TSTP Solution File: SWC245+1 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : SWC245+1 : TPTP v8.2.0. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n018.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 05:06:44 EDT 2024
% Result : Theorem 38.13s 5.85s
% Output : Refutation 38.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 329
% Syntax : Number of formulae : 2012 ( 82 unt; 0 def)
% Number of atoms : 8006 (1054 equ)
% Maximal formula atoms : 44 ( 3 avg)
% Number of connectives : 10598 (4604 ~;4682 |; 805 &)
% ( 241 <=>; 266 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 209 ( 207 usr; 171 prp; 0-3 aty)
% Number of functors : 56 ( 56 usr; 8 con; 0-3 aty)
% Number of variables : 1870 (1527 !; 343 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f45281,plain,
$false,
inference(avatar_sat_refutation,[],[f848,f899,f1280,f1284,f1299,f1303,f1382,f1386,f1401,f1405,f1424,f1446,f1448,f1608,f1612,f2006,f2010,f2055,f2059,f2381,f2390,f2633,f2638,f2714,f2719,f2993,f3127,f3131,f3191,f3195,f3232,f3236,f3284,f3370,f3382,f3386,f4124,f4129,f4632,f4637,f4991,f5035,f5038,f5042,f5054,f5057,f5076,f5120,f5123,f5127,f5139,f5142,f5262,f5264,f5266,f6375,f6379,f6550,f6557,f6696,f6701,f6932,f6936,f6939,f7017,f7246,f7250,f7253,f7261,f7289,f7294,f7297,f7300,f7308,f7430,f7434,f7437,f7445,f7474,f7479,f7482,f7485,f7564,f7622,f7627,f7629,f7637,f7929,f7934,f7936,f7944,f7975,f7980,f7982,f7990,f8021,f8026,f8028,f8036,f8067,f8072,f8074,f8082,f8722,f9221,f9257,f9336,f9348,f10815,f10860,f11862,f11866,f12570,f12580,f13662,f13667,f13671,f13703,f13768,f13775,f13777,f13785,f13972,f13981,f14054,f14124,f14744,f14750,f14753,f14770,f14774,f15060,f15074,f15335,f15361,f15365,f15374,f15400,f15404,f15413,f15425,f15445,f15457,f15501,f15538,f15556,f15560,f15569,f15587,f15591,f15606,f15632,f15636,f16998,f17002,f17205,f17227,f17234,f17238,f17281,f18905,f18909,f18983,f18987,f19156,f19160,f19740,f19744,f26934,f27085,f27094,f27104,f27138,f28187,f35483,f35486,f35492,f35938,f35941,f35947,f39071,f39074,f39081,f40014,f40020,f40023,f40043,f45251]) ).
fof(f45251,plain,
( ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_29 ),
inference(avatar_contradiction_clause,[],[f45250]) ).
fof(f45250,plain,
( $false
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f45249,f1775]) ).
fof(f1775,plain,
( ssList(tl(sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(superposition,[],[f1602,f1769]) ).
fof(f1769,plain,
( tl(sK20) = sK25(sK20)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f1744,f1700]) ).
fof(f1700,plain,
( sK20 = cons(hd(sK20),sK25(sK20))
| ~ spl72_5
| ~ spl72_13 ),
inference(superposition,[],[f1246,f1698]) ).
fof(f1698,plain,
( hd(sK20) = sK26(sK20)
| ~ spl72_5
| ~ spl72_13 ),
inference(forward_demodulation,[],[f1677,f1246]) ).
fof(f1677,plain,
( sK26(sK20) = hd(cons(sK26(sK20),sK25(sK20)))
| ~ spl72_5
| ~ spl72_13 ),
inference(resolution,[],[f1620,f1274]) ).
fof(f1274,plain,
( ssItem(sK26(sK20))
| ~ spl72_5 ),
inference(avatar_component_clause,[],[f1273]) ).
fof(f1273,plain,
( spl72_5
<=> ssItem(sK26(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_5])]) ).
fof(f1620,plain,
( ! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK25(sK20))) = X0 )
| ~ spl72_13 ),
inference(resolution,[],[f1602,f573]) ).
fof(f573,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/sandbox/benchmark/theBenchmark.p',ax23) ).
fof(f1246,plain,
sK20 = cons(sK26(sK20),sK25(sK20)),
inference(subsumption_resolution,[],[f1212,f392]) ).
fof(f392,plain,
nil != sK20,
inference(cnf_transformation,[],[f261]) ).
fof(f261,plain,
( ( nil != sK22
| nil = sK23 )
& ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK22
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != sK24
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK22)
& sK23 = app(sK22,sK24)
& ssList(sK24)
& ! [X8] :
( ! [X9] :
( ! [X10] :
( sP0(X8,X10,X9)
| app(app(X9,cons(X8,nil)),X10) != sK20
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != sK20
& sK20 = sK22
& sK21 = sK23
& ssList(sK23)
& ssList(sK22)
& ssList(sK21)
& ssList(sK20) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK20,sK21,sK22,sK23,sK24])],[f224,f260,f259,f258,f257,f256]) ).
fof(f256,plain,
( ? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3
& ssList(X4) )
& ! [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) )
=> ( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( sP0(X8,X10,X9)
| app(app(X9,cons(X8,nil)),X10) != sK20
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != sK20
& sK20 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
& ssList(sK20) ) ),
introduced(choice_axiom,[]) ).
fof(f257,plain,
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( sP0(X8,X10,X9)
| app(app(X9,cons(X8,nil)),X10) != sK20
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != sK20
& sK20 = X2
& X1 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(X1) )
=> ( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( sP0(X8,X10,X9)
| app(app(X9,cons(X8,nil)),X10) != sK20
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != sK20
& sK20 = X2
& sK21 = X3
& ssList(X3) )
& ssList(X2) )
& ssList(sK21) ) ),
introduced(choice_axiom,[]) ).
fof(f258,plain,
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( sP0(X8,X10,X9)
| app(app(X9,cons(X8,nil)),X10) != sK20
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != sK20
& sK20 = X2
& sK21 = X3
& ssList(X3) )
& ssList(X2) )
=> ( ? [X3] :
( ( nil != sK22
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK22
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK22)
& app(sK22,X4) = X3
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( sP0(X8,X10,X9)
| app(app(X9,cons(X8,nil)),X10) != sK20
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != sK20
& sK20 = sK22
& sK21 = X3
& ssList(X3) )
& ssList(sK22) ) ),
introduced(choice_axiom,[]) ).
fof(f259,plain,
( ? [X3] :
( ( nil != sK22
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK22
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK22)
& app(sK22,X4) = X3
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( sP0(X8,X10,X9)
| app(app(X9,cons(X8,nil)),X10) != sK20
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != sK20
& sK20 = sK22
& sK21 = X3
& ssList(X3) )
=> ( ( nil != sK22
| nil = sK23 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK22
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK22)
& app(sK22,X4) = sK23
& ssList(X4) )
& ! [X8] :
( ! [X9] :
( ! [X10] :
( sP0(X8,X10,X9)
| app(app(X9,cons(X8,nil)),X10) != sK20
| ~ ssList(X10) )
| ~ ssList(X9) )
| ~ ssItem(X8) )
& nil != sK20
& sK20 = sK22
& sK21 = sK23
& ssList(sK23) ) ),
introduced(choice_axiom,[]) ).
fof(f260,plain,
( ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK22
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK22)
& app(sK22,X4) = sK23
& ssList(X4) )
=> ( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != sK22
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != sK24
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(sK22)
& sK23 = app(sK22,sK24)
& ssList(sK24) ) ),
introduced(choice_axiom,[]) ).
fof(f224,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3
& ssList(X4) )
& ! [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,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(f99,plain,
? [X0] :
( ? [X1] :
( ? [X2] :
( ? [X3] :
( ( nil != X2
| nil = X3 )
& ? [X4] :
( ! [X5] :
( ! [X6] :
( ! [X7] :
( app(X7,cons(X5,nil)) != X2
| ~ ssList(X7) )
| app(cons(X5,nil),X6) != X4
| ~ ssList(X6) )
| ~ ssItem(X5) )
& equalelemsP(X2)
& app(X2,X4) = X3
& ssList(X4) )
& ! [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] :
( ( nil = X2
& nil != X3 )
| ! [X4] :
( ? [X5] :
( ? [X6] :
( ? [X7] :
( app(X7,cons(X5,nil)) = X2
& ssList(X7) )
& app(cons(X5,nil),X6) = X4
& ssList(X6) )
& ssItem(X5) )
| ~ equalelemsP(X2)
| app(X2,X4) != X3
| ~ ssList(X4) )
| ? [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] :
( ( nil = X2
& nil != X3 )
| ! [X8] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( app(X11,cons(X9,nil)) = X2
& ssList(X11) )
& app(cons(X9,nil),X10) = X8
& ssList(X10) )
& ssItem(X9) )
| ~ equalelemsP(X2)
| app(X2,X8) != X3
| ~ ssList(X8) )
| ? [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] :
( ( nil = X2
& nil != X3 )
| ! [X8] :
( ? [X9] :
( ? [X10] :
( ? [X11] :
( app(X11,cons(X9,nil)) = X2
& ssList(X11) )
& app(cons(X9,nil),X10) = X8
& ssList(X10) )
& ssItem(X9) )
| ~ equalelemsP(X2)
| app(X2,X8) != X3
| ~ ssList(X8) )
| ? [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/sandbox/benchmark/theBenchmark.p',co1) ).
fof(f1212,plain,
( nil = sK20
| sK20 = cons(sK26(sK20),sK25(sK20)) ),
inference(resolution,[],[f473,f386]) ).
fof(f386,plain,
ssList(sK20),
inference(cnf_transformation,[],[f261]) ).
fof(f473,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| cons(sK26(X0),sK25(X0)) = X0 ),
inference(cnf_transformation,[],[f283]) ).
fof(f283,plain,
! [X0] :
( ( cons(sK26(X0),sK25(X0)) = X0
& ssItem(sK26(X0))
& ssList(sK25(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f149,f282,f281]) ).
fof(f281,plain,
! [X0] :
( ? [X1] :
( ? [X2] :
( cons(X2,X1) = X0
& ssItem(X2) )
& ssList(X1) )
=> ( ? [X2] :
( cons(X2,sK25(X0)) = X0
& ssItem(X2) )
& ssList(sK25(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f282,plain,
! [X0] :
( ? [X2] :
( cons(X2,sK25(X0)) = X0
& ssItem(X2) )
=> ( cons(sK26(X0),sK25(X0)) = X0
& ssItem(sK26(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/sandbox/benchmark/theBenchmark.p',ax20) ).
fof(f1744,plain,
( sK25(sK20) = tl(cons(hd(sK20),sK25(sK20)))
| ~ spl72_9
| ~ spl72_13 ),
inference(resolution,[],[f1619,f1376]) ).
fof(f1376,plain,
( ssItem(hd(sK20))
| ~ spl72_9 ),
inference(avatar_component_clause,[],[f1375]) ).
fof(f1375,plain,
( spl72_9
<=> ssItem(hd(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_9])]) ).
fof(f1619,plain,
( ! [X0] :
( ~ ssItem(X0)
| sK25(sK20) = tl(cons(X0,sK25(sK20))) )
| ~ spl72_13 ),
inference(resolution,[],[f1602,f572]) ).
fof(f572,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/sandbox/benchmark/theBenchmark.p',ax25) ).
fof(f1602,plain,
( ssList(sK25(sK20))
| ~ spl72_13 ),
inference(avatar_component_clause,[],[f1601]) ).
fof(f1601,plain,
( spl72_13
<=> ssList(sK25(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_13])]) ).
fof(f45249,plain,
( ~ ssList(tl(sK20))
| ~ spl72_9
| ~ spl72_29 ),
inference(trivial_inequality_removal,[],[f45222]) ).
fof(f45222,plain,
( sK20 != sK20
| ~ ssList(tl(sK20))
| ~ spl72_9
| ~ spl72_29 ),
inference(superposition,[],[f5464,f45212]) ).
fof(f45212,plain,
( sK20 = app(cons(hd(sK20),nil),tl(sK20))
| ~ spl72_9 ),
inference(forward_demodulation,[],[f45187,f1348]) ).
fof(f1348,plain,
sK20 = cons(hd(sK20),tl(sK20)),
inference(subsumption_resolution,[],[f1314,f392]) ).
fof(f1314,plain,
( nil = sK20
| sK20 = cons(hd(sK20),tl(sK20)) ),
inference(resolution,[],[f476,f386]) ).
fof(f476,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/sandbox/benchmark/theBenchmark.p',ax78) ).
fof(f45187,plain,
( cons(hd(sK20),tl(sK20)) = app(cons(hd(sK20),nil),tl(sK20))
| ~ spl72_9 ),
inference(resolution,[],[f44444,f1376]) ).
fof(f44444,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,tl(sK20)) = app(cons(X0,nil),tl(sK20)) ),
inference(subsumption_resolution,[],[f44360,f392]) ).
fof(f44360,plain,
! [X0] :
( cons(X0,tl(sK20)) = app(cons(X0,nil),tl(sK20))
| nil = sK20
| ~ ssItem(X0) ),
inference(resolution,[],[f1624,f386]) ).
fof(f1624,plain,
! [X0,X1] :
( ~ ssList(X1)
| cons(X0,tl(X1)) = app(cons(X0,nil),tl(X1))
| nil = X1
| ~ ssItem(X0) ),
inference(resolution,[],[f574,f475]) ).
fof(f475,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/sandbox/benchmark/theBenchmark.p',ax24) ).
fof(f574,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/sandbox/benchmark/theBenchmark.p',ax81) ).
fof(f5464,plain,
( ! [X0] :
( sK20 != app(cons(hd(sK20),nil),X0)
| ~ ssList(X0) )
| ~ spl72_9
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f5463,f1376]) ).
fof(f5463,plain,
( ! [X0] :
( sK20 != app(cons(hd(sK20),nil),X0)
| ~ ssList(X0)
| ~ ssItem(hd(sK20)) )
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f5448,f407]) ).
fof(f407,plain,
ssList(nil),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax17) ).
fof(f5448,plain,
( ! [X0] :
( sK20 != app(cons(hd(sK20),nil),X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssItem(hd(sK20)) )
| ~ spl72_29 ),
inference(superposition,[],[f3009,f3133]) ).
fof(f3133,plain,
( cons(hd(sK20),nil) = app(nil,cons(hd(sK20),nil))
| ~ spl72_29 ),
inference(resolution,[],[f3121,f470]) ).
fof(f470,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/sandbox/benchmark/theBenchmark.p',ax28) ).
fof(f3121,plain,
( ssList(cons(hd(sK20),nil))
| ~ spl72_29 ),
inference(avatar_component_clause,[],[f3120]) ).
fof(f3120,plain,
( spl72_29
<=> ssList(cons(hd(sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_29])]) ).
fof(f3009,plain,
! [X10,X8,X9] :
( app(app(X9,cons(X8,nil)),X10) != sK20
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssItem(X8) ),
inference(subsumption_resolution,[],[f393,f791]) ).
fof(f791,plain,
! [X2,X0,X1] :
( ~ sP0(X0,X1,X2)
| ~ ssItem(X0) ),
inference(subsumption_resolution,[],[f790,f381]) ).
fof(f381,plain,
! [X2,X0,X1] :
( ssItem(sK19(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f255]) ).
fof(f255,plain,
! [X0,X1,X2] :
( ( ~ leq(X0,sK19(X0,X1,X2))
& lt(X0,sK19(X0,X1,X2))
& memberP(X1,sK19(X0,X1,X2))
& memberP(X2,sK19(X0,X1,X2))
& ssItem(sK19(X0,X1,X2)) )
| ~ sP0(X0,X1,X2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK19])],[f253,f254]) ).
fof(f254,plain,
! [X0,X1,X2] :
( ? [X3] :
( ~ leq(X0,X3)
& lt(X0,X3)
& memberP(X1,X3)
& memberP(X2,X3)
& ssItem(X3) )
=> ( ~ leq(X0,sK19(X0,X1,X2))
& lt(X0,sK19(X0,X1,X2))
& memberP(X1,sK19(X0,X1,X2))
& memberP(X2,sK19(X0,X1,X2))
& ssItem(sK19(X0,X1,X2)) ) ),
introduced(choice_axiom,[]) ).
fof(f253,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,[],[f252]) ).
fof(f252,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(f790,plain,
! [X2,X0,X1] :
( ~ ssItem(sK19(X0,X1,X2))
| ~ ssItem(X0)
| ~ sP0(X0,X1,X2) ),
inference(subsumption_resolution,[],[f789,f385]) ).
fof(f385,plain,
! [X2,X0,X1] :
( ~ leq(X0,sK19(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f255]) ).
fof(f789,plain,
! [X2,X0,X1] :
( leq(X0,sK19(X0,X1,X2))
| ~ ssItem(sK19(X0,X1,X2))
| ~ ssItem(X0)
| ~ sP0(X0,X1,X2) ),
inference(resolution,[],[f431,f384]) ).
fof(f384,plain,
! [X2,X0,X1] :
( lt(X0,sK19(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f255]) ).
fof(f431,plain,
! [X0,X1] :
( ~ lt(X0,X1)
| leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f266,plain,
! [X0] :
( ! [X1] :
( ( ( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1 )
& ( ( leq(X0,X1)
& X0 != X1 )
| ~ lt(X0,X1) ) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f265]) ).
fof(f265,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/sandbox/benchmark/theBenchmark.p',ax93) ).
fof(f393,plain,
! [X10,X8,X9] :
( sP0(X8,X10,X9)
| app(app(X9,cons(X8,nil)),X10) != sK20
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssItem(X8) ),
inference(cnf_transformation,[],[f261]) ).
fof(f40043,plain,
( ~ spl72_86
| spl72_169
| ~ spl72_170 ),
inference(avatar_contradiction_clause,[],[f40042]) ).
fof(f40042,plain,
( $false
| ~ spl72_86
| spl72_169
| ~ spl72_170 ),
inference(subsumption_resolution,[],[f40041,f11860]) ).
fof(f11860,plain,
( ssList(app(sK20,sK20))
| ~ spl72_86 ),
inference(avatar_component_clause,[],[f11859]) ).
fof(f11859,plain,
( spl72_86
<=> ssList(app(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_86])]) ).
fof(f40041,plain,
( ~ ssList(app(sK20,sK20))
| spl72_169
| ~ spl72_170 ),
inference(subsumption_resolution,[],[f40040,f386]) ).
fof(f40040,plain,
( ~ ssList(sK20)
| ~ ssList(app(sK20,sK20))
| spl72_169
| ~ spl72_170 ),
inference(subsumption_resolution,[],[f40039,f40013]) ).
fof(f40013,plain,
( rearsegP(app(sK20,sK20),sK20)
| ~ spl72_170 ),
inference(avatar_component_clause,[],[f40011]) ).
fof(f40011,plain,
( spl72_170
<=> rearsegP(app(sK20,sK20),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_170])]) ).
fof(f40039,plain,
( ~ rearsegP(app(sK20,sK20),sK20)
| ~ ssList(sK20)
| ~ ssList(app(sK20,sK20))
| spl72_169 ),
inference(resolution,[],[f40009,f588]) ).
fof(f588,plain,
! [X0,X1] :
( ssList(sK66(X0,X1))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f366]) ).
fof(f366,plain,
! [X0] :
( ! [X1] :
( ( ( rearsegP(X0,X1)
| ! [X2] :
( app(X2,X1) != X0
| ~ ssList(X2) ) )
& ( ( app(sK66(X0,X1),X1) = X0
& ssList(sK66(X0,X1)) )
| ~ rearsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK66])],[f364,f365]) ).
fof(f365,plain,
! [X0,X1] :
( ? [X3] :
( app(X3,X1) = X0
& ssList(X3) )
=> ( app(sK66(X0,X1),X1) = X0
& ssList(sK66(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f364,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,[],[f363]) ).
fof(f363,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/sandbox/benchmark/theBenchmark.p',ax6) ).
fof(f40009,plain,
( ~ ssList(sK66(app(sK20,sK20),sK20))
| spl72_169 ),
inference(avatar_component_clause,[],[f40007]) ).
fof(f40007,plain,
( spl72_169
<=> ssList(sK66(app(sK20,sK20),sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_169])]) ).
fof(f40023,plain,
( ~ spl72_49
| ~ spl72_50
| ~ spl72_51
| ~ spl72_52
| spl72_170 ),
inference(avatar_contradiction_clause,[],[f40022]) ).
fof(f40022,plain,
( $false
| ~ spl72_49
| ~ spl72_50
| ~ spl72_51
| ~ spl72_52
| spl72_170 ),
inference(subsumption_resolution,[],[f40021,f386]) ).
fof(f40021,plain,
( ~ ssList(sK20)
| ~ spl72_49
| ~ spl72_50
| ~ spl72_51
| ~ spl72_52
| spl72_170 ),
inference(subsumption_resolution,[],[f40017,f6791]) ).
fof(f6791,plain,
( rearsegP(sK20,sK20)
| ~ spl72_49
| ~ spl72_50
| ~ spl72_51
| ~ spl72_52 ),
inference(forward_demodulation,[],[f6790,f6695]) ).
fof(f6695,plain,
( sK20 = sK69(sK20,nil)
| ~ spl72_52 ),
inference(avatar_component_clause,[],[f6693]) ).
fof(f6693,plain,
( spl72_52
<=> sK20 = sK69(sK20,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_52])]) ).
fof(f6790,plain,
( rearsegP(sK20,sK69(sK20,nil))
| ~ spl72_49
| ~ spl72_50
| ~ spl72_51 ),
inference(subsumption_resolution,[],[f6685,f6690]) ).
fof(f6690,plain,
( ssList(sK69(sK20,nil))
| ~ spl72_51 ),
inference(avatar_component_clause,[],[f6689]) ).
fof(f6689,plain,
( spl72_51
<=> ssList(sK69(sK20,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_51])]) ).
fof(f6685,plain,
( rearsegP(sK20,sK69(sK20,nil))
| ~ ssList(sK69(sK20,nil))
| ~ spl72_49
| ~ spl72_50 ),
inference(subsumption_resolution,[],[f6671,f407]) ).
fof(f6671,plain,
( rearsegP(sK20,sK69(sK20,nil))
| ~ ssList(nil)
| ~ ssList(sK69(sK20,nil))
| ~ spl72_49
| ~ spl72_50 ),
inference(superposition,[],[f1990,f6654]) ).
fof(f6654,plain,
( sK20 = app(nil,sK69(sK20,nil))
| ~ spl72_49
| ~ spl72_50 ),
inference(subsumption_resolution,[],[f6653,f386]) ).
fof(f6653,plain,
( sK20 = app(nil,sK69(sK20,nil))
| ~ ssList(sK20)
| ~ spl72_49
| ~ spl72_50 ),
inference(subsumption_resolution,[],[f6651,f407]) ).
fof(f6651,plain,
( sK20 = app(nil,sK69(sK20,nil))
| ~ ssList(nil)
| ~ ssList(sK20)
| ~ spl72_49
| ~ spl72_50 ),
inference(resolution,[],[f6649,f596]) ).
fof(f596,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| app(X1,sK69(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f375]) ).
fof(f375,plain,
! [X0] :
( ! [X1] :
( ( ( frontsegP(X0,X1)
| ! [X2] :
( app(X1,X2) != X0
| ~ ssList(X2) ) )
& ( ( app(X1,sK69(X0,X1)) = X0
& ssList(sK69(X0,X1)) )
| ~ frontsegP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK69])],[f373,f374]) ).
fof(f374,plain,
! [X0,X1] :
( ? [X3] :
( app(X1,X3) = X0
& ssList(X3) )
=> ( app(X1,sK69(X0,X1)) = X0
& ssList(sK69(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f373,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,[],[f372]) ).
fof(f372,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/sandbox/benchmark/theBenchmark.p',ax5) ).
fof(f6649,plain,
( frontsegP(sK20,nil)
| ~ spl72_49
| ~ spl72_50 ),
inference(forward_demodulation,[],[f6648,f6549]) ).
fof(f6549,plain,
( nil = sK66(sK20,sK20)
| ~ spl72_50 ),
inference(avatar_component_clause,[],[f6547]) ).
fof(f6547,plain,
( spl72_50
<=> nil = sK66(sK20,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_50])]) ).
fof(f6648,plain,
( frontsegP(sK20,sK66(sK20,sK20))
| ~ spl72_49 ),
inference(subsumption_resolution,[],[f6473,f6544]) ).
fof(f6544,plain,
( ssList(sK66(sK20,sK20))
| ~ spl72_49 ),
inference(avatar_component_clause,[],[f6543]) ).
fof(f6543,plain,
( spl72_49
<=> ssList(sK66(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_49])]) ).
fof(f6473,plain,
( frontsegP(sK20,sK66(sK20,sK20))
| ~ ssList(sK66(sK20,sK20)) ),
inference(subsumption_resolution,[],[f6461,f386]) ).
fof(f6461,plain,
( frontsegP(sK20,sK66(sK20,sK20))
| ~ ssList(sK20)
| ~ ssList(sK66(sK20,sK20)) ),
inference(superposition,[],[f2128,f6397]) ).
fof(f6397,plain,
sK20 = app(sK66(sK20,sK20),sK20),
inference(resolution,[],[f2606,f386]) ).
fof(f2606,plain,
! [X0] :
( ~ ssList(X0)
| app(sK66(X0,X0),X0) = X0 ),
inference(duplicate_literal_removal,[],[f2596]) ).
fof(f2596,plain,
! [X0] :
( app(sK66(X0,X0),X0) = X0
| ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f589,f467]) ).
fof(f467,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f144]) ).
fof(f144,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f49]) ).
fof(f49,axiom,
! [X0] :
( ssList(X0)
=> rearsegP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax49) ).
fof(f589,plain,
! [X0,X1] :
( ~ rearsegP(X0,X1)
| app(sK66(X0,X1),X1) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f366]) ).
fof(f2128,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f640,f579]) ).
fof(f579,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/sandbox/benchmark/theBenchmark.p',ax26) ).
fof(f640,plain,
! [X2,X1] :
( frontsegP(app(X1,X2),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2)) ),
inference(equality_resolution,[],[f597]) ).
fof(f597,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| app(X1,X2) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f375]) ).
fof(f1990,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f638,f579]) ).
fof(f638,plain,
! [X2,X1] :
( rearsegP(app(X2,X1),X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X2,X1)) ),
inference(equality_resolution,[],[f590]) ).
fof(f590,plain,
! [X2,X0,X1] :
( rearsegP(X0,X1)
| app(X2,X1) != X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f366]) ).
fof(f40017,plain,
( ~ rearsegP(sK20,sK20)
| ~ ssList(sK20)
| spl72_170 ),
inference(duplicate_literal_removal,[],[f40016]) ).
fof(f40016,plain,
( ~ rearsegP(sK20,sK20)
| ~ ssList(sK20)
| ~ ssList(sK20)
| ~ ssList(sK20)
| spl72_170 ),
inference(resolution,[],[f40012,f605]) ).
fof(f605,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/sandbox/benchmark/theBenchmark.p',ax50) ).
fof(f40012,plain,
( ~ rearsegP(app(sK20,sK20),sK20)
| spl72_170 ),
inference(avatar_component_clause,[],[f40011]) ).
fof(f40020,plain,
spl72_170,
inference(avatar_contradiction_clause,[],[f40019]) ).
fof(f40019,plain,
( $false
| spl72_170 ),
inference(subsumption_resolution,[],[f40018,f386]) ).
fof(f40018,plain,
( ~ ssList(sK20)
| spl72_170 ),
inference(duplicate_literal_removal,[],[f40015]) ).
fof(f40015,plain,
( ~ ssList(sK20)
| ~ ssList(sK20)
| spl72_170 ),
inference(resolution,[],[f40012,f1990]) ).
fof(f40014,plain,
( ~ spl72_169
| spl72_170 ),
inference(avatar_split_clause,[],[f39957,f40011,f40007]) ).
fof(f39957,plain,
( rearsegP(app(sK20,sK20),sK20)
| ~ ssList(sK66(app(sK20,sK20),sK20)) ),
inference(subsumption_resolution,[],[f39935,f386]) ).
fof(f39935,plain,
( rearsegP(app(sK20,sK20),sK20)
| ~ ssList(sK66(app(sK20,sK20),sK20))
| ~ ssList(sK20) ),
inference(superposition,[],[f1990,f39816]) ).
fof(f39816,plain,
app(sK20,sK20) = app(sK66(app(sK20,sK20),sK20),sK20),
inference(resolution,[],[f33889,f386]) ).
fof(f33889,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,sK20) = app(sK66(app(X0,sK20),sK20),sK20) ),
inference(resolution,[],[f2607,f386]) ).
fof(f2607,plain,
! [X0,X1] :
( ~ ssList(X1)
| app(X0,X1) = app(sK66(app(X0,X1),X1),X1)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f2605,f579]) ).
fof(f2605,plain,
! [X0,X1] :
( app(X0,X1) = app(sK66(app(X0,X1),X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X0) ),
inference(duplicate_literal_removal,[],[f2597]) ).
fof(f2597,plain,
! [X0,X1] :
( app(X0,X1) = app(sK66(app(X0,X1),X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(resolution,[],[f589,f1990]) ).
fof(f39081,plain,
( ~ spl72_9
| ~ spl72_29
| spl72_167 ),
inference(avatar_contradiction_clause,[],[f39080]) ).
fof(f39080,plain,
( $false
| ~ spl72_9
| ~ spl72_29
| spl72_167 ),
inference(subsumption_resolution,[],[f39079,f3121]) ).
fof(f39079,plain,
( ~ ssList(cons(hd(sK20),nil))
| ~ spl72_9
| ~ spl72_29
| spl72_167 ),
inference(subsumption_resolution,[],[f39078,f1376]) ).
fof(f39078,plain,
( ~ ssItem(hd(sK20))
| ~ ssList(cons(hd(sK20),nil))
| ~ spl72_29
| spl72_167 ),
inference(resolution,[],[f39077,f624]) ).
fof(f624,plain,
! [X1] :
( singletonP(cons(X1,nil))
| ~ ssItem(X1)
| ~ ssList(cons(X1,nil)) ),
inference(equality_resolution,[],[f483]) ).
fof(f483,plain,
! [X0,X1] :
( singletonP(X0)
| cons(X1,nil) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f291]) ).
fof(f291,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ( cons(sK29(X0),nil) = X0
& ssItem(sK29(X0)) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29])],[f289,f290]) ).
fof(f290,plain,
! [X0] :
( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
=> ( cons(sK29(X0),nil) = X0
& ssItem(sK29(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f289,plain,
! [X0] :
( ( ( singletonP(X0)
| ! [X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1) ) )
& ( ? [X2] :
( cons(X2,nil) = X0
& ssItem(X2) )
| ~ singletonP(X0) ) )
| ~ ssList(X0) ),
inference(rectify,[],[f288]) ).
fof(f288,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/sandbox/benchmark/theBenchmark.p',ax4) ).
fof(f39077,plain,
( ~ singletonP(cons(hd(sK20),nil))
| ~ spl72_29
| spl72_167 ),
inference(subsumption_resolution,[],[f39076,f3121]) ).
fof(f39076,plain,
( ~ singletonP(cons(hd(sK20),nil))
| ~ ssList(cons(hd(sK20),nil))
| spl72_167 ),
inference(resolution,[],[f39066,f481]) ).
fof(f481,plain,
! [X0] :
( ssItem(sK29(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f291]) ).
fof(f39066,plain,
( ~ ssItem(sK29(cons(hd(sK20),nil)))
| spl72_167 ),
inference(avatar_component_clause,[],[f39064]) ).
fof(f39064,plain,
( spl72_167
<=> ssItem(sK29(cons(hd(sK20),nil))) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_167])]) ).
fof(f39074,plain,
( ~ spl72_9
| spl72_168 ),
inference(avatar_contradiction_clause,[],[f39073]) ).
fof(f39073,plain,
( $false
| ~ spl72_9
| spl72_168 ),
inference(subsumption_resolution,[],[f39072,f1376]) ).
fof(f39072,plain,
( ~ ssItem(hd(sK20))
| spl72_168 ),
inference(resolution,[],[f39069,f412]) ).
fof(f412,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f104]) ).
fof(f104,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/sandbox/benchmark/theBenchmark.p',ax59) ).
fof(f39069,plain,
( ~ cyclefreeP(cons(hd(sK20),nil))
| spl72_168 ),
inference(avatar_component_clause,[],[f39068]) ).
fof(f39068,plain,
( spl72_168
<=> cyclefreeP(cons(hd(sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_168])]) ).
fof(f39071,plain,
( ~ spl72_167
| spl72_168
| ~ spl72_9
| ~ spl72_29 ),
inference(avatar_split_clause,[],[f38969,f3120,f1375,f39068,f39064]) ).
fof(f38969,plain,
( cyclefreeP(cons(hd(sK20),nil))
| ~ ssItem(sK29(cons(hd(sK20),nil)))
| ~ spl72_9
| ~ spl72_29 ),
inference(superposition,[],[f412,f35383]) ).
fof(f35383,plain,
( cons(hd(sK20),nil) = cons(sK29(cons(hd(sK20),nil)),nil)
| ~ spl72_9
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f35378,f1376]) ).
fof(f35378,plain,
( ~ ssItem(hd(sK20))
| cons(hd(sK20),nil) = cons(sK29(cons(hd(sK20),nil)),nil)
| ~ spl72_29 ),
inference(resolution,[],[f1064,f3121]) ).
fof(f1064,plain,
! [X0] :
( ~ ssList(cons(X0,nil))
| ~ ssItem(X0)
| cons(X0,nil) = cons(sK29(cons(X0,nil)),nil) ),
inference(duplicate_literal_removal,[],[f1063]) ).
fof(f1063,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssList(cons(X0,nil))
| cons(X0,nil) = cons(sK29(cons(X0,nil)),nil)
| ~ ssList(cons(X0,nil)) ),
inference(resolution,[],[f624,f482]) ).
fof(f482,plain,
! [X0] :
( ~ singletonP(X0)
| cons(sK29(X0),nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f291]) ).
fof(f35947,plain,
( ~ spl72_17
| spl72_165 ),
inference(avatar_contradiction_clause,[],[f35946]) ).
fof(f35946,plain,
( $false
| ~ spl72_17
| spl72_165 ),
inference(subsumption_resolution,[],[f35945,f2049]) ).
fof(f2049,plain,
( ssList(cons(sK71,nil))
| ~ spl72_17 ),
inference(avatar_component_clause,[],[f2048]) ).
fof(f2048,plain,
( spl72_17
<=> ssList(cons(sK71,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_17])]) ).
fof(f35945,plain,
( ~ ssList(cons(sK71,nil))
| ~ spl72_17
| spl72_165 ),
inference(subsumption_resolution,[],[f35944,f614]) ).
fof(f614,plain,
ssItem(sK71),
inference(cnf_transformation,[],[f380]) ).
fof(f380,plain,
( sK70 != sK71
& ssItem(sK71)
& ssItem(sK70) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK70,sK71])],[f2,f379,f378]) ).
fof(f378,plain,
( ? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) )
=> ( ? [X1] :
( sK70 != X1
& ssItem(X1) )
& ssItem(sK70) ) ),
introduced(choice_axiom,[]) ).
fof(f379,plain,
( ? [X1] :
( sK70 != X1
& ssItem(X1) )
=> ( sK70 != sK71
& ssItem(sK71) ) ),
introduced(choice_axiom,[]) ).
fof(f2,axiom,
? [X0] :
( ? [X1] :
( X0 != X1
& ssItem(X1) )
& ssItem(X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax2) ).
fof(f35944,plain,
( ~ ssItem(sK71)
| ~ ssList(cons(sK71,nil))
| ~ spl72_17
| spl72_165 ),
inference(resolution,[],[f35943,f624]) ).
fof(f35943,plain,
( ~ singletonP(cons(sK71,nil))
| ~ spl72_17
| spl72_165 ),
inference(subsumption_resolution,[],[f35942,f2049]) ).
fof(f35942,plain,
( ~ singletonP(cons(sK71,nil))
| ~ ssList(cons(sK71,nil))
| spl72_165 ),
inference(resolution,[],[f35933,f481]) ).
fof(f35933,plain,
( ~ ssItem(sK29(cons(sK71,nil)))
| spl72_165 ),
inference(avatar_component_clause,[],[f35931]) ).
fof(f35931,plain,
( spl72_165
<=> ssItem(sK29(cons(sK71,nil))) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_165])]) ).
fof(f35941,plain,
spl72_166,
inference(avatar_contradiction_clause,[],[f35940]) ).
fof(f35940,plain,
( $false
| spl72_166 ),
inference(subsumption_resolution,[],[f35939,f614]) ).
fof(f35939,plain,
( ~ ssItem(sK71)
| spl72_166 ),
inference(resolution,[],[f35936,f412]) ).
fof(f35936,plain,
( ~ cyclefreeP(cons(sK71,nil))
| spl72_166 ),
inference(avatar_component_clause,[],[f35935]) ).
fof(f35935,plain,
( spl72_166
<=> cyclefreeP(cons(sK71,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_166])]) ).
fof(f35938,plain,
( ~ spl72_165
| spl72_166
| ~ spl72_17 ),
inference(avatar_split_clause,[],[f35841,f2048,f35935,f35931]) ).
fof(f35841,plain,
( cyclefreeP(cons(sK71,nil))
| ~ ssItem(sK29(cons(sK71,nil)))
| ~ spl72_17 ),
inference(superposition,[],[f412,f35385]) ).
fof(f35385,plain,
( cons(sK71,nil) = cons(sK29(cons(sK71,nil)),nil)
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f35380,f614]) ).
fof(f35380,plain,
( ~ ssItem(sK71)
| cons(sK71,nil) = cons(sK29(cons(sK71,nil)),nil)
| ~ spl72_17 ),
inference(resolution,[],[f1064,f2049]) ).
fof(f35492,plain,
( ~ spl72_15
| spl72_163 ),
inference(avatar_contradiction_clause,[],[f35491]) ).
fof(f35491,plain,
( $false
| ~ spl72_15
| spl72_163 ),
inference(subsumption_resolution,[],[f35490,f2000]) ).
fof(f2000,plain,
( ssList(cons(sK70,nil))
| ~ spl72_15 ),
inference(avatar_component_clause,[],[f1999]) ).
fof(f1999,plain,
( spl72_15
<=> ssList(cons(sK70,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_15])]) ).
fof(f35490,plain,
( ~ ssList(cons(sK70,nil))
| ~ spl72_15
| spl72_163 ),
inference(subsumption_resolution,[],[f35489,f613]) ).
fof(f613,plain,
ssItem(sK70),
inference(cnf_transformation,[],[f380]) ).
fof(f35489,plain,
( ~ ssItem(sK70)
| ~ ssList(cons(sK70,nil))
| ~ spl72_15
| spl72_163 ),
inference(resolution,[],[f35488,f624]) ).
fof(f35488,plain,
( ~ singletonP(cons(sK70,nil))
| ~ spl72_15
| spl72_163 ),
inference(subsumption_resolution,[],[f35487,f2000]) ).
fof(f35487,plain,
( ~ singletonP(cons(sK70,nil))
| ~ ssList(cons(sK70,nil))
| spl72_163 ),
inference(resolution,[],[f35478,f481]) ).
fof(f35478,plain,
( ~ ssItem(sK29(cons(sK70,nil)))
| spl72_163 ),
inference(avatar_component_clause,[],[f35476]) ).
fof(f35476,plain,
( spl72_163
<=> ssItem(sK29(cons(sK70,nil))) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_163])]) ).
fof(f35486,plain,
spl72_164,
inference(avatar_contradiction_clause,[],[f35485]) ).
fof(f35485,plain,
( $false
| spl72_164 ),
inference(subsumption_resolution,[],[f35484,f613]) ).
fof(f35484,plain,
( ~ ssItem(sK70)
| spl72_164 ),
inference(resolution,[],[f35481,f412]) ).
fof(f35481,plain,
( ~ cyclefreeP(cons(sK70,nil))
| spl72_164 ),
inference(avatar_component_clause,[],[f35480]) ).
fof(f35480,plain,
( spl72_164
<=> cyclefreeP(cons(sK70,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_164])]) ).
fof(f35483,plain,
( ~ spl72_163
| spl72_164
| ~ spl72_15 ),
inference(avatar_split_clause,[],[f35386,f1999,f35480,f35476]) ).
fof(f35386,plain,
( cyclefreeP(cons(sK70,nil))
| ~ ssItem(sK29(cons(sK70,nil)))
| ~ spl72_15 ),
inference(superposition,[],[f412,f35384]) ).
fof(f35384,plain,
( cons(sK70,nil) = cons(sK29(cons(sK70,nil)),nil)
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f35379,f613]) ).
fof(f35379,plain,
( ~ ssItem(sK70)
| cons(sK70,nil) = cons(sK29(cons(sK70,nil)),nil)
| ~ spl72_15 ),
inference(resolution,[],[f1064,f2000]) ).
fof(f28187,plain,
( ~ spl72_161
| spl72_162
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_156 ),
inference(avatar_split_clause,[],[f27768,f27091,f1601,f1375,f1273,f28184,f28180]) ).
fof(f28180,plain,
( spl72_161
<=> totalorderedP(app(sK20,tl(sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_161])]) ).
fof(f28184,plain,
( spl72_162
<=> sP1(app(sK20,tl(sK20)),hd(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_162])]) ).
fof(f27091,plain,
( spl72_156
<=> nil = app(sK20,tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_156])]) ).
fof(f27768,plain,
( sP1(app(sK20,tl(sK20)),hd(sK20))
| ~ totalorderedP(app(sK20,tl(sK20)))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_156 ),
inference(subsumption_resolution,[],[f27767,f1376]) ).
fof(f27767,plain,
( ~ ssItem(hd(sK20))
| sP1(app(sK20,tl(sK20)),hd(sK20))
| ~ totalorderedP(app(sK20,tl(sK20)))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_156 ),
inference(forward_demodulation,[],[f27766,f27679]) ).
fof(f27679,plain,
( hd(sK20) = hd(app(sK20,tl(sK20)))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f27592,f392]) ).
fof(f27592,plain,
( nil = sK20
| hd(sK20) = hd(app(sK20,tl(sK20)))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(resolution,[],[f2560,f386]) ).
fof(f2560,plain,
( ! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = hd(app(X0,tl(sK20))) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f2527,f1769]) ).
fof(f2527,plain,
( ! [X0] :
( nil = X0
| hd(X0) = hd(app(X0,sK25(sK20)))
| ~ ssList(X0) )
| ~ spl72_13 ),
inference(resolution,[],[f580,f1602]) ).
fof(f580,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/sandbox/benchmark/theBenchmark.p',ax85) ).
fof(f27766,plain,
( sP1(app(sK20,tl(sK20)),hd(sK20))
| ~ totalorderedP(app(sK20,tl(sK20)))
| ~ ssItem(hd(app(sK20,tl(sK20))))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_156 ),
inference(subsumption_resolution,[],[f27752,f27092]) ).
fof(f27092,plain,
( nil != app(sK20,tl(sK20))
| spl72_156 ),
inference(avatar_component_clause,[],[f27091]) ).
fof(f27752,plain,
( sP1(app(sK20,tl(sK20)),hd(sK20))
| ~ totalorderedP(app(sK20,tl(sK20)))
| nil = app(sK20,tl(sK20))
| ~ ssItem(hd(app(sK20,tl(sK20))))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(superposition,[],[f1181,f27679]) ).
fof(f1181,plain,
! [X0] :
( sP1(X0,hd(X0))
| ~ totalorderedP(X0)
| nil = X0
| ~ ssItem(hd(X0)) ),
inference(resolution,[],[f450,f411]) ).
fof(f411,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/sandbox/benchmark/theBenchmark.p',ax31) ).
fof(f450,plain,
! [X0,X1] :
( ~ leq(X1,hd(X0))
| sP1(X0,X1)
| ~ totalorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f274]) ).
fof(f274,plain,
! [X0,X1] :
( ( sP1(X0,X1)
| ( ( ~ leq(X1,hd(X0))
| ~ totalorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( leq(X1,hd(X0))
& totalorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP1(X0,X1) ) ),
inference(rectify,[],[f273]) ).
fof(f273,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP1(X1,X0) ) ),
inference(flattening,[],[f272]) ).
fof(f272,plain,
! [X1,X0] :
( ( sP1(X1,X0)
| ( ( ~ leq(X0,hd(X1))
| ~ totalorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP1(X1,X0) ) ),
inference(nnf_transformation,[],[f225]) ).
fof(f225,plain,
! [X1,X0] :
( sP1(X1,X0)
<=> ( ( leq(X0,hd(X1))
& totalorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP1])]) ).
fof(f27138,plain,
( spl72_159
| ~ spl72_160
| ~ spl72_18 ),
inference(avatar_split_clause,[],[f25193,f2052,f27135,f27131]) ).
fof(f27131,plain,
( spl72_159
<=> frontsegP(sK20,cons(sK71,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_159])]) ).
fof(f27135,plain,
( spl72_160
<=> frontsegP(nil,cons(sK71,app(sK20,sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_160])]) ).
fof(f2052,plain,
( spl72_18
<=> ssList(cons(sK71,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_18])]) ).
fof(f25193,plain,
( ~ frontsegP(nil,cons(sK71,app(sK20,sK20)))
| frontsegP(sK20,cons(sK71,sK20))
| ~ spl72_18 ),
inference(subsumption_resolution,[],[f25192,f386]) ).
fof(f25192,plain,
( ~ frontsegP(nil,cons(sK71,app(sK20,sK20)))
| ~ ssList(sK20)
| frontsegP(sK20,cons(sK71,sK20))
| ~ spl72_18 ),
inference(subsumption_resolution,[],[f25115,f2054]) ).
fof(f2054,plain,
( ssList(cons(sK71,sK20))
| ~ spl72_18 ),
inference(avatar_component_clause,[],[f2052]) ).
fof(f25115,plain,
( ~ frontsegP(nil,cons(sK71,app(sK20,sK20)))
| ~ ssList(cons(sK71,sK20))
| ~ ssList(sK20)
| frontsegP(sK20,cons(sK71,sK20)) ),
inference(superposition,[],[f24965,f19909]) ).
fof(f19909,plain,
cons(sK71,app(sK20,sK20)) = app(cons(sK71,sK20),sK20),
inference(resolution,[],[f10964,f614]) ).
fof(f10964,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,app(sK20,sK20)) = app(cons(X0,sK20),sK20) ),
inference(resolution,[],[f4671,f386]) ).
fof(f4671,plain,
! [X0,X1] :
( ~ ssList(X1)
| cons(X0,app(sK20,X1)) = app(cons(X0,sK20),X1)
| ~ ssItem(X0) ),
inference(resolution,[],[f601,f386]) ).
fof(f601,plain,
! [X2,X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X2)
| cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f203]) ).
fof(f203,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f27]) ).
fof(f27,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssItem(X2)
=> cons(X2,app(X1,X0)) = app(cons(X2,X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax27) ).
fof(f24965,plain,
! [X0,X1] :
( ~ frontsegP(nil,app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(sK20,X0) ),
inference(subsumption_resolution,[],[f24964,f579]) ).
fof(f24964,plain,
! [X0,X1] :
( frontsegP(sK20,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(nil,app(X0,X1))
| ~ ssList(app(X0,X1)) ),
inference(subsumption_resolution,[],[f24857,f386]) ).
fof(f24857,plain,
! [X0,X1] :
( frontsegP(sK20,X0)
| ~ ssList(X0)
| ~ ssList(sK20)
| ~ ssList(X1)
| ~ frontsegP(nil,app(X0,X1))
| ~ ssList(app(X0,X1)) ),
inference(resolution,[],[f3693,f2951]) ).
fof(f2951,plain,
! [X0] :
( frontsegP(sK20,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f2950,f407]) ).
fof(f2950,plain,
! [X0] :
( frontsegP(sK20,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(subsumption_resolution,[],[f2915,f386]) ).
fof(f2915,plain,
! [X0] :
( frontsegP(sK20,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sK20)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(superposition,[],[f606,f700]) ).
fof(f700,plain,
sK20 = app(nil,sK20),
inference(resolution,[],[f470,f386]) ).
fof(f606,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/sandbox/benchmark/theBenchmark.p',ax43) ).
fof(f3693,plain,
! [X2,X0,X1] :
( ~ frontsegP(X0,app(X1,X2))
| frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2) ),
inference(subsumption_resolution,[],[f3678,f579]) ).
fof(f3678,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| ~ frontsegP(X0,app(X1,X2))
| ~ ssList(X1)
| ~ ssList(app(X1,X2))
| ~ ssList(X0)
| ~ ssList(X2) ),
inference(duplicate_literal_removal,[],[f3664]) ).
fof(f3664,plain,
! [X2,X0,X1] :
( frontsegP(X0,X1)
| ~ frontsegP(X0,app(X1,X2))
| ~ ssList(X1)
| ~ ssList(app(X1,X2))
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1) ),
inference(resolution,[],[f611,f2128]) ).
fof(f611,plain,
! [X2,X0,X1] :
( ~ frontsegP(X1,X2)
| frontsegP(X0,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f220]) ).
fof(f220,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f219]) ).
fof(f219,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f40]) ).
fof(f40,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( frontsegP(X1,X2)
& frontsegP(X0,X1) )
=> frontsegP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax40) ).
fof(f27104,plain,
( spl72_157
| ~ spl72_158
| ~ spl72_16 ),
inference(avatar_split_clause,[],[f25191,f2003,f27101,f27097]) ).
fof(f27097,plain,
( spl72_157
<=> frontsegP(sK20,cons(sK70,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_157])]) ).
fof(f27101,plain,
( spl72_158
<=> frontsegP(nil,cons(sK70,app(sK20,sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_158])]) ).
fof(f2003,plain,
( spl72_16
<=> ssList(cons(sK70,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_16])]) ).
fof(f25191,plain,
( ~ frontsegP(nil,cons(sK70,app(sK20,sK20)))
| frontsegP(sK20,cons(sK70,sK20))
| ~ spl72_16 ),
inference(subsumption_resolution,[],[f25190,f386]) ).
fof(f25190,plain,
( ~ frontsegP(nil,cons(sK70,app(sK20,sK20)))
| ~ ssList(sK20)
| frontsegP(sK20,cons(sK70,sK20))
| ~ spl72_16 ),
inference(subsumption_resolution,[],[f25114,f2005]) ).
fof(f2005,plain,
( ssList(cons(sK70,sK20))
| ~ spl72_16 ),
inference(avatar_component_clause,[],[f2003]) ).
fof(f25114,plain,
( ~ frontsegP(nil,cons(sK70,app(sK20,sK20)))
| ~ ssList(cons(sK70,sK20))
| ~ ssList(sK20)
| frontsegP(sK20,cons(sK70,sK20)) ),
inference(superposition,[],[f24965,f19908]) ).
fof(f19908,plain,
cons(sK70,app(sK20,sK20)) = app(cons(sK70,sK20),sK20),
inference(resolution,[],[f10964,f613]) ).
fof(f27094,plain,
( ~ spl72_155
| spl72_156
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_136 ),
inference(avatar_split_clause,[],[f24343,f16995,f1601,f1375,f1273,f27091,f27087]) ).
fof(f27087,plain,
( spl72_155
<=> rearsegP(nil,app(sK20,tl(sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_155])]) ).
fof(f16995,plain,
( spl72_136
<=> ssList(app(sK20,tl(sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_136])]) ).
fof(f24343,plain,
( nil = app(sK20,tl(sK20))
| ~ rearsegP(nil,app(sK20,tl(sK20)))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_136 ),
inference(forward_demodulation,[],[f24342,f16812]) ).
fof(f16812,plain,
( app(sK20,tl(sK20)) = app(app(sK20,tl(sK20)),nil)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f16760,f1769]) ).
fof(f16760,plain,
( app(sK20,sK25(sK20)) = app(app(sK20,sK25(sK20)),nil)
| ~ spl72_13 ),
inference(resolution,[],[f16665,f1602]) ).
fof(f16665,plain,
! [X0] :
( ~ ssList(X0)
| app(sK20,X0) = app(app(sK20,X0),nil) ),
inference(resolution,[],[f753,f386]) ).
fof(f753,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| app(X1,X0) = app(app(X1,X0),nil) ),
inference(resolution,[],[f579,f469]) ).
fof(f469,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/sandbox/benchmark/theBenchmark.p',ax84) ).
fof(f24342,plain,
( ~ rearsegP(nil,app(sK20,tl(sK20)))
| nil = app(app(sK20,tl(sK20)),nil)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_136 ),
inference(subsumption_resolution,[],[f24341,f16996]) ).
fof(f16996,plain,
( ssList(app(sK20,tl(sK20)))
| ~ spl72_136 ),
inference(avatar_component_clause,[],[f16995]) ).
fof(f24341,plain,
( ~ rearsegP(nil,app(sK20,tl(sK20)))
| nil = app(app(sK20,tl(sK20)),nil)
| ~ ssList(app(sK20,tl(sK20)))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f24233,f407]) ).
fof(f24233,plain,
( ~ rearsegP(nil,app(sK20,tl(sK20)))
| ~ ssList(nil)
| nil = app(app(sK20,tl(sK20)),nil)
| ~ ssList(app(sK20,tl(sK20)))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(superposition,[],[f2089,f16812]) ).
fof(f2089,plain,
! [X0,X1] :
( ~ rearsegP(X1,app(X0,X1))
| ~ ssList(X1)
| app(X0,X1) = X1
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f2088,f579]) ).
fof(f2088,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) = X1
| ~ rearsegP(X1,app(X0,X1))
| ~ ssList(app(X0,X1)) ),
inference(duplicate_literal_removal,[],[f2072]) ).
fof(f2072,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) = X1
| ~ rearsegP(X1,app(X0,X1))
| ~ ssList(app(X0,X1))
| ~ ssList(X1) ),
inference(resolution,[],[f1990,f583]) ).
fof(f583,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/sandbox/benchmark/theBenchmark.p',ax48) ).
fof(f27085,plain,
( ~ spl72_153
| spl72_154
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(avatar_split_clause,[],[f24340,f11859,f8715,f1601,f1375,f1273,f896,f27082,f27078]) ).
fof(f27078,plain,
( spl72_153
<=> rearsegP(nil,app(tl(sK20),sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_153])]) ).
fof(f27082,plain,
( spl72_154
<=> nil = app(tl(sK20),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_154])]) ).
fof(f896,plain,
( spl72_4
<=> nil = sK24 ),
introduced(avatar_definition,[new_symbols(naming,[spl72_4])]) ).
fof(f8715,plain,
( spl72_73
<=> nil = app(sK20,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_73])]) ).
fof(f24340,plain,
( nil = app(tl(sK20),sK20)
| ~ rearsegP(nil,app(tl(sK20),sK20))
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(forward_demodulation,[],[f24339,f11797]) ).
fof(f11797,plain,
( app(tl(sK20),sK20) = app(app(tl(sK20),sK20),nil)
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f11743,f1769]) ).
fof(f11743,plain,
( app(sK25(sK20),sK20) = app(app(sK25(sK20),sK20),nil)
| ~ spl72_4
| ~ spl72_13 ),
inference(resolution,[],[f11581,f1602]) ).
fof(f11581,plain,
( ! [X0] :
( ~ ssList(X0)
| app(X0,sK20) = app(app(X0,sK20),nil) )
| ~ spl72_4 ),
inference(forward_demodulation,[],[f11523,f672]) ).
fof(f672,plain,
sK20 = app(sK20,nil),
inference(resolution,[],[f469,f386]) ).
fof(f11523,plain,
( ! [X0] :
( app(app(X0,sK20),nil) = app(X0,app(sK20,nil))
| ~ ssList(X0) )
| ~ spl72_4 ),
inference(resolution,[],[f4780,f386]) ).
fof(f4780,plain,
( ! [X0,X1] :
( ~ ssList(X1)
| app(app(X0,X1),nil) = app(X0,app(X1,nil))
| ~ ssList(X0) )
| ~ spl72_4 ),
inference(forward_demodulation,[],[f4739,f898]) ).
fof(f898,plain,
( nil = sK24
| ~ spl72_4 ),
inference(avatar_component_clause,[],[f896]) ).
fof(f4739,plain,
! [X0,X1] :
( app(app(X0,X1),sK24) = app(X0,app(X1,sK24))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[],[f604,f394]) ).
fof(f394,plain,
ssList(sK24),
inference(cnf_transformation,[],[f261]) ).
fof(f604,plain,
! [X2,X0,X1] :
( ~ ssList(X2)
| app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f206]) ).
fof(f206,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f82]) ).
fof(f82,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(X0,X1),X2) = app(X0,app(X1,X2)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax82) ).
fof(f24339,plain,
( ~ rearsegP(nil,app(tl(sK20),sK20))
| nil = app(app(tl(sK20),sK20),nil)
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f24338,f12119]) ).
fof(f12119,plain,
( ssList(app(tl(sK20),sK20))
| spl72_73
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f12118,f11860]) ).
fof(f12118,plain,
( ssList(app(tl(sK20),sK20))
| ~ ssList(app(sK20,sK20))
| spl72_73
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f12117,f8716]) ).
fof(f8716,plain,
( nil != app(sK20,sK20)
| spl72_73 ),
inference(avatar_component_clause,[],[f8715]) ).
fof(f12117,plain,
( ssList(app(tl(sK20),sK20))
| nil = app(sK20,sK20)
| ~ ssList(app(sK20,sK20))
| spl72_73
| ~ spl72_86 ),
inference(superposition,[],[f479,f11908]) ).
fof(f11908,plain,
( sK28(app(sK20,sK20)) = app(tl(sK20),sK20)
| spl72_73
| ~ spl72_86 ),
inference(forward_demodulation,[],[f11907,f8642]) ).
fof(f8642,plain,
tl(app(sK20,sK20)) = app(tl(sK20),sK20),
inference(subsumption_resolution,[],[f8573,f392]) ).
fof(f8573,plain,
( tl(app(sK20,sK20)) = app(tl(sK20),sK20)
| nil = sK20 ),
inference(resolution,[],[f3786,f386]) ).
fof(f3786,plain,
! [X0] :
( ~ ssList(X0)
| tl(app(X0,sK20)) = app(tl(X0),sK20)
| nil = X0 ),
inference(resolution,[],[f581,f386]) ).
fof(f581,plain,
! [X0,X1] :
( ~ ssList(X1)
| nil = X0
| tl(app(X0,X1)) = app(tl(X0),X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f189]) ).
fof(f189,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f188]) ).
fof(f188,plain,
! [X0] :
( ! [X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f86]) ).
fof(f86,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil != X0
=> tl(app(X0,X1)) = app(tl(X0),X1) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax86) ).
fof(f11907,plain,
( sK28(app(sK20,sK20)) = tl(app(sK20,sK20))
| spl72_73
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f11872,f8716]) ).
fof(f11872,plain,
( nil = app(sK20,sK20)
| sK28(app(sK20,sK20)) = tl(app(sK20,sK20))
| ~ spl72_86 ),
inference(resolution,[],[f11860,f480]) ).
fof(f480,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| tl(X0) = sK28(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f287,plain,
! [X0] :
( ( tl(X0) = sK28(X0)
& ssList(sK28(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK28])],[f159,f286]) ).
fof(f286,plain,
! [X0] :
( ? [X1] :
( tl(X0) = X1
& ssList(X1) )
=> ( tl(X0) = sK28(X0)
& ssList(sK28(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/sandbox/benchmark/theBenchmark.p',ax76) ).
fof(f479,plain,
! [X0] :
( ssList(sK28(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f287]) ).
fof(f24338,plain,
( ~ rearsegP(nil,app(tl(sK20),sK20))
| nil = app(app(tl(sK20),sK20),nil)
| ~ ssList(app(tl(sK20),sK20))
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f24232,f407]) ).
fof(f24232,plain,
( ~ rearsegP(nil,app(tl(sK20),sK20))
| ~ ssList(nil)
| nil = app(app(tl(sK20),sK20),nil)
| ~ ssList(app(tl(sK20),sK20))
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(superposition,[],[f2089,f11797]) ).
fof(f26934,plain,
( ~ spl72_151
| spl72_152
| ~ spl72_4
| ~ spl72_9
| ~ spl72_29 ),
inference(avatar_split_clause,[],[f24329,f3120,f1375,f896,f26931,f26927]) ).
fof(f26927,plain,
( spl72_151
<=> rearsegP(nil,cons(hd(sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_151])]) ).
fof(f26931,plain,
( spl72_152
<=> nil = cons(hd(sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_152])]) ).
fof(f24329,plain,
( nil = cons(hd(sK20),nil)
| ~ rearsegP(nil,cons(hd(sK20),nil))
| ~ spl72_4
| ~ spl72_9
| ~ spl72_29 ),
inference(forward_demodulation,[],[f24328,f2563]) ).
fof(f2563,plain,
( cons(hd(sK20),nil) = app(cons(hd(sK20),nil),nil)
| ~ spl72_4
| ~ spl72_9 ),
inference(resolution,[],[f1663,f1376]) ).
fof(f1663,plain,
( ! [X0] :
( ~ ssItem(X0)
| cons(X0,nil) = app(cons(X0,nil),nil) )
| ~ spl72_4 ),
inference(forward_demodulation,[],[f1629,f898]) ).
fof(f1629,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,sK24) = app(cons(X0,nil),sK24) ),
inference(resolution,[],[f574,f394]) ).
fof(f24328,plain,
( ~ rearsegP(nil,cons(hd(sK20),nil))
| nil = app(cons(hd(sK20),nil),nil)
| ~ spl72_4
| ~ spl72_9
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f24327,f3121]) ).
fof(f24327,plain,
( ~ rearsegP(nil,cons(hd(sK20),nil))
| nil = app(cons(hd(sK20),nil),nil)
| ~ ssList(cons(hd(sK20),nil))
| ~ spl72_4
| ~ spl72_9 ),
inference(subsumption_resolution,[],[f24222,f407]) ).
fof(f24222,plain,
( ~ rearsegP(nil,cons(hd(sK20),nil))
| ~ ssList(nil)
| nil = app(cons(hd(sK20),nil),nil)
| ~ ssList(cons(hd(sK20),nil))
| ~ spl72_4
| ~ spl72_9 ),
inference(superposition,[],[f2089,f2563]) ).
fof(f19744,plain,
( ~ spl72_86
| spl72_149 ),
inference(avatar_contradiction_clause,[],[f19743]) ).
fof(f19743,plain,
( $false
| ~ spl72_86
| spl72_149 ),
inference(subsumption_resolution,[],[f19742,f11860]) ).
fof(f19742,plain,
( ~ ssList(app(sK20,sK20))
| spl72_149 ),
inference(subsumption_resolution,[],[f19741,f386]) ).
fof(f19741,plain,
( ~ ssList(sK20)
| ~ ssList(app(sK20,sK20))
| spl72_149 ),
inference(resolution,[],[f19735,f579]) ).
fof(f19735,plain,
( ~ ssList(app(app(sK20,sK20),sK20))
| spl72_149 ),
inference(avatar_component_clause,[],[f19733]) ).
fof(f19733,plain,
( spl72_149
<=> ssList(app(app(sK20,sK20),sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_149])]) ).
fof(f19740,plain,
( ~ spl72_149
| ~ spl72_150
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(avatar_split_clause,[],[f19422,f11859,f8715,f1601,f1375,f1273,f19737,f19733]) ).
fof(f19737,plain,
( spl72_150
<=> duplicatefreeP(app(app(sK20,sK20),sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_150])]) ).
fof(f19422,plain,
( ~ duplicatefreeP(app(app(sK20,sK20),sK20))
| ~ ssList(app(app(sK20,sK20),sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(resolution,[],[f19419,f658]) ).
fof(f658,plain,
! [X0] :
( sP5(X0)
| ~ duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f484,f494]) ).
fof(f494,plain,
! [X0] :
( sP6(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f233]) ).
fof(f233,plain,
! [X0] :
( sP6(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f162,f232,f231]) ).
fof(f231,plain,
! [X0] :
( sP5(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,[sP5])]) ).
fof(f232,plain,
! [X0] :
( ( duplicatefreeP(X0)
<=> sP5(X0) )
| ~ sP6(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP6])]) ).
fof(f162,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,[],[f161]) ).
fof(f161,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/sandbox/benchmark/theBenchmark.p',ax13) ).
fof(f484,plain,
! [X0] :
( ~ sP6(X0)
| ~ duplicatefreeP(X0)
| sP5(X0) ),
inference(cnf_transformation,[],[f292]) ).
fof(f292,plain,
! [X0] :
( ( ( duplicatefreeP(X0)
| ~ sP5(X0) )
& ( sP5(X0)
| ~ duplicatefreeP(X0) ) )
| ~ sP6(X0) ),
inference(nnf_transformation,[],[f232]) ).
fof(f19419,plain,
( ~ sP5(app(app(sK20,sK20),sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f19414,f407]) ).
fof(f19414,plain,
( ~ sP5(app(app(sK20,sK20),sK20))
| ~ ssList(nil)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(superposition,[],[f19357,f11868]) ).
fof(f11868,plain,
( app(sK20,sK20) = app(nil,app(sK20,sK20))
| ~ spl72_86 ),
inference(resolution,[],[f11860,f470]) ).
fof(f19357,plain,
( ! [X0] :
( ~ sP5(app(app(X0,app(sK20,sK20)),sK20))
| ~ ssList(X0) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f19347,f12119]) ).
fof(f19347,plain,
( ! [X0] :
( ~ sP5(app(app(X0,app(sK20,sK20)),sK20))
| ~ ssList(app(tl(sK20),sK20))
| ~ ssList(X0) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(superposition,[],[f5813,f11904]) ).
fof(f11904,plain,
( app(sK20,sK20) = cons(hd(sK20),app(tl(sK20),sK20))
| spl72_73
| ~ spl72_86 ),
inference(forward_demodulation,[],[f11903,f7732]) ).
fof(f7732,plain,
hd(sK20) = hd(app(sK20,sK20)),
inference(subsumption_resolution,[],[f7670,f392]) ).
fof(f7670,plain,
( hd(sK20) = hd(app(sK20,sK20))
| nil = sK20 ),
inference(resolution,[],[f2521,f386]) ).
fof(f2521,plain,
! [X0] :
( ~ ssList(X0)
| hd(X0) = hd(app(X0,sK20))
| nil = X0 ),
inference(resolution,[],[f580,f386]) ).
fof(f11903,plain,
( app(sK20,sK20) = cons(hd(app(sK20,sK20)),app(tl(sK20),sK20))
| spl72_73
| ~ spl72_86 ),
inference(forward_demodulation,[],[f11902,f8642]) ).
fof(f11902,plain,
( app(sK20,sK20) = cons(hd(app(sK20,sK20)),tl(app(sK20,sK20)))
| spl72_73
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f11870,f8716]) ).
fof(f11870,plain,
( nil = app(sK20,sK20)
| app(sK20,sK20) = cons(hd(app(sK20,sK20)),tl(app(sK20,sK20)))
| ~ spl72_86 ),
inference(resolution,[],[f11860,f476]) ).
fof(f5813,plain,
( ! [X0,X1] :
( ~ sP5(app(app(X0,cons(hd(sK20),X1)),sK20))
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f5812,f1775]) ).
fof(f5812,plain,
( ! [X0,X1] :
( ~ sP5(app(app(X0,cons(hd(sK20),X1)),sK20))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(tl(sK20)) )
| ~ spl72_9 ),
inference(subsumption_resolution,[],[f5780,f1376]) ).
fof(f5780,plain,
! [X0,X1] :
( ~ sP5(app(app(X0,cons(hd(sK20),X1)),sK20))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(hd(sK20))
| ~ ssList(tl(sK20)) ),
inference(superposition,[],[f644,f1348]) ).
fof(f644,plain,
! [X10,X8,X9,X7] :
( ~ sP5(app(app(X8,cons(X7,X9)),cons(X7,X10)))
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssList(X10) ),
inference(duplicate_literal_removal,[],[f626]) ).
fof(f626,plain,
! [X10,X8,X9,X7] :
( ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X7)
| ~ sP5(app(app(X8,cons(X7,X9)),cons(X7,X10))) ),
inference(equality_resolution,[],[f625]) ).
fof(f625,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)
| ~ sP5(X0) ),
inference(equality_resolution,[],[f486]) ).
fof(f486,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)
| ~ sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f300,plain,
! [X0] :
( ( sP5(X0)
| ( sK30(X0) = sK31(X0)
& app(app(sK32(X0),cons(sK30(X0),sK33(X0))),cons(sK31(X0),sK34(X0))) = X0
& ssList(sK34(X0))
& ssList(sK33(X0))
& ssList(sK32(X0))
& ssItem(sK31(X0))
& ssItem(sK30(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) )
| ~ sP5(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK30,sK31,sK32,sK33,sK34])],[f294,f299,f298,f297,f296,f295]) ).
fof(f295,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] :
( sK30(X0) = X2
& app(app(X3,cons(sK30(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK30(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f296,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK30(X0) = X2
& app(app(X3,cons(sK30(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK30(X0) = sK31(X0)
& app(app(X3,cons(sK30(X0),X4)),cons(sK31(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK31(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f297,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( sK30(X0) = sK31(X0)
& app(app(X3,cons(sK30(X0),X4)),cons(sK31(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( sK30(X0) = sK31(X0)
& app(app(sK32(X0),cons(sK30(X0),X4)),cons(sK31(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK32(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f298,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( sK30(X0) = sK31(X0)
& app(app(sK32(X0),cons(sK30(X0),X4)),cons(sK31(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( sK30(X0) = sK31(X0)
& app(app(sK32(X0),cons(sK30(X0),sK33(X0))),cons(sK31(X0),X5)) = X0
& ssList(X5) )
& ssList(sK33(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f299,plain,
! [X0] :
( ? [X5] :
( sK30(X0) = sK31(X0)
& app(app(sK32(X0),cons(sK30(X0),sK33(X0))),cons(sK31(X0),X5)) = X0
& ssList(X5) )
=> ( sK30(X0) = sK31(X0)
& app(app(sK32(X0),cons(sK30(X0),sK33(X0))),cons(sK31(X0),sK34(X0))) = X0
& ssList(sK34(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f294,plain,
! [X0] :
( ( sP5(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) )
| ~ sP5(X0) ) ),
inference(rectify,[],[f293]) ).
fof(f293,plain,
! [X0] :
( ( sP5(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) )
| ~ sP5(X0) ) ),
inference(nnf_transformation,[],[f231]) ).
fof(f19160,plain,
( ~ spl72_86
| spl72_147 ),
inference(avatar_contradiction_clause,[],[f19159]) ).
fof(f19159,plain,
( $false
| ~ spl72_86
| spl72_147 ),
inference(subsumption_resolution,[],[f19158,f386]) ).
fof(f19158,plain,
( ~ ssList(sK20)
| ~ spl72_86
| spl72_147 ),
inference(subsumption_resolution,[],[f19157,f11860]) ).
fof(f19157,plain,
( ~ ssList(app(sK20,sK20))
| ~ ssList(sK20)
| spl72_147 ),
inference(resolution,[],[f19151,f579]) ).
fof(f19151,plain,
( ~ ssList(app(sK20,app(sK20,sK20)))
| spl72_147 ),
inference(avatar_component_clause,[],[f19149]) ).
fof(f19149,plain,
( spl72_147
<=> ssList(app(sK20,app(sK20,sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_147])]) ).
fof(f19156,plain,
( ~ spl72_147
| ~ spl72_148
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(avatar_split_clause,[],[f17992,f11859,f8715,f1601,f1375,f1273,f19153,f19149]) ).
fof(f19153,plain,
( spl72_148
<=> duplicatefreeP(app(sK20,app(sK20,sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_148])]) ).
fof(f17992,plain,
( ~ duplicatefreeP(app(sK20,app(sK20,sK20)))
| ~ ssList(app(sK20,app(sK20,sK20)))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(resolution,[],[f17989,f658]) ).
fof(f17989,plain,
( ~ sP5(app(sK20,app(sK20,sK20)))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f17982,f12119]) ).
fof(f17982,plain,
( ~ sP5(app(sK20,app(sK20,sK20)))
| ~ ssList(app(tl(sK20),sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(superposition,[],[f17674,f11904]) ).
fof(f17674,plain,
( ! [X0] :
( ~ sP5(app(sK20,cons(hd(sK20),X0)))
| ~ ssList(X0) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f17661,f407]) ).
fof(f17661,plain,
( ! [X0] :
( ~ sP5(app(sK20,cons(hd(sK20),X0)))
| ~ ssList(nil)
| ~ ssList(X0) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(superposition,[],[f5791,f700]) ).
fof(f5791,plain,
( ! [X0,X1] :
( ~ sP5(app(app(X0,sK20),cons(hd(sK20),X1)))
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f5790,f1376]) ).
fof(f5790,plain,
( ! [X0,X1] :
( ~ sP5(app(app(X0,sK20),cons(hd(sK20),X1)))
| ~ ssList(X0)
| ~ ssItem(hd(sK20))
| ~ ssList(X1) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f5771,f1775]) ).
fof(f5771,plain,
! [X0,X1] :
( ~ sP5(app(app(X0,sK20),cons(hd(sK20),X1)))
| ~ ssList(tl(sK20))
| ~ ssList(X0)
| ~ ssItem(hd(sK20))
| ~ ssList(X1) ),
inference(superposition,[],[f644,f1348]) ).
fof(f18987,plain,
( ~ spl72_18
| spl72_145 ),
inference(avatar_contradiction_clause,[],[f18986]) ).
fof(f18986,plain,
( $false
| ~ spl72_18
| spl72_145 ),
inference(subsumption_resolution,[],[f18985,f2054]) ).
fof(f18985,plain,
( ~ ssList(cons(sK71,sK20))
| spl72_145 ),
inference(subsumption_resolution,[],[f18984,f386]) ).
fof(f18984,plain,
( ~ ssList(sK20)
| ~ ssList(cons(sK71,sK20))
| spl72_145 ),
inference(resolution,[],[f18978,f579]) ).
fof(f18978,plain,
( ~ ssList(app(cons(sK71,sK20),sK20))
| spl72_145 ),
inference(avatar_component_clause,[],[f18976]) ).
fof(f18976,plain,
( spl72_145
<=> ssList(app(cons(sK71,sK20),sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_145])]) ).
fof(f18983,plain,
( ~ spl72_145
| ~ spl72_146
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_17 ),
inference(avatar_split_clause,[],[f17872,f2048,f1601,f1375,f1273,f18980,f18976]) ).
fof(f18980,plain,
( spl72_146
<=> duplicatefreeP(app(cons(sK71,sK20),sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_146])]) ).
fof(f17872,plain,
( ~ duplicatefreeP(app(cons(sK71,sK20),sK20))
| ~ ssList(app(cons(sK71,sK20),sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_17 ),
inference(resolution,[],[f17747,f658]) ).
fof(f17747,plain,
( ~ sP5(app(cons(sK71,sK20),sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f17737,f2049]) ).
fof(f17737,plain,
( ~ sP5(app(cons(sK71,sK20),sK20))
| ~ ssList(cons(sK71,nil))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(superposition,[],[f17679,f1986]) ).
fof(f1986,plain,
cons(sK71,sK20) = app(cons(sK71,nil),sK20),
inference(resolution,[],[f1625,f614]) ).
fof(f1625,plain,
! [X0] :
( ~ ssItem(X0)
| cons(X0,sK20) = app(cons(X0,nil),sK20) ),
inference(resolution,[],[f574,f386]) ).
fof(f17679,plain,
( ! [X0] :
( ~ sP5(app(app(X0,sK20),sK20))
| ~ ssList(X0) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f17666,f1775]) ).
fof(f17666,plain,
( ! [X0] :
( ~ sP5(app(app(X0,sK20),sK20))
| ~ ssList(X0)
| ~ ssList(tl(sK20)) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(superposition,[],[f5791,f1348]) ).
fof(f18909,plain,
( ~ spl72_16
| spl72_143 ),
inference(avatar_contradiction_clause,[],[f18908]) ).
fof(f18908,plain,
( $false
| ~ spl72_16
| spl72_143 ),
inference(subsumption_resolution,[],[f18907,f2005]) ).
fof(f18907,plain,
( ~ ssList(cons(sK70,sK20))
| spl72_143 ),
inference(subsumption_resolution,[],[f18906,f386]) ).
fof(f18906,plain,
( ~ ssList(sK20)
| ~ ssList(cons(sK70,sK20))
| spl72_143 ),
inference(resolution,[],[f18900,f579]) ).
fof(f18900,plain,
( ~ ssList(app(cons(sK70,sK20),sK20))
| spl72_143 ),
inference(avatar_component_clause,[],[f18898]) ).
fof(f18898,plain,
( spl72_143
<=> ssList(app(cons(sK70,sK20),sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_143])]) ).
fof(f18905,plain,
( ~ spl72_143
| ~ spl72_144
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_15 ),
inference(avatar_split_clause,[],[f17814,f1999,f1601,f1375,f1273,f18902,f18898]) ).
fof(f18902,plain,
( spl72_144
<=> duplicatefreeP(app(cons(sK70,sK20),sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_144])]) ).
fof(f17814,plain,
( ~ duplicatefreeP(app(cons(sK70,sK20),sK20))
| ~ ssList(app(cons(sK70,sK20),sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_15 ),
inference(resolution,[],[f17746,f658]) ).
fof(f17746,plain,
( ~ sP5(app(cons(sK70,sK20),sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f17736,f2000]) ).
fof(f17736,plain,
( ~ sP5(app(cons(sK70,sK20),sK20))
| ~ ssList(cons(sK70,nil))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(superposition,[],[f17679,f1985]) ).
fof(f1985,plain,
cons(sK70,sK20) = app(cons(sK70,nil),sK20),
inference(resolution,[],[f1625,f613]) ).
fof(f17281,plain,
( ~ spl72_141
| spl72_142
| ~ spl72_136
| ~ spl72_139 ),
inference(avatar_split_clause,[],[f17247,f17220,f16995,f17278,f17274]) ).
fof(f17274,plain,
( spl72_141
<=> segmentP(sK20,app(sK20,tl(sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_141])]) ).
fof(f17278,plain,
( spl72_142
<=> sK20 = app(sK20,tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_142])]) ).
fof(f17220,plain,
( spl72_139
<=> segmentP(app(sK20,tl(sK20)),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_139])]) ).
fof(f17247,plain,
( sK20 = app(sK20,tl(sK20))
| ~ segmentP(sK20,app(sK20,tl(sK20)))
| ~ spl72_136
| ~ spl72_139 ),
inference(subsumption_resolution,[],[f17246,f386]) ).
fof(f17246,plain,
( sK20 = app(sK20,tl(sK20))
| ~ segmentP(sK20,app(sK20,tl(sK20)))
| ~ ssList(sK20)
| ~ spl72_136
| ~ spl72_139 ),
inference(subsumption_resolution,[],[f17241,f16996]) ).
fof(f17241,plain,
( sK20 = app(sK20,tl(sK20))
| ~ segmentP(sK20,app(sK20,tl(sK20)))
| ~ ssList(app(sK20,tl(sK20)))
| ~ ssList(sK20)
| ~ spl72_139 ),
inference(resolution,[],[f17222,f584]) ).
fof(f584,plain,
! [X0,X1] :
( ~ segmentP(X1,X0)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f195]) ).
fof(f195,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f194]) ).
fof(f194,plain,
! [X0] :
( ! [X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f54]) ).
fof(f54,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( ( segmentP(X1,X0)
& segmentP(X0,X1) )
=> X0 = X1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax54) ).
fof(f17222,plain,
( segmentP(app(sK20,tl(sK20)),sK20)
| ~ spl72_139 ),
inference(avatar_component_clause,[],[f17220]) ).
fof(f17238,plain,
( ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_139 ),
inference(avatar_contradiction_clause,[],[f17237]) ).
fof(f17237,plain,
( $false
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_139 ),
inference(subsumption_resolution,[],[f17236,f386]) ).
fof(f17236,plain,
( ~ ssList(sK20)
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_139 ),
inference(subsumption_resolution,[],[f17235,f1775]) ).
fof(f17235,plain,
( ~ ssList(tl(sK20))
| ~ ssList(sK20)
| ~ spl72_4
| spl72_139 ),
inference(subsumption_resolution,[],[f17230,f6169]) ).
fof(f6169,plain,
( segmentP(sK20,sK20)
| ~ spl72_4 ),
inference(subsumption_resolution,[],[f6168,f387]) ).
fof(f387,plain,
ssList(sK21),
inference(cnf_transformation,[],[f261]) ).
fof(f6168,plain,
( ~ ssList(sK21)
| segmentP(sK20,sK20)
| ~ spl72_4 ),
inference(forward_demodulation,[],[f6167,f656]) ).
fof(f656,plain,
sK21 = app(sK20,sK24),
inference(forward_demodulation,[],[f655,f390]) ).
fof(f390,plain,
sK21 = sK23,
inference(cnf_transformation,[],[f261]) ).
fof(f655,plain,
sK23 = app(sK20,sK24),
inference(forward_demodulation,[],[f395,f391]) ).
fof(f391,plain,
sK20 = sK22,
inference(cnf_transformation,[],[f261]) ).
fof(f395,plain,
sK23 = app(sK22,sK24),
inference(cnf_transformation,[],[f261]) ).
fof(f6167,plain,
( segmentP(sK20,sK20)
| ~ ssList(app(sK20,sK24))
| ~ spl72_4 ),
inference(forward_demodulation,[],[f6166,f1443]) ).
fof(f1443,plain,
( sK20 = sK21
| ~ spl72_4 ),
inference(forward_demodulation,[],[f1431,f672]) ).
fof(f1431,plain,
( sK21 = app(sK20,nil)
| ~ spl72_4 ),
inference(superposition,[],[f656,f898]) ).
fof(f6166,plain,
( segmentP(sK21,sK20)
| ~ ssList(app(sK20,sK24)) ),
inference(subsumption_resolution,[],[f6157,f394]) ).
fof(f6157,plain,
( segmentP(sK21,sK20)
| ~ ssList(app(sK20,sK24))
| ~ ssList(sK24) ),
inference(superposition,[],[f6081,f656]) ).
fof(f6081,plain,
! [X0] :
( segmentP(app(sK20,X0),sK20)
| ~ ssList(app(sK20,X0))
| ~ ssList(X0) ),
inference(forward_demodulation,[],[f6080,f700]) ).
fof(f6080,plain,
! [X0] :
( segmentP(app(sK20,X0),sK20)
| ~ ssList(X0)
| ~ ssList(app(app(nil,sK20),X0)) ),
inference(subsumption_resolution,[],[f6079,f386]) ).
fof(f6079,plain,
! [X0] :
( segmentP(app(sK20,X0),sK20)
| ~ ssList(X0)
| ~ ssList(sK20)
| ~ ssList(app(app(nil,sK20),X0)) ),
inference(subsumption_resolution,[],[f6007,f407]) ).
fof(f6007,plain,
! [X0] :
( segmentP(app(sK20,X0),sK20)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK20)
| ~ ssList(app(app(nil,sK20),X0)) ),
inference(superposition,[],[f639,f700]) ).
fof(f639,plain,
! [X2,X3,X1] :
( segmentP(app(app(X2,X1),X3),X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(app(X2,X1),X3)) ),
inference(equality_resolution,[],[f594]) ).
fof(f594,plain,
! [X2,X3,X0,X1] :
( segmentP(X0,X1)
| app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f371]) ).
fof(f371,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
& ssList(sK68(X0,X1))
& ssList(sK67(X0,X1)) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK67,sK68])],[f368,f370,f369]) ).
fof(f369,plain,
! [X0,X1] :
( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( app(app(sK67(X0,X1),X1),X5) = X0
& ssList(X5) )
& ssList(sK67(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f370,plain,
! [X0,X1] :
( ? [X5] :
( app(app(sK67(X0,X1),X1),X5) = X0
& ssList(X5) )
=> ( app(app(sK67(X0,X1),X1),sK68(X0,X1)) = X0
& ssList(sK68(X0,X1)) ) ),
introduced(choice_axiom,[]) ).
fof(f368,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X4] :
( ? [X5] :
( app(app(X4,X1),X5) = X0
& ssList(X5) )
& ssList(X4) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(rectify,[],[f367]) ).
fof(f367,plain,
! [X0] :
( ! [X1] :
( ( ( segmentP(X0,X1)
| ! [X2] :
( ! [X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3) )
| ~ ssList(X2) ) )
& ( ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) )
| ~ segmentP(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f200]) ).
fof(f200,plain,
! [X0] :
( ! [X1] :
( ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( segmentP(X0,X1)
<=> ? [X2] :
( ? [X3] :
( app(app(X2,X1),X3) = X0
& ssList(X3) )
& ssList(X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax7) ).
fof(f17230,plain,
( ~ segmentP(sK20,sK20)
| ~ ssList(tl(sK20))
| ~ ssList(sK20)
| spl72_139 ),
inference(resolution,[],[f17221,f5547]) ).
fof(f5547,plain,
! [X0,X1] :
( segmentP(app(sK20,X0),X1)
| ~ segmentP(sK20,X1)
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f5546,f386]) ).
fof(f5546,plain,
! [X0,X1] :
( segmentP(app(sK20,X0),X1)
| ~ segmentP(sK20,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sK20) ),
inference(subsumption_resolution,[],[f5495,f407]) ).
fof(f5495,plain,
! [X0,X1] :
( segmentP(app(sK20,X0),X1)
| ~ segmentP(sK20,X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(sK20) ),
inference(superposition,[],[f612,f700]) ).
fof(f612,plain,
! [X2,X3,X0,X1] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f222]) ).
fof(f222,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f221]) ).
fof(f221,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f56]) ).
fof(f56,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ! [X3] :
( ssList(X3)
=> ( segmentP(X0,X1)
=> segmentP(app(app(X2,X0),X3),X1) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax56) ).
fof(f17221,plain,
( ~ segmentP(app(sK20,tl(sK20)),sK20)
| spl72_139 ),
inference(avatar_component_clause,[],[f17220]) ).
fof(f17234,plain,
( ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_136
| spl72_139 ),
inference(avatar_contradiction_clause,[],[f17233]) ).
fof(f17233,plain,
( $false
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_136
| spl72_139 ),
inference(subsumption_resolution,[],[f17232,f1775]) ).
fof(f17232,plain,
( ~ ssList(tl(sK20))
| ~ spl72_136
| spl72_139 ),
inference(subsumption_resolution,[],[f17228,f16996]) ).
fof(f17228,plain,
( ~ ssList(app(sK20,tl(sK20)))
| ~ ssList(tl(sK20))
| spl72_139 ),
inference(resolution,[],[f17221,f6081]) ).
fof(f17227,plain,
( spl72_139
| ~ spl72_140
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_85
| ~ spl72_86
| ~ spl72_136 ),
inference(avatar_split_clause,[],[f17148,f16995,f11859,f11855,f1601,f1375,f1273,f17224,f17220]) ).
fof(f17224,plain,
( spl72_140
<=> segmentP(tl(sK20),app(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_140])]) ).
fof(f11855,plain,
( spl72_85
<=> segmentP(app(sK20,sK20),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_85])]) ).
fof(f17148,plain,
( ~ segmentP(tl(sK20),app(sK20,sK20))
| segmentP(app(sK20,tl(sK20)),sK20)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_85
| ~ spl72_86
| ~ spl72_136 ),
inference(subsumption_resolution,[],[f17147,f16996]) ).
fof(f17147,plain,
( ~ segmentP(tl(sK20),app(sK20,sK20))
| segmentP(app(sK20,tl(sK20)),sK20)
| ~ ssList(app(sK20,tl(sK20)))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_85
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f17139,f11860]) ).
fof(f17139,plain,
( ~ segmentP(tl(sK20),app(sK20,sK20))
| ~ ssList(app(sK20,sK20))
| segmentP(app(sK20,tl(sK20)),sK20)
| ~ ssList(app(sK20,tl(sK20)))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_85
| ~ spl72_86 ),
inference(resolution,[],[f16971,f11933]) ).
fof(f11933,plain,
( ! [X0] :
( ~ segmentP(X0,app(sK20,sK20))
| segmentP(X0,sK20)
| ~ ssList(X0) )
| ~ spl72_85
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f11932,f11860]) ).
fof(f11932,plain,
( ! [X0] :
( segmentP(X0,sK20)
| ~ segmentP(X0,app(sK20,sK20))
| ~ ssList(app(sK20,sK20))
| ~ ssList(X0) )
| ~ spl72_85 ),
inference(subsumption_resolution,[],[f11928,f386]) ).
fof(f11928,plain,
( ! [X0] :
( segmentP(X0,sK20)
| ~ segmentP(X0,app(sK20,sK20))
| ~ ssList(sK20)
| ~ ssList(app(sK20,sK20))
| ~ ssList(X0) )
| ~ spl72_85 ),
inference(resolution,[],[f11857,f609]) ).
fof(f609,plain,
! [X2,X0,X1] :
( ~ segmentP(X1,X2)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f216]) ).
fof(f216,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f215]) ).
fof(f215,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f53]) ).
fof(f53,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ( segmentP(X1,X2)
& segmentP(X0,X1) )
=> segmentP(X0,X2) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax53) ).
fof(f11857,plain,
( segmentP(app(sK20,sK20),sK20)
| ~ spl72_85 ),
inference(avatar_component_clause,[],[f11855]) ).
fof(f16971,plain,
( ! [X0] :
( segmentP(app(sK20,tl(sK20)),X0)
| ~ segmentP(tl(sK20),X0)
| ~ ssList(X0) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f16970,f1775]) ).
fof(f16970,plain,
( ! [X0] :
( segmentP(app(sK20,tl(sK20)),X0)
| ~ segmentP(tl(sK20),X0)
| ~ ssList(X0)
| ~ ssList(tl(sK20)) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f16969,f386]) ).
fof(f16969,plain,
( ! [X0] :
( segmentP(app(sK20,tl(sK20)),X0)
| ~ segmentP(tl(sK20),X0)
| ~ ssList(sK20)
| ~ ssList(X0)
| ~ ssList(tl(sK20)) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f16945,f407]) ).
fof(f16945,plain,
( ! [X0] :
( segmentP(app(sK20,tl(sK20)),X0)
| ~ segmentP(tl(sK20),X0)
| ~ ssList(nil)
| ~ ssList(sK20)
| ~ ssList(X0)
| ~ ssList(tl(sK20)) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(superposition,[],[f612,f16812]) ).
fof(f17205,plain,
( ~ spl72_137
| spl72_138
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_135
| ~ spl72_136 ),
inference(avatar_split_clause,[],[f17191,f16995,f16991,f1601,f1375,f1273,f896,f17202,f17198]) ).
fof(f17198,plain,
( spl72_137
<=> segmentP(nil,app(sK20,tl(sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_137])]) ).
fof(f17202,plain,
( spl72_138
<=> segmentP(sK20,tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_138])]) ).
fof(f16991,plain,
( spl72_135
<=> segmentP(app(sK20,tl(sK20)),tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_135])]) ).
fof(f17191,plain,
( segmentP(sK20,tl(sK20))
| ~ segmentP(nil,app(sK20,tl(sK20)))
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_135
| ~ spl72_136 ),
inference(subsumption_resolution,[],[f17190,f16996]) ).
fof(f17190,plain,
( segmentP(sK20,tl(sK20))
| ~ segmentP(nil,app(sK20,tl(sK20)))
| ~ ssList(app(sK20,tl(sK20)))
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_135
| ~ spl72_136 ),
inference(subsumption_resolution,[],[f17163,f386]) ).
fof(f17163,plain,
( segmentP(sK20,tl(sK20))
| ~ ssList(sK20)
| ~ segmentP(nil,app(sK20,tl(sK20)))
| ~ ssList(app(sK20,tl(sK20)))
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_135
| ~ spl72_136 ),
inference(resolution,[],[f17076,f8239]) ).
fof(f8239,plain,
( ! [X0] :
( segmentP(sK20,X0)
| ~ segmentP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_4 ),
inference(forward_demodulation,[],[f8238,f1443]) ).
fof(f8238,plain,
( ! [X0] :
( segmentP(sK21,X0)
| ~ segmentP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_4 ),
inference(subsumption_resolution,[],[f8232,f394]) ).
fof(f8232,plain,
( ! [X0] :
( segmentP(sK21,X0)
| ~ segmentP(nil,X0)
| ~ ssList(sK24)
| ~ ssList(X0) )
| ~ spl72_4 ),
inference(superposition,[],[f5572,f656]) ).
fof(f5572,plain,
( ! [X0,X1] :
( segmentP(app(sK20,X0),X1)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl72_4 ),
inference(forward_demodulation,[],[f5571,f898]) ).
fof(f5571,plain,
( ! [X0,X1] :
( segmentP(app(sK20,X0),X1)
| ~ segmentP(sK24,X1)
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl72_4 ),
inference(forward_demodulation,[],[f5570,f1443]) ).
fof(f5570,plain,
! [X0,X1] :
( segmentP(app(sK21,X0),X1)
| ~ segmentP(sK24,X1)
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f5569,f394]) ).
fof(f5569,plain,
! [X0,X1] :
( segmentP(app(sK21,X0),X1)
| ~ segmentP(sK24,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sK24) ),
inference(subsumption_resolution,[],[f5502,f386]) ).
fof(f5502,plain,
! [X0,X1] :
( segmentP(app(sK21,X0),X1)
| ~ segmentP(sK24,X1)
| ~ ssList(X0)
| ~ ssList(sK20)
| ~ ssList(X1)
| ~ ssList(sK24) ),
inference(superposition,[],[f612,f656]) ).
fof(f17076,plain,
( ! [X0] :
( ~ segmentP(X0,app(sK20,tl(sK20)))
| segmentP(X0,tl(sK20))
| ~ ssList(X0) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_135
| ~ spl72_136 ),
inference(subsumption_resolution,[],[f17075,f16996]) ).
fof(f17075,plain,
( ! [X0] :
( segmentP(X0,tl(sK20))
| ~ segmentP(X0,app(sK20,tl(sK20)))
| ~ ssList(app(sK20,tl(sK20)))
| ~ ssList(X0) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_135 ),
inference(subsumption_resolution,[],[f17071,f1775]) ).
fof(f17071,plain,
( ! [X0] :
( segmentP(X0,tl(sK20))
| ~ segmentP(X0,app(sK20,tl(sK20)))
| ~ ssList(tl(sK20))
| ~ ssList(app(sK20,tl(sK20)))
| ~ ssList(X0) )
| ~ spl72_135 ),
inference(resolution,[],[f16993,f609]) ).
fof(f16993,plain,
( segmentP(app(sK20,tl(sK20)),tl(sK20))
| ~ spl72_135 ),
inference(avatar_component_clause,[],[f16991]) ).
fof(f17002,plain,
( ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_136 ),
inference(avatar_contradiction_clause,[],[f17001]) ).
fof(f17001,plain,
( $false
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_136 ),
inference(subsumption_resolution,[],[f17000,f386]) ).
fof(f17000,plain,
( ~ ssList(sK20)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_136 ),
inference(subsumption_resolution,[],[f16999,f1775]) ).
fof(f16999,plain,
( ~ ssList(tl(sK20))
| ~ ssList(sK20)
| spl72_136 ),
inference(resolution,[],[f16997,f579]) ).
fof(f16997,plain,
( ~ ssList(app(sK20,tl(sK20)))
| spl72_136 ),
inference(avatar_component_clause,[],[f16995]) ).
fof(f16998,plain,
( spl72_135
| ~ spl72_136
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(avatar_split_clause,[],[f16968,f1601,f1375,f1273,f16995,f16991]) ).
fof(f16968,plain,
( ~ ssList(app(sK20,tl(sK20)))
| segmentP(app(sK20,tl(sK20)),tl(sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f16967,f16812]) ).
fof(f16967,plain,
( segmentP(app(sK20,tl(sK20)),tl(sK20))
| ~ ssList(app(app(sK20,tl(sK20)),nil))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f16966,f1775]) ).
fof(f16966,plain,
( segmentP(app(sK20,tl(sK20)),tl(sK20))
| ~ ssList(tl(sK20))
| ~ ssList(app(app(sK20,tl(sK20)),nil))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f16965,f386]) ).
fof(f16965,plain,
( segmentP(app(sK20,tl(sK20)),tl(sK20))
| ~ ssList(sK20)
| ~ ssList(tl(sK20))
| ~ ssList(app(app(sK20,tl(sK20)),nil))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f16944,f407]) ).
fof(f16944,plain,
( segmentP(app(sK20,tl(sK20)),tl(sK20))
| ~ ssList(nil)
| ~ ssList(sK20)
| ~ ssList(tl(sK20))
| ~ ssList(app(app(sK20,tl(sK20)),nil))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(superposition,[],[f639,f16812]) ).
fof(f15636,plain,
( ~ spl72_9
| spl72_133 ),
inference(avatar_contradiction_clause,[],[f15635]) ).
fof(f15635,plain,
( $false
| ~ spl72_9
| spl72_133 ),
inference(subsumption_resolution,[],[f15634,f1376]) ).
fof(f15634,plain,
( ~ ssItem(hd(sK20))
| spl72_133 ),
inference(subsumption_resolution,[],[f15633,f386]) ).
fof(f15633,plain,
( ~ ssList(sK20)
| ~ ssItem(hd(sK20))
| spl72_133 ),
inference(resolution,[],[f15627,f451]) ).
fof(f451,plain,
! [X0,X1] :
( sP2(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f227]) ).
fof(f227,plain,
! [X0] :
( ! [X1] :
( sP2(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f137,f226,f225]) ).
fof(f226,plain,
! [X0,X1] :
( ( totalorderedP(cons(X0,X1))
<=> sP1(X1,X0) )
| ~ sP2(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP2])]) ).
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/sandbox/benchmark/theBenchmark.p',ax67) ).
fof(f15627,plain,
( ~ sP2(hd(sK20),sK20)
| spl72_133 ),
inference(avatar_component_clause,[],[f15625]) ).
fof(f15625,plain,
( spl72_133
<=> sP2(hd(sK20),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_133])]) ).
fof(f15632,plain,
( ~ spl72_133
| ~ spl72_134
| spl72_131 ),
inference(avatar_split_clause,[],[f15607,f15599,f15629,f15625]) ).
fof(f15629,plain,
( spl72_134
<=> sP1(sK20,hd(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_134])]) ).
fof(f15599,plain,
( spl72_131
<=> totalorderedP(cons(hd(sK20),sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_131])]) ).
fof(f15607,plain,
( ~ sP1(sK20,hd(sK20))
| ~ sP2(hd(sK20),sK20)
| spl72_131 ),
inference(resolution,[],[f15601,f445]) ).
fof(f445,plain,
! [X0,X1] :
( totalorderedP(cons(X0,X1))
| ~ sP1(X1,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f271]) ).
fof(f271,plain,
! [X0,X1] :
( ( ( totalorderedP(cons(X0,X1))
| ~ sP1(X1,X0) )
& ( sP1(X1,X0)
| ~ totalorderedP(cons(X0,X1)) ) )
| ~ sP2(X0,X1) ),
inference(nnf_transformation,[],[f226]) ).
fof(f15601,plain,
( ~ totalorderedP(cons(hd(sK20),sK20))
| spl72_131 ),
inference(avatar_component_clause,[],[f15599]) ).
fof(f15606,plain,
( ~ spl72_131
| spl72_132
| ~ spl72_9
| ~ spl72_29 ),
inference(avatar_split_clause,[],[f15226,f3120,f1375,f15603,f15599]) ).
fof(f15603,plain,
( spl72_132
<=> sP1(cons(hd(sK20),sK20),hd(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_132])]) ).
fof(f15226,plain,
( sP1(cons(hd(sK20),sK20),hd(sK20))
| ~ totalorderedP(cons(hd(sK20),sK20))
| ~ spl72_9
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f15225,f1376]) ).
fof(f15225,plain,
( ~ ssItem(hd(sK20))
| sP1(cons(hd(sK20),sK20),hd(sK20))
| ~ totalorderedP(cons(hd(sK20),sK20))
| ~ spl72_9
| ~ spl72_29 ),
inference(forward_demodulation,[],[f15224,f1389]) ).
fof(f1389,plain,
( hd(sK20) = hd(cons(hd(sK20),sK20))
| ~ spl72_9 ),
inference(resolution,[],[f1376,f963]) ).
fof(f963,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK20)) = X0 ),
inference(resolution,[],[f573,f386]) ).
fof(f15224,plain,
( sP1(cons(hd(sK20),sK20),hd(sK20))
| ~ totalorderedP(cons(hd(sK20),sK20))
| ~ ssItem(hd(cons(hd(sK20),sK20)))
| ~ spl72_9
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f15114,f5200]) ).
fof(f5200,plain,
( nil != cons(hd(sK20),sK20)
| ~ spl72_9
| ~ spl72_29 ),
inference(subsumption_resolution,[],[f3112,f3121]) ).
fof(f3112,plain,
( nil != cons(hd(sK20),sK20)
| ~ ssList(cons(hd(sK20),nil))
| ~ spl72_9 ),
inference(subsumption_resolution,[],[f3111,f386]) ).
fof(f3111,plain,
( nil != cons(hd(sK20),sK20)
| ~ ssList(sK20)
| ~ ssList(cons(hd(sK20),nil))
| ~ spl72_9 ),
inference(subsumption_resolution,[],[f3102,f392]) ).
fof(f3102,plain,
( nil != cons(hd(sK20),sK20)
| nil = sK20
| ~ ssList(sK20)
| ~ ssList(cons(hd(sK20),nil))
| ~ spl72_9 ),
inference(superposition,[],[f598,f1962]) ).
fof(f1962,plain,
( cons(hd(sK20),sK20) = app(cons(hd(sK20),nil),sK20)
| ~ spl72_9 ),
inference(resolution,[],[f1625,f1376]) ).
fof(f598,plain,
! [X0,X1] :
( nil != app(X0,X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f377]) ).
fof(f377,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(flattening,[],[f376]) ).
fof(f376,plain,
! [X0] :
( ! [X1] :
( ( ( nil = app(X0,X1)
| nil != X0
| nil != X1 )
& ( ( nil = X0
& nil = X1 )
| nil != app(X0,X1) ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f202]) ).
fof(f202,plain,
! [X0] :
( ! [X1] :
( ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) )
| ~ ssList(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f83]) ).
fof(f83,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssList(X1)
=> ( nil = app(X0,X1)
<=> ( nil = X0
& nil = X1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax83) ).
fof(f15114,plain,
( sP1(cons(hd(sK20),sK20),hd(sK20))
| ~ totalorderedP(cons(hd(sK20),sK20))
| nil = cons(hd(sK20),sK20)
| ~ ssItem(hd(cons(hd(sK20),sK20)))
| ~ spl72_9 ),
inference(superposition,[],[f1181,f1389]) ).
fof(f15591,plain,
( ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_129 ),
inference(avatar_contradiction_clause,[],[f15590]) ).
fof(f15590,plain,
( $false
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_129 ),
inference(subsumption_resolution,[],[f15589,f614]) ).
fof(f15589,plain,
( ~ ssItem(sK71)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_129 ),
inference(subsumption_resolution,[],[f15588,f1775]) ).
fof(f15588,plain,
( ~ ssList(tl(sK20))
| ~ ssItem(sK71)
| spl72_129 ),
inference(resolution,[],[f15582,f451]) ).
fof(f15582,plain,
( ~ sP2(sK71,tl(sK20))
| spl72_129 ),
inference(avatar_component_clause,[],[f15580]) ).
fof(f15580,plain,
( spl72_129
<=> sP2(sK71,tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_129])]) ).
fof(f15587,plain,
( ~ spl72_129
| ~ spl72_130
| spl72_128 ),
inference(avatar_split_clause,[],[f15570,f15566,f15584,f15580]) ).
fof(f15584,plain,
( spl72_130
<=> sP1(tl(sK20),sK71) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_130])]) ).
fof(f15566,plain,
( spl72_128
<=> totalorderedP(cons(sK71,tl(sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_128])]) ).
fof(f15570,plain,
( ~ sP1(tl(sK20),sK71)
| ~ sP2(sK71,tl(sK20))
| spl72_128 ),
inference(resolution,[],[f15568,f445]) ).
fof(f15568,plain,
( ~ totalorderedP(cons(sK71,tl(sK20)))
| spl72_128 ),
inference(avatar_component_clause,[],[f15566]) ).
fof(f15569,plain,
( spl72_127
| ~ spl72_128
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_98 ),
inference(avatar_split_clause,[],[f15266,f13978,f1601,f1375,f1273,f15566,f15562]) ).
fof(f15562,plain,
( spl72_127
<=> sP1(cons(sK71,tl(sK20)),sK71) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_127])]) ).
fof(f13978,plain,
( spl72_98
<=> nil = cons(sK71,tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_98])]) ).
fof(f15266,plain,
( ~ totalorderedP(cons(sK71,tl(sK20)))
| sP1(cons(sK71,tl(sK20)),sK71)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_98 ),
inference(subsumption_resolution,[],[f15265,f614]) ).
fof(f15265,plain,
( ~ ssItem(sK71)
| ~ totalorderedP(cons(sK71,tl(sK20)))
| sP1(cons(sK71,tl(sK20)),sK71)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_98 ),
inference(forward_demodulation,[],[f15264,f1696]) ).
fof(f1696,plain,
( sK71 = hd(cons(sK71,sK25(sK20)))
| ~ spl72_13 ),
inference(resolution,[],[f1620,f614]) ).
fof(f15264,plain,
( ~ totalorderedP(cons(sK71,tl(sK20)))
| sP1(cons(sK71,tl(sK20)),sK71)
| ~ ssItem(hd(cons(sK71,sK25(sK20))))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_98 ),
inference(subsumption_resolution,[],[f15263,f13979]) ).
fof(f13979,plain,
( nil != cons(sK71,tl(sK20))
| spl72_98 ),
inference(avatar_component_clause,[],[f13978]) ).
fof(f15263,plain,
( nil = cons(sK71,tl(sK20))
| ~ totalorderedP(cons(sK71,tl(sK20)))
| sP1(cons(sK71,tl(sK20)),sK71)
| ~ ssItem(hd(cons(sK71,sK25(sK20))))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f15262,f1769]) ).
fof(f15262,plain,
( ~ totalorderedP(cons(sK71,tl(sK20)))
| sP1(cons(sK71,tl(sK20)),sK71)
| nil = cons(sK71,sK25(sK20))
| ~ ssItem(hd(cons(sK71,sK25(sK20))))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f15261,f1769]) ).
fof(f15261,plain,
( sP1(cons(sK71,tl(sK20)),sK71)
| ~ totalorderedP(cons(sK71,sK25(sK20)))
| nil = cons(sK71,sK25(sK20))
| ~ ssItem(hd(cons(sK71,sK25(sK20))))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f15125,f1769]) ).
fof(f15125,plain,
( sP1(cons(sK71,sK25(sK20)),sK71)
| ~ totalorderedP(cons(sK71,sK25(sK20)))
| nil = cons(sK71,sK25(sK20))
| ~ ssItem(hd(cons(sK71,sK25(sK20))))
| ~ spl72_13 ),
inference(superposition,[],[f1181,f1696]) ).
fof(f15560,plain,
( ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_125 ),
inference(avatar_contradiction_clause,[],[f15559]) ).
fof(f15559,plain,
( $false
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_125 ),
inference(subsumption_resolution,[],[f15558,f613]) ).
fof(f15558,plain,
( ~ ssItem(sK70)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_125 ),
inference(subsumption_resolution,[],[f15557,f1775]) ).
fof(f15557,plain,
( ~ ssList(tl(sK20))
| ~ ssItem(sK70)
| spl72_125 ),
inference(resolution,[],[f15551,f451]) ).
fof(f15551,plain,
( ~ sP2(sK70,tl(sK20))
| spl72_125 ),
inference(avatar_component_clause,[],[f15549]) ).
fof(f15549,plain,
( spl72_125
<=> sP2(sK70,tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_125])]) ).
fof(f15556,plain,
( ~ spl72_125
| ~ spl72_126
| spl72_124 ),
inference(avatar_split_clause,[],[f15539,f15535,f15553,f15549]) ).
fof(f15553,plain,
( spl72_126
<=> sP1(tl(sK20),sK70) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_126])]) ).
fof(f15535,plain,
( spl72_124
<=> totalorderedP(cons(sK70,tl(sK20))) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_124])]) ).
fof(f15539,plain,
( ~ sP1(tl(sK20),sK70)
| ~ sP2(sK70,tl(sK20))
| spl72_124 ),
inference(resolution,[],[f15537,f445]) ).
fof(f15537,plain,
( ~ totalorderedP(cons(sK70,tl(sK20)))
| spl72_124 ),
inference(avatar_component_clause,[],[f15535]) ).
fof(f15538,plain,
( spl72_123
| ~ spl72_124
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_96 ),
inference(avatar_split_clause,[],[f15260,f13969,f1601,f1375,f1273,f15535,f15531]) ).
fof(f15531,plain,
( spl72_123
<=> sP1(cons(sK70,tl(sK20)),sK70) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_123])]) ).
fof(f13969,plain,
( spl72_96
<=> nil = cons(sK70,tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_96])]) ).
fof(f15260,plain,
( ~ totalorderedP(cons(sK70,tl(sK20)))
| sP1(cons(sK70,tl(sK20)),sK70)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_96 ),
inference(subsumption_resolution,[],[f15259,f613]) ).
fof(f15259,plain,
( ~ ssItem(sK70)
| ~ totalorderedP(cons(sK70,tl(sK20)))
| sP1(cons(sK70,tl(sK20)),sK70)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_96 ),
inference(forward_demodulation,[],[f15258,f1695]) ).
fof(f1695,plain,
( sK70 = hd(cons(sK70,sK25(sK20)))
| ~ spl72_13 ),
inference(resolution,[],[f1620,f613]) ).
fof(f15258,plain,
( ~ totalorderedP(cons(sK70,tl(sK20)))
| sP1(cons(sK70,tl(sK20)),sK70)
| ~ ssItem(hd(cons(sK70,sK25(sK20))))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_96 ),
inference(subsumption_resolution,[],[f15257,f13970]) ).
fof(f13970,plain,
( nil != cons(sK70,tl(sK20))
| spl72_96 ),
inference(avatar_component_clause,[],[f13969]) ).
fof(f15257,plain,
( nil = cons(sK70,tl(sK20))
| ~ totalorderedP(cons(sK70,tl(sK20)))
| sP1(cons(sK70,tl(sK20)),sK70)
| ~ ssItem(hd(cons(sK70,sK25(sK20))))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f15256,f1769]) ).
fof(f15256,plain,
( ~ totalorderedP(cons(sK70,tl(sK20)))
| sP1(cons(sK70,tl(sK20)),sK70)
| nil = cons(sK70,sK25(sK20))
| ~ ssItem(hd(cons(sK70,sK25(sK20))))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f15255,f1769]) ).
fof(f15255,plain,
( sP1(cons(sK70,tl(sK20)),sK70)
| ~ totalorderedP(cons(sK70,sK25(sK20)))
| nil = cons(sK70,sK25(sK20))
| ~ ssItem(hd(cons(sK70,sK25(sK20))))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f15124,f1769]) ).
fof(f15124,plain,
( sP1(cons(sK70,sK25(sK20)),sK70)
| ~ totalorderedP(cons(sK70,sK25(sK20)))
| nil = cons(sK70,sK25(sK20))
| ~ ssItem(hd(cons(sK70,sK25(sK20))))
| ~ spl72_13 ),
inference(superposition,[],[f1181,f1695]) ).
fof(f15501,plain,
( ~ spl72_121
| spl72_122
| ~ spl72_9
| spl72_73 ),
inference(avatar_split_clause,[],[f15326,f8715,f1375,f15498,f15494]) ).
fof(f15494,plain,
( spl72_121
<=> totalorderedP(app(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_121])]) ).
fof(f15498,plain,
( spl72_122
<=> sP1(app(sK20,sK20),hd(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_122])]) ).
fof(f15326,plain,
( sP1(app(sK20,sK20),hd(sK20))
| ~ totalorderedP(app(sK20,sK20))
| ~ spl72_9
| spl72_73 ),
inference(subsumption_resolution,[],[f15325,f1376]) ).
fof(f15325,plain,
( ~ ssItem(hd(sK20))
| sP1(app(sK20,sK20),hd(sK20))
| ~ totalorderedP(app(sK20,sK20))
| spl72_73 ),
inference(forward_demodulation,[],[f15324,f7732]) ).
fof(f15324,plain,
( sP1(app(sK20,sK20),hd(sK20))
| ~ totalorderedP(app(sK20,sK20))
| ~ ssItem(hd(app(sK20,sK20)))
| spl72_73 ),
inference(subsumption_resolution,[],[f15149,f8716]) ).
fof(f15149,plain,
( sP1(app(sK20,sK20),hd(sK20))
| ~ totalorderedP(app(sK20,sK20))
| nil = app(sK20,sK20)
| ~ ssItem(hd(app(sK20,sK20))) ),
inference(superposition,[],[f1181,f7732]) ).
fof(f15457,plain,
spl72_120,
inference(avatar_contradiction_clause,[],[f15456]) ).
fof(f15456,plain,
( $false
| spl72_120 ),
inference(subsumption_resolution,[],[f15446,f614]) ).
fof(f15446,plain,
( ~ ssItem(sK71)
| spl72_120 ),
inference(resolution,[],[f15444,f416]) ).
fof(f416,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f108]) ).
fof(f108,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/sandbox/benchmark/theBenchmark.p',ax65) ).
fof(f15444,plain,
( ~ totalorderedP(cons(sK71,nil))
| spl72_120 ),
inference(avatar_component_clause,[],[f15442]) ).
fof(f15442,plain,
( spl72_120
<=> totalorderedP(cons(sK71,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_120])]) ).
fof(f15445,plain,
( spl72_119
| ~ spl72_120
| ~ spl72_4
| spl72_45 ),
inference(avatar_split_clause,[],[f15254,f5069,f896,f15442,f15438]) ).
fof(f15438,plain,
( spl72_119
<=> sP1(cons(sK71,nil),sK71) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_119])]) ).
fof(f5069,plain,
( spl72_45
<=> nil = cons(sK71,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_45])]) ).
fof(f15254,plain,
( ~ totalorderedP(cons(sK71,nil))
| sP1(cons(sK71,nil),sK71)
| ~ spl72_4
| spl72_45 ),
inference(subsumption_resolution,[],[f15253,f614]) ).
fof(f15253,plain,
( ~ ssItem(sK71)
| ~ totalorderedP(cons(sK71,nil))
| sP1(cons(sK71,nil),sK71)
| ~ spl72_4
| spl72_45 ),
inference(forward_demodulation,[],[f15252,f1091]) ).
fof(f1091,plain,
sK71 = hd(cons(sK71,sK24)),
inference(resolution,[],[f967,f614]) ).
fof(f967,plain,
! [X0] :
( ~ ssItem(X0)
| hd(cons(X0,sK24)) = X0 ),
inference(resolution,[],[f573,f394]) ).
fof(f15252,plain,
( ~ totalorderedP(cons(sK71,nil))
| sP1(cons(sK71,nil),sK71)
| ~ ssItem(hd(cons(sK71,sK24)))
| ~ spl72_4
| spl72_45 ),
inference(subsumption_resolution,[],[f15251,f5070]) ).
fof(f5070,plain,
( nil != cons(sK71,nil)
| spl72_45 ),
inference(avatar_component_clause,[],[f5069]) ).
fof(f15251,plain,
( nil = cons(sK71,nil)
| ~ totalorderedP(cons(sK71,nil))
| sP1(cons(sK71,nil),sK71)
| ~ ssItem(hd(cons(sK71,sK24)))
| ~ spl72_4 ),
inference(forward_demodulation,[],[f15250,f898]) ).
fof(f15250,plain,
( ~ totalorderedP(cons(sK71,nil))
| sP1(cons(sK71,nil),sK71)
| nil = cons(sK71,sK24)
| ~ ssItem(hd(cons(sK71,sK24)))
| ~ spl72_4 ),
inference(forward_demodulation,[],[f15249,f898]) ).
fof(f15249,plain,
( sP1(cons(sK71,nil),sK71)
| ~ totalorderedP(cons(sK71,sK24))
| nil = cons(sK71,sK24)
| ~ ssItem(hd(cons(sK71,sK24)))
| ~ spl72_4 ),
inference(forward_demodulation,[],[f15123,f898]) ).
fof(f15123,plain,
( sP1(cons(sK71,sK24),sK71)
| ~ totalorderedP(cons(sK71,sK24))
| nil = cons(sK71,sK24)
| ~ ssItem(hd(cons(sK71,sK24))) ),
inference(superposition,[],[f1181,f1091]) ).
fof(f15425,plain,
spl72_118,
inference(avatar_contradiction_clause,[],[f15424]) ).
fof(f15424,plain,
( $false
| spl72_118 ),
inference(subsumption_resolution,[],[f15414,f613]) ).
fof(f15414,plain,
( ~ ssItem(sK70)
| spl72_118 ),
inference(resolution,[],[f15412,f416]) ).
fof(f15412,plain,
( ~ totalorderedP(cons(sK70,nil))
| spl72_118 ),
inference(avatar_component_clause,[],[f15410]) ).
fof(f15410,plain,
( spl72_118
<=> totalorderedP(cons(sK70,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_118])]) ).
fof(f15413,plain,
( spl72_117
| ~ spl72_118
| ~ spl72_4
| spl72_43 ),
inference(avatar_split_clause,[],[f15248,f4984,f896,f15410,f15406]) ).
fof(f15406,plain,
( spl72_117
<=> sP1(cons(sK70,nil),sK70) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_117])]) ).
fof(f4984,plain,
( spl72_43
<=> nil = cons(sK70,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_43])]) ).
fof(f15248,plain,
( ~ totalorderedP(cons(sK70,nil))
| sP1(cons(sK70,nil),sK70)
| ~ spl72_4
| spl72_43 ),
inference(subsumption_resolution,[],[f15247,f613]) ).
fof(f15247,plain,
( ~ ssItem(sK70)
| ~ totalorderedP(cons(sK70,nil))
| sP1(cons(sK70,nil),sK70)
| ~ spl72_4
| spl72_43 ),
inference(forward_demodulation,[],[f15246,f1090]) ).
fof(f1090,plain,
sK70 = hd(cons(sK70,sK24)),
inference(resolution,[],[f967,f613]) ).
fof(f15246,plain,
( ~ totalorderedP(cons(sK70,nil))
| sP1(cons(sK70,nil),sK70)
| ~ ssItem(hd(cons(sK70,sK24)))
| ~ spl72_4
| spl72_43 ),
inference(subsumption_resolution,[],[f15245,f4985]) ).
fof(f4985,plain,
( nil != cons(sK70,nil)
| spl72_43 ),
inference(avatar_component_clause,[],[f4984]) ).
fof(f15245,plain,
( nil = cons(sK70,nil)
| ~ totalorderedP(cons(sK70,nil))
| sP1(cons(sK70,nil),sK70)
| ~ ssItem(hd(cons(sK70,sK24)))
| ~ spl72_4 ),
inference(forward_demodulation,[],[f15244,f898]) ).
fof(f15244,plain,
( ~ totalorderedP(cons(sK70,nil))
| sP1(cons(sK70,nil),sK70)
| nil = cons(sK70,sK24)
| ~ ssItem(hd(cons(sK70,sK24)))
| ~ spl72_4 ),
inference(forward_demodulation,[],[f15243,f898]) ).
fof(f15243,plain,
( sP1(cons(sK70,nil),sK70)
| ~ totalorderedP(cons(sK70,sK24))
| nil = cons(sK70,sK24)
| ~ ssItem(hd(cons(sK70,sK24)))
| ~ spl72_4 ),
inference(forward_demodulation,[],[f15122,f898]) ).
fof(f15122,plain,
( sP1(cons(sK70,sK24),sK70)
| ~ totalorderedP(cons(sK70,sK24))
| nil = cons(sK70,sK24)
| ~ ssItem(hd(cons(sK70,sK24))) ),
inference(superposition,[],[f1181,f1090]) ).
fof(f15404,plain,
spl72_115,
inference(avatar_contradiction_clause,[],[f15403]) ).
fof(f15403,plain,
( $false
| spl72_115 ),
inference(subsumption_resolution,[],[f15402,f614]) ).
fof(f15402,plain,
( ~ ssItem(sK71)
| spl72_115 ),
inference(subsumption_resolution,[],[f15401,f386]) ).
fof(f15401,plain,
( ~ ssList(sK20)
| ~ ssItem(sK71)
| spl72_115 ),
inference(resolution,[],[f15395,f451]) ).
fof(f15395,plain,
( ~ sP2(sK71,sK20)
| spl72_115 ),
inference(avatar_component_clause,[],[f15393]) ).
fof(f15393,plain,
( spl72_115
<=> sP2(sK71,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_115])]) ).
fof(f15400,plain,
( ~ spl72_115
| ~ spl72_116
| spl72_113 ),
inference(avatar_split_clause,[],[f15375,f15367,f15397,f15393]) ).
fof(f15397,plain,
( spl72_116
<=> sP1(sK20,sK71) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_116])]) ).
fof(f15367,plain,
( spl72_113
<=> totalorderedP(cons(sK71,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_113])]) ).
fof(f15375,plain,
( ~ sP1(sK20,sK71)
| ~ sP2(sK71,sK20)
| spl72_113 ),
inference(resolution,[],[f15369,f445]) ).
fof(f15369,plain,
( ~ totalorderedP(cons(sK71,sK20))
| spl72_113 ),
inference(avatar_component_clause,[],[f15367]) ).
fof(f15374,plain,
( ~ spl72_113
| spl72_114
| ~ spl72_17 ),
inference(avatar_split_clause,[],[f15242,f2048,f15371,f15367]) ).
fof(f15371,plain,
( spl72_114
<=> sP1(cons(sK71,sK20),sK71) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_114])]) ).
fof(f15242,plain,
( sP1(cons(sK71,sK20),sK71)
| ~ totalorderedP(cons(sK71,sK20))
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f15241,f614]) ).
fof(f15241,plain,
( ~ ssItem(sK71)
| sP1(cons(sK71,sK20),sK71)
| ~ totalorderedP(cons(sK71,sK20))
| ~ spl72_17 ),
inference(forward_demodulation,[],[f15240,f1062]) ).
fof(f1062,plain,
sK71 = hd(cons(sK71,sK20)),
inference(resolution,[],[f963,f614]) ).
fof(f15240,plain,
( sP1(cons(sK71,sK20),sK71)
| ~ totalorderedP(cons(sK71,sK20))
| ~ ssItem(hd(cons(sK71,sK20)))
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f15121,f2123]) ).
fof(f2123,plain,
( nil != cons(sK71,sK20)
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f2045,f2049]) ).
fof(f2045,plain,
( nil != cons(sK71,sK20)
| ~ ssList(cons(sK71,nil)) ),
inference(subsumption_resolution,[],[f2044,f386]) ).
fof(f2044,plain,
( nil != cons(sK71,sK20)
| ~ ssList(sK20)
| ~ ssList(cons(sK71,nil)) ),
inference(subsumption_resolution,[],[f2041,f392]) ).
fof(f2041,plain,
( nil != cons(sK71,sK20)
| nil = sK20
| ~ ssList(sK20)
| ~ ssList(cons(sK71,nil)) ),
inference(superposition,[],[f598,f1986]) ).
fof(f15121,plain,
( sP1(cons(sK71,sK20),sK71)
| ~ totalorderedP(cons(sK71,sK20))
| nil = cons(sK71,sK20)
| ~ ssItem(hd(cons(sK71,sK20))) ),
inference(superposition,[],[f1181,f1062]) ).
fof(f15365,plain,
spl72_111,
inference(avatar_contradiction_clause,[],[f15364]) ).
fof(f15364,plain,
( $false
| spl72_111 ),
inference(subsumption_resolution,[],[f15363,f613]) ).
fof(f15363,plain,
( ~ ssItem(sK70)
| spl72_111 ),
inference(subsumption_resolution,[],[f15362,f386]) ).
fof(f15362,plain,
( ~ ssList(sK20)
| ~ ssItem(sK70)
| spl72_111 ),
inference(resolution,[],[f15356,f451]) ).
fof(f15356,plain,
( ~ sP2(sK70,sK20)
| spl72_111 ),
inference(avatar_component_clause,[],[f15354]) ).
fof(f15354,plain,
( spl72_111
<=> sP2(sK70,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_111])]) ).
fof(f15361,plain,
( ~ spl72_111
| ~ spl72_112
| spl72_109 ),
inference(avatar_split_clause,[],[f15336,f15328,f15358,f15354]) ).
fof(f15358,plain,
( spl72_112
<=> sP1(sK20,sK70) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_112])]) ).
fof(f15328,plain,
( spl72_109
<=> totalorderedP(cons(sK70,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_109])]) ).
fof(f15336,plain,
( ~ sP1(sK20,sK70)
| ~ sP2(sK70,sK20)
| spl72_109 ),
inference(resolution,[],[f15330,f445]) ).
fof(f15330,plain,
( ~ totalorderedP(cons(sK70,sK20))
| spl72_109 ),
inference(avatar_component_clause,[],[f15328]) ).
fof(f15335,plain,
( ~ spl72_109
| spl72_110
| ~ spl72_15 ),
inference(avatar_split_clause,[],[f15239,f1999,f15332,f15328]) ).
fof(f15332,plain,
( spl72_110
<=> sP1(cons(sK70,sK20),sK70) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_110])]) ).
fof(f15239,plain,
( sP1(cons(sK70,sK20),sK70)
| ~ totalorderedP(cons(sK70,sK20))
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f15238,f613]) ).
fof(f15238,plain,
( ~ ssItem(sK70)
| sP1(cons(sK70,sK20),sK70)
| ~ totalorderedP(cons(sK70,sK20))
| ~ spl72_15 ),
inference(forward_demodulation,[],[f15237,f1061]) ).
fof(f1061,plain,
sK70 = hd(cons(sK70,sK20)),
inference(resolution,[],[f963,f613]) ).
fof(f15237,plain,
( sP1(cons(sK70,sK20),sK70)
| ~ totalorderedP(cons(sK70,sK20))
| ~ ssItem(hd(cons(sK70,sK20)))
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f15120,f2122]) ).
fof(f2122,plain,
( nil != cons(sK70,sK20)
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f1996,f2000]) ).
fof(f1996,plain,
( nil != cons(sK70,sK20)
| ~ ssList(cons(sK70,nil)) ),
inference(subsumption_resolution,[],[f1995,f386]) ).
fof(f1995,plain,
( nil != cons(sK70,sK20)
| ~ ssList(sK20)
| ~ ssList(cons(sK70,nil)) ),
inference(subsumption_resolution,[],[f1992,f392]) ).
fof(f1992,plain,
( nil != cons(sK70,sK20)
| nil = sK20
| ~ ssList(sK20)
| ~ ssList(cons(sK70,nil)) ),
inference(superposition,[],[f598,f1985]) ).
fof(f15120,plain,
( sP1(cons(sK70,sK20),sK70)
| ~ totalorderedP(cons(sK70,sK20))
| nil = cons(sK70,sK20)
| ~ ssItem(hd(cons(sK70,sK20))) ),
inference(superposition,[],[f1181,f1061]) ).
fof(f15074,plain,
( ~ spl72_107
| spl72_108
| ~ spl72_17
| ~ spl72_18
| ~ spl72_86
| ~ spl72_104 ),
inference(avatar_split_clause,[],[f14827,f14741,f11859,f2052,f2048,f15071,f15067]) ).
fof(f15067,plain,
( spl72_107
<=> frontsegP(cons(sK71,nil),app(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_107])]) ).
fof(f15071,plain,
( spl72_108
<=> frontsegP(cons(sK71,sK20),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_108])]) ).
fof(f14741,plain,
( spl72_104
<=> frontsegP(app(sK20,sK20),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_104])]) ).
fof(f14827,plain,
( frontsegP(cons(sK71,sK20),sK20)
| ~ frontsegP(cons(sK71,nil),app(sK20,sK20))
| ~ spl72_17
| ~ spl72_18
| ~ spl72_86
| ~ spl72_104 ),
inference(subsumption_resolution,[],[f14826,f11860]) ).
fof(f14826,plain,
( frontsegP(cons(sK71,sK20),sK20)
| ~ frontsegP(cons(sK71,nil),app(sK20,sK20))
| ~ ssList(app(sK20,sK20))
| ~ spl72_17
| ~ spl72_18
| ~ spl72_86
| ~ spl72_104 ),
inference(subsumption_resolution,[],[f14816,f2054]) ).
fof(f14816,plain,
( frontsegP(cons(sK71,sK20),sK20)
| ~ ssList(cons(sK71,sK20))
| ~ frontsegP(cons(sK71,nil),app(sK20,sK20))
| ~ ssList(app(sK20,sK20))
| ~ spl72_17
| ~ spl72_86
| ~ spl72_104 ),
inference(resolution,[],[f14758,f2939]) ).
fof(f2939,plain,
( ! [X0] :
( frontsegP(cons(sK71,sK20),X0)
| ~ frontsegP(cons(sK71,nil),X0)
| ~ ssList(X0) )
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f2938,f2049]) ).
fof(f2938,plain,
! [X0] :
( frontsegP(cons(sK71,sK20),X0)
| ~ frontsegP(cons(sK71,nil),X0)
| ~ ssList(X0)
| ~ ssList(cons(sK71,nil)) ),
inference(subsumption_resolution,[],[f2904,f386]) ).
fof(f2904,plain,
! [X0] :
( frontsegP(cons(sK71,sK20),X0)
| ~ frontsegP(cons(sK71,nil),X0)
| ~ ssList(sK20)
| ~ ssList(X0)
| ~ ssList(cons(sK71,nil)) ),
inference(superposition,[],[f606,f1986]) ).
fof(f14758,plain,
( ! [X0] :
( ~ frontsegP(X0,app(sK20,sK20))
| frontsegP(X0,sK20)
| ~ ssList(X0) )
| ~ spl72_86
| ~ spl72_104 ),
inference(subsumption_resolution,[],[f14757,f11860]) ).
fof(f14757,plain,
( ! [X0] :
( frontsegP(X0,sK20)
| ~ frontsegP(X0,app(sK20,sK20))
| ~ ssList(app(sK20,sK20))
| ~ ssList(X0) )
| ~ spl72_104 ),
inference(subsumption_resolution,[],[f14754,f386]) ).
fof(f14754,plain,
( ! [X0] :
( frontsegP(X0,sK20)
| ~ frontsegP(X0,app(sK20,sK20))
| ~ ssList(sK20)
| ~ ssList(app(sK20,sK20))
| ~ ssList(X0) )
| ~ spl72_104 ),
inference(resolution,[],[f14743,f611]) ).
fof(f14743,plain,
( frontsegP(app(sK20,sK20),sK20)
| ~ spl72_104 ),
inference(avatar_component_clause,[],[f14741]) ).
fof(f15060,plain,
( ~ spl72_105
| spl72_106
| ~ spl72_15
| ~ spl72_16
| ~ spl72_86
| ~ spl72_104 ),
inference(avatar_split_clause,[],[f14825,f14741,f11859,f2003,f1999,f15057,f15053]) ).
fof(f15053,plain,
( spl72_105
<=> frontsegP(cons(sK70,nil),app(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_105])]) ).
fof(f15057,plain,
( spl72_106
<=> frontsegP(cons(sK70,sK20),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_106])]) ).
fof(f14825,plain,
( frontsegP(cons(sK70,sK20),sK20)
| ~ frontsegP(cons(sK70,nil),app(sK20,sK20))
| ~ spl72_15
| ~ spl72_16
| ~ spl72_86
| ~ spl72_104 ),
inference(subsumption_resolution,[],[f14824,f11860]) ).
fof(f14824,plain,
( frontsegP(cons(sK70,sK20),sK20)
| ~ frontsegP(cons(sK70,nil),app(sK20,sK20))
| ~ ssList(app(sK20,sK20))
| ~ spl72_15
| ~ spl72_16
| ~ spl72_86
| ~ spl72_104 ),
inference(subsumption_resolution,[],[f14813,f2005]) ).
fof(f14813,plain,
( frontsegP(cons(sK70,sK20),sK20)
| ~ ssList(cons(sK70,sK20))
| ~ frontsegP(cons(sK70,nil),app(sK20,sK20))
| ~ ssList(app(sK20,sK20))
| ~ spl72_15
| ~ spl72_86
| ~ spl72_104 ),
inference(resolution,[],[f14758,f2937]) ).
fof(f2937,plain,
( ! [X0] :
( frontsegP(cons(sK70,sK20),X0)
| ~ frontsegP(cons(sK70,nil),X0)
| ~ ssList(X0) )
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f2936,f2000]) ).
fof(f2936,plain,
! [X0] :
( frontsegP(cons(sK70,sK20),X0)
| ~ frontsegP(cons(sK70,nil),X0)
| ~ ssList(X0)
| ~ ssList(cons(sK70,nil)) ),
inference(subsumption_resolution,[],[f2903,f386]) ).
fof(f2903,plain,
! [X0] :
( frontsegP(cons(sK70,sK20),X0)
| ~ frontsegP(cons(sK70,nil),X0)
| ~ ssList(sK20)
| ~ ssList(X0)
| ~ ssList(cons(sK70,nil)) ),
inference(superposition,[],[f606,f1985]) ).
fof(f14774,plain,
( ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_53
| spl72_103 ),
inference(avatar_contradiction_clause,[],[f14773]) ).
fof(f14773,plain,
( $false
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_53
| spl72_103 ),
inference(subsumption_resolution,[],[f14772,f1775]) ).
fof(f14772,plain,
( ~ ssList(tl(sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_53
| spl72_103 ),
inference(subsumption_resolution,[],[f14771,f386]) ).
fof(f14771,plain,
( ~ ssList(sK20)
| ~ ssList(tl(sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_53
| spl72_103 ),
inference(subsumption_resolution,[],[f14767,f11068]) ).
fof(f11068,plain,
( frontsegP(tl(sK20),tl(sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_53 ),
inference(forward_demodulation,[],[f11067,f7033]) ).
fof(f7033,plain,
( tl(sK20) = sK66(tl(sK20),nil)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_53 ),
inference(forward_demodulation,[],[f7018,f6885]) ).
fof(f6885,plain,
( tl(sK20) = app(sK66(tl(sK20),nil),nil)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f6846,f1769]) ).
fof(f6846,plain,
( sK25(sK20) = app(sK66(sK25(sK20),nil),nil)
| ~ spl72_13 ),
inference(resolution,[],[f2609,f1602]) ).
fof(f2609,plain,
! [X0] :
( ~ ssList(X0)
| app(sK66(X0,nil),nil) = X0 ),
inference(subsumption_resolution,[],[f2603,f407]) ).
fof(f2603,plain,
! [X0] :
( app(sK66(X0,nil),nil) = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(duplicate_literal_removal,[],[f2599]) ).
fof(f2599,plain,
! [X0] :
( app(sK66(X0,nil),nil) = X0
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f589,f464]) ).
fof(f464,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/sandbox/benchmark/theBenchmark.p',ax51) ).
fof(f7018,plain,
( sK66(tl(sK20),nil) = app(sK66(tl(sK20),nil),nil)
| ~ spl72_53 ),
inference(resolution,[],[f6926,f469]) ).
fof(f6926,plain,
( ssList(sK66(tl(sK20),nil))
| ~ spl72_53 ),
inference(avatar_component_clause,[],[f6925]) ).
fof(f6925,plain,
( spl72_53
<=> ssList(sK66(tl(sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_53])]) ).
fof(f11067,plain,
( frontsegP(tl(sK20),sK66(tl(sK20),nil))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_53 ),
inference(subsumption_resolution,[],[f6923,f6926]) ).
fof(f6923,plain,
( frontsegP(tl(sK20),sK66(tl(sK20),nil))
| ~ ssList(sK66(tl(sK20),nil))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f6909,f407]) ).
fof(f6909,plain,
( frontsegP(tl(sK20),sK66(tl(sK20),nil))
| ~ ssList(nil)
| ~ ssList(sK66(tl(sK20),nil))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(superposition,[],[f2128,f6885]) ).
fof(f14767,plain,
( ~ frontsegP(tl(sK20),tl(sK20))
| ~ ssList(sK20)
| ~ ssList(tl(sK20))
| spl72_103 ),
inference(duplicate_literal_removal,[],[f14766]) ).
fof(f14766,plain,
( ~ frontsegP(tl(sK20),tl(sK20))
| ~ ssList(sK20)
| ~ ssList(tl(sK20))
| ~ ssList(tl(sK20))
| spl72_103 ),
inference(resolution,[],[f14739,f606]) ).
fof(f14739,plain,
( ~ frontsegP(app(tl(sK20),sK20),tl(sK20))
| spl72_103 ),
inference(avatar_component_clause,[],[f14737]) ).
fof(f14737,plain,
( spl72_103
<=> frontsegP(app(tl(sK20),sK20),tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_103])]) ).
fof(f14770,plain,
( ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_103 ),
inference(avatar_contradiction_clause,[],[f14769]) ).
fof(f14769,plain,
( $false
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_103 ),
inference(subsumption_resolution,[],[f14768,f1775]) ).
fof(f14768,plain,
( ~ ssList(tl(sK20))
| spl72_103 ),
inference(subsumption_resolution,[],[f14765,f386]) ).
fof(f14765,plain,
( ~ ssList(sK20)
| ~ ssList(tl(sK20))
| spl72_103 ),
inference(resolution,[],[f14739,f2128]) ).
fof(f14753,plain,
( ~ spl72_4
| spl72_104 ),
inference(avatar_contradiction_clause,[],[f14752]) ).
fof(f14752,plain,
( $false
| ~ spl72_4
| spl72_104 ),
inference(subsumption_resolution,[],[f14751,f386]) ).
fof(f14751,plain,
( ~ ssList(sK20)
| ~ spl72_4
| spl72_104 ),
inference(subsumption_resolution,[],[f14747,f2259]) ).
fof(f2259,plain,
( frontsegP(sK20,sK20)
| ~ spl72_4 ),
inference(forward_demodulation,[],[f2258,f1443]) ).
fof(f2258,plain,
frontsegP(sK21,sK20),
inference(subsumption_resolution,[],[f2257,f386]) ).
fof(f2257,plain,
( frontsegP(sK21,sK20)
| ~ ssList(sK20) ),
inference(subsumption_resolution,[],[f2245,f394]) ).
fof(f2245,plain,
( frontsegP(sK21,sK20)
| ~ ssList(sK24)
| ~ ssList(sK20) ),
inference(superposition,[],[f2128,f656]) ).
fof(f14747,plain,
( ~ frontsegP(sK20,sK20)
| ~ ssList(sK20)
| spl72_104 ),
inference(duplicate_literal_removal,[],[f14746]) ).
fof(f14746,plain,
( ~ frontsegP(sK20,sK20)
| ~ ssList(sK20)
| ~ ssList(sK20)
| ~ ssList(sK20)
| spl72_104 ),
inference(resolution,[],[f14742,f606]) ).
fof(f14742,plain,
( ~ frontsegP(app(sK20,sK20),sK20)
| spl72_104 ),
inference(avatar_component_clause,[],[f14741]) ).
fof(f14750,plain,
spl72_104,
inference(avatar_contradiction_clause,[],[f14749]) ).
fof(f14749,plain,
( $false
| spl72_104 ),
inference(subsumption_resolution,[],[f14748,f386]) ).
fof(f14748,plain,
( ~ ssList(sK20)
| spl72_104 ),
inference(duplicate_literal_removal,[],[f14745]) ).
fof(f14745,plain,
( ~ ssList(sK20)
| ~ ssList(sK20)
| spl72_104 ),
inference(resolution,[],[f14742,f2128]) ).
fof(f14744,plain,
( ~ spl72_103
| spl72_104
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(avatar_split_clause,[],[f13406,f11859,f8715,f1601,f1375,f1273,f14741,f14737]) ).
fof(f13406,plain,
( frontsegP(app(sK20,sK20),sK20)
| ~ frontsegP(app(tl(sK20),sK20),tl(sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f13370,f12119]) ).
fof(f13370,plain,
( frontsegP(app(sK20,sK20),sK20)
| ~ frontsegP(app(tl(sK20),sK20),tl(sK20))
| ~ ssList(app(tl(sK20),sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(superposition,[],[f4443,f11904]) ).
fof(f4443,plain,
( ! [X0] :
( frontsegP(cons(hd(sK20),X0),sK20)
| ~ frontsegP(X0,tl(sK20))
| ~ ssList(X0) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f4442,f1769]) ).
fof(f4442,plain,
( ! [X0] :
( frontsegP(cons(hd(sK20),X0),sK20)
| ~ frontsegP(X0,sK25(sK20))
| ~ ssList(X0) )
| ~ spl72_5
| ~ spl72_13 ),
inference(forward_demodulation,[],[f4441,f1698]) ).
fof(f4441,plain,
( ! [X0] :
( frontsegP(cons(sK26(sK20),X0),sK20)
| ~ frontsegP(X0,sK25(sK20))
| ~ ssList(X0) )
| ~ spl72_5
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f4440,f1274]) ).
fof(f4440,plain,
( ! [X0] :
( frontsegP(cons(sK26(sK20),X0),sK20)
| ~ frontsegP(X0,sK25(sK20))
| ~ ssList(X0)
| ~ ssItem(sK26(sK20)) )
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f4409,f1602]) ).
fof(f4409,plain,
! [X0] :
( frontsegP(cons(sK26(sK20),X0),sK20)
| ~ frontsegP(X0,sK25(sK20))
| ~ ssList(sK25(sK20))
| ~ ssList(X0)
| ~ ssItem(sK26(sK20)) ),
inference(superposition,[],[f645,f1246]) ).
fof(f645,plain,
! [X2,X3,X1] :
( frontsegP(cons(X1,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f619]) ).
fof(f619,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,[],[f443]) ).
fof(f443,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,[],[f270]) ).
fof(f270,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ! [X3] :
( ( ( frontsegP(cons(X0,X2),cons(X1,X3))
| ~ frontsegP(X2,X3)
| X0 != X1 )
& ( ( frontsegP(X2,X3)
& X0 = X1 )
| ~ frontsegP(cons(X0,X2),cons(X1,X3)) ) )
| ~ ssList(X3) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f269]) ).
fof(f269,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/sandbox/benchmark/theBenchmark.p',ax44) ).
fof(f14124,plain,
( spl72_101
| ~ spl72_102
| ~ spl72_9
| ~ spl72_15
| spl72_73
| ~ spl72_86 ),
inference(avatar_split_clause,[],[f14115,f11859,f8715,f1999,f1375,f14121,f14117]) ).
fof(f14117,plain,
( spl72_101
<=> sK70 = hd(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_101])]) ).
fof(f14121,plain,
( spl72_102
<=> frontsegP(nil,app(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_102])]) ).
fof(f14115,plain,
( ~ frontsegP(nil,app(sK20,sK20))
| sK70 = hd(sK20)
| ~ spl72_9
| ~ spl72_15
| spl72_73
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f14114,f1376]) ).
fof(f14114,plain,
( ~ frontsegP(nil,app(sK20,sK20))
| ~ ssItem(hd(sK20))
| sK70 = hd(sK20)
| ~ spl72_15
| spl72_73
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f14110,f12119]) ).
fof(f14110,plain,
( ~ frontsegP(nil,app(sK20,sK20))
| ~ ssList(app(tl(sK20),sK20))
| ~ ssItem(hd(sK20))
| sK70 = hd(sK20)
| ~ spl72_15
| spl72_73
| ~ spl72_86 ),
inference(superposition,[],[f4814,f11904]) ).
fof(f4814,plain,
( ! [X0,X1] :
( ~ frontsegP(nil,cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0)
| sK70 = X0 )
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f4813,f569]) ).
fof(f569,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/sandbox/benchmark/theBenchmark.p',ax16) ).
fof(f4813,plain,
( ! [X0,X1] :
( sK70 = X0
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ frontsegP(nil,cons(X0,X1))
| ~ ssList(cons(X0,X1)) )
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f4812,f613]) ).
fof(f4812,plain,
( ! [X0,X1] :
( sK70 = X0
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(sK70)
| ~ frontsegP(nil,cons(X0,X1))
| ~ ssList(cons(X0,X1)) )
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f4791,f407]) ).
fof(f4791,plain,
( ! [X0,X1] :
( sK70 = X0
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK70)
| ~ frontsegP(nil,cons(X0,X1))
| ~ ssList(cons(X0,X1)) )
| ~ spl72_15 ),
inference(resolution,[],[f441,f2941]) ).
fof(f2941,plain,
( ! [X0] :
( frontsegP(cons(sK70,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f2940,f407]) ).
fof(f2940,plain,
( ! [X0] :
( frontsegP(cons(sK70,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f2909,f2000]) ).
fof(f2909,plain,
( ! [X0] :
( frontsegP(cons(sK70,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(cons(sK70,nil))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_15 ),
inference(superposition,[],[f606,f2012]) ).
fof(f2012,plain,
( cons(sK70,nil) = app(nil,cons(sK70,nil))
| ~ spl72_15 ),
inference(resolution,[],[f2000,f470]) ).
fof(f441,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,[],[f270]) ).
fof(f14054,plain,
( ~ spl72_99
| spl72_100
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(avatar_split_clause,[],[f12929,f11859,f8715,f1601,f1375,f1273,f896,f14051,f14047]) ).
fof(f14047,plain,
( spl72_99
<=> segmentP(sK20,app(tl(sK20),sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_99])]) ).
fof(f14051,plain,
( spl72_100
<=> sK20 = app(tl(sK20),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_100])]) ).
fof(f12929,plain,
( sK20 = app(tl(sK20),sK20)
| ~ segmentP(sK20,app(tl(sK20),sK20))
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f12928,f386]) ).
fof(f12928,plain,
( sK20 = app(tl(sK20),sK20)
| ~ segmentP(sK20,app(tl(sK20),sK20))
| ~ ssList(sK20)
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f12923,f12119]) ).
fof(f12923,plain,
( sK20 = app(tl(sK20),sK20)
| ~ segmentP(sK20,app(tl(sK20),sK20))
| ~ ssList(app(tl(sK20),sK20))
| ~ ssList(sK20)
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(resolution,[],[f12760,f584]) ).
fof(f12760,plain,
( segmentP(app(tl(sK20),sK20),sK20)
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_73
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f12759,f12119]) ).
fof(f12759,plain,
( ~ ssList(app(tl(sK20),sK20))
| segmentP(app(tl(sK20),sK20),sK20)
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f12758,f11797]) ).
fof(f12758,plain,
( segmentP(app(tl(sK20),sK20),sK20)
| ~ ssList(app(app(tl(sK20),sK20),nil))
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f12757,f386]) ).
fof(f12757,plain,
( segmentP(app(tl(sK20),sK20),sK20)
| ~ ssList(sK20)
| ~ ssList(app(app(tl(sK20),sK20),nil))
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f12756,f1775]) ).
fof(f12756,plain,
( segmentP(app(tl(sK20),sK20),sK20)
| ~ ssList(tl(sK20))
| ~ ssList(sK20)
| ~ ssList(app(app(tl(sK20),sK20),nil))
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f12735,f407]) ).
fof(f12735,plain,
( segmentP(app(tl(sK20),sK20),sK20)
| ~ ssList(nil)
| ~ ssList(tl(sK20))
| ~ ssList(sK20)
| ~ ssList(app(app(tl(sK20),sK20),nil))
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(superposition,[],[f639,f11797]) ).
fof(f13981,plain,
( ~ spl72_97
| spl72_98
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(avatar_split_clause,[],[f8538,f1601,f1375,f1273,f13978,f13974]) ).
fof(f13974,plain,
( spl72_97
<=> sP3(cons(sK71,tl(sK20)),sK71) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_97])]) ).
fof(f8538,plain,
( nil = cons(sK71,tl(sK20))
| ~ sP3(cons(sK71,tl(sK20)),sK71)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f8537,f614]) ).
fof(f8537,plain,
( ~ ssItem(sK71)
| nil = cons(sK71,tl(sK20))
| ~ sP3(cons(sK71,tl(sK20)),sK71)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f8536,f1696]) ).
fof(f8536,plain,
( nil = cons(sK71,tl(sK20))
| ~ sP3(cons(sK71,tl(sK20)),sK71)
| ~ ssItem(hd(cons(sK71,sK25(sK20))))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f8535,f1769]) ).
fof(f8535,plain,
( ~ sP3(cons(sK71,tl(sK20)),sK71)
| nil = cons(sK71,sK25(sK20))
| ~ ssItem(hd(cons(sK71,sK25(sK20))))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f8446,f1769]) ).
fof(f8446,plain,
( ~ sP3(cons(sK71,sK25(sK20)),sK71)
| nil = cons(sK71,sK25(sK20))
| ~ ssItem(hd(cons(sK71,sK25(sK20))))
| ~ spl72_13 ),
inference(superposition,[],[f798,f1696]) ).
fof(f798,plain,
! [X0] :
( ~ sP3(X0,hd(X0))
| nil = X0
| ~ ssItem(hd(X0)) ),
inference(resolution,[],[f456,f409]) ).
fof(f409,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/sandbox/benchmark/theBenchmark.p',ax90) ).
fof(f456,plain,
! [X0,X1] :
( lt(X1,hd(X0))
| nil = X0
| ~ sP3(X0,X1) ),
inference(cnf_transformation,[],[f278]) ).
fof(f278,plain,
! [X0,X1] :
( ( sP3(X0,X1)
| ( ( ~ lt(X1,hd(X0))
| ~ strictorderedP(X0)
| nil = X0 )
& nil != X0 ) )
& ( ( lt(X1,hd(X0))
& strictorderedP(X0)
& nil != X0 )
| nil = X0
| ~ sP3(X0,X1) ) ),
inference(rectify,[],[f277]) ).
fof(f277,plain,
! [X1,X0] :
( ( sP3(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP3(X1,X0) ) ),
inference(flattening,[],[f276]) ).
fof(f276,plain,
! [X1,X0] :
( ( sP3(X1,X0)
| ( ( ~ lt(X0,hd(X1))
| ~ strictorderedP(X1)
| nil = X1 )
& nil != X1 ) )
& ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1
| ~ sP3(X1,X0) ) ),
inference(nnf_transformation,[],[f228]) ).
fof(f228,plain,
! [X1,X0] :
( sP3(X1,X0)
<=> ( ( lt(X0,hd(X1))
& strictorderedP(X1)
& nil != X1 )
| nil = X1 ) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP3])]) ).
fof(f13972,plain,
( ~ spl72_95
| spl72_96
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(avatar_split_clause,[],[f8534,f1601,f1375,f1273,f13969,f13965]) ).
fof(f13965,plain,
( spl72_95
<=> sP3(cons(sK70,tl(sK20)),sK70) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_95])]) ).
fof(f8534,plain,
( nil = cons(sK70,tl(sK20))
| ~ sP3(cons(sK70,tl(sK20)),sK70)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f8533,f613]) ).
fof(f8533,plain,
( ~ ssItem(sK70)
| nil = cons(sK70,tl(sK20))
| ~ sP3(cons(sK70,tl(sK20)),sK70)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f8532,f1695]) ).
fof(f8532,plain,
( nil = cons(sK70,tl(sK20))
| ~ sP3(cons(sK70,tl(sK20)),sK70)
| ~ ssItem(hd(cons(sK70,sK25(sK20))))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f8531,f1769]) ).
fof(f8531,plain,
( ~ sP3(cons(sK70,tl(sK20)),sK70)
| nil = cons(sK70,sK25(sK20))
| ~ ssItem(hd(cons(sK70,sK25(sK20))))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f8445,f1769]) ).
fof(f8445,plain,
( ~ sP3(cons(sK70,sK25(sK20)),sK70)
| nil = cons(sK70,sK25(sK20))
| ~ ssItem(hd(cons(sK70,sK25(sK20))))
| ~ spl72_13 ),
inference(superposition,[],[f798,f1695]) ).
fof(f13785,plain,
( ~ spl72_86
| spl72_93
| ~ spl72_94 ),
inference(avatar_contradiction_clause,[],[f13784]) ).
fof(f13784,plain,
( $false
| ~ spl72_86
| spl72_93
| ~ spl72_94 ),
inference(subsumption_resolution,[],[f13783,f11860]) ).
fof(f13783,plain,
( ~ ssList(app(sK20,sK20))
| spl72_93
| ~ spl72_94 ),
inference(subsumption_resolution,[],[f13782,f407]) ).
fof(f13782,plain,
( ~ ssList(nil)
| ~ ssList(app(sK20,sK20))
| spl72_93
| ~ spl72_94 ),
inference(subsumption_resolution,[],[f13781,f13767]) ).
fof(f13767,plain,
( frontsegP(app(sK20,sK20),nil)
| ~ spl72_94 ),
inference(avatar_component_clause,[],[f13765]) ).
fof(f13765,plain,
( spl72_94
<=> frontsegP(app(sK20,sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_94])]) ).
fof(f13781,plain,
( ~ frontsegP(app(sK20,sK20),nil)
| ~ ssList(nil)
| ~ ssList(app(sK20,sK20))
| spl72_93 ),
inference(resolution,[],[f13763,f595]) ).
fof(f595,plain,
! [X0,X1] :
( ssList(sK69(X0,X1))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f375]) ).
fof(f13763,plain,
( ~ ssList(sK69(app(sK20,sK20),nil))
| spl72_93 ),
inference(avatar_component_clause,[],[f13761]) ).
fof(f13761,plain,
( spl72_93
<=> ssList(sK69(app(sK20,sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_93])]) ).
fof(f13777,plain,
( ~ spl72_86
| spl72_94 ),
inference(avatar_contradiction_clause,[],[f13776]) ).
fof(f13776,plain,
( $false
| ~ spl72_86
| spl72_94 ),
inference(subsumption_resolution,[],[f13770,f11860]) ).
fof(f13770,plain,
( ~ ssList(app(sK20,sK20))
| spl72_94 ),
inference(resolution,[],[f13766,f466]) ).
fof(f466,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/sandbox/benchmark/theBenchmark.p',ax45) ).
fof(f13766,plain,
( ~ frontsegP(app(sK20,sK20),nil)
| spl72_94 ),
inference(avatar_component_clause,[],[f13765]) ).
fof(f13775,plain,
( ~ spl72_49
| ~ spl72_50
| spl72_94 ),
inference(avatar_contradiction_clause,[],[f13774]) ).
fof(f13774,plain,
( $false
| ~ spl72_49
| ~ spl72_50
| spl72_94 ),
inference(subsumption_resolution,[],[f13773,f407]) ).
fof(f13773,plain,
( ~ ssList(nil)
| ~ spl72_49
| ~ spl72_50
| spl72_94 ),
inference(subsumption_resolution,[],[f13772,f386]) ).
fof(f13772,plain,
( ~ ssList(sK20)
| ~ ssList(nil)
| ~ spl72_49
| ~ spl72_50
| spl72_94 ),
inference(subsumption_resolution,[],[f13771,f6649]) ).
fof(f13771,plain,
( ~ frontsegP(sK20,nil)
| ~ ssList(sK20)
| ~ ssList(nil)
| spl72_94 ),
inference(duplicate_literal_removal,[],[f13769]) ).
fof(f13769,plain,
( ~ frontsegP(sK20,nil)
| ~ ssList(sK20)
| ~ ssList(nil)
| ~ ssList(sK20)
| spl72_94 ),
inference(resolution,[],[f13766,f606]) ).
fof(f13768,plain,
( ~ spl72_93
| spl72_94
| ~ spl72_86 ),
inference(avatar_split_clause,[],[f13369,f11859,f13765,f13761]) ).
fof(f13369,plain,
( frontsegP(app(sK20,sK20),nil)
| ~ ssList(sK69(app(sK20,sK20),nil))
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f13354,f407]) ).
fof(f13354,plain,
( frontsegP(app(sK20,sK20),nil)
| ~ ssList(sK69(app(sK20,sK20),nil))
| ~ ssList(nil)
| ~ spl72_86 ),
inference(superposition,[],[f2128,f11888]) ).
fof(f11888,plain,
( app(sK20,sK20) = app(nil,sK69(app(sK20,sK20),nil))
| ~ spl72_86 ),
inference(resolution,[],[f11860,f2686]) ).
fof(f2686,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,sK69(X0,nil)) = X0 ),
inference(subsumption_resolution,[],[f2684,f407]) ).
fof(f2684,plain,
! [X0] :
( app(nil,sK69(X0,nil)) = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(duplicate_literal_removal,[],[f2674]) ).
fof(f2674,plain,
! [X0] :
( app(nil,sK69(X0,nil)) = X0
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[],[f596,f466]) ).
fof(f13703,plain,
( ~ spl72_86
| spl72_91
| ~ spl72_92 ),
inference(avatar_contradiction_clause,[],[f13702]) ).
fof(f13702,plain,
( $false
| ~ spl72_86
| spl72_91
| ~ spl72_92 ),
inference(subsumption_resolution,[],[f13701,f11860]) ).
fof(f13701,plain,
( ~ ssList(app(sK20,sK20))
| spl72_91
| ~ spl72_92 ),
inference(subsumption_resolution,[],[f13700,f407]) ).
fof(f13700,plain,
( ~ ssList(nil)
| ~ ssList(app(sK20,sK20))
| spl72_91
| ~ spl72_92 ),
inference(subsumption_resolution,[],[f13699,f13661]) ).
fof(f13661,plain,
( rearsegP(app(sK20,sK20),nil)
| ~ spl72_92 ),
inference(avatar_component_clause,[],[f13659]) ).
fof(f13659,plain,
( spl72_92
<=> rearsegP(app(sK20,sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_92])]) ).
fof(f13699,plain,
( ~ rearsegP(app(sK20,sK20),nil)
| ~ ssList(nil)
| ~ ssList(app(sK20,sK20))
| spl72_91 ),
inference(resolution,[],[f13657,f588]) ).
fof(f13657,plain,
( ~ ssList(sK66(app(sK20,sK20),nil))
| spl72_91 ),
inference(avatar_component_clause,[],[f13655]) ).
fof(f13655,plain,
( spl72_91
<=> ssList(sK66(app(sK20,sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_91])]) ).
fof(f13671,plain,
( ~ spl72_4
| spl72_92 ),
inference(avatar_contradiction_clause,[],[f13670]) ).
fof(f13670,plain,
( $false
| ~ spl72_4
| spl72_92 ),
inference(subsumption_resolution,[],[f13669,f407]) ).
fof(f13669,plain,
( ~ ssList(nil)
| ~ spl72_4
| spl72_92 ),
inference(subsumption_resolution,[],[f13668,f386]) ).
fof(f13668,plain,
( ~ ssList(sK20)
| ~ ssList(nil)
| ~ spl72_4
| spl72_92 ),
inference(subsumption_resolution,[],[f13665,f2097]) ).
fof(f2097,plain,
( rearsegP(sK20,nil)
| ~ spl72_4 ),
inference(forward_demodulation,[],[f2096,f1443]) ).
fof(f2096,plain,
( rearsegP(sK21,nil)
| ~ spl72_4 ),
inference(forward_demodulation,[],[f2095,f898]) ).
fof(f2095,plain,
rearsegP(sK21,sK24),
inference(subsumption_resolution,[],[f2094,f394]) ).
fof(f2094,plain,
( rearsegP(sK21,sK24)
| ~ ssList(sK24) ),
inference(subsumption_resolution,[],[f2082,f386]) ).
fof(f2082,plain,
( rearsegP(sK21,sK24)
| ~ ssList(sK20)
| ~ ssList(sK24) ),
inference(superposition,[],[f1990,f656]) ).
fof(f13665,plain,
( ~ rearsegP(sK20,nil)
| ~ ssList(sK20)
| ~ ssList(nil)
| spl72_92 ),
inference(duplicate_literal_removal,[],[f13664]) ).
fof(f13664,plain,
( ~ rearsegP(sK20,nil)
| ~ ssList(sK20)
| ~ ssList(nil)
| ~ ssList(sK20)
| spl72_92 ),
inference(resolution,[],[f13660,f605]) ).
fof(f13660,plain,
( ~ rearsegP(app(sK20,sK20),nil)
| spl72_92 ),
inference(avatar_component_clause,[],[f13659]) ).
fof(f13667,plain,
( ~ spl72_86
| spl72_92 ),
inference(avatar_contradiction_clause,[],[f13666]) ).
fof(f13666,plain,
( $false
| ~ spl72_86
| spl72_92 ),
inference(subsumption_resolution,[],[f13663,f11860]) ).
fof(f13663,plain,
( ~ ssList(app(sK20,sK20))
| spl72_92 ),
inference(resolution,[],[f13660,f464]) ).
fof(f13662,plain,
( ~ spl72_91
| spl72_92
| ~ spl72_86 ),
inference(avatar_split_clause,[],[f13333,f11859,f13659,f13655]) ).
fof(f13333,plain,
( rearsegP(app(sK20,sK20),nil)
| ~ ssList(sK66(app(sK20,sK20),nil))
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f13317,f407]) ).
fof(f13317,plain,
( rearsegP(app(sK20,sK20),nil)
| ~ ssList(sK66(app(sK20,sK20),nil))
| ~ ssList(nil)
| ~ spl72_86 ),
inference(superposition,[],[f1990,f11886]) ).
fof(f11886,plain,
( app(sK20,sK20) = app(sK66(app(sK20,sK20),nil),nil)
| ~ spl72_86 ),
inference(resolution,[],[f11860,f2609]) ).
fof(f12580,plain,
( ~ spl72_89
| spl72_90
| ~ spl72_85
| ~ spl72_86 ),
inference(avatar_split_clause,[],[f11935,f11859,f11855,f12577,f12573]) ).
fof(f12573,plain,
( spl72_89
<=> segmentP(sK20,app(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_89])]) ).
fof(f12577,plain,
( spl72_90
<=> sK20 = app(sK20,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_90])]) ).
fof(f11935,plain,
( sK20 = app(sK20,sK20)
| ~ segmentP(sK20,app(sK20,sK20))
| ~ spl72_85
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f11934,f386]) ).
fof(f11934,plain,
( sK20 = app(sK20,sK20)
| ~ segmentP(sK20,app(sK20,sK20))
| ~ ssList(sK20)
| ~ spl72_85
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f11929,f11860]) ).
fof(f11929,plain,
( sK20 = app(sK20,sK20)
| ~ segmentP(sK20,app(sK20,sK20))
| ~ ssList(app(sK20,sK20))
| ~ ssList(sK20)
| ~ spl72_85 ),
inference(resolution,[],[f11857,f584]) ).
fof(f12570,plain,
( ~ spl72_87
| spl72_88
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_85
| ~ spl72_86 ),
inference(avatar_split_clause,[],[f12395,f11859,f11855,f1601,f1375,f1273,f896,f12567,f12563]) ).
fof(f12563,plain,
( spl72_87
<=> segmentP(nil,app(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_87])]) ).
fof(f12567,plain,
( spl72_88
<=> segmentP(tl(sK20),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_88])]) ).
fof(f12395,plain,
( segmentP(tl(sK20),sK20)
| ~ segmentP(nil,app(sK20,sK20))
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_85
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f12394,f11860]) ).
fof(f12394,plain,
( segmentP(tl(sK20),sK20)
| ~ segmentP(nil,app(sK20,sK20))
| ~ ssList(app(sK20,sK20))
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_85
| ~ spl72_86 ),
inference(subsumption_resolution,[],[f12373,f1775]) ).
fof(f12373,plain,
( segmentP(tl(sK20),sK20)
| ~ ssList(tl(sK20))
| ~ segmentP(nil,app(sK20,sK20))
| ~ ssList(app(sK20,sK20))
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| ~ spl72_85
| ~ spl72_86 ),
inference(resolution,[],[f11933,f9498]) ).
fof(f9498,plain,
( ! [X0] :
( segmentP(tl(sK20),X0)
| ~ segmentP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_4
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f9497,f1769]) ).
fof(f9497,plain,
( ! [X0] :
( segmentP(sK25(sK20),X0)
| ~ segmentP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_4
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f9474,f1602]) ).
fof(f9474,plain,
( ! [X0] :
( segmentP(sK25(sK20),X0)
| ~ segmentP(nil,X0)
| ~ ssList(sK25(sK20))
| ~ ssList(X0) )
| ~ spl72_4
| ~ spl72_13 ),
inference(superposition,[],[f5555,f1614]) ).
fof(f1614,plain,
( sK25(sK20) = app(nil,sK25(sK20))
| ~ spl72_13 ),
inference(resolution,[],[f1602,f470]) ).
fof(f5555,plain,
( ! [X0,X1] :
( segmentP(app(nil,X0),X1)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl72_4 ),
inference(forward_demodulation,[],[f5554,f898]) ).
fof(f5554,plain,
( ! [X0,X1] :
( segmentP(app(nil,X0),X1)
| ~ segmentP(sK24,X1)
| ~ ssList(X0)
| ~ ssList(X1) )
| ~ spl72_4 ),
inference(forward_demodulation,[],[f5553,f898]) ).
fof(f5553,plain,
! [X0,X1] :
( segmentP(app(sK24,X0),X1)
| ~ segmentP(sK24,X1)
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(subsumption_resolution,[],[f5552,f394]) ).
fof(f5552,plain,
! [X0,X1] :
( segmentP(app(sK24,X0),X1)
| ~ segmentP(sK24,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sK24) ),
inference(subsumption_resolution,[],[f5497,f407]) ).
fof(f5497,plain,
! [X0,X1] :
( segmentP(app(sK24,X0),X1)
| ~ segmentP(sK24,X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(sK24) ),
inference(superposition,[],[f612,f704]) ).
fof(f704,plain,
sK24 = app(nil,sK24),
inference(resolution,[],[f470,f394]) ).
fof(f11866,plain,
spl72_86,
inference(avatar_contradiction_clause,[],[f11865]) ).
fof(f11865,plain,
( $false
| spl72_86 ),
inference(subsumption_resolution,[],[f11864,f386]) ).
fof(f11864,plain,
( ~ ssList(sK20)
| spl72_86 ),
inference(duplicate_literal_removal,[],[f11863]) ).
fof(f11863,plain,
( ~ ssList(sK20)
| ~ ssList(sK20)
| spl72_86 ),
inference(resolution,[],[f11861,f579]) ).
fof(f11861,plain,
( ~ ssList(app(sK20,sK20))
| spl72_86 ),
inference(avatar_component_clause,[],[f11859]) ).
fof(f11862,plain,
( spl72_85
| ~ spl72_86
| ~ spl72_4 ),
inference(avatar_split_clause,[],[f11846,f896,f11859,f11855]) ).
fof(f11846,plain,
( ~ ssList(app(sK20,sK20))
| segmentP(app(sK20,sK20),sK20)
| ~ spl72_4 ),
inference(forward_demodulation,[],[f11845,f11737]) ).
fof(f11737,plain,
( app(sK20,sK20) = app(app(sK20,sK20),nil)
| ~ spl72_4 ),
inference(resolution,[],[f11581,f386]) ).
fof(f11845,plain,
( segmentP(app(sK20,sK20),sK20)
| ~ ssList(app(app(sK20,sK20),nil))
| ~ spl72_4 ),
inference(subsumption_resolution,[],[f11844,f386]) ).
fof(f11844,plain,
( segmentP(app(sK20,sK20),sK20)
| ~ ssList(sK20)
| ~ ssList(app(app(sK20,sK20),nil))
| ~ spl72_4 ),
inference(subsumption_resolution,[],[f11843,f407]) ).
fof(f11843,plain,
( segmentP(app(sK20,sK20),sK20)
| ~ ssList(nil)
| ~ ssList(sK20)
| ~ ssList(app(app(sK20,sK20),nil))
| ~ spl72_4 ),
inference(duplicate_literal_removal,[],[f11821]) ).
fof(f11821,plain,
( segmentP(app(sK20,sK20),sK20)
| ~ ssList(nil)
| ~ ssList(sK20)
| ~ ssList(sK20)
| ~ ssList(app(app(sK20,sK20),nil))
| ~ spl72_4 ),
inference(superposition,[],[f639,f11737]) ).
fof(f10860,plain,
( ~ spl72_83
| spl72_84
| ~ spl72_17
| ~ spl72_18 ),
inference(avatar_split_clause,[],[f10848,f2052,f2048,f10857,f10853]) ).
fof(f10853,plain,
( spl72_83
<=> frontsegP(nil,cons(sK71,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_83])]) ).
fof(f10857,plain,
( spl72_84
<=> frontsegP(sK20,cons(sK71,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_84])]) ).
fof(f10848,plain,
( frontsegP(sK20,cons(sK71,nil))
| ~ frontsegP(nil,cons(sK71,sK20))
| ~ spl72_17
| ~ spl72_18 ),
inference(subsumption_resolution,[],[f10847,f2054]) ).
fof(f10847,plain,
( frontsegP(sK20,cons(sK71,nil))
| ~ frontsegP(nil,cons(sK71,sK20))
| ~ ssList(cons(sK71,sK20))
| ~ spl72_17
| ~ spl72_18 ),
inference(subsumption_resolution,[],[f10829,f386]) ).
fof(f10829,plain,
( frontsegP(sK20,cons(sK71,nil))
| ~ ssList(sK20)
| ~ frontsegP(nil,cons(sK71,sK20))
| ~ ssList(cons(sK71,sK20))
| ~ spl72_17
| ~ spl72_18 ),
inference(resolution,[],[f3688,f2951]) ).
fof(f3688,plain,
( ! [X0] :
( ~ frontsegP(X0,cons(sK71,sK20))
| frontsegP(X0,cons(sK71,nil))
| ~ ssList(X0) )
| ~ spl72_17
| ~ spl72_18 ),
inference(subsumption_resolution,[],[f3687,f2054]) ).
fof(f3687,plain,
( ! [X0] :
( frontsegP(X0,cons(sK71,nil))
| ~ frontsegP(X0,cons(sK71,sK20))
| ~ ssList(cons(sK71,sK20))
| ~ ssList(X0) )
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f3659,f2049]) ).
fof(f3659,plain,
( ! [X0] :
( frontsegP(X0,cons(sK71,nil))
| ~ frontsegP(X0,cons(sK71,sK20))
| ~ ssList(cons(sK71,nil))
| ~ ssList(cons(sK71,sK20))
| ~ ssList(X0) )
| ~ spl72_17 ),
inference(resolution,[],[f611,f2256]) ).
fof(f2256,plain,
( frontsegP(cons(sK71,sK20),cons(sK71,nil))
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f2255,f2049]) ).
fof(f2255,plain,
( frontsegP(cons(sK71,sK20),cons(sK71,nil))
| ~ ssList(cons(sK71,nil)) ),
inference(subsumption_resolution,[],[f2229,f386]) ).
fof(f2229,plain,
( frontsegP(cons(sK71,sK20),cons(sK71,nil))
| ~ ssList(sK20)
| ~ ssList(cons(sK71,nil)) ),
inference(superposition,[],[f2128,f1986]) ).
fof(f10815,plain,
( ~ spl72_81
| spl72_82
| ~ spl72_15
| ~ spl72_16 ),
inference(avatar_split_clause,[],[f10803,f2003,f1999,f10812,f10808]) ).
fof(f10808,plain,
( spl72_81
<=> frontsegP(nil,cons(sK70,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_81])]) ).
fof(f10812,plain,
( spl72_82
<=> frontsegP(sK20,cons(sK70,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_82])]) ).
fof(f10803,plain,
( frontsegP(sK20,cons(sK70,nil))
| ~ frontsegP(nil,cons(sK70,sK20))
| ~ spl72_15
| ~ spl72_16 ),
inference(subsumption_resolution,[],[f10802,f2005]) ).
fof(f10802,plain,
( frontsegP(sK20,cons(sK70,nil))
| ~ frontsegP(nil,cons(sK70,sK20))
| ~ ssList(cons(sK70,sK20))
| ~ spl72_15
| ~ spl72_16 ),
inference(subsumption_resolution,[],[f10784,f386]) ).
fof(f10784,plain,
( frontsegP(sK20,cons(sK70,nil))
| ~ ssList(sK20)
| ~ frontsegP(nil,cons(sK70,sK20))
| ~ ssList(cons(sK70,sK20))
| ~ spl72_15
| ~ spl72_16 ),
inference(resolution,[],[f3686,f2951]) ).
fof(f3686,plain,
( ! [X0] :
( ~ frontsegP(X0,cons(sK70,sK20))
| frontsegP(X0,cons(sK70,nil))
| ~ ssList(X0) )
| ~ spl72_15
| ~ spl72_16 ),
inference(subsumption_resolution,[],[f3685,f2005]) ).
fof(f3685,plain,
( ! [X0] :
( frontsegP(X0,cons(sK70,nil))
| ~ frontsegP(X0,cons(sK70,sK20))
| ~ ssList(cons(sK70,sK20))
| ~ ssList(X0) )
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f3658,f2000]) ).
fof(f3658,plain,
( ! [X0] :
( frontsegP(X0,cons(sK70,nil))
| ~ frontsegP(X0,cons(sK70,sK20))
| ~ ssList(cons(sK70,nil))
| ~ ssList(cons(sK70,sK20))
| ~ ssList(X0) )
| ~ spl72_15 ),
inference(resolution,[],[f611,f2254]) ).
fof(f2254,plain,
( frontsegP(cons(sK70,sK20),cons(sK70,nil))
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f2253,f2000]) ).
fof(f2253,plain,
( frontsegP(cons(sK70,sK20),cons(sK70,nil))
| ~ ssList(cons(sK70,nil)) ),
inference(subsumption_resolution,[],[f2228,f386]) ).
fof(f2228,plain,
( frontsegP(cons(sK70,sK20),cons(sK70,nil))
| ~ ssList(sK20)
| ~ ssList(cons(sK70,nil)) ),
inference(superposition,[],[f2128,f1985]) ).
fof(f9348,plain,
( ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_78 ),
inference(avatar_contradiction_clause,[],[f9347]) ).
fof(f9347,plain,
( $false
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_78 ),
inference(subsumption_resolution,[],[f9346,f1376]) ).
fof(f9346,plain,
( ~ ssItem(hd(sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_78 ),
inference(subsumption_resolution,[],[f9345,f1775]) ).
fof(f9345,plain,
( ~ ssList(tl(sK20))
| ~ ssItem(hd(sK20))
| spl72_78 ),
inference(resolution,[],[f9327,f459]) ).
fof(f459,plain,
! [X0,X1] :
( sP4(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f230]) ).
fof(f230,plain,
! [X0] :
( ! [X1] :
( sP4(X0,X1)
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(definition_folding,[],[f138,f229,f228]) ).
fof(f229,plain,
! [X0,X1] :
( ( strictorderedP(cons(X0,X1))
<=> sP3(X1,X0) )
| ~ sP4(X0,X1) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP4])]) ).
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/sandbox/benchmark/theBenchmark.p',ax70) ).
fof(f9327,plain,
( ~ sP4(hd(sK20),tl(sK20))
| spl72_78 ),
inference(avatar_component_clause,[],[f9325]) ).
fof(f9325,plain,
( spl72_78
<=> sP4(hd(sK20),tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_78])]) ).
fof(f9336,plain,
( ~ spl72_78
| spl72_79
| ~ spl72_80 ),
inference(avatar_split_clause,[],[f1356,f9333,f9329,f9325]) ).
fof(f9329,plain,
( spl72_79
<=> sP3(tl(sK20),hd(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_79])]) ).
fof(f9333,plain,
( spl72_80
<=> strictorderedP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_80])]) ).
fof(f1356,plain,
( ~ strictorderedP(sK20)
| sP3(tl(sK20),hd(sK20))
| ~ sP4(hd(sK20),tl(sK20)) ),
inference(superposition,[],[f452,f1348]) ).
fof(f452,plain,
! [X0,X1] :
( ~ strictorderedP(cons(X0,X1))
| sP3(X1,X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f275]) ).
fof(f275,plain,
! [X0,X1] :
( ( ( strictorderedP(cons(X0,X1))
| ~ sP3(X1,X0) )
& ( sP3(X1,X0)
| ~ strictorderedP(cons(X0,X1)) ) )
| ~ sP4(X0,X1) ),
inference(nnf_transformation,[],[f229]) ).
fof(f9257,plain,
( ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_75 ),
inference(avatar_contradiction_clause,[],[f9256]) ).
fof(f9256,plain,
( $false
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_75 ),
inference(subsumption_resolution,[],[f9255,f1376]) ).
fof(f9255,plain,
( ~ ssItem(hd(sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_75 ),
inference(subsumption_resolution,[],[f9254,f1775]) ).
fof(f9254,plain,
( ~ ssList(tl(sK20))
| ~ ssItem(hd(sK20))
| spl72_75 ),
inference(resolution,[],[f9212,f451]) ).
fof(f9212,plain,
( ~ sP2(hd(sK20),tl(sK20))
| spl72_75 ),
inference(avatar_component_clause,[],[f9210]) ).
fof(f9210,plain,
( spl72_75
<=> sP2(hd(sK20),tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_75])]) ).
fof(f9221,plain,
( ~ spl72_75
| spl72_76
| ~ spl72_77 ),
inference(avatar_split_clause,[],[f1354,f9218,f9214,f9210]) ).
fof(f9214,plain,
( spl72_76
<=> sP1(tl(sK20),hd(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_76])]) ).
fof(f9218,plain,
( spl72_77
<=> totalorderedP(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_77])]) ).
fof(f1354,plain,
( ~ totalorderedP(sK20)
| sP1(tl(sK20),hd(sK20))
| ~ sP2(hd(sK20),tl(sK20)) ),
inference(superposition,[],[f444,f1348]) ).
fof(f444,plain,
! [X0,X1] :
( ~ totalorderedP(cons(X0,X1))
| sP1(X1,X0)
| ~ sP2(X0,X1) ),
inference(cnf_transformation,[],[f271]) ).
fof(f8722,plain,
( spl72_73
| ~ spl72_74
| ~ spl72_9 ),
inference(avatar_split_clause,[],[f8554,f1375,f8719,f8715]) ).
fof(f8719,plain,
( spl72_74
<=> sP3(app(sK20,sK20),hd(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_74])]) ).
fof(f8554,plain,
( ~ sP3(app(sK20,sK20),hd(sK20))
| nil = app(sK20,sK20)
| ~ spl72_9 ),
inference(subsumption_resolution,[],[f8553,f1376]) ).
fof(f8553,plain,
( ~ ssItem(hd(sK20))
| ~ sP3(app(sK20,sK20),hd(sK20))
| nil = app(sK20,sK20) ),
inference(forward_demodulation,[],[f8450,f7732]) ).
fof(f8450,plain,
( ~ sP3(app(sK20,sK20),hd(sK20))
| nil = app(sK20,sK20)
| ~ ssItem(hd(app(sK20,sK20))) ),
inference(superposition,[],[f798,f7732]) ).
fof(f8082,plain,
( ~ spl72_18
| spl72_71
| ~ spl72_72 ),
inference(avatar_contradiction_clause,[],[f8081]) ).
fof(f8081,plain,
( $false
| ~ spl72_18
| spl72_71
| ~ spl72_72 ),
inference(subsumption_resolution,[],[f8080,f2054]) ).
fof(f8080,plain,
( ~ ssList(cons(sK71,sK20))
| spl72_71
| ~ spl72_72 ),
inference(subsumption_resolution,[],[f8079,f407]) ).
fof(f8079,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK71,sK20))
| spl72_71
| ~ spl72_72 ),
inference(subsumption_resolution,[],[f8078,f8066]) ).
fof(f8066,plain,
( frontsegP(cons(sK71,sK20),nil)
| ~ spl72_72 ),
inference(avatar_component_clause,[],[f8064]) ).
fof(f8064,plain,
( spl72_72
<=> frontsegP(cons(sK71,sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_72])]) ).
fof(f8078,plain,
( ~ frontsegP(cons(sK71,sK20),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK71,sK20))
| spl72_71 ),
inference(resolution,[],[f8062,f595]) ).
fof(f8062,plain,
( ~ ssList(sK69(cons(sK71,sK20),nil))
| spl72_71 ),
inference(avatar_component_clause,[],[f8060]) ).
fof(f8060,plain,
( spl72_71
<=> ssList(sK69(cons(sK71,sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_71])]) ).
fof(f8074,plain,
( ~ spl72_18
| spl72_72 ),
inference(avatar_contradiction_clause,[],[f8073]) ).
fof(f8073,plain,
( $false
| ~ spl72_18
| spl72_72 ),
inference(subsumption_resolution,[],[f8069,f2054]) ).
fof(f8069,plain,
( ~ ssList(cons(sK71,sK20))
| spl72_72 ),
inference(resolution,[],[f8065,f466]) ).
fof(f8065,plain,
( ~ frontsegP(cons(sK71,sK20),nil)
| spl72_72 ),
inference(avatar_component_clause,[],[f8064]) ).
fof(f8072,plain,
( ~ spl72_18
| spl72_72 ),
inference(avatar_contradiction_clause,[],[f8071]) ).
fof(f8071,plain,
( $false
| ~ spl72_18
| spl72_72 ),
inference(subsumption_resolution,[],[f8070,f407]) ).
fof(f8070,plain,
( ~ ssList(nil)
| ~ spl72_18
| spl72_72 ),
inference(subsumption_resolution,[],[f8068,f650]) ).
fof(f650,plain,
frontsegP(nil,nil),
inference(global_subsumption,[],[f385,f384,f383,f382,f381,f398,f397,f396,f395,f394,f393,f392,f391,f390,f389,f388,f387,f386,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f422,f423,f427,f426,f429,f428,f432,f431,f647,f433,f434,f435,f436,f437,f440,f646,f438,f645,f442,f441,f445,f444,f450,f620,f448,f447,f451,f453,f452,f458,f622,f456,f455,f459,f462,f461,f460,f463,f464,f465,f466,f467,f468,f469,f470,f473,f472,f471,f474,f475,f476,f478,f477,f480,f479,f624,f482,f481,f484,f493,f492,f491,f490,f489,f488,f487,f644,f494,f495,f505,f504,f503,f502,f501,f500,f499,f498,f627,f506,f507,f517,f516,f515,f514,f513,f512,f511,f510,f628,f518,f519,f529,f528,f527,f526,f525,f524,f523,f522,f629,f530,f532,f531,f540,f539,f538,f537,f536,f535,f534,f630,f541,f543,f542,f551,f550,f549,f548,f547,f546,f545,f631,f552,f553,f561,f560,f559,f558,f557,f556,f632,f562,f633,f648,f563,f634,f649,f565,f635]) ).
fof(f635,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f568]) ).
fof(f568,plain,
! [X0] :
( frontsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f356]) ).
fof(f356,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/sandbox/benchmark/theBenchmark.p',ax46) ).
fof(f565,plain,
! [X0] :
( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f355,plain,
! [X0] :
( ( ( segmentP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ segmentP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f176]) ).
fof(f176,plain,
! [X0] :
( ( segmentP(nil,X0)
<=> nil = X0 )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f58]) ).
fof(f58,axiom,
! [X0] :
( ssList(X0)
=> ( segmentP(nil,X0)
<=> nil = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax58) ).
fof(f649,plain,
segmentP(nil,nil),
inference(global_subsumption,[],[f385,f384,f383,f382,f381,f398,f397,f396,f395,f394,f393,f392,f391,f390,f389,f388,f387,f386,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f422,f423,f427,f426,f429,f428,f432,f431,f647,f433,f434,f435,f436,f437,f440,f646,f438,f645,f442,f441,f445,f444,f450,f620,f448,f447,f451,f453,f452,f458,f622,f456,f455,f459,f462,f461,f460,f463,f464,f465,f466,f467,f468,f469,f470,f473,f472,f471,f474,f475,f476,f478,f477,f480,f479,f624,f482,f481,f484,f493,f492,f491,f490,f489,f488,f487,f644,f494,f495,f505,f504,f503,f502,f501,f500,f499,f498,f627,f506,f507,f517,f516,f515,f514,f513,f512,f511,f510,f628,f518,f519,f529,f528,f527,f526,f525,f524,f523,f522,f629,f530,f532,f531,f540,f539,f538,f537,f536,f535,f534,f630,f541,f543,f542,f551,f550,f549,f548,f547,f546,f545,f631,f552,f553,f561,f560,f559,f558,f557,f556,f632,f562,f633,f648,f563,f634]) ).
fof(f634,plain,
( segmentP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f566]) ).
fof(f566,plain,
! [X0] :
( segmentP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f355]) ).
fof(f563,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f354,plain,
! [X0] :
( ( ( rearsegP(nil,X0)
| nil != X0 )
& ( nil = X0
| ~ rearsegP(nil,X0) ) )
| ~ ssList(X0) ),
inference(nnf_transformation,[],[f175]) ).
fof(f175,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/sandbox/benchmark/theBenchmark.p',ax52) ).
fof(f648,plain,
rearsegP(nil,nil),
inference(global_subsumption,[],[f385,f384,f383,f382,f381,f398,f397,f396,f395,f394,f393,f392,f391,f390,f389,f388,f387,f386,f399,f400,f401,f402,f403,f404,f405,f406,f407,f408,f409,f410,f411,f412,f413,f414,f415,f416,f417,f418,f419,f420,f421,f422,f423,f427,f426,f429,f428,f432,f431,f647,f433,f434,f435,f436,f437,f440,f646,f438,f645,f442,f441,f445,f444,f450,f620,f448,f447,f451,f453,f452,f458,f622,f456,f455,f459,f462,f461,f460,f463,f464,f465,f466,f467,f468,f469,f470,f473,f472,f471,f474,f475,f476,f478,f477,f480,f479,f624,f482,f481,f484,f493,f492,f491,f490,f489,f488,f487,f644,f494,f495,f505,f504,f503,f502,f501,f500,f499,f498,f627,f506,f507,f517,f516,f515,f514,f513,f512,f511,f510,f628,f518,f519,f529,f528,f527,f526,f525,f524,f523,f522,f629,f530,f532,f531,f540,f539,f538,f537,f536,f535,f534,f630,f541,f543,f542,f551,f550,f549,f548,f547,f546,f545,f631,f552,f553,f561,f560,f559,f558,f557,f556,f632,f562,f633]) ).
fof(f633,plain,
( rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(equality_resolution,[],[f564]) ).
fof(f564,plain,
! [X0] :
( rearsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f354]) ).
fof(f562,plain,
! [X0] :
( sP18(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f251]) ).
fof(f251,plain,
! [X0] :
( sP18(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f174,f250,f249]) ).
fof(f249,plain,
! [X0] :
( sP17(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,[sP17])]) ).
fof(f250,plain,
! [X0] :
( ( equalelemsP(X0)
<=> sP17(X0) )
| ~ sP18(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP18])]) ).
fof(f174,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,[],[f173]) ).
fof(f173,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/sandbox/benchmark/theBenchmark.p',ax14) ).
fof(f632,plain,
! [X8,X6,X7,X5] :
( ~ sP17(app(X7,cons(X5,cons(X6,X8))))
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| X5 = X6 ),
inference(equality_resolution,[],[f555]) ).
fof(f555,plain,
! [X0,X8,X6,X7,X5] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8)
| ~ ssList(X7)
| ~ ssItem(X6)
| ~ ssItem(X5)
| ~ sP17(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f353,plain,
! [X0] :
( ( sP17(X0)
| ( sK60(X0) != sK61(X0)
& app(sK62(X0),cons(sK60(X0),cons(sK61(X0),sK63(X0)))) = X0
& ssList(sK63(X0))
& ssList(sK62(X0))
& ssItem(sK61(X0))
& ssItem(sK60(X0)) ) )
& ( ! [X5] :
( ! [X6] :
( ! [X7] :
( ! [X8] :
( X5 = X6
| app(X7,cons(X5,cons(X6,X8))) != X0
| ~ ssList(X8) )
| ~ ssList(X7) )
| ~ ssItem(X6) )
| ~ ssItem(X5) )
| ~ sP17(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK60,sK61,sK62,sK63])],[f348,f352,f351,f350,f349]) ).
fof(f349,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] :
( sK60(X0) != X2
& app(X3,cons(sK60(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK60(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f350,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( sK60(X0) != X2
& app(X3,cons(sK60(X0),cons(X2,X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( sK60(X0) != sK61(X0)
& app(X3,cons(sK60(X0),cons(sK61(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
& ssItem(sK61(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f351,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( sK60(X0) != sK61(X0)
& app(X3,cons(sK60(X0),cons(sK61(X0),X4))) = X0
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( sK60(X0) != sK61(X0)
& app(sK62(X0),cons(sK60(X0),cons(sK61(X0),X4))) = X0
& ssList(X4) )
& ssList(sK62(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f352,plain,
! [X0] :
( ? [X4] :
( sK60(X0) != sK61(X0)
& app(sK62(X0),cons(sK60(X0),cons(sK61(X0),X4))) = X0
& ssList(X4) )
=> ( sK60(X0) != sK61(X0)
& app(sK62(X0),cons(sK60(X0),cons(sK61(X0),sK63(X0)))) = X0
& ssList(sK63(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f348,plain,
! [X0] :
( ( sP17(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) )
| ~ sP17(X0) ) ),
inference(rectify,[],[f347]) ).
fof(f347,plain,
! [X0] :
( ( sP17(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) )
| ~ sP17(X0) ) ),
inference(nnf_transformation,[],[f249]) ).
fof(f556,plain,
! [X0] :
( ssItem(sK60(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f557,plain,
! [X0] :
( ssItem(sK61(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f558,plain,
! [X0] :
( ssList(sK62(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f559,plain,
! [X0] :
( ssList(sK63(X0))
| sP17(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f560,plain,
! [X0] :
( sP17(X0)
| app(sK62(X0),cons(sK60(X0),cons(sK61(X0),sK63(X0)))) = X0 ),
inference(cnf_transformation,[],[f353]) ).
fof(f561,plain,
! [X0] :
( sK60(X0) != sK61(X0)
| sP17(X0) ),
inference(cnf_transformation,[],[f353]) ).
fof(f553,plain,
! [X0] :
( ~ sP18(X0)
| ~ equalelemsP(X0)
| sP17(X0) ),
inference(cnf_transformation,[],[f346]) ).
fof(f346,plain,
! [X0] :
( ( ( equalelemsP(X0)
| ~ sP17(X0) )
& ( sP17(X0)
| ~ equalelemsP(X0) ) )
| ~ sP18(X0) ),
inference(nnf_transformation,[],[f250]) ).
fof(f552,plain,
! [X0] :
( sP16(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f248]) ).
fof(f248,plain,
! [X0] :
( sP16(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f172,f247,f246]) ).
fof(f246,plain,
! [X0] :
( sP15(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,[sP15])]) ).
fof(f247,plain,
! [X0] :
( ( strictorderedP(X0)
<=> sP15(X0) )
| ~ sP16(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP16])]) ).
fof(f172,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,[],[f171]) ).
fof(f171,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/sandbox/benchmark/theBenchmark.p',ax12) ).
fof(f631,plain,
! [X10,X8,X6,X9,X7] :
( ~ sP15(app(app(X8,cons(X6,X9)),cons(X7,X10)))
| ~ ssList(X10)
| ~ ssList(X9)
| ~ ssList(X8)
| ~ ssItem(X7)
| ~ ssItem(X6)
| lt(X6,X7) ),
inference(equality_resolution,[],[f544]) ).
fof(f544,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)
| ~ sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f345,plain,
! [X0] :
( ( sP15(X0)
| ( ~ lt(sK55(X0),sK56(X0))
& app(app(sK57(X0),cons(sK55(X0),sK58(X0))),cons(sK56(X0),sK59(X0))) = X0
& ssList(sK59(X0))
& ssList(sK58(X0))
& ssList(sK57(X0))
& ssItem(sK56(X0))
& ssItem(sK55(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) )
| ~ sP15(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK55,sK56,sK57,sK58,sK59])],[f339,f344,f343,f342,f341,f340]) ).
fof(f340,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(sK55(X0),X2)
& app(app(X3,cons(sK55(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK55(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f341,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK55(X0),X2)
& app(app(X3,cons(sK55(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK55(X0),sK56(X0))
& app(app(X3,cons(sK55(X0),X4)),cons(sK56(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK56(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f342,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK55(X0),sK56(X0))
& app(app(X3,cons(sK55(X0),X4)),cons(sK56(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK55(X0),sK56(X0))
& app(app(sK57(X0),cons(sK55(X0),X4)),cons(sK56(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK57(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f343,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK55(X0),sK56(X0))
& app(app(sK57(X0),cons(sK55(X0),X4)),cons(sK56(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK55(X0),sK56(X0))
& app(app(sK57(X0),cons(sK55(X0),sK58(X0))),cons(sK56(X0),X5)) = X0
& ssList(X5) )
& ssList(sK58(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f344,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK55(X0),sK56(X0))
& app(app(sK57(X0),cons(sK55(X0),sK58(X0))),cons(sK56(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK55(X0),sK56(X0))
& app(app(sK57(X0),cons(sK55(X0),sK58(X0))),cons(sK56(X0),sK59(X0))) = X0
& ssList(sK59(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f339,plain,
! [X0] :
( ( sP15(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) )
| ~ sP15(X0) ) ),
inference(rectify,[],[f338]) ).
fof(f338,plain,
! [X0] :
( ( sP15(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) )
| ~ sP15(X0) ) ),
inference(nnf_transformation,[],[f246]) ).
fof(f545,plain,
! [X0] :
( ssItem(sK55(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f546,plain,
! [X0] :
( ssItem(sK56(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f547,plain,
! [X0] :
( ssList(sK57(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f548,plain,
! [X0] :
( ssList(sK58(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f549,plain,
! [X0] :
( ssList(sK59(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f550,plain,
! [X0] :
( sP15(X0)
| app(app(sK57(X0),cons(sK55(X0),sK58(X0))),cons(sK56(X0),sK59(X0))) = X0 ),
inference(cnf_transformation,[],[f345]) ).
fof(f551,plain,
! [X0] :
( ~ lt(sK55(X0),sK56(X0))
| sP15(X0) ),
inference(cnf_transformation,[],[f345]) ).
fof(f542,plain,
! [X0] :
( ~ sP16(X0)
| ~ strictorderedP(X0)
| sP15(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f337,plain,
! [X0] :
( ( ( strictorderedP(X0)
| ~ sP15(X0) )
& ( sP15(X0)
| ~ strictorderedP(X0) ) )
| ~ sP16(X0) ),
inference(nnf_transformation,[],[f247]) ).
fof(f543,plain,
! [X0] :
( ~ sP16(X0)
| ~ sP15(X0)
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f337]) ).
fof(f541,plain,
! [X0] :
( sP14(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f245]) ).
fof(f245,plain,
! [X0] :
( sP14(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f170,f244,f243]) ).
fof(f243,plain,
! [X0] :
( sP13(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,[sP13])]) ).
fof(f244,plain,
! [X0] :
( ( totalorderedP(X0)
<=> sP13(X0) )
| ~ sP14(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP14])]) ).
fof(f170,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,[],[f169]) ).
fof(f169,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/sandbox/benchmark/theBenchmark.p',ax11) ).
fof(f630,plain,
! [X10,X8,X6,X9,X7] :
( ~ sP13(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,[],[f533]) ).
fof(f533,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)
| ~ sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f336,plain,
! [X0] :
( ( sP13(X0)
| ( ~ leq(sK50(X0),sK51(X0))
& app(app(sK52(X0),cons(sK50(X0),sK53(X0))),cons(sK51(X0),sK54(X0))) = X0
& ssList(sK54(X0))
& ssList(sK53(X0))
& ssList(sK52(X0))
& ssItem(sK51(X0))
& ssItem(sK50(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) )
| ~ sP13(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK50,sK51,sK52,sK53,sK54])],[f330,f335,f334,f333,f332,f331]) ).
fof(f331,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(sK50(X0),X2)
& app(app(X3,cons(sK50(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK50(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f332,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK50(X0),X2)
& app(app(X3,cons(sK50(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK50(X0),sK51(X0))
& app(app(X3,cons(sK50(X0),X4)),cons(sK51(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK51(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f333,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK50(X0),sK51(X0))
& app(app(X3,cons(sK50(X0),X4)),cons(sK51(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK50(X0),sK51(X0))
& app(app(sK52(X0),cons(sK50(X0),X4)),cons(sK51(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK52(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f334,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK50(X0),sK51(X0))
& app(app(sK52(X0),cons(sK50(X0),X4)),cons(sK51(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK50(X0),sK51(X0))
& app(app(sK52(X0),cons(sK50(X0),sK53(X0))),cons(sK51(X0),X5)) = X0
& ssList(X5) )
& ssList(sK53(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f335,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK50(X0),sK51(X0))
& app(app(sK52(X0),cons(sK50(X0),sK53(X0))),cons(sK51(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK50(X0),sK51(X0))
& app(app(sK52(X0),cons(sK50(X0),sK53(X0))),cons(sK51(X0),sK54(X0))) = X0
& ssList(sK54(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f330,plain,
! [X0] :
( ( sP13(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) )
| ~ sP13(X0) ) ),
inference(rectify,[],[f329]) ).
fof(f329,plain,
! [X0] :
( ( sP13(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) )
| ~ sP13(X0) ) ),
inference(nnf_transformation,[],[f243]) ).
fof(f534,plain,
! [X0] :
( ssItem(sK50(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f535,plain,
! [X0] :
( ssItem(sK51(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f536,plain,
! [X0] :
( ssList(sK52(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f537,plain,
! [X0] :
( ssList(sK53(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f538,plain,
! [X0] :
( ssList(sK54(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f539,plain,
! [X0] :
( sP13(X0)
| app(app(sK52(X0),cons(sK50(X0),sK53(X0))),cons(sK51(X0),sK54(X0))) = X0 ),
inference(cnf_transformation,[],[f336]) ).
fof(f540,plain,
! [X0] :
( ~ leq(sK50(X0),sK51(X0))
| sP13(X0) ),
inference(cnf_transformation,[],[f336]) ).
fof(f531,plain,
! [X0] :
( ~ sP14(X0)
| ~ totalorderedP(X0)
| sP13(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f328,plain,
! [X0] :
( ( ( totalorderedP(X0)
| ~ sP13(X0) )
& ( sP13(X0)
| ~ totalorderedP(X0) ) )
| ~ sP14(X0) ),
inference(nnf_transformation,[],[f244]) ).
fof(f532,plain,
! [X0] :
( ~ sP14(X0)
| ~ sP13(X0)
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f328]) ).
fof(f530,plain,
! [X0] :
( sP12(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f242]) ).
fof(f242,plain,
! [X0] :
( sP12(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f168,f241,f240]) ).
fof(f240,plain,
! [X0] :
( sP11(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,[sP11])]) ).
fof(f241,plain,
! [X0] :
( ( cyclefreeP(X0)
<=> sP11(X0) )
| ~ sP12(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP12])]) ).
fof(f168,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,[],[f167]) ).
fof(f167,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/sandbox/benchmark/theBenchmark.p',ax8) ).
fof(f629,plain,
! [X10,X8,X6,X9,X7] :
( ~ sP11(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,[],[f521]) ).
fof(f521,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)
| ~ sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f327,plain,
! [X0] :
( ( sP11(X0)
| ( leq(sK46(X0),sK45(X0))
& leq(sK45(X0),sK46(X0))
& app(app(sK47(X0),cons(sK45(X0),sK48(X0))),cons(sK46(X0),sK49(X0))) = X0
& ssList(sK49(X0))
& ssList(sK48(X0))
& ssList(sK47(X0))
& ssItem(sK46(X0))
& ssItem(sK45(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) )
| ~ sP11(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK45,sK46,sK47,sK48,sK49])],[f321,f326,f325,f324,f323,f322]) ).
fof(f322,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,sK45(X0))
& leq(sK45(X0),X2)
& app(app(X3,cons(sK45(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK45(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f323,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(X2,sK45(X0))
& leq(sK45(X0),X2)
& app(app(X3,cons(sK45(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK46(X0),sK45(X0))
& leq(sK45(X0),sK46(X0))
& app(app(X3,cons(sK45(X0),X4)),cons(sK46(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK46(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f324,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( leq(sK46(X0),sK45(X0))
& leq(sK45(X0),sK46(X0))
& app(app(X3,cons(sK45(X0),X4)),cons(sK46(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( leq(sK46(X0),sK45(X0))
& leq(sK45(X0),sK46(X0))
& app(app(sK47(X0),cons(sK45(X0),X4)),cons(sK46(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK47(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f325,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( leq(sK46(X0),sK45(X0))
& leq(sK45(X0),sK46(X0))
& app(app(sK47(X0),cons(sK45(X0),X4)),cons(sK46(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( leq(sK46(X0),sK45(X0))
& leq(sK45(X0),sK46(X0))
& app(app(sK47(X0),cons(sK45(X0),sK48(X0))),cons(sK46(X0),X5)) = X0
& ssList(X5) )
& ssList(sK48(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f326,plain,
! [X0] :
( ? [X5] :
( leq(sK46(X0),sK45(X0))
& leq(sK45(X0),sK46(X0))
& app(app(sK47(X0),cons(sK45(X0),sK48(X0))),cons(sK46(X0),X5)) = X0
& ssList(X5) )
=> ( leq(sK46(X0),sK45(X0))
& leq(sK45(X0),sK46(X0))
& app(app(sK47(X0),cons(sK45(X0),sK48(X0))),cons(sK46(X0),sK49(X0))) = X0
& ssList(sK49(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f321,plain,
! [X0] :
( ( sP11(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) )
| ~ sP11(X0) ) ),
inference(rectify,[],[f320]) ).
fof(f320,plain,
! [X0] :
( ( sP11(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) )
| ~ sP11(X0) ) ),
inference(nnf_transformation,[],[f240]) ).
fof(f522,plain,
! [X0] :
( ssItem(sK45(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f523,plain,
! [X0] :
( ssItem(sK46(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f524,plain,
! [X0] :
( ssList(sK47(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f525,plain,
! [X0] :
( ssList(sK48(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f526,plain,
! [X0] :
( ssList(sK49(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f527,plain,
! [X0] :
( sP11(X0)
| app(app(sK47(X0),cons(sK45(X0),sK48(X0))),cons(sK46(X0),sK49(X0))) = X0 ),
inference(cnf_transformation,[],[f327]) ).
fof(f528,plain,
! [X0] :
( leq(sK45(X0),sK46(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f529,plain,
! [X0] :
( leq(sK46(X0),sK45(X0))
| sP11(X0) ),
inference(cnf_transformation,[],[f327]) ).
fof(f519,plain,
! [X0] :
( ~ sP12(X0)
| ~ cyclefreeP(X0)
| sP11(X0) ),
inference(cnf_transformation,[],[f319]) ).
fof(f319,plain,
! [X0] :
( ( ( cyclefreeP(X0)
| ~ sP11(X0) )
& ( sP11(X0)
| ~ cyclefreeP(X0) ) )
| ~ sP12(X0) ),
inference(nnf_transformation,[],[f241]) ).
fof(f518,plain,
! [X0] :
( sP10(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f239]) ).
fof(f239,plain,
! [X0] :
( sP10(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f166,f238,f237]) ).
fof(f237,plain,
! [X0] :
( sP9(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,[sP9])]) ).
fof(f238,plain,
! [X0] :
( ( strictorderP(X0)
<=> sP9(X0) )
| ~ sP10(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP10])]) ).
fof(f166,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,[],[f165]) ).
fof(f165,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/sandbox/benchmark/theBenchmark.p',ax10) ).
fof(f628,plain,
! [X10,X8,X6,X9,X7] :
( ~ sP9(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,[],[f509]) ).
fof(f509,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)
| ~ sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f318,plain,
! [X0] :
( ( sP9(X0)
| ( ~ lt(sK41(X0),sK40(X0))
& ~ lt(sK40(X0),sK41(X0))
& app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),sK44(X0))) = X0
& ssList(sK44(X0))
& ssList(sK43(X0))
& ssList(sK42(X0))
& ssItem(sK41(X0))
& ssItem(sK40(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) )
| ~ sP9(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK40,sK41,sK42,sK43,sK44])],[f312,f317,f316,f315,f314,f313]) ).
fof(f313,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,sK40(X0))
& ~ lt(sK40(X0),X2)
& app(app(X3,cons(sK40(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK40(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f314,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(X2,sK40(X0))
& ~ lt(sK40(X0),X2)
& app(app(X3,cons(sK40(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK41(X0),sK40(X0))
& ~ lt(sK40(X0),sK41(X0))
& app(app(X3,cons(sK40(X0),X4)),cons(sK41(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK41(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f315,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK41(X0),sK40(X0))
& ~ lt(sK40(X0),sK41(X0))
& app(app(X3,cons(sK40(X0),X4)),cons(sK41(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ lt(sK41(X0),sK40(X0))
& ~ lt(sK40(X0),sK41(X0))
& app(app(sK42(X0),cons(sK40(X0),X4)),cons(sK41(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK42(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f316,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ lt(sK41(X0),sK40(X0))
& ~ lt(sK40(X0),sK41(X0))
& app(app(sK42(X0),cons(sK40(X0),X4)),cons(sK41(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ lt(sK41(X0),sK40(X0))
& ~ lt(sK40(X0),sK41(X0))
& app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),X5)) = X0
& ssList(X5) )
& ssList(sK43(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f317,plain,
! [X0] :
( ? [X5] :
( ~ lt(sK41(X0),sK40(X0))
& ~ lt(sK40(X0),sK41(X0))
& app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),X5)) = X0
& ssList(X5) )
=> ( ~ lt(sK41(X0),sK40(X0))
& ~ lt(sK40(X0),sK41(X0))
& app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),sK44(X0))) = X0
& ssList(sK44(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f312,plain,
! [X0] :
( ( sP9(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) )
| ~ sP9(X0) ) ),
inference(rectify,[],[f311]) ).
fof(f311,plain,
! [X0] :
( ( sP9(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) )
| ~ sP9(X0) ) ),
inference(nnf_transformation,[],[f237]) ).
fof(f510,plain,
! [X0] :
( ssItem(sK40(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f511,plain,
! [X0] :
( ssItem(sK41(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f512,plain,
! [X0] :
( ssList(sK42(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f513,plain,
! [X0] :
( ssList(sK43(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f514,plain,
! [X0] :
( ssList(sK44(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f515,plain,
! [X0] :
( sP9(X0)
| app(app(sK42(X0),cons(sK40(X0),sK43(X0))),cons(sK41(X0),sK44(X0))) = X0 ),
inference(cnf_transformation,[],[f318]) ).
fof(f516,plain,
! [X0] :
( ~ lt(sK40(X0),sK41(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f517,plain,
! [X0] :
( ~ lt(sK41(X0),sK40(X0))
| sP9(X0) ),
inference(cnf_transformation,[],[f318]) ).
fof(f507,plain,
! [X0] :
( ~ sP10(X0)
| ~ strictorderP(X0)
| sP9(X0) ),
inference(cnf_transformation,[],[f310]) ).
fof(f310,plain,
! [X0] :
( ( ( strictorderP(X0)
| ~ sP9(X0) )
& ( sP9(X0)
| ~ strictorderP(X0) ) )
| ~ sP10(X0) ),
inference(nnf_transformation,[],[f238]) ).
fof(f506,plain,
! [X0] :
( sP8(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f236]) ).
fof(f236,plain,
! [X0] :
( sP8(X0)
| ~ ssList(X0) ),
inference(definition_folding,[],[f164,f235,f234]) ).
fof(f234,plain,
! [X0] :
( sP7(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,[sP7])]) ).
fof(f235,plain,
! [X0] :
( ( totalorderP(X0)
<=> sP7(X0) )
| ~ sP8(X0) ),
introduced(predicate_definition_introduction,[new_symbols(naming,[sP8])]) ).
fof(f164,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,[],[f163]) ).
fof(f163,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/sandbox/benchmark/theBenchmark.p',ax9) ).
fof(f627,plain,
! [X10,X8,X6,X9,X7] :
( ~ sP7(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,[],[f497]) ).
fof(f497,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)
| ~ sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f309,plain,
! [X0] :
( ( sP7(X0)
| ( ~ leq(sK36(X0),sK35(X0))
& ~ leq(sK35(X0),sK36(X0))
& app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),sK39(X0))) = X0
& ssList(sK39(X0))
& ssList(sK38(X0))
& ssList(sK37(X0))
& ssItem(sK36(X0))
& ssItem(sK35(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) )
| ~ sP7(X0) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK35,sK36,sK37,sK38,sK39])],[f303,f308,f307,f306,f305,f304]) ).
fof(f304,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,sK35(X0))
& ~ leq(sK35(X0),X2)
& app(app(X3,cons(sK35(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
& ssItem(sK35(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f305,plain,
! [X0] :
( ? [X2] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(X2,sK35(X0))
& ~ leq(sK35(X0),X2)
& app(app(X3,cons(sK35(X0),X4)),cons(X2,X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(X2) )
=> ( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK36(X0),sK35(X0))
& ~ leq(sK35(X0),sK36(X0))
& app(app(X3,cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
& ssItem(sK36(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f306,plain,
! [X0] :
( ? [X3] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK36(X0),sK35(X0))
& ~ leq(sK35(X0),sK36(X0))
& app(app(X3,cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(X3) )
=> ( ? [X4] :
( ? [X5] :
( ~ leq(sK36(X0),sK35(X0))
& ~ leq(sK35(X0),sK36(X0))
& app(app(sK37(X0),cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
& ssList(sK37(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f307,plain,
! [X0] :
( ? [X4] :
( ? [X5] :
( ~ leq(sK36(X0),sK35(X0))
& ~ leq(sK35(X0),sK36(X0))
& app(app(sK37(X0),cons(sK35(X0),X4)),cons(sK36(X0),X5)) = X0
& ssList(X5) )
& ssList(X4) )
=> ( ? [X5] :
( ~ leq(sK36(X0),sK35(X0))
& ~ leq(sK35(X0),sK36(X0))
& app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),X5)) = X0
& ssList(X5) )
& ssList(sK38(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f308,plain,
! [X0] :
( ? [X5] :
( ~ leq(sK36(X0),sK35(X0))
& ~ leq(sK35(X0),sK36(X0))
& app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),X5)) = X0
& ssList(X5) )
=> ( ~ leq(sK36(X0),sK35(X0))
& ~ leq(sK35(X0),sK36(X0))
& app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),sK39(X0))) = X0
& ssList(sK39(X0)) ) ),
introduced(choice_axiom,[]) ).
fof(f303,plain,
! [X0] :
( ( sP7(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) )
| ~ sP7(X0) ) ),
inference(rectify,[],[f302]) ).
fof(f302,plain,
! [X0] :
( ( sP7(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) )
| ~ sP7(X0) ) ),
inference(nnf_transformation,[],[f234]) ).
fof(f498,plain,
! [X0] :
( ssItem(sK35(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f499,plain,
! [X0] :
( ssItem(sK36(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f500,plain,
! [X0] :
( ssList(sK37(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f501,plain,
! [X0] :
( ssList(sK38(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f502,plain,
! [X0] :
( ssList(sK39(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f503,plain,
! [X0] :
( sP7(X0)
| app(app(sK37(X0),cons(sK35(X0),sK38(X0))),cons(sK36(X0),sK39(X0))) = X0 ),
inference(cnf_transformation,[],[f309]) ).
fof(f504,plain,
! [X0] :
( ~ leq(sK35(X0),sK36(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f505,plain,
! [X0] :
( ~ leq(sK36(X0),sK35(X0))
| sP7(X0) ),
inference(cnf_transformation,[],[f309]) ).
fof(f495,plain,
! [X0] :
( ~ sP8(X0)
| ~ totalorderP(X0)
| sP7(X0) ),
inference(cnf_transformation,[],[f301]) ).
fof(f301,plain,
! [X0] :
( ( ( totalorderP(X0)
| ~ sP7(X0) )
& ( sP7(X0)
| ~ totalorderP(X0) ) )
| ~ sP8(X0) ),
inference(nnf_transformation,[],[f235]) ).
fof(f487,plain,
! [X0] :
( ssItem(sK30(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f488,plain,
! [X0] :
( ssItem(sK31(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f489,plain,
! [X0] :
( ssList(sK32(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f490,plain,
! [X0] :
( ssList(sK33(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f491,plain,
! [X0] :
( ssList(sK34(X0))
| sP5(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f492,plain,
! [X0] :
( sP5(X0)
| app(app(sK32(X0),cons(sK30(X0),sK33(X0))),cons(sK31(X0),sK34(X0))) = X0 ),
inference(cnf_transformation,[],[f300]) ).
fof(f493,plain,
! [X0] :
( sP5(X0)
| sK30(X0) = sK31(X0) ),
inference(cnf_transformation,[],[f300]) ).
fof(f477,plain,
! [X0] :
( ssItem(sK27(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f285,plain,
! [X0] :
( ( hd(X0) = sK27(X0)
& ssItem(sK27(X0)) )
| nil = X0
| ~ ssList(X0) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK27])],[f157,f284]) ).
fof(f284,plain,
! [X0] :
( ? [X1] :
( hd(X0) = X1
& ssItem(X1) )
=> ( hd(X0) = sK27(X0)
& ssItem(sK27(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/sandbox/benchmark/theBenchmark.p',ax75) ).
fof(f478,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| hd(X0) = sK27(X0) ),
inference(cnf_transformation,[],[f285]) ).
fof(f474,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/sandbox/benchmark/theBenchmark.p',ax22) ).
fof(f471,plain,
! [X0] :
( ssList(sK25(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f472,plain,
! [X0] :
( ssItem(sK26(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f283]) ).
fof(f468,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f145]) ).
fof(f145,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f55]) ).
fof(f55,axiom,
! [X0] :
( ssList(X0)
=> segmentP(X0,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax55) ).
fof(f465,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/sandbox/benchmark/theBenchmark.p',ax42) ).
fof(f463,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/sandbox/benchmark/theBenchmark.p',ax57) ).
fof(f460,plain,
! [X2,X0,X1] :
( ~ memberP(app(X1,X2),X0)
| memberP(X1,X0)
| memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f280,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(app(X1,X2),X0)
| ( ~ memberP(X2,X0)
& ~ memberP(X1,X0) ) )
& ( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f279]) ).
fof(f279,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/sandbox/benchmark/theBenchmark.p',ax36) ).
fof(f461,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f462,plain,
! [X2,X0,X1] :
( memberP(app(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f280]) ).
fof(f455,plain,
! [X0,X1] :
( ~ sP3(X0,X1)
| nil = X0
| strictorderedP(X0) ),
inference(cnf_transformation,[],[f278]) ).
fof(f622,plain,
! [X1] : sP3(nil,X1),
inference(equality_resolution,[],[f457]) ).
fof(f457,plain,
! [X0,X1] :
( sP3(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f278]) ).
fof(f458,plain,
! [X0,X1] :
( ~ lt(X1,hd(X0))
| sP3(X0,X1)
| ~ strictorderedP(X0)
| nil = X0 ),
inference(cnf_transformation,[],[f278]) ).
fof(f453,plain,
! [X0,X1] :
( strictorderedP(cons(X0,X1))
| ~ sP3(X1,X0)
| ~ sP4(X0,X1) ),
inference(cnf_transformation,[],[f275]) ).
fof(f447,plain,
! [X0,X1] :
( ~ sP1(X0,X1)
| nil = X0
| totalorderedP(X0) ),
inference(cnf_transformation,[],[f274]) ).
fof(f448,plain,
! [X0,X1] :
( leq(X1,hd(X0))
| nil = X0
| ~ sP1(X0,X1) ),
inference(cnf_transformation,[],[f274]) ).
fof(f620,plain,
! [X1] : sP1(nil,X1),
inference(equality_resolution,[],[f449]) ).
fof(f449,plain,
! [X0,X1] :
( sP1(X0,X1)
| nil != X0 ),
inference(cnf_transformation,[],[f274]) ).
fof(f442,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,[],[f270]) ).
fof(f438,plain,
! [X2,X0,X1] :
( ~ memberP(cons(X1,X2),X0)
| X0 = X1
| memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f268,plain,
! [X0] :
( ! [X1] :
( ! [X2] :
( ( ( memberP(cons(X1,X2),X0)
| ( ~ memberP(X2,X0)
& X0 != X1 ) )
& ( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0) ) )
| ~ ssList(X2) )
| ~ ssItem(X1) )
| ~ ssItem(X0) ),
inference(flattening,[],[f267]) ).
fof(f267,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/sandbox/benchmark/theBenchmark.p',ax37) ).
fof(f646,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f618]) ).
fof(f618,plain,
! [X2,X1] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f439]) ).
fof(f439,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| X0 != X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f440,plain,
! [X2,X0,X1] :
( memberP(cons(X1,X2),X0)
| ~ memberP(X2,X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f268]) ).
fof(f437,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/sandbox/benchmark/theBenchmark.p',ax34) ).
fof(f436,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/sandbox/benchmark/theBenchmark.p',ax91) ).
fof(f435,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/sandbox/benchmark/theBenchmark.p',ax30) ).
fof(f434,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/sandbox/benchmark/theBenchmark.p',ax88) ).
fof(f433,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/sandbox/benchmark/theBenchmark.p',ax95) ).
fof(f647,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1) ),
inference(duplicate_literal_removal,[],[f617]) ).
fof(f617,plain,
! [X1] :
( ~ lt(X1,X1)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(equality_resolution,[],[f430]) ).
fof(f430,plain,
! [X0,X1] :
( X0 != X1
| ~ lt(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f432,plain,
! [X0,X1] :
( lt(X0,X1)
| ~ leq(X0,X1)
| X0 = X1
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f266]) ).
fof(f428,plain,
! [X0,X1] :
( ~ geq(X0,X1)
| leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f264,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/sandbox/benchmark/theBenchmark.p',ax32) ).
fof(f429,plain,
! [X0,X1] :
( geq(X0,X1)
| ~ leq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f264]) ).
fof(f426,plain,
! [X0,X1] :
( ~ gt(X0,X1)
| lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f263]) ).
fof(f263,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/sandbox/benchmark/theBenchmark.p',ax35) ).
fof(f427,plain,
! [X0,X1] :
( gt(X0,X1)
| ~ lt(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f263]) ).
fof(f423,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/sandbox/benchmark/theBenchmark.p',ax29) ).
fof(f422,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/sandbox/benchmark/theBenchmark.p',ax87) ).
fof(f421,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/sandbox/benchmark/theBenchmark.p',ax33) ).
fof(f420,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/sandbox/benchmark/theBenchmark.p',ax92) ).
fof(f419,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/sandbox/benchmark/theBenchmark.p',ax94) ).
fof(f418,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f110]) ).
fof(f110,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/sandbox/benchmark/theBenchmark.p',ax73) ).
fof(f417,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/sandbox/benchmark/theBenchmark.p',ax68) ).
fof(f415,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/sandbox/benchmark/theBenchmark.p',ax61) ).
fof(f414,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[],[f106]) ).
fof(f106,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/sandbox/benchmark/theBenchmark.p',ax63) ).
fof(f413,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/sandbox/benchmark/theBenchmark.p',ax71) ).
fof(f410,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/sandbox/benchmark/theBenchmark.p',ax89) ).
fof(f408,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/sandbox/benchmark/theBenchmark.p',ax38) ).
fof(f406,plain,
equalelemsP(nil),
inference(cnf_transformation,[],[f74]) ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax74) ).
fof(f405,plain,
totalorderedP(nil),
inference(cnf_transformation,[],[f66]) ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax66) ).
fof(f404,plain,
strictorderedP(nil),
inference(cnf_transformation,[],[f69]) ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax69) ).
fof(f403,plain,
strictorderP(nil),
inference(cnf_transformation,[],[f64]) ).
fof(f64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax64) ).
fof(f402,plain,
cyclefreeP(nil),
inference(cnf_transformation,[],[f60]) ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax60) ).
fof(f401,plain,
totalorderP(nil),
inference(cnf_transformation,[],[f62]) ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax62) ).
fof(f400,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[],[f72]) ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax72) ).
fof(f399,plain,
~ singletonP(nil),
inference(cnf_transformation,[],[f39]) ).
fof(f39,axiom,
~ singletonP(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax39) ).
fof(f388,plain,
ssList(sK22),
inference(cnf_transformation,[],[f261]) ).
fof(f389,plain,
ssList(sK23),
inference(cnf_transformation,[],[f261]) ).
fof(f396,plain,
equalelemsP(sK22),
inference(cnf_transformation,[],[f261]) ).
fof(f397,plain,
! [X6,X7,X5] :
( app(X7,cons(X5,nil)) != sK22
| ~ ssList(X7)
| app(cons(X5,nil),X6) != sK24
| ~ ssList(X6)
| ~ ssItem(X5) ),
inference(cnf_transformation,[],[f261]) ).
fof(f398,plain,
( nil != sK22
| nil = sK23 ),
inference(cnf_transformation,[],[f261]) ).
fof(f382,plain,
! [X2,X0,X1] :
( memberP(X2,sK19(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f255]) ).
fof(f383,plain,
! [X2,X0,X1] :
( memberP(X1,sK19(X0,X1,X2))
| ~ sP0(X0,X1,X2) ),
inference(cnf_transformation,[],[f255]) ).
fof(f8068,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_18
| spl72_72 ),
inference(resolution,[],[f8065,f2947]) ).
fof(f2947,plain,
( ! [X0] :
( frontsegP(cons(sK71,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_18 ),
inference(subsumption_resolution,[],[f2946,f407]) ).
fof(f2946,plain,
( ! [X0] :
( frontsegP(cons(sK71,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_18 ),
inference(subsumption_resolution,[],[f2912,f2054]) ).
fof(f2912,plain,
( ! [X0] :
( frontsegP(cons(sK71,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(cons(sK71,sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_18 ),
inference(superposition,[],[f606,f2100]) ).
fof(f2100,plain,
( cons(sK71,sK20) = app(nil,cons(sK71,sK20))
| ~ spl72_18 ),
inference(resolution,[],[f2054,f470]) ).
fof(f8067,plain,
( ~ spl72_71
| spl72_72
| ~ spl72_18 ),
inference(avatar_split_clause,[],[f7918,f2052,f8064,f8060]) ).
fof(f7918,plain,
( frontsegP(cons(sK71,sK20),nil)
| ~ ssList(sK69(cons(sK71,sK20),nil))
| ~ spl72_18 ),
inference(subsumption_resolution,[],[f7905,f407]) ).
fof(f7905,plain,
( frontsegP(cons(sK71,sK20),nil)
| ~ ssList(sK69(cons(sK71,sK20),nil))
| ~ ssList(nil)
| ~ spl72_18 ),
inference(superposition,[],[f2128,f7495]) ).
fof(f7495,plain,
( cons(sK71,sK20) = app(nil,sK69(cons(sK71,sK20),nil))
| ~ spl72_18 ),
inference(resolution,[],[f2686,f2054]) ).
fof(f8036,plain,
( ~ spl72_17
| spl72_69
| ~ spl72_70 ),
inference(avatar_contradiction_clause,[],[f8035]) ).
fof(f8035,plain,
( $false
| ~ spl72_17
| spl72_69
| ~ spl72_70 ),
inference(subsumption_resolution,[],[f8034,f2049]) ).
fof(f8034,plain,
( ~ ssList(cons(sK71,nil))
| spl72_69
| ~ spl72_70 ),
inference(subsumption_resolution,[],[f8033,f407]) ).
fof(f8033,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK71,nil))
| spl72_69
| ~ spl72_70 ),
inference(subsumption_resolution,[],[f8032,f8020]) ).
fof(f8020,plain,
( frontsegP(cons(sK71,nil),nil)
| ~ spl72_70 ),
inference(avatar_component_clause,[],[f8018]) ).
fof(f8018,plain,
( spl72_70
<=> frontsegP(cons(sK71,nil),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_70])]) ).
fof(f8032,plain,
( ~ frontsegP(cons(sK71,nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK71,nil))
| spl72_69 ),
inference(resolution,[],[f8016,f595]) ).
fof(f8016,plain,
( ~ ssList(sK69(cons(sK71,nil),nil))
| spl72_69 ),
inference(avatar_component_clause,[],[f8014]) ).
fof(f8014,plain,
( spl72_69
<=> ssList(sK69(cons(sK71,nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_69])]) ).
fof(f8028,plain,
( ~ spl72_17
| spl72_70 ),
inference(avatar_contradiction_clause,[],[f8027]) ).
fof(f8027,plain,
( $false
| ~ spl72_17
| spl72_70 ),
inference(subsumption_resolution,[],[f8023,f2049]) ).
fof(f8023,plain,
( ~ ssList(cons(sK71,nil))
| spl72_70 ),
inference(resolution,[],[f8019,f466]) ).
fof(f8019,plain,
( ~ frontsegP(cons(sK71,nil),nil)
| spl72_70 ),
inference(avatar_component_clause,[],[f8018]) ).
fof(f8026,plain,
( ~ spl72_17
| spl72_70 ),
inference(avatar_contradiction_clause,[],[f8025]) ).
fof(f8025,plain,
( $false
| ~ spl72_17
| spl72_70 ),
inference(subsumption_resolution,[],[f8024,f407]) ).
fof(f8024,plain,
( ~ ssList(nil)
| ~ spl72_17
| spl72_70 ),
inference(subsumption_resolution,[],[f8022,f650]) ).
fof(f8022,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_17
| spl72_70 ),
inference(resolution,[],[f8019,f2945]) ).
fof(f2945,plain,
( ! [X0] :
( frontsegP(cons(sK71,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f2944,f407]) ).
fof(f2944,plain,
( ! [X0] :
( frontsegP(cons(sK71,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f2911,f2049]) ).
fof(f2911,plain,
( ! [X0] :
( frontsegP(cons(sK71,nil),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(cons(sK71,nil))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_17 ),
inference(superposition,[],[f606,f2061]) ).
fof(f2061,plain,
( cons(sK71,nil) = app(nil,cons(sK71,nil))
| ~ spl72_17 ),
inference(resolution,[],[f2049,f470]) ).
fof(f8021,plain,
( ~ spl72_69
| spl72_70
| ~ spl72_17 ),
inference(avatar_split_clause,[],[f7887,f2048,f8018,f8014]) ).
fof(f7887,plain,
( frontsegP(cons(sK71,nil),nil)
| ~ ssList(sK69(cons(sK71,nil),nil))
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f7874,f407]) ).
fof(f7874,plain,
( frontsegP(cons(sK71,nil),nil)
| ~ ssList(sK69(cons(sK71,nil),nil))
| ~ ssList(nil)
| ~ spl72_17 ),
inference(superposition,[],[f2128,f7494]) ).
fof(f7494,plain,
( cons(sK71,nil) = app(nil,sK69(cons(sK71,nil),nil))
| ~ spl72_17 ),
inference(resolution,[],[f2686,f2049]) ).
fof(f7990,plain,
( ~ spl72_16
| spl72_67
| ~ spl72_68 ),
inference(avatar_contradiction_clause,[],[f7989]) ).
fof(f7989,plain,
( $false
| ~ spl72_16
| spl72_67
| ~ spl72_68 ),
inference(subsumption_resolution,[],[f7988,f2005]) ).
fof(f7988,plain,
( ~ ssList(cons(sK70,sK20))
| spl72_67
| ~ spl72_68 ),
inference(subsumption_resolution,[],[f7987,f407]) ).
fof(f7987,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK70,sK20))
| spl72_67
| ~ spl72_68 ),
inference(subsumption_resolution,[],[f7986,f7974]) ).
fof(f7974,plain,
( frontsegP(cons(sK70,sK20),nil)
| ~ spl72_68 ),
inference(avatar_component_clause,[],[f7972]) ).
fof(f7972,plain,
( spl72_68
<=> frontsegP(cons(sK70,sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_68])]) ).
fof(f7986,plain,
( ~ frontsegP(cons(sK70,sK20),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK70,sK20))
| spl72_67 ),
inference(resolution,[],[f7970,f595]) ).
fof(f7970,plain,
( ~ ssList(sK69(cons(sK70,sK20),nil))
| spl72_67 ),
inference(avatar_component_clause,[],[f7968]) ).
fof(f7968,plain,
( spl72_67
<=> ssList(sK69(cons(sK70,sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_67])]) ).
fof(f7982,plain,
( ~ spl72_16
| spl72_68 ),
inference(avatar_contradiction_clause,[],[f7981]) ).
fof(f7981,plain,
( $false
| ~ spl72_16
| spl72_68 ),
inference(subsumption_resolution,[],[f7977,f2005]) ).
fof(f7977,plain,
( ~ ssList(cons(sK70,sK20))
| spl72_68 ),
inference(resolution,[],[f7973,f466]) ).
fof(f7973,plain,
( ~ frontsegP(cons(sK70,sK20),nil)
| spl72_68 ),
inference(avatar_component_clause,[],[f7972]) ).
fof(f7980,plain,
( ~ spl72_16
| spl72_68 ),
inference(avatar_contradiction_clause,[],[f7979]) ).
fof(f7979,plain,
( $false
| ~ spl72_16
| spl72_68 ),
inference(subsumption_resolution,[],[f7978,f407]) ).
fof(f7978,plain,
( ~ ssList(nil)
| ~ spl72_16
| spl72_68 ),
inference(subsumption_resolution,[],[f7976,f650]) ).
fof(f7976,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_16
| spl72_68 ),
inference(resolution,[],[f7973,f2943]) ).
fof(f2943,plain,
( ! [X0] :
( frontsegP(cons(sK70,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_16 ),
inference(subsumption_resolution,[],[f2942,f407]) ).
fof(f2942,plain,
( ! [X0] :
( frontsegP(cons(sK70,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_16 ),
inference(subsumption_resolution,[],[f2910,f2005]) ).
fof(f2910,plain,
( ! [X0] :
( frontsegP(cons(sK70,sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(cons(sK70,sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_16 ),
inference(superposition,[],[f606,f2024]) ).
fof(f2024,plain,
( cons(sK70,sK20) = app(nil,cons(sK70,sK20))
| ~ spl72_16 ),
inference(resolution,[],[f2005,f470]) ).
fof(f7975,plain,
( ~ spl72_67
| spl72_68
| ~ spl72_16 ),
inference(avatar_split_clause,[],[f7856,f2003,f7972,f7968]) ).
fof(f7856,plain,
( frontsegP(cons(sK70,sK20),nil)
| ~ ssList(sK69(cons(sK70,sK20),nil))
| ~ spl72_16 ),
inference(subsumption_resolution,[],[f7843,f407]) ).
fof(f7843,plain,
( frontsegP(cons(sK70,sK20),nil)
| ~ ssList(sK69(cons(sK70,sK20),nil))
| ~ ssList(nil)
| ~ spl72_16 ),
inference(superposition,[],[f2128,f7493]) ).
fof(f7493,plain,
( cons(sK70,sK20) = app(nil,sK69(cons(sK70,sK20),nil))
| ~ spl72_16 ),
inference(resolution,[],[f2686,f2005]) ).
fof(f7944,plain,
( ~ spl72_15
| spl72_65
| ~ spl72_66 ),
inference(avatar_contradiction_clause,[],[f7943]) ).
fof(f7943,plain,
( $false
| ~ spl72_15
| spl72_65
| ~ spl72_66 ),
inference(subsumption_resolution,[],[f7942,f2000]) ).
fof(f7942,plain,
( ~ ssList(cons(sK70,nil))
| spl72_65
| ~ spl72_66 ),
inference(subsumption_resolution,[],[f7941,f407]) ).
fof(f7941,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK70,nil))
| spl72_65
| ~ spl72_66 ),
inference(subsumption_resolution,[],[f7940,f7928]) ).
fof(f7928,plain,
( frontsegP(cons(sK70,nil),nil)
| ~ spl72_66 ),
inference(avatar_component_clause,[],[f7926]) ).
fof(f7926,plain,
( spl72_66
<=> frontsegP(cons(sK70,nil),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_66])]) ).
fof(f7940,plain,
( ~ frontsegP(cons(sK70,nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK70,nil))
| spl72_65 ),
inference(resolution,[],[f7924,f595]) ).
fof(f7924,plain,
( ~ ssList(sK69(cons(sK70,nil),nil))
| spl72_65 ),
inference(avatar_component_clause,[],[f7922]) ).
fof(f7922,plain,
( spl72_65
<=> ssList(sK69(cons(sK70,nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_65])]) ).
fof(f7936,plain,
( ~ spl72_15
| spl72_66 ),
inference(avatar_contradiction_clause,[],[f7935]) ).
fof(f7935,plain,
( $false
| ~ spl72_15
| spl72_66 ),
inference(subsumption_resolution,[],[f7931,f2000]) ).
fof(f7931,plain,
( ~ ssList(cons(sK70,nil))
| spl72_66 ),
inference(resolution,[],[f7927,f466]) ).
fof(f7927,plain,
( ~ frontsegP(cons(sK70,nil),nil)
| spl72_66 ),
inference(avatar_component_clause,[],[f7926]) ).
fof(f7934,plain,
( ~ spl72_15
| spl72_66 ),
inference(avatar_contradiction_clause,[],[f7933]) ).
fof(f7933,plain,
( $false
| ~ spl72_15
| spl72_66 ),
inference(subsumption_resolution,[],[f7932,f407]) ).
fof(f7932,plain,
( ~ ssList(nil)
| ~ spl72_15
| spl72_66 ),
inference(subsumption_resolution,[],[f7930,f650]) ).
fof(f7930,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_15
| spl72_66 ),
inference(resolution,[],[f7927,f2941]) ).
fof(f7929,plain,
( ~ spl72_65
| spl72_66
| ~ spl72_15 ),
inference(avatar_split_clause,[],[f7825,f1999,f7926,f7922]) ).
fof(f7825,plain,
( frontsegP(cons(sK70,nil),nil)
| ~ ssList(sK69(cons(sK70,nil),nil))
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f7812,f407]) ).
fof(f7812,plain,
( frontsegP(cons(sK70,nil),nil)
| ~ ssList(sK69(cons(sK70,nil),nil))
| ~ ssList(nil)
| ~ spl72_15 ),
inference(superposition,[],[f2128,f7492]) ).
fof(f7492,plain,
( cons(sK70,nil) = app(nil,sK69(cons(sK70,nil),nil))
| ~ spl72_15 ),
inference(resolution,[],[f2686,f2000]) ).
fof(f7637,plain,
( ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_63
| ~ spl72_64 ),
inference(avatar_contradiction_clause,[],[f7636]) ).
fof(f7636,plain,
( $false
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_63
| ~ spl72_64 ),
inference(subsumption_resolution,[],[f7635,f1775]) ).
fof(f7635,plain,
( ~ ssList(tl(sK20))
| spl72_63
| ~ spl72_64 ),
inference(subsumption_resolution,[],[f7634,f407]) ).
fof(f7634,plain,
( ~ ssList(nil)
| ~ ssList(tl(sK20))
| spl72_63
| ~ spl72_64 ),
inference(subsumption_resolution,[],[f7633,f7621]) ).
fof(f7621,plain,
( frontsegP(tl(sK20),nil)
| ~ spl72_64 ),
inference(avatar_component_clause,[],[f7619]) ).
fof(f7619,plain,
( spl72_64
<=> frontsegP(tl(sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_64])]) ).
fof(f7633,plain,
( ~ frontsegP(tl(sK20),nil)
| ~ ssList(nil)
| ~ ssList(tl(sK20))
| spl72_63 ),
inference(resolution,[],[f7617,f595]) ).
fof(f7617,plain,
( ~ ssList(sK69(tl(sK20),nil))
| spl72_63 ),
inference(avatar_component_clause,[],[f7615]) ).
fof(f7615,plain,
( spl72_63
<=> ssList(sK69(tl(sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_63])]) ).
fof(f7629,plain,
( ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_64 ),
inference(avatar_contradiction_clause,[],[f7628]) ).
fof(f7628,plain,
( $false
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_64 ),
inference(subsumption_resolution,[],[f7624,f1775]) ).
fof(f7624,plain,
( ~ ssList(tl(sK20))
| spl72_64 ),
inference(resolution,[],[f7620,f466]) ).
fof(f7620,plain,
( ~ frontsegP(tl(sK20),nil)
| spl72_64 ),
inference(avatar_component_clause,[],[f7619]) ).
fof(f7627,plain,
( ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_64 ),
inference(avatar_contradiction_clause,[],[f7626]) ).
fof(f7626,plain,
( $false
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_64 ),
inference(subsumption_resolution,[],[f7625,f407]) ).
fof(f7625,plain,
( ~ ssList(nil)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_64 ),
inference(subsumption_resolution,[],[f7623,f650]) ).
fof(f7623,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_64 ),
inference(resolution,[],[f7620,f2960]) ).
fof(f2960,plain,
( ! [X0] :
( frontsegP(tl(sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f2959,f1769]) ).
fof(f2959,plain,
( ! [X0] :
( frontsegP(sK25(sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f2958,f407]) ).
fof(f2958,plain,
( ! [X0] :
( frontsegP(sK25(sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f2918,f1602]) ).
fof(f2918,plain,
( ! [X0] :
( frontsegP(sK25(sK20),X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sK25(sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_13 ),
inference(superposition,[],[f606,f1614]) ).
fof(f7622,plain,
( ~ spl72_63
| spl72_64
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(avatar_split_clause,[],[f7613,f1601,f1375,f1273,f7619,f7615]) ).
fof(f7613,plain,
( frontsegP(tl(sK20),nil)
| ~ ssList(sK69(tl(sK20),nil))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f7600,f407]) ).
fof(f7600,plain,
( frontsegP(tl(sK20),nil)
| ~ ssList(sK69(tl(sK20),nil))
| ~ ssList(nil)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(superposition,[],[f2128,f7549]) ).
fof(f7549,plain,
( tl(sK20) = app(nil,sK69(tl(sK20),nil))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f7506,f1769]) ).
fof(f7506,plain,
( sK25(sK20) = app(nil,sK69(sK25(sK20),nil))
| ~ spl72_13 ),
inference(resolution,[],[f2686,f1602]) ).
fof(f7564,plain,
( ~ spl72_18
| spl72_61
| ~ spl72_62 ),
inference(avatar_contradiction_clause,[],[f7563]) ).
fof(f7563,plain,
( $false
| ~ spl72_18
| spl72_61
| ~ spl72_62 ),
inference(subsumption_resolution,[],[f7562,f2054]) ).
fof(f7562,plain,
( ~ ssList(cons(sK71,sK20))
| spl72_61
| ~ spl72_62 ),
inference(subsumption_resolution,[],[f7561,f407]) ).
fof(f7561,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK71,sK20))
| spl72_61
| ~ spl72_62 ),
inference(subsumption_resolution,[],[f7560,f7473]) ).
fof(f7473,plain,
( rearsegP(cons(sK71,sK20),nil)
| ~ spl72_62 ),
inference(avatar_component_clause,[],[f7471]) ).
fof(f7471,plain,
( spl72_62
<=> rearsegP(cons(sK71,sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_62])]) ).
fof(f7560,plain,
( ~ rearsegP(cons(sK71,sK20),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK71,sK20))
| spl72_61 ),
inference(resolution,[],[f7469,f588]) ).
fof(f7469,plain,
( ~ ssList(sK66(cons(sK71,sK20),nil))
| spl72_61 ),
inference(avatar_component_clause,[],[f7467]) ).
fof(f7467,plain,
( spl72_61
<=> ssList(sK66(cons(sK71,sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_61])]) ).
fof(f7485,plain,
( ~ spl72_4
| ~ spl72_17
| spl72_62 ),
inference(avatar_contradiction_clause,[],[f7484]) ).
fof(f7484,plain,
( $false
| ~ spl72_4
| ~ spl72_17
| spl72_62 ),
inference(subsumption_resolution,[],[f7483,f407]) ).
fof(f7483,plain,
( ~ ssList(nil)
| ~ spl72_4
| ~ spl72_17
| spl72_62 ),
inference(subsumption_resolution,[],[f7477,f2097]) ).
fof(f7477,plain,
( ~ rearsegP(sK20,nil)
| ~ ssList(nil)
| ~ spl72_17
| spl72_62 ),
inference(resolution,[],[f7472,f2835]) ).
fof(f2835,plain,
( ! [X0] :
( rearsegP(cons(sK71,sK20),X0)
| ~ rearsegP(sK20,X0)
| ~ ssList(X0) )
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f2834,f386]) ).
fof(f2834,plain,
( ! [X0] :
( rearsegP(cons(sK71,sK20),X0)
| ~ rearsegP(sK20,X0)
| ~ ssList(X0)
| ~ ssList(sK20) )
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f2800,f2049]) ).
fof(f2800,plain,
! [X0] :
( rearsegP(cons(sK71,sK20),X0)
| ~ rearsegP(sK20,X0)
| ~ ssList(cons(sK71,nil))
| ~ ssList(X0)
| ~ ssList(sK20) ),
inference(superposition,[],[f605,f1986]) ).
fof(f7472,plain,
( ~ rearsegP(cons(sK71,sK20),nil)
| spl72_62 ),
inference(avatar_component_clause,[],[f7471]) ).
fof(f7482,plain,
( ~ spl72_18
| spl72_62 ),
inference(avatar_contradiction_clause,[],[f7481]) ).
fof(f7481,plain,
( $false
| ~ spl72_18
| spl72_62 ),
inference(subsumption_resolution,[],[f7480,f407]) ).
fof(f7480,plain,
( ~ ssList(nil)
| ~ spl72_18
| spl72_62 ),
inference(subsumption_resolution,[],[f7476,f648]) ).
fof(f7476,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_18
| spl72_62 ),
inference(resolution,[],[f7472,f2843]) ).
fof(f2843,plain,
( ! [X0] :
( rearsegP(cons(sK71,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_18 ),
inference(subsumption_resolution,[],[f2842,f407]) ).
fof(f2842,plain,
( ! [X0] :
( rearsegP(cons(sK71,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_18 ),
inference(subsumption_resolution,[],[f2804,f2054]) ).
fof(f2804,plain,
( ! [X0] :
( rearsegP(cons(sK71,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(cons(sK71,sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_18 ),
inference(superposition,[],[f605,f2099]) ).
fof(f2099,plain,
( cons(sK71,sK20) = app(cons(sK71,sK20),nil)
| ~ spl72_18 ),
inference(resolution,[],[f2054,f469]) ).
fof(f7479,plain,
( ~ spl72_18
| spl72_62 ),
inference(avatar_contradiction_clause,[],[f7478]) ).
fof(f7478,plain,
( $false
| ~ spl72_18
| spl72_62 ),
inference(subsumption_resolution,[],[f7475,f2054]) ).
fof(f7475,plain,
( ~ ssList(cons(sK71,sK20))
| spl72_62 ),
inference(resolution,[],[f7472,f464]) ).
fof(f7474,plain,
( ~ spl72_61
| spl72_62
| ~ spl72_18 ),
inference(avatar_split_clause,[],[f7163,f2052,f7471,f7467]) ).
fof(f7163,plain,
( rearsegP(cons(sK71,sK20),nil)
| ~ ssList(sK66(cons(sK71,sK20),nil))
| ~ spl72_18 ),
inference(subsumption_resolution,[],[f7149,f407]) ).
fof(f7149,plain,
( rearsegP(cons(sK71,sK20),nil)
| ~ ssList(sK66(cons(sK71,sK20),nil))
| ~ ssList(nil)
| ~ spl72_18 ),
inference(superposition,[],[f1990,f6835]) ).
fof(f6835,plain,
( cons(sK71,sK20) = app(sK66(cons(sK71,sK20),nil),nil)
| ~ spl72_18 ),
inference(resolution,[],[f2609,f2054]) ).
fof(f7445,plain,
( ~ spl72_17
| spl72_59
| ~ spl72_60 ),
inference(avatar_contradiction_clause,[],[f7444]) ).
fof(f7444,plain,
( $false
| ~ spl72_17
| spl72_59
| ~ spl72_60 ),
inference(subsumption_resolution,[],[f7443,f2049]) ).
fof(f7443,plain,
( ~ ssList(cons(sK71,nil))
| spl72_59
| ~ spl72_60 ),
inference(subsumption_resolution,[],[f7442,f407]) ).
fof(f7442,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK71,nil))
| spl72_59
| ~ spl72_60 ),
inference(subsumption_resolution,[],[f7441,f7429]) ).
fof(f7429,plain,
( rearsegP(cons(sK71,nil),nil)
| ~ spl72_60 ),
inference(avatar_component_clause,[],[f7427]) ).
fof(f7427,plain,
( spl72_60
<=> rearsegP(cons(sK71,nil),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_60])]) ).
fof(f7441,plain,
( ~ rearsegP(cons(sK71,nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK71,nil))
| spl72_59 ),
inference(resolution,[],[f7425,f588]) ).
fof(f7425,plain,
( ~ ssList(sK66(cons(sK71,nil),nil))
| spl72_59 ),
inference(avatar_component_clause,[],[f7423]) ).
fof(f7423,plain,
( spl72_59
<=> ssList(sK66(cons(sK71,nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_59])]) ).
fof(f7437,plain,
( ~ spl72_17
| spl72_60 ),
inference(avatar_contradiction_clause,[],[f7436]) ).
fof(f7436,plain,
( $false
| ~ spl72_17
| spl72_60 ),
inference(subsumption_resolution,[],[f7435,f407]) ).
fof(f7435,plain,
( ~ ssList(nil)
| ~ spl72_17
| spl72_60 ),
inference(subsumption_resolution,[],[f7432,f648]) ).
fof(f7432,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_17
| spl72_60 ),
inference(resolution,[],[f7428,f2839]) ).
fof(f2839,plain,
( ! [X0] :
( rearsegP(cons(sK71,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f2838,f407]) ).
fof(f2838,plain,
( ! [X0] :
( rearsegP(cons(sK71,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f2802,f2049]) ).
fof(f2802,plain,
( ! [X0] :
( rearsegP(cons(sK71,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(cons(sK71,nil))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_17 ),
inference(superposition,[],[f605,f2060]) ).
fof(f2060,plain,
( cons(sK71,nil) = app(cons(sK71,nil),nil)
| ~ spl72_17 ),
inference(resolution,[],[f2049,f469]) ).
fof(f7428,plain,
( ~ rearsegP(cons(sK71,nil),nil)
| spl72_60 ),
inference(avatar_component_clause,[],[f7427]) ).
fof(f7434,plain,
( ~ spl72_17
| spl72_60 ),
inference(avatar_contradiction_clause,[],[f7433]) ).
fof(f7433,plain,
( $false
| ~ spl72_17
| spl72_60 ),
inference(subsumption_resolution,[],[f7431,f2049]) ).
fof(f7431,plain,
( ~ ssList(cons(sK71,nil))
| spl72_60 ),
inference(resolution,[],[f7428,f464]) ).
fof(f7430,plain,
( ~ spl72_59
| spl72_60
| ~ spl72_17 ),
inference(avatar_split_clause,[],[f7131,f2048,f7427,f7423]) ).
fof(f7131,plain,
( rearsegP(cons(sK71,nil),nil)
| ~ ssList(sK66(cons(sK71,nil),nil))
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f7117,f407]) ).
fof(f7117,plain,
( rearsegP(cons(sK71,nil),nil)
| ~ ssList(sK66(cons(sK71,nil),nil))
| ~ ssList(nil)
| ~ spl72_17 ),
inference(superposition,[],[f1990,f6834]) ).
fof(f6834,plain,
( cons(sK71,nil) = app(sK66(cons(sK71,nil),nil),nil)
| ~ spl72_17 ),
inference(resolution,[],[f2609,f2049]) ).
fof(f7308,plain,
( ~ spl72_16
| spl72_57
| ~ spl72_58 ),
inference(avatar_contradiction_clause,[],[f7307]) ).
fof(f7307,plain,
( $false
| ~ spl72_16
| spl72_57
| ~ spl72_58 ),
inference(subsumption_resolution,[],[f7306,f2005]) ).
fof(f7306,plain,
( ~ ssList(cons(sK70,sK20))
| spl72_57
| ~ spl72_58 ),
inference(subsumption_resolution,[],[f7305,f407]) ).
fof(f7305,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK70,sK20))
| spl72_57
| ~ spl72_58 ),
inference(subsumption_resolution,[],[f7304,f7288]) ).
fof(f7288,plain,
( rearsegP(cons(sK70,sK20),nil)
| ~ spl72_58 ),
inference(avatar_component_clause,[],[f7286]) ).
fof(f7286,plain,
( spl72_58
<=> rearsegP(cons(sK70,sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_58])]) ).
fof(f7304,plain,
( ~ rearsegP(cons(sK70,sK20),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK70,sK20))
| spl72_57 ),
inference(resolution,[],[f7284,f588]) ).
fof(f7284,plain,
( ~ ssList(sK66(cons(sK70,sK20),nil))
| spl72_57 ),
inference(avatar_component_clause,[],[f7282]) ).
fof(f7282,plain,
( spl72_57
<=> ssList(sK66(cons(sK70,sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_57])]) ).
fof(f7300,plain,
( ~ spl72_4
| ~ spl72_15
| spl72_58 ),
inference(avatar_contradiction_clause,[],[f7299]) ).
fof(f7299,plain,
( $false
| ~ spl72_4
| ~ spl72_15
| spl72_58 ),
inference(subsumption_resolution,[],[f7298,f407]) ).
fof(f7298,plain,
( ~ ssList(nil)
| ~ spl72_4
| ~ spl72_15
| spl72_58 ),
inference(subsumption_resolution,[],[f7292,f2097]) ).
fof(f7292,plain,
( ~ rearsegP(sK20,nil)
| ~ ssList(nil)
| ~ spl72_15
| spl72_58 ),
inference(resolution,[],[f7287,f2833]) ).
fof(f2833,plain,
( ! [X0] :
( rearsegP(cons(sK70,sK20),X0)
| ~ rearsegP(sK20,X0)
| ~ ssList(X0) )
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f2832,f386]) ).
fof(f2832,plain,
( ! [X0] :
( rearsegP(cons(sK70,sK20),X0)
| ~ rearsegP(sK20,X0)
| ~ ssList(X0)
| ~ ssList(sK20) )
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f2799,f2000]) ).
fof(f2799,plain,
! [X0] :
( rearsegP(cons(sK70,sK20),X0)
| ~ rearsegP(sK20,X0)
| ~ ssList(cons(sK70,nil))
| ~ ssList(X0)
| ~ ssList(sK20) ),
inference(superposition,[],[f605,f1985]) ).
fof(f7287,plain,
( ~ rearsegP(cons(sK70,sK20),nil)
| spl72_58 ),
inference(avatar_component_clause,[],[f7286]) ).
fof(f7297,plain,
( ~ spl72_16
| spl72_58 ),
inference(avatar_contradiction_clause,[],[f7296]) ).
fof(f7296,plain,
( $false
| ~ spl72_16
| spl72_58 ),
inference(subsumption_resolution,[],[f7295,f407]) ).
fof(f7295,plain,
( ~ ssList(nil)
| ~ spl72_16
| spl72_58 ),
inference(subsumption_resolution,[],[f7291,f648]) ).
fof(f7291,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_16
| spl72_58 ),
inference(resolution,[],[f7287,f2841]) ).
fof(f2841,plain,
( ! [X0] :
( rearsegP(cons(sK70,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_16 ),
inference(subsumption_resolution,[],[f2840,f407]) ).
fof(f2840,plain,
( ! [X0] :
( rearsegP(cons(sK70,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_16 ),
inference(subsumption_resolution,[],[f2803,f2005]) ).
fof(f2803,plain,
( ! [X0] :
( rearsegP(cons(sK70,sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(cons(sK70,sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_16 ),
inference(superposition,[],[f605,f2023]) ).
fof(f2023,plain,
( cons(sK70,sK20) = app(cons(sK70,sK20),nil)
| ~ spl72_16 ),
inference(resolution,[],[f2005,f469]) ).
fof(f7294,plain,
( ~ spl72_16
| spl72_58 ),
inference(avatar_contradiction_clause,[],[f7293]) ).
fof(f7293,plain,
( $false
| ~ spl72_16
| spl72_58 ),
inference(subsumption_resolution,[],[f7290,f2005]) ).
fof(f7290,plain,
( ~ ssList(cons(sK70,sK20))
| spl72_58 ),
inference(resolution,[],[f7287,f464]) ).
fof(f7289,plain,
( ~ spl72_57
| spl72_58
| ~ spl72_16 ),
inference(avatar_split_clause,[],[f7099,f2003,f7286,f7282]) ).
fof(f7099,plain,
( rearsegP(cons(sK70,sK20),nil)
| ~ ssList(sK66(cons(sK70,sK20),nil))
| ~ spl72_16 ),
inference(subsumption_resolution,[],[f7085,f407]) ).
fof(f7085,plain,
( rearsegP(cons(sK70,sK20),nil)
| ~ ssList(sK66(cons(sK70,sK20),nil))
| ~ ssList(nil)
| ~ spl72_16 ),
inference(superposition,[],[f1990,f6833]) ).
fof(f6833,plain,
( cons(sK70,sK20) = app(sK66(cons(sK70,sK20),nil),nil)
| ~ spl72_16 ),
inference(resolution,[],[f2609,f2005]) ).
fof(f7261,plain,
( ~ spl72_15
| spl72_55
| ~ spl72_56 ),
inference(avatar_contradiction_clause,[],[f7260]) ).
fof(f7260,plain,
( $false
| ~ spl72_15
| spl72_55
| ~ spl72_56 ),
inference(subsumption_resolution,[],[f7259,f2000]) ).
fof(f7259,plain,
( ~ ssList(cons(sK70,nil))
| spl72_55
| ~ spl72_56 ),
inference(subsumption_resolution,[],[f7258,f407]) ).
fof(f7258,plain,
( ~ ssList(nil)
| ~ ssList(cons(sK70,nil))
| spl72_55
| ~ spl72_56 ),
inference(subsumption_resolution,[],[f7257,f7245]) ).
fof(f7245,plain,
( rearsegP(cons(sK70,nil),nil)
| ~ spl72_56 ),
inference(avatar_component_clause,[],[f7243]) ).
fof(f7243,plain,
( spl72_56
<=> rearsegP(cons(sK70,nil),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_56])]) ).
fof(f7257,plain,
( ~ rearsegP(cons(sK70,nil),nil)
| ~ ssList(nil)
| ~ ssList(cons(sK70,nil))
| spl72_55 ),
inference(resolution,[],[f7241,f588]) ).
fof(f7241,plain,
( ~ ssList(sK66(cons(sK70,nil),nil))
| spl72_55 ),
inference(avatar_component_clause,[],[f7239]) ).
fof(f7239,plain,
( spl72_55
<=> ssList(sK66(cons(sK70,nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_55])]) ).
fof(f7253,plain,
( ~ spl72_15
| spl72_56 ),
inference(avatar_contradiction_clause,[],[f7252]) ).
fof(f7252,plain,
( $false
| ~ spl72_15
| spl72_56 ),
inference(subsumption_resolution,[],[f7251,f407]) ).
fof(f7251,plain,
( ~ ssList(nil)
| ~ spl72_15
| spl72_56 ),
inference(subsumption_resolution,[],[f7248,f648]) ).
fof(f7248,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_15
| spl72_56 ),
inference(resolution,[],[f7244,f2837]) ).
fof(f2837,plain,
( ! [X0] :
( rearsegP(cons(sK70,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f2836,f407]) ).
fof(f2836,plain,
( ! [X0] :
( rearsegP(cons(sK70,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f2801,f2000]) ).
fof(f2801,plain,
( ! [X0] :
( rearsegP(cons(sK70,nil),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(cons(sK70,nil))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_15 ),
inference(superposition,[],[f605,f2011]) ).
fof(f2011,plain,
( cons(sK70,nil) = app(cons(sK70,nil),nil)
| ~ spl72_15 ),
inference(resolution,[],[f2000,f469]) ).
fof(f7244,plain,
( ~ rearsegP(cons(sK70,nil),nil)
| spl72_56 ),
inference(avatar_component_clause,[],[f7243]) ).
fof(f7250,plain,
( ~ spl72_15
| spl72_56 ),
inference(avatar_contradiction_clause,[],[f7249]) ).
fof(f7249,plain,
( $false
| ~ spl72_15
| spl72_56 ),
inference(subsumption_resolution,[],[f7247,f2000]) ).
fof(f7247,plain,
( ~ ssList(cons(sK70,nil))
| spl72_56 ),
inference(resolution,[],[f7244,f464]) ).
fof(f7246,plain,
( ~ spl72_55
| spl72_56
| ~ spl72_15 ),
inference(avatar_split_clause,[],[f7067,f1999,f7243,f7239]) ).
fof(f7067,plain,
( rearsegP(cons(sK70,nil),nil)
| ~ ssList(sK66(cons(sK70,nil),nil))
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f7053,f407]) ).
fof(f7053,plain,
( rearsegP(cons(sK70,nil),nil)
| ~ ssList(sK66(cons(sK70,nil),nil))
| ~ ssList(nil)
| ~ spl72_15 ),
inference(superposition,[],[f1990,f6832]) ).
fof(f6832,plain,
( cons(sK70,nil) = app(sK66(cons(sK70,nil),nil),nil)
| ~ spl72_15 ),
inference(resolution,[],[f2609,f2000]) ).
fof(f7017,plain,
( ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_53
| ~ spl72_54 ),
inference(avatar_contradiction_clause,[],[f7016]) ).
fof(f7016,plain,
( $false
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_53
| ~ spl72_54 ),
inference(subsumption_resolution,[],[f7015,f1775]) ).
fof(f7015,plain,
( ~ ssList(tl(sK20))
| spl72_53
| ~ spl72_54 ),
inference(subsumption_resolution,[],[f7014,f407]) ).
fof(f7014,plain,
( ~ ssList(nil)
| ~ ssList(tl(sK20))
| spl72_53
| ~ spl72_54 ),
inference(subsumption_resolution,[],[f7013,f6931]) ).
fof(f6931,plain,
( rearsegP(tl(sK20),nil)
| ~ spl72_54 ),
inference(avatar_component_clause,[],[f6929]) ).
fof(f6929,plain,
( spl72_54
<=> rearsegP(tl(sK20),nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_54])]) ).
fof(f7013,plain,
( ~ rearsegP(tl(sK20),nil)
| ~ ssList(nil)
| ~ ssList(tl(sK20))
| spl72_53 ),
inference(resolution,[],[f6927,f588]) ).
fof(f6927,plain,
( ~ ssList(sK66(tl(sK20),nil))
| spl72_53 ),
inference(avatar_component_clause,[],[f6925]) ).
fof(f6939,plain,
( ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_54 ),
inference(avatar_contradiction_clause,[],[f6938]) ).
fof(f6938,plain,
( $false
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_54 ),
inference(subsumption_resolution,[],[f6937,f407]) ).
fof(f6937,plain,
( ~ ssList(nil)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_54 ),
inference(subsumption_resolution,[],[f6934,f648]) ).
fof(f6934,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_54 ),
inference(resolution,[],[f6930,f2863]) ).
fof(f2863,plain,
( ! [X0] :
( rearsegP(tl(sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f2862,f1769]) ).
fof(f2862,plain,
( ! [X0] :
( rearsegP(sK25(sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) )
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f2861,f407]) ).
fof(f2861,plain,
( ! [X0] :
( rearsegP(sK25(sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f2823,f1602]) ).
fof(f2823,plain,
( ! [X0] :
( rearsegP(sK25(sK20),X0)
| ~ rearsegP(nil,X0)
| ~ ssList(sK25(sK20))
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_13 ),
inference(superposition,[],[f605,f1613]) ).
fof(f1613,plain,
( sK25(sK20) = app(sK25(sK20),nil)
| ~ spl72_13 ),
inference(resolution,[],[f1602,f469]) ).
fof(f6930,plain,
( ~ rearsegP(tl(sK20),nil)
| spl72_54 ),
inference(avatar_component_clause,[],[f6929]) ).
fof(f6936,plain,
( ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_54 ),
inference(avatar_contradiction_clause,[],[f6935]) ).
fof(f6935,plain,
( $false
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13
| spl72_54 ),
inference(subsumption_resolution,[],[f6933,f1775]) ).
fof(f6933,plain,
( ~ ssList(tl(sK20))
| spl72_54 ),
inference(resolution,[],[f6930,f464]) ).
fof(f6932,plain,
( ~ spl72_53
| spl72_54
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(avatar_split_clause,[],[f6922,f1601,f1375,f1273,f6929,f6925]) ).
fof(f6922,plain,
( rearsegP(tl(sK20),nil)
| ~ ssList(sK66(tl(sK20),nil))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(subsumption_resolution,[],[f6908,f407]) ).
fof(f6908,plain,
( rearsegP(tl(sK20),nil)
| ~ ssList(sK66(tl(sK20),nil))
| ~ ssList(nil)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(superposition,[],[f1990,f6885]) ).
fof(f6701,plain,
( ~ spl72_49
| ~ spl72_50
| spl72_51 ),
inference(avatar_contradiction_clause,[],[f6700]) ).
fof(f6700,plain,
( $false
| ~ spl72_49
| ~ spl72_50
| spl72_51 ),
inference(subsumption_resolution,[],[f6699,f386]) ).
fof(f6699,plain,
( ~ ssList(sK20)
| ~ spl72_49
| ~ spl72_50
| spl72_51 ),
inference(subsumption_resolution,[],[f6698,f407]) ).
fof(f6698,plain,
( ~ ssList(nil)
| ~ ssList(sK20)
| ~ spl72_49
| ~ spl72_50
| spl72_51 ),
inference(subsumption_resolution,[],[f6697,f6649]) ).
fof(f6697,plain,
( ~ frontsegP(sK20,nil)
| ~ ssList(nil)
| ~ ssList(sK20)
| spl72_51 ),
inference(resolution,[],[f6691,f595]) ).
fof(f6691,plain,
( ~ ssList(sK69(sK20,nil))
| spl72_51 ),
inference(avatar_component_clause,[],[f6689]) ).
fof(f6696,plain,
( ~ spl72_51
| spl72_52
| ~ spl72_49
| ~ spl72_50 ),
inference(avatar_split_clause,[],[f6673,f6547,f6543,f6693,f6689]) ).
fof(f6673,plain,
( sK20 = sK69(sK20,nil)
| ~ ssList(sK69(sK20,nil))
| ~ spl72_49
| ~ spl72_50 ),
inference(trivial_inequality_removal,[],[f6656]) ).
fof(f6656,plain,
( sK20 != sK20
| sK20 = sK69(sK20,nil)
| ~ ssList(sK69(sK20,nil))
| ~ spl72_49
| ~ spl72_50 ),
inference(superposition,[],[f4254,f6654]) ).
fof(f4254,plain,
! [X0] :
( app(nil,X0) != sK20
| sK20 = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4253,f407]) ).
fof(f4253,plain,
! [X0] :
( app(nil,X0) != sK20
| sK20 = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4166,f386]) ).
fof(f4166,plain,
! [X0] :
( app(nil,X0) != sK20
| sK20 = X0
| ~ ssList(sK20)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[],[f608,f700]) ).
fof(f608,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/sandbox/benchmark/theBenchmark.p',ax80) ).
fof(f6557,plain,
spl72_49,
inference(avatar_contradiction_clause,[],[f6556]) ).
fof(f6556,plain,
( $false
| spl72_49 ),
inference(subsumption_resolution,[],[f6555,f386]) ).
fof(f6555,plain,
( ~ ssList(sK20)
| spl72_49 ),
inference(resolution,[],[f6553,f467]) ).
fof(f6553,plain,
( ~ rearsegP(sK20,sK20)
| spl72_49 ),
inference(subsumption_resolution,[],[f6552,f386]) ).
fof(f6552,plain,
( ~ rearsegP(sK20,sK20)
| ~ ssList(sK20)
| spl72_49 ),
inference(duplicate_literal_removal,[],[f6551]) ).
fof(f6551,plain,
( ~ rearsegP(sK20,sK20)
| ~ ssList(sK20)
| ~ ssList(sK20)
| spl72_49 ),
inference(resolution,[],[f6545,f588]) ).
fof(f6545,plain,
( ~ ssList(sK66(sK20,sK20))
| spl72_49 ),
inference(avatar_component_clause,[],[f6543]) ).
fof(f6550,plain,
( ~ spl72_49
| spl72_50 ),
inference(avatar_split_clause,[],[f6462,f6547,f6543]) ).
fof(f6462,plain,
( nil = sK66(sK20,sK20)
| ~ ssList(sK66(sK20,sK20)) ),
inference(trivial_inequality_removal,[],[f6445]) ).
fof(f6445,plain,
( sK20 != sK20
| nil = sK66(sK20,sK20)
| ~ ssList(sK66(sK20,sK20)) ),
inference(superposition,[],[f3950,f6397]) ).
fof(f3950,plain,
! [X0] :
( sK20 != app(X0,sK20)
| nil = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f3949,f386]) ).
fof(f3949,plain,
! [X0] :
( sK20 != app(X0,sK20)
| nil = X0
| ~ ssList(sK20)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f3862,f407]) ).
fof(f3862,plain,
! [X0] :
( sK20 != app(X0,sK20)
| nil = X0
| ~ ssList(nil)
| ~ ssList(sK20)
| ~ ssList(X0) ),
inference(superposition,[],[f607,f700]) ).
fof(f607,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/sandbox/benchmark/theBenchmark.p',ax79) ).
fof(f6379,plain,
( ~ spl72_37
| spl72_47 ),
inference(avatar_contradiction_clause,[],[f6378]) ).
fof(f6378,plain,
( $false
| ~ spl72_37
| spl72_47 ),
inference(subsumption_resolution,[],[f6377,f407]) ).
fof(f6377,plain,
( ~ ssList(nil)
| ~ spl72_37
| spl72_47 ),
inference(subsumption_resolution,[],[f6376,f3376]) ).
fof(f3376,plain,
( ssItem(sK29(sK20))
| ~ spl72_37 ),
inference(avatar_component_clause,[],[f3375]) ).
fof(f3375,plain,
( spl72_37
<=> ssItem(sK29(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_37])]) ).
fof(f6376,plain,
( ~ ssItem(sK29(sK20))
| ~ ssList(nil)
| spl72_47 ),
inference(resolution,[],[f6370,f569]) ).
fof(f6370,plain,
( ~ ssList(cons(sK29(sK20),nil))
| spl72_47 ),
inference(avatar_component_clause,[],[f6368]) ).
fof(f6368,plain,
( spl72_47
<=> ssList(cons(sK29(sK20),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_47])]) ).
fof(f6375,plain,
( ~ spl72_47
| spl72_48
| ~ spl72_37 ),
inference(avatar_split_clause,[],[f6351,f3375,f6372,f6368]) ).
fof(f6372,plain,
( spl72_48
<=> ssList(cons(sK29(sK20),sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_48])]) ).
fof(f6351,plain,
( ssList(cons(sK29(sK20),sK20))
| ~ ssList(cons(sK29(sK20),nil))
| ~ spl72_37 ),
inference(subsumption_resolution,[],[f6335,f386]) ).
fof(f6335,plain,
( ssList(cons(sK29(sK20),sK20))
| ~ ssList(sK20)
| ~ ssList(cons(sK29(sK20),nil))
| ~ spl72_37 ),
inference(superposition,[],[f579,f3395]) ).
fof(f3395,plain,
( cons(sK29(sK20),sK20) = app(cons(sK29(sK20),nil),sK20)
| ~ spl72_37 ),
inference(resolution,[],[f3376,f1625]) ).
fof(f5266,plain,
( ~ spl72_4
| ~ spl72_9
| ~ spl72_25
| ~ spl72_35 ),
inference(avatar_contradiction_clause,[],[f5265]) ).
fof(f5265,plain,
( $false
| ~ spl72_4
| ~ spl72_9
| ~ spl72_25
| ~ spl72_35 ),
inference(subsumption_resolution,[],[f5258,f2708]) ).
fof(f2708,plain,
( ssList(sK69(sK20,sK20))
| ~ spl72_25 ),
inference(avatar_component_clause,[],[f2707]) ).
fof(f2707,plain,
( spl72_25
<=> ssList(sK69(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_25])]) ).
fof(f5258,plain,
( ~ ssList(sK69(sK20,sK20))
| ~ spl72_4
| ~ spl72_9
| ~ spl72_35 ),
inference(trivial_inequality_removal,[],[f5257]) ).
fof(f5257,plain,
( sK20 != sK20
| ~ ssList(sK69(sK20,sK20))
| ~ spl72_4
| ~ spl72_9
| ~ spl72_35 ),
inference(superposition,[],[f5252,f2693]) ).
fof(f2693,plain,
( sK20 = app(sK20,sK69(sK20,sK20))
| ~ spl72_4 ),
inference(subsumption_resolution,[],[f2681,f386]) ).
fof(f2681,plain,
( sK20 = app(sK20,sK69(sK20,sK20))
| ~ ssList(sK20)
| ~ spl72_4 ),
inference(duplicate_literal_removal,[],[f2679]) ).
fof(f2679,plain,
( sK20 = app(sK20,sK69(sK20,sK20))
| ~ ssList(sK20)
| ~ ssList(sK20)
| ~ spl72_4 ),
inference(resolution,[],[f596,f2259]) ).
fof(f5252,plain,
( ! [X0] :
( sK20 != app(sK20,X0)
| ~ ssList(X0) )
| ~ spl72_9
| ~ spl72_35 ),
inference(subsumption_resolution,[],[f5244,f407]) ).
fof(f5244,plain,
( ! [X0] :
( sK20 != app(sK20,X0)
| ~ ssList(X0)
| ~ ssList(nil) )
| ~ spl72_9
| ~ spl72_35 ),
inference(superposition,[],[f3332,f700]) ).
fof(f3332,plain,
( ! [X0,X1] :
( sK20 != app(app(X0,sK20),X1)
| ~ ssList(X1)
| ~ ssList(X0) )
| ~ spl72_9
| ~ spl72_35 ),
inference(subsumption_resolution,[],[f3314,f1376]) ).
fof(f3314,plain,
( ! [X0,X1] :
( sK20 != app(app(X0,sK20),X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(hd(sK20)) )
| ~ spl72_35 ),
inference(superposition,[],[f3009,f3285]) ).
fof(f3285,plain,
( sK20 = cons(hd(sK20),nil)
| ~ spl72_35 ),
inference(superposition,[],[f1348,f3279]) ).
fof(f3279,plain,
( nil = tl(sK20)
| ~ spl72_35 ),
inference(avatar_component_clause,[],[f3277]) ).
fof(f3277,plain,
( spl72_35
<=> nil = tl(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_35])]) ).
fof(f5264,plain,
( ~ spl72_9
| ~ spl72_35 ),
inference(avatar_contradiction_clause,[],[f5263]) ).
fof(f5263,plain,
( $false
| ~ spl72_9
| ~ spl72_35 ),
inference(subsumption_resolution,[],[f5259,f407]) ).
fof(f5259,plain,
( ~ ssList(nil)
| ~ spl72_9
| ~ spl72_35 ),
inference(trivial_inequality_removal,[],[f5256]) ).
fof(f5256,plain,
( sK20 != sK20
| ~ ssList(nil)
| ~ spl72_9
| ~ spl72_35 ),
inference(superposition,[],[f5252,f672]) ).
fof(f5262,plain,
( ~ spl72_4
| ~ spl72_9
| ~ spl72_35 ),
inference(avatar_contradiction_clause,[],[f5261]) ).
fof(f5261,plain,
( $false
| ~ spl72_4
| ~ spl72_9
| ~ spl72_35 ),
inference(subsumption_resolution,[],[f5260,f394]) ).
fof(f5260,plain,
( ~ ssList(sK24)
| ~ spl72_4
| ~ spl72_9
| ~ spl72_35 ),
inference(subsumption_resolution,[],[f5255,f1443]) ).
fof(f5255,plain,
( sK20 != sK21
| ~ ssList(sK24)
| ~ spl72_9
| ~ spl72_35 ),
inference(superposition,[],[f5252,f656]) ).
fof(f5142,plain,
~ spl72_45,
inference(avatar_contradiction_clause,[],[f5141]) ).
fof(f5141,plain,
( $false
| ~ spl72_45 ),
inference(subsumption_resolution,[],[f5140,f407]) ).
fof(f5140,plain,
( ~ ssList(nil)
| ~ spl72_45 ),
inference(subsumption_resolution,[],[f5117,f614]) ).
fof(f5117,plain,
( ~ ssItem(sK71)
| ~ ssList(nil)
| ~ spl72_45 ),
inference(trivial_inequality_removal,[],[f5113]) ).
fof(f5113,plain,
( nil != nil
| ~ ssItem(sK71)
| ~ ssList(nil)
| ~ spl72_45 ),
inference(superposition,[],[f571,f5071]) ).
fof(f5071,plain,
( nil = cons(sK71,nil)
| ~ spl72_45 ),
inference(avatar_component_clause,[],[f5069]) ).
fof(f571,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/sandbox/benchmark/theBenchmark.p',ax18) ).
fof(f5139,plain,
~ spl72_45,
inference(avatar_contradiction_clause,[],[f5138]) ).
fof(f5138,plain,
( $false
| ~ spl72_45 ),
inference(subsumption_resolution,[],[f5137,f407]) ).
fof(f5137,plain,
( ~ ssList(nil)
| ~ spl72_45 ),
inference(subsumption_resolution,[],[f5118,f614]) ).
fof(f5118,plain,
( ~ ssItem(sK71)
| ~ ssList(nil)
| ~ spl72_45 ),
inference(trivial_inequality_removal,[],[f5112]) ).
fof(f5112,plain,
( nil != nil
| ~ ssItem(sK71)
| ~ ssList(nil)
| ~ spl72_45 ),
inference(superposition,[],[f570,f5071]) ).
fof(f570,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[],[f179]) ).
fof(f179,plain,
! [X0] :
( ! [X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1) )
| ~ ssList(X0) ),
inference(ennf_transformation,[],[f21]) ).
fof(f21,axiom,
! [X0] :
( ssList(X0)
=> ! [X1] :
( ssItem(X1)
=> nil != cons(X1,X0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax21) ).
fof(f5127,plain,
( ~ spl72_17
| ~ spl72_45 ),
inference(avatar_contradiction_clause,[],[f5126]) ).
fof(f5126,plain,
( $false
| ~ spl72_17
| ~ spl72_45 ),
inference(subsumption_resolution,[],[f5125,f2049]) ).
fof(f5125,plain,
( ~ ssList(cons(sK71,nil))
| ~ spl72_45 ),
inference(subsumption_resolution,[],[f5124,f614]) ).
fof(f5124,plain,
( ~ ssItem(sK71)
| ~ ssList(cons(sK71,nil))
| ~ spl72_45 ),
inference(subsumption_resolution,[],[f5098,f399]) ).
fof(f5098,plain,
( singletonP(nil)
| ~ ssItem(sK71)
| ~ ssList(cons(sK71,nil))
| ~ spl72_45 ),
inference(superposition,[],[f624,f5071]) ).
fof(f5123,plain,
( spl72_22
| ~ spl72_45 ),
inference(avatar_contradiction_clause,[],[f5122]) ).
fof(f5122,plain,
( $false
| spl72_22
| ~ spl72_45 ),
inference(subsumption_resolution,[],[f5121,f2388]) ).
fof(f2388,plain,
( sK20 != cons(sK71,sK20)
| spl72_22 ),
inference(avatar_component_clause,[],[f2387]) ).
fof(f2387,plain,
( spl72_22
<=> sK20 = cons(sK71,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_22])]) ).
fof(f5121,plain,
( sK20 = cons(sK71,sK20)
| ~ spl72_45 ),
inference(forward_demodulation,[],[f5079,f700]) ).
fof(f5079,plain,
( app(nil,sK20) = cons(sK71,sK20)
| ~ spl72_45 ),
inference(superposition,[],[f1986,f5071]) ).
fof(f5120,plain,
( ~ spl72_4
| spl72_12
| ~ spl72_45 ),
inference(avatar_contradiction_clause,[],[f5119]) ).
fof(f5119,plain,
( $false
| ~ spl72_4
| spl72_12
| ~ spl72_45 ),
inference(subsumption_resolution,[],[f5077,f1442]) ).
fof(f1442,plain,
( nil != tl(nil)
| ~ spl72_4
| spl72_12 ),
inference(superposition,[],[f1400,f898]) ).
fof(f1400,plain,
( sK24 != tl(sK24)
| spl72_12 ),
inference(avatar_component_clause,[],[f1398]) ).
fof(f1398,plain,
( spl72_12
<=> sK24 = tl(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_12])]) ).
fof(f5077,plain,
( nil = tl(nil)
| ~ spl72_4
| ~ spl72_45 ),
inference(superposition,[],[f1436,f5071]) ).
fof(f1436,plain,
( nil = tl(cons(sK71,nil))
| ~ spl72_4 ),
inference(superposition,[],[f1016,f898]) ).
fof(f1016,plain,
sK24 = tl(cons(sK71,sK24)),
inference(resolution,[],[f911,f614]) ).
fof(f911,plain,
! [X0] :
( ~ ssItem(X0)
| sK24 = tl(cons(X0,sK24)) ),
inference(resolution,[],[f572,f394]) ).
fof(f5076,plain,
( spl72_45
| spl72_46
| ~ spl72_4
| ~ spl72_17 ),
inference(avatar_split_clause,[],[f2070,f2048,f896,f5073,f5069]) ).
fof(f5073,plain,
( spl72_46
<=> sK71 = sK27(cons(sK71,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_46])]) ).
fof(f2070,plain,
( sK71 = sK27(cons(sK71,nil))
| nil = cons(sK71,nil)
| ~ spl72_4
| ~ spl72_17 ),
inference(forward_demodulation,[],[f2064,f1438]) ).
fof(f1438,plain,
( sK71 = hd(cons(sK71,nil))
| ~ spl72_4 ),
inference(superposition,[],[f1091,f898]) ).
fof(f2064,plain,
( nil = cons(sK71,nil)
| hd(cons(sK71,nil)) = sK27(cons(sK71,nil))
| ~ spl72_17 ),
inference(resolution,[],[f2049,f478]) ).
fof(f5057,plain,
~ spl72_43,
inference(avatar_contradiction_clause,[],[f5056]) ).
fof(f5056,plain,
( $false
| ~ spl72_43 ),
inference(subsumption_resolution,[],[f5055,f407]) ).
fof(f5055,plain,
( ~ ssList(nil)
| ~ spl72_43 ),
inference(subsumption_resolution,[],[f5032,f613]) ).
fof(f5032,plain,
( ~ ssItem(sK70)
| ~ ssList(nil)
| ~ spl72_43 ),
inference(trivial_inequality_removal,[],[f5028]) ).
fof(f5028,plain,
( nil != nil
| ~ ssItem(sK70)
| ~ ssList(nil)
| ~ spl72_43 ),
inference(superposition,[],[f571,f4986]) ).
fof(f4986,plain,
( nil = cons(sK70,nil)
| ~ spl72_43 ),
inference(avatar_component_clause,[],[f4984]) ).
fof(f5054,plain,
~ spl72_43,
inference(avatar_contradiction_clause,[],[f5053]) ).
fof(f5053,plain,
( $false
| ~ spl72_43 ),
inference(subsumption_resolution,[],[f5052,f407]) ).
fof(f5052,plain,
( ~ ssList(nil)
| ~ spl72_43 ),
inference(subsumption_resolution,[],[f5033,f613]) ).
fof(f5033,plain,
( ~ ssItem(sK70)
| ~ ssList(nil)
| ~ spl72_43 ),
inference(trivial_inequality_removal,[],[f5027]) ).
fof(f5027,plain,
( nil != nil
| ~ ssItem(sK70)
| ~ ssList(nil)
| ~ spl72_43 ),
inference(superposition,[],[f570,f4986]) ).
fof(f5042,plain,
( ~ spl72_15
| ~ spl72_43 ),
inference(avatar_contradiction_clause,[],[f5041]) ).
fof(f5041,plain,
( $false
| ~ spl72_15
| ~ spl72_43 ),
inference(subsumption_resolution,[],[f5040,f2000]) ).
fof(f5040,plain,
( ~ ssList(cons(sK70,nil))
| ~ spl72_43 ),
inference(subsumption_resolution,[],[f5039,f613]) ).
fof(f5039,plain,
( ~ ssItem(sK70)
| ~ ssList(cons(sK70,nil))
| ~ spl72_43 ),
inference(subsumption_resolution,[],[f5013,f399]) ).
fof(f5013,plain,
( singletonP(nil)
| ~ ssItem(sK70)
| ~ ssList(cons(sK70,nil))
| ~ spl72_43 ),
inference(superposition,[],[f624,f4986]) ).
fof(f5038,plain,
( spl72_20
| ~ spl72_43 ),
inference(avatar_contradiction_clause,[],[f5037]) ).
fof(f5037,plain,
( $false
| spl72_20
| ~ spl72_43 ),
inference(subsumption_resolution,[],[f5036,f2379]) ).
fof(f2379,plain,
( sK20 != cons(sK70,sK20)
| spl72_20 ),
inference(avatar_component_clause,[],[f2378]) ).
fof(f2378,plain,
( spl72_20
<=> sK20 = cons(sK70,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_20])]) ).
fof(f5036,plain,
( sK20 = cons(sK70,sK20)
| ~ spl72_43 ),
inference(forward_demodulation,[],[f4994,f700]) ).
fof(f4994,plain,
( app(nil,sK20) = cons(sK70,sK20)
| ~ spl72_43 ),
inference(superposition,[],[f1985,f4986]) ).
fof(f5035,plain,
( ~ spl72_4
| spl72_12
| ~ spl72_43 ),
inference(avatar_contradiction_clause,[],[f5034]) ).
fof(f5034,plain,
( $false
| ~ spl72_4
| spl72_12
| ~ spl72_43 ),
inference(subsumption_resolution,[],[f4992,f1442]) ).
fof(f4992,plain,
( nil = tl(nil)
| ~ spl72_4
| ~ spl72_43 ),
inference(superposition,[],[f1435,f4986]) ).
fof(f1435,plain,
( nil = tl(cons(sK70,nil))
| ~ spl72_4 ),
inference(superposition,[],[f1015,f898]) ).
fof(f1015,plain,
sK24 = tl(cons(sK70,sK24)),
inference(resolution,[],[f911,f613]) ).
fof(f4991,plain,
( spl72_43
| spl72_44
| ~ spl72_4
| ~ spl72_15 ),
inference(avatar_split_clause,[],[f2021,f1999,f896,f4988,f4984]) ).
fof(f4988,plain,
( spl72_44
<=> sK70 = sK27(cons(sK70,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_44])]) ).
fof(f2021,plain,
( sK70 = sK27(cons(sK70,nil))
| nil = cons(sK70,nil)
| ~ spl72_4
| ~ spl72_15 ),
inference(forward_demodulation,[],[f2015,f1437]) ).
fof(f1437,plain,
( sK70 = hd(cons(sK70,nil))
| ~ spl72_4 ),
inference(superposition,[],[f1090,f898]) ).
fof(f2015,plain,
( nil = cons(sK70,nil)
| hd(cons(sK70,nil)) = sK27(cons(sK70,nil))
| ~ spl72_15 ),
inference(resolution,[],[f2000,f478]) ).
fof(f4637,plain,
spl72_41,
inference(avatar_contradiction_clause,[],[f4636]) ).
fof(f4636,plain,
( $false
| spl72_41 ),
inference(subsumption_resolution,[],[f4635,f407]) ).
fof(f4635,plain,
( ~ ssList(nil)
| spl72_41 ),
inference(subsumption_resolution,[],[f4634,f650]) ).
fof(f4634,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| spl72_41 ),
inference(duplicate_literal_removal,[],[f4633]) ).
fof(f4633,plain,
( ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| spl72_41 ),
inference(resolution,[],[f4627,f595]) ).
fof(f4627,plain,
( ~ ssList(sK69(nil,nil))
| spl72_41 ),
inference(avatar_component_clause,[],[f4625]) ).
fof(f4625,plain,
( spl72_41
<=> ssList(sK69(nil,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_41])]) ).
fof(f4632,plain,
( ~ spl72_41
| spl72_42
| ~ spl72_4 ),
inference(avatar_split_clause,[],[f4623,f896,f4629,f4625]) ).
fof(f4629,plain,
( spl72_42
<=> nil = sK69(nil,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_42])]) ).
fof(f4623,plain,
( nil = sK69(nil,nil)
| ~ ssList(sK69(nil,nil))
| ~ spl72_4 ),
inference(trivial_inequality_removal,[],[f4622]) ).
fof(f4622,plain,
( nil != nil
| nil = sK69(nil,nil)
| ~ ssList(sK69(nil,nil))
| ~ spl72_4 ),
inference(superposition,[],[f4262,f2692]) ).
fof(f2692,plain,
nil = app(nil,sK69(nil,nil)),
inference(subsumption_resolution,[],[f2682,f407]) ).
fof(f2682,plain,
( nil = app(nil,sK69(nil,nil))
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f2678]) ).
fof(f2678,plain,
( nil = app(nil,sK69(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[],[f596,f650]) ).
fof(f4262,plain,
( ! [X0] :
( nil != app(nil,X0)
| nil = X0
| ~ ssList(X0) )
| ~ spl72_4 ),
inference(forward_demodulation,[],[f4261,f898]) ).
fof(f4261,plain,
( ! [X0] :
( nil != app(nil,X0)
| sK24 = X0
| ~ ssList(X0) )
| ~ spl72_4 ),
inference(forward_demodulation,[],[f4260,f898]) ).
fof(f4260,plain,
! [X0] :
( app(nil,X0) != sK24
| sK24 = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4259,f407]) ).
fof(f4259,plain,
! [X0] :
( app(nil,X0) != sK24
| sK24 = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f4168,f394]) ).
fof(f4168,plain,
! [X0] :
( app(nil,X0) != sK24
| sK24 = X0
| ~ ssList(sK24)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(superposition,[],[f608,f704]) ).
fof(f4129,plain,
spl72_39,
inference(avatar_contradiction_clause,[],[f4128]) ).
fof(f4128,plain,
( $false
| spl72_39 ),
inference(subsumption_resolution,[],[f4127,f407]) ).
fof(f4127,plain,
( ~ ssList(nil)
| spl72_39 ),
inference(subsumption_resolution,[],[f4126,f648]) ).
fof(f4126,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| spl72_39 ),
inference(duplicate_literal_removal,[],[f4125]) ).
fof(f4125,plain,
( ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| spl72_39 ),
inference(resolution,[],[f4119,f588]) ).
fof(f4119,plain,
( ~ ssList(sK66(nil,nil))
| spl72_39 ),
inference(avatar_component_clause,[],[f4117]) ).
fof(f4117,plain,
( spl72_39
<=> ssList(sK66(nil,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_39])]) ).
fof(f4124,plain,
( ~ spl72_39
| spl72_40
| ~ spl72_4 ),
inference(avatar_split_clause,[],[f4115,f896,f4121,f4117]) ).
fof(f4121,plain,
( spl72_40
<=> nil = sK66(nil,nil) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_40])]) ).
fof(f4115,plain,
( nil = sK66(nil,nil)
| ~ ssList(sK66(nil,nil))
| ~ spl72_4 ),
inference(trivial_inequality_removal,[],[f4113]) ).
fof(f4113,plain,
( nil != nil
| nil = sK66(nil,nil)
| ~ ssList(sK66(nil,nil))
| ~ spl72_4 ),
inference(superposition,[],[f3956,f2608]) ).
fof(f2608,plain,
nil = app(sK66(nil,nil),nil),
inference(subsumption_resolution,[],[f2604,f407]) ).
fof(f2604,plain,
( nil = app(sK66(nil,nil),nil)
| ~ ssList(nil) ),
inference(duplicate_literal_removal,[],[f2598]) ).
fof(f2598,plain,
( nil = app(sK66(nil,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[],[f589,f648]) ).
fof(f3956,plain,
( ! [X0] :
( nil != app(X0,nil)
| nil = X0
| ~ ssList(X0) )
| ~ spl72_4 ),
inference(forward_demodulation,[],[f3955,f898]) ).
fof(f3955,plain,
! [X0] :
( sK24 != app(X0,sK24)
| nil = X0
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f3954,f394]) ).
fof(f3954,plain,
! [X0] :
( sK24 != app(X0,sK24)
| nil = X0
| ~ ssList(sK24)
| ~ ssList(X0) ),
inference(subsumption_resolution,[],[f3864,f407]) ).
fof(f3864,plain,
! [X0] :
( sK24 != app(X0,sK24)
| nil = X0
| ~ ssList(nil)
| ~ ssList(sK24)
| ~ ssList(X0) ),
inference(superposition,[],[f607,f704]) ).
fof(f3386,plain,
( ~ spl72_9
| ~ spl72_29
| ~ spl72_35
| spl72_37 ),
inference(avatar_contradiction_clause,[],[f3385]) ).
fof(f3385,plain,
( $false
| ~ spl72_9
| ~ spl72_29
| ~ spl72_35
| spl72_37 ),
inference(subsumption_resolution,[],[f3384,f386]) ).
fof(f3384,plain,
( ~ ssList(sK20)
| ~ spl72_9
| ~ spl72_29
| ~ spl72_35
| spl72_37 ),
inference(subsumption_resolution,[],[f3383,f3331]) ).
fof(f3331,plain,
( singletonP(sK20)
| ~ spl72_9
| ~ spl72_29
| ~ spl72_35 ),
inference(subsumption_resolution,[],[f3330,f3121]) ).
fof(f3330,plain,
( singletonP(sK20)
| ~ ssList(cons(hd(sK20),nil))
| ~ spl72_9
| ~ spl72_35 ),
inference(subsumption_resolution,[],[f3313,f1376]) ).
fof(f3313,plain,
( singletonP(sK20)
| ~ ssItem(hd(sK20))
| ~ ssList(cons(hd(sK20),nil))
| ~ spl72_35 ),
inference(superposition,[],[f624,f3285]) ).
fof(f3383,plain,
( ~ singletonP(sK20)
| ~ ssList(sK20)
| spl72_37 ),
inference(resolution,[],[f3377,f481]) ).
fof(f3377,plain,
( ~ ssItem(sK29(sK20))
| spl72_37 ),
inference(avatar_component_clause,[],[f3375]) ).
fof(f3382,plain,
( ~ spl72_37
| spl72_38
| ~ spl72_9
| ~ spl72_29
| ~ spl72_35 ),
inference(avatar_split_clause,[],[f3363,f3277,f3120,f1375,f3379,f3375]) ).
fof(f3379,plain,
( spl72_38
<=> memberP(sK20,sK29(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_38])]) ).
fof(f3363,plain,
( memberP(sK20,sK29(sK20))
| ~ ssItem(sK29(sK20))
| ~ spl72_9
| ~ spl72_29
| ~ spl72_35 ),
inference(subsumption_resolution,[],[f3361,f407]) ).
fof(f3361,plain,
( memberP(sK20,sK29(sK20))
| ~ ssList(nil)
| ~ ssItem(sK29(sK20))
| ~ spl72_9
| ~ spl72_29
| ~ spl72_35 ),
inference(superposition,[],[f646,f3343]) ).
fof(f3343,plain,
( sK20 = cons(sK29(sK20),nil)
| ~ spl72_9
| ~ spl72_29
| ~ spl72_35 ),
inference(subsumption_resolution,[],[f3339,f386]) ).
fof(f3339,plain,
( sK20 = cons(sK29(sK20),nil)
| ~ ssList(sK20)
| ~ spl72_9
| ~ spl72_29
| ~ spl72_35 ),
inference(resolution,[],[f3331,f482]) ).
fof(f3370,plain,
( ~ spl72_3
| ~ spl72_4
| ~ spl72_35
| spl72_36 ),
inference(avatar_contradiction_clause,[],[f3369]) ).
fof(f3369,plain,
( $false
| ~ spl72_3
| ~ spl72_4
| ~ spl72_35
| spl72_36 ),
inference(subsumption_resolution,[],[f3368,f1434]) ).
fof(f1434,plain,
( hd(nil) = sK27(nil)
| ~ spl72_3
| ~ spl72_4 ),
inference(superposition,[],[f894,f898]) ).
fof(f894,plain,
( hd(sK24) = sK27(sK24)
| ~ spl72_3 ),
inference(avatar_component_clause,[],[f892]) ).
fof(f892,plain,
( spl72_3
<=> hd(sK24) = sK27(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_3])]) ).
fof(f3368,plain,
( hd(nil) != sK27(nil)
| ~ spl72_35
| spl72_36 ),
inference(forward_demodulation,[],[f3282,f3279]) ).
fof(f3282,plain,
( hd(tl(sK20)) != sK27(tl(sK20))
| spl72_36 ),
inference(avatar_component_clause,[],[f3281]) ).
fof(f3281,plain,
( spl72_36
<=> hd(tl(sK20)) = sK27(tl(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_36])]) ).
fof(f3284,plain,
( spl72_35
| spl72_36
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(avatar_split_clause,[],[f3094,f1601,f1375,f1273,f3281,f3277]) ).
fof(f3094,plain,
( hd(tl(sK20)) = sK27(tl(sK20))
| nil = tl(sK20)
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f3093,f1769]) ).
fof(f3093,plain,
( nil = tl(sK20)
| hd(sK25(sK20)) = sK27(sK25(sK20))
| ~ spl72_5
| ~ spl72_9
| ~ spl72_13 ),
inference(forward_demodulation,[],[f1617,f1769]) ).
fof(f1617,plain,
( nil = sK25(sK20)
| hd(sK25(sK20)) = sK27(sK25(sK20))
| ~ spl72_13 ),
inference(resolution,[],[f1602,f478]) ).
fof(f3236,plain,
( ~ spl72_4
| ~ spl72_7
| spl72_33 ),
inference(avatar_contradiction_clause,[],[f3235]) ).
fof(f3235,plain,
( $false
| ~ spl72_4
| ~ spl72_7
| spl72_33 ),
inference(subsumption_resolution,[],[f3234,f407]) ).
fof(f3234,plain,
( ~ ssList(nil)
| ~ spl72_4
| ~ spl72_7
| spl72_33 ),
inference(subsumption_resolution,[],[f3233,f1439]) ).
fof(f1439,plain,
( ssItem(sK26(nil))
| ~ spl72_4
| ~ spl72_7 ),
inference(superposition,[],[f1293,f898]) ).
fof(f1293,plain,
( ssItem(sK26(sK24))
| ~ spl72_7 ),
inference(avatar_component_clause,[],[f1292]) ).
fof(f1292,plain,
( spl72_7
<=> ssItem(sK26(sK24)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_7])]) ).
fof(f3233,plain,
( ~ ssItem(sK26(nil))
| ~ ssList(nil)
| spl72_33 ),
inference(resolution,[],[f3227,f569]) ).
fof(f3227,plain,
( ~ ssList(cons(sK26(nil),nil))
| spl72_33 ),
inference(avatar_component_clause,[],[f3225]) ).
fof(f3225,plain,
( spl72_33
<=> ssList(cons(sK26(nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_33])]) ).
fof(f3232,plain,
( ~ spl72_33
| spl72_34
| ~ spl72_4
| ~ spl72_7 ),
inference(avatar_split_clause,[],[f3215,f1292,f896,f3229,f3225]) ).
fof(f3229,plain,
( spl72_34
<=> ssList(cons(sK26(nil),sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_34])]) ).
fof(f3215,plain,
( ssList(cons(sK26(nil),sK20))
| ~ ssList(cons(sK26(nil),nil))
| ~ spl72_4
| ~ spl72_7 ),
inference(subsumption_resolution,[],[f3206,f386]) ).
fof(f3206,plain,
( ssList(cons(sK26(nil),sK20))
| ~ ssList(sK20)
| ~ ssList(cons(sK26(nil),nil))
| ~ spl72_4
| ~ spl72_7 ),
inference(superposition,[],[f579,f1989]) ).
fof(f1989,plain,
( cons(sK26(nil),sK20) = app(cons(sK26(nil),nil),sK20)
| ~ spl72_4
| ~ spl72_7 ),
inference(forward_demodulation,[],[f1968,f898]) ).
fof(f1968,plain,
( cons(sK26(sK24),sK20) = app(cons(sK26(sK24),nil),sK20)
| ~ spl72_7 ),
inference(resolution,[],[f1625,f1293]) ).
fof(f3195,plain,
( ~ spl72_4
| ~ spl72_11
| spl72_31 ),
inference(avatar_contradiction_clause,[],[f3194]) ).
fof(f3194,plain,
( $false
| ~ spl72_4
| ~ spl72_11
| spl72_31 ),
inference(subsumption_resolution,[],[f3193,f407]) ).
fof(f3193,plain,
( ~ ssList(nil)
| ~ spl72_4
| ~ spl72_11
| spl72_31 ),
inference(subsumption_resolution,[],[f3192,f1441]) ).
fof(f1441,plain,
( ssItem(hd(nil))
| ~ spl72_4
| ~ spl72_11 ),
inference(superposition,[],[f1395,f898]) ).
fof(f1395,plain,
( ssItem(hd(sK24))
| ~ spl72_11 ),
inference(avatar_component_clause,[],[f1394]) ).
fof(f1394,plain,
( spl72_11
<=> ssItem(hd(sK24)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_11])]) ).
fof(f3192,plain,
( ~ ssItem(hd(nil))
| ~ ssList(nil)
| spl72_31 ),
inference(resolution,[],[f3186,f569]) ).
fof(f3186,plain,
( ~ ssList(cons(hd(nil),nil))
| spl72_31 ),
inference(avatar_component_clause,[],[f3184]) ).
fof(f3184,plain,
( spl72_31
<=> ssList(cons(hd(nil),nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_31])]) ).
fof(f3191,plain,
( ~ spl72_31
| spl72_32
| ~ spl72_4
| ~ spl72_11 ),
inference(avatar_split_clause,[],[f3174,f1394,f896,f3188,f3184]) ).
fof(f3188,plain,
( spl72_32
<=> ssList(cons(hd(nil),sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_32])]) ).
fof(f3174,plain,
( ssList(cons(hd(nil),sK20))
| ~ ssList(cons(hd(nil),nil))
| ~ spl72_4
| ~ spl72_11 ),
inference(subsumption_resolution,[],[f3165,f386]) ).
fof(f3165,plain,
( ssList(cons(hd(nil),sK20))
| ~ ssList(sK20)
| ~ ssList(cons(hd(nil),nil))
| ~ spl72_4
| ~ spl72_11 ),
inference(superposition,[],[f579,f1987]) ).
fof(f1987,plain,
( cons(hd(nil),sK20) = app(cons(hd(nil),nil),sK20)
| ~ spl72_4
| ~ spl72_11 ),
inference(forward_demodulation,[],[f1963,f898]) ).
fof(f1963,plain,
( cons(hd(sK24),sK20) = app(cons(hd(sK24),nil),sK20)
| ~ spl72_11 ),
inference(resolution,[],[f1625,f1395]) ).
fof(f3131,plain,
( ~ spl72_9
| spl72_29 ),
inference(avatar_contradiction_clause,[],[f3130]) ).
fof(f3130,plain,
( $false
| ~ spl72_9
| spl72_29 ),
inference(subsumption_resolution,[],[f3129,f407]) ).
fof(f3129,plain,
( ~ ssList(nil)
| ~ spl72_9
| spl72_29 ),
inference(subsumption_resolution,[],[f3128,f1376]) ).
fof(f3128,plain,
( ~ ssItem(hd(sK20))
| ~ ssList(nil)
| spl72_29 ),
inference(resolution,[],[f3122,f569]) ).
fof(f3122,plain,
( ~ ssList(cons(hd(sK20),nil))
| spl72_29 ),
inference(avatar_component_clause,[],[f3120]) ).
fof(f3127,plain,
( ~ spl72_29
| spl72_30
| ~ spl72_9 ),
inference(avatar_split_clause,[],[f3110,f1375,f3124,f3120]) ).
fof(f3124,plain,
( spl72_30
<=> ssList(cons(hd(sK20),sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_30])]) ).
fof(f3110,plain,
( ssList(cons(hd(sK20),sK20))
| ~ ssList(cons(hd(sK20),nil))
| ~ spl72_9 ),
inference(subsumption_resolution,[],[f3101,f386]) ).
fof(f3101,plain,
( ssList(cons(hd(sK20),sK20))
| ~ ssList(sK20)
| ~ ssList(cons(hd(sK20),nil))
| ~ spl72_9 ),
inference(superposition,[],[f579,f1962]) ).
fof(f2993,plain,
( ~ spl72_27
| spl72_28
| ~ spl72_25
| ~ spl72_26 ),
inference(avatar_split_clause,[],[f2735,f2711,f2707,f2990,f2986]) ).
fof(f2986,plain,
( spl72_27
<=> rearsegP(sK69(sK20,sK20),sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_27])]) ).
fof(f2990,plain,
( spl72_28
<=> sK20 = sK69(sK20,sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_28])]) ).
fof(f2711,plain,
( spl72_26
<=> rearsegP(sK20,sK69(sK20,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_26])]) ).
fof(f2735,plain,
( sK20 = sK69(sK20,sK20)
| ~ rearsegP(sK69(sK20,sK20),sK20)
| ~ spl72_25
| ~ spl72_26 ),
inference(subsumption_resolution,[],[f2734,f2708]) ).
fof(f2734,plain,
( sK20 = sK69(sK20,sK20)
| ~ rearsegP(sK69(sK20,sK20),sK20)
| ~ ssList(sK69(sK20,sK20))
| ~ spl72_26 ),
inference(subsumption_resolution,[],[f2731,f386]) ).
fof(f2731,plain,
( sK20 = sK69(sK20,sK20)
| ~ rearsegP(sK69(sK20,sK20),sK20)
| ~ ssList(sK20)
| ~ ssList(sK69(sK20,sK20))
| ~ spl72_26 ),
inference(resolution,[],[f2713,f583]) ).
fof(f2713,plain,
( rearsegP(sK20,sK69(sK20,sK20))
| ~ spl72_26 ),
inference(avatar_component_clause,[],[f2711]) ).
fof(f2719,plain,
( ~ spl72_4
| spl72_25 ),
inference(avatar_contradiction_clause,[],[f2718]) ).
fof(f2718,plain,
( $false
| ~ spl72_4
| spl72_25 ),
inference(subsumption_resolution,[],[f2717,f386]) ).
fof(f2717,plain,
( ~ ssList(sK20)
| ~ spl72_4
| spl72_25 ),
inference(subsumption_resolution,[],[f2716,f2259]) ).
fof(f2716,plain,
( ~ frontsegP(sK20,sK20)
| ~ ssList(sK20)
| spl72_25 ),
inference(duplicate_literal_removal,[],[f2715]) ).
fof(f2715,plain,
( ~ frontsegP(sK20,sK20)
| ~ ssList(sK20)
| ~ ssList(sK20)
| spl72_25 ),
inference(resolution,[],[f2709,f595]) ).
fof(f2709,plain,
( ~ ssList(sK69(sK20,sK20))
| spl72_25 ),
inference(avatar_component_clause,[],[f2707]) ).
fof(f2714,plain,
( ~ spl72_25
| spl72_26
| ~ spl72_4 ),
inference(avatar_split_clause,[],[f2705,f896,f2711,f2707]) ).
fof(f2705,plain,
( rearsegP(sK20,sK69(sK20,sK20))
| ~ ssList(sK69(sK20,sK20))
| ~ spl72_4 ),
inference(subsumption_resolution,[],[f2702,f386]) ).
fof(f2702,plain,
( rearsegP(sK20,sK69(sK20,sK20))
| ~ ssList(sK20)
| ~ ssList(sK69(sK20,sK20))
| ~ spl72_4 ),
inference(superposition,[],[f1990,f2693]) ).
fof(f2638,plain,
( ~ spl72_4
| spl72_23 ),
inference(avatar_contradiction_clause,[],[f2637]) ).
fof(f2637,plain,
( $false
| ~ spl72_4
| spl72_23 ),
inference(subsumption_resolution,[],[f2636,f386]) ).
fof(f2636,plain,
( ~ ssList(sK20)
| ~ spl72_4
| spl72_23 ),
inference(subsumption_resolution,[],[f2635,f407]) ).
fof(f2635,plain,
( ~ ssList(nil)
| ~ ssList(sK20)
| ~ spl72_4
| spl72_23 ),
inference(subsumption_resolution,[],[f2634,f2097]) ).
fof(f2634,plain,
( ~ rearsegP(sK20,nil)
| ~ ssList(nil)
| ~ ssList(sK20)
| spl72_23 ),
inference(resolution,[],[f2628,f588]) ).
fof(f2628,plain,
( ~ ssList(sK66(sK20,nil))
| spl72_23 ),
inference(avatar_component_clause,[],[f2626]) ).
fof(f2626,plain,
( spl72_23
<=> ssList(sK66(sK20,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_23])]) ).
fof(f2633,plain,
( ~ spl72_23
| spl72_24
| ~ spl72_4 ),
inference(avatar_split_clause,[],[f2624,f896,f2630,f2626]) ).
fof(f2630,plain,
( spl72_24
<=> frontsegP(sK20,sK66(sK20,nil)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_24])]) ).
fof(f2624,plain,
( frontsegP(sK20,sK66(sK20,nil))
| ~ ssList(sK66(sK20,nil))
| ~ spl72_4 ),
inference(subsumption_resolution,[],[f2622,f407]) ).
fof(f2622,plain,
( frontsegP(sK20,sK66(sK20,nil))
| ~ ssList(nil)
| ~ ssList(sK66(sK20,nil))
| ~ spl72_4 ),
inference(superposition,[],[f2128,f2611]) ).
fof(f2611,plain,
( sK20 = app(sK66(sK20,nil),nil)
| ~ spl72_4 ),
inference(subsumption_resolution,[],[f2610,f386]) ).
fof(f2610,plain,
( sK20 = app(sK66(sK20,nil),nil)
| ~ ssList(sK20)
| ~ spl72_4 ),
inference(subsumption_resolution,[],[f2600,f407]) ).
fof(f2600,plain,
( sK20 = app(sK66(sK20,nil),nil)
| ~ ssList(nil)
| ~ ssList(sK20)
| ~ spl72_4 ),
inference(resolution,[],[f589,f2097]) ).
fof(f2390,plain,
( ~ spl72_21
| spl72_22
| ~ spl72_17
| ~ spl72_18 ),
inference(avatar_split_clause,[],[f2119,f2052,f2048,f2387,f2383]) ).
fof(f2383,plain,
( spl72_21
<=> rearsegP(sK20,cons(sK71,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_21])]) ).
fof(f2119,plain,
( sK20 = cons(sK71,sK20)
| ~ rearsegP(sK20,cons(sK71,sK20))
| ~ spl72_17
| ~ spl72_18 ),
inference(subsumption_resolution,[],[f2118,f386]) ).
fof(f2118,plain,
( sK20 = cons(sK71,sK20)
| ~ rearsegP(sK20,cons(sK71,sK20))
| ~ ssList(sK20)
| ~ spl72_17
| ~ spl72_18 ),
inference(subsumption_resolution,[],[f2117,f2054]) ).
fof(f2117,plain,
( sK20 = cons(sK71,sK20)
| ~ rearsegP(sK20,cons(sK71,sK20))
| ~ ssList(cons(sK71,sK20))
| ~ ssList(sK20)
| ~ spl72_17 ),
inference(resolution,[],[f2093,f583]) ).
fof(f2093,plain,
( rearsegP(cons(sK71,sK20),sK20)
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f2092,f386]) ).
fof(f2092,plain,
( rearsegP(cons(sK71,sK20),sK20)
| ~ ssList(sK20)
| ~ spl72_17 ),
inference(subsumption_resolution,[],[f2074,f2049]) ).
fof(f2074,plain,
( rearsegP(cons(sK71,sK20),sK20)
| ~ ssList(cons(sK71,nil))
| ~ ssList(sK20) ),
inference(superposition,[],[f1990,f1986]) ).
fof(f2381,plain,
( ~ spl72_19
| spl72_20
| ~ spl72_15
| ~ spl72_16 ),
inference(avatar_split_clause,[],[f2116,f2003,f1999,f2378,f2374]) ).
fof(f2374,plain,
( spl72_19
<=> rearsegP(sK20,cons(sK70,sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_19])]) ).
fof(f2116,plain,
( sK20 = cons(sK70,sK20)
| ~ rearsegP(sK20,cons(sK70,sK20))
| ~ spl72_15
| ~ spl72_16 ),
inference(subsumption_resolution,[],[f2115,f386]) ).
fof(f2115,plain,
( sK20 = cons(sK70,sK20)
| ~ rearsegP(sK20,cons(sK70,sK20))
| ~ ssList(sK20)
| ~ spl72_15
| ~ spl72_16 ),
inference(subsumption_resolution,[],[f2114,f2005]) ).
fof(f2114,plain,
( sK20 = cons(sK70,sK20)
| ~ rearsegP(sK20,cons(sK70,sK20))
| ~ ssList(cons(sK70,sK20))
| ~ ssList(sK20)
| ~ spl72_15 ),
inference(resolution,[],[f2091,f583]) ).
fof(f2091,plain,
( rearsegP(cons(sK70,sK20),sK20)
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f2090,f386]) ).
fof(f2090,plain,
( rearsegP(cons(sK70,sK20),sK20)
| ~ ssList(sK20)
| ~ spl72_15 ),
inference(subsumption_resolution,[],[f2073,f2000]) ).
fof(f2073,plain,
( rearsegP(cons(sK70,sK20),sK20)
| ~ ssList(cons(sK70,nil))
| ~ ssList(sK20) ),
inference(superposition,[],[f1990,f1985]) ).
fof(f2059,plain,
spl72_17,
inference(avatar_contradiction_clause,[],[f2058]) ).
fof(f2058,plain,
( $false
| spl72_17 ),
inference(subsumption_resolution,[],[f2057,f407]) ).
fof(f2057,plain,
( ~ ssList(nil)
| spl72_17 ),
inference(subsumption_resolution,[],[f2056,f614]) ).
fof(f2056,plain,
( ~ ssItem(sK71)
| ~ ssList(nil)
| spl72_17 ),
inference(resolution,[],[f2050,f569]) ).
fof(f2050,plain,
( ~ ssList(cons(sK71,nil))
| spl72_17 ),
inference(avatar_component_clause,[],[f2048]) ).
fof(f2055,plain,
( ~ spl72_17
| spl72_18 ),
inference(avatar_split_clause,[],[f2046,f2052,f2048]) ).
fof(f2046,plain,
( ssList(cons(sK71,sK20))
| ~ ssList(cons(sK71,nil)) ),
inference(subsumption_resolution,[],[f2042,f386]) ).
fof(f2042,plain,
( ssList(cons(sK71,sK20))
| ~ ssList(sK20)
| ~ ssList(cons(sK71,nil)) ),
inference(superposition,[],[f579,f1986]) ).
fof(f2010,plain,
spl72_15,
inference(avatar_contradiction_clause,[],[f2009]) ).
fof(f2009,plain,
( $false
| spl72_15 ),
inference(subsumption_resolution,[],[f2008,f407]) ).
fof(f2008,plain,
( ~ ssList(nil)
| spl72_15 ),
inference(subsumption_resolution,[],[f2007,f613]) ).
fof(f2007,plain,
( ~ ssItem(sK70)
| ~ ssList(nil)
| spl72_15 ),
inference(resolution,[],[f2001,f569]) ).
fof(f2001,plain,
( ~ ssList(cons(sK70,nil))
| spl72_15 ),
inference(avatar_component_clause,[],[f1999]) ).
fof(f2006,plain,
( ~ spl72_15
| spl72_16 ),
inference(avatar_split_clause,[],[f1997,f2003,f1999]) ).
fof(f1997,plain,
( ssList(cons(sK70,sK20))
| ~ ssList(cons(sK70,nil)) ),
inference(subsumption_resolution,[],[f1993,f386]) ).
fof(f1993,plain,
( ssList(cons(sK70,sK20))
| ~ ssList(sK20)
| ~ ssList(cons(sK70,nil)) ),
inference(superposition,[],[f579,f1985]) ).
fof(f1612,plain,
spl72_13,
inference(avatar_contradiction_clause,[],[f1611]) ).
fof(f1611,plain,
( $false
| spl72_13 ),
inference(subsumption_resolution,[],[f1610,f386]) ).
fof(f1610,plain,
( ~ ssList(sK20)
| spl72_13 ),
inference(subsumption_resolution,[],[f1609,f392]) ).
fof(f1609,plain,
( nil = sK20
| ~ ssList(sK20)
| spl72_13 ),
inference(resolution,[],[f1603,f471]) ).
fof(f1603,plain,
( ~ ssList(sK25(sK20))
| spl72_13 ),
inference(avatar_component_clause,[],[f1601]) ).
fof(f1608,plain,
( ~ spl72_13
| spl72_14
| ~ spl72_5 ),
inference(avatar_split_clause,[],[f1599,f1273,f1605,f1601]) ).
fof(f1605,plain,
( spl72_14
<=> memberP(sK20,sK26(sK20)) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_14])]) ).
fof(f1599,plain,
( memberP(sK20,sK26(sK20))
| ~ ssList(sK25(sK20))
| ~ spl72_5 ),
inference(subsumption_resolution,[],[f1259,f1274]) ).
fof(f1259,plain,
( memberP(sK20,sK26(sK20))
| ~ ssList(sK25(sK20))
| ~ ssItem(sK26(sK20)) ),
inference(superposition,[],[f646,f1246]) ).
fof(f1448,plain,
( spl72_1
| ~ spl72_2
| ~ spl72_3
| ~ spl72_4 ),
inference(avatar_contradiction_clause,[],[f1447]) ).
fof(f1447,plain,
( $false
| spl72_1
| ~ spl72_2
| ~ spl72_3
| ~ spl72_4 ),
inference(subsumption_resolution,[],[f1434,f852]) ).
fof(f852,plain,
( hd(nil) != sK27(nil)
| spl72_1
| ~ spl72_2 ),
inference(forward_demodulation,[],[f842,f847]) ).
fof(f847,plain,
( nil = sK21
| ~ spl72_2 ),
inference(avatar_component_clause,[],[f845]) ).
fof(f845,plain,
( spl72_2
<=> nil = sK21 ),
introduced(avatar_definition,[new_symbols(naming,[spl72_2])]) ).
fof(f842,plain,
( hd(sK21) != sK27(sK21)
| spl72_1 ),
inference(avatar_component_clause,[],[f841]) ).
fof(f841,plain,
( spl72_1
<=> hd(sK21) = sK27(sK21) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_1])]) ).
fof(f1446,plain,
( ~ spl72_2
| ~ spl72_4 ),
inference(avatar_contradiction_clause,[],[f1445]) ).
fof(f1445,plain,
( $false
| ~ spl72_2
| ~ spl72_4 ),
inference(subsumption_resolution,[],[f1444,f392]) ).
fof(f1444,plain,
( nil = sK20
| ~ spl72_2
| ~ spl72_4 ),
inference(forward_demodulation,[],[f1443,f847]) ).
fof(f1424,plain,
( ~ spl72_2
| spl72_4 ),
inference(avatar_contradiction_clause,[],[f1423]) ).
fof(f1423,plain,
( $false
| ~ spl72_2
| spl72_4 ),
inference(subsumption_resolution,[],[f1422,f386]) ).
fof(f1422,plain,
( ~ ssList(sK20)
| ~ spl72_2
| spl72_4 ),
inference(subsumption_resolution,[],[f1421,f394]) ).
fof(f1421,plain,
( ~ ssList(sK24)
| ~ ssList(sK20)
| ~ spl72_2
| spl72_4 ),
inference(subsumption_resolution,[],[f1420,f897]) ).
fof(f897,plain,
( nil != sK24
| spl72_4 ),
inference(avatar_component_clause,[],[f896]) ).
fof(f1420,plain,
( nil = sK24
| ~ ssList(sK24)
| ~ ssList(sK20)
| ~ spl72_2 ),
inference(subsumption_resolution,[],[f1416,f847]) ).
fof(f1416,plain,
( nil != sK21
| nil = sK24
| ~ ssList(sK24)
| ~ ssList(sK20) ),
inference(superposition,[],[f598,f656]) ).
fof(f1405,plain,
( spl72_4
| spl72_11 ),
inference(avatar_contradiction_clause,[],[f1404]) ).
fof(f1404,plain,
( $false
| spl72_4
| spl72_11 ),
inference(subsumption_resolution,[],[f1403,f394]) ).
fof(f1403,plain,
( ~ ssList(sK24)
| spl72_4
| spl72_11 ),
inference(subsumption_resolution,[],[f1402,f897]) ).
fof(f1402,plain,
( nil = sK24
| ~ ssList(sK24)
| spl72_11 ),
inference(resolution,[],[f1396,f474]) ).
fof(f1396,plain,
( ~ ssItem(hd(sK24))
| spl72_11 ),
inference(avatar_component_clause,[],[f1394]) ).
fof(f1401,plain,
( ~ spl72_11
| ~ spl72_12
| spl72_4 ),
inference(avatar_split_clause,[],[f1373,f896,f1398,f1394]) ).
fof(f1373,plain,
( sK24 != tl(sK24)
| ~ ssItem(hd(sK24))
| spl72_4 ),
inference(subsumption_resolution,[],[f1372,f394]) ).
fof(f1372,plain,
( sK24 != tl(sK24)
| ~ ssItem(hd(sK24))
| ~ ssList(sK24)
| spl72_4 ),
inference(inner_rewriting,[],[f1370]) ).
fof(f1370,plain,
( sK24 != tl(sK24)
| ~ ssItem(hd(sK24))
| ~ ssList(tl(sK24))
| spl72_4 ),
inference(superposition,[],[f571,f1353]) ).
fof(f1353,plain,
( sK24 = cons(hd(sK24),tl(sK24))
| spl72_4 ),
inference(subsumption_resolution,[],[f1318,f897]) ).
fof(f1318,plain,
( nil = sK24
| sK24 = cons(hd(sK24),tl(sK24)) ),
inference(resolution,[],[f476,f394]) ).
fof(f1386,plain,
spl72_9,
inference(avatar_contradiction_clause,[],[f1385]) ).
fof(f1385,plain,
( $false
| spl72_9 ),
inference(subsumption_resolution,[],[f1384,f386]) ).
fof(f1384,plain,
( ~ ssList(sK20)
| spl72_9 ),
inference(subsumption_resolution,[],[f1383,f392]) ).
fof(f1383,plain,
( nil = sK20
| ~ ssList(sK20)
| spl72_9 ),
inference(resolution,[],[f1377,f474]) ).
fof(f1377,plain,
( ~ ssItem(hd(sK20))
| spl72_9 ),
inference(avatar_component_clause,[],[f1375]) ).
fof(f1382,plain,
( ~ spl72_9
| ~ spl72_10 ),
inference(avatar_split_clause,[],[f1363,f1379,f1375]) ).
fof(f1379,plain,
( spl72_10
<=> sK20 = tl(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_10])]) ).
fof(f1363,plain,
( sK20 != tl(sK20)
| ~ ssItem(hd(sK20)) ),
inference(subsumption_resolution,[],[f1362,f386]) ).
fof(f1362,plain,
( sK20 != tl(sK20)
| ~ ssItem(hd(sK20))
| ~ ssList(sK20) ),
inference(inner_rewriting,[],[f1360]) ).
fof(f1360,plain,
( sK20 != tl(sK20)
| ~ ssItem(hd(sK20))
| ~ ssList(tl(sK20)) ),
inference(superposition,[],[f571,f1348]) ).
fof(f1303,plain,
( spl72_4
| spl72_7 ),
inference(avatar_contradiction_clause,[],[f1302]) ).
fof(f1302,plain,
( $false
| spl72_4
| spl72_7 ),
inference(subsumption_resolution,[],[f1301,f394]) ).
fof(f1301,plain,
( ~ ssList(sK24)
| spl72_4
| spl72_7 ),
inference(subsumption_resolution,[],[f1300,f897]) ).
fof(f1300,plain,
( nil = sK24
| ~ ssList(sK24)
| spl72_7 ),
inference(resolution,[],[f1294,f472]) ).
fof(f1294,plain,
( ~ ssItem(sK26(sK24))
| spl72_7 ),
inference(avatar_component_clause,[],[f1292]) ).
fof(f1299,plain,
( ~ spl72_7
| ~ spl72_8
| spl72_4 ),
inference(avatar_split_clause,[],[f1271,f896,f1296,f1292]) ).
fof(f1296,plain,
( spl72_8
<=> sK24 = sK25(sK24) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_8])]) ).
fof(f1271,plain,
( sK24 != sK25(sK24)
| ~ ssItem(sK26(sK24))
| spl72_4 ),
inference(subsumption_resolution,[],[f1270,f394]) ).
fof(f1270,plain,
( sK24 != sK25(sK24)
| ~ ssItem(sK26(sK24))
| ~ ssList(sK24)
| spl72_4 ),
inference(inner_rewriting,[],[f1268]) ).
fof(f1268,plain,
( sK24 != sK25(sK24)
| ~ ssItem(sK26(sK24))
| ~ ssList(sK25(sK24))
| spl72_4 ),
inference(superposition,[],[f571,f1251]) ).
fof(f1251,plain,
( sK24 = cons(sK26(sK24),sK25(sK24))
| spl72_4 ),
inference(subsumption_resolution,[],[f1216,f897]) ).
fof(f1216,plain,
( nil = sK24
| sK24 = cons(sK26(sK24),sK25(sK24)) ),
inference(resolution,[],[f473,f394]) ).
fof(f1284,plain,
spl72_5,
inference(avatar_contradiction_clause,[],[f1283]) ).
fof(f1283,plain,
( $false
| spl72_5 ),
inference(subsumption_resolution,[],[f1282,f386]) ).
fof(f1282,plain,
( ~ ssList(sK20)
| spl72_5 ),
inference(subsumption_resolution,[],[f1281,f392]) ).
fof(f1281,plain,
( nil = sK20
| ~ ssList(sK20)
| spl72_5 ),
inference(resolution,[],[f1275,f472]) ).
fof(f1275,plain,
( ~ ssItem(sK26(sK20))
| spl72_5 ),
inference(avatar_component_clause,[],[f1273]) ).
fof(f1280,plain,
( ~ spl72_5
| ~ spl72_6 ),
inference(avatar_split_clause,[],[f1261,f1277,f1273]) ).
fof(f1277,plain,
( spl72_6
<=> sK20 = sK25(sK20) ),
introduced(avatar_definition,[new_symbols(naming,[spl72_6])]) ).
fof(f1261,plain,
( sK20 != sK25(sK20)
| ~ ssItem(sK26(sK20)) ),
inference(subsumption_resolution,[],[f1260,f386]) ).
fof(f1260,plain,
( sK20 != sK25(sK20)
| ~ ssItem(sK26(sK20))
| ~ ssList(sK20) ),
inference(inner_rewriting,[],[f1258]) ).
fof(f1258,plain,
( sK20 != sK25(sK20)
| ~ ssItem(sK26(sK20))
| ~ ssList(sK25(sK20)) ),
inference(superposition,[],[f571,f1246]) ).
fof(f899,plain,
( spl72_3
| spl72_4 ),
inference(avatar_split_clause,[],[f809,f896,f892]) ).
fof(f809,plain,
( nil = sK24
| hd(sK24) = sK27(sK24) ),
inference(resolution,[],[f478,f394]) ).
fof(f848,plain,
( spl72_1
| spl72_2 ),
inference(avatar_split_clause,[],[f806,f845,f841]) ).
fof(f806,plain,
( nil = sK21
| hd(sK21) = sK27(sK21) ),
inference(resolution,[],[f478,f387]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12 % Problem : SWC245+1 : TPTP v8.2.0. Released v2.4.0.
% 0.12/0.14 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.14/0.35 % Computer : n018.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Sun May 19 03:03:08 EDT 2024
% 0.14/0.36 % CPUTime :
% 0.14/0.36 % (20126)Running in auto input_syntax mode. Trying TPTP
% 0.14/0.39 % (20129)WARNING: value z3 for option sas not known
% 0.14/0.39 % (20129)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.14/0.40 % (20128)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.14/0.40 % (20127)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.14/0.40 % (20130)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.14/0.40 % (20131)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.14/0.40 % (20132)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.14/0.40 % (20133)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)
% 0.21/0.43 TRYING [1]
% 0.21/0.43 TRYING [1]
% 0.21/0.43 TRYING [2]
% 0.21/0.43 TRYING [2]
% 0.21/0.44 TRYING [3]
% 0.21/0.44 TRYING [3]
% 0.21/0.48 TRYING [4]
% 0.21/0.50 TRYING [4]
% 1.76/0.62 TRYING [5]
% 1.98/0.69 TRYING [5]
% 4.09/0.96 TRYING [6]
% 5.21/1.11 TRYING [6]
% 7.90/1.50 TRYING [1]
% 7.90/1.51 TRYING [2]
% 7.90/1.51 TRYING [3]
% 8.28/1.56 TRYING [4]
% 9.39/1.70 TRYING [7]
% 9.39/1.71 TRYING [5]
% 12.10/2.09 TRYING [7]
% 12.25/2.11 TRYING [6]
% 18.59/3.08 TRYING [7]
% 20.00/3.29 TRYING [8]
% 25.35/4.07 TRYING [8]
% 33.25/5.15 TRYING [8]
% 38.13/5.81 % (20129)First to succeed.
% 38.13/5.84 % (20129)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-20126"
% 38.13/5.85 % (20129)Refutation found. Thanks to Tanya!
% 38.13/5.85 % SZS status Theorem for theBenchmark
% 38.13/5.85 % SZS output start Proof for theBenchmark
% See solution above
% 38.13/5.86 % (20129)------------------------------
% 38.13/5.86 % (20129)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 38.13/5.86 % (20129)Termination reason: Refutation
% 38.13/5.86
% 38.13/5.86 % (20129)Memory used [KB]: 25030
% 38.13/5.86 % (20129)Time elapsed: 5.453 s
% 38.13/5.86 % (20129)Instructions burned: 13501 (million)
% 38.13/5.86 % (20126)Success in time 5.476 s
%------------------------------------------------------------------------------