TSTP Solution File: SWV408+1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV408+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 : n003.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 16:46:43 EDT 2024
% Result : Theorem 0.22s 0.44s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 159
% Syntax : Number of formulae : 514 ( 98 unt; 0 def)
% Number of atoms : 1470 ( 289 equ)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 1602 ( 646 ~; 745 |; 59 &)
% ( 122 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 125 ( 123 usr; 115 prp; 0-3 aty)
% Number of functors : 23 ( 23 usr; 7 con; 0-3 aty)
% Number of variables : 1148 (1130 !; 18 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1176,plain,
$false,
inference(avatar_sat_refutation,[],[f164,f169,f174,f179,f183,f187,f191,f195,f199,f203,f207,f211,f215,f219,f223,f227,f231,f239,f243,f247,f251,f255,f259,f263,f267,f272,f277,f281,f285,f289,f293,f297,f314,f318,f322,f333,f343,f347,f351,f362,f366,f372,f376,f384,f388,f392,f396,f416,f421,f425,f439,f446,f452,f462,f466,f477,f481,f485,f493,f501,f520,f528,f532,f536,f551,f570,f575,f589,f593,f600,f605,f610,f615,f622,f626,f630,f669,f684,f688,f692,f700,f713,f717,f725,f729,f741,f753,f764,f768,f772,f810,f814,f818,f846,f850,f888,f895,f944,f954,f1010,f1015,f1019,f1053,f1057,f1071,f1077,f1094,f1098,f1107,f1111,f1112,f1130,f1134,f1151,f1159,f1174]) ).
fof(f1174,plain,
( ~ spl5_1
| ~ spl5_109 ),
inference(avatar_contradiction_clause,[],[f1169]) ).
fof(f1169,plain,
( $false
| ~ spl5_1
| ~ spl5_109 ),
inference(resolution,[],[f1097,f163]) ).
fof(f163,plain,
( contains_slb(sK1,sK3)
| ~ spl5_1 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f161,plain,
( spl5_1
<=> contains_slb(sK1,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f1097,plain,
( ! [X0] : ~ contains_slb(sK1,X0)
| ~ spl5_109 ),
inference(avatar_component_clause,[],[f1096]) ).
fof(f1096,plain,
( spl5_109
<=> ! [X0] : ~ contains_slb(sK1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_109])]) ).
fof(f1159,plain,
( ~ spl5_1
| ~ spl5_41
| spl5_3
| ~ spl5_49
| spl5_62 ),
inference(avatar_split_clause,[],[f521,f517,f414,f171,f359,f161]) ).
fof(f359,plain,
( spl5_41
<=> strictly_less_than(sK3,findmin_pqp_res(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_41])]) ).
fof(f171,plain,
( spl5_3
<=> pair_in_list(update_slb(sK1,findmin_pqp_res(sK0)),sK3,findmin_pqp_res(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f414,plain,
( spl5_49
<=> ! [X2,X0,X1] :
( less_than(X2,sK4(X0,X1,X2))
| pair_in_list(update_slb(X0,X2),X1,X2)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_49])]) ).
fof(f517,plain,
( spl5_62
<=> less_than(findmin_pqp_res(sK0),sK4(sK1,sK3,findmin_pqp_res(sK0))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_62])]) ).
fof(f521,plain,
( pair_in_list(update_slb(sK1,findmin_pqp_res(sK0)),sK3,findmin_pqp_res(sK0))
| ~ strictly_less_than(sK3,findmin_pqp_res(sK0))
| ~ contains_slb(sK1,sK3)
| ~ spl5_49
| spl5_62 ),
inference(resolution,[],[f519,f415]) ).
fof(f415,plain,
( ! [X2,X0,X1] :
( less_than(X2,sK4(X0,X1,X2))
| pair_in_list(update_slb(X0,X2),X1,X2)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1) )
| ~ spl5_49 ),
inference(avatar_component_clause,[],[f414]) ).
fof(f519,plain,
( ~ less_than(findmin_pqp_res(sK0),sK4(sK1,sK3,findmin_pqp_res(sK0)))
| spl5_62 ),
inference(avatar_component_clause,[],[f517]) ).
fof(f1151,plain,
( spl5_114
| ~ spl5_29
| ~ spl5_61 ),
inference(avatar_split_clause,[],[f506,f499,f283,f1149]) ).
fof(f1149,plain,
( spl5_114
<=> ! [X0,X1] :
( lookup_slb(remove_slb(insert_slb(sK1,pair(X0,X1)),sK3),X0) = X1
| sK3 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_114])]) ).
fof(f283,plain,
( spl5_29
<=> ! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_29])]) ).
fof(f499,plain,
( spl5_61
<=> ! [X0,X1] :
( remove_slb(insert_slb(sK1,pair(X0,X1)),sK3) = insert_slb(remove_slb(sK1,sK3),pair(X0,X1))
| sK3 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_61])]) ).
fof(f506,plain,
( ! [X0,X1] :
( lookup_slb(remove_slb(insert_slb(sK1,pair(X0,X1)),sK3),X0) = X1
| sK3 = X0 )
| ~ spl5_29
| ~ spl5_61 ),
inference(superposition,[],[f284,f500]) ).
fof(f500,plain,
( ! [X0,X1] :
( remove_slb(insert_slb(sK1,pair(X0,X1)),sK3) = insert_slb(remove_slb(sK1,sK3),pair(X0,X1))
| sK3 = X0 )
| ~ spl5_61 ),
inference(avatar_component_clause,[],[f499]) ).
fof(f284,plain,
( ! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2
| ~ spl5_29 ),
inference(avatar_component_clause,[],[f283]) ).
fof(f1134,plain,
( spl5_113
| ~ spl5_21
| ~ spl5_66 ),
inference(avatar_split_clause,[],[f555,f549,f249,f1132]) ).
fof(f1132,plain,
( spl5_113
<=> ! [X0,X1] : contains_slb(update_slb(insert_slb(X0,pair(X1,sK3)),removemin_cpq_res(triple(sK0,sK1,sK2))),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_113])]) ).
fof(f249,plain,
( spl5_21
<=> ! [X2,X0,X3] : contains_slb(insert_slb(X0,pair(X2,X3)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_21])]) ).
fof(f549,plain,
( spl5_66
<=> ! [X0,X1] : update_slb(insert_slb(X0,pair(X1,sK3)),removemin_cpq_res(triple(sK0,sK1,sK2))) = insert_slb(update_slb(X0,removemin_cpq_res(triple(sK0,sK1,sK2))),pair(X1,removemin_cpq_res(triple(sK0,sK1,sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_66])]) ).
fof(f555,plain,
( ! [X0,X1] : contains_slb(update_slb(insert_slb(X0,pair(X1,sK3)),removemin_cpq_res(triple(sK0,sK1,sK2))),X1)
| ~ spl5_21
| ~ spl5_66 ),
inference(superposition,[],[f250,f550]) ).
fof(f550,plain,
( ! [X0,X1] : update_slb(insert_slb(X0,pair(X1,sK3)),removemin_cpq_res(triple(sK0,sK1,sK2))) = insert_slb(update_slb(X0,removemin_cpq_res(triple(sK0,sK1,sK2))),pair(X1,removemin_cpq_res(triple(sK0,sK1,sK2))))
| ~ spl5_66 ),
inference(avatar_component_clause,[],[f549]) ).
fof(f250,plain,
( ! [X2,X3,X0] : contains_slb(insert_slb(X0,pair(X2,X3)),X2)
| ~ spl5_21 ),
inference(avatar_component_clause,[],[f249]) ).
fof(f1130,plain,
( spl5_112
| ~ spl5_25
| ~ spl5_61 ),
inference(avatar_split_clause,[],[f504,f499,f265,f1128]) ).
fof(f1128,plain,
( spl5_112
<=> ! [X0,X1] :
( pair_in_list(remove_slb(insert_slb(sK1,pair(X0,X1)),sK3),X0,X1)
| sK3 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_112])]) ).
fof(f265,plain,
( spl5_25
<=> ! [X4,X0,X2] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_25])]) ).
fof(f504,plain,
( ! [X0,X1] :
( pair_in_list(remove_slb(insert_slb(sK1,pair(X0,X1)),sK3),X0,X1)
| sK3 = X0 )
| ~ spl5_25
| ~ spl5_61 ),
inference(superposition,[],[f266,f500]) ).
fof(f266,plain,
( ! [X2,X0,X4] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4)
| ~ spl5_25 ),
inference(avatar_component_clause,[],[f265]) ).
fof(f1112,plain,
( spl5_41
| spl5_57
| ~ spl5_64 ),
inference(avatar_split_clause,[],[f583,f530,f474,f359]) ).
fof(f474,plain,
( spl5_57
<=> less_than(findmin_pqp_res(sK0),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_57])]) ).
fof(f530,plain,
( spl5_64
<=> ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_64])]) ).
fof(f583,plain,
( strictly_less_than(sK3,findmin_pqp_res(sK0))
| spl5_57
| ~ spl5_64 ),
inference(resolution,[],[f476,f531]) ).
fof(f531,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(X1,X0) )
| ~ spl5_64 ),
inference(avatar_component_clause,[],[f530]) ).
fof(f476,plain,
( ~ less_than(findmin_pqp_res(sK0),sK3)
| spl5_57 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f1111,plain,
( spl5_111
| ~ spl5_17
| ~ spl5_66 ),
inference(avatar_split_clause,[],[f554,f549,f229,f1109]) ).
fof(f1109,plain,
( spl5_111
<=> ! [X0,X1] : isnonempty_slb(update_slb(insert_slb(X0,pair(X1,sK3)),removemin_cpq_res(triple(sK0,sK1,sK2)))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_111])]) ).
fof(f229,plain,
( spl5_17
<=> ! [X2,X0,X1] : isnonempty_slb(insert_slb(X0,pair(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_17])]) ).
fof(f554,plain,
( ! [X0,X1] : isnonempty_slb(update_slb(insert_slb(X0,pair(X1,sK3)),removemin_cpq_res(triple(sK0,sK1,sK2))))
| ~ spl5_17
| ~ spl5_66 ),
inference(superposition,[],[f230,f550]) ).
fof(f230,plain,
( ! [X2,X0,X1] : isnonempty_slb(insert_slb(X0,pair(X1,X2)))
| ~ spl5_17 ),
inference(avatar_component_clause,[],[f229]) ).
fof(f1107,plain,
( spl5_110
| ~ spl5_21
| ~ spl5_61 ),
inference(avatar_split_clause,[],[f503,f499,f249,f1105]) ).
fof(f1105,plain,
( spl5_110
<=> ! [X0,X1] :
( contains_slb(remove_slb(insert_slb(sK1,pair(X0,X1)),sK3),X0)
| sK3 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_110])]) ).
fof(f503,plain,
( ! [X0,X1] :
( contains_slb(remove_slb(insert_slb(sK1,pair(X0,X1)),sK3),X0)
| sK3 = X0 )
| ~ spl5_21
| ~ spl5_61 ),
inference(superposition,[],[f250,f500]) ).
fof(f1098,plain,
( spl5_109
| ~ spl5_6
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f1079,f355,f185,f1096]) ).
fof(f185,plain,
( spl5_6
<=> ! [X0] : ~ contains_slb(create_slb,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
fof(f355,plain,
( spl5_40
<=> create_slb = sK1 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_40])]) ).
fof(f1079,plain,
( ! [X0] : ~ contains_slb(sK1,X0)
| ~ spl5_6
| ~ spl5_40 ),
inference(superposition,[],[f186,f357]) ).
fof(f357,plain,
( create_slb = sK1
| ~ spl5_40 ),
inference(avatar_component_clause,[],[f355]) ).
fof(f186,plain,
( ! [X0] : ~ contains_slb(create_slb,X0)
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f185]) ).
fof(f1094,plain,
( ~ spl5_108
| spl5_4
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f1078,f355,f176,f1091]) ).
fof(f1091,plain,
( spl5_108
<=> isnonempty_slb(sK1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_108])]) ).
fof(f176,plain,
( spl5_4
<=> isnonempty_slb(create_slb) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f1078,plain,
( ~ isnonempty_slb(sK1)
| spl5_4
| ~ spl5_40 ),
inference(superposition,[],[f178,f357]) ).
fof(f178,plain,
( ~ isnonempty_slb(create_slb)
| spl5_4 ),
inference(avatar_component_clause,[],[f176]) ).
fof(f1077,plain,
( spl5_107
| ~ spl5_15
| ~ spl5_102 ),
inference(avatar_split_clause,[],[f1048,f1012,f221,f1074]) ).
fof(f1074,plain,
( spl5_107
<=> less_than(sK4(sK1,sK3,findmin_pqp_res(sK0)),findmin_pqp_res(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_107])]) ).
fof(f221,plain,
( spl5_15
<=> ! [X0,X1] :
( less_than(X0,X1)
| ~ strictly_less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_15])]) ).
fof(f1012,plain,
( spl5_102
<=> strictly_less_than(sK4(sK1,sK3,findmin_pqp_res(sK0)),findmin_pqp_res(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_102])]) ).
fof(f1048,plain,
( less_than(sK4(sK1,sK3,findmin_pqp_res(sK0)),findmin_pqp_res(sK0))
| ~ spl5_15
| ~ spl5_102 ),
inference(resolution,[],[f1014,f222]) ).
fof(f222,plain,
( ! [X0,X1] :
( ~ strictly_less_than(X0,X1)
| less_than(X0,X1) )
| ~ spl5_15 ),
inference(avatar_component_clause,[],[f221]) ).
fof(f1014,plain,
( strictly_less_than(sK4(sK1,sK3,findmin_pqp_res(sK0)),findmin_pqp_res(sK0))
| ~ spl5_102 ),
inference(avatar_component_clause,[],[f1012]) ).
fof(f1071,plain,
( spl5_106
| ~ spl5_17
| ~ spl5_61 ),
inference(avatar_split_clause,[],[f502,f499,f229,f1069]) ).
fof(f1069,plain,
( spl5_106
<=> ! [X0,X1] :
( isnonempty_slb(remove_slb(insert_slb(sK1,pair(X0,X1)),sK3))
| sK3 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_106])]) ).
fof(f502,plain,
( ! [X0,X1] :
( isnonempty_slb(remove_slb(insert_slb(sK1,pair(X0,X1)),sK3))
| sK3 = X0 )
| ~ spl5_17
| ~ spl5_61 ),
inference(superposition,[],[f230,f500]) ).
fof(f1057,plain,
( spl5_105
| ~ spl5_18
| ~ spl5_68 ),
inference(avatar_split_clause,[],[f581,f573,f236,f1055]) ).
fof(f1055,plain,
( spl5_105
<=> ! [X0] :
( less_than(sK3,X0)
| less_than(X0,removemin_cpq_res(triple(sK0,sK1,sK2))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_105])]) ).
fof(f236,plain,
( spl5_18
<=> less_than(sK3,removemin_cpq_res(triple(sK0,sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_18])]) ).
fof(f573,plain,
( spl5_68
<=> ! [X2,X0,X1] :
( less_than(X0,X1)
| ~ less_than(X0,X2)
| less_than(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_68])]) ).
fof(f581,plain,
( ! [X0] :
( less_than(sK3,X0)
| less_than(X0,removemin_cpq_res(triple(sK0,sK1,sK2))) )
| ~ spl5_18
| ~ spl5_68 ),
inference(resolution,[],[f574,f238]) ).
fof(f238,plain,
( less_than(sK3,removemin_cpq_res(triple(sK0,sK1,sK2)))
| ~ spl5_18 ),
inference(avatar_component_clause,[],[f236]) ).
fof(f574,plain,
( ! [X2,X0,X1] :
( ~ less_than(X0,X2)
| less_than(X0,X1)
| less_than(X1,X2) )
| ~ spl5_68 ),
inference(avatar_component_clause,[],[f573]) ).
fof(f1053,plain,
( spl5_104
| ~ spl5_18
| ~ spl5_30 ),
inference(avatar_split_clause,[],[f309,f287,f236,f1051]) ).
fof(f1051,plain,
( spl5_104
<=> ! [X0] :
( less_than(X0,removemin_cpq_res(triple(sK0,sK1,sK2)))
| ~ less_than(X0,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_104])]) ).
fof(f287,plain,
( spl5_30
<=> ! [X2,X0,X1] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_30])]) ).
fof(f309,plain,
( ! [X0] :
( less_than(X0,removemin_cpq_res(triple(sK0,sK1,sK2)))
| ~ less_than(X0,sK3) )
| ~ spl5_18
| ~ spl5_30 ),
inference(resolution,[],[f288,f238]) ).
fof(f288,plain,
( ! [X2,X0,X1] :
( ~ less_than(X1,X2)
| less_than(X0,X2)
| ~ less_than(X0,X1) )
| ~ spl5_30 ),
inference(avatar_component_clause,[],[f287]) ).
fof(f1019,plain,
( spl5_103
| ~ spl5_29
| ~ spl5_59 ),
inference(avatar_split_clause,[],[f489,f483,f283,f1017]) ).
fof(f1017,plain,
( spl5_103
<=> ! [X0,X3,X2,X1] :
( ~ less_than(X2,findmin_pqp_res(X1))
| findmin_cpq_eff(triple(X1,insert_slb(X0,pair(findmin_pqp_res(X1),X2)),X3)) = triple(X1,update_slb(insert_slb(X0,pair(findmin_pqp_res(X1),X2)),findmin_pqp_res(X1)),X3)
| ~ contains_slb(insert_slb(X0,pair(findmin_pqp_res(X1),X2)),findmin_pqp_res(X1))
| create_slb = insert_slb(X0,pair(findmin_pqp_res(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_103])]) ).
fof(f483,plain,
( spl5_59
<=> ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_59])]) ).
fof(f489,plain,
( ! [X2,X3,X0,X1] :
( ~ less_than(X2,findmin_pqp_res(X1))
| findmin_cpq_eff(triple(X1,insert_slb(X0,pair(findmin_pqp_res(X1),X2)),X3)) = triple(X1,update_slb(insert_slb(X0,pair(findmin_pqp_res(X1),X2)),findmin_pqp_res(X1)),X3)
| ~ contains_slb(insert_slb(X0,pair(findmin_pqp_res(X1),X2)),findmin_pqp_res(X1))
| create_slb = insert_slb(X0,pair(findmin_pqp_res(X1),X2)) )
| ~ spl5_29
| ~ spl5_59 ),
inference(superposition,[],[f484,f284]) ).
fof(f484,plain,
( ! [X2,X0,X1] :
( ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
| findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 )
| ~ spl5_59 ),
inference(avatar_component_clause,[],[f483]) ).
fof(f1015,plain,
( spl5_102
| spl5_62
| ~ spl5_64 ),
inference(avatar_split_clause,[],[f541,f530,f517,f1012]) ).
fof(f541,plain,
( strictly_less_than(sK4(sK1,sK3,findmin_pqp_res(sK0)),findmin_pqp_res(sK0))
| spl5_62
| ~ spl5_64 ),
inference(resolution,[],[f531,f519]) ).
fof(f1010,plain,
( spl5_101
| ~ spl5_29
| ~ spl5_58 ),
inference(avatar_split_clause,[],[f486,f479,f283,f1008]) ).
fof(f1008,plain,
( spl5_101
<=> ! [X0,X3,X2,X1] :
( ~ strictly_less_than(findmin_pqp_res(X1),X2)
| findmin_cpq_eff(triple(X1,insert_slb(X0,pair(findmin_pqp_res(X1),X2)),X3)) = triple(X1,update_slb(insert_slb(X0,pair(findmin_pqp_res(X1),X2)),findmin_pqp_res(X1)),bad)
| ~ contains_slb(insert_slb(X0,pair(findmin_pqp_res(X1),X2)),findmin_pqp_res(X1))
| create_slb = insert_slb(X0,pair(findmin_pqp_res(X1),X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_101])]) ).
fof(f479,plain,
( spl5_58
<=> ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_58])]) ).
fof(f486,plain,
( ! [X2,X3,X0,X1] :
( ~ strictly_less_than(findmin_pqp_res(X1),X2)
| findmin_cpq_eff(triple(X1,insert_slb(X0,pair(findmin_pqp_res(X1),X2)),X3)) = triple(X1,update_slb(insert_slb(X0,pair(findmin_pqp_res(X1),X2)),findmin_pqp_res(X1)),bad)
| ~ contains_slb(insert_slb(X0,pair(findmin_pqp_res(X1),X2)),findmin_pqp_res(X1))
| create_slb = insert_slb(X0,pair(findmin_pqp_res(X1),X2)) )
| ~ spl5_29
| ~ spl5_58 ),
inference(superposition,[],[f480,f284]) ).
fof(f480,plain,
( ! [X2,X0,X1] :
( ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 )
| ~ spl5_58 ),
inference(avatar_component_clause,[],[f479]) ).
fof(f954,plain,
( spl5_100
| ~ spl5_52
| ~ spl5_54 ),
inference(avatar_split_clause,[],[f457,f450,f437,f952]) ).
fof(f952,plain,
( spl5_100
<=> ! [X4,X0,X3,X2,X1] :
( remove_slb(insert_slb(X0,pair(X1,X2)),findmin_pqp_res(X3)) = insert_slb(remove_slb(X0,findmin_pqp_res(X3)),pair(X1,X2))
| findmin_pqp_res(X3) = X1
| findmin_cpq_eff(triple(X3,X0,X4)) = triple(X3,update_slb(X0,findmin_pqp_res(X3)),bad)
| create_slb = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_100])]) ).
fof(f437,plain,
( spl5_52
<=> ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_52])]) ).
fof(f450,plain,
( spl5_54
<=> ! [X0,X3,X2,X1] :
( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
| ~ contains_slb(X0,X2)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_54])]) ).
fof(f457,plain,
( ! [X2,X3,X0,X1,X4] :
( remove_slb(insert_slb(X0,pair(X1,X2)),findmin_pqp_res(X3)) = insert_slb(remove_slb(X0,findmin_pqp_res(X3)),pair(X1,X2))
| findmin_pqp_res(X3) = X1
| findmin_cpq_eff(triple(X3,X0,X4)) = triple(X3,update_slb(X0,findmin_pqp_res(X3)),bad)
| create_slb = X0 )
| ~ spl5_52
| ~ spl5_54 ),
inference(resolution,[],[f451,f438]) ).
fof(f438,plain,
( ! [X2,X0,X1] :
( contains_slb(X1,findmin_pqp_res(X0))
| findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| create_slb = X1 )
| ~ spl5_52 ),
inference(avatar_component_clause,[],[f437]) ).
fof(f451,plain,
( ! [X2,X3,X0,X1] :
( ~ contains_slb(X0,X2)
| remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
| X1 = X2 )
| ~ spl5_54 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f944,plain,
( spl5_99
| ~ spl5_39
| ~ spl5_52 ),
inference(avatar_split_clause,[],[f441,f437,f349,f942]) ).
fof(f942,plain,
( spl5_99
<=> ! [X4,X0,X3,X2,X1] :
( findmin_cpq_eff(triple(X0,insert_slb(X1,pair(X2,X3)),X4)) = triple(X0,update_slb(insert_slb(X1,pair(X2,X3)),findmin_pqp_res(X0)),bad)
| create_slb = insert_slb(X1,pair(X2,X3))
| contains_slb(X1,findmin_pqp_res(X0))
| findmin_pqp_res(X0) = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_99])]) ).
fof(f349,plain,
( spl5_39
<=> ! [X0,X3,X2,X1] :
( X1 = X2
| contains_slb(X0,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_39])]) ).
fof(f441,plain,
( ! [X2,X3,X0,X1,X4] :
( findmin_cpq_eff(triple(X0,insert_slb(X1,pair(X2,X3)),X4)) = triple(X0,update_slb(insert_slb(X1,pair(X2,X3)),findmin_pqp_res(X0)),bad)
| create_slb = insert_slb(X1,pair(X2,X3))
| contains_slb(X1,findmin_pqp_res(X0))
| findmin_pqp_res(X0) = X2 )
| ~ spl5_39
| ~ spl5_52 ),
inference(resolution,[],[f438,f350]) ).
fof(f350,plain,
( ! [X2,X3,X0,X1] :
( ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| contains_slb(X0,X2)
| X1 = X2 )
| ~ spl5_39 ),
inference(avatar_component_clause,[],[f349]) ).
fof(f895,plain,
( spl5_98
| ~ spl5_46
| ~ spl5_52 ),
inference(avatar_split_clause,[],[f442,f437,f386,f893]) ).
fof(f893,plain,
( spl5_98
<=> ! [X4,X0,X3,X2,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| create_slb = X1
| lookup_slb(X1,findmin_pqp_res(X0)) = lookup_slb(insert_slb(X1,pair(X3,X4)),findmin_pqp_res(X0))
| findmin_pqp_res(X0) = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_98])]) ).
fof(f386,plain,
( spl5_46
<=> ! [X0,X3,X2,X1] :
( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
| ~ contains_slb(X0,X2)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_46])]) ).
fof(f442,plain,
( ! [X2,X3,X0,X1,X4] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| create_slb = X1
| lookup_slb(X1,findmin_pqp_res(X0)) = lookup_slb(insert_slb(X1,pair(X3,X4)),findmin_pqp_res(X0))
| findmin_pqp_res(X0) = X3 )
| ~ spl5_46
| ~ spl5_52 ),
inference(resolution,[],[f438,f387]) ).
fof(f387,plain,
( ! [X2,X3,X0,X1] :
( ~ contains_slb(X0,X2)
| lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
| X1 = X2 )
| ~ spl5_46 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f888,plain,
( spl5_97
| ~ spl5_49
| ~ spl5_51 ),
inference(avatar_split_clause,[],[f432,f423,f414,f886]) ).
fof(f886,plain,
( spl5_97
<=> ! [X4,X0,X3,X2,X1] :
( update_slb(insert_slb(X0,pair(X1,sK4(X2,X3,X4))),X4) = insert_slb(update_slb(X0,X4),pair(X1,sK4(X2,X3,X4)))
| pair_in_list(update_slb(X2,X4),X3,X4)
| ~ strictly_less_than(X3,X4)
| ~ contains_slb(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_97])]) ).
fof(f423,plain,
( spl5_51
<=> ! [X0,X3,X2,X1] :
( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3))
| ~ less_than(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_51])]) ).
fof(f432,plain,
( ! [X2,X3,X0,X1,X4] :
( update_slb(insert_slb(X0,pair(X1,sK4(X2,X3,X4))),X4) = insert_slb(update_slb(X0,X4),pair(X1,sK4(X2,X3,X4)))
| pair_in_list(update_slb(X2,X4),X3,X4)
| ~ strictly_less_than(X3,X4)
| ~ contains_slb(X2,X3) )
| ~ spl5_49
| ~ spl5_51 ),
inference(resolution,[],[f424,f415]) ).
fof(f424,plain,
( ! [X2,X3,X0,X1] :
( ~ less_than(X2,X3)
| update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3)) )
| ~ spl5_51 ),
inference(avatar_component_clause,[],[f423]) ).
fof(f850,plain,
( spl5_96
| ~ spl5_42
| ~ spl5_54 ),
inference(avatar_split_clause,[],[f456,f450,f364,f848]) ).
fof(f848,plain,
( spl5_96
<=> ! [X5,X4,X0,X3,X2,X1] :
( remove_slb(insert_slb(X0,pair(X1,X2)),X3) = insert_slb(remove_slb(X0,X3),pair(X1,X2))
| X1 = X3
| triple(X4,X0,bad) = remove_cpq(triple(X4,X0,X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_96])]) ).
fof(f364,plain,
( spl5_42
<=> ! [X0,X3,X2,X1] :
( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_42])]) ).
fof(f456,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( remove_slb(insert_slb(X0,pair(X1,X2)),X3) = insert_slb(remove_slb(X0,X3),pair(X1,X2))
| X1 = X3
| triple(X4,X0,bad) = remove_cpq(triple(X4,X0,X5),X3) )
| ~ spl5_42
| ~ spl5_54 ),
inference(resolution,[],[f451,f365]) ).
fof(f365,plain,
( ! [X2,X3,X0,X1] :
( contains_slb(X1,X3)
| triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3) )
| ~ spl5_42 ),
inference(avatar_component_clause,[],[f364]) ).
fof(f846,plain,
( spl5_95
| ~ spl5_34
| ~ spl5_54 ),
inference(avatar_split_clause,[],[f455,f450,f316,f844]) ).
fof(f844,plain,
( spl5_95
<=> ! [X3,X4,X0,X5,X2,X1] :
( remove_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X5) = insert_slb(remove_slb(insert_slb(X0,pair(X1,X2)),X5),pair(X3,X4))
| X3 = X5
| ~ contains_slb(X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_95])]) ).
fof(f316,plain,
( spl5_34
<=> ! [X0,X3,X2,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ~ contains_slb(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_34])]) ).
fof(f455,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( remove_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X5) = insert_slb(remove_slb(insert_slb(X0,pair(X1,X2)),X5),pair(X3,X4))
| X3 = X5
| ~ contains_slb(X0,X5) )
| ~ spl5_34
| ~ spl5_54 ),
inference(resolution,[],[f451,f317]) ).
fof(f317,plain,
( ! [X2,X3,X0,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ~ contains_slb(X0,X2) )
| ~ spl5_34 ),
inference(avatar_component_clause,[],[f316]) ).
fof(f818,plain,
( spl5_94
| ~ spl5_14
| ~ spl5_59 ),
inference(avatar_split_clause,[],[f487,f483,f217,f816]) ).
fof(f816,plain,
( spl5_94
<=> ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1
| less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_94])]) ).
fof(f217,plain,
( spl5_14
<=> ! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_14])]) ).
fof(f487,plain,
( ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1
| less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0))) )
| ~ spl5_14
| ~ spl5_59 ),
inference(resolution,[],[f484,f218]) ).
fof(f218,plain,
( ! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) )
| ~ spl5_14 ),
inference(avatar_component_clause,[],[f217]) ).
fof(f814,plain,
( spl5_93
| ~ spl5_28
| ~ spl5_29
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f472,f464,f283,f279,f812]) ).
fof(f812,plain,
( spl5_93
<=> ! [X2,X4,X0,X3,X1] :
( remove_cpq(triple(X3,insert_slb(X0,pair(X1,X2)),X4),X1) = triple(remove_pqp(X3,X1),X0,X4)
| ~ less_than(X2,X1)
| ~ contains_slb(insert_slb(X0,pair(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_93])]) ).
fof(f279,plain,
( spl5_28
<=> ! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_28])]) ).
fof(f464,plain,
( spl5_56
<=> ! [X0,X3,X2,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
| ~ less_than(lookup_slb(X1,X3),X3)
| ~ contains_slb(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_56])]) ).
fof(f472,plain,
( ! [X2,X3,X0,X1,X4] :
( remove_cpq(triple(X3,insert_slb(X0,pair(X1,X2)),X4),X1) = triple(remove_pqp(X3,X1),X0,X4)
| ~ less_than(X2,X1)
| ~ contains_slb(insert_slb(X0,pair(X1,X2)),X1) )
| ~ spl5_28
| ~ spl5_29
| ~ spl5_56 ),
inference(forward_demodulation,[],[f471,f280]) ).
fof(f280,plain,
( ! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0
| ~ spl5_28 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f471,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ less_than(X2,X1)
| remove_cpq(triple(X3,insert_slb(X0,pair(X1,X2)),X4),X1) = triple(remove_pqp(X3,X1),remove_slb(insert_slb(X0,pair(X1,X2)),X1),X4)
| ~ contains_slb(insert_slb(X0,pair(X1,X2)),X1) )
| ~ spl5_29
| ~ spl5_56 ),
inference(superposition,[],[f465,f284]) ).
fof(f465,plain,
( ! [X2,X3,X0,X1] :
( ~ less_than(lookup_slb(X1,X3),X3)
| remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
| ~ contains_slb(X1,X3) )
| ~ spl5_56 ),
inference(avatar_component_clause,[],[f464]) ).
fof(f810,plain,
( spl5_92
| ~ spl5_28
| ~ spl5_29
| ~ spl5_55 ),
inference(avatar_split_clause,[],[f468,f460,f283,f279,f808]) ).
fof(f808,plain,
( spl5_92
<=> ! [X2,X4,X0,X3,X1] :
( remove_cpq(triple(X3,insert_slb(X0,pair(X1,X2)),X4),X1) = triple(remove_pqp(X3,X1),X0,bad)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_92])]) ).
fof(f460,plain,
( spl5_55
<=> ! [X0,X3,X2,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
| ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_slb(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_55])]) ).
fof(f468,plain,
( ! [X2,X3,X0,X1,X4] :
( remove_cpq(triple(X3,insert_slb(X0,pair(X1,X2)),X4),X1) = triple(remove_pqp(X3,X1),X0,bad)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X2)),X1) )
| ~ spl5_28
| ~ spl5_29
| ~ spl5_55 ),
inference(forward_demodulation,[],[f467,f280]) ).
fof(f467,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ strictly_less_than(X1,X2)
| remove_cpq(triple(X3,insert_slb(X0,pair(X1,X2)),X4),X1) = triple(remove_pqp(X3,X1),remove_slb(insert_slb(X0,pair(X1,X2)),X1),bad)
| ~ contains_slb(insert_slb(X0,pair(X1,X2)),X1) )
| ~ spl5_29
| ~ spl5_55 ),
inference(superposition,[],[f461,f284]) ).
fof(f461,plain,
( ! [X2,X3,X0,X1] :
( ~ strictly_less_than(X3,lookup_slb(X1,X3))
| remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
| ~ contains_slb(X1,X3) )
| ~ spl5_55 ),
inference(avatar_component_clause,[],[f460]) ).
fof(f772,plain,
( spl5_91
| ~ spl5_42
| ~ spl5_46 ),
inference(avatar_split_clause,[],[f406,f386,f364,f770]) ).
fof(f770,plain,
( spl5_91
<=> ! [X5,X4,X0,X3,X2,X1] :
( lookup_slb(insert_slb(X0,pair(X1,X2)),X3) = lookup_slb(X0,X3)
| X1 = X3
| triple(X4,X0,bad) = remove_cpq(triple(X4,X0,X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_91])]) ).
fof(f406,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( lookup_slb(insert_slb(X0,pair(X1,X2)),X3) = lookup_slb(X0,X3)
| X1 = X3
| triple(X4,X0,bad) = remove_cpq(triple(X4,X0,X5),X3) )
| ~ spl5_42
| ~ spl5_46 ),
inference(resolution,[],[f387,f365]) ).
fof(f768,plain,
( spl5_90
| ~ spl5_34
| ~ spl5_46 ),
inference(avatar_split_clause,[],[f405,f386,f316,f766]) ).
fof(f766,plain,
( spl5_90
<=> ! [X3,X4,X0,X5,X2,X1] :
( lookup_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X5) = lookup_slb(insert_slb(X0,pair(X1,X2)),X5)
| X3 = X5
| ~ contains_slb(X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_90])]) ).
fof(f405,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( lookup_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X5) = lookup_slb(insert_slb(X0,pair(X1,X2)),X5)
| X3 = X5
| ~ contains_slb(X0,X5) )
| ~ spl5_34
| ~ spl5_46 ),
inference(resolution,[],[f387,f317]) ).
fof(f764,plain,
( spl5_89
| ~ spl5_39
| ~ spl5_42 ),
inference(avatar_split_clause,[],[f368,f364,f349,f762]) ).
fof(f762,plain,
( spl5_89
<=> ! [X3,X4,X0,X5,X2,X1] :
( triple(X0,insert_slb(X1,pair(X2,X3)),bad) = remove_cpq(triple(X0,insert_slb(X1,pair(X2,X3)),X4),X5)
| contains_slb(X1,X5)
| X2 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_89])]) ).
fof(f368,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( triple(X0,insert_slb(X1,pair(X2,X3)),bad) = remove_cpq(triple(X0,insert_slb(X1,pair(X2,X3)),X4),X5)
| contains_slb(X1,X5)
| X2 = X5 )
| ~ spl5_39
| ~ spl5_42 ),
inference(resolution,[],[f365,f350]) ).
fof(f753,plain,
( spl5_88
| ~ spl5_14
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f469,f464,f217,f751]) ).
fof(f751,plain,
( spl5_88
<=> ! [X0,X3,X2,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
| ~ contains_slb(X1,X3)
| less_than(X3,lookup_slb(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_88])]) ).
fof(f469,plain,
( ! [X2,X3,X0,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
| ~ contains_slb(X1,X3)
| less_than(X3,lookup_slb(X1,X3)) )
| ~ spl5_14
| ~ spl5_56 ),
inference(resolution,[],[f465,f218]) ).
fof(f741,plain,
( spl5_87
| ~ spl5_30
| ~ spl5_49 ),
inference(avatar_split_clause,[],[f417,f414,f287,f739]) ).
fof(f739,plain,
( spl5_87
<=> ! [X0,X3,X2,X1] :
( pair_in_list(update_slb(X0,X1),X2,X1)
| ~ strictly_less_than(X2,X1)
| ~ contains_slb(X0,X2)
| less_than(X3,sK4(X0,X2,X1))
| ~ less_than(X3,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_87])]) ).
fof(f417,plain,
( ! [X2,X3,X0,X1] :
( pair_in_list(update_slb(X0,X1),X2,X1)
| ~ strictly_less_than(X2,X1)
| ~ contains_slb(X0,X2)
| less_than(X3,sK4(X0,X2,X1))
| ~ less_than(X3,X1) )
| ~ spl5_30
| ~ spl5_49 ),
inference(resolution,[],[f415,f288]) ).
fof(f729,plain,
( spl5_86
| ~ spl5_30
| ~ spl5_63 ),
inference(avatar_split_clause,[],[f618,f525,f287,f727]) ).
fof(f727,plain,
( spl5_86
<=> ! [X0] :
( less_than(X0,findmin_pqp_res(sK0))
| ~ less_than(X0,sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_86])]) ).
fof(f525,plain,
( spl5_63
<=> less_than(sK3,findmin_pqp_res(sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_63])]) ).
fof(f618,plain,
( ! [X0] :
( less_than(X0,findmin_pqp_res(sK0))
| ~ less_than(X0,sK3) )
| ~ spl5_30
| ~ spl5_63 ),
inference(resolution,[],[f527,f288]) ).
fof(f527,plain,
( less_than(sK3,findmin_pqp_res(sK0))
| ~ spl5_63 ),
inference(avatar_component_clause,[],[f525]) ).
fof(f725,plain,
( spl5_85
| ~ spl5_21
| ~ spl5_28
| ~ spl5_54 ),
inference(avatar_split_clause,[],[f458,f450,f279,f249,f723]) ).
fof(f723,plain,
( spl5_85
<=> ! [X2,X4,X0,X3,X1] :
( remove_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X1) = insert_slb(X0,pair(X3,X4))
| X1 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_85])]) ).
fof(f458,plain,
( ! [X2,X3,X0,X1,X4] :
( remove_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X1) = insert_slb(X0,pair(X3,X4))
| X1 = X3 )
| ~ spl5_21
| ~ spl5_28
| ~ spl5_54 ),
inference(forward_demodulation,[],[f454,f280]) ).
fof(f454,plain,
( ! [X2,X3,X0,X1,X4] :
( remove_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X1) = insert_slb(remove_slb(insert_slb(X0,pair(X1,X2)),X1),pair(X3,X4))
| X1 = X3 )
| ~ spl5_21
| ~ spl5_54 ),
inference(resolution,[],[f451,f250]) ).
fof(f717,plain,
( spl5_84
| ~ spl5_36
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f399,f382,f331,f715]) ).
fof(f715,plain,
( spl5_84
<=> ! [X0,X3,X2,X1] :
( findmin_pqp_res(insert_pqp(X0,X1)) = removemin_cpq_res(insert_cpq(triple(X0,X2,X3),X1))
| create_slb = insert_slb(X2,pair(X1,bottom)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_84])]) ).
fof(f331,plain,
( spl5_36
<=> ! [X2,X0,X1] :
( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_36])]) ).
fof(f382,plain,
( spl5_45
<=> ! [X0,X3,X2,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_45])]) ).
fof(f399,plain,
( ! [X2,X3,X0,X1] :
( findmin_pqp_res(insert_pqp(X0,X1)) = removemin_cpq_res(insert_cpq(triple(X0,X2,X3),X1))
| create_slb = insert_slb(X2,pair(X1,bottom)) )
| ~ spl5_36
| ~ spl5_45 ),
inference(superposition,[],[f332,f383]) ).
fof(f383,plain,
( ! [X2,X3,X0,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2)
| ~ spl5_45 ),
inference(avatar_component_clause,[],[f382]) ).
fof(f332,plain,
( ! [X2,X0,X1] :
( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 )
| ~ spl5_36 ),
inference(avatar_component_clause,[],[f331]) ).
fof(f713,plain,
( spl5_83
| ~ spl5_35
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f339,f331,f320,f711]) ).
fof(f711,plain,
( spl5_83
<=> ! [X0,X3,X2,X1] :
( succ_cpq(X3,remove_cpq(findmin_cpq_eff(triple(X0,X1,X2)),findmin_pqp_res(X0)))
| ~ succ_cpq(X3,triple(X0,X1,X2))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_83])]) ).
fof(f320,plain,
( spl5_35
<=> ! [X0,X1] :
( succ_cpq(X0,remove_cpq(findmin_cpq_eff(X1),removemin_cpq_res(X1)))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_35])]) ).
fof(f339,plain,
( ! [X2,X3,X0,X1] :
( succ_cpq(X3,remove_cpq(findmin_cpq_eff(triple(X0,X1,X2)),findmin_pqp_res(X0)))
| ~ succ_cpq(X3,triple(X0,X1,X2))
| create_slb = X1 )
| ~ spl5_35
| ~ spl5_36 ),
inference(superposition,[],[f321,f332]) ).
fof(f321,plain,
( ! [X0,X1] :
( succ_cpq(X0,remove_cpq(findmin_cpq_eff(X1),removemin_cpq_res(X1)))
| ~ succ_cpq(X0,X1) )
| ~ spl5_35 ),
inference(avatar_component_clause,[],[f320]) ).
fof(f700,plain,
( spl5_82
| ~ spl5_14
| ~ spl5_51 ),
inference(avatar_split_clause,[],[f429,f423,f217,f698]) ).
fof(f698,plain,
( spl5_82
<=> ! [X0,X3,X2,X1] :
( update_slb(insert_slb(X0,pair(X1,X2)),X3) = insert_slb(update_slb(X0,X3),pair(X1,X2))
| less_than(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_82])]) ).
fof(f429,plain,
( ! [X2,X3,X0,X1] :
( update_slb(insert_slb(X0,pair(X1,X2)),X3) = insert_slb(update_slb(X0,X3),pair(X1,X2))
| less_than(X2,X3) )
| ~ spl5_14
| ~ spl5_51 ),
inference(resolution,[],[f424,f218]) ).
fof(f692,plain,
( spl5_81
| ~ spl5_45
| ~ spl5_48 ),
inference(avatar_split_clause,[],[f411,f394,f382,f690]) ).
fof(f690,plain,
( spl5_81
<=> ! [X0,X3,X2,X1] :
( check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| ~ check_cpq(triple(insert_pqp(X0,X1),X2,X3))
| ~ less_than(bottom,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_81])]) ).
fof(f394,plain,
( spl5_48
<=> ! [X4,X0,X3,X2,X1] :
( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ check_cpq(triple(X0,X1,X2))
| ~ less_than(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_48])]) ).
fof(f411,plain,
( ! [X2,X3,X0,X1] :
( check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| ~ check_cpq(triple(insert_pqp(X0,X1),X2,X3))
| ~ less_than(bottom,X1) )
| ~ spl5_45
| ~ spl5_48 ),
inference(superposition,[],[f395,f383]) ).
fof(f395,plain,
( ! [X2,X3,X0,X1,X4] :
( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ check_cpq(triple(X0,X1,X2))
| ~ less_than(X4,X3) )
| ~ spl5_48 ),
inference(avatar_component_clause,[],[f394]) ).
fof(f688,plain,
( spl5_80
| ~ spl5_63
| ~ spl5_68 ),
inference(avatar_split_clause,[],[f616,f573,f525,f686]) ).
fof(f686,plain,
( spl5_80
<=> ! [X0] :
( less_than(sK3,X0)
| less_than(X0,findmin_pqp_res(sK0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_80])]) ).
fof(f616,plain,
( ! [X0] :
( less_than(sK3,X0)
| less_than(X0,findmin_pqp_res(sK0)) )
| ~ spl5_63
| ~ spl5_68 ),
inference(resolution,[],[f527,f574]) ).
fof(f684,plain,
( spl5_79
| ~ spl5_45
| ~ spl5_47 ),
inference(avatar_split_clause,[],[f408,f390,f382,f682]) ).
fof(f682,plain,
( spl5_79
<=> ! [X0,X3,X2,X1] :
( ~ check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| check_cpq(triple(insert_pqp(X0,X1),X2,X3))
| ~ less_than(bottom,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_79])]) ).
fof(f390,plain,
( spl5_47
<=> ! [X4,X0,X3,X2,X1] :
( check_cpq(triple(X0,X1,X2))
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ less_than(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_47])]) ).
fof(f408,plain,
( ! [X2,X3,X0,X1] :
( ~ check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| check_cpq(triple(insert_pqp(X0,X1),X2,X3))
| ~ less_than(bottom,X1) )
| ~ spl5_45
| ~ spl5_47 ),
inference(superposition,[],[f391,f383]) ).
fof(f391,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| check_cpq(triple(X0,X1,X2))
| ~ less_than(X4,X3) )
| ~ spl5_47 ),
inference(avatar_component_clause,[],[f390]) ).
fof(f669,plain,
( spl5_78
| ~ spl5_21
| ~ spl5_29
| ~ spl5_46 ),
inference(avatar_split_clause,[],[f407,f386,f283,f249,f667]) ).
fof(f667,plain,
( spl5_78
<=> ! [X4,X0,X3,X2,X1] :
( lookup_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X1) = X2
| X1 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_78])]) ).
fof(f407,plain,
( ! [X2,X3,X0,X1,X4] :
( lookup_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X1) = X2
| X1 = X3 )
| ~ spl5_21
| ~ spl5_29
| ~ spl5_46 ),
inference(forward_demodulation,[],[f404,f284]) ).
fof(f404,plain,
( ! [X2,X3,X0,X1,X4] :
( lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = lookup_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X1)
| X1 = X3 )
| ~ spl5_21
| ~ spl5_46 ),
inference(resolution,[],[f387,f250]) ).
fof(f630,plain,
( spl5_77
| ~ spl5_9
| ~ spl5_51 ),
inference(avatar_split_clause,[],[f428,f423,f197,f628]) ).
fof(f628,plain,
( spl5_77
<=> ! [X2,X0,X1] : update_slb(insert_slb(X0,pair(X1,X2)),bottom) = insert_slb(update_slb(X0,bottom),pair(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_77])]) ).
fof(f197,plain,
( spl5_9
<=> ! [X0] : less_than(bottom,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).
fof(f428,plain,
( ! [X2,X0,X1] : update_slb(insert_slb(X0,pair(X1,X2)),bottom) = insert_slb(update_slb(X0,bottom),pair(X1,X2))
| ~ spl5_9
| ~ spl5_51 ),
inference(resolution,[],[f424,f198]) ).
fof(f198,plain,
( ! [X0] : less_than(bottom,X0)
| ~ spl5_9 ),
inference(avatar_component_clause,[],[f197]) ).
fof(f626,plain,
( spl5_76
| ~ spl5_8
| ~ spl5_51 ),
inference(avatar_split_clause,[],[f427,f423,f193,f624]) ).
fof(f624,plain,
( spl5_76
<=> ! [X2,X0,X1] : insert_slb(update_slb(X0,X2),pair(X1,X2)) = update_slb(insert_slb(X0,pair(X1,X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_76])]) ).
fof(f193,plain,
( spl5_8
<=> ! [X0] : less_than(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).
fof(f427,plain,
( ! [X2,X0,X1] : insert_slb(update_slb(X0,X2),pair(X1,X2)) = update_slb(insert_slb(X0,pair(X1,X2)),X2)
| ~ spl5_8
| ~ spl5_51 ),
inference(resolution,[],[f424,f194]) ).
fof(f194,plain,
( ! [X0] : less_than(X0,X0)
| ~ spl5_8 ),
inference(avatar_component_clause,[],[f193]) ).
fof(f622,plain,
( spl5_75
| ~ spl5_31
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f401,f382,f291,f620]) ).
fof(f620,plain,
( spl5_75
<=> ! [X4,X0,X3,X2,X1] :
( ~ contains_cpq(insert_cpq(triple(X0,X2,X3),X1),X4)
| contains_slb(insert_slb(X2,pair(X1,bottom)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_75])]) ).
fof(f291,plain,
( spl5_31
<=> ! [X2,X0,X1,X3] :
( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_31])]) ).
fof(f401,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ contains_cpq(insert_cpq(triple(X0,X2,X3),X1),X4)
| contains_slb(insert_slb(X2,pair(X1,bottom)),X4) )
| ~ spl5_31
| ~ spl5_45 ),
inference(superposition,[],[f292,f383]) ).
fof(f292,plain,
( ! [X2,X3,X0,X1] :
( ~ contains_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) )
| ~ spl5_31 ),
inference(avatar_component_clause,[],[f291]) ).
fof(f615,plain,
( spl5_74
| ~ spl5_32
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f400,f382,f295,f613]) ).
fof(f613,plain,
( spl5_74
<=> ! [X4,X0,X3,X2,X1] :
( contains_cpq(insert_cpq(triple(X0,X2,X3),X1),X4)
| ~ contains_slb(insert_slb(X2,pair(X1,bottom)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_74])]) ).
fof(f295,plain,
( spl5_32
<=> ! [X0,X3,X2,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_32])]) ).
fof(f400,plain,
( ! [X2,X3,X0,X1,X4] :
( contains_cpq(insert_cpq(triple(X0,X2,X3),X1),X4)
| ~ contains_slb(insert_slb(X2,pair(X1,bottom)),X4) )
| ~ spl5_32
| ~ spl5_45 ),
inference(superposition,[],[f296,f383]) ).
fof(f296,plain,
( ! [X2,X3,X0,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) )
| ~ spl5_32 ),
inference(avatar_component_clause,[],[f295]) ).
fof(f610,plain,
( spl5_73
| ~ spl5_20
| ~ spl5_33
| ~ spl5_35 ),
inference(avatar_split_clause,[],[f328,f320,f312,f245,f608]) ).
fof(f608,plain,
( spl5_73
<=> ! [X2,X0,X1] :
( succ_cpq(X2,remove_cpq(triple(X0,create_slb,bad),bottom))
| ~ succ_cpq(X2,triple(X0,create_slb,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_73])]) ).
fof(f245,plain,
( spl5_20
<=> ! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_20])]) ).
fof(f312,plain,
( spl5_33
<=> ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_33])]) ).
fof(f328,plain,
( ! [X2,X0,X1] :
( succ_cpq(X2,remove_cpq(triple(X0,create_slb,bad),bottom))
| ~ succ_cpq(X2,triple(X0,create_slb,X1)) )
| ~ spl5_20
| ~ spl5_33
| ~ spl5_35 ),
inference(forward_demodulation,[],[f326,f246]) ).
fof(f246,plain,
( ! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1))
| ~ spl5_20 ),
inference(avatar_component_clause,[],[f245]) ).
fof(f326,plain,
( ! [X2,X0,X1] :
( succ_cpq(X2,remove_cpq(triple(X0,create_slb,bad),removemin_cpq_res(triple(X0,create_slb,X1))))
| ~ succ_cpq(X2,triple(X0,create_slb,X1)) )
| ~ spl5_33
| ~ spl5_35 ),
inference(superposition,[],[f321,f313]) ).
fof(f313,plain,
( ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad)
| ~ spl5_33 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f605,plain,
( spl5_72
| ~ spl5_19
| ~ spl5_33 ),
inference(avatar_split_clause,[],[f323,f312,f241,f603]) ).
fof(f603,plain,
( spl5_72
<=> ! [X2,X0,X1] :
( succ_cpq(X2,triple(X0,create_slb,bad))
| ~ succ_cpq(X2,triple(X0,create_slb,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_72])]) ).
fof(f241,plain,
( spl5_19
<=> ! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_19])]) ).
fof(f323,plain,
( ! [X2,X0,X1] :
( succ_cpq(X2,triple(X0,create_slb,bad))
| ~ succ_cpq(X2,triple(X0,create_slb,X1)) )
| ~ spl5_19
| ~ spl5_33 ),
inference(superposition,[],[f242,f313]) ).
fof(f242,plain,
( ! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) )
| ~ spl5_19 ),
inference(avatar_component_clause,[],[f241]) ).
fof(f600,plain,
( spl5_71
| ~ spl5_6
| ~ spl5_42 ),
inference(avatar_split_clause,[],[f367,f364,f185,f598]) ).
fof(f598,plain,
( spl5_71
<=> ! [X2,X0,X1] : triple(X0,create_slb,bad) = remove_cpq(triple(X0,create_slb,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_71])]) ).
fof(f367,plain,
( ! [X2,X0,X1] : triple(X0,create_slb,bad) = remove_cpq(triple(X0,create_slb,X1),X2)
| ~ spl5_6
| ~ spl5_42 ),
inference(resolution,[],[f365,f186]) ).
fof(f593,plain,
( spl5_70
| ~ spl5_24
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f402,f382,f261,f591]) ).
fof(f591,plain,
( spl5_70
<=> ! [X0,X3,X2,X1] :
( ok(insert_cpq(triple(X0,X2,X3),X1))
| bad = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_70])]) ).
fof(f261,plain,
( spl5_24
<=> ! [X2,X0,X1] :
( bad = X2
| ok(triple(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_24])]) ).
fof(f402,plain,
( ! [X2,X3,X0,X1] :
( ok(insert_cpq(triple(X0,X2,X3),X1))
| bad = X3 )
| ~ spl5_24
| ~ spl5_45 ),
inference(superposition,[],[f262,f383]) ).
fof(f262,plain,
( ! [X2,X0,X1] :
( ok(triple(X0,X1,X2))
| bad = X2 )
| ~ spl5_24 ),
inference(avatar_component_clause,[],[f261]) ).
fof(f589,plain,
( spl5_69
| ~ spl5_37
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f397,f382,f341,f587]) ).
fof(f587,plain,
( spl5_69
<=> ! [X0,X3,X2,X1] :
( ~ check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| ~ strictly_less_than(X1,bottom) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_69])]) ).
fof(f341,plain,
( spl5_37
<=> ! [X4,X0,X3,X2,X1] :
( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ strictly_less_than(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_37])]) ).
fof(f397,plain,
( ! [X2,X3,X0,X1] :
( ~ check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| ~ strictly_less_than(X1,bottom) )
| ~ spl5_37
| ~ spl5_45 ),
inference(superposition,[],[f342,f383]) ).
fof(f342,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ strictly_less_than(X3,X4) )
| ~ spl5_37 ),
inference(avatar_component_clause,[],[f341]) ).
fof(f575,plain,
( spl5_68
| ~ spl5_14
| ~ spl5_30 ),
inference(avatar_split_clause,[],[f307,f287,f217,f573]) ).
fof(f307,plain,
( ! [X2,X0,X1] :
( less_than(X0,X1)
| ~ less_than(X0,X2)
| less_than(X1,X2) )
| ~ spl5_14
| ~ spl5_30 ),
inference(resolution,[],[f288,f218]) ).
fof(f570,plain,
( spl5_67
| ~ spl5_13
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f398,f382,f213,f568]) ).
fof(f568,plain,
( spl5_67
<=> ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,bad),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_67])]) ).
fof(f213,plain,
( spl5_13
<=> ! [X0,X1] : ~ ok(triple(X0,X1,bad)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).
fof(f398,plain,
( ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,bad),X1))
| ~ spl5_13
| ~ spl5_45 ),
inference(superposition,[],[f214,f383]) ).
fof(f214,plain,
( ! [X0,X1] : ~ ok(triple(X0,X1,bad))
| ~ spl5_13 ),
inference(avatar_component_clause,[],[f213]) ).
fof(f551,plain,
( spl5_66
| ~ spl5_2
| ~ spl5_50 ),
inference(avatar_split_clause,[],[f426,f419,f166,f549]) ).
fof(f166,plain,
( spl5_2
<=> strictly_less_than(sK3,removemin_cpq_res(triple(sK0,sK1,sK2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f419,plain,
( spl5_50
<=> ! [X0,X3,X2,X1] :
( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2))
| ~ strictly_less_than(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_50])]) ).
fof(f426,plain,
( ! [X0,X1] : update_slb(insert_slb(X0,pair(X1,sK3)),removemin_cpq_res(triple(sK0,sK1,sK2))) = insert_slb(update_slb(X0,removemin_cpq_res(triple(sK0,sK1,sK2))),pair(X1,removemin_cpq_res(triple(sK0,sK1,sK2))))
| ~ spl5_2
| ~ spl5_50 ),
inference(resolution,[],[f420,f168]) ).
fof(f168,plain,
( strictly_less_than(sK3,removemin_cpq_res(triple(sK0,sK1,sK2)))
| ~ spl5_2 ),
inference(avatar_component_clause,[],[f166]) ).
fof(f420,plain,
( ! [X2,X3,X0,X1] :
( ~ strictly_less_than(X3,X2)
| update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2)) )
| ~ spl5_50 ),
inference(avatar_component_clause,[],[f419]) ).
fof(f536,plain,
( spl5_65
| ~ spl5_9
| ~ spl5_30 ),
inference(avatar_split_clause,[],[f306,f287,f197,f534]) ).
fof(f534,plain,
( spl5_65
<=> ! [X0,X1] :
( less_than(X0,X1)
| ~ less_than(X0,bottom) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_65])]) ).
fof(f306,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| ~ less_than(X0,bottom) )
| ~ spl5_9
| ~ spl5_30 ),
inference(resolution,[],[f288,f198]) ).
fof(f532,plain,
( spl5_64
| ~ spl5_14
| ~ spl5_27 ),
inference(avatar_split_clause,[],[f304,f275,f217,f530]) ).
fof(f275,plain,
( spl5_27
<=> ! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_27])]) ).
fof(f304,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(X1,X0) )
| ~ spl5_14
| ~ spl5_27 ),
inference(duplicate_literal_removal,[],[f300]) ).
fof(f300,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(X1,X0)
| less_than(X0,X1) )
| ~ spl5_14
| ~ spl5_27 ),
inference(resolution,[],[f276,f218]) ).
fof(f276,plain,
( ! [X0,X1] :
( ~ less_than(X0,X1)
| less_than(X1,X0)
| strictly_less_than(X0,X1) )
| ~ spl5_27 ),
inference(avatar_component_clause,[],[f275]) ).
fof(f528,plain,
( spl5_63
| ~ spl5_15
| ~ spl5_41 ),
inference(avatar_split_clause,[],[f435,f359,f221,f525]) ).
fof(f435,plain,
( less_than(sK3,findmin_pqp_res(sK0))
| ~ spl5_15
| ~ spl5_41 ),
inference(resolution,[],[f361,f222]) ).
fof(f361,plain,
( strictly_less_than(sK3,findmin_pqp_res(sK0))
| ~ spl5_41 ),
inference(avatar_component_clause,[],[f359]) ).
fof(f520,plain,
( ~ spl5_62
| ~ spl5_1
| ~ spl5_41
| spl5_3
| ~ spl5_5
| ~ spl5_53 ),
inference(avatar_split_clause,[],[f447,f444,f181,f171,f359,f161,f517]) ).
fof(f181,plain,
( spl5_5
<=> ! [X4] :
( ~ less_than(findmin_pqp_res(sK0),X4)
| ~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK0)),sK3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
fof(f444,plain,
( spl5_53
<=> ! [X2,X0,X1] :
( pair_in_list(update_slb(X0,X2),X1,sK4(X0,X1,X2))
| pair_in_list(update_slb(X0,X2),X1,X2)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_53])]) ).
fof(f447,plain,
( pair_in_list(update_slb(sK1,findmin_pqp_res(sK0)),sK3,findmin_pqp_res(sK0))
| ~ strictly_less_than(sK3,findmin_pqp_res(sK0))
| ~ contains_slb(sK1,sK3)
| ~ less_than(findmin_pqp_res(sK0),sK4(sK1,sK3,findmin_pqp_res(sK0)))
| ~ spl5_5
| ~ spl5_53 ),
inference(resolution,[],[f445,f182]) ).
fof(f182,plain,
( ! [X4] :
( ~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK0)),sK3,X4)
| ~ less_than(findmin_pqp_res(sK0),X4) )
| ~ spl5_5 ),
inference(avatar_component_clause,[],[f181]) ).
fof(f445,plain,
( ! [X2,X0,X1] :
( pair_in_list(update_slb(X0,X2),X1,sK4(X0,X1,X2))
| pair_in_list(update_slb(X0,X2),X1,X2)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1) )
| ~ spl5_53 ),
inference(avatar_component_clause,[],[f444]) ).
fof(f501,plain,
( spl5_61
| ~ spl5_1
| ~ spl5_54 ),
inference(avatar_split_clause,[],[f453,f450,f161,f499]) ).
fof(f453,plain,
( ! [X0,X1] :
( remove_slb(insert_slb(sK1,pair(X0,X1)),sK3) = insert_slb(remove_slb(sK1,sK3),pair(X0,X1))
| sK3 = X0 )
| ~ spl5_1
| ~ spl5_54 ),
inference(resolution,[],[f451,f163]) ).
fof(f493,plain,
( spl5_60
| ~ spl5_1
| ~ spl5_46 ),
inference(avatar_split_clause,[],[f403,f386,f161,f491]) ).
fof(f491,plain,
( spl5_60
<=> ! [X0,X1] :
( lookup_slb(insert_slb(sK1,pair(X0,X1)),sK3) = lookup_slb(sK1,sK3)
| sK3 = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_60])]) ).
fof(f403,plain,
( ! [X0,X1] :
( lookup_slb(insert_slb(sK1,pair(X0,X1)),sK3) = lookup_slb(sK1,sK3)
| sK3 = X0 )
| ~ spl5_1
| ~ spl5_46 ),
inference(resolution,[],[f387,f163]) ).
fof(f485,plain,
spl5_59,
inference(avatar_split_clause,[],[f137,f483]) ).
fof(f137,plain,
! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(flattening,[],[f76]) ).
fof(f76,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ( less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
& contains_slb(X1,findmin_pqp_res(X0))
& create_slb != X1 )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2) ),
inference(rectify,[],[f37]) ).
fof(f37,axiom,
! [X0,X1,X2,X3] :
( ( less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
& contains_slb(X1,findmin_pqp_res(X0))
& create_slb != X1 )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
fof(f481,plain,
spl5_58,
inference(avatar_split_clause,[],[f136,f479]) ).
fof(f136,plain,
! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(cnf_transformation,[],[f75]) ).
fof(f75,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(flattening,[],[f74]) ).
fof(f74,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ( strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
& contains_slb(X1,findmin_pqp_res(X0))
& create_slb != X1 )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
inference(rectify,[],[f36]) ).
fof(f36,axiom,
! [X0,X1,X2,X3] :
( ( strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
& contains_slb(X1,findmin_pqp_res(X0))
& create_slb != X1 )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax48) ).
fof(f477,plain,
( ~ spl5_57
| ~ spl5_16
| ~ spl5_41 ),
inference(avatar_split_clause,[],[f434,f359,f225,f474]) ).
fof(f225,plain,
( spl5_16
<=> ! [X0,X1] :
( ~ less_than(X1,X0)
| ~ strictly_less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_16])]) ).
fof(f434,plain,
( ~ less_than(findmin_pqp_res(sK0),sK3)
| ~ spl5_16
| ~ spl5_41 ),
inference(resolution,[],[f361,f226]) ).
fof(f226,plain,
( ! [X0,X1] :
( ~ strictly_less_than(X0,X1)
| ~ less_than(X1,X0) )
| ~ spl5_16 ),
inference(avatar_component_clause,[],[f225]) ).
fof(f466,plain,
spl5_56,
inference(avatar_split_clause,[],[f139,f464]) ).
fof(f139,plain,
! [X2,X3,X0,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
| ~ less_than(lookup_slb(X1,X3),X3)
| ~ contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f81]) ).
fof(f81,plain,
! [X0,X1,X2,X3] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
| ~ less_than(lookup_slb(X1,X3),X3)
| ~ contains_slb(X1,X3) ),
inference(flattening,[],[f80]) ).
fof(f80,plain,
! [X0,X1,X2,X3] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
| ~ less_than(lookup_slb(X1,X3),X3)
| ~ contains_slb(X1,X3) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1,X2,X3] :
( ( less_than(lookup_slb(X1,X3),X3)
& contains_slb(X1,X3) )
=> remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax44) ).
fof(f462,plain,
spl5_55,
inference(avatar_split_clause,[],[f138,f460]) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
| ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,plain,
! [X0,X1,X2,X3] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
| ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_slb(X1,X3) ),
inference(flattening,[],[f78]) ).
fof(f78,plain,
! [X0,X1,X2,X3] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
| ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_slb(X1,X3) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1,X2,X3] :
( ( strictly_less_than(X3,lookup_slb(X1,X3))
& contains_slb(X1,X3) )
=> remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax45) ).
fof(f452,plain,
spl5_54,
inference(avatar_split_clause,[],[f134,f450]) ).
fof(f134,plain,
! [X2,X3,X0,X1] :
( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
| ~ contains_slb(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f71]) ).
fof(f71,plain,
! [X0,X1,X2,X3] :
( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
| ~ contains_slb(X0,X2)
| X1 = X2 ),
inference(flattening,[],[f70]) ).
fof(f70,plain,
! [X0,X1,X2,X3] :
( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
| ~ contains_slb(X0,X2)
| X1 = X2 ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2,X3] :
( ( contains_slb(X0,X2)
& X1 != X2 )
=> remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax25) ).
fof(f446,plain,
spl5_53,
inference(avatar_split_clause,[],[f100,f444]) ).
fof(f100,plain,
! [X2,X0,X1] :
( pair_in_list(update_slb(X0,X2),X1,sK4(X0,X1,X2))
| pair_in_list(update_slb(X0,X2),X1,X2)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
! [X0,X1,X2] :
( ( less_than(X2,sK4(X0,X1,X2))
& pair_in_list(update_slb(X0,X2),X1,sK4(X0,X1,X2)) )
| pair_in_list(update_slb(X0,X2),X1,X2)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f56,f86]) ).
fof(f86,plain,
! [X0,X1,X2] :
( ? [X3] :
( less_than(X2,X3)
& pair_in_list(update_slb(X0,X2),X1,X3) )
=> ( less_than(X2,sK4(X0,X1,X2))
& pair_in_list(update_slb(X0,X2),X1,sK4(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ? [X3] :
( less_than(X2,X3)
& pair_in_list(update_slb(X0,X2),X1,X3) )
| pair_in_list(update_slb(X0,X2),X1,X2)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1) ),
inference(flattening,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X2] :
( ? [X3] :
( less_than(X2,X3)
& pair_in_list(update_slb(X0,X2),X1,X3) )
| pair_in_list(update_slb(X0,X2),X1,X2)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1,X2] :
( ( strictly_less_than(X1,X2)
& contains_slb(X0,X1) )
=> ( ? [X3] :
( less_than(X2,X3)
& pair_in_list(update_slb(X0,X2),X1,X3) )
| pair_in_list(update_slb(X0,X2),X1,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l44_l45) ).
fof(f439,plain,
spl5_52,
inference(avatar_split_clause,[],[f135,f437]) ).
fof(f135,plain,
! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(cnf_transformation,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(flattening,[],[f72]) ).
fof(f72,plain,
! [X0,X1,X2] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,plain,
! [X0,X1,X2] :
( ( ~ contains_slb(X1,findmin_pqp_res(X0))
& create_slb != X1 )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
inference(rectify,[],[f35]) ).
fof(f35,axiom,
! [X0,X1,X2,X3] :
( ( ~ contains_slb(X1,findmin_pqp_res(X0))
& create_slb != X1 )
=> findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax47) ).
fof(f425,plain,
spl5_51,
inference(avatar_split_clause,[],[f132,f423]) ).
fof(f132,plain,
! [X2,X3,X0,X1] :
( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3))
| ~ less_than(X2,X3) ),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1,X2,X3] :
( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3))
| ~ less_than(X2,X3) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0,X1,X2,X3] :
( less_than(X2,X3)
=> update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax30) ).
fof(f421,plain,
spl5_50,
inference(avatar_split_clause,[],[f131,f419]) ).
fof(f131,plain,
! [X2,X3,X0,X1] :
( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2))
| ~ strictly_less_than(X3,X2) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,plain,
! [X0,X1,X2,X3] :
( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2))
| ~ strictly_less_than(X3,X2) ),
inference(ennf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1,X2,X3] :
( strictly_less_than(X3,X2)
=> update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax29) ).
fof(f416,plain,
spl5_49,
inference(avatar_split_clause,[],[f101,f414]) ).
fof(f101,plain,
! [X2,X0,X1] :
( less_than(X2,sK4(X0,X1,X2))
| pair_in_list(update_slb(X0,X2),X1,X2)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(X0,X1) ),
inference(cnf_transformation,[],[f87]) ).
fof(f396,plain,
spl5_48,
inference(avatar_split_clause,[],[f147,f394]) ).
fof(f147,plain,
! [X2,X3,X0,X1,X4] :
( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ check_cpq(triple(X0,X1,X2))
| ~ less_than(X4,X3) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2,X3,X4] :
( ( ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ check_cpq(triple(X0,X1,X2)) )
& ( check_cpq(triple(X0,X1,X2))
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ) )
| ~ less_than(X4,X3) ),
inference(nnf_transformation,[],[f83]) ).
fof(f83,plain,
! [X0,X1,X2,X3,X4] :
( ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
<=> check_cpq(triple(X0,X1,X2)) )
| ~ less_than(X4,X3) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0,X1,X2,X3,X4] :
( less_than(X4,X3)
=> ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
<=> check_cpq(triple(X0,X1,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax37) ).
fof(f392,plain,
spl5_47,
inference(avatar_split_clause,[],[f146,f390]) ).
fof(f146,plain,
! [X2,X3,X0,X1,X4] :
( check_cpq(triple(X0,X1,X2))
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ less_than(X4,X3) ),
inference(cnf_transformation,[],[f93]) ).
fof(f388,plain,
spl5_46,
inference(avatar_split_clause,[],[f133,f386]) ).
fof(f133,plain,
! [X2,X3,X0,X1] :
( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
| ~ contains_slb(X0,X2)
| X1 = X2 ),
inference(cnf_transformation,[],[f69]) ).
fof(f69,plain,
! [X0,X1,X2,X3] :
( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
| ~ contains_slb(X0,X2)
| X1 = X2 ),
inference(flattening,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2,X3] :
( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
| ~ contains_slb(X0,X2)
| X1 = X2 ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1,X2,X3] :
( ( contains_slb(X0,X2)
& X1 != X2 )
=> lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
fof(f384,plain,
spl5_45,
inference(avatar_split_clause,[],[f128,f382]) ).
fof(f128,plain,
! [X2,X3,X0,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
inference(cnf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0,X1,X2,X3] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax42) ).
fof(f376,plain,
spl5_44,
inference(avatar_split_clause,[],[f149,f374]) ).
fof(f374,plain,
( spl5_44
<=> ! [X4,X0,X3,X2,X1] :
( X3 = X4
| pair_in_list(X0,X2,X4)
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_44])]) ).
fof(f149,plain,
! [X2,X3,X0,X1,X4] :
( X3 = X4
| pair_in_list(X0,X2,X4)
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
inference(cnf_transformation,[],[f95]) ).
fof(f95,plain,
! [X0,X1,X2,X3,X4] :
( ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ( ( X3 != X4
| X1 != X2 )
& ~ pair_in_list(X0,X2,X4) ) )
& ( ( X3 = X4
& X1 = X2 )
| pair_in_list(X0,X2,X4)
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
inference(flattening,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2,X3,X4] :
( ( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ( ( X3 != X4
| X1 != X2 )
& ~ pair_in_list(X0,X2,X4) ) )
& ( ( X3 = X4
& X1 = X2 )
| pair_in_list(X0,X2,X4)
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
inference(nnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1,X2,X3,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
<=> ( ( X3 = X4
& X1 = X2 )
| pair_in_list(X0,X2,X4) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax23) ).
fof(f372,plain,
spl5_43,
inference(avatar_split_clause,[],[f148,f370]) ).
fof(f370,plain,
( spl5_43
<=> ! [X4,X0,X3,X2,X1] :
( X1 = X2
| pair_in_list(X0,X2,X4)
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_43])]) ).
fof(f148,plain,
! [X2,X3,X0,X1,X4] :
( X1 = X2
| pair_in_list(X0,X2,X4)
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ),
inference(cnf_transformation,[],[f95]) ).
fof(f366,plain,
spl5_42,
inference(avatar_split_clause,[],[f130,f364]) ).
fof(f130,plain,
! [X2,X3,X0,X1] :
( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,plain,
! [X0,X1,X2,X3] :
( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0,X1,X2,X3] :
( ~ contains_slb(X1,X3)
=> triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax43) ).
fof(f362,plain,
( spl5_40
| spl5_41
| ~ spl5_2
| ~ spl5_36 ),
inference(avatar_split_clause,[],[f337,f331,f166,f359,f355]) ).
fof(f337,plain,
( strictly_less_than(sK3,findmin_pqp_res(sK0))
| create_slb = sK1
| ~ spl5_2
| ~ spl5_36 ),
inference(superposition,[],[f168,f332]) ).
fof(f351,plain,
spl5_39,
inference(avatar_split_clause,[],[f142,f349]) ).
fof(f142,plain,
! [X2,X3,X0,X1] :
( X1 = X2
| contains_slb(X0,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2,X3] :
( ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ( X1 != X2
& ~ contains_slb(X0,X2) ) )
& ( X1 = X2
| contains_slb(X0,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
inference(flattening,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2,X3] :
( ( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ( X1 != X2
& ~ contains_slb(X0,X2) ) )
& ( X1 = X2
| contains_slb(X0,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X2,X3] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
<=> ( X1 = X2
| contains_slb(X0,X2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f347,plain,
spl5_38,
inference(avatar_split_clause,[],[f150,f345]) ).
fof(f345,plain,
( spl5_38
<=> ! [X4,X0,X3,X2,X1] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ~ pair_in_list(X0,X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_38])]) ).
fof(f150,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ~ pair_in_list(X0,X2,X4) ),
inference(cnf_transformation,[],[f95]) ).
fof(f343,plain,
spl5_37,
inference(avatar_split_clause,[],[f145,f341]) ).
fof(f145,plain,
! [X2,X3,X0,X1,X4] :
( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ strictly_less_than(X3,X4) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1,X2,X3,X4] :
( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ strictly_less_than(X3,X4) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,plain,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X3,X4)
=> ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
inference(flattening,[],[f51]) ).
fof(f51,plain,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X3,X4)
=> ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
inference(true_and_false_elimination,[],[f26]) ).
fof(f26,axiom,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X3,X4)
=> ( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
<=> $false ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f333,plain,
spl5_36,
inference(avatar_split_clause,[],[f156,f331]) ).
fof(f156,plain,
! [X2,X0,X1] :
( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(definition_unfolding,[],[f129,f108]) ).
fof(f108,plain,
! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
inference(cnf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
fof(f129,plain,
! [X2,X0,X1] :
( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,plain,
! [X0,X1,X2] :
( create_slb != X1
=> findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
inference(rectify,[],[f39]) ).
fof(f39,axiom,
! [X0,X1,X2,X3] :
( create_slb != X1
=> findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax51) ).
fof(f322,plain,
spl5_35,
inference(avatar_split_clause,[],[f155,f320]) ).
fof(f155,plain,
! [X0,X1] :
( succ_cpq(X0,remove_cpq(findmin_cpq_eff(X1),removemin_cpq_res(X1)))
| ~ succ_cpq(X0,X1) ),
inference(definition_unfolding,[],[f115,f152]) ).
fof(f152,plain,
! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),removemin_cpq_res(X0)),
inference(definition_unfolding,[],[f109,f108]) ).
fof(f109,plain,
! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),findmin_cpq_res(X0)),
inference(cnf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),findmin_cpq_res(X0)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax52) ).
fof(f115,plain,
! [X0,X1] :
( succ_cpq(X0,removemin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,plain,
! [X0,X1] :
( succ_cpq(X0,removemin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0,X1] :
( succ_cpq(X0,X1)
=> succ_cpq(X0,removemin_cpq_eff(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax35) ).
fof(f318,plain,
spl5_34,
inference(avatar_split_clause,[],[f143,f316]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ~ contains_slb(X0,X2) ),
inference(cnf_transformation,[],[f92]) ).
fof(f314,plain,
spl5_33,
inference(avatar_split_clause,[],[f113,f312]) ).
fof(f113,plain,
! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
inference(cnf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax46) ).
fof(f297,plain,
spl5_32,
inference(avatar_split_clause,[],[f141,f295]) ).
fof(f141,plain,
! [X2,X3,X0,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2,X3] :
( ( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) )
& ( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
inference(nnf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0,X1,X2,X3] :
( contains_cpq(triple(X0,X1,X2),X3)
<=> contains_slb(X1,X3) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
fof(f293,plain,
spl5_31,
inference(avatar_split_clause,[],[f140,f291]) ).
fof(f140,plain,
! [X2,X3,X0,X1] :
( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f90]) ).
fof(f289,plain,
spl5_30,
inference(avatar_split_clause,[],[f127,f287]) ).
fof(f127,plain,
! [X2,X0,X1] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f63]) ).
fof(f63,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(flattening,[],[f62]) ).
fof(f62,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(ennf_transformation,[],[f1]) ).
fof(f1,axiom,
! [X0,X1,X2] :
( ( less_than(X1,X2)
& less_than(X0,X1) )
=> less_than(X0,X2) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',transitivity) ).
fof(f285,plain,
spl5_29,
inference(avatar_split_clause,[],[f123,f283]) ).
fof(f123,plain,
! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2,
inference(cnf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f281,plain,
spl5_28,
inference(avatar_split_clause,[],[f122,f279]) ).
fof(f122,plain,
! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0,
inference(cnf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1,X2] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax24) ).
fof(f277,plain,
spl5_27,
inference(avatar_split_clause,[],[f119,f275]) ).
fof(f119,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( ( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) )
& ( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
| ~ strictly_less_than(X0,X1) ) ),
inference(flattening,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( ( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) )
& ( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
| ~ strictly_less_than(X0,X1) ) ),
inference(nnf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( strictly_less_than(X0,X1)
<=> ( ~ less_than(X1,X0)
& less_than(X0,X1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',stricly_smaller_definition) ).
fof(f272,plain,
( ~ spl5_26
| ~ spl5_2
| ~ spl5_16 ),
inference(avatar_split_clause,[],[f234,f225,f166,f269]) ).
fof(f269,plain,
( spl5_26
<=> less_than(removemin_cpq_res(triple(sK0,sK1,sK2)),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_26])]) ).
fof(f234,plain,
( ~ less_than(removemin_cpq_res(triple(sK0,sK1,sK2)),sK3)
| ~ spl5_2
| ~ spl5_16 ),
inference(resolution,[],[f226,f168]) ).
fof(f267,plain,
spl5_25,
inference(avatar_split_clause,[],[f159,f265]) ).
fof(f159,plain,
! [X2,X0,X4] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4),
inference(equality_resolution,[],[f158]) ).
fof(f158,plain,
! [X2,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X4)),X2,X4)
| X1 != X2 ),
inference(equality_resolution,[],[f151]) ).
fof(f151,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| X3 != X4
| X1 != X2 ),
inference(cnf_transformation,[],[f95]) ).
fof(f263,plain,
spl5_24,
inference(avatar_split_clause,[],[f126,f261]) ).
fof(f126,plain,
! [X2,X0,X1] :
( bad = X2
| ok(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,plain,
! [X0,X1,X2] :
( bad = X2
| ok(triple(X0,X1,X2)) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0,X1,X2] :
( ~ ok(triple(X0,X1,X2))
=> bad = X2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax41) ).
fof(f259,plain,
spl5_23,
inference(avatar_split_clause,[],[f125,f257]) ).
fof(f257,plain,
( spl5_23
<=> ! [X2,X0,X1] :
( succ_cpq(X0,remove_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_23])]) ).
fof(f125,plain,
! [X2,X0,X1] :
( succ_cpq(X0,remove_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,plain,
! [X0,X1,X2] :
( succ_cpq(X0,remove_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0,X1,X2] :
( succ_cpq(X0,X1)
=> succ_cpq(X0,remove_cpq(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax33) ).
fof(f255,plain,
spl5_22,
inference(avatar_split_clause,[],[f124,f253]) ).
fof(f253,plain,
( spl5_22
<=> ! [X2,X0,X1] :
( succ_cpq(X0,insert_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_22])]) ).
fof(f124,plain,
! [X2,X0,X1] :
( succ_cpq(X0,insert_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1,X2] :
( succ_cpq(X0,insert_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0,X1,X2] :
( succ_cpq(X0,X1)
=> succ_cpq(X0,insert_cpq(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax32) ).
fof(f251,plain,
spl5_21,
inference(avatar_split_clause,[],[f157,f249]) ).
fof(f157,plain,
! [X2,X3,X0] : contains_slb(insert_slb(X0,pair(X2,X3)),X2),
inference(equality_resolution,[],[f144]) ).
fof(f144,plain,
! [X2,X3,X0,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| X1 != X2 ),
inference(cnf_transformation,[],[f92]) ).
fof(f247,plain,
spl5_20,
inference(avatar_split_clause,[],[f154,f245]) ).
fof(f154,plain,
! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)),
inference(definition_unfolding,[],[f112,f108]) ).
fof(f112,plain,
! [X0,X1] : bottom = findmin_cpq_res(triple(X0,create_slb,X1)),
inference(cnf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0,X1] : bottom = findmin_cpq_res(triple(X0,create_slb,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax50) ).
fof(f243,plain,
spl5_19,
inference(avatar_split_clause,[],[f116,f241]) ).
fof(f116,plain,
! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] :
( succ_cpq(X0,X1)
=> succ_cpq(X0,findmin_cpq_eff(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax34) ).
fof(f239,plain,
( spl5_18
| ~ spl5_2
| ~ spl5_15 ),
inference(avatar_split_clause,[],[f233,f221,f166,f236]) ).
fof(f233,plain,
( less_than(sK3,removemin_cpq_res(triple(sK0,sK1,sK2)))
| ~ spl5_2
| ~ spl5_15 ),
inference(resolution,[],[f222,f168]) ).
fof(f231,plain,
spl5_17,
inference(avatar_split_clause,[],[f121,f229]) ).
fof(f121,plain,
! [X2,X0,X1] : isnonempty_slb(insert_slb(X0,pair(X1,X2))),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] : isnonempty_slb(insert_slb(X0,pair(X1,X2))),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax19) ).
fof(f227,plain,
spl5_16,
inference(avatar_split_clause,[],[f118,f225]) ).
fof(f118,plain,
! [X0,X1] :
( ~ less_than(X1,X0)
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f223,plain,
spl5_15,
inference(avatar_split_clause,[],[f117,f221]) ).
fof(f117,plain,
! [X0,X1] :
( less_than(X0,X1)
| ~ strictly_less_than(X0,X1) ),
inference(cnf_transformation,[],[f89]) ).
fof(f219,plain,
spl5_14,
inference(avatar_split_clause,[],[f114,f217]) ).
fof(f114,plain,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',totality) ).
fof(f215,plain,
spl5_13,
inference(avatar_split_clause,[],[f120,f213]) ).
fof(f120,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(cnf_transformation,[],[f46]) ).
fof(f46,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(flattening,[],[f45]) ).
fof(f45,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(true_and_false_elimination,[],[f28]) ).
fof(f28,axiom,
! [X0,X1] :
( ok(triple(X0,X1,bad))
<=> $false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
fof(f211,plain,
spl5_12,
inference(avatar_split_clause,[],[f111,f209]) ).
fof(f209,plain,
( spl5_12
<=> ! [X0,X1] : check_cpq(triple(X0,create_slb,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).
fof(f111,plain,
! [X0,X1] : check_cpq(triple(X0,create_slb,X1)),
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0,X1] : check_cpq(triple(X0,create_slb,X1)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax36) ).
fof(f207,plain,
spl5_11,
inference(avatar_split_clause,[],[f107,f205]) ).
fof(f205,plain,
( spl5_11
<=> ! [X0] : create_slb = update_slb(create_slb,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).
fof(f107,plain,
! [X0] : create_slb = update_slb(create_slb,X0),
inference(cnf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] : create_slb = update_slb(create_slb,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f203,plain,
spl5_10,
inference(avatar_split_clause,[],[f110,f201]) ).
fof(f201,plain,
( spl5_10
<=> ! [X0,X1] : ~ pair_in_list(create_slb,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).
fof(f110,plain,
! [X0,X1] : ~ pair_in_list(create_slb,X0,X1),
inference(cnf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] : ~ pair_in_list(create_slb,X0,X1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f199,plain,
spl5_9,
inference(avatar_split_clause,[],[f106,f197]) ).
fof(f106,plain,
! [X0] : less_than(bottom,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] : less_than(bottom,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',bottom_smallest) ).
fof(f195,plain,
spl5_8,
inference(avatar_split_clause,[],[f105,f193]) ).
fof(f105,plain,
! [X0] : less_than(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : less_than(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',reflexivity) ).
fof(f191,plain,
spl5_7,
inference(avatar_split_clause,[],[f104,f189]) ).
fof(f189,plain,
( spl5_7
<=> ! [X0] : succ_cpq(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
fof(f104,plain,
! [X0] : succ_cpq(X0,X0),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0] : succ_cpq(X0,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax31) ).
fof(f187,plain,
spl5_6,
inference(avatar_split_clause,[],[f103,f185]) ).
fof(f103,plain,
! [X0] : ~ contains_slb(create_slb,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] : ~ contains_slb(create_slb,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax20) ).
fof(f183,plain,
spl5_5,
inference(avatar_split_clause,[],[f99,f181]) ).
fof(f99,plain,
! [X4] :
( ~ less_than(findmin_pqp_res(sK0),X4)
| ~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK0)),sK3,X4) ),
inference(cnf_transformation,[],[f85]) ).
fof(f85,plain,
( ! [X4] :
( ~ less_than(findmin_pqp_res(sK0),X4)
| ~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK0)),sK3,X4) )
& ~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK0)),sK3,findmin_pqp_res(sK0))
& strictly_less_than(sK3,findmin_cpq_res(triple(sK0,sK1,sK2)))
& contains_slb(sK1,sK3) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f54,f84]) ).
fof(f84,plain,
( ? [X0,X1,X2,X3] :
( ! [X4] :
( ~ less_than(findmin_pqp_res(X0),X4)
| ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) )
& ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_slb(X1,X3) )
=> ( ! [X4] :
( ~ less_than(findmin_pqp_res(sK0),X4)
| ~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK0)),sK3,X4) )
& ~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK0)),sK3,findmin_pqp_res(sK0))
& strictly_less_than(sK3,findmin_cpq_res(triple(sK0,sK1,sK2)))
& contains_slb(sK1,sK3) ) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
? [X0,X1,X2,X3] :
( ! [X4] :
( ~ less_than(findmin_pqp_res(X0),X4)
| ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) )
& ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_slb(X1,X3) ),
inference(flattening,[],[f53]) ).
fof(f53,plain,
? [X0,X1,X2,X3] :
( ! [X4] :
( ~ less_than(findmin_pqp_res(X0),X4)
| ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) )
& ~ pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0))
& strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_slb(X1,X3) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,negated_conjecture,
~ ! [X0,X1,X2,X3] :
( ( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_slb(X1,X3) )
=> ( ? [X4] :
( less_than(findmin_pqp_res(X0),X4)
& pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) )
| pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) ) ),
inference(negated_conjecture,[],[f43]) ).
fof(f43,conjecture,
! [X0,X1,X2,X3] :
( ( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_slb(X1,X3) )
=> ( ? [X4] :
( less_than(findmin_pqp_res(X0),X4)
& pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,X4) )
| pair_in_list(update_slb(X1,findmin_pqp_res(X0)),X3,findmin_pqp_res(X0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l44_co) ).
fof(f179,plain,
~ spl5_4,
inference(avatar_split_clause,[],[f102,f176]) ).
fof(f102,plain,
~ isnonempty_slb(create_slb),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
~ isnonempty_slb(create_slb),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax18) ).
fof(f174,plain,
~ spl5_3,
inference(avatar_split_clause,[],[f98,f171]) ).
fof(f98,plain,
~ pair_in_list(update_slb(sK1,findmin_pqp_res(sK0)),sK3,findmin_pqp_res(sK0)),
inference(cnf_transformation,[],[f85]) ).
fof(f169,plain,
spl5_2,
inference(avatar_split_clause,[],[f153,f166]) ).
fof(f153,plain,
strictly_less_than(sK3,removemin_cpq_res(triple(sK0,sK1,sK2))),
inference(definition_unfolding,[],[f97,f108]) ).
fof(f97,plain,
strictly_less_than(sK3,findmin_cpq_res(triple(sK0,sK1,sK2))),
inference(cnf_transformation,[],[f85]) ).
fof(f164,plain,
spl5_1,
inference(avatar_split_clause,[],[f96,f161]) ).
fof(f96,plain,
contains_slb(sK1,sK3),
inference(cnf_transformation,[],[f85]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV408+1 : TPTP v8.1.2. Released v3.3.0.
% 0.12/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 05:01:48 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.15/0.36 % (8728)Running in auto input_syntax mode. Trying TPTP
% 0.15/0.38 % (8731)WARNING: value z3 for option sas not known
% 0.15/0.38 % (8732)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.15/0.38 % (8734)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.15/0.38 % (8733)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.15/0.38 % (8730)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.15/0.38 % (8735)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.15/0.38 % (8731)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.15/0.38 % (8729)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.15/0.39 TRYING [1]
% 0.15/0.39 TRYING [2]
% 0.15/0.40 TRYING [1]
% 0.15/0.40 TRYING [2]
% 0.15/0.40 TRYING [3]
% 0.15/0.41 TRYING [1]
% 0.15/0.41 TRYING [2]
% 0.15/0.42 TRYING [3]
% 0.22/0.43 % (8733)First to succeed.
% 0.22/0.44 % (8733)Refutation found. Thanks to Tanya!
% 0.22/0.44 % SZS status Theorem for theBenchmark
% 0.22/0.44 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.45 % (8733)------------------------------
% 0.22/0.45 % (8733)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.22/0.45 % (8733)Termination reason: Refutation
% 0.22/0.45
% 0.22/0.45 % (8733)Memory used [KB]: 1642
% 0.22/0.45 % (8733)Time elapsed: 0.062 s
% 0.22/0.45 % (8733)Instructions burned: 99 (million)
% 0.22/0.45 % (8733)------------------------------
% 0.22/0.45 % (8733)------------------------------
% 0.22/0.45 % (8728)Success in time 0.071 s
%------------------------------------------------------------------------------