TSTP Solution File: DAT061_1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : DAT061_1 : TPTP v8.1.2. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n008.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 11:03:56 EDT 2024

% Result   : Theorem 0.21s 0.41s
% Output   : Refutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   62
% Syntax   : Number of formulae    :  143 (  37 unt;  11 typ;   0 def)
%            Number of atoms       :  294 (  83 equ)
%            Maximal formula atoms :    4 (   2 avg)
%            Number of connectives :  285 ( 123   ~; 118   |;   7   &)
%                                         (  33 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number arithmetic     :  346 (  77 atm;  99 fun;  22 num; 148 var)
%            Number of types       :    3 (   2 usr;   1 ari)
%            Number of type conns  :    7 (   3   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :   34 (  31 usr;  32 prp; 0-2 aty)
%            Number of functors    :   13 (   9 usr;   8 con; 0-3 aty)
%            Number of variables   :  206 ( 195   !;  11   ?; 206   :)

% Comments : 
%------------------------------------------------------------------------------
tff(type_def_5,type,
    data: $tType ).

tff(type_def_6,type,
    array: $tType ).

tff(func_def_0,type,
    mkarray: array ).

tff(func_def_1,type,
    none: data ).

tff(func_def_2,type,
    put: ( array * $int * data ) > array ).

tff(func_def_3,type,
    get: ( array * $int ) > data ).

tff(func_def_8,type,
    sK0: data ).

tff(func_def_9,type,
    sK1: array ).

tff(func_def_10,type,
    sK2: $int ).

tff(func_def_11,type,
    sK3: $int ).

tff(func_def_12,type,
    sK4: ( array * array ) > $int ).

tff(f298,plain,
    $false,
    inference(avatar_sat_refutation,[],[f46,f51,f55,f59,f63,f67,f71,f75,f79,f83,f87,f97,f101,f107,f118,f122,f147,f169,f176,f187,f197,f204,f213,f217,f221,f226,f262,f266,f285,f289,f293,f297]) ).

tff(f297,plain,
    ( ~ spl5_3
    | ~ spl5_26 ),
    inference(avatar_contradiction_clause,[],[f295]) ).

tff(f295,plain,
    ( $false
    | ~ spl5_3
    | ~ spl5_26 ),
    inference(resolution,[],[f225,f54]) ).

tff(f54,plain,
    ( ! [X0: $int] : ~ $less(X0,X0)
    | ~ spl5_3 ),
    inference(avatar_component_clause,[],[f53]) ).

tff(f53,plain,
    ( spl5_3
  <=> ! [X0: $int] : ~ $less(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).

tff(f225,plain,
    ( $less(sK2,sK2)
    | ~ spl5_26 ),
    inference(avatar_component_clause,[],[f223]) ).

tff(f223,plain,
    ( spl5_26
  <=> $less(sK2,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_26])]) ).

tff(f293,plain,
    ( spl5_31
    | ~ spl5_8
    | ~ spl5_16 ),
    inference(avatar_split_clause,[],[f141,f120,f73,f291]) ).

tff(f291,plain,
    ( spl5_31
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X2,X1),$sum(X1,X0))
        | ~ $less(X2,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_31])]) ).

tff(f73,plain,
    ( spl5_8
  <=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).

tff(f120,plain,
    ( spl5_16
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | $less($sum(X0,X2),$sum(X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_16])]) ).

tff(f141,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X2,X1),$sum(X1,X0))
        | ~ $less(X2,X0) )
    | ~ spl5_8
    | ~ spl5_16 ),
    inference(superposition,[],[f121,f74]) ).

tff(f74,plain,
    ( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
    | ~ spl5_8 ),
    inference(avatar_component_clause,[],[f73]) ).

tff(f121,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X0,X2),$sum(X1,X2))
        | ~ $less(X0,X1) )
    | ~ spl5_16 ),
    inference(avatar_component_clause,[],[f120]) ).

tff(f289,plain,
    ( spl5_30
    | ~ spl5_8
    | ~ spl5_16 ),
    inference(avatar_split_clause,[],[f137,f120,f73,f287]) ).

tff(f287,plain,
    ( spl5_30
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X1,X0),$sum(X2,X1))
        | ~ $less(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_30])]) ).

tff(f137,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( $less($sum(X1,X0),$sum(X2,X1))
        | ~ $less(X0,X2) )
    | ~ spl5_8
    | ~ spl5_16 ),
    inference(superposition,[],[f121,f74]) ).

tff(f285,plain,
    ( spl5_29
    | ~ spl5_8
    | ~ spl5_15 ),
    inference(avatar_split_clause,[],[f124,f116,f73,f283]) ).

tff(f283,plain,
    ( spl5_29
  <=> ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_29])]) ).

tff(f116,plain,
    ( spl5_15
  <=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_15])]) ).

tff(f124,plain,
    ( ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) )
    | ~ spl5_8
    | ~ spl5_15 ),
    inference(superposition,[],[f117,f74]) ).

tff(f117,plain,
    ( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) )
    | ~ spl5_15 ),
    inference(avatar_component_clause,[],[f116]) ).

tff(f266,plain,
    ( spl5_28
    | ~ spl5_7
    | ~ spl5_16 ),
    inference(avatar_split_clause,[],[f140,f120,f69,f264]) ).

tff(f264,plain,
    ( spl5_28
  <=> ! [X0: $int,X1: $int] :
        ( $less($sum(X1,$uminus(X0)),0)
        | ~ $less(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_28])]) ).

tff(f69,plain,
    ( spl5_7
  <=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).

tff(f140,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less($sum(X1,$uminus(X0)),0)
        | ~ $less(X1,X0) )
    | ~ spl5_7
    | ~ spl5_16 ),
    inference(superposition,[],[f121,f70]) ).

tff(f70,plain,
    ( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
    | ~ spl5_7 ),
    inference(avatar_component_clause,[],[f69]) ).

tff(f262,plain,
    ( spl5_27
    | ~ spl5_7
    | ~ spl5_16 ),
    inference(avatar_split_clause,[],[f136,f120,f69,f260]) ).

tff(f260,plain,
    ( spl5_27
  <=> ! [X0: $int,X1: $int] :
        ( $less(0,$sum(X1,$uminus(X0)))
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_27])]) ).

tff(f136,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less(0,$sum(X1,$uminus(X0)))
        | ~ $less(X0,X1) )
    | ~ spl5_7
    | ~ spl5_16 ),
    inference(superposition,[],[f121,f70]) ).

tff(f226,plain,
    ( spl5_26
    | ~ spl5_1
    | ~ spl5_21 ),
    inference(avatar_split_clause,[],[f199,f194,f43,f223]) ).

tff(f43,plain,
    ( spl5_1
  <=> $less(sK2,sK3) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).

tff(f194,plain,
    ( spl5_21
  <=> ( sK2 = sK3 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_21])]) ).

tff(f199,plain,
    ( $less(sK2,sK2)
    | ~ spl5_1
    | ~ spl5_21 ),
    inference(superposition,[],[f45,f196]) ).

tff(f196,plain,
    ( ( sK2 = sK3 )
    | ~ spl5_21 ),
    inference(avatar_component_clause,[],[f194]) ).

tff(f45,plain,
    ( $less(sK2,sK3)
    | ~ spl5_1 ),
    inference(avatar_component_clause,[],[f43]) ).

tff(f221,plain,
    ( spl5_25
    | ~ spl5_7
    | ~ spl5_17 ),
    inference(avatar_split_clause,[],[f163,f145,f69,f219]) ).

tff(f219,plain,
    ( spl5_25
  <=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_25])]) ).

tff(f145,plain,
    ( spl5_17
  <=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_17])]) ).

tff(f163,plain,
    ( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
    | ~ spl5_7
    | ~ spl5_17 ),
    inference(evaluation,[],[f148]) ).

tff(f148,plain,
    ( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
    | ~ spl5_7
    | ~ spl5_17 ),
    inference(superposition,[],[f146,f70]) ).

tff(f146,plain,
    ( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
    | ~ spl5_17 ),
    inference(avatar_component_clause,[],[f145]) ).

tff(f217,plain,
    ( spl5_24
    | ~ spl5_8
    | ~ spl5_10 ),
    inference(avatar_split_clause,[],[f92,f81,f73,f215]) ).

tff(f215,plain,
    ( spl5_24
  <=> ! [X0: $int,X1: $int] :
        ( ~ $less(X1,$sum(1,X0))
        | ~ $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_24])]) ).

tff(f81,plain,
    ( spl5_10
  <=> ! [X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,$sum(X0,1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).

tff(f92,plain,
    ( ! [X0: $int,X1: $int] :
        ( ~ $less(X1,$sum(1,X0))
        | ~ $less(X0,X1) )
    | ~ spl5_8
    | ~ spl5_10 ),
    inference(superposition,[],[f82,f74]) ).

tff(f82,plain,
    ( ! [X0: $int,X1: $int] :
        ( ~ $less(X1,$sum(X0,1))
        | ~ $less(X0,X1) )
    | ~ spl5_10 ),
    inference(avatar_component_clause,[],[f81]) ).

tff(f213,plain,
    ( spl5_23
    | ~ spl5_8
    | ~ spl5_9 ),
    inference(avatar_split_clause,[],[f89,f77,f73,f211]) ).

tff(f211,plain,
    ( spl5_23
  <=> ! [X0: $int,X1: $int] :
        ( $less(X1,$sum(1,X0))
        | $less(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_23])]) ).

tff(f77,plain,
    ( spl5_9
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,X1)
        | $less(X1,$sum(X0,1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).

tff(f89,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less(X1,$sum(1,X0))
        | $less(X0,X1) )
    | ~ spl5_8
    | ~ spl5_9 ),
    inference(superposition,[],[f78,f74]) ).

tff(f78,plain,
    ( ! [X0: $int,X1: $int] :
        ( $less(X1,$sum(X0,1))
        | $less(X0,X1) )
    | ~ spl5_9 ),
    inference(avatar_component_clause,[],[f77]) ).

tff(f204,plain,
    ( spl5_22
    | ~ spl5_3
    | ~ spl5_9 ),
    inference(avatar_split_clause,[],[f88,f77,f53,f202]) ).

tff(f202,plain,
    ( spl5_22
  <=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_22])]) ).

tff(f88,plain,
    ( ! [X0: $int] : $less(X0,$sum(X0,1))
    | ~ spl5_3
    | ~ spl5_9 ),
    inference(resolution,[],[f78,f54]) ).

tff(f197,plain,
    ( spl5_21
    | spl5_2
    | ~ spl5_19 ),
    inference(avatar_split_clause,[],[f183,f174,f48,f194]) ).

tff(f48,plain,
    ( spl5_2
  <=> ( get(sK1,sK3) = get(put(sK1,sK2,sK0),sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).

tff(f174,plain,
    ( spl5_19
  <=> ! [X0: $int,X3: $int,X2: array,X1: data] :
        ( ( get(put(X2,X0,X1),X3) = get(X2,X3) )
        | ( X0 = X3 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_19])]) ).

tff(f183,plain,
    ( ( sK2 = sK3 )
    | spl5_2
    | ~ spl5_19 ),
    inference(trivial_inequality_removal,[],[f181]) ).

tff(f181,plain,
    ( ( get(sK1,sK3) != get(sK1,sK3) )
    | ( sK2 = sK3 )
    | spl5_2
    | ~ spl5_19 ),
    inference(superposition,[],[f50,f175]) ).

tff(f175,plain,
    ( ! [X2: array,X3: $int,X0: $int,X1: data] :
        ( ( get(put(X2,X0,X1),X3) = get(X2,X3) )
        | ( X0 = X3 ) )
    | ~ spl5_19 ),
    inference(avatar_component_clause,[],[f174]) ).

tff(f50,plain,
    ( ( get(sK1,sK3) != get(put(sK1,sK2,sK0),sK3) )
    | spl5_2 ),
    inference(avatar_component_clause,[],[f48]) ).

tff(f187,plain,
    spl5_20,
    inference(avatar_split_clause,[],[f37,f185]) ).

tff(f185,plain,
    ( spl5_20
  <=> ! [X0: array,X1: array] :
        ( ( X0 = X1 )
        | ( get(X0,sK4(X0,X1)) != get(X1,sK4(X0,X1)) ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_20])]) ).

tff(f37,plain,
    ! [X0: array,X1: array] :
      ( ( X0 = X1 )
      | ( get(X0,sK4(X0,X1)) != get(X1,sK4(X0,X1)) ) ),
    inference(cnf_transformation,[],[f32]) ).

tff(f32,plain,
    ! [X0: array,X1: array] :
      ( ( ( X0 = X1 )
        | ( get(X0,sK4(X0,X1)) != get(X1,sK4(X0,X1)) ) )
      & ( ! [X3: $int] : ( get(X1,X3) = get(X0,X3) )
        | ( X0 != X1 ) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f30,f31]) ).

tff(f31,plain,
    ! [X0: array,X1: array] :
      ( ? [X2: $int] : ( get(X0,X2) != get(X1,X2) )
     => ( get(X0,sK4(X0,X1)) != get(X1,sK4(X0,X1)) ) ),
    introduced(choice_axiom,[]) ).

tff(f30,plain,
    ! [X0: array,X1: array] :
      ( ( ( X0 = X1 )
        | ? [X2: $int] : ( get(X0,X2) != get(X1,X2) ) )
      & ( ! [X3: $int] : ( get(X1,X3) = get(X0,X3) )
        | ( X0 != X1 ) ) ),
    inference(rectify,[],[f29]) ).

tff(f29,plain,
    ! [X0: array,X1: array] :
      ( ( ( X0 = X1 )
        | ? [X2: $int] : ( get(X0,X2) != get(X1,X2) ) )
      & ( ! [X2: $int] : ( get(X0,X2) = get(X1,X2) )
        | ( X0 != X1 ) ) ),
    inference(nnf_transformation,[],[f21]) ).

tff(f21,plain,
    ! [X0: array,X1: array] :
      ( ( X0 = X1 )
    <=> ! [X2: $int] : ( get(X0,X2) = get(X1,X2) ) ),
    inference(rectify,[],[f5]) ).

tff(f5,axiom,
    ! [X1: array,X6: array] :
      ( ( X1 = X6 )
    <=> ! [X3: $int] : ( get(X1,X3) = get(X6,X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_21) ).

tff(f176,plain,
    spl5_19,
    inference(avatar_split_clause,[],[f40,f174]) ).

tff(f40,plain,
    ! [X2: array,X3: $int,X0: $int,X1: data] :
      ( ( get(put(X2,X0,X1),X3) = get(X2,X3) )
      | ( X0 = X3 ) ),
    inference(cnf_transformation,[],[f26]) ).

tff(f26,plain,
    ! [X0: $int,X1: data,X2: array,X3: $int] :
      ( ( get(put(X2,X0,X1),X3) = get(X2,X3) )
      | ( X0 = X3 ) ),
    inference(ennf_transformation,[],[f24]) ).

tff(f24,plain,
    ! [X0: $int,X1: data,X2: array,X3: $int] :
      ( ( X0 != X3 )
     => ( get(put(X2,X0,X1),X3) = get(X2,X3) ) ),
    inference(rectify,[],[f3]) ).

tff(f3,axiom,
    ! [X3: $int,X2: data,X1: array,X0: $int] :
      ( ( X0 != X3 )
     => ( get(put(X1,X3,X2),X0) = get(X1,X0) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_19) ).

tff(f169,plain,
    spl5_18,
    inference(avatar_split_clause,[],[f39,f167]) ).

tff(f167,plain,
    ( spl5_18
  <=> ! [X0: data,X3: data,X2: $int,X1: array] : ( put(put(X1,X2,X0),X2,X3) = put(X1,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_18])]) ).

tff(f39,plain,
    ! [X2: $int,X3: data,X0: data,X1: array] : ( put(put(X1,X2,X0),X2,X3) = put(X1,X2,X3) ),
    inference(cnf_transformation,[],[f23]) ).

tff(f23,plain,
    ! [X0: data,X1: array,X2: $int,X3: data] : ( put(put(X1,X2,X0),X2,X3) = put(X1,X2,X3) ),
    inference(rectify,[],[f4]) ).

tff(f4,axiom,
    ! [X4: data,X1: array,X0: $int,X5: data] : ( put(put(X1,X0,X4),X0,X5) = put(X1,X0,X5) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_20) ).

tff(f147,plain,
    spl5_17,
    inference(avatar_split_clause,[],[f9,f145]) ).

tff(f9,plain,
    ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
    introduced(theory_axiom_136,[]) ).

tff(f122,plain,
    spl5_16,
    inference(avatar_split_clause,[],[f16,f120]) ).

tff(f16,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | $less($sum(X0,X2),$sum(X1,X2)) ),
    introduced(theory_axiom_145,[]) ).

tff(f118,plain,
    spl5_15,
    inference(avatar_split_clause,[],[f11,f116]) ).

tff(f11,plain,
    ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
    introduced(theory_axiom_139,[]) ).

tff(f107,plain,
    ( spl5_14
    | ~ spl5_1
    | ~ spl5_12 ),
    inference(avatar_split_clause,[],[f102,f95,f43,f105]) ).

tff(f105,plain,
    ( spl5_14
  <=> ! [X0: $int] :
        ( ~ $less(X0,sK2)
        | $less(X0,sK3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_14])]) ).

tff(f95,plain,
    ( spl5_12
  <=> ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X0,X1)
        | ~ $less(X1,X2)
        | $less(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).

tff(f102,plain,
    ( ! [X0: $int] :
        ( ~ $less(X0,sK2)
        | $less(X0,sK3) )
    | ~ spl5_1
    | ~ spl5_12 ),
    inference(resolution,[],[f96,f45]) ).

tff(f96,plain,
    ( ! [X2: $int,X0: $int,X1: $int] :
        ( ~ $less(X1,X2)
        | ~ $less(X0,X1)
        | $less(X0,X2) )
    | ~ spl5_12 ),
    inference(avatar_component_clause,[],[f95]) ).

tff(f101,plain,
    spl5_13,
    inference(avatar_split_clause,[],[f15,f99]) ).

tff(f99,plain,
    ( spl5_13
  <=> ! [X0: $int,X1: $int] :
        ( $less(X0,X1)
        | $less(X1,X0)
        | ( X0 = X1 ) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).

tff(f15,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,X0)
      | ( X0 = X1 ) ),
    introduced(theory_axiom_144,[]) ).

tff(f97,plain,
    spl5_12,
    inference(avatar_split_clause,[],[f14,f95]) ).

tff(f14,plain,
    ! [X2: $int,X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,X2)
      | $less(X0,X2) ),
    introduced(theory_axiom_143,[]) ).

tff(f87,plain,
    spl5_11,
    inference(avatar_split_clause,[],[f38,f85]) ).

tff(f85,plain,
    ( spl5_11
  <=> ! [X2: data,X0: array,X1: $int] : ( get(put(X0,X1,X2),X1) = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).

tff(f38,plain,
    ! [X2: data,X0: array,X1: $int] : ( get(put(X0,X1,X2),X1) = X2 ),
    inference(cnf_transformation,[],[f22]) ).

tff(f22,plain,
    ! [X0: array,X1: $int,X2: data] : ( get(put(X0,X1,X2),X1) = X2 ),
    inference(rectify,[],[f2]) ).

tff(f2,axiom,
    ! [X1: array,X0: $int,X2: data] : ( get(put(X1,X0,X2),X0) = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_18) ).

tff(f83,plain,
    spl5_10,
    inference(avatar_split_clause,[],[f19,f81]) ).

tff(f19,plain,
    ! [X0: $int,X1: $int] :
      ( ~ $less(X0,X1)
      | ~ $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_161,[]) ).

tff(f79,plain,
    spl5_9,
    inference(avatar_split_clause,[],[f17,f77]) ).

tff(f17,plain,
    ! [X0: $int,X1: $int] :
      ( $less(X0,X1)
      | $less(X1,$sum(X0,1)) ),
    introduced(theory_axiom_147,[]) ).

tff(f75,plain,
    spl5_8,
    inference(avatar_split_clause,[],[f8,f73]) ).

tff(f8,plain,
    ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
    introduced(theory_axiom_135,[]) ).

tff(f71,plain,
    spl5_7,
    inference(avatar_split_clause,[],[f12,f69]) ).

tff(f12,plain,
    ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
    introduced(theory_axiom_140,[]) ).

tff(f67,plain,
    spl5_6,
    inference(avatar_split_clause,[],[f35,f65]) ).

tff(f65,plain,
    ( spl5_6
  <=> ! [X0: $int] : ( get(mkarray,X0) = none ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).

tff(f35,plain,
    ! [X0: $int] : ( get(mkarray,X0) = none ),
    inference(cnf_transformation,[],[f1]) ).

tff(f1,axiom,
    ! [X0: $int] : ( get(mkarray,X0) = none ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax_17) ).

tff(f63,plain,
    spl5_5,
    inference(avatar_split_clause,[],[f18,f61]) ).

tff(f61,plain,
    ( spl5_5
  <=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).

tff(f18,plain,
    ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
    introduced(theory_axiom_148,[]) ).

tff(f59,plain,
    spl5_4,
    inference(avatar_split_clause,[],[f10,f57]) ).

tff(f57,plain,
    ( spl5_4
  <=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).

tff(f10,plain,
    ! [X0: $int] : ( $sum(X0,0) = X0 ),
    introduced(theory_axiom_137,[]) ).

tff(f55,plain,
    spl5_3,
    inference(avatar_split_clause,[],[f13,f53]) ).

tff(f13,plain,
    ! [X0: $int] : ~ $less(X0,X0),
    introduced(theory_axiom_142,[]) ).

tff(f51,plain,
    ~ spl5_2,
    inference(avatar_split_clause,[],[f33,f48]) ).

tff(f33,plain,
    get(sK1,sK3) != get(put(sK1,sK2,sK0),sK3),
    inference(cnf_transformation,[],[f28]) ).

tff(f28,plain,
    ( $less(sK2,sK3)
    & ( get(sK1,sK3) != get(put(sK1,sK2,sK0),sK3) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f25,f27]) ).

tff(f27,plain,
    ( ? [X0: data,X1: array,X2: $int,X3: $int] :
        ( $less(X2,X3)
        & ( get(X1,X3) != get(put(X1,X2,X0),X3) ) )
   => ( $less(sK2,sK3)
      & ( get(sK1,sK3) != get(put(sK1,sK2,sK0),sK3) ) ) ),
    introduced(choice_axiom,[]) ).

tff(f25,plain,
    ? [X0: data,X1: array,X2: $int,X3: $int] :
      ( $less(X2,X3)
      & ( get(X1,X3) != get(put(X1,X2,X0),X3) ) ),
    inference(ennf_transformation,[],[f20]) ).

tff(f20,plain,
    ~ ! [X0: data,X1: array,X2: $int,X3: $int] :
        ( ~ $less(X2,X3)
        | ( get(X1,X3) = get(put(X1,X2,X0),X3) ) ),
    inference(rectify,[],[f7]) ).

tff(f7,negated_conjecture,
    ~ ! [X2: data,X1: array,X0: $int,X3: $int] :
        ( ~ $less(X0,X3)
        | ( get(X1,X3) = get(put(X1,X0,X2),X3) ) ),
    inference(negated_conjecture,[],[f6]) ).

tff(f6,conjecture,
    ! [X2: data,X1: array,X0: $int,X3: $int] :
      ( ~ $less(X0,X3)
      | ( get(X1,X3) = get(put(X1,X0,X2),X3) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',th_lem_7) ).

tff(f46,plain,
    spl5_1,
    inference(avatar_split_clause,[],[f34,f43]) ).

tff(f34,plain,
    $less(sK2,sK3),
    inference(cnf_transformation,[],[f28]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12  % Problem    : DAT061_1 : TPTP v8.1.2. Released v5.5.0.
% 0.07/0.14  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n008.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 22:13:43 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.36  % (31870)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38  % (31873)WARNING: value z3 for option sas not known
% 0.14/0.38  % (31873)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)
% 0.14/0.39  % (31872)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.39  % (31872)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.39  % (31872)Terminated due to inappropriate strategy.
% 0.14/0.39  % (31872)------------------------------
% 0.14/0.39  % (31872)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.39  % (31872)Termination reason: Inappropriate
% 0.14/0.39  
% 0.14/0.39  % (31872)Memory used [KB]: 744
% 0.14/0.39  % (31872)Time elapsed: 0.003 s
% 0.14/0.39  % (31872)Instructions burned: 2 (million)
% 0.14/0.39  % (31872)------------------------------
% 0.14/0.39  % (31872)------------------------------
% 0.14/0.39  % (31871)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.39  % (31874)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.39  % (31875)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)
% 0.14/0.39  % (31876)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)
% 0.14/0.39  % (31877)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)
% 0.14/0.39  % (31871)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.39  % (31871)Terminated due to inappropriate strategy.
% 0.14/0.39  % (31871)------------------------------
% 0.14/0.39  % (31871)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.39  % (31871)Termination reason: Inappropriate
% 0.14/0.39  
% 0.14/0.39  % (31871)Memory used [KB]: 744
% 0.14/0.39  % (31871)Time elapsed: 0.004 s
% 0.14/0.39  % (31871)Instructions burned: 2 (million)
% 0.14/0.39  % (31871)------------------------------
% 0.14/0.39  % (31871)------------------------------
% 0.14/0.39  % (31874)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.14/0.39  % (31874)Terminated due to inappropriate strategy.
% 0.14/0.39  % (31874)------------------------------
% 0.14/0.39  % (31874)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.14/0.39  % (31874)Termination reason: Inappropriate
% 0.14/0.39  
% 0.14/0.39  % (31874)Memory used [KB]: 744
% 0.14/0.39  % (31874)Time elapsed: 0.004 s
% 0.14/0.39  % (31874)Instructions burned: 2 (million)
% 0.14/0.39  % (31874)------------------------------
% 0.14/0.39  % (31874)------------------------------
% 0.21/0.40  % (31875)First to succeed.
% 0.21/0.41  % (31875)Refutation found. Thanks to Tanya!
% 0.21/0.41  % SZS status Theorem for theBenchmark
% 0.21/0.41  % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.41  % (31875)------------------------------
% 0.21/0.41  % (31875)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.41  % (31875)Termination reason: Refutation
% 0.21/0.41  
% 0.21/0.41  % (31875)Memory used [KB]: 929
% 0.21/0.41  % (31875)Time elapsed: 0.020 s
% 0.21/0.41  % (31875)Instructions burned: 15 (million)
% 0.21/0.41  % (31875)------------------------------
% 0.21/0.41  % (31875)------------------------------
% 0.21/0.41  % (31870)Success in time 0.029 s
%------------------------------------------------------------------------------