TSTP Solution File: SEU239+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU239+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 : n027.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 09:30:20 EDT 2024
% Result : Theorem 0.14s 0.37s
% Output : Refutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 100
% Syntax : Number of formulae : 311 ( 66 unt; 0 def)
% Number of atoms : 844 ( 52 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 951 ( 418 ~; 386 |; 51 &)
% ( 71 <=>; 24 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 75 ( 73 usr; 66 prp; 0-2 aty)
% Number of functors : 17 ( 17 usr; 8 con; 0-2 aty)
% Number of variables : 286 ( 259 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f522,plain,
$false,
inference(avatar_sat_refutation,[],[f127,f136,f141,f146,f151,f156,f161,f166,f171,f176,f181,f186,f190,f195,f199,f203,f210,f214,f219,f223,f227,f236,f240,f244,f248,f256,f266,f270,f274,f278,f299,f305,f309,f313,f320,f325,f329,f341,f346,f352,f357,f363,f369,f375,f379,f388,f393,f398,f410,f415,f420,f430,f434,f449,f456,f460,f473,f478,f483,f493,f497,f498,f506,f508,f513,f521]) ).
fof(f521,plain,
( ~ spl9_2
| ~ spl9_1
| ~ spl9_3
| spl9_48
| ~ spl9_65 ),
inference(avatar_split_clause,[],[f515,f511,f385,f133,f124,f129]) ).
fof(f129,plain,
( spl9_2
<=> reflexive(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_2])]) ).
fof(f124,plain,
( spl9_1
<=> relation(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_1])]) ).
fof(f133,plain,
( spl9_3
<=> in(sK1,relation_field(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_3])]) ).
fof(f385,plain,
( spl9_48
<=> in(unordered_pair(singleton(sK1),unordered_pair(sK1,sK1)),sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_48])]) ).
fof(f511,plain,
( spl9_65
<=> ! [X0,X1] :
( ~ in(X0,relation_field(X1))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ reflexive(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_65])]) ).
fof(f515,plain,
( ~ in(sK1,relation_field(sK0))
| ~ relation(sK0)
| ~ reflexive(sK0)
| spl9_48
| ~ spl9_65 ),
inference(resolution,[],[f512,f387]) ).
fof(f387,plain,
( ~ in(unordered_pair(singleton(sK1),unordered_pair(sK1,sK1)),sK0)
| spl9_48 ),
inference(avatar_component_clause,[],[f385]) ).
fof(f512,plain,
( ! [X0,X1] :
( in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),X1)
| ~ in(X0,relation_field(X1))
| ~ relation(X1)
| ~ reflexive(X1) )
| ~ spl9_65 ),
inference(avatar_component_clause,[],[f511]) ).
fof(f513,plain,
( spl9_65
| ~ spl9_34
| ~ spl9_41 ),
inference(avatar_split_clause,[],[f348,f344,f303,f511]) ).
fof(f303,plain,
( spl9_34
<=> ! [X0] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_34])]) ).
fof(f344,plain,
( spl9_41
<=> ! [X0,X1,X3] :
( in(unordered_pair(singleton(X3),unordered_pair(X3,X3)),X0)
| ~ in(X3,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_41])]) ).
fof(f348,plain,
( ! [X0,X1] :
( ~ in(X0,relation_field(X1))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ reflexive(X1) )
| ~ spl9_34
| ~ spl9_41 ),
inference(duplicate_literal_removal,[],[f347]) ).
fof(f347,plain,
( ! [X0,X1] :
( ~ in(X0,relation_field(X1))
| in(unordered_pair(singleton(X0),unordered_pair(X0,X0)),X1)
| ~ relation(X1)
| ~ reflexive(X1)
| ~ relation(X1) )
| ~ spl9_34
| ~ spl9_41 ),
inference(resolution,[],[f345,f304]) ).
fof(f304,plain,
( ! [X0] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) )
| ~ spl9_34 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f345,plain,
( ! [X3,X0,X1] :
( ~ is_reflexive_in(X0,X1)
| ~ in(X3,X1)
| in(unordered_pair(singleton(X3),unordered_pair(X3,X3)),X0)
| ~ relation(X0) )
| ~ spl9_41 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f508,plain,
( ~ spl9_3
| ~ spl9_15
| spl9_48 ),
inference(avatar_split_clause,[],[f400,f385,f193,f133]) ).
fof(f193,plain,
( spl9_15
<=> ! [X2] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X2)),sK0)
| ~ in(X2,relation_field(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_15])]) ).
fof(f400,plain,
( ~ in(sK1,relation_field(sK0))
| ~ spl9_15
| spl9_48 ),
inference(resolution,[],[f194,f387]) ).
fof(f194,plain,
( ! [X2] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X2)),sK0)
| ~ in(X2,relation_field(sK0)) )
| ~ spl9_15 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f506,plain,
( ~ spl9_64
| ~ spl9_3
| ~ spl9_25 ),
inference(avatar_split_clause,[],[f382,f242,f133,f503]) ).
fof(f503,plain,
( spl9_64
<=> in(relation_field(sK0),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_64])]) ).
fof(f242,plain,
( spl9_25
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_25])]) ).
fof(f382,plain,
( ~ in(relation_field(sK0),sK1)
| ~ spl9_3
| ~ spl9_25 ),
inference(resolution,[],[f135,f243]) ).
fof(f243,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl9_25 ),
inference(avatar_component_clause,[],[f242]) ).
fof(f135,plain,
( in(sK1,relation_field(sK0))
| ~ spl9_3 ),
inference(avatar_component_clause,[],[f133]) ).
fof(f498,plain,
( ~ spl9_1
| spl9_2
| ~ spl9_35
| ~ spl9_53 ),
inference(avatar_split_clause,[],[f461,f417,f307,f129,f124]) ).
fof(f307,plain,
( spl9_35
<=> ! [X0] :
( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_35])]) ).
fof(f417,plain,
( spl9_53
<=> is_reflexive_in(sK0,relation_field(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_53])]) ).
fof(f461,plain,
( reflexive(sK0)
| ~ relation(sK0)
| ~ spl9_35
| ~ spl9_53 ),
inference(resolution,[],[f419,f308]) ).
fof(f308,plain,
( ! [X0] :
( ~ is_reflexive_in(X0,relation_field(X0))
| reflexive(X0)
| ~ relation(X0) )
| ~ spl9_35 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f419,plain,
( is_reflexive_in(sK0,relation_field(sK0))
| ~ spl9_53 ),
inference(avatar_component_clause,[],[f417]) ).
fof(f497,plain,
( spl9_63
| ~ spl9_25
| ~ spl9_39 ),
inference(avatar_split_clause,[],[f336,f327,f242,f495]) ).
fof(f495,plain,
( spl9_63
<=> ! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ relation(X0)
| ~ in(X1,sK2(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_63])]) ).
fof(f327,plain,
( spl9_39
<=> ! [X0,X1] :
( is_reflexive_in(X0,X1)
| in(sK2(X0,X1),X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_39])]) ).
fof(f336,plain,
( ! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ relation(X0)
| ~ in(X1,sK2(X0,X1)) )
| ~ spl9_25
| ~ spl9_39 ),
inference(resolution,[],[f328,f243]) ).
fof(f328,plain,
( ! [X0,X1] :
( in(sK2(X0,X1),X1)
| is_reflexive_in(X0,X1)
| ~ relation(X0) )
| ~ spl9_39 ),
inference(avatar_component_clause,[],[f327]) ).
fof(f493,plain,
( spl9_62
| ~ spl9_26
| ~ spl9_39 ),
inference(avatar_split_clause,[],[f335,f327,f246,f491]) ).
fof(f491,plain,
( spl9_62
<=> ! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ relation(X0)
| element(sK2(X0,X1),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_62])]) ).
fof(f246,plain,
( spl9_26
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_26])]) ).
fof(f335,plain,
( ! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ relation(X0)
| element(sK2(X0,X1),X1) )
| ~ spl9_26
| ~ spl9_39 ),
inference(resolution,[],[f328,f247]) ).
fof(f247,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| element(X0,X1) )
| ~ spl9_26 ),
inference(avatar_component_clause,[],[f246]) ).
fof(f483,plain,
( spl9_61
| ~ spl9_6
| ~ spl9_11
| ~ spl9_12
| ~ spl9_19
| ~ spl9_37 ),
inference(avatar_split_clause,[],[f334,f318,f212,f178,f173,f148,f480]) ).
fof(f480,plain,
( spl9_61
<=> relation_field(sK5) = set_union2(relation_dom(sK5),relation_rng(sK5)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_61])]) ).
fof(f148,plain,
( spl9_6
<=> empty(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_6])]) ).
fof(f173,plain,
( spl9_11
<=> relation(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_11])]) ).
fof(f178,plain,
( spl9_12
<=> empty(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_12])]) ).
fof(f212,plain,
( spl9_19
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_19])]) ).
fof(f318,plain,
( spl9_37
<=> ! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_37])]) ).
fof(f334,plain,
( relation_field(sK5) = set_union2(relation_dom(sK5),relation_rng(sK5))
| ~ spl9_6
| ~ spl9_11
| ~ spl9_12
| ~ spl9_19
| ~ spl9_37 ),
inference(forward_demodulation,[],[f333,f231]) ).
fof(f231,plain,
( sK5 = sK8
| ~ spl9_6
| ~ spl9_12
| ~ spl9_19 ),
inference(forward_demodulation,[],[f230,f229]) ).
fof(f229,plain,
( empty_set = sK5
| ~ spl9_6
| ~ spl9_19 ),
inference(resolution,[],[f213,f150]) ).
fof(f150,plain,
( empty(sK5)
| ~ spl9_6 ),
inference(avatar_component_clause,[],[f148]) ).
fof(f213,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl9_19 ),
inference(avatar_component_clause,[],[f212]) ).
fof(f230,plain,
( empty_set = sK8
| ~ spl9_12
| ~ spl9_19 ),
inference(resolution,[],[f213,f180]) ).
fof(f180,plain,
( empty(sK8)
| ~ spl9_12 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f333,plain,
( relation_field(sK8) = set_union2(relation_dom(sK8),relation_rng(sK8))
| ~ spl9_11
| ~ spl9_37 ),
inference(resolution,[],[f319,f175]) ).
fof(f175,plain,
( relation(sK8)
| ~ spl9_11 ),
inference(avatar_component_clause,[],[f173]) ).
fof(f319,plain,
( ! [X0] :
( ~ relation(X0)
| relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) )
| ~ spl9_37 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f478,plain,
( spl9_60
| ~ spl9_9
| ~ spl9_37 ),
inference(avatar_split_clause,[],[f332,f318,f163,f475]) ).
fof(f475,plain,
( spl9_60
<=> relation_field(sK7) = set_union2(relation_dom(sK7),relation_rng(sK7)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_60])]) ).
fof(f163,plain,
( spl9_9
<=> relation(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_9])]) ).
fof(f332,plain,
( relation_field(sK7) = set_union2(relation_dom(sK7),relation_rng(sK7))
| ~ spl9_9
| ~ spl9_37 ),
inference(resolution,[],[f319,f165]) ).
fof(f165,plain,
( relation(sK7)
| ~ spl9_9 ),
inference(avatar_component_clause,[],[f163]) ).
fof(f473,plain,
( spl9_59
| ~ spl9_7
| ~ spl9_37 ),
inference(avatar_split_clause,[],[f331,f318,f153,f470]) ).
fof(f470,plain,
( spl9_59
<=> relation_field(sK6) = set_union2(relation_dom(sK6),relation_rng(sK6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_59])]) ).
fof(f153,plain,
( spl9_7
<=> relation(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_7])]) ).
fof(f331,plain,
( relation_field(sK6) = set_union2(relation_dom(sK6),relation_rng(sK6))
| ~ spl9_7
| ~ spl9_37 ),
inference(resolution,[],[f319,f155]) ).
fof(f155,plain,
( relation(sK6)
| ~ spl9_7 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f460,plain,
( spl9_58
| ~ spl9_22
| ~ spl9_39 ),
inference(avatar_split_clause,[],[f337,f327,f225,f458]) ).
fof(f458,plain,
( spl9_58
<=> ! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ relation(X0)
| ~ empty(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_58])]) ).
fof(f225,plain,
( spl9_22
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_22])]) ).
fof(f337,plain,
( ! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ relation(X0)
| ~ empty(X1) )
| ~ spl9_22
| ~ spl9_39 ),
inference(resolution,[],[f328,f226]) ).
fof(f226,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl9_22 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f456,plain,
( spl9_57
| ~ spl9_29
| ~ spl9_33 ),
inference(avatar_split_clause,[],[f300,f297,f264,f454]) ).
fof(f454,plain,
( spl9_57
<=> ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X1,X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_57])]) ).
fof(f264,plain,
( spl9_29
<=> ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_29])]) ).
fof(f297,plain,
( spl9_33
<=> ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X0,X1))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_33])]) ).
fof(f300,plain,
( ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X1,X0)))
| ~ spl9_29
| ~ spl9_33 ),
inference(superposition,[],[f298,f265]) ).
fof(f265,plain,
( ! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0)
| ~ spl9_29 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f298,plain,
( ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X0,X1)))
| ~ spl9_33 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f449,plain,
( spl9_56
| ~ spl9_17
| ~ spl9_36 ),
inference(avatar_split_clause,[],[f316,f311,f201,f447]) ).
fof(f447,plain,
( spl9_56
<=> ! [X0] :
( empty(X0)
| in(sK3(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_56])]) ).
fof(f201,plain,
( spl9_17
<=> ! [X0] : element(sK3(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_17])]) ).
fof(f311,plain,
( spl9_36
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_36])]) ).
fof(f316,plain,
( ! [X0] :
( empty(X0)
| in(sK3(X0),X0) )
| ~ spl9_17
| ~ spl9_36 ),
inference(resolution,[],[f312,f202]) ).
fof(f202,plain,
( ! [X0] : element(sK3(X0),X0)
| ~ spl9_17 ),
inference(avatar_component_clause,[],[f201]) ).
fof(f312,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl9_36 ),
inference(avatar_component_clause,[],[f311]) ).
fof(f434,plain,
( spl9_55
| ~ spl9_6
| ~ spl9_31 ),
inference(avatar_split_clause,[],[f293,f272,f148,f432]) ).
fof(f432,plain,
( spl9_55
<=> ! [X0] :
( sK5 = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_55])]) ).
fof(f272,plain,
( spl9_31
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_31])]) ).
fof(f293,plain,
( ! [X0] :
( sK5 = X0
| ~ empty(X0) )
| ~ spl9_6
| ~ spl9_31 ),
inference(resolution,[],[f273,f150]) ).
fof(f273,plain,
( ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) )
| ~ spl9_31 ),
inference(avatar_component_clause,[],[f272]) ).
fof(f430,plain,
( spl9_54
| ~ spl9_6
| ~ spl9_18
| ~ spl9_19
| ~ spl9_30 ),
inference(avatar_split_clause,[],[f288,f268,f212,f208,f148,f428]) ).
fof(f428,plain,
( spl9_54
<=> ! [X0] : set_union2(sK5,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl9_54])]) ).
fof(f208,plain,
( spl9_18
<=> ! [X0] : set_union2(X0,empty_set) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl9_18])]) ).
fof(f268,plain,
( spl9_30
<=> ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_30])]) ).
fof(f288,plain,
( ! [X0] : set_union2(sK5,X0) = X0
| ~ spl9_6
| ~ spl9_18
| ~ spl9_19
| ~ spl9_30 ),
inference(forward_demodulation,[],[f280,f229]) ).
fof(f280,plain,
( ! [X0] : set_union2(empty_set,X0) = X0
| ~ spl9_18
| ~ spl9_30 ),
inference(superposition,[],[f269,f209]) ).
fof(f209,plain,
( ! [X0] : set_union2(X0,empty_set) = X0
| ~ spl9_18 ),
inference(avatar_component_clause,[],[f208]) ).
fof(f269,plain,
( ! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0)
| ~ spl9_30 ),
inference(avatar_component_clause,[],[f268]) ).
fof(f420,plain,
( ~ spl9_1
| spl9_53
| ~ spl9_39
| ~ spl9_45 ),
inference(avatar_split_clause,[],[f371,f367,f327,f417,f124]) ).
fof(f367,plain,
( spl9_45
<=> ! [X0] :
( is_reflexive_in(sK0,X0)
| ~ in(sK2(sK0,X0),relation_field(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_45])]) ).
fof(f371,plain,
( is_reflexive_in(sK0,relation_field(sK0))
| ~ relation(sK0)
| ~ spl9_39
| ~ spl9_45 ),
inference(duplicate_literal_removal,[],[f370]) ).
fof(f370,plain,
( is_reflexive_in(sK0,relation_field(sK0))
| is_reflexive_in(sK0,relation_field(sK0))
| ~ relation(sK0)
| ~ spl9_39
| ~ spl9_45 ),
inference(resolution,[],[f368,f328]) ).
fof(f368,plain,
( ! [X0] :
( ~ in(sK2(sK0,X0),relation_field(sK0))
| is_reflexive_in(sK0,X0) )
| ~ spl9_45 ),
inference(avatar_component_clause,[],[f367]) ).
fof(f415,plain,
( spl9_52
| ~ spl9_6
| ~ spl9_12
| ~ spl9_19 ),
inference(avatar_split_clause,[],[f231,f212,f178,f148,f412]) ).
fof(f412,plain,
( spl9_52
<=> sK5 = sK8 ),
introduced(avatar_definition,[new_symbols(naming,[spl9_52])]) ).
fof(f410,plain,
( spl9_51
| ~ spl9_6
| ~ spl9_19 ),
inference(avatar_split_clause,[],[f229,f212,f148,f407]) ).
fof(f407,plain,
( spl9_51
<=> empty_set = sK5 ),
introduced(avatar_definition,[new_symbols(naming,[spl9_51])]) ).
fof(f398,plain,
( spl9_50
| ~ spl9_3
| ~ spl9_26 ),
inference(avatar_split_clause,[],[f381,f246,f133,f395]) ).
fof(f395,plain,
( spl9_50
<=> element(sK1,relation_field(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_50])]) ).
fof(f381,plain,
( element(sK1,relation_field(sK0))
| ~ spl9_3
| ~ spl9_26 ),
inference(resolution,[],[f135,f247]) ).
fof(f393,plain,
( ~ spl9_49
| ~ spl9_3
| ~ spl9_22 ),
inference(avatar_split_clause,[],[f383,f225,f133,f390]) ).
fof(f390,plain,
( spl9_49
<=> empty(relation_field(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_49])]) ).
fof(f383,plain,
( ~ empty(relation_field(sK0))
| ~ spl9_3
| ~ spl9_22 ),
inference(resolution,[],[f135,f226]) ).
fof(f388,plain,
( ~ spl9_2
| ~ spl9_48
| ~ spl9_29 ),
inference(avatar_split_clause,[],[f380,f264,f385,f129]) ).
fof(f380,plain,
( ~ in(unordered_pair(singleton(sK1),unordered_pair(sK1,sK1)),sK0)
| ~ reflexive(sK0)
| ~ spl9_29 ),
inference(forward_demodulation,[],[f118,f265]) ).
fof(f118,plain,
( ~ in(unordered_pair(unordered_pair(sK1,sK1),singleton(sK1)),sK0)
| ~ reflexive(sK0) ),
inference(definition_unfolding,[],[f83,f101]) ).
fof(f101,plain,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : ordered_pair(X0,X1) = unordered_pair(unordered_pair(X0,X1),singleton(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d5_tarski) ).
fof(f83,plain,
( ~ in(ordered_pair(sK1,sK1),sK0)
| ~ reflexive(sK0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,plain,
( ( ( ~ in(ordered_pair(sK1,sK1),sK0)
& in(sK1,relation_field(sK0)) )
| ~ reflexive(sK0) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),sK0)
| ~ in(X2,relation_field(sK0)) )
| reflexive(sK0) )
& relation(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f59,f61,f60]) ).
fof(f60,plain,
( ? [X0] :
( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
| ~ reflexive(X0) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0)) )
| reflexive(X0) )
& relation(X0) )
=> ( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),sK0)
& in(X1,relation_field(sK0)) )
| ~ reflexive(sK0) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),sK0)
| ~ in(X2,relation_field(sK0)) )
| reflexive(sK0) )
& relation(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f61,plain,
( ? [X1] :
( ~ in(ordered_pair(X1,X1),sK0)
& in(X1,relation_field(sK0)) )
=> ( ~ in(ordered_pair(sK1,sK1),sK0)
& in(sK1,relation_field(sK0)) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
? [X0] :
( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
| ~ reflexive(X0) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,relation_field(X0)) )
| reflexive(X0) )
& relation(X0) ),
inference(rectify,[],[f58]) ).
fof(f58,plain,
? [X0] :
( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
| ~ reflexive(X0) )
& ( ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) )
| reflexive(X0) )
& relation(X0) ),
inference(flattening,[],[f57]) ).
fof(f57,plain,
? [X0] :
( ( ? [X1] :
( ~ in(ordered_pair(X1,X1),X0)
& in(X1,relation_field(X0)) )
| ~ reflexive(X0) )
& ( ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) )
| reflexive(X0) )
& relation(X0) ),
inference(nnf_transformation,[],[f41]) ).
fof(f41,plain,
? [X0] :
( ( reflexive(X0)
<~> ! [X1] :
( in(ordered_pair(X1,X1),X0)
| ~ in(X1,relation_field(X0)) ) )
& relation(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,negated_conjecture,
~ ! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
inference(negated_conjecture,[],[f25]) ).
fof(f25,conjecture,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> ! [X1] :
( in(X1,relation_field(X0))
=> in(ordered_pair(X1,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l1_wellord1) ).
fof(f379,plain,
( spl9_47
| ~ spl9_15
| ~ spl9_26 ),
inference(avatar_split_clause,[],[f262,f246,f193,f377]) ).
fof(f377,plain,
( spl9_47
<=> ! [X0] :
( element(unordered_pair(singleton(X0),unordered_pair(X0,X0)),sK0)
| ~ in(X0,relation_field(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_47])]) ).
fof(f262,plain,
( ! [X0] :
( element(unordered_pair(singleton(X0),unordered_pair(X0,X0)),sK0)
| ~ in(X0,relation_field(sK0)) )
| ~ spl9_15
| ~ spl9_26 ),
inference(resolution,[],[f247,f194]) ).
fof(f375,plain,
( spl9_46
| ~ spl9_15
| ~ spl9_25 ),
inference(avatar_split_clause,[],[f261,f242,f193,f373]) ).
fof(f373,plain,
( spl9_46
<=> ! [X0] :
( ~ in(sK0,unordered_pair(singleton(X0),unordered_pair(X0,X0)))
| ~ in(X0,relation_field(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_46])]) ).
fof(f261,plain,
( ! [X0] :
( ~ in(sK0,unordered_pair(singleton(X0),unordered_pair(X0,X0)))
| ~ in(X0,relation_field(sK0)) )
| ~ spl9_15
| ~ spl9_25 ),
inference(resolution,[],[f243,f194]) ).
fof(f369,plain,
( ~ spl9_1
| spl9_45
| ~ spl9_15
| ~ spl9_43 ),
inference(avatar_split_clause,[],[f358,f355,f193,f367,f124]) ).
fof(f355,plain,
( spl9_43
<=> ! [X0,X1] :
( ~ in(unordered_pair(singleton(sK2(X0,X1)),unordered_pair(sK2(X0,X1),sK2(X0,X1))),X0)
| is_reflexive_in(X0,X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_43])]) ).
fof(f358,plain,
( ! [X0] :
( is_reflexive_in(sK0,X0)
| ~ relation(sK0)
| ~ in(sK2(sK0,X0),relation_field(sK0)) )
| ~ spl9_15
| ~ spl9_43 ),
inference(resolution,[],[f356,f194]) ).
fof(f356,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(sK2(X0,X1)),unordered_pair(sK2(X0,X1),sK2(X0,X1))),X0)
| is_reflexive_in(X0,X1)
| ~ relation(X0) )
| ~ spl9_43 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f363,plain,
( spl9_44
| ~ spl9_1
| ~ spl9_37 ),
inference(avatar_split_clause,[],[f330,f318,f124,f360]) ).
fof(f360,plain,
( spl9_44
<=> relation_field(sK0) = set_union2(relation_dom(sK0),relation_rng(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_44])]) ).
fof(f330,plain,
( relation_field(sK0) = set_union2(relation_dom(sK0),relation_rng(sK0))
| ~ spl9_1
| ~ spl9_37 ),
inference(resolution,[],[f319,f126]) ).
fof(f126,plain,
( relation(sK0)
| ~ spl9_1 ),
inference(avatar_component_clause,[],[f124]) ).
fof(f357,plain,
( spl9_43
| ~ spl9_29
| ~ spl9_42 ),
inference(avatar_split_clause,[],[f353,f350,f264,f355]) ).
fof(f350,plain,
( spl9_42
<=> ! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK2(X0,X1)),singleton(sK2(X0,X1))),X0)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_42])]) ).
fof(f353,plain,
( ! [X0,X1] :
( ~ in(unordered_pair(singleton(sK2(X0,X1)),unordered_pair(sK2(X0,X1),sK2(X0,X1))),X0)
| is_reflexive_in(X0,X1)
| ~ relation(X0) )
| ~ spl9_29
| ~ spl9_42 ),
inference(forward_demodulation,[],[f351,f265]) ).
fof(f351,plain,
( ! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK2(X0,X1)),singleton(sK2(X0,X1))),X0)
| ~ relation(X0) )
| ~ spl9_42 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f352,plain,
spl9_42,
inference(avatar_split_clause,[],[f120,f350]) ).
fof(f120,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(unordered_pair(unordered_pair(sK2(X0,X1),sK2(X0,X1)),singleton(sK2(X0,X1))),X0)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f91,f101]) ).
fof(f91,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| ~ in(ordered_pair(sK2(X0,X1),sK2(X0,X1)),X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ( ~ in(ordered_pair(sK2(X0,X1),sK2(X0,X1)),X0)
& in(sK2(X0,X1),X1) ) )
& ( ! [X3] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2])],[f65,f66]) ).
fof(f66,plain,
! [X0,X1] :
( ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) )
=> ( ~ in(ordered_pair(sK2(X0,X1),sK2(X0,X1)),X0)
& in(sK2(X0,X1),X1) ) ),
introduced(choice_axiom,[]) ).
fof(f65,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) ) )
& ( ! [X3] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(rectify,[],[f64]) ).
fof(f64,plain,
! [X0] :
( ! [X1] :
( ( is_reflexive_in(X0,X1)
| ? [X2] :
( ~ in(ordered_pair(X2,X2),X0)
& in(X2,X1) ) )
& ( ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1) )
| ~ is_reflexive_in(X0,X1) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] :
( ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(ordered_pair(X2,X2),X0)
| ~ in(X2,X1) ) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( relation(X0)
=> ! [X1] :
( is_reflexive_in(X0,X1)
<=> ! [X2] :
( in(X2,X1)
=> in(ordered_pair(X2,X2),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_relat_2) ).
fof(f346,plain,
( spl9_41
| ~ spl9_29
| ~ spl9_40 ),
inference(avatar_split_clause,[],[f342,f339,f264,f344]) ).
fof(f339,plain,
( spl9_40
<=> ! [X0,X1,X3] :
( in(unordered_pair(unordered_pair(X3,X3),singleton(X3)),X0)
| ~ in(X3,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_40])]) ).
fof(f342,plain,
( ! [X3,X0,X1] :
( in(unordered_pair(singleton(X3),unordered_pair(X3,X3)),X0)
| ~ in(X3,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) )
| ~ spl9_29
| ~ spl9_40 ),
inference(forward_demodulation,[],[f340,f265]) ).
fof(f340,plain,
( ! [X3,X0,X1] :
( in(unordered_pair(unordered_pair(X3,X3),singleton(X3)),X0)
| ~ in(X3,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) )
| ~ spl9_40 ),
inference(avatar_component_clause,[],[f339]) ).
fof(f341,plain,
spl9_40,
inference(avatar_split_clause,[],[f121,f339]) ).
fof(f121,plain,
! [X3,X0,X1] :
( in(unordered_pair(unordered_pair(X3,X3),singleton(X3)),X0)
| ~ in(X3,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(definition_unfolding,[],[f89,f101]) ).
fof(f89,plain,
! [X3,X0,X1] :
( in(ordered_pair(X3,X3),X0)
| ~ in(X3,X1)
| ~ is_reflexive_in(X0,X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f329,plain,
spl9_39,
inference(avatar_split_clause,[],[f90,f327]) ).
fof(f90,plain,
! [X0,X1] :
( is_reflexive_in(X0,X1)
| in(sK2(X0,X1),X1)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f325,plain,
( spl9_38
| ~ spl9_6
| ~ spl9_16 ),
inference(avatar_split_clause,[],[f205,f197,f148,f322]) ).
fof(f322,plain,
( spl9_38
<=> function(sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_38])]) ).
fof(f197,plain,
( spl9_16
<=> ! [X0] :
( function(X0)
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_16])]) ).
fof(f205,plain,
( function(sK5)
| ~ spl9_6
| ~ spl9_16 ),
inference(resolution,[],[f198,f150]) ).
fof(f198,plain,
( ! [X0] :
( ~ empty(X0)
| function(X0) )
| ~ spl9_16 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f320,plain,
spl9_37,
inference(avatar_split_clause,[],[f86,f318]) ).
fof(f86,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f42]) ).
fof(f42,plain,
! [X0] :
( relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0))
| ~ relation(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( relation(X0)
=> relation_field(X0) = set_union2(relation_dom(X0),relation_rng(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d6_relat_1) ).
fof(f313,plain,
spl9_36,
inference(avatar_split_clause,[],[f106,f311]) ).
fof(f106,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f54]) ).
fof(f54,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f309,plain,
spl9_35,
inference(avatar_split_clause,[],[f88,f307]) ).
fof(f88,plain,
! [X0] :
( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0))
| ~ relation(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0] :
( ( ( reflexive(X0)
| ~ is_reflexive_in(X0,relation_field(X0)) )
& ( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0) ) )
| ~ relation(X0) ),
inference(nnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0] :
( ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) )
| ~ relation(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( relation(X0)
=> ( reflexive(X0)
<=> is_reflexive_in(X0,relation_field(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d9_relat_2) ).
fof(f305,plain,
spl9_34,
inference(avatar_split_clause,[],[f87,f303]) ).
fof(f87,plain,
! [X0] :
( is_reflexive_in(X0,relation_field(X0))
| ~ reflexive(X0)
| ~ relation(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f299,plain,
( spl9_33
| ~ spl9_29
| ~ spl9_32 ),
inference(avatar_split_clause,[],[f279,f276,f264,f297]) ).
fof(f276,plain,
( spl9_32
<=> ! [X0,X1] : ~ empty(unordered_pair(unordered_pair(X0,X1),singleton(X0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_32])]) ).
fof(f279,plain,
( ! [X0,X1] : ~ empty(unordered_pair(singleton(X0),unordered_pair(X0,X1)))
| ~ spl9_29
| ~ spl9_32 ),
inference(forward_demodulation,[],[f277,f265]) ).
fof(f277,plain,
( ! [X0,X1] : ~ empty(unordered_pair(unordered_pair(X0,X1),singleton(X0)))
| ~ spl9_32 ),
inference(avatar_component_clause,[],[f276]) ).
fof(f278,plain,
spl9_32,
inference(avatar_split_clause,[],[f122,f276]) ).
fof(f122,plain,
! [X0,X1] : ~ empty(unordered_pair(unordered_pair(X0,X1),singleton(X0))),
inference(definition_unfolding,[],[f97,f101]) ).
fof(f97,plain,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
inference(cnf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1] : ~ empty(ordered_pair(X0,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_zfmisc_1) ).
fof(f274,plain,
spl9_31,
inference(avatar_split_clause,[],[f107,f272]) ).
fof(f107,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f270,plain,
spl9_30,
inference(avatar_split_clause,[],[f100,f268]) ).
fof(f100,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f266,plain,
spl9_29,
inference(avatar_split_clause,[],[f99,f264]) ).
fof(f99,plain,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] : unordered_pair(X0,X1) = unordered_pair(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_tarski) ).
fof(f256,plain,
( spl9_27
| ~ spl9_28
| ~ spl9_15
| ~ spl9_22 ),
inference(avatar_split_clause,[],[f232,f225,f193,f253,f250]) ).
fof(f250,plain,
( spl9_27
<=> ! [X0] : ~ in(X0,relation_field(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_27])]) ).
fof(f253,plain,
( spl9_28
<=> empty(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_28])]) ).
fof(f232,plain,
( ! [X0] :
( ~ empty(sK0)
| ~ in(X0,relation_field(sK0)) )
| ~ spl9_15
| ~ spl9_22 ),
inference(resolution,[],[f226,f194]) ).
fof(f248,plain,
spl9_26,
inference(avatar_split_clause,[],[f105,f246]) ).
fof(f105,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f244,plain,
spl9_25,
inference(avatar_split_clause,[],[f104,f242]) ).
fof(f104,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1] :
( in(X0,X1)
=> ~ in(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',antisymmetry_r2_hidden) ).
fof(f240,plain,
spl9_24,
inference(avatar_split_clause,[],[f103,f238]) ).
fof(f238,plain,
( spl9_24
<=> ! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_24])]) ).
fof(f103,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1] :
( ~ empty(set_union2(X1,X0))
| empty(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X1,X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc3_xboole_0) ).
fof(f236,plain,
spl9_23,
inference(avatar_split_clause,[],[f102,f234]) ).
fof(f234,plain,
( spl9_23
<=> ! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_23])]) ).
fof(f102,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1] :
( ~ empty(set_union2(X0,X1))
| empty(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
( ~ empty(X0)
=> ~ empty(set_union2(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc2_xboole_0) ).
fof(f227,plain,
spl9_22,
inference(avatar_split_clause,[],[f108,f225]) ).
fof(f108,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f223,plain,
spl9_21,
inference(avatar_split_clause,[],[f98,f221]) ).
fof(f221,plain,
( spl9_21
<=> ! [X0] : set_union2(X0,X0) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl9_21])]) ).
fof(f98,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[],[f38]) ).
fof(f38,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(rectify,[],[f24]) ).
fof(f24,axiom,
! [X0,X1] : set_union2(X0,X0) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence_k2_xboole_0) ).
fof(f219,plain,
( spl9_20
| ~ spl9_4
| ~ spl9_16 ),
inference(avatar_split_clause,[],[f204,f197,f138,f216]) ).
fof(f216,plain,
( spl9_20
<=> function(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_20])]) ).
fof(f138,plain,
( spl9_4
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_4])]) ).
fof(f204,plain,
( function(empty_set)
| ~ spl9_4
| ~ spl9_16 ),
inference(resolution,[],[f198,f140]) ).
fof(f140,plain,
( empty(empty_set)
| ~ spl9_4 ),
inference(avatar_component_clause,[],[f138]) ).
fof(f214,plain,
spl9_19,
inference(avatar_split_clause,[],[f93,f212]) ).
fof(f93,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f210,plain,
spl9_18,
inference(avatar_split_clause,[],[f85,f208]) ).
fof(f85,plain,
! [X0] : set_union2(X0,empty_set) = X0,
inference(cnf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] : set_union2(X0,empty_set) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_boole) ).
fof(f203,plain,
spl9_17,
inference(avatar_split_clause,[],[f96,f201]) ).
fof(f96,plain,
! [X0] : element(sK3(X0),X0),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0] : element(sK3(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f19,f68]) ).
fof(f68,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK3(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f19,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f199,plain,
spl9_16,
inference(avatar_split_clause,[],[f92,f197]) ).
fof(f92,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0] :
( function(X0)
| ~ empty(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( empty(X0)
=> function(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_funct_1) ).
fof(f195,plain,
( spl9_15
| ~ spl9_14 ),
inference(avatar_split_clause,[],[f191,f188,f193]) ).
fof(f188,plain,
( spl9_14
<=> ! [X2] :
( in(unordered_pair(unordered_pair(X2,X2),singleton(X2)),sK0)
| ~ in(X2,relation_field(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_14])]) ).
fof(f191,plain,
( ! [X2] :
( in(unordered_pair(singleton(X2),unordered_pair(X2,X2)),sK0)
| ~ in(X2,relation_field(sK0)) )
| ~ spl9_14 ),
inference(forward_demodulation,[],[f189,f99]) ).
fof(f189,plain,
( ! [X2] :
( in(unordered_pair(unordered_pair(X2,X2),singleton(X2)),sK0)
| ~ in(X2,relation_field(sK0)) )
| ~ spl9_14 ),
inference(avatar_component_clause,[],[f188]) ).
fof(f190,plain,
( spl9_2
| spl9_14 ),
inference(avatar_split_clause,[],[f119,f188,f129]) ).
fof(f119,plain,
! [X2] :
( in(unordered_pair(unordered_pair(X2,X2),singleton(X2)),sK0)
| ~ in(X2,relation_field(sK0))
| reflexive(sK0) ),
inference(definition_unfolding,[],[f81,f101]) ).
fof(f81,plain,
! [X2] :
( in(ordered_pair(X2,X2),sK0)
| ~ in(X2,relation_field(sK0))
| reflexive(sK0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f186,plain,
spl9_13,
inference(avatar_split_clause,[],[f117,f183]) ).
fof(f183,plain,
( spl9_13
<=> function(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_13])]) ).
fof(f117,plain,
function(sK8),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
( function(sK8)
& empty(sK8)
& relation(sK8) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f29,f78]) ).
fof(f78,plain,
( ? [X0] :
( function(X0)
& empty(X0)
& relation(X0) )
=> ( function(sK8)
& empty(sK8)
& relation(sK8) ) ),
introduced(choice_axiom,[]) ).
fof(f29,axiom,
? [X0] :
( function(X0)
& empty(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_funct_1) ).
fof(f181,plain,
spl9_12,
inference(avatar_split_clause,[],[f116,f178]) ).
fof(f116,plain,
empty(sK8),
inference(cnf_transformation,[],[f79]) ).
fof(f176,plain,
spl9_11,
inference(avatar_split_clause,[],[f115,f173]) ).
fof(f115,plain,
relation(sK8),
inference(cnf_transformation,[],[f79]) ).
fof(f171,plain,
spl9_10,
inference(avatar_split_clause,[],[f114,f168]) ).
fof(f168,plain,
( spl9_10
<=> function(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_10])]) ).
fof(f114,plain,
function(sK7),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
( function(sK7)
& relation(sK7) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f39,f76]) ).
fof(f76,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK7)
& relation(sK7) ) ),
introduced(choice_axiom,[]) ).
fof(f39,plain,
? [X0] :
( function(X0)
& relation(X0) ),
inference(pure_predicate_removal,[],[f31]) ).
fof(f31,axiom,
? [X0] :
( one_to_one(X0)
& function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_funct_1) ).
fof(f166,plain,
spl9_9,
inference(avatar_split_clause,[],[f113,f163]) ).
fof(f113,plain,
relation(sK7),
inference(cnf_transformation,[],[f77]) ).
fof(f161,plain,
spl9_8,
inference(avatar_split_clause,[],[f112,f158]) ).
fof(f158,plain,
( spl9_8
<=> function(sK6) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_8])]) ).
fof(f112,plain,
function(sK6),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
( function(sK6)
& relation(sK6) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f27,f74]) ).
fof(f74,plain,
( ? [X0] :
( function(X0)
& relation(X0) )
=> ( function(sK6)
& relation(sK6) ) ),
introduced(choice_axiom,[]) ).
fof(f27,axiom,
? [X0] :
( function(X0)
& relation(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_funct_1) ).
fof(f156,plain,
spl9_7,
inference(avatar_split_clause,[],[f111,f153]) ).
fof(f111,plain,
relation(sK6),
inference(cnf_transformation,[],[f75]) ).
fof(f151,plain,
spl9_6,
inference(avatar_split_clause,[],[f110,f148]) ).
fof(f110,plain,
empty(sK5),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
empty(sK5),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f28,f72]) ).
fof(f72,plain,
( ? [X0] : empty(X0)
=> empty(sK5) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] : empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc1_xboole_0) ).
fof(f146,plain,
~ spl9_5,
inference(avatar_split_clause,[],[f109,f143]) ).
fof(f143,plain,
( spl9_5
<=> empty(sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl9_5])]) ).
fof(f109,plain,
~ empty(sK4),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
~ empty(sK4),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f30,f70]) ).
fof(f70,plain,
( ? [X0] : ~ empty(X0)
=> ~ empty(sK4) ),
introduced(choice_axiom,[]) ).
fof(f30,axiom,
? [X0] : ~ empty(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc2_xboole_0) ).
fof(f141,plain,
spl9_4,
inference(avatar_split_clause,[],[f84,f138]) ).
fof(f84,plain,
empty(empty_set),
inference(cnf_transformation,[],[f20]) ).
fof(f20,axiom,
empty(empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_xboole_0) ).
fof(f136,plain,
( ~ spl9_2
| spl9_3 ),
inference(avatar_split_clause,[],[f82,f133,f129]) ).
fof(f82,plain,
( in(sK1,relation_field(sK0))
| ~ reflexive(sK0) ),
inference(cnf_transformation,[],[f62]) ).
fof(f127,plain,
spl9_1,
inference(avatar_split_clause,[],[f80,f124]) ).
fof(f80,plain,
relation(sK0),
inference(cnf_transformation,[],[f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU239+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n027.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 3 11:58:35 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.35 % (24847)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (24848)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.36 % (24852)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.37 % (24850)WARNING: value z3 for option sas not known
% 0.14/0.37 % (24849)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.37 % (24851)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.37 % (24850)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.37 % (24853)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 % (24854)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.37 % (24852)First to succeed.
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.37 TRYING [3]
% 0.14/0.37 % (24852)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-24847"
% 0.14/0.37 TRYING [3]
% 0.14/0.37 % (24852)Refutation found. Thanks to Tanya!
% 0.14/0.37 % SZS status Theorem for theBenchmark
% 0.14/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.14/0.38 % (24852)------------------------------
% 0.14/0.38 % (24852)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.14/0.38 % (24852)Termination reason: Refutation
% 0.14/0.38
% 0.14/0.38 % (24852)Memory used [KB]: 997
% 0.14/0.38 % (24852)Time elapsed: 0.011 s
% 0.14/0.38 % (24852)Instructions burned: 19 (million)
% 0.14/0.38 % (24847)Success in time 0.022 s
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