TSTP Solution File: SWV381+1 by Vampire---4.8
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%------------------------------------------------------------------------------
% File : Vampire---4.8
% Problem : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% Computer : n002.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 : Thu Aug 31 23:10:08 EDT 2023
% Result : Theorem 0.17s 0.41s
% Output : Refutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 39
% Syntax : Number of formulae : 378 ( 50 unt; 0 def)
% Number of atoms : 1311 ( 284 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 1605 ( 672 ~; 837 |; 56 &)
% ( 7 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 8 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-2 aty)
% Number of functors : 31 ( 31 usr; 7 con; 0-3 aty)
% Number of variables : 1459 (;1446 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f491,plain,
$false,
inference(global_subsumption,[],[f214,f136,f215,f140,f139,f216,f217,f218,f220,f221,f222,f223,f224,f225,f226,f230,f228,f229,f231,f232,f233,f234,f235,f241,f237,f238,f240,f242,f243,f244,f245,f249,f247,f248,f251,f252,f253,f254,f256,f257,f258,f259,f260,f261,f262,f263,f264,f265,f267,f268,f269,f270,f274,f275,f276,f277,f278,f279,f280,f282,f284,f285,f286,f290,f288,f289,f291,f292,f293,f294,f295,f299,f297,f298,f302,f303,f305,f306,f312,f308,f309,f310,f311,f313,f315,f317,f318,f324,f320,f321,f322,f323,f325,f327,f328,f329,f330,f331,f333,f334,f335,f344,f337,f338,f347,f348,f349,f358,f351,f352,f359,f360,f361,f362,f365,f364,f366,f367,f368,f369,f372,f371,f373,f374,f375,f377,f378,f379,f380,f381,f382,f383,f384,f385,f388,f387,f389,f390,f391,f392,f395,f394,f396,f397,f398,f400,f401,f402,f403,f404,f408,f406,f407,f415,f410,f411,f412,f416,f414,f423,f418,f419,f420,f424,f422,f425,f426,f427,f436,f429,f430,f437,f438,f439,f441,f442,f443,f444,f445,f446,f449,f448,f450,f451,f452,f453,f456,f455,f458,f465,f460,f461,f462,f466,f464,f467,f468,f469,f470,f472,f473,f474,f475,f477,f478,f479,f480,f482,f483,f484,f485,f490]) ).
fof(f490,plain,
~ strictly_less_than(sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2))),removemin_cpq_res(triple(sK0,sK1,sK2))),
inference(subsumption_resolution,[],[f487,f136]) ).
fof(f487,plain,
( ~ phi(findmin_cpq_eff(triple(sK0,sK1,sK2)))
| ~ strictly_less_than(sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2))),removemin_cpq_res(triple(sK0,sK1,sK2))) ),
inference(resolution,[],[f256,f215]) ).
fof(f485,plain,
! [X5] : succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),removemin_cpq_eff(insert_cpq(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))),X5))),
inference(resolution,[],[f252,f163]) ).
fof(f163,plain,
! [X0,X1] :
( succ_cpq(X0,removemin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f79]) ).
fof(f79,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax35) ).
fof(f484,plain,
! [X4] : succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),findmin_cpq_eff(insert_cpq(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))),X4))),
inference(resolution,[],[f252,f164]) ).
fof(f164,plain,
! [X0,X1] :
( succ_cpq(X0,findmin_cpq_eff(X1))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f80]) ).
fof(f80,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax34) ).
fof(f483,plain,
! [X2,X3] : succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),insert_cpq(insert_cpq(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))),X2),X3)),
inference(resolution,[],[f252,f177]) ).
fof(f177,plain,
! [X2,X0,X1] :
( succ_cpq(X0,insert_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f92]) ).
fof(f92,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax32) ).
fof(f482,plain,
! [X0,X1] : succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),remove_cpq(insert_cpq(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))),X0),X1)),
inference(resolution,[],[f252,f178]) ).
fof(f178,plain,
! [X2,X0,X1] :
( succ_cpq(X0,remove_cpq(X1,X2))
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f93]) ).
fof(f93,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax33) ).
fof(f480,plain,
! [X5] : succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),removemin_cpq_eff(remove_cpq(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))),X5))),
inference(resolution,[],[f251,f163]) ).
fof(f479,plain,
! [X4] : succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),findmin_cpq_eff(remove_cpq(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))),X4))),
inference(resolution,[],[f251,f164]) ).
fof(f478,plain,
! [X2,X3] : succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),insert_cpq(remove_cpq(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))),X2),X3)),
inference(resolution,[],[f251,f177]) ).
fof(f477,plain,
! [X0,X1] : succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),remove_cpq(remove_cpq(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))),X0),X1)),
inference(resolution,[],[f251,f178]) ).
fof(f475,plain,
succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),removemin_cpq_eff(removemin_cpq_eff(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2)))))),
inference(resolution,[],[f254,f163]) ).
fof(f474,plain,
succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),findmin_cpq_eff(removemin_cpq_eff(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2)))))),
inference(resolution,[],[f254,f164]) ).
fof(f473,plain,
! [X1] : succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),insert_cpq(removemin_cpq_eff(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2)))),X1)),
inference(resolution,[],[f254,f177]) ).
fof(f472,plain,
! [X0] : succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),remove_cpq(removemin_cpq_eff(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2)))),X0)),
inference(resolution,[],[f254,f178]) ).
fof(f470,plain,
succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),removemin_cpq_eff(findmin_cpq_eff(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2)))))),
inference(resolution,[],[f253,f163]) ).
fof(f469,plain,
succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),findmin_cpq_eff(findmin_cpq_eff(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2)))))),
inference(resolution,[],[f253,f164]) ).
fof(f468,plain,
! [X1] : succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),insert_cpq(findmin_cpq_eff(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2)))),X1)),
inference(resolution,[],[f253,f177]) ).
fof(f467,plain,
! [X0] : succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),remove_cpq(findmin_cpq_eff(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2)))),X0)),
inference(resolution,[],[f253,f178]) ).
fof(f464,plain,
! [X31,X28,X29,X32,X30,X33] :
( ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X28,insert_slb(X29,pair(X30,X31)),X32))))
| ~ strictly_less_than(X33,removemin_cpq_res(findmin_cpq_eff(triple(X28,insert_slb(X29,pair(X30,X31)),X32))))
| ~ strictly_less_than(findmin_pqp_res(X28),lookup_slb(insert_slb(X29,pair(X30,X31)),findmin_pqp_res(X28)))
| ~ contains_cpq(findmin_cpq_eff(triple(X28,insert_slb(X29,pair(X30,X31)),X32)),X33)
| create_slb = insert_slb(X29,pair(X30,X31))
| ~ contains_slb(X29,findmin_pqp_res(X28)) ),
inference(resolution,[],[f244,f200]) ).
fof(f200,plain,
! [X2,X3,X0,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| ~ contains_slb(X0,X2) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,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,[],[f131]) ).
fof(f131,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax21) ).
fof(f466,plain,
! [X26,X27,X24,X25,X23] :
( ~ strictly_less_than(findmin_pqp_res(X23),X25)
| ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X23,insert_slb(X24,pair(findmin_pqp_res(X23),X25)),X26))))
| ~ strictly_less_than(X27,removemin_cpq_res(findmin_cpq_eff(triple(X23,insert_slb(X24,pair(findmin_pqp_res(X23),X25)),X26))))
| ~ contains_cpq(findmin_cpq_eff(triple(X23,insert_slb(X24,pair(findmin_pqp_res(X23),X25)),X26)),X27)
| create_slb = insert_slb(X24,pair(findmin_pqp_res(X23),X25)) ),
inference(forward_demodulation,[],[f463,f175]) ).
fof(f175,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax26) ).
fof(f463,plain,
! [X26,X27,X24,X25,X23] :
( ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X23,insert_slb(X24,pair(findmin_pqp_res(X23),X25)),X26))))
| ~ strictly_less_than(X27,removemin_cpq_res(findmin_cpq_eff(triple(X23,insert_slb(X24,pair(findmin_pqp_res(X23),X25)),X26))))
| ~ strictly_less_than(findmin_pqp_res(X23),lookup_slb(insert_slb(X24,pair(findmin_pqp_res(X23),X25)),findmin_pqp_res(X23)))
| ~ contains_cpq(findmin_cpq_eff(triple(X23,insert_slb(X24,pair(findmin_pqp_res(X23),X25)),X26)),X27)
| create_slb = insert_slb(X24,pair(findmin_pqp_res(X23),X25)) ),
inference(resolution,[],[f244,f211]) ).
fof(f211,plain,
! [X2,X3,X0] : contains_slb(insert_slb(X0,pair(X2,X3)),X2),
inference(equality_resolution,[],[f201]) ).
fof(f201,plain,
! [X2,X3,X0,X1] :
( contains_slb(insert_slb(X0,pair(X1,X3)),X2)
| X1 != X2 ),
inference(cnf_transformation,[],[f132]) ).
fof(f462,plain,
! [X21,X18,X19,X17,X22,X20] :
( ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X17,X18,X19))))
| ~ strictly_less_than(X20,removemin_cpq_res(findmin_cpq_eff(triple(X17,X18,X19))))
| ~ strictly_less_than(findmin_pqp_res(X17),lookup_slb(X18,findmin_pqp_res(X17)))
| ~ contains_cpq(findmin_cpq_eff(triple(X17,X18,X19)),X20)
| create_slb = X18
| triple(X21,X18,bad) = remove_cpq(triple(X21,X18,X22),findmin_pqp_res(X17)) ),
inference(resolution,[],[f244,f187]) ).
fof(f187,plain,
! [X2,X3,X0,X1] :
( triple(X0,X1,bad) = remove_cpq(triple(X0,X1,X2),X3)
| contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax43) ).
fof(f461,plain,
! [X11,X16,X14,X15,X12,X13] :
( ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X11,X12,X13))))
| ~ strictly_less_than(X14,removemin_cpq_res(findmin_cpq_eff(triple(X11,X12,X13))))
| ~ strictly_less_than(findmin_pqp_res(X11),lookup_slb(X12,findmin_pqp_res(X11)))
| ~ contains_cpq(findmin_cpq_eff(triple(X11,X12,X13)),X14)
| create_slb = X12
| ~ contains_cpq(triple(X15,X12,X16),findmin_pqp_res(X11)) ),
inference(resolution,[],[f244,f197]) ).
fof(f197,plain,
! [X2,X3,X0,X1] :
( contains_slb(X1,X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax39) ).
fof(f460,plain,
! [X10,X8,X6,X9,X7,X5] :
( ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X5,X6,X7))))
| ~ strictly_less_than(X8,removemin_cpq_res(findmin_cpq_eff(triple(X5,X6,X7))))
| ~ strictly_less_than(findmin_pqp_res(X5),lookup_slb(X6,findmin_pqp_res(X5)))
| ~ contains_cpq(findmin_cpq_eff(triple(X5,X6,X7)),X8)
| create_slb = X6
| findmin_pqp_res(X5) = X9
| ~ contains_slb(insert_slb(X6,pair(X9,X10)),findmin_pqp_res(X5)) ),
inference(resolution,[],[f244,f199]) ).
fof(f199,plain,
! [X2,X3,X0,X1] :
( X1 = X2
| contains_slb(X0,X2)
| ~ contains_slb(insert_slb(X0,pair(X1,X3)),X2) ),
inference(cnf_transformation,[],[f132]) ).
fof(f465,plain,
! [X2,X3,X0,X1,X4] :
( ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X0,X1,X2))))
| ~ strictly_less_than(X3,removemin_cpq_res(findmin_cpq_eff(triple(X0,X1,X2))))
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_cpq(findmin_cpq_eff(triple(X0,X1,X2)),X3)
| create_slb = X1
| triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) = findmin_cpq_eff(triple(X0,X1,X4)) ),
inference(duplicate_literal_removal,[],[f459]) ).
fof(f459,plain,
! [X2,X3,X0,X1,X4] :
( ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X0,X1,X2))))
| ~ strictly_less_than(X3,removemin_cpq_res(findmin_cpq_eff(triple(X0,X1,X2))))
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_cpq(findmin_cpq_eff(triple(X0,X1,X2)),X3)
| create_slb = X1
| triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) = findmin_cpq_eff(triple(X0,X1,X4))
| create_slb = X1 ),
inference(resolution,[],[f244,f192]) ).
fof(f192,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,[],[f108]) ).
fof(f108,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,[],[f107]) ).
fof(f107,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,[],[f70]) ).
fof(f70,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax47) ).
fof(f458,plain,
! [X0] :
( phi(X0)
| ~ succ_cpq(X0,sK3(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))))) ),
inference(subsumption_resolution,[],[f457,f381]) ).
fof(f457,plain,
! [X0] :
( phi(X0)
| ~ check_cpq(sK3(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2)))))
| ~ succ_cpq(X0,sK3(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))))) ),
inference(resolution,[],[f380,f154]) ).
fof(f154,plain,
! [X0,X1] :
( phi(X0)
| ~ check_cpq(X1)
| ~ ok(X1)
| ~ succ_cpq(X0,X1) ),
inference(cnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ( phi(X0)
| ! [X1] :
( ~ check_cpq(X1)
| ~ ok(X1)
| ~ succ_cpq(X0,X1) ) )
& ( ( check_cpq(sK3(X0))
& ok(sK3(X0))
& succ_cpq(X0,sK3(X0)) )
| ~ phi(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3])],[f123,f124]) ).
fof(f124,plain,
! [X0] :
( ? [X2] :
( check_cpq(X2)
& ok(X2)
& succ_cpq(X0,X2) )
=> ( check_cpq(sK3(X0))
& ok(sK3(X0))
& succ_cpq(X0,sK3(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f123,plain,
! [X0] :
( ( phi(X0)
| ! [X1] :
( ~ check_cpq(X1)
| ~ ok(X1)
| ~ succ_cpq(X0,X1) ) )
& ( ? [X2] :
( check_cpq(X2)
& ok(X2)
& succ_cpq(X0,X2) )
| ~ phi(X0) ) ),
inference(rectify,[],[f122]) ).
fof(f122,plain,
! [X0] :
( ( phi(X0)
| ! [X1] :
( ~ check_cpq(X1)
| ~ ok(X1)
| ~ succ_cpq(X0,X1) ) )
& ( ? [X1] :
( check_cpq(X1)
& ok(X1)
& succ_cpq(X0,X1) )
| ~ phi(X0) ) ),
inference(nnf_transformation,[],[f62]) ).
fof(f62,axiom,
! [X0] :
( phi(X0)
<=> ? [X1] :
( check_cpq(X1)
& ok(X1)
& succ_cpq(X0,X1) ) ),
file('/export/starexec/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax62) ).
fof(f455,plain,
! [X38,X39,X36,X37,X34,X35,X33] :
( ~ phi(findmin_cpq_eff(remove_cpq(triple(X33,insert_slb(X34,pair(X35,X36)),X37),X38)))
| ~ strictly_less_than(X39,removemin_cpq_res(remove_cpq(triple(X33,insert_slb(X34,pair(X35,X36)),X37),X38)))
| ~ less_than(lookup_slb(insert_slb(X34,pair(X35,X36)),X38),X38)
| ~ contains_cpq(remove_cpq(triple(X33,insert_slb(X34,pair(X35,X36)),X37),X38),X39)
| ~ contains_slb(X34,X38) ),
inference(resolution,[],[f248,f200]) ).
fof(f456,plain,
! [X31,X28,X29,X27,X32,X30] :
( ~ less_than(X30,X29)
| ~ phi(findmin_cpq_eff(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29)))
| ~ strictly_less_than(X32,removemin_cpq_res(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29)))
| ~ contains_cpq(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29),X32) ),
inference(forward_demodulation,[],[f454,f175]) ).
fof(f454,plain,
! [X31,X28,X29,X27,X32,X30] :
( ~ phi(findmin_cpq_eff(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29)))
| ~ strictly_less_than(X32,removemin_cpq_res(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29)))
| ~ less_than(lookup_slb(insert_slb(X28,pair(X29,X30)),X29),X29)
| ~ contains_cpq(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29),X32) ),
inference(resolution,[],[f248,f211]) ).
fof(f453,plain,
! [X21,X26,X24,X22,X25,X23] :
( ~ phi(findmin_cpq_eff(remove_cpq(triple(X21,X22,X23),findmin_pqp_res(X24))))
| ~ strictly_less_than(X25,removemin_cpq_res(remove_cpq(triple(X21,X22,X23),findmin_pqp_res(X24))))
| ~ less_than(lookup_slb(X22,findmin_pqp_res(X24)),findmin_pqp_res(X24))
| ~ contains_cpq(remove_cpq(triple(X21,X22,X23),findmin_pqp_res(X24)),X25)
| findmin_cpq_eff(triple(X24,X22,X26)) = triple(X24,update_slb(X22,findmin_pqp_res(X24)),bad)
| create_slb = X22 ),
inference(resolution,[],[f248,f192]) ).
fof(f452,plain,
! [X18,X19,X16,X14,X17,X15,X20] :
( ~ phi(findmin_cpq_eff(remove_cpq(triple(X14,X15,X16),X17)))
| ~ strictly_less_than(X18,removemin_cpq_res(remove_cpq(triple(X14,X15,X16),X17)))
| ~ less_than(lookup_slb(X15,X17),X17)
| ~ contains_cpq(remove_cpq(triple(X14,X15,X16),X17),X18)
| triple(X19,X15,bad) = remove_cpq(triple(X19,X15,X20),X17) ),
inference(resolution,[],[f248,f187]) ).
fof(f451,plain,
! [X10,X11,X8,X9,X7,X12,X13] :
( ~ phi(findmin_cpq_eff(remove_cpq(triple(X7,X8,X9),X10)))
| ~ strictly_less_than(X11,removemin_cpq_res(remove_cpq(triple(X7,X8,X9),X10)))
| ~ less_than(lookup_slb(X8,X10),X10)
| ~ contains_cpq(remove_cpq(triple(X7,X8,X9),X10),X11)
| ~ contains_cpq(triple(X12,X8,X13),X10) ),
inference(resolution,[],[f248,f197]) ).
fof(f450,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ phi(findmin_cpq_eff(remove_cpq(triple(X0,X1,X2),X3)))
| ~ strictly_less_than(X4,removemin_cpq_res(remove_cpq(triple(X0,X1,X2),X3)))
| ~ less_than(lookup_slb(X1,X3),X3)
| ~ contains_cpq(remove_cpq(triple(X0,X1,X2),X3),X4)
| X3 = X5
| ~ contains_slb(insert_slb(X1,pair(X5,X6)),X3) ),
inference(resolution,[],[f248,f199]) ).
fof(f448,plain,
! [X38,X39,X36,X37,X34,X35,X33] :
( ~ phi(findmin_cpq_eff(remove_cpq(triple(X33,insert_slb(X34,pair(X35,X36)),X37),X38)))
| ~ strictly_less_than(X39,removemin_cpq_res(remove_cpq(triple(X33,insert_slb(X34,pair(X35,X36)),X37),X38)))
| ~ strictly_less_than(X38,lookup_slb(insert_slb(X34,pair(X35,X36)),X38))
| ~ contains_cpq(remove_cpq(triple(X33,insert_slb(X34,pair(X35,X36)),X37),X38),X39)
| ~ contains_slb(X34,X38) ),
inference(resolution,[],[f247,f200]) ).
fof(f449,plain,
! [X31,X28,X29,X27,X32,X30] :
( ~ strictly_less_than(X29,X30)
| ~ phi(findmin_cpq_eff(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29)))
| ~ strictly_less_than(X32,removemin_cpq_res(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29)))
| ~ contains_cpq(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29),X32) ),
inference(forward_demodulation,[],[f447,f175]) ).
fof(f447,plain,
! [X31,X28,X29,X27,X32,X30] :
( ~ phi(findmin_cpq_eff(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29)))
| ~ strictly_less_than(X32,removemin_cpq_res(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29)))
| ~ strictly_less_than(X29,lookup_slb(insert_slb(X28,pair(X29,X30)),X29))
| ~ contains_cpq(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29),X32) ),
inference(resolution,[],[f247,f211]) ).
fof(f446,plain,
! [X21,X26,X24,X22,X25,X23] :
( ~ phi(findmin_cpq_eff(remove_cpq(triple(X21,X22,X23),findmin_pqp_res(X24))))
| ~ strictly_less_than(X25,removemin_cpq_res(remove_cpq(triple(X21,X22,X23),findmin_pqp_res(X24))))
| ~ strictly_less_than(findmin_pqp_res(X24),lookup_slb(X22,findmin_pqp_res(X24)))
| ~ contains_cpq(remove_cpq(triple(X21,X22,X23),findmin_pqp_res(X24)),X25)
| findmin_cpq_eff(triple(X24,X22,X26)) = triple(X24,update_slb(X22,findmin_pqp_res(X24)),bad)
| create_slb = X22 ),
inference(resolution,[],[f247,f192]) ).
fof(f445,plain,
! [X18,X19,X16,X14,X17,X15,X20] :
( ~ phi(findmin_cpq_eff(remove_cpq(triple(X14,X15,X16),X17)))
| ~ strictly_less_than(X18,removemin_cpq_res(remove_cpq(triple(X14,X15,X16),X17)))
| ~ strictly_less_than(X17,lookup_slb(X15,X17))
| ~ contains_cpq(remove_cpq(triple(X14,X15,X16),X17),X18)
| triple(X19,X15,bad) = remove_cpq(triple(X19,X15,X20),X17) ),
inference(resolution,[],[f247,f187]) ).
fof(f444,plain,
! [X10,X11,X8,X9,X7,X12,X13] :
( ~ phi(findmin_cpq_eff(remove_cpq(triple(X7,X8,X9),X10)))
| ~ strictly_less_than(X11,removemin_cpq_res(remove_cpq(triple(X7,X8,X9),X10)))
| ~ strictly_less_than(X10,lookup_slb(X8,X10))
| ~ contains_cpq(remove_cpq(triple(X7,X8,X9),X10),X11)
| ~ contains_cpq(triple(X12,X8,X13),X10) ),
inference(resolution,[],[f247,f197]) ).
fof(f443,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( ~ phi(findmin_cpq_eff(remove_cpq(triple(X0,X1,X2),X3)))
| ~ strictly_less_than(X4,removemin_cpq_res(remove_cpq(triple(X0,X1,X2),X3)))
| ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_cpq(remove_cpq(triple(X0,X1,X2),X3),X4)
| X3 = X5
| ~ contains_slb(insert_slb(X1,pair(X5,X6)),X3) ),
inference(resolution,[],[f247,f199]) ).
fof(f442,plain,
! [X10,X8,X6,X9,X7,X5] :
( ~ less_than(lookup_slb(X5,findmin_pqp_res(X8)),findmin_pqp_res(X8))
| ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X8,insert_slb(X5,pair(X6,X7)),X9))))
| ~ strictly_less_than(X10,removemin_cpq_res(findmin_cpq_eff(triple(X8,insert_slb(X5,pair(X6,X7)),X9))))
| ~ contains_cpq(findmin_cpq_eff(triple(X8,insert_slb(X5,pair(X6,X7)),X9)),X10)
| create_slb = insert_slb(X5,pair(X6,X7))
| ~ contains_slb(X5,findmin_pqp_res(X8))
| findmin_pqp_res(X8) = X6 ),
inference(superposition,[],[f249,f190]) ).
fof(f190,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,[],[f104]) ).
fof(f104,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,[],[f103]) ).
fof(f103,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax27) ).
fof(f441,plain,
! [X2,X3,X0,X1,X4] :
( ~ less_than(X2,findmin_pqp_res(X1))
| ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X1,insert_slb(X0,pair(findmin_pqp_res(X1),X2)),X3))))
| ~ strictly_less_than(X4,removemin_cpq_res(findmin_cpq_eff(triple(X1,insert_slb(X0,pair(findmin_pqp_res(X1),X2)),X3))))
| ~ contains_cpq(findmin_cpq_eff(triple(X1,insert_slb(X0,pair(findmin_pqp_res(X1),X2)),X3)),X4)
| create_slb = insert_slb(X0,pair(findmin_pqp_res(X1),X2)) ),
inference(superposition,[],[f249,f175]) ).
fof(f439,plain,
! [X10,X11,X9,X12] :
( ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X9,X10,X11))))
| ~ strictly_less_than(X12,removemin_cpq_res(findmin_cpq_eff(triple(X9,X10,X11))))
| ~ contains_cpq(findmin_cpq_eff(triple(X9,X10,X11)),X12)
| create_slb = X10
| less_than(findmin_pqp_res(X9),lookup_slb(X10,findmin_pqp_res(X9))) ),
inference(resolution,[],[f249,f162]) ).
fof(f162,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/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',totality) ).
fof(f438,plain,
! [X8,X6,X7,X5] :
( ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X5,X6,X7))))
| ~ strictly_less_than(X8,removemin_cpq_res(findmin_cpq_eff(triple(X5,X6,X7))))
| ~ contains_cpq(findmin_cpq_eff(triple(X5,X6,X7)),X8)
| create_slb = X6
| strictly_less_than(findmin_pqp_res(X5),lookup_slb(X6,findmin_pqp_res(X5)))
| ~ less_than(findmin_pqp_res(X5),lookup_slb(X6,findmin_pqp_res(X5))) ),
inference(resolution,[],[f249,f169]) ).
fof(f169,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f90]) ).
fof(f90,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(flattening,[],[f89]) ).
fof(f89,plain,
! [X0,X1] :
( strictly_less_than(X0,X1)
| less_than(X1,X0)
| ~ less_than(X0,X1) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,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/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',stricly_smaller_definition) ).
fof(f437,plain,
! [X2,X3,X0,X1,X4] :
( ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X0,X1,X2))))
| ~ strictly_less_than(X3,removemin_cpq_res(findmin_cpq_eff(triple(X0,X1,X2))))
| ~ contains_cpq(findmin_cpq_eff(triple(X0,X1,X2)),X3)
| create_slb = X1
| ~ less_than(X4,findmin_pqp_res(X0))
| ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),X4) ),
inference(resolution,[],[f249,f181]) ).
fof(f181,plain,
! [X2,X0,X1] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(cnf_transformation,[],[f98]) ).
fof(f98,plain,
! [X0,X1,X2] :
( less_than(X0,X2)
| ~ less_than(X1,X2)
| ~ less_than(X0,X1) ),
inference(flattening,[],[f97]) ).
fof(f97,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/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',transitivity) ).
fof(f430,plain,
! [X26,X24,X22,X25,X23] :
( ~ contains_cpq(findmin_cpq_eff(remove_cpq(triple(X22,X24,X25),X23)),X26)
| ~ phi(findmin_cpq_eff(findmin_cpq_eff(remove_cpq(triple(X22,X24,X25),X23))))
| ~ strictly_less_than(X26,removemin_cpq_res(findmin_cpq_eff(remove_cpq(triple(X22,X24,X25),X23))))
| contains_slb(remove_slb(X24,X23),findmin_pqp_res(remove_pqp(X22,X23)))
| create_slb = remove_slb(X24,X23)
| ~ less_than(lookup_slb(X24,X23),X23)
| ~ contains_slb(X24,X23) ),
inference(superposition,[],[f245,f196]) ).
fof(f196,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,[],[f116]) ).
fof(f116,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,[],[f115]) ).
fof(f115,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax44) ).
fof(f429,plain,
! [X21,X18,X19,X17,X20] :
( ~ contains_cpq(findmin_cpq_eff(remove_cpq(triple(X17,X19,X20),X18)),X21)
| ~ phi(findmin_cpq_eff(findmin_cpq_eff(remove_cpq(triple(X17,X19,X20),X18))))
| ~ strictly_less_than(X21,removemin_cpq_res(findmin_cpq_eff(remove_cpq(triple(X17,X19,X20),X18))))
| contains_slb(remove_slb(X19,X18),findmin_pqp_res(remove_pqp(X17,X18)))
| create_slb = remove_slb(X19,X18)
| ~ strictly_less_than(X18,lookup_slb(X19,X18))
| ~ contains_slb(X19,X18) ),
inference(superposition,[],[f245,f195]) ).
fof(f195,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,[],[f114]) ).
fof(f114,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,[],[f113]) ).
fof(f113,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax45) ).
fof(f436,plain,
! [X16,X14,X15,X13] :
( ~ contains_cpq(findmin_cpq_eff(findmin_cpq_eff(triple(X13,X14,X15))),X16)
| ~ phi(findmin_cpq_eff(findmin_cpq_eff(findmin_cpq_eff(triple(X13,X14,X15)))))
| ~ strictly_less_than(X16,removemin_cpq_res(findmin_cpq_eff(findmin_cpq_eff(triple(X13,X14,X15)))))
| contains_slb(update_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| create_slb = update_slb(X14,findmin_pqp_res(X13))
| ~ less_than(lookup_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| create_slb = X14 ),
inference(subsumption_resolution,[],[f428,f427]) ).
fof(f428,plain,
! [X16,X14,X15,X13] :
( ~ contains_cpq(findmin_cpq_eff(findmin_cpq_eff(triple(X13,X14,X15))),X16)
| ~ phi(findmin_cpq_eff(findmin_cpq_eff(findmin_cpq_eff(triple(X13,X14,X15)))))
| ~ strictly_less_than(X16,removemin_cpq_res(findmin_cpq_eff(findmin_cpq_eff(triple(X13,X14,X15)))))
| contains_slb(update_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| create_slb = update_slb(X14,findmin_pqp_res(X13))
| ~ less_than(lookup_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| ~ contains_slb(X14,findmin_pqp_res(X13))
| create_slb = X14 ),
inference(superposition,[],[f245,f194]) ).
fof(f194,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,[],[f112]) ).
fof(f112,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,[],[f111]) ).
fof(f111,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,[],[f72]) ).
fof(f72,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax49) ).
fof(f427,plain,
! [X10,X11,X9,X12] :
( ~ contains_cpq(findmin_cpq_eff(findmin_cpq_eff(triple(X9,X10,X11))),X12)
| ~ phi(findmin_cpq_eff(findmin_cpq_eff(findmin_cpq_eff(triple(X9,X10,X11)))))
| ~ strictly_less_than(X12,removemin_cpq_res(findmin_cpq_eff(findmin_cpq_eff(triple(X9,X10,X11)))))
| contains_slb(update_slb(X10,findmin_pqp_res(X9)),findmin_pqp_res(X9))
| create_slb = update_slb(X10,findmin_pqp_res(X9))
| contains_slb(X10,findmin_pqp_res(X9))
| create_slb = X10 ),
inference(superposition,[],[f245,f192]) ).
fof(f426,plain,
! [X8,X6,X7,X5] :
( ~ contains_cpq(findmin_cpq_eff(findmin_cpq_eff(triple(X5,X6,X7))),X8)
| ~ phi(findmin_cpq_eff(findmin_cpq_eff(findmin_cpq_eff(triple(X5,X6,X7)))))
| ~ strictly_less_than(X8,removemin_cpq_res(findmin_cpq_eff(findmin_cpq_eff(triple(X5,X6,X7)))))
| contains_slb(update_slb(X6,findmin_pqp_res(X5)),findmin_pqp_res(X5))
| create_slb = update_slb(X6,findmin_pqp_res(X5))
| ~ strictly_less_than(findmin_pqp_res(X5),lookup_slb(X6,findmin_pqp_res(X5)))
| ~ contains_slb(X6,findmin_pqp_res(X5))
| create_slb = X6 ),
inference(superposition,[],[f245,f193]) ).
fof(f193,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,[],[f110]) ).
fof(f110,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,[],[f109]) ).
fof(f109,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,[],[f71]) ).
fof(f71,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax48) ).
fof(f425,plain,
! [X2,X3,X0,X1,X4] :
( ~ contains_cpq(findmin_cpq_eff(insert_cpq(triple(X0,X2,X3),X1)),X4)
| ~ phi(findmin_cpq_eff(findmin_cpq_eff(insert_cpq(triple(X0,X2,X3),X1))))
| ~ strictly_less_than(X4,removemin_cpq_res(findmin_cpq_eff(insert_cpq(triple(X0,X2,X3),X1))))
| contains_slb(insert_slb(X2,pair(X1,bottom)),findmin_pqp_res(insert_pqp(X0,X1)))
| create_slb = insert_slb(X2,pair(X1,bottom)) ),
inference(superposition,[],[f245,f185]) ).
fof(f185,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax42) ).
fof(f422,plain,
! [X31,X28,X29,X32,X30,X33] :
( contains_cpq(findmin_cpq_eff(triple(X28,insert_slb(X29,pair(X30,X31)),X32)),X33)
| ~ strictly_less_than(findmin_pqp_res(X28),lookup_slb(insert_slb(X29,pair(X30,X31)),findmin_pqp_res(X28)))
| ~ contains_pq(i(findmin_cpq_eff(triple(X28,insert_slb(X29,pair(X30,X31)),X32))),X33)
| create_slb = insert_slb(X29,pair(X30,X31))
| ~ contains_slb(X29,findmin_pqp_res(X28)) ),
inference(resolution,[],[f234,f200]) ).
fof(f424,plain,
! [X26,X27,X24,X25,X23] :
( ~ strictly_less_than(findmin_pqp_res(X23),X25)
| contains_cpq(findmin_cpq_eff(triple(X23,insert_slb(X24,pair(findmin_pqp_res(X23),X25)),X26)),X27)
| ~ contains_pq(i(findmin_cpq_eff(triple(X23,insert_slb(X24,pair(findmin_pqp_res(X23),X25)),X26))),X27)
| create_slb = insert_slb(X24,pair(findmin_pqp_res(X23),X25)) ),
inference(forward_demodulation,[],[f421,f175]) ).
fof(f421,plain,
! [X26,X27,X24,X25,X23] :
( contains_cpq(findmin_cpq_eff(triple(X23,insert_slb(X24,pair(findmin_pqp_res(X23),X25)),X26)),X27)
| ~ strictly_less_than(findmin_pqp_res(X23),lookup_slb(insert_slb(X24,pair(findmin_pqp_res(X23),X25)),findmin_pqp_res(X23)))
| ~ contains_pq(i(findmin_cpq_eff(triple(X23,insert_slb(X24,pair(findmin_pqp_res(X23),X25)),X26))),X27)
| create_slb = insert_slb(X24,pair(findmin_pqp_res(X23),X25)) ),
inference(resolution,[],[f234,f211]) ).
fof(f420,plain,
! [X21,X18,X19,X17,X22,X20] :
( contains_cpq(findmin_cpq_eff(triple(X17,X18,X19)),X20)
| ~ strictly_less_than(findmin_pqp_res(X17),lookup_slb(X18,findmin_pqp_res(X17)))
| ~ contains_pq(i(findmin_cpq_eff(triple(X17,X18,X19))),X20)
| create_slb = X18
| triple(X21,X18,bad) = remove_cpq(triple(X21,X18,X22),findmin_pqp_res(X17)) ),
inference(resolution,[],[f234,f187]) ).
fof(f419,plain,
! [X11,X16,X14,X15,X12,X13] :
( contains_cpq(findmin_cpq_eff(triple(X11,X12,X13)),X14)
| ~ strictly_less_than(findmin_pqp_res(X11),lookup_slb(X12,findmin_pqp_res(X11)))
| ~ contains_pq(i(findmin_cpq_eff(triple(X11,X12,X13))),X14)
| create_slb = X12
| ~ contains_cpq(triple(X15,X12,X16),findmin_pqp_res(X11)) ),
inference(resolution,[],[f234,f197]) ).
fof(f418,plain,
! [X10,X8,X6,X9,X7,X5] :
( contains_cpq(findmin_cpq_eff(triple(X5,X6,X7)),X8)
| ~ strictly_less_than(findmin_pqp_res(X5),lookup_slb(X6,findmin_pqp_res(X5)))
| ~ contains_pq(i(findmin_cpq_eff(triple(X5,X6,X7))),X8)
| create_slb = X6
| findmin_pqp_res(X5) = X9
| ~ contains_slb(insert_slb(X6,pair(X9,X10)),findmin_pqp_res(X5)) ),
inference(resolution,[],[f234,f199]) ).
fof(f423,plain,
! [X2,X3,X0,X1,X4] :
( contains_cpq(findmin_cpq_eff(triple(X0,X1,X2)),X3)
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_pq(i(findmin_cpq_eff(triple(X0,X1,X2))),X3)
| create_slb = X1
| triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) = findmin_cpq_eff(triple(X0,X1,X4)) ),
inference(duplicate_literal_removal,[],[f417]) ).
fof(f417,plain,
! [X2,X3,X0,X1,X4] :
( contains_cpq(findmin_cpq_eff(triple(X0,X1,X2)),X3)
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_pq(i(findmin_cpq_eff(triple(X0,X1,X2))),X3)
| create_slb = X1
| triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) = findmin_cpq_eff(triple(X0,X1,X4))
| create_slb = X1 ),
inference(resolution,[],[f234,f192]) ).
fof(f414,plain,
! [X31,X28,X29,X32,X30,X33] :
( contains_pq(i(findmin_cpq_eff(triple(X28,insert_slb(X29,pair(X30,X31)),X32))),X33)
| ~ strictly_less_than(findmin_pqp_res(X28),lookup_slb(insert_slb(X29,pair(X30,X31)),findmin_pqp_res(X28)))
| ~ contains_cpq(findmin_cpq_eff(triple(X28,insert_slb(X29,pair(X30,X31)),X32)),X33)
| create_slb = insert_slb(X29,pair(X30,X31))
| ~ contains_slb(X29,findmin_pqp_res(X28)) ),
inference(resolution,[],[f225,f200]) ).
fof(f416,plain,
! [X26,X27,X24,X25,X23] :
( ~ strictly_less_than(findmin_pqp_res(X23),X25)
| contains_pq(i(findmin_cpq_eff(triple(X23,insert_slb(X24,pair(findmin_pqp_res(X23),X25)),X26))),X27)
| ~ contains_cpq(findmin_cpq_eff(triple(X23,insert_slb(X24,pair(findmin_pqp_res(X23),X25)),X26)),X27)
| create_slb = insert_slb(X24,pair(findmin_pqp_res(X23),X25)) ),
inference(forward_demodulation,[],[f413,f175]) ).
fof(f413,plain,
! [X26,X27,X24,X25,X23] :
( contains_pq(i(findmin_cpq_eff(triple(X23,insert_slb(X24,pair(findmin_pqp_res(X23),X25)),X26))),X27)
| ~ strictly_less_than(findmin_pqp_res(X23),lookup_slb(insert_slb(X24,pair(findmin_pqp_res(X23),X25)),findmin_pqp_res(X23)))
| ~ contains_cpq(findmin_cpq_eff(triple(X23,insert_slb(X24,pair(findmin_pqp_res(X23),X25)),X26)),X27)
| create_slb = insert_slb(X24,pair(findmin_pqp_res(X23),X25)) ),
inference(resolution,[],[f225,f211]) ).
fof(f412,plain,
! [X21,X18,X19,X17,X22,X20] :
( contains_pq(i(findmin_cpq_eff(triple(X17,X18,X19))),X20)
| ~ strictly_less_than(findmin_pqp_res(X17),lookup_slb(X18,findmin_pqp_res(X17)))
| ~ contains_cpq(findmin_cpq_eff(triple(X17,X18,X19)),X20)
| create_slb = X18
| triple(X21,X18,bad) = remove_cpq(triple(X21,X18,X22),findmin_pqp_res(X17)) ),
inference(resolution,[],[f225,f187]) ).
fof(f411,plain,
! [X11,X16,X14,X15,X12,X13] :
( contains_pq(i(findmin_cpq_eff(triple(X11,X12,X13))),X14)
| ~ strictly_less_than(findmin_pqp_res(X11),lookup_slb(X12,findmin_pqp_res(X11)))
| ~ contains_cpq(findmin_cpq_eff(triple(X11,X12,X13)),X14)
| create_slb = X12
| ~ contains_cpq(triple(X15,X12,X16),findmin_pqp_res(X11)) ),
inference(resolution,[],[f225,f197]) ).
fof(f410,plain,
! [X10,X8,X6,X9,X7,X5] :
( contains_pq(i(findmin_cpq_eff(triple(X5,X6,X7))),X8)
| ~ strictly_less_than(findmin_pqp_res(X5),lookup_slb(X6,findmin_pqp_res(X5)))
| ~ contains_cpq(findmin_cpq_eff(triple(X5,X6,X7)),X8)
| create_slb = X6
| findmin_pqp_res(X5) = X9
| ~ contains_slb(insert_slb(X6,pair(X9,X10)),findmin_pqp_res(X5)) ),
inference(resolution,[],[f225,f199]) ).
fof(f415,plain,
! [X2,X3,X0,X1,X4] :
( contains_pq(i(findmin_cpq_eff(triple(X0,X1,X2))),X3)
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_cpq(findmin_cpq_eff(triple(X0,X1,X2)),X3)
| create_slb = X1
| triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) = findmin_cpq_eff(triple(X0,X1,X4)) ),
inference(duplicate_literal_removal,[],[f409]) ).
fof(f409,plain,
! [X2,X3,X0,X1,X4] :
( contains_pq(i(findmin_cpq_eff(triple(X0,X1,X2))),X3)
| ~ strictly_less_than(findmin_pqp_res(X0),lookup_slb(X1,findmin_pqp_res(X0)))
| ~ contains_cpq(findmin_cpq_eff(triple(X0,X1,X2)),X3)
| create_slb = X1
| triple(X0,update_slb(X1,findmin_pqp_res(X0)),bad) = findmin_cpq_eff(triple(X0,X1,X4))
| create_slb = X1 ),
inference(resolution,[],[f225,f192]) ).
fof(f407,plain,
! [X31,X28,X29,X27,X32,X30] :
( ~ contains_cpq(insert_cpq(remove_cpq(triple(X27,X29,X30),X28),X31),X32)
| ~ phi(findmin_cpq_eff(insert_cpq(remove_cpq(triple(X27,X29,X30),X28),X31)))
| ~ strictly_less_than(X32,removemin_cpq_res(insert_cpq(remove_cpq(triple(X27,X29,X30),X28),X31)))
| ~ less_than(lookup_slb(X29,X28),X28)
| ~ contains_slb(X29,X28) ),
inference(superposition,[],[f243,f196]) ).
fof(f406,plain,
! [X21,X26,X24,X22,X25,X23] :
( ~ contains_cpq(insert_cpq(remove_cpq(triple(X21,X23,X24),X22),X25),X26)
| ~ phi(findmin_cpq_eff(insert_cpq(remove_cpq(triple(X21,X23,X24),X22),X25)))
| ~ strictly_less_than(X26,removemin_cpq_res(insert_cpq(remove_cpq(triple(X21,X23,X24),X22),X25)))
| ~ strictly_less_than(X22,lookup_slb(X23,X22))
| ~ contains_slb(X23,X22) ),
inference(superposition,[],[f243,f195]) ).
fof(f408,plain,
! [X18,X19,X16,X17,X20] :
( ~ contains_cpq(insert_cpq(findmin_cpq_eff(triple(X16,X17,X18)),X19),X20)
| ~ phi(findmin_cpq_eff(insert_cpq(findmin_cpq_eff(triple(X16,X17,X18)),X19)))
| ~ strictly_less_than(X20,removemin_cpq_res(insert_cpq(findmin_cpq_eff(triple(X16,X17,X18)),X19)))
| ~ less_than(lookup_slb(X17,findmin_pqp_res(X16)),findmin_pqp_res(X16))
| create_slb = X17 ),
inference(subsumption_resolution,[],[f405,f404]) ).
fof(f405,plain,
! [X18,X19,X16,X17,X20] :
( ~ contains_cpq(insert_cpq(findmin_cpq_eff(triple(X16,X17,X18)),X19),X20)
| ~ phi(findmin_cpq_eff(insert_cpq(findmin_cpq_eff(triple(X16,X17,X18)),X19)))
| ~ strictly_less_than(X20,removemin_cpq_res(insert_cpq(findmin_cpq_eff(triple(X16,X17,X18)),X19)))
| ~ less_than(lookup_slb(X17,findmin_pqp_res(X16)),findmin_pqp_res(X16))
| ~ contains_slb(X17,findmin_pqp_res(X16))
| create_slb = X17 ),
inference(superposition,[],[f243,f194]) ).
fof(f404,plain,
! [X11,X14,X15,X12,X13] :
( ~ contains_cpq(insert_cpq(findmin_cpq_eff(triple(X11,X12,X13)),X14),X15)
| ~ phi(findmin_cpq_eff(insert_cpq(findmin_cpq_eff(triple(X11,X12,X13)),X14)))
| ~ strictly_less_than(X15,removemin_cpq_res(insert_cpq(findmin_cpq_eff(triple(X11,X12,X13)),X14)))
| contains_slb(X12,findmin_pqp_res(X11))
| create_slb = X12 ),
inference(superposition,[],[f243,f192]) ).
fof(f403,plain,
! [X10,X8,X6,X9,X7] :
( ~ contains_cpq(insert_cpq(findmin_cpq_eff(triple(X6,X7,X8)),X9),X10)
| ~ phi(findmin_cpq_eff(insert_cpq(findmin_cpq_eff(triple(X6,X7,X8)),X9)))
| ~ strictly_less_than(X10,removemin_cpq_res(insert_cpq(findmin_cpq_eff(triple(X6,X7,X8)),X9)))
| ~ strictly_less_than(findmin_pqp_res(X6),lookup_slb(X7,findmin_pqp_res(X6)))
| ~ contains_slb(X7,findmin_pqp_res(X6))
| create_slb = X7 ),
inference(superposition,[],[f243,f193]) ).
fof(f402,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ contains_cpq(insert_cpq(insert_cpq(triple(X0,X2,X3),X1),X4),X5)
| ~ phi(findmin_cpq_eff(insert_cpq(insert_cpq(triple(X0,X2,X3),X1),X4)))
| ~ strictly_less_than(X5,removemin_cpq_res(insert_cpq(insert_cpq(triple(X0,X2,X3),X1),X4))) ),
inference(superposition,[],[f243,f185]) ).
fof(f401,plain,
! [X10,X8,X6,X9,X7,X5] :
( ~ less_than(lookup_slb(X5,findmin_pqp_res(X8)),findmin_pqp_res(X8))
| contains_cpq(findmin_cpq_eff(triple(X8,insert_slb(X5,pair(X6,X7)),X9)),X10)
| ~ contains_pq(i(findmin_cpq_eff(triple(X8,insert_slb(X5,pair(X6,X7)),X9))),X10)
| create_slb = insert_slb(X5,pair(X6,X7))
| ~ contains_slb(X5,findmin_pqp_res(X8))
| findmin_pqp_res(X8) = X6 ),
inference(superposition,[],[f241,f190]) ).
fof(f400,plain,
! [X2,X3,X0,X1,X4] :
( ~ less_than(X2,findmin_pqp_res(X1))
| contains_cpq(findmin_cpq_eff(triple(X1,insert_slb(X0,pair(findmin_pqp_res(X1),X2)),X3)),X4)
| ~ contains_pq(i(findmin_cpq_eff(triple(X1,insert_slb(X0,pair(findmin_pqp_res(X1),X2)),X3))),X4)
| create_slb = insert_slb(X0,pair(findmin_pqp_res(X1),X2)) ),
inference(superposition,[],[f241,f175]) ).
fof(f398,plain,
! [X10,X11,X9,X12] :
( contains_cpq(findmin_cpq_eff(triple(X9,X10,X11)),X12)
| ~ contains_pq(i(findmin_cpq_eff(triple(X9,X10,X11))),X12)
| create_slb = X10
| less_than(findmin_pqp_res(X9),lookup_slb(X10,findmin_pqp_res(X9))) ),
inference(resolution,[],[f241,f162]) ).
fof(f397,plain,
! [X8,X6,X7,X5] :
( contains_cpq(findmin_cpq_eff(triple(X5,X6,X7)),X8)
| ~ contains_pq(i(findmin_cpq_eff(triple(X5,X6,X7))),X8)
| create_slb = X6
| strictly_less_than(findmin_pqp_res(X5),lookup_slb(X6,findmin_pqp_res(X5)))
| ~ less_than(findmin_pqp_res(X5),lookup_slb(X6,findmin_pqp_res(X5))) ),
inference(resolution,[],[f241,f169]) ).
fof(f396,plain,
! [X2,X3,X0,X1,X4] :
( contains_cpq(findmin_cpq_eff(triple(X0,X1,X2)),X3)
| ~ contains_pq(i(findmin_cpq_eff(triple(X0,X1,X2))),X3)
| create_slb = X1
| ~ less_than(X4,findmin_pqp_res(X0))
| ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),X4) ),
inference(resolution,[],[f241,f181]) ).
fof(f394,plain,
! [X38,X39,X36,X37,X34,X35,X33] :
( contains_cpq(remove_cpq(triple(X33,insert_slb(X34,pair(X35,X36)),X37),X38),X39)
| ~ less_than(lookup_slb(insert_slb(X34,pair(X35,X36)),X38),X38)
| ~ contains_pq(i(remove_cpq(triple(X33,insert_slb(X34,pair(X35,X36)),X37),X38)),X39)
| ~ contains_slb(X34,X38) ),
inference(resolution,[],[f238,f200]) ).
fof(f395,plain,
! [X31,X28,X29,X27,X32,X30] :
( ~ less_than(X30,X29)
| contains_cpq(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29),X32)
| ~ contains_pq(i(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29)),X32) ),
inference(forward_demodulation,[],[f393,f175]) ).
fof(f393,plain,
! [X31,X28,X29,X27,X32,X30] :
( contains_cpq(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29),X32)
| ~ less_than(lookup_slb(insert_slb(X28,pair(X29,X30)),X29),X29)
| ~ contains_pq(i(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29)),X32) ),
inference(resolution,[],[f238,f211]) ).
fof(f392,plain,
! [X21,X26,X24,X22,X25,X23] :
( contains_cpq(remove_cpq(triple(X21,X22,X23),findmin_pqp_res(X24)),X25)
| ~ less_than(lookup_slb(X22,findmin_pqp_res(X24)),findmin_pqp_res(X24))
| ~ contains_pq(i(remove_cpq(triple(X21,X22,X23),findmin_pqp_res(X24))),X25)
| findmin_cpq_eff(triple(X24,X22,X26)) = triple(X24,update_slb(X22,findmin_pqp_res(X24)),bad)
| create_slb = X22 ),
inference(resolution,[],[f238,f192]) ).
fof(f391,plain,
! [X18,X19,X16,X14,X17,X15,X20] :
( contains_cpq(remove_cpq(triple(X14,X15,X16),X17),X18)
| ~ less_than(lookup_slb(X15,X17),X17)
| ~ contains_pq(i(remove_cpq(triple(X14,X15,X16),X17)),X18)
| triple(X19,X15,bad) = remove_cpq(triple(X19,X15,X20),X17) ),
inference(resolution,[],[f238,f187]) ).
fof(f390,plain,
! [X10,X11,X8,X9,X7,X12,X13] :
( contains_cpq(remove_cpq(triple(X7,X8,X9),X10),X11)
| ~ less_than(lookup_slb(X8,X10),X10)
| ~ contains_pq(i(remove_cpq(triple(X7,X8,X9),X10)),X11)
| ~ contains_cpq(triple(X12,X8,X13),X10) ),
inference(resolution,[],[f238,f197]) ).
fof(f389,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( contains_cpq(remove_cpq(triple(X0,X1,X2),X3),X4)
| ~ less_than(lookup_slb(X1,X3),X3)
| ~ contains_pq(i(remove_cpq(triple(X0,X1,X2),X3)),X4)
| X3 = X5
| ~ contains_slb(insert_slb(X1,pair(X5,X6)),X3) ),
inference(resolution,[],[f238,f199]) ).
fof(f387,plain,
! [X38,X39,X36,X37,X34,X35,X33] :
( contains_cpq(remove_cpq(triple(X33,insert_slb(X34,pair(X35,X36)),X37),X38),X39)
| ~ strictly_less_than(X38,lookup_slb(insert_slb(X34,pair(X35,X36)),X38))
| ~ contains_pq(i(remove_cpq(triple(X33,insert_slb(X34,pair(X35,X36)),X37),X38)),X39)
| ~ contains_slb(X34,X38) ),
inference(resolution,[],[f237,f200]) ).
fof(f388,plain,
! [X31,X28,X29,X27,X32,X30] :
( ~ strictly_less_than(X29,X30)
| contains_cpq(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29),X32)
| ~ contains_pq(i(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29)),X32) ),
inference(forward_demodulation,[],[f386,f175]) ).
fof(f386,plain,
! [X31,X28,X29,X27,X32,X30] :
( contains_cpq(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29),X32)
| ~ strictly_less_than(X29,lookup_slb(insert_slb(X28,pair(X29,X30)),X29))
| ~ contains_pq(i(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29)),X32) ),
inference(resolution,[],[f237,f211]) ).
fof(f385,plain,
! [X21,X26,X24,X22,X25,X23] :
( contains_cpq(remove_cpq(triple(X21,X22,X23),findmin_pqp_res(X24)),X25)
| ~ strictly_less_than(findmin_pqp_res(X24),lookup_slb(X22,findmin_pqp_res(X24)))
| ~ contains_pq(i(remove_cpq(triple(X21,X22,X23),findmin_pqp_res(X24))),X25)
| findmin_cpq_eff(triple(X24,X22,X26)) = triple(X24,update_slb(X22,findmin_pqp_res(X24)),bad)
| create_slb = X22 ),
inference(resolution,[],[f237,f192]) ).
fof(f384,plain,
! [X18,X19,X16,X14,X17,X15,X20] :
( contains_cpq(remove_cpq(triple(X14,X15,X16),X17),X18)
| ~ strictly_less_than(X17,lookup_slb(X15,X17))
| ~ contains_pq(i(remove_cpq(triple(X14,X15,X16),X17)),X18)
| triple(X19,X15,bad) = remove_cpq(triple(X19,X15,X20),X17) ),
inference(resolution,[],[f237,f187]) ).
fof(f383,plain,
! [X10,X11,X8,X9,X7,X12,X13] :
( contains_cpq(remove_cpq(triple(X7,X8,X9),X10),X11)
| ~ strictly_less_than(X10,lookup_slb(X8,X10))
| ~ contains_pq(i(remove_cpq(triple(X7,X8,X9),X10)),X11)
| ~ contains_cpq(triple(X12,X8,X13),X10) ),
inference(resolution,[],[f237,f197]) ).
fof(f382,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( contains_cpq(remove_cpq(triple(X0,X1,X2),X3),X4)
| ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_pq(i(remove_cpq(triple(X0,X1,X2),X3)),X4)
| X3 = X5
| ~ contains_slb(insert_slb(X1,pair(X5,X6)),X3) ),
inference(resolution,[],[f237,f199]) ).
fof(f381,plain,
check_cpq(sK3(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))))),
inference(resolution,[],[f282,f153]) ).
fof(f153,plain,
! [X0] :
( check_cpq(sK3(X0))
| ~ phi(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f380,plain,
ok(sK3(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))))),
inference(resolution,[],[f282,f152]) ).
fof(f152,plain,
! [X0] :
( ok(sK3(X0))
| ~ phi(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f379,plain,
succ_cpq(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))),sK3(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))))),
inference(resolution,[],[f282,f151]) ).
fof(f151,plain,
! [X0] :
( succ_cpq(X0,sK3(X0))
| ~ phi(X0) ),
inference(cnf_transformation,[],[f125]) ).
fof(f378,plain,
! [X10,X8,X6,X9,X7,X5] :
( ~ less_than(lookup_slb(X5,findmin_pqp_res(X8)),findmin_pqp_res(X8))
| contains_pq(i(findmin_cpq_eff(triple(X8,insert_slb(X5,pair(X6,X7)),X9))),X10)
| ~ contains_cpq(findmin_cpq_eff(triple(X8,insert_slb(X5,pair(X6,X7)),X9)),X10)
| create_slb = insert_slb(X5,pair(X6,X7))
| ~ contains_slb(X5,findmin_pqp_res(X8))
| findmin_pqp_res(X8) = X6 ),
inference(superposition,[],[f230,f190]) ).
fof(f377,plain,
! [X2,X3,X0,X1,X4] :
( ~ less_than(X2,findmin_pqp_res(X1))
| contains_pq(i(findmin_cpq_eff(triple(X1,insert_slb(X0,pair(findmin_pqp_res(X1),X2)),X3))),X4)
| ~ contains_cpq(findmin_cpq_eff(triple(X1,insert_slb(X0,pair(findmin_pqp_res(X1),X2)),X3)),X4)
| create_slb = insert_slb(X0,pair(findmin_pqp_res(X1),X2)) ),
inference(superposition,[],[f230,f175]) ).
fof(f375,plain,
! [X10,X11,X9,X12] :
( contains_pq(i(findmin_cpq_eff(triple(X9,X10,X11))),X12)
| ~ contains_cpq(findmin_cpq_eff(triple(X9,X10,X11)),X12)
| create_slb = X10
| less_than(findmin_pqp_res(X9),lookup_slb(X10,findmin_pqp_res(X9))) ),
inference(resolution,[],[f230,f162]) ).
fof(f374,plain,
! [X8,X6,X7,X5] :
( contains_pq(i(findmin_cpq_eff(triple(X5,X6,X7))),X8)
| ~ contains_cpq(findmin_cpq_eff(triple(X5,X6,X7)),X8)
| create_slb = X6
| strictly_less_than(findmin_pqp_res(X5),lookup_slb(X6,findmin_pqp_res(X5)))
| ~ less_than(findmin_pqp_res(X5),lookup_slb(X6,findmin_pqp_res(X5))) ),
inference(resolution,[],[f230,f169]) ).
fof(f373,plain,
! [X2,X3,X0,X1,X4] :
( contains_pq(i(findmin_cpq_eff(triple(X0,X1,X2))),X3)
| ~ contains_cpq(findmin_cpq_eff(triple(X0,X1,X2)),X3)
| create_slb = X1
| ~ less_than(X4,findmin_pqp_res(X0))
| ~ less_than(lookup_slb(X1,findmin_pqp_res(X0)),X4) ),
inference(resolution,[],[f230,f181]) ).
fof(f371,plain,
! [X38,X39,X36,X37,X34,X35,X33] :
( contains_pq(i(remove_cpq(triple(X33,insert_slb(X34,pair(X35,X36)),X37),X38)),X39)
| ~ less_than(lookup_slb(insert_slb(X34,pair(X35,X36)),X38),X38)
| ~ contains_cpq(remove_cpq(triple(X33,insert_slb(X34,pair(X35,X36)),X37),X38),X39)
| ~ contains_slb(X34,X38) ),
inference(resolution,[],[f229,f200]) ).
fof(f372,plain,
! [X31,X28,X29,X27,X32,X30] :
( ~ less_than(X30,X29)
| contains_pq(i(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29)),X32)
| ~ contains_cpq(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29),X32) ),
inference(forward_demodulation,[],[f370,f175]) ).
fof(f370,plain,
! [X31,X28,X29,X27,X32,X30] :
( contains_pq(i(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29)),X32)
| ~ less_than(lookup_slb(insert_slb(X28,pair(X29,X30)),X29),X29)
| ~ contains_cpq(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29),X32) ),
inference(resolution,[],[f229,f211]) ).
fof(f369,plain,
! [X21,X26,X24,X22,X25,X23] :
( contains_pq(i(remove_cpq(triple(X21,X22,X23),findmin_pqp_res(X24))),X25)
| ~ less_than(lookup_slb(X22,findmin_pqp_res(X24)),findmin_pqp_res(X24))
| ~ contains_cpq(remove_cpq(triple(X21,X22,X23),findmin_pqp_res(X24)),X25)
| findmin_cpq_eff(triple(X24,X22,X26)) = triple(X24,update_slb(X22,findmin_pqp_res(X24)),bad)
| create_slb = X22 ),
inference(resolution,[],[f229,f192]) ).
fof(f368,plain,
! [X18,X19,X16,X14,X17,X15,X20] :
( contains_pq(i(remove_cpq(triple(X14,X15,X16),X17)),X18)
| ~ less_than(lookup_slb(X15,X17),X17)
| ~ contains_cpq(remove_cpq(triple(X14,X15,X16),X17),X18)
| triple(X19,X15,bad) = remove_cpq(triple(X19,X15,X20),X17) ),
inference(resolution,[],[f229,f187]) ).
fof(f367,plain,
! [X10,X11,X8,X9,X7,X12,X13] :
( contains_pq(i(remove_cpq(triple(X7,X8,X9),X10)),X11)
| ~ less_than(lookup_slb(X8,X10),X10)
| ~ contains_cpq(remove_cpq(triple(X7,X8,X9),X10),X11)
| ~ contains_cpq(triple(X12,X8,X13),X10) ),
inference(resolution,[],[f229,f197]) ).
fof(f366,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( contains_pq(i(remove_cpq(triple(X0,X1,X2),X3)),X4)
| ~ less_than(lookup_slb(X1,X3),X3)
| ~ contains_cpq(remove_cpq(triple(X0,X1,X2),X3),X4)
| X3 = X5
| ~ contains_slb(insert_slb(X1,pair(X5,X6)),X3) ),
inference(resolution,[],[f229,f199]) ).
fof(f364,plain,
! [X38,X39,X36,X37,X34,X35,X33] :
( contains_pq(i(remove_cpq(triple(X33,insert_slb(X34,pair(X35,X36)),X37),X38)),X39)
| ~ strictly_less_than(X38,lookup_slb(insert_slb(X34,pair(X35,X36)),X38))
| ~ contains_cpq(remove_cpq(triple(X33,insert_slb(X34,pair(X35,X36)),X37),X38),X39)
| ~ contains_slb(X34,X38) ),
inference(resolution,[],[f228,f200]) ).
fof(f365,plain,
! [X31,X28,X29,X27,X32,X30] :
( ~ strictly_less_than(X29,X30)
| contains_pq(i(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29)),X32)
| ~ contains_cpq(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29),X32) ),
inference(forward_demodulation,[],[f363,f175]) ).
fof(f363,plain,
! [X31,X28,X29,X27,X32,X30] :
( contains_pq(i(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29)),X32)
| ~ strictly_less_than(X29,lookup_slb(insert_slb(X28,pair(X29,X30)),X29))
| ~ contains_cpq(remove_cpq(triple(X27,insert_slb(X28,pair(X29,X30)),X31),X29),X32) ),
inference(resolution,[],[f228,f211]) ).
fof(f362,plain,
! [X21,X26,X24,X22,X25,X23] :
( contains_pq(i(remove_cpq(triple(X21,X22,X23),findmin_pqp_res(X24))),X25)
| ~ strictly_less_than(findmin_pqp_res(X24),lookup_slb(X22,findmin_pqp_res(X24)))
| ~ contains_cpq(remove_cpq(triple(X21,X22,X23),findmin_pqp_res(X24)),X25)
| findmin_cpq_eff(triple(X24,X22,X26)) = triple(X24,update_slb(X22,findmin_pqp_res(X24)),bad)
| create_slb = X22 ),
inference(resolution,[],[f228,f192]) ).
fof(f361,plain,
! [X18,X19,X16,X14,X17,X15,X20] :
( contains_pq(i(remove_cpq(triple(X14,X15,X16),X17)),X18)
| ~ strictly_less_than(X17,lookup_slb(X15,X17))
| ~ contains_cpq(remove_cpq(triple(X14,X15,X16),X17),X18)
| triple(X19,X15,bad) = remove_cpq(triple(X19,X15,X20),X17) ),
inference(resolution,[],[f228,f187]) ).
fof(f360,plain,
! [X10,X11,X8,X9,X7,X12,X13] :
( contains_pq(i(remove_cpq(triple(X7,X8,X9),X10)),X11)
| ~ strictly_less_than(X10,lookup_slb(X8,X10))
| ~ contains_cpq(remove_cpq(triple(X7,X8,X9),X10),X11)
| ~ contains_cpq(triple(X12,X8,X13),X10) ),
inference(resolution,[],[f228,f197]) ).
fof(f359,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( contains_pq(i(remove_cpq(triple(X0,X1,X2),X3)),X4)
| ~ strictly_less_than(X3,lookup_slb(X1,X3))
| ~ contains_cpq(remove_cpq(triple(X0,X1,X2),X3),X4)
| X3 = X5
| ~ contains_slb(insert_slb(X1,pair(X5,X6)),X3) ),
inference(resolution,[],[f228,f199]) ).
fof(f352,plain,
! [X26,X24,X22,X25,X23] :
( ~ contains_pq(i(findmin_cpq_eff(remove_cpq(triple(X22,X24,X25),X23))),X26)
| contains_cpq(findmin_cpq_eff(remove_cpq(triple(X22,X24,X25),X23)),X26)
| contains_slb(remove_slb(X24,X23),findmin_pqp_res(remove_pqp(X22,X23)))
| create_slb = remove_slb(X24,X23)
| ~ less_than(lookup_slb(X24,X23),X23)
| ~ contains_slb(X24,X23) ),
inference(superposition,[],[f235,f196]) ).
fof(f351,plain,
! [X21,X18,X19,X17,X20] :
( ~ contains_pq(i(findmin_cpq_eff(remove_cpq(triple(X17,X19,X20),X18))),X21)
| contains_cpq(findmin_cpq_eff(remove_cpq(triple(X17,X19,X20),X18)),X21)
| contains_slb(remove_slb(X19,X18),findmin_pqp_res(remove_pqp(X17,X18)))
| create_slb = remove_slb(X19,X18)
| ~ strictly_less_than(X18,lookup_slb(X19,X18))
| ~ contains_slb(X19,X18) ),
inference(superposition,[],[f235,f195]) ).
fof(f358,plain,
! [X16,X14,X15,X13] :
( ~ contains_pq(i(findmin_cpq_eff(findmin_cpq_eff(triple(X13,X14,X15)))),X16)
| contains_cpq(findmin_cpq_eff(findmin_cpq_eff(triple(X13,X14,X15))),X16)
| contains_slb(update_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| create_slb = update_slb(X14,findmin_pqp_res(X13))
| ~ less_than(lookup_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| create_slb = X14 ),
inference(subsumption_resolution,[],[f350,f349]) ).
fof(f350,plain,
! [X16,X14,X15,X13] :
( ~ contains_pq(i(findmin_cpq_eff(findmin_cpq_eff(triple(X13,X14,X15)))),X16)
| contains_cpq(findmin_cpq_eff(findmin_cpq_eff(triple(X13,X14,X15))),X16)
| contains_slb(update_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| create_slb = update_slb(X14,findmin_pqp_res(X13))
| ~ less_than(lookup_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| ~ contains_slb(X14,findmin_pqp_res(X13))
| create_slb = X14 ),
inference(superposition,[],[f235,f194]) ).
fof(f349,plain,
! [X10,X11,X9,X12] :
( ~ contains_pq(i(findmin_cpq_eff(findmin_cpq_eff(triple(X9,X10,X11)))),X12)
| contains_cpq(findmin_cpq_eff(findmin_cpq_eff(triple(X9,X10,X11))),X12)
| contains_slb(update_slb(X10,findmin_pqp_res(X9)),findmin_pqp_res(X9))
| create_slb = update_slb(X10,findmin_pqp_res(X9))
| contains_slb(X10,findmin_pqp_res(X9))
| create_slb = X10 ),
inference(superposition,[],[f235,f192]) ).
fof(f348,plain,
! [X8,X6,X7,X5] :
( ~ contains_pq(i(findmin_cpq_eff(findmin_cpq_eff(triple(X5,X6,X7)))),X8)
| contains_cpq(findmin_cpq_eff(findmin_cpq_eff(triple(X5,X6,X7))),X8)
| contains_slb(update_slb(X6,findmin_pqp_res(X5)),findmin_pqp_res(X5))
| create_slb = update_slb(X6,findmin_pqp_res(X5))
| ~ strictly_less_than(findmin_pqp_res(X5),lookup_slb(X6,findmin_pqp_res(X5)))
| ~ contains_slb(X6,findmin_pqp_res(X5))
| create_slb = X6 ),
inference(superposition,[],[f235,f193]) ).
fof(f347,plain,
! [X2,X3,X0,X1,X4] :
( ~ contains_pq(i(findmin_cpq_eff(insert_cpq(triple(X0,X2,X3),X1))),X4)
| contains_cpq(findmin_cpq_eff(insert_cpq(triple(X0,X2,X3),X1)),X4)
| contains_slb(insert_slb(X2,pair(X1,bottom)),findmin_pqp_res(insert_pqp(X0,X1)))
| create_slb = insert_slb(X2,pair(X1,bottom)) ),
inference(superposition,[],[f235,f185]) ).
fof(f338,plain,
! [X26,X24,X22,X25,X23] :
( ~ contains_cpq(findmin_cpq_eff(remove_cpq(triple(X22,X24,X25),X23)),X26)
| contains_pq(i(findmin_cpq_eff(remove_cpq(triple(X22,X24,X25),X23))),X26)
| contains_slb(remove_slb(X24,X23),findmin_pqp_res(remove_pqp(X22,X23)))
| create_slb = remove_slb(X24,X23)
| ~ less_than(lookup_slb(X24,X23),X23)
| ~ contains_slb(X24,X23) ),
inference(superposition,[],[f226,f196]) ).
fof(f337,plain,
! [X21,X18,X19,X17,X20] :
( ~ contains_cpq(findmin_cpq_eff(remove_cpq(triple(X17,X19,X20),X18)),X21)
| contains_pq(i(findmin_cpq_eff(remove_cpq(triple(X17,X19,X20),X18))),X21)
| contains_slb(remove_slb(X19,X18),findmin_pqp_res(remove_pqp(X17,X18)))
| create_slb = remove_slb(X19,X18)
| ~ strictly_less_than(X18,lookup_slb(X19,X18))
| ~ contains_slb(X19,X18) ),
inference(superposition,[],[f226,f195]) ).
fof(f344,plain,
! [X16,X14,X15,X13] :
( ~ contains_cpq(findmin_cpq_eff(findmin_cpq_eff(triple(X13,X14,X15))),X16)
| contains_pq(i(findmin_cpq_eff(findmin_cpq_eff(triple(X13,X14,X15)))),X16)
| contains_slb(update_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| create_slb = update_slb(X14,findmin_pqp_res(X13))
| ~ less_than(lookup_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| create_slb = X14 ),
inference(subsumption_resolution,[],[f336,f335]) ).
fof(f336,plain,
! [X16,X14,X15,X13] :
( ~ contains_cpq(findmin_cpq_eff(findmin_cpq_eff(triple(X13,X14,X15))),X16)
| contains_pq(i(findmin_cpq_eff(findmin_cpq_eff(triple(X13,X14,X15)))),X16)
| contains_slb(update_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| create_slb = update_slb(X14,findmin_pqp_res(X13))
| ~ less_than(lookup_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| ~ contains_slb(X14,findmin_pqp_res(X13))
| create_slb = X14 ),
inference(superposition,[],[f226,f194]) ).
fof(f335,plain,
! [X10,X11,X9,X12] :
( ~ contains_cpq(findmin_cpq_eff(findmin_cpq_eff(triple(X9,X10,X11))),X12)
| contains_pq(i(findmin_cpq_eff(findmin_cpq_eff(triple(X9,X10,X11)))),X12)
| contains_slb(update_slb(X10,findmin_pqp_res(X9)),findmin_pqp_res(X9))
| create_slb = update_slb(X10,findmin_pqp_res(X9))
| contains_slb(X10,findmin_pqp_res(X9))
| create_slb = X10 ),
inference(superposition,[],[f226,f192]) ).
fof(f334,plain,
! [X8,X6,X7,X5] :
( ~ contains_cpq(findmin_cpq_eff(findmin_cpq_eff(triple(X5,X6,X7))),X8)
| contains_pq(i(findmin_cpq_eff(findmin_cpq_eff(triple(X5,X6,X7)))),X8)
| contains_slb(update_slb(X6,findmin_pqp_res(X5)),findmin_pqp_res(X5))
| create_slb = update_slb(X6,findmin_pqp_res(X5))
| ~ strictly_less_than(findmin_pqp_res(X5),lookup_slb(X6,findmin_pqp_res(X5)))
| ~ contains_slb(X6,findmin_pqp_res(X5))
| create_slb = X6 ),
inference(superposition,[],[f226,f193]) ).
fof(f333,plain,
! [X2,X3,X0,X1,X4] :
( ~ contains_cpq(findmin_cpq_eff(insert_cpq(triple(X0,X2,X3),X1)),X4)
| contains_pq(i(findmin_cpq_eff(insert_cpq(triple(X0,X2,X3),X1))),X4)
| contains_slb(insert_slb(X2,pair(X1,bottom)),findmin_pqp_res(insert_pqp(X0,X1)))
| create_slb = insert_slb(X2,pair(X1,bottom)) ),
inference(superposition,[],[f226,f185]) ).
fof(f331,plain,
! [X2,X3,X0,X1,X4] :
( contains_cpq(insert_cpq(triple(X0,X2,X3),X1),X4)
| ~ contains_pq(insert_pq(i(triple(insert_pqp(X0,X1),X2,X3)),X1),X4) ),
inference(superposition,[],[f240,f185]) ).
fof(f330,plain,
! [X18,X19,X16,X14,X17,X15,X20] :
( contains_cpq(triple(X18,remove_slb(insert_slb(X14,pair(X16,X17)),X15),X19),X20)
| ~ contains_pq(insert_pq(i(triple(X18,remove_slb(X14,X15),X19)),X16),X20)
| ~ contains_slb(X14,X15)
| X15 = X16 ),
inference(superposition,[],[f240,f191]) ).
fof(f191,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,[],[f106]) ).
fof(f106,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,[],[f105]) ).
fof(f105,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax25) ).
fof(f329,plain,
! [X10,X11,X8,X9,X7,X12,X13] :
( contains_cpq(triple(X11,update_slb(insert_slb(X7,pair(X9,X10)),X8),X12),X13)
| ~ contains_pq(insert_pq(i(triple(X11,update_slb(X7,X8),X12)),X9),X13)
| ~ less_than(X8,X10) ),
inference(superposition,[],[f240,f189]) ).
fof(f189,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,[],[f102]) ).
fof(f102,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax30) ).
fof(f328,plain,
! [X2,X3,X0,X1,X6,X4,X5] :
( contains_cpq(triple(X4,update_slb(insert_slb(X0,pair(X2,X3)),X1),X5),X6)
| ~ contains_pq(insert_pq(i(triple(X4,update_slb(X0,X1),X5)),X2),X6)
| ~ strictly_less_than(X3,X1) ),
inference(superposition,[],[f240,f188]) ).
fof(f188,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,[],[f101]) ).
fof(f101,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax29) ).
fof(f327,plain,
! [X16,X14,X17,X15,X12,X13] :
( ~ contains_pq(insert_pq(i(triple(X12,X13,X14)),X15),X16)
| contains_slb(insert_slb(X13,pair(X15,X17)),X16) ),
inference(resolution,[],[f240,f197]) ).
fof(f325,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ contains_pq(insert_pq(i(triple(X0,X1,X2)),X3),X4)
| ~ phi(findmin_cpq_eff(triple(X0,insert_slb(X1,pair(X3,X5)),X2)))
| ~ strictly_less_than(X4,removemin_cpq_res(triple(X0,insert_slb(X1,pair(X3,X5)),X2))) ),
inference(resolution,[],[f240,f215]) ).
fof(f323,plain,
! [X3,X8,X6,X7,X4,X5] :
( contains_cpq(triple(X3,insert_slb(X4,pair(X5,X6)),X7),sK4(insert_pq(i(triple(X3,X4,X7)),X5),X8))
| issmallestelement_pq(insert_pq(i(triple(X3,X4,X7)),X5),X8) ),
inference(superposition,[],[f231,f202]) ).
fof(f202,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax55) ).
fof(f322,plain,
! [X2,X0,X1] :
( contains_cpq(triple(X0,create_slb,X1),sK4(create_pq,X2))
| issmallestelement_pq(create_pq,X2) ),
inference(superposition,[],[f231,f159]) ).
fof(f159,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax54) ).
fof(f321,plain,
! [X26,X24,X22,X25,X23] :
( contains_cpq(remove_cpq(triple(X22,X24,X25),X23),sK4(i(remove_cpq(triple(X22,X24,X25),X23)),X26))
| issmallestelement_pq(i(remove_cpq(triple(X22,X24,X25),X23)),X26)
| ~ less_than(lookup_slb(X24,X23),X23)
| ~ contains_slb(X24,X23) ),
inference(superposition,[],[f231,f196]) ).
fof(f320,plain,
! [X21,X18,X19,X17,X20] :
( contains_cpq(remove_cpq(triple(X17,X19,X20),X18),sK4(i(remove_cpq(triple(X17,X19,X20),X18)),X21))
| issmallestelement_pq(i(remove_cpq(triple(X17,X19,X20),X18)),X21)
| ~ strictly_less_than(X18,lookup_slb(X19,X18))
| ~ contains_slb(X19,X18) ),
inference(superposition,[],[f231,f195]) ).
fof(f324,plain,
! [X16,X14,X15,X13] :
( contains_cpq(findmin_cpq_eff(triple(X13,X14,X15)),sK4(i(findmin_cpq_eff(triple(X13,X14,X15))),X16))
| issmallestelement_pq(i(findmin_cpq_eff(triple(X13,X14,X15))),X16)
| ~ less_than(lookup_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| create_slb = X14 ),
inference(subsumption_resolution,[],[f319,f318]) ).
fof(f319,plain,
! [X16,X14,X15,X13] :
( contains_cpq(findmin_cpq_eff(triple(X13,X14,X15)),sK4(i(findmin_cpq_eff(triple(X13,X14,X15))),X16))
| issmallestelement_pq(i(findmin_cpq_eff(triple(X13,X14,X15))),X16)
| ~ less_than(lookup_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| ~ contains_slb(X14,findmin_pqp_res(X13))
| create_slb = X14 ),
inference(superposition,[],[f231,f194]) ).
fof(f318,plain,
! [X10,X11,X9,X12] :
( contains_cpq(findmin_cpq_eff(triple(X9,X10,X11)),sK4(i(findmin_cpq_eff(triple(X9,X10,X11))),X12))
| issmallestelement_pq(i(findmin_cpq_eff(triple(X9,X10,X11))),X12)
| contains_slb(X10,findmin_pqp_res(X9))
| create_slb = X10 ),
inference(superposition,[],[f231,f192]) ).
fof(f317,plain,
! [X8,X6,X7,X5] :
( contains_cpq(findmin_cpq_eff(triple(X5,X6,X7)),sK4(i(findmin_cpq_eff(triple(X5,X6,X7))),X8))
| issmallestelement_pq(i(findmin_cpq_eff(triple(X5,X6,X7))),X8)
| ~ strictly_less_than(findmin_pqp_res(X5),lookup_slb(X6,findmin_pqp_res(X5)))
| ~ contains_slb(X6,findmin_pqp_res(X5))
| create_slb = X6 ),
inference(superposition,[],[f231,f193]) ).
fof(f315,plain,
! [X10,X11,X8,X9] :
( issmallestelement_pq(i(triple(X8,X9,X10)),X11)
| contains_slb(X9,sK4(i(triple(X8,X9,X10)),X11)) ),
inference(resolution,[],[f231,f197]) ).
fof(f313,plain,
! [X2,X3,X0,X1] :
( issmallestelement_pq(i(triple(X0,X1,X2)),X3)
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ~ strictly_less_than(sK4(i(triple(X0,X1,X2)),X3),removemin_cpq_res(triple(X0,X1,X2))) ),
inference(resolution,[],[f231,f215]) ).
fof(f311,plain,
! [X10,X8,X6,X9,X7,X4,X5] :
( ~ contains_pq(insert_pq(insert_pq(i(triple(X4,X5,X8)),X6),X9),X10)
| X9 = X10
| contains_cpq(triple(X4,insert_slb(X5,pair(X6,X7)),X8),X10) ),
inference(superposition,[],[f232,f202]) ).
fof(f310,plain,
! [X2,X3,X0,X1] :
( ~ contains_pq(insert_pq(create_pq,X2),X3)
| X2 = X3
| contains_cpq(triple(X0,create_slb,X1),X3) ),
inference(superposition,[],[f232,f159]) ).
fof(f309,plain,
! [X31,X28,X29,X27,X32,X30] :
( ~ contains_pq(insert_pq(i(remove_cpq(triple(X27,X29,X30),X28)),X31),X32)
| X31 = X32
| contains_cpq(remove_cpq(triple(X27,X29,X30),X28),X32)
| ~ less_than(lookup_slb(X29,X28),X28)
| ~ contains_slb(X29,X28) ),
inference(superposition,[],[f232,f196]) ).
fof(f308,plain,
! [X21,X26,X24,X22,X25,X23] :
( ~ contains_pq(insert_pq(i(remove_cpq(triple(X21,X23,X24),X22)),X25),X26)
| X25 = X26
| contains_cpq(remove_cpq(triple(X21,X23,X24),X22),X26)
| ~ strictly_less_than(X22,lookup_slb(X23,X22))
| ~ contains_slb(X23,X22) ),
inference(superposition,[],[f232,f195]) ).
fof(f312,plain,
! [X18,X19,X16,X17,X20] :
( ~ contains_pq(insert_pq(i(findmin_cpq_eff(triple(X16,X17,X18))),X19),X20)
| X19 = X20
| contains_cpq(findmin_cpq_eff(triple(X16,X17,X18)),X20)
| ~ less_than(lookup_slb(X17,findmin_pqp_res(X16)),findmin_pqp_res(X16))
| create_slb = X17 ),
inference(subsumption_resolution,[],[f307,f306]) ).
fof(f307,plain,
! [X18,X19,X16,X17,X20] :
( ~ contains_pq(insert_pq(i(findmin_cpq_eff(triple(X16,X17,X18))),X19),X20)
| X19 = X20
| contains_cpq(findmin_cpq_eff(triple(X16,X17,X18)),X20)
| ~ less_than(lookup_slb(X17,findmin_pqp_res(X16)),findmin_pqp_res(X16))
| ~ contains_slb(X17,findmin_pqp_res(X16))
| create_slb = X17 ),
inference(superposition,[],[f232,f194]) ).
fof(f306,plain,
! [X11,X14,X15,X12,X13] :
( ~ contains_pq(insert_pq(i(findmin_cpq_eff(triple(X11,X12,X13))),X14),X15)
| X14 = X15
| contains_cpq(findmin_cpq_eff(triple(X11,X12,X13)),X15)
| contains_slb(X12,findmin_pqp_res(X11))
| create_slb = X12 ),
inference(superposition,[],[f232,f192]) ).
fof(f305,plain,
! [X10,X8,X6,X9,X7] :
( ~ contains_pq(insert_pq(i(findmin_cpq_eff(triple(X6,X7,X8))),X9),X10)
| X9 = X10
| contains_cpq(findmin_cpq_eff(triple(X6,X7,X8)),X10)
| ~ strictly_less_than(findmin_pqp_res(X6),lookup_slb(X7,findmin_pqp_res(X6)))
| ~ contains_slb(X7,findmin_pqp_res(X6))
| create_slb = X7 ),
inference(superposition,[],[f232,f193]) ).
fof(f303,plain,
! [X18,X19,X16,X14,X17,X15] :
( X14 = X15
| contains_cpq(triple(X16,X17,X18),X14)
| X14 = X19
| ~ contains_pq(insert_pq(insert_pq(i(triple(X16,X17,X18)),X15),X19),X14) ),
inference(resolution,[],[f232,f182]) ).
fof(f182,plain,
! [X2,X0,X1] :
( X1 = X2
| contains_pq(X0,X2)
| ~ contains_pq(insert_pq(X0,X1),X2) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,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,[],[f128]) ).
fof(f128,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax9) ).
fof(f302,plain,
! [X10,X11,X9,X12,X13] :
( sK4(insert_pq(i(triple(X9,X10,X11)),X12),X13) = X12
| contains_cpq(triple(X9,X10,X11),sK4(insert_pq(i(triple(X9,X10,X11)),X12),X13))
| issmallestelement_pq(insert_pq(i(triple(X9,X10,X11)),X12),X13) ),
inference(resolution,[],[f232,f170]) ).
fof(f170,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| contains_pq(X0,sK4(X0,X1)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,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])],[f91,f126]) ).
fof(f126,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(f91,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| ? [X2] :
( ~ less_than(X1,X2)
& contains_pq(X0,X2) ) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax10) ).
fof(f298,plain,
! [X31,X28,X29,X27,X32,X30] :
( ~ contains_pq(i(insert_cpq(remove_cpq(triple(X27,X29,X30),X28),X31)),X32)
| contains_cpq(insert_cpq(remove_cpq(triple(X27,X29,X30),X28),X31),X32)
| ~ less_than(lookup_slb(X29,X28),X28)
| ~ contains_slb(X29,X28) ),
inference(superposition,[],[f233,f196]) ).
fof(f297,plain,
! [X21,X26,X24,X22,X25,X23] :
( ~ contains_pq(i(insert_cpq(remove_cpq(triple(X21,X23,X24),X22),X25)),X26)
| contains_cpq(insert_cpq(remove_cpq(triple(X21,X23,X24),X22),X25),X26)
| ~ strictly_less_than(X22,lookup_slb(X23,X22))
| ~ contains_slb(X23,X22) ),
inference(superposition,[],[f233,f195]) ).
fof(f299,plain,
! [X18,X19,X16,X17,X20] :
( ~ contains_pq(i(insert_cpq(findmin_cpq_eff(triple(X16,X17,X18)),X19)),X20)
| contains_cpq(insert_cpq(findmin_cpq_eff(triple(X16,X17,X18)),X19),X20)
| ~ less_than(lookup_slb(X17,findmin_pqp_res(X16)),findmin_pqp_res(X16))
| create_slb = X17 ),
inference(subsumption_resolution,[],[f296,f295]) ).
fof(f296,plain,
! [X18,X19,X16,X17,X20] :
( ~ contains_pq(i(insert_cpq(findmin_cpq_eff(triple(X16,X17,X18)),X19)),X20)
| contains_cpq(insert_cpq(findmin_cpq_eff(triple(X16,X17,X18)),X19),X20)
| ~ less_than(lookup_slb(X17,findmin_pqp_res(X16)),findmin_pqp_res(X16))
| ~ contains_slb(X17,findmin_pqp_res(X16))
| create_slb = X17 ),
inference(superposition,[],[f233,f194]) ).
fof(f295,plain,
! [X11,X14,X15,X12,X13] :
( ~ contains_pq(i(insert_cpq(findmin_cpq_eff(triple(X11,X12,X13)),X14)),X15)
| contains_cpq(insert_cpq(findmin_cpq_eff(triple(X11,X12,X13)),X14),X15)
| contains_slb(X12,findmin_pqp_res(X11))
| create_slb = X12 ),
inference(superposition,[],[f233,f192]) ).
fof(f294,plain,
! [X10,X8,X6,X9,X7] :
( ~ contains_pq(i(insert_cpq(findmin_cpq_eff(triple(X6,X7,X8)),X9)),X10)
| contains_cpq(insert_cpq(findmin_cpq_eff(triple(X6,X7,X8)),X9),X10)
| ~ strictly_less_than(findmin_pqp_res(X6),lookup_slb(X7,findmin_pqp_res(X6)))
| ~ contains_slb(X7,findmin_pqp_res(X6))
| create_slb = X7 ),
inference(superposition,[],[f233,f193]) ).
fof(f293,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ contains_pq(i(insert_cpq(insert_cpq(triple(X0,X2,X3),X1),X4)),X5)
| contains_cpq(insert_cpq(insert_cpq(triple(X0,X2,X3),X1),X4),X5) ),
inference(superposition,[],[f233,f185]) ).
fof(f292,plain,
! [X10,X8,X6,X9,X7,X5] :
( contains_cpq(insert_cpq(triple(X5,X6,X7),X8),X9)
| X9 = X10
| ~ contains_pq(insert_pq(i(insert_cpq(triple(X5,X6,X7),X8)),X10),X9) ),
inference(resolution,[],[f233,f182]) ).
fof(f291,plain,
! [X2,X3,X0,X1,X4] :
( contains_cpq(insert_cpq(triple(X0,X1,X2),X3),sK4(i(insert_cpq(triple(X0,X1,X2),X3)),X4))
| issmallestelement_pq(i(insert_cpq(triple(X0,X1,X2),X3)),X4) ),
inference(resolution,[],[f233,f170]) ).
fof(f289,plain,
! [X31,X28,X29,X27,X32,X30] :
( ~ contains_cpq(insert_cpq(remove_cpq(triple(X27,X29,X30),X28),X31),X32)
| contains_pq(i(insert_cpq(remove_cpq(triple(X27,X29,X30),X28),X31)),X32)
| ~ less_than(lookup_slb(X29,X28),X28)
| ~ contains_slb(X29,X28) ),
inference(superposition,[],[f224,f196]) ).
fof(f288,plain,
! [X21,X26,X24,X22,X25,X23] :
( ~ contains_cpq(insert_cpq(remove_cpq(triple(X21,X23,X24),X22),X25),X26)
| contains_pq(i(insert_cpq(remove_cpq(triple(X21,X23,X24),X22),X25)),X26)
| ~ strictly_less_than(X22,lookup_slb(X23,X22))
| ~ contains_slb(X23,X22) ),
inference(superposition,[],[f224,f195]) ).
fof(f290,plain,
! [X18,X19,X16,X17,X20] :
( ~ contains_cpq(insert_cpq(findmin_cpq_eff(triple(X16,X17,X18)),X19),X20)
| contains_pq(i(insert_cpq(findmin_cpq_eff(triple(X16,X17,X18)),X19)),X20)
| ~ less_than(lookup_slb(X17,findmin_pqp_res(X16)),findmin_pqp_res(X16))
| create_slb = X17 ),
inference(subsumption_resolution,[],[f287,f286]) ).
fof(f287,plain,
! [X18,X19,X16,X17,X20] :
( ~ contains_cpq(insert_cpq(findmin_cpq_eff(triple(X16,X17,X18)),X19),X20)
| contains_pq(i(insert_cpq(findmin_cpq_eff(triple(X16,X17,X18)),X19)),X20)
| ~ less_than(lookup_slb(X17,findmin_pqp_res(X16)),findmin_pqp_res(X16))
| ~ contains_slb(X17,findmin_pqp_res(X16))
| create_slb = X17 ),
inference(superposition,[],[f224,f194]) ).
fof(f286,plain,
! [X11,X14,X15,X12,X13] :
( ~ contains_cpq(insert_cpq(findmin_cpq_eff(triple(X11,X12,X13)),X14),X15)
| contains_pq(i(insert_cpq(findmin_cpq_eff(triple(X11,X12,X13)),X14)),X15)
| contains_slb(X12,findmin_pqp_res(X11))
| create_slb = X12 ),
inference(superposition,[],[f224,f192]) ).
fof(f285,plain,
! [X10,X8,X6,X9,X7] :
( ~ contains_cpq(insert_cpq(findmin_cpq_eff(triple(X6,X7,X8)),X9),X10)
| contains_pq(i(insert_cpq(findmin_cpq_eff(triple(X6,X7,X8)),X9)),X10)
| ~ strictly_less_than(findmin_pqp_res(X6),lookup_slb(X7,findmin_pqp_res(X6)))
| ~ contains_slb(X7,findmin_pqp_res(X6))
| create_slb = X7 ),
inference(superposition,[],[f224,f193]) ).
fof(f284,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ contains_cpq(insert_cpq(insert_cpq(triple(X0,X2,X3),X1),X4),X5)
| contains_pq(i(insert_cpq(insert_cpq(triple(X0,X2,X3),X1),X4)),X5) ),
inference(superposition,[],[f224,f185]) ).
fof(f282,plain,
phi(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2)))),
inference(resolution,[],[f220,f147]) ).
fof(f147,plain,
! [X0] : succ_cpq(X0,X0),
inference(cnf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] : succ_cpq(X0,X0),
file('/export/starexec/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax31) ).
fof(f280,plain,
! [X31,X28,X29,X32,X30,X33] :
( ~ strictly_less_than(X28,removemin_cpq_res(triple(X29,insert_slb(X30,pair(X31,X32)),X33)))
| ~ phi(findmin_cpq_eff(triple(X29,insert_slb(X30,pair(X31,X32)),X33)))
| ~ contains_slb(X30,X28) ),
inference(resolution,[],[f242,f200]) ).
fof(f279,plain,
! [X26,X27,X24,X25,X23] :
( ~ strictly_less_than(X23,removemin_cpq_res(triple(X24,insert_slb(X25,pair(X23,X26)),X27)))
| ~ phi(findmin_cpq_eff(triple(X24,insert_slb(X25,pair(X23,X26)),X27))) ),
inference(resolution,[],[f242,f211]) ).
fof(f278,plain,
! [X21,X18,X19,X22,X20] :
( ~ strictly_less_than(findmin_pqp_res(X18),removemin_cpq_res(triple(X19,X20,X21)))
| ~ phi(findmin_cpq_eff(triple(X19,X20,X21)))
| findmin_cpq_eff(triple(X18,X20,X22)) = triple(X18,update_slb(X20,findmin_pqp_res(X18)),bad)
| create_slb = X20 ),
inference(resolution,[],[f242,f192]) ).
fof(f277,plain,
! [X16,X14,X17,X15,X12,X13] :
( ~ strictly_less_than(X12,removemin_cpq_res(triple(X13,X14,X15)))
| ~ phi(findmin_cpq_eff(triple(X13,X14,X15)))
| triple(X16,X14,bad) = remove_cpq(triple(X16,X14,X17),X12) ),
inference(resolution,[],[f242,f187]) ).
fof(f276,plain,
! [X10,X11,X8,X6,X9,X7] :
( ~ strictly_less_than(X6,removemin_cpq_res(triple(X7,X8,X9)))
| ~ phi(findmin_cpq_eff(triple(X7,X8,X9)))
| ~ contains_cpq(triple(X10,X8,X11),X6) ),
inference(resolution,[],[f242,f197]) ).
fof(f275,plain,
! [X2,X3,X0,X1,X4,X5] :
( ~ strictly_less_than(X0,removemin_cpq_res(triple(X1,X2,X3)))
| ~ phi(findmin_cpq_eff(triple(X1,X2,X3)))
| X0 = X4
| ~ contains_slb(insert_slb(X2,pair(X4,X5)),X0) ),
inference(resolution,[],[f242,f199]) ).
fof(f274,plain,
! [X28,X29,X32,X30,X33] :
( contains_pq(insert_pq(i(triple(X28,X29,X32)),X30),X33)
| ~ contains_slb(X29,X33) ),
inference(forward_demodulation,[],[f272,f202]) ).
fof(f272,plain,
! [X31,X28,X29,X32,X30,X33] :
( contains_pq(i(triple(X28,insert_slb(X29,pair(X30,X31)),X32)),X33)
| ~ contains_slb(X29,X33) ),
inference(resolution,[],[f223,f200]) ).
fof(f270,plain,
! [X21,X18,X19,X22,X20] :
( contains_pq(i(triple(X18,X19,X20)),findmin_pqp_res(X21))
| findmin_cpq_eff(triple(X21,X19,X22)) = triple(X21,update_slb(X19,findmin_pqp_res(X21)),bad)
| create_slb = X19 ),
inference(resolution,[],[f223,f192]) ).
fof(f269,plain,
! [X16,X14,X17,X15,X12,X13] :
( contains_pq(i(triple(X12,X13,X14)),X15)
| triple(X16,X13,bad) = remove_cpq(triple(X16,X13,X17),X15) ),
inference(resolution,[],[f223,f187]) ).
fof(f268,plain,
! [X10,X11,X8,X6,X9,X7] :
( contains_pq(i(triple(X6,X7,X8)),X9)
| ~ contains_cpq(triple(X10,X7,X11),X9) ),
inference(resolution,[],[f223,f197]) ).
fof(f267,plain,
! [X2,X3,X0,X1,X4,X5] :
( contains_pq(i(triple(X0,X1,X2)),X3)
| X3 = X4
| ~ contains_slb(insert_slb(X1,pair(X4,X5)),X3) ),
inference(resolution,[],[f223,f199]) ).
fof(f265,plain,
less_than(sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2))),removemin_cpq_res(triple(sK0,sK1,sK2))),
inference(resolution,[],[f222,f162]) ).
fof(f264,plain,
( strictly_less_than(sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2))),removemin_cpq_res(triple(sK0,sK1,sK2)))
| ~ less_than(sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2))),removemin_cpq_res(triple(sK0,sK1,sK2))) ),
inference(resolution,[],[f222,f169]) ).
fof(f263,plain,
! [X0] :
( ~ less_than(X0,sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2))))
| ~ less_than(removemin_cpq_res(triple(sK0,sK1,sK2)),X0) ),
inference(resolution,[],[f222,f181]) ).
fof(f262,plain,
( sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2))) = findmin_pq_res(i(triple(sK0,sK1,sK2)),sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2))))
| ~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2)))) ),
inference(resolution,[],[f221,f165]) ).
fof(f165,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax14) ).
fof(f261,plain,
( i(triple(sK0,sK1,sK2)) = findmin_pq_eff(i(triple(sK0,sK1,sK2)),sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2))))
| ~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2)))) ),
inference(resolution,[],[f221,f166]) ).
fof(f166,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax13) ).
fof(f260,plain,
( sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2))) = removemin_pq_res(i(triple(sK0,sK1,sK2)),sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2))))
| ~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2)))) ),
inference(resolution,[],[f221,f167]) ).
fof(f167,plain,
! [X0,X1] :
( removemin_pq_res(X0,X1) = X1
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(cnf_transformation,[],[f86]) ).
fof(f86,plain,
! [X0,X1] :
( removemin_pq_res(X0,X1) = X1
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(flattening,[],[f85]) ).
fof(f85,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax16) ).
fof(f259,plain,
( remove_pq(i(triple(sK0,sK1,sK2)),sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2)))) = removemin_pq_eff(i(triple(sK0,sK1,sK2)),sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2))))
| ~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2)))) ),
inference(resolution,[],[f221,f168]) ).
fof(f168,plain,
! [X0,X1] :
( removemin_pq_eff(X0,X1) = remove_pq(X0,X1)
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(cnf_transformation,[],[f88]) ).
fof(f88,plain,
! [X0,X1] :
( removemin_pq_eff(X0,X1) = remove_pq(X0,X1)
| ~ issmallestelement_pq(X0,X1)
| ~ contains_pq(X0,X1) ),
inference(flattening,[],[f87]) ).
fof(f87,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax15) ).
fof(f258,plain,
! [X1] :
( remove_pq(insert_pq(i(triple(sK0,sK1,sK2)),X1),sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2)))) = insert_pq(remove_pq(i(triple(sK0,sK1,sK2)),sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2)))),X1)
| sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2))) = X1 ),
inference(resolution,[],[f221,f180]) ).
fof(f180,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,[],[f96]) ).
fof(f96,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,[],[f95]) ).
fof(f95,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax12) ).
fof(f257,plain,
! [X0] : contains_pq(insert_pq(i(triple(sK0,sK1,sK2)),X0),sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2)))),
inference(resolution,[],[f221,f183]) ).
fof(f183,plain,
! [X2,X0,X1] :
( contains_pq(insert_pq(X0,X1),X2)
| ~ contains_pq(X0,X2) ),
inference(cnf_transformation,[],[f129]) ).
fof(f256,plain,
contains_cpq(triple(sK0,sK1,sK2),sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2)))),
inference(resolution,[],[f221,f140]) ).
fof(f254,plain,
succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),removemin_cpq_eff(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))))),
inference(resolution,[],[f216,f163]) ).
fof(f253,plain,
succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),findmin_cpq_eff(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))))),
inference(resolution,[],[f216,f164]) ).
fof(f252,plain,
! [X1] : succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),insert_cpq(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))),X1)),
inference(resolution,[],[f216,f177]) ).
fof(f251,plain,
! [X0] : succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),remove_cpq(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))),X0)),
inference(resolution,[],[f216,f178]) ).
fof(f248,plain,
! [X26,X24,X22,X25,X23] :
( ~ contains_slb(X24,X23)
| ~ phi(findmin_cpq_eff(remove_cpq(triple(X22,X24,X25),X23)))
| ~ strictly_less_than(X26,removemin_cpq_res(remove_cpq(triple(X22,X24,X25),X23)))
| ~ less_than(lookup_slb(X24,X23),X23)
| ~ contains_cpq(remove_cpq(triple(X22,X24,X25),X23),X26) ),
inference(superposition,[],[f215,f196]) ).
fof(f247,plain,
! [X21,X18,X19,X17,X20] :
( ~ contains_slb(X19,X18)
| ~ phi(findmin_cpq_eff(remove_cpq(triple(X17,X19,X20),X18)))
| ~ strictly_less_than(X21,removemin_cpq_res(remove_cpq(triple(X17,X19,X20),X18)))
| ~ strictly_less_than(X18,lookup_slb(X19,X18))
| ~ contains_cpq(remove_cpq(triple(X17,X19,X20),X18),X21) ),
inference(superposition,[],[f215,f195]) ).
fof(f249,plain,
! [X16,X14,X15,X13] :
( ~ less_than(lookup_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X13,X14,X15))))
| ~ strictly_less_than(X16,removemin_cpq_res(findmin_cpq_eff(triple(X13,X14,X15))))
| ~ contains_cpq(findmin_cpq_eff(triple(X13,X14,X15)),X16)
| create_slb = X14 ),
inference(subsumption_resolution,[],[f246,f245]) ).
fof(f246,plain,
! [X16,X14,X15,X13] :
( ~ contains_cpq(findmin_cpq_eff(triple(X13,X14,X15)),X16)
| ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X13,X14,X15))))
| ~ strictly_less_than(X16,removemin_cpq_res(findmin_cpq_eff(triple(X13,X14,X15))))
| ~ less_than(lookup_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| ~ contains_slb(X14,findmin_pqp_res(X13))
| create_slb = X14 ),
inference(superposition,[],[f215,f194]) ).
fof(f245,plain,
! [X10,X11,X9,X12] :
( ~ contains_cpq(findmin_cpq_eff(triple(X9,X10,X11)),X12)
| ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X9,X10,X11))))
| ~ strictly_less_than(X12,removemin_cpq_res(findmin_cpq_eff(triple(X9,X10,X11))))
| contains_slb(X10,findmin_pqp_res(X9))
| create_slb = X10 ),
inference(superposition,[],[f215,f192]) ).
fof(f244,plain,
! [X8,X6,X7,X5] :
( ~ contains_slb(X6,findmin_pqp_res(X5))
| ~ phi(findmin_cpq_eff(findmin_cpq_eff(triple(X5,X6,X7))))
| ~ strictly_less_than(X8,removemin_cpq_res(findmin_cpq_eff(triple(X5,X6,X7))))
| ~ strictly_less_than(findmin_pqp_res(X5),lookup_slb(X6,findmin_pqp_res(X5)))
| ~ contains_cpq(findmin_cpq_eff(triple(X5,X6,X7)),X8)
| create_slb = X6 ),
inference(superposition,[],[f215,f193]) ).
fof(f243,plain,
! [X2,X3,X0,X1,X4] :
( ~ contains_cpq(insert_cpq(triple(X0,X2,X3),X1),X4)
| ~ phi(findmin_cpq_eff(insert_cpq(triple(X0,X2,X3),X1)))
| ~ strictly_less_than(X4,removemin_cpq_res(insert_cpq(triple(X0,X2,X3),X1))) ),
inference(superposition,[],[f215,f185]) ).
fof(f242,plain,
! [X2,X3,X0,X1] :
( ~ contains_slb(X1,X3)
| ~ strictly_less_than(X3,removemin_cpq_res(triple(X0,X1,X2)))
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(resolution,[],[f215,f198]) ).
fof(f198,plain,
! [X2,X3,X0,X1] :
( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_slb(X1,X3) ),
inference(cnf_transformation,[],[f130]) ).
fof(f240,plain,
! [X3,X8,X6,X7,X4,X5] :
( contains_cpq(triple(X3,insert_slb(X4,pair(X5,X6)),X7),X8)
| ~ contains_pq(insert_pq(i(triple(X3,X4,X7)),X5),X8) ),
inference(superposition,[],[f140,f202]) ).
fof(f238,plain,
! [X26,X24,X22,X25,X23] :
( ~ contains_slb(X24,X23)
| contains_cpq(remove_cpq(triple(X22,X24,X25),X23),X26)
| ~ less_than(lookup_slb(X24,X23),X23)
| ~ contains_pq(i(remove_cpq(triple(X22,X24,X25),X23)),X26) ),
inference(superposition,[],[f140,f196]) ).
fof(f237,plain,
! [X21,X18,X19,X17,X20] :
( ~ contains_slb(X19,X18)
| contains_cpq(remove_cpq(triple(X17,X19,X20),X18),X21)
| ~ strictly_less_than(X18,lookup_slb(X19,X18))
| ~ contains_pq(i(remove_cpq(triple(X17,X19,X20),X18)),X21) ),
inference(superposition,[],[f140,f195]) ).
fof(f241,plain,
! [X16,X14,X15,X13] :
( ~ less_than(lookup_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| contains_cpq(findmin_cpq_eff(triple(X13,X14,X15)),X16)
| ~ contains_pq(i(findmin_cpq_eff(triple(X13,X14,X15))),X16)
| create_slb = X14 ),
inference(subsumption_resolution,[],[f236,f235]) ).
fof(f236,plain,
! [X16,X14,X15,X13] :
( ~ contains_pq(i(findmin_cpq_eff(triple(X13,X14,X15))),X16)
| contains_cpq(findmin_cpq_eff(triple(X13,X14,X15)),X16)
| ~ less_than(lookup_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| ~ contains_slb(X14,findmin_pqp_res(X13))
| create_slb = X14 ),
inference(superposition,[],[f140,f194]) ).
fof(f235,plain,
! [X10,X11,X9,X12] :
( ~ contains_pq(i(findmin_cpq_eff(triple(X9,X10,X11))),X12)
| contains_cpq(findmin_cpq_eff(triple(X9,X10,X11)),X12)
| contains_slb(X10,findmin_pqp_res(X9))
| create_slb = X10 ),
inference(superposition,[],[f140,f192]) ).
fof(f234,plain,
! [X8,X6,X7,X5] :
( ~ contains_slb(X6,findmin_pqp_res(X5))
| contains_cpq(findmin_cpq_eff(triple(X5,X6,X7)),X8)
| ~ strictly_less_than(findmin_pqp_res(X5),lookup_slb(X6,findmin_pqp_res(X5)))
| ~ contains_pq(i(findmin_cpq_eff(triple(X5,X6,X7))),X8)
| create_slb = X6 ),
inference(superposition,[],[f140,f193]) ).
fof(f233,plain,
! [X2,X3,X0,X1,X4] :
( ~ contains_pq(i(insert_cpq(triple(X0,X2,X3),X1)),X4)
| contains_cpq(insert_cpq(triple(X0,X2,X3),X1),X4) ),
inference(superposition,[],[f140,f185]) ).
fof(f232,plain,
! [X8,X6,X7,X4,X5] :
( ~ contains_pq(insert_pq(i(triple(X4,X5,X6)),X8),X7)
| X7 = X8
| contains_cpq(triple(X4,X5,X6),X7) ),
inference(resolution,[],[f140,f182]) ).
fof(f231,plain,
! [X2,X3,X0,X1] :
( contains_cpq(triple(X0,X1,X2),sK4(i(triple(X0,X1,X2)),X3))
| issmallestelement_pq(i(triple(X0,X1,X2)),X3) ),
inference(resolution,[],[f140,f170]) ).
fof(f229,plain,
! [X26,X24,X22,X25,X23] :
( ~ contains_slb(X24,X23)
| contains_pq(i(remove_cpq(triple(X22,X24,X25),X23)),X26)
| ~ less_than(lookup_slb(X24,X23),X23)
| ~ contains_cpq(remove_cpq(triple(X22,X24,X25),X23),X26) ),
inference(superposition,[],[f139,f196]) ).
fof(f228,plain,
! [X21,X18,X19,X17,X20] :
( ~ contains_slb(X19,X18)
| contains_pq(i(remove_cpq(triple(X17,X19,X20),X18)),X21)
| ~ strictly_less_than(X18,lookup_slb(X19,X18))
| ~ contains_cpq(remove_cpq(triple(X17,X19,X20),X18),X21) ),
inference(superposition,[],[f139,f195]) ).
fof(f230,plain,
! [X16,X14,X15,X13] :
( ~ less_than(lookup_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| contains_pq(i(findmin_cpq_eff(triple(X13,X14,X15))),X16)
| ~ contains_cpq(findmin_cpq_eff(triple(X13,X14,X15)),X16)
| create_slb = X14 ),
inference(subsumption_resolution,[],[f227,f226]) ).
fof(f227,plain,
! [X16,X14,X15,X13] :
( ~ contains_cpq(findmin_cpq_eff(triple(X13,X14,X15)),X16)
| contains_pq(i(findmin_cpq_eff(triple(X13,X14,X15))),X16)
| ~ less_than(lookup_slb(X14,findmin_pqp_res(X13)),findmin_pqp_res(X13))
| ~ contains_slb(X14,findmin_pqp_res(X13))
| create_slb = X14 ),
inference(superposition,[],[f139,f194]) ).
fof(f226,plain,
! [X10,X11,X9,X12] :
( ~ contains_cpq(findmin_cpq_eff(triple(X9,X10,X11)),X12)
| contains_pq(i(findmin_cpq_eff(triple(X9,X10,X11))),X12)
| contains_slb(X10,findmin_pqp_res(X9))
| create_slb = X10 ),
inference(superposition,[],[f139,f192]) ).
fof(f225,plain,
! [X8,X6,X7,X5] :
( ~ contains_slb(X6,findmin_pqp_res(X5))
| contains_pq(i(findmin_cpq_eff(triple(X5,X6,X7))),X8)
| ~ strictly_less_than(findmin_pqp_res(X5),lookup_slb(X6,findmin_pqp_res(X5)))
| ~ contains_cpq(findmin_cpq_eff(triple(X5,X6,X7)),X8)
| create_slb = X6 ),
inference(superposition,[],[f139,f193]) ).
fof(f224,plain,
! [X2,X3,X0,X1,X4] :
( ~ contains_cpq(insert_cpq(triple(X0,X2,X3),X1),X4)
| contains_pq(i(insert_cpq(triple(X0,X2,X3),X1)),X4) ),
inference(superposition,[],[f139,f185]) ).
fof(f223,plain,
! [X2,X3,X0,X1] :
( ~ contains_slb(X1,X3)
| contains_pq(i(triple(X0,X1,X2)),X3) ),
inference(resolution,[],[f139,f198]) ).
fof(f222,plain,
~ less_than(removemin_cpq_res(triple(sK0,sK1,sK2)),sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2)))),
inference(resolution,[],[f214,f171]) ).
fof(f171,plain,
! [X0,X1] :
( issmallestelement_pq(X0,X1)
| ~ less_than(X1,sK4(X0,X1)) ),
inference(cnf_transformation,[],[f127]) ).
fof(f221,plain,
contains_pq(i(triple(sK0,sK1,sK2)),sK4(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2)))),
inference(resolution,[],[f214,f170]) ).
fof(f220,plain,
! [X0] :
( ~ succ_cpq(X0,sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))))
| phi(X0) ),
inference(subsumption_resolution,[],[f219,f218]) ).
fof(f219,plain,
! [X0] :
( phi(X0)
| ~ check_cpq(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2))))
| ~ succ_cpq(X0,sK3(findmin_cpq_eff(triple(sK0,sK1,sK2)))) ),
inference(resolution,[],[f217,f154]) ).
fof(f218,plain,
check_cpq(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2)))),
inference(resolution,[],[f136,f153]) ).
fof(f217,plain,
ok(sK3(findmin_cpq_eff(triple(sK0,sK1,sK2)))),
inference(resolution,[],[f136,f152]) ).
fof(f216,plain,
succ_cpq(findmin_cpq_eff(triple(sK0,sK1,sK2)),sK3(findmin_cpq_eff(triple(sK0,sK1,sK2)))),
inference(resolution,[],[f136,f151]) ).
fof(f139,plain,
! [X2,X3,X0,X1] :
( ~ contains_cpq(triple(X0,X1,X2),X3)
| contains_pq(i(triple(X0,X1,X2)),X3) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0,X1,X2,X3] :
( ( contains_cpq(triple(X0,X1,X2),X3)
| ~ contains_pq(i(triple(X0,X1,X2)),X3) )
& ( contains_pq(i(triple(X0,X1,X2)),X3)
| ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
inference(nnf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0,X1,X2,X3] :
( contains_cpq(triple(X0,X1,X2),X3)
<=> contains_pq(i(triple(X0,X1,X2)),X3) ),
file('/export/starexec/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',l17_li56) ).
fof(f140,plain,
! [X2,X3,X0,X1] :
( ~ contains_pq(i(triple(X0,X1,X2)),X3)
| contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f121]) ).
fof(f215,plain,
! [X2,X3,X0,X1] :
( ~ contains_cpq(triple(X0,X1,X2),X3)
| ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ~ strictly_less_than(X3,removemin_cpq_res(triple(X0,X1,X2))) ),
inference(forward_demodulation,[],[f138,f149]) ).
fof(f149,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/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',ax53) ).
fof(f138,plain,
! [X2,X3,X0,X1] :
( ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ contains_cpq(triple(X0,X1,X2),X3) ),
inference(cnf_transformation,[],[f78]) ).
fof(f78,plain,
! [X0,X1,X2] :
( ~ phi(findmin_cpq_eff(triple(X0,X1,X2)))
| ! [X3] :
( ~ strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
| ~ contains_cpq(triple(X0,X1,X2),X3) ) ),
inference(ennf_transformation,[],[f64]) ).
fof(f64,axiom,
! [X0,X1,X2] :
( ? [X3] :
( strictly_less_than(X3,findmin_cpq_res(triple(X0,X1,X2)))
& contains_cpq(triple(X0,X1,X2),X3) )
=> ~ phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',l17_l18) ).
fof(f136,plain,
phi(findmin_cpq_eff(triple(sK0,sK1,sK2))),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
( ~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))
& phi(findmin_cpq_eff(triple(sK0,sK1,sK2))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f77,f119]) ).
fof(f119,plain,
( ? [X0,X1,X2] :
( ~ issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2)))
& phi(findmin_cpq_eff(triple(X0,X1,X2))) )
=> ( ~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2)))
& phi(findmin_cpq_eff(triple(sK0,sK1,sK2))) ) ),
introduced(choice_axiom,[]) ).
fof(f77,plain,
? [X0,X1,X2] :
( ~ issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2)))
& phi(findmin_cpq_eff(triple(X0,X1,X2))) ),
inference(ennf_transformation,[],[f66]) ).
fof(f66,negated_conjecture,
~ ! [X0,X1,X2] :
( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
inference(negated_conjecture,[],[f65]) ).
fof(f65,conjecture,
! [X0,X1,X2] :
( phi(findmin_cpq_eff(triple(X0,X1,X2)))
=> issmallestelement_pq(i(triple(X0,X1,X2)),findmin_cpq_res(triple(X0,X1,X2))) ),
file('/export/starexec/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515',l17_co) ).
fof(f214,plain,
~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),removemin_cpq_res(triple(sK0,sK1,sK2))),
inference(forward_demodulation,[],[f137,f149]) ).
fof(f137,plain,
~ issmallestelement_pq(i(triple(sK0,sK1,sK2)),findmin_cpq_res(triple(sK0,sK1,sK2))),
inference(cnf_transformation,[],[f120]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10 % Problem : SWV381+1 : TPTP v8.1.2. Released v3.3.0.
% 0.10/0.11 % Command : vampire --ignore_missing on --mode portfolio/casc [--schedule casc_hol_2020] -p tptp -om szs -t %d %s
% 0.11/0.31 % Computer : n002.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Tue Aug 29 03:56:34 EDT 2023
% 0.11/0.31 % CPUTime :
% 0.11/0.31 This is a FOF_THM_RFO_SEQ problem
% 0.11/0.32 Running vampire_casc2023 --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/tmp/tmp.eYxed7STBn/Vampire---4.8_1515
% 0.11/0.32 % (1636)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.38 % (1638)ott+3_2:7_add=large:amm=off:anc=all:bce=on:drc=off:fsd=off:fde=unused:gs=on:irw=on:lcm=predicate:lma=on:msp=off:nwc=10.0:sac=on_598 on Vampire---4 for (598ds/0Mi)
% 0.11/0.38 % (1644)ott+1010_1_aac=none:bce=on:ep=RS:fsd=off:nm=4:nwc=2.0:nicw=on:sas=z3:sims=off_453 on Vampire---4 for (453ds/0Mi)
% 0.11/0.38 % (1640)lrs+11_10:1_bs=unit_only:drc=off:fsd=off:fde=none:gs=on:msp=off:nm=16:nwc=2.0:nicw=on:sos=all:sac=on:sp=reverse_frequency:stl=62_575 on Vampire---4 for (575ds/0Mi)
% 0.11/0.38 % (1643)lrs-1010_2_av=off:bce=on:cond=on:er=filter:fde=unused:lcm=predicate:nm=2:nwc=3.0:sims=off:sp=frequency:urr=on:stl=188_520 on Vampire---4 for (520ds/0Mi)
% 0.11/0.38 % (1641)lrs+2_5:4_anc=none:br=off:fde=unused:gsp=on:nm=32:nwc=1.3:sims=off:sos=all:urr=on:stl=62_558 on Vampire---4 for (558ds/0Mi)
% 0.11/0.38 % (1637)lrs+1010_20_av=off:bd=off:bs=on:bsr=on:bce=on:flr=on:fde=none:gsp=on:nwc=3.0:tgt=ground:urr=ec_only:stl=125_1192 on Vampire---4 for (1192ds/0Mi)
% 0.11/0.38 % (1642)lrs-1010_20_afr=on:anc=all_dependent:bs=on:bsr=on:cond=on:er=known:fde=none:nm=4:nwc=1.3:sims=off:sp=frequency:urr=on:stl=62_533 on Vampire---4 for (533ds/0Mi)
% 0.17/0.40 % (1640)First to succeed.
% 0.17/0.41 % (1641)Also succeeded, but the first one will report.
% 0.17/0.41 % (1643)Also succeeded, but the first one will report.
% 0.17/0.41 % (1640)Refutation found. Thanks to Tanya!
% 0.17/0.41 % SZS status Theorem for Vampire---4
% 0.17/0.41 % SZS output start Proof for Vampire---4
% See solution above
% 0.17/0.42 % (1640)------------------------------
% 0.17/0.42 % (1640)Version: Vampire 4.7 (commit 05ef610bd on 2023-06-21 19:03:17 +0100)
% 0.17/0.42 % (1640)Linked with Z3 4.9.1.0 6ed071b44407cf6623b8d3c0dceb2a8fb7040cee z3-4.8.4-6427-g6ed071b44
% 0.17/0.42 % (1640)Termination reason: Refutation
% 0.17/0.42
% 0.17/0.42 % (1640)Memory used [KB]: 10874
% 0.17/0.42 % (1640)Time elapsed: 0.035 s
% 0.17/0.42 % (1640)------------------------------
% 0.17/0.42 % (1640)------------------------------
% 0.17/0.42 % (1636)Success in time 0.092 s
% 0.17/0.42 % Vampire---4.8 exiting
%------------------------------------------------------------------------------