TSTP Solution File: SWV390+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV390+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 : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 10:51:38 EDT 2024
% Result : Theorem 0.20s 0.42s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 178
% Syntax : Number of formulae : 578 ( 93 unt; 0 def)
% Number of atoms : 1661 ( 284 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1840 ( 757 ~; 867 |; 42 &)
% ( 142 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 6 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 143 ( 141 usr; 133 prp; 0-3 aty)
% Number of functors : 24 ( 24 usr; 7 con; 0-3 aty)
% Number of variables : 1445 (1429 !; 16 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1488,plain,
$false,
inference(avatar_sat_refutation,[],[f162,f167,f172,f176,f180,f184,f188,f192,f196,f200,f204,f208,f212,f217,f221,f225,f229,f233,f237,f241,f246,f250,f254,f258,f262,f266,f281,f287,f291,f295,f299,f308,f314,f321,f327,f331,f335,f340,f346,f352,f356,f368,f372,f376,f380,f408,f412,f421,f428,f437,f441,f445,f456,f460,f469,f474,f490,f502,f506,f514,f521,f526,f531,f563,f568,f575,f580,f584,f588,f592,f599,f633,f646,f650,f661,f675,f679,f690,f699,f703,f711,f724,f728,f739,f749,f763,f767,f771,f803,f821,f825,f829,f853,f857,f861,f898,f902,f940,f995,f1005,f1075,f1079,f1105,f1109,f1117,f1129,f1133,f1137,f1141,f1155,f1159,f1252,f1267,f1271,f1275,f1280,f1297,f1301,f1331,f1345,f1351,f1362,f1366,f1402,f1406,f1410,f1411,f1415,f1465,f1475,f1479,f1483,f1487]) ).
fof(f1487,plain,
( spl6_1
| ~ spl6_105 ),
inference(avatar_contradiction_clause,[],[f1484]) ).
fof(f1484,plain,
( $false
| spl6_1
| ~ spl6_105 ),
inference(resolution,[],[f1112,f161]) ).
fof(f161,plain,
( ~ check_cpq(triple(sK0,sK1,sK2))
| spl6_1 ),
inference(avatar_component_clause,[],[f159]) ).
fof(f159,plain,
( spl6_1
<=> check_cpq(triple(sK0,sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_1])]) ).
fof(f1112,plain,
( ! [X0,X1] : check_cpq(triple(X0,sK1,X1))
| ~ spl6_105 ),
inference(avatar_component_clause,[],[f1111]) ).
fof(f1111,plain,
( spl6_105
<=> ! [X0,X1] : check_cpq(triple(X0,sK1,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_105])]) ).
fof(f1483,plain,
( spl6_132
| ~ spl6_29
| ~ spl6_70 ),
inference(avatar_split_clause,[],[f621,f590,f289,f1481]) ).
fof(f1481,plain,
( spl6_132
<=> ! [X0,X3,X2,X1] :
( contains_slb(update_slb(insert_slb(X0,pair(X1,X2)),bottom),X3)
| ~ contains_slb(update_slb(X0,bottom),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_132])]) ).
fof(f289,plain,
( spl6_29
<=> ! [X0,X3,X2,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ~ contains_slb(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_29])]) ).
fof(f590,plain,
( spl6_70
<=> ! [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,[spl6_70])]) ).
fof(f621,plain,
( ! [X2,X3,X0,X1] :
( contains_slb(update_slb(insert_slb(X0,pair(X1,X2)),bottom),X3)
| ~ contains_slb(update_slb(X0,bottom),X3) )
| ~ spl6_29
| ~ spl6_70 ),
inference(superposition,[],[f290,f591]) ).
fof(f591,plain,
( ! [X2,X0,X1] : update_slb(insert_slb(X0,pair(X1,X2)),bottom) = insert_slb(update_slb(X0,bottom),pair(X1,X2))
| ~ spl6_70 ),
inference(avatar_component_clause,[],[f590]) ).
fof(f290,plain,
( ! [X2,X3,X0,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ~ contains_slb(X0,X2) )
| ~ spl6_29 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f1479,plain,
( spl6_131
| ~ spl6_36
| ~ spl6_69 ),
inference(avatar_split_clause,[],[f607,f586,f329,f1477]) ).
fof(f1477,plain,
( spl6_131
<=> ! [X2,X4,X0,X3,X1] :
( ~ check_cpq(triple(X3,update_slb(insert_slb(X0,pair(X2,X1)),X1),X4))
| ~ strictly_less_than(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_131])]) ).
fof(f329,plain,
( spl6_36
<=> ! [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,[spl6_36])]) ).
fof(f586,plain,
( spl6_69
<=> ! [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,[spl6_69])]) ).
fof(f607,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ check_cpq(triple(X3,update_slb(insert_slb(X0,pair(X2,X1)),X1),X4))
| ~ strictly_less_than(X2,X1) )
| ~ spl6_36
| ~ spl6_69 ),
inference(superposition,[],[f330,f587]) ).
fof(f587,plain,
( ! [X2,X0,X1] : insert_slb(update_slb(X0,X2),pair(X1,X2)) = update_slb(insert_slb(X0,pair(X1,X2)),X2)
| ~ spl6_69 ),
inference(avatar_component_clause,[],[f586]) ).
fof(f330,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ strictly_less_than(X3,X4) )
| ~ spl6_36 ),
inference(avatar_component_clause,[],[f329]) ).
fof(f1475,plain,
( spl6_130
| ~ spl6_29
| ~ spl6_69 ),
inference(avatar_split_clause,[],[f606,f586,f289,f1473]) ).
fof(f1473,plain,
( spl6_130
<=> ! [X0,X3,X2,X1] :
( contains_slb(update_slb(insert_slb(X0,pair(X2,X1)),X1),X3)
| ~ contains_slb(update_slb(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_130])]) ).
fof(f606,plain,
( ! [X2,X3,X0,X1] :
( contains_slb(update_slb(insert_slb(X0,pair(X2,X1)),X1),X3)
| ~ contains_slb(update_slb(X0,X1),X3) )
| ~ spl6_29
| ~ spl6_69 ),
inference(superposition,[],[f290,f587]) ).
fof(f1465,plain,
( spl6_129
| ~ spl6_37
| ~ spl6_75 ),
inference(avatar_split_clause,[],[f663,f659,f333,f1463]) ).
fof(f1463,plain,
( spl6_129
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ check_cpq(insert_cpq(triple(X0,X1,X2),X3))
| less_than(X4,X5)
| ~ pair_in_list(X1,X5,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_129])]) ).
fof(f333,plain,
( spl6_37
<=> ! [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,[spl6_37])]) ).
fof(f659,plain,
( spl6_75
<=> ! [X5,X4,X0,X3,X2,X1] :
( ~ check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| ~ pair_in_list(insert_slb(X2,pair(X1,bottom)),X4,X5)
| less_than(X5,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_75])]) ).
fof(f663,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ check_cpq(insert_cpq(triple(X0,X1,X2),X3))
| less_than(X4,X5)
| ~ pair_in_list(X1,X5,X4) )
| ~ spl6_37
| ~ spl6_75 ),
inference(resolution,[],[f660,f334]) ).
fof(f334,plain,
( ! [X2,X3,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ~ pair_in_list(X0,X2,X4) )
| ~ spl6_37 ),
inference(avatar_component_clause,[],[f333]) ).
fof(f660,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ pair_in_list(insert_slb(X2,pair(X1,bottom)),X4,X5)
| ~ check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| less_than(X5,X4) )
| ~ spl6_75 ),
inference(avatar_component_clause,[],[f659]) ).
fof(f1415,plain,
( spl6_128
| ~ spl6_22
| ~ spl6_70 ),
inference(avatar_split_clause,[],[f619,f590,f248,f1413]) ).
fof(f1413,plain,
( spl6_128
<=> ! [X2,X0,X1] : update_slb(X0,bottom) = remove_slb(update_slb(insert_slb(X0,pair(X1,X2)),bottom),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_128])]) ).
fof(f248,plain,
( spl6_22
<=> ! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_22])]) ).
fof(f619,plain,
( ! [X2,X0,X1] : update_slb(X0,bottom) = remove_slb(update_slb(insert_slb(X0,pair(X1,X2)),bottom),X1)
| ~ spl6_22
| ~ spl6_70 ),
inference(superposition,[],[f249,f591]) ).
fof(f249,plain,
( ! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0
| ~ spl6_22 ),
inference(avatar_component_clause,[],[f248]) ).
fof(f1411,plain,
( ~ spl6_106
| ~ spl6_61
| ~ spl6_117 ),
inference(avatar_split_clause,[],[f1346,f1277,f516,f1114]) ).
fof(f1114,plain,
( spl6_106
<=> less_than(sK5(sK1),sK4(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_106])]) ).
fof(f516,plain,
( spl6_61
<=> ! [X4,X3] :
( ~ less_than(X3,X4)
| ~ strictly_less_than(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_61])]) ).
fof(f1277,plain,
( spl6_117
<=> strictly_less_than(sK4(sK1),sK5(sK1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_117])]) ).
fof(f1346,plain,
( ~ less_than(sK5(sK1),sK4(sK1))
| ~ spl6_61
| ~ spl6_117 ),
inference(resolution,[],[f1279,f517]) ).
fof(f517,plain,
( ! [X3,X4] :
( ~ strictly_less_than(X4,X3)
| ~ less_than(X3,X4) )
| ~ spl6_61 ),
inference(avatar_component_clause,[],[f516]) ).
fof(f1279,plain,
( strictly_less_than(sK4(sK1),sK5(sK1))
| ~ spl6_117 ),
inference(avatar_component_clause,[],[f1277]) ).
fof(f1410,plain,
( spl6_127
| ~ spl6_9
| ~ spl6_70 ),
inference(avatar_split_clause,[],[f615,f590,f194,f1408]) ).
fof(f1408,plain,
( spl6_127
<=> ! [X0,X1] : insert_slb(create_slb,pair(X0,X1)) = update_slb(insert_slb(create_slb,pair(X0,X1)),bottom) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_127])]) ).
fof(f194,plain,
( spl6_9
<=> ! [X0] : create_slb = update_slb(create_slb,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_9])]) ).
fof(f615,plain,
( ! [X0,X1] : insert_slb(create_slb,pair(X0,X1)) = update_slb(insert_slb(create_slb,pair(X0,X1)),bottom)
| ~ spl6_9
| ~ spl6_70 ),
inference(superposition,[],[f591,f195]) ).
fof(f195,plain,
( ! [X0] : create_slb = update_slb(create_slb,X0)
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f194]) ).
fof(f1406,plain,
( spl6_126
| ~ spl6_22
| ~ spl6_69 ),
inference(avatar_split_clause,[],[f604,f586,f248,f1404]) ).
fof(f1404,plain,
( spl6_126
<=> ! [X2,X0,X1] : update_slb(X0,X1) = remove_slb(update_slb(insert_slb(X0,pair(X2,X1)),X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_126])]) ).
fof(f604,plain,
( ! [X2,X0,X1] : update_slb(X0,X1) = remove_slb(update_slb(insert_slb(X0,pair(X2,X1)),X1),X2)
| ~ spl6_22
| ~ spl6_69 ),
inference(superposition,[],[f249,f587]) ).
fof(f1402,plain,
( spl6_125
| ~ spl6_9
| ~ spl6_69 ),
inference(avatar_split_clause,[],[f600,f586,f194,f1400]) ).
fof(f1400,plain,
( spl6_125
<=> ! [X0,X1] : insert_slb(create_slb,pair(X1,X0)) = update_slb(insert_slb(create_slb,pair(X1,X0)),X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_125])]) ).
fof(f600,plain,
( ! [X0,X1] : insert_slb(create_slb,pair(X1,X0)) = update_slb(insert_slb(create_slb,pair(X1,X0)),X0)
| ~ spl6_9
| ~ spl6_69 ),
inference(superposition,[],[f587,f195]) ).
fof(f1366,plain,
( spl6_124
| ~ spl6_24
| ~ spl6_57 ),
inference(avatar_split_clause,[],[f497,f488,f256,f1364]) ).
fof(f1364,plain,
( spl6_124
<=> ! [X0,X3,X2,X1] :
( check_cpq(triple(X1,X0,X2))
| less_than(X3,sK5(X0))
| ~ less_than(X3,sK4(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_124])]) ).
fof(f256,plain,
( spl6_24
<=> ! [X2,X0,X1] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_24])]) ).
fof(f488,plain,
( spl6_57
<=> ! [X2,X0,X1] :
( check_cpq(triple(X0,X1,X2))
| less_than(sK4(X1),sK5(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_57])]) ).
fof(f497,plain,
( ! [X2,X3,X0,X1] :
( check_cpq(triple(X1,X0,X2))
| less_than(X3,sK5(X0))
| ~ less_than(X3,sK4(X0)) )
| ~ spl6_24
| ~ spl6_57 ),
inference(resolution,[],[f489,f257]) ).
fof(f257,plain,
( ! [X2,X0,X1] :
( ~ less_than(X1,X2)
| less_than(X0,X2)
| ~ less_than(X0,X1) )
| ~ spl6_24 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f489,plain,
( ! [X2,X0,X1] :
( check_cpq(triple(X0,X1,X2))
| less_than(sK4(X1),sK5(X1)) )
| ~ spl6_57 ),
inference(avatar_component_clause,[],[f488]) ).
fof(f1362,plain,
( spl6_123
| ~ spl6_56
| ~ spl6_57 ),
inference(avatar_split_clause,[],[f495,f488,f472,f1360]) ).
fof(f1360,plain,
( spl6_123
<=> ! [X0,X3,X2,X1] :
( check_cpq(triple(X1,X0,X2))
| less_than(sK4(X0),X3)
| less_than(X3,sK5(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_123])]) ).
fof(f472,plain,
( spl6_56
<=> ! [X2,X0,X1] :
( less_than(X0,X1)
| ~ less_than(X0,X2)
| less_than(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_56])]) ).
fof(f495,plain,
( ! [X2,X3,X0,X1] :
( check_cpq(triple(X1,X0,X2))
| less_than(sK4(X0),X3)
| less_than(X3,sK5(X0)) )
| ~ spl6_56
| ~ spl6_57 ),
inference(resolution,[],[f489,f473]) ).
fof(f473,plain,
( ! [X2,X0,X1] :
( ~ less_than(X0,X2)
| less_than(X0,X1)
| less_than(X1,X2) )
| ~ spl6_56 ),
inference(avatar_component_clause,[],[f472]) ).
fof(f1351,plain,
( spl6_122
| ~ spl6_42
| ~ spl6_59 ),
inference(avatar_split_clause,[],[f510,f504,f366,f1349]) ).
fof(f1349,plain,
( spl6_122
<=> ! [X4,X0,X3,X2,X1] :
( ok(insert_cpq(insert_cpq(triple(X0,X2,X3),X1),X4))
| bad = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_122])]) ).
fof(f366,plain,
( spl6_42
<=> ! [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,[spl6_42])]) ).
fof(f504,plain,
( spl6_59
<=> ! [X0,X3,X2,X1] :
( ok(insert_cpq(triple(X0,X2,X3),X1))
| bad = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_59])]) ).
fof(f510,plain,
( ! [X2,X3,X0,X1,X4] :
( ok(insert_cpq(insert_cpq(triple(X0,X2,X3),X1),X4))
| bad = X3 )
| ~ spl6_42
| ~ spl6_59 ),
inference(superposition,[],[f505,f367]) ).
fof(f367,plain,
( ! [X2,X3,X0,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2)
| ~ spl6_42 ),
inference(avatar_component_clause,[],[f366]) ).
fof(f505,plain,
( ! [X2,X3,X0,X1] :
( ok(insert_cpq(triple(X0,X2,X3),X1))
| bad = X3 )
| ~ spl6_59 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f1345,plain,
( spl6_121
| ~ spl6_42
| ~ spl6_58 ),
inference(avatar_split_clause,[],[f508,f500,f366,f1343]) ).
fof(f1343,plain,
( spl6_121
<=> ! [X4,X0,X3,X2,X1] :
( ~ check_cpq(insert_cpq(insert_cpq(triple(X0,X2,X3),X1),X4))
| ~ strictly_less_than(X4,bottom) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_121])]) ).
fof(f500,plain,
( spl6_58
<=> ! [X0,X3,X2,X1] :
( ~ check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| ~ strictly_less_than(X1,bottom) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_58])]) ).
fof(f508,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ check_cpq(insert_cpq(insert_cpq(triple(X0,X2,X3),X1),X4))
| ~ strictly_less_than(X4,bottom) )
| ~ spl6_42
| ~ spl6_58 ),
inference(superposition,[],[f501,f367]) ).
fof(f501,plain,
( ! [X2,X3,X0,X1] :
( ~ check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| ~ strictly_less_than(X1,bottom) )
| ~ spl6_58 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f1331,plain,
( spl6_120
| ~ spl6_34
| ~ spl6_57 ),
inference(avatar_split_clause,[],[f492,f488,f319,f1329]) ).
fof(f1329,plain,
( spl6_120
<=> ! [X4,X1,X3] :
( less_than(sK4(X1),sK5(X1))
| ~ pair_in_list(X1,X3,X4)
| less_than(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_120])]) ).
fof(f319,plain,
( spl6_34
<=> ! [X5,X0,X6,X2,X1] :
( less_than(X6,X5)
| ~ pair_in_list(X1,X5,X6)
| ~ check_cpq(triple(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_34])]) ).
fof(f492,plain,
( ! [X3,X1,X4] :
( less_than(sK4(X1),sK5(X1))
| ~ pair_in_list(X1,X3,X4)
| less_than(X4,X3) )
| ~ spl6_34
| ~ spl6_57 ),
inference(resolution,[],[f489,f320]) ).
fof(f320,plain,
( ! [X2,X0,X1,X6,X5] :
( ~ check_cpq(triple(X0,X1,X2))
| ~ pair_in_list(X1,X5,X6)
| less_than(X6,X5) )
| ~ spl6_34 ),
inference(avatar_component_clause,[],[f319]) ).
fof(f1301,plain,
( spl6_119
| ~ spl6_23
| ~ spl6_70 ),
inference(avatar_split_clause,[],[f620,f590,f252,f1299]) ).
fof(f1299,plain,
( spl6_119
<=> ! [X2,X0,X1] : lookup_slb(update_slb(insert_slb(X0,pair(X1,X2)),bottom),X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_119])]) ).
fof(f252,plain,
( spl6_23
<=> ! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_23])]) ).
fof(f620,plain,
( ! [X2,X0,X1] : lookup_slb(update_slb(insert_slb(X0,pair(X1,X2)),bottom),X1) = X2
| ~ spl6_23
| ~ spl6_70 ),
inference(superposition,[],[f253,f591]) ).
fof(f253,plain,
( ! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2
| ~ spl6_23 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f1297,plain,
( spl6_118
| ~ spl6_23
| ~ spl6_69 ),
inference(avatar_split_clause,[],[f605,f586,f252,f1295]) ).
fof(f1295,plain,
( spl6_118
<=> ! [X2,X0,X1] : lookup_slb(update_slb(insert_slb(X0,pair(X2,X1)),X1),X2) = X1 ),
introduced(avatar_definition,[new_symbols(naming,[spl6_118])]) ).
fof(f605,plain,
( ! [X2,X0,X1] : lookup_slb(update_slb(insert_slb(X0,pair(X2,X1)),X1),X2) = X1
| ~ spl6_23
| ~ spl6_69 ),
inference(superposition,[],[f253,f587]) ).
fof(f1280,plain,
( spl6_117
| spl6_1
| ~ spl6_113 ),
inference(avatar_split_clause,[],[f1255,f1250,f159,f1277]) ).
fof(f1250,plain,
( spl6_113
<=> ! [X2,X0,X1] :
( strictly_less_than(sK4(X0),sK5(X0))
| check_cpq(triple(X1,X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_113])]) ).
fof(f1255,plain,
( strictly_less_than(sK4(sK1),sK5(sK1))
| spl6_1
| ~ spl6_113 ),
inference(resolution,[],[f1251,f161]) ).
fof(f1251,plain,
( ! [X2,X0,X1] :
( strictly_less_than(sK4(X0),sK5(X0))
| check_cpq(triple(X1,X0,X2)) )
| ~ spl6_113 ),
inference(avatar_component_clause,[],[f1250]) ).
fof(f1275,plain,
( spl6_116
| ~ spl6_10
| ~ spl6_74 ),
inference(avatar_split_clause,[],[f653,f648,f198,f1273]) ).
fof(f1273,plain,
( spl6_116
<=> ! [X2,X0,X1] :
( check_cpq(insert_cpq(triple(X0,create_slb,X1),X2))
| ~ less_than(bottom,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_116])]) ).
fof(f198,plain,
( spl6_10
<=> ! [X0,X1] : check_cpq(triple(X0,create_slb,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_10])]) ).
fof(f648,plain,
( spl6_74
<=> ! [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,[spl6_74])]) ).
fof(f653,plain,
( ! [X2,X0,X1] :
( check_cpq(insert_cpq(triple(X0,create_slb,X1),X2))
| ~ less_than(bottom,X2) )
| ~ spl6_10
| ~ spl6_74 ),
inference(resolution,[],[f649,f199]) ).
fof(f199,plain,
( ! [X0,X1] : check_cpq(triple(X0,create_slb,X1))
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f198]) ).
fof(f649,plain,
( ! [X2,X3,X0,X1] :
( ~ check_cpq(triple(insert_pqp(X0,X1),X2,X3))
| check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| ~ less_than(bottom,X1) )
| ~ spl6_74 ),
inference(avatar_component_clause,[],[f648]) ).
fof(f1271,plain,
( spl6_115
| ~ spl6_20
| ~ spl6_70 ),
inference(avatar_split_clause,[],[f618,f590,f239,f1269]) ).
fof(f1269,plain,
( spl6_115
<=> ! [X2,X0,X1] : pair_in_list(update_slb(insert_slb(X0,pair(X1,X2)),bottom),X1,X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_115])]) ).
fof(f239,plain,
( spl6_20
<=> ! [X4,X0,X2] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_20])]) ).
fof(f618,plain,
( ! [X2,X0,X1] : pair_in_list(update_slb(insert_slb(X0,pair(X1,X2)),bottom),X1,X2)
| ~ spl6_20
| ~ spl6_70 ),
inference(superposition,[],[f240,f591]) ).
fof(f240,plain,
( ! [X2,X0,X4] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4)
| ~ spl6_20 ),
inference(avatar_component_clause,[],[f239]) ).
fof(f1267,plain,
( spl6_114
| ~ spl6_20
| ~ spl6_69 ),
inference(avatar_split_clause,[],[f603,f586,f239,f1265]) ).
fof(f1265,plain,
( spl6_114
<=> ! [X2,X0,X1] : pair_in_list(update_slb(insert_slb(X0,pair(X2,X1)),X1),X2,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_114])]) ).
fof(f603,plain,
( ! [X2,X0,X1] : pair_in_list(update_slb(insert_slb(X0,pair(X2,X1)),X1),X2,X1)
| ~ spl6_20
| ~ spl6_69 ),
inference(superposition,[],[f240,f587]) ).
fof(f1252,plain,
( spl6_113
| ~ spl6_27
| ~ spl6_30 ),
inference(avatar_split_clause,[],[f358,f293,f279,f1250]) ).
fof(f279,plain,
( spl6_27
<=> ! [X2,X0,X1] :
( check_cpq(triple(X0,X1,X2))
| ~ less_than(sK5(X1),sK4(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_27])]) ).
fof(f293,plain,
( spl6_30
<=> ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_30])]) ).
fof(f358,plain,
( ! [X2,X0,X1] :
( strictly_less_than(sK4(X0),sK5(X0))
| check_cpq(triple(X1,X0,X2)) )
| ~ spl6_27
| ~ spl6_30 ),
inference(resolution,[],[f294,f280]) ).
fof(f280,plain,
( ! [X2,X0,X1] :
( ~ less_than(sK5(X1),sK4(X1))
| check_cpq(triple(X0,X1,X2)) )
| ~ spl6_27 ),
inference(avatar_component_clause,[],[f279]) ).
fof(f294,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(X1,X0) )
| ~ spl6_30 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f1159,plain,
( spl6_112
| ~ spl6_16
| ~ spl6_70 ),
inference(avatar_split_clause,[],[f617,f590,f223,f1157]) ).
fof(f1157,plain,
( spl6_112
<=> ! [X2,X0,X1] : contains_slb(update_slb(insert_slb(X0,pair(X1,X2)),bottom),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_112])]) ).
fof(f223,plain,
( spl6_16
<=> ! [X2,X0,X3] : contains_slb(insert_slb(X0,pair(X2,X3)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_16])]) ).
fof(f617,plain,
( ! [X2,X0,X1] : contains_slb(update_slb(insert_slb(X0,pair(X1,X2)),bottom),X1)
| ~ spl6_16
| ~ spl6_70 ),
inference(superposition,[],[f224,f591]) ).
fof(f224,plain,
( ! [X2,X3,X0] : contains_slb(insert_slb(X0,pair(X2,X3)),X2)
| ~ spl6_16 ),
inference(avatar_component_clause,[],[f223]) ).
fof(f1155,plain,
( spl6_111
| ~ spl6_16
| ~ spl6_69 ),
inference(avatar_split_clause,[],[f602,f586,f223,f1153]) ).
fof(f1153,plain,
( spl6_111
<=> ! [X2,X0,X1] : contains_slb(update_slb(insert_slb(X0,pair(X2,X1)),X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_111])]) ).
fof(f602,plain,
( ! [X2,X0,X1] : contains_slb(update_slb(insert_slb(X0,pair(X2,X1)),X1),X2)
| ~ spl6_16
| ~ spl6_69 ),
inference(superposition,[],[f224,f587]) ).
fof(f1141,plain,
( spl6_110
| ~ spl6_5
| ~ spl6_64 ),
inference(avatar_split_clause,[],[f564,f561,f178,f1139]) ).
fof(f1139,plain,
( spl6_110
<=> ! [X0,X1] : succ_cpq(triple(X0,create_slb,X1),triple(X0,create_slb,bad)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_110])]) ).
fof(f178,plain,
( spl6_5
<=> ! [X0] : succ_cpq(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_5])]) ).
fof(f561,plain,
( spl6_64
<=> ! [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,[spl6_64])]) ).
fof(f564,plain,
( ! [X0,X1] : succ_cpq(triple(X0,create_slb,X1),triple(X0,create_slb,bad))
| ~ spl6_5
| ~ spl6_64 ),
inference(resolution,[],[f562,f179]) ).
fof(f179,plain,
( ! [X0] : succ_cpq(X0,X0)
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f178]) ).
fof(f562,plain,
( ! [X2,X0,X1] :
( ~ succ_cpq(X2,triple(X0,create_slb,X1))
| succ_cpq(X2,triple(X0,create_slb,bad)) )
| ~ spl6_64 ),
inference(avatar_component_clause,[],[f561]) ).
fof(f1137,plain,
( spl6_109
| ~ spl6_12
| ~ spl6_56 ),
inference(avatar_split_clause,[],[f478,f472,f206,f1135]) ).
fof(f1135,plain,
( spl6_109
<=> ! [X2,X0,X1] :
( less_than(X0,X1)
| less_than(X1,X2)
| less_than(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_109])]) ).
fof(f206,plain,
( spl6_12
<=> ! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_12])]) ).
fof(f478,plain,
( ! [X2,X0,X1] :
( less_than(X0,X1)
| less_than(X1,X2)
| less_than(X2,X0) )
| ~ spl6_12
| ~ spl6_56 ),
inference(resolution,[],[f473,f207]) ).
fof(f207,plain,
( ! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) )
| ~ spl6_12 ),
inference(avatar_component_clause,[],[f206]) ).
fof(f1133,plain,
( spl6_108
| ~ spl6_30
| ~ spl6_56 ),
inference(avatar_split_clause,[],[f477,f472,f293,f1131]) ).
fof(f1131,plain,
( spl6_108
<=> ! [X2,X0,X1] :
( less_than(X0,X1)
| less_than(X1,X2)
| strictly_less_than(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_108])]) ).
fof(f477,plain,
( ! [X2,X0,X1] :
( less_than(X0,X1)
| less_than(X1,X2)
| strictly_less_than(X2,X0) )
| ~ spl6_30
| ~ spl6_56 ),
inference(resolution,[],[f473,f294]) ).
fof(f1129,plain,
( spl6_107
| ~ spl6_42
| ~ spl6_55 ),
inference(avatar_split_clause,[],[f470,f467,f366,f1127]) ).
fof(f1127,plain,
( spl6_107
<=> ! [X2,X0,X1,X3] : ~ ok(insert_cpq(insert_cpq(triple(X0,X2,bad),X1),X3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_107])]) ).
fof(f467,plain,
( spl6_55
<=> ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,bad),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_55])]) ).
fof(f470,plain,
( ! [X2,X3,X0,X1] : ~ ok(insert_cpq(insert_cpq(triple(X0,X2,bad),X1),X3))
| ~ spl6_42
| ~ spl6_55 ),
inference(superposition,[],[f468,f367]) ).
fof(f468,plain,
( ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,bad),X1))
| ~ spl6_55 ),
inference(avatar_component_clause,[],[f467]) ).
fof(f1117,plain,
( spl6_105
| spl6_106
| ~ spl6_32
| ~ spl6_93 ),
inference(avatar_split_clause,[],[f989,f851,f306,f1114,f1111]) ).
fof(f306,plain,
( spl6_32
<=> ! [X2,X0,X1] :
( check_cpq(triple(X0,X1,X2))
| pair_in_list(X1,sK4(X1),sK5(X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_32])]) ).
fof(f851,plain,
( spl6_93
<=> ! [X0,X1] :
( ~ pair_in_list(sK1,X0,X1)
| less_than(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_93])]) ).
fof(f989,plain,
( ! [X0,X1] :
( less_than(sK5(sK1),sK4(sK1))
| check_cpq(triple(X0,sK1,X1)) )
| ~ spl6_32
| ~ spl6_93 ),
inference(resolution,[],[f852,f307]) ).
fof(f307,plain,
( ! [X2,X0,X1] :
( check_cpq(triple(X0,X1,X2))
| pair_in_list(X1,sK4(X1),sK5(X1)) )
| ~ spl6_32 ),
inference(avatar_component_clause,[],[f306]) ).
fof(f852,plain,
( ! [X0,X1] :
( ~ pair_in_list(sK1,X0,X1)
| less_than(X1,X0) )
| ~ spl6_93 ),
inference(avatar_component_clause,[],[f851]) ).
fof(f1109,plain,
( spl6_104
| ~ spl6_13
| ~ spl6_70 ),
inference(avatar_split_clause,[],[f616,f590,f210,f1107]) ).
fof(f1107,plain,
( spl6_104
<=> ! [X2,X0,X1] : isnonempty_slb(update_slb(insert_slb(X0,pair(X1,X2)),bottom)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_104])]) ).
fof(f210,plain,
( spl6_13
<=> ! [X2,X0,X1] : isnonempty_slb(insert_slb(X0,pair(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_13])]) ).
fof(f616,plain,
( ! [X2,X0,X1] : isnonempty_slb(update_slb(insert_slb(X0,pair(X1,X2)),bottom))
| ~ spl6_13
| ~ spl6_70 ),
inference(superposition,[],[f211,f591]) ).
fof(f211,plain,
( ! [X2,X0,X1] : isnonempty_slb(insert_slb(X0,pair(X1,X2)))
| ~ spl6_13 ),
inference(avatar_component_clause,[],[f210]) ).
fof(f1105,plain,
( spl6_103
| ~ spl6_13
| ~ spl6_69 ),
inference(avatar_split_clause,[],[f601,f586,f210,f1103]) ).
fof(f1103,plain,
( spl6_103
<=> ! [X2,X0,X1] : isnonempty_slb(update_slb(insert_slb(X0,pair(X2,X1)),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_103])]) ).
fof(f601,plain,
( ! [X2,X0,X1] : isnonempty_slb(update_slb(insert_slb(X0,pair(X2,X1)),X1))
| ~ spl6_13
| ~ spl6_69 ),
inference(superposition,[],[f211,f587]) ).
fof(f1079,plain,
( spl6_102
| ~ spl6_23
| ~ spl6_54 ),
inference(avatar_split_clause,[],[f465,f458,f252,f1077]) ).
fof(f1077,plain,
( spl6_102
<=> ! [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,[spl6_102])]) ).
fof(f458,plain,
( spl6_54
<=> ! [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,[spl6_54])]) ).
fof(f465,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)) )
| ~ spl6_23
| ~ spl6_54 ),
inference(superposition,[],[f459,f253]) ).
fof(f459,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 )
| ~ spl6_54 ),
inference(avatar_component_clause,[],[f458]) ).
fof(f1075,plain,
( spl6_101
| ~ spl6_23
| ~ spl6_53 ),
inference(avatar_split_clause,[],[f461,f454,f252,f1073]) ).
fof(f1073,plain,
( spl6_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,[spl6_101])]) ).
fof(f454,plain,
( spl6_53
<=> ! [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,[spl6_53])]) ).
fof(f461,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)) )
| ~ spl6_23
| ~ spl6_53 ),
inference(superposition,[],[f455,f253]) ).
fof(f455,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 )
| ~ spl6_53 ),
inference(avatar_component_clause,[],[f454]) ).
fof(f1005,plain,
( spl6_100
| ~ spl6_48
| ~ spl6_49 ),
inference(avatar_split_clause,[],[f432,f426,f419,f1003]) ).
fof(f1003,plain,
( spl6_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,[spl6_100])]) ).
fof(f419,plain,
( spl6_48
<=> ! [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,[spl6_48])]) ).
fof(f426,plain,
( spl6_49
<=> ! [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,[spl6_49])]) ).
fof(f432,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 )
| ~ spl6_48
| ~ spl6_49 ),
inference(resolution,[],[f427,f420]) ).
fof(f420,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 )
| ~ spl6_48 ),
inference(avatar_component_clause,[],[f419]) ).
fof(f427,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 )
| ~ spl6_49 ),
inference(avatar_component_clause,[],[f426]) ).
fof(f995,plain,
( spl6_99
| ~ spl6_38
| ~ spl6_48 ),
inference(avatar_split_clause,[],[f423,f419,f338,f993]) ).
fof(f993,plain,
( spl6_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,[spl6_99])]) ).
fof(f338,plain,
( spl6_38
<=> ! [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,[spl6_38])]) ).
fof(f423,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 )
| ~ spl6_38
| ~ spl6_48 ),
inference(resolution,[],[f420,f339]) ).
fof(f339,plain,
( ! [X2,X3,X0,X1] :
( ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| contains_slb(X0,X2)
| X1 = X2 )
| ~ spl6_38 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f940,plain,
( spl6_98
| ~ spl6_43
| ~ spl6_48 ),
inference(avatar_split_clause,[],[f424,f419,f370,f938]) ).
fof(f938,plain,
( spl6_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,[spl6_98])]) ).
fof(f370,plain,
( spl6_43
<=> ! [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,[spl6_43])]) ).
fof(f424,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 )
| ~ spl6_43
| ~ spl6_48 ),
inference(resolution,[],[f420,f371]) ).
fof(f371,plain,
( ! [X2,X3,X0,X1] :
( ~ contains_slb(X0,X2)
| lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
| X1 = X2 )
| ~ spl6_43 ),
inference(avatar_component_clause,[],[f370]) ).
fof(f902,plain,
( spl6_97
| ~ spl6_32
| ~ spl6_41 ),
inference(avatar_split_clause,[],[f364,f354,f306,f900]) ).
fof(f900,plain,
( spl6_97
<=> ! [X4,X0,X3,X2,X1] :
( pair_in_list(X0,sK4(insert_slb(X0,pair(X1,X2))),sK5(insert_slb(X0,pair(X1,X2))))
| sK5(insert_slb(X0,pair(X1,X2))) = X2
| check_cpq(triple(X3,insert_slb(X0,pair(X1,X2)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_97])]) ).
fof(f354,plain,
( spl6_41
<=> ! [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,[spl6_41])]) ).
fof(f364,plain,
( ! [X2,X3,X0,X1,X4] :
( pair_in_list(X0,sK4(insert_slb(X0,pair(X1,X2))),sK5(insert_slb(X0,pair(X1,X2))))
| sK5(insert_slb(X0,pair(X1,X2))) = X2
| check_cpq(triple(X3,insert_slb(X0,pair(X1,X2)),X4)) )
| ~ spl6_32
| ~ spl6_41 ),
inference(resolution,[],[f355,f307]) ).
fof(f355,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| pair_in_list(X0,X2,X4)
| X3 = X4 )
| ~ spl6_41 ),
inference(avatar_component_clause,[],[f354]) ).
fof(f898,plain,
( spl6_96
| ~ spl6_32
| ~ spl6_40 ),
inference(avatar_split_clause,[],[f361,f350,f306,f896]) ).
fof(f896,plain,
( spl6_96
<=> ! [X4,X0,X3,X2,X1] :
( pair_in_list(X0,sK4(insert_slb(X0,pair(X1,X2))),sK5(insert_slb(X0,pair(X1,X2))))
| sK4(insert_slb(X0,pair(X1,X2))) = X1
| check_cpq(triple(X3,insert_slb(X0,pair(X1,X2)),X4)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_96])]) ).
fof(f350,plain,
( spl6_40
<=> ! [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,[spl6_40])]) ).
fof(f361,plain,
( ! [X2,X3,X0,X1,X4] :
( pair_in_list(X0,sK4(insert_slb(X0,pair(X1,X2))),sK5(insert_slb(X0,pair(X1,X2))))
| sK4(insert_slb(X0,pair(X1,X2))) = X1
| check_cpq(triple(X3,insert_slb(X0,pair(X1,X2)),X4)) )
| ~ spl6_32
| ~ spl6_40 ),
inference(resolution,[],[f351,f307]) ).
fof(f351,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| pair_in_list(X0,X2,X4)
| X1 = X2 )
| ~ spl6_40 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f861,plain,
( spl6_95
| ~ spl6_39
| ~ spl6_49 ),
inference(avatar_split_clause,[],[f431,f426,f344,f859]) ).
fof(f859,plain,
( spl6_95
<=> ! [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,[spl6_95])]) ).
fof(f344,plain,
( spl6_39
<=> ! [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,[spl6_39])]) ).
fof(f431,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) )
| ~ spl6_39
| ~ spl6_49 ),
inference(resolution,[],[f427,f345]) ).
fof(f345,plain,
( ! [X2,X3,X0,X1] :
( contains_slb(X1,X3)
| triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3) )
| ~ spl6_39 ),
inference(avatar_component_clause,[],[f344]) ).
fof(f857,plain,
( spl6_94
| ~ spl6_29
| ~ spl6_49 ),
inference(avatar_split_clause,[],[f430,f426,f289,f855]) ).
fof(f855,plain,
( spl6_94
<=> ! [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,[spl6_94])]) ).
fof(f430,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) )
| ~ spl6_29
| ~ spl6_49 ),
inference(resolution,[],[f427,f290]) ).
fof(f853,plain,
( spl6_93
| ~ spl6_34
| ~ spl6_77 ),
inference(avatar_split_clause,[],[f777,f672,f319,f851]) ).
fof(f672,plain,
( spl6_77
<=> check_cpq(triple(insert_pqp(sK0,sK3),sK1,sK2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_77])]) ).
fof(f777,plain,
( ! [X0,X1] :
( ~ pair_in_list(sK1,X0,X1)
| less_than(X1,X0) )
| ~ spl6_34
| ~ spl6_77 ),
inference(resolution,[],[f674,f320]) ).
fof(f674,plain,
( check_cpq(triple(insert_pqp(sK0,sK3),sK1,sK2))
| ~ spl6_77 ),
inference(avatar_component_clause,[],[f672]) ).
fof(f829,plain,
( spl6_92
| ~ spl6_12
| ~ spl6_54 ),
inference(avatar_split_clause,[],[f463,f458,f206,f827]) ).
fof(f827,plain,
( spl6_92
<=> ! [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,[spl6_92])]) ).
fof(f463,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))) )
| ~ spl6_12
| ~ spl6_54 ),
inference(resolution,[],[f459,f207]) ).
fof(f825,plain,
( spl6_91
| ~ spl6_22
| ~ spl6_23
| ~ spl6_51 ),
inference(avatar_split_clause,[],[f452,f439,f252,f248,f823]) ).
fof(f823,plain,
( spl6_91
<=> ! [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,[spl6_91])]) ).
fof(f439,plain,
( spl6_51
<=> ! [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,[spl6_51])]) ).
fof(f452,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) )
| ~ spl6_22
| ~ spl6_23
| ~ spl6_51 ),
inference(forward_demodulation,[],[f451,f249]) ).
fof(f451,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) )
| ~ spl6_23
| ~ spl6_51 ),
inference(superposition,[],[f440,f253]) ).
fof(f440,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) )
| ~ spl6_51 ),
inference(avatar_component_clause,[],[f439]) ).
fof(f821,plain,
( spl6_90
| ~ spl6_22
| ~ spl6_23
| ~ spl6_50 ),
inference(avatar_split_clause,[],[f447,f435,f252,f248,f819]) ).
fof(f819,plain,
( spl6_90
<=> ! [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,[spl6_90])]) ).
fof(f435,plain,
( spl6_50
<=> ! [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,[spl6_50])]) ).
fof(f447,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) )
| ~ spl6_22
| ~ spl6_23
| ~ spl6_50 ),
inference(forward_demodulation,[],[f446,f249]) ).
fof(f446,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) )
| ~ spl6_23
| ~ spl6_50 ),
inference(superposition,[],[f436,f253]) ).
fof(f436,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) )
| ~ spl6_50 ),
inference(avatar_component_clause,[],[f435]) ).
fof(f803,plain,
( spl6_89
| ~ spl6_32
| ~ spl6_44 ),
inference(avatar_split_clause,[],[f393,f374,f306,f801]) ).
fof(f801,plain,
( spl6_89
<=> ! [X4,X0,X3,X2,X1] :
( check_cpq(triple(X0,X1,X2))
| ~ less_than(X3,X4)
| pair_in_list(insert_slb(X1,pair(X4,X3)),sK4(insert_slb(X1,pair(X4,X3))),sK5(insert_slb(X1,pair(X4,X3)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_89])]) ).
fof(f374,plain,
( spl6_44
<=> ! [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,[spl6_44])]) ).
fof(f393,plain,
( ! [X2,X3,X0,X1,X4] :
( check_cpq(triple(X0,X1,X2))
| ~ less_than(X3,X4)
| pair_in_list(insert_slb(X1,pair(X4,X3)),sK4(insert_slb(X1,pair(X4,X3))),sK5(insert_slb(X1,pair(X4,X3)))) )
| ~ spl6_32
| ~ spl6_44 ),
inference(resolution,[],[f375,f307]) ).
fof(f375,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) )
| ~ spl6_44 ),
inference(avatar_component_clause,[],[f374]) ).
fof(f771,plain,
( spl6_88
| ~ spl6_39
| ~ spl6_43 ),
inference(avatar_split_clause,[],[f391,f370,f344,f769]) ).
fof(f769,plain,
( spl6_88
<=> ! [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,[spl6_88])]) ).
fof(f391,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) )
| ~ spl6_39
| ~ spl6_43 ),
inference(resolution,[],[f371,f345]) ).
fof(f767,plain,
( spl6_87
| ~ spl6_29
| ~ spl6_43 ),
inference(avatar_split_clause,[],[f390,f370,f289,f765]) ).
fof(f765,plain,
( spl6_87
<=> ! [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,[spl6_87])]) ).
fof(f390,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) )
| ~ spl6_29
| ~ spl6_43 ),
inference(resolution,[],[f371,f290]) ).
fof(f763,plain,
( spl6_86
| ~ spl6_38
| ~ spl6_39 ),
inference(avatar_split_clause,[],[f348,f344,f338,f761]) ).
fof(f761,plain,
( spl6_86
<=> ! [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,[spl6_86])]) ).
fof(f348,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 )
| ~ spl6_38
| ~ spl6_39 ),
inference(resolution,[],[f345,f339]) ).
fof(f749,plain,
( spl6_85
| ~ spl6_32
| ~ spl6_42 ),
inference(avatar_split_clause,[],[f385,f366,f306,f747]) ).
fof(f747,plain,
( spl6_85
<=> ! [X0,X3,X2,X1] :
( check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| pair_in_list(insert_slb(X2,pair(X1,bottom)),sK4(insert_slb(X2,pair(X1,bottom))),sK5(insert_slb(X2,pair(X1,bottom)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_85])]) ).
fof(f385,plain,
( ! [X2,X3,X0,X1] :
( check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| pair_in_list(insert_slb(X2,pair(X1,bottom)),sK4(insert_slb(X2,pair(X1,bottom))),sK5(insert_slb(X2,pair(X1,bottom)))) )
| ~ spl6_32
| ~ spl6_42 ),
inference(superposition,[],[f307,f367]) ).
fof(f739,plain,
( spl6_84
| ~ spl6_12
| ~ spl6_51 ),
inference(avatar_split_clause,[],[f449,f439,f206,f737]) ).
fof(f737,plain,
( spl6_84
<=> ! [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,[spl6_84])]) ).
fof(f449,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)) )
| ~ spl6_12
| ~ spl6_51 ),
inference(resolution,[],[f440,f207]) ).
fof(f728,plain,
( spl6_83
| ~ spl6_32
| ~ spl6_36 ),
inference(avatar_split_clause,[],[f336,f329,f306,f726]) ).
fof(f726,plain,
( spl6_83
<=> ! [X0,X1,X3] :
( ~ strictly_less_than(X0,X1)
| pair_in_list(insert_slb(X3,pair(X0,X1)),sK4(insert_slb(X3,pair(X0,X1))),sK5(insert_slb(X3,pair(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_83])]) ).
fof(f336,plain,
( ! [X3,X0,X1] :
( ~ strictly_less_than(X0,X1)
| pair_in_list(insert_slb(X3,pair(X0,X1)),sK4(insert_slb(X3,pair(X0,X1))),sK5(insert_slb(X3,pair(X0,X1)))) )
| ~ spl6_32
| ~ spl6_36 ),
inference(resolution,[],[f330,f307]) ).
fof(f724,plain,
( ~ spl6_7
| spl6_76 ),
inference(avatar_contradiction_clause,[],[f718]) ).
fof(f718,plain,
( $false
| ~ spl6_7
| spl6_76 ),
inference(resolution,[],[f670,f187]) ).
fof(f187,plain,
( ! [X0] : less_than(bottom,X0)
| ~ spl6_7 ),
inference(avatar_component_clause,[],[f186]) ).
fof(f186,plain,
( spl6_7
<=> ! [X0] : less_than(bottom,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_7])]) ).
fof(f670,plain,
( ~ less_than(bottom,sK3)
| spl6_76 ),
inference(avatar_component_clause,[],[f668]) ).
fof(f668,plain,
( spl6_76
<=> less_than(bottom,sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_76])]) ).
fof(f711,plain,
( spl6_82
| ~ spl6_16
| ~ spl6_22
| ~ spl6_49 ),
inference(avatar_split_clause,[],[f433,f426,f248,f223,f709]) ).
fof(f709,plain,
( spl6_82
<=> ! [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,[spl6_82])]) ).
fof(f433,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 )
| ~ spl6_16
| ~ spl6_22
| ~ spl6_49 ),
inference(forward_demodulation,[],[f429,f249]) ).
fof(f429,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 )
| ~ spl6_16
| ~ spl6_49 ),
inference(resolution,[],[f427,f224]) ).
fof(f703,plain,
( spl6_81
| ~ spl6_33
| ~ spl6_42 ),
inference(avatar_split_clause,[],[f384,f366,f312,f701]) ).
fof(f701,plain,
( spl6_81
<=> ! [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,[spl6_81])]) ).
fof(f312,plain,
( spl6_33
<=> ! [X2,X0,X1] :
( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_33])]) ).
fof(f384,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)) )
| ~ spl6_33
| ~ spl6_42 ),
inference(superposition,[],[f313,f367]) ).
fof(f313,plain,
( ! [X2,X0,X1] :
( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 )
| ~ spl6_33 ),
inference(avatar_component_clause,[],[f312]) ).
fof(f699,plain,
( spl6_80
| ~ spl6_31
| ~ spl6_33 ),
inference(avatar_split_clause,[],[f317,f312,f297,f697]) ).
fof(f697,plain,
( spl6_80
<=> ! [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,[spl6_80])]) ).
fof(f297,plain,
( spl6_31
<=> ! [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,[spl6_31])]) ).
fof(f317,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 )
| ~ spl6_31
| ~ spl6_33 ),
inference(superposition,[],[f298,f313]) ).
fof(f298,plain,
( ! [X0,X1] :
( succ_cpq(X0,remove_cpq(findmin_cpq_eff(X1),removemin_cpq_res(X1)))
| ~ succ_cpq(X0,X1) )
| ~ spl6_31 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f690,plain,
( spl6_79
| ~ spl6_34
| ~ spl6_45 ),
inference(avatar_split_clause,[],[f397,f378,f319,f688]) ).
fof(f688,plain,
( spl6_79
<=> ! [X5,X6,X4,X0,X3,X2,X1] :
( ~ check_cpq(triple(X0,X1,X2))
| ~ less_than(X3,X4)
| ~ pair_in_list(insert_slb(X1,pair(X4,X3)),X5,X6)
| less_than(X6,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_79])]) ).
fof(f378,plain,
( spl6_45
<=> ! [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,[spl6_45])]) ).
fof(f397,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] :
( ~ check_cpq(triple(X0,X1,X2))
| ~ less_than(X3,X4)
| ~ pair_in_list(insert_slb(X1,pair(X4,X3)),X5,X6)
| less_than(X6,X5) )
| ~ spl6_34
| ~ spl6_45 ),
inference(resolution,[],[f379,f320]) ).
fof(f379,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) )
| ~ spl6_45 ),
inference(avatar_component_clause,[],[f378]) ).
fof(f679,plain,
( spl6_78
| ~ spl6_12
| ~ spl6_47 ),
inference(avatar_split_clause,[],[f416,f410,f206,f677]) ).
fof(f677,plain,
( spl6_78
<=> ! [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,[spl6_78])]) ).
fof(f410,plain,
( spl6_47
<=> ! [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,[spl6_47])]) ).
fof(f416,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) )
| ~ spl6_12
| ~ spl6_47 ),
inference(resolution,[],[f411,f207]) ).
fof(f411,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)) )
| ~ spl6_47 ),
inference(avatar_component_clause,[],[f410]) ).
fof(f675,plain,
( ~ spl6_76
| spl6_77
| ~ spl6_2
| ~ spl6_73 ),
inference(avatar_split_clause,[],[f651,f644,f164,f672,f668]) ).
fof(f164,plain,
( spl6_2
<=> check_cpq(insert_cpq(triple(sK0,sK1,sK2),sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_2])]) ).
fof(f644,plain,
( spl6_73
<=> ! [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,[spl6_73])]) ).
fof(f651,plain,
( check_cpq(triple(insert_pqp(sK0,sK3),sK1,sK2))
| ~ less_than(bottom,sK3)
| ~ spl6_2
| ~ spl6_73 ),
inference(resolution,[],[f645,f166]) ).
fof(f166,plain,
( check_cpq(insert_cpq(triple(sK0,sK1,sK2),sK3))
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f645,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) )
| ~ spl6_73 ),
inference(avatar_component_clause,[],[f644]) ).
fof(f661,plain,
( spl6_75
| ~ spl6_34
| ~ spl6_42 ),
inference(avatar_split_clause,[],[f383,f366,f319,f659]) ).
fof(f383,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( ~ check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| ~ pair_in_list(insert_slb(X2,pair(X1,bottom)),X4,X5)
| less_than(X5,X4) )
| ~ spl6_34
| ~ spl6_42 ),
inference(superposition,[],[f320,f367]) ).
fof(f650,plain,
( spl6_74
| ~ spl6_42
| ~ spl6_45 ),
inference(avatar_split_clause,[],[f398,f378,f366,f648]) ).
fof(f398,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) )
| ~ spl6_42
| ~ spl6_45 ),
inference(superposition,[],[f379,f367]) ).
fof(f646,plain,
( spl6_73
| ~ spl6_42
| ~ spl6_44 ),
inference(avatar_split_clause,[],[f394,f374,f366,f644]) ).
fof(f394,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) )
| ~ spl6_42
| ~ spl6_44 ),
inference(superposition,[],[f375,f367]) ).
fof(f633,plain,
( spl6_72
| ~ spl6_16
| ~ spl6_23
| ~ spl6_43 ),
inference(avatar_split_clause,[],[f392,f370,f252,f223,f631]) ).
fof(f631,plain,
( spl6_72
<=> ! [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,[spl6_72])]) ).
fof(f392,plain,
( ! [X2,X3,X0,X1,X4] :
( lookup_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X1) = X2
| X1 = X3 )
| ~ spl6_16
| ~ spl6_23
| ~ spl6_43 ),
inference(forward_demodulation,[],[f389,f253]) ).
fof(f389,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 )
| ~ spl6_16
| ~ spl6_43 ),
inference(resolution,[],[f371,f224]) ).
fof(f599,plain,
( spl6_71
| ~ spl6_24
| ~ spl6_30 ),
inference(avatar_split_clause,[],[f357,f293,f256,f597]) ).
fof(f597,plain,
( spl6_71
<=> ! [X2,X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X2,X0)
| ~ less_than(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_71])]) ).
fof(f357,plain,
( ! [X2,X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X2,X0)
| ~ less_than(X2,X1) )
| ~ spl6_24
| ~ spl6_30 ),
inference(resolution,[],[f294,f257]) ).
fof(f592,plain,
( spl6_70
| ~ spl6_7
| ~ spl6_47 ),
inference(avatar_split_clause,[],[f414,f410,f186,f590]) ).
fof(f414,plain,
( ! [X2,X0,X1] : update_slb(insert_slb(X0,pair(X1,X2)),bottom) = insert_slb(update_slb(X0,bottom),pair(X1,X2))
| ~ spl6_7
| ~ spl6_47 ),
inference(resolution,[],[f411,f187]) ).
fof(f588,plain,
( spl6_69
| ~ spl6_6
| ~ spl6_47 ),
inference(avatar_split_clause,[],[f413,f410,f182,f586]) ).
fof(f182,plain,
( spl6_6
<=> ! [X0] : less_than(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_6])]) ).
fof(f413,plain,
( ! [X2,X0,X1] : insert_slb(update_slb(X0,X2),pair(X1,X2)) = update_slb(insert_slb(X0,pair(X1,X2)),X2)
| ~ spl6_6
| ~ spl6_47 ),
inference(resolution,[],[f411,f183]) ).
fof(f183,plain,
( ! [X0] : less_than(X0,X0)
| ~ spl6_6 ),
inference(avatar_component_clause,[],[f182]) ).
fof(f584,plain,
( spl6_68
| ~ spl6_25
| ~ spl6_42 ),
inference(avatar_split_clause,[],[f387,f366,f260,f582]) ).
fof(f582,plain,
( spl6_68
<=> ! [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,[spl6_68])]) ).
fof(f260,plain,
( spl6_25
<=> ! [X2,X0,X1,X3] :
( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_25])]) ).
fof(f387,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) )
| ~ spl6_25
| ~ spl6_42 ),
inference(superposition,[],[f261,f367]) ).
fof(f261,plain,
( ! [X2,X3,X0,X1] :
( ~ contains_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) )
| ~ spl6_25 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f580,plain,
( spl6_67
| ~ spl6_26
| ~ spl6_42 ),
inference(avatar_split_clause,[],[f386,f366,f264,f578]) ).
fof(f578,plain,
( spl6_67
<=> ! [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,[spl6_67])]) ).
fof(f264,plain,
( spl6_26
<=> ! [X0,X3,X2,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_26])]) ).
fof(f386,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) )
| ~ spl6_26
| ~ spl6_42 ),
inference(superposition,[],[f265,f367]) ).
fof(f265,plain,
( ! [X2,X3,X0,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) )
| ~ spl6_26 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f575,plain,
( spl6_66
| ~ spl6_15
| ~ spl6_28
| ~ spl6_31 ),
inference(avatar_split_clause,[],[f303,f297,f285,f219,f573]) ).
fof(f573,plain,
( spl6_66
<=> ! [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,[spl6_66])]) ).
fof(f219,plain,
( spl6_15
<=> ! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_15])]) ).
fof(f285,plain,
( spl6_28
<=> ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_28])]) ).
fof(f303,plain,
( ! [X2,X0,X1] :
( succ_cpq(X2,remove_cpq(triple(X0,create_slb,bad),bottom))
| ~ succ_cpq(X2,triple(X0,create_slb,X1)) )
| ~ spl6_15
| ~ spl6_28
| ~ spl6_31 ),
inference(forward_demodulation,[],[f301,f220]) ).
fof(f220,plain,
( ! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1))
| ~ spl6_15 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f301,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)) )
| ~ spl6_28
| ~ spl6_31 ),
inference(superposition,[],[f298,f286]) ).
fof(f286,plain,
( ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad)
| ~ spl6_28 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f568,plain,
( spl6_65
| ~ spl6_32
| ~ spl6_34 ),
inference(avatar_split_clause,[],[f323,f319,f306,f566]) ).
fof(f566,plain,
( spl6_65
<=> ! [X2,X0,X1] :
( ~ pair_in_list(X0,X1,X2)
| less_than(X2,X1)
| pair_in_list(X0,sK4(X0),sK5(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_65])]) ).
fof(f323,plain,
( ! [X2,X0,X1] :
( ~ pair_in_list(X0,X1,X2)
| less_than(X2,X1)
| pair_in_list(X0,sK4(X0),sK5(X0)) )
| ~ spl6_32
| ~ spl6_34 ),
inference(resolution,[],[f320,f307]) ).
fof(f563,plain,
( spl6_64
| ~ spl6_14
| ~ spl6_28 ),
inference(avatar_split_clause,[],[f300,f285,f215,f561]) ).
fof(f215,plain,
( spl6_14
<=> ! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_14])]) ).
fof(f300,plain,
( ! [X2,X0,X1] :
( succ_cpq(X2,triple(X0,create_slb,bad))
| ~ succ_cpq(X2,triple(X0,create_slb,X1)) )
| ~ spl6_14
| ~ spl6_28 ),
inference(superposition,[],[f216,f286]) ).
fof(f216,plain,
( ! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) )
| ~ spl6_14 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f531,plain,
( ~ spl6_63
| ~ spl6_2
| ~ spl6_58 ),
inference(avatar_split_clause,[],[f507,f500,f164,f528]) ).
fof(f528,plain,
( spl6_63
<=> strictly_less_than(sK3,bottom) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_63])]) ).
fof(f507,plain,
( ~ strictly_less_than(sK3,bottom)
| ~ spl6_2
| ~ spl6_58 ),
inference(resolution,[],[f501,f166]) ).
fof(f526,plain,
( ~ spl6_10
| ~ spl6_62 ),
inference(avatar_contradiction_clause,[],[f522]) ).
fof(f522,plain,
( $false
| ~ spl6_10
| ~ spl6_62 ),
inference(resolution,[],[f520,f199]) ).
fof(f520,plain,
( ! [X2,X0,X1] : ~ check_cpq(triple(X0,X1,X2))
| ~ spl6_62 ),
inference(avatar_component_clause,[],[f519]) ).
fof(f519,plain,
( spl6_62
<=> ! [X2,X0,X1] : ~ check_cpq(triple(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_62])]) ).
fof(f521,plain,
( spl6_61
| spl6_62
| ~ spl6_36
| ~ spl6_45 ),
inference(avatar_split_clause,[],[f396,f378,f329,f519,f516]) ).
fof(f396,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ check_cpq(triple(X0,X1,X2))
| ~ less_than(X3,X4)
| ~ strictly_less_than(X4,X3) )
| ~ spl6_36
| ~ spl6_45 ),
inference(resolution,[],[f379,f330]) ).
fof(f514,plain,
( spl6_60
| ~ spl6_4
| ~ spl6_39 ),
inference(avatar_split_clause,[],[f347,f344,f174,f512]) ).
fof(f512,plain,
( spl6_60
<=> ! [X2,X0,X1] : triple(X0,create_slb,bad) = remove_cpq(triple(X0,create_slb,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_60])]) ).
fof(f174,plain,
( spl6_4
<=> ! [X0] : ~ contains_slb(create_slb,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_4])]) ).
fof(f347,plain,
( ! [X2,X0,X1] : triple(X0,create_slb,bad) = remove_cpq(triple(X0,create_slb,X1),X2)
| ~ spl6_4
| ~ spl6_39 ),
inference(resolution,[],[f345,f175]) ).
fof(f175,plain,
( ! [X0] : ~ contains_slb(create_slb,X0)
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f174]) ).
fof(f506,plain,
( spl6_59
| ~ spl6_19
| ~ spl6_42 ),
inference(avatar_split_clause,[],[f388,f366,f235,f504]) ).
fof(f235,plain,
( spl6_19
<=> ! [X2,X0,X1] :
( bad = X2
| ok(triple(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_19])]) ).
fof(f388,plain,
( ! [X2,X3,X0,X1] :
( ok(insert_cpq(triple(X0,X2,X3),X1))
| bad = X3 )
| ~ spl6_19
| ~ spl6_42 ),
inference(superposition,[],[f236,f367]) ).
fof(f236,plain,
( ! [X2,X0,X1] :
( ok(triple(X0,X1,X2))
| bad = X2 )
| ~ spl6_19 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f502,plain,
( spl6_58
| ~ spl6_36
| ~ spl6_42 ),
inference(avatar_split_clause,[],[f381,f366,f329,f500]) ).
fof(f381,plain,
( ! [X2,X3,X0,X1] :
( ~ check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| ~ strictly_less_than(X1,bottom) )
| ~ spl6_36
| ~ spl6_42 ),
inference(superposition,[],[f330,f367]) ).
fof(f490,plain,
( spl6_57
| ~ spl6_12
| ~ spl6_27 ),
inference(avatar_split_clause,[],[f282,f279,f206,f488]) ).
fof(f282,plain,
( ! [X2,X0,X1] :
( check_cpq(triple(X0,X1,X2))
| less_than(sK4(X1),sK5(X1)) )
| ~ spl6_12
| ~ spl6_27 ),
inference(resolution,[],[f280,f207]) ).
fof(f474,plain,
( spl6_56
| ~ spl6_12
| ~ spl6_24 ),
inference(avatar_split_clause,[],[f275,f256,f206,f472]) ).
fof(f275,plain,
( ! [X2,X0,X1] :
( less_than(X0,X1)
| ~ less_than(X0,X2)
| less_than(X1,X2) )
| ~ spl6_12
| ~ spl6_24 ),
inference(resolution,[],[f257,f207]) ).
fof(f469,plain,
( spl6_55
| ~ spl6_11
| ~ spl6_42 ),
inference(avatar_split_clause,[],[f382,f366,f202,f467]) ).
fof(f202,plain,
( spl6_11
<=> ! [X0,X1] : ~ ok(triple(X0,X1,bad)) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_11])]) ).
fof(f382,plain,
( ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,bad),X1))
| ~ spl6_11
| ~ spl6_42 ),
inference(superposition,[],[f203,f367]) ).
fof(f203,plain,
( ! [X0,X1] : ~ ok(triple(X0,X1,bad))
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f202]) ).
fof(f460,plain,
spl6_54,
inference(avatar_split_clause,[],[f136,f458]) ).
fof(f136,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,[],[f78]) ).
fof(f78,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,[],[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(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(f456,plain,
spl6_53,
inference(avatar_split_clause,[],[f135,f454]) ).
fof(f135,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,[],[f76]) ).
fof(f76,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,[],[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(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(f445,plain,
( spl6_52
| ~ spl6_30
| ~ spl6_35 ),
inference(avatar_split_clause,[],[f402,f325,f293,f443]) ).
fof(f443,plain,
( spl6_52
<=> ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(bottom,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_52])]) ).
fof(f325,plain,
( spl6_35
<=> ! [X0,X1] :
( less_than(X0,X1)
| ~ less_than(X0,bottom) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_35])]) ).
fof(f402,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(bottom,X0) )
| ~ spl6_30
| ~ spl6_35 ),
inference(resolution,[],[f326,f294]) ).
fof(f326,plain,
( ! [X0,X1] :
( ~ less_than(X0,bottom)
| less_than(X0,X1) )
| ~ spl6_35 ),
inference(avatar_component_clause,[],[f325]) ).
fof(f441,plain,
spl6_51,
inference(avatar_split_clause,[],[f138,f439]) ).
fof(f138,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,[],[f82]) ).
fof(f82,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,[],[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(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(f437,plain,
spl6_50,
inference(avatar_split_clause,[],[f137,f435]) ).
fof(f137,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,[],[f80]) ).
fof(f80,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,[],[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(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(f428,plain,
spl6_49,
inference(avatar_split_clause,[],[f133,f426]) ).
fof(f133,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,[],[f72]) ).
fof(f72,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,[],[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(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(f421,plain,
spl6_48,
inference(avatar_split_clause,[],[f134,f419]) ).
fof(f134,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,[],[f74]) ).
fof(f74,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,[],[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(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(f412,plain,
spl6_47,
inference(avatar_split_clause,[],[f131,f410]) ).
fof(f131,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,[],[f68]) ).
fof(f68,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(f408,plain,
spl6_46,
inference(avatar_split_clause,[],[f130,f406]) ).
fof(f406,plain,
( spl6_46
<=> ! [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,[spl6_46])]) ).
fof(f130,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,[],[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,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(f380,plain,
spl6_45,
inference(avatar_split_clause,[],[f146,f378]) ).
fof(f146,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,[],[f95]) ).
fof(f95,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,[],[f84]) ).
fof(f84,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(f376,plain,
spl6_44,
inference(avatar_split_clause,[],[f145,f374]) ).
fof(f145,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,[],[f95]) ).
fof(f372,plain,
spl6_43,
inference(avatar_split_clause,[],[f132,f370]) ).
fof(f132,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,[],[f70]) ).
fof(f70,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,[],[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(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(f368,plain,
spl6_42,
inference(avatar_split_clause,[],[f127,f366]) ).
fof(f127,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(f356,plain,
spl6_41,
inference(avatar_split_clause,[],[f148,f354]) ).
fof(f148,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,[],[f97]) ).
fof(f97,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,[],[f96]) ).
fof(f96,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(f352,plain,
spl6_40,
inference(avatar_split_clause,[],[f147,f350]) ).
fof(f147,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,[],[f97]) ).
fof(f346,plain,
spl6_39,
inference(avatar_split_clause,[],[f129,f344]) ).
fof(f129,plain,
! [X2,X3,X0,X1] :
( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f66]) ).
fof(f66,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(f340,plain,
spl6_38,
inference(avatar_split_clause,[],[f141,f338]) ).
fof(f141,plain,
! [X2,X3,X0,X1] :
( X1 = X2
| contains_slb(X0,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,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,[],[f93]) ).
fof(f93,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(f335,plain,
spl6_37,
inference(avatar_split_clause,[],[f149,f333]) ).
fof(f149,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,[],[f97]) ).
fof(f331,plain,
spl6_36,
inference(avatar_split_clause,[],[f144,f329]) ).
fof(f144,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,[],[f83]) ).
fof(f83,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(f327,plain,
( spl6_35
| ~ spl6_7
| ~ spl6_24 ),
inference(avatar_split_clause,[],[f274,f256,f186,f325]) ).
fof(f274,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| ~ less_than(X0,bottom) )
| ~ spl6_7
| ~ spl6_24 ),
inference(resolution,[],[f257,f187]) ).
fof(f321,plain,
spl6_34,
inference(avatar_split_clause,[],[f100,f319]) ).
fof(f100,plain,
! [X2,X0,X1,X6,X5] :
( less_than(X6,X5)
| ~ pair_in_list(X1,X5,X6)
| ~ check_cpq(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( ( check_cpq(triple(X0,X1,X2))
| ( ~ less_than(sK5(X1),sK4(X1))
& pair_in_list(X1,sK4(X1),sK5(X1)) ) )
& ( ! [X5,X6] :
( less_than(X6,X5)
| ~ pair_in_list(X1,X5,X6) )
| ~ check_cpq(triple(X0,X1,X2)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f89,f90]) ).
fof(f90,plain,
! [X1] :
( ? [X3,X4] :
( ~ less_than(X4,X3)
& pair_in_list(X1,X3,X4) )
=> ( ~ less_than(sK5(X1),sK4(X1))
& pair_in_list(X1,sK4(X1),sK5(X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
! [X0,X1,X2] :
( ( check_cpq(triple(X0,X1,X2))
| ? [X3,X4] :
( ~ less_than(X4,X3)
& pair_in_list(X1,X3,X4) ) )
& ( ! [X5,X6] :
( less_than(X6,X5)
| ~ pair_in_list(X1,X5,X6) )
| ~ check_cpq(triple(X0,X1,X2)) ) ),
inference(rectify,[],[f88]) ).
fof(f88,plain,
! [X0,X1,X2] :
( ( check_cpq(triple(X0,X1,X2))
| ? [X3,X4] :
( ~ less_than(X4,X3)
& pair_in_list(X1,X3,X4) ) )
& ( ! [X3,X4] :
( less_than(X4,X3)
| ~ pair_in_list(X1,X3,X4) )
| ~ check_cpq(triple(X0,X1,X2)) ) ),
inference(nnf_transformation,[],[f55]) ).
fof(f55,plain,
! [X0,X1,X2] :
( check_cpq(triple(X0,X1,X2))
<=> ! [X3,X4] :
( less_than(X4,X3)
| ~ pair_in_list(X1,X3,X4) ) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0,X1,X2] :
( check_cpq(triple(X0,X1,X2))
<=> ! [X3,X4] :
( pair_in_list(X1,X3,X4)
=> less_than(X4,X3) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l26_li4142) ).
fof(f314,plain,
spl6_33,
inference(avatar_split_clause,[],[f154,f312]) ).
fof(f154,plain,
! [X2,X0,X1] :
( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(definition_unfolding,[],[f128,f109]) ).
fof(f109,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(f128,plain,
! [X2,X0,X1] :
( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(cnf_transformation,[],[f65]) ).
fof(f65,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(f308,plain,
spl6_32,
inference(avatar_split_clause,[],[f101,f306]) ).
fof(f101,plain,
! [X2,X0,X1] :
( check_cpq(triple(X0,X1,X2))
| pair_in_list(X1,sK4(X1),sK5(X1)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f299,plain,
spl6_31,
inference(avatar_split_clause,[],[f153,f297]) ).
fof(f153,plain,
! [X0,X1] :
( succ_cpq(X0,remove_cpq(findmin_cpq_eff(X1),removemin_cpq_res(X1)))
| ~ succ_cpq(X0,X1) ),
inference(definition_unfolding,[],[f116,f151]) ).
fof(f151,plain,
! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),removemin_cpq_res(X0)),
inference(definition_unfolding,[],[f110,f109]) ).
fof(f110,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(f116,plain,
! [X0,X1] :
( succ_cpq(X0,removemin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f56]) ).
fof(f56,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(f295,plain,
( spl6_30
| ~ spl6_12
| ~ spl6_21 ),
inference(avatar_split_clause,[],[f272,f244,f206,f293]) ).
fof(f244,plain,
( spl6_21
<=> ! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_21])]) ).
fof(f272,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(X1,X0) )
| ~ spl6_12
| ~ spl6_21 ),
inference(duplicate_literal_removal,[],[f269]) ).
fof(f269,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(X1,X0)
| less_than(X0,X1) )
| ~ spl6_12
| ~ spl6_21 ),
inference(resolution,[],[f245,f207]) ).
fof(f245,plain,
( ! [X0,X1] :
( ~ less_than(X0,X1)
| less_than(X1,X0)
| strictly_less_than(X0,X1) )
| ~ spl6_21 ),
inference(avatar_component_clause,[],[f244]) ).
fof(f291,plain,
spl6_29,
inference(avatar_split_clause,[],[f142,f289]) ).
fof(f142,plain,
! [X2,X3,X0,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ~ contains_slb(X0,X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f287,plain,
spl6_28,
inference(avatar_split_clause,[],[f114,f285]) ).
fof(f114,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(f281,plain,
spl6_27,
inference(avatar_split_clause,[],[f102,f279]) ).
fof(f102,plain,
! [X2,X0,X1] :
( check_cpq(triple(X0,X1,X2))
| ~ less_than(sK5(X1),sK4(X1)) ),
inference(cnf_transformation,[],[f91]) ).
fof(f266,plain,
spl6_26,
inference(avatar_split_clause,[],[f140,f264]) ).
fof(f140,plain,
! [X2,X3,X0,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,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(f262,plain,
spl6_25,
inference(avatar_split_clause,[],[f139,f260]) ).
fof(f139,plain,
! [X2,X3,X0,X1] :
( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f92]) ).
fof(f258,plain,
spl6_24,
inference(avatar_split_clause,[],[f126,f256]) ).
fof(f126,plain,
! [X2,X0,X1] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f64]) ).
fof(f64,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(flattening,[],[f63]) ).
fof(f63,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(f254,plain,
spl6_23,
inference(avatar_split_clause,[],[f122,f252]) ).
fof(f122,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(f250,plain,
spl6_22,
inference(avatar_split_clause,[],[f121,f248]) ).
fof(f121,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(f246,plain,
spl6_21,
inference(avatar_split_clause,[],[f118,f244]) ).
fof(f118,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f59]) ).
fof(f59,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(flattening,[],[f58]) ).
fof(f58,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,plain,
! [X0,X1] :
( ( ~ less_than(X1,X0)
& less_than(X0,X1) )
=> strictly_less_than(X0,X1) ),
inference(unused_predicate_definition_removal,[],[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(f241,plain,
spl6_20,
inference(avatar_split_clause,[],[f157,f239]) ).
fof(f157,plain,
! [X2,X0,X4] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4),
inference(equality_resolution,[],[f156]) ).
fof(f156,plain,
! [X2,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X4)),X2,X4)
| X1 != X2 ),
inference(equality_resolution,[],[f150]) ).
fof(f150,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| X3 != X4
| X1 != X2 ),
inference(cnf_transformation,[],[f97]) ).
fof(f237,plain,
spl6_19,
inference(avatar_split_clause,[],[f125,f235]) ).
fof(f125,plain,
! [X2,X0,X1] :
( bad = X2
| ok(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f62]) ).
fof(f62,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(f233,plain,
spl6_18,
inference(avatar_split_clause,[],[f124,f231]) ).
fof(f231,plain,
( spl6_18
<=> ! [X2,X0,X1] :
( succ_cpq(X0,remove_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_18])]) ).
fof(f124,plain,
! [X2,X0,X1] :
( succ_cpq(X0,remove_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f61]) ).
fof(f61,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(f229,plain,
spl6_17,
inference(avatar_split_clause,[],[f123,f227]) ).
fof(f227,plain,
( spl6_17
<=> ! [X2,X0,X1] :
( succ_cpq(X0,insert_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_17])]) ).
fof(f123,plain,
! [X2,X0,X1] :
( succ_cpq(X0,insert_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f60]) ).
fof(f60,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(f225,plain,
spl6_16,
inference(avatar_split_clause,[],[f155,f223]) ).
fof(f155,plain,
! [X2,X3,X0] : contains_slb(insert_slb(X0,pair(X2,X3)),X2),
inference(equality_resolution,[],[f143]) ).
fof(f143,plain,
! [X2,X3,X0,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| X1 != X2 ),
inference(cnf_transformation,[],[f94]) ).
fof(f221,plain,
spl6_15,
inference(avatar_split_clause,[],[f152,f219]) ).
fof(f152,plain,
! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)),
inference(definition_unfolding,[],[f113,f109]) ).
fof(f113,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(f217,plain,
spl6_14,
inference(avatar_split_clause,[],[f117,f215]) ).
fof(f117,plain,
! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f57]) ).
fof(f57,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(f212,plain,
spl6_13,
inference(avatar_split_clause,[],[f120,f210]) ).
fof(f120,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(f208,plain,
spl6_12,
inference(avatar_split_clause,[],[f115,f206]) ).
fof(f115,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(f204,plain,
spl6_11,
inference(avatar_split_clause,[],[f119,f202]) ).
fof(f119,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(f200,plain,
spl6_10,
inference(avatar_split_clause,[],[f112,f198]) ).
fof(f112,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(f196,plain,
spl6_9,
inference(avatar_split_clause,[],[f108,f194]) ).
fof(f108,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(f192,plain,
spl6_8,
inference(avatar_split_clause,[],[f111,f190]) ).
fof(f190,plain,
( spl6_8
<=> ! [X0,X1] : ~ pair_in_list(create_slb,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_8])]) ).
fof(f111,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(f188,plain,
spl6_7,
inference(avatar_split_clause,[],[f107,f186]) ).
fof(f107,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(f184,plain,
spl6_6,
inference(avatar_split_clause,[],[f106,f182]) ).
fof(f106,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(f180,plain,
spl6_5,
inference(avatar_split_clause,[],[f105,f178]) ).
fof(f105,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(f176,plain,
spl6_4,
inference(avatar_split_clause,[],[f104,f174]) ).
fof(f104,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(f172,plain,
~ spl6_3,
inference(avatar_split_clause,[],[f103,f169]) ).
fof(f169,plain,
( spl6_3
<=> isnonempty_slb(create_slb) ),
introduced(avatar_definition,[new_symbols(naming,[spl6_3])]) ).
fof(f103,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(f167,plain,
spl6_2,
inference(avatar_split_clause,[],[f99,f164]) ).
fof(f99,plain,
check_cpq(insert_cpq(triple(sK0,sK1,sK2),sK3)),
inference(cnf_transformation,[],[f87]) ).
fof(f87,plain,
( check_cpq(insert_cpq(triple(sK0,sK1,sK2),sK3))
& ~ check_cpq(triple(sK0,sK1,sK2)) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f54,f86,f85]) ).
fof(f85,plain,
( ? [X0,X1,X2] :
( ? [X3] : check_cpq(insert_cpq(triple(X0,X1,X2),X3))
& ~ check_cpq(triple(X0,X1,X2)) )
=> ( ? [X3] : check_cpq(insert_cpq(triple(sK0,sK1,sK2),X3))
& ~ check_cpq(triple(sK0,sK1,sK2)) ) ),
introduced(choice_axiom,[]) ).
fof(f86,plain,
( ? [X3] : check_cpq(insert_cpq(triple(sK0,sK1,sK2),X3))
=> check_cpq(insert_cpq(triple(sK0,sK1,sK2),sK3)) ),
introduced(choice_axiom,[]) ).
fof(f54,plain,
? [X0,X1,X2] :
( ? [X3] : check_cpq(insert_cpq(triple(X0,X1,X2),X3))
& ~ check_cpq(triple(X0,X1,X2)) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,negated_conjecture,
~ ! [X0,X1,X2] :
( ~ check_cpq(triple(X0,X1,X2))
=> ! [X3] : ~ check_cpq(insert_cpq(triple(X0,X1,X2),X3)) ),
inference(negated_conjecture,[],[f43]) ).
fof(f43,conjecture,
! [X0,X1,X2] :
( ~ check_cpq(triple(X0,X1,X2))
=> ! [X3] : ~ check_cpq(insert_cpq(triple(X0,X1,X2),X3)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l26_co) ).
fof(f162,plain,
~ spl6_1,
inference(avatar_split_clause,[],[f98,f159]) ).
fof(f98,plain,
~ check_cpq(triple(sK0,sK1,sK2)),
inference(cnf_transformation,[],[f87]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWV390+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.34 % Computer : n018.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Fri May 3 20:59:23 EDT 2024
% 0.14/0.34 % CPUTime :
% 0.14/0.34 % (6413)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.36 % (6418)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.36 % (6416)WARNING: value z3 for option sas not known
% 0.14/0.36 % (6414)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.36 % (6415)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.36 % (6416)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.36 % (6417)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.36 % (6420)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.36 % (6419)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.37 TRYING [1]
% 0.14/0.37 TRYING [2]
% 0.14/0.38 TRYING [3]
% 0.14/0.38 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [2]
% 0.14/0.40 TRYING [3]
% 0.20/0.41 % (6418)First to succeed.
% 0.20/0.41 % (6416)Also succeeded, but the first one will report.
% 0.20/0.42 % (6418)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-6413"
% 0.20/0.42 % (6418)Refutation found. Thanks to Tanya!
% 0.20/0.42 % SZS status Theorem for theBenchmark
% 0.20/0.42 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.42 % (6418)------------------------------
% 0.20/0.42 % (6418)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.20/0.42 % (6418)Termination reason: Refutation
% 0.20/0.42
% 0.20/0.42 % (6418)Memory used [KB]: 1705
% 0.20/0.42 % (6418)Time elapsed: 0.058 s
% 0.20/0.42 % (6418)Instructions burned: 125 (million)
% 0.20/0.42 % (6413)Success in time 0.072 s
%------------------------------------------------------------------------------