TSTP Solution File: SEU305+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SEU305+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 : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 15:28:03 EDT 2024
% Result : Theorem 0.11s 0.37s
% Output : Refutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 155
% Syntax : Number of formulae : 486 ( 84 unt; 0 def)
% Number of atoms : 1864 ( 143 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 2385 (1007 ~;1105 |; 114 &)
% ( 116 <=>; 43 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 129 ( 127 usr; 112 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 7 con; 0-6 aty)
% Number of variables : 719 ( 688 !; 31 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f920,plain,
$false,
inference(avatar_sat_refutation,[],[f160,f165,f170,f175,f180,f185,f190,f195,f200,f205,f210,f215,f219,f223,f227,f231,f235,f239,f243,f247,f251,f259,f263,f267,f272,f276,f280,f284,f288,f292,f297,f301,f305,f309,f314,f318,f322,f326,f336,f342,f351,f355,f359,f371,f375,f380,f388,f393,f397,f407,f411,f433,f448,f458,f472,f476,f482,f490,f497,f501,f504,f512,f519,f529,f540,f544,f557,f569,f582,f595,f599,f604,f608,f618,f623,f627,f633,f638,f645,f652,f656,f660,f671,f678,f685,f694,f698,f703,f723,f730,f742,f746,f750,f754,f759,f795,f805,f809,f825,f831,f843,f847,f851,f868,f877,f884,f893,f899,f911,f918,f919]) ).
fof(f919,plain,
( spl10_4
| ~ spl10_56
| ~ spl10_96 ),
inference(avatar_split_clause,[],[f860,f756,f461,f172]) ).
fof(f172,plain,
( spl10_4
<=> sK1 = sK2 ),
introduced(avatar_definition,[new_symbols(naming,[spl10_4])]) ).
fof(f461,plain,
( spl10_56
<=> sK2 = join(sK0,sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_56])]) ).
fof(f756,plain,
( spl10_96
<=> sK1 = join(sK0,sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_96])]) ).
fof(f860,plain,
( sK1 = sK2
| ~ spl10_56
| ~ spl10_96 ),
inference(superposition,[],[f758,f463]) ).
fof(f463,plain,
( sK2 = join(sK0,sK1,sK2)
| ~ spl10_56 ),
inference(avatar_component_clause,[],[f461]) ).
fof(f758,plain,
( sK1 = join(sK0,sK1,sK2)
| ~ spl10_96 ),
inference(avatar_component_clause,[],[f756]) ).
fof(f918,plain,
( spl10_111
| ~ spl10_21
| ~ spl10_59 ),
inference(avatar_split_clause,[],[f477,f474,f249,f915]) ).
fof(f915,plain,
( spl10_111
<=> join_commut(sK0,sK4(empty_set),sK1) = join_commut(sK0,sK1,sK4(empty_set)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_111])]) ).
fof(f249,plain,
( spl10_21
<=> ! [X0] : element(sK4(X0),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_21])]) ).
fof(f474,plain,
( spl10_59
<=> ! [X0] :
( ~ element(X0,empty_set)
| join_commut(sK0,X0,sK1) = join_commut(sK0,sK1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_59])]) ).
fof(f477,plain,
( join_commut(sK0,sK4(empty_set),sK1) = join_commut(sK0,sK1,sK4(empty_set))
| ~ spl10_21
| ~ spl10_59 ),
inference(resolution,[],[f475,f250]) ).
fof(f250,plain,
( ! [X0] : element(sK4(X0),X0)
| ~ spl10_21 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f475,plain,
( ! [X0] :
( ~ element(X0,empty_set)
| join_commut(sK0,X0,sK1) = join_commut(sK0,sK1,X0) )
| ~ spl10_59 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f911,plain,
( spl10_110
| ~ spl10_6
| ~ spl10_68 ),
inference(avatar_split_clause,[],[f559,f555,f182,f908]) ).
fof(f908,plain,
( spl10_110
<=> join_commut(sK0,sK2,sK2) = join(sK0,sK2,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_110])]) ).
fof(f182,plain,
( spl10_6
<=> element(sK2,the_carrier(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_6])]) ).
fof(f555,plain,
( spl10_68
<=> ! [X0] :
( join_commut(sK0,X0,sK2) = join(sK0,X0,sK2)
| ~ element(X0,the_carrier(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_68])]) ).
fof(f559,plain,
( join_commut(sK0,sK2,sK2) = join(sK0,sK2,sK2)
| ~ spl10_6
| ~ spl10_68 ),
inference(resolution,[],[f556,f184]) ).
fof(f184,plain,
( element(sK2,the_carrier(sK0))
| ~ spl10_6 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f556,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK0))
| join_commut(sK0,X0,sK2) = join(sK0,X0,sK2) )
| ~ spl10_68 ),
inference(avatar_component_clause,[],[f555]) ).
fof(f899,plain,
( spl10_109
| ~ spl10_107
| ~ spl10_108 ),
inference(avatar_split_clause,[],[f894,f890,f881,f896]) ).
fof(f896,plain,
( spl10_109
<=> sK1 = join(sK0,sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_109])]) ).
fof(f881,plain,
( spl10_107
<=> sK1 = join_commut(sK0,sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_107])]) ).
fof(f890,plain,
( spl10_108
<=> join_commut(sK0,sK1,sK1) = join(sK0,sK1,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_108])]) ).
fof(f894,plain,
( sK1 = join(sK0,sK1,sK1)
| ~ spl10_107
| ~ spl10_108 ),
inference(forward_demodulation,[],[f892,f883]) ).
fof(f883,plain,
( sK1 = join_commut(sK0,sK1,sK1)
| ~ spl10_107 ),
inference(avatar_component_clause,[],[f881]) ).
fof(f892,plain,
( join_commut(sK0,sK1,sK1) = join(sK0,sK1,sK1)
| ~ spl10_108 ),
inference(avatar_component_clause,[],[f890]) ).
fof(f893,plain,
( spl10_108
| ~ spl10_5
| ~ spl10_67 ),
inference(avatar_split_clause,[],[f545,f542,f177,f890]) ).
fof(f177,plain,
( spl10_5
<=> element(sK1,the_carrier(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_5])]) ).
fof(f542,plain,
( spl10_67
<=> ! [X0] :
( join_commut(sK0,X0,sK1) = join(sK0,X0,sK1)
| ~ element(X0,the_carrier(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_67])]) ).
fof(f545,plain,
( join_commut(sK0,sK1,sK1) = join(sK0,sK1,sK1)
| ~ spl10_5
| ~ spl10_67 ),
inference(resolution,[],[f543,f179]) ).
fof(f179,plain,
( element(sK1,the_carrier(sK0))
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f177]) ).
fof(f543,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK0))
| join_commut(sK0,X0,sK1) = join(sK0,X0,sK1) )
| ~ spl10_67 ),
inference(avatar_component_clause,[],[f542]) ).
fof(f884,plain,
( spl10_107
| ~ spl10_56
| ~ spl10_89
| ~ spl10_96
| ~ spl10_106 ),
inference(avatar_split_clause,[],[f879,f874,f756,f700,f461,f881]) ).
fof(f700,plain,
( spl10_89
<=> sK1 = join_commut(sK0,sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_89])]) ).
fof(f874,plain,
( spl10_106
<=> join_commut(sK0,sK2,sK1) = join_commut(sK0,sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_106])]) ).
fof(f879,plain,
( sK1 = join_commut(sK0,sK1,sK1)
| ~ spl10_56
| ~ spl10_89
| ~ spl10_96
| ~ spl10_106 ),
inference(forward_demodulation,[],[f878,f860]) ).
fof(f878,plain,
( sK1 = join_commut(sK0,sK2,sK1)
| ~ spl10_89
| ~ spl10_106 ),
inference(forward_demodulation,[],[f876,f702]) ).
fof(f702,plain,
( sK1 = join_commut(sK0,sK1,sK2)
| ~ spl10_89 ),
inference(avatar_component_clause,[],[f700]) ).
fof(f876,plain,
( join_commut(sK0,sK2,sK1) = join_commut(sK0,sK1,sK2)
| ~ spl10_106 ),
inference(avatar_component_clause,[],[f874]) ).
fof(f877,plain,
( spl10_106
| ~ spl10_6
| ~ spl10_64 ),
inference(avatar_split_clause,[],[f521,f517,f182,f874]) ).
fof(f517,plain,
( spl10_64
<=> ! [X0] :
( join_commut(sK0,X0,sK1) = join_commut(sK0,sK1,X0)
| ~ element(X0,the_carrier(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_64])]) ).
fof(f521,plain,
( join_commut(sK0,sK2,sK1) = join_commut(sK0,sK1,sK2)
| ~ spl10_6
| ~ spl10_64 ),
inference(resolution,[],[f518,f184]) ).
fof(f518,plain,
( ! [X0] :
( ~ element(X0,the_carrier(sK0))
| join_commut(sK0,X0,sK1) = join_commut(sK0,sK1,X0) )
| ~ spl10_64 ),
inference(avatar_component_clause,[],[f517]) ).
fof(f868,plain,
( spl10_105
| ~ spl10_53
| ~ spl10_54 ),
inference(avatar_split_clause,[],[f452,f446,f431,f866]) ).
fof(f866,plain,
( spl10_105
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),the_carrier(X5))
| ~ quasi_total(X4,cartesian_product2(X3,X1),the_carrier(X5))
| ~ function(X4)
| empty(X1)
| empty(X3)
| join(X5,X6,apply_binary_as_element(X3,X1,the_carrier(X5),X4,X2,X0)) = apply_binary_as_element(the_carrier(X5),the_carrier(X5),the_carrier(X5),the_L_join(X5),X6,apply_binary_as_element(X3,X1,the_carrier(X5),X4,X2,X0))
| ~ element(X6,the_carrier(X5))
| ~ join_semilatt_str(X5)
| empty_carrier(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_105])]) ).
fof(f431,plain,
( spl10_53
<=> ! [X2,X0,X1] :
( join(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_53])]) ).
fof(f446,plain,
( spl10_54
<=> ! [X3,X4,X0,X5,X2,X1] :
( element(apply_binary_as_element(X0,X1,X2,X3,X4,X5),X2)
| ~ element(X5,X1)
| ~ element(X4,X0)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_54])]) ).
fof(f452,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),the_carrier(X5))
| ~ quasi_total(X4,cartesian_product2(X3,X1),the_carrier(X5))
| ~ function(X4)
| empty(X1)
| empty(X3)
| join(X5,X6,apply_binary_as_element(X3,X1,the_carrier(X5),X4,X2,X0)) = apply_binary_as_element(the_carrier(X5),the_carrier(X5),the_carrier(X5),the_L_join(X5),X6,apply_binary_as_element(X3,X1,the_carrier(X5),X4,X2,X0))
| ~ element(X6,the_carrier(X5))
| ~ join_semilatt_str(X5)
| empty_carrier(X5) )
| ~ spl10_53
| ~ spl10_54 ),
inference(resolution,[],[f447,f432]) ).
fof(f432,plain,
( ! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| join(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) )
| ~ spl10_53 ),
inference(avatar_component_clause,[],[f431]) ).
fof(f447,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( element(apply_binary_as_element(X0,X1,X2,X3,X4,X5),X2)
| ~ element(X5,X1)
| ~ element(X4,X0)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) )
| ~ spl10_54 ),
inference(avatar_component_clause,[],[f446]) ).
fof(f851,plain,
( spl10_104
| ~ spl10_51
| ~ spl10_54 ),
inference(avatar_split_clause,[],[f454,f446,f405,f849]) ).
fof(f849,plain,
( spl10_104
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),the_carrier(X5))
| ~ quasi_total(X4,cartesian_product2(X3,X1),the_carrier(X5))
| ~ function(X4)
| empty(X1)
| empty(X3)
| join_commut(X5,X6,apply_binary_as_element(X3,X1,the_carrier(X5),X4,X2,X0)) = join_commut(X5,apply_binary_as_element(X3,X1,the_carrier(X5),X4,X2,X0),X6)
| ~ element(X6,the_carrier(X5))
| ~ join_semilatt_str(X5)
| ~ join_commutative(X5)
| empty_carrier(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_104])]) ).
fof(f405,plain,
( spl10_51
<=> ! [X2,X0,X1] :
( join_commut(X0,X1,X2) = join_commut(X0,X2,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_51])]) ).
fof(f454,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),the_carrier(X5))
| ~ quasi_total(X4,cartesian_product2(X3,X1),the_carrier(X5))
| ~ function(X4)
| empty(X1)
| empty(X3)
| join_commut(X5,X6,apply_binary_as_element(X3,X1,the_carrier(X5),X4,X2,X0)) = join_commut(X5,apply_binary_as_element(X3,X1,the_carrier(X5),X4,X2,X0),X6)
| ~ element(X6,the_carrier(X5))
| ~ join_semilatt_str(X5)
| ~ join_commutative(X5)
| empty_carrier(X5) )
| ~ spl10_51
| ~ spl10_54 ),
inference(resolution,[],[f447,f406]) ).
fof(f406,plain,
( ! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| join_commut(X0,X1,X2) = join_commut(X0,X2,X1)
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) )
| ~ spl10_51 ),
inference(avatar_component_clause,[],[f405]) ).
fof(f847,plain,
( spl10_103
| ~ spl10_52
| ~ spl10_54 ),
inference(avatar_split_clause,[],[f453,f446,f409,f845]) ).
fof(f845,plain,
( spl10_103
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),the_carrier(X5))
| ~ quasi_total(X4,cartesian_product2(X3,X1),the_carrier(X5))
| ~ function(X4)
| empty(X1)
| empty(X3)
| join(X5,X6,apply_binary_as_element(X3,X1,the_carrier(X5),X4,X2,X0)) = join_commut(X5,X6,apply_binary_as_element(X3,X1,the_carrier(X5),X4,X2,X0))
| ~ element(X6,the_carrier(X5))
| ~ join_semilatt_str(X5)
| ~ join_commutative(X5)
| empty_carrier(X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_103])]) ).
fof(f409,plain,
( spl10_52
<=> ! [X2,X0,X1] :
( join_commut(X0,X1,X2) = join(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_52])]) ).
fof(f453,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),the_carrier(X5))
| ~ quasi_total(X4,cartesian_product2(X3,X1),the_carrier(X5))
| ~ function(X4)
| empty(X1)
| empty(X3)
| join(X5,X6,apply_binary_as_element(X3,X1,the_carrier(X5),X4,X2,X0)) = join_commut(X5,X6,apply_binary_as_element(X3,X1,the_carrier(X5),X4,X2,X0))
| ~ element(X6,the_carrier(X5))
| ~ join_semilatt_str(X5)
| ~ join_commutative(X5)
| empty_carrier(X5) )
| ~ spl10_52
| ~ spl10_54 ),
inference(resolution,[],[f447,f410]) ).
fof(f410,plain,
( ! [X2,X0,X1] :
( ~ element(X2,the_carrier(X0))
| join_commut(X0,X1,X2) = join(X0,X1,X2)
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) )
| ~ spl10_52 ),
inference(avatar_component_clause,[],[f409]) ).
fof(f843,plain,
( spl10_102
| ~ spl10_29
| ~ spl10_55 ),
inference(avatar_split_clause,[],[f459,f456,f286,f841]) ).
fof(f841,plain,
( spl10_102
<=> ! [X4,X0,X3,X2,X1] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| apply_binary_as_element(X3,X1,X4,sK5(cartesian_product2(X3,X1),X4),X2,X0) = apply_binary(sK5(cartesian_product2(X3,X1),X4),X2,X0)
| ~ quasi_total(sK5(cartesian_product2(X3,X1),X4),cartesian_product2(X3,X1),X4)
| ~ function(sK5(cartesian_product2(X3,X1),X4))
| empty(X1)
| empty(X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_102])]) ).
fof(f286,plain,
( spl10_29
<=> ! [X0,X1] : relation_of2(sK5(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_29])]) ).
fof(f456,plain,
( spl10_55
<=> ! [X3,X4,X0,X5,X2,X1] :
( apply_binary_as_element(X0,X1,X2,X3,X4,X5) = apply_binary(X3,X4,X5)
| ~ element(X5,X1)
| ~ element(X4,X0)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_55])]) ).
fof(f459,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| apply_binary_as_element(X3,X1,X4,sK5(cartesian_product2(X3,X1),X4),X2,X0) = apply_binary(sK5(cartesian_product2(X3,X1),X4),X2,X0)
| ~ quasi_total(sK5(cartesian_product2(X3,X1),X4),cartesian_product2(X3,X1),X4)
| ~ function(sK5(cartesian_product2(X3,X1),X4))
| empty(X1)
| empty(X3) )
| ~ spl10_29
| ~ spl10_55 ),
inference(resolution,[],[f457,f287]) ).
fof(f287,plain,
( ! [X0,X1] : relation_of2(sK5(X0,X1),X0,X1)
| ~ spl10_29 ),
inference(avatar_component_clause,[],[f286]) ).
fof(f457,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ element(X5,X1)
| ~ element(X4,X0)
| apply_binary_as_element(X0,X1,X2,X3,X4,X5) = apply_binary(X3,X4,X5)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) )
| ~ spl10_55 ),
inference(avatar_component_clause,[],[f456]) ).
fof(f831,plain,
( spl10_101
| ~ spl10_48
| ~ spl10_53 ),
inference(avatar_split_clause,[],[f439,f431,f386,f829]) ).
fof(f829,plain,
( spl10_101
<=> ! [X0,X3,X2,X1] :
( join(X0,X1,join_commut(X0,X2,X3)) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,join_commut(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_commutative(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_101])]) ).
fof(f386,plain,
( spl10_48
<=> ! [X2,X0,X1] :
( element(join_commut(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_48])]) ).
fof(f439,plain,
( ! [X2,X3,X0,X1] :
( join(X0,X1,join_commut(X0,X2,X3)) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,join_commut(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_commutative(X0) )
| ~ spl10_48
| ~ spl10_53 ),
inference(duplicate_literal_removal,[],[f437]) ).
fof(f437,plain,
( ! [X2,X3,X0,X1] :
( join(X0,X1,join_commut(X0,X2,X3)) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,join_commut(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) )
| ~ spl10_48
| ~ spl10_53 ),
inference(resolution,[],[f432,f387]) ).
fof(f387,plain,
( ! [X2,X0,X1] :
( element(join_commut(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) )
| ~ spl10_48 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f825,plain,
( spl10_100
| ~ spl10_44
| ~ spl10_54 ),
inference(avatar_split_clause,[],[f450,f446,f357,f823]) ).
fof(f823,plain,
( spl10_100
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),powerset(X5))
| ~ quasi_total(X4,cartesian_product2(X3,X1),powerset(X5))
| ~ function(X4)
| empty(X1)
| empty(X3)
| element(X6,X5)
| ~ in(X6,apply_binary_as_element(X3,X1,powerset(X5),X4,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_100])]) ).
fof(f357,plain,
( spl10_44
<=> ! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_44])]) ).
fof(f450,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),powerset(X5))
| ~ quasi_total(X4,cartesian_product2(X3,X1),powerset(X5))
| ~ function(X4)
| empty(X1)
| empty(X3)
| element(X6,X5)
| ~ in(X6,apply_binary_as_element(X3,X1,powerset(X5),X4,X2,X0)) )
| ~ spl10_44
| ~ spl10_54 ),
inference(resolution,[],[f447,f358]) ).
fof(f358,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| element(X0,X2)
| ~ in(X0,X1) )
| ~ spl10_44 ),
inference(avatar_component_clause,[],[f357]) ).
fof(f809,plain,
( spl10_99
| ~ spl10_39
| ~ spl10_54 ),
inference(avatar_split_clause,[],[f451,f446,f334,f807]) ).
fof(f807,plain,
( spl10_99
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),powerset(X5))
| ~ quasi_total(X4,cartesian_product2(X3,X1),powerset(X5))
| ~ function(X4)
| empty(X1)
| empty(X3)
| ~ empty(X5)
| ~ in(X6,apply_binary_as_element(X3,X1,powerset(X5),X4,X2,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_99])]) ).
fof(f334,plain,
( spl10_39
<=> ! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_39])]) ).
fof(f451,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),powerset(X5))
| ~ quasi_total(X4,cartesian_product2(X3,X1),powerset(X5))
| ~ function(X4)
| empty(X1)
| empty(X3)
| ~ empty(X5)
| ~ in(X6,apply_binary_as_element(X3,X1,powerset(X5),X4,X2,X0)) )
| ~ spl10_39
| ~ spl10_54 ),
inference(resolution,[],[f447,f335]) ).
fof(f335,plain,
( ! [X2,X0,X1] :
( ~ element(X1,powerset(X2))
| ~ empty(X2)
| ~ in(X0,X1) )
| ~ spl10_39 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f805,plain,
( spl10_98
| ~ spl10_47
| ~ spl10_53 ),
inference(avatar_split_clause,[],[f440,f431,f378,f803]) ).
fof(f803,plain,
( spl10_98
<=> ! [X0,X3,X2,X1] :
( join(X0,X1,join(X0,X2,X3)) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,join(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_98])]) ).
fof(f378,plain,
( spl10_47
<=> ! [X2,X0,X1] :
( element(join(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_47])]) ).
fof(f440,plain,
( ! [X2,X3,X0,X1] :
( join(X0,X1,join(X0,X2,X3)) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,join(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) )
| ~ spl10_47
| ~ spl10_53 ),
inference(duplicate_literal_removal,[],[f436]) ).
fof(f436,plain,
( ! [X2,X3,X0,X1] :
( join(X0,X1,join(X0,X2,X3)) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,join(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) )
| ~ spl10_47
| ~ spl10_53 ),
inference(resolution,[],[f432,f379]) ).
fof(f379,plain,
( ! [X2,X0,X1] :
( element(join(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) )
| ~ spl10_47 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f795,plain,
( spl10_97
| ~ spl10_36
| ~ spl10_54 ),
inference(avatar_split_clause,[],[f449,f446,f316,f793]) ).
fof(f793,plain,
( spl10_97
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),X5)
| ~ quasi_total(X4,cartesian_product2(X3,X1),X5)
| ~ function(X4)
| empty(X1)
| empty(X3)
| empty(X5)
| in(apply_binary_as_element(X3,X1,X5,X4,X2,X0),X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_97])]) ).
fof(f316,plain,
( spl10_36
<=> ! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_36])]) ).
fof(f449,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ element(X0,X1)
| ~ element(X2,X3)
| ~ relation_of2(X4,cartesian_product2(X3,X1),X5)
| ~ quasi_total(X4,cartesian_product2(X3,X1),X5)
| ~ function(X4)
| empty(X1)
| empty(X3)
| empty(X5)
| in(apply_binary_as_element(X3,X1,X5,X4,X2,X0),X5) )
| ~ spl10_36
| ~ spl10_54 ),
inference(resolution,[],[f447,f317]) ).
fof(f317,plain,
( ! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) )
| ~ spl10_36 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f759,plain,
( spl10_96
| ~ spl10_5
| ~ spl10_6
| ~ spl10_63
| ~ spl10_64
| ~ spl10_67
| ~ spl10_68 ),
inference(avatar_split_clause,[],[f564,f555,f542,f517,f509,f182,f177,f756]) ).
fof(f509,plain,
( spl10_63
<=> sK1 = join(sK0,sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_63])]) ).
fof(f564,plain,
( sK1 = join(sK0,sK1,sK2)
| ~ spl10_5
| ~ spl10_6
| ~ spl10_63
| ~ spl10_64
| ~ spl10_67
| ~ spl10_68 ),
inference(forward_demodulation,[],[f558,f552]) ).
fof(f552,plain,
( sK1 = join_commut(sK0,sK1,sK2)
| ~ spl10_6
| ~ spl10_63
| ~ spl10_64
| ~ spl10_67 ),
inference(forward_demodulation,[],[f551,f511]) ).
fof(f511,plain,
( sK1 = join(sK0,sK2,sK1)
| ~ spl10_63 ),
inference(avatar_component_clause,[],[f509]) ).
fof(f551,plain,
( join(sK0,sK2,sK1) = join_commut(sK0,sK1,sK2)
| ~ spl10_6
| ~ spl10_64
| ~ spl10_67 ),
inference(forward_demodulation,[],[f546,f521]) ).
fof(f546,plain,
( join(sK0,sK2,sK1) = join_commut(sK0,sK2,sK1)
| ~ spl10_6
| ~ spl10_67 ),
inference(resolution,[],[f543,f184]) ).
fof(f558,plain,
( join(sK0,sK1,sK2) = join_commut(sK0,sK1,sK2)
| ~ spl10_5
| ~ spl10_68 ),
inference(resolution,[],[f556,f179]) ).
fof(f754,plain,
( spl10_95
| ~ spl10_47
| ~ spl10_52 ),
inference(avatar_split_clause,[],[f427,f409,f378,f752]) ).
fof(f752,plain,
( spl10_95
<=> ! [X0,X3,X2,X1] :
( join_commut(X0,X1,join(X0,X2,X3)) = join(X0,X1,join(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_95])]) ).
fof(f427,plain,
( ! [X2,X3,X0,X1] :
( join_commut(X0,X1,join(X0,X2,X3)) = join(X0,X1,join(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) )
| ~ spl10_47
| ~ spl10_52 ),
inference(duplicate_literal_removal,[],[f423]) ).
fof(f423,plain,
( ! [X2,X3,X0,X1] :
( join_commut(X0,X1,join(X0,X2,X3)) = join(X0,X1,join(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) )
| ~ spl10_47
| ~ spl10_52 ),
inference(resolution,[],[f410,f379]) ).
fof(f750,plain,
( spl10_94
| ~ spl10_48
| ~ spl10_52 ),
inference(avatar_split_clause,[],[f426,f409,f386,f748]) ).
fof(f748,plain,
( spl10_94
<=> ! [X0,X3,X2,X1] :
( join_commut(X0,X1,join_commut(X0,X2,X3)) = join(X0,X1,join_commut(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_94])]) ).
fof(f426,plain,
( ! [X2,X3,X0,X1] :
( join_commut(X0,X1,join_commut(X0,X2,X3)) = join(X0,X1,join_commut(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) )
| ~ spl10_48
| ~ spl10_52 ),
inference(duplicate_literal_removal,[],[f424]) ).
fof(f424,plain,
( ! [X2,X3,X0,X1] :
( join_commut(X0,X1,join_commut(X0,X2,X3)) = join(X0,X1,join_commut(X0,X2,X3))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) )
| ~ spl10_48
| ~ spl10_52 ),
inference(resolution,[],[f410,f387]) ).
fof(f746,plain,
( spl10_93
| ~ spl10_47
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f418,f405,f378,f744]) ).
fof(f744,plain,
( spl10_93
<=> ! [X0,X3,X2,X1] :
( join_commut(X0,X1,join(X0,X2,X3)) = join_commut(X0,join(X0,X2,X3),X1)
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_93])]) ).
fof(f418,plain,
( ! [X2,X3,X0,X1] :
( join_commut(X0,X1,join(X0,X2,X3)) = join_commut(X0,join(X0,X2,X3),X1)
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) )
| ~ spl10_47
| ~ spl10_51 ),
inference(duplicate_literal_removal,[],[f414]) ).
fof(f414,plain,
( ! [X2,X3,X0,X1] :
( join_commut(X0,X1,join(X0,X2,X3)) = join_commut(X0,join(X0,X2,X3),X1)
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) )
| ~ spl10_47
| ~ spl10_51 ),
inference(resolution,[],[f406,f379]) ).
fof(f742,plain,
( spl10_92
| ~ spl10_48
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f417,f405,f386,f740]) ).
fof(f740,plain,
( spl10_92
<=> ! [X0,X3,X2,X1] :
( join_commut(X0,X1,join_commut(X0,X2,X3)) = join_commut(X0,join_commut(X0,X2,X3),X1)
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_92])]) ).
fof(f417,plain,
( ! [X2,X3,X0,X1] :
( join_commut(X0,X1,join_commut(X0,X2,X3)) = join_commut(X0,join_commut(X0,X2,X3),X1)
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0)) )
| ~ spl10_48
| ~ spl10_51 ),
inference(duplicate_literal_removal,[],[f415]) ).
fof(f415,plain,
( ! [X2,X3,X0,X1] :
( join_commut(X0,X1,join_commut(X0,X2,X3)) = join_commut(X0,join_commut(X0,X2,X3),X1)
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0)
| ~ element(X3,the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) )
| ~ spl10_48
| ~ spl10_51 ),
inference(resolution,[],[f406,f387]) ).
fof(f730,plain,
( spl10_91
| ~ spl10_21
| ~ spl10_53 ),
inference(avatar_split_clause,[],[f438,f431,f249,f728]) ).
fof(f728,plain,
( spl10_91
<=> ! [X0,X1] :
( join(X0,X1,sK4(the_carrier(X0))) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,sK4(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_91])]) ).
fof(f438,plain,
( ! [X0,X1] :
( join(X0,X1,sK4(the_carrier(X0))) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,sK4(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) )
| ~ spl10_21
| ~ spl10_53 ),
inference(resolution,[],[f432,f250]) ).
fof(f723,plain,
( spl10_90
| ~ spl10_36
| ~ spl10_48 ),
inference(avatar_split_clause,[],[f389,f386,f316,f721]) ).
fof(f721,plain,
( spl10_90
<=> ! [X2,X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1)
| empty_carrier(X1)
| empty(the_carrier(X1))
| in(join_commut(X1,X2,X0),the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_90])]) ).
fof(f389,plain,
( ! [X2,X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| ~ join_commutative(X1)
| empty_carrier(X1)
| empty(the_carrier(X1))
| in(join_commut(X1,X2,X0),the_carrier(X1)) )
| ~ spl10_36
| ~ spl10_48 ),
inference(resolution,[],[f387,f317]) ).
fof(f703,plain,
( spl10_89
| ~ spl10_6
| ~ spl10_63
| ~ spl10_64
| ~ spl10_67 ),
inference(avatar_split_clause,[],[f552,f542,f517,f509,f182,f700]) ).
fof(f698,plain,
( spl10_88
| ~ spl10_21
| ~ spl10_52 ),
inference(avatar_split_clause,[],[f425,f409,f249,f696]) ).
fof(f696,plain,
( spl10_88
<=> ! [X0,X1] :
( join_commut(X0,X1,sK4(the_carrier(X0))) = join(X0,X1,sK4(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_88])]) ).
fof(f425,plain,
( ! [X0,X1] :
( join_commut(X0,X1,sK4(the_carrier(X0))) = join(X0,X1,sK4(the_carrier(X0)))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) )
| ~ spl10_21
| ~ spl10_52 ),
inference(resolution,[],[f410,f250]) ).
fof(f694,plain,
( spl10_87
| ~ spl10_21
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f416,f405,f249,f692]) ).
fof(f692,plain,
( spl10_87
<=> ! [X0,X1] :
( join_commut(X0,X1,sK4(the_carrier(X0))) = join_commut(X0,sK4(the_carrier(X0)),X1)
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_87])]) ).
fof(f416,plain,
( ! [X0,X1] :
( join_commut(X0,X1,sK4(the_carrier(X0))) = join_commut(X0,sK4(the_carrier(X0)),X1)
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) )
| ~ spl10_21
| ~ spl10_51 ),
inference(resolution,[],[f406,f250]) ).
fof(f685,plain,
( spl10_86
| ~ spl10_36
| ~ spl10_47 ),
inference(avatar_split_clause,[],[f384,f378,f316,f683]) ).
fof(f683,plain,
( spl10_86
<=> ! [X2,X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| empty_carrier(X1)
| empty(the_carrier(X1))
| in(join(X1,X2,X0),the_carrier(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_86])]) ).
fof(f384,plain,
( ! [X2,X0,X1] :
( ~ element(X0,the_carrier(X1))
| ~ element(X2,the_carrier(X1))
| ~ join_semilatt_str(X1)
| empty_carrier(X1)
| empty(the_carrier(X1))
| in(join(X1,X2,X0),the_carrier(X1)) )
| ~ spl10_36
| ~ spl10_47 ),
inference(resolution,[],[f379,f317]) ).
fof(f678,plain,
( spl10_85
| ~ spl10_36
| ~ spl10_43 ),
inference(avatar_split_clause,[],[f363,f353,f316,f676]) ).
fof(f676,plain,
( spl10_85
<=> ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| empty(powerset(cartesian_product2(X1,X2)))
| in(X0,powerset(cartesian_product2(X1,X2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_85])]) ).
fof(f353,plain,
( spl10_43
<=> ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_43])]) ).
fof(f363,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| empty(powerset(cartesian_product2(X1,X2)))
| in(X0,powerset(cartesian_product2(X1,X2))) )
| ~ spl10_36
| ~ spl10_43 ),
inference(resolution,[],[f354,f317]) ).
fof(f354,plain,
( ! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) )
| ~ spl10_43 ),
inference(avatar_component_clause,[],[f353]) ).
fof(f671,plain,
( spl10_84
| ~ spl10_36
| ~ spl10_40 ),
inference(avatar_split_clause,[],[f361,f340,f316,f669]) ).
fof(f669,plain,
( spl10_84
<=> ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| empty(powerset(the_carrier(X0)))
| in(sK3(X0),powerset(the_carrier(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_84])]) ).
fof(f340,plain,
( spl10_40
<=> ! [X0] :
( element(sK3(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_40])]) ).
fof(f361,plain,
( ! [X0] :
( ~ one_sorted_str(X0)
| empty_carrier(X0)
| empty(powerset(the_carrier(X0)))
| in(sK3(X0),powerset(the_carrier(X0))) )
| ~ spl10_36
| ~ spl10_40 ),
inference(resolution,[],[f341,f317]) ).
fof(f341,plain,
( ! [X0] :
( element(sK3(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| empty_carrier(X0) )
| ~ spl10_40 ),
inference(avatar_component_clause,[],[f340]) ).
fof(f660,plain,
( spl10_83
| ~ spl10_37
| ~ spl10_46 ),
inference(avatar_split_clause,[],[f376,f373,f320,f658]) ).
fof(f658,plain,
( spl10_83
<=> ! [X0] :
( ~ join_semilatt_str(X0)
| relation_of2(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_83])]) ).
fof(f320,plain,
( spl10_37
<=> ! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_37])]) ).
fof(f373,plain,
( spl10_46
<=> ! [X0] :
( relation_of2_as_subset(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ join_semilatt_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_46])]) ).
fof(f376,plain,
( ! [X0] :
( ~ join_semilatt_str(X0)
| relation_of2(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0)) )
| ~ spl10_37
| ~ spl10_46 ),
inference(resolution,[],[f374,f321]) ).
fof(f321,plain,
( ! [X2,X0,X1] :
( ~ relation_of2_as_subset(X2,X0,X1)
| relation_of2(X2,X0,X1) )
| ~ spl10_37 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f374,plain,
( ! [X0] :
( relation_of2_as_subset(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ join_semilatt_str(X0) )
| ~ spl10_46 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f656,plain,
( spl10_82
| ~ spl10_40
| ~ spl10_44 ),
inference(avatar_split_clause,[],[f366,f357,f340,f654]) ).
fof(f654,plain,
( spl10_82
<=> ! [X0,X1] :
( element(X0,the_carrier(X1))
| ~ in(X0,sK3(X1))
| ~ one_sorted_str(X1)
| empty_carrier(X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_82])]) ).
fof(f366,plain,
( ! [X0,X1] :
( element(X0,the_carrier(X1))
| ~ in(X0,sK3(X1))
| ~ one_sorted_str(X1)
| empty_carrier(X1) )
| ~ spl10_40
| ~ spl10_44 ),
inference(resolution,[],[f358,f341]) ).
fof(f652,plain,
( spl10_81
| ~ spl10_43
| ~ spl10_44 ),
inference(avatar_split_clause,[],[f365,f357,f353,f650]) ).
fof(f650,plain,
( spl10_81
<=> ! [X0,X3,X2,X1] :
( element(X0,cartesian_product2(X1,X2))
| ~ in(X0,X3)
| ~ relation_of2_as_subset(X3,X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_81])]) ).
fof(f365,plain,
( ! [X2,X3,X0,X1] :
( element(X0,cartesian_product2(X1,X2))
| ~ in(X0,X3)
| ~ relation_of2_as_subset(X3,X1,X2) )
| ~ spl10_43
| ~ spl10_44 ),
inference(resolution,[],[f358,f354]) ).
fof(f645,plain,
( spl10_80
| ~ spl10_39
| ~ spl10_43 ),
inference(avatar_split_clause,[],[f362,f353,f334,f643]) ).
fof(f643,plain,
( spl10_80
<=> ! [X2,X0,X1,X3] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_80])]) ).
fof(f362,plain,
( ! [X2,X3,X0,X1] :
( ~ relation_of2_as_subset(X0,X1,X2)
| ~ empty(cartesian_product2(X1,X2))
| ~ in(X3,X0) )
| ~ spl10_39
| ~ spl10_43 ),
inference(resolution,[],[f354,f335]) ).
fof(f638,plain,
( spl10_79
| ~ spl10_33
| ~ spl10_36 ),
inference(avatar_split_clause,[],[f330,f316,f303,f636]) ).
fof(f636,plain,
( spl10_79
<=> ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_79])]) ).
fof(f303,plain,
( spl10_33
<=> ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_33])]) ).
fof(f330,plain,
( ! [X0,X1] :
( empty(powerset(X0))
| in(X1,powerset(X0))
| ~ subset(X1,X0) )
| ~ spl10_33
| ~ spl10_36 ),
inference(resolution,[],[f317,f304]) ).
fof(f304,plain,
( ! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) )
| ~ spl10_33 ),
inference(avatar_component_clause,[],[f303]) ).
fof(f633,plain,
( spl10_78
| ~ spl10_33
| ~ spl10_44 ),
inference(avatar_split_clause,[],[f364,f357,f303,f631]) ).
fof(f631,plain,
( spl10_78
<=> ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_78])]) ).
fof(f364,plain,
( ! [X2,X0,X1] :
( element(X0,X1)
| ~ in(X0,X2)
| ~ subset(X2,X1) )
| ~ spl10_33
| ~ spl10_44 ),
inference(resolution,[],[f358,f304]) ).
fof(f627,plain,
( spl10_77
| ~ spl10_21
| ~ spl10_44 ),
inference(avatar_split_clause,[],[f367,f357,f249,f625]) ).
fof(f625,plain,
( spl10_77
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(powerset(X1))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_77])]) ).
fof(f367,plain,
( ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,sK4(powerset(X1))) )
| ~ spl10_21
| ~ spl10_44 ),
inference(resolution,[],[f358,f250]) ).
fof(f623,plain,
( spl10_76
| ~ spl10_33
| ~ spl10_39 ),
inference(avatar_split_clause,[],[f337,f334,f303,f621]) ).
fof(f621,plain,
( spl10_76
<=> ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_76])]) ).
fof(f337,plain,
( ! [X2,X0,X1] :
( ~ empty(X0)
| ~ in(X1,X2)
| ~ subset(X2,X0) )
| ~ spl10_33
| ~ spl10_39 ),
inference(resolution,[],[f335,f304]) ).
fof(f618,plain,
( spl10_75
| ~ spl10_21
| ~ spl10_39 ),
inference(avatar_split_clause,[],[f338,f334,f249,f616]) ).
fof(f616,plain,
( spl10_75
<=> ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK4(powerset(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_75])]) ).
fof(f338,plain,
( ! [X0,X1] :
( ~ empty(X0)
| ~ in(X1,sK4(powerset(X0))) )
| ~ spl10_21
| ~ spl10_39 ),
inference(resolution,[],[f335,f250]) ).
fof(f608,plain,
( spl10_74
| ~ spl10_29
| ~ spl10_38 ),
inference(avatar_split_clause,[],[f332,f324,f286,f606]) ).
fof(f606,plain,
( spl10_74
<=> ! [X0,X1] : relation_of2_as_subset(sK5(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_74])]) ).
fof(f324,plain,
( spl10_38
<=> ! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_38])]) ).
fof(f332,plain,
( ! [X0,X1] : relation_of2_as_subset(sK5(X0,X1),X0,X1)
| ~ spl10_29
| ~ spl10_38 ),
inference(resolution,[],[f325,f287]) ).
fof(f325,plain,
( ! [X2,X0,X1] :
( ~ relation_of2(X2,X0,X1)
| relation_of2_as_subset(X2,X0,X1) )
| ~ spl10_38 ),
inference(avatar_component_clause,[],[f324]) ).
fof(f604,plain,
( ~ spl10_73
| ~ spl10_27
| ~ spl10_61 ),
inference(avatar_split_clause,[],[f499,f487,f278,f601]) ).
fof(f601,plain,
( spl10_73
<=> in(the_carrier(sK0),sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_73])]) ).
fof(f278,plain,
( spl10_27
<=> ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_27])]) ).
fof(f487,plain,
( spl10_61
<=> in(sK2,the_carrier(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_61])]) ).
fof(f499,plain,
( ~ in(the_carrier(sK0),sK2)
| ~ spl10_27
| ~ spl10_61 ),
inference(resolution,[],[f489,f279]) ).
fof(f279,plain,
( ! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) )
| ~ spl10_27 ),
inference(avatar_component_clause,[],[f278]) ).
fof(f489,plain,
( in(sK2,the_carrier(sK0))
| ~ spl10_61 ),
inference(avatar_component_clause,[],[f487]) ).
fof(f599,plain,
( spl10_72
| ~ spl10_30
| ~ spl10_37 ),
inference(avatar_split_clause,[],[f331,f320,f290,f597]) ).
fof(f597,plain,
( spl10_72
<=> ! [X0,X1] : relation_of2(sK6(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_72])]) ).
fof(f290,plain,
( spl10_30
<=> ! [X0,X1] : relation_of2_as_subset(sK6(X0,X1),X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_30])]) ).
fof(f331,plain,
( ! [X0,X1] : relation_of2(sK6(X0,X1),X0,X1)
| ~ spl10_30
| ~ spl10_37 ),
inference(resolution,[],[f321,f291]) ).
fof(f291,plain,
( ! [X0,X1] : relation_of2_as_subset(sK6(X0,X1),X0,X1)
| ~ spl10_30 ),
inference(avatar_component_clause,[],[f290]) ).
fof(f595,plain,
( spl10_71
| ~ spl10_21
| ~ spl10_36 ),
inference(avatar_split_clause,[],[f329,f316,f249,f593]) ).
fof(f593,plain,
( spl10_71
<=> ! [X0] :
( empty(X0)
| in(sK4(X0),X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_71])]) ).
fof(f329,plain,
( ! [X0] :
( empty(X0)
| in(sK4(X0),X0) )
| ~ spl10_21
| ~ spl10_36 ),
inference(resolution,[],[f317,f250]) ).
fof(f582,plain,
( spl10_1
| ~ spl10_3
| spl10_70
| ~ spl10_6
| ~ spl10_53 ),
inference(avatar_split_clause,[],[f435,f431,f182,f580,f167,f157]) ).
fof(f157,plain,
( spl10_1
<=> empty_carrier(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_1])]) ).
fof(f167,plain,
( spl10_3
<=> join_semilatt_str(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_3])]) ).
fof(f580,plain,
( spl10_70
<=> ! [X0] :
( join(sK0,X0,sK2) = apply_binary_as_element(the_carrier(sK0),the_carrier(sK0),the_carrier(sK0),the_L_join(sK0),X0,sK2)
| ~ element(X0,the_carrier(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_70])]) ).
fof(f435,plain,
( ! [X0] :
( join(sK0,X0,sK2) = apply_binary_as_element(the_carrier(sK0),the_carrier(sK0),the_carrier(sK0),the_L_join(sK0),X0,sK2)
| ~ element(X0,the_carrier(sK0))
| ~ join_semilatt_str(sK0)
| empty_carrier(sK0) )
| ~ spl10_6
| ~ spl10_53 ),
inference(resolution,[],[f432,f184]) ).
fof(f569,plain,
( spl10_1
| ~ spl10_3
| spl10_69
| ~ spl10_5
| ~ spl10_53 ),
inference(avatar_split_clause,[],[f434,f431,f177,f567,f167,f157]) ).
fof(f567,plain,
( spl10_69
<=> ! [X0] :
( join(sK0,X0,sK1) = apply_binary_as_element(the_carrier(sK0),the_carrier(sK0),the_carrier(sK0),the_L_join(sK0),X0,sK1)
| ~ element(X0,the_carrier(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_69])]) ).
fof(f434,plain,
( ! [X0] :
( join(sK0,X0,sK1) = apply_binary_as_element(the_carrier(sK0),the_carrier(sK0),the_carrier(sK0),the_L_join(sK0),X0,sK1)
| ~ element(X0,the_carrier(sK0))
| ~ join_semilatt_str(sK0)
| empty_carrier(sK0) )
| ~ spl10_5
| ~ spl10_53 ),
inference(resolution,[],[f432,f179]) ).
fof(f557,plain,
( spl10_1
| ~ spl10_2
| ~ spl10_3
| spl10_68
| ~ spl10_6
| ~ spl10_52 ),
inference(avatar_split_clause,[],[f422,f409,f182,f555,f167,f162,f157]) ).
fof(f162,plain,
( spl10_2
<=> join_commutative(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_2])]) ).
fof(f422,plain,
( ! [X0] :
( join_commut(sK0,X0,sK2) = join(sK0,X0,sK2)
| ~ element(X0,the_carrier(sK0))
| ~ join_semilatt_str(sK0)
| ~ join_commutative(sK0)
| empty_carrier(sK0) )
| ~ spl10_6
| ~ spl10_52 ),
inference(resolution,[],[f410,f184]) ).
fof(f544,plain,
( spl10_1
| ~ spl10_2
| ~ spl10_3
| spl10_67
| ~ spl10_5
| ~ spl10_52 ),
inference(avatar_split_clause,[],[f421,f409,f177,f542,f167,f162,f157]) ).
fof(f421,plain,
( ! [X0] :
( join_commut(sK0,X0,sK1) = join(sK0,X0,sK1)
| ~ element(X0,the_carrier(sK0))
| ~ join_semilatt_str(sK0)
| ~ join_commutative(sK0)
| empty_carrier(sK0) )
| ~ spl10_5
| ~ spl10_52 ),
inference(resolution,[],[f410,f179]) ).
fof(f540,plain,
( ~ spl10_66
| ~ spl10_27
| ~ spl10_41 ),
inference(avatar_split_clause,[],[f484,f344,f278,f537]) ).
fof(f537,plain,
( spl10_66
<=> in(the_carrier(sK0),sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_66])]) ).
fof(f344,plain,
( spl10_41
<=> in(sK1,the_carrier(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_41])]) ).
fof(f484,plain,
( ~ in(the_carrier(sK0),sK1)
| ~ spl10_27
| ~ spl10_41 ),
inference(resolution,[],[f346,f279]) ).
fof(f346,plain,
( in(sK1,the_carrier(sK0))
| ~ spl10_41 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f529,plain,
( spl10_1
| ~ spl10_2
| ~ spl10_3
| spl10_65
| ~ spl10_6
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f413,f405,f182,f527,f167,f162,f157]) ).
fof(f527,plain,
( spl10_65
<=> ! [X0] :
( join_commut(sK0,X0,sK2) = join_commut(sK0,sK2,X0)
| ~ element(X0,the_carrier(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_65])]) ).
fof(f413,plain,
( ! [X0] :
( join_commut(sK0,X0,sK2) = join_commut(sK0,sK2,X0)
| ~ element(X0,the_carrier(sK0))
| ~ join_semilatt_str(sK0)
| ~ join_commutative(sK0)
| empty_carrier(sK0) )
| ~ spl10_6
| ~ spl10_51 ),
inference(resolution,[],[f406,f184]) ).
fof(f519,plain,
( spl10_1
| ~ spl10_2
| ~ spl10_3
| spl10_64
| ~ spl10_5
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f412,f405,f177,f517,f167,f162,f157]) ).
fof(f412,plain,
( ! [X0] :
( join_commut(sK0,X0,sK1) = join_commut(sK0,sK1,X0)
| ~ element(X0,the_carrier(sK0))
| ~ join_semilatt_str(sK0)
| ~ join_commutative(sK0)
| empty_carrier(sK0) )
| ~ spl10_5
| ~ spl10_51 ),
inference(resolution,[],[f406,f179]) ).
fof(f512,plain,
( spl10_1
| ~ spl10_3
| ~ spl10_6
| ~ spl10_5
| spl10_63
| ~ spl10_8
| ~ spl10_49 ),
inference(avatar_split_clause,[],[f399,f391,f192,f509,f177,f182,f167,f157]) ).
fof(f192,plain,
( spl10_8
<=> below(sK0,sK2,sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_8])]) ).
fof(f391,plain,
( spl10_49
<=> ! [X2,X0,X1] :
( join(X0,X1,X2) = X2
| ~ below(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_49])]) ).
fof(f399,plain,
( sK1 = join(sK0,sK2,sK1)
| ~ element(sK1,the_carrier(sK0))
| ~ element(sK2,the_carrier(sK0))
| ~ join_semilatt_str(sK0)
| empty_carrier(sK0)
| ~ spl10_8
| ~ spl10_49 ),
inference(resolution,[],[f392,f194]) ).
fof(f194,plain,
( below(sK0,sK2,sK1)
| ~ spl10_8 ),
inference(avatar_component_clause,[],[f192]) ).
fof(f392,plain,
( ! [X2,X0,X1] :
( ~ below(X0,X1,X2)
| join(X0,X1,X2) = X2
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) )
| ~ spl10_49 ),
inference(avatar_component_clause,[],[f391]) ).
fof(f504,plain,
( spl10_1
| ~ spl10_3
| ~ spl10_5
| ~ spl10_6
| spl10_56
| ~ spl10_7
| ~ spl10_49 ),
inference(avatar_split_clause,[],[f398,f391,f187,f461,f182,f177,f167,f157]) ).
fof(f187,plain,
( spl10_7
<=> below(sK0,sK1,sK2) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_7])]) ).
fof(f398,plain,
( sK2 = join(sK0,sK1,sK2)
| ~ element(sK2,the_carrier(sK0))
| ~ element(sK1,the_carrier(sK0))
| ~ join_semilatt_str(sK0)
| empty_carrier(sK0)
| ~ spl10_7
| ~ spl10_49 ),
inference(resolution,[],[f392,f189]) ).
fof(f189,plain,
( below(sK0,sK1,sK2)
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f187]) ).
fof(f501,plain,
( ~ spl10_42
| ~ spl10_24
| ~ spl10_41 ),
inference(avatar_split_clause,[],[f485,f344,f265,f348]) ).
fof(f348,plain,
( spl10_42
<=> empty(the_carrier(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_42])]) ).
fof(f265,plain,
( spl10_24
<=> ! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_24])]) ).
fof(f485,plain,
( ~ empty(the_carrier(sK0))
| ~ spl10_24
| ~ spl10_41 ),
inference(resolution,[],[f346,f266]) ).
fof(f266,plain,
( ! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) )
| ~ spl10_24 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f497,plain,
( spl10_62
| ~ spl10_23
| ~ spl10_42 ),
inference(avatar_split_clause,[],[f492,f348,f261,f494]) ).
fof(f494,plain,
( spl10_62
<=> empty(empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_62])]) ).
fof(f261,plain,
( spl10_23
<=> ! [X0] :
( empty_set = X0
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_23])]) ).
fof(f492,plain,
( empty(empty_set)
| ~ spl10_23
| ~ spl10_42 ),
inference(forward_demodulation,[],[f350,f383]) ).
fof(f383,plain,
( empty_set = the_carrier(sK0)
| ~ spl10_23
| ~ spl10_42 ),
inference(resolution,[],[f350,f262]) ).
fof(f262,plain,
( ! [X0] :
( ~ empty(X0)
| empty_set = X0 )
| ~ spl10_23 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f350,plain,
( empty(the_carrier(sK0))
| ~ spl10_42 ),
inference(avatar_component_clause,[],[f348]) ).
fof(f490,plain,
( spl10_61
| spl10_42
| ~ spl10_6
| ~ spl10_36 ),
inference(avatar_split_clause,[],[f328,f316,f182,f348,f487]) ).
fof(f328,plain,
( empty(the_carrier(sK0))
| in(sK2,the_carrier(sK0))
| ~ spl10_6
| ~ spl10_36 ),
inference(resolution,[],[f317,f184]) ).
fof(f482,plain,
( spl10_1
| ~ spl10_2
| ~ spl10_3
| spl10_60
| ~ spl10_6
| ~ spl10_23
| ~ spl10_42
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f420,f405,f348,f261,f182,f480,f167,f162,f157]) ).
fof(f480,plain,
( spl10_60
<=> ! [X0] :
( ~ element(X0,empty_set)
| join_commut(sK0,X0,sK2) = join_commut(sK0,sK2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_60])]) ).
fof(f420,plain,
( ! [X0] :
( ~ element(X0,empty_set)
| join_commut(sK0,X0,sK2) = join_commut(sK0,sK2,X0)
| ~ join_semilatt_str(sK0)
| ~ join_commutative(sK0)
| empty_carrier(sK0) )
| ~ spl10_6
| ~ spl10_23
| ~ spl10_42
| ~ spl10_51 ),
inference(forward_demodulation,[],[f413,f383]) ).
fof(f476,plain,
( spl10_1
| ~ spl10_2
| ~ spl10_3
| spl10_59
| ~ spl10_5
| ~ spl10_23
| ~ spl10_42
| ~ spl10_51 ),
inference(avatar_split_clause,[],[f419,f405,f348,f261,f177,f474,f167,f162,f157]) ).
fof(f419,plain,
( ! [X0] :
( ~ element(X0,empty_set)
| join_commut(sK0,X0,sK1) = join_commut(sK0,sK1,X0)
| ~ join_semilatt_str(sK0)
| ~ join_commutative(sK0)
| empty_carrier(sK0) )
| ~ spl10_5
| ~ spl10_23
| ~ spl10_42
| ~ spl10_51 ),
inference(forward_demodulation,[],[f412,f383]) ).
fof(f472,plain,
( spl10_1
| ~ spl10_3
| spl10_56
| ~ spl10_57
| ~ spl10_58
| ~ spl10_7
| ~ spl10_23
| ~ spl10_42
| ~ spl10_49 ),
inference(avatar_split_clause,[],[f401,f391,f348,f261,f187,f469,f465,f461,f167,f157]) ).
fof(f465,plain,
( spl10_57
<=> element(sK2,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_57])]) ).
fof(f469,plain,
( spl10_58
<=> element(sK1,empty_set) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_58])]) ).
fof(f401,plain,
( ~ element(sK1,empty_set)
| ~ element(sK2,empty_set)
| sK2 = join(sK0,sK1,sK2)
| ~ join_semilatt_str(sK0)
| empty_carrier(sK0)
| ~ spl10_7
| ~ spl10_23
| ~ spl10_42
| ~ spl10_49 ),
inference(forward_demodulation,[],[f400,f383]) ).
fof(f400,plain,
( ~ element(sK2,empty_set)
| sK2 = join(sK0,sK1,sK2)
| ~ element(sK1,the_carrier(sK0))
| ~ join_semilatt_str(sK0)
| empty_carrier(sK0)
| ~ spl10_7
| ~ spl10_23
| ~ spl10_42
| ~ spl10_49 ),
inference(forward_demodulation,[],[f398,f383]) ).
fof(f458,plain,
spl10_55,
inference(avatar_split_clause,[],[f151,f456]) ).
fof(f151,plain,
! [X2,X3,X0,X1,X4,X5] :
( apply_binary_as_element(X0,X1,X2,X3,X4,X5) = apply_binary(X3,X4,X5)
| ~ element(X5,X1)
| ~ element(X4,X0)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1,X2,X3,X4,X5] :
( apply_binary_as_element(X0,X1,X2,X3,X4,X5) = apply_binary(X3,X4,X5)
| ~ element(X5,X1)
| ~ element(X4,X0)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2,X3,X4,X5] :
( apply_binary_as_element(X0,X1,X2,X3,X4,X5) = apply_binary(X3,X4,X5)
| ~ element(X5,X1)
| ~ element(X4,X0)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( element(X5,X1)
& element(X4,X0)
& relation_of2(X3,cartesian_product2(X0,X1),X2)
& quasi_total(X3,cartesian_product2(X0,X1),X2)
& function(X3)
& ~ empty(X1)
& ~ empty(X0) )
=> apply_binary_as_element(X0,X1,X2,X3,X4,X5) = apply_binary(X3,X4,X5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k2_binop_1) ).
fof(f448,plain,
spl10_54,
inference(avatar_split_clause,[],[f150,f446]) ).
fof(f150,plain,
! [X2,X3,X0,X1,X4,X5] :
( element(apply_binary_as_element(X0,X1,X2,X3,X4,X5),X2)
| ~ element(X5,X1)
| ~ element(X4,X0)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2,X3,X4,X5] :
( element(apply_binary_as_element(X0,X1,X2,X3,X4,X5),X2)
| ~ element(X5,X1)
| ~ element(X4,X0)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2,X3,X4,X5] :
( element(apply_binary_as_element(X0,X1,X2,X3,X4,X5),X2)
| ~ element(X5,X1)
| ~ element(X4,X0)
| ~ relation_of2(X3,cartesian_product2(X0,X1),X2)
| ~ quasi_total(X3,cartesian_product2(X0,X1),X2)
| ~ function(X3)
| empty(X1)
| empty(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1,X2,X3,X4,X5] :
( ( element(X5,X1)
& element(X4,X0)
& relation_of2(X3,cartesian_product2(X0,X1),X2)
& quasi_total(X3,cartesian_product2(X0,X1),X2)
& function(X3)
& ~ empty(X1)
& ~ empty(X0) )
=> element(apply_binary_as_element(X0,X1,X2,X3,X4,X5),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k2_binop_1) ).
fof(f433,plain,
spl10_53,
inference(avatar_split_clause,[],[f124,f431]) ).
fof(f124,plain,
! [X2,X0,X1] :
( join(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( join(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,X2)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f52]) ).
fof(f52,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( join(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,X2)
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ( join_semilatt_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> join(X0,X1,X2) = apply_binary_as_element(the_carrier(X0),the_carrier(X0),the_carrier(X0),the_L_join(X0),X1,X2) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d1_lattices) ).
fof(f411,plain,
spl10_52,
inference(avatar_split_clause,[],[f144,f409]) ).
fof(f144,plain,
! [X2,X0,X1] :
( join_commut(X0,X1,X2) = join(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2] :
( join_commut(X0,X1,X2) = join(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2] :
( join_commut(X0,X1,X2) = join(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& join_semilatt_str(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
=> join_commut(X0,X1,X2) = join(X0,X1,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_k3_lattices) ).
fof(f407,plain,
spl10_51,
inference(avatar_split_clause,[],[f143,f405]) ).
fof(f143,plain,
! [X2,X0,X1] :
( join_commut(X0,X1,X2) = join_commut(X0,X2,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2] :
( join_commut(X0,X1,X2) = join_commut(X0,X2,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( join_commut(X0,X1,X2) = join_commut(X0,X2,X1)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& join_semilatt_str(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
=> join_commut(X0,X1,X2) = join_commut(X0,X2,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k3_lattices) ).
fof(f397,plain,
spl10_50,
inference(avatar_split_clause,[],[f126,f395]) ).
fof(f395,plain,
( spl10_50
<=> ! [X2,X0,X1] :
( below(X0,X1,X2)
| join(X0,X1,X2) != X2
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_50])]) ).
fof(f126,plain,
! [X2,X0,X1] :
( below(X0,X1,X2)
| join(X0,X1,X2) != X2
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( below(X0,X1,X2)
| join(X0,X1,X2) != X2 )
& ( join(X0,X1,X2) = X2
| ~ below(X0,X1,X2) ) )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(nnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( below(X0,X1,X2)
<=> join(X0,X1,X2) = X2 )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f54]) ).
fof(f54,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( below(X0,X1,X2)
<=> join(X0,X1,X2) = X2 )
| ~ element(X2,the_carrier(X0)) )
| ~ element(X1,the_carrier(X0)) )
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ( join_semilatt_str(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( below(X0,X1,X2)
<=> join(X0,X1,X2) = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d3_lattices) ).
fof(f393,plain,
spl10_49,
inference(avatar_split_clause,[],[f125,f391]) ).
fof(f125,plain,
! [X2,X0,X1] :
( join(X0,X1,X2) = X2
| ~ below(X0,X1,X2)
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f89]) ).
fof(f388,plain,
spl10_48,
inference(avatar_split_clause,[],[f142,f386]) ).
fof(f142,plain,
! [X2,X0,X1] :
( element(join_commut(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2] :
( element(join_commut(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2] :
( element(join_commut(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| ~ join_commutative(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& join_semilatt_str(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
=> element(join_commut(X0,X1,X2),the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k3_lattices) ).
fof(f380,plain,
spl10_47,
inference(avatar_split_clause,[],[f145,f378]) ).
fof(f145,plain,
! [X2,X0,X1] :
( element(join(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( element(join(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( element(join(X0,X1,X2),the_carrier(X0))
| ~ element(X2,the_carrier(X0))
| ~ element(X1,the_carrier(X0))
| ~ join_semilatt_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0,X1,X2] :
( ( element(X2,the_carrier(X0))
& element(X1,the_carrier(X0))
& join_semilatt_str(X0)
& ~ empty_carrier(X0) )
=> element(join(X0,X1,X2),the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k1_lattices) ).
fof(f375,plain,
spl10_46,
inference(avatar_split_clause,[],[f122,f373]) ).
fof(f122,plain,
! [X0] :
( relation_of2_as_subset(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0] :
( ( relation_of2_as_subset(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
& quasi_total(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
& function(the_L_join(X0)) )
| ~ join_semilatt_str(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( join_semilatt_str(X0)
=> ( relation_of2_as_subset(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
& quasi_total(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
& function(the_L_join(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_u2_lattices) ).
fof(f371,plain,
spl10_45,
inference(avatar_split_clause,[],[f121,f369]) ).
fof(f369,plain,
( spl10_45
<=> ! [X0] :
( quasi_total(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ join_semilatt_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_45])]) ).
fof(f121,plain,
! [X0] :
( quasi_total(the_L_join(X0),cartesian_product2(the_carrier(X0),the_carrier(X0)),the_carrier(X0))
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f359,plain,
spl10_44,
inference(avatar_split_clause,[],[f146,f357]) ).
fof(f146,plain,
! [X2,X0,X1] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f39]) ).
fof(f39,axiom,
! [X0,X1,X2] :
( ( element(X1,powerset(X2))
& in(X0,X1) )
=> element(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t4_subset) ).
fof(f355,plain,
spl10_43,
inference(avatar_split_clause,[],[f141,f353]) ).
fof(f141,plain,
! [X2,X0,X1] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1,X2] :
( element(X2,powerset(cartesian_product2(X0,X1)))
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
=> element(X2,powerset(cartesian_product2(X0,X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_m2_relset_1) ).
fof(f351,plain,
( spl10_41
| spl10_42
| ~ spl10_5
| ~ spl10_36 ),
inference(avatar_split_clause,[],[f327,f316,f177,f348,f344]) ).
fof(f327,plain,
( empty(the_carrier(sK0))
| in(sK1,the_carrier(sK0))
| ~ spl10_5
| ~ spl10_36 ),
inference(resolution,[],[f317,f179]) ).
fof(f342,plain,
spl10_40,
inference(avatar_split_clause,[],[f128,f340]) ).
fof(f128,plain,
! [X0] :
( element(sK3(X0),powerset(the_carrier(X0)))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0] :
( ( ~ empty(sK3(X0))
& element(sK3(X0),powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f59,f90]) ).
fof(f90,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
=> ( ~ empty(sK3(X0))
& element(sK3(X0),powerset(the_carrier(X0))) ) ),
introduced(choice_axiom,[]) ).
fof(f59,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X0] :
( ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) )
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ? [X1] :
( ~ empty(X1)
& element(X1,powerset(the_carrier(X0))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc5_struct_0) ).
fof(f336,plain,
spl10_39,
inference(avatar_split_clause,[],[f149,f334]) ).
fof(f149,plain,
! [X2,X0,X1] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ~ empty(X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0,X1,X2] :
~ ( empty(X2)
& element(X1,powerset(X2))
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t5_subset) ).
fof(f326,plain,
spl10_38,
inference(avatar_split_clause,[],[f148,f324]) ).
fof(f148,plain,
! [X2,X0,X1] :
( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2] :
( ( relation_of2_as_subset(X2,X0,X1)
| ~ relation_of2(X2,X0,X1) )
& ( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ) ),
inference(nnf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1,X2] :
( relation_of2_as_subset(X2,X0,X1)
<=> relation_of2(X2,X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',redefinition_m2_relset_1) ).
fof(f322,plain,
spl10_37,
inference(avatar_split_clause,[],[f147,f320]) ).
fof(f147,plain,
! [X2,X0,X1] :
( relation_of2(X2,X0,X1)
| ~ relation_of2_as_subset(X2,X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f318,plain,
spl10_36,
inference(avatar_split_clause,[],[f135,f316]) ).
fof(f135,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(flattening,[],[f64]) ).
fof(f64,plain,
! [X0,X1] :
( in(X0,X1)
| empty(X1)
| ~ element(X0,X1) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0,X1] :
( element(X0,X1)
=> ( in(X0,X1)
| empty(X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t2_subset) ).
fof(f314,plain,
( spl10_35
| ~ spl10_9
| ~ spl10_20 ),
inference(avatar_split_clause,[],[f255,f245,f197,f311]) ).
fof(f311,plain,
( spl10_35
<=> one_sorted_str(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_35])]) ).
fof(f197,plain,
( spl10_9
<=> join_semilatt_str(sK7) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_9])]) ).
fof(f245,plain,
( spl10_20
<=> ! [X0] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_20])]) ).
fof(f255,plain,
( one_sorted_str(sK7)
| ~ spl10_9
| ~ spl10_20 ),
inference(resolution,[],[f246,f199]) ).
fof(f199,plain,
( join_semilatt_str(sK7)
| ~ spl10_9 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f246,plain,
( ! [X0] :
( ~ join_semilatt_str(X0)
| one_sorted_str(X0) )
| ~ spl10_20 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f309,plain,
spl10_34,
inference(avatar_split_clause,[],[f137,f307]) ).
fof(f307,plain,
( spl10_34
<=> ! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_34])]) ).
fof(f137,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] :
( ~ empty(X1)
| X0 = X1
| ~ empty(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1] :
~ ( empty(X1)
& X0 != X1
& empty(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t8_boole) ).
fof(f305,plain,
spl10_33,
inference(avatar_split_clause,[],[f136,f303]) ).
fof(f136,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1] :
( element(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1] :
( subset(X0,X1)
=> element(X0,powerset(X1)) ),
inference(unused_predicate_definition_removal,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t3_subset) ).
fof(f301,plain,
spl10_32,
inference(avatar_split_clause,[],[f129,f299]) ).
fof(f299,plain,
( spl10_32
<=> ! [X0] :
( ~ empty(sK3(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_32])]) ).
fof(f129,plain,
! [X0] :
( ~ empty(sK3(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f91]) ).
fof(f297,plain,
spl10_31,
inference(avatar_split_clause,[],[f127,f295]) ).
fof(f295,plain,
( spl10_31
<=> ! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_31])]) ).
fof(f127,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(flattening,[],[f56]) ).
fof(f56,plain,
! [X0] :
( ~ empty(the_carrier(X0))
| ~ one_sorted_str(X0)
| empty_carrier(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( ( one_sorted_str(X0)
& ~ empty_carrier(X0) )
=> ~ empty(the_carrier(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_struct_0) ).
fof(f292,plain,
spl10_30,
inference(avatar_split_clause,[],[f140,f290]) ).
fof(f140,plain,
! [X0,X1] : relation_of2_as_subset(sK6(X0,X1),X0,X1),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1] : relation_of2_as_subset(sK6(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6])],[f25,f96]) ).
fof(f96,plain,
! [X0,X1] :
( ? [X2] : relation_of2_as_subset(X2,X0,X1)
=> relation_of2_as_subset(sK6(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f25,axiom,
! [X0,X1] :
? [X2] : relation_of2_as_subset(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m2_relset_1) ).
fof(f288,plain,
spl10_29,
inference(avatar_split_clause,[],[f139,f286]) ).
fof(f139,plain,
! [X0,X1] : relation_of2(sK5(X0,X1),X0,X1),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1] : relation_of2(sK5(X0,X1),X0,X1),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK5])],[f23,f94]) ).
fof(f94,plain,
! [X0,X1] :
( ? [X2] : relation_of2(X2,X0,X1)
=> relation_of2(sK5(X0,X1),X0,X1) ),
introduced(choice_axiom,[]) ).
fof(f23,axiom,
! [X0,X1] :
? [X2] : relation_of2(X2,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_relset_1) ).
fof(f284,plain,
spl10_28,
inference(avatar_split_clause,[],[f134,f282]) ).
fof(f282,plain,
( spl10_28
<=> ! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_28])]) ).
fof(f134,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( in(X0,X1)
=> element(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t1_subset) ).
fof(f280,plain,
spl10_27,
inference(avatar_split_clause,[],[f133,f278]) ).
fof(f133,plain,
! [X0,X1] :
( ~ in(X1,X0)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,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(f276,plain,
spl10_26,
inference(avatar_split_clause,[],[f130,f274]) ).
fof(f274,plain,
( spl10_26
<=> ! [X0] :
( preboolean(X0)
| ~ diff_closed(X0)
| ~ cup_closed(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_26])]) ).
fof(f130,plain,
! [X0] :
( preboolean(X0)
| ~ diff_closed(X0)
| ~ cup_closed(X0) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0] :
( preboolean(X0)
| ~ diff_closed(X0)
| ~ cup_closed(X0) ),
inference(flattening,[],[f60]) ).
fof(f60,plain,
! [X0] :
( preboolean(X0)
| ~ diff_closed(X0)
| ~ cup_closed(X0) ),
inference(ennf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] :
( ( diff_closed(X0)
& cup_closed(X0) )
=> preboolean(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc2_finsub_1) ).
fof(f272,plain,
( spl10_25
| ~ spl10_3
| ~ spl10_20 ),
inference(avatar_split_clause,[],[f254,f245,f167,f269]) ).
fof(f269,plain,
( spl10_25
<=> one_sorted_str(sK0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_25])]) ).
fof(f254,plain,
( one_sorted_str(sK0)
| ~ spl10_3
| ~ spl10_20 ),
inference(resolution,[],[f246,f169]) ).
fof(f169,plain,
( join_semilatt_str(sK0)
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f267,plain,
spl10_24,
inference(avatar_split_clause,[],[f138,f265]) ).
fof(f138,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t7_boole) ).
fof(f263,plain,
spl10_23,
inference(avatar_split_clause,[],[f123,f261]) ).
fof(f123,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(cnf_transformation,[],[f51]) ).
fof(f51,plain,
! [X0] :
( empty_set = X0
| ~ empty(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( empty(X0)
=> empty_set = X0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t6_boole) ).
fof(f259,plain,
spl10_22,
inference(avatar_split_clause,[],[f120,f257]) ).
fof(f257,plain,
( spl10_22
<=> ! [X0] :
( function(the_L_join(X0))
| ~ join_semilatt_str(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_22])]) ).
fof(f120,plain,
! [X0] :
( function(the_L_join(X0))
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f50]) ).
fof(f251,plain,
spl10_21,
inference(avatar_split_clause,[],[f131,f249]) ).
fof(f131,plain,
! [X0] : element(sK4(X0),X0),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0] : element(sK4(X0),X0),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f24,f92]) ).
fof(f92,plain,
! [X0] :
( ? [X1] : element(X1,X0)
=> element(sK4(X0),X0) ),
introduced(choice_axiom,[]) ).
fof(f24,axiom,
! [X0] :
? [X1] : element(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_m1_subset_1) ).
fof(f247,plain,
spl10_20,
inference(avatar_split_clause,[],[f119,f245]) ).
fof(f119,plain,
! [X0] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(cnf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0] :
( one_sorted_str(X0)
| ~ join_semilatt_str(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( join_semilatt_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_l2_lattices) ).
fof(f243,plain,
spl10_19,
inference(avatar_split_clause,[],[f118,f241]) ).
fof(f241,plain,
( spl10_19
<=> ! [X0] :
( diff_closed(X0)
| ~ preboolean(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_19])]) ).
fof(f118,plain,
! [X0] :
( diff_closed(X0)
| ~ preboolean(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0] :
( ( diff_closed(X0)
& cup_closed(X0) )
| ~ preboolean(X0) ),
inference(ennf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0] :
( preboolean(X0)
=> ( diff_closed(X0)
& cup_closed(X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cc1_finsub_1) ).
fof(f239,plain,
spl10_18,
inference(avatar_split_clause,[],[f117,f237]) ).
fof(f237,plain,
( spl10_18
<=> ! [X0] :
( cup_closed(X0)
| ~ preboolean(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_18])]) ).
fof(f117,plain,
! [X0] :
( cup_closed(X0)
| ~ preboolean(X0) ),
inference(cnf_transformation,[],[f48]) ).
fof(f235,plain,
spl10_17,
inference(avatar_split_clause,[],[f132,f233]) ).
fof(f233,plain,
( spl10_17
<=> ! [X0] : subset(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_17])]) ).
fof(f132,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[],[f44]) ).
fof(f44,plain,
! [X0] : subset(X0,X0),
inference(rectify,[],[f33]) ).
fof(f33,axiom,
! [X0,X1] : subset(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity_r1_tarski) ).
fof(f231,plain,
spl10_16,
inference(avatar_split_clause,[],[f116,f229]) ).
fof(f229,plain,
( spl10_16
<=> ! [X0] : preboolean(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_16])]) ).
fof(f116,plain,
! [X0] : preboolean(powerset(X0)),
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( preboolean(powerset(X0))
& diff_closed(powerset(X0))
& cup_closed(powerset(X0))
& ~ empty(powerset(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fc1_finsub_1) ).
fof(f227,plain,
spl10_15,
inference(avatar_split_clause,[],[f115,f225]) ).
fof(f225,plain,
( spl10_15
<=> ! [X0] : diff_closed(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_15])]) ).
fof(f115,plain,
! [X0] : diff_closed(powerset(X0)),
inference(cnf_transformation,[],[f26]) ).
fof(f223,plain,
spl10_14,
inference(avatar_split_clause,[],[f114,f221]) ).
fof(f221,plain,
( spl10_14
<=> ! [X0] : cup_closed(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_14])]) ).
fof(f114,plain,
! [X0] : cup_closed(powerset(X0)),
inference(cnf_transformation,[],[f26]) ).
fof(f219,plain,
spl10_13,
inference(avatar_split_clause,[],[f113,f217]) ).
fof(f217,plain,
( spl10_13
<=> ! [X0] : ~ empty(powerset(X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_13])]) ).
fof(f113,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f26]) ).
fof(f215,plain,
~ spl10_12,
inference(avatar_split_clause,[],[f155,f212]) ).
fof(f212,plain,
( spl10_12
<=> empty_carrier(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_12])]) ).
fof(f155,plain,
~ empty_carrier(sK9),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
( ~ empty_carrier(sK9)
& one_sorted_str(sK9) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK9])],[f28,f103]) ).
fof(f103,plain,
( ? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) )
=> ( ~ empty_carrier(sK9)
& one_sorted_str(sK9) ) ),
introduced(choice_axiom,[]) ).
fof(f28,axiom,
? [X0] :
( ~ empty_carrier(X0)
& one_sorted_str(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rc3_struct_0) ).
fof(f210,plain,
spl10_11,
inference(avatar_split_clause,[],[f154,f207]) ).
fof(f207,plain,
( spl10_11
<=> one_sorted_str(sK9) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_11])]) ).
fof(f154,plain,
one_sorted_str(sK9),
inference(cnf_transformation,[],[f104]) ).
fof(f205,plain,
spl10_10,
inference(avatar_split_clause,[],[f153,f202]) ).
fof(f202,plain,
( spl10_10
<=> one_sorted_str(sK8) ),
introduced(avatar_definition,[new_symbols(naming,[spl10_10])]) ).
fof(f153,plain,
one_sorted_str(sK8),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
one_sorted_str(sK8),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK8])],[f21,f101]) ).
fof(f101,plain,
( ? [X0] : one_sorted_str(X0)
=> one_sorted_str(sK8) ),
introduced(choice_axiom,[]) ).
fof(f21,axiom,
? [X0] : one_sorted_str(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l1_struct_0) ).
fof(f200,plain,
spl10_9,
inference(avatar_split_clause,[],[f152,f197]) ).
fof(f152,plain,
join_semilatt_str(sK7),
inference(cnf_transformation,[],[f100]) ).
fof(f100,plain,
join_semilatt_str(sK7),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK7])],[f22,f99]) ).
fof(f99,plain,
( ? [X0] : join_semilatt_str(X0)
=> join_semilatt_str(sK7) ),
introduced(choice_axiom,[]) ).
fof(f22,axiom,
? [X0] : join_semilatt_str(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',existence_l2_lattices) ).
fof(f195,plain,
spl10_8,
inference(avatar_split_clause,[],[f111,f192]) ).
fof(f111,plain,
below(sK0,sK2,sK1),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
( sK1 != sK2
& below(sK0,sK2,sK1)
& below(sK0,sK1,sK2)
& element(sK2,the_carrier(sK0))
& element(sK1,the_carrier(sK0))
& join_semilatt_str(sK0)
& join_commutative(sK0)
& ~ empty_carrier(sK0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f47,f87,f86,f85]) ).
fof(f85,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( X1 != X2
& below(X0,X2,X1)
& below(X0,X1,X2)
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& join_semilatt_str(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
=> ( ? [X1] :
( ? [X2] :
( X1 != X2
& below(sK0,X2,X1)
& below(sK0,X1,X2)
& element(X2,the_carrier(sK0)) )
& element(X1,the_carrier(sK0)) )
& join_semilatt_str(sK0)
& join_commutative(sK0)
& ~ empty_carrier(sK0) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
( ? [X1] :
( ? [X2] :
( X1 != X2
& below(sK0,X2,X1)
& below(sK0,X1,X2)
& element(X2,the_carrier(sK0)) )
& element(X1,the_carrier(sK0)) )
=> ( ? [X2] :
( sK1 != X2
& below(sK0,X2,sK1)
& below(sK0,sK1,X2)
& element(X2,the_carrier(sK0)) )
& element(sK1,the_carrier(sK0)) ) ),
introduced(choice_axiom,[]) ).
fof(f87,plain,
( ? [X2] :
( sK1 != X2
& below(sK0,X2,sK1)
& below(sK0,sK1,X2)
& element(X2,the_carrier(sK0)) )
=> ( sK1 != sK2
& below(sK0,sK2,sK1)
& below(sK0,sK1,sK2)
& element(sK2,the_carrier(sK0)) ) ),
introduced(choice_axiom,[]) ).
fof(f47,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( X1 != X2
& below(X0,X2,X1)
& below(X0,X1,X2)
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& join_semilatt_str(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) ),
inference(flattening,[],[f46]) ).
fof(f46,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( X1 != X2
& below(X0,X2,X1)
& below(X0,X1,X2)
& element(X2,the_carrier(X0)) )
& element(X1,the_carrier(X0)) )
& join_semilatt_str(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,negated_conjecture,
~ ! [X0] :
( ( join_semilatt_str(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( below(X0,X2,X1)
& below(X0,X1,X2) )
=> X1 = X2 ) ) ) ),
inference(negated_conjecture,[],[f35]) ).
fof(f35,conjecture,
! [X0] :
( ( join_semilatt_str(X0)
& join_commutative(X0)
& ~ empty_carrier(X0) )
=> ! [X1] :
( element(X1,the_carrier(X0))
=> ! [X2] :
( element(X2,the_carrier(X0))
=> ( ( below(X0,X2,X1)
& below(X0,X1,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t26_lattices) ).
fof(f190,plain,
spl10_7,
inference(avatar_split_clause,[],[f110,f187]) ).
fof(f110,plain,
below(sK0,sK1,sK2),
inference(cnf_transformation,[],[f88]) ).
fof(f185,plain,
spl10_6,
inference(avatar_split_clause,[],[f109,f182]) ).
fof(f109,plain,
element(sK2,the_carrier(sK0)),
inference(cnf_transformation,[],[f88]) ).
fof(f180,plain,
spl10_5,
inference(avatar_split_clause,[],[f108,f177]) ).
fof(f108,plain,
element(sK1,the_carrier(sK0)),
inference(cnf_transformation,[],[f88]) ).
fof(f175,plain,
~ spl10_4,
inference(avatar_split_clause,[],[f112,f172]) ).
fof(f112,plain,
sK1 != sK2,
inference(cnf_transformation,[],[f88]) ).
fof(f170,plain,
spl10_3,
inference(avatar_split_clause,[],[f107,f167]) ).
fof(f107,plain,
join_semilatt_str(sK0),
inference(cnf_transformation,[],[f88]) ).
fof(f165,plain,
spl10_2,
inference(avatar_split_clause,[],[f106,f162]) ).
fof(f106,plain,
join_commutative(sK0),
inference(cnf_transformation,[],[f88]) ).
fof(f160,plain,
~ spl10_1,
inference(avatar_split_clause,[],[f105,f157]) ).
fof(f105,plain,
~ empty_carrier(sK0),
inference(cnf_transformation,[],[f88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SEU305+1 : TPTP v8.1.2. Released v3.3.0.
% 0.09/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n023.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 : Mon Apr 29 20:27:55 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (31202)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (31207)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)
% 0.11/0.34 % (31209)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)
% 0.11/0.34 % (31208)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)
% 0.11/0.35 % (31204)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.36 % (31203)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.36 % (31207)First to succeed.
% 0.11/0.37 TRYING [1]
% 0.11/0.37 TRYING [2]
% 0.11/0.37 % (31207)Refutation found. Thanks to Tanya!
% 0.11/0.37 % SZS status Theorem for theBenchmark
% 0.11/0.37 % SZS output start Proof for theBenchmark
% See solution above
% 0.11/0.38 % (31207)------------------------------
% 0.11/0.38 % (31207)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.11/0.38 % (31207)Termination reason: Refutation
% 0.11/0.38
% 0.11/0.38 % (31207)Memory used [KB]: 1335
% 0.11/0.38 % (31207)Time elapsed: 0.033 s
% 0.11/0.38 % (31207)Instructions burned: 52 (million)
% 0.11/0.38 % (31207)------------------------------
% 0.11/0.38 % (31207)------------------------------
% 0.11/0.38 % (31202)Success in time 0.052 s
%------------------------------------------------------------------------------