TSTP Solution File: SWC242+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC242+1 : TPTP v8.1.2. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun May 5 10:18:26 EDT 2024
% Result : Theorem 2.76s 0.76s
% Output : Refutation 2.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 241
% Syntax : Number of formulae : 1336 ( 65 unt; 0 def)
% Number of atoms : 5311 ( 743 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 6732 (2757 ~;2798 |; 775 &)
% ( 157 <=>; 245 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 130 ( 128 usr; 91 prp; 0-3 aty)
% Number of functors : 56 ( 56 usr; 8 con; 0-3 aty)
% Number of variables : 1625 (1283 !; 342 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8947,plain,
$false,
inference(avatar_sat_refutation,[],[f857,f1481,f1490,f1553,f1557,f1641,f1645,f1668,f1672,f1782,f1791,f1800,f1809,f1990,f2072,f2076,f2161,f2165,f2248,f2252,f2335,f2339,f2906,f2915,f2924,f3106,f3130,f4001,f4181,f4188,f4499,f4504,f4845,f4850,f4943,f4948,f5376,f5380,f5383,f5391,f5548,f5552,f5555,f5563,f5597,f5602,f5811,f5815,f5818,f5826,f5860,f5865,f5868,f5871,f5879,f5913,f5917,f5920,f5928,f5963,f5968,f5971,f5974,f5982,f6016,f6020,f6023,f6031,f6066,f6071,f6074,f6077,f6085,f6357,f6362,f6364,f6372,f6574,f6579,f6581,f6611,f6647,f6652,f6654,f6662,f6698,f6727,f6729,f6737,f6773,f6778,f6780,f6788,f7012,f7017,f7019,f7027,f7063,f7068,f7070,f7078,f7841,f8006,f8026,f8213,f8233,f8915,f8918,f8946]) ).
fof(f8946,plain,
spl75_90,
inference(avatar_contradiction_clause,[],[f8945]) ).
fof(f8945,plain,
( $false
| spl75_90 ),
inference(subsumption_resolution,[],[f8944,f666]) ).
fof(f666,plain,
sP1(sK27,sK23),
inference(subsumption_resolution,[],[f665,f403]) ).
fof(f403,plain,
nil != sK23,
inference(cnf_transformation,[],[f268]) ).
fof(f268,plain,
( ( ( sP1(sK27,sK25)
& ssItem(sK27) )
| nil = sK25 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( sP0(X5,X7,X6)
| app(app(X6,cons(X5,nil)),X7) != sK23
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
& nil != sK23
& sK23 = sK25
& sK24 = sK26
& ssList(sK26)
& ssList(sK25)
& ssList(sK24)
& ssList(sK23) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK23,sK24,sK25,sK26,sK27])],[f262,f267,f266,f265,f264,f263]) ).
fof(f263,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ? [X4] :
( sP1(X4,X2)
& ssItem(X4) )
| nil = X2 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( sP0(X5,X7,X6)
| app(app(X6,cons(X5,nil)),X7) != X0
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
& nil != X0
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ? [X4] :
( sP1(X4,X2)
& ssItem(X4) )
| nil = X2 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( sP0(X5,X7,X6)
| app(app(X6,cons(X5,nil)),X7) != sK23
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
& nil != sK23
& sK23 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f264,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ? [X4] :
( sP1(X4,X2)
& ssItem(X4) )
| nil = X2 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( sP0(X5,X7,X6)
| app(app(X6,cons(X5,nil)),X7) != sK23
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
& nil != sK23
& sK23 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( ? [X4] :
( sP1(X4,X2)
& ssItem(X4) )
| nil = X2 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( sP0(X5,X7,X6)
| app(app(X6,cons(X5,nil)),X7) != sK23
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
& nil != sK23
& sK23 = X2
& sK24 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f265,plain,
( ? [X2] :
( ? [X3] :
( ( ? [X4] :
( sP1(X4,X2)
& ssItem(X4) )
| nil = X2 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( sP0(X5,X7,X6)
| app(app(X6,cons(X5,nil)),X7) != sK23
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
& nil != sK23
& sK23 = X2
& sK24 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( ? [X4] :
( sP1(X4,sK25)
& ssItem(X4) )
| nil = sK25 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( sP0(X5,X7,X6)
| app(app(X6,cons(X5,nil)),X7) != sK23
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
& nil != sK23
& sK23 = sK25
& sK24 = X3
& ssList(X3) )
& ssList(sK25) ) ),
introduced(choice_axiom,[]) ).
fof(f266,plain,
( ? [X3] :
( ( ? [X4] :
( sP1(X4,sK25)
& ssItem(X4) )
| nil = sK25 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( sP0(X5,X7,X6)
| app(app(X6,cons(X5,nil)),X7) != sK23
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
& nil != sK23
& sK23 = sK25
& sK24 = X3
& ssList(X3) )
=> ( ( ? [X4] :
( sP1(X4,sK25)
& ssItem(X4) )
| nil = sK25 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( sP0(X5,X7,X6)
| app(app(X6,cons(X5,nil)),X7) != sK23
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
& nil != sK23
& sK23 = sK25
& sK24 = sK26
& ssList(sK26) ) ),
introduced(choice_axiom,[]) ).
fof(f267,plain,
( ? [X4] :
( sP1(X4,sK25)
& ssItem(X4) )
=> ( sP1(sK27,sK25)
& ssItem(sK27) ) ),
introduced(choice_axiom,[]) ).
fof(f262,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ? [X4] :
( sP1(X4,X2)
& ssItem(X4) )
| nil = X2 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( sP0(X5,X7,X6)
| app(app(X6,cons(X5,nil)),X7) != X0
| ~ ssList(X7) )
| ~ ssList(X6) )
| ~ ssItem(X5) )
& nil != X0
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(rectify,[],[f225]) ).
fof(f225,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ? [X4] :
( sP1(X4,X2)
& ssItem(X4) )
| nil = X2 )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( sP0(X8,X10,X9)
| app(app(X9,cons(X8,nil)),X10) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != X0
& X0 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(X0) ),
inference(definition_folding,[],[f99,f224,f223]) ).
fof(f223,plain,
! [X8,X10,X9] :
( ? [X11] :
( ~ leq(X8,X11)
& lt(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ssItem(X11) )
| ~ sP0(X8,X10,X9) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP0])]) ).
fof(f224,plain,
! [X4,X2] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7)
| leq(X4,X7)
| ~ ssItem(X7) )
& app(app(X5,cons(X4,nil)),X6) = X2
& ssList(X6) )
& ssList(X5) )
| ~ sP1(X4,X2) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7)
| leq(X4,X7)
| ~ ssItem(X7) )
& app(app(X5,cons(X4,nil)),X6) = X2
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X2 )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( ? [X11] :
( ~ leq(X8,X11)
& lt(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ssItem(X11) )
| app(app(X9,cons(X8,nil)),X10) != X0
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& 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] :
( ( ! [X4] :
( ssItem(X4)
=> ! [X5] :
( ssList(X5)
=> ! [X6] :
( ? [X7] :
( lt(X4,X7)
& memberP(X6,X7)
& memberP(X5,X7)
& ~ leq(X4,X7)
& ssItem(X7) )
| app(app(X5,cons(X4,nil)),X6) != X2
| ~ ssList(X6) ) ) )
& nil != X2 )
| ? [X8] :
( ? [X9] :
( ? [X10] :
( ! [X11] :
( leq(X8,X11)
| ~ lt(X8,X11)
| ~ memberP(X10,X11)
| ~ memberP(X9,X11)
| ~ ssItem(X11) )
& app(app(X9,cons(X8,nil)),X10) = X0
& ssList(X10) )
& ssList(X9) )
& ssItem(X8) )
| nil = X0
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(rectify,[],[f97]) ).
fof(f97,negated_conjecture,
~ ! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ? [X11] :
( lt(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ~ leq(X8,X11)
& ssItem(X11) )
| app(app(X9,cons(X8,nil)),X10) != X2
| ~ ssList(X10) ) ) )
& nil != X2 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( leq(X4,X7)
| ~ lt(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
inference(negated_conjecture,[],[f96]) ).
fof(f96,conjecture,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ( ! [X8] :
( ssItem(X8)
=> ! [X9] :
( ssList(X9)
=> ! [X10] :
( ? [X11] :
( lt(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ~ leq(X8,X11)
& ssItem(X11) )
| app(app(X9,cons(X8,nil)),X10) != X2
| ~ ssList(X10) ) ) )
& nil != X2 )
| ? [X4] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( leq(X4,X7)
| ~ lt(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& app(app(X5,cons(X4,nil)),X6) = X0
& ssList(X6) )
& ssList(X5) )
& ssItem(X4) )
| nil = X0
| X0 != X2
| X1 != X3
| ~ ssList(X3) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',co1) ).
fof(f665,plain,
( nil = sK23
| sP1(sK27,sK23) ),
inference(forward_demodulation,[],[f664,f402]) ).
fof(f402,plain,
sK23 = sK25,
inference(cnf_transformation,[],[f268]) ).
fof(f664,plain,
( sP1(sK27,sK23)
| nil = sK25 ),
inference(forward_demodulation,[],[f406,f402]) ).
fof(f406,plain,
( sP1(sK27,sK25)
| nil = sK25 ),
inference(cnf_transformation,[],[f268]) ).
fof(f8944,plain,
( ~ sP1(sK27,sK23)
| spl75_90 ),
inference(resolution,[],[f8914,f389]) ).
fof(f389,plain,
! [X0,X1] :
( ssList(sK21(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f257]) ).
fof(f257,plain,
! [X0,X1] :
( ( ! [X4] :
( ~ lt(X0,X4)
| ~ memberP(sK21(X0,X1),X4)
| ~ memberP(sK20(X0,X1),X4)
| leq(X0,X4)
| ~ ssItem(X4) )
& app(app(sK20(X0,X1),cons(X0,nil)),sK21(X0,X1)) = X1
& ssList(sK21(X0,X1))
& ssList(sK20(X0,X1)) )
| ~ sP1(X0,X1) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21])],[f254,f256,f255]) ).
fof(f255,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ~ lt(X0,X4)
| ~ memberP(X3,X4)
| ~ memberP(X2,X4)
| leq(X0,X4)
| ~ ssItem(X4) )
& app(app(X2,cons(X0,nil)),X3) = X1
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ! [X4] :
( ~ lt(X0,X4)
| ~ memberP(X3,X4)
| ~ memberP(sK20(X0,X1),X4)
| leq(X0,X4)
| ~ ssItem(X4) )
& app(app(sK20(X0,X1),cons(X0,nil)),X3) = X1
& ssList(X3) )
& ssList(sK20(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f256,plain,
! [X0,X1] :
( ? [X3] :
( ! [X4] :
( ~ lt(X0,X4)
| ~ memberP(X3,X4)
| ~ memberP(sK20(X0,X1),X4)
| leq(X0,X4)
| ~ ssItem(X4) )
& app(app(sK20(X0,X1),cons(X0,nil)),X3) = X1
& ssList(X3) )
=> ( ! [X4] :
( ~ lt(X0,X4)
| ~ memberP(sK21(X0,X1),X4)
| ~ memberP(sK20(X0,X1),X4)
| leq(X0,X4)
| ~ ssItem(X4) )
& app(app(sK20(X0,X1),cons(X0,nil)),sK21(X0,X1)) = X1
& ssList(sK21(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f254,plain,
! [X0,X1] :
( ? [X2] :
( ? [X3] :
( ! [X4] :
( ~ lt(X0,X4)
| ~ memberP(X3,X4)
| ~ memberP(X2,X4)
| leq(X0,X4)
| ~ ssItem(X4) )
& app(app(X2,cons(X0,nil)),X3) = X1
& ssList(X3) )
& ssList(X2) )
| ~ sP1(X0,X1) ),
inference(rectify,[],[f253]) ).
fof(f253,plain,
! [X4,X2] :
( ? [X5] :
( ? [X6] :
( ! [X7] :
( ~ lt(X4,X7)
| ~ memberP(X6,X7)
| ~ memberP(X5,X7)
| leq(X4,X7)
| ~ ssItem(X7) )
& app(app(X5,cons(X4,nil)),X6) = X2
& ssList(X6) )
& ssList(X5) )
| ~ sP1(X4,X2) ),
inference(nnf_transformation,[],[f224]) ).
fof(f8914,plain,
( ~ ssList(sK21(sK27,sK23))
| spl75_90 ),
inference(avatar_component_clause,[],[f8912]) ).
fof(f8912,plain,
( spl75_90
<=> ssList(sK21(sK27,sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_90])]) ).
fof(f8918,plain,
spl75_89,
inference(avatar_contradiction_clause,[],[f8917]) ).
fof(f8917,plain,
( $false
| spl75_89 ),
inference(subsumption_resolution,[],[f8916,f666]) ).
fof(f8916,plain,
( ~ sP1(sK27,sK23)
| spl75_89 ),
inference(resolution,[],[f8910,f388]) ).
fof(f388,plain,
! [X0,X1] :
( ssList(sK20(X0,X1))
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f257]) ).
fof(f8910,plain,
( ~ ssList(sK20(sK27,sK23))
| spl75_89 ),
inference(avatar_component_clause,[],[f8908]) ).
fof(f8908,plain,
( spl75_89
<=> ssList(sK20(sK27,sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_89])]) ).
fof(f8915,plain,
( ~ spl75_89
| ~ spl75_90 ),
inference(avatar_split_clause,[],[f8900,f8912,f8908]) ).
fof(f8900,plain,
( ~ ssList(sK21(sK27,sK23))
| ~ ssList(sK20(sK27,sK23)) ),
inference(subsumption_resolution,[],[f8898,f663]) ).
fof(f663,plain,
ssItem(sK27),
inference(subsumption_resolution,[],[f662,f403]) ).
fof(f662,plain,
( nil = sK23
| ssItem(sK27) ),
inference(forward_demodulation,[],[f405,f402]) ).
fof(f405,plain,
( ssItem(sK27)
| nil = sK25 ),
inference(cnf_transformation,[],[f268]) ).
fof(f8898,plain,
( ~ ssList(sK21(sK27,sK23))
| ~ ssList(sK20(sK27,sK23))
| ~ ssItem(sK27) ),
inference(trivial_inequality_removal,[],[f8895]) ).
fof(f8895,plain,
( sK23 != sK23
| ~ ssList(sK21(sK27,sK23))
| ~ ssList(sK20(sK27,sK23))
| ~ ssItem(sK27) ),
inference(superposition,[],[f3487,f4054]) ).
fof(f4054,plain,
sK23 = app(app(sK20(sK27,sK23),cons(sK27,nil)),sK21(sK27,sK23)),
inference(resolution,[],[f390,f666]) ).
fof(f390,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| app(app(sK20(X0,X1),cons(X0,nil)),sK21(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f257]) ).
fof(f3487,plain,
! [X6,X7,X5] :
( app(app(X6,cons(X5,nil)),X7) != sK23
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssItem(X5) ),
inference(subsumption_resolution,[],[f404,f799]) ).
fof(f799,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| ~ ssItem(X0) ),
inference(subsumption_resolution,[],[f798,f392]) ).
fof(f392,plain,
! [X2,X0,X1] :
( ssItem(sK22(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f261]) ).
fof(f261,plain,
! [X0,X1,X2] :
( ( ~ leq(X0,sK22(X0,X1,X2))
& lt(X0,sK22(X0,X1,X2))
& memberP(X1,sK22(X0,X1,X2))
& memberP(X2,sK22(X0,X1,X2))
& ssItem(sK22(X0,X1,X2)) )
| ~ sP0(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22])],[f259,f260]) ).
fof(f260,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ leq(X0,X3)
& lt(X0,X3)
& memberP(X1,X3)
& memberP(X2,X3)
& ssItem(X3) )
=> ( ~ leq(X0,sK22(X0,X1,X2))
& lt(X0,sK22(X0,X1,X2))
& memberP(X1,sK22(X0,X1,X2))
& memberP(X2,sK22(X0,X1,X2))
& ssItem(sK22(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f259,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,[],[f258]) ).
fof(f258,plain,
! [X8,X10,X9] :
( ? [X11] :
( ~ leq(X8,X11)
& lt(X8,X11)
& memberP(X10,X11)
& memberP(X9,X11)
& ssItem(X11) )
| ~ sP0(X8,X10,X9) ),
inference(nnf_transformation,[],[f223]) ).
fof(f798,plain,
! [X2,X0,X1] :
( ~ ssItem(sK22(X0,X1,X2))
| ~ ssItem(X0)
| ~ sP0(X0,X1,X2) ),
inference(subsumption_resolution,[],[f797,f396]) ).
fof(f396,plain,
! [X2,X0,X1] :
( ~ leq(X0,sK22(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f261]) ).
fof(f797,plain,
! [X2,X0,X1] :
( leq(X0,sK22(X0,X1,X2))
| ~ ssItem(sK22(X0,X1,X2))
| ~ ssItem(X0)
| ~ sP0(X0,X1,X2) ),
inference(resolution,[],[f439,f395]) ).
fof(f395,plain,
! [X2,X0,X1] :
( lt(X0,sK22(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f261]) ).
fof(f439,plain,
! [X0,X1] :
( ~ lt(X0,X1)
| leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f273,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,[],[f272]) ).
fof(f272,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,[],[f124]) ).
fof(f124,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(f404,plain,
! [X6,X7,X5] :
( sP0(X5,X7,X6)
| app(app(X6,cons(X5,nil)),X7) != sK23
| ~ ssList(X7)
| ~ ssList(X6)
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f268]) ).
fof(f8233,plain,
( ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_86 ),
inference(avatar_contradiction_clause,[],[f8232]) ).
fof(f8232,plain,
( $false
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_86 ),
inference(subsumption_resolution,[],[f8231,f1662]) ).
fof(f1662,plain,
( ssItem(hd(sK23))
| ~ spl75_11 ),
inference(avatar_component_clause,[],[f1661]) ).
fof(f1661,plain,
( spl75_11
<=> ssItem(hd(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_11])]) ).
fof(f8231,plain,
( ~ ssItem(hd(sK23))
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_86 ),
inference(subsumption_resolution,[],[f8230,f1854]) ).
fof(f1854,plain,
( ssList(tl(sK23))
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11 ),
inference(superposition,[],[f1635,f1850]) ).
fof(f1850,plain,
( tl(sK23) = sK28(sK23)
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11 ),
inference(forward_demodulation,[],[f1827,f1729]) ).
fof(f1729,plain,
( sK23 = cons(hd(sK23),sK28(sK23))
| ~ spl75_7
| ~ spl75_9 ),
inference(superposition,[],[f1530,f1726]) ).
fof(f1726,plain,
( hd(sK23) = sK29(sK23)
| ~ spl75_7
| ~ spl75_9 ),
inference(forward_demodulation,[],[f1707,f1530]) ).
fof(f1707,plain,
( sK29(sK23) = hd(cons(sK29(sK23),sK28(sK23)))
| ~ spl75_7
| ~ spl75_9 ),
inference(resolution,[],[f1653,f1547]) ).
fof(f1547,plain,
( ssItem(sK29(sK23))
| ~ spl75_7 ),
inference(avatar_component_clause,[],[f1546]) ).
fof(f1546,plain,
( spl75_7
<=> ssItem(sK29(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_7])]) ).
fof(f1653,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK28(sK23))) = X0 )
| ~ spl75_9 ),
inference(resolution,[],[f1635,f581]) ).
fof(f581,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| hd(cons(X1,X0)) = X1 ),
inference(cnf_transformation,[],[f182]) ).
fof(f182,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(f1530,plain,
sK23 = cons(sK29(sK23),sK28(sK23)),
inference(subsumption_resolution,[],[f1497,f403]) ).
fof(f1497,plain,
( nil = sK23
| sK23 = cons(sK29(sK23),sK28(sK23)) ),
inference(resolution,[],[f481,f397]) ).
fof(f397,plain,
ssList(sK23),
inference(cnf_transformation,[],[f268]) ).
fof(f481,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(sK29(X0),sK28(X0)) = X0 ),
inference(cnf_transformation,[],[f290]) ).
fof(f290,plain,
! [X0] :
( ( cons(sK29(X0),sK28(X0)) = X0
& ssItem(sK29(X0))
& ssList(sK28(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28,sK29])],[f149,f289,f288]) ).
fof(f288,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK28(X0)) = X0
& ssItem(X2) )
& ssList(sK28(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f289,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK28(X0)) = X0
& ssItem(X2) )
=> ( cons(sK29(X0),sK28(X0)) = X0
& ssItem(sK29(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f149,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f148]) ).
fof(f148,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(f1827,plain,
( sK28(sK23) = tl(cons(hd(sK23),sK28(sK23)))
| ~ spl75_9
| ~ spl75_11 ),
inference(resolution,[],[f1652,f1662]) ).
fof(f1652,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK28(sK23) = tl(cons(X0,sK28(sK23))) )
| ~ spl75_9 ),
inference(resolution,[],[f1635,f580]) ).
fof(f580,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| tl(cons(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f181]) ).
fof(f181,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(f1635,plain,
( ssList(sK28(sK23))
| ~ spl75_9 ),
inference(avatar_component_clause,[],[f1634]) ).
fof(f1634,plain,
( spl75_9
<=> ssList(sK28(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_9])]) ).
fof(f8230,plain,
( ~ ssList(tl(sK23))
| ~ ssItem(hd(sK23))
| spl75_86 ),
inference(resolution,[],[f8204,f467]) ).
fof(f467,plain,
! [X0,X1] :
( sP5(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f231]) ).
fof(f231,plain,
! [X0] :
( ! [X1] :
( sP5(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f138,f230,f229]) ).
fof(f229,plain,
! [X1,X0] :
( sP4(X1,X0)
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
fof(f230,plain,
! [X0,X1] :
( ( strictorderedP(cons(X0,X1))
<=> sP4(X1,X0) )
| ~ sP5(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP5])]) ).
fof(f138,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(f8204,plain,
( ~ sP5(hd(sK23),tl(sK23))
| spl75_86 ),
inference(avatar_component_clause,[],[f8202]) ).
fof(f8202,plain,
( spl75_86
<=> sP5(hd(sK23),tl(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_86])]) ).
fof(f8213,plain,
( ~ spl75_86
| spl75_87
| ~ spl75_88 ),
inference(avatar_split_clause,[],[f1625,f8210,f8206,f8202]) ).
fof(f8206,plain,
( spl75_87
<=> sP4(tl(sK23),hd(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_87])]) ).
fof(f8210,plain,
( spl75_88
<=> strictorderedP(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_88])]) ).
fof(f1625,plain,
( ~ strictorderedP(sK23)
| sP4(tl(sK23),hd(sK23))
| ~ sP5(hd(sK23),tl(sK23)) ),
inference(superposition,[],[f460,f1618]) ).
fof(f1618,plain,
sK23 = cons(hd(sK23),tl(sK23)),
inference(subsumption_resolution,[],[f1585,f403]) ).
fof(f1585,plain,
( nil = sK23
| sK23 = cons(hd(sK23),tl(sK23)) ),
inference(resolution,[],[f484,f397]) ).
fof(f484,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(hd(X0),tl(X0)) = X0 ),
inference(cnf_transformation,[],[f155]) ).
fof(f155,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f154]) ).
fof(f154,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(f460,plain,
! [X0,X1] :
( ~ strictorderedP(cons(X0,X1))
| sP4(X1,X0)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f282]) ).
fof(f282,plain,
! [X0,X1] :
( ( ( strictorderedP(cons(X0,X1))
| ~ sP4(X1,X0) )
& ( sP4(X1,X0)
| ~ strictorderedP(cons(X0,X1)) ) )
| ~ sP5(X0,X1) ),
inference(nnf_transformation,[],[f230]) ).
fof(f8026,plain,
( ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_83 ),
inference(avatar_contradiction_clause,[],[f8025]) ).
fof(f8025,plain,
( $false
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_83 ),
inference(subsumption_resolution,[],[f8024,f1662]) ).
fof(f8024,plain,
( ~ ssItem(hd(sK23))
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_83 ),
inference(subsumption_resolution,[],[f8023,f1854]) ).
fof(f8023,plain,
( ~ ssList(tl(sK23))
| ~ ssItem(hd(sK23))
| spl75_83 ),
inference(resolution,[],[f7997,f459]) ).
fof(f459,plain,
! [X0,X1] :
( sP3(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X0] :
( ! [X1] :
( sP3(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f137,f227,f226]) ).
fof(f226,plain,
! [X1,X0] :
( sP2(X1,X0)
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
fof(f227,plain,
! [X0,X1] :
( ( totalorderedP(cons(X0,X1))
<=> sP2(X1,X0) )
| ~ sP3(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f137,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(f7997,plain,
( ~ sP3(hd(sK23),tl(sK23))
| spl75_83 ),
inference(avatar_component_clause,[],[f7995]) ).
fof(f7995,plain,
( spl75_83
<=> sP3(hd(sK23),tl(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_83])]) ).
fof(f8006,plain,
( ~ spl75_83
| spl75_84
| ~ spl75_85 ),
inference(avatar_split_clause,[],[f1623,f8003,f7999,f7995]) ).
fof(f7999,plain,
( spl75_84
<=> sP2(tl(sK23),hd(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_84])]) ).
fof(f8003,plain,
( spl75_85
<=> totalorderedP(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_85])]) ).
fof(f1623,plain,
( ~ totalorderedP(sK23)
| sP2(tl(sK23),hd(sK23))
| ~ sP3(hd(sK23),tl(sK23)) ),
inference(superposition,[],[f452,f1618]) ).
fof(f452,plain,
! [X0,X1] :
( ~ totalorderedP(cons(X0,X1))
| sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f278]) ).
fof(f278,plain,
! [X0,X1] :
( ( ( totalorderedP(cons(X0,X1))
| ~ sP2(X1,X0) )
& ( sP2(X1,X0)
| ~ totalorderedP(cons(X0,X1)) ) )
| ~ sP3(X0,X1) ),
inference(nnf_transformation,[],[f227]) ).
fof(f7841,plain,
( spl75_81
| ~ spl75_82
| ~ spl75_11 ),
inference(avatar_split_clause,[],[f7498,f1661,f7838,f7834]) ).
fof(f7834,plain,
( spl75_81
<=> nil = app(sK23,sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_81])]) ).
fof(f7838,plain,
( spl75_82
<=> sP4(app(sK23,sK23),hd(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_82])]) ).
fof(f7498,plain,
( ~ sP4(app(sK23,sK23),hd(sK23))
| nil = app(sK23,sK23)
| ~ spl75_11 ),
inference(subsumption_resolution,[],[f7497,f1662]) ).
fof(f7497,plain,
( ~ ssItem(hd(sK23))
| ~ sP4(app(sK23,sK23),hd(sK23))
| nil = app(sK23,sK23) ),
inference(forward_demodulation,[],[f7491,f7426]) ).
fof(f7426,plain,
hd(sK23) = hd(app(sK23,sK23)),
inference(subsumption_resolution,[],[f7352,f403]) ).
fof(f7352,plain,
( hd(sK23) = hd(app(sK23,sK23))
| nil = sK23 ),
inference(resolution,[],[f3001,f397]) ).
fof(f3001,plain,
! [X0] :
( ~ ssList(X0)
| hd(X0) = hd(app(X0,sK23))
| nil = X0 ),
inference(resolution,[],[f588,f397]) ).
fof(f588,plain,
! [X0,X1] :
( ~ ssList(X1)
| nil = X0
| hd(X0) = hd(app(X0,X1))
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f187]) ).
fof(f187,plain,
! [X0] :
( ! [X1] :
( hd(X0) = hd(app(X0,X1))
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f186]) ).
fof(f186,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(f7491,plain,
( ~ sP4(app(sK23,sK23),hd(sK23))
| nil = app(sK23,sK23)
| ~ ssItem(hd(app(sK23,sK23))) ),
inference(superposition,[],[f806,f7426]) ).
fof(f806,plain,
! [X0] :
( ~ sP4(X0,hd(X0))
| nil = X0
| ~ ssItem(hd(X0)) ),
inference(resolution,[],[f464,f417]) ).
fof(f417,plain,
! [X0] :
( ~ lt(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f101]) ).
fof(f101,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(f464,plain,
! [X0,X1] :
( lt(X1,hd(X0))
| nil = X0
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f285]) ).
fof(f285,plain,
! [X0,X1] :
( ( sP4(X0,X1)
| ( ( ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( lt(X1,hd(X0))
& strictorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP4(X0,X1) ) ),
inference(rectify,[],[f284]) ).
fof(f284,plain,
! [X1,X0] :
( ( sP4(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP4(X1,X0) ) ),
inference(flattening,[],[f283]) ).
fof(f283,plain,
! [X1,X0] :
( ( sP4(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP4(X1,X0) ) ),
inference(nnf_transformation,[],[f229]) ).
fof(f7078,plain,
( ~ spl75_30
| spl75_79
| ~ spl75_80 ),
inference(avatar_contradiction_clause,[],[f7077]) ).
fof(f7077,plain,
( $false
| ~ spl75_30
| spl75_79
| ~ spl75_80 ),
inference(subsumption_resolution,[],[f7076,f2334]) ).
fof(f2334,plain,
( ssList(cons(sK74,sK23))
| ~ spl75_30 ),
inference(avatar_component_clause,[],[f2332]) ).
fof(f2332,plain,
( spl75_30
<=> ssList(cons(sK74,sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_30])]) ).
fof(f7076,plain,
( ~ ssList(cons(sK74,sK23))
| spl75_79
| ~ spl75_80 ),
inference(subsumption_resolution,[],[f7075,f415]) ).
fof(f415,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax17) ).
fof(f7075,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK74,sK23))
| spl75_79
| ~ spl75_80 ),
inference(subsumption_resolution,[],[f7074,f7062]) ).
fof(f7062,plain,
( frontsegP(cons(sK74,sK23),nil)
| ~ spl75_80 ),
inference(avatar_component_clause,[],[f7060]) ).
fof(f7060,plain,
( spl75_80
<=> frontsegP(cons(sK74,sK23),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_80])]) ).
fof(f7074,plain,
( ~ frontsegP(cons(sK74,sK23),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK74,sK23))
| spl75_79 ),
inference(resolution,[],[f7058,f603]) ).
fof(f603,plain,
! [X0,X1] :
( ssList(sK72(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f382]) ).
fof(f382,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK72(X0,X1)) = X0
& ssList(sK72(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK72])],[f380,f381]) ).
fof(f381,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK72(X0,X1)) = X0
& ssList(sK72(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f380,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,[],[f379]) ).
fof(f379,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,[],[f201]) ).
fof(f201,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(f7058,plain,
( ~ ssList(sK72(cons(sK74,sK23),nil))
| spl75_79 ),
inference(avatar_component_clause,[],[f7056]) ).
fof(f7056,plain,
( spl75_79
<=> ssList(sK72(cons(sK74,sK23),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_79])]) ).
fof(f7070,plain,
( ~ spl75_30
| spl75_80 ),
inference(avatar_contradiction_clause,[],[f7069]) ).
fof(f7069,plain,
( $false
| ~ spl75_30
| spl75_80 ),
inference(subsumption_resolution,[],[f7065,f2334]) ).
fof(f7065,plain,
( ~ ssList(cons(sK74,sK23))
| spl75_80 ),
inference(resolution,[],[f7061,f474]) ).
fof(f474,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f143]) ).
fof(f143,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(f7061,plain,
( ~ frontsegP(cons(sK74,sK23),nil)
| spl75_80 ),
inference(avatar_component_clause,[],[f7060]) ).
fof(f7068,plain,
( ~ spl75_30
| spl75_80 ),
inference(avatar_contradiction_clause,[],[f7067]) ).
fof(f7067,plain,
( $false
| ~ spl75_30
| spl75_80 ),
inference(subsumption_resolution,[],[f7066,f415]) ).
fof(f7066,plain,
( ~ ssList(nil)
| ~ spl75_30
| spl75_80 ),
inference(subsumption_resolution,[],[f7064,f658]) ).
fof(f658,plain,
frontsegP(nil,nil),
inference(global_subsumption,[],[f391,f390,f389,f388,f396,f395,f394,f393,f392,f406,f405,f404,f403,f402,f401,f400,f399,f398,f397,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f422,f423,f424,f425,f426,f427,f428,f429,f430,f431,f435,f434,f437,f436,f440,f439,f655,f441,f442,f443,f444,f445,f448,f654,f446,f653,f450,f449,f453,f452,f458,f628,f456,f455,f459,f461,f460,f466,f630,f464,f463,f467,f470,f469,f468,f471,f472,f473,f474,f475,f476,f477,f478,f481,f480,f479,f482,f483,f484,f486,f485,f488,f487,f632,f490,f489,f492,f500,f499,f498,f497,f496,f495,f633,f501,f502,f511,f510,f509,f508,f507,f506,f505,f652,f512,f513,f523,f522,f521,f520,f519,f518,f517,f516,f636,f524,f525,f535,f534,f533,f532,f531,f530,f529,f528,f637,f536,f537,f547,f546,f545,f544,f543,f542,f541,f540,f638,f548,f550,f549,f558,f557,f556,f555,f554,f553,f552,f639,f559,f561,f560,f569,f568,f567,f566,f565,f564,f563,f640,f570,f641,f656,f571,f642,f657,f573,f643]) ).
fof(f643,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f576]) ).
fof(f576,plain,
! [X0] :
( frontsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f363]) ).
fof(f363,plain,
! [X0] :
( ( ( frontsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ frontsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f177]) ).
fof(f177,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(f573,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f362]) ).
fof(f362,plain,
! [X0] :
( ( ( rearsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ rearsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f176,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(f657,plain,
rearsegP(nil,nil),
inference(global_subsumption,[],[f391,f390,f389,f388,f396,f395,f394,f393,f392,f406,f405,f404,f403,f402,f401,f400,f399,f398,f397,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f422,f423,f424,f425,f426,f427,f428,f429,f430,f431,f435,f434,f437,f436,f440,f439,f655,f441,f442,f443,f444,f445,f448,f654,f446,f653,f450,f449,f453,f452,f458,f628,f456,f455,f459,f461,f460,f466,f630,f464,f463,f467,f470,f469,f468,f471,f472,f473,f474,f475,f476,f477,f478,f481,f480,f479,f482,f483,f484,f486,f485,f488,f487,f632,f490,f489,f492,f500,f499,f498,f497,f496,f495,f633,f501,f502,f511,f510,f509,f508,f507,f506,f505,f652,f512,f513,f523,f522,f521,f520,f519,f518,f517,f516,f636,f524,f525,f535,f534,f533,f532,f531,f530,f529,f528,f637,f536,f537,f547,f546,f545,f544,f543,f542,f541,f540,f638,f548,f550,f549,f558,f557,f556,f555,f554,f553,f552,f639,f559,f561,f560,f569,f568,f567,f566,f565,f564,f563,f640,f570,f641,f656,f571,f642]) ).
fof(f642,plain,
( rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f574]) ).
fof(f574,plain,
! [X0] :
( rearsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f362]) ).
fof(f571,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f361]) ).
fof(f361,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f175]) ).
fof(f175,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(f656,plain,
segmentP(nil,nil),
inference(global_subsumption,[],[f391,f390,f389,f388,f396,f395,f394,f393,f392,f406,f405,f404,f403,f402,f401,f400,f399,f398,f397,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f422,f423,f424,f425,f426,f427,f428,f429,f430,f431,f435,f434,f437,f436,f440,f439,f655,f441,f442,f443,f444,f445,f448,f654,f446,f653,f450,f449,f453,f452,f458,f628,f456,f455,f459,f461,f460,f466,f630,f464,f463,f467,f470,f469,f468,f471,f472,f473,f474,f475,f476,f477,f478,f481,f480,f479,f482,f483,f484,f486,f485,f488,f487,f632,f490,f489,f492,f500,f499,f498,f497,f496,f495,f633,f501,f502,f511,f510,f509,f508,f507,f506,f505,f652,f512,f513,f523,f522,f521,f520,f519,f518,f517,f516,f636,f524,f525,f535,f534,f533,f532,f531,f530,f529,f528,f637,f536,f537,f547,f546,f545,f544,f543,f542,f541,f540,f638,f548,f550,f549,f558,f557,f556,f555,f554,f553,f552,f639,f559,f561,f560,f569,f568,f567,f566,f565,f564,f563,f640,f570,f641]) ).
fof(f641,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f572]) ).
fof(f572,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f361]) ).
fof(f570,plain,
! [X0] :
( sP19(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f252]) ).
fof(f252,plain,
! [X0] :
( sP19(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f174,f251,f250]) ).
fof(f250,plain,
! [X0] :
( sP18(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,[sP18])]) ).
fof(f251,plain,
! [X0] :
( ( strictorderedP(X0)
<=> sP18(X0) )
| ~ sP19(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP19])]) ).
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(flattening,[],[f173]) ).
fof(f173,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(f640,plain,
! [X10,X8,X6,X9,X7] :
( ~ sP18(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,[],[f562]) ).
fof(f562,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)
| ~ sP18(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f360,plain,
! [X0] :
( ( sP18(X0)
| ( ~ lt(sK62(X0),sK63(X0))
& app(app(sK64(X0),cons(sK62(X0),sK65(X0))),cons(sK63(X0),sK66(X0))) = X0
& ssList(sK66(X0))
& ssList(sK65(X0))
& ssList(sK64(X0))
& ssItem(sK63(X0))
& ssItem(sK62(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) )
| ~ sP18(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK62,sK63,sK64,sK65,sK66])],[f354,f359,f358,f357,f356,f355]) ).
fof(f355,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(sK62(X0),X2)
& app(app(X3,cons(sK62(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK62(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f356,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK62(X0),X2)
& app(app(X3,cons(sK62(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK62(X0),sK63(X0))
& app(app(X3,cons(sK62(X0),X4)),cons(sK63(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK63(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f357,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK62(X0),sK63(X0))
& app(app(X3,cons(sK62(X0),X4)),cons(sK63(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK62(X0),sK63(X0))
& app(app(sK64(X0),cons(sK62(X0),X4)),cons(sK63(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK64(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f358,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK62(X0),sK63(X0))
& app(app(sK64(X0),cons(sK62(X0),X4)),cons(sK63(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK62(X0),sK63(X0))
& app(app(sK64(X0),cons(sK62(X0),sK65(X0))),cons(sK63(X0),X5)) = X0
& ssList(X5) )
& ssList(sK65(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f359,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK62(X0),sK63(X0))
& app(app(sK64(X0),cons(sK62(X0),sK65(X0))),cons(sK63(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK62(X0),sK63(X0))
& app(app(sK64(X0),cons(sK62(X0),sK65(X0))),cons(sK63(X0),sK66(X0))) = X0
& ssList(sK66(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f354,plain,
! [X0] :
( ( sP18(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) )
| ~ sP18(X0) ) ),
inference(rectify,[],[f353]) ).
fof(f353,plain,
! [X0] :
( ( sP18(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) )
| ~ sP18(X0) ) ),
inference(nnf_transformation,[],[f250]) ).
fof(f563,plain,
! [X0] :
( ssItem(sK62(X0))
| sP18(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f564,plain,
! [X0] :
( ssItem(sK63(X0))
| sP18(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f565,plain,
! [X0] :
( ssList(sK64(X0))
| sP18(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f566,plain,
! [X0] :
( ssList(sK65(X0))
| sP18(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f567,plain,
! [X0] :
( ssList(sK66(X0))
| sP18(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f568,plain,
! [X0] :
( sP18(X0)
| app(app(sK64(X0),cons(sK62(X0),sK65(X0))),cons(sK63(X0),sK66(X0))) = X0 ),
inference(cnf_transformation,[],[f360]) ).
fof(f569,plain,
! [X0] :
( ~ lt(sK62(X0),sK63(X0))
| sP18(X0) ),
inference(cnf_transformation,[],[f360]) ).
fof(f560,plain,
! [X0] :
( ~ sP19(X0)
| ~ strictorderedP(X0)
| sP18(X0) ),
inference(cnf_transformation,[],[f352]) ).
fof(f352,plain,
! [X0] :
( ( ( strictorderedP(X0)
| ~ sP18(X0) )
& ( sP18(X0)
| ~ strictorderedP(X0) ) )
| ~ sP19(X0) ),
inference(nnf_transformation,[],[f251]) ).
fof(f561,plain,
! [X0] :
( ~ sP19(X0)
| ~ sP18(X0)
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f352]) ).
fof(f559,plain,
! [X0] :
( sP17(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f249]) ).
fof(f249,plain,
! [X0] :
( sP17(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f172,f248,f247]) ).
fof(f247,plain,
! [X0] :
( sP16(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,[sP16])]) ).
fof(f248,plain,
! [X0] :
( ( totalorderedP(X0)
<=> sP16(X0) )
| ~ sP17(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP17])]) ).
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(flattening,[],[f171]) ).
fof(f171,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(f639,plain,
! [X10,X8,X6,X9,X7] :
( ~ sP16(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,[],[f551]) ).
fof(f551,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)
| ~ sP16(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f351,plain,
! [X0] :
( ( sP16(X0)
| ( ~ leq(sK57(X0),sK58(X0))
& app(app(sK59(X0),cons(sK57(X0),sK60(X0))),cons(sK58(X0),sK61(X0))) = X0
& ssList(sK61(X0))
& ssList(sK60(X0))
& ssList(sK59(X0))
& ssItem(sK58(X0))
& ssItem(sK57(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) )
| ~ sP16(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57,sK58,sK59,sK60,sK61])],[f345,f350,f349,f348,f347,f346]) ).
fof(f346,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(sK57(X0),X2)
& app(app(X3,cons(sK57(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK57(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f347,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK57(X0),X2)
& app(app(X3,cons(sK57(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK57(X0),sK58(X0))
& app(app(X3,cons(sK57(X0),X4)),cons(sK58(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK58(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK57(X0),sK58(X0))
& app(app(X3,cons(sK57(X0),X4)),cons(sK58(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK57(X0),sK58(X0))
& app(app(sK59(X0),cons(sK57(X0),X4)),cons(sK58(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK59(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f349,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK57(X0),sK58(X0))
& app(app(sK59(X0),cons(sK57(X0),X4)),cons(sK58(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK57(X0),sK58(X0))
& app(app(sK59(X0),cons(sK57(X0),sK60(X0))),cons(sK58(X0),X5)) = X0
& ssList(X5) )
& ssList(sK60(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f350,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK57(X0),sK58(X0))
& app(app(sK59(X0),cons(sK57(X0),sK60(X0))),cons(sK58(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK57(X0),sK58(X0))
& app(app(sK59(X0),cons(sK57(X0),sK60(X0))),cons(sK58(X0),sK61(X0))) = X0
& ssList(sK61(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f345,plain,
! [X0] :
( ( sP16(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) )
| ~ sP16(X0) ) ),
inference(rectify,[],[f344]) ).
fof(f344,plain,
! [X0] :
( ( sP16(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) )
| ~ sP16(X0) ) ),
inference(nnf_transformation,[],[f247]) ).
fof(f552,plain,
! [X0] :
( ssItem(sK57(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f553,plain,
! [X0] :
( ssItem(sK58(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f554,plain,
! [X0] :
( ssList(sK59(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f555,plain,
! [X0] :
( ssList(sK60(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f556,plain,
! [X0] :
( ssList(sK61(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f557,plain,
! [X0] :
( sP16(X0)
| app(app(sK59(X0),cons(sK57(X0),sK60(X0))),cons(sK58(X0),sK61(X0))) = X0 ),
inference(cnf_transformation,[],[f351]) ).
fof(f558,plain,
! [X0] :
( ~ leq(sK57(X0),sK58(X0))
| sP16(X0) ),
inference(cnf_transformation,[],[f351]) ).
fof(f549,plain,
! [X0] :
( ~ sP17(X0)
| ~ totalorderedP(X0)
| sP16(X0) ),
inference(cnf_transformation,[],[f343]) ).
fof(f343,plain,
! [X0] :
( ( ( totalorderedP(X0)
| ~ sP16(X0) )
& ( sP16(X0)
| ~ totalorderedP(X0) ) )
| ~ sP17(X0) ),
inference(nnf_transformation,[],[f248]) ).
fof(f550,plain,
! [X0] :
( ~ sP17(X0)
| ~ sP16(X0)
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f343]) ).
fof(f548,plain,
! [X0] :
( sP15(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f246]) ).
fof(f246,plain,
! [X0] :
( sP15(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f170,f245,f244]) ).
fof(f244,plain,
! [X0] :
( sP14(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,[sP14])]) ).
fof(f245,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> sP14(X0) )
| ~ sP15(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP15])]) ).
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(flattening,[],[f169]) ).
fof(f169,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(f638,plain,
! [X10,X8,X6,X9,X7] :
( ~ sP14(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,[],[f539]) ).
fof(f539,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)
| ~ sP14(X0) ),
inference(cnf_transformation,[],[f342]) ).
fof(f342,plain,
! [X0] :
( ( sP14(X0)
| ( leq(sK53(X0),sK52(X0))
& leq(sK52(X0),sK53(X0))
& app(app(sK54(X0),cons(sK52(X0),sK55(X0))),cons(sK53(X0),sK56(X0))) = X0
& ssList(sK56(X0))
& ssList(sK55(X0))
& ssList(sK54(X0))
& ssItem(sK53(X0))
& ssItem(sK52(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) )
| ~ sP14(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK52,sK53,sK54,sK55,sK56])],[f336,f341,f340,f339,f338,f337]) ).
fof(f337,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,sK52(X0))
& leq(sK52(X0),X2)
& app(app(X3,cons(sK52(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f338,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK52(X0))
& leq(sK52(X0),X2)
& app(app(X3,cons(sK52(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK53(X0),sK52(X0))
& leq(sK52(X0),sK53(X0))
& app(app(X3,cons(sK52(X0),X4)),cons(sK53(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK53(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f339,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK53(X0),sK52(X0))
& leq(sK52(X0),sK53(X0))
& app(app(X3,cons(sK52(X0),X4)),cons(sK53(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( leq(sK53(X0),sK52(X0))
& leq(sK52(X0),sK53(X0))
& app(app(sK54(X0),cons(sK52(X0),X4)),cons(sK53(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK54(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f340,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( leq(sK53(X0),sK52(X0))
& leq(sK52(X0),sK53(X0))
& app(app(sK54(X0),cons(sK52(X0),X4)),cons(sK53(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( leq(sK53(X0),sK52(X0))
& leq(sK52(X0),sK53(X0))
& app(app(sK54(X0),cons(sK52(X0),sK55(X0))),cons(sK53(X0),X5)) = X0
& ssList(X5) )
& ssList(sK55(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f341,plain,
! [X0] :
( ? [X5] :
( leq(sK53(X0),sK52(X0))
& leq(sK52(X0),sK53(X0))
& app(app(sK54(X0),cons(sK52(X0),sK55(X0))),cons(sK53(X0),X5)) = X0
& ssList(X5) )
=> ( leq(sK53(X0),sK52(X0))
& leq(sK52(X0),sK53(X0))
& app(app(sK54(X0),cons(sK52(X0),sK55(X0))),cons(sK53(X0),sK56(X0))) = X0
& ssList(sK56(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f336,plain,
! [X0] :
( ( sP14(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) )
| ~ sP14(X0) ) ),
inference(rectify,[],[f335]) ).
fof(f335,plain,
! [X0] :
( ( sP14(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) )
| ~ sP14(X0) ) ),
inference(nnf_transformation,[],[f244]) ).
fof(f540,plain,
! [X0] :
( ssItem(sK52(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f342]) ).
fof(f541,plain,
! [X0] :
( ssItem(sK53(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f342]) ).
fof(f542,plain,
! [X0] :
( ssList(sK54(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f342]) ).
fof(f543,plain,
! [X0] :
( ssList(sK55(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f342]) ).
fof(f544,plain,
! [X0] :
( ssList(sK56(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f342]) ).
fof(f545,plain,
! [X0] :
( sP14(X0)
| app(app(sK54(X0),cons(sK52(X0),sK55(X0))),cons(sK53(X0),sK56(X0))) = X0 ),
inference(cnf_transformation,[],[f342]) ).
fof(f546,plain,
! [X0] :
( leq(sK52(X0),sK53(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f342]) ).
fof(f547,plain,
! [X0] :
( leq(sK53(X0),sK52(X0))
| sP14(X0) ),
inference(cnf_transformation,[],[f342]) ).
fof(f537,plain,
! [X0] :
( ~ sP15(X0)
| ~ cyclefreeP(X0)
| sP14(X0) ),
inference(cnf_transformation,[],[f334]) ).
fof(f334,plain,
! [X0] :
( ( ( cyclefreeP(X0)
| ~ sP14(X0) )
& ( sP14(X0)
| ~ cyclefreeP(X0) ) )
| ~ sP15(X0) ),
inference(nnf_transformation,[],[f245]) ).
fof(f536,plain,
! [X0] :
( sP13(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f243]) ).
fof(f243,plain,
! [X0] :
( sP13(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f168,f242,f241]) ).
fof(f241,plain,
! [X0] :
( sP12(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,[sP12])]) ).
fof(f242,plain,
! [X0] :
( ( strictorderP(X0)
<=> sP12(X0) )
| ~ sP13(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP13])]) ).
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(flattening,[],[f167]) ).
fof(f167,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(f637,plain,
! [X10,X8,X6,X9,X7] :
( ~ sP12(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,[],[f527]) ).
fof(f527,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)
| ~ sP12(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f333,plain,
! [X0] :
( ( sP12(X0)
| ( ~ lt(sK48(X0),sK47(X0))
& ~ lt(sK47(X0),sK48(X0))
& app(app(sK49(X0),cons(sK47(X0),sK50(X0))),cons(sK48(X0),sK51(X0))) = X0
& ssList(sK51(X0))
& ssList(sK50(X0))
& ssList(sK49(X0))
& ssItem(sK48(X0))
& ssItem(sK47(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) )
| ~ sP12(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK47,sK48,sK49,sK50,sK51])],[f327,f332,f331,f330,f329,f328]) ).
fof(f328,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,sK47(X0))
& ~ lt(sK47(X0),X2)
& app(app(X3,cons(sK47(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK47(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f329,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK47(X0))
& ~ lt(sK47(X0),X2)
& app(app(X3,cons(sK47(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK48(X0),sK47(X0))
& ~ lt(sK47(X0),sK48(X0))
& app(app(X3,cons(sK47(X0),X4)),cons(sK48(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK48(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f330,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK48(X0),sK47(X0))
& ~ lt(sK47(X0),sK48(X0))
& app(app(X3,cons(sK47(X0),X4)),cons(sK48(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK48(X0),sK47(X0))
& ~ lt(sK47(X0),sK48(X0))
& app(app(sK49(X0),cons(sK47(X0),X4)),cons(sK48(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK49(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f331,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK48(X0),sK47(X0))
& ~ lt(sK47(X0),sK48(X0))
& app(app(sK49(X0),cons(sK47(X0),X4)),cons(sK48(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK48(X0),sK47(X0))
& ~ lt(sK47(X0),sK48(X0))
& app(app(sK49(X0),cons(sK47(X0),sK50(X0))),cons(sK48(X0),X5)) = X0
& ssList(X5) )
& ssList(sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f332,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK48(X0),sK47(X0))
& ~ lt(sK47(X0),sK48(X0))
& app(app(sK49(X0),cons(sK47(X0),sK50(X0))),cons(sK48(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK48(X0),sK47(X0))
& ~ lt(sK47(X0),sK48(X0))
& app(app(sK49(X0),cons(sK47(X0),sK50(X0))),cons(sK48(X0),sK51(X0))) = X0
& ssList(sK51(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f327,plain,
! [X0] :
( ( sP12(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) )
| ~ sP12(X0) ) ),
inference(rectify,[],[f326]) ).
fof(f326,plain,
! [X0] :
( ( sP12(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) )
| ~ sP12(X0) ) ),
inference(nnf_transformation,[],[f241]) ).
fof(f528,plain,
! [X0] :
( ssItem(sK47(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f529,plain,
! [X0] :
( ssItem(sK48(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f530,plain,
! [X0] :
( ssList(sK49(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f531,plain,
! [X0] :
( ssList(sK50(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f532,plain,
! [X0] :
( ssList(sK51(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f533,plain,
! [X0] :
( sP12(X0)
| app(app(sK49(X0),cons(sK47(X0),sK50(X0))),cons(sK48(X0),sK51(X0))) = X0 ),
inference(cnf_transformation,[],[f333]) ).
fof(f534,plain,
! [X0] :
( ~ lt(sK47(X0),sK48(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f535,plain,
! [X0] :
( ~ lt(sK48(X0),sK47(X0))
| sP12(X0) ),
inference(cnf_transformation,[],[f333]) ).
fof(f525,plain,
! [X0] :
( ~ sP13(X0)
| ~ strictorderP(X0)
| sP12(X0) ),
inference(cnf_transformation,[],[f325]) ).
fof(f325,plain,
! [X0] :
( ( ( strictorderP(X0)
| ~ sP12(X0) )
& ( sP12(X0)
| ~ strictorderP(X0) ) )
| ~ sP13(X0) ),
inference(nnf_transformation,[],[f242]) ).
fof(f524,plain,
! [X0] :
( sP11(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f240]) ).
fof(f240,plain,
! [X0] :
( sP11(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f166,f239,f238]) ).
fof(f238,plain,
! [X0] :
( sP10(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,[sP10])]) ).
fof(f239,plain,
! [X0] :
( ( totalorderP(X0)
<=> sP10(X0) )
| ~ sP11(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP11])]) ).
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(flattening,[],[f165]) ).
fof(f165,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(f636,plain,
! [X10,X8,X6,X9,X7] :
( ~ sP10(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,[],[f515]) ).
fof(f515,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)
| ~ sP10(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f324,plain,
! [X0] :
( ( sP10(X0)
| ( ~ leq(sK43(X0),sK42(X0))
& ~ leq(sK42(X0),sK43(X0))
& app(app(sK44(X0),cons(sK42(X0),sK45(X0))),cons(sK43(X0),sK46(X0))) = X0
& ssList(sK46(X0))
& ssList(sK45(X0))
& ssList(sK44(X0))
& ssItem(sK43(X0))
& ssItem(sK42(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) )
| ~ sP10(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK42,sK43,sK44,sK45,sK46])],[f318,f323,f322,f321,f320,f319]) ).
fof(f319,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,sK42(X0))
& ~ leq(sK42(X0),X2)
& app(app(X3,cons(sK42(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK42(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f320,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK42(X0))
& ~ leq(sK42(X0),X2)
& app(app(X3,cons(sK42(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK43(X0),sK42(X0))
& ~ leq(sK42(X0),sK43(X0))
& app(app(X3,cons(sK42(X0),X4)),cons(sK43(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK43(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f321,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK43(X0),sK42(X0))
& ~ leq(sK42(X0),sK43(X0))
& app(app(X3,cons(sK42(X0),X4)),cons(sK43(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK43(X0),sK42(X0))
& ~ leq(sK42(X0),sK43(X0))
& app(app(sK44(X0),cons(sK42(X0),X4)),cons(sK43(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK44(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f322,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK43(X0),sK42(X0))
& ~ leq(sK42(X0),sK43(X0))
& app(app(sK44(X0),cons(sK42(X0),X4)),cons(sK43(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK43(X0),sK42(X0))
& ~ leq(sK42(X0),sK43(X0))
& app(app(sK44(X0),cons(sK42(X0),sK45(X0))),cons(sK43(X0),X5)) = X0
& ssList(X5) )
& ssList(sK45(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f323,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK43(X0),sK42(X0))
& ~ leq(sK42(X0),sK43(X0))
& app(app(sK44(X0),cons(sK42(X0),sK45(X0))),cons(sK43(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK43(X0),sK42(X0))
& ~ leq(sK42(X0),sK43(X0))
& app(app(sK44(X0),cons(sK42(X0),sK45(X0))),cons(sK43(X0),sK46(X0))) = X0
& ssList(sK46(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f318,plain,
! [X0] :
( ( sP10(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) )
| ~ sP10(X0) ) ),
inference(rectify,[],[f317]) ).
fof(f317,plain,
! [X0] :
( ( sP10(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) )
| ~ sP10(X0) ) ),
inference(nnf_transformation,[],[f238]) ).
fof(f516,plain,
! [X0] :
( ssItem(sK42(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f517,plain,
! [X0] :
( ssItem(sK43(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f518,plain,
! [X0] :
( ssList(sK44(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f519,plain,
! [X0] :
( ssList(sK45(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f520,plain,
! [X0] :
( ssList(sK46(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f521,plain,
! [X0] :
( sP10(X0)
| app(app(sK44(X0),cons(sK42(X0),sK45(X0))),cons(sK43(X0),sK46(X0))) = X0 ),
inference(cnf_transformation,[],[f324]) ).
fof(f522,plain,
! [X0] :
( ~ leq(sK42(X0),sK43(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f523,plain,
! [X0] :
( ~ leq(sK43(X0),sK42(X0))
| sP10(X0) ),
inference(cnf_transformation,[],[f324]) ).
fof(f513,plain,
! [X0] :
( ~ sP11(X0)
| ~ totalorderP(X0)
| sP10(X0) ),
inference(cnf_transformation,[],[f316]) ).
fof(f316,plain,
! [X0] :
( ( ( totalorderP(X0)
| ~ sP10(X0) )
& ( sP10(X0)
| ~ totalorderP(X0) ) )
| ~ sP11(X0) ),
inference(nnf_transformation,[],[f239]) ).
fof(f512,plain,
! [X0] :
( sP9(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f237]) ).
fof(f237,plain,
! [X0] :
( sP9(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f164,f236,f235]) ).
fof(f235,plain,
! [X0] :
( sP8(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,[sP8])]) ).
fof(f236,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> sP8(X0) )
| ~ sP9(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP9])]) ).
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(flattening,[],[f163]) ).
fof(f163,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(f652,plain,
! [X10,X8,X9,X7] :
( ~ sP8(app(app(X8,cons(X7,X9)),cons(X7,X10)))
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssList(X10) ),
inference(duplicate_literal_removal,[],[f635]) ).
fof(f635,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP8(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f634]) ).
fof(f634,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)
| ~ sP8(X0) ),
inference(equality_resolution,[],[f504]) ).
fof(f504,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)
| ~ sP8(X0) ),
inference(cnf_transformation,[],[f315]) ).
fof(f315,plain,
! [X0] :
( ( sP8(X0)
| ( sK37(X0) = sK38(X0)
& app(app(sK39(X0),cons(sK37(X0),sK40(X0))),cons(sK38(X0),sK41(X0))) = X0
& ssList(sK41(X0))
& ssList(sK40(X0))
& ssList(sK39(X0))
& ssItem(sK38(X0))
& ssItem(sK37(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) )
| ~ sP8(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37,sK38,sK39,sK40,sK41])],[f309,f314,f313,f312,f311,f310]) ).
fof(f310,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] :
( sK37(X0) = X2
& app(app(X3,cons(sK37(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK37(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f311,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK37(X0) = X2
& app(app(X3,cons(sK37(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK37(X0) = sK38(X0)
& app(app(X3,cons(sK37(X0),X4)),cons(sK38(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK38(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f312,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK37(X0) = sK38(X0)
& app(app(X3,cons(sK37(X0),X4)),cons(sK38(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( sK37(X0) = sK38(X0)
& app(app(sK39(X0),cons(sK37(X0),X4)),cons(sK38(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK39(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f313,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( sK37(X0) = sK38(X0)
& app(app(sK39(X0),cons(sK37(X0),X4)),cons(sK38(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( sK37(X0) = sK38(X0)
& app(app(sK39(X0),cons(sK37(X0),sK40(X0))),cons(sK38(X0),X5)) = X0
& ssList(X5) )
& ssList(sK40(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f314,plain,
! [X0] :
( ? [X5] :
( sK37(X0) = sK38(X0)
& app(app(sK39(X0),cons(sK37(X0),sK40(X0))),cons(sK38(X0),X5)) = X0
& ssList(X5) )
=> ( sK37(X0) = sK38(X0)
& app(app(sK39(X0),cons(sK37(X0),sK40(X0))),cons(sK38(X0),sK41(X0))) = X0
& ssList(sK41(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f309,plain,
! [X0] :
( ( sP8(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) )
| ~ sP8(X0) ) ),
inference(rectify,[],[f308]) ).
fof(f308,plain,
! [X0] :
( ( sP8(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) )
| ~ sP8(X0) ) ),
inference(nnf_transformation,[],[f235]) ).
fof(f505,plain,
! [X0] :
( ssItem(sK37(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f315]) ).
fof(f506,plain,
! [X0] :
( ssItem(sK38(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f315]) ).
fof(f507,plain,
! [X0] :
( ssList(sK39(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f315]) ).
fof(f508,plain,
! [X0] :
( ssList(sK40(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f315]) ).
fof(f509,plain,
! [X0] :
( ssList(sK41(X0))
| sP8(X0) ),
inference(cnf_transformation,[],[f315]) ).
fof(f510,plain,
! [X0] :
( sP8(X0)
| app(app(sK39(X0),cons(sK37(X0),sK40(X0))),cons(sK38(X0),sK41(X0))) = X0 ),
inference(cnf_transformation,[],[f315]) ).
fof(f511,plain,
! [X0] :
( sP8(X0)
| sK37(X0) = sK38(X0) ),
inference(cnf_transformation,[],[f315]) ).
fof(f502,plain,
! [X0] :
( ~ sP9(X0)
| ~ duplicatefreeP(X0)
| sP8(X0) ),
inference(cnf_transformation,[],[f307]) ).
fof(f307,plain,
! [X0] :
( ( ( duplicatefreeP(X0)
| ~ sP8(X0) )
& ( sP8(X0)
| ~ duplicatefreeP(X0) ) )
| ~ sP9(X0) ),
inference(nnf_transformation,[],[f236]) ).
fof(f501,plain,
! [X0] :
( sP7(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f234]) ).
fof(f234,plain,
! [X0] :
( sP7(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f162,f233,f232]) ).
fof(f232,plain,
! [X0] :
( sP6(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,[sP6])]) ).
fof(f233,plain,
! [X0] :
( ( equalelemsP(X0)
<=> sP6(X0) )
| ~ sP7(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP7])]) ).
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(flattening,[],[f161]) ).
fof(f161,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(f633,plain,
! [X8,X6,X7,X5] :
( ~ sP6(app(X7,cons(X5,cons(X6,X8))))
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| X5 = X6 ),
inference(equality_resolution,[],[f494]) ).
fof(f494,plain,
! [X0,X8,X6,X7,X5] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP6(X0) ),
inference(cnf_transformation,[],[f306]) ).
fof(f306,plain,
! [X0] :
( ( sP6(X0)
| ( sK33(X0) != sK34(X0)
& app(sK35(X0),cons(sK33(X0),cons(sK34(X0),sK36(X0)))) = X0
& ssList(sK36(X0))
& ssList(sK35(X0))
& ssItem(sK34(X0))
& ssItem(sK33(X0)) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP6(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK33,sK34,sK35,sK36])],[f301,f305,f304,f303,f302]) ).
fof(f302,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] :
( sK33(X0) != X2
& app(X3,cons(sK33(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK33(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f303,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK33(X0) != X2
& app(X3,cons(sK33(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( sK33(X0) != sK34(X0)
& app(X3,cons(sK33(X0),cons(sK34(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(sK34(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f304,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( sK33(X0) != sK34(X0)
& app(X3,cons(sK33(X0),cons(sK34(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( sK33(X0) != sK34(X0)
& app(sK35(X0),cons(sK33(X0),cons(sK34(X0),X4))) = X0
& ssList(X4) )
& ssList(sK35(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f305,plain,
! [X0] :
( ? [X4] :
( sK33(X0) != sK34(X0)
& app(sK35(X0),cons(sK33(X0),cons(sK34(X0),X4))) = X0
& ssList(X4) )
=> ( sK33(X0) != sK34(X0)
& app(sK35(X0),cons(sK33(X0),cons(sK34(X0),sK36(X0)))) = X0
& ssList(sK36(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f301,plain,
! [X0] :
( ( sP6(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) )
| ~ sP6(X0) ) ),
inference(rectify,[],[f300]) ).
fof(f300,plain,
! [X0] :
( ( sP6(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) )
| ~ sP6(X0) ) ),
inference(nnf_transformation,[],[f232]) ).
fof(f495,plain,
! [X0] :
( ssItem(sK33(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f306]) ).
fof(f496,plain,
! [X0] :
( ssItem(sK34(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f306]) ).
fof(f497,plain,
! [X0] :
( ssList(sK35(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f306]) ).
fof(f498,plain,
! [X0] :
( ssList(sK36(X0))
| sP6(X0) ),
inference(cnf_transformation,[],[f306]) ).
fof(f499,plain,
! [X0] :
( sP6(X0)
| app(sK35(X0),cons(sK33(X0),cons(sK34(X0),sK36(X0)))) = X0 ),
inference(cnf_transformation,[],[f306]) ).
fof(f500,plain,
! [X0] :
( sK33(X0) != sK34(X0)
| sP6(X0) ),
inference(cnf_transformation,[],[f306]) ).
fof(f492,plain,
! [X0] :
( ~ sP7(X0)
| ~ equalelemsP(X0)
| sP6(X0) ),
inference(cnf_transformation,[],[f299]) ).
fof(f299,plain,
! [X0] :
( ( ( equalelemsP(X0)
| ~ sP6(X0) )
& ( sP6(X0)
| ~ equalelemsP(X0) ) )
| ~ sP7(X0) ),
inference(nnf_transformation,[],[f233]) ).
fof(f489,plain,
! [X0] :
( ssItem(sK32(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f298]) ).
fof(f298,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK32(X0),nil) = X0
& ssItem(sK32(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK32])],[f296,f297]) ).
fof(f297,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK32(X0),nil) = X0
& ssItem(sK32(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f296,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f295]) ).
fof(f295,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,[],[f160]) ).
fof(f160,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(f490,plain,
! [X0] :
( ~ singletonP(X0)
| cons(sK32(X0),nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f298]) ).
fof(f632,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f491]) ).
fof(f491,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f298]) ).
fof(f487,plain,
! [X0] :
( ssList(sK31(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f294]) ).
fof(f294,plain,
! [X0] :
( ( tl(X0) = sK31(X0)
& ssList(sK31(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f159,f293]) ).
fof(f293,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK31(X0)
& ssList(sK31(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f159,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f158]) ).
fof(f158,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(f488,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK31(X0) ),
inference(cnf_transformation,[],[f294]) ).
fof(f485,plain,
! [X0] :
( ssItem(sK30(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f292,plain,
! [X0] :
( ( hd(X0) = sK30(X0)
& ssItem(sK30(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30])],[f157,f291]) ).
fof(f291,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK30(X0)
& ssItem(sK30(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f157,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f156]) ).
fof(f156,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(f486,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK30(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f483,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f153]) ).
fof(f153,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f152]) ).
fof(f152,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(f482,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f151]) ).
fof(f151,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(flattening,[],[f150]) ).
fof(f150,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(f479,plain,
! [X0] :
( ssList(sK28(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f290]) ).
fof(f480,plain,
! [X0] :
( ssItem(sK29(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f290]) ).
fof(f478,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,X0) = X0 ),
inference(cnf_transformation,[],[f147]) ).
fof(f147,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(f477,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,nil) = X0 ),
inference(cnf_transformation,[],[f146]) ).
fof(f146,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(f476,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,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(f475,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,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(f473,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f142]) ).
fof(f142,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(f472,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f141]) ).
fof(f141,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(f471,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f140]) ).
fof(f140,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(f468,plain,
! [X2,X0,X1] :
( ~ memberP(app(X1,X2),X0)
| memberP(X1,X0)
| memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f287,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,[],[f286]) ).
fof(f286,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,[],[f139]) ).
fof(f139,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(f469,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f470,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f463,plain,
! [X0,X1] :
( ~ sP4(X0,X1)
| nil = X0
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f630,plain,
! [X1] : sP4(nil,X1),
inference(equality_resolution,[],[f465]) ).
fof(f465,plain,
! [X0,X1] :
( sP4(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f285]) ).
fof(f466,plain,
! [X0,X1] :
( ~ lt(X1,hd(X0))
| sP4(X0,X1)
| ~ strictorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f285]) ).
fof(f461,plain,
! [X0,X1] :
( strictorderedP(cons(X0,X1))
| ~ sP4(X1,X0)
| ~ sP5(X0,X1) ),
inference(cnf_transformation,[],[f282]) ).
fof(f455,plain,
! [X0,X1] :
( ~ sP2(X0,X1)
| nil = X0
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f281]) ).
fof(f281,plain,
! [X0,X1] :
( ( sP2(X0,X1)
| ( ( ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( leq(X1,hd(X0))
& totalorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP2(X0,X1) ) ),
inference(rectify,[],[f280]) ).
fof(f280,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(flattening,[],[f279]) ).
fof(f279,plain,
! [X1,X0] :
( ( sP2(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP2(X1,X0) ) ),
inference(nnf_transformation,[],[f226]) ).
fof(f456,plain,
! [X0,X1] :
( leq(X1,hd(X0))
| nil = X0
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f281]) ).
fof(f628,plain,
! [X1] : sP2(nil,X1),
inference(equality_resolution,[],[f457]) ).
fof(f457,plain,
! [X0,X1] :
( sP2(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f281]) ).
fof(f458,plain,
! [X0,X1] :
( ~ leq(X1,hd(X0))
| sP2(X0,X1)
| ~ totalorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f281]) ).
fof(f453,plain,
! [X0,X1] :
( totalorderedP(cons(X0,X1))
| ~ sP2(X1,X0)
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f278]) ).
fof(f449,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,[],[f277]) ).
fof(f277,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,[],[f276]) ).
fof(f276,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,[],[f136]) ).
fof(f136,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(f450,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,[],[f277]) ).
fof(f653,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f627]) ).
fof(f627,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,[],[f451]) ).
fof(f451,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,[],[f277]) ).
fof(f446,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X1,X2),X0)
| X0 = X1
| memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f275,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,[],[f274]) ).
fof(f274,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,[],[f135]) ).
fof(f135,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(f654,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f626]) ).
fof(f626,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f447]) ).
fof(f447,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f448,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f275]) ).
fof(f445,plain,
! [X2,X0,X1] :
( ~ lt(X1,X2)
| lt(X0,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f134]) ).
fof(f134,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ lt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f133]) ).
fof(f133,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(f444,plain,
! [X2,X0,X1] :
( ~ lt(X1,X2)
| lt(X0,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f132]) ).
fof(f132,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f131]) ).
fof(f131,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(f443,plain,
! [X2,X0,X1] :
( ~ leq(X1,X2)
| leq(X0,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f130]) ).
fof(f130,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f129]) ).
fof(f129,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(f442,plain,
! [X2,X0,X1] :
( ~ geq(X1,X2)
| geq(X0,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f128,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f127]) ).
fof(f127,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(f441,plain,
! [X2,X0,X1] :
( ~ gt(X1,X2)
| gt(X0,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f126]) ).
fof(f126,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( gt(X0,X2)
| ~ gt(X1,X2)
| ~ gt(X0,X1)
| ~ ssItem(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f125]) ).
fof(f125,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(f655,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f625]) ).
fof(f625,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f438]) ).
fof(f438,plain,
! [X0,X1] :
( X0 != X1
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f440,plain,
! [X0,X1] :
( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f273]) ).
fof(f436,plain,
! [X0,X1] :
( ~ geq(X0,X1)
| leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f271,plain,
! [X0] :
( ! [X1] :
( ( ( geq(X0,X1)
| ~ leq(X1,X0) )
& ( leq(X1,X0)
| ~ geq(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f123]) ).
fof(f123,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(f437,plain,
! [X0,X1] :
( geq(X0,X1)
| ~ leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f271]) ).
fof(f434,plain,
! [X0,X1] :
( ~ gt(X0,X1)
| lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f270]) ).
fof(f270,plain,
! [X0] :
( ! [X1] :
( ( ( gt(X0,X1)
| ~ lt(X1,X0) )
& ( lt(X1,X0)
| ~ gt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(nnf_transformation,[],[f122]) ).
fof(f122,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(f435,plain,
! [X0,X1] :
( gt(X0,X1)
| ~ lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f270]) ).
fof(f431,plain,
! [X0,X1] :
( ~ leq(X1,X0)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f120,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f119]) ).
fof(f119,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(f430,plain,
! [X0,X1] :
( ~ geq(X1,X0)
| X0 = X1
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f118]) ).
fof(f118,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f117]) ).
fof(f117,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(f429,plain,
! [X0,X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f116]) ).
fof(f116,plain,
! [X0] :
( ! [X1] :
( ~ lt(X1,X0)
| ~ lt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f115]) ).
fof(f115,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(f428,plain,
! [X0,X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f114]) ).
fof(f114,plain,
! [X0] :
( ! [X1] :
( lt(X0,X1)
| X0 = X1
| ~ leq(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f113]) ).
fof(f113,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(f427,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f112]) ).
fof(f112,plain,
! [X0] :
( ! [X1] :
( ~ gt(X1,X0)
| ~ gt(X0,X1)
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f111]) ).
fof(f111,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(f426,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,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(f425,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f109]) ).
fof(f109,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(f424,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,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(f423,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f107,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(f422,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,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(f421,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f105]) ).
fof(f105,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(f420,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,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(f419,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f103]) ).
fof(f103,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(f418,plain,
! [X0] :
( geq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f102]) ).
fof(f102,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(f416,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f100]) ).
fof(f100,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(f414,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax66) ).
fof(f413,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax69) ).
fof(f412,plain,
totalorderP(nil),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax62) ).
fof(f411,plain,
strictorderP(nil),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax64) ).
fof(f410,plain,
cyclefreeP(nil),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax60) ).
fof(f409,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax72) ).
fof(f408,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax74) ).
fof(f407,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax39) ).
fof(f398,plain,
ssList(sK24),
inference(cnf_transformation,[],[f268]) ).
fof(f399,plain,
ssList(sK25),
inference(cnf_transformation,[],[f268]) ).
fof(f400,plain,
ssList(sK26),
inference(cnf_transformation,[],[f268]) ).
fof(f401,plain,
sK24 = sK26,
inference(cnf_transformation,[],[f268]) ).
fof(f393,plain,
! [X2,X0,X1] :
( memberP(X2,sK22(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f261]) ).
fof(f394,plain,
! [X2,X0,X1] :
( memberP(X1,sK22(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f261]) ).
fof(f391,plain,
! [X0,X1,X4] :
( ~ memberP(sK21(X0,X1),X4)
| ~ lt(X0,X4)
| ~ memberP(sK20(X0,X1),X4)
| leq(X0,X4)
| ~ ssItem(X4)
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f257]) ).
fof(f7064,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl75_30
| spl75_80 ),
inference(resolution,[],[f7061,f3407]) ).
fof(f3407,plain,
( ! [X0] :
( frontsegP(cons(sK74,sK23),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl75_30 ),
inference(subsumption_resolution,[],[f3406,f415]) ).
fof(f3406,plain,
( ! [X0] :
( frontsegP(cons(sK74,sK23),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_30 ),
inference(subsumption_resolution,[],[f3368,f2334]) ).
fof(f3368,plain,
( ! [X0] :
( frontsegP(cons(sK74,sK23),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(cons(sK74,sK23))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_30 ),
inference(superposition,[],[f614,f2371]) ).
fof(f2371,plain,
( cons(sK74,sK23) = app(nil,cons(sK74,sK23))
| ~ spl75_30 ),
inference(resolution,[],[f2334,f478]) ).
fof(f614,plain,
! [X2,X0,X1] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f210]) ).
fof(f210,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f209]) ).
fof(f209,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(f7063,plain,
( ~ spl75_79
| spl75_80
| ~ spl75_30 ),
inference(avatar_split_clause,[],[f6563,f2332,f7060,f7056]) ).
fof(f6563,plain,
( frontsegP(cons(sK74,sK23),nil)
| ~ ssList(sK72(cons(sK74,sK23),nil))
| ~ spl75_30 ),
inference(subsumption_resolution,[],[f6553,f415]) ).
fof(f6553,plain,
( frontsegP(cons(sK74,sK23),nil)
| ~ ssList(sK72(cons(sK74,sK23),nil))
| ~ ssList(nil)
| ~ spl75_30 ),
inference(superposition,[],[f2506,f6252]) ).
fof(f6252,plain,
( cons(sK74,sK23) = app(nil,sK72(cons(sK74,sK23),nil))
| ~ spl75_30 ),
inference(resolution,[],[f3209,f2334]) ).
fof(f3209,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,sK72(X0,nil)) = X0 ),
inference(subsumption_resolution,[],[f3207,f415]) ).
fof(f3207,plain,
! [X0] :
( app(nil,sK72(X0,nil)) = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(duplicate_literal_removal,[],[f3199]) ).
fof(f3199,plain,
! [X0] :
( app(nil,sK72(X0,nil)) = X0
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f604,f474]) ).
fof(f604,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| app(X1,sK72(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f382]) ).
fof(f2506,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f648,f587]) ).
fof(f587,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f185,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(f648,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f605]) ).
fof(f605,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f382]) ).
fof(f7027,plain,
( ~ spl75_29
| spl75_77
| ~ spl75_78 ),
inference(avatar_contradiction_clause,[],[f7026]) ).
fof(f7026,plain,
( $false
| ~ spl75_29
| spl75_77
| ~ spl75_78 ),
inference(subsumption_resolution,[],[f7025,f2329]) ).
fof(f2329,plain,
( ssList(cons(sK74,nil))
| ~ spl75_29 ),
inference(avatar_component_clause,[],[f2328]) ).
fof(f2328,plain,
( spl75_29
<=> ssList(cons(sK74,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_29])]) ).
fof(f7025,plain,
( ~ ssList(cons(sK74,nil))
| spl75_77
| ~ spl75_78 ),
inference(subsumption_resolution,[],[f7024,f415]) ).
fof(f7024,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK74,nil))
| spl75_77
| ~ spl75_78 ),
inference(subsumption_resolution,[],[f7023,f7011]) ).
fof(f7011,plain,
( frontsegP(cons(sK74,nil),nil)
| ~ spl75_78 ),
inference(avatar_component_clause,[],[f7009]) ).
fof(f7009,plain,
( spl75_78
<=> frontsegP(cons(sK74,nil),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_78])]) ).
fof(f7023,plain,
( ~ frontsegP(cons(sK74,nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK74,nil))
| spl75_77 ),
inference(resolution,[],[f7007,f603]) ).
fof(f7007,plain,
( ~ ssList(sK72(cons(sK74,nil),nil))
| spl75_77 ),
inference(avatar_component_clause,[],[f7005]) ).
fof(f7005,plain,
( spl75_77
<=> ssList(sK72(cons(sK74,nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_77])]) ).
fof(f7019,plain,
( ~ spl75_29
| spl75_78 ),
inference(avatar_contradiction_clause,[],[f7018]) ).
fof(f7018,plain,
( $false
| ~ spl75_29
| spl75_78 ),
inference(subsumption_resolution,[],[f7014,f2329]) ).
fof(f7014,plain,
( ~ ssList(cons(sK74,nil))
| spl75_78 ),
inference(resolution,[],[f7010,f474]) ).
fof(f7010,plain,
( ~ frontsegP(cons(sK74,nil),nil)
| spl75_78 ),
inference(avatar_component_clause,[],[f7009]) ).
fof(f7017,plain,
( ~ spl75_29
| spl75_78 ),
inference(avatar_contradiction_clause,[],[f7016]) ).
fof(f7016,plain,
( $false
| ~ spl75_29
| spl75_78 ),
inference(subsumption_resolution,[],[f7015,f415]) ).
fof(f7015,plain,
( ~ ssList(nil)
| ~ spl75_29
| spl75_78 ),
inference(subsumption_resolution,[],[f7013,f658]) ).
fof(f7013,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl75_29
| spl75_78 ),
inference(resolution,[],[f7010,f3405]) ).
fof(f3405,plain,
( ! [X0] :
( frontsegP(cons(sK74,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl75_29 ),
inference(subsumption_resolution,[],[f3404,f415]) ).
fof(f3404,plain,
( ! [X0] :
( frontsegP(cons(sK74,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_29 ),
inference(subsumption_resolution,[],[f3367,f2329]) ).
fof(f3367,plain,
( ! [X0] :
( frontsegP(cons(sK74,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(cons(sK74,nil))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_29 ),
inference(superposition,[],[f614,f2341]) ).
fof(f2341,plain,
( cons(sK74,nil) = app(nil,cons(sK74,nil))
| ~ spl75_29 ),
inference(resolution,[],[f2329,f478]) ).
fof(f7012,plain,
( ~ spl75_77
| spl75_78
| ~ spl75_29 ),
inference(avatar_split_clause,[],[f6537,f2328,f7009,f7005]) ).
fof(f6537,plain,
( frontsegP(cons(sK74,nil),nil)
| ~ ssList(sK72(cons(sK74,nil),nil))
| ~ spl75_29 ),
inference(subsumption_resolution,[],[f6527,f415]) ).
fof(f6527,plain,
( frontsegP(cons(sK74,nil),nil)
| ~ ssList(sK72(cons(sK74,nil),nil))
| ~ ssList(nil)
| ~ spl75_29 ),
inference(superposition,[],[f2506,f6251]) ).
fof(f6251,plain,
( cons(sK74,nil) = app(nil,sK72(cons(sK74,nil),nil))
| ~ spl75_29 ),
inference(resolution,[],[f3209,f2329]) ).
fof(f6788,plain,
( ~ spl75_28
| spl75_75
| ~ spl75_76 ),
inference(avatar_contradiction_clause,[],[f6787]) ).
fof(f6787,plain,
( $false
| ~ spl75_28
| spl75_75
| ~ spl75_76 ),
inference(subsumption_resolution,[],[f6786,f2247]) ).
fof(f2247,plain,
( ssList(cons(sK73,sK23))
| ~ spl75_28 ),
inference(avatar_component_clause,[],[f2245]) ).
fof(f2245,plain,
( spl75_28
<=> ssList(cons(sK73,sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_28])]) ).
fof(f6786,plain,
( ~ ssList(cons(sK73,sK23))
| spl75_75
| ~ spl75_76 ),
inference(subsumption_resolution,[],[f6785,f415]) ).
fof(f6785,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK73,sK23))
| spl75_75
| ~ spl75_76 ),
inference(subsumption_resolution,[],[f6784,f6772]) ).
fof(f6772,plain,
( frontsegP(cons(sK73,sK23),nil)
| ~ spl75_76 ),
inference(avatar_component_clause,[],[f6770]) ).
fof(f6770,plain,
( spl75_76
<=> frontsegP(cons(sK73,sK23),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_76])]) ).
fof(f6784,plain,
( ~ frontsegP(cons(sK73,sK23),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK73,sK23))
| spl75_75 ),
inference(resolution,[],[f6768,f603]) ).
fof(f6768,plain,
( ~ ssList(sK72(cons(sK73,sK23),nil))
| spl75_75 ),
inference(avatar_component_clause,[],[f6766]) ).
fof(f6766,plain,
( spl75_75
<=> ssList(sK72(cons(sK73,sK23),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_75])]) ).
fof(f6780,plain,
( ~ spl75_28
| spl75_76 ),
inference(avatar_contradiction_clause,[],[f6779]) ).
fof(f6779,plain,
( $false
| ~ spl75_28
| spl75_76 ),
inference(subsumption_resolution,[],[f6775,f2247]) ).
fof(f6775,plain,
( ~ ssList(cons(sK73,sK23))
| spl75_76 ),
inference(resolution,[],[f6771,f474]) ).
fof(f6771,plain,
( ~ frontsegP(cons(sK73,sK23),nil)
| spl75_76 ),
inference(avatar_component_clause,[],[f6770]) ).
fof(f6778,plain,
( ~ spl75_28
| spl75_76 ),
inference(avatar_contradiction_clause,[],[f6777]) ).
fof(f6777,plain,
( $false
| ~ spl75_28
| spl75_76 ),
inference(subsumption_resolution,[],[f6776,f415]) ).
fof(f6776,plain,
( ~ ssList(nil)
| ~ spl75_28
| spl75_76 ),
inference(subsumption_resolution,[],[f6774,f658]) ).
fof(f6774,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl75_28
| spl75_76 ),
inference(resolution,[],[f6771,f3403]) ).
fof(f3403,plain,
( ! [X0] :
( frontsegP(cons(sK73,sK23),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl75_28 ),
inference(subsumption_resolution,[],[f3402,f415]) ).
fof(f3402,plain,
( ! [X0] :
( frontsegP(cons(sK73,sK23),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_28 ),
inference(subsumption_resolution,[],[f3366,f2247]) ).
fof(f3366,plain,
( ! [X0] :
( frontsegP(cons(sK73,sK23),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(cons(sK73,sK23))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_28 ),
inference(superposition,[],[f614,f2284]) ).
fof(f2284,plain,
( cons(sK73,sK23) = app(nil,cons(sK73,sK23))
| ~ spl75_28 ),
inference(resolution,[],[f2247,f478]) ).
fof(f6773,plain,
( ~ spl75_75
| spl75_76
| ~ spl75_28 ),
inference(avatar_split_clause,[],[f6511,f2245,f6770,f6766]) ).
fof(f6511,plain,
( frontsegP(cons(sK73,sK23),nil)
| ~ ssList(sK72(cons(sK73,sK23),nil))
| ~ spl75_28 ),
inference(subsumption_resolution,[],[f6501,f415]) ).
fof(f6501,plain,
( frontsegP(cons(sK73,sK23),nil)
| ~ ssList(sK72(cons(sK73,sK23),nil))
| ~ ssList(nil)
| ~ spl75_28 ),
inference(superposition,[],[f2506,f6250]) ).
fof(f6250,plain,
( cons(sK73,sK23) = app(nil,sK72(cons(sK73,sK23),nil))
| ~ spl75_28 ),
inference(resolution,[],[f3209,f2247]) ).
fof(f6737,plain,
( ~ spl75_27
| spl75_73
| ~ spl75_74 ),
inference(avatar_contradiction_clause,[],[f6736]) ).
fof(f6736,plain,
( $false
| ~ spl75_27
| spl75_73
| ~ spl75_74 ),
inference(subsumption_resolution,[],[f6735,f2242]) ).
fof(f2242,plain,
( ssList(cons(sK73,nil))
| ~ spl75_27 ),
inference(avatar_component_clause,[],[f2241]) ).
fof(f2241,plain,
( spl75_27
<=> ssList(cons(sK73,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_27])]) ).
fof(f6735,plain,
( ~ ssList(cons(sK73,nil))
| spl75_73
| ~ spl75_74 ),
inference(subsumption_resolution,[],[f6734,f415]) ).
fof(f6734,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK73,nil))
| spl75_73
| ~ spl75_74 ),
inference(subsumption_resolution,[],[f6733,f6697]) ).
fof(f6697,plain,
( frontsegP(cons(sK73,nil),nil)
| ~ spl75_74 ),
inference(avatar_component_clause,[],[f6695]) ).
fof(f6695,plain,
( spl75_74
<=> frontsegP(cons(sK73,nil),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_74])]) ).
fof(f6733,plain,
( ~ frontsegP(cons(sK73,nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK73,nil))
| spl75_73 ),
inference(resolution,[],[f6693,f603]) ).
fof(f6693,plain,
( ~ ssList(sK72(cons(sK73,nil),nil))
| spl75_73 ),
inference(avatar_component_clause,[],[f6691]) ).
fof(f6691,plain,
( spl75_73
<=> ssList(sK72(cons(sK73,nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_73])]) ).
fof(f6729,plain,
( ~ spl75_27
| spl75_74 ),
inference(avatar_contradiction_clause,[],[f6728]) ).
fof(f6728,plain,
( $false
| ~ spl75_27
| spl75_74 ),
inference(subsumption_resolution,[],[f6724,f2242]) ).
fof(f6724,plain,
( ~ ssList(cons(sK73,nil))
| spl75_74 ),
inference(resolution,[],[f6696,f474]) ).
fof(f6696,plain,
( ~ frontsegP(cons(sK73,nil),nil)
| spl75_74 ),
inference(avatar_component_clause,[],[f6695]) ).
fof(f6727,plain,
( ~ spl75_27
| spl75_74 ),
inference(avatar_contradiction_clause,[],[f6726]) ).
fof(f6726,plain,
( $false
| ~ spl75_27
| spl75_74 ),
inference(subsumption_resolution,[],[f6725,f415]) ).
fof(f6725,plain,
( ~ ssList(nil)
| ~ spl75_27
| spl75_74 ),
inference(subsumption_resolution,[],[f6723,f658]) ).
fof(f6723,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl75_27
| spl75_74 ),
inference(resolution,[],[f6696,f3401]) ).
fof(f3401,plain,
( ! [X0] :
( frontsegP(cons(sK73,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl75_27 ),
inference(subsumption_resolution,[],[f3400,f415]) ).
fof(f3400,plain,
( ! [X0] :
( frontsegP(cons(sK73,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_27 ),
inference(subsumption_resolution,[],[f3365,f2242]) ).
fof(f3365,plain,
( ! [X0] :
( frontsegP(cons(sK73,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(cons(sK73,nil))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_27 ),
inference(superposition,[],[f614,f2254]) ).
fof(f2254,plain,
( cons(sK73,nil) = app(nil,cons(sK73,nil))
| ~ spl75_27 ),
inference(resolution,[],[f2242,f478]) ).
fof(f6698,plain,
( ~ spl75_73
| spl75_74
| ~ spl75_27 ),
inference(avatar_split_clause,[],[f6485,f2241,f6695,f6691]) ).
fof(f6485,plain,
( frontsegP(cons(sK73,nil),nil)
| ~ ssList(sK72(cons(sK73,nil),nil))
| ~ spl75_27 ),
inference(subsumption_resolution,[],[f6475,f415]) ).
fof(f6475,plain,
( frontsegP(cons(sK73,nil),nil)
| ~ ssList(sK72(cons(sK73,nil),nil))
| ~ ssList(nil)
| ~ spl75_27 ),
inference(superposition,[],[f2506,f6249]) ).
fof(f6249,plain,
( cons(sK73,nil) = app(nil,sK72(cons(sK73,nil),nil))
| ~ spl75_27 ),
inference(resolution,[],[f3209,f2242]) ).
fof(f6662,plain,
( ~ spl75_26
| spl75_71
| ~ spl75_72 ),
inference(avatar_contradiction_clause,[],[f6661]) ).
fof(f6661,plain,
( $false
| ~ spl75_26
| spl75_71
| ~ spl75_72 ),
inference(subsumption_resolution,[],[f6660,f2160]) ).
fof(f2160,plain,
( ssList(cons(sK27,sK23))
| ~ spl75_26 ),
inference(avatar_component_clause,[],[f2158]) ).
fof(f2158,plain,
( spl75_26
<=> ssList(cons(sK27,sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_26])]) ).
fof(f6660,plain,
( ~ ssList(cons(sK27,sK23))
| spl75_71
| ~ spl75_72 ),
inference(subsumption_resolution,[],[f6659,f415]) ).
fof(f6659,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK27,sK23))
| spl75_71
| ~ spl75_72 ),
inference(subsumption_resolution,[],[f6658,f6646]) ).
fof(f6646,plain,
( frontsegP(cons(sK27,sK23),nil)
| ~ spl75_72 ),
inference(avatar_component_clause,[],[f6644]) ).
fof(f6644,plain,
( spl75_72
<=> frontsegP(cons(sK27,sK23),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_72])]) ).
fof(f6658,plain,
( ~ frontsegP(cons(sK27,sK23),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK27,sK23))
| spl75_71 ),
inference(resolution,[],[f6642,f603]) ).
fof(f6642,plain,
( ~ ssList(sK72(cons(sK27,sK23),nil))
| spl75_71 ),
inference(avatar_component_clause,[],[f6640]) ).
fof(f6640,plain,
( spl75_71
<=> ssList(sK72(cons(sK27,sK23),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_71])]) ).
fof(f6654,plain,
( ~ spl75_26
| spl75_72 ),
inference(avatar_contradiction_clause,[],[f6653]) ).
fof(f6653,plain,
( $false
| ~ spl75_26
| spl75_72 ),
inference(subsumption_resolution,[],[f6649,f2160]) ).
fof(f6649,plain,
( ~ ssList(cons(sK27,sK23))
| spl75_72 ),
inference(resolution,[],[f6645,f474]) ).
fof(f6645,plain,
( ~ frontsegP(cons(sK27,sK23),nil)
| spl75_72 ),
inference(avatar_component_clause,[],[f6644]) ).
fof(f6652,plain,
( ~ spl75_26
| spl75_72 ),
inference(avatar_contradiction_clause,[],[f6651]) ).
fof(f6651,plain,
( $false
| ~ spl75_26
| spl75_72 ),
inference(subsumption_resolution,[],[f6650,f415]) ).
fof(f6650,plain,
( ~ ssList(nil)
| ~ spl75_26
| spl75_72 ),
inference(subsumption_resolution,[],[f6648,f658]) ).
fof(f6648,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl75_26
| spl75_72 ),
inference(resolution,[],[f6645,f3399]) ).
fof(f3399,plain,
( ! [X0] :
( frontsegP(cons(sK27,sK23),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl75_26 ),
inference(subsumption_resolution,[],[f3398,f415]) ).
fof(f3398,plain,
( ! [X0] :
( frontsegP(cons(sK27,sK23),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_26 ),
inference(subsumption_resolution,[],[f3364,f2160]) ).
fof(f3364,plain,
( ! [X0] :
( frontsegP(cons(sK27,sK23),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(cons(sK27,sK23))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_26 ),
inference(superposition,[],[f614,f2197]) ).
fof(f2197,plain,
( cons(sK27,sK23) = app(nil,cons(sK27,sK23))
| ~ spl75_26 ),
inference(resolution,[],[f2160,f478]) ).
fof(f6647,plain,
( ~ spl75_71
| spl75_72
| ~ spl75_26 ),
inference(avatar_split_clause,[],[f6459,f2158,f6644,f6640]) ).
fof(f6459,plain,
( frontsegP(cons(sK27,sK23),nil)
| ~ ssList(sK72(cons(sK27,sK23),nil))
| ~ spl75_26 ),
inference(subsumption_resolution,[],[f6449,f415]) ).
fof(f6449,plain,
( frontsegP(cons(sK27,sK23),nil)
| ~ ssList(sK72(cons(sK27,sK23),nil))
| ~ ssList(nil)
| ~ spl75_26 ),
inference(superposition,[],[f2506,f6248]) ).
fof(f6248,plain,
( cons(sK27,sK23) = app(nil,sK72(cons(sK27,sK23),nil))
| ~ spl75_26 ),
inference(resolution,[],[f3209,f2160]) ).
fof(f6611,plain,
( ~ spl75_25
| spl75_69
| ~ spl75_70 ),
inference(avatar_contradiction_clause,[],[f6610]) ).
fof(f6610,plain,
( $false
| ~ spl75_25
| spl75_69
| ~ spl75_70 ),
inference(subsumption_resolution,[],[f6609,f2155]) ).
fof(f2155,plain,
( ssList(cons(sK27,nil))
| ~ spl75_25 ),
inference(avatar_component_clause,[],[f2154]) ).
fof(f2154,plain,
( spl75_25
<=> ssList(cons(sK27,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_25])]) ).
fof(f6609,plain,
( ~ ssList(cons(sK27,nil))
| spl75_69
| ~ spl75_70 ),
inference(subsumption_resolution,[],[f6608,f415]) ).
fof(f6608,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK27,nil))
| spl75_69
| ~ spl75_70 ),
inference(subsumption_resolution,[],[f6607,f6573]) ).
fof(f6573,plain,
( frontsegP(cons(sK27,nil),nil)
| ~ spl75_70 ),
inference(avatar_component_clause,[],[f6571]) ).
fof(f6571,plain,
( spl75_70
<=> frontsegP(cons(sK27,nil),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_70])]) ).
fof(f6607,plain,
( ~ frontsegP(cons(sK27,nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK27,nil))
| spl75_69 ),
inference(resolution,[],[f6569,f603]) ).
fof(f6569,plain,
( ~ ssList(sK72(cons(sK27,nil),nil))
| spl75_69 ),
inference(avatar_component_clause,[],[f6567]) ).
fof(f6567,plain,
( spl75_69
<=> ssList(sK72(cons(sK27,nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_69])]) ).
fof(f6581,plain,
( ~ spl75_25
| spl75_70 ),
inference(avatar_contradiction_clause,[],[f6580]) ).
fof(f6580,plain,
( $false
| ~ spl75_25
| spl75_70 ),
inference(subsumption_resolution,[],[f6576,f2155]) ).
fof(f6576,plain,
( ~ ssList(cons(sK27,nil))
| spl75_70 ),
inference(resolution,[],[f6572,f474]) ).
fof(f6572,plain,
( ~ frontsegP(cons(sK27,nil),nil)
| spl75_70 ),
inference(avatar_component_clause,[],[f6571]) ).
fof(f6579,plain,
( ~ spl75_25
| spl75_70 ),
inference(avatar_contradiction_clause,[],[f6578]) ).
fof(f6578,plain,
( $false
| ~ spl75_25
| spl75_70 ),
inference(subsumption_resolution,[],[f6577,f415]) ).
fof(f6577,plain,
( ~ ssList(nil)
| ~ spl75_25
| spl75_70 ),
inference(subsumption_resolution,[],[f6575,f658]) ).
fof(f6575,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl75_25
| spl75_70 ),
inference(resolution,[],[f6572,f3397]) ).
fof(f3397,plain,
( ! [X0] :
( frontsegP(cons(sK27,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl75_25 ),
inference(subsumption_resolution,[],[f3396,f415]) ).
fof(f3396,plain,
( ! [X0] :
( frontsegP(cons(sK27,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_25 ),
inference(subsumption_resolution,[],[f3363,f2155]) ).
fof(f3363,plain,
( ! [X0] :
( frontsegP(cons(sK27,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(cons(sK27,nil))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_25 ),
inference(superposition,[],[f614,f2167]) ).
fof(f2167,plain,
( cons(sK27,nil) = app(nil,cons(sK27,nil))
| ~ spl75_25 ),
inference(resolution,[],[f2155,f478]) ).
fof(f6574,plain,
( ~ spl75_69
| spl75_70
| ~ spl75_25 ),
inference(avatar_split_clause,[],[f6433,f2154,f6571,f6567]) ).
fof(f6433,plain,
( frontsegP(cons(sK27,nil),nil)
| ~ ssList(sK72(cons(sK27,nil),nil))
| ~ spl75_25 ),
inference(subsumption_resolution,[],[f6423,f415]) ).
fof(f6423,plain,
( frontsegP(cons(sK27,nil),nil)
| ~ ssList(sK72(cons(sK27,nil),nil))
| ~ ssList(nil)
| ~ spl75_25 ),
inference(superposition,[],[f2506,f6247]) ).
fof(f6247,plain,
( cons(sK27,nil) = app(nil,sK72(cons(sK27,nil),nil))
| ~ spl75_25 ),
inference(resolution,[],[f3209,f2155]) ).
fof(f6372,plain,
( ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_67
| ~ spl75_68 ),
inference(avatar_contradiction_clause,[],[f6371]) ).
fof(f6371,plain,
( $false
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_67
| ~ spl75_68 ),
inference(subsumption_resolution,[],[f6370,f1854]) ).
fof(f6370,plain,
( ~ ssList(tl(sK23))
| spl75_67
| ~ spl75_68 ),
inference(subsumption_resolution,[],[f6369,f415]) ).
fof(f6369,plain,
( ~ ssList(nil)
| ~ ssList(tl(sK23))
| spl75_67
| ~ spl75_68 ),
inference(subsumption_resolution,[],[f6368,f6356]) ).
fof(f6356,plain,
( frontsegP(tl(sK23),nil)
| ~ spl75_68 ),
inference(avatar_component_clause,[],[f6354]) ).
fof(f6354,plain,
( spl75_68
<=> frontsegP(tl(sK23),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_68])]) ).
fof(f6368,plain,
( ~ frontsegP(tl(sK23),nil)
| ~ ssList(nil)
| ~ ssList(tl(sK23))
| spl75_67 ),
inference(resolution,[],[f6352,f603]) ).
fof(f6352,plain,
( ~ ssList(sK72(tl(sK23),nil))
| spl75_67 ),
inference(avatar_component_clause,[],[f6350]) ).
fof(f6350,plain,
( spl75_67
<=> ssList(sK72(tl(sK23),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_67])]) ).
fof(f6364,plain,
( ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_68 ),
inference(avatar_contradiction_clause,[],[f6363]) ).
fof(f6363,plain,
( $false
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_68 ),
inference(subsumption_resolution,[],[f6359,f1854]) ).
fof(f6359,plain,
( ~ ssList(tl(sK23))
| spl75_68 ),
inference(resolution,[],[f6355,f474]) ).
fof(f6355,plain,
( ~ frontsegP(tl(sK23),nil)
| spl75_68 ),
inference(avatar_component_clause,[],[f6354]) ).
fof(f6362,plain,
( ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_68 ),
inference(avatar_contradiction_clause,[],[f6361]) ).
fof(f6361,plain,
( $false
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_68 ),
inference(subsumption_resolution,[],[f6360,f415]) ).
fof(f6360,plain,
( ~ ssList(nil)
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_68 ),
inference(subsumption_resolution,[],[f6358,f658]) ).
fof(f6358,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_68 ),
inference(resolution,[],[f6355,f3426]) ).
fof(f3426,plain,
( ! [X0] :
( frontsegP(tl(sK23),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11 ),
inference(forward_demodulation,[],[f3425,f1850]) ).
fof(f3425,plain,
( ! [X0] :
( frontsegP(sK28(sK23),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl75_9 ),
inference(subsumption_resolution,[],[f3424,f415]) ).
fof(f3424,plain,
( ! [X0] :
( frontsegP(sK28(sK23),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_9 ),
inference(subsumption_resolution,[],[f3389,f1635]) ).
fof(f3389,plain,
( ! [X0] :
( frontsegP(sK28(sK23),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sK28(sK23))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_9 ),
inference(superposition,[],[f614,f1647]) ).
fof(f1647,plain,
( sK28(sK23) = app(nil,sK28(sK23))
| ~ spl75_9 ),
inference(resolution,[],[f1635,f478]) ).
fof(f6357,plain,
( ~ spl75_67
| spl75_68
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11 ),
inference(avatar_split_clause,[],[f6348,f1661,f1634,f1546,f6354,f6350]) ).
fof(f6348,plain,
( frontsegP(tl(sK23),nil)
| ~ ssList(sK72(tl(sK23),nil))
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11 ),
inference(subsumption_resolution,[],[f6338,f415]) ).
fof(f6338,plain,
( frontsegP(tl(sK23),nil)
| ~ ssList(sK72(tl(sK23),nil))
| ~ ssList(nil)
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11 ),
inference(superposition,[],[f2506,f6309]) ).
fof(f6309,plain,
( tl(sK23) = app(nil,sK72(tl(sK23),nil))
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11 ),
inference(forward_demodulation,[],[f6264,f1850]) ).
fof(f6264,plain,
( sK28(sK23) = app(nil,sK72(sK28(sK23),nil))
| ~ spl75_9 ),
inference(resolution,[],[f3209,f1635]) ).
fof(f6085,plain,
( ~ spl75_30
| spl75_65
| ~ spl75_66 ),
inference(avatar_contradiction_clause,[],[f6084]) ).
fof(f6084,plain,
( $false
| ~ spl75_30
| spl75_65
| ~ spl75_66 ),
inference(subsumption_resolution,[],[f6083,f2334]) ).
fof(f6083,plain,
( ~ ssList(cons(sK74,sK23))
| spl75_65
| ~ spl75_66 ),
inference(subsumption_resolution,[],[f6082,f415]) ).
fof(f6082,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK74,sK23))
| spl75_65
| ~ spl75_66 ),
inference(subsumption_resolution,[],[f6081,f6065]) ).
fof(f6065,plain,
( rearsegP(cons(sK74,sK23),nil)
| ~ spl75_66 ),
inference(avatar_component_clause,[],[f6063]) ).
fof(f6063,plain,
( spl75_66
<=> rearsegP(cons(sK74,sK23),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_66])]) ).
fof(f6081,plain,
( ~ rearsegP(cons(sK74,sK23),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK74,sK23))
| spl75_65 ),
inference(resolution,[],[f6061,f596]) ).
fof(f596,plain,
! [X0,X1] :
( ssList(sK69(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f373,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ( app(sK69(X0,X1),X1) = X0
& ssList(sK69(X0,X1)) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69])],[f371,f372]) ).
fof(f372,plain,
! [X0,X1] :
( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
=> ( app(sK69(X0,X1),X1) = X0
& ssList(sK69(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f371,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,[],[f370]) ).
fof(f370,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,[],[f199]) ).
fof(f199,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(f6061,plain,
( ~ ssList(sK69(cons(sK74,sK23),nil))
| spl75_65 ),
inference(avatar_component_clause,[],[f6059]) ).
fof(f6059,plain,
( spl75_65
<=> ssList(sK69(cons(sK74,sK23),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_65])]) ).
fof(f6077,plain,
( ~ spl75_29
| ~ spl75_50
| spl75_66 ),
inference(avatar_contradiction_clause,[],[f6076]) ).
fof(f6076,plain,
( $false
| ~ spl75_29
| ~ spl75_50
| spl75_66 ),
inference(subsumption_resolution,[],[f6075,f415]) ).
fof(f6075,plain,
( ~ ssList(nil)
| ~ spl75_29
| ~ spl75_50
| spl75_66 ),
inference(subsumption_resolution,[],[f6069,f5375]) ).
fof(f5375,plain,
( rearsegP(sK23,nil)
| ~ spl75_50 ),
inference(avatar_component_clause,[],[f5373]) ).
fof(f5373,plain,
( spl75_50
<=> rearsegP(sK23,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_50])]) ).
fof(f6069,plain,
( ~ rearsegP(sK23,nil)
| ~ ssList(nil)
| ~ spl75_29
| spl75_66 ),
inference(resolution,[],[f6064,f3311]) ).
fof(f3311,plain,
( ! [X0] :
( rearsegP(cons(sK74,sK23),X0)
| ~ rearsegP(sK23,X0)
| ~ ssList(X0) )
| ~ spl75_29 ),
inference(subsumption_resolution,[],[f3310,f397]) ).
fof(f3310,plain,
( ! [X0] :
( rearsegP(cons(sK74,sK23),X0)
| ~ rearsegP(sK23,X0)
| ~ ssList(X0)
| ~ ssList(sK23) )
| ~ spl75_29 ),
inference(subsumption_resolution,[],[f3271,f2329]) ).
fof(f3271,plain,
! [X0] :
( rearsegP(cons(sK74,sK23),X0)
| ~ rearsegP(sK23,X0)
| ~ ssList(cons(sK74,nil))
| ~ ssList(X0)
| ~ ssList(sK23) ),
inference(superposition,[],[f613,f2147]) ).
fof(f2147,plain,
cons(sK74,sK23) = app(cons(sK74,nil),sK23),
inference(resolution,[],[f2085,f622]) ).
fof(f622,plain,
ssItem(sK74),
inference(cnf_transformation,[],[f387]) ).
fof(f387,plain,
( sK73 != sK74
& ssItem(sK74)
& ssItem(sK73) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK73,sK74])],[f2,f386,f385]) ).
fof(f385,plain,
( ? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) )
=> ( ? [X1] :
( sK73 != X1
& ssItem(X1) )
& ssItem(sK73) ) ),
introduced(choice_axiom,[]) ).
fof(f386,plain,
( ? [X1] :
( sK73 != X1
& ssItem(X1) )
=> ( sK73 != sK74
& ssItem(sK74) ) ),
introduced(choice_axiom,[]) ).
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax2) ).
fof(f2085,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,sK23) = app(cons(X0,nil),sK23) ),
inference(resolution,[],[f582,f397]) ).
fof(f582,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssItem(X1)
| cons(X1,X0) = app(cons(X1,nil),X0) ),
inference(cnf_transformation,[],[f183]) ).
fof(f183,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(f613,plain,
! [X2,X0,X1] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f208]) ).
fof(f208,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f207]) ).
fof(f207,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(f6064,plain,
( ~ rearsegP(cons(sK74,sK23),nil)
| spl75_66 ),
inference(avatar_component_clause,[],[f6063]) ).
fof(f6074,plain,
( ~ spl75_30
| spl75_66 ),
inference(avatar_contradiction_clause,[],[f6073]) ).
fof(f6073,plain,
( $false
| ~ spl75_30
| spl75_66 ),
inference(subsumption_resolution,[],[f6072,f415]) ).
fof(f6072,plain,
( ~ ssList(nil)
| ~ spl75_30
| spl75_66 ),
inference(subsumption_resolution,[],[f6068,f657]) ).
fof(f6068,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl75_30
| spl75_66 ),
inference(resolution,[],[f6064,f3293]) ).
fof(f3293,plain,
( ! [X0] :
( rearsegP(cons(sK74,sK23),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl75_30 ),
inference(subsumption_resolution,[],[f3292,f415]) ).
fof(f3292,plain,
( ! [X0] :
( rearsegP(cons(sK74,sK23),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_30 ),
inference(subsumption_resolution,[],[f3259,f2334]) ).
fof(f3259,plain,
( ! [X0] :
( rearsegP(cons(sK74,sK23),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(cons(sK74,sK23))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_30 ),
inference(superposition,[],[f613,f2370]) ).
fof(f2370,plain,
( cons(sK74,sK23) = app(cons(sK74,sK23),nil)
| ~ spl75_30 ),
inference(resolution,[],[f2334,f477]) ).
fof(f6071,plain,
( ~ spl75_30
| spl75_66 ),
inference(avatar_contradiction_clause,[],[f6070]) ).
fof(f6070,plain,
( $false
| ~ spl75_30
| spl75_66 ),
inference(subsumption_resolution,[],[f6067,f2334]) ).
fof(f6067,plain,
( ~ ssList(cons(sK74,sK23))
| spl75_66 ),
inference(resolution,[],[f6064,f472]) ).
fof(f6066,plain,
( ~ spl75_65
| spl75_66
| ~ spl75_30 ),
inference(avatar_split_clause,[],[f5798,f2332,f6063,f6059]) ).
fof(f5798,plain,
( rearsegP(cons(sK74,sK23),nil)
| ~ ssList(sK69(cons(sK74,sK23),nil))
| ~ spl75_30 ),
inference(subsumption_resolution,[],[f5788,f415]) ).
fof(f5788,plain,
( rearsegP(cons(sK74,sK23),nil)
| ~ ssList(sK69(cons(sK74,sK23),nil))
| ~ ssList(nil)
| ~ spl75_30 ),
inference(superposition,[],[f2430,f5226]) ).
fof(f5226,plain,
( cons(sK74,sK23) = app(sK69(cons(sK74,sK23),nil),nil)
| ~ spl75_30 ),
inference(resolution,[],[f3120,f2334]) ).
fof(f3120,plain,
! [X0] :
( ~ ssList(X0)
| app(sK69(X0,nil),nil) = X0 ),
inference(subsumption_resolution,[],[f3114,f415]) ).
fof(f3114,plain,
! [X0] :
( app(sK69(X0,nil),nil) = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(duplicate_literal_removal,[],[f3110]) ).
fof(f3110,plain,
! [X0] :
( app(sK69(X0,nil),nil) = X0
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f597,f472]) ).
fof(f597,plain,
! [X0,X1] :
( ~ rearsegP(X0,X1)
| app(sK69(X0,X1),X1) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f2430,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f646,f587]) ).
fof(f646,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ),
inference(equality_resolution,[],[f598]) ).
fof(f598,plain,
! [X2,X0,X1] :
( rearsegP(X0,X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f373]) ).
fof(f6031,plain,
( ~ spl75_29
| spl75_63
| ~ spl75_64 ),
inference(avatar_contradiction_clause,[],[f6030]) ).
fof(f6030,plain,
( $false
| ~ spl75_29
| spl75_63
| ~ spl75_64 ),
inference(subsumption_resolution,[],[f6029,f2329]) ).
fof(f6029,plain,
( ~ ssList(cons(sK74,nil))
| spl75_63
| ~ spl75_64 ),
inference(subsumption_resolution,[],[f6028,f415]) ).
fof(f6028,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK74,nil))
| spl75_63
| ~ spl75_64 ),
inference(subsumption_resolution,[],[f6027,f6015]) ).
fof(f6015,plain,
( rearsegP(cons(sK74,nil),nil)
| ~ spl75_64 ),
inference(avatar_component_clause,[],[f6013]) ).
fof(f6013,plain,
( spl75_64
<=> rearsegP(cons(sK74,nil),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_64])]) ).
fof(f6027,plain,
( ~ rearsegP(cons(sK74,nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK74,nil))
| spl75_63 ),
inference(resolution,[],[f6011,f596]) ).
fof(f6011,plain,
( ~ ssList(sK69(cons(sK74,nil),nil))
| spl75_63 ),
inference(avatar_component_clause,[],[f6009]) ).
fof(f6009,plain,
( spl75_63
<=> ssList(sK69(cons(sK74,nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_63])]) ).
fof(f6023,plain,
( ~ spl75_29
| spl75_64 ),
inference(avatar_contradiction_clause,[],[f6022]) ).
fof(f6022,plain,
( $false
| ~ spl75_29
| spl75_64 ),
inference(subsumption_resolution,[],[f6021,f415]) ).
fof(f6021,plain,
( ~ ssList(nil)
| ~ spl75_29
| spl75_64 ),
inference(subsumption_resolution,[],[f6018,f657]) ).
fof(f6018,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl75_29
| spl75_64 ),
inference(resolution,[],[f6014,f3291]) ).
fof(f3291,plain,
( ! [X0] :
( rearsegP(cons(sK74,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl75_29 ),
inference(subsumption_resolution,[],[f3290,f415]) ).
fof(f3290,plain,
( ! [X0] :
( rearsegP(cons(sK74,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_29 ),
inference(subsumption_resolution,[],[f3258,f2329]) ).
fof(f3258,plain,
( ! [X0] :
( rearsegP(cons(sK74,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(cons(sK74,nil))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_29 ),
inference(superposition,[],[f613,f2340]) ).
fof(f2340,plain,
( cons(sK74,nil) = app(cons(sK74,nil),nil)
| ~ spl75_29 ),
inference(resolution,[],[f2329,f477]) ).
fof(f6014,plain,
( ~ rearsegP(cons(sK74,nil),nil)
| spl75_64 ),
inference(avatar_component_clause,[],[f6013]) ).
fof(f6020,plain,
( ~ spl75_29
| spl75_64 ),
inference(avatar_contradiction_clause,[],[f6019]) ).
fof(f6019,plain,
( $false
| ~ spl75_29
| spl75_64 ),
inference(subsumption_resolution,[],[f6017,f2329]) ).
fof(f6017,plain,
( ~ ssList(cons(sK74,nil))
| spl75_64 ),
inference(resolution,[],[f6014,f472]) ).
fof(f6016,plain,
( ~ spl75_63
| spl75_64
| ~ spl75_29 ),
inference(avatar_split_clause,[],[f5772,f2328,f6013,f6009]) ).
fof(f5772,plain,
( rearsegP(cons(sK74,nil),nil)
| ~ ssList(sK69(cons(sK74,nil),nil))
| ~ spl75_29 ),
inference(subsumption_resolution,[],[f5762,f415]) ).
fof(f5762,plain,
( rearsegP(cons(sK74,nil),nil)
| ~ ssList(sK69(cons(sK74,nil),nil))
| ~ ssList(nil)
| ~ spl75_29 ),
inference(superposition,[],[f2430,f5225]) ).
fof(f5225,plain,
( cons(sK74,nil) = app(sK69(cons(sK74,nil),nil),nil)
| ~ spl75_29 ),
inference(resolution,[],[f3120,f2329]) ).
fof(f5982,plain,
( ~ spl75_28
| spl75_61
| ~ spl75_62 ),
inference(avatar_contradiction_clause,[],[f5981]) ).
fof(f5981,plain,
( $false
| ~ spl75_28
| spl75_61
| ~ spl75_62 ),
inference(subsumption_resolution,[],[f5980,f2247]) ).
fof(f5980,plain,
( ~ ssList(cons(sK73,sK23))
| spl75_61
| ~ spl75_62 ),
inference(subsumption_resolution,[],[f5979,f415]) ).
fof(f5979,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK73,sK23))
| spl75_61
| ~ spl75_62 ),
inference(subsumption_resolution,[],[f5978,f5962]) ).
fof(f5962,plain,
( rearsegP(cons(sK73,sK23),nil)
| ~ spl75_62 ),
inference(avatar_component_clause,[],[f5960]) ).
fof(f5960,plain,
( spl75_62
<=> rearsegP(cons(sK73,sK23),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_62])]) ).
fof(f5978,plain,
( ~ rearsegP(cons(sK73,sK23),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK73,sK23))
| spl75_61 ),
inference(resolution,[],[f5958,f596]) ).
fof(f5958,plain,
( ~ ssList(sK69(cons(sK73,sK23),nil))
| spl75_61 ),
inference(avatar_component_clause,[],[f5956]) ).
fof(f5956,plain,
( spl75_61
<=> ssList(sK69(cons(sK73,sK23),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_61])]) ).
fof(f5974,plain,
( ~ spl75_27
| ~ spl75_50
| spl75_62 ),
inference(avatar_contradiction_clause,[],[f5973]) ).
fof(f5973,plain,
( $false
| ~ spl75_27
| ~ spl75_50
| spl75_62 ),
inference(subsumption_resolution,[],[f5972,f415]) ).
fof(f5972,plain,
( ~ ssList(nil)
| ~ spl75_27
| ~ spl75_50
| spl75_62 ),
inference(subsumption_resolution,[],[f5966,f5375]) ).
fof(f5966,plain,
( ~ rearsegP(sK23,nil)
| ~ ssList(nil)
| ~ spl75_27
| spl75_62 ),
inference(resolution,[],[f5961,f3309]) ).
fof(f3309,plain,
( ! [X0] :
( rearsegP(cons(sK73,sK23),X0)
| ~ rearsegP(sK23,X0)
| ~ ssList(X0) )
| ~ spl75_27 ),
inference(subsumption_resolution,[],[f3308,f397]) ).
fof(f3308,plain,
( ! [X0] :
( rearsegP(cons(sK73,sK23),X0)
| ~ rearsegP(sK23,X0)
| ~ ssList(X0)
| ~ ssList(sK23) )
| ~ spl75_27 ),
inference(subsumption_resolution,[],[f3270,f2242]) ).
fof(f3270,plain,
! [X0] :
( rearsegP(cons(sK73,sK23),X0)
| ~ rearsegP(sK23,X0)
| ~ ssList(cons(sK73,nil))
| ~ ssList(X0)
| ~ ssList(sK23) ),
inference(superposition,[],[f613,f2146]) ).
fof(f2146,plain,
cons(sK73,sK23) = app(cons(sK73,nil),sK23),
inference(resolution,[],[f2085,f621]) ).
fof(f621,plain,
ssItem(sK73),
inference(cnf_transformation,[],[f387]) ).
fof(f5961,plain,
( ~ rearsegP(cons(sK73,sK23),nil)
| spl75_62 ),
inference(avatar_component_clause,[],[f5960]) ).
fof(f5971,plain,
( ~ spl75_28
| spl75_62 ),
inference(avatar_contradiction_clause,[],[f5970]) ).
fof(f5970,plain,
( $false
| ~ spl75_28
| spl75_62 ),
inference(subsumption_resolution,[],[f5969,f415]) ).
fof(f5969,plain,
( ~ ssList(nil)
| ~ spl75_28
| spl75_62 ),
inference(subsumption_resolution,[],[f5965,f657]) ).
fof(f5965,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl75_28
| spl75_62 ),
inference(resolution,[],[f5961,f3289]) ).
fof(f3289,plain,
( ! [X0] :
( rearsegP(cons(sK73,sK23),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl75_28 ),
inference(subsumption_resolution,[],[f3288,f415]) ).
fof(f3288,plain,
( ! [X0] :
( rearsegP(cons(sK73,sK23),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_28 ),
inference(subsumption_resolution,[],[f3257,f2247]) ).
fof(f3257,plain,
( ! [X0] :
( rearsegP(cons(sK73,sK23),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(cons(sK73,sK23))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_28 ),
inference(superposition,[],[f613,f2283]) ).
fof(f2283,plain,
( cons(sK73,sK23) = app(cons(sK73,sK23),nil)
| ~ spl75_28 ),
inference(resolution,[],[f2247,f477]) ).
fof(f5968,plain,
( ~ spl75_28
| spl75_62 ),
inference(avatar_contradiction_clause,[],[f5967]) ).
fof(f5967,plain,
( $false
| ~ spl75_28
| spl75_62 ),
inference(subsumption_resolution,[],[f5964,f2247]) ).
fof(f5964,plain,
( ~ ssList(cons(sK73,sK23))
| spl75_62 ),
inference(resolution,[],[f5961,f472]) ).
fof(f5963,plain,
( ~ spl75_61
| spl75_62
| ~ spl75_28 ),
inference(avatar_split_clause,[],[f5746,f2245,f5960,f5956]) ).
fof(f5746,plain,
( rearsegP(cons(sK73,sK23),nil)
| ~ ssList(sK69(cons(sK73,sK23),nil))
| ~ spl75_28 ),
inference(subsumption_resolution,[],[f5736,f415]) ).
fof(f5736,plain,
( rearsegP(cons(sK73,sK23),nil)
| ~ ssList(sK69(cons(sK73,sK23),nil))
| ~ ssList(nil)
| ~ spl75_28 ),
inference(superposition,[],[f2430,f5224]) ).
fof(f5224,plain,
( cons(sK73,sK23) = app(sK69(cons(sK73,sK23),nil),nil)
| ~ spl75_28 ),
inference(resolution,[],[f3120,f2247]) ).
fof(f5928,plain,
( ~ spl75_27
| spl75_59
| ~ spl75_60 ),
inference(avatar_contradiction_clause,[],[f5927]) ).
fof(f5927,plain,
( $false
| ~ spl75_27
| spl75_59
| ~ spl75_60 ),
inference(subsumption_resolution,[],[f5926,f2242]) ).
fof(f5926,plain,
( ~ ssList(cons(sK73,nil))
| spl75_59
| ~ spl75_60 ),
inference(subsumption_resolution,[],[f5925,f415]) ).
fof(f5925,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK73,nil))
| spl75_59
| ~ spl75_60 ),
inference(subsumption_resolution,[],[f5924,f5912]) ).
fof(f5912,plain,
( rearsegP(cons(sK73,nil),nil)
| ~ spl75_60 ),
inference(avatar_component_clause,[],[f5910]) ).
fof(f5910,plain,
( spl75_60
<=> rearsegP(cons(sK73,nil),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_60])]) ).
fof(f5924,plain,
( ~ rearsegP(cons(sK73,nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK73,nil))
| spl75_59 ),
inference(resolution,[],[f5908,f596]) ).
fof(f5908,plain,
( ~ ssList(sK69(cons(sK73,nil),nil))
| spl75_59 ),
inference(avatar_component_clause,[],[f5906]) ).
fof(f5906,plain,
( spl75_59
<=> ssList(sK69(cons(sK73,nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_59])]) ).
fof(f5920,plain,
( ~ spl75_27
| spl75_60 ),
inference(avatar_contradiction_clause,[],[f5919]) ).
fof(f5919,plain,
( $false
| ~ spl75_27
| spl75_60 ),
inference(subsumption_resolution,[],[f5918,f415]) ).
fof(f5918,plain,
( ~ ssList(nil)
| ~ spl75_27
| spl75_60 ),
inference(subsumption_resolution,[],[f5915,f657]) ).
fof(f5915,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl75_27
| spl75_60 ),
inference(resolution,[],[f5911,f3287]) ).
fof(f3287,plain,
( ! [X0] :
( rearsegP(cons(sK73,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl75_27 ),
inference(subsumption_resolution,[],[f3286,f415]) ).
fof(f3286,plain,
( ! [X0] :
( rearsegP(cons(sK73,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_27 ),
inference(subsumption_resolution,[],[f3256,f2242]) ).
fof(f3256,plain,
( ! [X0] :
( rearsegP(cons(sK73,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(cons(sK73,nil))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_27 ),
inference(superposition,[],[f613,f2253]) ).
fof(f2253,plain,
( cons(sK73,nil) = app(cons(sK73,nil),nil)
| ~ spl75_27 ),
inference(resolution,[],[f2242,f477]) ).
fof(f5911,plain,
( ~ rearsegP(cons(sK73,nil),nil)
| spl75_60 ),
inference(avatar_component_clause,[],[f5910]) ).
fof(f5917,plain,
( ~ spl75_27
| spl75_60 ),
inference(avatar_contradiction_clause,[],[f5916]) ).
fof(f5916,plain,
( $false
| ~ spl75_27
| spl75_60 ),
inference(subsumption_resolution,[],[f5914,f2242]) ).
fof(f5914,plain,
( ~ ssList(cons(sK73,nil))
| spl75_60 ),
inference(resolution,[],[f5911,f472]) ).
fof(f5913,plain,
( ~ spl75_59
| spl75_60
| ~ spl75_27 ),
inference(avatar_split_clause,[],[f5720,f2241,f5910,f5906]) ).
fof(f5720,plain,
( rearsegP(cons(sK73,nil),nil)
| ~ ssList(sK69(cons(sK73,nil),nil))
| ~ spl75_27 ),
inference(subsumption_resolution,[],[f5710,f415]) ).
fof(f5710,plain,
( rearsegP(cons(sK73,nil),nil)
| ~ ssList(sK69(cons(sK73,nil),nil))
| ~ ssList(nil)
| ~ spl75_27 ),
inference(superposition,[],[f2430,f5223]) ).
fof(f5223,plain,
( cons(sK73,nil) = app(sK69(cons(sK73,nil),nil),nil)
| ~ spl75_27 ),
inference(resolution,[],[f3120,f2242]) ).
fof(f5879,plain,
( ~ spl75_26
| spl75_57
| ~ spl75_58 ),
inference(avatar_contradiction_clause,[],[f5878]) ).
fof(f5878,plain,
( $false
| ~ spl75_26
| spl75_57
| ~ spl75_58 ),
inference(subsumption_resolution,[],[f5877,f2160]) ).
fof(f5877,plain,
( ~ ssList(cons(sK27,sK23))
| spl75_57
| ~ spl75_58 ),
inference(subsumption_resolution,[],[f5876,f415]) ).
fof(f5876,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK27,sK23))
| spl75_57
| ~ spl75_58 ),
inference(subsumption_resolution,[],[f5875,f5859]) ).
fof(f5859,plain,
( rearsegP(cons(sK27,sK23),nil)
| ~ spl75_58 ),
inference(avatar_component_clause,[],[f5857]) ).
fof(f5857,plain,
( spl75_58
<=> rearsegP(cons(sK27,sK23),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_58])]) ).
fof(f5875,plain,
( ~ rearsegP(cons(sK27,sK23),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK27,sK23))
| spl75_57 ),
inference(resolution,[],[f5855,f596]) ).
fof(f5855,plain,
( ~ ssList(sK69(cons(sK27,sK23),nil))
| spl75_57 ),
inference(avatar_component_clause,[],[f5853]) ).
fof(f5853,plain,
( spl75_57
<=> ssList(sK69(cons(sK27,sK23),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_57])]) ).
fof(f5871,plain,
( ~ spl75_25
| ~ spl75_50
| spl75_58 ),
inference(avatar_contradiction_clause,[],[f5870]) ).
fof(f5870,plain,
( $false
| ~ spl75_25
| ~ spl75_50
| spl75_58 ),
inference(subsumption_resolution,[],[f5869,f415]) ).
fof(f5869,plain,
( ~ ssList(nil)
| ~ spl75_25
| ~ spl75_50
| spl75_58 ),
inference(subsumption_resolution,[],[f5863,f5375]) ).
fof(f5863,plain,
( ~ rearsegP(sK23,nil)
| ~ ssList(nil)
| ~ spl75_25
| spl75_58 ),
inference(resolution,[],[f5858,f3307]) ).
fof(f3307,plain,
( ! [X0] :
( rearsegP(cons(sK27,sK23),X0)
| ~ rearsegP(sK23,X0)
| ~ ssList(X0) )
| ~ spl75_25 ),
inference(subsumption_resolution,[],[f3306,f397]) ).
fof(f3306,plain,
( ! [X0] :
( rearsegP(cons(sK27,sK23),X0)
| ~ rearsegP(sK23,X0)
| ~ ssList(X0)
| ~ ssList(sK23) )
| ~ spl75_25 ),
inference(subsumption_resolution,[],[f3269,f2155]) ).
fof(f3269,plain,
! [X0] :
( rearsegP(cons(sK27,sK23),X0)
| ~ rearsegP(sK23,X0)
| ~ ssList(cons(sK27,nil))
| ~ ssList(X0)
| ~ ssList(sK23) ),
inference(superposition,[],[f613,f2127]) ).
fof(f2127,plain,
cons(sK27,sK23) = app(cons(sK27,nil),sK23),
inference(resolution,[],[f2085,f663]) ).
fof(f5858,plain,
( ~ rearsegP(cons(sK27,sK23),nil)
| spl75_58 ),
inference(avatar_component_clause,[],[f5857]) ).
fof(f5868,plain,
( ~ spl75_26
| spl75_58 ),
inference(avatar_contradiction_clause,[],[f5867]) ).
fof(f5867,plain,
( $false
| ~ spl75_26
| spl75_58 ),
inference(subsumption_resolution,[],[f5866,f415]) ).
fof(f5866,plain,
( ~ ssList(nil)
| ~ spl75_26
| spl75_58 ),
inference(subsumption_resolution,[],[f5862,f657]) ).
fof(f5862,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl75_26
| spl75_58 ),
inference(resolution,[],[f5858,f3285]) ).
fof(f3285,plain,
( ! [X0] :
( rearsegP(cons(sK27,sK23),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl75_26 ),
inference(subsumption_resolution,[],[f3284,f415]) ).
fof(f3284,plain,
( ! [X0] :
( rearsegP(cons(sK27,sK23),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_26 ),
inference(subsumption_resolution,[],[f3255,f2160]) ).
fof(f3255,plain,
( ! [X0] :
( rearsegP(cons(sK27,sK23),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(cons(sK27,sK23))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_26 ),
inference(superposition,[],[f613,f2196]) ).
fof(f2196,plain,
( cons(sK27,sK23) = app(cons(sK27,sK23),nil)
| ~ spl75_26 ),
inference(resolution,[],[f2160,f477]) ).
fof(f5865,plain,
( ~ spl75_26
| spl75_58 ),
inference(avatar_contradiction_clause,[],[f5864]) ).
fof(f5864,plain,
( $false
| ~ spl75_26
| spl75_58 ),
inference(subsumption_resolution,[],[f5861,f2160]) ).
fof(f5861,plain,
( ~ ssList(cons(sK27,sK23))
| spl75_58 ),
inference(resolution,[],[f5858,f472]) ).
fof(f5860,plain,
( ~ spl75_57
| spl75_58
| ~ spl75_26 ),
inference(avatar_split_clause,[],[f5694,f2158,f5857,f5853]) ).
fof(f5694,plain,
( rearsegP(cons(sK27,sK23),nil)
| ~ ssList(sK69(cons(sK27,sK23),nil))
| ~ spl75_26 ),
inference(subsumption_resolution,[],[f5684,f415]) ).
fof(f5684,plain,
( rearsegP(cons(sK27,sK23),nil)
| ~ ssList(sK69(cons(sK27,sK23),nil))
| ~ ssList(nil)
| ~ spl75_26 ),
inference(superposition,[],[f2430,f5222]) ).
fof(f5222,plain,
( cons(sK27,sK23) = app(sK69(cons(sK27,sK23),nil),nil)
| ~ spl75_26 ),
inference(resolution,[],[f3120,f2160]) ).
fof(f5826,plain,
( ~ spl75_25
| spl75_55
| ~ spl75_56 ),
inference(avatar_contradiction_clause,[],[f5825]) ).
fof(f5825,plain,
( $false
| ~ spl75_25
| spl75_55
| ~ spl75_56 ),
inference(subsumption_resolution,[],[f5824,f2155]) ).
fof(f5824,plain,
( ~ ssList(cons(sK27,nil))
| spl75_55
| ~ spl75_56 ),
inference(subsumption_resolution,[],[f5823,f415]) ).
fof(f5823,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK27,nil))
| spl75_55
| ~ spl75_56 ),
inference(subsumption_resolution,[],[f5822,f5810]) ).
fof(f5810,plain,
( rearsegP(cons(sK27,nil),nil)
| ~ spl75_56 ),
inference(avatar_component_clause,[],[f5808]) ).
fof(f5808,plain,
( spl75_56
<=> rearsegP(cons(sK27,nil),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_56])]) ).
fof(f5822,plain,
( ~ rearsegP(cons(sK27,nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK27,nil))
| spl75_55 ),
inference(resolution,[],[f5806,f596]) ).
fof(f5806,plain,
( ~ ssList(sK69(cons(sK27,nil),nil))
| spl75_55 ),
inference(avatar_component_clause,[],[f5804]) ).
fof(f5804,plain,
( spl75_55
<=> ssList(sK69(cons(sK27,nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_55])]) ).
fof(f5818,plain,
( ~ spl75_25
| spl75_56 ),
inference(avatar_contradiction_clause,[],[f5817]) ).
fof(f5817,plain,
( $false
| ~ spl75_25
| spl75_56 ),
inference(subsumption_resolution,[],[f5816,f415]) ).
fof(f5816,plain,
( ~ ssList(nil)
| ~ spl75_25
| spl75_56 ),
inference(subsumption_resolution,[],[f5813,f657]) ).
fof(f5813,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl75_25
| spl75_56 ),
inference(resolution,[],[f5809,f3283]) ).
fof(f3283,plain,
( ! [X0] :
( rearsegP(cons(sK27,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl75_25 ),
inference(subsumption_resolution,[],[f3282,f415]) ).
fof(f3282,plain,
( ! [X0] :
( rearsegP(cons(sK27,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_25 ),
inference(subsumption_resolution,[],[f3254,f2155]) ).
fof(f3254,plain,
( ! [X0] :
( rearsegP(cons(sK27,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(cons(sK27,nil))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_25 ),
inference(superposition,[],[f613,f2166]) ).
fof(f2166,plain,
( cons(sK27,nil) = app(cons(sK27,nil),nil)
| ~ spl75_25 ),
inference(resolution,[],[f2155,f477]) ).
fof(f5809,plain,
( ~ rearsegP(cons(sK27,nil),nil)
| spl75_56 ),
inference(avatar_component_clause,[],[f5808]) ).
fof(f5815,plain,
( ~ spl75_25
| spl75_56 ),
inference(avatar_contradiction_clause,[],[f5814]) ).
fof(f5814,plain,
( $false
| ~ spl75_25
| spl75_56 ),
inference(subsumption_resolution,[],[f5812,f2155]) ).
fof(f5812,plain,
( ~ ssList(cons(sK27,nil))
| spl75_56 ),
inference(resolution,[],[f5809,f472]) ).
fof(f5811,plain,
( ~ spl75_55
| spl75_56
| ~ spl75_25 ),
inference(avatar_split_clause,[],[f5668,f2154,f5808,f5804]) ).
fof(f5668,plain,
( rearsegP(cons(sK27,nil),nil)
| ~ ssList(sK69(cons(sK27,nil),nil))
| ~ spl75_25 ),
inference(subsumption_resolution,[],[f5658,f415]) ).
fof(f5658,plain,
( rearsegP(cons(sK27,nil),nil)
| ~ ssList(sK69(cons(sK27,nil),nil))
| ~ ssList(nil)
| ~ spl75_25 ),
inference(superposition,[],[f2430,f5221]) ).
fof(f5221,plain,
( cons(sK27,nil) = app(sK69(cons(sK27,nil),nil),nil)
| ~ spl75_25 ),
inference(resolution,[],[f3120,f2155]) ).
fof(f5602,plain,
( ~ spl75_49
| spl75_53 ),
inference(avatar_contradiction_clause,[],[f5601]) ).
fof(f5601,plain,
( $false
| ~ spl75_49
| spl75_53 ),
inference(subsumption_resolution,[],[f5600,f397]) ).
fof(f5600,plain,
( ~ ssList(sK23)
| ~ spl75_49
| spl75_53 ),
inference(subsumption_resolution,[],[f5599,f5444]) ).
fof(f5444,plain,
( frontsegP(sK23,sK23)
| ~ spl75_49 ),
inference(forward_demodulation,[],[f5443,f5413]) ).
fof(f5413,plain,
( sK23 = sK69(sK23,nil)
| ~ spl75_49 ),
inference(forward_demodulation,[],[f5392,f5233]) ).
fof(f5233,plain,
sK23 = app(sK69(sK23,nil),nil),
inference(resolution,[],[f3120,f397]) ).
fof(f5392,plain,
( sK69(sK23,nil) = app(sK69(sK23,nil),nil)
| ~ spl75_49 ),
inference(resolution,[],[f5370,f477]) ).
fof(f5370,plain,
( ssList(sK69(sK23,nil))
| ~ spl75_49 ),
inference(avatar_component_clause,[],[f5369]) ).
fof(f5369,plain,
( spl75_49
<=> ssList(sK69(sK23,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_49])]) ).
fof(f5443,plain,
( frontsegP(sK23,sK69(sK23,nil))
| ~ spl75_49 ),
inference(subsumption_resolution,[],[f5305,f5370]) ).
fof(f5305,plain,
( frontsegP(sK23,sK69(sK23,nil))
| ~ ssList(sK69(sK23,nil)) ),
inference(subsumption_resolution,[],[f5294,f415]) ).
fof(f5294,plain,
( frontsegP(sK23,sK69(sK23,nil))
| ~ ssList(nil)
| ~ ssList(sK69(sK23,nil)) ),
inference(superposition,[],[f2506,f5233]) ).
fof(f5599,plain,
( ~ frontsegP(sK23,sK23)
| ~ ssList(sK23)
| spl75_53 ),
inference(duplicate_literal_removal,[],[f5598]) ).
fof(f5598,plain,
( ~ frontsegP(sK23,sK23)
| ~ ssList(sK23)
| ~ ssList(sK23)
| spl75_53 ),
inference(resolution,[],[f5592,f603]) ).
fof(f5592,plain,
( ~ ssList(sK72(sK23,sK23))
| spl75_53 ),
inference(avatar_component_clause,[],[f5590]) ).
fof(f5590,plain,
( spl75_53
<=> ssList(sK72(sK23,sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_53])]) ).
fof(f5597,plain,
( ~ spl75_53
| spl75_54
| ~ spl75_49 ),
inference(avatar_split_clause,[],[f5531,f5369,f5594,f5590]) ).
fof(f5594,plain,
( spl75_54
<=> nil = sK72(sK23,sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_54])]) ).
fof(f5531,plain,
( nil = sK72(sK23,sK23)
| ~ ssList(sK72(sK23,sK23))
| ~ spl75_49 ),
inference(trivial_inequality_removal,[],[f5516]) ).
fof(f5516,plain,
( sK23 != sK23
| nil = sK72(sK23,sK23)
| ~ ssList(sK72(sK23,sK23))
| ~ spl75_49 ),
inference(superposition,[],[f4651,f5515]) ).
fof(f5515,plain,
( sK23 = app(sK23,sK72(sK23,sK23))
| ~ spl75_49 ),
inference(subsumption_resolution,[],[f5513,f397]) ).
fof(f5513,plain,
( sK23 = app(sK23,sK72(sK23,sK23))
| ~ ssList(sK23)
| ~ spl75_49 ),
inference(duplicate_literal_removal,[],[f5510]) ).
fof(f5510,plain,
( sK23 = app(sK23,sK72(sK23,sK23))
| ~ ssList(sK23)
| ~ ssList(sK23)
| ~ spl75_49 ),
inference(resolution,[],[f5444,f604]) ).
fof(f4651,plain,
! [X0] :
( sK23 != app(sK23,X0)
| nil = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4650,f397]) ).
fof(f4650,plain,
! [X0] :
( sK23 != app(sK23,X0)
| nil = X0
| ~ ssList(sK23)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4556,f415]) ).
fof(f4556,plain,
! [X0] :
( sK23 != app(sK23,X0)
| nil = X0
| ~ ssList(nil)
| ~ ssList(sK23)
| ~ ssList(X0) ),
inference(superposition,[],[f616,f683]) ).
fof(f683,plain,
sK23 = app(sK23,nil),
inference(resolution,[],[f477,f397]) ).
fof(f616,plain,
! [X2,X0,X1] :
( app(X1,X2) != app(X1,X0)
| X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f214]) ).
fof(f214,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f213]) ).
fof(f213,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(f5563,plain,
( ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_51
| ~ spl75_52 ),
inference(avatar_contradiction_clause,[],[f5562]) ).
fof(f5562,plain,
( $false
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_51
| ~ spl75_52 ),
inference(subsumption_resolution,[],[f5561,f1854]) ).
fof(f5561,plain,
( ~ ssList(tl(sK23))
| spl75_51
| ~ spl75_52 ),
inference(subsumption_resolution,[],[f5560,f415]) ).
fof(f5560,plain,
( ~ ssList(nil)
| ~ ssList(tl(sK23))
| spl75_51
| ~ spl75_52 ),
inference(subsumption_resolution,[],[f5559,f5547]) ).
fof(f5547,plain,
( rearsegP(tl(sK23),nil)
| ~ spl75_52 ),
inference(avatar_component_clause,[],[f5545]) ).
fof(f5545,plain,
( spl75_52
<=> rearsegP(tl(sK23),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_52])]) ).
fof(f5559,plain,
( ~ rearsegP(tl(sK23),nil)
| ~ ssList(nil)
| ~ ssList(tl(sK23))
| spl75_51 ),
inference(resolution,[],[f5543,f596]) ).
fof(f5543,plain,
( ~ ssList(sK69(tl(sK23),nil))
| spl75_51 ),
inference(avatar_component_clause,[],[f5541]) ).
fof(f5541,plain,
( spl75_51
<=> ssList(sK69(tl(sK23),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_51])]) ).
fof(f5555,plain,
( ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_52 ),
inference(avatar_contradiction_clause,[],[f5554]) ).
fof(f5554,plain,
( $false
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_52 ),
inference(subsumption_resolution,[],[f5553,f415]) ).
fof(f5553,plain,
( ~ ssList(nil)
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_52 ),
inference(subsumption_resolution,[],[f5550,f657]) ).
fof(f5550,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_52 ),
inference(resolution,[],[f5546,f3303]) ).
fof(f3303,plain,
( ! [X0] :
( rearsegP(tl(sK23),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11 ),
inference(forward_demodulation,[],[f3302,f1850]) ).
fof(f3302,plain,
( ! [X0] :
( rearsegP(sK28(sK23),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl75_9 ),
inference(subsumption_resolution,[],[f3301,f415]) ).
fof(f3301,plain,
( ! [X0] :
( rearsegP(sK28(sK23),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_9 ),
inference(subsumption_resolution,[],[f3264,f1635]) ).
fof(f3264,plain,
( ! [X0] :
( rearsegP(sK28(sK23),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(sK28(sK23))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl75_9 ),
inference(superposition,[],[f613,f1646]) ).
fof(f1646,plain,
( sK28(sK23) = app(sK28(sK23),nil)
| ~ spl75_9 ),
inference(resolution,[],[f1635,f477]) ).
fof(f5546,plain,
( ~ rearsegP(tl(sK23),nil)
| spl75_52 ),
inference(avatar_component_clause,[],[f5545]) ).
fof(f5552,plain,
( ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_52 ),
inference(avatar_contradiction_clause,[],[f5551]) ).
fof(f5551,plain,
( $false
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| spl75_52 ),
inference(subsumption_resolution,[],[f5549,f1854]) ).
fof(f5549,plain,
( ~ ssList(tl(sK23))
| spl75_52 ),
inference(resolution,[],[f5546,f472]) ).
fof(f5548,plain,
( ~ spl75_51
| spl75_52
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11 ),
inference(avatar_split_clause,[],[f5441,f1661,f1634,f1546,f5545,f5541]) ).
fof(f5441,plain,
( rearsegP(tl(sK23),nil)
| ~ ssList(sK69(tl(sK23),nil))
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11 ),
inference(subsumption_resolution,[],[f5431,f415]) ).
fof(f5431,plain,
( rearsegP(tl(sK23),nil)
| ~ ssList(sK69(tl(sK23),nil))
| ~ ssList(nil)
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11 ),
inference(superposition,[],[f2430,f5274]) ).
fof(f5274,plain,
( tl(sK23) = app(sK69(tl(sK23),nil),nil)
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11 ),
inference(forward_demodulation,[],[f5238,f1850]) ).
fof(f5238,plain,
( sK28(sK23) = app(sK69(sK28(sK23),nil),nil)
| ~ spl75_9 ),
inference(resolution,[],[f3120,f1635]) ).
fof(f5391,plain,
( spl75_49
| ~ spl75_50 ),
inference(avatar_contradiction_clause,[],[f5390]) ).
fof(f5390,plain,
( $false
| spl75_49
| ~ spl75_50 ),
inference(subsumption_resolution,[],[f5389,f397]) ).
fof(f5389,plain,
( ~ ssList(sK23)
| spl75_49
| ~ spl75_50 ),
inference(subsumption_resolution,[],[f5388,f415]) ).
fof(f5388,plain,
( ~ ssList(nil)
| ~ ssList(sK23)
| spl75_49
| ~ spl75_50 ),
inference(subsumption_resolution,[],[f5387,f5375]) ).
fof(f5387,plain,
( ~ rearsegP(sK23,nil)
| ~ ssList(nil)
| ~ ssList(sK23)
| spl75_49 ),
inference(resolution,[],[f5371,f596]) ).
fof(f5371,plain,
( ~ ssList(sK69(sK23,nil))
| spl75_49 ),
inference(avatar_component_clause,[],[f5369]) ).
fof(f5383,plain,
spl75_50,
inference(avatar_contradiction_clause,[],[f5382]) ).
fof(f5382,plain,
( $false
| spl75_50 ),
inference(subsumption_resolution,[],[f5381,f415]) ).
fof(f5381,plain,
( ~ ssList(nil)
| spl75_50 ),
inference(subsumption_resolution,[],[f5378,f657]) ).
fof(f5378,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| spl75_50 ),
inference(resolution,[],[f5374,f3297]) ).
fof(f3297,plain,
! [X0] :
( rearsegP(sK23,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f3296,f415]) ).
fof(f3296,plain,
! [X0] :
( rearsegP(sK23,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(subsumption_resolution,[],[f3262,f397]) ).
fof(f3262,plain,
! [X0] :
( rearsegP(sK23,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(sK23)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(superposition,[],[f613,f683]) ).
fof(f5374,plain,
( ~ rearsegP(sK23,nil)
| spl75_50 ),
inference(avatar_component_clause,[],[f5373]) ).
fof(f5380,plain,
spl75_50,
inference(avatar_contradiction_clause,[],[f5379]) ).
fof(f5379,plain,
( $false
| spl75_50 ),
inference(subsumption_resolution,[],[f5377,f397]) ).
fof(f5377,plain,
( ~ ssList(sK23)
| spl75_50 ),
inference(resolution,[],[f5374,f472]) ).
fof(f5376,plain,
( ~ spl75_49
| spl75_50 ),
inference(avatar_split_clause,[],[f5304,f5373,f5369]) ).
fof(f5304,plain,
( rearsegP(sK23,nil)
| ~ ssList(sK69(sK23,nil)) ),
inference(subsumption_resolution,[],[f5293,f415]) ).
fof(f5293,plain,
( rearsegP(sK23,nil)
| ~ ssList(sK69(sK23,nil))
| ~ ssList(nil) ),
inference(superposition,[],[f2430,f5233]) ).
fof(f4948,plain,
spl75_47,
inference(avatar_contradiction_clause,[],[f4947]) ).
fof(f4947,plain,
( $false
| spl75_47 ),
inference(subsumption_resolution,[],[f4946,f415]) ).
fof(f4946,plain,
( ~ ssList(nil)
| spl75_47 ),
inference(subsumption_resolution,[],[f4945,f658]) ).
fof(f4945,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| spl75_47 ),
inference(duplicate_literal_removal,[],[f4944]) ).
fof(f4944,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| spl75_47 ),
inference(resolution,[],[f4938,f603]) ).
fof(f4938,plain,
( ~ ssList(sK72(nil,nil))
| spl75_47 ),
inference(avatar_component_clause,[],[f4936]) ).
fof(f4936,plain,
( spl75_47
<=> ssList(sK72(nil,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_47])]) ).
fof(f4943,plain,
( ~ spl75_47
| spl75_48
| ~ spl75_2 ),
inference(avatar_split_clause,[],[f4934,f854,f4940,f4936]) ).
fof(f4940,plain,
( spl75_48
<=> nil = sK72(nil,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_48])]) ).
fof(f854,plain,
( spl75_2
<=> nil = sK24 ),
introduced(avatar_definition,[new_symbols(naming,[spl75_2])]) ).
fof(f4934,plain,
( nil = sK72(nil,nil)
| ~ ssList(sK72(nil,nil))
| ~ spl75_2 ),
inference(trivial_inequality_removal,[],[f4932]) ).
fof(f4932,plain,
( nil != nil
| nil = sK72(nil,nil)
| ~ ssList(sK72(nil,nil))
| ~ spl75_2 ),
inference(superposition,[],[f4654,f3217]) ).
fof(f3217,plain,
nil = app(nil,sK72(nil,nil)),
inference(subsumption_resolution,[],[f3205,f415]) ).
fof(f3205,plain,
( nil = app(nil,sK72(nil,nil))
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f3204]) ).
fof(f3204,plain,
( nil = app(nil,sK72(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[],[f604,f658]) ).
fof(f4654,plain,
( ! [X0] :
( nil != app(nil,X0)
| nil = X0
| ~ ssList(X0) )
| ~ spl75_2 ),
inference(forward_demodulation,[],[f4653,f856]) ).
fof(f856,plain,
( nil = sK24
| ~ spl75_2 ),
inference(avatar_component_clause,[],[f854]) ).
fof(f4653,plain,
! [X0] :
( sK24 != app(sK24,X0)
| nil = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4652,f398]) ).
fof(f4652,plain,
! [X0] :
( sK24 != app(sK24,X0)
| nil = X0
| ~ ssList(sK24)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4557,f415]) ).
fof(f4557,plain,
! [X0] :
( sK24 != app(sK24,X0)
| nil = X0
| ~ ssList(nil)
| ~ ssList(sK24)
| ~ ssList(X0) ),
inference(superposition,[],[f616,f684]) ).
fof(f684,plain,
sK24 = app(sK24,nil),
inference(resolution,[],[f477,f398]) ).
fof(f4850,plain,
( ~ spl75_41
| ~ spl75_42
| spl75_45 ),
inference(avatar_contradiction_clause,[],[f4849]) ).
fof(f4849,plain,
( $false
| ~ spl75_41
| ~ spl75_42
| spl75_45 ),
inference(subsumption_resolution,[],[f4848,f397]) ).
fof(f4848,plain,
( ~ ssList(sK23)
| ~ spl75_41
| ~ spl75_42
| spl75_45 ),
inference(subsumption_resolution,[],[f4847,f415]) ).
fof(f4847,plain,
( ~ ssList(nil)
| ~ ssList(sK23)
| ~ spl75_41
| ~ spl75_42
| spl75_45 ),
inference(subsumption_resolution,[],[f4846,f4807]) ).
fof(f4807,plain,
( frontsegP(sK23,nil)
| ~ spl75_41
| ~ spl75_42 ),
inference(superposition,[],[f4180,f4771]) ).
fof(f4771,plain,
( nil = sK69(sK23,sK23)
| ~ spl75_41 ),
inference(subsumption_resolution,[],[f4770,f4175]) ).
fof(f4175,plain,
( ssList(sK69(sK23,sK23))
| ~ spl75_41 ),
inference(avatar_component_clause,[],[f4174]) ).
fof(f4174,plain,
( spl75_41
<=> ssList(sK69(sK23,sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_41])]) ).
fof(f4770,plain,
( nil = sK69(sK23,sK23)
| ~ ssList(sK69(sK23,sK23)) ),
inference(trivial_inequality_removal,[],[f4769]) ).
fof(f4769,plain,
( sK23 != sK23
| nil = sK69(sK23,sK23)
| ~ ssList(sK69(sK23,sK23)) ),
inference(superposition,[],[f4329,f4123]) ).
fof(f4123,plain,
sK23 = app(sK69(sK23,sK23),sK23),
inference(resolution,[],[f3117,f397]) ).
fof(f3117,plain,
! [X0] :
( ~ ssList(X0)
| app(sK69(X0,X0),X0) = X0 ),
inference(duplicate_literal_removal,[],[f3107]) ).
fof(f3107,plain,
! [X0] :
( app(sK69(X0,X0),X0) = X0
| ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f597,f476]) ).
fof(f4329,plain,
! [X0] :
( sK23 != app(X0,sK23)
| nil = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4328,f397]) ).
fof(f4328,plain,
! [X0] :
( sK23 != app(X0,sK23)
| nil = X0
| ~ ssList(sK23)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4230,f415]) ).
fof(f4230,plain,
! [X0] :
( sK23 != app(X0,sK23)
| nil = X0
| ~ ssList(nil)
| ~ ssList(sK23)
| ~ ssList(X0) ),
inference(superposition,[],[f615,f712]) ).
fof(f712,plain,
sK23 = app(nil,sK23),
inference(resolution,[],[f478,f397]) ).
fof(f615,plain,
! [X2,X0,X1] :
( app(X2,X1) != app(X0,X1)
| X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f212]) ).
fof(f212,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( X0 = X2
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f211]) ).
fof(f211,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(f4180,plain,
( frontsegP(sK23,sK69(sK23,sK23))
| ~ spl75_42 ),
inference(avatar_component_clause,[],[f4178]) ).
fof(f4178,plain,
( spl75_42
<=> frontsegP(sK23,sK69(sK23,sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_42])]) ).
fof(f4846,plain,
( ~ frontsegP(sK23,nil)
| ~ ssList(nil)
| ~ ssList(sK23)
| spl75_45 ),
inference(resolution,[],[f4840,f603]) ).
fof(f4840,plain,
( ~ ssList(sK72(sK23,nil))
| spl75_45 ),
inference(avatar_component_clause,[],[f4838]) ).
fof(f4838,plain,
( spl75_45
<=> ssList(sK72(sK23,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_45])]) ).
fof(f4845,plain,
( ~ spl75_45
| spl75_46
| ~ spl75_41
| ~ spl75_42 ),
inference(avatar_split_clause,[],[f4836,f4178,f4174,f4842,f4838]) ).
fof(f4842,plain,
( spl75_46
<=> rearsegP(sK23,sK72(sK23,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_46])]) ).
fof(f4836,plain,
( rearsegP(sK23,sK72(sK23,nil))
| ~ ssList(sK72(sK23,nil))
| ~ spl75_41
| ~ spl75_42 ),
inference(subsumption_resolution,[],[f4828,f415]) ).
fof(f4828,plain,
( rearsegP(sK23,sK72(sK23,nil))
| ~ ssList(nil)
| ~ ssList(sK72(sK23,nil))
| ~ spl75_41
| ~ spl75_42 ),
inference(superposition,[],[f2430,f4816]) ).
fof(f4816,plain,
( sK23 = app(nil,sK72(sK23,nil))
| ~ spl75_41
| ~ spl75_42 ),
inference(subsumption_resolution,[],[f4815,f397]) ).
fof(f4815,plain,
( sK23 = app(nil,sK72(sK23,nil))
| ~ ssList(sK23)
| ~ spl75_41
| ~ spl75_42 ),
inference(subsumption_resolution,[],[f4813,f415]) ).
fof(f4813,plain,
( sK23 = app(nil,sK72(sK23,nil))
| ~ ssList(nil)
| ~ ssList(sK23)
| ~ spl75_41
| ~ spl75_42 ),
inference(resolution,[],[f4807,f604]) ).
fof(f4504,plain,
spl75_43,
inference(avatar_contradiction_clause,[],[f4503]) ).
fof(f4503,plain,
( $false
| spl75_43 ),
inference(subsumption_resolution,[],[f4502,f415]) ).
fof(f4502,plain,
( ~ ssList(nil)
| spl75_43 ),
inference(subsumption_resolution,[],[f4501,f657]) ).
fof(f4501,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| spl75_43 ),
inference(duplicate_literal_removal,[],[f4500]) ).
fof(f4500,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| spl75_43 ),
inference(resolution,[],[f4494,f596]) ).
fof(f4494,plain,
( ~ ssList(sK69(nil,nil))
| spl75_43 ),
inference(avatar_component_clause,[],[f4492]) ).
fof(f4492,plain,
( spl75_43
<=> ssList(sK69(nil,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_43])]) ).
fof(f4499,plain,
( ~ spl75_43
| spl75_44
| ~ spl75_2 ),
inference(avatar_split_clause,[],[f4490,f854,f4496,f4492]) ).
fof(f4496,plain,
( spl75_44
<=> nil = sK69(nil,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_44])]) ).
fof(f4490,plain,
( nil = sK69(nil,nil)
| ~ ssList(sK69(nil,nil))
| ~ spl75_2 ),
inference(trivial_inequality_removal,[],[f4488]) ).
fof(f4488,plain,
( nil != nil
| nil = sK69(nil,nil)
| ~ ssList(sK69(nil,nil))
| ~ spl75_2 ),
inference(superposition,[],[f4320,f3119]) ).
fof(f3119,plain,
nil = app(sK69(nil,nil),nil),
inference(subsumption_resolution,[],[f3115,f415]) ).
fof(f3115,plain,
( nil = app(sK69(nil,nil),nil)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f3109]) ).
fof(f3109,plain,
( nil = app(sK69(nil,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[],[f597,f657]) ).
fof(f4320,plain,
( ! [X0] :
( nil != app(X0,nil)
| nil = X0
| ~ ssList(X0) )
| ~ spl75_2 ),
inference(forward_demodulation,[],[f4319,f856]) ).
fof(f4319,plain,
( ! [X0] :
( nil != app(X0,nil)
| sK24 = X0
| ~ ssList(X0) )
| ~ spl75_2 ),
inference(forward_demodulation,[],[f4318,f856]) ).
fof(f4318,plain,
! [X0] :
( app(X0,nil) != sK24
| sK24 = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4317,f415]) ).
fof(f4317,plain,
! [X0] :
( app(X0,nil) != sK24
| sK24 = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4226,f398]) ).
fof(f4226,plain,
! [X0] :
( app(X0,nil) != sK24
| sK24 = X0
| ~ ssList(sK24)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[],[f615,f684]) ).
fof(f4188,plain,
spl75_41,
inference(avatar_contradiction_clause,[],[f4187]) ).
fof(f4187,plain,
( $false
| spl75_41 ),
inference(subsumption_resolution,[],[f4186,f397]) ).
fof(f4186,plain,
( ~ ssList(sK23)
| spl75_41 ),
inference(resolution,[],[f4184,f476]) ).
fof(f4184,plain,
( ~ rearsegP(sK23,sK23)
| spl75_41 ),
inference(subsumption_resolution,[],[f4183,f397]) ).
fof(f4183,plain,
( ~ rearsegP(sK23,sK23)
| ~ ssList(sK23)
| spl75_41 ),
inference(duplicate_literal_removal,[],[f4182]) ).
fof(f4182,plain,
( ~ rearsegP(sK23,sK23)
| ~ ssList(sK23)
| ~ ssList(sK23)
| spl75_41 ),
inference(resolution,[],[f4176,f596]) ).
fof(f4176,plain,
( ~ ssList(sK69(sK23,sK23))
| spl75_41 ),
inference(avatar_component_clause,[],[f4174]) ).
fof(f4181,plain,
( ~ spl75_41
| spl75_42 ),
inference(avatar_split_clause,[],[f4172,f4178,f4174]) ).
fof(f4172,plain,
( frontsegP(sK23,sK69(sK23,sK23))
| ~ ssList(sK69(sK23,sK23)) ),
inference(subsumption_resolution,[],[f4169,f397]) ).
fof(f4169,plain,
( frontsegP(sK23,sK69(sK23,sK23))
| ~ ssList(sK23)
| ~ ssList(sK69(sK23,sK23)) ),
inference(superposition,[],[f2506,f4123]) ).
fof(f4001,plain,
( ~ spl75_39
| spl75_40
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| ~ spl75_37
| ~ spl75_38 ),
inference(avatar_split_clause,[],[f3989,f3103,f3099,f1661,f1634,f1546,f3998,f3994]) ).
fof(f3994,plain,
( spl75_39
<=> rearsegP(nil,cons(hd(sK23),sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_39])]) ).
fof(f3998,plain,
( spl75_40
<=> rearsegP(tl(sK23),sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_40])]) ).
fof(f3099,plain,
( spl75_37
<=> ssList(cons(hd(sK23),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_37])]) ).
fof(f3103,plain,
( spl75_38
<=> ssList(cons(hd(sK23),sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_38])]) ).
fof(f3989,plain,
( rearsegP(tl(sK23),sK23)
| ~ rearsegP(nil,cons(hd(sK23),sK23))
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| ~ spl75_37
| ~ spl75_38 ),
inference(subsumption_resolution,[],[f3988,f3105]) ).
fof(f3105,plain,
( ssList(cons(hd(sK23),sK23))
| ~ spl75_38 ),
inference(avatar_component_clause,[],[f3103]) ).
fof(f3988,plain,
( rearsegP(tl(sK23),sK23)
| ~ rearsegP(nil,cons(hd(sK23),sK23))
| ~ ssList(cons(hd(sK23),sK23))
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| ~ spl75_37
| ~ spl75_38 ),
inference(subsumption_resolution,[],[f3973,f1854]) ).
fof(f3973,plain,
( rearsegP(tl(sK23),sK23)
| ~ ssList(tl(sK23))
| ~ rearsegP(nil,cons(hd(sK23),sK23))
| ~ ssList(cons(hd(sK23),sK23))
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11
| ~ spl75_37
| ~ spl75_38 ),
inference(resolution,[],[f3884,f3303]) ).
fof(f3884,plain,
( ! [X0] :
( ~ rearsegP(X0,cons(hd(sK23),sK23))
| rearsegP(X0,sK23)
| ~ ssList(X0) )
| ~ spl75_11
| ~ spl75_37
| ~ spl75_38 ),
inference(subsumption_resolution,[],[f3883,f3105]) ).
fof(f3883,plain,
( ! [X0] :
( rearsegP(X0,sK23)
| ~ rearsegP(X0,cons(hd(sK23),sK23))
| ~ ssList(cons(hd(sK23),sK23))
| ~ ssList(X0) )
| ~ spl75_11
| ~ spl75_37 ),
inference(subsumption_resolution,[],[f3844,f397]) ).
fof(f3844,plain,
( ! [X0] :
( rearsegP(X0,sK23)
| ~ rearsegP(X0,cons(hd(sK23),sK23))
| ~ ssList(sK23)
| ~ ssList(cons(hd(sK23),sK23))
| ~ ssList(X0) )
| ~ spl75_11
| ~ spl75_37 ),
inference(resolution,[],[f618,f3567]) ).
fof(f3567,plain,
( rearsegP(cons(hd(sK23),sK23),sK23)
| ~ spl75_11
| ~ spl75_37 ),
inference(subsumption_resolution,[],[f3096,f3100]) ).
fof(f3100,plain,
( ssList(cons(hd(sK23),nil))
| ~ spl75_37 ),
inference(avatar_component_clause,[],[f3099]) ).
fof(f3096,plain,
( rearsegP(cons(hd(sK23),sK23),sK23)
| ~ ssList(cons(hd(sK23),nil))
| ~ spl75_11 ),
inference(subsumption_resolution,[],[f3087,f397]) ).
fof(f3087,plain,
( rearsegP(cons(hd(sK23),sK23),sK23)
| ~ ssList(cons(hd(sK23),nil))
| ~ ssList(sK23)
| ~ spl75_11 ),
inference(superposition,[],[f2430,f2125]) ).
fof(f2125,plain,
( cons(hd(sK23),sK23) = app(cons(hd(sK23),nil),sK23)
| ~ spl75_11 ),
inference(resolution,[],[f2085,f1662]) ).
fof(f618,plain,
! [X2,X0,X1] :
( ~ rearsegP(X1,X2)
| rearsegP(X0,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f218]) ).
fof(f218,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f217]) ).
fof(f217,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f47]) ).
fof(f47,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( rearsegP(X1,X2)
& rearsegP(X0,X1) )
=> rearsegP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ax47) ).
fof(f3130,plain,
( ~ spl75_11
| spl75_37 ),
inference(avatar_contradiction_clause,[],[f3129]) ).
fof(f3129,plain,
( $false
| ~ spl75_11
| spl75_37 ),
inference(subsumption_resolution,[],[f3128,f415]) ).
fof(f3128,plain,
( ~ ssList(nil)
| ~ spl75_11
| spl75_37 ),
inference(subsumption_resolution,[],[f3127,f1662]) ).
fof(f3127,plain,
( ~ ssItem(hd(sK23))
| ~ ssList(nil)
| spl75_37 ),
inference(resolution,[],[f3101,f577]) ).
fof(f577,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f178]) ).
fof(f178,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(f3101,plain,
( ~ ssList(cons(hd(sK23),nil))
| spl75_37 ),
inference(avatar_component_clause,[],[f3099]) ).
fof(f3106,plain,
( ~ spl75_37
| spl75_38
| ~ spl75_11 ),
inference(avatar_split_clause,[],[f3091,f1661,f3103,f3099]) ).
fof(f3091,plain,
( ssList(cons(hd(sK23),sK23))
| ~ ssList(cons(hd(sK23),nil))
| ~ spl75_11 ),
inference(subsumption_resolution,[],[f3084,f397]) ).
fof(f3084,plain,
( ssList(cons(hd(sK23),sK23))
| ~ ssList(sK23)
| ~ ssList(cons(hd(sK23),nil))
| ~ spl75_11 ),
inference(superposition,[],[f587,f2125]) ).
fof(f2924,plain,
( ~ spl75_35
| spl75_36
| ~ spl75_29
| ~ spl75_30 ),
inference(avatar_split_clause,[],[f2488,f2332,f2328,f2921,f2917]) ).
fof(f2917,plain,
( spl75_35
<=> rearsegP(sK23,cons(sK74,sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_35])]) ).
fof(f2921,plain,
( spl75_36
<=> sK23 = cons(sK74,sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_36])]) ).
fof(f2488,plain,
( sK23 = cons(sK74,sK23)
| ~ rearsegP(sK23,cons(sK74,sK23))
| ~ spl75_29
| ~ spl75_30 ),
inference(subsumption_resolution,[],[f2487,f397]) ).
fof(f2487,plain,
( sK23 = cons(sK74,sK23)
| ~ rearsegP(sK23,cons(sK74,sK23))
| ~ ssList(sK23)
| ~ spl75_29
| ~ spl75_30 ),
inference(subsumption_resolution,[],[f2486,f2334]) ).
fof(f2486,plain,
( sK23 = cons(sK74,sK23)
| ~ rearsegP(sK23,cons(sK74,sK23))
| ~ ssList(cons(sK74,sK23))
| ~ ssList(sK23)
| ~ spl75_29 ),
inference(resolution,[],[f2479,f591]) ).
fof(f591,plain,
! [X0,X1] :
( ~ rearsegP(X1,X0)
| X0 = X1
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f193]) ).
fof(f193,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f192]) ).
fof(f192,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(f2479,plain,
( rearsegP(cons(sK74,sK23),sK23)
| ~ spl75_29 ),
inference(subsumption_resolution,[],[f2478,f397]) ).
fof(f2478,plain,
( rearsegP(cons(sK74,sK23),sK23)
| ~ ssList(sK23)
| ~ spl75_29 ),
inference(subsumption_resolution,[],[f2468,f2329]) ).
fof(f2468,plain,
( rearsegP(cons(sK74,sK23),sK23)
| ~ ssList(cons(sK74,nil))
| ~ ssList(sK23) ),
inference(superposition,[],[f2430,f2147]) ).
fof(f2915,plain,
( ~ spl75_33
| spl75_34
| ~ spl75_27
| ~ spl75_28 ),
inference(avatar_split_clause,[],[f2485,f2245,f2241,f2912,f2908]) ).
fof(f2908,plain,
( spl75_33
<=> rearsegP(sK23,cons(sK73,sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_33])]) ).
fof(f2912,plain,
( spl75_34
<=> sK23 = cons(sK73,sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_34])]) ).
fof(f2485,plain,
( sK23 = cons(sK73,sK23)
| ~ rearsegP(sK23,cons(sK73,sK23))
| ~ spl75_27
| ~ spl75_28 ),
inference(subsumption_resolution,[],[f2484,f397]) ).
fof(f2484,plain,
( sK23 = cons(sK73,sK23)
| ~ rearsegP(sK23,cons(sK73,sK23))
| ~ ssList(sK23)
| ~ spl75_27
| ~ spl75_28 ),
inference(subsumption_resolution,[],[f2483,f2247]) ).
fof(f2483,plain,
( sK23 = cons(sK73,sK23)
| ~ rearsegP(sK23,cons(sK73,sK23))
| ~ ssList(cons(sK73,sK23))
| ~ ssList(sK23)
| ~ spl75_27 ),
inference(resolution,[],[f2477,f591]) ).
fof(f2477,plain,
( rearsegP(cons(sK73,sK23),sK23)
| ~ spl75_27 ),
inference(subsumption_resolution,[],[f2476,f397]) ).
fof(f2476,plain,
( rearsegP(cons(sK73,sK23),sK23)
| ~ ssList(sK23)
| ~ spl75_27 ),
inference(subsumption_resolution,[],[f2467,f2242]) ).
fof(f2467,plain,
( rearsegP(cons(sK73,sK23),sK23)
| ~ ssList(cons(sK73,nil))
| ~ ssList(sK23) ),
inference(superposition,[],[f2430,f2146]) ).
fof(f2906,plain,
( ~ spl75_31
| spl75_32
| ~ spl75_25
| ~ spl75_26 ),
inference(avatar_split_clause,[],[f2482,f2158,f2154,f2903,f2899]) ).
fof(f2899,plain,
( spl75_31
<=> rearsegP(sK23,cons(sK27,sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_31])]) ).
fof(f2903,plain,
( spl75_32
<=> sK23 = cons(sK27,sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_32])]) ).
fof(f2482,plain,
( sK23 = cons(sK27,sK23)
| ~ rearsegP(sK23,cons(sK27,sK23))
| ~ spl75_25
| ~ spl75_26 ),
inference(subsumption_resolution,[],[f2481,f397]) ).
fof(f2481,plain,
( sK23 = cons(sK27,sK23)
| ~ rearsegP(sK23,cons(sK27,sK23))
| ~ ssList(sK23)
| ~ spl75_25
| ~ spl75_26 ),
inference(subsumption_resolution,[],[f2480,f2160]) ).
fof(f2480,plain,
( sK23 = cons(sK27,sK23)
| ~ rearsegP(sK23,cons(sK27,sK23))
| ~ ssList(cons(sK27,sK23))
| ~ ssList(sK23)
| ~ spl75_25 ),
inference(resolution,[],[f2475,f591]) ).
fof(f2475,plain,
( rearsegP(cons(sK27,sK23),sK23)
| ~ spl75_25 ),
inference(subsumption_resolution,[],[f2474,f397]) ).
fof(f2474,plain,
( rearsegP(cons(sK27,sK23),sK23)
| ~ ssList(sK23)
| ~ spl75_25 ),
inference(subsumption_resolution,[],[f2466,f2155]) ).
fof(f2466,plain,
( rearsegP(cons(sK27,sK23),sK23)
| ~ ssList(cons(sK27,nil))
| ~ ssList(sK23) ),
inference(superposition,[],[f2430,f2127]) ).
fof(f2339,plain,
spl75_29,
inference(avatar_contradiction_clause,[],[f2338]) ).
fof(f2338,plain,
( $false
| spl75_29 ),
inference(subsumption_resolution,[],[f2337,f415]) ).
fof(f2337,plain,
( ~ ssList(nil)
| spl75_29 ),
inference(subsumption_resolution,[],[f2336,f622]) ).
fof(f2336,plain,
( ~ ssItem(sK74)
| ~ ssList(nil)
| spl75_29 ),
inference(resolution,[],[f2330,f577]) ).
fof(f2330,plain,
( ~ ssList(cons(sK74,nil))
| spl75_29 ),
inference(avatar_component_clause,[],[f2328]) ).
fof(f2335,plain,
( ~ spl75_29
| spl75_30 ),
inference(avatar_split_clause,[],[f2326,f2332,f2328]) ).
fof(f2326,plain,
( ssList(cons(sK74,sK23))
| ~ ssList(cons(sK74,nil)) ),
inference(subsumption_resolution,[],[f2325,f397]) ).
fof(f2325,plain,
( ssList(cons(sK74,sK23))
| ~ ssList(sK23)
| ~ ssList(cons(sK74,nil)) ),
inference(superposition,[],[f587,f2147]) ).
fof(f2252,plain,
spl75_27,
inference(avatar_contradiction_clause,[],[f2251]) ).
fof(f2251,plain,
( $false
| spl75_27 ),
inference(subsumption_resolution,[],[f2250,f415]) ).
fof(f2250,plain,
( ~ ssList(nil)
| spl75_27 ),
inference(subsumption_resolution,[],[f2249,f621]) ).
fof(f2249,plain,
( ~ ssItem(sK73)
| ~ ssList(nil)
| spl75_27 ),
inference(resolution,[],[f2243,f577]) ).
fof(f2243,plain,
( ~ ssList(cons(sK73,nil))
| spl75_27 ),
inference(avatar_component_clause,[],[f2241]) ).
fof(f2248,plain,
( ~ spl75_27
| spl75_28 ),
inference(avatar_split_clause,[],[f2239,f2245,f2241]) ).
fof(f2239,plain,
( ssList(cons(sK73,sK23))
| ~ ssList(cons(sK73,nil)) ),
inference(subsumption_resolution,[],[f2238,f397]) ).
fof(f2238,plain,
( ssList(cons(sK73,sK23))
| ~ ssList(sK23)
| ~ ssList(cons(sK73,nil)) ),
inference(superposition,[],[f587,f2146]) ).
fof(f2165,plain,
spl75_25,
inference(avatar_contradiction_clause,[],[f2164]) ).
fof(f2164,plain,
( $false
| spl75_25 ),
inference(subsumption_resolution,[],[f2163,f415]) ).
fof(f2163,plain,
( ~ ssList(nil)
| spl75_25 ),
inference(subsumption_resolution,[],[f2162,f663]) ).
fof(f2162,plain,
( ~ ssItem(sK27)
| ~ ssList(nil)
| spl75_25 ),
inference(resolution,[],[f2156,f577]) ).
fof(f2156,plain,
( ~ ssList(cons(sK27,nil))
| spl75_25 ),
inference(avatar_component_clause,[],[f2154]) ).
fof(f2161,plain,
( ~ spl75_25
| spl75_26 ),
inference(avatar_split_clause,[],[f2152,f2158,f2154]) ).
fof(f2152,plain,
( ssList(cons(sK27,sK23))
| ~ ssList(cons(sK27,nil)) ),
inference(subsumption_resolution,[],[f2151,f397]) ).
fof(f2151,plain,
( ssList(cons(sK27,sK23))
| ~ ssList(sK23)
| ~ ssList(cons(sK27,nil)) ),
inference(superposition,[],[f587,f2127]) ).
fof(f2076,plain,
( ~ spl75_11
| ~ spl75_21
| spl75_23 ),
inference(avatar_contradiction_clause,[],[f2075]) ).
fof(f2075,plain,
( $false
| ~ spl75_11
| ~ spl75_21
| spl75_23 ),
inference(subsumption_resolution,[],[f2074,f397]) ).
fof(f2074,plain,
( ~ ssList(sK23)
| ~ spl75_11
| ~ spl75_21
| spl75_23 ),
inference(subsumption_resolution,[],[f2073,f2029]) ).
fof(f2029,plain,
( singletonP(sK23)
| ~ spl75_11
| ~ spl75_21 ),
inference(subsumption_resolution,[],[f2028,f397]) ).
fof(f2028,plain,
( ~ ssList(sK23)
| singletonP(sK23)
| ~ spl75_11
| ~ spl75_21 ),
inference(forward_demodulation,[],[f2027,f1991]) ).
fof(f1991,plain,
( sK23 = cons(hd(sK23),nil)
| ~ spl75_21 ),
inference(superposition,[],[f1618,f1985]) ).
fof(f1985,plain,
( nil = tl(sK23)
| ~ spl75_21 ),
inference(avatar_component_clause,[],[f1983]) ).
fof(f1983,plain,
( spl75_21
<=> nil = tl(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_21])]) ).
fof(f2027,plain,
( singletonP(sK23)
| ~ ssList(cons(hd(sK23),nil))
| ~ spl75_11
| ~ spl75_21 ),
inference(subsumption_resolution,[],[f2011,f1662]) ).
fof(f2011,plain,
( singletonP(sK23)
| ~ ssItem(hd(sK23))
| ~ ssList(cons(hd(sK23),nil))
| ~ spl75_21 ),
inference(superposition,[],[f632,f1991]) ).
fof(f2073,plain,
( ~ singletonP(sK23)
| ~ ssList(sK23)
| spl75_23 ),
inference(resolution,[],[f2067,f489]) ).
fof(f2067,plain,
( ~ ssItem(sK32(sK23))
| spl75_23 ),
inference(avatar_component_clause,[],[f2065]) ).
fof(f2065,plain,
( spl75_23
<=> ssItem(sK32(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_23])]) ).
fof(f2072,plain,
( ~ spl75_23
| spl75_24
| ~ spl75_11
| ~ spl75_21 ),
inference(avatar_split_clause,[],[f2060,f1983,f1661,f2069,f2065]) ).
fof(f2069,plain,
( spl75_24
<=> memberP(sK23,sK32(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_24])]) ).
fof(f2060,plain,
( memberP(sK23,sK32(sK23))
| ~ ssItem(sK32(sK23))
| ~ spl75_11
| ~ spl75_21 ),
inference(subsumption_resolution,[],[f2059,f415]) ).
fof(f2059,plain,
( memberP(sK23,sK32(sK23))
| ~ ssList(nil)
| ~ ssItem(sK32(sK23))
| ~ spl75_11
| ~ spl75_21 ),
inference(superposition,[],[f654,f2043]) ).
fof(f2043,plain,
( sK23 = cons(sK32(sK23),nil)
| ~ spl75_11
| ~ spl75_21 ),
inference(subsumption_resolution,[],[f2038,f397]) ).
fof(f2038,plain,
( sK23 = cons(sK32(sK23),nil)
| ~ ssList(sK23)
| ~ spl75_11
| ~ spl75_21 ),
inference(resolution,[],[f2029,f490]) ).
fof(f1990,plain,
( spl75_21
| spl75_22
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11 ),
inference(avatar_split_clause,[],[f1968,f1661,f1634,f1546,f1987,f1983]) ).
fof(f1987,plain,
( spl75_22
<=> hd(tl(sK23)) = sK30(tl(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_22])]) ).
fof(f1968,plain,
( hd(tl(sK23)) = sK30(tl(sK23))
| nil = tl(sK23)
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11 ),
inference(forward_demodulation,[],[f1967,f1850]) ).
fof(f1967,plain,
( nil = tl(sK23)
| hd(sK28(sK23)) = sK30(sK28(sK23))
| ~ spl75_7
| ~ spl75_9
| ~ spl75_11 ),
inference(forward_demodulation,[],[f1650,f1850]) ).
fof(f1650,plain,
( nil = sK28(sK23)
| hd(sK28(sK23)) = sK30(sK28(sK23))
| ~ spl75_9 ),
inference(resolution,[],[f1635,f486]) ).
fof(f1809,plain,
( spl75_19
| ~ spl75_20
| ~ spl75_2 ),
inference(avatar_split_clause,[],[f1472,f854,f1806,f1802]) ).
fof(f1802,plain,
( spl75_19
<=> nil = cons(sK74,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_19])]) ).
fof(f1806,plain,
( spl75_20
<=> sP4(cons(sK74,nil),sK74) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_20])]) ).
fof(f1472,plain,
( ~ sP4(cons(sK74,nil),sK74)
| nil = cons(sK74,nil)
| ~ spl75_2 ),
inference(subsumption_resolution,[],[f1471,f622]) ).
fof(f1471,plain,
( ~ ssItem(sK74)
| ~ sP4(cons(sK74,nil),sK74)
| nil = cons(sK74,nil)
| ~ spl75_2 ),
inference(forward_demodulation,[],[f1460,f1075]) ).
fof(f1075,plain,
( sK74 = hd(cons(sK74,nil))
| ~ spl75_2 ),
inference(resolution,[],[f1019,f622]) ).
fof(f1019,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,nil)) = X0 )
| ~ spl75_2 ),
inference(forward_demodulation,[],[f994,f856]) ).
fof(f994,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK24)) = X0 ),
inference(resolution,[],[f581,f398]) ).
fof(f1460,plain,
( ~ sP4(cons(sK74,nil),sK74)
| nil = cons(sK74,nil)
| ~ ssItem(hd(cons(sK74,nil)))
| ~ spl75_2 ),
inference(superposition,[],[f806,f1075]) ).
fof(f1800,plain,
( spl75_17
| ~ spl75_18
| ~ spl75_2 ),
inference(avatar_split_clause,[],[f1470,f854,f1797,f1793]) ).
fof(f1793,plain,
( spl75_17
<=> nil = cons(sK73,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_17])]) ).
fof(f1797,plain,
( spl75_18
<=> sP4(cons(sK73,nil),sK73) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_18])]) ).
fof(f1470,plain,
( ~ sP4(cons(sK73,nil),sK73)
| nil = cons(sK73,nil)
| ~ spl75_2 ),
inference(subsumption_resolution,[],[f1469,f621]) ).
fof(f1469,plain,
( ~ ssItem(sK73)
| ~ sP4(cons(sK73,nil),sK73)
| nil = cons(sK73,nil)
| ~ spl75_2 ),
inference(forward_demodulation,[],[f1459,f1074]) ).
fof(f1074,plain,
( sK73 = hd(cons(sK73,nil))
| ~ spl75_2 ),
inference(resolution,[],[f1019,f621]) ).
fof(f1459,plain,
( ~ sP4(cons(sK73,nil),sK73)
| nil = cons(sK73,nil)
| ~ ssItem(hd(cons(sK73,nil)))
| ~ spl75_2 ),
inference(superposition,[],[f806,f1074]) ).
fof(f1791,plain,
( spl75_15
| ~ spl75_16
| ~ spl75_2 ),
inference(avatar_split_clause,[],[f1468,f854,f1788,f1784]) ).
fof(f1784,plain,
( spl75_15
<=> nil = cons(sK27,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_15])]) ).
fof(f1788,plain,
( spl75_16
<=> sP4(cons(sK27,nil),sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_16])]) ).
fof(f1468,plain,
( ~ sP4(cons(sK27,nil),sK27)
| nil = cons(sK27,nil)
| ~ spl75_2 ),
inference(subsumption_resolution,[],[f1467,f663]) ).
fof(f1467,plain,
( ~ ssItem(sK27)
| ~ sP4(cons(sK27,nil),sK27)
| nil = cons(sK27,nil)
| ~ spl75_2 ),
inference(forward_demodulation,[],[f1458,f1056]) ).
fof(f1056,plain,
( sK27 = hd(cons(sK27,nil))
| ~ spl75_2 ),
inference(resolution,[],[f1019,f663]) ).
fof(f1458,plain,
( ~ sP4(cons(sK27,nil),sK27)
| nil = cons(sK27,nil)
| ~ ssItem(hd(cons(sK27,nil)))
| ~ spl75_2 ),
inference(superposition,[],[f806,f1056]) ).
fof(f1782,plain,
( spl75_13
| ~ spl75_14 ),
inference(avatar_split_clause,[],[f1466,f1779,f1775]) ).
fof(f1775,plain,
( spl75_13
<=> nil = cons(sK74,sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_13])]) ).
fof(f1779,plain,
( spl75_14
<=> sP4(cons(sK74,sK23),sK74) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_14])]) ).
fof(f1466,plain,
( ~ sP4(cons(sK74,sK23),sK74)
| nil = cons(sK74,sK23) ),
inference(subsumption_resolution,[],[f1465,f622]) ).
fof(f1465,plain,
( ~ ssItem(sK74)
| ~ sP4(cons(sK74,sK23),sK74)
| nil = cons(sK74,sK23) ),
inference(forward_demodulation,[],[f1457,f1044]) ).
fof(f1044,plain,
sK74 = hd(cons(sK74,sK23)),
inference(resolution,[],[f993,f622]) ).
fof(f993,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK23)) = X0 ),
inference(resolution,[],[f581,f397]) ).
fof(f1457,plain,
( ~ sP4(cons(sK74,sK23),sK74)
| nil = cons(sK74,sK23)
| ~ ssItem(hd(cons(sK74,sK23))) ),
inference(superposition,[],[f806,f1044]) ).
fof(f1672,plain,
spl75_11,
inference(avatar_contradiction_clause,[],[f1671]) ).
fof(f1671,plain,
( $false
| spl75_11 ),
inference(subsumption_resolution,[],[f1670,f397]) ).
fof(f1670,plain,
( ~ ssList(sK23)
| spl75_11 ),
inference(subsumption_resolution,[],[f1669,f403]) ).
fof(f1669,plain,
( nil = sK23
| ~ ssList(sK23)
| spl75_11 ),
inference(resolution,[],[f1663,f482]) ).
fof(f1663,plain,
( ~ ssItem(hd(sK23))
| spl75_11 ),
inference(avatar_component_clause,[],[f1661]) ).
fof(f1668,plain,
( ~ spl75_11
| ~ spl75_12 ),
inference(avatar_split_clause,[],[f1632,f1665,f1661]) ).
fof(f1665,plain,
( spl75_12
<=> sK23 = tl(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_12])]) ).
fof(f1632,plain,
( sK23 != tl(sK23)
| ~ ssItem(hd(sK23)) ),
inference(subsumption_resolution,[],[f1631,f397]) ).
fof(f1631,plain,
( sK23 != tl(sK23)
| ~ ssItem(hd(sK23))
| ~ ssList(sK23) ),
inference(inner_rewriting,[],[f1629]) ).
fof(f1629,plain,
( sK23 != tl(sK23)
| ~ ssItem(hd(sK23))
| ~ ssList(tl(sK23)) ),
inference(superposition,[],[f579,f1618]) ).
fof(f579,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f180,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(f1645,plain,
spl75_9,
inference(avatar_contradiction_clause,[],[f1644]) ).
fof(f1644,plain,
( $false
| spl75_9 ),
inference(subsumption_resolution,[],[f1643,f397]) ).
fof(f1643,plain,
( ~ ssList(sK23)
| spl75_9 ),
inference(subsumption_resolution,[],[f1642,f403]) ).
fof(f1642,plain,
( nil = sK23
| ~ ssList(sK23)
| spl75_9 ),
inference(resolution,[],[f1636,f479]) ).
fof(f1636,plain,
( ~ ssList(sK28(sK23))
| spl75_9 ),
inference(avatar_component_clause,[],[f1634]) ).
fof(f1641,plain,
( ~ spl75_9
| spl75_10
| ~ spl75_7 ),
inference(avatar_split_clause,[],[f1578,f1546,f1638,f1634]) ).
fof(f1638,plain,
( spl75_10
<=> memberP(sK23,sK29(sK23)) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_10])]) ).
fof(f1578,plain,
( memberP(sK23,sK29(sK23))
| ~ ssList(sK28(sK23))
| ~ spl75_7 ),
inference(subsumption_resolution,[],[f1542,f1547]) ).
fof(f1542,plain,
( memberP(sK23,sK29(sK23))
| ~ ssList(sK28(sK23))
| ~ ssItem(sK29(sK23)) ),
inference(superposition,[],[f654,f1530]) ).
fof(f1557,plain,
spl75_7,
inference(avatar_contradiction_clause,[],[f1556]) ).
fof(f1556,plain,
( $false
| spl75_7 ),
inference(subsumption_resolution,[],[f1555,f397]) ).
fof(f1555,plain,
( ~ ssList(sK23)
| spl75_7 ),
inference(subsumption_resolution,[],[f1554,f403]) ).
fof(f1554,plain,
( nil = sK23
| ~ ssList(sK23)
| spl75_7 ),
inference(resolution,[],[f1548,f480]) ).
fof(f1548,plain,
( ~ ssItem(sK29(sK23))
| spl75_7 ),
inference(avatar_component_clause,[],[f1546]) ).
fof(f1553,plain,
( ~ spl75_7
| ~ spl75_8 ),
inference(avatar_split_clause,[],[f1544,f1550,f1546]) ).
fof(f1550,plain,
( spl75_8
<=> sK23 = sK28(sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_8])]) ).
fof(f1544,plain,
( sK23 != sK28(sK23)
| ~ ssItem(sK29(sK23)) ),
inference(subsumption_resolution,[],[f1543,f397]) ).
fof(f1543,plain,
( sK23 != sK28(sK23)
| ~ ssItem(sK29(sK23))
| ~ ssList(sK23) ),
inference(inner_rewriting,[],[f1541]) ).
fof(f1541,plain,
( sK23 != sK28(sK23)
| ~ ssItem(sK29(sK23))
| ~ ssList(sK28(sK23)) ),
inference(superposition,[],[f579,f1530]) ).
fof(f1490,plain,
( spl75_5
| ~ spl75_6 ),
inference(avatar_split_clause,[],[f1464,f1487,f1483]) ).
fof(f1483,plain,
( spl75_5
<=> nil = cons(sK73,sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_5])]) ).
fof(f1487,plain,
( spl75_6
<=> sP4(cons(sK73,sK23),sK73) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_6])]) ).
fof(f1464,plain,
( ~ sP4(cons(sK73,sK23),sK73)
| nil = cons(sK73,sK23) ),
inference(subsumption_resolution,[],[f1463,f621]) ).
fof(f1463,plain,
( ~ ssItem(sK73)
| ~ sP4(cons(sK73,sK23),sK73)
| nil = cons(sK73,sK23) ),
inference(forward_demodulation,[],[f1456,f1043]) ).
fof(f1043,plain,
sK73 = hd(cons(sK73,sK23)),
inference(resolution,[],[f993,f621]) ).
fof(f1456,plain,
( ~ sP4(cons(sK73,sK23),sK73)
| nil = cons(sK73,sK23)
| ~ ssItem(hd(cons(sK73,sK23))) ),
inference(superposition,[],[f806,f1043]) ).
fof(f1481,plain,
( spl75_3
| ~ spl75_4 ),
inference(avatar_split_clause,[],[f1462,f1478,f1474]) ).
fof(f1474,plain,
( spl75_3
<=> nil = cons(sK27,sK23) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_3])]) ).
fof(f1478,plain,
( spl75_4
<=> sP4(cons(sK27,sK23),sK27) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_4])]) ).
fof(f1462,plain,
( ~ sP4(cons(sK27,sK23),sK27)
| nil = cons(sK27,sK23) ),
inference(subsumption_resolution,[],[f1461,f663]) ).
fof(f1461,plain,
( ~ ssItem(sK27)
| ~ sP4(cons(sK27,sK23),sK27)
| nil = cons(sK27,sK23) ),
inference(forward_demodulation,[],[f1455,f1025]) ).
fof(f1025,plain,
sK27 = hd(cons(sK27,sK23)),
inference(resolution,[],[f993,f663]) ).
fof(f1455,plain,
( ~ sP4(cons(sK27,sK23),sK27)
| nil = cons(sK27,sK23)
| ~ ssItem(hd(cons(sK27,sK23))) ),
inference(superposition,[],[f806,f1025]) ).
fof(f857,plain,
( spl75_1
| spl75_2 ),
inference(avatar_split_clause,[],[f816,f854,f850]) ).
fof(f850,plain,
( spl75_1
<=> hd(sK24) = sK30(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl75_1])]) ).
fof(f816,plain,
( nil = sK24
| hd(sK24) = sK30(sK24) ),
inference(resolution,[],[f486,f398]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SWC242+1 : TPTP v8.1.2. Released v2.4.0.
% 0.11/0.12 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.11/0.32 % Computer : n002.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Fri May 3 20:27:23 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.33 % (13248)Running in auto input_syntax mode. Trying TPTP
% 0.11/0.35 % (13251)WARNING: value z3 for option sas not known
% 0.11/0.35 % (13252)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.11/0.35 % (13250)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.11/0.35 % (13249)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.11/0.35 % (13254)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.11/0.35 % (13255)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.11/0.35 % (13253)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.11/0.35 % (13251)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.11/0.36 TRYING [1]
% 0.11/0.36 TRYING [1]
% 0.11/0.36 TRYING [2]
% 0.11/0.36 TRYING [2]
% 0.11/0.37 TRYING [3]
% 0.11/0.37 TRYING [3]
% 0.17/0.42 TRYING [4]
% 0.17/0.43 TRYING [4]
% 0.17/0.43 TRYING [1]
% 0.17/0.44 TRYING [2]
% 0.17/0.44 TRYING [3]
% 0.17/0.49 TRYING [4]
% 0.17/0.55 TRYING [5]
% 1.92/0.60 TRYING [5]
% 2.19/0.65 TRYING [5]
% 2.76/0.74 % (13251)First to succeed.
% 2.76/0.76 % (13251)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13248"
% 2.76/0.76 % (13251)Refutation found. Thanks to Tanya!
% 2.76/0.76 % SZS status Theorem for theBenchmark
% 2.76/0.76 % SZS output start Proof for theBenchmark
% See solution above
% 2.76/0.77 % (13251)------------------------------
% 2.76/0.77 % (13251)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 2.76/0.77 % (13251)Termination reason: Refutation
% 2.76/0.77
% 2.76/0.77 % (13251)Memory used [KB]: 6010
% 2.76/0.77 % (13251)Time elapsed: 0.415 s
% 2.76/0.77 % (13251)Instructions burned: 852 (million)
% 2.76/0.77 % (13248)Success in time 0.426 s
%------------------------------------------------------------------------------