TSTP Solution File: SWV387+1 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : SWV387+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 : n026.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 : Sun May  5 10:51:38 EDT 2024

% Result   : Theorem 0.15s 0.40s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   93
% Syntax   : Number of formulae    :  255 (  91 unt;   0 def)
%            Number of atoms       :  563 ( 119 equ)
%            Maximal formula atoms :    8 (   2 avg)
%            Number of connectives :  492 ( 184   ~; 190   |;  33   &)
%                                         (  58 <=>;  27  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   5 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :   61 (  59 usr;  51 prp; 0-3 aty)
%            Number of functors    :   22 (  22 usr;   7 con; 0-3 aty)
%            Number of variables   :  595 ( 585   !;  10   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f431,plain,
    $false,
    inference(avatar_sat_refutation,[],[f158,f163,f168,f173,f177,f181,f185,f189,f193,f197,f201,f205,f209,f213,f218,f222,f226,f230,f234,f238,f242,f247,f251,f255,f259,f263,f267,f282,f286,f290,f294,f303,f310,f314,f318,f322,f328,f334,f338,f346,f350,f355,f359,f378,f382,f396,f402,f409,f418,f422,f430]) ).

fof(f430,plain,
    ( ~ spl4_2
    | spl4_1
    | ~ spl4_3
    | ~ spl4_46 ),
    inference(avatar_split_clause,[],[f397,f394,f165,f155,f160]) ).

fof(f160,plain,
    ( spl4_2
  <=> check_cpq(remove_cpq(triple(sK0,sK1,sK2),sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_2])]) ).

fof(f155,plain,
    ( spl4_1
  <=> check_cpq(triple(sK0,sK1,sK2)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_1])]) ).

fof(f165,plain,
    ( spl4_3
  <=> ok(remove_cpq(triple(sK0,sK1,sK2),sK3)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_3])]) ).

fof(f394,plain,
    ( spl4_46
  <=> ! [X0,X3,X2,X1] :
        ( check_cpq(triple(X0,X1,X2))
        | ~ ok(remove_cpq(triple(X0,X1,X2),X3))
        | ~ check_cpq(remove_cpq(triple(X0,X1,X2),X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_46])]) ).

fof(f397,plain,
    ( check_cpq(triple(sK0,sK1,sK2))
    | ~ check_cpq(remove_cpq(triple(sK0,sK1,sK2),sK3))
    | ~ spl4_3
    | ~ spl4_46 ),
    inference(resolution,[],[f395,f167]) ).

fof(f167,plain,
    ( ok(remove_cpq(triple(sK0,sK1,sK2),sK3))
    | ~ spl4_3 ),
    inference(avatar_component_clause,[],[f165]) ).

fof(f395,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ ok(remove_cpq(triple(X0,X1,X2),X3))
        | check_cpq(triple(X0,X1,X2))
        | ~ check_cpq(remove_cpq(triple(X0,X1,X2),X3)) )
    | ~ spl4_46 ),
    inference(avatar_component_clause,[],[f394]) ).

fof(f422,plain,
    spl4_50,
    inference(avatar_split_clause,[],[f134,f420]) ).

fof(f420,plain,
    ( spl4_50
  <=> ! [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,[spl4_50])]) ).

fof(f134,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,[],[f83]) ).

fof(f83,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,[],[f82]) ).

fof(f82,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/sandbox/benchmark/theBenchmark.p',ax44) ).

fof(f418,plain,
    spl4_49,
    inference(avatar_split_clause,[],[f133,f416]) ).

fof(f416,plain,
    ( spl4_49
  <=> ! [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,[spl4_49])]) ).

fof(f133,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,[],[f81]) ).

fof(f81,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,[],[f80]) ).

fof(f80,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/sandbox/benchmark/theBenchmark.p',ax45) ).

fof(f409,plain,
    spl4_48,
    inference(avatar_split_clause,[],[f129,f407]) ).

fof(f407,plain,
    ( spl4_48
  <=> ! [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,[spl4_48])]) ).

fof(f129,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,[],[f73]) ).

fof(f73,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,[],[f72]) ).

fof(f72,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/sandbox/benchmark/theBenchmark.p',ax25) ).

fof(f402,plain,
    spl4_47,
    inference(avatar_split_clause,[],[f130,f400]) ).

fof(f400,plain,
    ( spl4_47
  <=> ! [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,[spl4_47])]) ).

fof(f130,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,[],[f75]) ).

fof(f75,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,[],[f74]) ).

fof(f74,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,[],[f48]) ).

fof(f48,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/sandbox/benchmark/theBenchmark.p',ax47) ).

fof(f396,plain,
    spl4_46,
    inference(avatar_split_clause,[],[f98,f394]) ).

fof(f98,plain,
    ! [X2,X3,X0,X1] :
      ( check_cpq(triple(X0,X1,X2))
      | ~ ok(remove_cpq(triple(X0,X1,X2),X3))
      | ~ check_cpq(remove_cpq(triple(X0,X1,X2),X3)) ),
    inference(cnf_transformation,[],[f56]) ).

fof(f56,plain,
    ! [X0,X1,X2,X3] :
      ( check_cpq(triple(X0,X1,X2))
      | ~ ok(remove_cpq(triple(X0,X1,X2),X3))
      | ~ check_cpq(remove_cpq(triple(X0,X1,X2),X3)) ),
    inference(flattening,[],[f55]) ).

fof(f55,plain,
    ! [X0,X1,X2,X3] :
      ( check_cpq(triple(X0,X1,X2))
      | ~ ok(remove_cpq(triple(X0,X1,X2),X3))
      | ~ check_cpq(remove_cpq(triple(X0,X1,X2),X3)) ),
    inference(ennf_transformation,[],[f42]) ).

fof(f42,axiom,
    ! [X0,X1,X2,X3] :
      ( ( ok(remove_cpq(triple(X0,X1,X2),X3))
        & check_cpq(remove_cpq(triple(X0,X1,X2),X3)) )
     => check_cpq(triple(X0,X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_l027) ).

fof(f382,plain,
    spl4_45,
    inference(avatar_split_clause,[],[f127,f380]) ).

fof(f380,plain,
    ( spl4_45
  <=> ! [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,[spl4_45])]) ).

fof(f127,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,[],[f69]) ).

fof(f69,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/sandbox/benchmark/theBenchmark.p',ax30) ).

fof(f378,plain,
    spl4_44,
    inference(avatar_split_clause,[],[f126,f376]) ).

fof(f376,plain,
    ( spl4_44
  <=> ! [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,[spl4_44])]) ).

fof(f126,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,[],[f68]) ).

fof(f68,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/sandbox/benchmark/theBenchmark.p',ax29) ).

fof(f359,plain,
    spl4_43,
    inference(avatar_split_clause,[],[f142,f357]) ).

fof(f357,plain,
    ( spl4_43
  <=> ! [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,[spl4_43])]) ).

fof(f142,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,[],[f92]) ).

fof(f92,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,[],[f85]) ).

fof(f85,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/sandbox/benchmark/theBenchmark.p',ax37) ).

fof(f355,plain,
    spl4_42,
    inference(avatar_split_clause,[],[f141,f353]) ).

fof(f353,plain,
    ( spl4_42
  <=> ! [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,[spl4_42])]) ).

fof(f141,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,[],[f92]) ).

fof(f350,plain,
    spl4_41,
    inference(avatar_split_clause,[],[f128,f348]) ).

fof(f348,plain,
    ( spl4_41
  <=> ! [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,[spl4_41])]) ).

fof(f128,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,[],[f71]) ).

fof(f71,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,[],[f70]) ).

fof(f70,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/sandbox/benchmark/theBenchmark.p',ax27) ).

fof(f346,plain,
    spl4_40,
    inference(avatar_split_clause,[],[f123,f344]) ).

fof(f344,plain,
    ( spl4_40
  <=> ! [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,[spl4_40])]) ).

fof(f123,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/sandbox/benchmark/theBenchmark.p',ax42) ).

fof(f338,plain,
    spl4_39,
    inference(avatar_split_clause,[],[f144,f336]) ).

fof(f336,plain,
    ( spl4_39
  <=> ! [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,[spl4_39])]) ).

fof(f144,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,[],[f94]) ).

fof(f94,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,[],[f93]) ).

fof(f93,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/sandbox/benchmark/theBenchmark.p',ax23) ).

fof(f334,plain,
    spl4_38,
    inference(avatar_split_clause,[],[f143,f332]) ).

fof(f332,plain,
    ( spl4_38
  <=> ! [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,[spl4_38])]) ).

fof(f143,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,[],[f94]) ).

fof(f328,plain,
    spl4_37,
    inference(avatar_split_clause,[],[f125,f326]) ).

fof(f326,plain,
    ( spl4_37
  <=> ! [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,[spl4_37])]) ).

fof(f125,plain,
    ! [X2,X3,X0,X1] :
      ( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
      | contains_slb(X1,X3) ),
    inference(cnf_transformation,[],[f67]) ).

fof(f67,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/sandbox/benchmark/theBenchmark.p',ax43) ).

fof(f322,plain,
    spl4_36,
    inference(avatar_split_clause,[],[f137,f320]) ).

fof(f320,plain,
    ( spl4_36
  <=> ! [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,[spl4_36])]) ).

fof(f137,plain,
    ! [X2,X3,X0,X1] :
      ( X1 = X2
      | contains_slb(X0,X2)
      | ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f91,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,[],[f90]) ).

fof(f90,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/sandbox/benchmark/theBenchmark.p',ax21) ).

fof(f318,plain,
    ( spl4_35
    | ~ spl4_8
    | ~ spl4_25 ),
    inference(avatar_split_clause,[],[f275,f257,f187,f316]) ).

fof(f316,plain,
    ( spl4_35
  <=> ! [X0,X1] :
        ( less_than(X0,X1)
        | ~ less_than(X0,bottom) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_35])]) ).

fof(f187,plain,
    ( spl4_8
  <=> ! [X0] : less_than(bottom,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_8])]) ).

fof(f257,plain,
    ( spl4_25
  <=> ! [X2,X0,X1] :
        ( less_than(X0,X2)
        | ~ less_than(X1,X2)
        | ~ less_than(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_25])]) ).

fof(f275,plain,
    ( ! [X0,X1] :
        ( less_than(X0,X1)
        | ~ less_than(X0,bottom) )
    | ~ spl4_8
    | ~ spl4_25 ),
    inference(resolution,[],[f258,f188]) ).

fof(f188,plain,
    ( ! [X0] : less_than(bottom,X0)
    | ~ spl4_8 ),
    inference(avatar_component_clause,[],[f187]) ).

fof(f258,plain,
    ( ! [X2,X0,X1] :
        ( ~ less_than(X1,X2)
        | less_than(X0,X2)
        | ~ less_than(X0,X1) )
    | ~ spl4_25 ),
    inference(avatar_component_clause,[],[f257]) ).

fof(f314,plain,
    spl4_34,
    inference(avatar_split_clause,[],[f145,f312]) ).

fof(f312,plain,
    ( spl4_34
  <=> ! [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,[spl4_34])]) ).

fof(f145,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,[],[f94]) ).

fof(f310,plain,
    spl4_33,
    inference(avatar_split_clause,[],[f140,f308]) ).

fof(f308,plain,
    ( spl4_33
  <=> ! [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,[spl4_33])]) ).

fof(f140,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,[],[f84]) ).

fof(f84,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,[],[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(flattening,[],[f51]) ).

fof(f51,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/sandbox/benchmark/theBenchmark.p',ax38) ).

fof(f303,plain,
    spl4_32,
    inference(avatar_split_clause,[],[f150,f301]) ).

fof(f301,plain,
    ( spl4_32
  <=> ! [X2,X0,X1] :
        ( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
        | create_slb = X1 ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_32])]) ).

fof(f150,plain,
    ! [X2,X0,X1] :
      ( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
      | create_slb = X1 ),
    inference(definition_unfolding,[],[f124,f105]) ).

fof(f105,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/sandbox/benchmark/theBenchmark.p',ax53) ).

fof(f124,plain,
    ! [X2,X0,X1] :
      ( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
      | create_slb = X1 ),
    inference(cnf_transformation,[],[f66]) ).

fof(f66,plain,
    ! [X0,X1,X2] :
      ( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
      | create_slb = X1 ),
    inference(ennf_transformation,[],[f47]) ).

fof(f47,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/sandbox/benchmark/theBenchmark.p',ax51) ).

fof(f294,plain,
    spl4_31,
    inference(avatar_split_clause,[],[f149,f292]) ).

fof(f292,plain,
    ( spl4_31
  <=> ! [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,[spl4_31])]) ).

fof(f149,plain,
    ! [X0,X1] :
      ( succ_cpq(X0,remove_cpq(findmin_cpq_eff(X1),removemin_cpq_res(X1)))
      | ~ succ_cpq(X0,X1) ),
    inference(definition_unfolding,[],[f112,f147]) ).

fof(f147,plain,
    ! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),removemin_cpq_res(X0)),
    inference(definition_unfolding,[],[f106,f105]) ).

fof(f106,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/sandbox/benchmark/theBenchmark.p',ax52) ).

fof(f112,plain,
    ! [X0,X1] :
      ( succ_cpq(X0,removemin_cpq_eff(X1))
      | ~ succ_cpq(X0,X1) ),
    inference(cnf_transformation,[],[f57]) ).

fof(f57,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/sandbox/benchmark/theBenchmark.p',ax35) ).

fof(f290,plain,
    ( spl4_30
    | ~ spl4_13
    | ~ spl4_22 ),
    inference(avatar_split_clause,[],[f273,f245,f207,f288]) ).

fof(f288,plain,
    ( spl4_30
  <=> ! [X0,X1] :
        ( less_than(X0,X1)
        | strictly_less_than(X1,X0) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_30])]) ).

fof(f207,plain,
    ( spl4_13
  <=> ! [X0,X1] :
        ( less_than(X1,X0)
        | less_than(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_13])]) ).

fof(f245,plain,
    ( spl4_22
  <=> ! [X0,X1] :
        ( strictly_less_than(X0,X1)
        | less_than(X1,X0)
        | ~ less_than(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_22])]) ).

fof(f273,plain,
    ( ! [X0,X1] :
        ( less_than(X0,X1)
        | strictly_less_than(X1,X0) )
    | ~ spl4_13
    | ~ spl4_22 ),
    inference(duplicate_literal_removal,[],[f270]) ).

fof(f270,plain,
    ( ! [X0,X1] :
        ( less_than(X0,X1)
        | strictly_less_than(X1,X0)
        | less_than(X0,X1) )
    | ~ spl4_13
    | ~ spl4_22 ),
    inference(resolution,[],[f246,f208]) ).

fof(f208,plain,
    ( ! [X0,X1] :
        ( less_than(X1,X0)
        | less_than(X0,X1) )
    | ~ spl4_13 ),
    inference(avatar_component_clause,[],[f207]) ).

fof(f246,plain,
    ( ! [X0,X1] :
        ( ~ less_than(X0,X1)
        | less_than(X1,X0)
        | strictly_less_than(X0,X1) )
    | ~ spl4_22 ),
    inference(avatar_component_clause,[],[f245]) ).

fof(f286,plain,
    spl4_29,
    inference(avatar_split_clause,[],[f138,f284]) ).

fof(f284,plain,
    ( spl4_29
  <=> ! [X0,X3,X2,X1] :
        ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
        | ~ contains_slb(X0,X2) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_29])]) ).

fof(f138,plain,
    ! [X2,X3,X0,X1] :
      ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
      | ~ contains_slb(X0,X2) ),
    inference(cnf_transformation,[],[f91]) ).

fof(f282,plain,
    spl4_28,
    inference(avatar_split_clause,[],[f110,f280]) ).

fof(f280,plain,
    ( spl4_28
  <=> ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_28])]) ).

fof(f110,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/sandbox/benchmark/theBenchmark.p',ax46) ).

fof(f267,plain,
    spl4_27,
    inference(avatar_split_clause,[],[f136,f265]) ).

fof(f265,plain,
    ( spl4_27
  <=> ! [X0,X3,X2,X1] :
        ( contains_cpq(triple(X0,X1,X2),X3)
        | ~ contains_slb(X1,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_27])]) ).

fof(f136,plain,
    ! [X2,X3,X0,X1] :
      ( contains_cpq(triple(X0,X1,X2),X3)
      | ~ contains_slb(X1,X3) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f89,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/sandbox/benchmark/theBenchmark.p',ax39) ).

fof(f263,plain,
    spl4_26,
    inference(avatar_split_clause,[],[f135,f261]) ).

fof(f261,plain,
    ( spl4_26
  <=> ! [X2,X0,X1,X3] :
        ( contains_slb(X1,X3)
        | ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_26])]) ).

fof(f135,plain,
    ! [X2,X3,X0,X1] :
      ( contains_slb(X1,X3)
      | ~ contains_cpq(triple(X0,X1,X2),X3) ),
    inference(cnf_transformation,[],[f89]) ).

fof(f259,plain,
    spl4_25,
    inference(avatar_split_clause,[],[f122,f257]) ).

fof(f122,plain,
    ! [X2,X0,X1] :
      ( less_than(X0,X2)
      | ~ less_than(X1,X2)
      | ~ less_than(X0,X1) ),
    inference(cnf_transformation,[],[f65]) ).

fof(f65,plain,
    ! [X0,X1,X2] :
      ( less_than(X0,X2)
      | ~ less_than(X1,X2)
      | ~ less_than(X0,X1) ),
    inference(flattening,[],[f64]) ).

fof(f64,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/sandbox/benchmark/theBenchmark.p',transitivity) ).

fof(f255,plain,
    spl4_24,
    inference(avatar_split_clause,[],[f118,f253]) ).

fof(f253,plain,
    ( spl4_24
  <=> ! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_24])]) ).

fof(f118,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/sandbox/benchmark/theBenchmark.p',ax26) ).

fof(f251,plain,
    spl4_23,
    inference(avatar_split_clause,[],[f117,f249]) ).

fof(f249,plain,
    ( spl4_23
  <=> ! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0 ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_23])]) ).

fof(f117,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/sandbox/benchmark/theBenchmark.p',ax24) ).

fof(f247,plain,
    spl4_22,
    inference(avatar_split_clause,[],[f114,f245]) ).

fof(f114,plain,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
      | less_than(X1,X0)
      | ~ less_than(X0,X1) ),
    inference(cnf_transformation,[],[f60]) ).

fof(f60,plain,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
      | less_than(X1,X0)
      | ~ less_than(X0,X1) ),
    inference(flattening,[],[f59]) ).

fof(f59,plain,
    ! [X0,X1] :
      ( strictly_less_than(X0,X1)
      | less_than(X1,X0)
      | ~ less_than(X0,X1) ),
    inference(ennf_transformation,[],[f53]) ).

fof(f53,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/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).

fof(f242,plain,
    spl4_21,
    inference(avatar_split_clause,[],[f153,f240]) ).

fof(f240,plain,
    ( spl4_21
  <=> ! [X4,X0,X2] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_21])]) ).

fof(f153,plain,
    ! [X2,X0,X4] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4),
    inference(equality_resolution,[],[f152]) ).

fof(f152,plain,
    ! [X2,X0,X1,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X4)),X2,X4)
      | X1 != X2 ),
    inference(equality_resolution,[],[f146]) ).

fof(f146,plain,
    ! [X2,X3,X0,X1,X4] :
      ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
      | X3 != X4
      | X1 != X2 ),
    inference(cnf_transformation,[],[f94]) ).

fof(f238,plain,
    spl4_20,
    inference(avatar_split_clause,[],[f121,f236]) ).

fof(f236,plain,
    ( spl4_20
  <=> ! [X2,X0,X1] :
        ( bad = X2
        | ok(triple(X0,X1,X2)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_20])]) ).

fof(f121,plain,
    ! [X2,X0,X1] :
      ( bad = X2
      | ok(triple(X0,X1,X2)) ),
    inference(cnf_transformation,[],[f63]) ).

fof(f63,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/sandbox/benchmark/theBenchmark.p',ax41) ).

fof(f234,plain,
    spl4_19,
    inference(avatar_split_clause,[],[f120,f232]) ).

fof(f232,plain,
    ( spl4_19
  <=> ! [X2,X0,X1] :
        ( succ_cpq(X0,remove_cpq(X1,X2))
        | ~ succ_cpq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_19])]) ).

fof(f120,plain,
    ! [X2,X0,X1] :
      ( succ_cpq(X0,remove_cpq(X1,X2))
      | ~ succ_cpq(X0,X1) ),
    inference(cnf_transformation,[],[f62]) ).

fof(f62,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/sandbox/benchmark/theBenchmark.p',ax33) ).

fof(f230,plain,
    spl4_18,
    inference(avatar_split_clause,[],[f119,f228]) ).

fof(f228,plain,
    ( spl4_18
  <=> ! [X2,X0,X1] :
        ( succ_cpq(X0,insert_cpq(X1,X2))
        | ~ succ_cpq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_18])]) ).

fof(f119,plain,
    ! [X2,X0,X1] :
      ( succ_cpq(X0,insert_cpq(X1,X2))
      | ~ succ_cpq(X0,X1) ),
    inference(cnf_transformation,[],[f61]) ).

fof(f61,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/sandbox/benchmark/theBenchmark.p',ax32) ).

fof(f226,plain,
    spl4_17,
    inference(avatar_split_clause,[],[f151,f224]) ).

fof(f224,plain,
    ( spl4_17
  <=> ! [X2,X0,X3] : contains_slb(insert_slb(X0,pair(X2,X3)),X2) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_17])]) ).

fof(f151,plain,
    ! [X2,X3,X0] : contains_slb(insert_slb(X0,pair(X2,X3)),X2),
    inference(equality_resolution,[],[f139]) ).

fof(f139,plain,
    ! [X2,X3,X0,X1] :
      ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
      | X1 != X2 ),
    inference(cnf_transformation,[],[f91]) ).

fof(f222,plain,
    spl4_16,
    inference(avatar_split_clause,[],[f148,f220]) ).

fof(f220,plain,
    ( spl4_16
  <=> ! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_16])]) ).

fof(f148,plain,
    ! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)),
    inference(definition_unfolding,[],[f109,f105]) ).

fof(f109,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/sandbox/benchmark/theBenchmark.p',ax50) ).

fof(f218,plain,
    spl4_15,
    inference(avatar_split_clause,[],[f113,f216]) ).

fof(f216,plain,
    ( spl4_15
  <=> ! [X0,X1] :
        ( succ_cpq(X0,findmin_cpq_eff(X1))
        | ~ succ_cpq(X0,X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_15])]) ).

fof(f113,plain,
    ! [X0,X1] :
      ( succ_cpq(X0,findmin_cpq_eff(X1))
      | ~ succ_cpq(X0,X1) ),
    inference(cnf_transformation,[],[f58]) ).

fof(f58,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/sandbox/benchmark/theBenchmark.p',ax34) ).

fof(f213,plain,
    spl4_14,
    inference(avatar_split_clause,[],[f116,f211]) ).

fof(f211,plain,
    ( spl4_14
  <=> ! [X2,X0,X1] : isnonempty_slb(insert_slb(X0,pair(X1,X2))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_14])]) ).

fof(f116,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/sandbox/benchmark/theBenchmark.p',ax19) ).

fof(f209,plain,
    spl4_13,
    inference(avatar_split_clause,[],[f111,f207]) ).

fof(f111,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/sandbox/benchmark/theBenchmark.p',totality) ).

fof(f205,plain,
    spl4_12,
    inference(avatar_split_clause,[],[f115,f203]) ).

fof(f203,plain,
    ( spl4_12
  <=> ! [X0,X1] : ~ ok(triple(X0,X1,bad)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_12])]) ).

fof(f115,plain,
    ! [X0,X1] : ~ ok(triple(X0,X1,bad)),
    inference(cnf_transformation,[],[f46]) ).

fof(f46,plain,
    ! [X0,X1] : ~ ok(triple(X0,X1,bad)),
    inference(flattening,[],[f45]) ).

fof(f45,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/sandbox/benchmark/theBenchmark.p',ax40) ).

fof(f201,plain,
    spl4_11,
    inference(avatar_split_clause,[],[f108,f199]) ).

fof(f199,plain,
    ( spl4_11
  <=> ! [X0,X1] : check_cpq(triple(X0,create_slb,X1)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_11])]) ).

fof(f108,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/sandbox/benchmark/theBenchmark.p',ax36) ).

fof(f197,plain,
    spl4_10,
    inference(avatar_split_clause,[],[f104,f195]) ).

fof(f195,plain,
    ( spl4_10
  <=> ! [X0] : create_slb = update_slb(create_slb,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_10])]) ).

fof(f104,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/sandbox/benchmark/theBenchmark.p',ax28) ).

fof(f193,plain,
    spl4_9,
    inference(avatar_split_clause,[],[f107,f191]) ).

fof(f191,plain,
    ( spl4_9
  <=> ! [X0,X1] : ~ pair_in_list(create_slb,X0,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_9])]) ).

fof(f107,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/sandbox/benchmark/theBenchmark.p',ax22) ).

fof(f189,plain,
    spl4_8,
    inference(avatar_split_clause,[],[f103,f187]) ).

fof(f103,plain,
    ! [X0] : less_than(bottom,X0),
    inference(cnf_transformation,[],[f5]) ).

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

fof(f185,plain,
    spl4_7,
    inference(avatar_split_clause,[],[f102,f183]) ).

fof(f183,plain,
    ( spl4_7
  <=> ! [X0] : less_than(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_7])]) ).

fof(f102,plain,
    ! [X0] : less_than(X0,X0),
    inference(cnf_transformation,[],[f3]) ).

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

fof(f181,plain,
    spl4_6,
    inference(avatar_split_clause,[],[f101,f179]) ).

fof(f179,plain,
    ( spl4_6
  <=> ! [X0] : succ_cpq(X0,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_6])]) ).

fof(f101,plain,
    ! [X0] : succ_cpq(X0,X0),
    inference(cnf_transformation,[],[f19]) ).

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

fof(f177,plain,
    spl4_5,
    inference(avatar_split_clause,[],[f100,f175]) ).

fof(f175,plain,
    ( spl4_5
  <=> ! [X0] : ~ contains_slb(create_slb,X0) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_5])]) ).

fof(f100,plain,
    ! [X0] : ~ contains_slb(create_slb,X0),
    inference(cnf_transformation,[],[f8]) ).

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

fof(f173,plain,
    ~ spl4_4,
    inference(avatar_split_clause,[],[f99,f170]) ).

fof(f170,plain,
    ( spl4_4
  <=> isnonempty_slb(create_slb) ),
    introduced(avatar_definition,[new_symbols(naming,[spl4_4])]) ).

fof(f99,plain,
    ~ isnonempty_slb(create_slb),
    inference(cnf_transformation,[],[f6]) ).

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

fof(f168,plain,
    spl4_3,
    inference(avatar_split_clause,[],[f97,f165]) ).

fof(f97,plain,
    ok(remove_cpq(triple(sK0,sK1,sK2),sK3)),
    inference(cnf_transformation,[],[f88]) ).

fof(f88,plain,
    ( ok(remove_cpq(triple(sK0,sK1,sK2),sK3))
    & check_cpq(remove_cpq(triple(sK0,sK1,sK2),sK3))
    & ~ check_cpq(triple(sK0,sK1,sK2)) ),
    inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f54,f87,f86]) ).

fof(f86,plain,
    ( ? [X0,X1,X2] :
        ( ? [X3] :
            ( ok(remove_cpq(triple(X0,X1,X2),X3))
            & check_cpq(remove_cpq(triple(X0,X1,X2),X3)) )
        & ~ check_cpq(triple(X0,X1,X2)) )
   => ( ? [X3] :
          ( ok(remove_cpq(triple(sK0,sK1,sK2),X3))
          & check_cpq(remove_cpq(triple(sK0,sK1,sK2),X3)) )
      & ~ check_cpq(triple(sK0,sK1,sK2)) ) ),
    introduced(choice_axiom,[]) ).

fof(f87,plain,
    ( ? [X3] :
        ( ok(remove_cpq(triple(sK0,sK1,sK2),X3))
        & check_cpq(remove_cpq(triple(sK0,sK1,sK2),X3)) )
   => ( ok(remove_cpq(triple(sK0,sK1,sK2),sK3))
      & check_cpq(remove_cpq(triple(sK0,sK1,sK2),sK3)) ) ),
    introduced(choice_axiom,[]) ).

fof(f54,plain,
    ? [X0,X1,X2] :
      ( ? [X3] :
          ( ok(remove_cpq(triple(X0,X1,X2),X3))
          & check_cpq(remove_cpq(triple(X0,X1,X2),X3)) )
      & ~ check_cpq(triple(X0,X1,X2)) ),
    inference(ennf_transformation,[],[f44]) ).

fof(f44,negated_conjecture,
    ~ ! [X0,X1,X2] :
        ( ~ check_cpq(triple(X0,X1,X2))
       => ! [X3] :
            ( ~ ok(remove_cpq(triple(X0,X1,X2),X3))
            | ~ check_cpq(remove_cpq(triple(X0,X1,X2),X3)) ) ),
    inference(negated_conjecture,[],[f43]) ).

fof(f43,conjecture,
    ! [X0,X1,X2] :
      ( ~ check_cpq(triple(X0,X1,X2))
     => ! [X3] :
          ( ~ ok(remove_cpq(triple(X0,X1,X2),X3))
          | ~ check_cpq(remove_cpq(triple(X0,X1,X2),X3)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_co) ).

fof(f163,plain,
    spl4_2,
    inference(avatar_split_clause,[],[f96,f160]) ).

fof(f96,plain,
    check_cpq(remove_cpq(triple(sK0,sK1,sK2),sK3)),
    inference(cnf_transformation,[],[f88]) ).

fof(f158,plain,
    ~ spl4_1,
    inference(avatar_split_clause,[],[f95,f155]) ).

fof(f95,plain,
    ~ check_cpq(triple(sK0,sK1,sK2)),
    inference(cnf_transformation,[],[f88]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : SWV387+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.15  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36  % Computer : n026.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Fri May  3 20:55:23 EDT 2024
% 0.15/0.36  % CPUTime    : 
% 0.15/0.37  % (8661)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38  % (8664)WARNING: value z3 for option sas not known
% 0.15/0.38  % (8665)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.39  % (8662)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39  % (8663)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.39  % (8664)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)
% 0.15/0.39  % (8666)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)
% 0.15/0.39  % (8667)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)
% 0.15/0.39  % (8668)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)
% 0.15/0.39  TRYING [1]
% 0.15/0.39  TRYING [2]
% 0.15/0.39  % (8666)First to succeed.
% 0.15/0.39  % (8667)Also succeeded, but the first one will report.
% 0.15/0.40  % (8666)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-8661"
% 0.15/0.40  TRYING [1]
% 0.15/0.40  % (8666)Refutation found. Thanks to Tanya!
% 0.15/0.40  % SZS status Theorem for theBenchmark
% 0.15/0.40  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.40  % (8666)------------------------------
% 0.15/0.40  % (8666)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.40  % (8666)Termination reason: Refutation
% 0.15/0.40  
% 0.15/0.40  % (8666)Memory used [KB]: 1039
% 0.15/0.40  % (8666)Time elapsed: 0.015 s
% 0.15/0.40  % (8666)Instructions burned: 20 (million)
% 0.15/0.40  % (8661)Success in time 0.031 s
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