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