TSTP Solution File: SWV415+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWV415+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 : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 16:46:44 EDT 2024
% Result : Theorem 0.16s 0.38s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 170
% Syntax : Number of formulae : 525 ( 128 unt; 0 def)
% Number of atoms : 1357 ( 315 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1410 ( 578 ~; 632 |; 43 &)
% ( 121 <=>; 36 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 125 ( 123 usr; 112 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 8 con; 0-3 aty)
% Number of variables : 1266 (1256 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1068,plain,
$false,
inference(avatar_sat_refutation,[],[f208,f213,f217,f221,f225,f229,f233,f238,f242,f246,f250,f254,f258,f262,f266,f270,f275,f279,f283,f287,f291,f295,f299,f303,f307,f311,f315,f319,f328,f332,f336,f340,f344,f348,f352,f366,f371,f375,f379,f388,f402,f406,f410,f414,f418,f422,f452,f456,f460,f464,f472,f476,f482,f486,f494,f498,f502,f506,f512,f516,f546,f550,f554,f562,f569,f578,f582,f592,f596,f600,f618,f622,f634,f638,f647,f651,f658,f662,f669,f672,f688,f692,f710,f715,f719,f723,f727,f731,f735,f805,f841,f854,f858,f903,f907,f911,f919,f930,f934,f938,f960,f970,f982,f986,f1000,f1004,f1008,f1012,f1042,f1046,f1050,f1067]) ).
fof(f1067,plain,
~ spl5_106,
inference(avatar_contradiction_clause,[],[f1066]) ).
fof(f1066,plain,
( $false
| ~ spl5_106 ),
inference(equality_resolution,[],[f1003]) ).
fof(f1003,plain,
( ! [X0,X1] : i(insert_cpq(triple(sK0,sK1,sK2),sK3)) != i(insert_cpq(triple(X0,sK1,X1),sK3))
| ~ spl5_106 ),
inference(avatar_component_clause,[],[f1002]) ).
fof(f1002,plain,
( spl5_106
<=> ! [X0,X1] : i(insert_cpq(triple(sK0,sK1,sK2),sK3)) != i(insert_cpq(triple(X0,sK1,X1),sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_106])]) ).
fof(f1050,plain,
( spl5_111
| ~ spl5_15
| ~ spl5_70 ),
inference(avatar_split_clause,[],[f602,f598,f264,f1048]) ).
fof(f1048,plain,
( spl5_111
<=> ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1
| less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_111])]) ).
fof(f264,plain,
( spl5_15
<=> ! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_15])]) ).
fof(f598,plain,
( spl5_70
<=> ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_70])]) ).
fof(f602,plain,
( ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1
| less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0))) )
| ~ spl5_15
| ~ spl5_70 ),
inference(resolution,[],[f599,f265]) ).
fof(f265,plain,
( ! [X0,X1] :
( less_than(X1,X0)
| less_than(X0,X1) )
| ~ spl5_15 ),
inference(avatar_component_clause,[],[f264]) ).
fof(f599,plain,
( ! [X2,X0,X1] :
( ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),findmin_pqp_res(X0))
| findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),X2)
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 )
| ~ spl5_70 ),
inference(avatar_component_clause,[],[f598]) ).
fof(f1046,plain,
( spl5_110
| ~ spl5_31
| ~ spl5_32
| ~ spl5_67 ),
inference(avatar_split_clause,[],[f588,f580,f338,f334,f1044]) ).
fof(f1044,plain,
( spl5_110
<=> ! [X2,X4,X0,X3,X1] :
( remove_cpq(triple(X3,insert_slb(X0,pair(X1,X2)),X4),X1) = triple(remove_pqp(X3,X1),X0,X4)
| ~ less_than(X2,X1)
| ~ contains_slb(insert_slb(X0,pair(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_110])]) ).
fof(f334,plain,
( spl5_31
<=> ! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_31])]) ).
fof(f338,plain,
( spl5_32
<=> ! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_32])]) ).
fof(f580,plain,
( spl5_67
<=> ! [X0,X3,X2,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
| ~ less_than(lookup_slb(X1,X3),X3)
| ~ contains_slb(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_67])]) ).
fof(f588,plain,
( ! [X2,X3,X0,X1,X4] :
( remove_cpq(triple(X3,insert_slb(X0,pair(X1,X2)),X4),X1) = triple(remove_pqp(X3,X1),X0,X4)
| ~ less_than(X2,X1)
| ~ contains_slb(insert_slb(X0,pair(X1,X2)),X1) )
| ~ spl5_31
| ~ spl5_32
| ~ spl5_67 ),
inference(forward_demodulation,[],[f587,f335]) ).
fof(f335,plain,
( ! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0
| ~ spl5_31 ),
inference(avatar_component_clause,[],[f334]) ).
fof(f587,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ less_than(X2,X1)
| remove_cpq(triple(X3,insert_slb(X0,pair(X1,X2)),X4),X1) = triple(remove_pqp(X3,X1),remove_slb(insert_slb(X0,pair(X1,X2)),X1),X4)
| ~ contains_slb(insert_slb(X0,pair(X1,X2)),X1) )
| ~ spl5_32
| ~ spl5_67 ),
inference(superposition,[],[f581,f339]) ).
fof(f339,plain,
( ! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2
| ~ spl5_32 ),
inference(avatar_component_clause,[],[f338]) ).
fof(f581,plain,
( ! [X2,X3,X0,X1] :
( ~ less_than(lookup_slb(X1,X3),X3)
| remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
| ~ contains_slb(X1,X3) )
| ~ spl5_67 ),
inference(avatar_component_clause,[],[f580]) ).
fof(f1042,plain,
( spl5_109
| ~ spl5_31
| ~ spl5_32
| ~ spl5_66 ),
inference(avatar_split_clause,[],[f584,f576,f338,f334,f1040]) ).
fof(f1040,plain,
( spl5_109
<=> ! [X2,X4,X0,X3,X1] :
( remove_cpq(triple(X3,insert_slb(X0,pair(X1,X2)),X4),X1) = triple(remove_pqp(X3,X1),X0,bad)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X2)),X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_109])]) ).
fof(f576,plain,
( spl5_66
<=> ! [X0,X3,X2,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
| ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_slb(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_66])]) ).
fof(f584,plain,
( ! [X2,X3,X0,X1,X4] :
( remove_cpq(triple(X3,insert_slb(X0,pair(X1,X2)),X4),X1) = triple(remove_pqp(X3,X1),X0,bad)
| ~ strictly_less_than(X1,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X2)),X1) )
| ~ spl5_31
| ~ spl5_32
| ~ spl5_66 ),
inference(forward_demodulation,[],[f583,f335]) ).
fof(f583,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ strictly_less_than(X1,X2)
| remove_cpq(triple(X3,insert_slb(X0,pair(X1,X2)),X4),X1) = triple(remove_pqp(X3,X1),remove_slb(insert_slb(X0,pair(X1,X2)),X1),bad)
| ~ contains_slb(insert_slb(X0,pair(X1,X2)),X1) )
| ~ spl5_32
| ~ spl5_66 ),
inference(superposition,[],[f577,f339]) ).
fof(f577,plain,
( ! [X2,X3,X0,X1] :
( ~ strictly_less_than(X3,lookup_slb(X1,X3))
| remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),bad)
| ~ contains_slb(X1,X3) )
| ~ spl5_66 ),
inference(avatar_component_clause,[],[f576]) ).
fof(f1012,plain,
( spl5_108
| ~ spl5_52
| ~ spl5_57 ),
inference(avatar_split_clause,[],[f531,f500,f474,f1010]) ).
fof(f1010,plain,
( spl5_108
<=> ! [X5,X4,X0,X3,X2,X1] :
( lookup_slb(insert_slb(X0,pair(X1,X2)),X3) = lookup_slb(X0,X3)
| X1 = X3
| triple(X4,X0,bad) = remove_cpq(triple(X4,X0,X5),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_108])]) ).
fof(f474,plain,
( spl5_52
<=> ! [X0,X3,X2,X1] :
( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_52])]) ).
fof(f500,plain,
( spl5_57
<=> ! [X0,X3,X2,X1] :
( lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
| ~ contains_slb(X0,X2)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_57])]) ).
fof(f531,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( lookup_slb(insert_slb(X0,pair(X1,X2)),X3) = lookup_slb(X0,X3)
| X1 = X3
| triple(X4,X0,bad) = remove_cpq(triple(X4,X0,X5),X3) )
| ~ spl5_52
| ~ spl5_57 ),
inference(resolution,[],[f501,f475]) ).
fof(f475,plain,
( ! [X2,X3,X0,X1] :
( contains_slb(X1,X3)
| triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3) )
| ~ spl5_52 ),
inference(avatar_component_clause,[],[f474]) ).
fof(f501,plain,
( ! [X2,X3,X0,X1] :
( ~ contains_slb(X0,X2)
| lookup_slb(insert_slb(X0,pair(X1,X3)),X2) = lookup_slb(X0,X2)
| X1 = X2 )
| ~ spl5_57 ),
inference(avatar_component_clause,[],[f500]) ).
fof(f1008,plain,
( spl5_107
| ~ spl5_38
| ~ spl5_57 ),
inference(avatar_split_clause,[],[f530,f500,f373,f1006]) ).
fof(f1006,plain,
( spl5_107
<=> ! [X3,X4,X0,X5,X2,X1] :
( lookup_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X5) = lookup_slb(insert_slb(X0,pair(X1,X2)),X5)
| X3 = X5
| ~ contains_slb(X0,X5) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_107])]) ).
fof(f373,plain,
( spl5_38
<=> ! [X0,X3,X2,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ~ contains_slb(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_38])]) ).
fof(f530,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( lookup_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X5) = lookup_slb(insert_slb(X0,pair(X1,X2)),X5)
| X3 = X5
| ~ contains_slb(X0,X5) )
| ~ spl5_38
| ~ spl5_57 ),
inference(resolution,[],[f501,f374]) ).
fof(f374,plain,
( ! [X2,X3,X0,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ~ contains_slb(X0,X2) )
| ~ spl5_38 ),
inference(avatar_component_clause,[],[f373]) ).
fof(f1004,plain,
( spl5_106
| ~ spl5_56
| ~ spl5_95 ),
inference(avatar_split_clause,[],[f950,f905,f496,f1002]) ).
fof(f496,plain,
( spl5_56
<=> ! [X0,X3,X2,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_56])]) ).
fof(f905,plain,
( spl5_95
<=> ! [X4,X2,X3] : i(insert_cpq(triple(sK0,sK1,sK2),sK3)) != i(triple(X2,insert_slb(sK1,pair(sK3,X3)),X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_95])]) ).
fof(f950,plain,
( ! [X0,X1] : i(insert_cpq(triple(sK0,sK1,sK2),sK3)) != i(insert_cpq(triple(X0,sK1,X1),sK3))
| ~ spl5_56
| ~ spl5_95 ),
inference(superposition,[],[f906,f497]) ).
fof(f497,plain,
( ! [X2,X3,X0,X1] : insert_cpq(triple(X0,X1,X2),X3) = triple(insert_pqp(X0,X3),insert_slb(X1,pair(X3,bottom)),X2)
| ~ spl5_56 ),
inference(avatar_component_clause,[],[f496]) ).
fof(f906,plain,
( ! [X2,X3,X4] : i(insert_cpq(triple(sK0,sK1,sK2),sK3)) != i(triple(X2,insert_slb(sK1,pair(sK3,X3)),X4))
| ~ spl5_95 ),
inference(avatar_component_clause,[],[f905]) ).
fof(f1000,plain,
( spl5_105
| ~ spl5_50
| ~ spl5_52 ),
inference(avatar_split_clause,[],[f478,f474,f462,f998]) ).
fof(f998,plain,
( spl5_105
<=> ! [X3,X4,X0,X5,X2,X1] :
( triple(X0,insert_slb(X1,pair(X2,X3)),bad) = remove_cpq(triple(X0,insert_slb(X1,pair(X2,X3)),X4),X5)
| contains_slb(X1,X5)
| X2 = X5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_105])]) ).
fof(f462,plain,
( spl5_50
<=> ! [X0,X3,X2,X1] :
( X1 = X2
| contains_slb(X0,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_50])]) ).
fof(f478,plain,
( ! [X2,X3,X0,X1,X4,X5] :
( triple(X0,insert_slb(X1,pair(X2,X3)),bad) = remove_cpq(triple(X0,insert_slb(X1,pair(X2,X3)),X4),X5)
| contains_slb(X1,X5)
| X2 = X5 )
| ~ spl5_50
| ~ spl5_52 ),
inference(resolution,[],[f475,f463]) ).
fof(f463,plain,
( ! [X2,X3,X0,X1] :
( ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| contains_slb(X0,X2)
| X1 = X2 )
| ~ spl5_50 ),
inference(avatar_component_clause,[],[f462]) ).
fof(f986,plain,
( spl5_104
| ~ spl5_15
| ~ spl5_67 ),
inference(avatar_split_clause,[],[f585,f580,f264,f984]) ).
fof(f984,plain,
( spl5_104
<=> ! [X0,X3,X2,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
| ~ contains_slb(X1,X3)
| less_than(X3,lookup_slb(X1,X3)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_104])]) ).
fof(f585,plain,
( ! [X2,X3,X0,X1] :
( remove_cpq(triple(X0,X1,X2),X3) = triple(remove_pqp(X0,X3),remove_slb(X1,X3),X2)
| ~ contains_slb(X1,X3)
| less_than(X3,lookup_slb(X1,X3)) )
| ~ spl5_15
| ~ spl5_67 ),
inference(resolution,[],[f581,f265]) ).
fof(f982,plain,
( spl5_103
| ~ spl5_22
| ~ spl5_55 ),
inference(avatar_split_clause,[],[f519,f492,f293,f980]) ).
fof(f980,plain,
( spl5_103
<=> ! [X2,X0,X1] :
( sK4(X1,X2) = X0
| remove_pq(insert_pq(X1,X0),sK4(X1,X2)) = insert_pq(remove_pq(X1,sK4(X1,X2)),X0)
| issmallestelement_pq(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_103])]) ).
fof(f293,plain,
( spl5_22
<=> ! [X0,X1] :
( issmallestelement_pq(X0,X1)
| contains_pq(X0,sK4(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_22])]) ).
fof(f492,plain,
( spl5_55
<=> ! [X2,X0,X1] :
( remove_pq(insert_pq(X0,X1),X2) = insert_pq(remove_pq(X0,X2),X1)
| X1 = X2
| ~ contains_pq(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_55])]) ).
fof(f519,plain,
( ! [X2,X0,X1] :
( sK4(X1,X2) = X0
| remove_pq(insert_pq(X1,X0),sK4(X1,X2)) = insert_pq(remove_pq(X1,sK4(X1,X2)),X0)
| issmallestelement_pq(X1,X2) )
| ~ spl5_22
| ~ spl5_55 ),
inference(resolution,[],[f493,f294]) ).
fof(f294,plain,
( ! [X0,X1] :
( contains_pq(X0,sK4(X0,X1))
| issmallestelement_pq(X0,X1) )
| ~ spl5_22 ),
inference(avatar_component_clause,[],[f293]) ).
fof(f493,plain,
( ! [X2,X0,X1] :
( ~ contains_pq(X0,X2)
| X1 = X2
| remove_pq(insert_pq(X0,X1),X2) = insert_pq(remove_pq(X0,X2),X1) )
| ~ spl5_55 ),
inference(avatar_component_clause,[],[f492]) ).
fof(f970,plain,
( spl5_102
| ~ spl5_27
| ~ spl5_55 ),
inference(avatar_split_clause,[],[f518,f492,f313,f968]) ).
fof(f968,plain,
( spl5_102
<=> ! [X0,X3,X2,X1] :
( X0 = X1
| remove_pq(insert_pq(insert_pq(X2,X3),X0),X1) = insert_pq(remove_pq(insert_pq(X2,X3),X1),X0)
| ~ contains_pq(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_102])]) ).
fof(f313,plain,
( spl5_27
<=> ! [X2,X0,X1] :
( contains_pq(insert_pq(X0,X1),X2)
| ~ contains_pq(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_27])]) ).
fof(f518,plain,
( ! [X2,X3,X0,X1] :
( X0 = X1
| remove_pq(insert_pq(insert_pq(X2,X3),X0),X1) = insert_pq(remove_pq(insert_pq(X2,X3),X1),X0)
| ~ contains_pq(X2,X1) )
| ~ spl5_27
| ~ spl5_55 ),
inference(resolution,[],[f493,f314]) ).
fof(f314,plain,
( ! [X2,X0,X1] :
( contains_pq(insert_pq(X0,X1),X2)
| ~ contains_pq(X0,X2) )
| ~ spl5_27 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f960,plain,
( spl5_101
| ~ spl5_21
| ~ spl5_31
| ~ spl5_65 ),
inference(avatar_split_clause,[],[f574,f567,f334,f289,f958]) ).
fof(f958,plain,
( spl5_101
<=> ! [X2,X4,X0,X3,X1] :
( remove_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X1) = insert_slb(X0,pair(X3,X4))
| X1 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_101])]) ).
fof(f289,plain,
( spl5_21
<=> ! [X2,X0,X3] : contains_slb(insert_slb(X0,pair(X2,X3)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_21])]) ).
fof(f567,plain,
( spl5_65
<=> ! [X0,X3,X2,X1] :
( remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
| ~ contains_slb(X0,X2)
| X1 = X2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_65])]) ).
fof(f574,plain,
( ! [X2,X3,X0,X1,X4] :
( remove_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X1) = insert_slb(X0,pair(X3,X4))
| X1 = X3 )
| ~ spl5_21
| ~ spl5_31
| ~ spl5_65 ),
inference(forward_demodulation,[],[f570,f335]) ).
fof(f570,plain,
( ! [X2,X3,X0,X1,X4] :
( remove_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X1) = insert_slb(remove_slb(insert_slb(X0,pair(X1,X2)),X1),pair(X3,X4))
| X1 = X3 )
| ~ spl5_21
| ~ spl5_65 ),
inference(resolution,[],[f568,f290]) ).
fof(f290,plain,
( ! [X2,X3,X0] : contains_slb(insert_slb(X0,pair(X2,X3)),X2)
| ~ spl5_21 ),
inference(avatar_component_clause,[],[f289]) ).
fof(f568,plain,
( ! [X2,X3,X0,X1] :
( ~ contains_slb(X0,X2)
| remove_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(remove_slb(X0,X2),pair(X1,X3))
| X1 = X2 )
| ~ spl5_65 ),
inference(avatar_component_clause,[],[f567]) ).
fof(f938,plain,
( spl5_100
| ~ spl5_46
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f523,f496,f420,f936]) ).
fof(f936,plain,
( spl5_100
<=> ! [X0,X3,X2,X1] :
( findmin_pqp_res(insert_pqp(X0,X1)) = removemin_cpq_res(insert_cpq(triple(X0,X2,X3),X1))
| create_slb = insert_slb(X2,pair(X1,bottom)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_100])]) ).
fof(f420,plain,
( spl5_46
<=> ! [X2,X0,X1] :
( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_46])]) ).
fof(f523,plain,
( ! [X2,X3,X0,X1] :
( findmin_pqp_res(insert_pqp(X0,X1)) = removemin_cpq_res(insert_cpq(triple(X0,X2,X3),X1))
| create_slb = insert_slb(X2,pair(X1,bottom)) )
| ~ spl5_46
| ~ spl5_56 ),
inference(superposition,[],[f421,f497]) ).
fof(f421,plain,
( ! [X2,X0,X1] :
( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 )
| ~ spl5_46 ),
inference(avatar_component_clause,[],[f420]) ).
fof(f934,plain,
( spl5_99
| ~ spl5_39
| ~ spl5_46 ),
inference(avatar_split_clause,[],[f448,f420,f377,f932]) ).
fof(f932,plain,
( spl5_99
<=> ! [X0,X3,X2,X1] :
( succ_cpq(X3,remove_cpq(findmin_cpq_eff(triple(X0,X1,X2)),findmin_pqp_res(X0)))
| ~ succ_cpq(X3,triple(X0,X1,X2))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_99])]) ).
fof(f377,plain,
( spl5_39
<=> ! [X0,X1] :
( succ_cpq(X0,remove_cpq(findmin_cpq_eff(X1),removemin_cpq_res(X1)))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_39])]) ).
fof(f448,plain,
( ! [X2,X3,X0,X1] :
( succ_cpq(X3,remove_cpq(findmin_cpq_eff(triple(X0,X1,X2)),findmin_pqp_res(X0)))
| ~ succ_cpq(X3,triple(X0,X1,X2))
| create_slb = X1 )
| ~ spl5_39
| ~ spl5_46 ),
inference(superposition,[],[f378,f421]) ).
fof(f378,plain,
( ! [X0,X1] :
( succ_cpq(X0,remove_cpq(findmin_cpq_eff(X1),removemin_cpq_res(X1)))
| ~ succ_cpq(X0,X1) )
| ~ spl5_39 ),
inference(avatar_component_clause,[],[f377]) ).
fof(f930,plain,
( spl5_98
| ~ spl5_22
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f443,f416,f293,f928]) ).
fof(f928,plain,
( spl5_98
<=> ! [X2,X0,X1] :
( contains_pq(X0,sK4(insert_pq(X0,X1),X2))
| sK4(insert_pq(X0,X1),X2) = X1
| issmallestelement_pq(insert_pq(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_98])]) ).
fof(f416,plain,
( spl5_45
<=> ! [X2,X0,X1] :
( X1 = X2
| contains_pq(X0,X2)
| ~ contains_pq(insert_pq(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_45])]) ).
fof(f443,plain,
( ! [X2,X0,X1] :
( contains_pq(X0,sK4(insert_pq(X0,X1),X2))
| sK4(insert_pq(X0,X1),X2) = X1
| issmallestelement_pq(insert_pq(X0,X1),X2) )
| ~ spl5_22
| ~ spl5_45 ),
inference(resolution,[],[f417,f294]) ).
fof(f417,plain,
( ! [X2,X0,X1] :
( ~ contains_pq(insert_pq(X0,X1),X2)
| contains_pq(X0,X2)
| X1 = X2 )
| ~ spl5_45 ),
inference(avatar_component_clause,[],[f416]) ).
fof(f919,plain,
( spl5_97
| ~ spl5_15
| ~ spl5_62 ),
inference(avatar_split_clause,[],[f557,f548,f264,f917]) ).
fof(f917,plain,
( spl5_97
<=> ! [X0,X3,X2,X1] :
( update_slb(insert_slb(X0,pair(X1,X2)),X3) = insert_slb(update_slb(X0,X3),pair(X1,X2))
| less_than(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_97])]) ).
fof(f548,plain,
( spl5_62
<=> ! [X0,X3,X2,X1] :
( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3))
| ~ less_than(X2,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_62])]) ).
fof(f557,plain,
( ! [X2,X3,X0,X1] :
( update_slb(insert_slb(X0,pair(X1,X2)),X3) = insert_slb(update_slb(X0,X3),pair(X1,X2))
| less_than(X2,X3) )
| ~ spl5_15
| ~ spl5_62 ),
inference(resolution,[],[f549,f265]) ).
fof(f549,plain,
( ! [X2,X3,X0,X1] :
( ~ less_than(X2,X3)
| update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X3)) )
| ~ spl5_62 ),
inference(avatar_component_clause,[],[f548]) ).
fof(f911,plain,
( spl5_96
| ~ spl5_56
| ~ spl5_60 ),
inference(avatar_split_clause,[],[f541,f514,f496,f909]) ).
fof(f909,plain,
( spl5_96
<=> ! [X0,X3,X2,X1] :
( check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| ~ check_cpq(triple(insert_pqp(X0,X1),X2,X3))
| ~ less_than(bottom,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_96])]) ).
fof(f514,plain,
( spl5_60
<=> ! [X4,X0,X3,X2,X1] :
( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ check_cpq(triple(X0,X1,X2))
| ~ less_than(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_60])]) ).
fof(f541,plain,
( ! [X2,X3,X0,X1] :
( check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| ~ check_cpq(triple(insert_pqp(X0,X1),X2,X3))
| ~ less_than(bottom,X1) )
| ~ spl5_56
| ~ spl5_60 ),
inference(superposition,[],[f515,f497]) ).
fof(f515,plain,
( ! [X2,X3,X0,X1,X4] :
( check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ check_cpq(triple(X0,X1,X2))
| ~ less_than(X4,X3) )
| ~ spl5_60 ),
inference(avatar_component_clause,[],[f514]) ).
fof(f907,plain,
( spl5_95
| ~ spl5_51
| ~ spl5_93 ),
inference(avatar_split_clause,[],[f883,f856,f470,f905]) ).
fof(f470,plain,
( spl5_51
<=> ! [X0,X1] : i(insert_cpq(triple(sK0,sK1,sK2),sK3)) != insert_pq(i(triple(X0,sK1,X1)),sK3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_51])]) ).
fof(f856,plain,
( spl5_93
<=> ! [X5,X3,X4,X0,X6,X2,X1] : insert_pq(i(triple(X0,X1,X4)),X2) = i(triple(X5,insert_slb(X1,pair(X2,X3)),X6)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_93])]) ).
fof(f883,plain,
( ! [X2,X3,X4] : i(insert_cpq(triple(sK0,sK1,sK2),sK3)) != i(triple(X2,insert_slb(sK1,pair(sK3,X3)),X4))
| ~ spl5_51
| ~ spl5_93 ),
inference(superposition,[],[f471,f857]) ).
fof(f857,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : insert_pq(i(triple(X0,X1,X4)),X2) = i(triple(X5,insert_slb(X1,pair(X2,X3)),X6))
| ~ spl5_93 ),
inference(avatar_component_clause,[],[f856]) ).
fof(f471,plain,
( ! [X0,X1] : i(insert_cpq(triple(sK0,sK1,sK2),sK3)) != insert_pq(i(triple(X0,sK1,X1)),sK3)
| ~ spl5_51 ),
inference(avatar_component_clause,[],[f470]) ).
fof(f903,plain,
( spl5_94
| ~ spl5_56
| ~ spl5_59 ),
inference(avatar_split_clause,[],[f538,f510,f496,f901]) ).
fof(f901,plain,
( spl5_94
<=> ! [X0,X3,X2,X1] :
( ~ check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| check_cpq(triple(insert_pqp(X0,X1),X2,X3))
| ~ less_than(bottom,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_94])]) ).
fof(f510,plain,
( spl5_59
<=> ! [X4,X0,X3,X2,X1] :
( check_cpq(triple(X0,X1,X2))
| ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ less_than(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_59])]) ).
fof(f538,plain,
( ! [X2,X3,X0,X1] :
( ~ check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| check_cpq(triple(insert_pqp(X0,X1),X2,X3))
| ~ less_than(bottom,X1) )
| ~ spl5_56
| ~ spl5_59 ),
inference(superposition,[],[f511,f497]) ).
fof(f511,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| check_cpq(triple(X0,X1,X2))
| ~ less_than(X4,X3) )
| ~ spl5_59 ),
inference(avatar_component_clause,[],[f510]) ).
fof(f858,plain,
( spl5_93
| ~ spl5_40
| ~ spl5_58 ),
inference(avatar_split_clause,[],[f534,f504,f386,f856]) ).
fof(f386,plain,
( spl5_40
<=> ! [X4,X0,X3,X2,X1] : i(triple(X0,X2,X3)) = i(triple(X1,X2,X4)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_40])]) ).
fof(f504,plain,
( spl5_58
<=> ! [X4,X0,X3,X2,X1] : i(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) = insert_pq(i(triple(X0,X1,X2)),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_58])]) ).
fof(f534,plain,
( ! [X2,X3,X0,X1,X6,X4,X5] : insert_pq(i(triple(X0,X1,X4)),X2) = i(triple(X5,insert_slb(X1,pair(X2,X3)),X6))
| ~ spl5_40
| ~ spl5_58 ),
inference(superposition,[],[f505,f387]) ).
fof(f387,plain,
( ! [X2,X3,X0,X1,X4] : i(triple(X0,X2,X3)) = i(triple(X1,X2,X4))
| ~ spl5_40 ),
inference(avatar_component_clause,[],[f386]) ).
fof(f505,plain,
( ! [X2,X3,X0,X1,X4] : i(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) = insert_pq(i(triple(X0,X1,X2)),X3)
| ~ spl5_58 ),
inference(avatar_component_clause,[],[f504]) ).
fof(f854,plain,
( spl5_92
| ~ spl5_40
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f524,f496,f386,f852]) ).
fof(f852,plain,
( spl5_92
<=> ! [X5,X4,X0,X3,X2,X1] : i(triple(X4,insert_slb(X2,pair(X1,bottom)),X5)) = i(insert_cpq(triple(X0,X2,X3),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_92])]) ).
fof(f524,plain,
( ! [X2,X3,X0,X1,X4,X5] : i(triple(X4,insert_slb(X2,pair(X1,bottom)),X5)) = i(insert_cpq(triple(X0,X2,X3),X1))
| ~ spl5_40
| ~ spl5_56 ),
inference(superposition,[],[f387,f497]) ).
fof(f841,plain,
( spl5_91
| ~ spl5_21
| ~ spl5_32
| ~ spl5_57 ),
inference(avatar_split_clause,[],[f532,f500,f338,f289,f839]) ).
fof(f839,plain,
( spl5_91
<=> ! [X4,X0,X3,X2,X1] :
( lookup_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X1) = X2
| X1 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_91])]) ).
fof(f532,plain,
( ! [X2,X3,X0,X1,X4] :
( lookup_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X1) = X2
| X1 = X3 )
| ~ spl5_21
| ~ spl5_32
| ~ spl5_57 ),
inference(forward_demodulation,[],[f529,f339]) ).
fof(f529,plain,
( ! [X2,X3,X0,X1,X4] :
( lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = lookup_slb(insert_slb(insert_slb(X0,pair(X1,X2)),pair(X3,X4)),X1)
| X1 = X3 )
| ~ spl5_21
| ~ spl5_57 ),
inference(resolution,[],[f501,f290]) ).
fof(f805,plain,
( spl5_90
| ~ spl5_23
| ~ spl5_73 ),
inference(avatar_split_clause,[],[f700,f632,f297,f803]) ).
fof(f803,plain,
( spl5_90
<=> ! [X0,X1] :
( strictly_less_than(bottom,X0)
| issmallestelement_pq(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_90])]) ).
fof(f297,plain,
( spl5_23
<=> ! [X0,X1] :
( issmallestelement_pq(X0,X1)
| ~ less_than(X1,sK4(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_23])]) ).
fof(f632,plain,
( spl5_73
<=> ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(bottom,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_73])]) ).
fof(f700,plain,
( ! [X0,X1] :
( strictly_less_than(bottom,X0)
| issmallestelement_pq(X1,X0) )
| ~ spl5_23
| ~ spl5_73 ),
inference(resolution,[],[f633,f298]) ).
fof(f298,plain,
( ! [X0,X1] :
( ~ less_than(X1,sK4(X0,X1))
| issmallestelement_pq(X0,X1) )
| ~ spl5_23 ),
inference(avatar_component_clause,[],[f297]) ).
fof(f633,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(bottom,X0) )
| ~ spl5_73 ),
inference(avatar_component_clause,[],[f632]) ).
fof(f735,plain,
( spl5_89
| ~ spl5_7
| ~ spl5_62 ),
inference(avatar_split_clause,[],[f556,f548,f231,f733]) ).
fof(f733,plain,
( spl5_89
<=> ! [X2,X0,X1] : update_slb(insert_slb(X0,pair(X1,X2)),bottom) = insert_slb(update_slb(X0,bottom),pair(X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_89])]) ).
fof(f231,plain,
( spl5_7
<=> ! [X0] : less_than(bottom,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_7])]) ).
fof(f556,plain,
( ! [X2,X0,X1] : update_slb(insert_slb(X0,pair(X1,X2)),bottom) = insert_slb(update_slb(X0,bottom),pair(X1,X2))
| ~ spl5_7
| ~ spl5_62 ),
inference(resolution,[],[f549,f232]) ).
fof(f232,plain,
( ! [X0] : less_than(bottom,X0)
| ~ spl5_7 ),
inference(avatar_component_clause,[],[f231]) ).
fof(f731,plain,
( spl5_88
| ~ spl5_6
| ~ spl5_62 ),
inference(avatar_split_clause,[],[f555,f548,f227,f729]) ).
fof(f729,plain,
( spl5_88
<=> ! [X2,X0,X1] : insert_slb(update_slb(X0,X2),pair(X1,X2)) = update_slb(insert_slb(X0,pair(X1,X2)),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_88])]) ).
fof(f227,plain,
( spl5_6
<=> ! [X0] : less_than(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_6])]) ).
fof(f555,plain,
( ! [X2,X0,X1] : insert_slb(update_slb(X0,X2),pair(X1,X2)) = update_slb(insert_slb(X0,pair(X1,X2)),X2)
| ~ spl5_6
| ~ spl5_62 ),
inference(resolution,[],[f549,f228]) ).
fof(f228,plain,
( ! [X0] : less_than(X0,X0)
| ~ spl5_6 ),
inference(avatar_component_clause,[],[f227]) ).
fof(f727,plain,
( spl5_87
| ~ spl5_34
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f527,f496,f346,f725]) ).
fof(f725,plain,
( spl5_87
<=> ! [X4,X0,X3,X2,X1] :
( ~ contains_cpq(insert_cpq(triple(X0,X2,X3),X1),X4)
| contains_slb(insert_slb(X2,pair(X1,bottom)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_87])]) ).
fof(f346,plain,
( spl5_34
<=> ! [X2,X0,X1,X3] :
( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_34])]) ).
fof(f527,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ contains_cpq(insert_cpq(triple(X0,X2,X3),X1),X4)
| contains_slb(insert_slb(X2,pair(X1,bottom)),X4) )
| ~ spl5_34
| ~ spl5_56 ),
inference(superposition,[],[f347,f497]) ).
fof(f347,plain,
( ! [X2,X3,X0,X1] :
( ~ contains_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) )
| ~ spl5_34 ),
inference(avatar_component_clause,[],[f346]) ).
fof(f723,plain,
( spl5_86
| ~ spl5_35
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f526,f496,f350,f721]) ).
fof(f721,plain,
( spl5_86
<=> ! [X4,X0,X3,X2,X1] :
( contains_cpq(insert_cpq(triple(X0,X2,X3),X1),X4)
| ~ contains_slb(insert_slb(X2,pair(X1,bottom)),X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_86])]) ).
fof(f350,plain,
( spl5_35
<=> ! [X0,X3,X2,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_35])]) ).
fof(f526,plain,
( ! [X2,X3,X0,X1,X4] :
( contains_cpq(insert_cpq(triple(X0,X2,X3),X1),X4)
| ~ contains_slb(insert_slb(X2,pair(X1,bottom)),X4) )
| ~ spl5_35
| ~ spl5_56 ),
inference(superposition,[],[f351,f497]) ).
fof(f351,plain,
( ! [X2,X3,X0,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) )
| ~ spl5_35 ),
inference(avatar_component_clause,[],[f350]) ).
fof(f719,plain,
( spl5_85
| ~ spl5_44
| ~ spl5_45 ),
inference(avatar_split_clause,[],[f444,f416,f412,f717]) ).
fof(f717,plain,
( spl5_85
<=> ! [X0,X3,X2,X1] :
( ~ contains_pq(insert_pq(insert_pq(X0,X2),X1),X3)
| contains_pq(insert_pq(X0,X1),X3)
| X2 = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_85])]) ).
fof(f412,plain,
( spl5_44
<=> ! [X2,X0,X1] : insert_pq(insert_pq(X0,X1),X2) = insert_pq(insert_pq(X0,X2),X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_44])]) ).
fof(f444,plain,
( ! [X2,X3,X0,X1] :
( ~ contains_pq(insert_pq(insert_pq(X0,X2),X1),X3)
| contains_pq(insert_pq(X0,X1),X3)
| X2 = X3 )
| ~ spl5_44
| ~ spl5_45 ),
inference(superposition,[],[f417,f413]) ).
fof(f413,plain,
( ! [X2,X0,X1] : insert_pq(insert_pq(X0,X1),X2) = insert_pq(insert_pq(X0,X2),X1)
| ~ spl5_44 ),
inference(avatar_component_clause,[],[f412]) ).
fof(f715,plain,
( spl5_84
| ~ spl5_44 ),
inference(avatar_split_clause,[],[f426,f412,f713]) ).
fof(f713,plain,
( spl5_84
<=> ! [X0,X3,X2,X1] : insert_pq(insert_pq(insert_pq(X0,X1),X3),X2) = insert_pq(insert_pq(insert_pq(X0,X2),X1),X3) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_84])]) ).
fof(f426,plain,
( ! [X2,X3,X0,X1] : insert_pq(insert_pq(insert_pq(X0,X1),X3),X2) = insert_pq(insert_pq(insert_pq(X0,X2),X1),X3)
| ~ spl5_44 ),
inference(superposition,[],[f413,f413]) ).
fof(f710,plain,
( spl5_83
| ~ spl5_20
| ~ spl5_37
| ~ spl5_39 ),
inference(avatar_split_clause,[],[f383,f377,f369,f285,f708]) ).
fof(f708,plain,
( spl5_83
<=> ! [X2,X0,X1] :
( succ_cpq(X2,remove_cpq(triple(X0,create_slb,bad),bottom))
| ~ succ_cpq(X2,triple(X0,create_slb,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_83])]) ).
fof(f285,plain,
( spl5_20
<=> ! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_20])]) ).
fof(f369,plain,
( spl5_37
<=> ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_37])]) ).
fof(f383,plain,
( ! [X2,X0,X1] :
( succ_cpq(X2,remove_cpq(triple(X0,create_slb,bad),bottom))
| ~ succ_cpq(X2,triple(X0,create_slb,X1)) )
| ~ spl5_20
| ~ spl5_37
| ~ spl5_39 ),
inference(forward_demodulation,[],[f381,f286]) ).
fof(f286,plain,
( ! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1))
| ~ spl5_20 ),
inference(avatar_component_clause,[],[f285]) ).
fof(f381,plain,
( ! [X2,X0,X1] :
( succ_cpq(X2,remove_cpq(triple(X0,create_slb,bad),removemin_cpq_res(triple(X0,create_slb,X1))))
| ~ succ_cpq(X2,triple(X0,create_slb,X1)) )
| ~ spl5_37
| ~ spl5_39 ),
inference(superposition,[],[f378,f370]) ).
fof(f370,plain,
( ! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad)
| ~ spl5_37 ),
inference(avatar_component_clause,[],[f369]) ).
fof(f692,plain,
( spl5_82
| ~ spl5_27
| ~ spl5_44 ),
inference(avatar_split_clause,[],[f430,f412,f313,f690]) ).
fof(f690,plain,
( spl5_82
<=> ! [X0,X3,X2,X1] :
( contains_pq(insert_pq(insert_pq(X0,X2),X1),X3)
| ~ contains_pq(insert_pq(X0,X1),X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_82])]) ).
fof(f430,plain,
( ! [X2,X3,X0,X1] :
( contains_pq(insert_pq(insert_pq(X0,X2),X1),X3)
| ~ contains_pq(insert_pq(X0,X1),X3) )
| ~ spl5_27
| ~ spl5_44 ),
inference(superposition,[],[f314,f413]) ).
fof(f688,plain,
( spl5_81
| ~ spl5_19
| ~ spl5_37 ),
inference(avatar_split_clause,[],[f380,f369,f281,f686]) ).
fof(f686,plain,
( spl5_81
<=> ! [X2,X0,X1] :
( succ_cpq(X2,triple(X0,create_slb,bad))
| ~ succ_cpq(X2,triple(X0,create_slb,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_81])]) ).
fof(f281,plain,
( spl5_19
<=> ! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_19])]) ).
fof(f380,plain,
( ! [X2,X0,X1] :
( succ_cpq(X2,triple(X0,create_slb,bad))
| ~ succ_cpq(X2,triple(X0,create_slb,X1)) )
| ~ spl5_19
| ~ spl5_37 ),
inference(superposition,[],[f282,f370]) ).
fof(f282,plain,
( ! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) )
| ~ spl5_19 ),
inference(avatar_component_clause,[],[f281]) ).
fof(f672,plain,
( ~ spl5_12
| ~ spl5_80 ),
inference(avatar_contradiction_clause,[],[f670]) ).
fof(f670,plain,
( $false
| ~ spl5_12
| ~ spl5_80 ),
inference(resolution,[],[f668,f253]) ).
fof(f253,plain,
( ! [X0,X1] : check_cpq(triple(X0,create_slb,X1))
| ~ spl5_12 ),
inference(avatar_component_clause,[],[f252]) ).
fof(f252,plain,
( spl5_12
<=> ! [X0,X1] : check_cpq(triple(X0,create_slb,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_12])]) ).
fof(f668,plain,
( ! [X2,X0,X1] : ~ check_cpq(triple(X0,X1,X2))
| ~ spl5_80 ),
inference(avatar_component_clause,[],[f667]) ).
fof(f667,plain,
( spl5_80
<=> ! [X2,X0,X1] : ~ check_cpq(triple(X0,X1,X2)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_80])]) ).
fof(f669,plain,
( spl5_79
| spl5_80
| ~ spl5_47
| ~ spl5_60 ),
inference(avatar_split_clause,[],[f540,f514,f450,f667,f664]) ).
fof(f664,plain,
( spl5_79
<=> ! [X4,X3] :
( ~ less_than(X3,X4)
| ~ strictly_less_than(X4,X3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_79])]) ).
fof(f450,plain,
( spl5_47
<=> ! [X4,X0,X3,X2,X1] :
( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ strictly_less_than(X3,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_47])]) ).
fof(f540,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ check_cpq(triple(X0,X1,X2))
| ~ less_than(X3,X4)
| ~ strictly_less_than(X4,X3) )
| ~ spl5_47
| ~ spl5_60 ),
inference(resolution,[],[f515,f451]) ).
fof(f451,plain,
( ! [X2,X3,X0,X1,X4] :
( ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2))
| ~ strictly_less_than(X3,X4) )
| ~ spl5_47 ),
inference(avatar_component_clause,[],[f450]) ).
fof(f662,plain,
( spl5_78
| ~ spl5_4
| ~ spl5_52 ),
inference(avatar_split_clause,[],[f477,f474,f219,f660]) ).
fof(f660,plain,
( spl5_78
<=> ! [X2,X0,X1] : triple(X0,create_slb,bad) = remove_cpq(triple(X0,create_slb,X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_78])]) ).
fof(f219,plain,
( spl5_4
<=> ! [X0] : ~ contains_slb(create_slb,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_4])]) ).
fof(f477,plain,
( ! [X2,X0,X1] : triple(X0,create_slb,bad) = remove_cpq(triple(X0,create_slb,X1),X2)
| ~ spl5_4
| ~ spl5_52 ),
inference(resolution,[],[f475,f220]) ).
fof(f220,plain,
( ! [X0] : ~ contains_slb(create_slb,X0)
| ~ spl5_4 ),
inference(avatar_component_clause,[],[f219]) ).
fof(f658,plain,
( spl5_77
| ~ spl5_18
| ~ spl5_44 ),
inference(avatar_split_clause,[],[f431,f412,f277,f656]) ).
fof(f656,plain,
( spl5_77
<=> ! [X2,X0,X1] : insert_pq(X0,X1) = remove_pq(insert_pq(insert_pq(X0,X2),X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_77])]) ).
fof(f277,plain,
( spl5_18
<=> ! [X0,X1] : remove_pq(insert_pq(X0,X1),X1) = X0 ),
introduced(avatar_definition,[new_symbols(naming,[spl5_18])]) ).
fof(f431,plain,
( ! [X2,X0,X1] : insert_pq(X0,X1) = remove_pq(insert_pq(insert_pq(X0,X2),X1),X2)
| ~ spl5_18
| ~ spl5_44 ),
inference(superposition,[],[f278,f413]) ).
fof(f278,plain,
( ! [X0,X1] : remove_pq(insert_pq(X0,X1),X1) = X0
| ~ spl5_18 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f651,plain,
( spl5_76
| ~ spl5_26
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f528,f496,f309,f649]) ).
fof(f649,plain,
( spl5_76
<=> ! [X0,X3,X2,X1] :
( ok(insert_cpq(triple(X0,X2,X3),X1))
| bad = X3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_76])]) ).
fof(f309,plain,
( spl5_26
<=> ! [X2,X0,X1] :
( bad = X2
| ok(triple(X0,X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_26])]) ).
fof(f528,plain,
( ! [X2,X3,X0,X1] :
( ok(insert_cpq(triple(X0,X2,X3),X1))
| bad = X3 )
| ~ spl5_26
| ~ spl5_56 ),
inference(superposition,[],[f310,f497]) ).
fof(f310,plain,
( ! [X2,X0,X1] :
( ok(triple(X0,X1,X2))
| bad = X2 )
| ~ spl5_26 ),
inference(avatar_component_clause,[],[f309]) ).
fof(f647,plain,
( spl5_75
| ~ spl5_47
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f521,f496,f450,f645]) ).
fof(f645,plain,
( spl5_75
<=> ! [X0,X3,X2,X1] :
( ~ check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| ~ strictly_less_than(X1,bottom) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_75])]) ).
fof(f521,plain,
( ! [X2,X3,X0,X1] :
( ~ check_cpq(insert_cpq(triple(X0,X2,X3),X1))
| ~ strictly_less_than(X1,bottom) )
| ~ spl5_47
| ~ spl5_56 ),
inference(superposition,[],[f451,f497]) ).
fof(f638,plain,
( spl5_74
| ~ spl5_15
| ~ spl5_33 ),
inference(avatar_split_clause,[],[f361,f342,f264,f636]) ).
fof(f636,plain,
( spl5_74
<=> ! [X2,X0,X1] :
( less_than(X0,X1)
| ~ less_than(X0,X2)
| less_than(X1,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_74])]) ).
fof(f342,plain,
( spl5_33
<=> ! [X2,X0,X1] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_33])]) ).
fof(f361,plain,
( ! [X2,X0,X1] :
( less_than(X0,X1)
| ~ less_than(X0,X2)
| less_than(X1,X2) )
| ~ spl5_15
| ~ spl5_33 ),
inference(resolution,[],[f343,f265]) ).
fof(f343,plain,
( ! [X2,X0,X1] :
( ~ less_than(X1,X2)
| less_than(X0,X2)
| ~ less_than(X0,X1) )
| ~ spl5_33 ),
inference(avatar_component_clause,[],[f342]) ).
fof(f634,plain,
( spl5_73
| ~ spl5_63
| ~ spl5_68 ),
inference(avatar_split_clause,[],[f612,f590,f552,f632]) ).
fof(f552,plain,
( spl5_63
<=> ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_63])]) ).
fof(f590,plain,
( spl5_68
<=> ! [X0,X1] :
( less_than(X0,X1)
| ~ less_than(X0,bottom) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_68])]) ).
fof(f612,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(bottom,X0) )
| ~ spl5_63
| ~ spl5_68 ),
inference(resolution,[],[f591,f553]) ).
fof(f553,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(X1,X0) )
| ~ spl5_63 ),
inference(avatar_component_clause,[],[f552]) ).
fof(f591,plain,
( ! [X0,X1] :
( ~ less_than(X0,bottom)
| less_than(X0,X1) )
| ~ spl5_68 ),
inference(avatar_component_clause,[],[f590]) ).
fof(f622,plain,
( spl5_72
| ~ spl5_13
| ~ spl5_56 ),
inference(avatar_split_clause,[],[f522,f496,f256,f620]) ).
fof(f620,plain,
( spl5_72
<=> ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,bad),X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_72])]) ).
fof(f256,plain,
( spl5_13
<=> ! [X0,X1] : ~ ok(triple(X0,X1,bad)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_13])]) ).
fof(f522,plain,
( ! [X2,X0,X1] : ~ ok(insert_cpq(triple(X0,X2,bad),X1))
| ~ spl5_13
| ~ spl5_56 ),
inference(superposition,[],[f257,f497]) ).
fof(f257,plain,
( ! [X0,X1] : ~ ok(triple(X0,X1,bad))
| ~ spl5_13 ),
inference(avatar_component_clause,[],[f256]) ).
fof(f618,plain,
( spl5_71
| ~ spl5_14
| ~ spl5_44 ),
inference(avatar_split_clause,[],[f432,f412,f260,f616]) ).
fof(f616,plain,
( spl5_71
<=> ! [X2,X0,X1] : contains_pq(insert_pq(insert_pq(X0,X2),X1),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_71])]) ).
fof(f260,plain,
( spl5_14
<=> ! [X2,X0] : contains_pq(insert_pq(X0,X2),X2) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_14])]) ).
fof(f432,plain,
( ! [X2,X0,X1] : contains_pq(insert_pq(insert_pq(X0,X2),X1),X2)
| ~ spl5_14
| ~ spl5_44 ),
inference(superposition,[],[f261,f413]) ).
fof(f261,plain,
( ! [X2,X0] : contains_pq(insert_pq(X0,X2),X2)
| ~ spl5_14 ),
inference(avatar_component_clause,[],[f260]) ).
fof(f600,plain,
spl5_70,
inference(avatar_split_clause,[],[f180,f598]) ).
fof(f180,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,[],[f110]) ).
fof(f110,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,[],[f109]) ).
fof(f109,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,[],[f71]) ).
fof(f71,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,[],[f49]) ).
fof(f49,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/sandbox2/benchmark/theBenchmark.p',ax49) ).
fof(f596,plain,
spl5_69,
inference(avatar_split_clause,[],[f179,f594]) ).
fof(f594,plain,
( spl5_69
<=> ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_69])]) ).
fof(f179,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,[],[f108]) ).
fof(f108,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,[],[f107]) ).
fof(f107,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,[],[f70]) ).
fof(f70,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,[],[f48]) ).
fof(f48,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/sandbox2/benchmark/theBenchmark.p',ax48) ).
fof(f592,plain,
( spl5_68
| ~ spl5_7
| ~ spl5_33 ),
inference(avatar_split_clause,[],[f360,f342,f231,f590]) ).
fof(f360,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| ~ less_than(X0,bottom) )
| ~ spl5_7
| ~ spl5_33 ),
inference(resolution,[],[f343,f232]) ).
fof(f582,plain,
spl5_67,
inference(avatar_split_clause,[],[f182,f580]) ).
fof(f182,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,[],[f114]) ).
fof(f114,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,[],[f113]) ).
fof(f113,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,[],[f44]) ).
fof(f44,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/sandbox2/benchmark/theBenchmark.p',ax44) ).
fof(f578,plain,
spl5_66,
inference(avatar_split_clause,[],[f181,f576]) ).
fof(f181,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,[],[f112]) ).
fof(f112,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,[],[f111]) ).
fof(f111,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,[],[f45]) ).
fof(f45,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/sandbox2/benchmark/theBenchmark.p',ax45) ).
fof(f569,plain,
spl5_65,
inference(avatar_split_clause,[],[f177,f567]) ).
fof(f177,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,[],[f104]) ).
fof(f104,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,[],[f103]) ).
fof(f103,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,[],[f25]) ).
fof(f25,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/sandbox2/benchmark/theBenchmark.p',ax25) ).
fof(f562,plain,
spl5_64,
inference(avatar_split_clause,[],[f178,f560]) ).
fof(f560,plain,
( spl5_64
<=> ! [X2,X0,X1] :
( findmin_cpq_eff(triple(X0,X1,X2)) = triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad)
| contains_slb(X1,findmin_pqp_res(X0))
| create_slb = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_64])]) ).
fof(f178,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,[],[f106]) ).
fof(f106,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,[],[f105]) ).
fof(f105,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,[],[f69]) ).
fof(f69,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,[],[f47]) ).
fof(f47,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/sandbox2/benchmark/theBenchmark.p',ax47) ).
fof(f554,plain,
( spl5_63
| ~ spl5_15
| ~ spl5_30 ),
inference(avatar_split_clause,[],[f358,f330,f264,f552]) ).
fof(f330,plain,
( spl5_30
<=> ! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_30])]) ).
fof(f358,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(X1,X0) )
| ~ spl5_15
| ~ spl5_30 ),
inference(duplicate_literal_removal,[],[f355]) ).
fof(f355,plain,
( ! [X0,X1] :
( less_than(X0,X1)
| strictly_less_than(X1,X0)
| less_than(X0,X1) )
| ~ spl5_15
| ~ spl5_30 ),
inference(resolution,[],[f331,f265]) ).
fof(f331,plain,
( ! [X0,X1] :
( ~ less_than(X0,X1)
| less_than(X1,X0)
| strictly_less_than(X0,X1) )
| ~ spl5_30 ),
inference(avatar_component_clause,[],[f330]) ).
fof(f550,plain,
spl5_62,
inference(avatar_split_clause,[],[f175,f548]) ).
fof(f175,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,[],[f100]) ).
fof(f100,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,[],[f30]) ).
fof(f30,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/sandbox2/benchmark/theBenchmark.p',ax30) ).
fof(f546,plain,
spl5_61,
inference(avatar_split_clause,[],[f174,f544]) ).
fof(f544,plain,
( spl5_61
<=> ! [X0,X3,X2,X1] :
( update_slb(insert_slb(X0,pair(X1,X3)),X2) = insert_slb(update_slb(X0,X2),pair(X1,X2))
| ~ strictly_less_than(X3,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_61])]) ).
fof(f174,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,[],[f99]) ).
fof(f99,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,[],[f29]) ).
fof(f29,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/sandbox2/benchmark/theBenchmark.p',ax29) ).
fof(f516,plain,
spl5_60,
inference(avatar_split_clause,[],[f191,f514]) ).
fof(f191,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,[],[f126]) ).
fof(f126,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,[],[f116]) ).
fof(f116,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,[],[f37]) ).
fof(f37,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/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f512,plain,
spl5_59,
inference(avatar_split_clause,[],[f190,f510]) ).
fof(f190,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,[],[f126]) ).
fof(f506,plain,
spl5_58,
inference(avatar_split_clause,[],[f188,f504]) ).
fof(f188,plain,
! [X2,X3,X0,X1,X4] : i(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) = insert_pq(i(triple(X0,X1,X2)),X3),
inference(cnf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0,X1,X2,X3,X4] : i(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) = insert_pq(i(triple(X0,X1,X2)),X3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
fof(f502,plain,
spl5_57,
inference(avatar_split_clause,[],[f176,f500]) ).
fof(f176,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,[],[f102]) ).
fof(f102,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,[],[f101]) ).
fof(f101,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,[],[f27]) ).
fof(f27,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/sandbox2/benchmark/theBenchmark.p',ax27) ).
fof(f498,plain,
spl5_56,
inference(avatar_split_clause,[],[f171,f496]) ).
fof(f171,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,[],[f42]) ).
fof(f42,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/sandbox2/benchmark/theBenchmark.p',ax42) ).
fof(f494,plain,
spl5_55,
inference(avatar_split_clause,[],[f166,f492]) ).
fof(f166,plain,
! [X2,X0,X1] :
( remove_pq(insert_pq(X0,X1),X2) = insert_pq(remove_pq(X0,X2),X1)
| X1 = X2
| ~ contains_pq(X0,X2) ),
inference(cnf_transformation,[],[f94]) ).
fof(f94,plain,
! [X0,X1,X2] :
( remove_pq(insert_pq(X0,X1),X2) = insert_pq(remove_pq(X0,X2),X1)
| X1 = X2
| ~ contains_pq(X0,X2) ),
inference(flattening,[],[f93]) ).
fof(f93,plain,
! [X0,X1,X2] :
( remove_pq(insert_pq(X0,X1),X2) = insert_pq(remove_pq(X0,X2),X1)
| X1 = X2
| ~ contains_pq(X0,X2) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0,X1,X2] :
( ( X1 != X2
& contains_pq(X0,X2) )
=> remove_pq(insert_pq(X0,X1),X2) = insert_pq(remove_pq(X0,X2),X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax12) ).
fof(f486,plain,
spl5_54,
inference(avatar_split_clause,[],[f193,f484]) ).
fof(f484,plain,
( spl5_54
<=> ! [X4,X0,X3,X2,X1] :
( X3 = X4
| pair_in_list(X0,X2,X4)
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_54])]) ).
fof(f193,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,[],[f128]) ).
fof(f128,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,[],[f127]) ).
fof(f127,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,[],[f23]) ).
fof(f23,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/sandbox2/benchmark/theBenchmark.p',ax23) ).
fof(f482,plain,
spl5_53,
inference(avatar_split_clause,[],[f192,f480]) ).
fof(f480,plain,
( spl5_53
<=> ! [X4,X0,X3,X2,X1] :
( X1 = X2
| pair_in_list(X0,X2,X4)
| ~ pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_53])]) ).
fof(f192,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,[],[f128]) ).
fof(f476,plain,
spl5_52,
inference(avatar_split_clause,[],[f173,f474]) ).
fof(f173,plain,
! [X2,X3,X0,X1] :
( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2,X3] :
( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0,X1,X2,X3] :
( ~ contains_slb(X1,X3)
=> triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43) ).
fof(f472,plain,
( spl5_51
| spl5_8
| ~ spl5_40 ),
inference(avatar_split_clause,[],[f395,f386,f235,f470]) ).
fof(f235,plain,
( spl5_8
<=> insert_pq(i(triple(sK0,sK1,sK2)),sK3) = i(insert_cpq(triple(sK0,sK1,sK2),sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_8])]) ).
fof(f395,plain,
( ! [X0,X1] : i(insert_cpq(triple(sK0,sK1,sK2),sK3)) != insert_pq(i(triple(X0,sK1,X1)),sK3)
| spl5_8
| ~ spl5_40 ),
inference(superposition,[],[f237,f387]) ).
fof(f237,plain,
( insert_pq(i(triple(sK0,sK1,sK2)),sK3) != i(insert_cpq(triple(sK0,sK1,sK2),sK3))
| spl5_8 ),
inference(avatar_component_clause,[],[f235]) ).
fof(f464,plain,
spl5_50,
inference(avatar_split_clause,[],[f185,f462]) ).
fof(f185,plain,
! [X2,X3,X0,X1] :
( X1 = X2
| contains_slb(X0,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,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,[],[f124]) ).
fof(f124,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,[],[f21]) ).
fof(f21,axiom,
! [X0,X1,X2,X3] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
<=> ( X1 = X2
| contains_slb(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax21) ).
fof(f460,plain,
spl5_49,
inference(avatar_split_clause,[],[f154,f458]) ).
fof(f458,plain,
( spl5_49
<=> ! [X0,X1] :
( removemin_pq_eff(X0,X1) = remove_pq(X0,X1)
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_49])]) ).
fof(f154,plain,
! [X0,X1] :
( removemin_pq_eff(X0,X1) = remove_pq(X0,X1)
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( removemin_pq_eff(X0,X1) = remove_pq(X0,X1)
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(flattening,[],[f85]) ).
fof(f85,plain,
! [X0,X1] :
( removemin_pq_eff(X0,X1) = remove_pq(X0,X1)
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0,X1] :
( ( issmallestelement_pq(X0,X1)
& contains_pq(X0,X1) )
=> removemin_pq_eff(X0,X1) = remove_pq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax15) ).
fof(f456,plain,
spl5_48,
inference(avatar_split_clause,[],[f194,f454]) ).
fof(f454,plain,
( spl5_48
<=> ! [X4,X0,X3,X2,X1] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| ~ pair_in_list(X0,X2,X4) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_48])]) ).
fof(f194,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,[],[f128]) ).
fof(f452,plain,
spl5_47,
inference(avatar_split_clause,[],[f189,f450]) ).
fof(f189,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,[],[f115]) ).
fof(f115,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,[],[f73]) ).
fof(f73,plain,
! [X0,X1,X2,X3,X4] :
( strictly_less_than(X3,X4)
=> ~ check_cpq(triple(X0,insert_slb(X1,pair(X3,X4)),X2)) ),
inference(flattening,[],[f72]) ).
fof(f72,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,[],[f38]) ).
fof(f38,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/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f422,plain,
spl5_46,
inference(avatar_split_clause,[],[f199,f420]) ).
fof(f199,plain,
! [X2,X0,X1] :
( findmin_pqp_res(X0) = removemin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(definition_unfolding,[],[f172,f139]) ).
fof(f139,plain,
! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
inference(cnf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] : findmin_cpq_res(X0) = removemin_cpq_res(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
fof(f172,plain,
! [X2,X0,X1] :
( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(cnf_transformation,[],[f97]) ).
fof(f97,plain,
! [X0,X1,X2] :
( findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2))
| create_slb = X1 ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,plain,
! [X0,X1,X2] :
( create_slb != X1
=> findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
inference(rectify,[],[f51]) ).
fof(f51,axiom,
! [X0,X1,X2,X3] :
( create_slb != X1
=> findmin_pqp_res(X0) = findmin_cpq_res(triple(X0,X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
fof(f418,plain,
spl5_45,
inference(avatar_split_clause,[],[f168,f416]) ).
fof(f168,plain,
! [X2,X0,X1] :
( X1 = X2
| contains_pq(X0,X2)
| ~ contains_pq(insert_pq(X0,X1),X2) ),
inference(cnf_transformation,[],[f122]) ).
fof(f122,plain,
! [X0,X1,X2] :
( ( contains_pq(insert_pq(X0,X1),X2)
| ( X1 != X2
& ~ contains_pq(X0,X2) ) )
& ( X1 = X2
| contains_pq(X0,X2)
| ~ contains_pq(insert_pq(X0,X1),X2) ) ),
inference(flattening,[],[f121]) ).
fof(f121,plain,
! [X0,X1,X2] :
( ( contains_pq(insert_pq(X0,X1),X2)
| ( X1 != X2
& ~ contains_pq(X0,X2) ) )
& ( X1 = X2
| contains_pq(X0,X2)
| ~ contains_pq(insert_pq(X0,X1),X2) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1,X2] :
( contains_pq(insert_pq(X0,X1),X2)
<=> ( X1 = X2
| contains_pq(X0,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9) ).
fof(f414,plain,
spl5_44,
inference(avatar_split_clause,[],[f162,f412]) ).
fof(f162,plain,
! [X2,X0,X1] : insert_pq(insert_pq(X0,X1),X2) = insert_pq(insert_pq(X0,X2),X1),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
! [X0,X1,X2] : insert_pq(insert_pq(X0,X1),X2) = insert_pq(insert_pq(X0,X2),X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f410,plain,
spl5_43,
inference(avatar_split_clause,[],[f153,f408]) ).
fof(f408,plain,
( spl5_43
<=> ! [X0,X1] :
( findmin_pq_eff(X0,X1) = X0
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_43])]) ).
fof(f153,plain,
! [X0,X1] :
( findmin_pq_eff(X0,X1) = X0
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(cnf_transformation,[],[f84]) ).
fof(f84,plain,
! [X0,X1] :
( findmin_pq_eff(X0,X1) = X0
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(flattening,[],[f83]) ).
fof(f83,plain,
! [X0,X1] :
( findmin_pq_eff(X0,X1) = X0
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1] :
( ( issmallestelement_pq(X0,X1)
& contains_pq(X0,X1) )
=> findmin_pq_eff(X0,X1) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).
fof(f406,plain,
spl5_42,
inference(avatar_split_clause,[],[f152,f404]) ).
fof(f404,plain,
( spl5_42
<=> ! [X0,X1] :
( findmin_pq_res(X0,X1) = X1
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_42])]) ).
fof(f152,plain,
! [X0,X1] :
( findmin_pq_res(X0,X1) = X1
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(cnf_transformation,[],[f82]) ).
fof(f82,plain,
! [X0,X1] :
( findmin_pq_res(X0,X1) = X1
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(flattening,[],[f81]) ).
fof(f81,plain,
! [X0,X1] :
( findmin_pq_res(X0,X1) = X1
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1] :
( ( issmallestelement_pq(X0,X1)
& contains_pq(X0,X1) )
=> findmin_pq_res(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).
fof(f402,plain,
spl5_41,
inference(avatar_split_clause,[],[f151,f400]) ).
fof(f400,plain,
( spl5_41
<=> ! [X0,X1] :
( removemin_pq_res(X0,X1) = X1
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_41])]) ).
fof(f151,plain,
! [X0,X1] :
( removemin_pq_res(X0,X1) = X1
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,plain,
! [X0,X1] :
( removemin_pq_res(X0,X1) = X1
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(flattening,[],[f79]) ).
fof(f79,plain,
! [X0,X1] :
( removemin_pq_res(X0,X1) = X1
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ( issmallestelement_pq(X0,X1)
& contains_pq(X0,X1) )
=> removemin_pq_res(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f388,plain,
spl5_40,
inference(avatar_split_clause,[],[f130,f386]) ).
fof(f130,plain,
! [X2,X3,X0,X1,X4] : i(triple(X0,X2,X3)) = i(triple(X1,X2,X4)),
inference(cnf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0,X1,X2,X3,X4] : i(triple(X0,X2,X3)) = i(triple(X1,X2,X4)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',main2_l12) ).
fof(f379,plain,
spl5_39,
inference(avatar_split_clause,[],[f198,f377]) ).
fof(f198,plain,
! [X0,X1] :
( succ_cpq(X0,remove_cpq(findmin_cpq_eff(X1),removemin_cpq_res(X1)))
| ~ succ_cpq(X0,X1) ),
inference(definition_unfolding,[],[f149,f196]) ).
fof(f196,plain,
! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),removemin_cpq_res(X0)),
inference(definition_unfolding,[],[f140,f139]) ).
fof(f140,plain,
! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),findmin_cpq_res(X0)),
inference(cnf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] : removemin_cpq_eff(X0) = remove_cpq(findmin_cpq_eff(X0),findmin_cpq_res(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
fof(f149,plain,
! [X0,X1] :
( succ_cpq(X0,removemin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f77]) ).
fof(f77,plain,
! [X0,X1] :
( succ_cpq(X0,removemin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0,X1] :
( succ_cpq(X0,X1)
=> succ_cpq(X0,removemin_cpq_eff(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35) ).
fof(f375,plain,
spl5_38,
inference(avatar_split_clause,[],[f186,f373]) ).
fof(f186,plain,
! [X2,X3,X0,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ~ contains_slb(X0,X2) ),
inference(cnf_transformation,[],[f125]) ).
fof(f371,plain,
spl5_37,
inference(avatar_split_clause,[],[f147,f369]) ).
fof(f147,plain,
! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
inference(cnf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0,X1] : findmin_cpq_eff(triple(X0,create_slb,X1)) = triple(X0,create_slb,bad),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
fof(f366,plain,
( spl5_36
| ~ spl5_7
| ~ spl5_23 ),
inference(avatar_split_clause,[],[f321,f297,f231,f364]) ).
fof(f364,plain,
( spl5_36
<=> ! [X0] : issmallestelement_pq(X0,bottom) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_36])]) ).
fof(f321,plain,
( ! [X0] : issmallestelement_pq(X0,bottom)
| ~ spl5_7
| ~ spl5_23 ),
inference(resolution,[],[f298,f232]) ).
fof(f352,plain,
spl5_35,
inference(avatar_split_clause,[],[f184,f350]) ).
fof(f184,plain,
! [X2,X3,X0,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f123]) ).
fof(f123,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,[],[f39]) ).
fof(f39,axiom,
! [X0,X1,X2,X3] :
( contains_cpq(triple(X0,X1,X2),X3)
<=> contains_slb(X1,X3) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
fof(f348,plain,
spl5_34,
inference(avatar_split_clause,[],[f183,f346]) ).
fof(f183,plain,
! [X2,X3,X0,X1] :
( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f123]) ).
fof(f344,plain,
spl5_33,
inference(avatar_split_clause,[],[f167,f342]) ).
fof(f167,plain,
! [X2,X0,X1] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f96]) ).
fof(f96,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(flattening,[],[f95]) ).
fof(f95,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/sandbox2/benchmark/theBenchmark.p',transitivity) ).
fof(f340,plain,
spl5_32,
inference(avatar_split_clause,[],[f161,f338]) ).
fof(f161,plain,
! [X2,X0,X1] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2,
inference(cnf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0,X1,X2] : lookup_slb(insert_slb(X0,pair(X1,X2)),X1) = X2,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f336,plain,
spl5_31,
inference(avatar_split_clause,[],[f160,f334]) ).
fof(f160,plain,
! [X2,X0,X1] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0,
inference(cnf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0,X1,X2] : remove_slb(insert_slb(X0,pair(X1,X2)),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f332,plain,
spl5_30,
inference(avatar_split_clause,[],[f155,f330]) ).
fof(f155,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(flattening,[],[f87]) ).
fof(f87,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,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/sandbox2/benchmark/theBenchmark.p',stricly_smaller_definition) ).
fof(f328,plain,
( spl5_29
| ~ spl5_3
| ~ spl5_22 ),
inference(avatar_split_clause,[],[f320,f293,f215,f326]) ).
fof(f326,plain,
( spl5_29
<=> ! [X0] : issmallestelement_pq(create_pq,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_29])]) ).
fof(f215,plain,
( spl5_3
<=> ! [X0] : ~ contains_pq(create_pq,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_3])]) ).
fof(f320,plain,
( ! [X0] : issmallestelement_pq(create_pq,X0)
| ~ spl5_3
| ~ spl5_22 ),
inference(resolution,[],[f294,f216]) ).
fof(f216,plain,
( ! [X0] : ~ contains_pq(create_pq,X0)
| ~ spl5_3 ),
inference(avatar_component_clause,[],[f215]) ).
fof(f319,plain,
spl5_28,
inference(avatar_split_clause,[],[f203,f317]) ).
fof(f317,plain,
( spl5_28
<=> ! [X4,X0,X2] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_28])]) ).
fof(f203,plain,
! [X2,X0,X4] : pair_in_list(insert_slb(X0,pair(X2,X4)),X2,X4),
inference(equality_resolution,[],[f202]) ).
fof(f202,plain,
! [X2,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X4)),X2,X4)
| X1 != X2 ),
inference(equality_resolution,[],[f195]) ).
fof(f195,plain,
! [X2,X3,X0,X1,X4] :
( pair_in_list(insert_slb(X0,pair(X1,X3)),X2,X4)
| X3 != X4
| X1 != X2 ),
inference(cnf_transformation,[],[f128]) ).
fof(f315,plain,
spl5_27,
inference(avatar_split_clause,[],[f169,f313]) ).
fof(f169,plain,
! [X2,X0,X1] :
( contains_pq(insert_pq(X0,X1),X2)
| ~ contains_pq(X0,X2) ),
inference(cnf_transformation,[],[f122]) ).
fof(f311,plain,
spl5_26,
inference(avatar_split_clause,[],[f165,f309]) ).
fof(f165,plain,
! [X2,X0,X1] :
( bad = X2
| ok(triple(X0,X1,X2)) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,plain,
! [X0,X1,X2] :
( bad = X2
| ok(triple(X0,X1,X2)) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0,X1,X2] :
( ~ ok(triple(X0,X1,X2))
=> bad = X2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
fof(f307,plain,
spl5_25,
inference(avatar_split_clause,[],[f164,f305]) ).
fof(f305,plain,
( spl5_25
<=> ! [X2,X0,X1] :
( succ_cpq(X0,remove_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_25])]) ).
fof(f164,plain,
! [X2,X0,X1] :
( succ_cpq(X0,remove_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f91]) ).
fof(f91,plain,
! [X0,X1,X2] :
( succ_cpq(X0,remove_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0,X1,X2] :
( succ_cpq(X0,X1)
=> succ_cpq(X0,remove_cpq(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).
fof(f303,plain,
spl5_24,
inference(avatar_split_clause,[],[f163,f301]) ).
fof(f301,plain,
( spl5_24
<=> ! [X2,X0,X1] :
( succ_cpq(X0,insert_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_24])]) ).
fof(f163,plain,
! [X2,X0,X1] :
( succ_cpq(X0,insert_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1,X2] :
( succ_cpq(X0,insert_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0,X1,X2] :
( succ_cpq(X0,X1)
=> succ_cpq(X0,insert_cpq(X1,X2)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32) ).
fof(f299,plain,
spl5_23,
inference(avatar_split_clause,[],[f157,f297]) ).
fof(f157,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| ~ less_than(X1,sK4(X0,X1)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| ( ~ less_than(X1,sK4(X0,X1))
& contains_pq(X0,sK4(X0,X1)) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4])],[f89,f119]) ).
fof(f119,plain,
! [X0,X1] :
( ? [X2] :
( ~ less_than(X1,X2)
& contains_pq(X0,X2) )
=> ( ~ less_than(X1,sK4(X0,X1))
& contains_pq(X0,sK4(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f89,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| ? [X2] :
( ~ less_than(X1,X2)
& contains_pq(X0,X2) ) ),
inference(ennf_transformation,[],[f74]) ).
fof(f74,plain,
! [X0,X1] :
( ! [X2] :
( contains_pq(X0,X2)
=> less_than(X1,X2) )
=> issmallestelement_pq(X0,X1) ),
inference(unused_predicate_definition_removal,[],[f10]) ).
fof(f10,axiom,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
<=> ! [X2] :
( contains_pq(X0,X2)
=> less_than(X1,X2) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10) ).
fof(f295,plain,
spl5_22,
inference(avatar_split_clause,[],[f156,f293]) ).
fof(f156,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| contains_pq(X0,sK4(X0,X1)) ),
inference(cnf_transformation,[],[f120]) ).
fof(f291,plain,
spl5_21,
inference(avatar_split_clause,[],[f201,f289]) ).
fof(f201,plain,
! [X2,X3,X0] : contains_slb(insert_slb(X0,pair(X2,X3)),X2),
inference(equality_resolution,[],[f187]) ).
fof(f187,plain,
! [X2,X3,X0,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| X1 != X2 ),
inference(cnf_transformation,[],[f125]) ).
fof(f287,plain,
spl5_20,
inference(avatar_split_clause,[],[f197,f285]) ).
fof(f197,plain,
! [X0,X1] : bottom = removemin_cpq_res(triple(X0,create_slb,X1)),
inference(definition_unfolding,[],[f144,f139]) ).
fof(f144,plain,
! [X0,X1] : bottom = findmin_cpq_res(triple(X0,create_slb,X1)),
inference(cnf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0,X1] : bottom = findmin_cpq_res(triple(X0,create_slb,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).
fof(f283,plain,
spl5_19,
inference(avatar_split_clause,[],[f150,f281]) ).
fof(f150,plain,
! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0,X1] :
( succ_cpq(X0,X1)
=> succ_cpq(X0,findmin_cpq_eff(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34) ).
fof(f279,plain,
spl5_18,
inference(avatar_split_clause,[],[f146,f277]) ).
fof(f146,plain,
! [X0,X1] : remove_pq(insert_pq(X0,X1),X1) = X0,
inference(cnf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0,X1] : remove_pq(insert_pq(X0,X1),X1) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11) ).
fof(f275,plain,
spl5_17,
inference(avatar_split_clause,[],[f145,f273]) ).
fof(f273,plain,
( spl5_17
<=> ! [X0,X1] : create_pq = i(triple(X0,create_slb,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_17])]) ).
fof(f145,plain,
! [X0,X1] : create_pq = i(triple(X0,create_slb,X1)),
inference(cnf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0,X1] : create_pq = i(triple(X0,create_slb,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
fof(f270,plain,
spl5_16,
inference(avatar_split_clause,[],[f159,f268]) ).
fof(f268,plain,
( spl5_16
<=> ! [X2,X0,X1] : isnonempty_slb(insert_slb(X0,pair(X1,X2))) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_16])]) ).
fof(f159,plain,
! [X2,X0,X1] : isnonempty_slb(insert_slb(X0,pair(X1,X2))),
inference(cnf_transformation,[],[f19]) ).
fof(f19,axiom,
! [X0,X1,X2] : isnonempty_slb(insert_slb(X0,pair(X1,X2))),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax19) ).
fof(f266,plain,
spl5_15,
inference(avatar_split_clause,[],[f148,f264]) ).
fof(f148,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/sandbox2/benchmark/theBenchmark.p',totality) ).
fof(f262,plain,
spl5_14,
inference(avatar_split_clause,[],[f200,f260]) ).
fof(f200,plain,
! [X2,X0] : contains_pq(insert_pq(X0,X2),X2),
inference(equality_resolution,[],[f170]) ).
fof(f170,plain,
! [X2,X0,X1] :
( contains_pq(insert_pq(X0,X1),X2)
| X1 != X2 ),
inference(cnf_transformation,[],[f122]) ).
fof(f258,plain,
spl5_13,
inference(avatar_split_clause,[],[f158,f256]) ).
fof(f158,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(cnf_transformation,[],[f67]) ).
fof(f67,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(flattening,[],[f66]) ).
fof(f66,plain,
! [X0,X1] : ~ ok(triple(X0,X1,bad)),
inference(true_and_false_elimination,[],[f40]) ).
fof(f40,axiom,
! [X0,X1] :
( ok(triple(X0,X1,bad))
<=> $false ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).
fof(f254,plain,
spl5_12,
inference(avatar_split_clause,[],[f143,f252]) ).
fof(f143,plain,
! [X0,X1] : check_cpq(triple(X0,create_slb,X1)),
inference(cnf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0,X1] : check_cpq(triple(X0,create_slb,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
fof(f250,plain,
spl5_11,
inference(avatar_split_clause,[],[f138,f248]) ).
fof(f248,plain,
( spl5_11
<=> ! [X0] : create_slb = update_slb(create_slb,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_11])]) ).
fof(f138,plain,
! [X0] : create_slb = update_slb(create_slb,X0),
inference(cnf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] : create_slb = update_slb(create_slb,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f246,plain,
spl5_10,
inference(avatar_split_clause,[],[f142,f244]) ).
fof(f244,plain,
( spl5_10
<=> ! [X0,X1] : isnonempty_pq(insert_pq(X0,X1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_10])]) ).
fof(f142,plain,
! [X0,X1] : isnonempty_pq(insert_pq(X0,X1)),
inference(cnf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1] : isnonempty_pq(insert_pq(X0,X1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f242,plain,
spl5_9,
inference(avatar_split_clause,[],[f141,f240]) ).
fof(f240,plain,
( spl5_9
<=> ! [X0,X1] : ~ pair_in_list(create_slb,X0,X1) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_9])]) ).
fof(f141,plain,
! [X0,X1] : ~ pair_in_list(create_slb,X0,X1),
inference(cnf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0,X1] : ~ pair_in_list(create_slb,X0,X1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f238,plain,
~ spl5_8,
inference(avatar_split_clause,[],[f129,f235]) ).
fof(f129,plain,
insert_pq(i(triple(sK0,sK1,sK2)),sK3) != i(insert_cpq(triple(sK0,sK1,sK2),sK3)),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
insert_pq(i(triple(sK0,sK1,sK2)),sK3) != i(insert_cpq(triple(sK0,sK1,sK2),sK3)),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f76,f117]) ).
fof(f117,plain,
( ? [X0,X1,X2,X3] : insert_pq(i(triple(X0,X1,X2)),X3) != i(insert_cpq(triple(X0,X1,X2),X3))
=> insert_pq(i(triple(sK0,sK1,sK2)),sK3) != i(insert_cpq(triple(sK0,sK1,sK2),sK3)) ),
introduced(choice_axiom,[]) ).
fof(f76,plain,
? [X0,X1,X2,X3] : insert_pq(i(triple(X0,X1,X2)),X3) != i(insert_cpq(triple(X0,X1,X2),X3)),
inference(ennf_transformation,[],[f65]) ).
fof(f65,negated_conjecture,
~ ! [X0,X1,X2,X3] : insert_pq(i(triple(X0,X1,X2)),X3) = i(insert_cpq(triple(X0,X1,X2),X3)),
inference(negated_conjecture,[],[f64]) ).
fof(f64,conjecture,
! [X0,X1,X2,X3] : insert_pq(i(triple(X0,X1,X2)),X3) = i(insert_cpq(triple(X0,X1,X2),X3)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co2) ).
fof(f233,plain,
spl5_7,
inference(avatar_split_clause,[],[f137,f231]) ).
fof(f137,plain,
! [X0] : less_than(bottom,X0),
inference(cnf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] : less_than(bottom,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bottom_smallest) ).
fof(f229,plain,
spl5_6,
inference(avatar_split_clause,[],[f136,f227]) ).
fof(f136,plain,
! [X0] : less_than(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
! [X0] : less_than(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',reflexivity) ).
fof(f225,plain,
spl5_5,
inference(avatar_split_clause,[],[f135,f223]) ).
fof(f223,plain,
( spl5_5
<=> ! [X0] : succ_cpq(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_5])]) ).
fof(f135,plain,
! [X0] : succ_cpq(X0,X0),
inference(cnf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] : succ_cpq(X0,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
fof(f221,plain,
spl5_4,
inference(avatar_split_clause,[],[f134,f219]) ).
fof(f134,plain,
! [X0] : ~ contains_slb(create_slb,X0),
inference(cnf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] : ~ contains_slb(create_slb,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
fof(f217,plain,
spl5_3,
inference(avatar_split_clause,[],[f133,f215]) ).
fof(f133,plain,
! [X0] : ~ contains_pq(create_pq,X0),
inference(cnf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] : ~ contains_pq(create_pq,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).
fof(f213,plain,
~ spl5_2,
inference(avatar_split_clause,[],[f132,f210]) ).
fof(f210,plain,
( spl5_2
<=> isnonempty_slb(create_slb) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_2])]) ).
fof(f132,plain,
~ isnonempty_slb(create_slb),
inference(cnf_transformation,[],[f18]) ).
fof(f18,axiom,
~ isnonempty_slb(create_slb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
fof(f208,plain,
~ spl5_1,
inference(avatar_split_clause,[],[f131,f205]) ).
fof(f205,plain,
( spl5_1
<=> isnonempty_pq(create_pq) ),
introduced(avatar_definition,[new_symbols(naming,[spl5_1])]) ).
fof(f131,plain,
~ isnonempty_pq(create_pq),
inference(cnf_transformation,[],[f6]) ).
fof(f6,axiom,
~ isnonempty_pq(create_pq),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SWV415+1 : TPTP v8.1.2. Released v3.3.0.
% 0.03/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n028.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Tue Apr 30 05:15:44 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.32 % (19350)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.34 % (19353)WARNING: value z3 for option sas not known
% 0.11/0.34 % (19354)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.34 % (19351)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.34 % (19357)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.11/0.34 % (19353)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)
% 0.11/0.34 % (19352)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.34 % (19355)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.11/0.34 % (19356)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.11/0.34 TRYING [1]
% 0.11/0.35 TRYING [2]
% 0.16/0.36 TRYING [3]
% 0.16/0.36 TRYING [1]
% 0.16/0.37 % (19355)First to succeed.
% 0.16/0.37 TRYING [2]
% 0.16/0.38 TRYING [1]
% 0.16/0.38 % (19355)Refutation found. Thanks to Tanya!
% 0.16/0.38 % SZS status Theorem for theBenchmark
% 0.16/0.38 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.38 % (19355)------------------------------
% 0.16/0.38 % (19355)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.16/0.38 % (19355)Termination reason: Refutation
% 0.16/0.38
% 0.16/0.38 % (19355)Memory used [KB]: 1484
% 0.16/0.38 % (19355)Time elapsed: 0.040 s
% 0.16/0.38 % (19355)Instructions burned: 69 (million)
% 0.16/0.38 % (19355)------------------------------
% 0.16/0.38 % (19355)------------------------------
% 0.16/0.38 % (19350)Success in time 0.057 s
%------------------------------------------------------------------------------