2: $int] : ( sK1 != $sum(X2,sK0) ),
    inference(cnf_transformation,[],[f17]) ).

tff(f17,plain,
    ! [X2: $int] : ( sK1 != $sum(X2,sK0) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f15,f16]) ).

tff(f16,plain,
    ( ? [X0: $int,X1: $int] :
      ! [X2: $int] : ( $sum(X2,X0) != X1 )
   => ! [X2: $int] : ( sK1 != $sum(X2,sK0) ) ),
    introduced(choice_axiom,[]) ).

tff(f15,plain,
    ? [X0: $int,X1: $int] :
    ! [X2: $int] : ( $sum(X2,X0) != X1 ),
    inference(ennf_transformation,[],[f2]) ).

tff(f2,negated_conjecture,
    ~ ! [X0: $int,X1: $int] :
      ? [X2: $int] : ( $sum(X2,X0) = X1 ),
    inference(negated_conjecture,[],[f1]) ).

tff(f1,conjecture,
    ! [X0: $int,X1: $int] :
    ? [X2: $int] : ( $sum(X2,X0) = X1 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem    : NUM916_1 : TPTP v8.1.2. Released v5.0.0.
% 0.13/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n015.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Apr 29 23:41:47 EDT 2024
% 0.14/0.36  % CPUTime    : 
% 0.14/0.36  % (26461)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.37  % (26466)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)
% 0.14/0.37  % (26464)WARNING: value z3 for option sas not known
% 0.14/0.38  % (26462)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38  % (26465)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38  % (26464)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)
% 0.14/0.38  % (26467)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)
% 0.14/0.38  % (26462)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38  % (26462)Terminated due to inappropriate strategy.
% 0.14/0.38  % (26462)------------------------------
% 0.14/0.38  % (26462)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38  % (26462)Termination reason: Inappropriate
% 0.14/0.38  
% 0.14/0.38  % (26462)Memory used [KB]: 722
% 0.14/0.38  % (26462)Time elapsed: 0.002 s
% 0.14/0.38  % (26462)Instructions burned: 2 (million)
% 0.14/0.38  % (26462)------------------------------
% 0.14/0.38  % (26462)------------------------------
% 0.14/0.38  % (26468)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)
% 0.14/0.38  % (26463)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38  % (26465)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38  % (26465)Terminated due to inappropriate strategy.
% 0.14/0.38  % (26465)------------------------------
% 0.14/0.38  % (26465)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38  % (26465)Termination reason: Inappropriate
% 0.14/0.38  
% 0.14/0.38  % (26465)Memory used [KB]: 722
% 0.14/0.38  % (26465)Time elapsed: 0.002 s
% 0.14/0.38  % (26465)Instructions burned: 2 (million)
% 0.14/0.38  % (26465)------------------------------
% 0.14/0.38  % (26465)------------------------------
% 0.14/0.38  % (26463)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.38  % (26463)Terminated due to inappropriate strategy.
% 0.14/0.38  % (26463)------------------------------
% 0.14/0.38  % (26463)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38  % (26463)Termination reason: Inappropriate
% 0.14/0.38  
% 0.14/0.38  % (26463)Memory used [KB]: 722
% 0.14/0.38  % (26463)Time elapsed: 0.002 s
% 0.14/0.38  % (26463)Instructions burned: 2 (million)
% 0.14/0.38  % (26463)------------------------------
% 0.14/0.38  % (26463)------------------------------
% 0.14/0.38  % (26466)First to succeed.
% 0.14/0.38  % (26466)Refutation found. Thanks to Tanya!
% 0.14/0.38  % SZS status Theorem for theBenchmark
% 0.14/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38  % (26466)------------------------------
% 0.14/0.38  % (26466)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.38  % (26466)Termination reason: Refutation
% 0.14/0.38  
% 0.14/0.38  % (26466)Memory used [KB]: 943
% 0.14/0.38  % (26466)Time elapsed: 0.012 s
% 0.14/0.38  % (26466)Instructions burned: 30 (million)
% 0.14/0.38  % (26466)------------------------------
% 0.14/0.38  % (26466)------------------------------
% 0.14/0.38  % (26461)Success in time 0.02 s
%------------------------------------------------------------------------------