%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC031-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:39:40 PM UTC 2026
% Result : Unsatisfiable 32.27s 4.60s
% Output : CNFRefutation 31.01s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 232
% Syntax : Number of formulae : 792 ( 127 unt; 156 def)
% Number of atoms : 2476 ( 345 equ)
% Maximal formula atoms : 9 ( 3 avg)
% Number of connectives : 3215 (1531 ~;1528 |; 0 &)
% ( 156 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 167 ( 165 usr; 157 prp; 0-2 aty)
% Number of functors : 37 ( 37 usr; 6 con; 0-2 aty)
% Number of variables : 791 ( 791 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
ssItem(skac2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [U] : ssList(skaf82(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [U] : ssList(skaf81(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] : ssList(skaf80(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] : ssList(skaf77(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [U] : ssList(skaf76(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [U] : ssList(skaf75(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [U] : ssList(skaf73(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [U] : ssList(skaf72(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U] : ssList(skaf71(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [U] : ssList(skaf68(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] : ssList(skaf67(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [U] : ssList(skaf66(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [U] : ssList(skaf63(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [U] : ssList(skaf62(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [U] : ssList(skaf61(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U] : ssList(skaf58(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] : ssList(skaf57(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [U] : ssList(skaf56(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [U] : ssList(skaf53(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [U] : ssList(skaf52(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [U] : ssList(skaf51(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [U] : ssItem(skaf49(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [U] : ssItem(skaf44(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [U,V] : ssList(skaf46(U,V)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( rearsegP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [U] :
( frontsegP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [U] :
( totalorderedP(cons(U,nil))
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f72,axiom,
! [U,V] :
( ssItem(V)
| duplicatefreeP(U)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [U] :
( nil = U
| ssList(tl(U))
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [U] :
( nil = U
| ~ ssList(U)
| ~ segmentP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( nil = U
| ~ ssList(U)
| ~ frontsegP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f98,axiom,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f100,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f102,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssItem(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f104,axiom,
! [U] :
( nil = U
| cons(hd(U),tl(U)) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f109,axiom,
! [U] :
( nil = U
| cons(skaf83(U),skaf82(U)) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f117,axiom,
! [U,V] :
( ~ ssItem(U)
| ~ ssItem(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f119,axiom,
! [U,V] :
( nil = V
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f123,axiom,
! [U,V] :
( hd(app(V,U)) = hd(V)
| nil = V
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f127,axiom,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ segmentP(V,U)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f128,axiom,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f129,axiom,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f131,axiom,
! [U,V] :
( app(skaf46(U,V),V) = U
| ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f133,axiom,
! [U,V] :
( tl(app(V,U)) = app(tl(V),U)
| nil = V
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f136,axiom,
! [U,V,W] :
( rearsegP(app(W,U),V)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ rearsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f137,axiom,
! [U,V,W] :
( frontsegP(app(U,W),V)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f143,axiom,
! [U,V,W] :
( rearsegP(W,V)
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| app(U,V) != W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f144,axiom,
! [U,V,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f149,axiom,
! [U,V,W] :
( app(app(W,V),U) = app(W,app(V,U))
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f150,axiom,
! [U,V,W] :
( V = W
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != app(U,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f151,axiom,
! [U,V,W] :
( U = W
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| app(U,V) != app(W,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f152,axiom,
! [U,V,W] :
( segmentP(U,W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ segmentP(V,W)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f154,axiom,
! [U,V,W] :
( frontsegP(U,W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ frontsegP(V,W)
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f168,axiom,
! [U,V] :
( app(app(skaf47(U,V),V),skaf48(V,U)) = U
| ~ ssList(U)
| ~ ssList(V)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f172,axiom,
! [U,V,W,X] :
( segmentP(app(app(X,U),W),V)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(X)
| ~ ssList(W)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f174,axiom,
! [U,V,W,X] :
( frontsegP(V,X)
| ~ ssItem(U)
| ~ ssItem(W)
| ~ ssList(V)
| ~ ssList(X)
| ~ frontsegP(cons(U,V),cons(W,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f176,axiom,
! [U,V,W,X] :
( U = W
| ~ ssItem(U)
| ~ ssItem(W)
| ~ ssList(V)
| ~ ssList(X)
| ~ frontsegP(cons(U,V),cons(W,X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f178,axiom,
! [U,V,W,X] :
( frontsegP(cons(W,U),cons(X,V))
| ~ ssItem(W)
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(V)
| W != X
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f179,axiom,
! [U,V,W,X,Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f182,axiom,
! [U,V,W,X,Y,Z] :
( leq(V,X)
| ~ ssList(Z)
| ~ totalorderedP(Z)
| ~ ssItem(V)
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(Y)
| app(app(U,cons(V,W)),cons(X,Y)) != Z ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f187,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
frontsegP(sk4,sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
! [A] :
( ~ totalorderedP(A)
| ~ segmentP(A,sk3)
| ~ frontsegP(sk4,A)
| ~ neq(sk3,A)
| ~ ssList(A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
( nil = sk1
| nil = sk2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( nil != sk2
| nil != sk1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f206,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f208,plain,
ssItem(skac2),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f211,plain,
! [X0] : ssList(skaf82(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f212,plain,
! [X0] : ssList(skaf81(X0)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f213,plain,
! [X0] : ssList(skaf80(X0)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f216,plain,
! [X0] : ssList(skaf77(X0)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f217,plain,
! [X0] : ssList(skaf76(X0)),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f218,plain,
! [X0] : ssList(skaf75(X0)),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f220,plain,
! [X0] : ssList(skaf73(X0)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f221,plain,
! [X0] : ssList(skaf72(X0)),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f222,plain,
! [X0] : ssList(skaf71(X0)),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f225,plain,
! [X0] : ssList(skaf68(X0)),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f226,plain,
! [X0] : ssList(skaf67(X0)),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f227,plain,
! [X0] : ssList(skaf66(X0)),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f230,plain,
! [X0] : ssList(skaf63(X0)),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f231,plain,
! [X0] : ssList(skaf62(X0)),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f232,plain,
! [X0] : ssList(skaf61(X0)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f235,plain,
! [X0] : ssList(skaf58(X0)),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f236,plain,
! [X0] : ssList(skaf57(X0)),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f237,plain,
! [X0] : ssList(skaf56(X0)),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f240,plain,
! [X0] : ssList(skaf53(X0)),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f241,plain,
! [X0] : ssList(skaf52(X0)),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f242,plain,
! [X0] : ssList(skaf51(X0)),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f244,plain,
! [X0] : ssItem(skaf49(X0)),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f245,plain,
! [X0] : ssItem(skaf44(X0)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f248,plain,
! [X0,X1] : ssList(skaf46(X0,X1)),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f254,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f256,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f258,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f259,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f265,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f67]) ).
fof(f270,plain,
( ! [V] : ssItem(V)
| ! [U] :
( duplicatefreeP(U)
| ~ ssList(U) ) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f271,plain,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f270]) ).
fof(f272,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f273,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f274,plain,
! [X0] :
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f279,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f283,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f84]) ).
fof(f284,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f285,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f297,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f298,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f301,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f100]) ).
fof(f303,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f305,plain,
! [X0] :
( nil = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f310,plain,
! [X0] :
( nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f323,plain,
! [U] :
( ~ ssItem(U)
| ! [V] :
( ~ ssItem(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f117]) ).
fof(f324,plain,
! [X0,X1] :
( ~ ssItem(X0)
| ~ ssItem(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f323]) ).
fof(f327,plain,
! [V] :
( nil = V
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f328,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f327]) ).
fof(f332,plain,
! [X0,X1] :
( hd(app(X1,X0)) = hd(X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f338,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f339,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f340,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f342,plain,
! [X0,X1] :
( app(skaf46(X0,X1),X1) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f131]) ).
fof(f344,plain,
! [X0,X1] :
( tl(app(X1,X0)) = app(tl(X1),X0)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f349,plain,
! [X0,X1,X2] :
( rearsegP(app(X2,X0),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f136]) ).
fof(f350,plain,
! [X0,X1,X2] :
( frontsegP(app(X0,X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f356,plain,
! [V,W] :
( rearsegP(W,V)
| ~ ssList(W)
| ~ ssList(V)
| ! [U] :
( ~ ssList(U)
| app(U,V) != W ) ),
inference(miniscoping,[status(thm)],[f143]) ).
fof(f357,plain,
! [X0,X1,X2] :
( rearsegP(X2,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f356]) ).
fof(f358,plain,
! [U,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != W ) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f359,plain,
! [X0,X1,X2] :
( frontsegP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f358]) ).
fof(f367,plain,
! [X0,X1,X2] :
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f368,plain,
! [V,W] :
( V = W
| ~ ssList(W)
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != app(U,W) ) ),
inference(miniscoping,[status(thm)],[f150]) ).
fof(f369,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != app(X0,X2) ),
inference(cnf_transformation,[status(thm)],[f368]) ).
fof(f370,plain,
! [U,W] :
( U = W
| ~ ssList(W)
| ! [V] :
( ~ ssList(V)
| ~ ssList(U)
| app(U,V) != app(W,V) ) ),
inference(miniscoping,[status(thm)],[f151]) ).
fof(f371,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != app(X2,X1) ),
inference(cnf_transformation,[status(thm)],[f370]) ).
fof(f372,plain,
! [U,W] :
( segmentP(U,W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ ssList(W)
| ~ segmentP(V,W)
| ~ segmentP(U,V) ) ),
inference(miniscoping,[status(thm)],[f152]) ).
fof(f373,plain,
! [X0,X1,X2] :
( segmentP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f372]) ).
fof(f376,plain,
! [U,W] :
( frontsegP(U,W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ ssList(W)
| ~ frontsegP(V,W)
| ~ frontsegP(U,V) ) ),
inference(miniscoping,[status(thm)],[f154]) ).
fof(f377,plain,
! [X0,X1,X2] :
( frontsegP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f376]) ).
fof(f397,plain,
! [X0,X1] :
( app(app(skaf47(X0,X1),X1),skaf48(X1,X0)) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f403,plain,
! [X0,X1,X2,X3] :
( segmentP(app(app(X3,X0),X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f406,plain,
! [V,X] :
( frontsegP(V,X)
| ! [U] :
( ~ ssItem(U)
| ! [W] :
( ~ ssItem(W)
| ~ ssList(V)
| ~ ssList(X)
| ~ frontsegP(cons(U,V),cons(W,X)) ) ) ),
inference(miniscoping,[status(thm)],[f174]) ).
fof(f407,plain,
! [X0,X1,X2,X3] :
( frontsegP(X1,X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f406]) ).
fof(f410,plain,
! [U,W] :
( U = W
| ~ ssItem(U)
| ~ ssItem(W)
| ! [V] :
( ~ ssList(V)
| ! [X] :
( ~ ssList(X)
| ~ frontsegP(cons(U,V),cons(W,X)) ) ) ),
inference(miniscoping,[status(thm)],[f176]) ).
fof(f411,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(cnf_transformation,[status(thm)],[f410]) ).
fof(f414,plain,
! [X0,X1,X2,X3] :
( frontsegP(cons(X2,X0),cons(X3,X1))
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X1)
| X2 != X3
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f415,plain,
! [Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ! [V] :
( ~ ssItem(V)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| ! [X] :
( ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ) ) ) ) ),
inference(miniscoping,[status(thm)],[f179]) ).
fof(f416,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(X4)
| ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
inference(cnf_transformation,[status(thm)],[f415]) ).
fof(f421,plain,
! [V,X] :
( leq(V,X)
| ! [Z] :
( ~ ssList(Z)
| ~ totalorderedP(Z)
| ~ ssItem(V)
| ~ ssItem(X)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| ! [Y] :
( ~ ssList(Y)
| app(app(U,cons(V,W)),cons(X,Y)) != Z ) ) ) ) ),
inference(miniscoping,[status(thm)],[f182]) ).
fof(f422,plain,
! [X0,X1,X2,X3,X4,X5] :
( leq(X1,X3)
| ~ ssList(X5)
| ~ totalorderedP(X5)
| ~ ssItem(X1)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X4)
| app(app(X0,cons(X1,X2)),cons(X3,X4)) != X5 ),
inference(cnf_transformation,[status(thm)],[f421]) ).
fof(f429,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f430,plain,
ssList(sk2),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f433,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f434,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f435,plain,
frontsegP(sk4,sk3),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f437,plain,
! [X0] :
( ~ totalorderedP(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0)
| ~ neq(sk3,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f438,plain,
( nil = sk1
| nil = sk2 ),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f441,plain,
( nil != sk2
| nil != sk1 ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f442,definition,
! [X0] :
( sQ0_spl
<=> ( duplicatefreeP(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f443,plain,
! [X0] :
( ~ sQ0_spl
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,definition,
! [X1] :
( sQ1_spl
<=> ssItem(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f446,plain,
! [X0] :
( ~ sQ1_spl
| ssItem(X0) ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f448,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f271,f442,f445]) ).
fof(f449,definition,
( sQ2_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( ~ sQ2_spl
| nil = sk2 ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,definition,
( sQ3_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( ~ sQ3_spl
| nil = sk1 ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f438,f449,f452]) ).
fof(f458,plain,
( ~ sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f441,f452,f449]) ).
fof(f469,plain,
! [X1] :
( ~ ssItem(X1)
| ~ ssItem(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f324]) ).
fof(f470,plain,
! [X0] :
( ~ ssItem(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f469]) ).
fof(f473,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f357]) ).
fof(f474,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f473,f284]) ).
fof(f475,plain,
! [X1,X0] :
( frontsegP(app(X0,X1),X0)
| ~ ssList(app(X0,X1))
| ~ ssList(X0)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f359]) ).
fof(f476,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f475,f284]) ).
fof(f481,plain,
! [X0,X1,X3] :
( frontsegP(cons(X3,X0),cons(X3,X1))
| ~ ssItem(X3)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f414]) ).
fof(f482,plain,
! [X0,X1,X2] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f481]) ).
fof(f483,plain,
! [X0,X1,X2,X3] :
( ~ ssList(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ duplicatefreeP(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f416]) ).
fof(f486,plain,
! [X0,X1,X2,X3,X4] :
( leq(X4,X3)
| ~ ssList(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ totalorderedP(app(app(X2,cons(X4,X1)),cons(X3,X0)))
| ~ ssItem(X4)
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f422]) ).
fof(f492,plain,
frontsegP(sk2,sk3),
inference(forward_demodulation,[status(thm)],[f433,f435]) ).
fof(f493,plain,
frontsegP(sk2,sk1),
inference(forward_demodulation,[status(thm)],[f434,f492]) ).
fof(f495,plain,
! [X0] :
( ~ totalorderedP(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk4,X0)
| ~ neq(sk1,X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f434,f437]) ).
fof(f496,plain,
! [X0] :
( ~ totalorderedP(X0)
| ~ segmentP(X0,sk3)
| ~ frontsegP(sk2,X0)
| ~ neq(sk1,X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f433,f495]) ).
fof(f497,plain,
! [X0] :
( ~ totalorderedP(X0)
| ~ segmentP(X0,sk1)
| ~ frontsegP(sk2,X0)
| ~ neq(sk1,X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f434,f496]) ).
fof(f498,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ ssList(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f483,f443]) ).
fof(f500,plain,
( ~ sQ2_spl
| frontsegP(nil,sk1) ),
inference(backward_demodulation,[status(thm)],[f450,f493]) ).
fof(f504,plain,
( nil = nil
| ~ segmentP(nil,nil) ),
inference(resolution,[status(thm)],[f279,f206]) ).
fof(f506,definition,
( sQ4_spl
<=> segmentP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f507,plain,
( ~ sQ4_spl
| segmentP(nil,nil) ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f508,plain,
( sQ4_spl
| ~ segmentP(nil,nil) ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f509,definition,
( sQ5_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f512,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f504,f506,f509]) ).
fof(f521,plain,
! [X0] :
( ~ sQ3_spl
| ~ totalorderedP(X0)
| ~ segmentP(X0,sk1)
| ~ frontsegP(sk2,X0)
| ~ neq(nil,X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f453,f497]) ).
fof(f522,plain,
! [X0] :
( ~ sQ3_spl
| ~ totalorderedP(X0)
| ~ segmentP(X0,nil)
| ~ frontsegP(sk2,X0)
| ~ neq(nil,X0)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f453,f521]) ).
fof(f523,plain,
! [X0] :
( ~ sQ3_spl
| ~ totalorderedP(X0)
| ~ frontsegP(sk2,X0)
| ~ neq(nil,X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f522,f254]) ).
fof(f526,plain,
~ neq(skac2,skac2),
inference(resolution,[status(thm)],[f208,f470]) ).
fof(f538,plain,
! [X0] :
( nil = skaf82(X0)
| ~ segmentP(nil,skaf82(X0)) ),
inference(resolution,[status(thm)],[f211,f279]) ).
fof(f539,plain,
! [X0] :
( nil = skaf81(X0)
| ~ segmentP(nil,skaf81(X0)) ),
inference(resolution,[status(thm)],[f212,f279]) ).
fof(f542,plain,
( sQ4_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f508,f254]) ).
fof(f544,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f542,f206]) ).
fof(f545,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f544]) ).
fof(f557,definition,
( sQ8_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f559,plain,
( sQ8_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f557]) ).
fof(f563,plain,
! [X0] :
( ~ ssList(X0)
| cons(skac2,X0) != nil ),
inference(resolution,[status(thm)],[f298,f208]) ).
fof(f565,plain,
! [X0] :
( nil = skaf80(X0)
| ~ segmentP(nil,skaf80(X0)) ),
inference(resolution,[status(thm)],[f213,f279]) ).
fof(f570,plain,
! [X0] :
( nil = skaf77(X0)
| ~ segmentP(nil,skaf77(X0)) ),
inference(resolution,[status(thm)],[f216,f279]) ).
fof(f571,plain,
! [X0] :
( nil = skaf76(X0)
| ~ segmentP(nil,skaf76(X0)) ),
inference(resolution,[status(thm)],[f217,f279]) ).
fof(f572,plain,
! [X0] :
( nil = skaf75(X0)
| ~ segmentP(nil,skaf75(X0)) ),
inference(resolution,[status(thm)],[f218,f279]) ).
fof(f575,plain,
! [X0] :
( nil = skaf73(X0)
| ~ segmentP(nil,skaf73(X0)) ),
inference(resolution,[status(thm)],[f220,f279]) ).
fof(f576,plain,
! [X0] :
( nil = skaf72(X0)
| ~ segmentP(nil,skaf72(X0)) ),
inference(resolution,[status(thm)],[f221,f279]) ).
fof(f577,plain,
! [X0] :
( nil = skaf71(X0)
| ~ segmentP(nil,skaf71(X0)) ),
inference(resolution,[status(thm)],[f222,f279]) ).
fof(f582,plain,
! [X0] :
( nil = skaf68(X0)
| ~ segmentP(nil,skaf68(X0)) ),
inference(resolution,[status(thm)],[f225,f279]) ).
fof(f583,plain,
! [X0] :
( nil = skaf67(X0)
| ~ segmentP(nil,skaf67(X0)) ),
inference(resolution,[status(thm)],[f226,f279]) ).
fof(f584,plain,
! [X0] :
( nil = skaf66(X0)
| ~ segmentP(nil,skaf66(X0)) ),
inference(resolution,[status(thm)],[f227,f279]) ).
fof(f593,plain,
! [X0] :
( ~ sQ3_spl
| ~ totalorderedP(X0)
| ~ frontsegP(sk2,X0)
| ~ ssList(X0)
| nil = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f523]) ).
fof(f597,definition,
! [X0] :
( sQ9_spl
<=> ( ~ totalorderedP(X0)
| ~ frontsegP(sk2,X0)
| ~ ssList(X0)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f598,plain,
! [X0] :
( ~ sQ9_spl
| ~ totalorderedP(X0)
| ~ frontsegP(sk2,X0)
| ~ ssList(X0)
| nil = X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f597]) ).
fof(f600,plain,
( ~ sQ3_spl
| ~ sQ8_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f593,f597,f557,f452]) ).
fof(f604,definition,
( sQ11_spl
<=> skac2 = skac2 ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f559,f206]) ).
fof(f616,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f615]) ).
fof(f617,plain,
! [X0] :
( ~ sQ9_spl
| ~ totalorderedP(X0)
| ~ frontsegP(sk2,X0)
| nil = X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f598]) ).
fof(f637,plain,
cons(skac2,nil) != nil,
inference(resolution,[status(thm)],[f563,f206]) ).
fof(f646,plain,
! [X0] :
( skac2 = X0
| neq(skac2,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f303,f208]) ).
fof(f691,plain,
! [X0] :
( ~ sQ9_spl
| ~ ssItem(X0)
| ~ frontsegP(sk2,cons(X0,nil))
| nil = cons(X0,nil)
| ~ ssList(cons(X0,nil)) ),
inference(resolution,[status(thm)],[f617,f265]) ).
fof(f694,definition,
( sQ14_spl
<=> frontsegP(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f695,plain,
( ~ sQ14_spl
| frontsegP(sk2,nil) ),
inference(component_clause,[status(thm)],[f694]) ).
fof(f709,plain,
! [X0] :
( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(resolution,[status(thm)],[f338,f254]) ).
fof(f712,definition,
! [X0] :
( sQ16_spl
<=> ( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f715,plain,
( ~ sQ8_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f709,f712,f557]) ).
fof(f725,plain,
! [X0] :
( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(nil,X0) ),
inference(resolution,[status(thm)],[f340,f258]) ).
fof(f730,definition,
( sQ18_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f732,plain,
( sQ18_spl
| ~ ssList(sk2) ),
inference(component_clause,[status(thm)],[f730]) ).
fof(f734,definition,
! [X0] :
( sQ19_spl
<=> ( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f737,plain,
( ~ sQ8_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f725,f734,f557]) ).
fof(f754,plain,
! [X0] : app(skaf51(X0),nil) = skaf51(X0),
inference(resolution,[status(thm)],[f272,f242]) ).
fof(f755,plain,
! [X0] : app(skaf52(X0),nil) = skaf52(X0),
inference(resolution,[status(thm)],[f272,f241]) ).
fof(f756,plain,
! [X0] : app(skaf53(X0),nil) = skaf53(X0),
inference(resolution,[status(thm)],[f272,f240]) ).
fof(f757,plain,
! [X0] : app(skaf56(X0),nil) = skaf56(X0),
inference(resolution,[status(thm)],[f272,f237]) ).
fof(f758,plain,
! [X0] : app(skaf57(X0),nil) = skaf57(X0),
inference(resolution,[status(thm)],[f272,f236]) ).
fof(f759,plain,
! [X0] : app(skaf58(X0),nil) = skaf58(X0),
inference(resolution,[status(thm)],[f272,f235]) ).
fof(f760,plain,
! [X0] : app(skaf61(X0),nil) = skaf61(X0),
inference(resolution,[status(thm)],[f272,f232]) ).
fof(f761,plain,
! [X0] : app(skaf62(X0),nil) = skaf62(X0),
inference(resolution,[status(thm)],[f272,f231]) ).
fof(f762,plain,
! [X0] : app(skaf63(X0),nil) = skaf63(X0),
inference(resolution,[status(thm)],[f272,f230]) ).
fof(f763,plain,
! [X0] : app(skaf66(X0),nil) = skaf66(X0),
inference(resolution,[status(thm)],[f272,f227]) ).
fof(f764,plain,
! [X0] : app(skaf67(X0),nil) = skaf67(X0),
inference(resolution,[status(thm)],[f272,f226]) ).
fof(f765,plain,
! [X0] : app(skaf68(X0),nil) = skaf68(X0),
inference(resolution,[status(thm)],[f272,f225]) ).
fof(f766,plain,
! [X0] : app(skaf71(X0),nil) = skaf71(X0),
inference(resolution,[status(thm)],[f272,f222]) ).
fof(f767,plain,
! [X0] : app(skaf72(X0),nil) = skaf72(X0),
inference(resolution,[status(thm)],[f272,f221]) ).
fof(f768,plain,
! [X0] : app(skaf73(X0),nil) = skaf73(X0),
inference(resolution,[status(thm)],[f272,f220]) ).
fof(f769,plain,
! [X0] : app(skaf75(X0),nil) = skaf75(X0),
inference(resolution,[status(thm)],[f272,f218]) ).
fof(f770,plain,
! [X0] : app(skaf76(X0),nil) = skaf76(X0),
inference(resolution,[status(thm)],[f272,f217]) ).
fof(f771,plain,
! [X0] : app(skaf77(X0),nil) = skaf77(X0),
inference(resolution,[status(thm)],[f272,f216]) ).
fof(f772,plain,
! [X0] : app(skaf80(X0),nil) = skaf80(X0),
inference(resolution,[status(thm)],[f272,f213]) ).
fof(f773,plain,
app(sk2,nil) = sk2,
inference(resolution,[status(thm)],[f272,f430]) ).
fof(f774,plain,
! [X0] : app(skaf81(X0),nil) = skaf81(X0),
inference(resolution,[status(thm)],[f272,f212]) ).
fof(f775,plain,
! [X0] : app(skaf82(X0),nil) = skaf82(X0),
inference(resolution,[status(thm)],[f272,f211]) ).
fof(f776,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f272,f206]) ).
fof(f777,plain,
! [X0] :
( frontsegP(sk2,X0)
| ~ ssList(sk2)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(sk2,X0) ),
inference(paramodulation,[status(thm)],[f773,f350]) ).
fof(f778,definition,
! [X0] :
( sQ20_spl
<=> ( frontsegP(sk2,X0)
| ~ ssList(X0)
| ~ frontsegP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f781,plain,
( ~ sQ18_spl
| ~ sQ8_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f777,f778,f557,f730]) ).
fof(f782,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f732,f430]) ).
fof(f783,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f782]) ).
fof(f784,plain,
! [X0] :
( frontsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f776,f350]) ).
fof(f785,definition,
! [X0] :
( sQ21_spl
<=> ( frontsegP(nil,X0)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f788,plain,
( ~ sQ8_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f784,f785,f557]) ).
fof(f790,plain,
( frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f776,f476]) ).
fof(f791,plain,
( frontsegP(sk2,sk2)
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f773,f476]) ).
fof(f794,definition,
( sQ22_spl
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f795,plain,
( ~ sQ22_spl
| frontsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f794]) ).
fof(f797,plain,
( sQ22_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f790,f557,f794]) ).
fof(f798,definition,
( sQ23_spl
<=> frontsegP(sk2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f799,plain,
( ~ sQ23_spl
| frontsegP(sk2,sk2) ),
inference(component_clause,[status(thm)],[f798]) ).
fof(f801,plain,
( sQ23_spl
| ~ sQ18_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f791,f557,f730,f798]) ).
fof(f807,definition,
( sQ24_spl
<=> sk2 = sk2 ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f819,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ frontsegP(nil,X0) ),
inference(resolution,[status(thm)],[f377,f283]) ).
fof(f825,definition,
! [X0,X1] :
( sQ27_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f828,plain,
( ~ sQ8_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f819,f825,f557]) ).
fof(f837,plain,
! [X0] : app(nil,skaf51(X0)) = skaf51(X0),
inference(resolution,[status(thm)],[f273,f242]) ).
fof(f838,plain,
! [X0] : app(nil,skaf52(X0)) = skaf52(X0),
inference(resolution,[status(thm)],[f273,f241]) ).
fof(f839,plain,
! [X0] : app(nil,skaf53(X0)) = skaf53(X0),
inference(resolution,[status(thm)],[f273,f240]) ).
fof(f840,plain,
! [X0] : app(nil,skaf56(X0)) = skaf56(X0),
inference(resolution,[status(thm)],[f273,f237]) ).
fof(f841,plain,
! [X0] : app(nil,skaf57(X0)) = skaf57(X0),
inference(resolution,[status(thm)],[f273,f236]) ).
fof(f842,plain,
! [X0] : app(nil,skaf58(X0)) = skaf58(X0),
inference(resolution,[status(thm)],[f273,f235]) ).
fof(f843,plain,
! [X0] : app(nil,skaf61(X0)) = skaf61(X0),
inference(resolution,[status(thm)],[f273,f232]) ).
fof(f844,plain,
! [X0] : app(nil,skaf62(X0)) = skaf62(X0),
inference(resolution,[status(thm)],[f273,f231]) ).
fof(f845,plain,
! [X0] : app(nil,skaf63(X0)) = skaf63(X0),
inference(resolution,[status(thm)],[f273,f230]) ).
fof(f846,plain,
! [X0] : app(nil,skaf66(X0)) = skaf66(X0),
inference(resolution,[status(thm)],[f273,f227]) ).
fof(f847,plain,
! [X0] : app(nil,skaf67(X0)) = skaf67(X0),
inference(resolution,[status(thm)],[f273,f226]) ).
fof(f848,plain,
! [X0] : app(nil,skaf68(X0)) = skaf68(X0),
inference(resolution,[status(thm)],[f273,f225]) ).
fof(f849,plain,
! [X0] : app(nil,skaf71(X0)) = skaf71(X0),
inference(resolution,[status(thm)],[f273,f222]) ).
fof(f850,plain,
! [X0] : app(nil,skaf72(X0)) = skaf72(X0),
inference(resolution,[status(thm)],[f273,f221]) ).
fof(f851,plain,
! [X0] : app(nil,skaf73(X0)) = skaf73(X0),
inference(resolution,[status(thm)],[f273,f220]) ).
fof(f852,plain,
! [X0] : app(nil,skaf75(X0)) = skaf75(X0),
inference(resolution,[status(thm)],[f273,f218]) ).
fof(f853,plain,
! [X0] : app(nil,skaf76(X0)) = skaf76(X0),
inference(resolution,[status(thm)],[f273,f217]) ).
fof(f854,plain,
! [X0] : app(nil,skaf77(X0)) = skaf77(X0),
inference(resolution,[status(thm)],[f273,f216]) ).
fof(f855,plain,
! [X0] : app(nil,skaf80(X0)) = skaf80(X0),
inference(resolution,[status(thm)],[f273,f213]) ).
fof(f856,plain,
app(nil,sk2) = sk2,
inference(resolution,[status(thm)],[f273,f430]) ).
fof(f857,plain,
! [X0] : app(nil,skaf81(X0)) = skaf81(X0),
inference(resolution,[status(thm)],[f273,f212]) ).
fof(f858,plain,
! [X0] : app(nil,skaf82(X0)) = skaf82(X0),
inference(resolution,[status(thm)],[f273,f211]) ).
fof(f860,plain,
( frontsegP(sk2,nil)
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(paramodulation,[status(thm)],[f856,f476]) ).
fof(f861,plain,
! [X0] :
( frontsegP(sk2,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ frontsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f856,f350]) ).
fof(f862,plain,
( sQ14_spl
| ~ sQ8_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f860,f730,f557,f694]) ).
fof(f863,definition,
! [X0] :
( sQ28_spl
<=> ( frontsegP(sk2,X0)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f864,plain,
! [X0] :
( ~ sQ28_spl
| frontsegP(sk2,X0)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(component_clause,[status(thm)],[f863]) ).
fof(f866,plain,
( ~ sQ8_spl
| ~ sQ18_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f861,f863,f730,f557]) ).
fof(f928,plain,
! [X0] :
( ~ sQ28_spl
| sk2 = X0
| ~ ssList(sk2)
| ~ ssList(X0)
| ~ frontsegP(X0,sk2)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ),
inference(resolution,[status(thm)],[f864,f340]) ).
fof(f929,definition,
! [X0] :
( sQ31_spl
<=> ( sk2 = X0
| ~ ssList(X0)
| ~ frontsegP(X0,sk2)
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f932,plain,
( ~ sQ28_spl
| ~ sQ18_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f928,f929,f730,f863]) ).
fof(f965,plain,
! [X0,X1] :
( ~ sQ4_spl
| segmentP(app(app(X1,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f403,f507]) ).
fof(f966,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| segmentP(app(app(X1,X2),X0),nil)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f403,f254]) ).
fof(f969,definition,
! [X0,X1] :
( sQ36_spl
<=> ( segmentP(app(app(X1,nil),X0),nil)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f972,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f965,f969,f557,f506]) ).
fof(f973,definition,
! [X0,X1,X2] :
( sQ37_spl
<=> ( ~ ssList(X2)
| segmentP(app(app(X1,X2),X0),nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f976,plain,
( ~ sQ8_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f966,f973,f557]) ).
fof(f996,plain,
! [X0] :
( ~ sQ9_spl
| ~ ssItem(X0)
| ~ frontsegP(sk2,cons(X0,nil))
| nil = cons(X0,nil)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f285,f691]) ).
fof(f1004,definition,
! [X0] :
( sQ38_spl
<=> ( ~ ssItem(X0)
| ~ frontsegP(sk2,cons(X0,nil))
| nil = cons(X0,nil)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f1005,plain,
! [X0] :
( ~ sQ38_spl
| ~ ssItem(X0)
| ~ frontsegP(sk2,cons(X0,nil))
| nil = cons(X0,nil)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1004]) ).
fof(f1007,plain,
( ~ sQ9_spl
| ~ sQ8_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f996,f1004,f557,f597]) ).
fof(f1009,plain,
! [X0] :
( ~ sQ38_spl
| ~ frontsegP(sk2,cons(X0,nil))
| nil = cons(X0,nil)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1005]) ).
fof(f1011,plain,
! [X0,X1] :
( ~ sQ38_spl
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ ssList(cons(X0,nil))
| ~ frontsegP(X1,cons(X0,nil))
| ~ frontsegP(sk2,X1)
| nil = cons(X0,nil)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1009,f377]) ).
fof(f1012,definition,
! [X0,X1] :
( sQ39_spl
<=> ( ~ ssList(X1)
| ~ ssList(cons(X0,nil))
| ~ frontsegP(X1,cons(X0,nil))
| ~ frontsegP(sk2,X1)
| nil = cons(X0,nil)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f1013,plain,
! [X0,X1] :
( ~ sQ39_spl
| ~ ssList(X1)
| ~ ssList(cons(X0,nil))
| ~ frontsegP(X1,cons(X0,nil))
| ~ frontsegP(sk2,X1)
| nil = cons(X0,nil)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1012]) ).
fof(f1015,plain,
( ~ sQ38_spl
| ~ sQ18_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f1011,f1012,f730,f1004]) ).
fof(f1031,plain,
! [X0,X1] :
( ~ sQ39_spl
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(X1,cons(X0,nil))
| ~ frontsegP(sk2,X1)
| nil = cons(X0,nil)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1013,f285]) ).
fof(f1032,definition,
! [X0,X1] :
( sQ42_spl
<=> ( ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(X1,cons(X0,nil))
| ~ frontsegP(sk2,X1)
| nil = cons(X0,nil)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f1033,plain,
! [X0,X1] :
( ~ sQ42_spl
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ frontsegP(X1,cons(X0,nil))
| ~ frontsegP(sk2,X1)
| nil = cons(X0,nil)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1032]) ).
fof(f1035,plain,
( ~ sQ39_spl
| ~ sQ8_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f1031,f1032,f557,f1012]) ).
fof(f1036,plain,
! [X0,X1] :
( ~ sQ42_spl
| ~ ssList(X1)
| ~ frontsegP(X1,cons(X0,nil))
| ~ frontsegP(sk2,X1)
| nil = cons(X0,nil)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1033]) ).
fof(f1102,plain,
! [X0,X1,X2] :
( X2 = X2
| ~ ssItem(X2)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f482,f411]) ).
fof(f1104,plain,
! [X0,X1] :
( ~ sQ42_spl
| ~ ssList(cons(X1,X0))
| ~ frontsegP(sk2,cons(X1,X0))
| nil = cons(X1,nil)
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(resolution,[status(thm)],[f482,f1036]) ).
fof(f1106,definition,
! [X0,X1] :
( sQ47_spl
<=> ( ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f1107,plain,
! [X0,X1] :
( ~ sQ47_spl
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(component_clause,[status(thm)],[f1106]) ).
fof(f1109,definition,
! [X2] :
( sQ48_spl
<=> ( X2 = X2
| ~ ssItem(X2)
| ~ ssItem(X2)
| ~ ssItem(X2) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1112,plain,
( sQ48_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f1102,f1106,f1109]) ).
fof(f1120,definition,
! [X0,X1] :
( sQ51_spl
<=> ( ~ ssList(cons(X1,X0))
| ~ frontsegP(sk2,cons(X1,X0))
| nil = cons(X1,nil)
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f1121,plain,
! [X0,X1] :
( ~ sQ51_spl
| ~ ssList(cons(X1,X0))
| ~ frontsegP(sk2,cons(X1,X0))
| nil = cons(X1,nil)
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(component_clause,[status(thm)],[f1120]) ).
fof(f1123,plain,
( ~ sQ42_spl
| ~ sQ8_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f1104,f1120,f557,f1032]) ).
fof(f1125,plain,
! [X0,X1,X2,X3] :
( ~ sQ47_spl
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[f407,f1126]) ).
fof(f1126,plain,
! [X0,X1] :
( ~ sQ47_spl
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f1107]) ).
fof(f1162,definition,
( sQ53_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f1164,plain,
( sQ53_spl
| ~ ssList(sk1) ),
inference(component_clause,[status(thm)],[f1162]) ).
fof(f1166,plain,
( ~ sQ2_spl
| nil = sk1
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f500,f283]) ).
fof(f1167,plain,
( ~ sQ2_spl
| sQ3_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f1166,f1162,f452,f449]) ).
fof(f1168,plain,
( sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1164,f429]) ).
fof(f1169,plain,
sQ53_spl,
inference(contradiction_clause,[status(thm)],[f1168]) ).
fof(f1170,plain,
! [X0,X1] :
( ~ sQ51_spl
| ~ ssList(cons(X1,X0))
| ~ frontsegP(sk2,cons(X1,X0))
| nil = cons(X1,nil)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(duplicate_literals_removal,[status(thm)],[f1121]) ).
fof(f1171,plain,
! [X0,X1] :
( ~ sQ51_spl
| ~ ssList(cons(X1,X0))
| ~ frontsegP(sk2,cons(X1,X0))
| nil = cons(X1,nil)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1170,f258]) ).
fof(f1217,plain,
! [X0,X1] :
( ~ sQ47_spl
| ~ ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1125,f259]) ).
fof(f1218,plain,
! [X0,X1] :
( ~ sQ47_spl
| ~ ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1217]) ).
fof(f1220,plain,
! [X0,X1] :
( ~ sQ47_spl
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1218,f285]) ).
fof(f1221,plain,
! [X0] :
( ~ sQ47_spl
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1220,f245]) ).
fof(f1238,plain,
( ~ sQ47_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f430,f1221]) ).
fof(f1267,plain,
~ sQ47_spl,
inference(contradiction_clause,[status(thm)],[f1238]) ).
fof(f1268,plain,
! [X0,X1] :
( ~ sQ51_spl
| ~ frontsegP(sk2,cons(X1,X0))
| nil = cons(X1,nil)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1171,f285]) ).
fof(f1291,plain,
! [X0] :
( ~ sQ4_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ segmentP(X0,nil) ),
inference(resolution,[status(thm)],[f373,f507]) ).
fof(f1292,plain,
! [X0,X1] :
( ~ ssList(X1)
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ segmentP(X0,X1) ),
inference(resolution,[status(thm)],[f373,f254]) ).
fof(f1299,definition,
! [X0] :
( sQ55_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ segmentP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1302,plain,
( ~ sQ4_spl
| ~ sQ8_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f1291,f1299,f557,f506]) ).
fof(f1303,definition,
! [X0,X1] :
( sQ56_spl
<=> ( ~ ssList(X1)
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f1306,plain,
( ~ sQ8_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f1292,f1303,f557]) ).
fof(f1455,plain,
! [X0] :
( frontsegP(skaf51(X0),skaf51(X0))
| ~ ssList(skaf51(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f754,f476]) ).
fof(f1456,definition,
! [X0] :
( sQ57_spl
<=> ( frontsegP(skaf51(X0),skaf51(X0))
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1459,plain,
( sQ57_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1455,f557,f1456]) ).
fof(f1460,plain,
! [X0] :
( frontsegP(skaf52(X0),skaf52(X0))
| ~ ssList(skaf52(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f755,f476]) ).
fof(f1461,definition,
! [X0] :
( sQ58_spl
<=> ( frontsegP(skaf52(X0),skaf52(X0))
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f1464,plain,
( sQ58_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1460,f557,f1461]) ).
fof(f1465,plain,
! [X0] :
( frontsegP(skaf53(X0),skaf53(X0))
| ~ ssList(skaf53(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f756,f476]) ).
fof(f1466,definition,
! [X0] :
( sQ59_spl
<=> ( frontsegP(skaf53(X0),skaf53(X0))
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1469,plain,
( sQ59_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1465,f557,f1466]) ).
fof(f1470,plain,
! [X0] :
( frontsegP(skaf56(X0),skaf56(X0))
| ~ ssList(skaf56(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f757,f476]) ).
fof(f1471,definition,
! [X0] :
( sQ60_spl
<=> ( frontsegP(skaf56(X0),skaf56(X0))
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1474,plain,
( sQ60_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1470,f557,f1471]) ).
fof(f1475,plain,
! [X0] :
( frontsegP(skaf57(X0),skaf57(X0))
| ~ ssList(skaf57(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f758,f476]) ).
fof(f1476,definition,
! [X0] :
( sQ61_spl
<=> ( frontsegP(skaf57(X0),skaf57(X0))
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1479,plain,
( sQ61_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1475,f557,f1476]) ).
fof(f1480,plain,
! [X0] :
( frontsegP(skaf58(X0),skaf58(X0))
| ~ ssList(skaf58(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f759,f476]) ).
fof(f1481,definition,
! [X0] :
( sQ62_spl
<=> ( frontsegP(skaf58(X0),skaf58(X0))
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1484,plain,
( sQ62_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1480,f557,f1481]) ).
fof(f1485,plain,
! [X0] :
( frontsegP(skaf61(X0),skaf61(X0))
| ~ ssList(skaf61(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f760,f476]) ).
fof(f1486,definition,
! [X0] :
( sQ63_spl
<=> ( frontsegP(skaf61(X0),skaf61(X0))
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1489,plain,
( sQ63_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1485,f557,f1486]) ).
fof(f1490,plain,
! [X0] :
( frontsegP(skaf62(X0),skaf62(X0))
| ~ ssList(skaf62(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f761,f476]) ).
fof(f1491,definition,
! [X0] :
( sQ64_spl
<=> ( frontsegP(skaf62(X0),skaf62(X0))
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1494,plain,
( sQ64_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1490,f557,f1491]) ).
fof(f1521,plain,
( skac2 = skac2
| ~ ssItem(skac2) ),
inference(resolution,[status(thm)],[f646,f526]) ).
fof(f1523,definition,
( sQ65_spl
<=> ssItem(skac2) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1525,plain,
( sQ65_spl
| ~ ssItem(skac2) ),
inference(component_clause,[status(thm)],[f1523]) ).
fof(f1526,plain,
( sQ11_spl
| ~ sQ65_spl ),
inference(split_clause,[status(thm)],[f1521,f1523,f604]) ).
fof(f1615,plain,
! [X0] :
( frontsegP(skaf63(X0),skaf63(X0))
| ~ ssList(skaf63(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f762,f476]) ).
fof(f1616,definition,
! [X0] :
( sQ67_spl
<=> ( frontsegP(skaf63(X0),skaf63(X0))
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1619,plain,
( sQ67_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1615,f557,f1616]) ).
fof(f1620,plain,
! [X0] :
( frontsegP(skaf66(X0),skaf66(X0))
| ~ ssList(skaf66(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f763,f476]) ).
fof(f1621,definition,
! [X0] :
( sQ68_spl
<=> ( frontsegP(skaf66(X0),skaf66(X0))
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1624,plain,
( sQ68_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1620,f557,f1621]) ).
fof(f1625,plain,
! [X0] :
( frontsegP(skaf67(X0),skaf67(X0))
| ~ ssList(skaf67(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f764,f476]) ).
fof(f1626,definition,
! [X0] :
( sQ69_spl
<=> ( frontsegP(skaf67(X0),skaf67(X0))
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1629,plain,
( sQ69_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1625,f557,f1626]) ).
fof(f1630,plain,
! [X0] :
( frontsegP(skaf68(X0),skaf68(X0))
| ~ ssList(skaf68(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f765,f476]) ).
fof(f1631,definition,
! [X0] :
( sQ70_spl
<=> ( frontsegP(skaf68(X0),skaf68(X0))
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1634,plain,
( sQ70_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1630,f557,f1631]) ).
fof(f1635,plain,
! [X0] :
( frontsegP(skaf71(X0),skaf71(X0))
| ~ ssList(skaf71(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f766,f476]) ).
fof(f1636,definition,
! [X0] :
( sQ71_spl
<=> ( frontsegP(skaf71(X0),skaf71(X0))
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1639,plain,
( sQ71_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1635,f557,f1636]) ).
fof(f1640,plain,
! [X0] :
( frontsegP(skaf72(X0),skaf72(X0))
| ~ ssList(skaf72(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f767,f476]) ).
fof(f1641,definition,
! [X0] :
( sQ72_spl
<=> ( frontsegP(skaf72(X0),skaf72(X0))
| ~ ssList(skaf72(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1644,plain,
( sQ72_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1640,f557,f1641]) ).
fof(f1645,plain,
! [X0] :
( frontsegP(skaf73(X0),skaf73(X0))
| ~ ssList(skaf73(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f768,f476]) ).
fof(f1646,definition,
! [X0] :
( sQ73_spl
<=> ( frontsegP(skaf73(X0),skaf73(X0))
| ~ ssList(skaf73(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1649,plain,
( sQ73_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1645,f557,f1646]) ).
fof(f1650,plain,
! [X0] :
( frontsegP(skaf75(X0),skaf75(X0))
| ~ ssList(skaf75(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f769,f476]) ).
fof(f1651,definition,
! [X0] :
( sQ74_spl
<=> ( frontsegP(skaf75(X0),skaf75(X0))
| ~ ssList(skaf75(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1654,plain,
( sQ74_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1650,f557,f1651]) ).
fof(f1655,plain,
! [X0] :
( frontsegP(skaf76(X0),skaf76(X0))
| ~ ssList(skaf76(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f770,f476]) ).
fof(f1656,definition,
! [X0] :
( sQ75_spl
<=> ( frontsegP(skaf76(X0),skaf76(X0))
| ~ ssList(skaf76(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1659,plain,
( sQ75_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1655,f557,f1656]) ).
fof(f1660,plain,
! [X0] :
( frontsegP(skaf77(X0),skaf77(X0))
| ~ ssList(skaf77(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f771,f476]) ).
fof(f1661,definition,
! [X0] :
( sQ76_spl
<=> ( frontsegP(skaf77(X0),skaf77(X0))
| ~ ssList(skaf77(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1664,plain,
( sQ76_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1660,f557,f1661]) ).
fof(f1665,plain,
! [X0] :
( frontsegP(skaf80(X0),skaf80(X0))
| ~ ssList(skaf80(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f772,f476]) ).
fof(f1666,definition,
! [X0] :
( sQ77_spl
<=> ( frontsegP(skaf80(X0),skaf80(X0))
| ~ ssList(skaf80(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1669,plain,
( sQ77_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1665,f557,f1666]) ).
fof(f1670,plain,
! [X0] :
( frontsegP(skaf81(X0),skaf81(X0))
| ~ ssList(skaf81(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f774,f476]) ).
fof(f1671,definition,
! [X0] :
( sQ78_spl
<=> ( frontsegP(skaf81(X0),skaf81(X0))
| ~ ssList(skaf81(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1674,plain,
( sQ78_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1670,f557,f1671]) ).
fof(f1675,plain,
! [X0] :
( frontsegP(skaf82(X0),skaf82(X0))
| ~ ssList(skaf82(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f775,f476]) ).
fof(f1676,definition,
! [X0] :
( sQ79_spl
<=> ( frontsegP(skaf82(X0),skaf82(X0))
| ~ ssList(skaf82(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1679,plain,
( sQ79_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1675,f557,f1676]) ).
fof(f1736,plain,
! [X0] :
( frontsegP(skaf51(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf51(X0)) ),
inference(paramodulation,[status(thm)],[f837,f476]) ).
fof(f1737,definition,
! [X0] :
( sQ86_spl
<=> ( frontsegP(skaf51(X0),nil)
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1740,plain,
( ~ sQ8_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f1736,f1737,f557]) ).
fof(f1741,plain,
! [X0] :
( frontsegP(skaf52(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf52(X0)) ),
inference(paramodulation,[status(thm)],[f838,f476]) ).
fof(f1742,definition,
! [X0] :
( sQ87_spl
<=> ( frontsegP(skaf52(X0),nil)
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1745,plain,
( ~ sQ8_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f1741,f1742,f557]) ).
fof(f1746,plain,
! [X0] :
( frontsegP(skaf53(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf53(X0)) ),
inference(paramodulation,[status(thm)],[f839,f476]) ).
fof(f1747,definition,
! [X0] :
( sQ88_spl
<=> ( frontsegP(skaf53(X0),nil)
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1750,plain,
( ~ sQ8_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f1746,f1747,f557]) ).
fof(f1751,plain,
! [X0] :
( frontsegP(skaf56(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf56(X0)) ),
inference(paramodulation,[status(thm)],[f840,f476]) ).
fof(f1752,definition,
! [X0] :
( sQ89_spl
<=> ( frontsegP(skaf56(X0),nil)
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1755,plain,
( ~ sQ8_spl
| sQ89_spl ),
inference(split_clause,[status(thm)],[f1751,f1752,f557]) ).
fof(f1756,plain,
! [X0] :
( frontsegP(skaf57(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf57(X0)) ),
inference(paramodulation,[status(thm)],[f841,f476]) ).
fof(f1757,definition,
! [X0] :
( sQ90_spl
<=> ( frontsegP(skaf57(X0),nil)
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1760,plain,
( ~ sQ8_spl
| sQ90_spl ),
inference(split_clause,[status(thm)],[f1756,f1757,f557]) ).
fof(f1761,plain,
! [X0] :
( frontsegP(skaf58(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf58(X0)) ),
inference(paramodulation,[status(thm)],[f842,f476]) ).
fof(f1762,definition,
! [X0] :
( sQ91_spl
<=> ( frontsegP(skaf58(X0),nil)
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1765,plain,
( ~ sQ8_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f1761,f1762,f557]) ).
fof(f1766,plain,
! [X0] :
( frontsegP(skaf61(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf61(X0)) ),
inference(paramodulation,[status(thm)],[f843,f476]) ).
fof(f1767,definition,
! [X0] :
( sQ92_spl
<=> ( frontsegP(skaf61(X0),nil)
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1770,plain,
( ~ sQ8_spl
| sQ92_spl ),
inference(split_clause,[status(thm)],[f1766,f1767,f557]) ).
fof(f1771,plain,
! [X0] :
( frontsegP(skaf62(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf62(X0)) ),
inference(paramodulation,[status(thm)],[f844,f476]) ).
fof(f1772,definition,
! [X0] :
( sQ93_spl
<=> ( frontsegP(skaf62(X0),nil)
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1775,plain,
( ~ sQ8_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f1771,f1772,f557]) ).
fof(f1776,plain,
! [X0] :
( frontsegP(skaf63(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf63(X0)) ),
inference(paramodulation,[status(thm)],[f845,f476]) ).
fof(f1777,definition,
! [X0] :
( sQ94_spl
<=> ( frontsegP(skaf63(X0),nil)
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1780,plain,
( ~ sQ8_spl
| sQ94_spl ),
inference(split_clause,[status(thm)],[f1776,f1777,f557]) ).
fof(f1781,plain,
! [X0] :
( frontsegP(skaf66(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf66(X0)) ),
inference(paramodulation,[status(thm)],[f846,f476]) ).
fof(f1782,definition,
! [X0] :
( sQ95_spl
<=> ( frontsegP(skaf66(X0),nil)
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1785,plain,
( ~ sQ8_spl
| sQ95_spl ),
inference(split_clause,[status(thm)],[f1781,f1782,f557]) ).
fof(f1786,plain,
! [X0] :
( frontsegP(skaf67(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf67(X0)) ),
inference(paramodulation,[status(thm)],[f847,f476]) ).
fof(f1787,definition,
! [X0] :
( sQ96_spl
<=> ( frontsegP(skaf67(X0),nil)
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f1790,plain,
( ~ sQ8_spl
| sQ96_spl ),
inference(split_clause,[status(thm)],[f1786,f1787,f557]) ).
fof(f1791,plain,
! [X0] :
( frontsegP(skaf68(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf68(X0)) ),
inference(paramodulation,[status(thm)],[f848,f476]) ).
fof(f1792,definition,
! [X0] :
( sQ97_spl
<=> ( frontsegP(skaf68(X0),nil)
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1795,plain,
( ~ sQ8_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f1791,f1792,f557]) ).
fof(f1796,plain,
! [X0] :
( frontsegP(skaf71(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf71(X0)) ),
inference(paramodulation,[status(thm)],[f849,f476]) ).
fof(f1797,definition,
! [X0] :
( sQ98_spl
<=> ( frontsegP(skaf71(X0),nil)
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1800,plain,
( ~ sQ8_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f1796,f1797,f557]) ).
fof(f1801,plain,
! [X0] :
( frontsegP(skaf72(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf72(X0)) ),
inference(paramodulation,[status(thm)],[f850,f476]) ).
fof(f1802,definition,
! [X0] :
( sQ99_spl
<=> ( frontsegP(skaf72(X0),nil)
| ~ ssList(skaf72(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1805,plain,
( ~ sQ8_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f1801,f1802,f557]) ).
fof(f1806,plain,
! [X0] :
( frontsegP(skaf73(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf73(X0)) ),
inference(paramodulation,[status(thm)],[f851,f476]) ).
fof(f1807,definition,
! [X0] :
( sQ100_spl
<=> ( frontsegP(skaf73(X0),nil)
| ~ ssList(skaf73(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1810,plain,
( ~ sQ8_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f1806,f1807,f557]) ).
fof(f1898,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f279,f373]) ).
fof(f1902,definition,
! [X0,X1] :
( sQ113_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1905,plain,
( ~ sQ8_spl
| sQ113_spl ),
inference(split_clause,[status(thm)],[f1898,f1902,f557]) ).
fof(f1908,plain,
! [X0] :
( frontsegP(skaf75(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf75(X0)) ),
inference(paramodulation,[status(thm)],[f852,f476]) ).
fof(f1909,definition,
! [X0] :
( sQ114_spl
<=> ( frontsegP(skaf75(X0),nil)
| ~ ssList(skaf75(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1912,plain,
( ~ sQ8_spl
| sQ114_spl ),
inference(split_clause,[status(thm)],[f1908,f1909,f557]) ).
fof(f1913,plain,
! [X0] :
( frontsegP(skaf76(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf76(X0)) ),
inference(paramodulation,[status(thm)],[f853,f476]) ).
fof(f1914,definition,
! [X0] :
( sQ115_spl
<=> ( frontsegP(skaf76(X0),nil)
| ~ ssList(skaf76(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f1917,plain,
( ~ sQ8_spl
| sQ115_spl ),
inference(split_clause,[status(thm)],[f1913,f1914,f557]) ).
fof(f1918,plain,
! [X0] :
( frontsegP(skaf77(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf77(X0)) ),
inference(paramodulation,[status(thm)],[f854,f476]) ).
fof(f1919,definition,
! [X0] :
( sQ116_spl
<=> ( frontsegP(skaf77(X0),nil)
| ~ ssList(skaf77(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1922,plain,
( ~ sQ8_spl
| sQ116_spl ),
inference(split_clause,[status(thm)],[f1918,f1919,f557]) ).
fof(f1923,plain,
! [X0] :
( frontsegP(skaf80(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf80(X0)) ),
inference(paramodulation,[status(thm)],[f855,f476]) ).
fof(f1924,definition,
! [X0] :
( sQ117_spl
<=> ( frontsegP(skaf80(X0),nil)
| ~ ssList(skaf80(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1927,plain,
( ~ sQ8_spl
| sQ117_spl ),
inference(split_clause,[status(thm)],[f1923,f1924,f557]) ).
fof(f1928,plain,
! [X0] :
( frontsegP(skaf81(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf81(X0)) ),
inference(paramodulation,[status(thm)],[f857,f476]) ).
fof(f1929,definition,
! [X0] :
( sQ118_spl
<=> ( frontsegP(skaf81(X0),nil)
| ~ ssList(skaf81(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1932,plain,
( ~ sQ8_spl
| sQ118_spl ),
inference(split_clause,[status(thm)],[f1928,f1929,f557]) ).
fof(f1933,plain,
! [X0] :
( frontsegP(skaf82(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf82(X0)) ),
inference(paramodulation,[status(thm)],[f858,f476]) ).
fof(f1934,definition,
! [X0] :
( sQ119_spl
<=> ( frontsegP(skaf82(X0),nil)
| ~ ssList(skaf82(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f1937,plain,
( ~ sQ8_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f1933,f1934,f557]) ).
fof(f2037,plain,
! [X0] :
( ~ sQ14_spl
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ frontsegP(X0,sk2) ),
inference(resolution,[status(thm)],[f377,f695]) ).
fof(f2038,plain,
! [X0] :
( ~ sQ23_spl
| frontsegP(X0,sk2)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ frontsegP(X0,sk2) ),
inference(resolution,[status(thm)],[f377,f799]) ).
fof(f2039,plain,
! [X0,X1] :
( ~ sQ28_spl
| ~ ssList(X1)
| ~ frontsegP(nil,X1)
| frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ frontsegP(X0,sk2) ),
inference(resolution,[status(thm)],[f377,f864]) ).
fof(f2040,plain,
! [X0] :
( ~ sQ22_spl
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(resolution,[status(thm)],[f377,f795]) ).
fof(f2041,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f377,f258]) ).
fof(f2046,definition,
! [X0] :
( sQ132_spl
<=> ( frontsegP(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f2049,plain,
( ~ sQ14_spl
| ~ sQ18_spl
| ~ sQ8_spl
| sQ132_spl ),
inference(split_clause,[status(thm)],[f2037,f2046,f557,f730,f694]) ).
fof(f2050,definition,
! [X0] :
( sQ133_spl
<=> ( frontsegP(X0,sk2)
| ~ ssList(X0)
| ~ frontsegP(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f2053,plain,
( ~ sQ23_spl
| ~ sQ18_spl
| sQ133_spl ),
inference(split_clause,[status(thm)],[f2038,f2050,f730,f798]) ).
fof(f2054,definition,
! [X0,X1] :
( sQ134_spl
<=> ( ~ ssList(X1)
| ~ frontsegP(nil,X1)
| frontsegP(X0,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f2057,plain,
( ~ sQ28_spl
| ~ sQ18_spl
| sQ134_spl ),
inference(split_clause,[status(thm)],[f2039,f2054,f730,f863]) ).
fof(f2058,definition,
! [X0] :
( sQ135_spl
<=> ( frontsegP(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f2061,plain,
( ~ sQ22_spl
| ~ sQ8_spl
| sQ135_spl ),
inference(split_clause,[status(thm)],[f2040,f2058,f557,f794]) ).
fof(f2062,definition,
! [X0,X1] :
( sQ136_spl
<=> ( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f2065,plain,
( ~ sQ8_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f2041,f2062,f557]) ).
fof(f2125,plain,
! [X0] :
( ssList(app(sk2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f284,f430]) ).
fof(f2126,plain,
( ~ sQ4_spl
| app(app(skaf47(nil,nil),nil),skaf48(nil,nil)) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f397,f507]) ).
fof(f2127,plain,
! [X0] :
( ~ ssList(X0)
| app(app(skaf47(X0,nil),nil),skaf48(nil,X0)) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f397,f254]) ).
fof(f2130,definition,
( sQ137_spl
<=> app(app(skaf47(nil,nil),nil),skaf48(nil,nil)) = nil ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f2133,plain,
( ~ sQ4_spl
| sQ137_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2126,f557,f2130,f506]) ).
fof(f2134,definition,
! [X0] :
( sQ138_spl
<=> ( ~ ssList(X0)
| app(app(skaf47(X0,nil),nil),skaf48(nil,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f2137,plain,
( sQ138_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2127,f557,f2134]) ).
fof(f2143,plain,
! [X0,X1] :
( ssList(app(app(sk2,X0),X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2125,f284]) ).
fof(f2185,plain,
! [X0,X1,X2,X3] :
( leq(X0,X2)
| ~ totalorderedP(app(app(sk2,cons(X0,X1)),cons(X2,X3)))
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(cons(X2,X3))
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f2143,f486]) ).
fof(f2196,plain,
! [X0] :
( ssList(app(sk2,X0))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f773,f2143]) ).
fof(f2197,definition,
! [X0,X1,X2,X3] :
( sQ139_spl
<=> ( leq(X0,X2)
| ~ totalorderedP(app(app(sk2,cons(X0,X1)),cons(X2,X3)))
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(cons(X2,X3))
| ~ ssList(cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f2200,plain,
( ~ sQ18_spl
| sQ139_spl ),
inference(split_clause,[status(thm)],[f2185,f2197,f730]) ).
fof(f2201,definition,
! [X0] :
( sQ140_spl
<=> ( ssList(app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f2204,plain,
( sQ140_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2196,f557,f2201]) ).
fof(f2208,plain,
! [X0] :
( ~ sQ14_spl
| frontsegP(app(sk2,X0),nil)
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f350,f695]) ).
fof(f2209,plain,
! [X0] :
( ~ sQ23_spl
| frontsegP(app(sk2,X0),sk2)
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f350,f799]) ).
fof(f2210,plain,
! [X0,X1] :
( ~ sQ28_spl
| ~ ssList(X1)
| ~ frontsegP(nil,X1)
| frontsegP(app(sk2,X0),X1)
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f350,f864]) ).
fof(f2211,plain,
! [X0] :
( ~ sQ22_spl
| frontsegP(app(nil,X0),nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f350,f795]) ).
fof(f2212,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X1,X0),nil)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f350,f258]) ).
fof(f2217,definition,
! [X0] :
( sQ141_spl
<=> ( frontsegP(app(sk2,X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f2218,plain,
! [X0] :
( ~ sQ141_spl
| frontsegP(app(sk2,X0),nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2217]) ).
fof(f2220,plain,
( ~ sQ14_spl
| ~ sQ18_spl
| ~ sQ8_spl
| sQ141_spl ),
inference(split_clause,[status(thm)],[f2208,f2217,f557,f730,f694]) ).
fof(f2221,definition,
! [X0] :
( sQ142_spl
<=> ( frontsegP(app(sk2,X0),sk2)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f2222,plain,
! [X0] :
( ~ sQ142_spl
| frontsegP(app(sk2,X0),sk2)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2221]) ).
fof(f2224,plain,
( ~ sQ23_spl
| ~ sQ18_spl
| sQ142_spl ),
inference(split_clause,[status(thm)],[f2209,f2221,f730,f798]) ).
fof(f2225,definition,
! [X0,X1] :
( sQ143_spl
<=> ( ~ ssList(X1)
| ~ frontsegP(nil,X1)
| frontsegP(app(sk2,X0),X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f2228,plain,
( ~ sQ28_spl
| ~ sQ18_spl
| sQ143_spl ),
inference(split_clause,[status(thm)],[f2210,f2225,f730,f863]) ).
fof(f2229,definition,
! [X0] :
( sQ144_spl
<=> ( frontsegP(app(nil,X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f2232,plain,
( ~ sQ22_spl
| ~ sQ8_spl
| sQ144_spl ),
inference(split_clause,[status(thm)],[f2211,f2229,f557,f794]) ).
fof(f2233,definition,
! [X0,X1] :
( sQ145_spl
<=> ( ~ ssList(X1)
| frontsegP(app(X1,X0),nil)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f2236,plain,
( ~ sQ8_spl
| sQ145_spl ),
inference(split_clause,[status(thm)],[f2212,f2233,f557]) ).
fof(f2345,plain,
! [X0] :
( ~ sQ142_spl
| app(sk2,X0) = sk2
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ frontsegP(sk2,app(sk2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2222,f340]) ).
fof(f2346,plain,
! [X0,X1] :
( ~ sQ142_spl
| frontsegP(app(app(sk2,X0),X1),sk2)
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2222,f350]) ).
fof(f2347,plain,
! [X0,X1] :
( ~ sQ142_spl
| frontsegP(X1,sk2)
| ~ ssList(X1)
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ frontsegP(X1,app(sk2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2222,f377]) ).
fof(f2349,definition,
! [X0] :
( sQ146_spl
<=> ( app(sk2,X0) = sk2
| ~ ssList(app(sk2,X0))
| ~ frontsegP(sk2,app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f2352,plain,
( ~ sQ142_spl
| ~ sQ18_spl
| sQ146_spl ),
inference(split_clause,[status(thm)],[f2345,f2349,f730,f2221]) ).
fof(f2353,definition,
! [X0,X1] :
( sQ147_spl
<=> ( frontsegP(app(app(sk2,X0),X1),sk2)
| ~ ssList(app(sk2,X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f2356,plain,
( ~ sQ142_spl
| ~ sQ18_spl
| sQ147_spl ),
inference(split_clause,[status(thm)],[f2346,f2353,f730,f2221]) ).
fof(f2357,definition,
! [X0,X1] :
( sQ148_spl
<=> ( frontsegP(X1,sk2)
| ~ ssList(X1)
| ~ ssList(app(sk2,X0))
| ~ frontsegP(X1,app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f2360,plain,
( ~ sQ142_spl
| ~ sQ18_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f2347,f2357,f730,f2221]) ).
fof(f2365,plain,
! [X0] :
( ~ sQ141_spl
| app(sk2,X0) = nil
| ~ ssList(app(sk2,X0))
| ~ ssList(nil)
| ~ frontsegP(nil,app(sk2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2218,f340]) ).
fof(f2366,plain,
! [X0,X1] :
( ~ sQ141_spl
| frontsegP(app(app(sk2,X0),X1),nil)
| ~ ssList(app(sk2,X0))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2218,f350]) ).
fof(f2367,plain,
! [X0,X1] :
( ~ sQ141_spl
| frontsegP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(sk2,X0))
| ~ ssList(nil)
| ~ frontsegP(X1,app(sk2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2218,f377]) ).
fof(f2369,definition,
! [X0] :
( sQ149_spl
<=> ( app(sk2,X0) = nil
| ~ ssList(app(sk2,X0))
| ~ frontsegP(nil,app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f2372,plain,
( ~ sQ141_spl
| ~ sQ8_spl
| sQ149_spl ),
inference(split_clause,[status(thm)],[f2365,f2369,f557,f2217]) ).
fof(f2373,definition,
! [X0,X1] :
( sQ150_spl
<=> ( frontsegP(app(app(sk2,X0),X1),nil)
| ~ ssList(app(sk2,X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f2376,plain,
( ~ sQ141_spl
| ~ sQ8_spl
| sQ150_spl ),
inference(split_clause,[status(thm)],[f2366,f2373,f557,f2217]) ).
fof(f2377,definition,
! [X0,X1] :
( sQ151_spl
<=> ( frontsegP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(sk2,X0))
| ~ frontsegP(X1,app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f2380,plain,
( ~ sQ141_spl
| ~ sQ8_spl
| sQ151_spl ),
inference(split_clause,[status(thm)],[f2367,f2377,f557,f2217]) ).
fof(f2492,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(skaf82(X0))
| ~ segmentP(X1,skaf82(X0))
| ~ segmentP(nil,X1)
| nil = skaf82(X0) ),
inference(resolution,[status(thm)],[f538,f373]) ).
fof(f2493,definition,
! [X0,X1] :
( sQ152_spl
<=> ( ~ ssList(X1)
| ~ ssList(skaf82(X0))
| ~ segmentP(X1,skaf82(X0))
| ~ segmentP(nil,X1)
| nil = skaf82(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f2496,plain,
( ~ sQ8_spl
| sQ152_spl ),
inference(split_clause,[status(thm)],[f2492,f2493,f557]) ).
fof(f2497,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(skaf81(X0))
| ~ segmentP(X1,skaf81(X0))
| ~ segmentP(nil,X1)
| nil = skaf81(X0) ),
inference(resolution,[status(thm)],[f539,f373]) ).
fof(f2498,definition,
! [X0,X1] :
( sQ153_spl
<=> ( ~ ssList(X1)
| ~ ssList(skaf81(X0))
| ~ segmentP(X1,skaf81(X0))
| ~ segmentP(nil,X1)
| nil = skaf81(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f2501,plain,
( ~ sQ8_spl
| sQ153_spl ),
inference(split_clause,[status(thm)],[f2497,f2498,f557]) ).
fof(f2594,plain,
! [X0,X1] :
( X0 = X1
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,sk2) != app(X1,sk2) ),
inference(resolution,[status(thm)],[f371,f430]) ).
fof(f2656,plain,
! [X0,X1] :
( X1 = nil
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != app(X0,nil) ),
inference(resolution,[status(thm)],[f369,f206]) ).
fof(f2718,plain,
! [X0] :
( app(app(sk2,sk2),X0) = app(sk2,app(sk2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f367,f430]) ).
fof(f2719,plain,
! [X0,X1] :
( app(app(X1,sk2),X0) = app(X1,app(sk2,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f367,f430]) ).
fof(f2754,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(skaf80(X0))
| ~ segmentP(X1,skaf80(X0))
| ~ segmentP(nil,X1)
| nil = skaf80(X0) ),
inference(resolution,[status(thm)],[f565,f373]) ).
fof(f2755,definition,
! [X0,X1] :
( sQ154_spl
<=> ( ~ ssList(X1)
| ~ ssList(skaf80(X0))
| ~ segmentP(X1,skaf80(X0))
| ~ segmentP(nil,X1)
| nil = skaf80(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f2758,plain,
( ~ sQ8_spl
| sQ154_spl ),
inference(split_clause,[status(thm)],[f2754,f2755,f557]) ).
fof(f2759,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(skaf77(X0))
| ~ segmentP(X1,skaf77(X0))
| ~ segmentP(nil,X1)
| nil = skaf77(X0) ),
inference(resolution,[status(thm)],[f570,f373]) ).
fof(f2760,definition,
! [X0,X1] :
( sQ155_spl
<=> ( ~ ssList(X1)
| ~ ssList(skaf77(X0))
| ~ segmentP(X1,skaf77(X0))
| ~ segmentP(nil,X1)
| nil = skaf77(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f2763,plain,
( ~ sQ8_spl
| sQ155_spl ),
inference(split_clause,[status(thm)],[f2759,f2760,f557]) ).
fof(f2825,plain,
! [X0] :
( rearsegP(app(X0,sk2),sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f474,f430]) ).
fof(f2826,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(app(X0,X1),nil)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f349,f256]) ).
fof(f2829,definition,
! [X0,X1] :
( sQ156_spl
<=> ( ~ ssList(X1)
| rearsegP(app(X0,X1),nil)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f2832,plain,
( ~ sQ8_spl
| sQ156_spl ),
inference(split_clause,[status(thm)],[f2826,f2829,f557]) ).
fof(f2836,plain,
! [X0,X1] :
( rearsegP(app(X1,app(X0,sk2)),sk2)
| ~ ssList(app(X0,sk2))
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2825,f349]) ).
fof(f2837,plain,
( rearsegP(sk2,sk2)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f856,f2825]) ).
fof(f2838,definition,
! [X0,X1] :
( sQ157_spl
<=> ( rearsegP(app(X1,app(X0,sk2)),sk2)
| ~ ssList(app(X0,sk2))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f2841,plain,
( ~ sQ18_spl
| sQ157_spl ),
inference(split_clause,[status(thm)],[f2836,f2838,f730]) ).
fof(f2842,definition,
( sQ158_spl
<=> rearsegP(sk2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f2843,plain,
( ~ sQ158_spl
| rearsegP(sk2,sk2) ),
inference(component_clause,[status(thm)],[f2842]) ).
fof(f2845,plain,
( sQ158_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2837,f557,f2842]) ).
fof(f2846,plain,
! [X0] :
( ~ sQ158_spl
| rearsegP(app(X0,sk2),sk2)
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2843,f349]) ).
fof(f2847,definition,
! [X0] :
( sQ159_spl
<=> ( rearsegP(app(X0,sk2),sk2)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f2850,plain,
( ~ sQ158_spl
| ~ sQ18_spl
| sQ159_spl ),
inference(split_clause,[status(thm)],[f2846,f2847,f730,f2842]) ).
fof(f2851,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(nil)
| sk2 != app(X0,sk2) ),
inference(paramodulation,[status(thm)],[f856,f2594]) ).
fof(f2854,definition,
! [X0] :
( sQ160_spl
<=> ( nil = X0
| ~ ssList(X0)
| sk2 != app(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f2855,plain,
! [X0] :
( ~ sQ160_spl
| nil = X0
| ~ ssList(X0)
| sk2 != app(X0,sk2) ),
inference(component_clause,[status(thm)],[f2854]) ).
fof(f2857,plain,
( ~ sQ8_spl
| sQ160_spl ),
inference(split_clause,[status(thm)],[f2851,f2854,f557]) ).
fof(f2859,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(skaf76(X0))
| ~ segmentP(X1,skaf76(X0))
| ~ segmentP(nil,X1)
| nil = skaf76(X0) ),
inference(resolution,[status(thm)],[f571,f373]) ).
fof(f2860,definition,
! [X0,X1] :
( sQ161_spl
<=> ( ~ ssList(X1)
| ~ ssList(skaf76(X0))
| ~ segmentP(X1,skaf76(X0))
| ~ segmentP(nil,X1)
| nil = skaf76(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f2863,plain,
( ~ sQ8_spl
| sQ161_spl ),
inference(split_clause,[status(thm)],[f2859,f2860,f557]) ).
fof(f2864,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(skaf75(X0))
| ~ segmentP(X1,skaf75(X0))
| ~ segmentP(nil,X1)
| nil = skaf75(X0) ),
inference(resolution,[status(thm)],[f572,f373]) ).
fof(f2865,definition,
! [X0,X1] :
( sQ162_spl
<=> ( ~ ssList(X1)
| ~ ssList(skaf75(X0))
| ~ segmentP(X1,skaf75(X0))
| ~ segmentP(nil,X1)
| nil = skaf75(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f2868,plain,
( ~ sQ8_spl
| sQ162_spl ),
inference(split_clause,[status(thm)],[f2864,f2865,f557]) ).
fof(f2900,plain,
( ~ sQ158_spl
| app(skaf46(sk2,sk2),sk2) = sk2
| ~ ssList(sk2)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f342,f2843]) ).
fof(f2901,plain,
! [X0] :
( ~ ssList(X0)
| app(skaf46(app(X0,sk2),sk2),sk2) = app(X0,sk2)
| ~ ssList(app(X0,sk2))
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f342,f2825]) ).
fof(f2902,plain,
! [X0] :
( ~ ssList(X0)
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f342,f256]) ).
fof(f2905,definition,
( sQ163_spl
<=> app(skaf46(sk2,sk2),sk2) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f2906,plain,
( ~ sQ163_spl
| app(skaf46(sk2,sk2),sk2) = sk2 ),
inference(component_clause,[status(thm)],[f2905]) ).
fof(f2908,plain,
( ~ sQ158_spl
| sQ163_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f2900,f730,f2905,f2842]) ).
fof(f2909,definition,
! [X0] :
( sQ164_spl
<=> ( ~ ssList(X0)
| app(skaf46(app(X0,sk2),sk2),sk2) = app(X0,sk2)
| ~ ssList(app(X0,sk2)) ) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f2912,plain,
( sQ164_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f2901,f730,f2909]) ).
fof(f2913,definition,
! [X0] :
( sQ165_spl
<=> ( ~ ssList(X0)
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f2916,plain,
( sQ165_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f2902,f557,f2913]) ).
fof(f2921,plain,
( ~ sQ158_spl
| sk2 = sk2
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ rearsegP(sk2,sk2) ),
inference(resolution,[status(thm)],[f339,f2843]) ).
fof(f2922,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,sk2) = sk2
| ~ ssList(app(X0,sk2))
| ~ ssList(sk2)
| ~ rearsegP(sk2,app(X0,sk2)) ),
inference(resolution,[status(thm)],[f339,f2825]) ).
fof(f2923,plain,
! [X0] :
( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f339,f256]) ).
fof(f2926,plain,
( sQ24_spl
| ~ sQ18_spl
| ~ sQ158_spl ),
inference(split_clause,[status(thm)],[f2921,f2842,f730,f807]) ).
fof(f2927,definition,
! [X0] :
( sQ166_spl
<=> ( ~ ssList(X0)
| app(X0,sk2) = sk2
| ~ ssList(app(X0,sk2))
| ~ rearsegP(sk2,app(X0,sk2)) ) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f2930,plain,
( ~ sQ18_spl
| sQ166_spl ),
inference(split_clause,[status(thm)],[f2922,f2927,f730]) ).
fof(f2931,definition,
! [X0] :
( sQ167_spl
<=> ( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f2934,plain,
( ~ sQ8_spl
| sQ167_spl ),
inference(split_clause,[status(thm)],[f2923,f2931,f557]) ).
fof(f2937,plain,
! [X0] :
( ~ sQ163_spl
| X0 = skaf46(sk2,sk2)
| ~ ssList(skaf46(sk2,sk2))
| ~ ssList(X0)
| app(X0,sk2) != sk2 ),
inference(paramodulation,[status(thm)],[f2906,f2594]) ).
fof(f2941,plain,
( ~ sQ163_spl
| frontsegP(sk2,skaf46(sk2,sk2))
| ~ ssList(skaf46(sk2,sk2))
| ~ ssList(sk2) ),
inference(paramodulation,[status(thm)],[f2906,f476]) ).
fof(f2942,definition,
! [X0] :
( sQ168_spl
<=> ( X0 = skaf46(sk2,sk2)
| ~ ssList(X0)
| app(X0,sk2) != sk2 ) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f2945,definition,
( sQ169_spl
<=> ssList(skaf46(sk2,sk2)) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f2947,plain,
( sQ169_spl
| ~ ssList(skaf46(sk2,sk2)) ),
inference(component_clause,[status(thm)],[f2945]) ).
fof(f2948,plain,
( ~ sQ163_spl
| ~ sQ169_spl
| sQ168_spl ),
inference(split_clause,[status(thm)],[f2937,f2942,f2945,f2905]) ).
fof(f2958,definition,
( sQ172_spl
<=> frontsegP(sk2,skaf46(sk2,sk2)) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f2959,plain,
( ~ sQ172_spl
| frontsegP(sk2,skaf46(sk2,sk2)) ),
inference(component_clause,[status(thm)],[f2958]) ).
fof(f2961,plain,
( ~ sQ163_spl
| sQ172_spl
| ~ sQ169_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f2941,f730,f2945,f2958,f2905]) ).
fof(f2962,plain,
( sQ169_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2947,f248]) ).
fof(f2963,plain,
sQ169_spl,
inference(contradiction_clause,[status(thm)],[f2962]) ).
fof(f2965,plain,
! [X0] :
( ~ sQ172_spl
| frontsegP(app(sk2,X0),skaf46(sk2,sk2))
| ~ ssList(sk2)
| ~ ssList(skaf46(sk2,sk2))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2959,f350]) ).
fof(f2966,plain,
! [X0] :
( ~ sQ172_spl
| frontsegP(X0,skaf46(sk2,sk2))
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(skaf46(sk2,sk2))
| ~ frontsegP(X0,sk2) ),
inference(resolution,[status(thm)],[f2959,f377]) ).
fof(f2971,definition,
! [X0] :
( sQ174_spl
<=> ( frontsegP(app(sk2,X0),skaf46(sk2,sk2))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f2974,plain,
( ~ sQ172_spl
| ~ sQ18_spl
| ~ sQ169_spl
| sQ174_spl ),
inference(split_clause,[status(thm)],[f2965,f2971,f2945,f730,f2958]) ).
fof(f2975,definition,
! [X0] :
( sQ175_spl
<=> ( frontsegP(X0,skaf46(sk2,sk2))
| ~ ssList(X0)
| ~ frontsegP(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f2978,plain,
( ~ sQ172_spl
| ~ sQ18_spl
| ~ sQ169_spl
| sQ175_spl ),
inference(split_clause,[status(thm)],[f2966,f2975,f2945,f730,f2958]) ).
fof(f3044,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(skaf73(X0))
| ~ segmentP(X1,skaf73(X0))
| ~ segmentP(nil,X1)
| nil = skaf73(X0) ),
inference(resolution,[status(thm)],[f575,f373]) ).
fof(f3045,definition,
! [X0,X1] :
( sQ177_spl
<=> ( ~ ssList(X1)
| ~ ssList(skaf73(X0))
| ~ segmentP(X1,skaf73(X0))
| ~ segmentP(nil,X1)
| nil = skaf73(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f3048,plain,
( ~ sQ8_spl
| sQ177_spl ),
inference(split_clause,[status(thm)],[f3044,f3045,f557]) ).
fof(f3049,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(skaf72(X0))
| ~ segmentP(X1,skaf72(X0))
| ~ segmentP(nil,X1)
| nil = skaf72(X0) ),
inference(resolution,[status(thm)],[f576,f373]) ).
fof(f3050,definition,
! [X0,X1] :
( sQ178_spl
<=> ( ~ ssList(X1)
| ~ ssList(skaf72(X0))
| ~ segmentP(X1,skaf72(X0))
| ~ segmentP(nil,X1)
| nil = skaf72(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f3053,plain,
( ~ sQ8_spl
| sQ178_spl ),
inference(split_clause,[status(thm)],[f3049,f3050,f557]) ).
fof(f3252,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(skaf71(X0))
| ~ segmentP(X1,skaf71(X0))
| ~ segmentP(nil,X1)
| nil = skaf71(X0) ),
inference(resolution,[status(thm)],[f577,f373]) ).
fof(f3253,definition,
! [X0,X1] :
( sQ182_spl
<=> ( ~ ssList(X1)
| ~ ssList(skaf71(X0))
| ~ segmentP(X1,skaf71(X0))
| ~ segmentP(nil,X1)
| nil = skaf71(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f3256,plain,
( ~ sQ8_spl
| sQ182_spl ),
inference(split_clause,[status(thm)],[f3252,f3253,f557]) ).
fof(f3257,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(skaf68(X0))
| ~ segmentP(X1,skaf68(X0))
| ~ segmentP(nil,X1)
| nil = skaf68(X0) ),
inference(resolution,[status(thm)],[f582,f373]) ).
fof(f3258,definition,
! [X0,X1] :
( sQ183_spl
<=> ( ~ ssList(X1)
| ~ ssList(skaf68(X0))
| ~ segmentP(X1,skaf68(X0))
| ~ segmentP(nil,X1)
| nil = skaf68(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f3261,plain,
( ~ sQ8_spl
| sQ183_spl ),
inference(split_clause,[status(thm)],[f3257,f3258,f557]) ).
fof(f3306,plain,
! [X0,X1] :
( ssList(cons(skaf44(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f285,f245]) ).
fof(f3321,plain,
! [X0] :
( ssList(cons(skac2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f285,f208]) ).
fof(f3371,plain,
! [X0] :
( ~ sQ163_spl
| app(sk2,X0) = app(skaf46(sk2,sk2),app(sk2,X0))
| ~ ssList(skaf46(sk2,sk2))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f2906,f2719]) ).
fof(f3372,plain,
! [X0] :
( app(app(X0,sk2),nil) = app(X0,sk2)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f773,f2719]) ).
fof(f3373,definition,
! [X0] :
( sQ186_spl
<=> ( app(sk2,X0) = app(skaf46(sk2,sk2),app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f3376,plain,
( ~ sQ163_spl
| ~ sQ169_spl
| sQ186_spl ),
inference(split_clause,[status(thm)],[f3371,f3373,f2945,f2905]) ).
fof(f3377,definition,
! [X0] :
( sQ187_spl
<=> ( app(app(X0,sk2),nil) = app(X0,sk2)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f3380,plain,
( sQ187_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f3372,f557,f3377]) ).
fof(f3381,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(skaf67(X0))
| ~ segmentP(X1,skaf67(X0))
| ~ segmentP(nil,X1)
| nil = skaf67(X0) ),
inference(resolution,[status(thm)],[f583,f373]) ).
fof(f3382,definition,
! [X0,X1] :
( sQ188_spl
<=> ( ~ ssList(X1)
| ~ ssList(skaf67(X0))
| ~ segmentP(X1,skaf67(X0))
| ~ segmentP(nil,X1)
| nil = skaf67(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f3385,plain,
( ~ sQ8_spl
| sQ188_spl ),
inference(split_clause,[status(thm)],[f3381,f3382,f557]) ).
fof(f3386,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(skaf66(X0))
| ~ segmentP(X1,skaf66(X0))
| ~ segmentP(nil,X1)
| nil = skaf66(X0) ),
inference(resolution,[status(thm)],[f584,f373]) ).
fof(f3387,definition,
! [X0,X1] :
( sQ189_spl
<=> ( ~ ssList(X1)
| ~ ssList(skaf66(X0))
| ~ segmentP(X1,skaf66(X0))
| ~ segmentP(nil,X1)
| nil = skaf66(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f3390,plain,
( ~ sQ8_spl
| sQ189_spl ),
inference(split_clause,[status(thm)],[f3386,f3387,f557]) ).
fof(f3400,plain,
! [X0] : ssList(cons(skac2,skaf81(X0))),
inference(resolution,[status(thm)],[f3321,f212]) ).
fof(f3420,plain,
ssList(cons(skac2,nil)),
inference(resolution,[status(thm)],[f3321,f206]) ).
fof(f3421,plain,
ssList(cons(skac2,sk2)),
inference(resolution,[status(thm)],[f3321,f430]) ).
fof(f3428,plain,
( ~ sQ160_spl
| nil = cons(skac2,nil)
| sk2 != app(cons(skac2,nil),sk2) ),
inference(resolution,[status(thm)],[f3420,f2855]) ).
fof(f3459,definition,
( sQ190_spl
<=> nil = cons(skac2,nil) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f3460,plain,
( ~ sQ190_spl
| nil = cons(skac2,nil) ),
inference(component_clause,[status(thm)],[f3459]) ).
fof(f3481,definition,
( sQ196_spl
<=> sk2 = app(cons(skac2,nil),sk2) ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f3484,plain,
( ~ sQ160_spl
| sQ190_spl
| ~ sQ196_spl ),
inference(split_clause,[status(thm)],[f3428,f3481,f3459,f2854]) ).
fof(f3486,plain,
( ~ sQ190_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3460,f637]) ).
fof(f3487,plain,
~ sQ190_spl,
inference(contradiction_clause,[status(thm)],[f3486]) ).
fof(f3519,plain,
( sQ65_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1525,f208]) ).
fof(f3520,plain,
sQ65_spl,
inference(contradiction_clause,[status(thm)],[f3519]) ).
fof(f3541,plain,
ssList(cons(skac2,cons(skac2,sk2))),
inference(resolution,[status(thm)],[f3421,f3321]) ).
fof(f3545,plain,
( ~ sQ160_spl
| nil = cons(skac2,sk2)
| sk2 != app(cons(skac2,sk2),sk2) ),
inference(resolution,[status(thm)],[f3421,f2855]) ).
fof(f3587,definition,
( sQ200_spl
<=> sk2 = app(cons(skac2,sk2),sk2) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f3590,definition,
( sQ201_spl
<=> nil = cons(skac2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f3591,plain,
( ~ sQ201_spl
| nil = cons(skac2,sk2) ),
inference(component_clause,[status(thm)],[f3590]) ).
fof(f3593,plain,
( ~ sQ160_spl
| sQ201_spl
| ~ sQ200_spl ),
inference(split_clause,[status(thm)],[f3545,f3587,f3590,f2854]) ).
fof(f3968,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ ssList(cons(X2,X0))
| ~ ssList(cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f498,f2143]) ).
fof(f3969,definition,
! [X0,X1,X2] :
( sQ229_spl
<=> ( ~ ssList(cons(X2,X0))
| ~ ssList(cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f3970,plain,
! [X0,X1,X2] :
( ~ sQ229_spl
| ~ ssList(cons(X2,X0))
| ~ ssList(cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3969]) ).
fof(f3972,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| sQ229_spl ),
inference(split_clause,[status(thm)],[f3968,f3969,f730,f442]) ).
fof(f3973,plain,
! [X0,X1,X2] :
( ~ sQ229_spl
| ~ ssList(cons(X2,X0))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3970,f285]) ).
fof(f3974,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| X0 = X2
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(backward_subsumption_resolution,[status(thm)],[f411,f446]) ).
fof(f3976,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f482,f446]) ).
fof(f3998,plain,
! [X0,X1] :
( ~ sQ51_spl
| ~ sQ1_spl
| ~ frontsegP(sk2,cons(X1,X0))
| nil = cons(X1,nil)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f1268,f446]) ).
fof(f4020,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ ssList(X1)
| cons(X0,X1) != nil ),
inference(backward_subsumption_resolution,[status(thm)],[f298,f446]) ).
fof(f4088,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| X0 = X2
| ~ ssList(X1)
| ~ ssList(X3)
| ~ frontsegP(cons(X0,X1),cons(X2,X3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f3974,f446]) ).
fof(f4110,definition,
! [X0,X2] :
( sQ230_spl
<=> ( ~ ssList(cons(X2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f4111,plain,
! [X0,X1] :
( ~ sQ230_spl
| ~ ssList(cons(X1,X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f4110]) ).
fof(f4113,definition,
! [X1] :
( sQ231_spl
<=> ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f4114,plain,
! [X0] :
( ~ sQ231_spl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f4113]) ).
fof(f4137,plain,
( ~ sQ231_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f3400,f4114]) ).
fof(f4199,definition,
! [X0,X2] :
( sQ232_spl
<=> ( ~ ssList(cons(X2,X0))
| ~ ssItem(X2)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f4200,plain,
! [X0,X1] :
( ~ sQ232_spl
| ~ ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f4199]) ).
fof(f4202,plain,
( ~ sQ229_spl
| sQ231_spl
| sQ232_spl ),
inference(split_clause,[status(thm)],[f3973,f4199,f4113,f3969]) ).
fof(f4203,plain,
~ sQ231_spl,
inference(contradiction_clause,[status(thm)],[f4137]) ).
fof(f4204,plain,
( ~ sQ230_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f430,f4266]) ).
fof(f4266,plain,
! [X0] :
( ~ sQ230_spl
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3306,f4111]) ).
fof(f4267,plain,
~ sQ230_spl,
inference(contradiction_clause,[status(thm)],[f4204]) ).
fof(f4270,plain,
! [X0,X1] :
( ~ sQ232_spl
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f285,f4200]) ).
fof(f4271,plain,
! [X0] :
( ~ sQ232_spl
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f4270,f430]) ).
fof(f4272,plain,
( ~ sQ232_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f244,f4271]) ).
fof(f4289,plain,
~ sQ232_spl,
inference(contradiction_clause,[status(thm)],[f4272]) ).
fof(f4354,plain,
! [X0] :
( ~ sQ1_spl
| cons(X0,nil) != nil ),
inference(resolution,[status(thm)],[f4020,f206]) ).
fof(f4357,plain,
! [X0] :
( ~ sQ1_spl
| cons(X0,cons(skac2,sk2)) != nil ),
inference(resolution,[status(thm)],[f4020,f3421]) ).
fof(f4358,plain,
! [X0] :
( ~ sQ1_spl
| cons(X0,sk2) != nil ),
inference(resolution,[status(thm)],[f4020,f430]) ).
fof(f4360,plain,
! [X0,X1] :
( ~ sQ51_spl
| ~ sQ1_spl
| ~ frontsegP(sk2,cons(X1,X0))
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f3998,f4354]) ).
fof(f4436,plain,
( nil = cons(skac2,nil)
| cons(hd(cons(skac2,nil)),tl(cons(skac2,nil))) = cons(skac2,nil) ),
inference(resolution,[status(thm)],[f305,f3420]) ).
fof(f4437,plain,
( nil = cons(skac2,sk2)
| cons(hd(cons(skac2,sk2)),tl(cons(skac2,sk2))) = cons(skac2,sk2) ),
inference(resolution,[status(thm)],[f305,f3421]) ).
fof(f4438,plain,
( nil = sk2
| cons(hd(sk2),tl(sk2)) = sk2 ),
inference(resolution,[status(thm)],[f305,f430]) ).
fof(f4443,definition,
( sQ234_spl
<=> cons(hd(cons(skac2,nil)),tl(cons(skac2,nil))) = cons(skac2,nil) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f4446,plain,
( sQ190_spl
| sQ234_spl ),
inference(split_clause,[status(thm)],[f4436,f4443,f3459]) ).
fof(f4447,definition,
( sQ235_spl
<=> cons(hd(cons(skac2,sk2)),tl(cons(skac2,sk2))) = cons(skac2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f4450,plain,
( sQ201_spl
| sQ235_spl ),
inference(split_clause,[status(thm)],[f4437,f4447,f3590]) ).
fof(f4451,definition,
( sQ236_spl
<=> cons(hd(sk2),tl(sk2)) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f4452,plain,
( ~ sQ236_spl
| cons(hd(sk2),tl(sk2)) = sk2 ),
inference(component_clause,[status(thm)],[f4451]) ).
fof(f4454,plain,
( sQ2_spl
| sQ236_spl ),
inference(split_clause,[status(thm)],[f4438,f4451,f449]) ).
fof(f4455,plain,
( ~ sQ201_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3591,f4358]) ).
fof(f4456,plain,
( ~ sQ201_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f4455]) ).
fof(f4474,plain,
( nil = cons(skac2,nil)
| cons(skaf83(cons(skac2,nil)),skaf82(cons(skac2,nil))) = cons(skac2,nil) ),
inference(resolution,[status(thm)],[f310,f3420]) ).
fof(f4475,plain,
( nil = cons(skac2,sk2)
| cons(skaf83(cons(skac2,sk2)),skaf82(cons(skac2,sk2))) = cons(skac2,sk2) ),
inference(resolution,[status(thm)],[f310,f3421]) ).
fof(f4481,definition,
( sQ238_spl
<=> cons(skaf83(cons(skac2,nil)),skaf82(cons(skac2,nil))) = cons(skac2,nil) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f4484,plain,
( sQ190_spl
| sQ238_spl ),
inference(split_clause,[status(thm)],[f4474,f4481,f3459]) ).
fof(f4485,definition,
( sQ239_spl
<=> cons(skaf83(cons(skac2,sk2)),skaf82(cons(skac2,sk2))) = cons(skac2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f4488,plain,
( sQ201_spl
| sQ239_spl ),
inference(split_clause,[status(thm)],[f4475,f4485,f3590]) ).
fof(f4522,plain,
( nil = cons(skac2,cons(skac2,sk2))
| cons(skaf83(cons(skac2,cons(skac2,sk2))),skaf82(cons(skac2,cons(skac2,sk2)))) = cons(skac2,cons(skac2,sk2)) ),
inference(resolution,[status(thm)],[f3541,f310]) ).
fof(f4523,plain,
( nil = cons(skac2,cons(skac2,sk2))
| cons(hd(cons(skac2,cons(skac2,sk2))),tl(cons(skac2,cons(skac2,sk2)))) = cons(skac2,cons(skac2,sk2)) ),
inference(resolution,[status(thm)],[f3541,f305]) ).
fof(f4526,definition,
( sQ241_spl
<=> cons(skaf83(cons(skac2,cons(skac2,sk2))),skaf82(cons(skac2,cons(skac2,sk2)))) = cons(skac2,cons(skac2,sk2)) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f4529,definition,
( sQ242_spl
<=> nil = cons(skac2,cons(skac2,sk2)) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f4530,plain,
( ~ sQ242_spl
| nil = cons(skac2,cons(skac2,sk2)) ),
inference(component_clause,[status(thm)],[f4529]) ).
fof(f4532,plain,
( sQ242_spl
| sQ241_spl ),
inference(split_clause,[status(thm)],[f4522,f4526,f4529]) ).
fof(f4533,definition,
( sQ243_spl
<=> cons(hd(cons(skac2,cons(skac2,sk2))),tl(cons(skac2,cons(skac2,sk2)))) = cons(skac2,cons(skac2,sk2)) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f4536,plain,
( sQ242_spl
| sQ243_spl ),
inference(split_clause,[status(thm)],[f4523,f4533,f4529]) ).
fof(f4537,plain,
( ~ sQ242_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4530,f4357]) ).
fof(f4538,plain,
( ~ sQ242_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f4537]) ).
fof(f4542,plain,
( ~ sQ236_spl
| ~ sQ51_spl
| ~ sQ1_spl
| ~ frontsegP(sk2,sk2)
| ~ ssList(tl(sk2)) ),
inference(paramodulation,[status(thm)],[f4452,f4360]) ).
fof(f4546,definition,
( sQ245_spl
<=> ssList(tl(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f4548,plain,
( sQ245_spl
| ~ ssList(tl(sk2)) ),
inference(component_clause,[status(thm)],[f4546]) ).
fof(f4555,plain,
( ~ sQ236_spl
| ~ sQ51_spl
| ~ sQ1_spl
| ~ sQ23_spl
| ~ sQ245_spl ),
inference(split_clause,[status(thm)],[f4542,f4546,f798,f445,f1120,f4451]) ).
fof(f4556,plain,
( app(app(sk2,sk2),nil) = app(sk2,sk2)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f773,f2718]) ).
fof(f4557,definition,
( sQ247_spl
<=> app(app(sk2,sk2),nil) = app(sk2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f4560,plain,
( sQ247_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f4556,f557,f4557]) ).
fof(f4612,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| X2 = X2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f3976,f4088]) ).
fof(f4615,definition,
! [X2] :
( sQ250_spl
<=> X2 = X2 ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f4618,plain,
( ~ sQ1_spl
| sQ250_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f4612,f1106,f4615,f445]) ).
fof(f4676,plain,
! [X0] :
( nil = cons(skac2,cons(skac2,sk2))
| ~ ssList(X0)
| app(X0,cons(skac2,cons(skac2,sk2))) != nil ),
inference(resolution,[status(thm)],[f328,f3541]) ).
fof(f4677,plain,
! [X0] :
( nil = cons(skac2,nil)
| ~ ssList(X0)
| app(X0,cons(skac2,nil)) != nil ),
inference(resolution,[status(thm)],[f328,f3420]) ).
fof(f4678,plain,
! [X0] :
( nil = cons(skac2,sk2)
| ~ ssList(X0)
| app(X0,cons(skac2,sk2)) != nil ),
inference(resolution,[status(thm)],[f328,f3421]) ).
fof(f4685,definition,
! [X0] :
( sQ254_spl
<=> ( ~ ssList(X0)
| app(X0,cons(skac2,cons(skac2,sk2))) != nil ) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f4688,plain,
( sQ242_spl
| sQ254_spl ),
inference(split_clause,[status(thm)],[f4676,f4685,f4529]) ).
fof(f4689,definition,
! [X0] :
( sQ255_spl
<=> ( ~ ssList(X0)
| app(X0,cons(skac2,nil)) != nil ) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f4692,plain,
( sQ190_spl
| sQ255_spl ),
inference(split_clause,[status(thm)],[f4677,f4689,f3459]) ).
fof(f4693,definition,
! [X0] :
( sQ256_spl
<=> ( ~ ssList(X0)
| app(X0,cons(skac2,sk2)) != nil ) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f4696,plain,
( sQ201_spl
| sQ256_spl ),
inference(split_clause,[status(thm)],[f4678,f4693,f3590]) ).
fof(f4719,plain,
! [X0] :
( hd(app(cons(skac2,cons(skac2,sk2)),X0)) = hd(cons(skac2,cons(skac2,sk2)))
| nil = cons(skac2,cons(skac2,sk2))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f332,f3541]) ).
fof(f4720,plain,
! [X0] :
( hd(app(cons(skac2,nil),X0)) = hd(cons(skac2,nil))
| nil = cons(skac2,nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f332,f3420]) ).
fof(f4721,plain,
! [X0] :
( hd(app(cons(skac2,sk2),X0)) = hd(cons(skac2,sk2))
| nil = cons(skac2,sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f332,f3421]) ).
fof(f4728,definition,
! [X0] :
( sQ259_spl
<=> ( hd(app(cons(skac2,cons(skac2,sk2)),X0)) = hd(cons(skac2,cons(skac2,sk2)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f4731,plain,
( sQ242_spl
| sQ259_spl ),
inference(split_clause,[status(thm)],[f4719,f4728,f4529]) ).
fof(f4732,definition,
! [X0] :
( sQ260_spl
<=> ( hd(app(cons(skac2,nil),X0)) = hd(cons(skac2,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f4735,plain,
( sQ190_spl
| sQ260_spl ),
inference(split_clause,[status(thm)],[f4720,f4732,f3459]) ).
fof(f4736,definition,
! [X0] :
( sQ261_spl
<=> ( hd(app(cons(skac2,sk2),X0)) = hd(cons(skac2,sk2))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f4739,plain,
( sQ201_spl
| sQ261_spl ),
inference(split_clause,[status(thm)],[f4721,f4736,f3590]) ).
fof(f4762,plain,
! [X0] :
( tl(app(cons(skac2,cons(skac2,sk2)),X0)) = app(tl(cons(skac2,cons(skac2,sk2))),X0)
| nil = cons(skac2,cons(skac2,sk2))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f344,f3541]) ).
fof(f4763,plain,
! [X0] :
( tl(app(cons(skac2,nil),X0)) = app(tl(cons(skac2,nil)),X0)
| nil = cons(skac2,nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f344,f3420]) ).
fof(f4764,plain,
! [X0] :
( tl(app(cons(skac2,sk2),X0)) = app(tl(cons(skac2,sk2)),X0)
| nil = cons(skac2,sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f344,f3421]) ).
fof(f4771,definition,
! [X0] :
( sQ264_spl
<=> ( tl(app(cons(skac2,cons(skac2,sk2)),X0)) = app(tl(cons(skac2,cons(skac2,sk2))),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f4774,plain,
( sQ242_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f4762,f4771,f4529]) ).
fof(f4775,definition,
! [X0] :
( sQ265_spl
<=> ( tl(app(cons(skac2,nil),X0)) = app(tl(cons(skac2,nil)),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f4778,plain,
( sQ190_spl
| sQ265_spl ),
inference(split_clause,[status(thm)],[f4763,f4775,f3459]) ).
fof(f4779,definition,
! [X0] :
( sQ266_spl
<=> ( tl(app(cons(skac2,sk2),X0)) = app(tl(cons(skac2,sk2)),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f4782,plain,
( sQ201_spl
| sQ266_spl ),
inference(split_clause,[status(thm)],[f4764,f4779,f3590]) ).
fof(f4833,plain,
! [X0] :
( cons(skac2,cons(skac2,sk2)) = nil
| ~ ssList(X0)
| app(X0,cons(skac2,cons(skac2,sk2))) != app(X0,nil) ),
inference(resolution,[status(thm)],[f2656,f3541]) ).
fof(f4834,plain,
! [X0] :
( cons(skac2,nil) = nil
| ~ ssList(X0)
| app(X0,cons(skac2,nil)) != app(X0,nil) ),
inference(resolution,[status(thm)],[f2656,f3420]) ).
fof(f4835,plain,
! [X0] :
( cons(skac2,sk2) = nil
| ~ ssList(X0)
| app(X0,cons(skac2,sk2)) != app(X0,nil) ),
inference(resolution,[status(thm)],[f2656,f3421]) ).
fof(f4842,definition,
! [X0] :
( sQ269_spl
<=> ( ~ ssList(X0)
| app(X0,cons(skac2,cons(skac2,sk2))) != app(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f4845,plain,
( sQ242_spl
| sQ269_spl ),
inference(split_clause,[status(thm)],[f4833,f4842,f4529]) ).
fof(f4846,definition,
! [X0] :
( sQ270_spl
<=> ( ~ ssList(X0)
| app(X0,cons(skac2,nil)) != app(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f4849,plain,
( sQ190_spl
| sQ270_spl ),
inference(split_clause,[status(thm)],[f4834,f4846,f3459]) ).
fof(f4850,definition,
! [X0] :
( sQ271_spl
<=> ( ~ ssList(X0)
| app(X0,cons(skac2,sk2)) != app(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f4853,plain,
( sQ201_spl
| sQ271_spl ),
inference(split_clause,[status(thm)],[f4835,f4850,f3590]) ).
fof(f4918,plain,
( sQ245_spl
| nil = sk2
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f274,f4548]) ).
fof(f4935,plain,
( sQ245_spl
| sQ2_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f4918,f730,f449,f4546]) ).
fof(f4944,plain,
$false,
inference(sat_refutation,[status(thm)],[f448,f455,f458,f512,f545,f600,f616,f715,f737,f781,f783,f788,f797,f801,f828,f862,f866,f932,f972,f976,f1007,f1015,f1035,f1112,f1123,f1167,f1169,f1267,f1302,f1306,f1459,f1464,f1469,f1474,f1479,f1484,f1489,f1494,f1526,f1619,f1624,f1629,f1634,f1639,f1644,f1649,f1654,f1659,f1664,f1669,f1674,f1679,f1740,f1745,f1750,f1755,f1760,f1765,f1770,f1775,f1780,f1785,f1790,f1795,f1800,f1805,f1810,f1905,f1912,f1917,f1922,f1927,f1932,f1937,f2049,f2053,f2057,f2061,f2065,f2133,f2137,f2200,f2204,f2220,f2224,f2228,f2232,f2236,f2352,f2356,f2360,f2372,f2376,f2380,f2496,f2501,f2758,f2763,f2832,f2841,f2845,f2850,f2857,f2863,f2868,f2908,f2912,f2916,f2926,f2930,f2934,f2948,f2961,f2963,f2974,f2978,f3048,f3053,f3256,f3261,f3376,f3380,f3385,f3390,f3484,f3487,f3520,f3593,f3972,f4202,f4203,f4267,f4289,f4446,f4450,f4454,f4456,f4484,f4488,f4532,f4536,f4538,f4555,f4560,f4618,f4688,f4692,f4696,f4731,f4735,f4739,f4774,f4778,f4782,f4845,f4849,f4853,f4935]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC031-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.36 % Computer : n015.cluster.edu
% 0.12/0.36 % Model : x86_64 x86_64
% 0.12/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.36 % Memory : 8046.5625MB
% 0.12/0.36 % OS : Linux 6.8.0-71-generic
% 0.12/0.36 % CPULimit : 300
% 0.12/0.36 % WCLimit : 300
% 0.12/0.36 % DateTime : Mon Sep 21 07:53:22 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.14/0.38 % Drodi V4.1.1
% 32.27/4.60 % Refutation found
% 32.27/4.60 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 32.27/4.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 31.01/4.65 % Elapsed time: 4.272347 seconds
% 31.01/4.65 % CPU time: 33.412246 seconds
% 31.01/4.65 % Total memory used: 357.127 MB
% 31.01/4.65 % Net memory used: 329.680 MB
%------------------------------------------------------------------------------