TSTP Solution File: PUZ062-2 by Vampire-SAT---4.8

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Vampire-SAT---4.8
% Problem  : PUZ062-2 : TPTP v8.2.0. Released v3.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s

% Computer : n032.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 May 21 02:29:21 EDT 2024

% Result   : Unsatisfiable 0.15s 0.34s
% Output   : Refutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   54
% Syntax   : Number of formulae    :  163 (  22 unt;   0 def)
%            Number of atoms       :  425 (  65 equ)
%            Maximal formula atoms :    5 (   2 avg)
%            Number of connectives :  455 ( 193   ~; 221   |;   0   &)
%                                         (  41 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   4 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of predicates  :   44 (  42 usr;  42 prp; 0-3 aty)
%            Number of functors    :   20 (  20 usr;  11 con; 0-4 aty)
%            Number of variables   :  143 ( 143   !;   0   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f242,plain,
    $false,
    inference(avatar_sat_refutation,[],[f18,f23,f27,f32,f37,f42,f46,f53,f57,f62,f67,f73,f82,f87,f89,f96,f102,f107,f112,f116,f124,f129,f138,f142,f147,f155,f166,f172,f176,f180,f187,f194,f199,f204,f208,f212,f216,f224,f232,f235,f237,f241]) ).

fof(f241,plain,
    ( ~ spl0_3
    | ~ spl0_29 ),
    inference(avatar_contradiction_clause,[],[f240]) ).

fof(f240,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_29 ),
    inference(resolution,[],[f165,f26]) ).

fof(f26,plain,
    ( ! [X1,X6] : ~ c_in(X6,c_emptyset,X1)
    | ~ spl0_3 ),
    inference(avatar_component_clause,[],[f25]) ).

fof(f25,plain,
    ( spl0_3
  <=> ! [X6,X1] : ~ c_in(X6,c_emptyset,X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).

fof(f165,plain,
    ( c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat))
    | ~ spl0_29 ),
    inference(avatar_component_clause,[],[f163]) ).

fof(f163,plain,
    ( spl0_29
  <=> c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).

fof(f237,plain,
    ( ~ spl0_3
    | ~ spl0_24 ),
    inference(avatar_contradiction_clause,[],[f236]) ).

fof(f236,plain,
    ( $false
    | ~ spl0_3
    | ~ spl0_24 ),
    inference(resolution,[],[f137,f26]) ).

fof(f137,plain,
    ( c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat))
    | ~ spl0_24 ),
    inference(avatar_component_clause,[],[f135]) ).

fof(f135,plain,
    ( spl0_24
  <=> c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).

fof(f235,plain,
    ( ~ spl0_38
    | spl0_41 ),
    inference(avatar_contradiction_clause,[],[f234]) ).

fof(f234,plain,
    ( $false
    | ~ spl0_38
    | spl0_41 ),
    inference(trivial_inequality_removal,[],[f233]) ).

fof(f233,plain,
    ( c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) != c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
    | ~ spl0_38
    | spl0_41 ),
    inference(superposition,[],[f231,f211]) ).

fof(f211,plain,
    ( ! [X0] : c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
    | ~ spl0_38 ),
    inference(avatar_component_clause,[],[f210]) ).

fof(f210,plain,
    ( spl0_38
  <=> ! [X0] : c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).

fof(f231,plain,
    ( c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
    | spl0_41 ),
    inference(avatar_component_clause,[],[f229]) ).

fof(f229,plain,
    ( spl0_41
  <=> c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).

fof(f232,plain,
    ( ~ spl0_41
    | ~ spl0_6
    | spl0_8
    | ~ spl0_39 ),
    inference(avatar_split_clause,[],[f220,f214,f50,f39,f229]) ).

fof(f39,plain,
    ( spl0_6
  <=> c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).

fof(f50,plain,
    ( spl0_8
  <=> c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).

fof(f214,plain,
    ( spl0_39
  <=> ! [X0] : c_Suc(c_Finite__Set_Ocard(c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) = c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).

fof(f220,plain,
    ( c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
    | ~ spl0_6
    | spl0_8
    | ~ spl0_39 ),
    inference(forward_demodulation,[],[f219,f41]) ).

fof(f41,plain,
    ( c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ spl0_6 ),
    inference(avatar_component_clause,[],[f39]) ).

fof(f219,plain,
    ( c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Suc(c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
    | spl0_8
    | ~ spl0_39 ),
    inference(superposition,[],[f52,f215]) ).

fof(f215,plain,
    ( ! [X0] : c_Suc(c_Finite__Set_Ocard(c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) = c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ spl0_39 ),
    inference(avatar_component_clause,[],[f214]) ).

fof(f52,plain,
    ( c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | spl0_8 ),
    inference(avatar_component_clause,[],[f50]) ).

fof(f224,plain,
    ( spl0_40
    | ~ spl0_9
    | ~ spl0_33 ),
    inference(avatar_split_clause,[],[f188,f185,f55,f222]) ).

fof(f222,plain,
    ( spl0_40
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,c_inter(X2,X3,X4),X4),X4),X4) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,c_inter(X2,X3,X4),X4),X4))
        | ~ c_in(X3,c_Finite__Set_OFinites,tc_set(X4))
        | c_in(X0,X3,X4) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).

fof(f55,plain,
    ( spl0_9
  <=> ! [X0,X6,X1,X7] :
        ( c_in(X6,X7,X1)
        | ~ c_in(X6,c_inter(X0,X7,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).

fof(f185,plain,
    ( spl0_33
  <=> ! [X4,X0,X3,X2,X1] :
        ( c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,c_inter(X2,X3,X4),X4),X4),X4) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,c_inter(X2,X3,X4),X4),X4))
        | c_in(X0,c_inter(X2,X3,X4),X4)
        | ~ c_in(X3,c_Finite__Set_OFinites,tc_set(X4)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).

fof(f188,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,c_inter(X2,X3,X4),X4),X4),X4) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,c_inter(X2,X3,X4),X4),X4))
        | ~ c_in(X3,c_Finite__Set_OFinites,tc_set(X4))
        | c_in(X0,X3,X4) )
    | ~ spl0_9
    | ~ spl0_33 ),
    inference(resolution,[],[f186,f56]) ).

fof(f56,plain,
    ( ! [X0,X1,X6,X7] :
        ( ~ c_in(X6,c_inter(X0,X7,X1),X1)
        | c_in(X6,X7,X1) )
    | ~ spl0_9 ),
    inference(avatar_component_clause,[],[f55]) ).

fof(f186,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_in(X0,c_inter(X2,X3,X4),X4)
        | c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,c_inter(X2,X3,X4),X4),X4),X4) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,c_inter(X2,X3,X4),X4),X4))
        | ~ c_in(X3,c_Finite__Set_OFinites,tc_set(X4)) )
    | ~ spl0_33 ),
    inference(avatar_component_clause,[],[f185]) ).

fof(f216,plain,
    ( spl0_39
    | spl0_28
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f183,f178,f159,f214]) ).

fof(f159,plain,
    ( spl0_28
  <=> c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).

fof(f178,plain,
    ( spl0_32
  <=> ! [X0,X1] :
        ( c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
        | c_in(X0,v_t,tc_prod(tc_nat,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).

fof(f183,plain,
    ( ! [X0] : c_Suc(c_Finite__Set_Ocard(c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) = c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | spl0_28
    | ~ spl0_32 ),
    inference(resolution,[],[f179,f161]) ).

fof(f161,plain,
    ( ~ c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat))
    | spl0_28 ),
    inference(avatar_component_clause,[],[f159]) ).

fof(f179,plain,
    ( ! [X0,X1] :
        ( c_in(X0,v_t,tc_prod(tc_nat,tc_nat))
        | c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) )
    | ~ spl0_32 ),
    inference(avatar_component_clause,[],[f178]) ).

fof(f212,plain,
    ( spl0_38
    | spl0_23
    | ~ spl0_32 ),
    inference(avatar_split_clause,[],[f182,f178,f131,f210]) ).

fof(f131,plain,
    ( spl0_23
  <=> c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).

fof(f182,plain,
    ( ! [X0] : c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
    | spl0_23
    | ~ spl0_32 ),
    inference(resolution,[],[f179,f133]) ).

fof(f133,plain,
    ( ~ c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat))
    | spl0_23 ),
    inference(avatar_component_clause,[],[f131]) ).

fof(f208,plain,
    ( spl0_37
    | ~ spl0_3
    | ~ spl0_31 ),
    inference(avatar_split_clause,[],[f181,f174,f25,f206]) ).

fof(f206,plain,
    ( spl0_37
  <=> ! [X0,X1] : c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).

fof(f174,plain,
    ( spl0_31
  <=> ! [X0,X1] :
        ( c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
        | c_in(X0,c_emptyset,tc_prod(tc_nat,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).

fof(f181,plain,
    ( ! [X0,X1] : c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
    | ~ spl0_3
    | ~ spl0_31 ),
    inference(resolution,[],[f175,f26]) ).

fof(f175,plain,
    ( ! [X0,X1] :
        ( c_in(X0,c_emptyset,tc_prod(tc_nat,tc_nat))
        | c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))) )
    | ~ spl0_31 ),
    inference(avatar_component_clause,[],[f174]) ).

fof(f204,plain,
    ( spl0_36
    | ~ spl0_22
    | spl0_28 ),
    inference(avatar_split_clause,[],[f167,f159,f127,f201]) ).

fof(f201,plain,
    ( spl0_36
  <=> c_Suc(c_Finite__Set_Ocard(v_t,tc_prod(tc_nat,tc_nat))) = c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).

fof(f127,plain,
    ( spl0_22
  <=> ! [X0] :
        ( c_in(X0,v_t,tc_prod(tc_nat,tc_nat))
        | c_Finite__Set_Ocard(c_insert(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(v_t,tc_prod(tc_nat,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).

fof(f167,plain,
    ( c_Suc(c_Finite__Set_Ocard(v_t,tc_prod(tc_nat,tc_nat))) = c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ spl0_22
    | spl0_28 ),
    inference(resolution,[],[f161,f128]) ).

fof(f128,plain,
    ( ! [X0] :
        ( c_in(X0,v_t,tc_prod(tc_nat,tc_nat))
        | c_Finite__Set_Ocard(c_insert(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(v_t,tc_prod(tc_nat,tc_nat))) )
    | ~ spl0_22 ),
    inference(avatar_component_clause,[],[f127]) ).

fof(f199,plain,
    ( spl0_35
    | ~ spl0_22
    | spl0_23 ),
    inference(avatar_split_clause,[],[f151,f131,f127,f196]) ).

fof(f196,plain,
    ( spl0_35
  <=> c_Suc(c_Finite__Set_Ocard(v_t,tc_prod(tc_nat,tc_nat))) = c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).

fof(f151,plain,
    ( c_Suc(c_Finite__Set_Ocard(v_t,tc_prod(tc_nat,tc_nat))) = c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ spl0_22
    | spl0_23 ),
    inference(resolution,[],[f133,f128]) ).

fof(f194,plain,
    ( spl0_34
    | ~ spl0_5
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f157,f153,f34,f191]) ).

fof(f191,plain,
    ( spl0_34
  <=> c_Suc(c_Finite__Set_Ocard(c_emptyset,tc_prod(tc_nat,tc_nat))) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).

fof(f34,plain,
    ( spl0_5
  <=> c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).

fof(f153,plain,
    ( spl0_27
  <=> ! [X0] : c_Finite__Set_Ocard(c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_emptyset,tc_prod(tc_nat,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).

fof(f157,plain,
    ( c_Suc(c_Finite__Set_Ocard(c_emptyset,tc_prod(tc_nat,tc_nat))) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ spl0_5
    | ~ spl0_27 ),
    inference(superposition,[],[f154,f36]) ).

fof(f36,plain,
    ( c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat))
    | ~ spl0_5 ),
    inference(avatar_component_clause,[],[f34]) ).

fof(f154,plain,
    ( ! [X0] : c_Finite__Set_Ocard(c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_emptyset,tc_prod(tc_nat,tc_nat)))
    | ~ spl0_27 ),
    inference(avatar_component_clause,[],[f153]) ).

fof(f187,plain,
    ( spl0_33
    | ~ spl0_10
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f148,f145,f60,f185]) ).

fof(f60,plain,
    ( spl0_10
  <=> ! [X4,X1,X3] :
        ( ~ c_in(X3,c_Finite__Set_OFinites,tc_set(X1))
        | c_in(c_inter(X4,X3,X1),c_Finite__Set_OFinites,tc_set(X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).

fof(f145,plain,
    ( spl0_26
  <=> ! [X0,X3,X2,X1] :
        ( c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,X2,X3),X3),X3) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,X2,X3),X3))
        | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
        | c_in(X0,X2,X3) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).

fof(f148,plain,
    ( ! [X2,X3,X0,X1,X4] :
        ( c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,c_inter(X2,X3,X4),X4),X4),X4) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,c_inter(X2,X3,X4),X4),X4))
        | c_in(X0,c_inter(X2,X3,X4),X4)
        | ~ c_in(X3,c_Finite__Set_OFinites,tc_set(X4)) )
    | ~ spl0_10
    | ~ spl0_26 ),
    inference(resolution,[],[f146,f61]) ).

fof(f61,plain,
    ( ! [X3,X1,X4] :
        ( c_in(c_inter(X4,X3,X1),c_Finite__Set_OFinites,tc_set(X1))
        | ~ c_in(X3,c_Finite__Set_OFinites,tc_set(X1)) )
    | ~ spl0_10 ),
    inference(avatar_component_clause,[],[f60]) ).

fof(f146,plain,
    ( ! [X2,X3,X0,X1] :
        ( ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
        | c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,X2,X3),X3),X3) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,X2,X3),X3))
        | c_in(X0,X2,X3) )
    | ~ spl0_26 ),
    inference(avatar_component_clause,[],[f145]) ).

fof(f180,plain,
    ( spl0_32
    | ~ spl0_13
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f150,f145,f75,f178]) ).

fof(f75,plain,
    ( spl0_13
  <=> c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).

fof(f150,plain,
    ( ! [X0,X1] :
        ( c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
        | c_in(X0,v_t,tc_prod(tc_nat,tc_nat)) )
    | ~ spl0_13
    | ~ spl0_26 ),
    inference(resolution,[],[f146,f76]) ).

fof(f76,plain,
    ( c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ spl0_13 ),
    inference(avatar_component_clause,[],[f75]) ).

fof(f176,plain,
    ( spl0_31
    | ~ spl0_14
    | ~ spl0_26 ),
    inference(avatar_split_clause,[],[f149,f145,f79,f174]) ).

fof(f79,plain,
    ( spl0_14
  <=> c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).

fof(f149,plain,
    ( ! [X0,X1] :
        ( c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)))
        | c_in(X0,c_emptyset,tc_prod(tc_nat,tc_nat)) )
    | ~ spl0_14
    | ~ spl0_26 ),
    inference(resolution,[],[f146,f81]) ).

fof(f81,plain,
    ( c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ spl0_14 ),
    inference(avatar_component_clause,[],[f79]) ).

fof(f172,plain,
    ( spl0_30
    | ~ spl0_4
    | ~ spl0_27 ),
    inference(avatar_split_clause,[],[f156,f153,f29,f169]) ).

fof(f169,plain,
    ( spl0_30
  <=> c_Suc(c_Finite__Set_Ocard(c_emptyset,tc_prod(tc_nat,tc_nat))) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).

fof(f29,plain,
    ( spl0_4
  <=> c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).

fof(f156,plain,
    ( c_Suc(c_Finite__Set_Ocard(c_emptyset,tc_prod(tc_nat,tc_nat))) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ spl0_4
    | ~ spl0_27 ),
    inference(superposition,[],[f154,f31]) ).

fof(f31,plain,
    ( c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat))
    | ~ spl0_4 ),
    inference(avatar_component_clause,[],[f29]) ).

fof(f166,plain,
    ( ~ spl0_28
    | spl0_29
    | ~ spl0_19
    | ~ spl0_21 ),
    inference(avatar_split_clause,[],[f125,f121,f110,f163,f159]) ).

fof(f110,plain,
    ( spl0_19
  <=> ! [X0] :
        ( c_in(X0,c_emptyset,tc_prod(tc_nat,tc_nat))
        | ~ c_in(X0,v_a,tc_prod(tc_nat,tc_nat))
        | ~ c_in(X0,v_t,tc_prod(tc_nat,tc_nat)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).

fof(f121,plain,
    ( spl0_21
  <=> c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).

fof(f125,plain,
    ( c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat))
    | ~ c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat))
    | ~ spl0_19
    | ~ spl0_21 ),
    inference(resolution,[],[f123,f111]) ).

fof(f111,plain,
    ( ! [X0] :
        ( ~ c_in(X0,v_a,tc_prod(tc_nat,tc_nat))
        | c_in(X0,c_emptyset,tc_prod(tc_nat,tc_nat))
        | ~ c_in(X0,v_t,tc_prod(tc_nat,tc_nat)) )
    | ~ spl0_19 ),
    inference(avatar_component_clause,[],[f110]) ).

fof(f123,plain,
    ( c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat))
    | ~ spl0_21 ),
    inference(avatar_component_clause,[],[f121]) ).

fof(f155,plain,
    ( spl0_27
    | ~ spl0_3
    | ~ spl0_25 ),
    inference(avatar_split_clause,[],[f143,f140,f25,f153]) ).

fof(f140,plain,
    ( spl0_25
  <=> ! [X0] :
        ( c_in(X0,c_emptyset,tc_prod(tc_nat,tc_nat))
        | c_Finite__Set_Ocard(c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_emptyset,tc_prod(tc_nat,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).

fof(f143,plain,
    ( ! [X0] : c_Finite__Set_Ocard(c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_emptyset,tc_prod(tc_nat,tc_nat)))
    | ~ spl0_3
    | ~ spl0_25 ),
    inference(resolution,[],[f141,f26]) ).

fof(f141,plain,
    ( ! [X0] :
        ( c_in(X0,c_emptyset,tc_prod(tc_nat,tc_nat))
        | c_Finite__Set_Ocard(c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_emptyset,tc_prod(tc_nat,tc_nat))) )
    | ~ spl0_25 ),
    inference(avatar_component_clause,[],[f140]) ).

fof(f147,plain,
    ( spl0_26
    | ~ spl0_9
    | ~ spl0_20 ),
    inference(avatar_split_clause,[],[f117,f114,f55,f145]) ).

fof(f114,plain,
    ( spl0_20
  <=> ! [X0,X3,X2,X1] :
        ( c_in(X0,c_inter(X1,X2,X3),X3)
        | c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,X2,X3),X3),X3) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,X2,X3),X3))
        | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).

fof(f117,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,X2,X3),X3),X3) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,X2,X3),X3))
        | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3))
        | c_in(X0,X2,X3) )
    | ~ spl0_9
    | ~ spl0_20 ),
    inference(resolution,[],[f115,f56]) ).

fof(f115,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_in(X0,c_inter(X1,X2,X3),X3)
        | c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,X2,X3),X3),X3) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,X2,X3),X3))
        | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) )
    | ~ spl0_20 ),
    inference(avatar_component_clause,[],[f114]) ).

fof(f142,plain,
    ( spl0_25
    | ~ spl0_14
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f91,f85,f79,f140]) ).

fof(f85,plain,
    ( spl0_15
  <=> ! [X2,X0,X1] :
        ( c_in(X2,X0,X1)
        | ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1))
        | c_Finite__Set_Ocard(c_insert(X2,X0,X1),X1) = c_Suc(c_Finite__Set_Ocard(X0,X1)) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).

fof(f91,plain,
    ( ! [X0] :
        ( c_in(X0,c_emptyset,tc_prod(tc_nat,tc_nat))
        | c_Finite__Set_Ocard(c_insert(X0,c_emptyset,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(c_emptyset,tc_prod(tc_nat,tc_nat))) )
    | ~ spl0_14
    | ~ spl0_15 ),
    inference(resolution,[],[f81,f86]) ).

fof(f86,plain,
    ( ! [X2,X0,X1] :
        ( ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1))
        | c_in(X2,X0,X1)
        | c_Finite__Set_Ocard(c_insert(X2,X0,X1),X1) = c_Suc(c_Finite__Set_Ocard(X0,X1)) )
    | ~ spl0_15 ),
    inference(avatar_component_clause,[],[f85]) ).

fof(f138,plain,
    ( ~ spl0_23
    | spl0_24
    | ~ spl0_17
    | ~ spl0_19 ),
    inference(avatar_split_clause,[],[f119,f110,f99,f135,f131]) ).

fof(f99,plain,
    ( spl0_17
  <=> c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).

fof(f119,plain,
    ( c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat))
    | ~ c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_t,tc_prod(tc_nat,tc_nat))
    | ~ spl0_17
    | ~ spl0_19 ),
    inference(resolution,[],[f101,f111]) ).

fof(f101,plain,
    ( c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat))
    | ~ spl0_17 ),
    inference(avatar_component_clause,[],[f99]) ).

fof(f129,plain,
    ( spl0_22
    | ~ spl0_13
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f90,f85,f75,f127]) ).

fof(f90,plain,
    ( ! [X0] :
        ( c_in(X0,v_t,tc_prod(tc_nat,tc_nat))
        | c_Finite__Set_Ocard(c_insert(X0,v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Suc(c_Finite__Set_Ocard(v_t,tc_prod(tc_nat,tc_nat))) )
    | ~ spl0_13
    | ~ spl0_15 ),
    inference(resolution,[],[f76,f86]) ).

fof(f124,plain,
    ( spl0_21
    | ~ spl0_9
    | ~ spl0_18 ),
    inference(avatar_split_clause,[],[f108,f104,f55,f121]) ).

fof(f104,plain,
    ( spl0_18
  <=> c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).

fof(f108,plain,
    ( c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat))
    | ~ spl0_9
    | ~ spl0_18 ),
    inference(resolution,[],[f106,f56]) ).

fof(f106,plain,
    ( c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ spl0_18 ),
    inference(avatar_component_clause,[],[f104]) ).

fof(f116,plain,
    ( spl0_20
    | ~ spl0_10
    | ~ spl0_15 ),
    inference(avatar_split_clause,[],[f88,f85,f60,f114]) ).

fof(f88,plain,
    ( ! [X2,X3,X0,X1] :
        ( c_in(X0,c_inter(X1,X2,X3),X3)
        | c_Finite__Set_Ocard(c_insert(X0,c_inter(X1,X2,X3),X3),X3) = c_Suc(c_Finite__Set_Ocard(c_inter(X1,X2,X3),X3))
        | ~ c_in(X2,c_Finite__Set_OFinites,tc_set(X3)) )
    | ~ spl0_10
    | ~ spl0_15 ),
    inference(resolution,[],[f86,f61]) ).

fof(f112,plain,
    ( spl0_19
    | ~ spl0_1
    | ~ spl0_11 ),
    inference(avatar_split_clause,[],[f69,f65,f15,f110]) ).

fof(f15,plain,
    ( spl0_1
  <=> c_emptyset = c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).

fof(f65,plain,
    ( spl0_11
  <=> ! [X0,X6,X1,X7] :
        ( ~ c_in(X6,X7,X1)
        | ~ c_in(X6,X0,X1)
        | c_in(X6,c_inter(X0,X7,X1),X1) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).

fof(f69,plain,
    ( ! [X0] :
        ( c_in(X0,c_emptyset,tc_prod(tc_nat,tc_nat))
        | ~ c_in(X0,v_a,tc_prod(tc_nat,tc_nat))
        | ~ c_in(X0,v_t,tc_prod(tc_nat,tc_nat)) )
    | ~ spl0_1
    | ~ spl0_11 ),
    inference(superposition,[],[f66,f17]) ).

fof(f17,plain,
    ( c_emptyset = c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat))
    | ~ spl0_1 ),
    inference(avatar_component_clause,[],[f15]) ).

fof(f66,plain,
    ( ! [X0,X1,X6,X7] :
        ( c_in(X6,c_inter(X0,X7,X1),X1)
        | ~ c_in(X6,X0,X1)
        | ~ c_in(X6,X7,X1) )
    | ~ spl0_11 ),
    inference(avatar_component_clause,[],[f65]) ).

fof(f107,plain,
    ( spl0_18
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f48,f44,f34,f104]) ).

fof(f44,plain,
    ( spl0_7
  <=> ! [X2,X0,X1] : c_in(X2,c_insert(X2,X0,X1),X1) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).

fof(f48,plain,
    ( c_in(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ spl0_5
    | ~ spl0_7 ),
    inference(superposition,[],[f45,f36]) ).

fof(f45,plain,
    ( ! [X2,X0,X1] : c_in(X2,c_insert(X2,X0,X1),X1)
    | ~ spl0_7 ),
    inference(avatar_component_clause,[],[f44]) ).

fof(f102,plain,
    ( spl0_17
    | ~ spl0_9
    | ~ spl0_16 ),
    inference(avatar_split_clause,[],[f97,f93,f55,f99]) ).

fof(f93,plain,
    ( spl0_16
  <=> c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).

fof(f97,plain,
    ( c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),v_a,tc_prod(tc_nat,tc_nat))
    | ~ spl0_9
    | ~ spl0_16 ),
    inference(resolution,[],[f95,f56]) ).

fof(f95,plain,
    ( c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ spl0_16 ),
    inference(avatar_component_clause,[],[f93]) ).

fof(f96,plain,
    ( spl0_16
    | ~ spl0_4
    | ~ spl0_7 ),
    inference(avatar_split_clause,[],[f47,f44,f29,f93]) ).

fof(f47,plain,
    ( c_in(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat))
    | ~ spl0_4
    | ~ spl0_7 ),
    inference(superposition,[],[f45,f31]) ).

fof(f89,plain,
    ( spl0_13
    | ~ spl0_2
    | ~ spl0_12 ),
    inference(avatar_split_clause,[],[f83,f71,f20,f75]) ).

fof(f20,plain,
    ( spl0_2
  <=> c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).

fof(f71,plain,
    ( spl0_12
  <=> ! [X5] :
        ( c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
        | ~ c_in(X5,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) ) ),
    introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).

fof(f83,plain,
    ( c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ spl0_2
    | ~ spl0_12 ),
    inference(resolution,[],[f72,f22]) ).

fof(f22,plain,
    ( c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ spl0_2 ),
    inference(avatar_component_clause,[],[f20]) ).

fof(f72,plain,
    ( ! [X5] :
        ( ~ c_in(X5,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat)))
        | c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat))) )
    | ~ spl0_12 ),
    inference(avatar_component_clause,[],[f71]) ).

fof(f87,plain,
    spl0_15,
    inference(avatar_split_clause,[],[f1,f85]) ).

fof(f1,axiom,
    ! [X2,X0,X1] :
      ( c_in(X2,X0,X1)
      | ~ c_in(X0,c_Finite__Set_OFinites,tc_set(X1))
      | c_Finite__Set_Ocard(c_insert(X2,X0,X1),X1) = c_Suc(c_Finite__Set_Ocard(X0,X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ocard__insert__disjoint_0) ).

fof(f82,plain,
    ( ~ spl0_13
    | spl0_14
    | ~ spl0_1
    | ~ spl0_10 ),
    inference(avatar_split_clause,[],[f63,f60,f15,f79,f75]) ).

fof(f63,plain,
    ( c_in(c_emptyset,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ c_in(v_t,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
    | ~ spl0_1
    | ~ spl0_10 ),
    inference(superposition,[],[f61,f17]) ).

fof(f73,plain,
    spl0_12,
    inference(avatar_split_clause,[],[f3,f71]) ).

fof(f3,axiom,
    ! [X5] :
      ( c_in(X5,c_Finite__Set_OFinites,tc_set(tc_prod(tc_nat,tc_nat)))
      | ~ c_in(X5,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Mutil_Otiling__domino__finite_0) ).

fof(f67,plain,
    spl0_11,
    inference(avatar_split_clause,[],[f5,f65]) ).

fof(f5,axiom,
    ! [X0,X1,X6,X7] :
      ( ~ c_in(X6,X7,X1)
      | ~ c_in(X6,X0,X1)
      | c_in(X6,c_inter(X0,X7,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_2) ).

fof(f62,plain,
    spl0_10,
    inference(avatar_split_clause,[],[f2,f60]) ).

fof(f2,axiom,
    ! [X3,X1,X4] :
      ( ~ c_in(X3,c_Finite__Set_OFinites,tc_set(X1))
      | c_in(c_inter(X4,X3,X1),c_Finite__Set_OFinites,tc_set(X1)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Finite__Set_Ofinite__Int_1) ).

fof(f57,plain,
    spl0_9,
    inference(avatar_split_clause,[],[f4,f55]) ).

fof(f4,axiom,
    ! [X0,X1,X6,X7] :
      ( c_in(X6,X7,X1)
      | ~ c_in(X6,c_inter(X0,X7,X1),X1) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_OInt__iff_1) ).

fof(f53,plain,
    ~ spl0_8,
    inference(avatar_split_clause,[],[f13,f50]) ).

fof(f13,axiom,
    c_Finite__Set_Ocard(c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) != c_Finite__Set_Ocard(c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).

fof(f46,plain,
    spl0_7,
    inference(avatar_split_clause,[],[f6,f44]) ).

fof(f6,axiom,
    ! [X2,X0,X1] : c_in(X2,c_insert(X2,X0,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oinsert__iff_1) ).

fof(f42,plain,
    spl0_6,
    inference(avatar_split_clause,[],[f9,f39]) ).

fof(f9,axiom,
    c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_0),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)) = c_Finite__Set_Ocard(c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_t,tc_prod(tc_nat,tc_nat)),tc_prod(tc_nat,tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

fof(f37,plain,
    spl0_5,
    inference(avatar_split_clause,[],[f12,f34]) ).

fof(f12,axiom,
    c_inter(c_Mutil_Ocoloured(c_Suc(c_0)),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_m,v_n,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).

fof(f32,plain,
    spl0_4,
    inference(avatar_split_clause,[],[f11,f29]) ).

fof(f11,axiom,
    c_inter(c_Mutil_Ocoloured(c_0),v_a,tc_prod(tc_nat,tc_nat)) = c_insert(c_Pair(v_i,v_j,tc_nat,tc_nat),c_emptyset,tc_prod(tc_nat,tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).

fof(f27,plain,
    spl0_3,
    inference(avatar_split_clause,[],[f7,f25]) ).

fof(f7,axiom,
    ! [X1,X6] : ~ c_in(X6,c_emptyset,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__iff_0) ).

fof(f23,plain,
    spl0_2,
    inference(avatar_split_clause,[],[f8,f20]) ).

fof(f8,axiom,
    c_in(v_t,c_Mutil_Otiling(c_Mutil_Odomino,tc_prod(tc_nat,tc_nat)),tc_set(tc_prod(tc_nat,tc_nat))),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

fof(f18,plain,
    spl0_1,
    inference(avatar_split_clause,[],[f10,f15]) ).

fof(f10,axiom,
    c_emptyset = c_inter(v_a,v_t,tc_prod(tc_nat,tc_nat)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11  % Problem    : PUZ062-2 : TPTP v8.2.0. Released v3.2.0.
% 0.05/0.12  % Command    : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32  % Computer : n032.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit   : 300
% 0.11/0.32  % WCLimit    : 300
% 0.11/0.32  % DateTime   : Sat May 18 10:42:38 EDT 2024
% 0.11/0.32  % CPUTime    : 
% 0.15/0.32  % (8727)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.33  % (8729)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.33  % (8728)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.33  TRYING [1]
% 0.15/0.33  % (8732)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)
% 0.15/0.33  TRYING [2]
% 0.15/0.33  TRYING [3]
% 0.15/0.34  % (8734)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)
% 0.15/0.34  % (8733)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)
% 0.15/0.34  % (8732)First to succeed.
% 0.15/0.34  TRYING [1]
% 0.15/0.34  TRYING [2]
% 0.15/0.34  TRYING [4]
% 0.15/0.34  % (8732)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-8727"
% 0.15/0.34  % (8732)Refutation found. Thanks to Tanya!
% 0.15/0.34  % SZS status Unsatisfiable for theBenchmark
% 0.15/0.34  % SZS output start Proof for theBenchmark
% See solution above
% 0.15/0.34  % (8732)------------------------------
% 0.15/0.34  % (8732)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.15/0.34  % (8732)Termination reason: Refutation
% 0.15/0.34  
% 0.15/0.34  % (8732)Memory used [KB]: 906
% 0.15/0.34  % (8732)Time elapsed: 0.009 s
% 0.15/0.34  % (8732)Instructions burned: 17 (million)
% 0.15/0.34  % (8727)Success in time 0.02 s
%------------------------------------------------------------------------------