TSTP Solution File: SWC240+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC240+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n022.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 05:06:29 EDT 2024
% Result : Theorem 4.71s 1.05s
% Output : Refutation 4.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 263
% Syntax : Number of formulae : 1586 ( 68 unt; 0 def)
% Number of atoms : 6470 ( 861 equ)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 8523 (3639 ~;3664 |; 773 &)
% ( 177 <=>; 270 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 145 ( 143 usr; 107 prp; 0-3 aty)
% Number of functors : 56 ( 56 usr; 8 con; 0-3 aty)
% Number of variables : 1776 (1433 !; 343 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f15187,plain,
$false,
inference(avatar_sat_refutation,[],[f841,f1447,f1456,f1517,f1521,f1551,f1597,f1649,f1653,f1766,f1794,f1903,f1912,f1921,f1941,f2101,f2105,f2117,f2121,f2191,f2195,f2278,f2282,f2365,f2369,f3051,f3060,f3069,f3140,f3159,f3161,f3779,f3786,f3954,f4240,f4245,f4580,f4585,f4674,f4679,f4930,f4934,f4946,f4985,f4990,f5192,f5197,f5352,f5356,f5359,f5367,f5559,f5563,f5566,f5574,f5608,f5613,f5616,f5619,f5627,f5661,f5665,f5668,f5677,f5711,f5716,f5719,f5722,f5730,f5764,f5769,f5772,f5780,f5814,f5819,f5822,f5825,f5833,f6089,f6094,f6096,f6104,f6306,f6341,f6343,f6351,f6387,f6392,f6394,f6402,f6468,f6473,f6475,f6483,f6519,f6524,f6526,f6534,f6749,f6754,f6756,f6764,f6800,f6805,f6807,f6815,f8172,f8879,f8883,f8979,f8985,f8992,f8995,f9007,f9010,f9781,f9799,f10130,f10136,f10139,f10143,f10151,f10222,f10229,f10233,f10235,f10243,f14476,f14507,f15040,f15072,f15097,f15186]) ).
fof(f15186,plain,
( ~ spl72_29
| ~ spl72_104 ),
inference(avatar_contradiction_clause,[],[f15185]) ).
fof(f15185,plain,
( $false
| ~ spl72_29
| ~ spl72_104 ),
inference(subsumption_resolution,[],[f15184,f387]) ).
fof(f387,plain,
ssList(sK20),
inference(cnf_transformation,[],[f262]) ).
fof(f262,plain,
( ! [X5] :
( ~ memberP(sK22,X5)
| sK24 = X5
| ~ ssItem(X5) )
& ssItem(sK24)
& ! [X6] :
( ! [X7] :
( ! [X8] :
( sP0(X6,X8,X7)
| app(app(X7,cons(X6,nil)),X8) != sK20
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
& nil != sK20
& sK20 = sK22
& sK21 = sK23
& ssList(sK23)
& ssList(sK22)
& ssList(sK21)
& ssList(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24])],[f225,f261,f260,f259,f258,f257]) ).
fof(f257,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ memberP(X2,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( sP0(X6,X8,X7)
| app(app(X7,cons(X6,nil)),X8) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
& nil != X0
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ memberP(X2,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( sP0(X6,X8,X7)
| app(app(X7,cons(X6,nil)),X8) != sK20
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
& nil != sK20
& sK20 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f258,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ memberP(X2,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( sP0(X6,X8,X7)
| app(app(X7,cons(X6,nil)),X8) != sK20
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
& nil != sK20
& sK20 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ memberP(X2,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( sP0(X6,X8,X7)
| app(app(X7,cons(X6,nil)),X8) != sK20
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
& nil != sK20
& sK20 = X2
& sK21 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f259,plain,
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ memberP(X2,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( sP0(X6,X8,X7)
| app(app(X7,cons(X6,nil)),X8) != sK20
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
& nil != sK20
& sK20 = X2
& sK21 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ memberP(sK22,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( sP0(X6,X8,X7)
| app(app(X7,cons(X6,nil)),X8) != sK20
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
& nil != sK20
& sK20 = sK22
& sK21 = X3
& ssList(X3) )
& ssList(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f260,plain,
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ memberP(sK22,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( sP0(X6,X8,X7)
| app(app(X7,cons(X6,nil)),X8) != sK20
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
& nil != sK20
& sK20 = sK22
& sK21 = X3
& ssList(X3) )
=> ( ? [X4] :
( ! [X5] :
( ~ memberP(sK22,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( sP0(X6,X8,X7)
| app(app(X7,cons(X6,nil)),X8) != sK20
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
& nil != sK20
& sK20 = sK22
& sK21 = sK23
& ssList(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f261,plain,
( ? [X4] :
( ! [X5] :
( ~ memberP(sK22,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
=> ( ! [X5] :
( ~ memberP(sK22,X5)
| sK24 = X5
| ~ ssItem(X5) )
& ssItem(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f225,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ memberP(X2,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( sP0(X6,X8,X7)
| app(app(X7,cons(X6,nil)),X8) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
& nil != X0
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f100,f224]) ).
fof(f224,plain,
! [X6,X8,X7] :
( ? [X9] :
( ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X8,X9)
& memberP(X7,X9)
& ssItem(X9) )
| ~ sP0(X6,X8,X7) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f100,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ memberP(X2,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ? [X9] :
( ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X8,X9)
& memberP(X7,X9)
& ssItem(X9) )
| app(app(X7,cons(X6,nil)),X8) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
& nil != X0
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(flattening,[],[f99]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ! [X5] :
( ~ memberP(X2,X5)
| X4 = X5
| ~ ssItem(X5) )
& ssItem(X4) )
& ! [X6] :
( ! [X7] :
( ! [X8] :
( ? [X9] :
( ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X8,X9)
& memberP(X7,X9)
& ssItem(X9) )
| app(app(X7,cons(X6,nil)),X8) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
& nil != X0
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(ennf_transformation,[],[f98]) ).
fof(f98,plain,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X4] :
( ssItem(X4)
=> ? [X5] :
( memberP(X2,X5)
& X4 != X5
& ssItem(X5) ) )
| ? [X6] :
( ? [X7] :
( ? [X8] :
( ! [X9] :
( ssItem(X9)
=> ( leq(X6,X9)
| ~ lt(X6,X9)
| ~ memberP(X8,X9)
| ~ memberP(X7,X9) ) )
& app(app(X7,cons(X6,nil)),X8) = X0
& ssList(X8) )
& ssList(X7) )
& ssItem(X6) )
| nil = X0
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X8] :
( ssItem(X8)
=> ? [X9] :
( memberP(X2,X9)
& X8 != X9
& ssItem(X9) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( leq(X4,X7)
| ~ lt(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3 ) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( ! [X8] :
( ssItem(X8)
=> ? [X9] :
( memberP(X2,X9)
& X8 != X9
& ssItem(X9) ) )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ssItem(X7)
=> ( leq(X4,X7)
| ~ lt(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7) ) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f15184,plain,
( ~ ssList(sK20)
| ~ spl72_29
| ~ spl72_104 ),
inference(subsumption_resolution,[],[f15183,f2185]) ).
fof(f2185,plain,
( ssList(cons(sK24,nil))
| ~ spl72_29 ),
inference(avatar_component_clause,[],[f2184]) ).
fof(f2184,plain,
( spl72_29
<=> ssList(cons(sK24,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_29])]) ).
fof(f15183,plain,
( ~ ssList(cons(sK24,nil))
| ~ ssList(sK20)
| ~ spl72_29
| ~ spl72_104 ),
inference(subsumption_resolution,[],[f15182,f15039]) ).
fof(f15039,plain,
( frontsegP(sK20,cons(sK24,nil))
| ~ spl72_104 ),
inference(avatar_component_clause,[],[f15037]) ).
fof(f15037,plain,
( spl72_104
<=> frontsegP(sK20,cons(sK24,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_104])]) ).
fof(f15182,plain,
( ~ frontsegP(sK20,cons(sK24,nil))
| ~ ssList(cons(sK24,nil))
| ~ ssList(sK20)
| ~ spl72_29
| ~ spl72_104 ),
inference(resolution,[],[f15160,f593]) ).
fof(f593,plain,
! [X0,X1] :
( ssList(sK69(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f376]) ).
fof(f376,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK69(X0,X1)) = X0
& ssList(sK69(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69])],[f374,f375]) ).
fof(f375,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK69(X0,X1)) = X0
& ssList(sK69(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f374,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f373]) ).
fof(f373,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X1,X2) = X0
& ssList(X2) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( frontsegP(X0,X1)
<=> ? [X2] :
( app(X1,X2) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax5) ).
fof(f15160,plain,
( ~ ssList(sK69(sK20,cons(sK24,nil)))
| ~ spl72_29
| ~ spl72_104 ),
inference(trivial_inequality_removal,[],[f15143]) ).
fof(f15143,plain,
( sK20 != sK20
| ~ ssList(sK69(sK20,cons(sK24,nil)))
| ~ spl72_29
| ~ spl72_104 ),
inference(superposition,[],[f3437,f15081]) ).
fof(f15081,plain,
( sK20 = app(cons(sK24,nil),sK69(sK20,cons(sK24,nil)))
| ~ spl72_29
| ~ spl72_104 ),
inference(subsumption_resolution,[],[f15080,f387]) ).
fof(f15080,plain,
( sK20 = app(cons(sK24,nil),sK69(sK20,cons(sK24,nil)))
| ~ ssList(sK20)
| ~ spl72_29
| ~ spl72_104 ),
inference(subsumption_resolution,[],[f15076,f2185]) ).
fof(f15076,plain,
( sK20 = app(cons(sK24,nil),sK69(sK20,cons(sK24,nil)))
| ~ ssList(cons(sK24,nil))
| ~ ssList(sK20)
| ~ spl72_104 ),
inference(resolution,[],[f15039,f594]) ).
fof(f594,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| app(X1,sK69(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f376]) ).
fof(f3437,plain,
( ! [X0] :
( sK20 != app(cons(sK24,nil),X0)
| ~ ssList(X0) )
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f3436,f395]) ).
fof(f395,plain,
ssItem(sK24),
inference(cnf_transformation,[],[f262]) ).
fof(f3436,plain,
( ! [X0] :
( sK20 != app(cons(sK24,nil),X0)
| ~ ssList(X0)
| ~ ssItem(sK24) )
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f3433,f405]) ).
fof(f405,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f3433,plain,
( ! [X0] :
( sK20 != app(cons(sK24,nil),X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssItem(sK24) )
| ~ spl72_29 ),
inference(superposition,[],[f3397,f2197]) ).
fof(f2197,plain,
( cons(sK24,nil) = app(nil,cons(sK24,nil))
| ~ spl72_29 ),
inference(resolution,[],[f2185,f468]) ).
fof(f468,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f148]) ).
fof(f148,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f28]) ).
fof(f28,axiom,
! [X0] :
( ssList(X0)
=> app(nil,X0) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax28) ).
fof(f3397,plain,
! [X8,X6,X7] :
( app(app(X7,cons(X6,nil)),X8) != sK20
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6) ),
inference(subsumption_resolution,[],[f394,f785]) ).
fof(f785,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| ~ ssItem(X0) ),
inference(subsumption_resolution,[],[f784,f382]) ).
fof(f382,plain,
! [X2,X0,X1] :
( ssItem(sK19(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f256]) ).
fof(f256,plain,
! [X0,X1,X2] :
( ( ~ leq(X0,sK19(X0,X1,X2))
& lt(X0,sK19(X0,X1,X2))
& memberP(X1,sK19(X0,X1,X2))
& memberP(X2,sK19(X0,X1,X2))
& ssItem(sK19(X0,X1,X2)) )
| ~ sP0(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f254,f255]) ).
fof(f255,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ leq(X0,X3)
& lt(X0,X3)
& memberP(X1,X3)
& memberP(X2,X3)
& ssItem(X3) )
=> ( ~ leq(X0,sK19(X0,X1,X2))
& lt(X0,sK19(X0,X1,X2))
& memberP(X1,sK19(X0,X1,X2))
& memberP(X2,sK19(X0,X1,X2))
& ssItem(sK19(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f254,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ leq(X0,X3)
& lt(X0,X3)
& memberP(X1,X3)
& memberP(X2,X3)
& ssItem(X3) )
| ~ sP0(X0,X1,X2) ),
inference(rectify,[],[f253]) ).
fof(f253,plain,
! [X6,X8,X7] :
( ? [X9] :
( ~ leq(X6,X9)
& lt(X6,X9)
& memberP(X8,X9)
& memberP(X7,X9)
& ssItem(X9) )
| ~ sP0(X6,X8,X7) ),
inference(nnf_transformation,[],[f224]) ).
fof(f784,plain,
! [X2,X0,X1] :
( ~ ssItem(sK19(X0,X1,X2))
| ~ ssItem(X0)
| ~ sP0(X0,X1,X2) ),
inference(subsumption_resolution,[],[f783,f386]) ).
fof(f386,plain,
! [X2,X0,X1] :
( ~ leq(X0,sK19(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f256]) ).
fof(f783,plain,
! [X2,X0,X1] :
( leq(X0,sK19(X0,X1,X2))
| ~ ssItem(sK19(X0,X1,X2))
| ~ ssItem(X0)
| ~ sP0(X0,X1,X2) ),
inference(resolution,[],[f429,f385]) ).
fof(f385,plain,
! [X2,X0,X1] :
( lt(X0,sK19(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f256]) ).
fof(f429,plain,
! [X0,X1] :
( ~ lt(X0,X1)
| leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f267]) ).
fof(f267,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f266]) ).
fof(f266,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f125]) ).
fof(f125,plain,
! [X0] :
( ! [X1] :
( ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f93]) ).
fof(f93,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
<=> ( leq(X0,X1)
& X0 != X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax93) ).
fof(f394,plain,
! [X8,X6,X7] :
( sP0(X6,X8,X7)
| app(app(X7,cons(X6,nil)),X8) != sK20
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6) ),
inference(cnf_transformation,[],[f262]) ).
fof(f15097,plain,
( ~ spl72_105
| spl72_106
| ~ spl72_29
| ~ spl72_30
| ~ spl72_43 ),
inference(avatar_split_clause,[],[f15031,f3772,f2188,f2184,f15094,f15090]) ).
fof(f15090,plain,
( spl72_105
<=> frontsegP(nil,cons(sK24,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_105])]) ).
fof(f15094,plain,
( spl72_106
<=> frontsegP(nil,cons(sK24,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_106])]) ).
fof(f2188,plain,
( spl72_30
<=> ssList(cons(sK24,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_30])]) ).
fof(f3772,plain,
( spl72_43
<=> ssList(sK66(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_43])]) ).
fof(f15031,plain,
( frontsegP(nil,cons(sK24,nil))
| ~ frontsegP(nil,cons(sK24,sK20))
| ~ spl72_29
| ~ spl72_30
| ~ spl72_43 ),
inference(forward_demodulation,[],[f15030,f4489]) ).
fof(f4489,plain,
( nil = sK66(sK20,sK20)
| ~ spl72_43 ),
inference(subsumption_resolution,[],[f4488,f3773]) ).
fof(f3773,plain,
( ssList(sK66(sK20,sK20))
| ~ spl72_43 ),
inference(avatar_component_clause,[],[f3772]) ).
fof(f4488,plain,
( nil = sK66(sK20,sK20)
| ~ ssList(sK66(sK20,sK20)) ),
inference(trivial_inequality_removal,[],[f4487]) ).
fof(f4487,plain,
( sK20 != sK20
| nil = sK66(sK20,sK20)
| ~ ssList(sK66(sK20,sK20)) ),
inference(superposition,[],[f4120,f3676]) ).
fof(f3676,plain,
sK20 = app(sK66(sK20,sK20),sK20),
inference(resolution,[],[f3021,f387]) ).
fof(f3021,plain,
! [X0] :
( ~ ssList(X0)
| app(sK66(X0,X0),X0) = X0 ),
inference(duplicate_literal_removal,[],[f3011]) ).
fof(f3011,plain,
! [X0] :
( app(sK66(X0,X0),X0) = X0
| ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f587,f466]) ).
fof(f466,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax49) ).
fof(f587,plain,
! [X0,X1] :
( ~ rearsegP(X0,X1)
| app(sK66(X0,X1),X1) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f367]) ).
fof(f367,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ( app(sK66(X0,X1),X1) = X0
& ssList(sK66(X0,X1)) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f365,f366]) ).
fof(f366,plain,
! [X0,X1] :
( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
=> ( app(sK66(X0,X1),X1) = X0
& ssList(sK66(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f365,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f364]) ).
fof(f364,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ? [X2] :
( app(X2,X1) = X0
& ssList(X2) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( rearsegP(X0,X1)
<=> ? [X2] :
( app(X2,X1) = X0
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax6) ).
fof(f4120,plain,
! [X0] :
( sK20 != app(X0,sK20)
| nil = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4119,f387]) ).
fof(f4119,plain,
! [X0] :
( sK20 != app(X0,sK20)
| nil = X0
| ~ ssList(sK20)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4026,f405]) ).
fof(f4026,plain,
! [X0] :
( sK20 != app(X0,sK20)
| nil = X0
| ~ ssList(nil)
| ~ ssList(sK20)
| ~ ssList(X0) ),
inference(superposition,[],[f605,f694]) ).
fof(f694,plain,
sK20 = app(nil,sK20),
inference(resolution,[],[f468,f387]) ).
fof(f605,plain,
! [X2,X0,X1] :
( app(X2,X1) != app(X0,X1)
| X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f213]) ).
fof(f213,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f212]) ).
fof(f212,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f79]) ).
fof(f79,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X2,X1) = app(X0,X1)
=> X0 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax79) ).
fof(f15030,plain,
( frontsegP(sK66(sK20,sK20),cons(sK24,nil))
| ~ frontsegP(nil,cons(sK24,sK20))
| ~ spl72_29
| ~ spl72_30
| ~ spl72_43 ),
inference(subsumption_resolution,[],[f15029,f2190]) ).
fof(f2190,plain,
( ssList(cons(sK24,sK20))
| ~ spl72_30 ),
inference(avatar_component_clause,[],[f2188]) ).
fof(f15029,plain,
( frontsegP(sK66(sK20,sK20),cons(sK24,nil))
| ~ frontsegP(nil,cons(sK24,sK20))
| ~ ssList(cons(sK24,sK20))
| ~ spl72_29
| ~ spl72_30
| ~ spl72_43 ),
inference(subsumption_resolution,[],[f14998,f3773]) ).
fof(f14998,plain,
( frontsegP(sK66(sK20,sK20),cons(sK24,nil))
| ~ ssList(sK66(sK20,sK20))
| ~ frontsegP(nil,cons(sK24,sK20))
| ~ ssList(cons(sK24,sK20))
| ~ spl72_29
| ~ spl72_30
| ~ spl72_43 ),
inference(resolution,[],[f3756,f3834]) ).
fof(f3834,plain,
( ! [X0] :
( frontsegP(sK66(sK20,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_43 ),
inference(subsumption_resolution,[],[f3833,f405]) ).
fof(f3833,plain,
( ! [X0] :
( frontsegP(sK66(sK20,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_43 ),
inference(subsumption_resolution,[],[f3830,f3773]) ).
fof(f3830,plain,
( ! [X0] :
( frontsegP(sK66(sK20,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sK66(sK20,sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_43 ),
inference(superposition,[],[f604,f3788]) ).
fof(f3788,plain,
( sK66(sK20,sK20) = app(nil,sK66(sK20,sK20))
| ~ spl72_43 ),
inference(resolution,[],[f3773,f468]) ).
fof(f604,plain,
! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f211]) ).
fof(f211,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f210]) ).
fof(f210,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f43]) ).
fof(f43,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( frontsegP(X0,X1)
=> frontsegP(app(X0,X2),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax43) ).
fof(f3756,plain,
( ! [X0] :
( ~ frontsegP(X0,cons(sK24,sK20))
| frontsegP(X0,cons(sK24,nil))
| ~ ssList(X0) )
| ~ spl72_29
| ~ spl72_30 ),
inference(subsumption_resolution,[],[f3755,f2190]) ).
fof(f3755,plain,
( ! [X0] :
( frontsegP(X0,cons(sK24,nil))
| ~ frontsegP(X0,cons(sK24,sK20))
| ~ ssList(cons(sK24,sK20))
| ~ ssList(X0) )
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f3728,f2185]) ).
fof(f3728,plain,
( ! [X0] :
( frontsegP(X0,cons(sK24,nil))
| ~ frontsegP(X0,cons(sK24,sK20))
| ~ ssList(cons(sK24,nil))
| ~ ssList(cons(sK24,sK20))
| ~ ssList(X0) )
| ~ spl72_29 ),
inference(resolution,[],[f609,f2551]) ).
fof(f2551,plain,
( frontsegP(cons(sK24,sK20),cons(sK24,nil))
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f2550,f2185]) ).
fof(f2550,plain,
( frontsegP(cons(sK24,sK20),cons(sK24,nil))
| ~ ssList(cons(sK24,nil)) ),
inference(subsumption_resolution,[],[f2542,f387]) ).
fof(f2542,plain,
( frontsegP(cons(sK24,sK20),cons(sK24,nil))
| ~ ssList(sK20)
| ~ ssList(cons(sK24,nil)) ),
inference(superposition,[],[f2500,f2156]) ).
fof(f2156,plain,
cons(sK24,sK20) = app(cons(sK24,nil),sK20),
inference(resolution,[],[f2052,f395]) ).
fof(f2052,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,sK20) = app(cons(X0,nil),sK20) ),
inference(resolution,[],[f572,f387]) ).
fof(f572,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f184]) ).
fof(f184,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f81]) ).
fof(f81,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) = app(cons(X1,nil),X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax81) ).
fof(f2500,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f638,f577]) ).
fof(f577,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f186]) ).
fof(f186,plain,
! [X0] :
( ! [X1] :
( ssList(app(X0,X1))
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f26]) ).
fof(f26,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ssList(app(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax26) ).
fof(f638,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f595]) ).
fof(f595,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f376]) ).
fof(f609,plain,
! [X2,X0,X1] :
( ~ frontsegP(X1,X2)
| frontsegP(X0,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f221]) ).
fof(f221,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f220]) ).
fof(f220,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( frontsegP(X1,X2)
& frontsegP(X0,X1) )
=> frontsegP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax40) ).
fof(f15072,plain,
( ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| ~ spl72_74
| spl72_104 ),
inference(avatar_contradiction_clause,[],[f15071]) ).
fof(f15071,plain,
( $false
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| ~ spl72_74
| spl72_104 ),
inference(subsumption_resolution,[],[f15070,f405]) ).
fof(f15070,plain,
( ~ ssList(nil)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| ~ spl72_74
| spl72_104 ),
inference(subsumption_resolution,[],[f15068,f6088]) ).
fof(f6088,plain,
( frontsegP(tl(sK20),nil)
| ~ spl72_74 ),
inference(avatar_component_clause,[],[f6086]) ).
fof(f6086,plain,
( spl72_74
<=> frontsegP(tl(sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_74])]) ).
fof(f15068,plain,
( ~ frontsegP(tl(sK20),nil)
| ~ ssList(nil)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_104 ),
inference(resolution,[],[f15038,f4551]) ).
fof(f4551,plain,
( ! [X0] :
( frontsegP(sK20,cons(sK24,X0))
| ~ frontsegP(tl(sK20),X0)
| ~ ssList(X0) )
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(forward_demodulation,[],[f4550,f1967]) ).
fof(f1967,plain,
( tl(sK20) = sK25(sK20)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(forward_demodulation,[],[f1966,f1616]) ).
fof(f1616,plain,
( sK20 = cons(sK24,sK25(sK20))
| ~ spl72_7
| ~ spl72_10 ),
inference(superposition,[],[f1494,f1613]) ).
fof(f1613,plain,
( sK24 = sK26(sK20)
| ~ spl72_7
| ~ spl72_10 ),
inference(subsumption_resolution,[],[f1612,f1511]) ).
fof(f1511,plain,
( ssItem(sK26(sK20))
| ~ spl72_7 ),
inference(avatar_component_clause,[],[f1510]) ).
fof(f1510,plain,
( spl72_7
<=> ssItem(sK26(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_7])]) ).
fof(f1612,plain,
( sK24 = sK26(sK20)
| ~ ssItem(sK26(sK20))
| ~ spl72_10 ),
inference(resolution,[],[f1550,f661]) ).
fof(f661,plain,
! [X5] :
( ~ memberP(sK20,X5)
| sK24 = X5
| ~ ssItem(X5) ),
inference(forward_demodulation,[],[f396,f392]) ).
fof(f392,plain,
sK20 = sK22,
inference(cnf_transformation,[],[f262]) ).
fof(f396,plain,
! [X5] :
( ~ memberP(sK22,X5)
| sK24 = X5
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f262]) ).
fof(f1550,plain,
( memberP(sK20,sK26(sK20))
| ~ spl72_10 ),
inference(avatar_component_clause,[],[f1548]) ).
fof(f1548,plain,
( spl72_10
<=> memberP(sK20,sK26(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_10])]) ).
fof(f1494,plain,
sK20 = cons(sK26(sK20),sK25(sK20)),
inference(subsumption_resolution,[],[f1461,f393]) ).
fof(f393,plain,
nil != sK20,
inference(cnf_transformation,[],[f262]) ).
fof(f1461,plain,
( nil = sK20
| sK20 = cons(sK26(sK20),sK25(sK20)) ),
inference(resolution,[],[f471,f387]) ).
fof(f471,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(sK26(X0),sK25(X0)) = X0 ),
inference(cnf_transformation,[],[f284]) ).
fof(f284,plain,
! [X0] :
( ( cons(sK26(X0),sK25(X0)) = X0
& ssItem(sK26(X0))
& ssList(sK25(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f150,f283,f282]) ).
fof(f282,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK25(X0)) = X0
& ssItem(X2) )
& ssList(sK25(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f283,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK25(X0)) = X0
& ssItem(X2) )
=> ( cons(sK26(X0),sK25(X0)) = X0
& ssItem(sK26(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f150,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f149]) ).
fof(f149,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f20]) ).
fof(f20,axiom,
! [X0] :
( ssList(X0)
=> ( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax20) ).
fof(f1966,plain,
( sK25(sK20) = tl(cons(sK24,sK25(sK20)))
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(forward_demodulation,[],[f1943,f1707]) ).
fof(f1707,plain,
( sK24 = hd(sK20)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10 ),
inference(forward_demodulation,[],[f1686,f1616]) ).
fof(f1686,plain,
( sK24 = hd(cons(sK24,sK25(sK20)))
| ~ spl72_9 ),
inference(resolution,[],[f1605,f395]) ).
fof(f1605,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK25(sK20))) = X0 )
| ~ spl72_9 ),
inference(resolution,[],[f1545,f571]) ).
fof(f571,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f183]) ).
fof(f183,plain,
! [X0] :
( ! [X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f23]) ).
fof(f23,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> hd(cons(X1,X0)) = X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax23) ).
fof(f1545,plain,
( ssList(sK25(sK20))
| ~ spl72_9 ),
inference(avatar_component_clause,[],[f1544]) ).
fof(f1544,plain,
( spl72_9
<=> ssList(sK25(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_9])]) ).
fof(f1943,plain,
( sK25(sK20) = tl(cons(hd(sK20),sK25(sK20)))
| ~ spl72_9
| ~ spl72_11 ),
inference(resolution,[],[f1604,f1643]) ).
fof(f1643,plain,
( ssItem(hd(sK20))
| ~ spl72_11 ),
inference(avatar_component_clause,[],[f1642]) ).
fof(f1642,plain,
( spl72_11
<=> ssItem(hd(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_11])]) ).
fof(f1604,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK25(sK20) = tl(cons(X0,sK25(sK20))) )
| ~ spl72_9 ),
inference(resolution,[],[f1545,f570]) ).
fof(f570,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f182]) ).
fof(f182,plain,
! [X0] :
( ! [X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f25]) ).
fof(f25,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> tl(cons(X1,X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax25) ).
fof(f4550,plain,
( ! [X0] :
( frontsegP(sK20,cons(sK24,X0))
| ~ frontsegP(sK25(sK20),X0)
| ~ ssList(X0) )
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10 ),
inference(forward_demodulation,[],[f4549,f1613]) ).
fof(f4549,plain,
( ! [X0] :
( frontsegP(sK20,cons(sK26(sK20),X0))
| ~ frontsegP(sK25(sK20),X0)
| ~ ssList(X0) )
| ~ spl72_7
| ~ spl72_9 ),
inference(subsumption_resolution,[],[f4548,f1511]) ).
fof(f4548,plain,
( ! [X0] :
( frontsegP(sK20,cons(sK26(sK20),X0))
| ~ frontsegP(sK25(sK20),X0)
| ~ ssList(X0)
| ~ ssItem(sK26(sK20)) )
| ~ spl72_9 ),
inference(subsumption_resolution,[],[f4534,f1545]) ).
fof(f4534,plain,
! [X0] :
( frontsegP(sK20,cons(sK26(sK20),X0))
| ~ frontsegP(sK25(sK20),X0)
| ~ ssList(X0)
| ~ ssList(sK25(sK20))
| ~ ssItem(sK26(sK20)) ),
inference(superposition,[],[f643,f1494]) ).
fof(f643,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f617]) ).
fof(f617,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f441]) ).
fof(f441,plain,
! [X2,X3,X0,X1] :
( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f271,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f270]) ).
fof(f270,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f137]) ).
fof(f137,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f44]) ).
fof(f44,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( frontsegP(cons(X0,X2),cons(X1,X3))
<=> ( frontsegP(X2,X3)
& X0 = X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax44) ).
fof(f15038,plain,
( ~ frontsegP(sK20,cons(sK24,nil))
| spl72_104 ),
inference(avatar_component_clause,[],[f15037]) ).
fof(f15040,plain,
( ~ spl72_103
| spl72_104
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| ~ spl72_29
| ~ spl72_30 ),
inference(avatar_split_clause,[],[f15026,f2188,f2184,f1642,f1548,f1544,f1510,f15037,f15033]) ).
fof(f15033,plain,
( spl72_103
<=> frontsegP(tl(sK20),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_103])]) ).
fof(f15026,plain,
( frontsegP(sK20,cons(sK24,nil))
| ~ frontsegP(tl(sK20),sK20)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| ~ spl72_29
| ~ spl72_30 ),
inference(subsumption_resolution,[],[f14999,f387]) ).
fof(f14999,plain,
( frontsegP(sK20,cons(sK24,nil))
| ~ ssList(sK20)
| ~ frontsegP(tl(sK20),sK20)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| ~ spl72_29
| ~ spl72_30 ),
inference(duplicate_literal_removal,[],[f14996]) ).
fof(f14996,plain,
( frontsegP(sK20,cons(sK24,nil))
| ~ ssList(sK20)
| ~ frontsegP(tl(sK20),sK20)
| ~ ssList(sK20)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| ~ spl72_29
| ~ spl72_30 ),
inference(resolution,[],[f3756,f4551]) ).
fof(f14507,plain,
( spl72_101
| ~ spl72_102
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_33 ),
inference(avatar_split_clause,[],[f14495,f2358,f1548,f1544,f1510,f14504,f14500]) ).
fof(f14500,plain,
( spl72_101
<=> sK24 = sK71 ),
introduced(avatar_definition,[new_symbols(naming,[spl72_101])]) ).
fof(f14504,plain,
( spl72_102
<=> frontsegP(cons(sK71,nil),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_102])]) ).
fof(f2358,plain,
( spl72_33
<=> ssList(cons(sK71,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_33])]) ).
fof(f14495,plain,
( ~ frontsegP(cons(sK71,nil),sK20)
| sK24 = sK71
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_33 ),
inference(subsumption_resolution,[],[f14494,f612]) ).
fof(f612,plain,
ssItem(sK71),
inference(cnf_transformation,[],[f381]) ).
fof(f381,plain,
( sK70 != sK71
& ssItem(sK71)
& ssItem(sK70) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK70,sK71])],[f2,f380,f379]) ).
fof(f379,plain,
( ? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) )
=> ( ? [X1] :
( sK70 != X1
& ssItem(X1) )
& ssItem(sK70) ) ),
introduced(choice_axiom,[]) ).
fof(f380,plain,
( ? [X1] :
( sK70 != X1
& ssItem(X1) )
=> ( sK70 != sK71
& ssItem(sK71) ) ),
introduced(choice_axiom,[]) ).
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f14494,plain,
( ~ frontsegP(cons(sK71,nil),sK20)
| sK24 = sK71
| ~ ssItem(sK71)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_33 ),
inference(subsumption_resolution,[],[f14487,f387]) ).
fof(f14487,plain,
( ~ frontsegP(cons(sK71,nil),sK20)
| ~ ssList(sK20)
| sK24 = sK71
| ~ ssItem(sK71)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_33 ),
inference(duplicate_literal_removal,[],[f14480]) ).
fof(f14480,plain,
( ~ frontsegP(cons(sK71,nil),sK20)
| ~ ssList(sK20)
| sK24 = sK71
| ~ ssList(sK20)
| ~ ssItem(sK71)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_33 ),
inference(resolution,[],[f3330,f5075]) ).
fof(f5075,plain,
( ! [X0,X1] :
( ~ frontsegP(cons(X0,X1),sK20)
| sK24 = X0
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10 ),
inference(forward_demodulation,[],[f5074,f1613]) ).
fof(f5074,plain,
( ! [X0,X1] :
( ~ frontsegP(cons(X0,X1),sK20)
| sK26(sK20) = X0
| ~ ssList(X1)
| ~ ssItem(X0) )
| ~ spl72_7
| ~ spl72_9 ),
inference(subsumption_resolution,[],[f5073,f1511]) ).
fof(f5073,plain,
( ! [X0,X1] :
( ~ frontsegP(cons(X0,X1),sK20)
| sK26(sK20) = X0
| ~ ssList(X1)
| ~ ssItem(sK26(sK20))
| ~ ssItem(X0) )
| ~ spl72_9 ),
inference(subsumption_resolution,[],[f5036,f1545]) ).
fof(f5036,plain,
! [X0,X1] :
( ~ frontsegP(cons(X0,X1),sK20)
| sK26(sK20) = X0
| ~ ssList(sK25(sK20))
| ~ ssList(X1)
| ~ ssItem(sK26(sK20))
| ~ ssItem(X0) ),
inference(superposition,[],[f439,f1494]) ).
fof(f439,plain,
! [X2,X3,X0,X1] :
( ~ frontsegP(cons(X0,X2),cons(X1,X3))
| X0 = X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f3330,plain,
( ! [X0] :
( frontsegP(cons(sK71,sK20),X0)
| ~ frontsegP(cons(sK71,nil),X0)
| ~ ssList(X0) )
| ~ spl72_33 ),
inference(subsumption_resolution,[],[f3329,f2359]) ).
fof(f2359,plain,
( ssList(cons(sK71,nil))
| ~ spl72_33 ),
inference(avatar_component_clause,[],[f2358]) ).
fof(f3329,plain,
! [X0] :
( frontsegP(cons(sK71,sK20),X0)
| ~ frontsegP(cons(sK71,nil),X0)
| ~ ssList(X0)
| ~ ssList(cons(sK71,nil)) ),
inference(subsumption_resolution,[],[f3299,f387]) ).
fof(f3299,plain,
! [X0] :
( frontsegP(cons(sK71,sK20),X0)
| ~ frontsegP(cons(sK71,nil),X0)
| ~ ssList(sK20)
| ~ ssList(X0)
| ~ ssList(cons(sK71,nil)) ),
inference(superposition,[],[f604,f2176]) ).
fof(f2176,plain,
cons(sK71,sK20) = app(cons(sK71,nil),sK20),
inference(resolution,[],[f2052,f612]) ).
fof(f14476,plain,
( spl72_99
| ~ spl72_100
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_31 ),
inference(avatar_split_clause,[],[f14464,f2271,f1548,f1544,f1510,f14473,f14469]) ).
fof(f14469,plain,
( spl72_99
<=> sK24 = sK70 ),
introduced(avatar_definition,[new_symbols(naming,[spl72_99])]) ).
fof(f14473,plain,
( spl72_100
<=> frontsegP(cons(sK70,nil),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_100])]) ).
fof(f2271,plain,
( spl72_31
<=> ssList(cons(sK70,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_31])]) ).
fof(f14464,plain,
( ~ frontsegP(cons(sK70,nil),sK20)
| sK24 = sK70
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_31 ),
inference(subsumption_resolution,[],[f14463,f611]) ).
fof(f611,plain,
ssItem(sK70),
inference(cnf_transformation,[],[f381]) ).
fof(f14463,plain,
( ~ frontsegP(cons(sK70,nil),sK20)
| sK24 = sK70
| ~ ssItem(sK70)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_31 ),
inference(subsumption_resolution,[],[f14456,f387]) ).
fof(f14456,plain,
( ~ frontsegP(cons(sK70,nil),sK20)
| ~ ssList(sK20)
| sK24 = sK70
| ~ ssItem(sK70)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_31 ),
inference(duplicate_literal_removal,[],[f14449]) ).
fof(f14449,plain,
( ~ frontsegP(cons(sK70,nil),sK20)
| ~ ssList(sK20)
| sK24 = sK70
| ~ ssList(sK20)
| ~ ssItem(sK70)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_31 ),
inference(resolution,[],[f3328,f5075]) ).
fof(f3328,plain,
( ! [X0] :
( frontsegP(cons(sK70,sK20),X0)
| ~ frontsegP(cons(sK70,nil),X0)
| ~ ssList(X0) )
| ~ spl72_31 ),
inference(subsumption_resolution,[],[f3327,f2272]) ).
fof(f2272,plain,
( ssList(cons(sK70,nil))
| ~ spl72_31 ),
inference(avatar_component_clause,[],[f2271]) ).
fof(f3327,plain,
! [X0] :
( frontsegP(cons(sK70,sK20),X0)
| ~ frontsegP(cons(sK70,nil),X0)
| ~ ssList(X0)
| ~ ssList(cons(sK70,nil)) ),
inference(subsumption_resolution,[],[f3298,f387]) ).
fof(f3298,plain,
! [X0] :
( frontsegP(cons(sK70,sK20),X0)
| ~ frontsegP(cons(sK70,nil),X0)
| ~ ssList(sK20)
| ~ ssList(X0)
| ~ ssList(cons(sK70,nil)) ),
inference(superposition,[],[f604,f2175]) ).
fof(f2175,plain,
cons(sK70,sK20) = app(cons(sK70,nil),sK20),
inference(resolution,[],[f2052,f611]) ).
fof(f10243,plain,
( ~ spl72_89
| spl72_97
| ~ spl72_98 ),
inference(avatar_contradiction_clause,[],[f10242]) ).
fof(f10242,plain,
( $false
| ~ spl72_89
| spl72_97
| ~ spl72_98 ),
inference(subsumption_resolution,[],[f10241,f8873]) ).
fof(f8873,plain,
( ssList(app(sK20,sK20))
| ~ spl72_89 ),
inference(avatar_component_clause,[],[f8872]) ).
fof(f8872,plain,
( spl72_89
<=> ssList(app(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_89])]) ).
fof(f10241,plain,
( ~ ssList(app(sK20,sK20))
| spl72_97
| ~ spl72_98 ),
inference(subsumption_resolution,[],[f10240,f405]) ).
fof(f10240,plain,
( ~ ssList(nil)
| ~ ssList(app(sK20,sK20))
| spl72_97
| ~ spl72_98 ),
inference(subsumption_resolution,[],[f10239,f10221]) ).
fof(f10221,plain,
( frontsegP(app(sK20,sK20),nil)
| ~ spl72_98 ),
inference(avatar_component_clause,[],[f10219]) ).
fof(f10219,plain,
( spl72_98
<=> frontsegP(app(sK20,sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_98])]) ).
fof(f10239,plain,
( ~ frontsegP(app(sK20,sK20),nil)
| ~ ssList(nil)
| ~ ssList(app(sK20,sK20))
| spl72_97 ),
inference(resolution,[],[f10217,f593]) ).
fof(f10217,plain,
( ~ ssList(sK69(app(sK20,sK20),nil))
| spl72_97 ),
inference(avatar_component_clause,[],[f10215]) ).
fof(f10215,plain,
( spl72_97
<=> ssList(sK69(app(sK20,sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_97])]) ).
fof(f10235,plain,
( ~ spl72_89
| spl72_98 ),
inference(avatar_contradiction_clause,[],[f10234]) ).
fof(f10234,plain,
( $false
| ~ spl72_89
| spl72_98 ),
inference(subsumption_resolution,[],[f10225,f8873]) ).
fof(f10225,plain,
( ~ ssList(app(sK20,sK20))
| spl72_98 ),
inference(resolution,[],[f10220,f464]) ).
fof(f464,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f45]) ).
fof(f45,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax45) ).
fof(f10220,plain,
( ~ frontsegP(app(sK20,sK20),nil)
| spl72_98 ),
inference(avatar_component_clause,[],[f10219]) ).
fof(f10233,plain,
( ~ spl72_43
| ~ spl72_44
| spl72_98 ),
inference(avatar_contradiction_clause,[],[f10232]) ).
fof(f10232,plain,
( $false
| ~ spl72_43
| ~ spl72_44
| spl72_98 ),
inference(subsumption_resolution,[],[f10231,f405]) ).
fof(f10231,plain,
( ~ ssList(nil)
| ~ spl72_43
| ~ spl72_44
| spl72_98 ),
inference(subsumption_resolution,[],[f10230,f387]) ).
fof(f10230,plain,
( ~ ssList(sK20)
| ~ ssList(nil)
| ~ spl72_43
| ~ spl72_44
| spl72_98 ),
inference(subsumption_resolution,[],[f10226,f4492]) ).
fof(f4492,plain,
( frontsegP(sK20,nil)
| ~ spl72_43
| ~ spl72_44 ),
inference(superposition,[],[f3778,f4489]) ).
fof(f3778,plain,
( frontsegP(sK20,sK66(sK20,sK20))
| ~ spl72_44 ),
inference(avatar_component_clause,[],[f3776]) ).
fof(f3776,plain,
( spl72_44
<=> frontsegP(sK20,sK66(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_44])]) ).
fof(f10226,plain,
( ~ frontsegP(sK20,nil)
| ~ ssList(sK20)
| ~ ssList(nil)
| spl72_98 ),
inference(duplicate_literal_removal,[],[f10224]) ).
fof(f10224,plain,
( ~ frontsegP(sK20,nil)
| ~ ssList(sK20)
| ~ ssList(nil)
| ~ ssList(sK20)
| spl72_98 ),
inference(resolution,[],[f10220,f604]) ).
fof(f10229,plain,
( ~ spl72_89
| spl72_98 ),
inference(avatar_contradiction_clause,[],[f10228]) ).
fof(f10228,plain,
( $false
| ~ spl72_89
| spl72_98 ),
inference(subsumption_resolution,[],[f10227,f405]) ).
fof(f10227,plain,
( ~ ssList(nil)
| ~ spl72_89
| spl72_98 ),
inference(subsumption_resolution,[],[f10223,f648]) ).
fof(f648,plain,
frontsegP(nil,nil),
inference(global_subsumption,[],[f386,f385,f384,f383,f382,f396,f395,f394,f393,f392,f391,f390,f389,f388,f387,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f425,f424,f427,f426,f430,f429,f645,f431,f432,f433,f434,f435,f438,f644,f436,f643,f440,f439,f443,f442,f448,f618,f446,f445,f449,f451,f450,f456,f620,f454,f453,f457,f460,f459,f458,f461,f462,f463,f464,f465,f466,f467,f468,f471,f470,f469,f472,f473,f474,f476,f475,f478,f477,f622,f480,f479,f482,f490,f489,f488,f487,f486,f485,f623,f491,f492,f501,f500,f499,f498,f497,f496,f495,f642,f502,f503,f513,f512,f511,f510,f509,f508,f507,f506,f626,f514,f515,f525,f524,f523,f522,f521,f520,f519,f518,f627,f526,f527,f537,f536,f535,f534,f533,f532,f531,f530,f628,f538,f540,f539,f548,f547,f546,f545,f544,f543,f542,f629,f549,f551,f550,f559,f558,f557,f556,f555,f554,f553,f630,f560,f631,f646,f561,f632,f647,f563,f633]) ).
fof(f633,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f566]) ).
fof(f566,plain,
! [X0] :
( frontsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f357]) ).
fof(f357,plain,
! [X0] :
( ( ( frontsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ frontsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f178]) ).
fof(f178,plain,
! [X0] :
( ( frontsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f46]) ).
fof(f46,axiom,
! [X0] :
( ssList(X0)
=> ( frontsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax46) ).
fof(f563,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f356,plain,
! [X0] :
( ( ( rearsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ rearsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f177,plain,
! [X0] :
( ( rearsegP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f52]) ).
fof(f52,axiom,
! [X0] :
( ssList(X0)
=> ( rearsegP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax52) ).
fof(f647,plain,
rearsegP(nil,nil),
inference(global_subsumption,[],[f386,f385,f384,f383,f382,f396,f395,f394,f393,f392,f391,f390,f389,f388,f387,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f425,f424,f427,f426,f430,f429,f645,f431,f432,f433,f434,f435,f438,f644,f436,f643,f440,f439,f443,f442,f448,f618,f446,f445,f449,f451,f450,f456,f620,f454,f453,f457,f460,f459,f458,f461,f462,f463,f464,f465,f466,f467,f468,f471,f470,f469,f472,f473,f474,f476,f475,f478,f477,f622,f480,f479,f482,f490,f489,f488,f487,f486,f485,f623,f491,f492,f501,f500,f499,f498,f497,f496,f495,f642,f502,f503,f513,f512,f511,f510,f509,f508,f507,f506,f626,f514,f515,f525,f524,f523,f522,f521,f520,f519,f518,f627,f526,f527,f537,f536,f535,f534,f533,f532,f531,f530,f628,f538,f540,f539,f548,f547,f546,f545,f544,f543,f542,f629,f549,f551,f550,f559,f558,f557,f556,f555,f554,f553,f630,f560,f631,f646,f561,f632]) ).
fof(f632,plain,
( rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f564]) ).
fof(f564,plain,
! [X0] :
( rearsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f561,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f355,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax58) ).
fof(f646,plain,
segmentP(nil,nil),
inference(global_subsumption,[],[f386,f385,f384,f383,f382,f396,f395,f394,f393,f392,f391,f390,f389,f388,f387,f397,f398,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f425,f424,f427,f426,f430,f429,f645,f431,f432,f433,f434,f435,f438,f644,f436,f643,f440,f439,f443,f442,f448,f618,f446,f445,f449,f451,f450,f456,f620,f454,f453,f457,f460,f459,f458,f461,f462,f463,f464,f465,f466,f467,f468,f471,f470,f469,f472,f473,f474,f476,f475,f478,f477,f622,f480,f479,f482,f490,f489,f488,f487,f486,f485,f623,f491,f492,f501,f500,f499,f498,f497,f496,f495,f642,f502,f503,f513,f512,f511,f510,f509,f508,f507,f506,f626,f514,f515,f525,f524,f523,f522,f521,f520,f519,f518,f627,f526,f527,f537,f536,f535,f534,f533,f532,f531,f530,f628,f538,f540,f539,f548,f547,f546,f545,f544,f543,f542,f629,f549,f551,f550,f559,f558,f557,f556,f555,f554,f553,f630,f560,f631]) ).
fof(f631,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f562]) ).
fof(f562,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f560,plain,
! [X0] :
( sP18(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f252]) ).
fof(f252,plain,
! [X0] :
( sP18(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f175,f251,f250]) ).
fof(f250,plain,
! [X0] :
( sP17(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
fof(f251,plain,
! [X0] :
( ( strictorderedP(X0)
<=> sP17(X0) )
| ~ sP18(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f175,plain,
! [X0] :
( ( strictorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f174]) ).
fof(f174,plain,
! [X0] :
( ( strictorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( ssList(X0)
=> ( strictorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> lt(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax12) ).
fof(f630,plain,
! [X10,X8,X6,X9,X7] :
( ~ sP17(app(app(X8,cons(X6,X9)),cons(X7,X10)))
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| lt(X6,X7) ),
inference(equality_resolution,[],[f552]) ).
fof(f552,plain,
! [X10,X0,X8,X6,X9,X7] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP17(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f354,plain,
! [X0] :
( ( sP17(X0)
| ( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),sK62(X0))),cons(sK60(X0),sK63(X0))) = X0
& ssList(sK63(X0))
& ssList(sK62(X0))
& ssList(sK61(X0))
& ssItem(sK60(X0))
& ssItem(sK59(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP17(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK59,sK60,sK61,sK62,sK63])],[f348,f353,f352,f351,f350,f349]) ).
fof(f349,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),X2)
& app(app(X3,cons(sK59(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK59(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f350,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),X2)
& app(app(X3,cons(sK59(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(X3,cons(sK59(X0),X4)),cons(sK60(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK60(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f351,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(X3,cons(sK59(X0),X4)),cons(sK60(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),X4)),cons(sK60(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK61(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f352,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),X4)),cons(sK60(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),sK62(X0))),cons(sK60(X0),X5)) = X0
& ssList(X5) )
& ssList(sK62(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f353,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),sK62(X0))),cons(sK60(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK59(X0),sK60(X0))
& app(app(sK61(X0),cons(sK59(X0),sK62(X0))),cons(sK60(X0),sK63(X0))) = X0
& ssList(sK63(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
! [X0] :
( ( sP17(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP17(X0) ) ),
inference(rectify,[],[f347]) ).
fof(f347,plain,
! [X0] :
( ( sP17(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP17(X0) ) ),
inference(nnf_transformation,[],[f250]) ).
fof(f553,plain,
! [X0] :
( ssItem(sK59(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f554,plain,
! [X0] :
( ssItem(sK60(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f555,plain,
! [X0] :
( ssList(sK61(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f556,plain,
! [X0] :
( ssList(sK62(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f557,plain,
! [X0] :
( ssList(sK63(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f558,plain,
! [X0] :
( sP17(X0)
| app(app(sK61(X0),cons(sK59(X0),sK62(X0))),cons(sK60(X0),sK63(X0))) = X0 ),
inference(cnf_transformation,[],[f354]) ).
fof(f559,plain,
! [X0] :
( ~ lt(sK59(X0),sK60(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f550,plain,
! [X0] :
( ~ sP18(X0)
| ~ strictorderedP(X0)
| sP17(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f346,plain,
! [X0] :
( ( ( strictorderedP(X0)
| ~ sP17(X0) )
& ( sP17(X0)
| ~ strictorderedP(X0) ) )
| ~ sP18(X0) ),
inference(nnf_transformation,[],[f251]) ).
fof(f551,plain,
! [X0] :
( ~ sP18(X0)
| ~ sP17(X0)
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f549,plain,
! [X0] :
( sP16(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f249]) ).
fof(f249,plain,
! [X0] :
( sP16(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f173,f248,f247]) ).
fof(f247,plain,
! [X0] :
( sP15(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
fof(f248,plain,
! [X0] :
( ( totalorderedP(X0)
<=> sP15(X0) )
| ~ sP16(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f173,plain,
! [X0] :
( ( totalorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f172]) ).
fof(f172,plain,
! [X0] :
( ( totalorderedP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( ssList(X0)
=> ( totalorderedP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> leq(X1,X2) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax11) ).
fof(f629,plain,
! [X10,X8,X6,X9,X7] :
( ~ sP15(app(app(X8,cons(X6,X9)),cons(X7,X10)))
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| leq(X6,X7) ),
inference(equality_resolution,[],[f541]) ).
fof(f541,plain,
! [X10,X0,X8,X6,X9,X7] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f345,plain,
! [X0] :
( ( sP15(X0)
| ( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),sK58(X0))) = X0
& ssList(sK58(X0))
& ssList(sK57(X0))
& ssList(sK56(X0))
& ssItem(sK55(X0))
& ssItem(sK54(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP15(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK54,sK55,sK56,sK57,sK58])],[f339,f344,f343,f342,f341,f340]) ).
fof(f340,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),X2)
& app(app(X3,cons(sK54(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK54(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f341,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),X2)
& app(app(X3,cons(sK54(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(X3,cons(sK54(X0),X4)),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK55(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f342,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(X3,cons(sK54(X0),X4)),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),X4)),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK56(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f343,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),X4)),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),X5)) = X0
& ssList(X5) )
& ssList(sK57(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK54(X0),sK55(X0))
& app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),sK58(X0))) = X0
& ssList(sK58(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f339,plain,
! [X0] :
( ( sP15(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP15(X0) ) ),
inference(rectify,[],[f338]) ).
fof(f338,plain,
! [X0] :
( ( sP15(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP15(X0) ) ),
inference(nnf_transformation,[],[f247]) ).
fof(f542,plain,
! [X0] :
( ssItem(sK54(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f543,plain,
! [X0] :
( ssItem(sK55(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f544,plain,
! [X0] :
( ssList(sK56(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f545,plain,
! [X0] :
( ssList(sK57(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f546,plain,
! [X0] :
( ssList(sK58(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f547,plain,
! [X0] :
( sP15(X0)
| app(app(sK56(X0),cons(sK54(X0),sK57(X0))),cons(sK55(X0),sK58(X0))) = X0 ),
inference(cnf_transformation,[],[f345]) ).
fof(f548,plain,
! [X0] :
( ~ leq(sK54(X0),sK55(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f539,plain,
! [X0] :
( ~ sP16(X0)
| ~ totalorderedP(X0)
| sP15(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f337,plain,
! [X0] :
( ( ( totalorderedP(X0)
| ~ sP15(X0) )
& ( sP15(X0)
| ~ totalorderedP(X0) ) )
| ~ sP16(X0) ),
inference(nnf_transformation,[],[f248]) ).
fof(f540,plain,
! [X0] :
( ~ sP16(X0)
| ~ sP15(X0)
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f538,plain,
! [X0] :
( sP14(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f246]) ).
fof(f246,plain,
! [X0] :
( sP14(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f171,f245,f244]) ).
fof(f244,plain,
! [X0] :
( sP13(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
fof(f245,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> sP13(X0) )
| ~ sP14(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f171,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f170]) ).
fof(f170,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( ssList(X0)
=> ( cyclefreeP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ~ ( leq(X2,X1)
& leq(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax8) ).
fof(f628,plain,
! [X10,X8,X6,X9,X7] :
( ~ sP13(app(app(X8,cons(X6,X9)),cons(X7,X10)))
| ~ leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ leq(X7,X6) ),
inference(equality_resolution,[],[f529]) ).
fof(f529,plain,
! [X10,X0,X8,X6,X9,X7] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f336,plain,
! [X0] :
( ( sP13(X0)
| ( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),sK53(X0))) = X0
& ssList(sK53(X0))
& ssList(sK52(X0))
& ssList(sK51(X0))
& ssItem(sK50(X0))
& ssItem(sK49(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP13(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK49,sK50,sK51,sK52,sK53])],[f330,f335,f334,f333,f332,f331]) ).
fof(f331,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK49(X0))
& leq(sK49(X0),X2)
& app(app(X3,cons(sK49(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK49(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f332,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK49(X0))
& leq(sK49(X0),X2)
& app(app(X3,cons(sK49(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(X3,cons(sK49(X0),X4)),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f333,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(X3,cons(sK49(X0),X4)),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),X4)),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK51(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f334,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),X4)),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),X5)) = X0
& ssList(X5) )
& ssList(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f335,plain,
! [X0] :
( ? [X5] :
( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),X5)) = X0
& ssList(X5) )
=> ( leq(sK50(X0),sK49(X0))
& leq(sK49(X0),sK50(X0))
& app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),sK53(X0))) = X0
& ssList(sK53(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f330,plain,
! [X0] :
( ( sP13(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( ~ leq(X7,X6)
| ~ leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP13(X0) ) ),
inference(rectify,[],[f329]) ).
fof(f329,plain,
! [X0] :
( ( sP13(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,X1)
& leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP13(X0) ) ),
inference(nnf_transformation,[],[f244]) ).
fof(f530,plain,
! [X0] :
( ssItem(sK49(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f531,plain,
! [X0] :
( ssItem(sK50(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f532,plain,
! [X0] :
( ssList(sK51(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f533,plain,
! [X0] :
( ssList(sK52(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f534,plain,
! [X0] :
( ssList(sK53(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f535,plain,
! [X0] :
( sP13(X0)
| app(app(sK51(X0),cons(sK49(X0),sK52(X0))),cons(sK50(X0),sK53(X0))) = X0 ),
inference(cnf_transformation,[],[f336]) ).
fof(f536,plain,
! [X0] :
( leq(sK49(X0),sK50(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f537,plain,
! [X0] :
( leq(sK50(X0),sK49(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f527,plain,
! [X0] :
( ~ sP14(X0)
| ~ cyclefreeP(X0)
| sP13(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f328,plain,
! [X0] :
( ( ( cyclefreeP(X0)
| ~ sP13(X0) )
& ( sP13(X0)
| ~ cyclefreeP(X0) ) )
| ~ sP14(X0) ),
inference(nnf_transformation,[],[f245]) ).
fof(f526,plain,
! [X0] :
( sP12(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f243]) ).
fof(f243,plain,
! [X0] :
( sP12(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f169,f242,f241]) ).
fof(f241,plain,
! [X0] :
( sP11(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
fof(f242,plain,
! [X0] :
( ( strictorderP(X0)
<=> sP11(X0) )
| ~ sP12(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f169,plain,
! [X0] :
( ( strictorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f168]) ).
fof(f168,plain,
! [X0] :
( ( strictorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0] :
( ssList(X0)
=> ( strictorderP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ( lt(X2,X1)
| lt(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax10) ).
fof(f627,plain,
! [X10,X8,X6,X9,X7] :
( ~ sP11(app(app(X8,cons(X6,X9)),cons(X7,X10)))
| lt(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| lt(X7,X6) ),
inference(equality_resolution,[],[f517]) ).
fof(f517,plain,
! [X10,X0,X8,X6,X9,X7] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f327,plain,
! [X0] :
( ( sP11(X0)
| ( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),sK48(X0))) = X0
& ssList(sK48(X0))
& ssList(sK47(X0))
& ssList(sK46(X0))
& ssItem(sK45(X0))
& ssItem(sK44(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP11(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK44,sK45,sK46,sK47,sK48])],[f321,f326,f325,f324,f323,f322]) ).
fof(f322,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK44(X0))
& ~ lt(sK44(X0),X2)
& app(app(X3,cons(sK44(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK44(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f323,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK44(X0))
& ~ lt(sK44(X0),X2)
& app(app(X3,cons(sK44(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(X3,cons(sK44(X0),X4)),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK45(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f324,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(X3,cons(sK44(X0),X4)),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),X4)),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK46(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f325,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),X4)),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),X5)) = X0
& ssList(X5) )
& ssList(sK47(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f326,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK45(X0),sK44(X0))
& ~ lt(sK44(X0),sK45(X0))
& app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),sK48(X0))) = X0
& ssList(sK48(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f321,plain,
! [X0] :
( ( sP11(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( lt(X7,X6)
| lt(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP11(X0) ) ),
inference(rectify,[],[f320]) ).
fof(f320,plain,
! [X0] :
( ( sP11(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,X1)
& ~ lt(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP11(X0) ) ),
inference(nnf_transformation,[],[f241]) ).
fof(f518,plain,
! [X0] :
( ssItem(sK44(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f519,plain,
! [X0] :
( ssItem(sK45(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f520,plain,
! [X0] :
( ssList(sK46(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f521,plain,
! [X0] :
( ssList(sK47(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f522,plain,
! [X0] :
( ssList(sK48(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f523,plain,
! [X0] :
( sP11(X0)
| app(app(sK46(X0),cons(sK44(X0),sK47(X0))),cons(sK45(X0),sK48(X0))) = X0 ),
inference(cnf_transformation,[],[f327]) ).
fof(f524,plain,
! [X0] :
( ~ lt(sK44(X0),sK45(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f525,plain,
! [X0] :
( ~ lt(sK45(X0),sK44(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f515,plain,
! [X0] :
( ~ sP12(X0)
| ~ strictorderP(X0)
| sP11(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f319,plain,
! [X0] :
( ( ( strictorderP(X0)
| ~ sP11(X0) )
& ( sP11(X0)
| ~ strictorderP(X0) ) )
| ~ sP12(X0) ),
inference(nnf_transformation,[],[f242]) ).
fof(f514,plain,
! [X0] :
( sP10(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0] :
( sP10(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f167,f239,f238]) ).
fof(f238,plain,
! [X0] :
( sP9(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
fof(f239,plain,
! [X0] :
( ( totalorderP(X0)
<=> sP9(X0) )
| ~ sP10(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f167,plain,
! [X0] :
( ( totalorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f166]) ).
fof(f166,plain,
! [X0] :
( ( totalorderP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0] :
( ssList(X0)
=> ( totalorderP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> ( leq(X2,X1)
| leq(X1,X2) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax9) ).
fof(f626,plain,
! [X10,X8,X6,X9,X7] :
( ~ sP9(app(app(X8,cons(X6,X9)),cons(X7,X10)))
| leq(X6,X7)
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| leq(X7,X6) ),
inference(equality_resolution,[],[f505]) ).
fof(f505,plain,
! [X10,X0,X8,X6,X9,X7] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f318,plain,
! [X0] :
( ( sP9(X0)
| ( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),sK43(X0))) = X0
& ssList(sK43(X0))
& ssList(sK42(X0))
& ssList(sK41(X0))
& ssItem(sK40(X0))
& ssItem(sK39(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP9(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK39,sK40,sK41,sK42,sK43])],[f312,f317,f316,f315,f314,f313]) ).
fof(f313,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK39(X0))
& ~ leq(sK39(X0),X2)
& app(app(X3,cons(sK39(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK39(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f314,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK39(X0))
& ~ leq(sK39(X0),X2)
& app(app(X3,cons(sK39(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(X3,cons(sK39(X0),X4)),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK40(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f315,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(X3,cons(sK39(X0),X4)),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),X4)),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK41(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f316,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),X4)),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),X5)) = X0
& ssList(X5) )
& ssList(sK42(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f317,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK40(X0),sK39(X0))
& ~ leq(sK39(X0),sK40(X0))
& app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),sK43(X0))) = X0
& ssList(sK43(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f312,plain,
! [X0] :
( ( sP9(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( leq(X7,X6)
| leq(X6,X7)
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP9(X0) ) ),
inference(rectify,[],[f311]) ).
fof(f311,plain,
! [X0] :
( ( sP9(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,X1)
& ~ leq(X1,X2)
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP9(X0) ) ),
inference(nnf_transformation,[],[f238]) ).
fof(f506,plain,
! [X0] :
( ssItem(sK39(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f507,plain,
! [X0] :
( ssItem(sK40(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f508,plain,
! [X0] :
( ssList(sK41(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f509,plain,
! [X0] :
( ssList(sK42(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f510,plain,
! [X0] :
( ssList(sK43(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f511,plain,
! [X0] :
( sP9(X0)
| app(app(sK41(X0),cons(sK39(X0),sK42(X0))),cons(sK40(X0),sK43(X0))) = X0 ),
inference(cnf_transformation,[],[f318]) ).
fof(f512,plain,
! [X0] :
( ~ leq(sK39(X0),sK40(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f513,plain,
! [X0] :
( ~ leq(sK40(X0),sK39(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f503,plain,
! [X0] :
( ~ sP10(X0)
| ~ totalorderP(X0)
| sP9(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f310,plain,
! [X0] :
( ( ( totalorderP(X0)
| ~ sP9(X0) )
& ( sP9(X0)
| ~ totalorderP(X0) ) )
| ~ sP10(X0) ),
inference(nnf_transformation,[],[f239]) ).
fof(f502,plain,
! [X0] :
( sP8(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f237]) ).
fof(f237,plain,
! [X0] :
( sP8(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f165,f236,f235]) ).
fof(f235,plain,
! [X0] :
( sP7(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
fof(f236,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> sP7(X0) )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f165,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f164]) ).
fof(f164,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0] :
( ssList(X0)
=> ( duplicatefreeP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
=> X1 != X2 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax13) ).
fof(f642,plain,
! [X10,X8,X9,X7] :
( ~ sP7(app(app(X8,cons(X7,X9)),cons(X7,X10)))
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssList(X10) ),
inference(duplicate_literal_removal,[],[f625]) ).
fof(f625,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP7(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f624]) ).
fof(f624,plain,
! [X10,X0,X8,X9,X7] :
( app(app(X8,cons(X7,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP7(X0) ),
inference(equality_resolution,[],[f494]) ).
fof(f494,plain,
! [X10,X0,X8,X6,X9,X7] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f309,plain,
! [X0] :
( ( sP7(X0)
| ( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),sK38(X0))) = X0
& ssList(sK38(X0))
& ssList(sK37(X0))
& ssList(sK36(X0))
& ssItem(sK35(X0))
& ssItem(sK34(X0)) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP7(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK34,sK35,sK36,sK37,sK38])],[f303,f308,f307,f306,f305,f304]) ).
fof(f304,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK34(X0) = X2
& app(app(X3,cons(sK34(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK34(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f305,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK34(X0) = X2
& app(app(X3,cons(sK34(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(X3,cons(sK34(X0),X4)),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK35(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f306,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(X3,cons(sK34(X0),X4)),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),X4)),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK36(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f307,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),X4)),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),X5)) = X0
& ssList(X5) )
& ssList(sK37(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f308,plain,
! [X0] :
( ? [X5] :
( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),X5)) = X0
& ssList(X5) )
=> ( sK34(X0) = sK35(X0)
& app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),sK38(X0))) = X0
& ssList(sK38(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f303,plain,
! [X0] :
( ( sP7(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X6] :
( ! [X7] :
( ! [X8] :
( ! [X9] :
( ! [X10] :
( X6 != X7
| app(app(X8,cons(X6,X9)),cons(X7,X10)) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssList(X8) )
| ~ ssItem(X7) )
| ~ ssItem(X6) )
| ~ sP7(X0) ) ),
inference(rectify,[],[f302]) ).
fof(f302,plain,
! [X0] :
( ( sP7(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( X1 = X2
& app(app(X3,cons(X1,X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( ! [X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP7(X0) ) ),
inference(nnf_transformation,[],[f235]) ).
fof(f495,plain,
! [X0] :
( ssItem(sK34(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f496,plain,
! [X0] :
( ssItem(sK35(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f497,plain,
! [X0] :
( ssList(sK36(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f498,plain,
! [X0] :
( ssList(sK37(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f499,plain,
! [X0] :
( ssList(sK38(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f500,plain,
! [X0] :
( sP7(X0)
| app(app(sK36(X0),cons(sK34(X0),sK37(X0))),cons(sK35(X0),sK38(X0))) = X0 ),
inference(cnf_transformation,[],[f309]) ).
fof(f501,plain,
! [X0] :
( sP7(X0)
| sK34(X0) = sK35(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f492,plain,
! [X0] :
( ~ sP8(X0)
| ~ duplicatefreeP(X0)
| sP7(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f301,plain,
! [X0] :
( ( ( duplicatefreeP(X0)
| ~ sP7(X0) )
& ( sP7(X0)
| ~ duplicatefreeP(X0) ) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f236]) ).
fof(f491,plain,
! [X0] :
( sP6(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f234]) ).
fof(f234,plain,
! [X0] :
( sP6(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f163,f233,f232]) ).
fof(f232,plain,
! [X0] :
( sP5(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f233,plain,
! [X0] :
( ( equalelemsP(X0)
<=> sP5(X0) )
| ~ sP6(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f163,plain,
! [X0] :
( ( equalelemsP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(flattening,[],[f162]) ).
fof(f162,plain,
! [X0] :
( ( equalelemsP(X0)
<=> ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0] :
( ssList(X0)
=> ( equalelemsP(X0)
<=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ! [X3] :
( ssList(X3)
=> ! [X4] :
( ssList(X4)
=> ( app(X3,cons(X1,cons(X2,X4))) = X0
=> X1 = X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax14) ).
fof(f623,plain,
! [X8,X6,X7,X5] :
( ~ sP5(app(X7,cons(X5,cons(X6,X8))))
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| X5 = X6 ),
inference(equality_resolution,[],[f484]) ).
fof(f484,plain,
! [X0,X8,X6,X7,X5] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f300,plain,
! [X0] :
( ( sP5(X0)
| ( sK30(X0) != sK31(X0)
& app(sK32(X0),cons(sK30(X0),cons(sK31(X0),sK33(X0)))) = X0
& ssList(sK33(X0))
& ssList(sK32(X0))
& ssItem(sK31(X0))
& ssItem(sK30(X0)) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP5(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31,sK32,sK33])],[f295,f299,f298,f297,f296]) ).
fof(f296,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) )
=> ( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK30(X0) != X2
& app(X3,cons(sK30(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK30(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f297,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK30(X0) != X2
& app(X3,cons(sK30(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( sK30(X0) != sK31(X0)
& app(X3,cons(sK30(X0),cons(sK31(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(sK31(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f298,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( sK30(X0) != sK31(X0)
& app(X3,cons(sK30(X0),cons(sK31(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( sK30(X0) != sK31(X0)
& app(sK32(X0),cons(sK30(X0),cons(sK31(X0),X4))) = X0
& ssList(X4) )
& ssList(sK32(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f299,plain,
! [X0] :
( ? [X4] :
( sK30(X0) != sK31(X0)
& app(sK32(X0),cons(sK30(X0),cons(sK31(X0),X4))) = X0
& ssList(X4) )
=> ( sK30(X0) != sK31(X0)
& app(sK32(X0),cons(sK30(X0),cons(sK31(X0),sK33(X0)))) = X0
& ssList(sK33(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f295,plain,
! [X0] :
( ( sP5(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP5(X0) ) ),
inference(rectify,[],[f294]) ).
fof(f294,plain,
! [X0] :
( ( sP5(X0)
| ? [X1] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( X1 != X2
& app(X3,cons(X1,cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(X1) ) )
& ( ! [X1] :
( ! [X2] :
( ! [X3] :
( ! [X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4) )
| ~ ssList(X3) )
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ sP5(X0) ) ),
inference(nnf_transformation,[],[f232]) ).
fof(f485,plain,
! [X0] :
( ssItem(sK30(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f486,plain,
! [X0] :
( ssItem(sK31(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f487,plain,
! [X0] :
( ssList(sK32(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f488,plain,
! [X0] :
( ssList(sK33(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f489,plain,
! [X0] :
( sP5(X0)
| app(sK32(X0),cons(sK30(X0),cons(sK31(X0),sK33(X0)))) = X0 ),
inference(cnf_transformation,[],[f300]) ).
fof(f490,plain,
! [X0] :
( sK30(X0) != sK31(X0)
| sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f482,plain,
! [X0] :
( ~ sP6(X0)
| ~ equalelemsP(X0)
| sP5(X0) ),
inference(cnf_transformation,[],[f293]) ).
fof(f293,plain,
! [X0] :
( ( ( equalelemsP(X0)
| ~ sP5(X0) )
& ( sP5(X0)
| ~ equalelemsP(X0) ) )
| ~ sP6(X0) ),
inference(nnf_transformation,[],[f233]) ).
fof(f479,plain,
! [X0] :
( ssItem(sK29(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f292,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK29(X0),nil) = X0
& ssItem(sK29(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f290,f291]) ).
fof(f291,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK29(X0),nil) = X0
& ssItem(sK29(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f290,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f289]) ).
fof(f289,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f161]) ).
fof(f161,plain,
! [X0] :
( ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0] :
( ssList(X0)
=> ( singletonP(X0)
<=> ? [X1] :
( cons(X1,nil) = X0
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax4) ).
fof(f480,plain,
! [X0] :
( ~ singletonP(X0)
| cons(sK29(X0),nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f622,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f481]) ).
fof(f481,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f477,plain,
! [X0] :
( ssList(sK28(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f288,plain,
! [X0] :
( ( tl(X0) = sK28(X0)
& ssList(sK28(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f160,f287]) ).
fof(f287,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK28(X0)
& ssList(sK28(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f160,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f159]) ).
fof(f159,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f76]) ).
fof(f76,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( tl(X0) = X1
& ssList(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax76) ).
fof(f478,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK28(X0) ),
inference(cnf_transformation,[],[f288]) ).
fof(f475,plain,
! [X0] :
( ssItem(sK27(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f286]) ).
fof(f286,plain,
! [X0] :
( ( hd(X0) = sK27(X0)
& ssItem(sK27(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f158,f285]) ).
fof(f285,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK27(X0)
& ssItem(sK27(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f158,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f157]) ).
fof(f157,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f75]) ).
fof(f75,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ? [X1] :
( hd(X0) = X1
& ssItem(X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax75) ).
fof(f476,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK27(X0) ),
inference(cnf_transformation,[],[f286]) ).
fof(f474,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f156]) ).
fof(f156,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f155]) ).
fof(f155,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f78]) ).
fof(f78,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> cons(hd(X0),tl(X0)) = X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax78) ).
fof(f473,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f154]) ).
fof(f154,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f24]) ).
fof(f24,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssList(tl(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax24) ).
fof(f472,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f152]) ).
fof(f152,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f22]) ).
fof(f22,axiom,
! [X0] :
( ssList(X0)
=> ( nil != X0
=> ssItem(hd(X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax22) ).
fof(f469,plain,
! [X0] :
( ssList(sK25(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f284]) ).
fof(f470,plain,
! [X0] :
( ssItem(sK26(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f284]) ).
fof(f467,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f84]) ).
fof(f84,axiom,
! [X0] :
( ssList(X0)
=> app(X0,nil) = X0 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax84) ).
fof(f465,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax55) ).
fof(f463,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f42]) ).
fof(f42,axiom,
! [X0] :
( ssList(X0)
=> frontsegP(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax42) ).
fof(f462,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f51]) ).
fof(f51,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax51) ).
fof(f461,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f57]) ).
fof(f57,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax57) ).
fof(f458,plain,
! [X2,X0,X1] :
( ~ memberP(app(X1,X2),X0)
| memberP(X1,X0)
| memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f281,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f280]) ).
fof(f280,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f140]) ).
fof(f140,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f36]) ).
fof(f36,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(app(X1,X2),X0)
<=> ( memberP(X2,X0)
| memberP(X1,X0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax36) ).
fof(f459,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f460,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f457,plain,
! [X0,X1] :
( sP4(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0] :
( ! [X1] :
( sP4(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f139,f230,f229]) ).
fof(f229,plain,
! [X1,X0] :
( sP3(X1,X0)
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f230,plain,
! [X0,X1] :
( ( strictorderedP(cons(X0,X1))
<=> sP3(X1,X0) )
| ~ sP4(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f139,plain,
! [X0] :
( ! [X1] :
( ( strictorderedP(cons(X0,X1))
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f70]) ).
fof(f70,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( strictorderedP(cons(X0,X1))
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax70) ).
fof(f453,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| nil = X0
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f279]) ).
fof(f279,plain,
! [X0,X1] :
( ( sP3(X0,X1)
| ( ( ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( lt(X1,hd(X0))
& strictorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP3(X0,X1) ) ),
inference(rectify,[],[f278]) ).
fof(f278,plain,
! [X1,X0] :
( ( sP3(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP3(X1,X0) ) ),
inference(flattening,[],[f277]) ).
fof(f277,plain,
! [X1,X0] :
( ( sP3(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP3(X1,X0) ) ),
inference(nnf_transformation,[],[f229]) ).
fof(f454,plain,
! [X0,X1] :
( lt(X1,hd(X0))
| nil = X0
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f279]) ).
fof(f620,plain,
! [X1] : sP3(nil,X1),
inference(equality_resolution,[],[f455]) ).
fof(f455,plain,
! [X0,X1] :
( sP3(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f279]) ).
fof(f456,plain,
! [X0,X1] :
( ~ lt(X1,hd(X0))
| sP3(X0,X1)
| ~ strictorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f279]) ).
fof(f450,plain,
! [X0,X1] :
( ~ strictorderedP(cons(X0,X1))
| sP3(X1,X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f276]) ).
fof(f276,plain,
! [X0,X1] :
( ( ( strictorderedP(cons(X0,X1))
| ~ sP3(X1,X0) )
& ( sP3(X1,X0)
| ~ strictorderedP(cons(X0,X1)) ) )
| ~ sP4(X0,X1) ),
inference(nnf_transformation,[],[f230]) ).
fof(f451,plain,
! [X0,X1] :
( strictorderedP(cons(X0,X1))
| ~ sP3(X1,X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f276]) ).
fof(f449,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X0] :
( ! [X1] :
( sP2(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f138,f227,f226]) ).
fof(f226,plain,
! [X1,X0] :
( sP1(X1,X0)
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f227,plain,
! [X0,X1] :
( ( totalorderedP(cons(X0,X1))
<=> sP1(X1,X0) )
| ~ sP2(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f138,plain,
! [X0] :
( ! [X1] :
( ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f67]) ).
fof(f67,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssList(X1)
=> ( totalorderedP(cons(X0,X1))
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax67) ).
fof(f445,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| nil = X0
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f275,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( ( ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( leq(X1,hd(X0))
& totalorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f274]) ).
fof(f274,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP1(X1,X0) ) ),
inference(flattening,[],[f273]) ).
fof(f273,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP1(X1,X0) ) ),
inference(nnf_transformation,[],[f226]) ).
fof(f446,plain,
! [X0,X1] :
( leq(X1,hd(X0))
| nil = X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f275]) ).
fof(f618,plain,
! [X1] : sP1(nil,X1),
inference(equality_resolution,[],[f447]) ).
fof(f447,plain,
! [X0,X1] :
( sP1(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f275]) ).
fof(f448,plain,
! [X0,X1] :
( ~ leq(X1,hd(X0))
| sP1(X0,X1)
| ~ totalorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f275]) ).
fof(f442,plain,
! [X0,X1] :
( ~ totalorderedP(cons(X0,X1))
| sP1(X1,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f272]) ).
fof(f272,plain,
! [X0,X1] :
( ( ( totalorderedP(cons(X0,X1))
| ~ sP1(X1,X0) )
& ( sP1(X1,X0)
| ~ totalorderedP(cons(X0,X1)) ) )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f227]) ).
fof(f443,plain,
! [X0,X1] :
( totalorderedP(cons(X0,X1))
| ~ sP1(X1,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f272]) ).
fof(f440,plain,
! [X2,X3,X0,X1] :
( ~ frontsegP(cons(X0,X2),cons(X1,X3))
| frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f436,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X1,X2),X0)
| X0 = X1
| memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f269]) ).
fof(f269,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f268]) ).
fof(f268,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f136]) ).
fof(f136,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f37]) ).
fof(f37,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssList(X2)
=> ( memberP(cons(X1,X2),X0)
<=> ( memberP(X2,X0)
| X0 = X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax37) ).
fof(f644,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f616]) ).
fof(f616,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f437]) ).
fof(f437,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f269]) ).
fof(f438,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f269]) ).
fof(f435,plain,
! [X2,X0,X1] :
( ~ lt(X1,X2)
| lt(X0,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f135]) ).
fof(f135,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f134]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f34]) ).
fof(f34,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( lt(X1,X2)
& lt(X0,X1) )
=> lt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax34) ).
fof(f434,plain,
! [X2,X0,X1] :
( ~ lt(X1,X2)
| lt(X0,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f133]) ).
fof(f133,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f91]) ).
fof(f91,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( lt(X1,X2)
& leq(X0,X1) )
=> lt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax91) ).
fof(f433,plain,
! [X2,X0,X1] :
( ~ leq(X1,X2)
| leq(X0,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f131]) ).
fof(f131,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f130]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f30]) ).
fof(f30,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( leq(X1,X2)
& leq(X0,X1) )
=> leq(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax30) ).
fof(f432,plain,
! [X2,X0,X1] :
( ~ geq(X1,X2)
| geq(X0,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f129]) ).
fof(f129,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f128]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f88]) ).
fof(f88,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( geq(X1,X2)
& geq(X0,X1) )
=> geq(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax88) ).
fof(f431,plain,
! [X2,X0,X1] :
( ~ gt(X1,X2)
| gt(X0,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f127]) ).
fof(f127,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f126]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f95]) ).
fof(f95,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ! [X2] :
( ssItem(X2)
=> ( ( gt(X1,X2)
& gt(X0,X1) )
=> gt(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax95) ).
fof(f645,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f615]) ).
fof(f615,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f428]) ).
fof(f428,plain,
! [X0,X1] :
( X0 != X1
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f267]) ).
fof(f430,plain,
! [X0,X1] :
( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f267]) ).
fof(f426,plain,
! [X0,X1] :
( ~ geq(X0,X1)
| leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f265]) ).
fof(f265,plain,
! [X0] :
( ! [X1] :
( ( ( geq(X0,X1)
| ~ leq(X1,X0) )
& ( leq(X1,X0)
| ~ geq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f124]) ).
fof(f124,plain,
! [X0] :
( ! [X1] :
( ( geq(X0,X1)
<=> leq(X1,X0) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f32]) ).
fof(f32,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( geq(X0,X1)
<=> leq(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax32) ).
fof(f427,plain,
! [X0,X1] :
( geq(X0,X1)
| ~ leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f265]) ).
fof(f424,plain,
! [X0,X1] :
( ~ gt(X0,X1)
| lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f264,plain,
! [X0] :
( ! [X1] :
( ( ( gt(X0,X1)
| ~ lt(X1,X0) )
& ( lt(X1,X0)
| ~ gt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f123]) ).
fof(f123,plain,
! [X0] :
( ! [X1] :
( ( gt(X0,X1)
<=> lt(X1,X0) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f35]) ).
fof(f35,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( gt(X0,X1)
<=> lt(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax35) ).
fof(f425,plain,
! [X0,X1] :
( gt(X0,X1)
| ~ lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f421,plain,
! [X0,X1] :
( ~ leq(X1,X0)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f121]) ).
fof(f121,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f120]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f29]) ).
fof(f29,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( ( leq(X1,X0)
& leq(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax29) ).
fof(f420,plain,
! [X0,X1] :
( ~ geq(X1,X0)
| X0 = X1
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f119]) ).
fof(f119,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f118]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f87]) ).
fof(f87,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( ( geq(X1,X0)
& geq(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax87) ).
fof(f419,plain,
! [X0,X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f117]) ).
fof(f117,plain,
! [X0] :
( ! [X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f116]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f33]) ).
fof(f33,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( lt(X0,X1)
=> ~ lt(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax33) ).
fof(f418,plain,
! [X0,X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f115]) ).
fof(f115,plain,
! [X0] :
( ! [X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f114]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f92]) ).
fof(f92,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( leq(X0,X1)
=> ( lt(X0,X1)
| X0 = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax92) ).
fof(f417,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f113]) ).
fof(f113,plain,
! [X0] :
( ! [X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f94]) ).
fof(f94,axiom,
! [X0] :
( ssItem(X0)
=> ! [X1] :
( ssItem(X1)
=> ( gt(X0,X1)
=> ~ gt(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax94) ).
fof(f416,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f111]) ).
fof(f111,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f65]) ).
fof(f65,axiom,
! [X0] :
( ssItem(X0)
=> totalorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax65) ).
fof(f415,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f68]) ).
fof(f68,axiom,
! [X0] :
( ssItem(X0)
=> strictorderedP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax68) ).
fof(f414,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f63]) ).
fof(f63,axiom,
! [X0] :
( ssItem(X0)
=> strictorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax63) ).
fof(f413,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f61]) ).
fof(f61,axiom,
! [X0] :
( ssItem(X0)
=> totalorderP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax61) ).
fof(f412,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f59]) ).
fof(f59,axiom,
! [X0] :
( ssItem(X0)
=> cyclefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax59) ).
fof(f411,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f71]) ).
fof(f71,axiom,
! [X0] :
( ssItem(X0)
=> duplicatefreeP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax71) ).
fof(f410,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f73]) ).
fof(f73,axiom,
! [X0] :
( ssItem(X0)
=> equalelemsP(cons(X0,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax73) ).
fof(f409,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f31]) ).
fof(f31,axiom,
! [X0] :
( ssItem(X0)
=> leq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax31) ).
fof(f408,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f89]) ).
fof(f89,axiom,
! [X0] :
( ssItem(X0)
=> geq(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax89) ).
fof(f407,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f90]) ).
fof(f90,axiom,
! [X0] :
( ssItem(X0)
=> ~ lt(X0,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax90) ).
fof(f406,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(ennf_transformation,[],[f38]) ).
fof(f38,axiom,
! [X0] :
( ssItem(X0)
=> ~ memberP(nil,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax38) ).
fof(f404,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
fof(f403,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).
fof(f402,plain,
totalorderP(nil),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
fof(f401,plain,
strictorderP(nil),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).
fof(f400,plain,
cyclefreeP(nil),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
fof(f399,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
fof(f398,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).
fof(f397,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
fof(f388,plain,
ssList(sK21),
inference(cnf_transformation,[],[f262]) ).
fof(f389,plain,
ssList(sK22),
inference(cnf_transformation,[],[f262]) ).
fof(f390,plain,
ssList(sK23),
inference(cnf_transformation,[],[f262]) ).
fof(f391,plain,
sK21 = sK23,
inference(cnf_transformation,[],[f262]) ).
fof(f383,plain,
! [X2,X0,X1] :
( memberP(X2,sK19(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f256]) ).
fof(f384,plain,
! [X2,X0,X1] :
( memberP(X1,sK19(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f256]) ).
fof(f10223,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_89
| spl72_98 ),
inference(resolution,[],[f10220,f9361]) ).
fof(f9361,plain,
( ! [X0] :
( frontsegP(app(sK20,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f9360,f405]) ).
fof(f9360,plain,
( ! [X0] :
( frontsegP(app(sK20,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f9350,f8873]) ).
fof(f9350,plain,
( ! [X0] :
( frontsegP(app(sK20,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(app(sK20,sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_89 ),
inference(superposition,[],[f604,f8890]) ).
fof(f8890,plain,
( app(sK20,sK20) = app(nil,app(sK20,sK20))
| ~ spl72_89 ),
inference(resolution,[],[f8873,f468]) ).
fof(f10222,plain,
( ~ spl72_97
| spl72_98
| ~ spl72_89 ),
inference(avatar_split_clause,[],[f9962,f8872,f10219,f10215]) ).
fof(f9962,plain,
( frontsegP(app(sK20,sK20),nil)
| ~ ssList(sK69(app(sK20,sK20),nil))
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f9949,f405]) ).
fof(f9949,plain,
( frontsegP(app(sK20,sK20),nil)
| ~ ssList(sK69(app(sK20,sK20),nil))
| ~ ssList(nil)
| ~ spl72_89 ),
inference(superposition,[],[f2500,f8913]) ).
fof(f8913,plain,
( app(sK20,sK20) = app(nil,sK69(app(sK20,sK20),nil))
| ~ spl72_89 ),
inference(resolution,[],[f8873,f3107]) ).
fof(f3107,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,sK69(X0,nil)) = X0 ),
inference(subsumption_resolution,[],[f3105,f405]) ).
fof(f3105,plain,
! [X0] :
( app(nil,sK69(X0,nil)) = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(duplicate_literal_removal,[],[f3097]) ).
fof(f3097,plain,
! [X0] :
( app(nil,sK69(X0,nil)) = X0
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f594,f464]) ).
fof(f10151,plain,
( ~ spl72_89
| spl72_95
| ~ spl72_96 ),
inference(avatar_contradiction_clause,[],[f10150]) ).
fof(f10150,plain,
( $false
| ~ spl72_89
| spl72_95
| ~ spl72_96 ),
inference(subsumption_resolution,[],[f10149,f8873]) ).
fof(f10149,plain,
( ~ ssList(app(sK20,sK20))
| spl72_95
| ~ spl72_96 ),
inference(subsumption_resolution,[],[f10148,f405]) ).
fof(f10148,plain,
( ~ ssList(nil)
| ~ ssList(app(sK20,sK20))
| spl72_95
| ~ spl72_96 ),
inference(subsumption_resolution,[],[f10147,f10129]) ).
fof(f10129,plain,
( rearsegP(app(sK20,sK20),nil)
| ~ spl72_96 ),
inference(avatar_component_clause,[],[f10127]) ).
fof(f10127,plain,
( spl72_96
<=> rearsegP(app(sK20,sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_96])]) ).
fof(f10147,plain,
( ~ rearsegP(app(sK20,sK20),nil)
| ~ ssList(nil)
| ~ ssList(app(sK20,sK20))
| spl72_95 ),
inference(resolution,[],[f10125,f586]) ).
fof(f586,plain,
! [X0,X1] :
( ssList(sK66(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f367]) ).
fof(f10125,plain,
( ~ ssList(sK66(app(sK20,sK20),nil))
| spl72_95 ),
inference(avatar_component_clause,[],[f10123]) ).
fof(f10123,plain,
( spl72_95
<=> ssList(sK66(app(sK20,sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_95])]) ).
fof(f10143,plain,
( ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_96 ),
inference(avatar_contradiction_clause,[],[f10142]) ).
fof(f10142,plain,
( $false
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_96 ),
inference(subsumption_resolution,[],[f10141,f405]) ).
fof(f10141,plain,
( ~ ssList(nil)
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_96 ),
inference(subsumption_resolution,[],[f10140,f387]) ).
fof(f10140,plain,
( ~ ssList(sK20)
| ~ ssList(nil)
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_96 ),
inference(subsumption_resolution,[],[f10134,f5150]) ).
fof(f5150,plain,
( rearsegP(sK20,nil)
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56 ),
inference(forward_demodulation,[],[f5149,f4984]) ).
fof(f4984,plain,
( nil = sK69(sK20,sK20)
| ~ spl72_56 ),
inference(avatar_component_clause,[],[f4982]) ).
fof(f4982,plain,
( spl72_56
<=> nil = sK69(sK20,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_56])]) ).
fof(f5149,plain,
( rearsegP(sK20,sK69(sK20,sK20))
| ~ spl72_53
| ~ spl72_55 ),
inference(subsumption_resolution,[],[f4976,f4979]) ).
fof(f4979,plain,
( ssList(sK69(sK20,sK20))
| ~ spl72_55 ),
inference(avatar_component_clause,[],[f4978]) ).
fof(f4978,plain,
( spl72_55
<=> ssList(sK69(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_55])]) ).
fof(f4976,plain,
( rearsegP(sK20,sK69(sK20,sK20))
| ~ ssList(sK69(sK20,sK20))
| ~ spl72_53 ),
inference(subsumption_resolution,[],[f4967,f387]) ).
fof(f4967,plain,
( rearsegP(sK20,sK69(sK20,sK20))
| ~ ssList(sK20)
| ~ ssList(sK69(sK20,sK20))
| ~ spl72_53 ),
inference(superposition,[],[f2433,f4941]) ).
fof(f4941,plain,
( sK20 = app(sK20,sK69(sK20,sK20))
| ~ spl72_53 ),
inference(subsumption_resolution,[],[f4939,f387]) ).
fof(f4939,plain,
( sK20 = app(sK20,sK69(sK20,sK20))
| ~ ssList(sK20)
| ~ spl72_53 ),
inference(duplicate_literal_removal,[],[f4936]) ).
fof(f4936,plain,
( sK20 = app(sK20,sK69(sK20,sK20))
| ~ ssList(sK20)
| ~ ssList(sK20)
| ~ spl72_53 ),
inference(resolution,[],[f4925,f594]) ).
fof(f4925,plain,
( frontsegP(sK20,sK20)
| ~ spl72_53 ),
inference(avatar_component_clause,[],[f4923]) ).
fof(f4923,plain,
( spl72_53
<=> frontsegP(sK20,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_53])]) ).
fof(f2433,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f636,f577]) ).
fof(f636,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ),
inference(equality_resolution,[],[f588]) ).
fof(f588,plain,
! [X2,X0,X1] :
( rearsegP(X0,X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f367]) ).
fof(f10134,plain,
( ~ rearsegP(sK20,nil)
| ~ ssList(sK20)
| ~ ssList(nil)
| spl72_96 ),
inference(duplicate_literal_removal,[],[f10133]) ).
fof(f10133,plain,
( ~ rearsegP(sK20,nil)
| ~ ssList(sK20)
| ~ ssList(nil)
| ~ ssList(sK20)
| spl72_96 ),
inference(resolution,[],[f10128,f603]) ).
fof(f603,plain,
! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f209]) ).
fof(f209,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f208]) ).
fof(f208,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f50]) ).
fof(f50,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( rearsegP(X0,X1)
=> rearsegP(app(X2,X0),X1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax50) ).
fof(f10128,plain,
( ~ rearsegP(app(sK20,sK20),nil)
| spl72_96 ),
inference(avatar_component_clause,[],[f10127]) ).
fof(f10139,plain,
( ~ spl72_89
| spl72_96 ),
inference(avatar_contradiction_clause,[],[f10138]) ).
fof(f10138,plain,
( $false
| ~ spl72_89
| spl72_96 ),
inference(subsumption_resolution,[],[f10137,f405]) ).
fof(f10137,plain,
( ~ ssList(nil)
| ~ spl72_89
| spl72_96 ),
inference(subsumption_resolution,[],[f10132,f647]) ).
fof(f10132,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_89
| spl72_96 ),
inference(resolution,[],[f10128,f9311]) ).
fof(f9311,plain,
( ! [X0] :
( rearsegP(app(sK20,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f9310,f405]) ).
fof(f9310,plain,
( ! [X0] :
( rearsegP(app(sK20,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f9296,f8873]) ).
fof(f9296,plain,
( ! [X0] :
( rearsegP(app(sK20,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(app(sK20,sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_89 ),
inference(superposition,[],[f603,f8889]) ).
fof(f8889,plain,
( app(sK20,sK20) = app(app(sK20,sK20),nil)
| ~ spl72_89 ),
inference(resolution,[],[f8873,f467]) ).
fof(f10136,plain,
( ~ spl72_89
| spl72_96 ),
inference(avatar_contradiction_clause,[],[f10135]) ).
fof(f10135,plain,
( $false
| ~ spl72_89
| spl72_96 ),
inference(subsumption_resolution,[],[f10131,f8873]) ).
fof(f10131,plain,
( ~ ssList(app(sK20,sK20))
| spl72_96 ),
inference(resolution,[],[f10128,f462]) ).
fof(f10130,plain,
( ~ spl72_95
| spl72_96
| ~ spl72_89 ),
inference(avatar_split_clause,[],[f9884,f8872,f10127,f10123]) ).
fof(f9884,plain,
( rearsegP(app(sK20,sK20),nil)
| ~ ssList(sK66(app(sK20,sK20),nil))
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f9870,f405]) ).
fof(f9870,plain,
( rearsegP(app(sK20,sK20),nil)
| ~ ssList(sK66(app(sK20,sK20),nil))
| ~ ssList(nil)
| ~ spl72_89 ),
inference(superposition,[],[f2433,f8911]) ).
fof(f8911,plain,
( app(sK20,sK20) = app(sK66(app(sK20,sK20),nil),nil)
| ~ spl72_89 ),
inference(resolution,[],[f8873,f3024]) ).
fof(f3024,plain,
! [X0] :
( ~ ssList(X0)
| app(sK66(X0,nil),nil) = X0 ),
inference(subsumption_resolution,[],[f3018,f405]) ).
fof(f3018,plain,
! [X0] :
( app(sK66(X0,nil),nil) = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(duplicate_literal_removal,[],[f3014]) ).
fof(f3014,plain,
! [X0] :
( app(sK66(X0,nil),nil) = X0
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f587,f462]) ).
fof(f9799,plain,
( ~ spl72_93
| spl72_94
| ~ spl72_89 ),
inference(avatar_split_clause,[],[f9339,f8872,f9796,f9792]) ).
fof(f9792,plain,
( spl72_93
<=> segmentP(sK20,app(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_93])]) ).
fof(f9796,plain,
( spl72_94
<=> sK20 = app(sK20,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_94])]) ).
fof(f9339,plain,
( sK20 = app(sK20,sK20)
| ~ segmentP(sK20,app(sK20,sK20))
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f9338,f387]) ).
fof(f9338,plain,
( sK20 = app(sK20,sK20)
| ~ segmentP(sK20,app(sK20,sK20))
| ~ ssList(sK20)
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f9333,f8873]) ).
fof(f9333,plain,
( sK20 = app(sK20,sK20)
| ~ segmentP(sK20,app(sK20,sK20))
| ~ ssList(app(sK20,sK20))
| ~ ssList(sK20)
| ~ spl72_89 ),
inference(resolution,[],[f9328,f582]) ).
fof(f582,plain,
! [X0,X1] :
( ~ segmentP(X1,X0)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f196]) ).
fof(f196,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f195]) ).
fof(f195,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( segmentP(X1,X0)
& segmentP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax54) ).
fof(f9328,plain,
( segmentP(app(sK20,sK20),sK20)
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f9327,f8873]) ).
fof(f9327,plain,
( ~ ssList(app(sK20,sK20))
| segmentP(app(sK20,sK20),sK20)
| ~ spl72_89 ),
inference(forward_demodulation,[],[f9326,f8889]) ).
fof(f9326,plain,
( segmentP(app(sK20,sK20),sK20)
| ~ ssList(app(app(sK20,sK20),nil))
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f9325,f387]) ).
fof(f9325,plain,
( segmentP(app(sK20,sK20),sK20)
| ~ ssList(sK20)
| ~ ssList(app(app(sK20,sK20),nil))
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f9309,f405]) ).
fof(f9309,plain,
( segmentP(app(sK20,sK20),sK20)
| ~ ssList(nil)
| ~ ssList(sK20)
| ~ ssList(app(app(sK20,sK20),nil))
| ~ spl72_89 ),
inference(duplicate_literal_removal,[],[f9306]) ).
fof(f9306,plain,
( segmentP(app(sK20,sK20),sK20)
| ~ ssList(nil)
| ~ ssList(sK20)
| ~ ssList(sK20)
| ~ ssList(app(app(sK20,sK20),nil))
| ~ spl72_89 ),
inference(superposition,[],[f637,f8889]) ).
fof(f637,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f592]) ).
fof(f592,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f372]) ).
fof(f372,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
& ssList(sK68(X0,X1))
& ssList(sK67(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f369,f371,f370]) ).
fof(f370,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK67(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK67(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f371,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK67(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
& ssList(sK68(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f369,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f368]) ).
fof(f368,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f201]) ).
fof(f201,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax7) ).
fof(f9781,plain,
( ~ spl72_91
| spl72_92
| ~ spl72_2
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| ~ spl72_89 ),
inference(avatar_split_clause,[],[f9732,f8872,f1642,f1548,f1544,f1510,f838,f9778,f9774]) ).
fof(f9774,plain,
( spl72_91
<=> segmentP(nil,app(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_91])]) ).
fof(f9778,plain,
( spl72_92
<=> segmentP(tl(sK20),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_92])]) ).
fof(f838,plain,
( spl72_2
<=> nil = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl72_2])]) ).
fof(f9732,plain,
( segmentP(tl(sK20),sK20)
| ~ segmentP(nil,app(sK20,sK20))
| ~ spl72_2
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f9731,f8873]) ).
fof(f9731,plain,
( segmentP(tl(sK20),sK20)
| ~ segmentP(nil,app(sK20,sK20))
| ~ ssList(app(sK20,sK20))
| ~ spl72_2
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f9709,f1972]) ).
fof(f1972,plain,
( ssList(tl(sK20))
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(superposition,[],[f1545,f1967]) ).
fof(f9709,plain,
( segmentP(tl(sK20),sK20)
| ~ ssList(tl(sK20))
| ~ segmentP(nil,app(sK20,sK20))
| ~ ssList(app(sK20,sK20))
| ~ spl72_2
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| ~ spl72_89 ),
inference(resolution,[],[f9337,f8644]) ).
fof(f8644,plain,
( ! [X0] :
( segmentP(tl(sK20),X0)
| ~ segmentP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_2
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(forward_demodulation,[],[f8643,f1967]) ).
fof(f8643,plain,
( ! [X0] :
( segmentP(sK25(sK20),X0)
| ~ segmentP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_2
| ~ spl72_9 ),
inference(subsumption_resolution,[],[f8617,f1545]) ).
fof(f8617,plain,
( ! [X0] :
( segmentP(sK25(sK20),X0)
| ~ segmentP(nil,X0)
| ~ ssList(sK25(sK20))
| ~ ssList(X0) )
| ~ spl72_2
| ~ spl72_9 ),
inference(superposition,[],[f6650,f1599]) ).
fof(f1599,plain,
( sK25(sK20) = app(nil,sK25(sK20))
| ~ spl72_9 ),
inference(resolution,[],[f1545,f468]) ).
fof(f6650,plain,
( ! [X0,X1] :
( segmentP(app(nil,X0),X1)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl72_2 ),
inference(forward_demodulation,[],[f6649,f840]) ).
fof(f840,plain,
( nil = sK21
| ~ spl72_2 ),
inference(avatar_component_clause,[],[f838]) ).
fof(f6649,plain,
! [X0,X1] :
( segmentP(app(sK21,X0),X1)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f6648,f405]) ).
fof(f6648,plain,
! [X0,X1] :
( segmentP(app(sK21,X0),X1)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(subsumption_resolution,[],[f6578,f388]) ).
fof(f6578,plain,
! [X0,X1] :
( segmentP(app(sK21,X0),X1)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(sK21)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(superposition,[],[f610,f668]) ).
fof(f668,plain,
sK21 = app(sK21,nil),
inference(resolution,[],[f467,f388]) ).
fof(f610,plain,
! [X2,X3,X0,X1] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f223]) ).
fof(f223,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f222]) ).
fof(f222,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax56) ).
fof(f9337,plain,
( ! [X0] :
( ~ segmentP(X0,app(sK20,sK20))
| segmentP(X0,sK20)
| ~ ssList(X0) )
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f9336,f8873]) ).
fof(f9336,plain,
( ! [X0] :
( segmentP(X0,sK20)
| ~ segmentP(X0,app(sK20,sK20))
| ~ ssList(app(sK20,sK20))
| ~ ssList(X0) )
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f9332,f387]) ).
fof(f9332,plain,
( ! [X0] :
( segmentP(X0,sK20)
| ~ segmentP(X0,app(sK20,sK20))
| ~ ssList(sK20)
| ~ ssList(app(sK20,sK20))
| ~ ssList(X0) )
| ~ spl72_89 ),
inference(resolution,[],[f9328,f607]) ).
fof(f607,plain,
! [X2,X0,X1] :
( ~ segmentP(X1,X2)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f217]) ).
fof(f217,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f216]) ).
fof(f216,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X0,X1) )
=> segmentP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax53) ).
fof(f9010,plain,
~ spl72_87,
inference(avatar_contradiction_clause,[],[f9009]) ).
fof(f9009,plain,
( $false
| ~ spl72_87 ),
inference(subsumption_resolution,[],[f9008,f387]) ).
fof(f9008,plain,
( ~ ssList(sK20)
| ~ spl72_87 ),
inference(subsumption_resolution,[],[f8960,f3427]) ).
fof(f3427,plain,
~ frontsegP(nil,sK20),
inference(subsumption_resolution,[],[f3426,f393]) ).
fof(f3426,plain,
( nil = sK20
| ~ frontsegP(nil,sK20) ),
inference(subsumption_resolution,[],[f3421,f405]) ).
fof(f3421,plain,
( ~ ssList(nil)
| nil = sK20
| ~ frontsegP(nil,sK20) ),
inference(resolution,[],[f3342,f648]) ).
fof(f3342,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| sK20 = X0
| ~ frontsegP(X0,sK20) ),
inference(subsumption_resolution,[],[f3339,f387]) ).
fof(f3339,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| sK20 = X0
| ~ frontsegP(X0,sK20)
| ~ ssList(sK20) ),
inference(duplicate_literal_removal,[],[f3338]) ).
fof(f3338,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| sK20 = X0
| ~ frontsegP(X0,sK20)
| ~ ssList(sK20)
| ~ ssList(X0) ),
inference(resolution,[],[f3324,f583]) ).
fof(f583,plain,
! [X0,X1] :
( ~ frontsegP(X1,X0)
| X0 = X1
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f198,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f197]) ).
fof(f197,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f41]) ).
fof(f41,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( frontsegP(X1,X0)
& frontsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax41) ).
fof(f3324,plain,
! [X0] :
( frontsegP(sK20,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f3323,f405]) ).
fof(f3323,plain,
! [X0] :
( frontsegP(sK20,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(subsumption_resolution,[],[f3296,f387]) ).
fof(f3296,plain,
! [X0] :
( frontsegP(sK20,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sK20)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(superposition,[],[f604,f694]) ).
fof(f8960,plain,
( frontsegP(nil,sK20)
| ~ ssList(sK20)
| ~ spl72_87 ),
inference(duplicate_literal_removal,[],[f8959]) ).
fof(f8959,plain,
( frontsegP(nil,sK20)
| ~ ssList(sK20)
| ~ ssList(sK20)
| ~ spl72_87 ),
inference(superposition,[],[f2500,f8167]) ).
fof(f8167,plain,
( nil = app(sK20,sK20)
| ~ spl72_87 ),
inference(avatar_component_clause,[],[f8165]) ).
fof(f8165,plain,
( spl72_87
<=> nil = app(sK20,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_87])]) ).
fof(f9007,plain,
~ spl72_87,
inference(avatar_contradiction_clause,[],[f9006]) ).
fof(f9006,plain,
( $false
| ~ spl72_87 ),
inference(subsumption_resolution,[],[f9005,f387]) ).
fof(f9005,plain,
( ~ ssList(sK20)
| ~ spl72_87 ),
inference(subsumption_resolution,[],[f8961,f3416]) ).
fof(f3416,plain,
~ rearsegP(nil,sK20),
inference(subsumption_resolution,[],[f3415,f393]) ).
fof(f3415,plain,
( nil = sK20
| ~ rearsegP(nil,sK20) ),
inference(subsumption_resolution,[],[f3414,f405]) ).
fof(f3414,plain,
( ~ ssList(nil)
| nil = sK20
| ~ rearsegP(nil,sK20) ),
inference(duplicate_literal_removal,[],[f3410]) ).
fof(f3410,plain,
( ~ ssList(nil)
| nil = sK20
| ~ rearsegP(nil,sK20)
| ~ ssList(nil) ),
inference(resolution,[],[f3238,f466]) ).
fof(f3238,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| sK20 = X0
| ~ rearsegP(X0,sK20) ),
inference(subsumption_resolution,[],[f3232,f387]) ).
fof(f3232,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| sK20 = X0
| ~ rearsegP(X0,sK20)
| ~ ssList(sK20) ),
inference(duplicate_literal_removal,[],[f3231]) ).
fof(f3231,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| sK20 = X0
| ~ rearsegP(X0,sK20)
| ~ ssList(sK20)
| ~ ssList(X0) ),
inference(resolution,[],[f3213,f581]) ).
fof(f581,plain,
! [X0,X1] :
( ~ rearsegP(X1,X0)
| X0 = X1
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f194]) ).
fof(f194,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f193]) ).
fof(f193,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f48]) ).
fof(f48,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( rearsegP(X1,X0)
& rearsegP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax48) ).
fof(f3213,plain,
! [X0] :
( rearsegP(sK20,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f3212,f405]) ).
fof(f3212,plain,
! [X0] :
( rearsegP(sK20,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(subsumption_resolution,[],[f3181,f387]) ).
fof(f3181,plain,
! [X0] :
( rearsegP(sK20,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(sK20)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(superposition,[],[f603,f667]) ).
fof(f667,plain,
sK20 = app(sK20,nil),
inference(resolution,[],[f467,f387]) ).
fof(f8961,plain,
( rearsegP(nil,sK20)
| ~ ssList(sK20)
| ~ spl72_87 ),
inference(duplicate_literal_removal,[],[f8958]) ).
fof(f8958,plain,
( rearsegP(nil,sK20)
| ~ ssList(sK20)
| ~ ssList(sK20)
| ~ spl72_87 ),
inference(superposition,[],[f2433,f8167]) ).
fof(f8995,plain,
~ spl72_87,
inference(avatar_contradiction_clause,[],[f8994]) ).
fof(f8994,plain,
( $false
| ~ spl72_87 ),
inference(subsumption_resolution,[],[f8993,f387]) ).
fof(f8993,plain,
( ~ ssList(sK20)
| ~ spl72_87 ),
inference(subsumption_resolution,[],[f8971,f393]) ).
fof(f8971,plain,
( nil = sK20
| ~ ssList(sK20)
| ~ spl72_87 ),
inference(trivial_inequality_removal,[],[f8970]) ).
fof(f8970,plain,
( nil != nil
| nil = sK20
| ~ ssList(sK20)
| ~ spl72_87 ),
inference(duplicate_literal_removal,[],[f8949]) ).
fof(f8949,plain,
( nil != nil
| nil = sK20
| ~ ssList(sK20)
| ~ ssList(sK20)
| ~ spl72_87 ),
inference(superposition,[],[f597,f8167]) ).
fof(f597,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f378]) ).
fof(f378,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f377]) ).
fof(f377,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f203]) ).
fof(f203,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax83) ).
fof(f8992,plain,
~ spl72_87,
inference(avatar_contradiction_clause,[],[f8991]) ).
fof(f8991,plain,
( $false
| ~ spl72_87 ),
inference(subsumption_resolution,[],[f8990,f387]) ).
fof(f8990,plain,
( ~ ssList(sK20)
| ~ spl72_87 ),
inference(subsumption_resolution,[],[f8973,f393]) ).
fof(f8973,plain,
( nil = sK20
| ~ ssList(sK20)
| ~ spl72_87 ),
inference(trivial_inequality_removal,[],[f8972]) ).
fof(f8972,plain,
( nil != nil
| nil = sK20
| ~ ssList(sK20)
| ~ spl72_87 ),
inference(duplicate_literal_removal,[],[f8948]) ).
fof(f8948,plain,
( nil != nil
| nil = sK20
| ~ ssList(sK20)
| ~ ssList(sK20)
| ~ spl72_87 ),
inference(superposition,[],[f596,f8167]) ).
fof(f596,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f378]) ).
fof(f8985,plain,
( ~ spl72_87
| ~ spl72_89 ),
inference(avatar_contradiction_clause,[],[f8984]) ).
fof(f8984,plain,
( $false
| ~ spl72_87
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f8983,f387]) ).
fof(f8983,plain,
( ~ ssList(sK20)
| ~ spl72_87
| ~ spl72_89 ),
inference(subsumption_resolution,[],[f8982,f8873]) ).
fof(f8982,plain,
( ~ ssList(app(sK20,sK20))
| ~ ssList(sK20)
| ~ spl72_87 ),
inference(subsumption_resolution,[],[f8942,f8520]) ).
fof(f8520,plain,
~ segmentP(nil,sK20),
inference(subsumption_resolution,[],[f8519,f393]) ).
fof(f8519,plain,
( nil = sK20
| ~ segmentP(nil,sK20) ),
inference(subsumption_resolution,[],[f8518,f405]) ).
fof(f8518,plain,
( ~ ssList(nil)
| nil = sK20
| ~ segmentP(nil,sK20) ),
inference(duplicate_literal_removal,[],[f8514]) ).
fof(f8514,plain,
( ~ ssList(nil)
| nil = sK20
| ~ segmentP(nil,sK20)
| ~ ssList(nil) ),
inference(resolution,[],[f8513,f465]) ).
fof(f8513,plain,
! [X0] :
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| sK20 = X0
| ~ segmentP(X0,sK20) ),
inference(subsumption_resolution,[],[f8508,f387]) ).
fof(f8508,plain,
! [X0] :
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| sK20 = X0
| ~ segmentP(X0,sK20)
| ~ ssList(sK20) ),
inference(duplicate_literal_removal,[],[f8507]) ).
fof(f8507,plain,
! [X0] :
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| sK20 = X0
| ~ segmentP(X0,sK20)
| ~ ssList(sK20)
| ~ ssList(X0) ),
inference(resolution,[],[f8503,f582]) ).
fof(f8503,plain,
! [X0] :
( segmentP(sK20,X0)
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f8498,f405]) ).
fof(f8498,plain,
! [X0] :
( segmentP(sK20,X0)
| ~ segmentP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[],[f6647,f667]) ).
fof(f6647,plain,
! [X0,X1] :
( segmentP(app(sK20,X0),X1)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f6646,f405]) ).
fof(f6646,plain,
! [X0,X1] :
( segmentP(app(sK20,X0),X1)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(subsumption_resolution,[],[f6577,f387]) ).
fof(f6577,plain,
! [X0,X1] :
( segmentP(app(sK20,X0),X1)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(sK20)
| ~ ssList(X1)
| ~ ssList(nil) ),
inference(superposition,[],[f610,f667]) ).
fof(f8942,plain,
( segmentP(nil,sK20)
| ~ ssList(app(sK20,sK20))
| ~ ssList(sK20)
| ~ spl72_87 ),
inference(superposition,[],[f7365,f8167]) ).
fof(f7365,plain,
! [X0] :
( segmentP(app(sK20,X0),sK20)
| ~ ssList(app(sK20,X0))
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f7364,f694]) ).
fof(f7364,plain,
! [X0] :
( segmentP(app(sK20,X0),sK20)
| ~ ssList(X0)
| ~ ssList(app(app(nil,sK20),X0)) ),
inference(subsumption_resolution,[],[f7363,f387]) ).
fof(f7363,plain,
! [X0] :
( segmentP(app(sK20,X0),sK20)
| ~ ssList(X0)
| ~ ssList(sK20)
| ~ ssList(app(app(nil,sK20),X0)) ),
inference(subsumption_resolution,[],[f7243,f405]) ).
fof(f7243,plain,
! [X0] :
( segmentP(app(sK20,X0),sK20)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK20)
| ~ ssList(app(app(nil,sK20),X0)) ),
inference(superposition,[],[f637,f694]) ).
fof(f8979,plain,
( ~ spl72_87
| spl72_88 ),
inference(avatar_contradiction_clause,[],[f8978]) ).
fof(f8978,plain,
( $false
| ~ spl72_87
| spl72_88 ),
inference(subsumption_resolution,[],[f8937,f620]) ).
fof(f8937,plain,
( ~ sP3(nil,sK24)
| ~ spl72_87
| spl72_88 ),
inference(superposition,[],[f8171,f8167]) ).
fof(f8171,plain,
( ~ sP3(app(sK20,sK20),sK24)
| spl72_88 ),
inference(avatar_component_clause,[],[f8169]) ).
fof(f8169,plain,
( spl72_88
<=> sP3(app(sK20,sK20),sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_88])]) ).
fof(f8883,plain,
spl72_89,
inference(avatar_contradiction_clause,[],[f8882]) ).
fof(f8882,plain,
( $false
| spl72_89 ),
inference(subsumption_resolution,[],[f8881,f387]) ).
fof(f8881,plain,
( ~ ssList(sK20)
| spl72_89 ),
inference(duplicate_literal_removal,[],[f8880]) ).
fof(f8880,plain,
( ~ ssList(sK20)
| ~ ssList(sK20)
| spl72_89 ),
inference(resolution,[],[f8874,f577]) ).
fof(f8874,plain,
( ~ ssList(app(sK20,sK20))
| spl72_89 ),
inference(avatar_component_clause,[],[f8872]) ).
fof(f8879,plain,
( ~ spl72_89
| spl72_90
| spl72_87 ),
inference(avatar_split_clause,[],[f8870,f8165,f8876,f8872]) ).
fof(f8876,plain,
( spl72_90
<=> ssList(app(tl(sK20),sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_90])]) ).
fof(f8870,plain,
( ssList(app(tl(sK20),sK20))
| ~ ssList(app(sK20,sK20))
| spl72_87 ),
inference(subsumption_resolution,[],[f8865,f8166]) ).
fof(f8166,plain,
( nil != app(sK20,sK20)
| spl72_87 ),
inference(avatar_component_clause,[],[f8165]) ).
fof(f8865,plain,
( ssList(app(tl(sK20),sK20))
| nil = app(sK20,sK20)
| ~ ssList(app(sK20,sK20)) ),
inference(superposition,[],[f473,f8792]) ).
fof(f8792,plain,
app(tl(sK20),sK20) = tl(app(sK20,sK20)),
inference(subsumption_resolution,[],[f8719,f393]) ).
fof(f8719,plain,
( app(tl(sK20),sK20) = tl(app(sK20,sK20))
| nil = sK20 ),
inference(resolution,[],[f3888,f387]) ).
fof(f3888,plain,
! [X0] :
( ~ ssList(X0)
| tl(app(X0,sK20)) = app(tl(X0),sK20)
| nil = X0 ),
inference(resolution,[],[f579,f387]) ).
fof(f579,plain,
! [X0,X1] :
( ~ ssList(X1)
| nil = X0
| tl(app(X0,X1)) = app(tl(X0),X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f190]) ).
fof(f190,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f189]) ).
fof(f189,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> tl(app(X0,X1)) = app(tl(X0),X1) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax86) ).
fof(f8172,plain,
( spl72_87
| ~ spl72_88
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10 ),
inference(avatar_split_clause,[],[f8058,f1548,f1544,f1510,f8169,f8165]) ).
fof(f8058,plain,
( ~ sP3(app(sK20,sK20),sK24)
| nil = app(sK20,sK20)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10 ),
inference(subsumption_resolution,[],[f8057,f395]) ).
fof(f8057,plain,
( ~ ssItem(sK24)
| ~ sP3(app(sK20,sK20),sK24)
| nil = app(sK20,sK20)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10 ),
inference(forward_demodulation,[],[f8051,f7908]) ).
fof(f7908,plain,
( sK24 = hd(app(sK20,sK20))
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10 ),
inference(forward_demodulation,[],[f7907,f1707]) ).
fof(f7907,plain,
hd(sK20) = hd(app(sK20,sK20)),
inference(subsumption_resolution,[],[f7837,f393]) ).
fof(f7837,plain,
( hd(sK20) = hd(app(sK20,sK20))
| nil = sK20 ),
inference(resolution,[],[f2899,f387]) ).
fof(f2899,plain,
! [X0] :
( ~ ssList(X0)
| hd(X0) = hd(app(X0,sK20))
| nil = X0 ),
inference(resolution,[],[f578,f387]) ).
fof(f578,plain,
! [X0,X1] :
( ~ ssList(X1)
| nil = X0
| hd(X0) = hd(app(X0,X1))
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f188]) ).
fof(f188,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f187]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f85]) ).
fof(f85,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> hd(X0) = hd(app(X0,X1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax85) ).
fof(f8051,plain,
( ~ sP3(app(sK20,sK20),sK24)
| nil = app(sK20,sK20)
| ~ ssItem(hd(app(sK20,sK20)))
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10 ),
inference(superposition,[],[f792,f7908]) ).
fof(f792,plain,
! [X0] :
( ~ sP3(X0,hd(X0))
| nil = X0
| ~ ssItem(hd(X0)) ),
inference(resolution,[],[f454,f407]) ).
fof(f6815,plain,
( ~ spl72_34
| spl72_85
| ~ spl72_86 ),
inference(avatar_contradiction_clause,[],[f6814]) ).
fof(f6814,plain,
( $false
| ~ spl72_34
| spl72_85
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f6813,f2364]) ).
fof(f2364,plain,
( ssList(cons(sK71,sK20))
| ~ spl72_34 ),
inference(avatar_component_clause,[],[f2362]) ).
fof(f2362,plain,
( spl72_34
<=> ssList(cons(sK71,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_34])]) ).
fof(f6813,plain,
( ~ ssList(cons(sK71,sK20))
| spl72_85
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f6812,f405]) ).
fof(f6812,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK71,sK20))
| spl72_85
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f6811,f6799]) ).
fof(f6799,plain,
( frontsegP(cons(sK71,sK20),nil)
| ~ spl72_86 ),
inference(avatar_component_clause,[],[f6797]) ).
fof(f6797,plain,
( spl72_86
<=> frontsegP(cons(sK71,sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_86])]) ).
fof(f6811,plain,
( ~ frontsegP(cons(sK71,sK20),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK71,sK20))
| spl72_85 ),
inference(resolution,[],[f6795,f593]) ).
fof(f6795,plain,
( ~ ssList(sK69(cons(sK71,sK20),nil))
| spl72_85 ),
inference(avatar_component_clause,[],[f6793]) ).
fof(f6793,plain,
( spl72_85
<=> ssList(sK69(cons(sK71,sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_85])]) ).
fof(f6807,plain,
( ~ spl72_34
| spl72_86 ),
inference(avatar_contradiction_clause,[],[f6806]) ).
fof(f6806,plain,
( $false
| ~ spl72_34
| spl72_86 ),
inference(subsumption_resolution,[],[f6802,f2364]) ).
fof(f6802,plain,
( ~ ssList(cons(sK71,sK20))
| spl72_86 ),
inference(resolution,[],[f6798,f464]) ).
fof(f6798,plain,
( ~ frontsegP(cons(sK71,sK20),nil)
| spl72_86 ),
inference(avatar_component_clause,[],[f6797]) ).
fof(f6805,plain,
( ~ spl72_34
| spl72_86 ),
inference(avatar_contradiction_clause,[],[f6804]) ).
fof(f6804,plain,
( $false
| ~ spl72_34
| spl72_86 ),
inference(subsumption_resolution,[],[f6803,f405]) ).
fof(f6803,plain,
( ~ ssList(nil)
| ~ spl72_34
| spl72_86 ),
inference(subsumption_resolution,[],[f6801,f648]) ).
fof(f6801,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_34
| spl72_86 ),
inference(resolution,[],[f6798,f3319]) ).
fof(f3319,plain,
( ! [X0] :
( frontsegP(cons(sK71,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_34 ),
inference(subsumption_resolution,[],[f3318,f405]) ).
fof(f3318,plain,
( ! [X0] :
( frontsegP(cons(sK71,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_34 ),
inference(subsumption_resolution,[],[f3282,f2364]) ).
fof(f3282,plain,
( ! [X0] :
( frontsegP(cons(sK71,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(cons(sK71,sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_34 ),
inference(superposition,[],[f604,f2401]) ).
fof(f2401,plain,
( cons(sK71,sK20) = app(nil,cons(sK71,sK20))
| ~ spl72_34 ),
inference(resolution,[],[f2364,f468]) ).
fof(f6800,plain,
( ~ spl72_85
| spl72_86
| ~ spl72_34 ),
inference(avatar_split_clause,[],[f6295,f2362,f6797,f6793]) ).
fof(f6295,plain,
( frontsegP(cons(sK71,sK20),nil)
| ~ ssList(sK69(cons(sK71,sK20),nil))
| ~ spl72_34 ),
inference(subsumption_resolution,[],[f6285,f405]) ).
fof(f6285,plain,
( frontsegP(cons(sK71,sK20),nil)
| ~ ssList(sK69(cons(sK71,sK20),nil))
| ~ ssList(nil)
| ~ spl72_34 ),
inference(superposition,[],[f2500,f5986]) ).
fof(f5986,plain,
( cons(sK71,sK20) = app(nil,sK69(cons(sK71,sK20),nil))
| ~ spl72_34 ),
inference(resolution,[],[f3107,f2364]) ).
fof(f6764,plain,
( ~ spl72_33
| spl72_83
| ~ spl72_84 ),
inference(avatar_contradiction_clause,[],[f6763]) ).
fof(f6763,plain,
( $false
| ~ spl72_33
| spl72_83
| ~ spl72_84 ),
inference(subsumption_resolution,[],[f6762,f2359]) ).
fof(f6762,plain,
( ~ ssList(cons(sK71,nil))
| spl72_83
| ~ spl72_84 ),
inference(subsumption_resolution,[],[f6761,f405]) ).
fof(f6761,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK71,nil))
| spl72_83
| ~ spl72_84 ),
inference(subsumption_resolution,[],[f6760,f6748]) ).
fof(f6748,plain,
( frontsegP(cons(sK71,nil),nil)
| ~ spl72_84 ),
inference(avatar_component_clause,[],[f6746]) ).
fof(f6746,plain,
( spl72_84
<=> frontsegP(cons(sK71,nil),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_84])]) ).
fof(f6760,plain,
( ~ frontsegP(cons(sK71,nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK71,nil))
| spl72_83 ),
inference(resolution,[],[f6744,f593]) ).
fof(f6744,plain,
( ~ ssList(sK69(cons(sK71,nil),nil))
| spl72_83 ),
inference(avatar_component_clause,[],[f6742]) ).
fof(f6742,plain,
( spl72_83
<=> ssList(sK69(cons(sK71,nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_83])]) ).
fof(f6756,plain,
( ~ spl72_33
| spl72_84 ),
inference(avatar_contradiction_clause,[],[f6755]) ).
fof(f6755,plain,
( $false
| ~ spl72_33
| spl72_84 ),
inference(subsumption_resolution,[],[f6751,f2359]) ).
fof(f6751,plain,
( ~ ssList(cons(sK71,nil))
| spl72_84 ),
inference(resolution,[],[f6747,f464]) ).
fof(f6747,plain,
( ~ frontsegP(cons(sK71,nil),nil)
| spl72_84 ),
inference(avatar_component_clause,[],[f6746]) ).
fof(f6754,plain,
( ~ spl72_33
| spl72_84 ),
inference(avatar_contradiction_clause,[],[f6753]) ).
fof(f6753,plain,
( $false
| ~ spl72_33
| spl72_84 ),
inference(subsumption_resolution,[],[f6752,f405]) ).
fof(f6752,plain,
( ~ ssList(nil)
| ~ spl72_33
| spl72_84 ),
inference(subsumption_resolution,[],[f6750,f648]) ).
fof(f6750,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_33
| spl72_84 ),
inference(resolution,[],[f6747,f3317]) ).
fof(f3317,plain,
( ! [X0] :
( frontsegP(cons(sK71,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_33 ),
inference(subsumption_resolution,[],[f3316,f405]) ).
fof(f3316,plain,
( ! [X0] :
( frontsegP(cons(sK71,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_33 ),
inference(subsumption_resolution,[],[f3281,f2359]) ).
fof(f3281,plain,
( ! [X0] :
( frontsegP(cons(sK71,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(cons(sK71,nil))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_33 ),
inference(superposition,[],[f604,f2371]) ).
fof(f2371,plain,
( cons(sK71,nil) = app(nil,cons(sK71,nil))
| ~ spl72_33 ),
inference(resolution,[],[f2359,f468]) ).
fof(f6749,plain,
( ~ spl72_83
| spl72_84
| ~ spl72_33 ),
inference(avatar_split_clause,[],[f6269,f2358,f6746,f6742]) ).
fof(f6269,plain,
( frontsegP(cons(sK71,nil),nil)
| ~ ssList(sK69(cons(sK71,nil),nil))
| ~ spl72_33 ),
inference(subsumption_resolution,[],[f6259,f405]) ).
fof(f6259,plain,
( frontsegP(cons(sK71,nil),nil)
| ~ ssList(sK69(cons(sK71,nil),nil))
| ~ ssList(nil)
| ~ spl72_33 ),
inference(superposition,[],[f2500,f5985]) ).
fof(f5985,plain,
( cons(sK71,nil) = app(nil,sK69(cons(sK71,nil),nil))
| ~ spl72_33 ),
inference(resolution,[],[f3107,f2359]) ).
fof(f6534,plain,
( ~ spl72_32
| spl72_81
| ~ spl72_82 ),
inference(avatar_contradiction_clause,[],[f6533]) ).
fof(f6533,plain,
( $false
| ~ spl72_32
| spl72_81
| ~ spl72_82 ),
inference(subsumption_resolution,[],[f6532,f2277]) ).
fof(f2277,plain,
( ssList(cons(sK70,sK20))
| ~ spl72_32 ),
inference(avatar_component_clause,[],[f2275]) ).
fof(f2275,plain,
( spl72_32
<=> ssList(cons(sK70,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_32])]) ).
fof(f6532,plain,
( ~ ssList(cons(sK70,sK20))
| spl72_81
| ~ spl72_82 ),
inference(subsumption_resolution,[],[f6531,f405]) ).
fof(f6531,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK70,sK20))
| spl72_81
| ~ spl72_82 ),
inference(subsumption_resolution,[],[f6530,f6518]) ).
fof(f6518,plain,
( frontsegP(cons(sK70,sK20),nil)
| ~ spl72_82 ),
inference(avatar_component_clause,[],[f6516]) ).
fof(f6516,plain,
( spl72_82
<=> frontsegP(cons(sK70,sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_82])]) ).
fof(f6530,plain,
( ~ frontsegP(cons(sK70,sK20),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK70,sK20))
| spl72_81 ),
inference(resolution,[],[f6514,f593]) ).
fof(f6514,plain,
( ~ ssList(sK69(cons(sK70,sK20),nil))
| spl72_81 ),
inference(avatar_component_clause,[],[f6512]) ).
fof(f6512,plain,
( spl72_81
<=> ssList(sK69(cons(sK70,sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_81])]) ).
fof(f6526,plain,
( ~ spl72_32
| spl72_82 ),
inference(avatar_contradiction_clause,[],[f6525]) ).
fof(f6525,plain,
( $false
| ~ spl72_32
| spl72_82 ),
inference(subsumption_resolution,[],[f6521,f2277]) ).
fof(f6521,plain,
( ~ ssList(cons(sK70,sK20))
| spl72_82 ),
inference(resolution,[],[f6517,f464]) ).
fof(f6517,plain,
( ~ frontsegP(cons(sK70,sK20),nil)
| spl72_82 ),
inference(avatar_component_clause,[],[f6516]) ).
fof(f6524,plain,
( ~ spl72_32
| spl72_82 ),
inference(avatar_contradiction_clause,[],[f6523]) ).
fof(f6523,plain,
( $false
| ~ spl72_32
| spl72_82 ),
inference(subsumption_resolution,[],[f6522,f405]) ).
fof(f6522,plain,
( ~ ssList(nil)
| ~ spl72_32
| spl72_82 ),
inference(subsumption_resolution,[],[f6520,f648]) ).
fof(f6520,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_32
| spl72_82 ),
inference(resolution,[],[f6517,f3315]) ).
fof(f3315,plain,
( ! [X0] :
( frontsegP(cons(sK70,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_32 ),
inference(subsumption_resolution,[],[f3314,f405]) ).
fof(f3314,plain,
( ! [X0] :
( frontsegP(cons(sK70,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_32 ),
inference(subsumption_resolution,[],[f3280,f2277]) ).
fof(f3280,plain,
( ! [X0] :
( frontsegP(cons(sK70,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(cons(sK70,sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_32 ),
inference(superposition,[],[f604,f2314]) ).
fof(f2314,plain,
( cons(sK70,sK20) = app(nil,cons(sK70,sK20))
| ~ spl72_32 ),
inference(resolution,[],[f2277,f468]) ).
fof(f6519,plain,
( ~ spl72_81
| spl72_82
| ~ spl72_32 ),
inference(avatar_split_clause,[],[f6243,f2275,f6516,f6512]) ).
fof(f6243,plain,
( frontsegP(cons(sK70,sK20),nil)
| ~ ssList(sK69(cons(sK70,sK20),nil))
| ~ spl72_32 ),
inference(subsumption_resolution,[],[f6233,f405]) ).
fof(f6233,plain,
( frontsegP(cons(sK70,sK20),nil)
| ~ ssList(sK69(cons(sK70,sK20),nil))
| ~ ssList(nil)
| ~ spl72_32 ),
inference(superposition,[],[f2500,f5984]) ).
fof(f5984,plain,
( cons(sK70,sK20) = app(nil,sK69(cons(sK70,sK20),nil))
| ~ spl72_32 ),
inference(resolution,[],[f3107,f2277]) ).
fof(f6483,plain,
( ~ spl72_31
| spl72_79
| ~ spl72_80 ),
inference(avatar_contradiction_clause,[],[f6482]) ).
fof(f6482,plain,
( $false
| ~ spl72_31
| spl72_79
| ~ spl72_80 ),
inference(subsumption_resolution,[],[f6481,f2272]) ).
fof(f6481,plain,
( ~ ssList(cons(sK70,nil))
| spl72_79
| ~ spl72_80 ),
inference(subsumption_resolution,[],[f6480,f405]) ).
fof(f6480,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK70,nil))
| spl72_79
| ~ spl72_80 ),
inference(subsumption_resolution,[],[f6479,f6467]) ).
fof(f6467,plain,
( frontsegP(cons(sK70,nil),nil)
| ~ spl72_80 ),
inference(avatar_component_clause,[],[f6465]) ).
fof(f6465,plain,
( spl72_80
<=> frontsegP(cons(sK70,nil),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_80])]) ).
fof(f6479,plain,
( ~ frontsegP(cons(sK70,nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK70,nil))
| spl72_79 ),
inference(resolution,[],[f6463,f593]) ).
fof(f6463,plain,
( ~ ssList(sK69(cons(sK70,nil),nil))
| spl72_79 ),
inference(avatar_component_clause,[],[f6461]) ).
fof(f6461,plain,
( spl72_79
<=> ssList(sK69(cons(sK70,nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_79])]) ).
fof(f6475,plain,
( ~ spl72_31
| spl72_80 ),
inference(avatar_contradiction_clause,[],[f6474]) ).
fof(f6474,plain,
( $false
| ~ spl72_31
| spl72_80 ),
inference(subsumption_resolution,[],[f6470,f2272]) ).
fof(f6470,plain,
( ~ ssList(cons(sK70,nil))
| spl72_80 ),
inference(resolution,[],[f6466,f464]) ).
fof(f6466,plain,
( ~ frontsegP(cons(sK70,nil),nil)
| spl72_80 ),
inference(avatar_component_clause,[],[f6465]) ).
fof(f6473,plain,
( ~ spl72_31
| spl72_80 ),
inference(avatar_contradiction_clause,[],[f6472]) ).
fof(f6472,plain,
( $false
| ~ spl72_31
| spl72_80 ),
inference(subsumption_resolution,[],[f6471,f405]) ).
fof(f6471,plain,
( ~ ssList(nil)
| ~ spl72_31
| spl72_80 ),
inference(subsumption_resolution,[],[f6469,f648]) ).
fof(f6469,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_31
| spl72_80 ),
inference(resolution,[],[f6466,f3313]) ).
fof(f3313,plain,
( ! [X0] :
( frontsegP(cons(sK70,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_31 ),
inference(subsumption_resolution,[],[f3312,f405]) ).
fof(f3312,plain,
( ! [X0] :
( frontsegP(cons(sK70,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_31 ),
inference(subsumption_resolution,[],[f3279,f2272]) ).
fof(f3279,plain,
( ! [X0] :
( frontsegP(cons(sK70,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(cons(sK70,nil))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_31 ),
inference(superposition,[],[f604,f2284]) ).
fof(f2284,plain,
( cons(sK70,nil) = app(nil,cons(sK70,nil))
| ~ spl72_31 ),
inference(resolution,[],[f2272,f468]) ).
fof(f6468,plain,
( ~ spl72_79
| spl72_80
| ~ spl72_31 ),
inference(avatar_split_clause,[],[f6217,f2271,f6465,f6461]) ).
fof(f6217,plain,
( frontsegP(cons(sK70,nil),nil)
| ~ ssList(sK69(cons(sK70,nil),nil))
| ~ spl72_31 ),
inference(subsumption_resolution,[],[f6207,f405]) ).
fof(f6207,plain,
( frontsegP(cons(sK70,nil),nil)
| ~ ssList(sK69(cons(sK70,nil),nil))
| ~ ssList(nil)
| ~ spl72_31 ),
inference(superposition,[],[f2500,f5983]) ).
fof(f5983,plain,
( cons(sK70,nil) = app(nil,sK69(cons(sK70,nil),nil))
| ~ spl72_31 ),
inference(resolution,[],[f3107,f2272]) ).
fof(f6402,plain,
( ~ spl72_30
| spl72_77
| ~ spl72_78 ),
inference(avatar_contradiction_clause,[],[f6401]) ).
fof(f6401,plain,
( $false
| ~ spl72_30
| spl72_77
| ~ spl72_78 ),
inference(subsumption_resolution,[],[f6400,f2190]) ).
fof(f6400,plain,
( ~ ssList(cons(sK24,sK20))
| spl72_77
| ~ spl72_78 ),
inference(subsumption_resolution,[],[f6399,f405]) ).
fof(f6399,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK24,sK20))
| spl72_77
| ~ spl72_78 ),
inference(subsumption_resolution,[],[f6398,f6386]) ).
fof(f6386,plain,
( frontsegP(cons(sK24,sK20),nil)
| ~ spl72_78 ),
inference(avatar_component_clause,[],[f6384]) ).
fof(f6384,plain,
( spl72_78
<=> frontsegP(cons(sK24,sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_78])]) ).
fof(f6398,plain,
( ~ frontsegP(cons(sK24,sK20),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK24,sK20))
| spl72_77 ),
inference(resolution,[],[f6382,f593]) ).
fof(f6382,plain,
( ~ ssList(sK69(cons(sK24,sK20),nil))
| spl72_77 ),
inference(avatar_component_clause,[],[f6380]) ).
fof(f6380,plain,
( spl72_77
<=> ssList(sK69(cons(sK24,sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_77])]) ).
fof(f6394,plain,
( ~ spl72_30
| spl72_78 ),
inference(avatar_contradiction_clause,[],[f6393]) ).
fof(f6393,plain,
( $false
| ~ spl72_30
| spl72_78 ),
inference(subsumption_resolution,[],[f6389,f2190]) ).
fof(f6389,plain,
( ~ ssList(cons(sK24,sK20))
| spl72_78 ),
inference(resolution,[],[f6385,f464]) ).
fof(f6385,plain,
( ~ frontsegP(cons(sK24,sK20),nil)
| spl72_78 ),
inference(avatar_component_clause,[],[f6384]) ).
fof(f6392,plain,
( ~ spl72_30
| spl72_78 ),
inference(avatar_contradiction_clause,[],[f6391]) ).
fof(f6391,plain,
( $false
| ~ spl72_30
| spl72_78 ),
inference(subsumption_resolution,[],[f6390,f405]) ).
fof(f6390,plain,
( ~ ssList(nil)
| ~ spl72_30
| spl72_78 ),
inference(subsumption_resolution,[],[f6388,f648]) ).
fof(f6388,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_30
| spl72_78 ),
inference(resolution,[],[f6385,f3311]) ).
fof(f3311,plain,
( ! [X0] :
( frontsegP(cons(sK24,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_30 ),
inference(subsumption_resolution,[],[f3310,f405]) ).
fof(f3310,plain,
( ! [X0] :
( frontsegP(cons(sK24,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_30 ),
inference(subsumption_resolution,[],[f3278,f2190]) ).
fof(f3278,plain,
( ! [X0] :
( frontsegP(cons(sK24,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(cons(sK24,sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_30 ),
inference(superposition,[],[f604,f2233]) ).
fof(f2233,plain,
( cons(sK24,sK20) = app(nil,cons(sK24,sK20))
| ~ spl72_30 ),
inference(resolution,[],[f2190,f468]) ).
fof(f6387,plain,
( ~ spl72_77
| spl72_78
| ~ spl72_30 ),
inference(avatar_split_clause,[],[f6191,f2188,f6384,f6380]) ).
fof(f6191,plain,
( frontsegP(cons(sK24,sK20),nil)
| ~ ssList(sK69(cons(sK24,sK20),nil))
| ~ spl72_30 ),
inference(subsumption_resolution,[],[f6181,f405]) ).
fof(f6181,plain,
( frontsegP(cons(sK24,sK20),nil)
| ~ ssList(sK69(cons(sK24,sK20),nil))
| ~ ssList(nil)
| ~ spl72_30 ),
inference(superposition,[],[f2500,f5982]) ).
fof(f5982,plain,
( cons(sK24,sK20) = app(nil,sK69(cons(sK24,sK20),nil))
| ~ spl72_30 ),
inference(resolution,[],[f3107,f2190]) ).
fof(f6351,plain,
( ~ spl72_29
| spl72_75
| ~ spl72_76 ),
inference(avatar_contradiction_clause,[],[f6350]) ).
fof(f6350,plain,
( $false
| ~ spl72_29
| spl72_75
| ~ spl72_76 ),
inference(subsumption_resolution,[],[f6349,f2185]) ).
fof(f6349,plain,
( ~ ssList(cons(sK24,nil))
| spl72_75
| ~ spl72_76 ),
inference(subsumption_resolution,[],[f6348,f405]) ).
fof(f6348,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK24,nil))
| spl72_75
| ~ spl72_76 ),
inference(subsumption_resolution,[],[f6347,f6305]) ).
fof(f6305,plain,
( frontsegP(cons(sK24,nil),nil)
| ~ spl72_76 ),
inference(avatar_component_clause,[],[f6303]) ).
fof(f6303,plain,
( spl72_76
<=> frontsegP(cons(sK24,nil),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_76])]) ).
fof(f6347,plain,
( ~ frontsegP(cons(sK24,nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK24,nil))
| spl72_75 ),
inference(resolution,[],[f6301,f593]) ).
fof(f6301,plain,
( ~ ssList(sK69(cons(sK24,nil),nil))
| spl72_75 ),
inference(avatar_component_clause,[],[f6299]) ).
fof(f6299,plain,
( spl72_75
<=> ssList(sK69(cons(sK24,nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_75])]) ).
fof(f6343,plain,
( ~ spl72_29
| spl72_76 ),
inference(avatar_contradiction_clause,[],[f6342]) ).
fof(f6342,plain,
( $false
| ~ spl72_29
| spl72_76 ),
inference(subsumption_resolution,[],[f6338,f2185]) ).
fof(f6338,plain,
( ~ ssList(cons(sK24,nil))
| spl72_76 ),
inference(resolution,[],[f6304,f464]) ).
fof(f6304,plain,
( ~ frontsegP(cons(sK24,nil),nil)
| spl72_76 ),
inference(avatar_component_clause,[],[f6303]) ).
fof(f6341,plain,
( ~ spl72_29
| spl72_76 ),
inference(avatar_contradiction_clause,[],[f6340]) ).
fof(f6340,plain,
( $false
| ~ spl72_29
| spl72_76 ),
inference(subsumption_resolution,[],[f6339,f405]) ).
fof(f6339,plain,
( ~ ssList(nil)
| ~ spl72_29
| spl72_76 ),
inference(subsumption_resolution,[],[f6337,f648]) ).
fof(f6337,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_29
| spl72_76 ),
inference(resolution,[],[f6304,f3309]) ).
fof(f3309,plain,
( ! [X0] :
( frontsegP(cons(sK24,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f3308,f405]) ).
fof(f3308,plain,
( ! [X0] :
( frontsegP(cons(sK24,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f3277,f2185]) ).
fof(f3277,plain,
( ! [X0] :
( frontsegP(cons(sK24,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(cons(sK24,nil))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_29 ),
inference(superposition,[],[f604,f2197]) ).
fof(f6306,plain,
( ~ spl72_75
| spl72_76
| ~ spl72_29 ),
inference(avatar_split_clause,[],[f6165,f2184,f6303,f6299]) ).
fof(f6165,plain,
( frontsegP(cons(sK24,nil),nil)
| ~ ssList(sK69(cons(sK24,nil),nil))
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f6155,f405]) ).
fof(f6155,plain,
( frontsegP(cons(sK24,nil),nil)
| ~ ssList(sK69(cons(sK24,nil),nil))
| ~ ssList(nil)
| ~ spl72_29 ),
inference(superposition,[],[f2500,f5981]) ).
fof(f5981,plain,
( cons(sK24,nil) = app(nil,sK69(cons(sK24,nil),nil))
| ~ spl72_29 ),
inference(resolution,[],[f3107,f2185]) ).
fof(f6104,plain,
( ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_73
| ~ spl72_74 ),
inference(avatar_contradiction_clause,[],[f6103]) ).
fof(f6103,plain,
( $false
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_73
| ~ spl72_74 ),
inference(subsumption_resolution,[],[f6102,f1972]) ).
fof(f6102,plain,
( ~ ssList(tl(sK20))
| spl72_73
| ~ spl72_74 ),
inference(subsumption_resolution,[],[f6101,f405]) ).
fof(f6101,plain,
( ~ ssList(nil)
| ~ ssList(tl(sK20))
| spl72_73
| ~ spl72_74 ),
inference(subsumption_resolution,[],[f6100,f6088]) ).
fof(f6100,plain,
( ~ frontsegP(tl(sK20),nil)
| ~ ssList(nil)
| ~ ssList(tl(sK20))
| spl72_73 ),
inference(resolution,[],[f6084,f593]) ).
fof(f6084,plain,
( ~ ssList(sK69(tl(sK20),nil))
| spl72_73 ),
inference(avatar_component_clause,[],[f6082]) ).
fof(f6082,plain,
( spl72_73
<=> ssList(sK69(tl(sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_73])]) ).
fof(f6096,plain,
( ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_74 ),
inference(avatar_contradiction_clause,[],[f6095]) ).
fof(f6095,plain,
( $false
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_74 ),
inference(subsumption_resolution,[],[f6091,f1972]) ).
fof(f6091,plain,
( ~ ssList(tl(sK20))
| spl72_74 ),
inference(resolution,[],[f6087,f464]) ).
fof(f6087,plain,
( ~ frontsegP(tl(sK20),nil)
| spl72_74 ),
inference(avatar_component_clause,[],[f6086]) ).
fof(f6094,plain,
( ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_74 ),
inference(avatar_contradiction_clause,[],[f6093]) ).
fof(f6093,plain,
( $false
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_74 ),
inference(subsumption_resolution,[],[f6092,f405]) ).
fof(f6092,plain,
( ~ ssList(nil)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_74 ),
inference(subsumption_resolution,[],[f6090,f648]) ).
fof(f6090,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_74 ),
inference(resolution,[],[f6087,f3336]) ).
fof(f3336,plain,
( ! [X0] :
( frontsegP(tl(sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(forward_demodulation,[],[f3335,f1967]) ).
fof(f3335,plain,
( ! [X0] :
( frontsegP(sK25(sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_9 ),
inference(subsumption_resolution,[],[f3334,f405]) ).
fof(f3334,plain,
( ! [X0] :
( frontsegP(sK25(sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_9 ),
inference(subsumption_resolution,[],[f3301,f1545]) ).
fof(f3301,plain,
( ! [X0] :
( frontsegP(sK25(sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sK25(sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_9 ),
inference(superposition,[],[f604,f1599]) ).
fof(f6089,plain,
( ~ spl72_73
| spl72_74
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(avatar_split_clause,[],[f6080,f1642,f1548,f1544,f1510,f6086,f6082]) ).
fof(f6080,plain,
( frontsegP(tl(sK20),nil)
| ~ ssList(sK69(tl(sK20),nil))
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(subsumption_resolution,[],[f6070,f405]) ).
fof(f6070,plain,
( frontsegP(tl(sK20),nil)
| ~ ssList(sK69(tl(sK20),nil))
| ~ ssList(nil)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(superposition,[],[f2500,f6041]) ).
fof(f6041,plain,
( tl(sK20) = app(nil,sK69(tl(sK20),nil))
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(forward_demodulation,[],[f5996,f1967]) ).
fof(f5996,plain,
( sK25(sK20) = app(nil,sK69(sK25(sK20),nil))
| ~ spl72_9 ),
inference(resolution,[],[f3107,f1545]) ).
fof(f5833,plain,
( ~ spl72_34
| spl72_71
| ~ spl72_72 ),
inference(avatar_contradiction_clause,[],[f5832]) ).
fof(f5832,plain,
( $false
| ~ spl72_34
| spl72_71
| ~ spl72_72 ),
inference(subsumption_resolution,[],[f5831,f2364]) ).
fof(f5831,plain,
( ~ ssList(cons(sK71,sK20))
| spl72_71
| ~ spl72_72 ),
inference(subsumption_resolution,[],[f5830,f405]) ).
fof(f5830,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK71,sK20))
| spl72_71
| ~ spl72_72 ),
inference(subsumption_resolution,[],[f5829,f5813]) ).
fof(f5813,plain,
( rearsegP(cons(sK71,sK20),nil)
| ~ spl72_72 ),
inference(avatar_component_clause,[],[f5811]) ).
fof(f5811,plain,
( spl72_72
<=> rearsegP(cons(sK71,sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_72])]) ).
fof(f5829,plain,
( ~ rearsegP(cons(sK71,sK20),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK71,sK20))
| spl72_71 ),
inference(resolution,[],[f5809,f586]) ).
fof(f5809,plain,
( ~ ssList(sK66(cons(sK71,sK20),nil))
| spl72_71 ),
inference(avatar_component_clause,[],[f5807]) ).
fof(f5807,plain,
( spl72_71
<=> ssList(sK66(cons(sK71,sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_71])]) ).
fof(f5825,plain,
( ~ spl72_33
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_72 ),
inference(avatar_contradiction_clause,[],[f5824]) ).
fof(f5824,plain,
( $false
| ~ spl72_33
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_72 ),
inference(subsumption_resolution,[],[f5823,f405]) ).
fof(f5823,plain,
( ~ ssList(nil)
| ~ spl72_33
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_72 ),
inference(subsumption_resolution,[],[f5817,f5150]) ).
fof(f5817,plain,
( ~ rearsegP(sK20,nil)
| ~ ssList(nil)
| ~ spl72_33
| spl72_72 ),
inference(resolution,[],[f5812,f3225]) ).
fof(f3225,plain,
( ! [X0] :
( rearsegP(cons(sK71,sK20),X0)
| ~ rearsegP(sK20,X0)
| ~ ssList(X0) )
| ~ spl72_33 ),
inference(subsumption_resolution,[],[f3224,f387]) ).
fof(f3224,plain,
( ! [X0] :
( rearsegP(cons(sK71,sK20),X0)
| ~ rearsegP(sK20,X0)
| ~ ssList(X0)
| ~ ssList(sK20) )
| ~ spl72_33 ),
inference(subsumption_resolution,[],[f3189,f2359]) ).
fof(f3189,plain,
! [X0] :
( rearsegP(cons(sK71,sK20),X0)
| ~ rearsegP(sK20,X0)
| ~ ssList(cons(sK71,nil))
| ~ ssList(X0)
| ~ ssList(sK20) ),
inference(superposition,[],[f603,f2176]) ).
fof(f5812,plain,
( ~ rearsegP(cons(sK71,sK20),nil)
| spl72_72 ),
inference(avatar_component_clause,[],[f5811]) ).
fof(f5822,plain,
( ~ spl72_34
| spl72_72 ),
inference(avatar_contradiction_clause,[],[f5821]) ).
fof(f5821,plain,
( $false
| ~ spl72_34
| spl72_72 ),
inference(subsumption_resolution,[],[f5820,f405]) ).
fof(f5820,plain,
( ~ ssList(nil)
| ~ spl72_34
| spl72_72 ),
inference(subsumption_resolution,[],[f5816,f647]) ).
fof(f5816,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_34
| spl72_72 ),
inference(resolution,[],[f5812,f3209]) ).
fof(f3209,plain,
( ! [X0] :
( rearsegP(cons(sK71,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_34 ),
inference(subsumption_resolution,[],[f3208,f405]) ).
fof(f3208,plain,
( ! [X0] :
( rearsegP(cons(sK71,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_34 ),
inference(subsumption_resolution,[],[f3178,f2364]) ).
fof(f3178,plain,
( ! [X0] :
( rearsegP(cons(sK71,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(cons(sK71,sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_34 ),
inference(superposition,[],[f603,f2400]) ).
fof(f2400,plain,
( cons(sK71,sK20) = app(cons(sK71,sK20),nil)
| ~ spl72_34 ),
inference(resolution,[],[f2364,f467]) ).
fof(f5819,plain,
( ~ spl72_34
| spl72_72 ),
inference(avatar_contradiction_clause,[],[f5818]) ).
fof(f5818,plain,
( $false
| ~ spl72_34
| spl72_72 ),
inference(subsumption_resolution,[],[f5815,f2364]) ).
fof(f5815,plain,
( ~ ssList(cons(sK71,sK20))
| spl72_72 ),
inference(resolution,[],[f5812,f462]) ).
fof(f5814,plain,
( ~ spl72_71
| spl72_72
| ~ spl72_34 ),
inference(avatar_split_clause,[],[f5547,f2362,f5811,f5807]) ).
fof(f5547,plain,
( rearsegP(cons(sK71,sK20),nil)
| ~ ssList(sK66(cons(sK71,sK20),nil))
| ~ spl72_34 ),
inference(subsumption_resolution,[],[f5537,f405]) ).
fof(f5537,plain,
( rearsegP(cons(sK71,sK20),nil)
| ~ ssList(sK66(cons(sK71,sK20),nil))
| ~ ssList(nil)
| ~ spl72_34 ),
inference(superposition,[],[f2433,f5263]) ).
fof(f5263,plain,
( cons(sK71,sK20) = app(sK66(cons(sK71,sK20),nil),nil)
| ~ spl72_34 ),
inference(resolution,[],[f3024,f2364]) ).
fof(f5780,plain,
( ~ spl72_33
| spl72_69
| ~ spl72_70 ),
inference(avatar_contradiction_clause,[],[f5779]) ).
fof(f5779,plain,
( $false
| ~ spl72_33
| spl72_69
| ~ spl72_70 ),
inference(subsumption_resolution,[],[f5778,f2359]) ).
fof(f5778,plain,
( ~ ssList(cons(sK71,nil))
| spl72_69
| ~ spl72_70 ),
inference(subsumption_resolution,[],[f5777,f405]) ).
fof(f5777,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK71,nil))
| spl72_69
| ~ spl72_70 ),
inference(subsumption_resolution,[],[f5776,f5763]) ).
fof(f5763,plain,
( rearsegP(cons(sK71,nil),nil)
| ~ spl72_70 ),
inference(avatar_component_clause,[],[f5761]) ).
fof(f5761,plain,
( spl72_70
<=> rearsegP(cons(sK71,nil),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_70])]) ).
fof(f5776,plain,
( ~ rearsegP(cons(sK71,nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK71,nil))
| spl72_69 ),
inference(resolution,[],[f5759,f586]) ).
fof(f5759,plain,
( ~ ssList(sK66(cons(sK71,nil),nil))
| spl72_69 ),
inference(avatar_component_clause,[],[f5757]) ).
fof(f5757,plain,
( spl72_69
<=> ssList(sK66(cons(sK71,nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_69])]) ).
fof(f5772,plain,
( ~ spl72_33
| spl72_70 ),
inference(avatar_contradiction_clause,[],[f5771]) ).
fof(f5771,plain,
( $false
| ~ spl72_33
| spl72_70 ),
inference(subsumption_resolution,[],[f5770,f405]) ).
fof(f5770,plain,
( ~ ssList(nil)
| ~ spl72_33
| spl72_70 ),
inference(subsumption_resolution,[],[f5767,f647]) ).
fof(f5767,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_33
| spl72_70 ),
inference(resolution,[],[f5762,f3207]) ).
fof(f3207,plain,
( ! [X0] :
( rearsegP(cons(sK71,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_33 ),
inference(subsumption_resolution,[],[f3206,f405]) ).
fof(f3206,plain,
( ! [X0] :
( rearsegP(cons(sK71,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_33 ),
inference(subsumption_resolution,[],[f3177,f2359]) ).
fof(f3177,plain,
( ! [X0] :
( rearsegP(cons(sK71,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(cons(sK71,nil))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_33 ),
inference(superposition,[],[f603,f2370]) ).
fof(f2370,plain,
( cons(sK71,nil) = app(cons(sK71,nil),nil)
| ~ spl72_33 ),
inference(resolution,[],[f2359,f467]) ).
fof(f5762,plain,
( ~ rearsegP(cons(sK71,nil),nil)
| spl72_70 ),
inference(avatar_component_clause,[],[f5761]) ).
fof(f5769,plain,
( ~ spl72_33
| spl72_70 ),
inference(avatar_contradiction_clause,[],[f5768]) ).
fof(f5768,plain,
( $false
| ~ spl72_33
| spl72_70 ),
inference(subsumption_resolution,[],[f5766,f2359]) ).
fof(f5766,plain,
( ~ ssList(cons(sK71,nil))
| spl72_70 ),
inference(resolution,[],[f5762,f462]) ).
fof(f5764,plain,
( ~ spl72_69
| spl72_70
| ~ spl72_33 ),
inference(avatar_split_clause,[],[f5521,f2358,f5761,f5757]) ).
fof(f5521,plain,
( rearsegP(cons(sK71,nil),nil)
| ~ ssList(sK66(cons(sK71,nil),nil))
| ~ spl72_33 ),
inference(subsumption_resolution,[],[f5511,f405]) ).
fof(f5511,plain,
( rearsegP(cons(sK71,nil),nil)
| ~ ssList(sK66(cons(sK71,nil),nil))
| ~ ssList(nil)
| ~ spl72_33 ),
inference(superposition,[],[f2433,f5262]) ).
fof(f5262,plain,
( cons(sK71,nil) = app(sK66(cons(sK71,nil),nil),nil)
| ~ spl72_33 ),
inference(resolution,[],[f3024,f2359]) ).
fof(f5730,plain,
( ~ spl72_32
| spl72_67
| ~ spl72_68 ),
inference(avatar_contradiction_clause,[],[f5729]) ).
fof(f5729,plain,
( $false
| ~ spl72_32
| spl72_67
| ~ spl72_68 ),
inference(subsumption_resolution,[],[f5728,f2277]) ).
fof(f5728,plain,
( ~ ssList(cons(sK70,sK20))
| spl72_67
| ~ spl72_68 ),
inference(subsumption_resolution,[],[f5727,f405]) ).
fof(f5727,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK70,sK20))
| spl72_67
| ~ spl72_68 ),
inference(subsumption_resolution,[],[f5726,f5710]) ).
fof(f5710,plain,
( rearsegP(cons(sK70,sK20),nil)
| ~ spl72_68 ),
inference(avatar_component_clause,[],[f5708]) ).
fof(f5708,plain,
( spl72_68
<=> rearsegP(cons(sK70,sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_68])]) ).
fof(f5726,plain,
( ~ rearsegP(cons(sK70,sK20),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK70,sK20))
| spl72_67 ),
inference(resolution,[],[f5706,f586]) ).
fof(f5706,plain,
( ~ ssList(sK66(cons(sK70,sK20),nil))
| spl72_67 ),
inference(avatar_component_clause,[],[f5704]) ).
fof(f5704,plain,
( spl72_67
<=> ssList(sK66(cons(sK70,sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_67])]) ).
fof(f5722,plain,
( ~ spl72_31
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_68 ),
inference(avatar_contradiction_clause,[],[f5721]) ).
fof(f5721,plain,
( $false
| ~ spl72_31
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_68 ),
inference(subsumption_resolution,[],[f5720,f405]) ).
fof(f5720,plain,
( ~ ssList(nil)
| ~ spl72_31
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_68 ),
inference(subsumption_resolution,[],[f5714,f5150]) ).
fof(f5714,plain,
( ~ rearsegP(sK20,nil)
| ~ ssList(nil)
| ~ spl72_31
| spl72_68 ),
inference(resolution,[],[f5709,f3223]) ).
fof(f3223,plain,
( ! [X0] :
( rearsegP(cons(sK70,sK20),X0)
| ~ rearsegP(sK20,X0)
| ~ ssList(X0) )
| ~ spl72_31 ),
inference(subsumption_resolution,[],[f3222,f387]) ).
fof(f3222,plain,
( ! [X0] :
( rearsegP(cons(sK70,sK20),X0)
| ~ rearsegP(sK20,X0)
| ~ ssList(X0)
| ~ ssList(sK20) )
| ~ spl72_31 ),
inference(subsumption_resolution,[],[f3188,f2272]) ).
fof(f3188,plain,
! [X0] :
( rearsegP(cons(sK70,sK20),X0)
| ~ rearsegP(sK20,X0)
| ~ ssList(cons(sK70,nil))
| ~ ssList(X0)
| ~ ssList(sK20) ),
inference(superposition,[],[f603,f2175]) ).
fof(f5709,plain,
( ~ rearsegP(cons(sK70,sK20),nil)
| spl72_68 ),
inference(avatar_component_clause,[],[f5708]) ).
fof(f5719,plain,
( ~ spl72_32
| spl72_68 ),
inference(avatar_contradiction_clause,[],[f5718]) ).
fof(f5718,plain,
( $false
| ~ spl72_32
| spl72_68 ),
inference(subsumption_resolution,[],[f5717,f405]) ).
fof(f5717,plain,
( ~ ssList(nil)
| ~ spl72_32
| spl72_68 ),
inference(subsumption_resolution,[],[f5713,f647]) ).
fof(f5713,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_32
| spl72_68 ),
inference(resolution,[],[f5709,f3205]) ).
fof(f3205,plain,
( ! [X0] :
( rearsegP(cons(sK70,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_32 ),
inference(subsumption_resolution,[],[f3204,f405]) ).
fof(f3204,plain,
( ! [X0] :
( rearsegP(cons(sK70,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_32 ),
inference(subsumption_resolution,[],[f3176,f2277]) ).
fof(f3176,plain,
( ! [X0] :
( rearsegP(cons(sK70,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(cons(sK70,sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_32 ),
inference(superposition,[],[f603,f2313]) ).
fof(f2313,plain,
( cons(sK70,sK20) = app(cons(sK70,sK20),nil)
| ~ spl72_32 ),
inference(resolution,[],[f2277,f467]) ).
fof(f5716,plain,
( ~ spl72_32
| spl72_68 ),
inference(avatar_contradiction_clause,[],[f5715]) ).
fof(f5715,plain,
( $false
| ~ spl72_32
| spl72_68 ),
inference(subsumption_resolution,[],[f5712,f2277]) ).
fof(f5712,plain,
( ~ ssList(cons(sK70,sK20))
| spl72_68 ),
inference(resolution,[],[f5709,f462]) ).
fof(f5711,plain,
( ~ spl72_67
| spl72_68
| ~ spl72_32 ),
inference(avatar_split_clause,[],[f5495,f2275,f5708,f5704]) ).
fof(f5495,plain,
( rearsegP(cons(sK70,sK20),nil)
| ~ ssList(sK66(cons(sK70,sK20),nil))
| ~ spl72_32 ),
inference(subsumption_resolution,[],[f5485,f405]) ).
fof(f5485,plain,
( rearsegP(cons(sK70,sK20),nil)
| ~ ssList(sK66(cons(sK70,sK20),nil))
| ~ ssList(nil)
| ~ spl72_32 ),
inference(superposition,[],[f2433,f5261]) ).
fof(f5261,plain,
( cons(sK70,sK20) = app(sK66(cons(sK70,sK20),nil),nil)
| ~ spl72_32 ),
inference(resolution,[],[f3024,f2277]) ).
fof(f5677,plain,
( ~ spl72_31
| spl72_65
| ~ spl72_66 ),
inference(avatar_contradiction_clause,[],[f5676]) ).
fof(f5676,plain,
( $false
| ~ spl72_31
| spl72_65
| ~ spl72_66 ),
inference(subsumption_resolution,[],[f5675,f2272]) ).
fof(f5675,plain,
( ~ ssList(cons(sK70,nil))
| spl72_65
| ~ spl72_66 ),
inference(subsumption_resolution,[],[f5674,f405]) ).
fof(f5674,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK70,nil))
| spl72_65
| ~ spl72_66 ),
inference(subsumption_resolution,[],[f5673,f5660]) ).
fof(f5660,plain,
( rearsegP(cons(sK70,nil),nil)
| ~ spl72_66 ),
inference(avatar_component_clause,[],[f5658]) ).
fof(f5658,plain,
( spl72_66
<=> rearsegP(cons(sK70,nil),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_66])]) ).
fof(f5673,plain,
( ~ rearsegP(cons(sK70,nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK70,nil))
| spl72_65 ),
inference(resolution,[],[f5656,f586]) ).
fof(f5656,plain,
( ~ ssList(sK66(cons(sK70,nil),nil))
| spl72_65 ),
inference(avatar_component_clause,[],[f5654]) ).
fof(f5654,plain,
( spl72_65
<=> ssList(sK66(cons(sK70,nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_65])]) ).
fof(f5668,plain,
( ~ spl72_31
| spl72_66 ),
inference(avatar_contradiction_clause,[],[f5667]) ).
fof(f5667,plain,
( $false
| ~ spl72_31
| spl72_66 ),
inference(subsumption_resolution,[],[f5666,f405]) ).
fof(f5666,plain,
( ~ ssList(nil)
| ~ spl72_31
| spl72_66 ),
inference(subsumption_resolution,[],[f5663,f647]) ).
fof(f5663,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_31
| spl72_66 ),
inference(resolution,[],[f5659,f3203]) ).
fof(f3203,plain,
( ! [X0] :
( rearsegP(cons(sK70,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_31 ),
inference(subsumption_resolution,[],[f3202,f405]) ).
fof(f3202,plain,
( ! [X0] :
( rearsegP(cons(sK70,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_31 ),
inference(subsumption_resolution,[],[f3175,f2272]) ).
fof(f3175,plain,
( ! [X0] :
( rearsegP(cons(sK70,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(cons(sK70,nil))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_31 ),
inference(superposition,[],[f603,f2283]) ).
fof(f2283,plain,
( cons(sK70,nil) = app(cons(sK70,nil),nil)
| ~ spl72_31 ),
inference(resolution,[],[f2272,f467]) ).
fof(f5659,plain,
( ~ rearsegP(cons(sK70,nil),nil)
| spl72_66 ),
inference(avatar_component_clause,[],[f5658]) ).
fof(f5665,plain,
( ~ spl72_31
| spl72_66 ),
inference(avatar_contradiction_clause,[],[f5664]) ).
fof(f5664,plain,
( $false
| ~ spl72_31
| spl72_66 ),
inference(subsumption_resolution,[],[f5662,f2272]) ).
fof(f5662,plain,
( ~ ssList(cons(sK70,nil))
| spl72_66 ),
inference(resolution,[],[f5659,f462]) ).
fof(f5661,plain,
( ~ spl72_65
| spl72_66
| ~ spl72_31 ),
inference(avatar_split_clause,[],[f5469,f2271,f5658,f5654]) ).
fof(f5469,plain,
( rearsegP(cons(sK70,nil),nil)
| ~ ssList(sK66(cons(sK70,nil),nil))
| ~ spl72_31 ),
inference(subsumption_resolution,[],[f5459,f405]) ).
fof(f5459,plain,
( rearsegP(cons(sK70,nil),nil)
| ~ ssList(sK66(cons(sK70,nil),nil))
| ~ ssList(nil)
| ~ spl72_31 ),
inference(superposition,[],[f2433,f5260]) ).
fof(f5260,plain,
( cons(sK70,nil) = app(sK66(cons(sK70,nil),nil),nil)
| ~ spl72_31 ),
inference(resolution,[],[f3024,f2272]) ).
fof(f5627,plain,
( ~ spl72_30
| spl72_63
| ~ spl72_64 ),
inference(avatar_contradiction_clause,[],[f5626]) ).
fof(f5626,plain,
( $false
| ~ spl72_30
| spl72_63
| ~ spl72_64 ),
inference(subsumption_resolution,[],[f5625,f2190]) ).
fof(f5625,plain,
( ~ ssList(cons(sK24,sK20))
| spl72_63
| ~ spl72_64 ),
inference(subsumption_resolution,[],[f5624,f405]) ).
fof(f5624,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK24,sK20))
| spl72_63
| ~ spl72_64 ),
inference(subsumption_resolution,[],[f5623,f5607]) ).
fof(f5607,plain,
( rearsegP(cons(sK24,sK20),nil)
| ~ spl72_64 ),
inference(avatar_component_clause,[],[f5605]) ).
fof(f5605,plain,
( spl72_64
<=> rearsegP(cons(sK24,sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_64])]) ).
fof(f5623,plain,
( ~ rearsegP(cons(sK24,sK20),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK24,sK20))
| spl72_63 ),
inference(resolution,[],[f5603,f586]) ).
fof(f5603,plain,
( ~ ssList(sK66(cons(sK24,sK20),nil))
| spl72_63 ),
inference(avatar_component_clause,[],[f5601]) ).
fof(f5601,plain,
( spl72_63
<=> ssList(sK66(cons(sK24,sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_63])]) ).
fof(f5619,plain,
( ~ spl72_29
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_64 ),
inference(avatar_contradiction_clause,[],[f5618]) ).
fof(f5618,plain,
( $false
| ~ spl72_29
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_64 ),
inference(subsumption_resolution,[],[f5617,f405]) ).
fof(f5617,plain,
( ~ ssList(nil)
| ~ spl72_29
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_64 ),
inference(subsumption_resolution,[],[f5611,f5150]) ).
fof(f5611,plain,
( ~ rearsegP(sK20,nil)
| ~ ssList(nil)
| ~ spl72_29
| spl72_64 ),
inference(resolution,[],[f5606,f3221]) ).
fof(f3221,plain,
( ! [X0] :
( rearsegP(cons(sK24,sK20),X0)
| ~ rearsegP(sK20,X0)
| ~ ssList(X0) )
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f3220,f387]) ).
fof(f3220,plain,
( ! [X0] :
( rearsegP(cons(sK24,sK20),X0)
| ~ rearsegP(sK20,X0)
| ~ ssList(X0)
| ~ ssList(sK20) )
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f3187,f2185]) ).
fof(f3187,plain,
! [X0] :
( rearsegP(cons(sK24,sK20),X0)
| ~ rearsegP(sK20,X0)
| ~ ssList(cons(sK24,nil))
| ~ ssList(X0)
| ~ ssList(sK20) ),
inference(superposition,[],[f603,f2156]) ).
fof(f5606,plain,
( ~ rearsegP(cons(sK24,sK20),nil)
| spl72_64 ),
inference(avatar_component_clause,[],[f5605]) ).
fof(f5616,plain,
( ~ spl72_30
| spl72_64 ),
inference(avatar_contradiction_clause,[],[f5615]) ).
fof(f5615,plain,
( $false
| ~ spl72_30
| spl72_64 ),
inference(subsumption_resolution,[],[f5614,f405]) ).
fof(f5614,plain,
( ~ ssList(nil)
| ~ spl72_30
| spl72_64 ),
inference(subsumption_resolution,[],[f5610,f647]) ).
fof(f5610,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_30
| spl72_64 ),
inference(resolution,[],[f5606,f3201]) ).
fof(f3201,plain,
( ! [X0] :
( rearsegP(cons(sK24,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_30 ),
inference(subsumption_resolution,[],[f3200,f405]) ).
fof(f3200,plain,
( ! [X0] :
( rearsegP(cons(sK24,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_30 ),
inference(subsumption_resolution,[],[f3174,f2190]) ).
fof(f3174,plain,
( ! [X0] :
( rearsegP(cons(sK24,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(cons(sK24,sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_30 ),
inference(superposition,[],[f603,f2232]) ).
fof(f2232,plain,
( cons(sK24,sK20) = app(cons(sK24,sK20),nil)
| ~ spl72_30 ),
inference(resolution,[],[f2190,f467]) ).
fof(f5613,plain,
( ~ spl72_30
| spl72_64 ),
inference(avatar_contradiction_clause,[],[f5612]) ).
fof(f5612,plain,
( $false
| ~ spl72_30
| spl72_64 ),
inference(subsumption_resolution,[],[f5609,f2190]) ).
fof(f5609,plain,
( ~ ssList(cons(sK24,sK20))
| spl72_64 ),
inference(resolution,[],[f5606,f462]) ).
fof(f5608,plain,
( ~ spl72_63
| spl72_64
| ~ spl72_30 ),
inference(avatar_split_clause,[],[f5443,f2188,f5605,f5601]) ).
fof(f5443,plain,
( rearsegP(cons(sK24,sK20),nil)
| ~ ssList(sK66(cons(sK24,sK20),nil))
| ~ spl72_30 ),
inference(subsumption_resolution,[],[f5433,f405]) ).
fof(f5433,plain,
( rearsegP(cons(sK24,sK20),nil)
| ~ ssList(sK66(cons(sK24,sK20),nil))
| ~ ssList(nil)
| ~ spl72_30 ),
inference(superposition,[],[f2433,f5259]) ).
fof(f5259,plain,
( cons(sK24,sK20) = app(sK66(cons(sK24,sK20),nil),nil)
| ~ spl72_30 ),
inference(resolution,[],[f3024,f2190]) ).
fof(f5574,plain,
( ~ spl72_29
| spl72_61
| ~ spl72_62 ),
inference(avatar_contradiction_clause,[],[f5573]) ).
fof(f5573,plain,
( $false
| ~ spl72_29
| spl72_61
| ~ spl72_62 ),
inference(subsumption_resolution,[],[f5572,f2185]) ).
fof(f5572,plain,
( ~ ssList(cons(sK24,nil))
| spl72_61
| ~ spl72_62 ),
inference(subsumption_resolution,[],[f5571,f405]) ).
fof(f5571,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK24,nil))
| spl72_61
| ~ spl72_62 ),
inference(subsumption_resolution,[],[f5570,f5558]) ).
fof(f5558,plain,
( rearsegP(cons(sK24,nil),nil)
| ~ spl72_62 ),
inference(avatar_component_clause,[],[f5556]) ).
fof(f5556,plain,
( spl72_62
<=> rearsegP(cons(sK24,nil),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_62])]) ).
fof(f5570,plain,
( ~ rearsegP(cons(sK24,nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK24,nil))
| spl72_61 ),
inference(resolution,[],[f5554,f586]) ).
fof(f5554,plain,
( ~ ssList(sK66(cons(sK24,nil),nil))
| spl72_61 ),
inference(avatar_component_clause,[],[f5552]) ).
fof(f5552,plain,
( spl72_61
<=> ssList(sK66(cons(sK24,nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_61])]) ).
fof(f5566,plain,
( ~ spl72_29
| spl72_62 ),
inference(avatar_contradiction_clause,[],[f5565]) ).
fof(f5565,plain,
( $false
| ~ spl72_29
| spl72_62 ),
inference(subsumption_resolution,[],[f5564,f405]) ).
fof(f5564,plain,
( ~ ssList(nil)
| ~ spl72_29
| spl72_62 ),
inference(subsumption_resolution,[],[f5561,f647]) ).
fof(f5561,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_29
| spl72_62 ),
inference(resolution,[],[f5557,f3199]) ).
fof(f3199,plain,
( ! [X0] :
( rearsegP(cons(sK24,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f3198,f405]) ).
fof(f3198,plain,
( ! [X0] :
( rearsegP(cons(sK24,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f3173,f2185]) ).
fof(f3173,plain,
( ! [X0] :
( rearsegP(cons(sK24,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(cons(sK24,nil))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_29 ),
inference(superposition,[],[f603,f2196]) ).
fof(f2196,plain,
( cons(sK24,nil) = app(cons(sK24,nil),nil)
| ~ spl72_29 ),
inference(resolution,[],[f2185,f467]) ).
fof(f5557,plain,
( ~ rearsegP(cons(sK24,nil),nil)
| spl72_62 ),
inference(avatar_component_clause,[],[f5556]) ).
fof(f5563,plain,
( ~ spl72_29
| spl72_62 ),
inference(avatar_contradiction_clause,[],[f5562]) ).
fof(f5562,plain,
( $false
| ~ spl72_29
| spl72_62 ),
inference(subsumption_resolution,[],[f5560,f2185]) ).
fof(f5560,plain,
( ~ ssList(cons(sK24,nil))
| spl72_62 ),
inference(resolution,[],[f5557,f462]) ).
fof(f5559,plain,
( ~ spl72_61
| spl72_62
| ~ spl72_29 ),
inference(avatar_split_clause,[],[f5417,f2184,f5556,f5552]) ).
fof(f5417,plain,
( rearsegP(cons(sK24,nil),nil)
| ~ ssList(sK66(cons(sK24,nil),nil))
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f5407,f405]) ).
fof(f5407,plain,
( rearsegP(cons(sK24,nil),nil)
| ~ ssList(sK66(cons(sK24,nil),nil))
| ~ ssList(nil)
| ~ spl72_29 ),
inference(superposition,[],[f2433,f5258]) ).
fof(f5258,plain,
( cons(sK24,nil) = app(sK66(cons(sK24,nil),nil),nil)
| ~ spl72_29 ),
inference(resolution,[],[f3024,f2185]) ).
fof(f5367,plain,
( ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_59
| ~ spl72_60 ),
inference(avatar_contradiction_clause,[],[f5366]) ).
fof(f5366,plain,
( $false
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_59
| ~ spl72_60 ),
inference(subsumption_resolution,[],[f5365,f1972]) ).
fof(f5365,plain,
( ~ ssList(tl(sK20))
| spl72_59
| ~ spl72_60 ),
inference(subsumption_resolution,[],[f5364,f405]) ).
fof(f5364,plain,
( ~ ssList(nil)
| ~ ssList(tl(sK20))
| spl72_59
| ~ spl72_60 ),
inference(subsumption_resolution,[],[f5363,f5351]) ).
fof(f5351,plain,
( rearsegP(tl(sK20),nil)
| ~ spl72_60 ),
inference(avatar_component_clause,[],[f5349]) ).
fof(f5349,plain,
( spl72_60
<=> rearsegP(tl(sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_60])]) ).
fof(f5363,plain,
( ~ rearsegP(tl(sK20),nil)
| ~ ssList(nil)
| ~ ssList(tl(sK20))
| spl72_59 ),
inference(resolution,[],[f5347,f586]) ).
fof(f5347,plain,
( ~ ssList(sK66(tl(sK20),nil))
| spl72_59 ),
inference(avatar_component_clause,[],[f5345]) ).
fof(f5345,plain,
( spl72_59
<=> ssList(sK66(tl(sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_59])]) ).
fof(f5359,plain,
( ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_60 ),
inference(avatar_contradiction_clause,[],[f5358]) ).
fof(f5358,plain,
( $false
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_60 ),
inference(subsumption_resolution,[],[f5357,f405]) ).
fof(f5357,plain,
( ~ ssList(nil)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_60 ),
inference(subsumption_resolution,[],[f5354,f647]) ).
fof(f5354,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_60 ),
inference(resolution,[],[f5350,f3219]) ).
fof(f3219,plain,
( ! [X0] :
( rearsegP(tl(sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(forward_demodulation,[],[f3218,f1967]) ).
fof(f3218,plain,
( ! [X0] :
( rearsegP(sK25(sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_9 ),
inference(subsumption_resolution,[],[f3217,f405]) ).
fof(f3217,plain,
( ! [X0] :
( rearsegP(sK25(sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_9 ),
inference(subsumption_resolution,[],[f3183,f1545]) ).
fof(f3183,plain,
( ! [X0] :
( rearsegP(sK25(sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(sK25(sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_9 ),
inference(superposition,[],[f603,f1598]) ).
fof(f1598,plain,
( sK25(sK20) = app(sK25(sK20),nil)
| ~ spl72_9 ),
inference(resolution,[],[f1545,f467]) ).
fof(f5350,plain,
( ~ rearsegP(tl(sK20),nil)
| spl72_60 ),
inference(avatar_component_clause,[],[f5349]) ).
fof(f5356,plain,
( ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_60 ),
inference(avatar_contradiction_clause,[],[f5355]) ).
fof(f5355,plain,
( $false
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_60 ),
inference(subsumption_resolution,[],[f5353,f1972]) ).
fof(f5353,plain,
( ~ ssList(tl(sK20))
| spl72_60 ),
inference(resolution,[],[f5350,f462]) ).
fof(f5352,plain,
( ~ spl72_59
| spl72_60
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(avatar_split_clause,[],[f5342,f1642,f1548,f1544,f1510,f5349,f5345]) ).
fof(f5342,plain,
( rearsegP(tl(sK20),nil)
| ~ ssList(sK66(tl(sK20),nil))
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(subsumption_resolution,[],[f5332,f405]) ).
fof(f5332,plain,
( rearsegP(tl(sK20),nil)
| ~ ssList(sK66(tl(sK20),nil))
| ~ ssList(nil)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(superposition,[],[f2433,f5311]) ).
fof(f5311,plain,
( tl(sK20) = app(sK66(tl(sK20),nil),nil)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(forward_demodulation,[],[f5273,f1967]) ).
fof(f5273,plain,
( sK25(sK20) = app(sK66(sK25(sK20),nil),nil)
| ~ spl72_9 ),
inference(resolution,[],[f3024,f1545]) ).
fof(f5197,plain,
( ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_57 ),
inference(avatar_contradiction_clause,[],[f5196]) ).
fof(f5196,plain,
( $false
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_57 ),
inference(subsumption_resolution,[],[f5195,f387]) ).
fof(f5195,plain,
( ~ ssList(sK20)
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_57 ),
inference(subsumption_resolution,[],[f5194,f405]) ).
fof(f5194,plain,
( ~ ssList(nil)
| ~ ssList(sK20)
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56
| spl72_57 ),
inference(subsumption_resolution,[],[f5193,f5150]) ).
fof(f5193,plain,
( ~ rearsegP(sK20,nil)
| ~ ssList(nil)
| ~ ssList(sK20)
| spl72_57 ),
inference(resolution,[],[f5187,f586]) ).
fof(f5187,plain,
( ~ ssList(sK66(sK20,nil))
| spl72_57 ),
inference(avatar_component_clause,[],[f5185]) ).
fof(f5185,plain,
( spl72_57
<=> ssList(sK66(sK20,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_57])]) ).
fof(f5192,plain,
( ~ spl72_57
| spl72_58
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56 ),
inference(avatar_split_clause,[],[f5172,f4982,f4978,f4923,f5189,f5185]) ).
fof(f5189,plain,
( spl72_58
<=> sK20 = sK66(sK20,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_58])]) ).
fof(f5172,plain,
( sK20 = sK66(sK20,nil)
| ~ ssList(sK66(sK20,nil))
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56 ),
inference(trivial_inequality_removal,[],[f5157]) ).
fof(f5157,plain,
( sK20 != sK20
| sK20 = sK66(sK20,nil)
| ~ ssList(sK66(sK20,nil))
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56 ),
inference(superposition,[],[f4104,f5155]) ).
fof(f5155,plain,
( sK20 = app(sK66(sK20,nil),nil)
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56 ),
inference(subsumption_resolution,[],[f5154,f387]) ).
fof(f5154,plain,
( sK20 = app(sK66(sK20,nil),nil)
| ~ ssList(sK20)
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56 ),
inference(subsumption_resolution,[],[f5152,f405]) ).
fof(f5152,plain,
( sK20 = app(sK66(sK20,nil),nil)
| ~ ssList(nil)
| ~ ssList(sK20)
| ~ spl72_53
| ~ spl72_55
| ~ spl72_56 ),
inference(resolution,[],[f5150,f587]) ).
fof(f4104,plain,
! [X0] :
( app(X0,nil) != sK20
| sK20 = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4103,f405]) ).
fof(f4103,plain,
! [X0] :
( app(X0,nil) != sK20
| sK20 = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4019,f387]) ).
fof(f4019,plain,
! [X0] :
( app(X0,nil) != sK20
| sK20 = X0
| ~ ssList(sK20)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[],[f605,f667]) ).
fof(f4990,plain,
( ~ spl72_53
| spl72_55 ),
inference(avatar_contradiction_clause,[],[f4989]) ).
fof(f4989,plain,
( $false
| ~ spl72_53
| spl72_55 ),
inference(subsumption_resolution,[],[f4988,f387]) ).
fof(f4988,plain,
( ~ ssList(sK20)
| ~ spl72_53
| spl72_55 ),
inference(subsumption_resolution,[],[f4987,f4925]) ).
fof(f4987,plain,
( ~ frontsegP(sK20,sK20)
| ~ ssList(sK20)
| spl72_55 ),
inference(duplicate_literal_removal,[],[f4986]) ).
fof(f4986,plain,
( ~ frontsegP(sK20,sK20)
| ~ ssList(sK20)
| ~ ssList(sK20)
| spl72_55 ),
inference(resolution,[],[f4980,f593]) ).
fof(f4980,plain,
( ~ ssList(sK69(sK20,sK20))
| spl72_55 ),
inference(avatar_component_clause,[],[f4978]) ).
fof(f4985,plain,
( ~ spl72_55
| spl72_56
| ~ spl72_53 ),
inference(avatar_split_clause,[],[f4969,f4923,f4982,f4978]) ).
fof(f4969,plain,
( nil = sK69(sK20,sK20)
| ~ ssList(sK69(sK20,sK20))
| ~ spl72_53 ),
inference(trivial_inequality_removal,[],[f4954]) ).
fof(f4954,plain,
( sK20 != sK20
| nil = sK69(sK20,sK20)
| ~ ssList(sK69(sK20,sK20))
| ~ spl72_53 ),
inference(superposition,[],[f4378,f4941]) ).
fof(f4378,plain,
! [X0] :
( sK20 != app(sK20,X0)
| nil = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4377,f387]) ).
fof(f4377,plain,
! [X0] :
( sK20 != app(sK20,X0)
| nil = X0
| ~ ssList(sK20)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4293,f405]) ).
fof(f4293,plain,
! [X0] :
( sK20 != app(sK20,X0)
| nil = X0
| ~ ssList(nil)
| ~ ssList(sK20)
| ~ ssList(X0) ),
inference(superposition,[],[f606,f667]) ).
fof(f606,plain,
! [X2,X0,X1] :
( app(X1,X2) != app(X1,X0)
| X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f215]) ).
fof(f215,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f214]) ).
fof(f214,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f80]) ).
fof(f80,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( app(X1,X2) = app(X1,X0)
=> X0 = X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax80) ).
fof(f4946,plain,
( ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_54 ),
inference(avatar_contradiction_clause,[],[f4945]) ).
fof(f4945,plain,
( $false
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_54 ),
inference(subsumption_resolution,[],[f4943,f1972]) ).
fof(f4943,plain,
( ~ ssList(tl(sK20))
| spl72_54 ),
inference(resolution,[],[f4929,f463]) ).
fof(f4929,plain,
( ~ frontsegP(tl(sK20),tl(sK20))
| spl72_54 ),
inference(avatar_component_clause,[],[f4927]) ).
fof(f4927,plain,
( spl72_54
<=> frontsegP(tl(sK20),tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_54])]) ).
fof(f4934,plain,
spl72_53,
inference(avatar_contradiction_clause,[],[f4933]) ).
fof(f4933,plain,
( $false
| spl72_53 ),
inference(subsumption_resolution,[],[f4932,f387]) ).
fof(f4932,plain,
( ~ ssList(sK20)
| spl72_53 ),
inference(resolution,[],[f4924,f463]) ).
fof(f4924,plain,
( ~ frontsegP(sK20,sK20)
| spl72_53 ),
inference(avatar_component_clause,[],[f4923]) ).
fof(f4930,plain,
( spl72_53
| ~ spl72_54
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(avatar_split_clause,[],[f4920,f1642,f1548,f1544,f1510,f4927,f4923]) ).
fof(f4920,plain,
( ~ frontsegP(tl(sK20),tl(sK20))
| frontsegP(sK20,sK20)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(forward_demodulation,[],[f4919,f1967]) ).
fof(f4919,plain,
( frontsegP(sK20,sK20)
| ~ frontsegP(tl(sK20),sK25(sK20))
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(subsumption_resolution,[],[f4914,f1545]) ).
fof(f4914,plain,
( frontsegP(sK20,sK20)
| ~ frontsegP(tl(sK20),sK25(sK20))
| ~ ssList(sK25(sK20))
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(superposition,[],[f4551,f1616]) ).
fof(f4679,plain,
spl72_51,
inference(avatar_contradiction_clause,[],[f4678]) ).
fof(f4678,plain,
( $false
| spl72_51 ),
inference(subsumption_resolution,[],[f4677,f405]) ).
fof(f4677,plain,
( ~ ssList(nil)
| spl72_51 ),
inference(subsumption_resolution,[],[f4676,f648]) ).
fof(f4676,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| spl72_51 ),
inference(duplicate_literal_removal,[],[f4675]) ).
fof(f4675,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| spl72_51 ),
inference(resolution,[],[f4669,f593]) ).
fof(f4669,plain,
( ~ ssList(sK69(nil,nil))
| spl72_51 ),
inference(avatar_component_clause,[],[f4667]) ).
fof(f4667,plain,
( spl72_51
<=> ssList(sK69(nil,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_51])]) ).
fof(f4674,plain,
( ~ spl72_51
| spl72_52
| ~ spl72_2 ),
inference(avatar_split_clause,[],[f4665,f838,f4671,f4667]) ).
fof(f4671,plain,
( spl72_52
<=> nil = sK69(nil,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_52])]) ).
fof(f4665,plain,
( nil = sK69(nil,nil)
| ~ ssList(sK69(nil,nil))
| ~ spl72_2 ),
inference(trivial_inequality_removal,[],[f4663]) ).
fof(f4663,plain,
( nil != nil
| nil = sK69(nil,nil)
| ~ ssList(sK69(nil,nil))
| ~ spl72_2 ),
inference(superposition,[],[f4381,f3115]) ).
fof(f3115,plain,
nil = app(nil,sK69(nil,nil)),
inference(subsumption_resolution,[],[f3103,f405]) ).
fof(f3103,plain,
( nil = app(nil,sK69(nil,nil))
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f3102]) ).
fof(f3102,plain,
( nil = app(nil,sK69(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[],[f594,f648]) ).
fof(f4381,plain,
( ! [X0] :
( nil != app(nil,X0)
| nil = X0
| ~ ssList(X0) )
| ~ spl72_2 ),
inference(forward_demodulation,[],[f4380,f840]) ).
fof(f4380,plain,
! [X0] :
( sK21 != app(sK21,X0)
| nil = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4379,f388]) ).
fof(f4379,plain,
! [X0] :
( sK21 != app(sK21,X0)
| nil = X0
| ~ ssList(sK21)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4294,f405]) ).
fof(f4294,plain,
! [X0] :
( sK21 != app(sK21,X0)
| nil = X0
| ~ ssList(nil)
| ~ ssList(sK21)
| ~ ssList(X0) ),
inference(superposition,[],[f606,f668]) ).
fof(f4585,plain,
( ~ spl72_43
| ~ spl72_44
| spl72_49 ),
inference(avatar_contradiction_clause,[],[f4584]) ).
fof(f4584,plain,
( $false
| ~ spl72_43
| ~ spl72_44
| spl72_49 ),
inference(subsumption_resolution,[],[f4583,f387]) ).
fof(f4583,plain,
( ~ ssList(sK20)
| ~ spl72_43
| ~ spl72_44
| spl72_49 ),
inference(subsumption_resolution,[],[f4582,f405]) ).
fof(f4582,plain,
( ~ ssList(nil)
| ~ ssList(sK20)
| ~ spl72_43
| ~ spl72_44
| spl72_49 ),
inference(subsumption_resolution,[],[f4581,f4492]) ).
fof(f4581,plain,
( ~ frontsegP(sK20,nil)
| ~ ssList(nil)
| ~ ssList(sK20)
| spl72_49 ),
inference(resolution,[],[f4575,f593]) ).
fof(f4575,plain,
( ~ ssList(sK69(sK20,nil))
| spl72_49 ),
inference(avatar_component_clause,[],[f4573]) ).
fof(f4573,plain,
( spl72_49
<=> ssList(sK69(sK20,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_49])]) ).
fof(f4580,plain,
( ~ spl72_49
| spl72_50
| ~ spl72_43
| ~ spl72_44 ),
inference(avatar_split_clause,[],[f4530,f3776,f3772,f4577,f4573]) ).
fof(f4577,plain,
( spl72_50
<=> rearsegP(sK20,sK69(sK20,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_50])]) ).
fof(f4530,plain,
( rearsegP(sK20,sK69(sK20,nil))
| ~ ssList(sK69(sK20,nil))
| ~ spl72_43
| ~ spl72_44 ),
inference(subsumption_resolution,[],[f4522,f405]) ).
fof(f4522,plain,
( rearsegP(sK20,sK69(sK20,nil))
| ~ ssList(nil)
| ~ ssList(sK69(sK20,nil))
| ~ spl72_43
| ~ spl72_44 ),
inference(superposition,[],[f2433,f4496]) ).
fof(f4496,plain,
( sK20 = app(nil,sK69(sK20,nil))
| ~ spl72_43
| ~ spl72_44 ),
inference(superposition,[],[f3810,f4489]) ).
fof(f3810,plain,
( sK20 = app(sK66(sK20,sK20),sK69(sK20,sK66(sK20,sK20)))
| ~ spl72_43
| ~ spl72_44 ),
inference(subsumption_resolution,[],[f3809,f387]) ).
fof(f3809,plain,
( sK20 = app(sK66(sK20,sK20),sK69(sK20,sK66(sK20,sK20)))
| ~ ssList(sK20)
| ~ spl72_43
| ~ spl72_44 ),
inference(subsumption_resolution,[],[f3805,f3773]) ).
fof(f3805,plain,
( sK20 = app(sK66(sK20,sK20),sK69(sK20,sK66(sK20,sK20)))
| ~ ssList(sK66(sK20,sK20))
| ~ ssList(sK20)
| ~ spl72_44 ),
inference(resolution,[],[f3778,f594]) ).
fof(f4245,plain,
spl72_47,
inference(avatar_contradiction_clause,[],[f4244]) ).
fof(f4244,plain,
( $false
| spl72_47 ),
inference(subsumption_resolution,[],[f4243,f405]) ).
fof(f4243,plain,
( ~ ssList(nil)
| spl72_47 ),
inference(subsumption_resolution,[],[f4242,f647]) ).
fof(f4242,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| spl72_47 ),
inference(duplicate_literal_removal,[],[f4241]) ).
fof(f4241,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| spl72_47 ),
inference(resolution,[],[f4235,f586]) ).
fof(f4235,plain,
( ~ ssList(sK66(nil,nil))
| spl72_47 ),
inference(avatar_component_clause,[],[f4233]) ).
fof(f4233,plain,
( spl72_47
<=> ssList(sK66(nil,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_47])]) ).
fof(f4240,plain,
( ~ spl72_47
| spl72_48
| ~ spl72_2 ),
inference(avatar_split_clause,[],[f4231,f838,f4237,f4233]) ).
fof(f4237,plain,
( spl72_48
<=> nil = sK66(nil,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_48])]) ).
fof(f4231,plain,
( nil = sK66(nil,nil)
| ~ ssList(sK66(nil,nil))
| ~ spl72_2 ),
inference(trivial_inequality_removal,[],[f4229]) ).
fof(f4229,plain,
( nil != nil
| nil = sK66(nil,nil)
| ~ ssList(sK66(nil,nil))
| ~ spl72_2 ),
inference(superposition,[],[f4108,f3023]) ).
fof(f3023,plain,
nil = app(sK66(nil,nil),nil),
inference(subsumption_resolution,[],[f3019,f405]) ).
fof(f3019,plain,
( nil = app(sK66(nil,nil),nil)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f3013]) ).
fof(f3013,plain,
( nil = app(sK66(nil,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[],[f587,f647]) ).
fof(f4108,plain,
( ! [X0] :
( nil != app(X0,nil)
| nil = X0
| ~ ssList(X0) )
| ~ spl72_2 ),
inference(forward_demodulation,[],[f4107,f840]) ).
fof(f4107,plain,
( ! [X0] :
( nil != app(X0,nil)
| sK21 = X0
| ~ ssList(X0) )
| ~ spl72_2 ),
inference(forward_demodulation,[],[f4106,f840]) ).
fof(f4106,plain,
! [X0] :
( app(X0,nil) != sK21
| sK21 = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4105,f405]) ).
fof(f4105,plain,
! [X0] :
( app(X0,nil) != sK21
| sK21 = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4020,f388]) ).
fof(f4020,plain,
! [X0] :
( app(X0,nil) != sK21
| sK21 = X0
| ~ ssList(sK21)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[],[f605,f668]) ).
fof(f3954,plain,
( ~ spl72_45
| spl72_46
| ~ spl72_43
| ~ spl72_44 ),
inference(avatar_split_clause,[],[f3812,f3776,f3772,f3951,f3947]) ).
fof(f3947,plain,
( spl72_45
<=> frontsegP(sK66(sK20,sK20),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_45])]) ).
fof(f3951,plain,
( spl72_46
<=> sK20 = sK66(sK20,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_46])]) ).
fof(f3812,plain,
( sK20 = sK66(sK20,sK20)
| ~ frontsegP(sK66(sK20,sK20),sK20)
| ~ spl72_43
| ~ spl72_44 ),
inference(subsumption_resolution,[],[f3811,f3773]) ).
fof(f3811,plain,
( sK20 = sK66(sK20,sK20)
| ~ frontsegP(sK66(sK20,sK20),sK20)
| ~ ssList(sK66(sK20,sK20))
| ~ spl72_44 ),
inference(subsumption_resolution,[],[f3806,f387]) ).
fof(f3806,plain,
( sK20 = sK66(sK20,sK20)
| ~ frontsegP(sK66(sK20,sK20),sK20)
| ~ ssList(sK20)
| ~ ssList(sK66(sK20,sK20))
| ~ spl72_44 ),
inference(resolution,[],[f3778,f583]) ).
fof(f3786,plain,
spl72_43,
inference(avatar_contradiction_clause,[],[f3785]) ).
fof(f3785,plain,
( $false
| spl72_43 ),
inference(subsumption_resolution,[],[f3784,f387]) ).
fof(f3784,plain,
( ~ ssList(sK20)
| spl72_43 ),
inference(resolution,[],[f3782,f466]) ).
fof(f3782,plain,
( ~ rearsegP(sK20,sK20)
| spl72_43 ),
inference(subsumption_resolution,[],[f3781,f387]) ).
fof(f3781,plain,
( ~ rearsegP(sK20,sK20)
| ~ ssList(sK20)
| spl72_43 ),
inference(duplicate_literal_removal,[],[f3780]) ).
fof(f3780,plain,
( ~ rearsegP(sK20,sK20)
| ~ ssList(sK20)
| ~ ssList(sK20)
| spl72_43 ),
inference(resolution,[],[f3774,f586]) ).
fof(f3774,plain,
( ~ ssList(sK66(sK20,sK20))
| spl72_43 ),
inference(avatar_component_clause,[],[f3772]) ).
fof(f3779,plain,
( ~ spl72_43
| spl72_44 ),
inference(avatar_split_clause,[],[f3725,f3776,f3772]) ).
fof(f3725,plain,
( frontsegP(sK20,sK66(sK20,sK20))
| ~ ssList(sK66(sK20,sK20)) ),
inference(subsumption_resolution,[],[f3722,f387]) ).
fof(f3722,plain,
( frontsegP(sK20,sK66(sK20,sK20))
| ~ ssList(sK20)
| ~ ssList(sK66(sK20,sK20)) ),
inference(superposition,[],[f2500,f3676]) ).
fof(f3161,plain,
( spl72_27
| ~ spl72_41 ),
inference(avatar_contradiction_clause,[],[f3160]) ).
fof(f3160,plain,
( $false
| spl72_27
| ~ spl72_41 ),
inference(subsumption_resolution,[],[f3153,f620]) ).
fof(f3153,plain,
( ~ sP3(nil,sK24)
| spl72_27
| ~ spl72_41 ),
inference(superposition,[],[f2112,f3135]) ).
fof(f3135,plain,
( nil = tl(sK20)
| ~ spl72_41 ),
inference(avatar_component_clause,[],[f3133]) ).
fof(f3133,plain,
( spl72_41
<=> nil = tl(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_41])]) ).
fof(f2112,plain,
( ~ sP3(tl(sK20),sK24)
| spl72_27 ),
inference(avatar_component_clause,[],[f2110]) ).
fof(f2110,plain,
( spl72_27
<=> sP3(tl(sK20),sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_27])]) ).
fof(f3159,plain,
( spl72_25
| ~ spl72_41 ),
inference(avatar_contradiction_clause,[],[f3158]) ).
fof(f3158,plain,
( $false
| spl72_25
| ~ spl72_41 ),
inference(subsumption_resolution,[],[f3151,f618]) ).
fof(f3151,plain,
( ~ sP1(nil,sK24)
| spl72_25
| ~ spl72_41 ),
inference(superposition,[],[f2096,f3135]) ).
fof(f2096,plain,
( ~ sP1(tl(sK20),sK24)
| spl72_25 ),
inference(avatar_component_clause,[],[f2094]) ).
fof(f2094,plain,
( spl72_25
<=> sP1(tl(sK20),sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_25])]) ).
fof(f3140,plain,
( spl72_41
| spl72_42
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(avatar_split_clause,[],[f3129,f1642,f1548,f1544,f1510,f3137,f3133]) ).
fof(f3137,plain,
( spl72_42
<=> hd(tl(sK20)) = sK27(tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_42])]) ).
fof(f3129,plain,
( hd(tl(sK20)) = sK27(tl(sK20))
| nil = tl(sK20)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(forward_demodulation,[],[f3128,f1967]) ).
fof(f3128,plain,
( nil = tl(sK20)
| hd(sK25(sK20)) = sK27(sK25(sK20))
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11 ),
inference(forward_demodulation,[],[f1602,f1967]) ).
fof(f1602,plain,
( nil = sK25(sK20)
| hd(sK25(sK20)) = sK27(sK25(sK20))
| ~ spl72_9 ),
inference(resolution,[],[f1545,f476]) ).
fof(f3069,plain,
( ~ spl72_39
| spl72_40
| ~ spl72_33
| ~ spl72_34 ),
inference(avatar_split_clause,[],[f2485,f2362,f2358,f3066,f3062]) ).
fof(f3062,plain,
( spl72_39
<=> rearsegP(sK20,cons(sK71,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_39])]) ).
fof(f3066,plain,
( spl72_40
<=> sK20 = cons(sK71,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_40])]) ).
fof(f2485,plain,
( sK20 = cons(sK71,sK20)
| ~ rearsegP(sK20,cons(sK71,sK20))
| ~ spl72_33
| ~ spl72_34 ),
inference(subsumption_resolution,[],[f2484,f387]) ).
fof(f2484,plain,
( sK20 = cons(sK71,sK20)
| ~ rearsegP(sK20,cons(sK71,sK20))
| ~ ssList(sK20)
| ~ spl72_33
| ~ spl72_34 ),
inference(subsumption_resolution,[],[f2483,f2364]) ).
fof(f2483,plain,
( sK20 = cons(sK71,sK20)
| ~ rearsegP(sK20,cons(sK71,sK20))
| ~ ssList(cons(sK71,sK20))
| ~ ssList(sK20)
| ~ spl72_33 ),
inference(resolution,[],[f2476,f581]) ).
fof(f2476,plain,
( rearsegP(cons(sK71,sK20),sK20)
| ~ spl72_33 ),
inference(subsumption_resolution,[],[f2475,f387]) ).
fof(f2475,plain,
( rearsegP(cons(sK71,sK20),sK20)
| ~ ssList(sK20)
| ~ spl72_33 ),
inference(subsumption_resolution,[],[f2465,f2359]) ).
fof(f2465,plain,
( rearsegP(cons(sK71,sK20),sK20)
| ~ ssList(cons(sK71,nil))
| ~ ssList(sK20) ),
inference(superposition,[],[f2433,f2176]) ).
fof(f3060,plain,
( ~ spl72_37
| spl72_38
| ~ spl72_31
| ~ spl72_32 ),
inference(avatar_split_clause,[],[f2482,f2275,f2271,f3057,f3053]) ).
fof(f3053,plain,
( spl72_37
<=> rearsegP(sK20,cons(sK70,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_37])]) ).
fof(f3057,plain,
( spl72_38
<=> sK20 = cons(sK70,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_38])]) ).
fof(f2482,plain,
( sK20 = cons(sK70,sK20)
| ~ rearsegP(sK20,cons(sK70,sK20))
| ~ spl72_31
| ~ spl72_32 ),
inference(subsumption_resolution,[],[f2481,f387]) ).
fof(f2481,plain,
( sK20 = cons(sK70,sK20)
| ~ rearsegP(sK20,cons(sK70,sK20))
| ~ ssList(sK20)
| ~ spl72_31
| ~ spl72_32 ),
inference(subsumption_resolution,[],[f2480,f2277]) ).
fof(f2480,plain,
( sK20 = cons(sK70,sK20)
| ~ rearsegP(sK20,cons(sK70,sK20))
| ~ ssList(cons(sK70,sK20))
| ~ ssList(sK20)
| ~ spl72_31 ),
inference(resolution,[],[f2474,f581]) ).
fof(f2474,plain,
( rearsegP(cons(sK70,sK20),sK20)
| ~ spl72_31 ),
inference(subsumption_resolution,[],[f2473,f387]) ).
fof(f2473,plain,
( rearsegP(cons(sK70,sK20),sK20)
| ~ ssList(sK20)
| ~ spl72_31 ),
inference(subsumption_resolution,[],[f2464,f2272]) ).
fof(f2464,plain,
( rearsegP(cons(sK70,sK20),sK20)
| ~ ssList(cons(sK70,nil))
| ~ ssList(sK20) ),
inference(superposition,[],[f2433,f2175]) ).
fof(f3051,plain,
( ~ spl72_35
| spl72_36
| ~ spl72_29
| ~ spl72_30 ),
inference(avatar_split_clause,[],[f2479,f2188,f2184,f3048,f3044]) ).
fof(f3044,plain,
( spl72_35
<=> rearsegP(sK20,cons(sK24,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_35])]) ).
fof(f3048,plain,
( spl72_36
<=> sK20 = cons(sK24,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_36])]) ).
fof(f2479,plain,
( sK20 = cons(sK24,sK20)
| ~ rearsegP(sK20,cons(sK24,sK20))
| ~ spl72_29
| ~ spl72_30 ),
inference(subsumption_resolution,[],[f2478,f387]) ).
fof(f2478,plain,
( sK20 = cons(sK24,sK20)
| ~ rearsegP(sK20,cons(sK24,sK20))
| ~ ssList(sK20)
| ~ spl72_29
| ~ spl72_30 ),
inference(subsumption_resolution,[],[f2477,f2190]) ).
fof(f2477,plain,
( sK20 = cons(sK24,sK20)
| ~ rearsegP(sK20,cons(sK24,sK20))
| ~ ssList(cons(sK24,sK20))
| ~ ssList(sK20)
| ~ spl72_29 ),
inference(resolution,[],[f2472,f581]) ).
fof(f2472,plain,
( rearsegP(cons(sK24,sK20),sK20)
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f2471,f387]) ).
fof(f2471,plain,
( rearsegP(cons(sK24,sK20),sK20)
| ~ ssList(sK20)
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f2463,f2185]) ).
fof(f2463,plain,
( rearsegP(cons(sK24,sK20),sK20)
| ~ ssList(cons(sK24,nil))
| ~ ssList(sK20) ),
inference(superposition,[],[f2433,f2156]) ).
fof(f2369,plain,
spl72_33,
inference(avatar_contradiction_clause,[],[f2368]) ).
fof(f2368,plain,
( $false
| spl72_33 ),
inference(subsumption_resolution,[],[f2367,f405]) ).
fof(f2367,plain,
( ~ ssList(nil)
| spl72_33 ),
inference(subsumption_resolution,[],[f2366,f612]) ).
fof(f2366,plain,
( ~ ssItem(sK71)
| ~ ssList(nil)
| spl72_33 ),
inference(resolution,[],[f2360,f567]) ).
fof(f567,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ! [X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> ssList(cons(X1,X0)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax16) ).
fof(f2360,plain,
( ~ ssList(cons(sK71,nil))
| spl72_33 ),
inference(avatar_component_clause,[],[f2358]) ).
fof(f2365,plain,
( ~ spl72_33
| spl72_34 ),
inference(avatar_split_clause,[],[f2356,f2362,f2358]) ).
fof(f2356,plain,
( ssList(cons(sK71,sK20))
| ~ ssList(cons(sK71,nil)) ),
inference(subsumption_resolution,[],[f2355,f387]) ).
fof(f2355,plain,
( ssList(cons(sK71,sK20))
| ~ ssList(sK20)
| ~ ssList(cons(sK71,nil)) ),
inference(superposition,[],[f577,f2176]) ).
fof(f2282,plain,
spl72_31,
inference(avatar_contradiction_clause,[],[f2281]) ).
fof(f2281,plain,
( $false
| spl72_31 ),
inference(subsumption_resolution,[],[f2280,f405]) ).
fof(f2280,plain,
( ~ ssList(nil)
| spl72_31 ),
inference(subsumption_resolution,[],[f2279,f611]) ).
fof(f2279,plain,
( ~ ssItem(sK70)
| ~ ssList(nil)
| spl72_31 ),
inference(resolution,[],[f2273,f567]) ).
fof(f2273,plain,
( ~ ssList(cons(sK70,nil))
| spl72_31 ),
inference(avatar_component_clause,[],[f2271]) ).
fof(f2278,plain,
( ~ spl72_31
| spl72_32 ),
inference(avatar_split_clause,[],[f2269,f2275,f2271]) ).
fof(f2269,plain,
( ssList(cons(sK70,sK20))
| ~ ssList(cons(sK70,nil)) ),
inference(subsumption_resolution,[],[f2268,f387]) ).
fof(f2268,plain,
( ssList(cons(sK70,sK20))
| ~ ssList(sK20)
| ~ ssList(cons(sK70,nil)) ),
inference(superposition,[],[f577,f2175]) ).
fof(f2195,plain,
spl72_29,
inference(avatar_contradiction_clause,[],[f2194]) ).
fof(f2194,plain,
( $false
| spl72_29 ),
inference(subsumption_resolution,[],[f2193,f405]) ).
fof(f2193,plain,
( ~ ssList(nil)
| spl72_29 ),
inference(subsumption_resolution,[],[f2192,f395]) ).
fof(f2192,plain,
( ~ ssItem(sK24)
| ~ ssList(nil)
| spl72_29 ),
inference(resolution,[],[f2186,f567]) ).
fof(f2186,plain,
( ~ ssList(cons(sK24,nil))
| spl72_29 ),
inference(avatar_component_clause,[],[f2184]) ).
fof(f2191,plain,
( ~ spl72_29
| spl72_30 ),
inference(avatar_split_clause,[],[f2182,f2188,f2184]) ).
fof(f2182,plain,
( ssList(cons(sK24,sK20))
| ~ ssList(cons(sK24,nil)) ),
inference(subsumption_resolution,[],[f2181,f387]) ).
fof(f2181,plain,
( ssList(cons(sK24,sK20))
| ~ ssList(sK20)
| ~ ssList(cons(sK24,nil)) ),
inference(superposition,[],[f577,f2156]) ).
fof(f2121,plain,
( ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_28 ),
inference(avatar_contradiction_clause,[],[f2120]) ).
fof(f2120,plain,
( $false
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_28 ),
inference(subsumption_resolution,[],[f2119,f395]) ).
fof(f2119,plain,
( ~ ssItem(sK24)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_28 ),
inference(subsumption_resolution,[],[f2118,f1972]) ).
fof(f2118,plain,
( ~ ssList(tl(sK20))
| ~ ssItem(sK24)
| spl72_28 ),
inference(resolution,[],[f2116,f457]) ).
fof(f2116,plain,
( ~ sP4(sK24,tl(sK20))
| spl72_28 ),
inference(avatar_component_clause,[],[f2114]) ).
fof(f2114,plain,
( spl72_28
<=> sP4(sK24,tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_28])]) ).
fof(f2117,plain,
( ~ spl72_27
| ~ spl72_28
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_13 ),
inference(avatar_split_clause,[],[f2108,f1760,f1642,f1548,f1544,f1510,f2114,f2110]) ).
fof(f1760,plain,
( spl72_13
<=> strictorderedP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_13])]) ).
fof(f2108,plain,
( ~ sP4(sK24,tl(sK20))
| ~ sP3(tl(sK20),sK24)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_13 ),
inference(forward_demodulation,[],[f2107,f1967]) ).
fof(f2107,plain,
( ~ sP3(tl(sK20),sK24)
| ~ sP4(sK24,sK25(sK20))
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_13 ),
inference(forward_demodulation,[],[f2106,f1967]) ).
fof(f2106,plain,
( ~ sP3(sK25(sK20),sK24)
| ~ sP4(sK24,sK25(sK20))
| ~ spl72_7
| ~ spl72_10
| spl72_13 ),
inference(subsumption_resolution,[],[f1626,f1762]) ).
fof(f1762,plain,
( ~ strictorderedP(sK20)
| spl72_13 ),
inference(avatar_component_clause,[],[f1760]) ).
fof(f1626,plain,
( strictorderedP(sK20)
| ~ sP3(sK25(sK20),sK24)
| ~ sP4(sK24,sK25(sK20))
| ~ spl72_7
| ~ spl72_10 ),
inference(superposition,[],[f451,f1616]) ).
fof(f2105,plain,
( ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_26 ),
inference(avatar_contradiction_clause,[],[f2104]) ).
fof(f2104,plain,
( $false
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_26 ),
inference(subsumption_resolution,[],[f2103,f395]) ).
fof(f2103,plain,
( ~ ssItem(sK24)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_26 ),
inference(subsumption_resolution,[],[f2102,f1972]) ).
fof(f2102,plain,
( ~ ssList(tl(sK20))
| ~ ssItem(sK24)
| spl72_26 ),
inference(resolution,[],[f2100,f449]) ).
fof(f2100,plain,
( ~ sP2(sK24,tl(sK20))
| spl72_26 ),
inference(avatar_component_clause,[],[f2098]) ).
fof(f2098,plain,
( spl72_26
<=> sP2(sK24,tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_26])]) ).
fof(f2101,plain,
( ~ spl72_25
| ~ spl72_26
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_15 ),
inference(avatar_split_clause,[],[f2092,f1788,f1642,f1548,f1544,f1510,f2098,f2094]) ).
fof(f1788,plain,
( spl72_15
<=> totalorderedP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_15])]) ).
fof(f2092,plain,
( ~ sP2(sK24,tl(sK20))
| ~ sP1(tl(sK20),sK24)
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_15 ),
inference(forward_demodulation,[],[f2091,f1967]) ).
fof(f2091,plain,
( ~ sP1(tl(sK20),sK24)
| ~ sP2(sK24,sK25(sK20))
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10
| ~ spl72_11
| spl72_15 ),
inference(forward_demodulation,[],[f2090,f1967]) ).
fof(f2090,plain,
( ~ sP1(sK25(sK20),sK24)
| ~ sP2(sK24,sK25(sK20))
| ~ spl72_7
| ~ spl72_10
| spl72_15 ),
inference(subsumption_resolution,[],[f1624,f1790]) ).
fof(f1790,plain,
( ~ totalorderedP(sK20)
| spl72_15 ),
inference(avatar_component_clause,[],[f1788]) ).
fof(f1624,plain,
( totalorderedP(sK20)
| ~ sP1(sK25(sK20),sK24)
| ~ sP2(sK24,sK25(sK20))
| ~ spl72_7
| ~ spl72_10 ),
inference(superposition,[],[f443,f1616]) ).
fof(f1941,plain,
( spl72_23
| ~ spl72_24
| ~ spl72_2 ),
inference(avatar_split_clause,[],[f1438,f838,f1938,f1934]) ).
fof(f1934,plain,
( spl72_23
<=> nil = cons(sK71,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_23])]) ).
fof(f1938,plain,
( spl72_24
<=> sP3(cons(sK71,nil),sK71) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_24])]) ).
fof(f1438,plain,
( ~ sP3(cons(sK71,nil),sK71)
| nil = cons(sK71,nil)
| ~ spl72_2 ),
inference(subsumption_resolution,[],[f1437,f612]) ).
fof(f1437,plain,
( ~ ssItem(sK71)
| ~ sP3(cons(sK71,nil),sK71)
| nil = cons(sK71,nil)
| ~ spl72_2 ),
inference(forward_demodulation,[],[f1426,f1053]) ).
fof(f1053,plain,
( sK71 = hd(cons(sK71,nil))
| ~ spl72_2 ),
inference(resolution,[],[f997,f612]) ).
fof(f997,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,nil)) = X0 )
| ~ spl72_2 ),
inference(forward_demodulation,[],[f972,f840]) ).
fof(f972,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK21)) = X0 ),
inference(resolution,[],[f571,f388]) ).
fof(f1426,plain,
( ~ sP3(cons(sK71,nil),sK71)
| nil = cons(sK71,nil)
| ~ ssItem(hd(cons(sK71,nil)))
| ~ spl72_2 ),
inference(superposition,[],[f792,f1053]) ).
fof(f1921,plain,
( spl72_21
| ~ spl72_22
| ~ spl72_2 ),
inference(avatar_split_clause,[],[f1436,f838,f1918,f1914]) ).
fof(f1914,plain,
( spl72_21
<=> nil = cons(sK70,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_21])]) ).
fof(f1918,plain,
( spl72_22
<=> sP3(cons(sK70,nil),sK70) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_22])]) ).
fof(f1436,plain,
( ~ sP3(cons(sK70,nil),sK70)
| nil = cons(sK70,nil)
| ~ spl72_2 ),
inference(subsumption_resolution,[],[f1435,f611]) ).
fof(f1435,plain,
( ~ ssItem(sK70)
| ~ sP3(cons(sK70,nil),sK70)
| nil = cons(sK70,nil)
| ~ spl72_2 ),
inference(forward_demodulation,[],[f1425,f1052]) ).
fof(f1052,plain,
( sK70 = hd(cons(sK70,nil))
| ~ spl72_2 ),
inference(resolution,[],[f997,f611]) ).
fof(f1425,plain,
( ~ sP3(cons(sK70,nil),sK70)
| nil = cons(sK70,nil)
| ~ ssItem(hd(cons(sK70,nil)))
| ~ spl72_2 ),
inference(superposition,[],[f792,f1052]) ).
fof(f1912,plain,
( spl72_19
| ~ spl72_20
| ~ spl72_2 ),
inference(avatar_split_clause,[],[f1434,f838,f1909,f1905]) ).
fof(f1905,plain,
( spl72_19
<=> nil = cons(sK24,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_19])]) ).
fof(f1909,plain,
( spl72_20
<=> sP3(cons(sK24,nil),sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_20])]) ).
fof(f1434,plain,
( ~ sP3(cons(sK24,nil),sK24)
| nil = cons(sK24,nil)
| ~ spl72_2 ),
inference(subsumption_resolution,[],[f1433,f395]) ).
fof(f1433,plain,
( ~ ssItem(sK24)
| ~ sP3(cons(sK24,nil),sK24)
| nil = cons(sK24,nil)
| ~ spl72_2 ),
inference(forward_demodulation,[],[f1424,f1034]) ).
fof(f1034,plain,
( sK24 = hd(cons(sK24,nil))
| ~ spl72_2 ),
inference(resolution,[],[f997,f395]) ).
fof(f1424,plain,
( ~ sP3(cons(sK24,nil),sK24)
| nil = cons(sK24,nil)
| ~ ssItem(hd(cons(sK24,nil)))
| ~ spl72_2 ),
inference(superposition,[],[f792,f1034]) ).
fof(f1903,plain,
( spl72_17
| ~ spl72_18 ),
inference(avatar_split_clause,[],[f1432,f1900,f1896]) ).
fof(f1896,plain,
( spl72_17
<=> nil = cons(sK71,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_17])]) ).
fof(f1900,plain,
( spl72_18
<=> sP3(cons(sK71,sK20),sK71) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_18])]) ).
fof(f1432,plain,
( ~ sP3(cons(sK71,sK20),sK71)
| nil = cons(sK71,sK20) ),
inference(subsumption_resolution,[],[f1431,f612]) ).
fof(f1431,plain,
( ~ ssItem(sK71)
| ~ sP3(cons(sK71,sK20),sK71)
| nil = cons(sK71,sK20) ),
inference(forward_demodulation,[],[f1423,f1022]) ).
fof(f1022,plain,
sK71 = hd(cons(sK71,sK20)),
inference(resolution,[],[f971,f612]) ).
fof(f971,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK20)) = X0 ),
inference(resolution,[],[f571,f387]) ).
fof(f1423,plain,
( ~ sP3(cons(sK71,sK20),sK71)
| nil = cons(sK71,sK20)
| ~ ssItem(hd(cons(sK71,sK20))) ),
inference(superposition,[],[f792,f1022]) ).
fof(f1794,plain,
( ~ spl72_15
| spl72_16
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10 ),
inference(avatar_split_clause,[],[f1725,f1548,f1544,f1510,f1792,f1788]) ).
fof(f1792,plain,
( spl72_16
<=> ! [X0] :
( ~ leq(X0,sK24)
| sP1(sK20,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_16])]) ).
fof(f1725,plain,
( ! [X0] :
( ~ leq(X0,sK24)
| sP1(sK20,X0)
| ~ totalorderedP(sK20) )
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10 ),
inference(subsumption_resolution,[],[f1718,f393]) ).
fof(f1718,plain,
( ! [X0] :
( ~ leq(X0,sK24)
| sP1(sK20,X0)
| ~ totalorderedP(sK20)
| nil = sK20 )
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10 ),
inference(superposition,[],[f448,f1707]) ).
fof(f1766,plain,
( ~ spl72_13
| spl72_14
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10 ),
inference(avatar_split_clause,[],[f1724,f1548,f1544,f1510,f1764,f1760]) ).
fof(f1764,plain,
( spl72_14
<=> ! [X0] :
( ~ lt(X0,sK24)
| sP3(sK20,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_14])]) ).
fof(f1724,plain,
( ! [X0] :
( ~ lt(X0,sK24)
| sP3(sK20,X0)
| ~ strictorderedP(sK20) )
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10 ),
inference(subsumption_resolution,[],[f1717,f393]) ).
fof(f1717,plain,
( ! [X0] :
( ~ lt(X0,sK24)
| sP3(sK20,X0)
| ~ strictorderedP(sK20)
| nil = sK20 )
| ~ spl72_7
| ~ spl72_9
| ~ spl72_10 ),
inference(superposition,[],[f456,f1707]) ).
fof(f1653,plain,
spl72_11,
inference(avatar_contradiction_clause,[],[f1652]) ).
fof(f1652,plain,
( $false
| spl72_11 ),
inference(subsumption_resolution,[],[f1651,f387]) ).
fof(f1651,plain,
( ~ ssList(sK20)
| spl72_11 ),
inference(subsumption_resolution,[],[f1650,f393]) ).
fof(f1650,plain,
( nil = sK20
| ~ ssList(sK20)
| spl72_11 ),
inference(resolution,[],[f1644,f472]) ).
fof(f1644,plain,
( ~ ssItem(hd(sK20))
| spl72_11 ),
inference(avatar_component_clause,[],[f1642]) ).
fof(f1649,plain,
( ~ spl72_11
| ~ spl72_12 ),
inference(avatar_split_clause,[],[f1640,f1646,f1642]) ).
fof(f1646,plain,
( spl72_12
<=> sK20 = tl(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_12])]) ).
fof(f1640,plain,
( sK20 != tl(sK20)
| ~ ssItem(hd(sK20)) ),
inference(subsumption_resolution,[],[f1639,f387]) ).
fof(f1639,plain,
( sK20 != tl(sK20)
| ~ ssItem(hd(sK20))
| ~ ssList(sK20) ),
inference(inner_rewriting,[],[f1637]) ).
fof(f1637,plain,
( sK20 != tl(sK20)
| ~ ssItem(hd(sK20))
| ~ ssList(tl(sK20)) ),
inference(superposition,[],[f569,f1589]) ).
fof(f1589,plain,
sK20 = cons(hd(sK20),tl(sK20)),
inference(subsumption_resolution,[],[f1556,f393]) ).
fof(f1556,plain,
( nil = sK20
| sK20 = cons(hd(sK20),tl(sK20)) ),
inference(resolution,[],[f474,f387]) ).
fof(f569,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,plain,
! [X0] :
( ! [X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f18,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> cons(X1,X0) != X0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax18) ).
fof(f1597,plain,
spl72_9,
inference(avatar_contradiction_clause,[],[f1596]) ).
fof(f1596,plain,
( $false
| spl72_9 ),
inference(subsumption_resolution,[],[f1595,f387]) ).
fof(f1595,plain,
( ~ ssList(sK20)
| spl72_9 ),
inference(subsumption_resolution,[],[f1594,f393]) ).
fof(f1594,plain,
( nil = sK20
| ~ ssList(sK20)
| spl72_9 ),
inference(resolution,[],[f1546,f469]) ).
fof(f1546,plain,
( ~ ssList(sK25(sK20))
| spl72_9 ),
inference(avatar_component_clause,[],[f1544]) ).
fof(f1551,plain,
( ~ spl72_9
| spl72_10
| ~ spl72_7 ),
inference(avatar_split_clause,[],[f1542,f1510,f1548,f1544]) ).
fof(f1542,plain,
( memberP(sK20,sK26(sK20))
| ~ ssList(sK25(sK20))
| ~ spl72_7 ),
inference(subsumption_resolution,[],[f1506,f1511]) ).
fof(f1506,plain,
( memberP(sK20,sK26(sK20))
| ~ ssList(sK25(sK20))
| ~ ssItem(sK26(sK20)) ),
inference(superposition,[],[f644,f1494]) ).
fof(f1521,plain,
spl72_7,
inference(avatar_contradiction_clause,[],[f1520]) ).
fof(f1520,plain,
( $false
| spl72_7 ),
inference(subsumption_resolution,[],[f1519,f387]) ).
fof(f1519,plain,
( ~ ssList(sK20)
| spl72_7 ),
inference(subsumption_resolution,[],[f1518,f393]) ).
fof(f1518,plain,
( nil = sK20
| ~ ssList(sK20)
| spl72_7 ),
inference(resolution,[],[f1512,f470]) ).
fof(f1512,plain,
( ~ ssItem(sK26(sK20))
| spl72_7 ),
inference(avatar_component_clause,[],[f1510]) ).
fof(f1517,plain,
( ~ spl72_7
| ~ spl72_8 ),
inference(avatar_split_clause,[],[f1508,f1514,f1510]) ).
fof(f1514,plain,
( spl72_8
<=> sK20 = sK25(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_8])]) ).
fof(f1508,plain,
( sK20 != sK25(sK20)
| ~ ssItem(sK26(sK20)) ),
inference(subsumption_resolution,[],[f1507,f387]) ).
fof(f1507,plain,
( sK20 != sK25(sK20)
| ~ ssItem(sK26(sK20))
| ~ ssList(sK20) ),
inference(inner_rewriting,[],[f1505]) ).
fof(f1505,plain,
( sK20 != sK25(sK20)
| ~ ssItem(sK26(sK20))
| ~ ssList(sK25(sK20)) ),
inference(superposition,[],[f569,f1494]) ).
fof(f1456,plain,
( spl72_5
| ~ spl72_6 ),
inference(avatar_split_clause,[],[f1430,f1453,f1449]) ).
fof(f1449,plain,
( spl72_5
<=> nil = cons(sK70,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_5])]) ).
fof(f1453,plain,
( spl72_6
<=> sP3(cons(sK70,sK20),sK70) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_6])]) ).
fof(f1430,plain,
( ~ sP3(cons(sK70,sK20),sK70)
| nil = cons(sK70,sK20) ),
inference(subsumption_resolution,[],[f1429,f611]) ).
fof(f1429,plain,
( ~ ssItem(sK70)
| ~ sP3(cons(sK70,sK20),sK70)
| nil = cons(sK70,sK20) ),
inference(forward_demodulation,[],[f1422,f1021]) ).
fof(f1021,plain,
sK70 = hd(cons(sK70,sK20)),
inference(resolution,[],[f971,f611]) ).
fof(f1422,plain,
( ~ sP3(cons(sK70,sK20),sK70)
| nil = cons(sK70,sK20)
| ~ ssItem(hd(cons(sK70,sK20))) ),
inference(superposition,[],[f792,f1021]) ).
fof(f1447,plain,
( spl72_3
| ~ spl72_4 ),
inference(avatar_split_clause,[],[f1428,f1444,f1440]) ).
fof(f1440,plain,
( spl72_3
<=> nil = cons(sK24,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_3])]) ).
fof(f1444,plain,
( spl72_4
<=> sP3(cons(sK24,sK20),sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_4])]) ).
fof(f1428,plain,
( ~ sP3(cons(sK24,sK20),sK24)
| nil = cons(sK24,sK20) ),
inference(subsumption_resolution,[],[f1427,f395]) ).
fof(f1427,plain,
( ~ ssItem(sK24)
| ~ sP3(cons(sK24,sK20),sK24)
| nil = cons(sK24,sK20) ),
inference(forward_demodulation,[],[f1421,f1003]) ).
fof(f1003,plain,
sK24 = hd(cons(sK24,sK20)),
inference(resolution,[],[f971,f395]) ).
fof(f1421,plain,
( ~ sP3(cons(sK24,sK20),sK24)
| nil = cons(sK24,sK20)
| ~ ssItem(hd(cons(sK24,sK20))) ),
inference(superposition,[],[f792,f1003]) ).
fof(f841,plain,
( spl72_1
| spl72_2 ),
inference(avatar_split_clause,[],[f800,f838,f834]) ).
fof(f834,plain,
( spl72_1
<=> hd(sK21) = sK27(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_1])]) ).
fof(f800,plain,
( nil = sK21
| hd(sK21) = sK27(sK21) ),
inference(resolution,[],[f476,f388]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWC240+1 : TPTP v8.2.0. Released v2.4.0.
% 0.07/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n022.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Sun May 19 02:49:38 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.14/0.36 % (21794)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.38 % (21801)WARNING: value z3 for option sas not known
% 0.14/0.38 % (21798)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.38 % (21801)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.38 % (21799)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.38 % (21802)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.38 % (21804)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.38 % (21803)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.38 % (21805)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.14/0.39 TRYING [1]
% 0.14/0.39 TRYING [1]
% 0.21/0.40 TRYING [2]
% 0.21/0.40 TRYING [2]
% 0.21/0.40 TRYING [3]
% 0.21/0.41 TRYING [3]
% 0.21/0.45 TRYING [4]
% 0.21/0.47 TRYING [4]
% 0.21/0.56 TRYING [5]
% 1.70/0.59 TRYING [5]
% 2.61/0.79 TRYING [6]
% 3.69/0.87 TRYING [6]
% 4.71/1.04 % (21801)First to succeed.
% 4.71/1.05 % (21801)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-21794"
% 4.71/1.05 % (21801)Refutation found. Thanks to Tanya!
% 4.71/1.05 % SZS status Theorem for theBenchmark
% 4.71/1.05 % SZS output start Proof for theBenchmark
% See solution above
% 4.71/1.06 % (21801)------------------------------
% 4.71/1.06 % (21801)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 4.71/1.06 % (21801)Termination reason: Refutation
% 4.71/1.06
% 4.71/1.06 % (21801)Memory used [KB]: 9824
% 4.71/1.06 % (21801)Time elapsed: 0.668 s
% 4.71/1.06 % (21801)Instructions burned: 2041 (million)
% 4.71/1.06 % (21794)Success in time 0.685 s
%------------------------------------------------------------------------------