TSTP Solution File: SWV376+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWV376+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n019.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 16:46:37 EDT 2024

% Result   : Theorem 0.20s 0.38s
% Output   : Refutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :  115
% Syntax   : Number of formulae    :  339 (  93 unt;   0 def)
%            Number of atoms       :  837 ( 176 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  817 ( 319   ~; 331   |;  52   &)
%                                         (  76 <=>;  39  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   79 (  77 usr;  69 prp; 0-3 aty)
%            Number of functors    :   31 (  31 usr;  15 con; 0-3 aty)
%            Number of variables   :  803 ( 761   !;  42   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f540,plain,
    $false,
    inference(avatar_sat_refutation,[],[f166,f171,f176,f181,f185,f189,f193,f197,f201,f205,f209,f213,f217,f221,f226,f230,f234,f238,f242,f246,f250,f256,f260,f264,f269,f273,f277,f281,f296,f302,f307,f311,f319,f323,f330,f334,f338,f342,f348,f353,f359,f364,f372,f376,f380,f384,f403,f411,f415,f423,f428,f435,f445,f450,f456,f468,f475,f481,f485,f494,f499,f504,f511,f512,f519,f525,f531,f537,f539]) ).

fof(f539,plain,
    ( ~ spl12_35
    | ~ spl12_68 ),
    inference(avatar_contradiction_clause,[],[f538]) ).

fof(f538,plain,
    ( $false
    | ~ spl12_35
    | ~ spl12_68 ),
    inference(resolution,[],[f536,f329]) ).

fof(f329,plain,
    ( ! [X0,X1] : ~ ok(triple(X0,X1,sK2))
    | ~ spl12_35 ),
    inference(avatar_component_clause,[],[f328]) ).

fof(f328,plain,
    ( spl12_35
  <=> ! [X0,X1] : ~ ok(triple(X0,X1,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_35])]) ).

fof(f536,plain,
    ( ok(triple(sK9,sK10,sK2))
    | ~ spl12_68 ),
    inference(avatar_component_clause,[],[f534]) ).

fof(f534,plain,
    ( spl12_68
  <=> ok(triple(sK9,sK10,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_68])]) ).

fof(f537,plain,
    ( spl12_68
    | ~ spl12_33
    | ~ spl12_59 ),
    inference(avatar_split_clause,[],[f520,f478,f317,f534]) ).

fof(f317,plain,
    ( spl12_33
  <=> ! [X2,X0,X1] :
        ( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
        | ok(triple(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_33])]) ).

fof(f478,plain,
    ( spl12_59
  <=> ok(im_succ_cpq(triple(sK9,sK10,sK2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_59])]) ).

fof(f520,plain,
    ( ok(triple(sK9,sK10,sK2))
    | ~ spl12_33
    | ~ spl12_59 ),
    inference(resolution,[],[f480,f318]) ).

fof(f318,plain,
    ( ! [X2,X0,X1] :
        ( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
        | ok(triple(X0,X1,X2)) )
    | ~ spl12_33 ),
    inference(avatar_component_clause,[],[f317]) ).

fof(f480,plain,
    ( ok(im_succ_cpq(triple(sK9,sK10,sK2)))
    | ~ spl12_59 ),
    inference(avatar_component_clause,[],[f478]) ).

fof(f531,plain,
    ( spl12_67
    | ~ spl12_65
    | ~ spl12_66 ),
    inference(avatar_split_clause,[],[f526,f522,f516,f528]) ).

fof(f528,plain,
    ( spl12_67
  <=> succ_cpq(triple(sK6,sK7,sK8),triple(sK9,sK10,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_67])]) ).

fof(f516,plain,
    ( spl12_65
  <=> sK2 = sK11 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_65])]) ).

fof(f522,plain,
    ( spl12_66
  <=> succ_cpq(triple(sK6,sK7,sK8),triple(sK9,sK10,sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_66])]) ).

fof(f526,plain,
    ( succ_cpq(triple(sK6,sK7,sK8),triple(sK9,sK10,sK2))
    | ~ spl12_65
    | ~ spl12_66 ),
    inference(forward_demodulation,[],[f524,f518]) ).

fof(f518,plain,
    ( sK2 = sK11
    | ~ spl12_65 ),
    inference(avatar_component_clause,[],[f516]) ).

fof(f524,plain,
    ( succ_cpq(triple(sK6,sK7,sK8),triple(sK9,sK10,sK11))
    | ~ spl12_66 ),
    inference(avatar_component_clause,[],[f522]) ).

fof(f525,plain,
    ( spl12_66
    | spl12_57 ),
    inference(avatar_split_clause,[],[f105,f466,f522]) ).

fof(f466,plain,
    ( spl12_57
  <=> ! [X3,X4,X0,X5,X2,X1] :
        ( ~ ok(triple(X3,X4,X5))
        | ok(triple(X0,X1,X2))
        | ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_57])]) ).

fof(f105,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ ok(triple(X3,X4,X5))
      | ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
      | ok(triple(X0,X1,X2))
      | succ_cpq(triple(sK6,sK7,sK8),triple(sK9,sK10,sK11)) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f93,plain,
    ( ! [X0,X1,X2] :
        ( ! [X3,X4,X5] :
            ( ~ ok(triple(X3,X4,X5))
            | ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
        | ok(triple(X0,X1,X2)) )
    | ( ok(im_succ_cpq(triple(sK9,sK10,sK11)))
      & ~ ok(triple(sK9,sK10,sK11))
      & succ_cpq(triple(sK6,sK7,sK8),triple(sK9,sK10,sK11)) ) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11])],[f91,f92]) ).

fof(f92,plain,
    ( ? [X6,X7,X8,X9,X10,X11] :
        ( ok(im_succ_cpq(triple(X9,X10,X11)))
        & ~ ok(triple(X9,X10,X11))
        & succ_cpq(triple(X6,X7,X8),triple(X9,X10,X11)) )
   => ( ok(im_succ_cpq(triple(sK9,sK10,sK11)))
      & ~ ok(triple(sK9,sK10,sK11))
      & succ_cpq(triple(sK6,sK7,sK8),triple(sK9,sK10,sK11)) ) ),
    introduced(choice_axiom,[]) ).

fof(f91,plain,
    ( ! [X0,X1,X2] :
        ( ! [X3,X4,X5] :
            ( ~ ok(triple(X3,X4,X5))
            | ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
        | ok(triple(X0,X1,X2)) )
    | ? [X6,X7,X8,X9,X10,X11] :
        ( ok(im_succ_cpq(triple(X9,X10,X11)))
        & ~ ok(triple(X9,X10,X11))
        & succ_cpq(triple(X6,X7,X8),triple(X9,X10,X11)) ) ),
    inference(rectify,[],[f58]) ).

fof(f58,plain,
    ( ! [X6,X7,X8] :
        ( ! [X9,X10,X11] :
            ( ~ ok(triple(X9,X10,X11))
            | ~ succ_cpq(triple(X6,X7,X8),triple(X9,X10,X11)) )
        | ok(triple(X6,X7,X8)) )
    | ? [X0,X1,X2,X3,X4,X5] :
        ( ok(im_succ_cpq(triple(X3,X4,X5)))
        & ~ ok(triple(X3,X4,X5))
        & succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) ) ),
    inference(flattening,[],[f57]) ).

fof(f57,plain,
    ( ! [X6,X7,X8] :
        ( ! [X9,X10,X11] :
            ( ~ ok(triple(X9,X10,X11))
            | ~ succ_cpq(triple(X6,X7,X8),triple(X9,X10,X11)) )
        | ok(triple(X6,X7,X8)) )
    | ? [X0,X1,X2,X3,X4,X5] :
        ( ok(im_succ_cpq(triple(X3,X4,X5)))
        & ~ ok(triple(X3,X4,X5))
        & succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) ) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,axiom,
    ( ! [X0,X1,X2,X3,X4,X5] :
        ( succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
       => ( ~ ok(triple(X3,X4,X5))
         => ~ ok(im_succ_cpq(triple(X3,X4,X5))) ) )
   => ! [X6,X7,X8] :
        ( ~ ok(triple(X6,X7,X8))
       => ! [X9,X10,X11] :
            ( succ_cpq(triple(X6,X7,X8),triple(X9,X10,X11))
           => ~ ok(triple(X9,X10,X11)) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12_induction) ).

fof(f519,plain,
    ( spl12_65
    | ~ spl12_20
    | ~ spl12_25
    | spl12_56 ),
    inference(avatar_split_clause,[],[f470,f462,f266,f244,f516]) ).

fof(f244,plain,
    ( spl12_20
  <=> ! [X2,X0,X1] :
        ( bad = X2
        | ok(triple(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_20])]) ).

fof(f266,plain,
    ( spl12_25
  <=> bad = sK2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_25])]) ).

fof(f462,plain,
    ( spl12_56
  <=> ok(triple(sK9,sK10,sK11)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_56])]) ).

fof(f470,plain,
    ( sK2 = sK11
    | ~ spl12_20
    | ~ spl12_25
    | spl12_56 ),
    inference(forward_demodulation,[],[f469,f268]) ).

fof(f268,plain,
    ( bad = sK2
    | ~ spl12_25 ),
    inference(avatar_component_clause,[],[f266]) ).

fof(f469,plain,
    ( bad = sK11
    | ~ spl12_20
    | spl12_56 ),
    inference(resolution,[],[f464,f245]) ).

fof(f245,plain,
    ( ! [X2,X0,X1] :
        ( ok(triple(X0,X1,X2))
        | bad = X2 )
    | ~ spl12_20 ),
    inference(avatar_component_clause,[],[f244]) ).

fof(f464,plain,
    ( ~ ok(triple(sK9,sK10,sK11))
    | spl12_56 ),
    inference(avatar_component_clause,[],[f462]) ).

fof(f512,plain,
    ( ~ spl12_2
    | spl12_1
    | ~ spl12_4
    | ~ spl12_57 ),
    inference(avatar_split_clause,[],[f487,f466,f178,f163,f168]) ).

fof(f168,plain,
    ( spl12_2
  <=> ok(triple(sK3,sK4,sK5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_2])]) ).

fof(f163,plain,
    ( spl12_1
  <=> ok(triple(sK0,sK1,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_1])]) ).

fof(f178,plain,
    ( spl12_4
  <=> succ_cpq(triple(sK0,sK1,sK2),triple(sK3,sK4,sK5)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_4])]) ).

fof(f487,plain,
    ( ok(triple(sK0,sK1,sK2))
    | ~ ok(triple(sK3,sK4,sK5))
    | ~ spl12_4
    | ~ spl12_57 ),
    inference(resolution,[],[f467,f180]) ).

fof(f180,plain,
    ( succ_cpq(triple(sK0,sK1,sK2),triple(sK3,sK4,sK5))
    | ~ spl12_4 ),
    inference(avatar_component_clause,[],[f178]) ).

fof(f467,plain,
    ( ! [X2,X3,X0,X1,X4,X5] :
        ( ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
        | ok(triple(X0,X1,X2))
        | ~ ok(triple(X3,X4,X5)) )
    | ~ spl12_57 ),
    inference(avatar_component_clause,[],[f466]) ).

fof(f511,plain,
    ( spl12_64
    | ~ spl12_20
    | ~ spl12_25
    | ~ spl12_43 ),
    inference(avatar_split_clause,[],[f394,f370,f266,f244,f509]) ).

fof(f509,plain,
    ( spl12_64
  <=> ! [X2,X0,X1,X3] :
        ( sK2 = X3
        | ok(insert_cpq(triple(X0,X2,X3),X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_64])]) ).

fof(f370,plain,
    ( spl12_43
  <=> ! [X0,X3,X2,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_43])]) ).

fof(f394,plain,
    ( ! [X2,X3,X0,X1] :
        ( sK2 = X3
        | ok(insert_cpq(triple(X0,X2,X3),X1)) )
    | ~ spl12_20
    | ~ spl12_25
    | ~ spl12_43 ),
    inference(forward_demodulation,[],[f391,f268]) ).

fof(f391,plain,
    ( ! [X2,X3,X0,X1] :
        ( ok(insert_cpq(triple(X0,X2,X3),X1))
        | bad = X3 )
    | ~ spl12_20
    | ~ spl12_43 ),
    inference(superposition,[],[f245,f371]) ).

fof(f371,plain,
    ( ! [X2,X3,X0,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2)
    | ~ spl12_43 ),
    inference(avatar_component_clause,[],[f370]) ).

fof(f504,plain,
    spl12_63,
    inference(avatar_split_clause,[],[f140,f502]) ).

fof(f502,plain,
    ( spl12_63
  <=> ! [X2,X0,X1] :
        ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
        | ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
        | ~ contains_slb(X1,findmin_pqp_res(X0))
        | create_slb = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_63])]) ).

fof(f140,plain,
    ! [X2,X0,X1] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
      | ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(cnf_transformation,[],[f81]) ).

fof(f81,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
      | ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(flattening,[],[f80]) ).

fof(f80,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
      | ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(ennf_transformation,[],[f51]) ).

fof(f51,plain,
    ! [X0,X1,X2] :
      ( ( less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
        & contains_slb(X1,findmin_pqp_res(X0))
        & create_slb != X1 )
     => findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2) ),
    inference(rectify,[],[f37]) ).

fof(f37,axiom,
    ! [X0,X1,X2,X3] :
      ( ( less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
        & contains_slb(X1,findmin_pqp_res(X0))
        & create_slb != X1 )
     => findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).

fof(f499,plain,
    ( spl12_62
    | ~ spl12_25
    | ~ spl12_61 ),
    inference(avatar_split_clause,[],[f495,f492,f266,f497]) ).

fof(f497,plain,
    ( spl12_62
  <=> ! [X2,X0,X1] :
        ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),sK2)
        | ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
        | ~ contains_slb(X1,findmin_pqp_res(X0))
        | create_slb = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_62])]) ).

fof(f492,plain,
    ( spl12_61
  <=> ! [X2,X0,X1] :
        ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
        | ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
        | ~ contains_slb(X1,findmin_pqp_res(X0))
        | create_slb = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_61])]) ).

fof(f495,plain,
    ( ! [X2,X0,X1] :
        ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),sK2)
        | ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
        | ~ contains_slb(X1,findmin_pqp_res(X0))
        | create_slb = X1 )
    | ~ spl12_25
    | ~ spl12_61 ),
    inference(forward_demodulation,[],[f493,f268]) ).

fof(f493,plain,
    ( ! [X2,X0,X1] :
        ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
        | ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
        | ~ contains_slb(X1,findmin_pqp_res(X0))
        | create_slb = X1 )
    | ~ spl12_61 ),
    inference(avatar_component_clause,[],[f492]) ).

fof(f494,plain,
    spl12_61,
    inference(avatar_split_clause,[],[f139,f492]) ).

fof(f139,plain,
    ! [X2,X0,X1] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(cnf_transformation,[],[f79]) ).

fof(f79,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(flattening,[],[f78]) ).

fof(f78,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
      | ~ contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(ennf_transformation,[],[f50]) ).

fof(f50,plain,
    ! [X0,X1,X2] :
      ( ( strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
        & contains_slb(X1,findmin_pqp_res(X0))
        & create_slb != X1 )
     => findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
    inference(rectify,[],[f36]) ).

fof(f36,axiom,
    ! [X0,X1,X2,X3] :
      ( ( strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
        & contains_slb(X1,findmin_pqp_res(X0))
        & create_slb != X1 )
     => findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).

fof(f485,plain,
    ( spl12_60
    | ~ spl12_43
    | ~ spl12_47 ),
    inference(avatar_split_clause,[],[f441,f401,f370,f483]) ).

fof(f483,plain,
    ( spl12_60
  <=> ! [X2,X0,X1,X3] : ~ ok(insert_cpq(insert_cpq(triple(X0,X2,sK2),X1),X3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_60])]) ).

fof(f401,plain,
    ( spl12_47
  <=> ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,sK2),X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_47])]) ).

fof(f441,plain,
    ( ! [X2,X3,X0,X1] : ~ ok(insert_cpq(insert_cpq(triple(X0,X2,sK2),X1),X3))
    | ~ spl12_43
    | ~ spl12_47 ),
    inference(superposition,[],[f402,f371]) ).

fof(f402,plain,
    ( ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,sK2),X1))
    | ~ spl12_47 ),
    inference(avatar_component_clause,[],[f401]) ).

fof(f481,plain,
    ( spl12_59
    | ~ spl12_20
    | ~ spl12_25
    | spl12_56
    | ~ spl12_58 ),
    inference(avatar_split_clause,[],[f476,f472,f462,f266,f244,f478]) ).

fof(f472,plain,
    ( spl12_58
  <=> ok(im_succ_cpq(triple(sK9,sK10,sK11))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_58])]) ).

fof(f476,plain,
    ( ok(im_succ_cpq(triple(sK9,sK10,sK2)))
    | ~ spl12_20
    | ~ spl12_25
    | spl12_56
    | ~ spl12_58 ),
    inference(forward_demodulation,[],[f474,f470]) ).

fof(f474,plain,
    ( ok(im_succ_cpq(triple(sK9,sK10,sK11)))
    | ~ spl12_58 ),
    inference(avatar_component_clause,[],[f472]) ).

fof(f475,plain,
    ( spl12_58
    | spl12_57 ),
    inference(avatar_split_clause,[],[f107,f466,f472]) ).

fof(f107,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ ok(triple(X3,X4,X5))
      | ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
      | ok(triple(X0,X1,X2))
      | ok(im_succ_cpq(triple(sK9,sK10,sK11))) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f468,plain,
    ( ~ spl12_56
    | spl12_57 ),
    inference(avatar_split_clause,[],[f106,f466,f462]) ).

fof(f106,plain,
    ! [X2,X3,X0,X1,X4,X5] :
      ( ~ ok(triple(X3,X4,X5))
      | ~ succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
      | ok(triple(X0,X1,X2))
      | ~ ok(triple(sK9,sK10,sK11)) ),
    inference(cnf_transformation,[],[f93]) ).

fof(f456,plain,
    spl12_55,
    inference(avatar_split_clause,[],[f142,f454]) ).

fof(f454,plain,
    ( spl12_55
  <=> ! [X0,X3,X2,X1] :
        ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
        | ~ less_than(lookup_slb(X1,X3),X3)
        | ~ contains_slb(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_55])]) ).

fof(f142,plain,
    ! [X2,X3,X0,X1] :
      ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
      | ~ less_than(lookup_slb(X1,X3),X3)
      | ~ contains_slb(X1,X3) ),
    inference(cnf_transformation,[],[f85]) ).

fof(f85,plain,
    ! [X0,X1,X2,X3] :
      ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
      | ~ less_than(lookup_slb(X1,X3),X3)
      | ~ contains_slb(X1,X3) ),
    inference(flattening,[],[f84]) ).

fof(f84,plain,
    ! [X0,X1,X2,X3] :
      ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
      | ~ less_than(lookup_slb(X1,X3),X3)
      | ~ contains_slb(X1,X3) ),
    inference(ennf_transformation,[],[f32]) ).

fof(f32,axiom,
    ! [X0,X1,X2,X3] :
      ( ( less_than(lookup_slb(X1,X3),X3)
        & contains_slb(X1,X3) )
     => remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax44) ).

fof(f450,plain,
    ( spl12_54
    | ~ spl12_25
    | ~ spl12_53 ),
    inference(avatar_split_clause,[],[f446,f443,f266,f448]) ).

fof(f448,plain,
    ( spl12_54
  <=> ! [X0,X3,X2,X1] :
        ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),sK2)
        | ~ strictly_less_than(X3,lookup_slb(X1,X3))
        | ~ contains_slb(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_54])]) ).

fof(f443,plain,
    ( spl12_53
  <=> ! [X0,X3,X2,X1] :
        ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
        | ~ strictly_less_than(X3,lookup_slb(X1,X3))
        | ~ contains_slb(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_53])]) ).

fof(f446,plain,
    ( ! [X2,X3,X0,X1] :
        ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),sK2)
        | ~ strictly_less_than(X3,lookup_slb(X1,X3))
        | ~ contains_slb(X1,X3) )
    | ~ spl12_25
    | ~ spl12_53 ),
    inference(forward_demodulation,[],[f444,f268]) ).

fof(f444,plain,
    ( ! [X2,X3,X0,X1] :
        ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
        | ~ strictly_less_than(X3,lookup_slb(X1,X3))
        | ~ contains_slb(X1,X3) )
    | ~ spl12_53 ),
    inference(avatar_component_clause,[],[f443]) ).

fof(f445,plain,
    spl12_53,
    inference(avatar_split_clause,[],[f141,f443]) ).

fof(f141,plain,
    ! [X2,X3,X0,X1] :
      ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
      | ~ strictly_less_than(X3,lookup_slb(X1,X3))
      | ~ contains_slb(X1,X3) ),
    inference(cnf_transformation,[],[f83]) ).

fof(f83,plain,
    ! [X0,X1,X2,X3] :
      ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
      | ~ strictly_less_than(X3,lookup_slb(X1,X3))
      | ~ contains_slb(X1,X3) ),
    inference(flattening,[],[f82]) ).

fof(f82,plain,
    ! [X0,X1,X2,X3] :
      ( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
      | ~ strictly_less_than(X3,lookup_slb(X1,X3))
      | ~ contains_slb(X1,X3) ),
    inference(ennf_transformation,[],[f33]) ).

fof(f33,axiom,
    ! [X0,X1,X2,X3] :
      ( ( strictly_less_than(X3,lookup_slb(X1,X3))
        & contains_slb(X1,X3) )
     => remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).

fof(f435,plain,
    spl12_52,
    inference(avatar_split_clause,[],[f137,f433]) ).

fof(f433,plain,
    ( spl12_52
  <=> ! [X0,X3,X2,X1] :
        ( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
        | ~ contains_slb(X0,X2)
        | X1 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_52])]) ).

fof(f137,plain,
    ! [X2,X3,X0,X1] :
      ( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
      | ~ contains_slb(X0,X2)
      | X1 = X2 ),
    inference(cnf_transformation,[],[f75]) ).

fof(f75,plain,
    ! [X0,X1,X2,X3] :
      ( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
      | ~ contains_slb(X0,X2)
      | X1 = X2 ),
    inference(flattening,[],[f74]) ).

fof(f74,plain,
    ! [X0,X1,X2,X3] :
      ( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
      | ~ contains_slb(X0,X2)
      | X1 = X2 ),
    inference(ennf_transformation,[],[f13]) ).

fof(f13,axiom,
    ! [X0,X1,X2,X3] :
      ( ( contains_slb(X0,X2)
        & X1 != X2 )
     => remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).

fof(f428,plain,
    ( spl12_51
    | ~ spl12_25
    | ~ spl12_50 ),
    inference(avatar_split_clause,[],[f424,f421,f266,f426]) ).

fof(f426,plain,
    ( spl12_51
  <=> ! [X2,X0,X1] :
        ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),sK2)
        | contains_slb(X1,findmin_pqp_res(X0))
        | create_slb = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_51])]) ).

fof(f421,plain,
    ( spl12_50
  <=> ! [X2,X0,X1] :
        ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
        | contains_slb(X1,findmin_pqp_res(X0))
        | create_slb = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_50])]) ).

fof(f424,plain,
    ( ! [X2,X0,X1] :
        ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),sK2)
        | contains_slb(X1,findmin_pqp_res(X0))
        | create_slb = X1 )
    | ~ spl12_25
    | ~ spl12_50 ),
    inference(forward_demodulation,[],[f422,f268]) ).

fof(f422,plain,
    ( ! [X2,X0,X1] :
        ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
        | contains_slb(X1,findmin_pqp_res(X0))
        | create_slb = X1 )
    | ~ spl12_50 ),
    inference(avatar_component_clause,[],[f421]) ).

fof(f423,plain,
    spl12_50,
    inference(avatar_split_clause,[],[f138,f421]) ).

fof(f138,plain,
    ! [X2,X0,X1] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(cnf_transformation,[],[f77]) ).

fof(f77,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(flattening,[],[f76]) ).

fof(f76,plain,
    ! [X0,X1,X2] :
      ( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
      | contains_slb(X1,findmin_pqp_res(X0))
      | create_slb = X1 ),
    inference(ennf_transformation,[],[f49]) ).

fof(f49,plain,
    ! [X0,X1,X2] :
      ( ( ~ contains_slb(X1,findmin_pqp_res(X0))
        & create_slb != X1 )
     => findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
    inference(rectify,[],[f35]) ).

fof(f35,axiom,
    ! [X0,X1,X2,X3] :
      ( ( ~ contains_slb(X1,findmin_pqp_res(X0))
        & create_slb != X1 )
     => findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).

fof(f415,plain,
    spl12_49,
    inference(avatar_split_clause,[],[f135,f413]) ).

fof(f413,plain,
    ( spl12_49
  <=> ! [X0,X3,X2,X1] :
        ( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3))
        | ~ less_than(X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_49])]) ).

fof(f135,plain,
    ! [X2,X3,X0,X1] :
      ( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3))
      | ~ less_than(X2,X3) ),
    inference(cnf_transformation,[],[f71]) ).

fof(f71,plain,
    ! [X0,X1,X2,X3] :
      ( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3))
      | ~ less_than(X2,X3) ),
    inference(ennf_transformation,[],[f18]) ).

fof(f18,axiom,
    ! [X0,X1,X2,X3] :
      ( less_than(X2,X3)
     => update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).

fof(f411,plain,
    spl12_48,
    inference(avatar_split_clause,[],[f134,f409]) ).

fof(f409,plain,
    ( spl12_48
  <=> ! [X0,X3,X2,X1] :
        ( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2))
        | ~ strictly_less_than(X3,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_48])]) ).

fof(f134,plain,
    ! [X2,X3,X0,X1] :
      ( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2))
      | ~ strictly_less_than(X3,X2) ),
    inference(cnf_transformation,[],[f70]) ).

fof(f70,plain,
    ! [X0,X1,X2,X3] :
      ( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2))
      | ~ strictly_less_than(X3,X2) ),
    inference(ennf_transformation,[],[f17]) ).

fof(f17,axiom,
    ! [X0,X1,X2,X3] :
      ( strictly_less_than(X3,X2)
     => update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).

fof(f403,plain,
    ( spl12_47
    | ~ spl12_12
    | ~ spl12_25
    | ~ spl12_43 ),
    inference(avatar_split_clause,[],[f393,f370,f266,f211,f401]) ).

fof(f211,plain,
    ( spl12_12
  <=> ! [X0,X1] : ~ ok(triple(X0,X1,bad)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_12])]) ).

fof(f393,plain,
    ( ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,sK2),X1))
    | ~ spl12_12
    | ~ spl12_25
    | ~ spl12_43 ),
    inference(forward_demodulation,[],[f386,f268]) ).

fof(f386,plain,
    ( ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,bad),X1))
    | ~ spl12_12
    | ~ spl12_43 ),
    inference(superposition,[],[f212,f371]) ).

fof(f212,plain,
    ( ! [X0,X1] : ~ ok(triple(X0,X1,bad))
    | ~ spl12_12 ),
    inference(avatar_component_clause,[],[f211]) ).

fof(f384,plain,
    spl12_46,
    inference(avatar_split_clause,[],[f150,f382]) ).

fof(f382,plain,
    ( spl12_46
  <=> ! [X4,X0,X3,X2,X1] :
        ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
        | ~ check_cpq(triple(X0,X1,X2))
        | ~ less_than(X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_46])]) ).

fof(f150,plain,
    ! [X2,X3,X0,X1,X4] :
      ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      | ~ check_cpq(triple(X0,X1,X2))
      | ~ less_than(X4,X3) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f97,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
          | ~ check_cpq(triple(X0,X1,X2)) )
        & ( check_cpq(triple(X0,X1,X2))
          | ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ) )
      | ~ less_than(X4,X3) ),
    inference(nnf_transformation,[],[f87]) ).

fof(f87,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      <=> check_cpq(triple(X0,X1,X2)) )
      | ~ less_than(X4,X3) ),
    inference(ennf_transformation,[],[f25]) ).

fof(f25,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( less_than(X4,X3)
     => ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      <=> check_cpq(triple(X0,X1,X2)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).

fof(f380,plain,
    spl12_45,
    inference(avatar_split_clause,[],[f149,f378]) ).

fof(f378,plain,
    ( spl12_45
  <=> ! [X4,X0,X3,X2,X1] :
        ( check_cpq(triple(X0,X1,X2))
        | ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
        | ~ less_than(X4,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_45])]) ).

fof(f149,plain,
    ! [X2,X3,X0,X1,X4] :
      ( check_cpq(triple(X0,X1,X2))
      | ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      | ~ less_than(X4,X3) ),
    inference(cnf_transformation,[],[f97]) ).

fof(f376,plain,
    spl12_44,
    inference(avatar_split_clause,[],[f136,f374]) ).

fof(f374,plain,
    ( spl12_44
  <=> ! [X0,X3,X2,X1] :
        ( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
        | ~ contains_slb(X0,X2)
        | X1 = X2 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_44])]) ).

fof(f136,plain,
    ! [X2,X3,X0,X1] :
      ( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
      | ~ contains_slb(X0,X2)
      | X1 = X2 ),
    inference(cnf_transformation,[],[f73]) ).

fof(f73,plain,
    ! [X0,X1,X2,X3] :
      ( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
      | ~ contains_slb(X0,X2)
      | X1 = X2 ),
    inference(flattening,[],[f72]) ).

fof(f72,plain,
    ! [X0,X1,X2,X3] :
      ( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
      | ~ contains_slb(X0,X2)
      | X1 = X2 ),
    inference(ennf_transformation,[],[f15]) ).

fof(f15,axiom,
    ! [X0,X1,X2,X3] :
      ( ( contains_slb(X0,X2)
        & X1 != X2 )
     => lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax27) ).

fof(f372,plain,
    spl12_43,
    inference(avatar_split_clause,[],[f131,f370]) ).

fof(f131,plain,
    ! [X2,X3,X0,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
    inference(cnf_transformation,[],[f30]) ).

fof(f30,axiom,
    ! [X0,X1,X2,X3] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).

fof(f364,plain,
    spl12_42,
    inference(avatar_split_clause,[],[f152,f362]) ).

fof(f362,plain,
    ( spl12_42
  <=> ! [X4,X0,X3,X2,X1] :
        ( X3 = X4
        | pair_in_list(X0,X2,X4)
        | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_42])]) ).

fof(f152,plain,
    ! [X2,X3,X0,X1,X4] :
      ( X3 = X4
      | pair_in_list(X0,X2,X4)
      | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f99,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
        | ( ( X3 != X4
            | X1 != X2 )
          & ~ pair_in_list(X0,X2,X4) ) )
      & ( ( X3 = X4
          & X1 = X2 )
        | pair_in_list(X0,X2,X4)
        | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
    inference(flattening,[],[f98]) ).

fof(f98,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
        | ( ( X3 != X4
            | X1 != X2 )
          & ~ pair_in_list(X0,X2,X4) ) )
      & ( ( X3 = X4
          & X1 = X2 )
        | pair_in_list(X0,X2,X4)
        | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
    inference(nnf_transformation,[],[f11]) ).

fof(f11,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
    <=> ( ( X3 = X4
          & X1 = X2 )
        | pair_in_list(X0,X2,X4) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).

fof(f359,plain,
    spl12_41,
    inference(avatar_split_clause,[],[f151,f357]) ).

fof(f357,plain,
    ( spl12_41
  <=> ! [X4,X0,X3,X2,X1] :
        ( X1 = X2
        | pair_in_list(X0,X2,X4)
        | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_41])]) ).

fof(f151,plain,
    ! [X2,X3,X0,X1,X4] :
      ( X1 = X2
      | pair_in_list(X0,X2,X4)
      | ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f353,plain,
    ( spl12_40
    | ~ spl12_25
    | ~ spl12_39 ),
    inference(avatar_split_clause,[],[f349,f346,f266,f351]) ).

fof(f351,plain,
    ( spl12_40
  <=> ! [X0,X3,X2,X1] :
        ( remove_cpq(triple(X0,X1,X2),X3) = triple(X0,X1,sK2)
        | contains_slb(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_40])]) ).

fof(f346,plain,
    ( spl12_39
  <=> ! [X0,X3,X2,X1] :
        ( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
        | contains_slb(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_39])]) ).

fof(f349,plain,
    ( ! [X2,X3,X0,X1] :
        ( remove_cpq(triple(X0,X1,X2),X3) = triple(X0,X1,sK2)
        | contains_slb(X1,X3) )
    | ~ spl12_25
    | ~ spl12_39 ),
    inference(forward_demodulation,[],[f347,f268]) ).

fof(f347,plain,
    ( ! [X2,X3,X0,X1] :
        ( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
        | contains_slb(X1,X3) )
    | ~ spl12_39 ),
    inference(avatar_component_clause,[],[f346]) ).

fof(f348,plain,
    spl12_39,
    inference(avatar_split_clause,[],[f133,f346]) ).

fof(f133,plain,
    ! [X2,X3,X0,X1] :
      ( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
      | contains_slb(X1,X3) ),
    inference(cnf_transformation,[],[f69]) ).

fof(f69,plain,
    ! [X0,X1,X2,X3] :
      ( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
      | contains_slb(X1,X3) ),
    inference(ennf_transformation,[],[f31]) ).

fof(f31,axiom,
    ! [X0,X1,X2,X3] :
      ( ~ contains_slb(X1,X3)
     => triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43) ).

fof(f342,plain,
    spl12_38,
    inference(avatar_split_clause,[],[f145,f340]) ).

fof(f340,plain,
    ( spl12_38
  <=> ! [X0,X3,X2,X1] :
        ( X1 = X2
        | contains_slb(X0,X2)
        | ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_38])]) ).

fof(f145,plain,
    ! [X2,X3,X0,X1] :
      ( X1 = X2
      | contains_slb(X0,X2)
      | ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f96,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
        | ( X1 != X2
          & ~ contains_slb(X0,X2) ) )
      & ( X1 = X2
        | contains_slb(X0,X2)
        | ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
    inference(flattening,[],[f95]) ).

fof(f95,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
        | ( X1 != X2
          & ~ contains_slb(X0,X2) ) )
      & ( X1 = X2
        | contains_slb(X0,X2)
        | ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
    inference(nnf_transformation,[],[f9]) ).

fof(f9,axiom,
    ! [X0,X1,X2,X3] :
      ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
    <=> ( X1 = X2
        | contains_slb(X0,X2) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).

fof(f338,plain,
    spl12_37,
    inference(avatar_split_clause,[],[f153,f336]) ).

fof(f336,plain,
    ( spl12_37
  <=> ! [X4,X0,X3,X2,X1] :
        ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
        | ~ pair_in_list(X0,X2,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_37])]) ).

fof(f153,plain,
    ! [X2,X3,X0,X1,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
      | ~ pair_in_list(X0,X2,X4) ),
    inference(cnf_transformation,[],[f99]) ).

fof(f334,plain,
    spl12_36,
    inference(avatar_split_clause,[],[f148,f332]) ).

fof(f332,plain,
    ( spl12_36
  <=> ! [X4,X0,X3,X2,X1] :
        ( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
        | ~ strictly_less_than(X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_36])]) ).

fof(f148,plain,
    ! [X2,X3,X0,X1,X4] :
      ( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      | ~ strictly_less_than(X3,X4) ),
    inference(cnf_transformation,[],[f86]) ).

fof(f86,plain,
    ! [X0,X1,X2,X3,X4] :
      ( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      | ~ strictly_less_than(X3,X4) ),
    inference(ennf_transformation,[],[f53]) ).

fof(f53,plain,
    ! [X0,X1,X2,X3,X4] :
      ( strictly_less_than(X3,X4)
     => ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
    inference(flattening,[],[f52]) ).

fof(f52,plain,
    ! [X0,X1,X2,X3,X4] :
      ( strictly_less_than(X3,X4)
     => ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
    inference(true_and_false_elimination,[],[f26]) ).

fof(f26,axiom,
    ! [X0,X1,X2,X3,X4] :
      ( strictly_less_than(X3,X4)
     => ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
      <=> $false ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).

fof(f330,plain,
    ( spl12_35
    | ~ spl12_12
    | ~ spl12_25 ),
    inference(avatar_split_clause,[],[f298,f266,f211,f328]) ).

fof(f298,plain,
    ( ! [X0,X1] : ~ ok(triple(X0,X1,sK2))
    | ~ spl12_12
    | ~ spl12_25 ),
    inference(superposition,[],[f212,f268]) ).

fof(f323,plain,
    spl12_34,
    inference(avatar_split_clause,[],[f158,f321]) ).

fof(f321,plain,
    ( spl12_34
  <=> ! [X2,X0,X1] :
        ( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
        | create_slb = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_34])]) ).

fof(f158,plain,
    ! [X2,X0,X1] :
      ( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
      | create_slb = X1 ),
    inference(definition_unfolding,[],[f132,f113]) ).

fof(f113,plain,
    ! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
    inference(cnf_transformation,[],[f41]) ).

fof(f41,axiom,
    ! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).

fof(f132,plain,
    ! [X2,X0,X1] :
      ( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
      | create_slb = X1 ),
    inference(cnf_transformation,[],[f68]) ).

fof(f68,plain,
    ! [X0,X1,X2] :
      ( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
      | create_slb = X1 ),
    inference(ennf_transformation,[],[f48]) ).

fof(f48,plain,
    ! [X0,X1,X2] :
      ( create_slb != X1
     => findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
    inference(rectify,[],[f39]) ).

fof(f39,axiom,
    ! [X0,X1,X2,X3] :
      ( create_slb != X1
     => findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).

fof(f319,plain,
    spl12_33,
    inference(avatar_split_clause,[],[f103,f317]) ).

fof(f103,plain,
    ! [X2,X0,X1] :
      ( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
      | ok(triple(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1,X2] :
      ( ~ ok(im_succ_cpq(triple(X0,X1,X2)))
      | ok(triple(X0,X1,X2)) ),
    inference(ennf_transformation,[],[f43]) ).

fof(f43,axiom,
    ! [X0,X1,X2] :
      ( ~ ok(triple(X0,X1,X2))
     => ~ ok(im_succ_cpq(triple(X0,X1,X2))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12_l13) ).

fof(f311,plain,
    spl12_32,
    inference(avatar_split_clause,[],[f157,f309]) ).

fof(f309,plain,
    ( spl12_32
  <=> ! [X0,X1] :
        ( succ_cpq(X0,remove_cpq(findmin_cpq_eff(X1),removemin_cpq_res(X1)))
        | ~ succ_cpq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_32])]) ).

fof(f157,plain,
    ! [X0,X1] :
      ( succ_cpq(X0,remove_cpq(findmin_cpq_eff(X1),removemin_cpq_res(X1)))
      | ~ succ_cpq(X0,X1) ),
    inference(definition_unfolding,[],[f120,f155]) ).

fof(f155,plain,
    ! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),removemin_cpq_res(X0)),
    inference(definition_unfolding,[],[f114,f113]) ).

fof(f114,plain,
    ! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),findmin_cpq_res(X0)),
    inference(cnf_transformation,[],[f40]) ).

fof(f40,axiom,
    ! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),findmin_cpq_res(X0)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).

fof(f120,plain,
    ! [X0,X1] :
      ( succ_cpq(X0,removemin_cpq_eff(X1))
      | ~ succ_cpq(X0,X1) ),
    inference(cnf_transformation,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( succ_cpq(X0,removemin_cpq_eff(X1))
      | ~ succ_cpq(X0,X1) ),
    inference(ennf_transformation,[],[f23]) ).

fof(f23,axiom,
    ! [X0,X1] :
      ( succ_cpq(X0,X1)
     => succ_cpq(X0,removemin_cpq_eff(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35) ).

fof(f307,plain,
    spl12_31,
    inference(avatar_split_clause,[],[f146,f305]) ).

fof(f305,plain,
    ( spl12_31
  <=> ! [X0,X3,X2,X1] :
        ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
        | ~ contains_slb(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_31])]) ).

fof(f146,plain,
    ! [X2,X3,X0,X1] :
      ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
      | ~ contains_slb(X0,X2) ),
    inference(cnf_transformation,[],[f96]) ).

fof(f302,plain,
    ( spl12_30
    | ~ spl12_25
    | ~ spl12_29 ),
    inference(avatar_split_clause,[],[f297,f294,f266,f300]) ).

fof(f300,plain,
    ( spl12_30
  <=> ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,sK2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_30])]) ).

fof(f294,plain,
    ( spl12_29
  <=> ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_29])]) ).

fof(f297,plain,
    ( ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,sK2)
    | ~ spl12_25
    | ~ spl12_29 ),
    inference(forward_demodulation,[],[f295,f268]) ).

fof(f295,plain,
    ( ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad)
    | ~ spl12_29 ),
    inference(avatar_component_clause,[],[f294]) ).

fof(f296,plain,
    spl12_29,
    inference(avatar_split_clause,[],[f118,f294]) ).

fof(f118,plain,
    ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
    inference(cnf_transformation,[],[f34]) ).

fof(f34,axiom,
    ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).

fof(f281,plain,
    spl12_28,
    inference(avatar_split_clause,[],[f144,f279]) ).

fof(f279,plain,
    ( spl12_28
  <=> ! [X0,X3,X2,X1] :
        ( contains_cpq(triple(X0,X1,X2),X3)
        | ~ contains_slb(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_28])]) ).

fof(f144,plain,
    ! [X2,X3,X0,X1] :
      ( contains_cpq(triple(X0,X1,X2),X3)
      | ~ contains_slb(X1,X3) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f94,plain,
    ! [X0,X1,X2,X3] :
      ( ( contains_cpq(triple(X0,X1,X2),X3)
        | ~ contains_slb(X1,X3) )
      & ( contains_slb(X1,X3)
        | ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
    inference(nnf_transformation,[],[f27]) ).

fof(f27,axiom,
    ! [X0,X1,X2,X3] :
      ( contains_cpq(triple(X0,X1,X2),X3)
    <=> contains_slb(X1,X3) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).

fof(f277,plain,
    spl12_27,
    inference(avatar_split_clause,[],[f143,f275]) ).

fof(f275,plain,
    ( spl12_27
  <=> ! [X2,X0,X1,X3] :
        ( contains_slb(X1,X3)
        | ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_27])]) ).

fof(f143,plain,
    ! [X2,X3,X0,X1] :
      ( contains_slb(X1,X3)
      | ~ contains_cpq(triple(X0,X1,X2),X3) ),
    inference(cnf_transformation,[],[f94]) ).

fof(f273,plain,
    spl12_26,
    inference(avatar_split_clause,[],[f130,f271]) ).

fof(f271,plain,
    ( spl12_26
  <=> ! [X2,X0,X1] :
        ( less_than(X0,X2)
        | ~ less_than(X1,X2)
        | ~ less_than(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_26])]) ).

fof(f130,plain,
    ! [X2,X0,X1] :
      ( less_than(X0,X2)
      | ~ less_than(X1,X2)
      | ~ less_than(X0,X1) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,plain,
    ! [X0,X1,X2] :
      ( less_than(X0,X2)
      | ~ less_than(X1,X2)
      | ~ less_than(X0,X1) ),
    inference(flattening,[],[f66]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( less_than(X0,X2)
      | ~ less_than(X1,X2)
      | ~ less_than(X0,X1) ),
    inference(ennf_transformation,[],[f1]) ).

fof(f1,axiom,
    ! [X0,X1,X2] :
      ( ( less_than(X1,X2)
        & less_than(X0,X1) )
     => less_than(X0,X2) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',transitivity) ).

fof(f269,plain,
    ( spl12_25
    | spl12_1
    | ~ spl12_20 ),
    inference(avatar_split_clause,[],[f251,f244,f163,f266]) ).

fof(f251,plain,
    ( bad = sK2
    | spl12_1
    | ~ spl12_20 ),
    inference(resolution,[],[f245,f165]) ).

fof(f165,plain,
    ( ~ ok(triple(sK0,sK1,sK2))
    | spl12_1 ),
    inference(avatar_component_clause,[],[f163]) ).

fof(f264,plain,
    spl12_24,
    inference(avatar_split_clause,[],[f126,f262]) ).

fof(f262,plain,
    ( spl12_24
  <=> ! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_24])]) ).

fof(f126,plain,
    ! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2,
    inference(cnf_transformation,[],[f14]) ).

fof(f14,axiom,
    ! [X0,X1,X2] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).

fof(f260,plain,
    spl12_23,
    inference(avatar_split_clause,[],[f125,f258]) ).

fof(f258,plain,
    ( spl12_23
  <=> ! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_23])]) ).

fof(f125,plain,
    ! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0,
    inference(cnf_transformation,[],[f12]) ).

fof(f12,axiom,
    ! [X0,X1,X2] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).

fof(f256,plain,
    spl12_22,
    inference(avatar_split_clause,[],[f122,f254]) ).

fof(f254,plain,
    ( spl12_22
  <=> ! [X0,X1] :
        ( strictly_less_than(X0,X1)
        | less_than(X1,X0)
        | ~ less_than(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_22])]) ).

fof(f122,plain,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
      | less_than(X1,X0)
      | ~ less_than(X0,X1) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,plain,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
      | less_than(X1,X0)
      | ~ less_than(X0,X1) ),
    inference(flattening,[],[f61]) ).

fof(f61,plain,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
      | less_than(X1,X0)
      | ~ less_than(X0,X1) ),
    inference(ennf_transformation,[],[f54]) ).

fof(f54,plain,
    ! [X0,X1] :
      ( ( ~ less_than(X1,X0)
        & less_than(X0,X1) )
     => strictly_less_than(X0,X1) ),
    inference(unused_predicate_definition_removal,[],[f4]) ).

fof(f4,axiom,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
    <=> ( ~ less_than(X1,X0)
        & less_than(X0,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).

fof(f250,plain,
    spl12_21,
    inference(avatar_split_clause,[],[f161,f248]) ).

fof(f248,plain,
    ( spl12_21
  <=> ! [X4,X0,X2] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_21])]) ).

fof(f161,plain,
    ! [X2,X0,X4] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4),
    inference(equality_resolution,[],[f160]) ).

fof(f160,plain,
    ! [X2,X0,X1,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X4)),X2,X4)
      | X1 != X2 ),
    inference(equality_resolution,[],[f154]) ).

fof(f154,plain,
    ! [X2,X3,X0,X1,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
      | X3 != X4
      | X1 != X2 ),
    inference(cnf_transformation,[],[f99]) ).

fof(f246,plain,
    spl12_20,
    inference(avatar_split_clause,[],[f129,f244]) ).

fof(f129,plain,
    ! [X2,X0,X1] :
      ( bad = X2
      | ok(triple(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0,X1,X2] :
      ( bad = X2
      | ok(triple(X0,X1,X2)) ),
    inference(ennf_transformation,[],[f29]) ).

fof(f29,axiom,
    ! [X0,X1,X2] :
      ( ~ ok(triple(X0,X1,X2))
     => bad = X2 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).

fof(f242,plain,
    spl12_19,
    inference(avatar_split_clause,[],[f128,f240]) ).

fof(f240,plain,
    ( spl12_19
  <=> ! [X2,X0,X1] :
        ( succ_cpq(X0,remove_cpq(X1,X2))
        | ~ succ_cpq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_19])]) ).

fof(f128,plain,
    ! [X2,X0,X1] :
      ( succ_cpq(X0,remove_cpq(X1,X2))
      | ~ succ_cpq(X0,X1) ),
    inference(cnf_transformation,[],[f64]) ).

fof(f64,plain,
    ! [X0,X1,X2] :
      ( succ_cpq(X0,remove_cpq(X1,X2))
      | ~ succ_cpq(X0,X1) ),
    inference(ennf_transformation,[],[f21]) ).

fof(f21,axiom,
    ! [X0,X1,X2] :
      ( succ_cpq(X0,X1)
     => succ_cpq(X0,remove_cpq(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).

fof(f238,plain,
    spl12_18,
    inference(avatar_split_clause,[],[f127,f236]) ).

fof(f236,plain,
    ( spl12_18
  <=> ! [X2,X0,X1] :
        ( succ_cpq(X0,insert_cpq(X1,X2))
        | ~ succ_cpq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_18])]) ).

fof(f127,plain,
    ! [X2,X0,X1] :
      ( succ_cpq(X0,insert_cpq(X1,X2))
      | ~ succ_cpq(X0,X1) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,plain,
    ! [X0,X1,X2] :
      ( succ_cpq(X0,insert_cpq(X1,X2))
      | ~ succ_cpq(X0,X1) ),
    inference(ennf_transformation,[],[f20]) ).

fof(f20,axiom,
    ! [X0,X1,X2] :
      ( succ_cpq(X0,X1)
     => succ_cpq(X0,insert_cpq(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32) ).

fof(f234,plain,
    spl12_17,
    inference(avatar_split_clause,[],[f159,f232]) ).

fof(f232,plain,
    ( spl12_17
  <=> ! [X2,X0,X3] : contains_slb(insert_slb(X0,pair(X2,X3)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_17])]) ).

fof(f159,plain,
    ! [X2,X3,X0] : contains_slb(insert_slb(X0,pair(X2,X3)),X2),
    inference(equality_resolution,[],[f147]) ).

fof(f147,plain,
    ! [X2,X3,X0,X1] :
      ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
      | X1 != X2 ),
    inference(cnf_transformation,[],[f96]) ).

fof(f230,plain,
    spl12_16,
    inference(avatar_split_clause,[],[f156,f228]) ).

fof(f228,plain,
    ( spl12_16
  <=> ! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_16])]) ).

fof(f156,plain,
    ! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)),
    inference(definition_unfolding,[],[f117,f113]) ).

fof(f117,plain,
    ! [X0,X1] : bottom = findmin_cpq_res(triple(X0,create_slb,X1)),
    inference(cnf_transformation,[],[f38]) ).

fof(f38,axiom,
    ! [X0,X1] : bottom = findmin_cpq_res(triple(X0,create_slb,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).

fof(f226,plain,
    spl12_15,
    inference(avatar_split_clause,[],[f121,f224]) ).

fof(f224,plain,
    ( spl12_15
  <=> ! [X0,X1] :
        ( succ_cpq(X0,findmin_cpq_eff(X1))
        | ~ succ_cpq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_15])]) ).

fof(f121,plain,
    ! [X0,X1] :
      ( succ_cpq(X0,findmin_cpq_eff(X1))
      | ~ succ_cpq(X0,X1) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( succ_cpq(X0,findmin_cpq_eff(X1))
      | ~ succ_cpq(X0,X1) ),
    inference(ennf_transformation,[],[f22]) ).

fof(f22,axiom,
    ! [X0,X1] :
      ( succ_cpq(X0,X1)
     => succ_cpq(X0,findmin_cpq_eff(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34) ).

fof(f221,plain,
    spl12_14,
    inference(avatar_split_clause,[],[f124,f219]) ).

fof(f219,plain,
    ( spl12_14
  <=> ! [X2,X0,X1] : isnonempty_slb(insert_slb(X0,pair(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_14])]) ).

fof(f124,plain,
    ! [X2,X0,X1] : isnonempty_slb(insert_slb(X0,pair(X1,X2))),
    inference(cnf_transformation,[],[f7]) ).

fof(f7,axiom,
    ! [X0,X1,X2] : isnonempty_slb(insert_slb(X0,pair(X1,X2))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).

fof(f217,plain,
    spl12_13,
    inference(avatar_split_clause,[],[f119,f215]) ).

fof(f215,plain,
    ( spl12_13
  <=> ! [X0,X1] :
        ( less_than(X1,X0)
        | less_than(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_13])]) ).

fof(f119,plain,
    ! [X0,X1] :
      ( less_than(X1,X0)
      | less_than(X0,X1) ),
    inference(cnf_transformation,[],[f2]) ).

fof(f2,axiom,
    ! [X0,X1] :
      ( less_than(X1,X0)
      | less_than(X0,X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',totality) ).

fof(f213,plain,
    spl12_12,
    inference(avatar_split_clause,[],[f123,f211]) ).

fof(f123,plain,
    ! [X0,X1] : ~ ok(triple(X0,X1,bad)),
    inference(cnf_transformation,[],[f47]) ).

fof(f47,plain,
    ! [X0,X1] : ~ ok(triple(X0,X1,bad)),
    inference(flattening,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] : ~ ok(triple(X0,X1,bad)),
    inference(true_and_false_elimination,[],[f28]) ).

fof(f28,axiom,
    ! [X0,X1] :
      ( ok(triple(X0,X1,bad))
    <=> $false ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).

fof(f209,plain,
    spl12_11,
    inference(avatar_split_clause,[],[f116,f207]) ).

fof(f207,plain,
    ( spl12_11
  <=> ! [X0,X1] : check_cpq(triple(X0,create_slb,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_11])]) ).

fof(f116,plain,
    ! [X0,X1] : check_cpq(triple(X0,create_slb,X1)),
    inference(cnf_transformation,[],[f24]) ).

fof(f24,axiom,
    ! [X0,X1] : check_cpq(triple(X0,create_slb,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).

fof(f205,plain,
    spl12_10,
    inference(avatar_split_clause,[],[f112,f203]) ).

fof(f203,plain,
    ( spl12_10
  <=> ! [X0] : create_slb = update_slb(create_slb,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_10])]) ).

fof(f112,plain,
    ! [X0] : create_slb = update_slb(create_slb,X0),
    inference(cnf_transformation,[],[f16]) ).

fof(f16,axiom,
    ! [X0] : create_slb = update_slb(create_slb,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).

fof(f201,plain,
    spl12_9,
    inference(avatar_split_clause,[],[f115,f199]) ).

fof(f199,plain,
    ( spl12_9
  <=> ! [X0,X1] : ~ pair_in_list(create_slb,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_9])]) ).

fof(f115,plain,
    ! [X0,X1] : ~ pair_in_list(create_slb,X0,X1),
    inference(cnf_transformation,[],[f10]) ).

fof(f10,axiom,
    ! [X0,X1] : ~ pair_in_list(create_slb,X0,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).

fof(f197,plain,
    spl12_8,
    inference(avatar_split_clause,[],[f111,f195]) ).

fof(f195,plain,
    ( spl12_8
  <=> ! [X0] : succ_cpq(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_8])]) ).

fof(f111,plain,
    ! [X0] : succ_cpq(X0,X0),
    inference(cnf_transformation,[],[f19]) ).

fof(f19,axiom,
    ! [X0] : succ_cpq(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).

fof(f193,plain,
    spl12_7,
    inference(avatar_split_clause,[],[f110,f191]) ).

fof(f191,plain,
    ( spl12_7
  <=> ! [X0] : less_than(bottom,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_7])]) ).

fof(f110,plain,
    ! [X0] : less_than(bottom,X0),
    inference(cnf_transformation,[],[f5]) ).

fof(f5,axiom,
    ! [X0] : less_than(bottom,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bottom_smallest) ).

fof(f189,plain,
    spl12_6,
    inference(avatar_split_clause,[],[f109,f187]) ).

fof(f187,plain,
    ( spl12_6
  <=> ! [X0] : less_than(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_6])]) ).

fof(f109,plain,
    ! [X0] : less_than(X0,X0),
    inference(cnf_transformation,[],[f3]) ).

fof(f3,axiom,
    ! [X0] : less_than(X0,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).

fof(f185,plain,
    spl12_5,
    inference(avatar_split_clause,[],[f108,f183]) ).

fof(f183,plain,
    ( spl12_5
  <=> ! [X0] : ~ contains_slb(create_slb,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_5])]) ).

fof(f108,plain,
    ! [X0] : ~ contains_slb(create_slb,X0),
    inference(cnf_transformation,[],[f8]) ).

fof(f8,axiom,
    ! [X0] : ~ contains_slb(create_slb,X0),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).

fof(f181,plain,
    spl12_4,
    inference(avatar_split_clause,[],[f101,f178]) ).

fof(f101,plain,
    succ_cpq(triple(sK0,sK1,sK2),triple(sK3,sK4,sK5)),
    inference(cnf_transformation,[],[f90]) ).

fof(f90,plain,
    ( ok(triple(sK3,sK4,sK5))
    & succ_cpq(triple(sK0,sK1,sK2),triple(sK3,sK4,sK5))
    & ~ ok(triple(sK0,sK1,sK2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f55,f89,f88]) ).

fof(f88,plain,
    ( ? [X0,X1,X2] :
        ( ? [X3,X4,X5] :
            ( ok(triple(X3,X4,X5))
            & succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
        & ~ ok(triple(X0,X1,X2)) )
   => ( ? [X5,X4,X3] :
          ( ok(triple(X3,X4,X5))
          & succ_cpq(triple(sK0,sK1,sK2),triple(X3,X4,X5)) )
      & ~ ok(triple(sK0,sK1,sK2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f89,plain,
    ( ? [X5,X4,X3] :
        ( ok(triple(X3,X4,X5))
        & succ_cpq(triple(sK0,sK1,sK2),triple(X3,X4,X5)) )
   => ( ok(triple(sK3,sK4,sK5))
      & succ_cpq(triple(sK0,sK1,sK2),triple(sK3,sK4,sK5)) ) ),
    introduced(choice_axiom,[]) ).

fof(f55,plain,
    ? [X0,X1,X2] :
      ( ? [X3,X4,X5] :
          ( ok(triple(X3,X4,X5))
          & succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5)) )
      & ~ ok(triple(X0,X1,X2)) ),
    inference(ennf_transformation,[],[f45]) ).

fof(f45,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ~ ok(triple(X0,X1,X2))
       => ! [X3,X4,X5] :
            ( succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
           => ~ ok(triple(X3,X4,X5)) ) ),
    inference(negated_conjecture,[],[f44]) ).

fof(f44,conjecture,
    ! [X0,X1,X2] :
      ( ~ ok(triple(X0,X1,X2))
     => ! [X3,X4,X5] :
          ( succ_cpq(triple(X0,X1,X2),triple(X3,X4,X5))
         => ~ ok(triple(X3,X4,X5)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l12_co) ).

fof(f176,plain,
    ~ spl12_3,
    inference(avatar_split_clause,[],[f104,f173]) ).

fof(f173,plain,
    ( spl12_3
  <=> isnonempty_slb(create_slb) ),
    introduced(avatar_definition,[new_symbols(naming,[spl12_3])]) ).

fof(f104,plain,
    ~ isnonempty_slb(create_slb),
    inference(cnf_transformation,[],[f6]) ).

fof(f6,axiom,
    ~ isnonempty_slb(create_slb),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).

fof(f171,plain,
    spl12_2,
    inference(avatar_split_clause,[],[f102,f168]) ).

fof(f102,plain,
    ok(triple(sK3,sK4,sK5)),
    inference(cnf_transformation,[],[f90]) ).

fof(f166,plain,
    ~ spl12_1,
    inference(avatar_split_clause,[],[f100,f163]) ).

fof(f100,plain,
    ~ ok(triple(sK0,sK1,sK2)),
    inference(cnf_transformation,[],[f90]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12  % Problem    : SWV376+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.13  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35  % Computer : n019.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   : Tue Apr 30 04:54:44 EDT 2024
% 0.14/0.35  % CPUTime    : 
% 0.14/0.35  % (31108)Running in auto input_syntax mode. Trying TPTP
% 0.20/0.37  % (31111)WARNING: value z3 for option sas not known
% 0.20/0.37  % (31112)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.20/0.37  % (31115)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)
% 0.20/0.37  % (31110)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.20/0.37  % (31113)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)
% 0.20/0.37  % (31114)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)
% 0.20/0.37  % (31111)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)
% 0.20/0.37  % (31109)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.20/0.37  TRYING [1]
% 0.20/0.38  TRYING [2]
% 0.20/0.38  % (31113)First to succeed.
% 0.20/0.38  TRYING [1]
% 0.20/0.38  % (31113)Refutation found. Thanks to Tanya!
% 0.20/0.38  % SZS status Theorem for theBenchmark
% 0.20/0.38  % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.39  % (31113)------------------------------
% 0.20/0.39  % (31113)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.20/0.39  % (31113)Termination reason: Refutation
% 0.20/0.39  
% 0.20/0.39  % (31113)Memory used [KB]: 1081
% 0.20/0.39  % (31113)Time elapsed: 0.016 s
% 0.20/0.39  % (31113)Instructions burned: 27 (million)
% 0.20/0.39  % (31113)------------------------------
% 0.20/0.39  % (31113)------------------------------
% 0.20/0.39  % (31108)Success in time 0.031 s
%------------------------------------------------------------------------------