%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC108-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 02:40:00 PM UTC 2026
% Result : Unsatisfiable 3.44s 1.29s
% Output : CNFRefutation 3.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 852
% Syntax : Number of formulae : 2859 ( 121 unt; 793 def)
% Number of atoms : 12636 ( 890 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 18741 (8964 ~;8984 |; 0 &)
% ( 793 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 801 ( 799 usr; 794 prp; 0-2 aty)
% Number of functors : 31 ( 31 usr; 5 con; 0-2 aty)
% Number of variables : 3726 (3726 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [U] : ssItem(skaf83(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [U] : ssList(skaf82(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [U] : ssList(skaf81(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] : ssList(skaf80(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] : ssList(skaf77(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [U] : ssList(skaf76(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [U] : ssList(skaf75(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [U] : ssList(skaf73(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [U] : ssList(skaf72(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U] : ssList(skaf71(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [U] : ssList(skaf68(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] : ssList(skaf67(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,axiom,
! [U] : ssList(skaf66(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [U] : ssList(skaf63(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [U] : ssList(skaf62(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [U] : ssList(skaf61(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U] : ssList(skaf58(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] : ssList(skaf57(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [U] : ssList(skaf56(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [U] : ssList(skaf53(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [U] : ssList(skaf52(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [U] : ssList(skaf51(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [U] : ssItem(skaf44(U)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [U,V] : ssList(skaf46(U,V)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( rearsegP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [U] :
( rearsegP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [U] :
( nil = U
| ~ ssList(U)
| ~ segmentP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f82,axiom,
! [U] :
( nil = U
| ~ ssList(U)
| ~ rearsegP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f115,axiom,
! [U,V] :
( ~ ssList(U)
| ~ ssList(V)
| ~ neq(U,V)
| U != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f127,axiom,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ segmentP(V,U)
| ~ segmentP(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f128,axiom,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ rearsegP(V,U)
| ~ rearsegP(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f129,axiom,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f131,axiom,
! [U,V] :
( app(skaf46(U,V),V) = U
| ~ ssList(U)
| ~ ssList(V)
| ~ rearsegP(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f132,axiom,
! [U,V] :
( app(V,skaf45(U,V)) = U
| ~ ssList(U)
| ~ ssList(V)
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f153,axiom,
! [U,V,W] :
( rearsegP(U,W)
| ~ ssList(U)
| ~ ssList(V)
| ~ ssList(W)
| ~ rearsegP(V,W)
| ~ rearsegP(U,V) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f173,axiom,
! [U,V,W,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ~ ssList(U)
| ~ ssList(W)
| app(app(U,V),W) != X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f187,negated_conjecture,
ssList(sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f190,negated_conjecture,
sk2 = sk4,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
( neq(sk2,nil)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
( neq(sk2,nil)
| nil != sk1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( neq(sk3,nil)
| nil = sk4 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f199,negated_conjecture,
( rearsegP(sk4,sk3)
| nil = sk3 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f207,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f211,plain,
! [X0] : ssItem(skaf83(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f212,plain,
! [X0] : ssList(skaf82(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f213,plain,
! [X0] : ssList(skaf81(X0)),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f214,plain,
! [X0] : ssList(skaf80(X0)),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f217,plain,
! [X0] : ssList(skaf77(X0)),
inference(cnf_transformation,[status(thm)],[f18]) ).
fof(f218,plain,
! [X0] : ssList(skaf76(X0)),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f219,plain,
! [X0] : ssList(skaf75(X0)),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f221,plain,
! [X0] : ssList(skaf73(X0)),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f222,plain,
! [X0] : ssList(skaf72(X0)),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f223,plain,
! [X0] : ssList(skaf71(X0)),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f226,plain,
! [X0] : ssList(skaf68(X0)),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f227,plain,
! [X0] : ssList(skaf67(X0)),
inference(cnf_transformation,[status(thm)],[f28]) ).
fof(f228,plain,
! [X0] : ssList(skaf66(X0)),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f231,plain,
! [X0] : ssList(skaf63(X0)),
inference(cnf_transformation,[status(thm)],[f32]) ).
fof(f232,plain,
! [X0] : ssList(skaf62(X0)),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f233,plain,
! [X0] : ssList(skaf61(X0)),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f236,plain,
! [X0] : ssList(skaf58(X0)),
inference(cnf_transformation,[status(thm)],[f37]) ).
fof(f237,plain,
! [X0] : ssList(skaf57(X0)),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f238,plain,
! [X0] : ssList(skaf56(X0)),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f241,plain,
! [X0] : ssList(skaf53(X0)),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f242,plain,
! [X0] : ssList(skaf52(X0)),
inference(cnf_transformation,[status(thm)],[f43]) ).
fof(f243,plain,
! [X0] : ssList(skaf51(X0)),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f246,plain,
! [X0] : ssItem(skaf44(X0)),
inference(cnf_transformation,[status(thm)],[f47]) ).
fof(f249,plain,
! [X0,X1] : ssList(skaf46(X0,X1)),
inference(cnf_transformation,[status(thm)],[f50]) ).
fof(f255,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
fof(f256,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f57]) ).
fof(f257,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
fof(f258,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f59]) ).
fof(f259,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f273,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f274,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f280,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f80]) ).
fof(f282,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f285,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f320,plain,
! [U] :
( ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ neq(U,V)
| U != V ) ),
inference(miniscoping,[status(thm)],[f115]) ).
fof(f321,plain,
! [X0,X1] :
( ~ ssList(X0)
| ~ ssList(X1)
| ~ neq(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f339,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f340,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f341,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f343,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] :
( app(X1,skaf45(X0,X1)) = X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
fof(f350,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(f351,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(f357,plain,
! [V,W] :
( rearsegP(W,V)
| ~ ssList(W)
| ~ ssList(V)
| ! [U] :
( ~ ssList(U)
| app(U,V) != W ) ),
inference(miniscoping,[status(thm)],[f143]) ).
fof(f358,plain,
! [X0,X1,X2] :
( rearsegP(X2,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f357]) ).
fof(f359,plain,
! [U,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != W ) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f360,plain,
! [X0,X1,X2] :
( frontsegP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f359]) ).
fof(f373,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(f374,plain,
! [X0,X1,X2] :
( segmentP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f373]) ).
fof(f375,plain,
! [U,W] :
( rearsegP(U,W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| ~ ssList(W)
| ~ rearsegP(V,W)
| ~ rearsegP(U,V) ) ),
inference(miniscoping,[status(thm)],[f153]) ).
fof(f376,plain,
! [X0,X1,X2] :
( rearsegP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f375]) ).
fof(f377,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(f378,plain,
! [X0,X1,X2] :
( frontsegP(X0,X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f377]) ).
fof(f404,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(f405,plain,
! [V,X] :
( segmentP(X,V)
| ~ ssList(X)
| ~ ssList(V)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| app(app(U,V),W) != X ) ) ),
inference(miniscoping,[status(thm)],[f173]) ).
fof(f406,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(app(X0,X1),X2) != X3 ),
inference(cnf_transformation,[status(thm)],[f405]) ).
fof(f430,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f431,plain,
ssList(sk2),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f434,plain,
sk2 = sk4,
inference(cnf_transformation,[status(thm)],[f190]) ).
fof(f435,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f436,plain,
( neq(sk2,nil)
| nil = sk2 ),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f437,plain,
( ~ segmentP(sk2,sk1)
| ~ neq(sk1,nil)
| nil = sk2 ),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f438,plain,
( neq(sk2,nil)
| nil != sk1 ),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f440,plain,
( neq(sk3,nil)
| nil = sk4 ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f443,plain,
( rearsegP(sk4,sk3)
| nil = sk3 ),
inference(cnf_transformation,[status(thm)],[f199]) ).
fof(f451,definition,
( sQ2_spl
<=> nil = sk2 ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ2_spl
| nil = sk2 ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,definition,
( sQ3_spl
<=> neq(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( ~ sQ3_spl
| neq(sk2,nil) ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f457,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f436,f451,f454]) ).
fof(f458,definition,
( sQ4_spl
<=> neq(sk1,nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f460,plain,
( sQ4_spl
| ~ neq(sk1,nil) ),
inference(component_clause,[status(thm)],[f458]) ).
fof(f461,definition,
( sQ5_spl
<=> segmentP(sk2,sk1) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f463,plain,
( sQ5_spl
| ~ segmentP(sk2,sk1) ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f464,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f437,f451,f458,f461]) ).
fof(f465,definition,
( sQ6_spl
<=> nil = sk1 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f466,plain,
( ~ sQ6_spl
| nil = sk1 ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f467,plain,
( sQ6_spl
| nil != sk1 ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f468,plain,
( sQ3_spl
| ~ sQ6_spl ),
inference(split_clause,[status(thm)],[f438,f465,f454]) ).
fof(f470,definition,
( sQ7_spl
<=> nil = sk4 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f471,plain,
( ~ sQ7_spl
| nil = sk4 ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f472,plain,
( sQ7_spl
| nil != sk4 ),
inference(component_clause,[status(thm)],[f470]) ).
fof(f473,definition,
( sQ8_spl
<=> neq(sk3,nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f474,plain,
( ~ sQ8_spl
| neq(sk3,nil) ),
inference(component_clause,[status(thm)],[f473]) ).
fof(f476,plain,
( sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f440,f470,f473]) ).
fof(f477,definition,
( sQ9_spl
<=> rearsegP(sk4,sk3) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f478,plain,
( ~ sQ9_spl
| rearsegP(sk4,sk3) ),
inference(component_clause,[status(thm)],[f477]) ).
fof(f481,definition,
( sQ10_spl
<=> nil = sk3 ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f482,plain,
( ~ sQ10_spl
| nil = sk3 ),
inference(component_clause,[status(thm)],[f481]) ).
fof(f485,plain,
( sQ9_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f443,f481,f477]) ).
fof(f493,plain,
! [X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ neq(X1,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f321]) ).
fof(f494,plain,
! [X0] :
( ~ ssList(X0)
| ~ neq(X0,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f493]) ).
fof(f500,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f358]) ).
fof(f501,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f360]) ).
fof(f504,plain,
! [X0,X1,X2] :
( segmentP(app(app(X1,X2),X0),X2)
| ~ ssList(app(app(X1,X2),X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f406]) ).
fof(f519,plain,
( ~ sQ10_spl
| nil = sk1 ),
inference(forward_demodulation,[status(thm)],[f435,f482]) ).
fof(f522,plain,
( ~ sQ7_spl
| nil = sk2 ),
inference(forward_demodulation,[status(thm)],[f434,f471]) ).
fof(f523,plain,
( sQ6_spl
| ~ sQ10_spl
| nil != nil ),
inference(forward_demodulation,[status(thm)],[f519,f467]) ).
fof(f524,plain,
( sQ6_spl
| ~ sQ10_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f523]) ).
fof(f525,plain,
( sQ6_spl
| ~ sQ10_spl ),
inference(contradiction_clause,[status(thm)],[f524]) ).
fof(f526,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| neq(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f522,f455]) ).
fof(f528,plain,
( ~ sQ8_spl
| neq(sk1,nil) ),
inference(forward_demodulation,[status(thm)],[f435,f474]) ).
fof(f532,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f494,f526]) ).
fof(f533,plain,
( ~ sQ3_spl
| ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f532,f207]) ).
fof(f534,plain,
( ~ sQ3_spl
| ~ sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f533]) ).
fof(f535,plain,
( ~ sQ9_spl
| rearsegP(sk4,sk1) ),
inference(forward_demodulation,[status(thm)],[f435,f478]) ).
fof(f536,plain,
( ~ sQ2_spl
| nil = sk4 ),
inference(forward_demodulation,[status(thm)],[f452,f434]) ).
fof(f537,plain,
( ~ sQ9_spl
| ~ sQ2_spl
| rearsegP(nil,sk1) ),
inference(forward_demodulation,[status(thm)],[f536,f535]) ).
fof(f539,plain,
( sQ7_spl
| ~ sQ2_spl
| nil != nil ),
inference(forward_demodulation,[status(thm)],[f536,f472]) ).
fof(f540,plain,
( sQ7_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f539]) ).
fof(f541,plain,
( sQ7_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f540]) ).
fof(f543,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f280,f255]) ).
fof(f545,definition,
( sQ11_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f547,plain,
( sQ11_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f545]) ).
fof(f548,definition,
( sQ12_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f551,plain,
( sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f543,f545,f548]) ).
fof(f553,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f547,f207]) ).
fof(f554,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f553]) ).
fof(f555,plain,
( ~ sQ9_spl
| ~ sQ2_spl
| nil = sk1
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f282,f537]) ).
fof(f558,definition,
( sQ13_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f560,plain,
( sQ13_spl
| ~ ssList(sk1) ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f561,plain,
( ~ sQ9_spl
| ~ sQ2_spl
| sQ6_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f555,f558,f465,f451,f477]) ).
fof(f564,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f560,f430]) ).
fof(f565,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f564]) ).
fof(f566,plain,
( sQ4_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f460,f528]) ).
fof(f567,plain,
( sQ4_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f566]) ).
fof(f571,plain,
( ~ sQ9_spl
| rearsegP(sk2,sk1) ),
inference(forward_demodulation,[status(thm)],[f434,f535]) ).
fof(f574,plain,
! [X0] :
( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(resolution,[status(thm)],[f339,f255]) ).
fof(f576,definition,
! [X0] :
( sQ14_spl
<=> ( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f579,plain,
( ~ sQ11_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f574,f576,f545]) ).
fof(f582,plain,
! [X0] :
( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f340,f257]) ).
fof(f587,definition,
( sQ16_spl
<=> ssList(sk2) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f589,plain,
( sQ16_spl
| ~ ssList(sk2) ),
inference(component_clause,[status(thm)],[f587]) ).
fof(f594,definition,
! [X0] :
( sQ18_spl
<=> ( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f597,plain,
( ~ sQ11_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f582,f594,f545]) ).
fof(f607,plain,
! [X0,X1,X2] :
( app(X2,X0) = X1
| ~ ssList(app(X2,X0))
| ~ ssList(X1)
| ~ rearsegP(X1,app(X2,X0))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f350,f340]) ).
fof(f608,plain,
! [X0,X1,X2] :
( app(X2,X0) = X1
| ~ ssList(app(X2,X0))
| ~ rearsegP(X1,app(X2,X0))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f607]) ).
fof(f611,plain,
! [X0,X1] :
( ~ ssList(X1)
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ segmentP(X0,X1) ),
inference(resolution,[status(thm)],[f374,f255]) ).
fof(f613,definition,
! [X0,X1] :
( sQ19_spl
<=> ( ~ ssList(X1)
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f616,plain,
( ~ sQ11_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f611,f613,f545]) ).
fof(f619,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f376,f282]) ).
fof(f620,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ ssList(X0)
| ~ ssList(X2)
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f376,f340]) ).
fof(f625,definition,
! [X0,X1] :
( sQ21_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f626,plain,
! [X0,X1] :
( ~ sQ21_spl
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ),
inference(component_clause,[status(thm)],[f625]) ).
fof(f628,plain,
( ~ sQ11_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f619,f625,f545]) ).
fof(f629,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f620]) ).
fof(f630,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f589,f431]) ).
fof(f631,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f630]) ).
fof(f632,plain,
! [X0,X1] :
( ~ sQ21_spl
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ),
inference(duplicate_literals_removal,[status(thm)],[f626]) ).
fof(f663,plain,
! [X0,X1,X2,X3,X4] :
( segmentP(X4,X1)
| ~ ssList(X4)
| ~ ssList(app(app(X3,X0),X2))
| ~ ssList(X1)
| ~ segmentP(X4,app(app(X3,X0),X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X0,X1) ),
inference(resolution,[status(thm)],[f404,f374]) ).
fof(f664,plain,
! [X0,X1,X2,X3] :
( app(app(X3,X0),X2) = X1
| ~ ssList(app(app(X3,X0),X2))
| ~ ssList(X1)
| ~ segmentP(X1,app(app(X3,X0),X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X0,X1) ),
inference(resolution,[status(thm)],[f404,f339]) ).
fof(f665,plain,
! [X0,X1,X2,X3,X4] :
( segmentP(X4,X1)
| ~ ssList(X4)
| ~ ssList(app(app(X3,X0),X2))
| ~ segmentP(X4,app(app(X3,X0),X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f663]) ).
fof(f666,plain,
! [X0,X1,X2,X3] :
( app(app(X3,X0),X2) = X1
| ~ ssList(app(app(X3,X0),X2))
| ~ segmentP(X1,app(app(X3,X0),X2))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ segmentP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f664]) ).
fof(f719,plain,
! [X0] :
( ~ sQ21_spl
| ~ ssList(nil)
| nil = X0
| ~ ssList(nil)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f632,f257]) ).
fof(f720,plain,
! [X0,X1,X2] :
( ~ sQ21_spl
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f632,f376]) ).
fof(f722,definition,
! [X0] :
( sQ34_spl
<=> ( nil = X0
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f725,plain,
( ~ sQ21_spl
| ~ sQ11_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f719,f722,f545,f625]) ).
fof(f726,definition,
! [X0,X1,X2] :
( sQ35_spl
<=> ( ~ ssList(X2)
| ~ ssList(X0)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f727,plain,
! [X0,X1,X2] :
( ~ sQ35_spl
| ~ ssList(X2)
| ~ ssList(X0)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ),
inference(component_clause,[status(thm)],[f726]) ).
fof(f729,plain,
( ~ sQ21_spl
| ~ sQ11_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f720,f726,f545,f625]) ).
fof(f731,plain,
! [X0,X1,X2] :
( ~ sQ35_spl
| ~ ssList(X2)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f727]) ).
fof(f734,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| ~ rearsegP(X2,X3)
| X0 = X3
| ~ rearsegP(X3,X0)
| ~ ssList(X0)
| ~ ssList(app(X1,X2))
| ~ ssList(X3)
| ~ rearsegP(X0,app(X1,X2)) ),
inference(resolution,[status(thm)],[f629,f350]) ).
fof(f736,plain,
! [X0,X1] :
( ~ ssList(X1)
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f629,f257]) ).
fof(f738,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ rearsegP(X3,X2)
| ~ rearsegP(X1,X3)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f629,f376]) ).
fof(f742,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X3)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ rearsegP(X3,X0)
| X0 = app(X2,X3)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(X2,X3))
| ~ rearsegP(X1,app(X2,X3))
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f629,f350]) ).
fof(f744,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X0)
| ~ rearsegP(X3,X0)
| ~ rearsegP(X2,X3)
| X0 = X2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f629,f376]) ).
fof(f750,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ rearsegP(X2,X3)
| X0 = X3
| ~ rearsegP(X3,X0)
| ~ ssList(X0)
| ~ ssList(app(X1,X2))
| ~ ssList(X3)
| ~ rearsegP(X0,app(X1,X2)) ),
inference(duplicate_literals_removal,[status(thm)],[f734]) ).
fof(f751,definition,
( sQ37_spl
<=> rearsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f755,definition,
! [X0,X1] :
( sQ38_spl
<=> ( ~ ssList(X1)
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f758,plain,
( ~ sQ11_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f736,f755,f545]) ).
fof(f759,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X3)
| ~ rearsegP(X3,X2)
| ~ rearsegP(X1,X3)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f738]) ).
fof(f762,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X3)
| ~ ssList(X2)
| ~ rearsegP(X3,X0)
| X0 = app(X2,X3)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(X2,X3))
| ~ rearsegP(X1,app(X2,X3))
| ~ rearsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f742]) ).
fof(f764,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X3)
| ~ rearsegP(X3,X0)
| ~ rearsegP(X2,X3)
| X0 = X2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f744]) ).
fof(f766,plain,
! [X0,X1] :
( ~ sQ35_spl
| ~ ssList(nil)
| ~ ssList(nil)
| ~ rearsegP(nil,X0)
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f731,f257]) ).
fof(f767,plain,
! [X0,X1,X2,X3] :
( ~ sQ35_spl
| ~ ssList(nil)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ rearsegP(X3,X2)
| ~ rearsegP(nil,X3)
| ~ ssList(X2)
| ~ rearsegP(X2,X0)
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f731,f376]) ).
fof(f769,definition,
! [X0,X1] :
( sQ39_spl
<=> ( ~ rearsegP(nil,X0)
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f772,plain,
( ~ sQ35_spl
| ~ sQ11_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f766,f769,f545,f726]) ).
fof(f773,definition,
! [X0,X1,X2,X3] :
( sQ40_spl
<=> ( ~ ssList(X3)
| ~ ssList(X2)
| ~ rearsegP(X3,X2)
| ~ rearsegP(nil,X3)
| ~ ssList(X2)
| ~ rearsegP(X2,X0)
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f776,plain,
( ~ sQ35_spl
| ~ sQ11_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f767,f773,f545,f726]) ).
fof(f794,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X2,X1)
| ~ rearsegP(X0,X2)
| nil = X1
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f759,f257]) ).
fof(f802,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssList(nil)
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ rearsegP(X0,nil) ),
inference(resolution,[status(thm)],[f759,f257]) ).
fof(f803,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f759,f257]) ).
fof(f810,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f759,f257]) ).
fof(f817,definition,
! [X0,X1,X2] :
( sQ42_spl
<=> ( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X2,X1)
| ~ rearsegP(X0,X2)
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f820,plain,
( ~ sQ11_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f794,f817,f545]) ).
fof(f828,definition,
! [X0] :
( sQ44_spl
<=> ( X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ rearsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f831,plain,
( ~ sQ11_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f802,f828,f545]) ).
fof(f832,definition,
! [X0,X1,X2] :
( sQ45_spl
<=> ( ~ ssList(X1)
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f833,plain,
! [X0,X1,X2] :
( ~ sQ45_spl
| ~ ssList(X1)
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ),
inference(component_clause,[status(thm)],[f832]) ).
fof(f835,plain,
( ~ sQ11_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f803,f832,f545]) ).
fof(f845,definition,
! [X0,X1,X2] :
( sQ47_spl
<=> ( ~ ssList(X2)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f848,plain,
( ~ sQ11_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f810,f845,f545]) ).
fof(f852,plain,
! [X0,X1,X2] :
( ~ sQ45_spl
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f833]) ).
fof(f860,plain,
( sQ5_spl
| ~ sQ6_spl
| ~ segmentP(sk2,nil) ),
inference(backward_demodulation,[status(thm)],[f466,f463]) ).
fof(f873,definition,
! [X0,X1] :
( sQ48_spl
<=> ( ~ rearsegP(X1,sk2)
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f878,definition,
! [X0,X1] :
( sQ49_spl
<=> ( ~ rearsegP(nil,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f885,definition,
! [X0] :
( sQ50_spl
<=> ( X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ rearsegP(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f890,plain,
( sQ5_spl
| ~ sQ6_spl
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f860,f255]) ).
fof(f891,plain,
( sQ5_spl
| ~ sQ6_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f890,f587,f465,f461]) ).
fof(f922,plain,
! [X0,X1] :
( ~ sQ45_spl
| ~ ssList(nil)
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f852,f257]) ).
fof(f923,plain,
! [X0,X1,X2,X3] :
( ~ sQ45_spl
| ~ ssList(nil)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ rearsegP(X3,X2)
| ~ rearsegP(nil,X3)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f852,f376]) ).
fof(f925,definition,
! [X0,X1] :
( sQ51_spl
<=> ( X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f928,plain,
( ~ sQ45_spl
| ~ sQ11_spl
| sQ51_spl ),
inference(split_clause,[status(thm)],[f922,f925,f545,f832]) ).
fof(f929,definition,
! [X0,X1,X2,X3] :
( sQ52_spl
<=> ( ~ ssList(X3)
| ~ ssList(X2)
| ~ rearsegP(X3,X2)
| ~ rearsegP(nil,X3)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f932,plain,
( ~ sQ45_spl
| ~ sQ11_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f923,f929,f545,f832]) ).
fof(f946,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f764,f257]) ).
fof(f955,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(nil)
| ~ rearsegP(nil,X0)
| X0 = X2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f764,f257]) ).
fof(f965,definition,
( sQ53_spl
<=> sk1 = sk1 ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f975,definition,
! [X0,X1,X2] :
( sQ55_spl
<=> ( ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f978,plain,
( ~ sQ11_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f946,f975,f545]) ).
fof(f990,definition,
! [X0,X1,X2] :
( sQ58_spl
<=> ( ~ ssList(X2)
| ~ rearsegP(nil,X0)
| X0 = X2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f991,plain,
! [X0,X1,X2] :
( ~ sQ58_spl
| ~ ssList(X2)
| ~ rearsegP(nil,X0)
| X0 = X2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1) ),
inference(component_clause,[status(thm)],[f990]) ).
fof(f993,plain,
( ~ sQ11_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f955,f990,f545]) ).
fof(f1002,plain,
! [X0,X1,X2] :
( ~ sQ58_spl
| ~ rearsegP(nil,X0)
| X0 = X2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f991]) ).
fof(f1004,plain,
! [X0,X1,X2,X3] :
( ~ sQ58_spl
| ~ ssList(nil)
| ~ ssList(X3)
| ~ ssList(X0)
| ~ rearsegP(X3,X0)
| ~ rearsegP(nil,X3)
| X0 = X2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f1002,f376]) ).
fof(f1007,definition,
! [X0,X1,X2,X3] :
( sQ59_spl
<=> ( ~ ssList(X3)
| ~ ssList(X0)
| ~ rearsegP(X3,X0)
| ~ rearsegP(nil,X3)
| X0 = X2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1010,plain,
( ~ sQ58_spl
| ~ sQ11_spl
| sQ59_spl ),
inference(split_clause,[status(thm)],[f1004,f1007,f545,f990]) ).
fof(f1013,plain,
app(sk1,nil) = sk1,
inference(resolution,[status(thm)],[f273,f430]) ).
fof(f1020,plain,
! [X0] : app(skaf51(X0),nil) = skaf51(X0),
inference(resolution,[status(thm)],[f273,f243]) ).
fof(f1021,plain,
! [X0] : app(skaf52(X0),nil) = skaf52(X0),
inference(resolution,[status(thm)],[f273,f242]) ).
fof(f1022,plain,
! [X0] : app(skaf53(X0),nil) = skaf53(X0),
inference(resolution,[status(thm)],[f273,f241]) ).
fof(f1023,plain,
! [X0] : app(skaf56(X0),nil) = skaf56(X0),
inference(resolution,[status(thm)],[f273,f238]) ).
fof(f1024,plain,
! [X0] : app(skaf57(X0),nil) = skaf57(X0),
inference(resolution,[status(thm)],[f273,f237]) ).
fof(f1025,plain,
! [X0] : app(skaf58(X0),nil) = skaf58(X0),
inference(resolution,[status(thm)],[f273,f236]) ).
fof(f1026,plain,
! [X0] : app(skaf61(X0),nil) = skaf61(X0),
inference(resolution,[status(thm)],[f273,f233]) ).
fof(f1027,plain,
! [X0] : app(skaf62(X0),nil) = skaf62(X0),
inference(resolution,[status(thm)],[f273,f232]) ).
fof(f1028,plain,
! [X0] : app(skaf63(X0),nil) = skaf63(X0),
inference(resolution,[status(thm)],[f273,f231]) ).
fof(f1029,plain,
app(sk2,nil) = sk2,
inference(resolution,[status(thm)],[f273,f431]) ).
fof(f1030,plain,
! [X0] : app(skaf66(X0),nil) = skaf66(X0),
inference(resolution,[status(thm)],[f273,f228]) ).
fof(f1031,plain,
! [X0] : app(skaf67(X0),nil) = skaf67(X0),
inference(resolution,[status(thm)],[f273,f227]) ).
fof(f1032,plain,
! [X0] : app(skaf68(X0),nil) = skaf68(X0),
inference(resolution,[status(thm)],[f273,f226]) ).
fof(f1033,plain,
! [X0] : app(skaf71(X0),nil) = skaf71(X0),
inference(resolution,[status(thm)],[f273,f223]) ).
fof(f1034,plain,
! [X0] : app(skaf72(X0),nil) = skaf72(X0),
inference(resolution,[status(thm)],[f273,f222]) ).
fof(f1035,plain,
! [X0] : app(skaf73(X0),nil) = skaf73(X0),
inference(resolution,[status(thm)],[f273,f221]) ).
fof(f1036,plain,
! [X0] : app(skaf75(X0),nil) = skaf75(X0),
inference(resolution,[status(thm)],[f273,f219]) ).
fof(f1037,plain,
! [X0] : app(skaf76(X0),nil) = skaf76(X0),
inference(resolution,[status(thm)],[f273,f218]) ).
fof(f1038,plain,
! [X0] : app(skaf77(X0),nil) = skaf77(X0),
inference(resolution,[status(thm)],[f273,f217]) ).
fof(f1039,plain,
! [X0] : app(skaf80(X0),nil) = skaf80(X0),
inference(resolution,[status(thm)],[f273,f214]) ).
fof(f1040,plain,
! [X0] : app(skaf81(X0),nil) = skaf81(X0),
inference(resolution,[status(thm)],[f273,f213]) ).
fof(f1041,plain,
! [X0] : app(skaf82(X0),nil) = skaf82(X0),
inference(resolution,[status(thm)],[f273,f212]) ).
fof(f1042,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f273,f207]) ).
fof(f1043,plain,
! [X0,X1,X2] :
( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk1,X1))
| ~ segmentP(X2,app(app(sk1,nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1013,f665]) ).
fof(f1044,plain,
! [X0] :
( app(sk1,nil) = X0
| ~ ssList(sk1)
| ~ rearsegP(X0,app(sk1,nil))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1013,f608]) ).
fof(f1045,plain,
! [X0] :
( segmentP(app(app(sk1,nil),X0),nil)
| ~ ssList(app(sk1,X0))
| ~ ssList(nil)
| ~ ssList(sk1)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1013,f504]) ).
fof(f1046,plain,
! [X0,X1] :
( segmentP(app(sk1,X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1013,f404]) ).
fof(f1047,plain,
( rearsegP(app(sk1,nil),nil)
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ ssList(sk1) ),
inference(paramodulation,[status(thm)],[f1013,f500]) ).
fof(f1049,definition,
! [X0,X1,X2] :
( sQ60_spl
<=> ( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk1,X1))
| ~ segmentP(X2,app(app(sk1,nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1050,plain,
! [X0,X1,X2] :
( ~ sQ60_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk1,X1))
| ~ segmentP(X2,app(app(sk1,nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1049]) ).
fof(f1052,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f1043,f1049,f558,f545]) ).
fof(f1053,definition,
! [X0] :
( sQ61_spl
<=> ( app(sk1,nil) = X0
| ~ rearsegP(X0,app(sk1,nil))
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1056,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f1044,f1053,f558,f545]) ).
fof(f1057,definition,
! [X0] :
( sQ62_spl
<=> ( segmentP(app(app(sk1,nil),X0),nil)
| ~ ssList(app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1060,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f1045,f1057,f558,f545]) ).
fof(f1061,definition,
! [X0,X1] :
( sQ63_spl
<=> ( segmentP(app(sk1,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1062,plain,
! [X0,X1] :
( ~ sQ63_spl
| segmentP(app(sk1,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1061]) ).
fof(f1064,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f1046,f1061,f558,f545]) ).
fof(f1065,definition,
( sQ64_spl
<=> rearsegP(app(sk1,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1066,plain,
( ~ sQ64_spl
| rearsegP(app(sk1,nil),nil) ),
inference(component_clause,[status(thm)],[f1065]) ).
fof(f1068,plain,
( sQ64_spl
| ~ sQ11_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1047,f558,f545,f1065]) ).
fof(f1069,definition,
! [X0] :
( sQ65_spl
<=> ( rearsegP(sk1,X0)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1070,plain,
! [X0] :
( ~ sQ65_spl
| rearsegP(sk1,X0)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ),
inference(component_clause,[status(thm)],[f1069]) ).
fof(f1073,plain,
! [X0,X1,X2] :
( ~ sQ60_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk1,X1))
| ~ segmentP(X2,app(sk1,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1013,f1050]) ).
fof(f1077,plain,
( ~ sQ64_spl
| rearsegP(sk1,nil) ),
inference(forward_demodulation,[status(thm)],[f1013,f1066]) ).
fof(f1082,plain,
! [X0,X1] :
( ~ sQ64_spl
| ~ ssList(sk1)
| ~ rearsegP(X1,sk1)
| nil = X1
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f1077,f764]) ).
fof(f1083,plain,
! [X0,X1] :
( ~ sQ64_spl
| ~ ssList(nil)
| ~ rearsegP(nil,X0)
| X0 = sk1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sk1)
| ~ rearsegP(X1,sk1)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f1077,f764]) ).
fof(f1086,plain,
! [X0,X1] :
( ~ sQ64_spl
| ~ ssList(sk1)
| ~ rearsegP(X1,sk1)
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f1077,f759]) ).
fof(f1088,plain,
! [X0,X1] :
( ~ sQ64_spl
| ~ ssList(nil)
| ~ rearsegP(nil,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(X1)
| ~ rearsegP(X0,sk1) ),
inference(resolution,[status(thm)],[f1077,f759]) ).
fof(f1092,plain,
! [X0] :
( ~ sQ64_spl
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ rearsegP(X0,sk1) ),
inference(resolution,[status(thm)],[f1077,f629]) ).
fof(f1101,definition,
! [X0,X1] :
( sQ67_spl
<=> ( ~ rearsegP(X1,sk1)
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1104,plain,
( ~ sQ64_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f1082,f1101,f545,f558,f1065]) ).
fof(f1105,definition,
! [X0,X1] :
( sQ68_spl
<=> ( ~ rearsegP(nil,X0)
| X0 = sk1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,sk1)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1108,plain,
( ~ sQ64_spl
| ~ sQ11_spl
| ~ sQ13_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f1083,f1105,f558,f545,f1065]) ).
fof(f1111,definition,
! [X0,X1] :
( sQ69_spl
<=> ( ~ rearsegP(X1,sk1)
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1114,plain,
( ~ sQ64_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f1086,f1111,f545,f558,f1065]) ).
fof(f1116,definition,
! [X0,X1] :
( sQ70_spl
<=> ( ~ rearsegP(nil,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1119,plain,
( ~ sQ64_spl
| ~ sQ11_spl
| ~ sQ13_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f1088,f1116,f558,f545,f1065]) ).
fof(f1129,definition,
! [X0] :
( sQ73_spl
<=> ( X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ rearsegP(X0,sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1132,plain,
( ~ sQ64_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f1092,f1129,f545,f558,f1065]) ).
fof(f1136,plain,
! [X0,X1,X2] :
( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk2,X1))
| ~ segmentP(X2,app(app(sk2,nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1029,f665]) ).
fof(f1137,plain,
! [X0] :
( app(sk2,nil) = X0
| ~ ssList(sk2)
| ~ rearsegP(X0,app(sk2,nil))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1029,f608]) ).
fof(f1138,plain,
! [X0] :
( segmentP(app(app(sk2,nil),X0),nil)
| ~ ssList(app(sk2,X0))
| ~ ssList(nil)
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1029,f504]) ).
fof(f1139,plain,
! [X0,X1] :
( segmentP(app(sk2,X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1029,f404]) ).
fof(f1140,plain,
( rearsegP(app(sk2,nil),nil)
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ ssList(sk2) ),
inference(paramodulation,[status(thm)],[f1029,f500]) ).
fof(f1142,definition,
! [X0,X1,X2] :
( sQ74_spl
<=> ( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk2,X1))
| ~ segmentP(X2,app(app(sk2,nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1143,plain,
! [X0,X1,X2] :
( ~ sQ74_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk2,X1))
| ~ segmentP(X2,app(app(sk2,nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1142]) ).
fof(f1145,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f1136,f1142,f587,f545]) ).
fof(f1146,definition,
! [X0] :
( sQ75_spl
<=> ( app(sk2,nil) = X0
| ~ rearsegP(X0,app(sk2,nil))
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1149,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f1137,f1146,f587,f545]) ).
fof(f1150,definition,
! [X0] :
( sQ76_spl
<=> ( segmentP(app(app(sk2,nil),X0),nil)
| ~ ssList(app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1153,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f1138,f1150,f587,f545]) ).
fof(f1154,definition,
! [X0,X1] :
( sQ77_spl
<=> ( segmentP(app(sk2,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1155,plain,
! [X0,X1] :
( ~ sQ77_spl
| segmentP(app(sk2,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1154]) ).
fof(f1157,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f1139,f1154,f587,f545]) ).
fof(f1158,definition,
( sQ78_spl
<=> rearsegP(app(sk2,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1159,plain,
( ~ sQ78_spl
| rearsegP(app(sk2,nil),nil) ),
inference(component_clause,[status(thm)],[f1158]) ).
fof(f1161,plain,
( sQ78_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1140,f587,f545,f1158]) ).
fof(f1162,definition,
! [X0] :
( sQ79_spl
<=> ( rearsegP(sk2,X0)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1163,plain,
! [X0] :
( ~ sQ79_spl
| rearsegP(sk2,X0)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ),
inference(component_clause,[status(thm)],[f1162]) ).
fof(f1166,plain,
! [X0,X1,X2] :
( ~ sQ74_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk2,X1))
| ~ segmentP(X2,app(sk2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1029,f1143]) ).
fof(f1170,plain,
( ~ sQ78_spl
| rearsegP(sk2,nil) ),
inference(forward_demodulation,[status(thm)],[f1029,f1159]) ).
fof(f1172,plain,
! [X0,X1] :
( ~ sQ78_spl
| ~ ssList(sk2)
| ~ rearsegP(X1,sk2)
| nil = X1
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f1170,f764]) ).
fof(f1173,plain,
! [X0,X1] :
( ~ sQ78_spl
| ~ ssList(nil)
| ~ rearsegP(nil,X0)
| X0 = sk2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sk2)
| ~ rearsegP(X1,sk2)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f1170,f764]) ).
fof(f1176,plain,
! [X0,X1] :
( ~ sQ78_spl
| ~ ssList(sk2)
| ~ rearsegP(X1,sk2)
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f1170,f759]) ).
fof(f1178,plain,
! [X0,X1] :
( ~ sQ78_spl
| ~ ssList(nil)
| ~ rearsegP(nil,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ rearsegP(X0,sk2) ),
inference(resolution,[status(thm)],[f1170,f759]) ).
fof(f1182,plain,
! [X0] :
( ~ sQ78_spl
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ rearsegP(X0,sk2) ),
inference(resolution,[status(thm)],[f1170,f629]) ).
fof(f1185,definition,
! [X0,X1] :
( sQ80_spl
<=> ( ~ rearsegP(X1,sk2)
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1188,plain,
( ~ sQ78_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sQ80_spl ),
inference(split_clause,[status(thm)],[f1172,f1185,f545,f587,f1158]) ).
fof(f1189,definition,
! [X0,X1] :
( sQ81_spl
<=> ( ~ rearsegP(nil,X0)
| X0 = sk2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,sk2)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1192,plain,
( ~ sQ78_spl
| ~ sQ11_spl
| ~ sQ16_spl
| sQ81_spl ),
inference(split_clause,[status(thm)],[f1173,f1189,f587,f545,f1158]) ).
fof(f1195,plain,
( ~ sQ78_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f1176,f873,f545,f587,f1158]) ).
fof(f1197,plain,
( ~ sQ78_spl
| ~ sQ11_spl
| ~ sQ16_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f1178,f878,f587,f545,f1158]) ).
fof(f1201,plain,
( ~ sQ78_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f1182,f885,f545,f587,f1158]) ).
fof(f1204,plain,
! [X0,X1] :
( ~ sQ65_spl
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| rearsegP(sk1,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1070,f376]) ).
fof(f1206,definition,
( sQ82_spl
<=> rearsegP(sk1,nil) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1210,definition,
! [X0,X1] :
( sQ83_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| rearsegP(sk1,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1211,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| rearsegP(sk1,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1210]) ).
fof(f1213,plain,
( ~ sQ65_spl
| ~ sQ11_spl
| sQ83_spl ),
inference(split_clause,[status(thm)],[f1204,f1210,f545,f1069]) ).
fof(f1215,plain,
! [X0,X1] :
( ~ sQ83_spl
| ~ ssList(X1)
| ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| rearsegP(sk1,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1211]) ).
fof(f1226,plain,
! [X0,X1] :
( ~ sQ60_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(sk1)
| ~ segmentP(X1,app(sk1,nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1013,f1073]) ).
fof(f1227,definition,
! [X0,X1] :
( sQ85_spl
<=> ( segmentP(X1,X0)
| ~ ssList(X1)
| ~ segmentP(X1,app(sk1,nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1228,plain,
! [X0,X1] :
( ~ sQ85_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| ~ segmentP(X1,app(sk1,nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1227]) ).
fof(f1230,plain,
( ~ sQ60_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f1226,f1227,f545,f558,f1049]) ).
fof(f1231,plain,
! [X0,X1] :
( ~ sQ85_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| ~ segmentP(X1,sk1)
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1013,f1228]) ).
fof(f1232,plain,
! [X0,X1,X2] :
( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(nil,X1))
| ~ segmentP(X2,app(app(nil,nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1042,f665]) ).
fof(f1233,plain,
! [X0] :
( app(nil,nil) = X0
| ~ ssList(nil)
| ~ rearsegP(X0,app(nil,nil))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1042,f608]) ).
fof(f1234,plain,
! [X0] :
( segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(app(nil,X0))
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1042,f504]) ).
fof(f1235,plain,
! [X0,X1] :
( segmentP(app(nil,X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1042,f404]) ).
fof(f1236,plain,
( rearsegP(app(nil,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1042,f500]) ).
fof(f1237,plain,
! [X0] :
( rearsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1042,f350]) ).
fof(f1238,definition,
! [X0,X1,X2] :
( sQ86_spl
<=> ( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(nil,X1))
| ~ segmentP(X2,app(app(nil,nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1239,plain,
! [X0,X1,X2] :
( ~ sQ86_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(nil,X1))
| ~ segmentP(X2,app(app(nil,nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1238]) ).
fof(f1241,plain,
( ~ sQ11_spl
| sQ86_spl ),
inference(split_clause,[status(thm)],[f1232,f1238,f545]) ).
fof(f1242,definition,
! [X0] :
( sQ87_spl
<=> ( app(nil,nil) = X0
| ~ rearsegP(X0,app(nil,nil))
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1245,plain,
( ~ sQ11_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f1233,f1242,f545]) ).
fof(f1246,definition,
! [X0] :
( sQ88_spl
<=> ( segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1249,plain,
( ~ sQ11_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f1234,f1246,f545]) ).
fof(f1250,definition,
! [X0,X1] :
( sQ89_spl
<=> ( segmentP(app(nil,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1253,plain,
( ~ sQ11_spl
| sQ89_spl ),
inference(split_clause,[status(thm)],[f1235,f1250,f545]) ).
fof(f1254,definition,
( sQ90_spl
<=> rearsegP(app(nil,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1255,plain,
( ~ sQ90_spl
| rearsegP(app(nil,nil),nil) ),
inference(component_clause,[status(thm)],[f1254]) ).
fof(f1257,plain,
( sQ90_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1236,f545,f1254]) ).
fof(f1258,definition,
! [X0] :
( sQ91_spl
<=> ( rearsegP(nil,X0)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1261,plain,
( ~ sQ11_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f1237,f1258,f545]) ).
fof(f1262,plain,
! [X0,X1,X2] :
( ~ sQ86_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(nil,X1))
| ~ segmentP(X2,app(nil,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1042,f1239]) ).
fof(f1266,plain,
( ~ sQ90_spl
| rearsegP(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f1042,f1255]) ).
fof(f1278,plain,
! [X0,X1] :
( ~ sQ90_spl
| ~ ssList(nil)
| ~ rearsegP(X1,nil)
| nil = X1
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f1266,f764]) ).
fof(f1280,plain,
! [X0,X1] :
( ~ sQ90_spl
| ~ ssList(nil)
| ~ rearsegP(nil,X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(X1,nil)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f1266,f764]) ).
fof(f1286,plain,
! [X0,X1] :
( ~ sQ90_spl
| ~ ssList(nil)
| ~ rearsegP(nil,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ rearsegP(X0,nil) ),
inference(resolution,[status(thm)],[f1266,f759]) ).
fof(f1305,definition,
! [X0,X1] :
( sQ92_spl
<=> ( ~ rearsegP(X1,nil)
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1308,plain,
( ~ sQ90_spl
| ~ sQ11_spl
| sQ92_spl ),
inference(split_clause,[status(thm)],[f1278,f1305,f545,f1254]) ).
fof(f1310,definition,
! [X0,X1] :
( sQ93_spl
<=> ( ~ rearsegP(nil,X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,nil)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1313,plain,
( ~ sQ90_spl
| ~ sQ11_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f1280,f1310,f545,f1254]) ).
fof(f1319,definition,
! [X0,X1] :
( sQ94_spl
<=> ( ~ rearsegP(nil,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1320,plain,
! [X0,X1] :
( ~ sQ94_spl
| ~ rearsegP(nil,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,nil) ),
inference(component_clause,[status(thm)],[f1319]) ).
fof(f1322,plain,
( ~ sQ90_spl
| ~ sQ11_spl
| sQ94_spl ),
inference(split_clause,[status(thm)],[f1286,f1319,f545,f1254]) ).
fof(f1333,plain,
! [X0,X1] :
( ~ sQ94_spl
| ~ rearsegP(nil,X0)
| X1 = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1320,f257]) ).
fof(f1336,plain,
! [X0,X1] :
( ~ sQ79_spl
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| rearsegP(sk2,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1163,f376]) ).
fof(f1338,definition,
( sQ96_spl
<=> rearsegP(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f1343,definition,
! [X0,X1] :
( sQ97_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| rearsegP(sk2,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1344,plain,
! [X0,X1] :
( ~ sQ97_spl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| rearsegP(sk2,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1343]) ).
fof(f1346,plain,
( ~ sQ79_spl
| ~ sQ11_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f1336,f1343,f545,f1162]) ).
fof(f1348,plain,
! [X0,X1] :
( ~ sQ97_spl
| ~ ssList(X1)
| ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| rearsegP(sk2,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1344]) ).
fof(f1351,plain,
! [X0,X1,X2] :
( ~ sQ94_spl
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| X1 = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1333,f376]) ).
fof(f1355,definition,
! [X0,X1,X2] :
( sQ98_spl
<=> ( ~ ssList(X2)
| ~ ssList(X0)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| X1 = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1358,plain,
( ~ sQ94_spl
| ~ sQ11_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f1351,f1355,f545,f1319]) ).
fof(f1361,plain,
! [X0] :
( ~ sQ63_spl
| ~ ssList(nil)
| segmentP(app(sk1,X0),nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1062,f255]) ).
fof(f1363,definition,
! [X0] :
( sQ99_spl
<=> ( segmentP(app(sk1,X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1364,plain,
! [X0] :
( ~ sQ99_spl
| segmentP(app(sk1,X0),nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1363]) ).
fof(f1366,plain,
( ~ sQ63_spl
| ~ sQ11_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f1361,f1363,f545,f1061]) ).
fof(f1368,plain,
! [X0,X1] :
( app(app(nil,nil),X1) = X0
| ~ ssList(app(nil,X1))
| ~ segmentP(X0,app(app(nil,nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1042,f666]) ).
fof(f1369,plain,
! [X0,X1] :
( app(app(sk2,nil),X1) = X0
| ~ ssList(app(sk2,X1))
| ~ segmentP(X0,app(app(sk2,nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1029,f666]) ).
fof(f1370,plain,
! [X0,X1] :
( app(app(sk1,nil),X1) = X0
| ~ ssList(app(sk1,X1))
| ~ segmentP(X0,app(app(sk1,nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1013,f666]) ).
fof(f1371,definition,
! [X0,X1] :
( sQ100_spl
<=> ( app(app(nil,nil),X1) = X0
| ~ ssList(app(nil,X1))
| ~ segmentP(X0,app(app(nil,nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1372,plain,
! [X0,X1] :
( ~ sQ100_spl
| app(app(nil,nil),X1) = X0
| ~ ssList(app(nil,X1))
| ~ segmentP(X0,app(app(nil,nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1371]) ).
fof(f1374,plain,
( ~ sQ11_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f1368,f1371,f545]) ).
fof(f1375,definition,
! [X0,X1] :
( sQ101_spl
<=> ( app(app(sk2,nil),X1) = X0
| ~ ssList(app(sk2,X1))
| ~ segmentP(X0,app(app(sk2,nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1376,plain,
! [X0,X1] :
( ~ sQ101_spl
| app(app(sk2,nil),X1) = X0
| ~ ssList(app(sk2,X1))
| ~ segmentP(X0,app(app(sk2,nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1375]) ).
fof(f1378,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| sQ101_spl ),
inference(split_clause,[status(thm)],[f1369,f1375,f587,f545]) ).
fof(f1379,definition,
! [X0,X1] :
( sQ102_spl
<=> ( app(app(sk1,nil),X1) = X0
| ~ ssList(app(sk1,X1))
| ~ segmentP(X0,app(app(sk1,nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1380,plain,
! [X0,X1] :
( ~ sQ102_spl
| app(app(sk1,nil),X1) = X0
| ~ ssList(app(sk1,X1))
| ~ segmentP(X0,app(app(sk1,nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1379]) ).
fof(f1382,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| sQ102_spl ),
inference(split_clause,[status(thm)],[f1370,f1379,f558,f545]) ).
fof(f1383,plain,
! [X0,X1] :
( ~ sQ100_spl
| app(app(nil,nil),X1) = X0
| ~ ssList(app(nil,X1))
| ~ segmentP(X0,app(nil,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1042,f1372]) ).
fof(f1384,plain,
! [X0,X1] :
( ~ sQ100_spl
| app(nil,X1) = X0
| ~ ssList(app(nil,X1))
| ~ segmentP(X0,app(nil,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1042,f1383]) ).
fof(f1385,plain,
! [X0,X1] :
( ~ sQ101_spl
| app(app(sk2,nil),X1) = X0
| ~ ssList(app(sk2,X1))
| ~ segmentP(X0,app(sk2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1029,f1376]) ).
fof(f1386,plain,
! [X0,X1] :
( ~ sQ101_spl
| app(sk2,X1) = X0
| ~ ssList(app(sk2,X1))
| ~ segmentP(X0,app(sk2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1029,f1385]) ).
fof(f1387,plain,
! [X0,X1] :
( ~ sQ102_spl
| app(app(sk1,nil),X1) = X0
| ~ ssList(app(sk1,X1))
| ~ segmentP(X0,app(sk1,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1013,f1380]) ).
fof(f1388,plain,
! [X0,X1] :
( ~ sQ102_spl
| app(sk1,X1) = X0
| ~ ssList(app(sk1,X1))
| ~ segmentP(X0,app(sk1,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1013,f1387]) ).
fof(f1389,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(nil)
| ~ rearsegP(nil,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ rearsegP(X0,app(nil,nil)) ),
inference(paramodulation,[status(thm)],[f1042,f750]) ).
fof(f1390,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(sk2)
| ~ rearsegP(nil,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ rearsegP(X0,app(sk2,nil)) ),
inference(paramodulation,[status(thm)],[f1029,f750]) ).
fof(f1391,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(sk1)
| ~ rearsegP(nil,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(X1)
| ~ rearsegP(X0,app(sk1,nil)) ),
inference(paramodulation,[status(thm)],[f1013,f750]) ).
fof(f1392,definition,
! [X0,X1] :
( sQ103_spl
<=> ( ~ rearsegP(nil,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,app(nil,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1395,plain,
( ~ sQ11_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f1389,f1392,f545]) ).
fof(f1396,definition,
! [X0,X1] :
( sQ104_spl
<=> ( ~ rearsegP(nil,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,app(sk2,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1399,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| sQ104_spl ),
inference(split_clause,[status(thm)],[f1390,f1396,f587,f545]) ).
fof(f1400,definition,
! [X0,X1] :
( sQ105_spl
<=> ( ~ rearsegP(nil,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,app(sk1,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1403,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| sQ105_spl ),
inference(split_clause,[status(thm)],[f1391,f1400,f558,f545]) ).
fof(f1407,plain,
app(nil,sk1) = sk1,
inference(resolution,[status(thm)],[f274,f430]) ).
fof(f1414,plain,
! [X0] : app(nil,skaf51(X0)) = skaf51(X0),
inference(resolution,[status(thm)],[f274,f243]) ).
fof(f1415,plain,
! [X0] : app(nil,skaf52(X0)) = skaf52(X0),
inference(resolution,[status(thm)],[f274,f242]) ).
fof(f1416,plain,
! [X0] : app(nil,skaf53(X0)) = skaf53(X0),
inference(resolution,[status(thm)],[f274,f241]) ).
fof(f1417,plain,
! [X0] : app(nil,skaf56(X0)) = skaf56(X0),
inference(resolution,[status(thm)],[f274,f238]) ).
fof(f1418,plain,
! [X0] : app(nil,skaf57(X0)) = skaf57(X0),
inference(resolution,[status(thm)],[f274,f237]) ).
fof(f1419,plain,
! [X0] : app(nil,skaf58(X0)) = skaf58(X0),
inference(resolution,[status(thm)],[f274,f236]) ).
fof(f1420,plain,
! [X0] : app(nil,skaf61(X0)) = skaf61(X0),
inference(resolution,[status(thm)],[f274,f233]) ).
fof(f1421,plain,
! [X0] : app(nil,skaf62(X0)) = skaf62(X0),
inference(resolution,[status(thm)],[f274,f232]) ).
fof(f1422,plain,
! [X0] : app(nil,skaf63(X0)) = skaf63(X0),
inference(resolution,[status(thm)],[f274,f231]) ).
fof(f1423,plain,
app(nil,sk2) = sk2,
inference(resolution,[status(thm)],[f274,f431]) ).
fof(f1424,plain,
! [X0] : app(nil,skaf66(X0)) = skaf66(X0),
inference(resolution,[status(thm)],[f274,f228]) ).
fof(f1425,plain,
! [X0] : app(nil,skaf67(X0)) = skaf67(X0),
inference(resolution,[status(thm)],[f274,f227]) ).
fof(f1426,plain,
! [X0] : app(nil,skaf68(X0)) = skaf68(X0),
inference(resolution,[status(thm)],[f274,f226]) ).
fof(f1427,plain,
! [X0] : app(nil,skaf71(X0)) = skaf71(X0),
inference(resolution,[status(thm)],[f274,f223]) ).
fof(f1428,plain,
! [X0] : app(nil,skaf72(X0)) = skaf72(X0),
inference(resolution,[status(thm)],[f274,f222]) ).
fof(f1429,plain,
! [X0] : app(nil,skaf73(X0)) = skaf73(X0),
inference(resolution,[status(thm)],[f274,f221]) ).
fof(f1430,plain,
! [X0] : app(nil,skaf75(X0)) = skaf75(X0),
inference(resolution,[status(thm)],[f274,f219]) ).
fof(f1431,plain,
! [X0] : app(nil,skaf76(X0)) = skaf76(X0),
inference(resolution,[status(thm)],[f274,f218]) ).
fof(f1432,plain,
! [X0] : app(nil,skaf77(X0)) = skaf77(X0),
inference(resolution,[status(thm)],[f274,f217]) ).
fof(f1433,plain,
! [X0] : app(nil,skaf80(X0)) = skaf80(X0),
inference(resolution,[status(thm)],[f274,f214]) ).
fof(f1434,plain,
! [X0] : app(nil,skaf81(X0)) = skaf81(X0),
inference(resolution,[status(thm)],[f274,f213]) ).
fof(f1435,plain,
! [X0] : app(nil,skaf82(X0)) = skaf82(X0),
inference(resolution,[status(thm)],[f274,f212]) ).
fof(f1437,plain,
! [X0,X1] :
( ~ ssList(sk1)
| ~ ssList(nil)
| ~ rearsegP(sk1,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(X1)
| ~ rearsegP(X0,app(nil,sk1)) ),
inference(paramodulation,[status(thm)],[f1407,f750]) ).
fof(f1438,plain,
! [X0,X1] :
( app(app(nil,sk1),X1) = X0
| ~ ssList(app(sk1,X1))
| ~ segmentP(X0,app(app(nil,sk1),X1))
| ~ ssList(sk1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ),
inference(paramodulation,[status(thm)],[f1407,f666]) ).
fof(f1439,plain,
! [X0,X1,X2] :
( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk1,X1))
| ~ segmentP(X2,app(app(nil,sk1),X1))
| ~ ssList(sk1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ),
inference(paramodulation,[status(thm)],[f1407,f665]) ).
fof(f1440,plain,
! [X0] :
( app(nil,sk1) = X0
| ~ ssList(sk1)
| ~ rearsegP(X0,app(nil,sk1))
| ~ ssList(sk1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ rearsegP(sk1,X0) ),
inference(paramodulation,[status(thm)],[f1407,f608]) ).
fof(f1441,plain,
! [X0] :
( segmentP(app(app(nil,sk1),X0),sk1)
| ~ ssList(app(sk1,X0))
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1407,f504]) ).
fof(f1442,plain,
! [X0,X1] :
( segmentP(app(sk1,X1),X0)
| ~ ssList(sk1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ),
inference(paramodulation,[status(thm)],[f1407,f404]) ).
fof(f1443,plain,
( rearsegP(app(nil,sk1),sk1)
| ~ ssList(sk1)
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1407,f500]) ).
fof(f1445,definition,
! [X0,X1] :
( sQ106_spl
<=> ( ~ rearsegP(sk1,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,app(nil,sk1)) ) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1446,plain,
! [X0,X1] :
( ~ sQ106_spl
| ~ rearsegP(sk1,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,app(nil,sk1)) ),
inference(component_clause,[status(thm)],[f1445]) ).
fof(f1448,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f1437,f1445,f558,f545]) ).
fof(f1449,definition,
! [X0,X1] :
( sQ107_spl
<=> ( app(app(nil,sk1),X1) = X0
| ~ ssList(app(sk1,X1))
| ~ segmentP(X0,app(app(nil,sk1),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1450,plain,
! [X0,X1] :
( ~ sQ107_spl
| app(app(nil,sk1),X1) = X0
| ~ ssList(app(sk1,X1))
| ~ segmentP(X0,app(app(nil,sk1),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ),
inference(component_clause,[status(thm)],[f1449]) ).
fof(f1452,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| sQ107_spl ),
inference(split_clause,[status(thm)],[f1438,f1449,f545,f558]) ).
fof(f1453,definition,
! [X0,X1,X2] :
( sQ108_spl
<=> ( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk1,X1))
| ~ segmentP(X2,app(app(nil,sk1),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1454,plain,
! [X0,X1,X2] :
( ~ sQ108_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk1,X1))
| ~ segmentP(X2,app(app(nil,sk1),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ),
inference(component_clause,[status(thm)],[f1453]) ).
fof(f1456,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| sQ108_spl ),
inference(split_clause,[status(thm)],[f1439,f1453,f545,f558]) ).
fof(f1457,definition,
! [X0] :
( sQ109_spl
<=> ( app(nil,sk1) = X0
| ~ rearsegP(X0,app(nil,sk1))
| ~ ssList(X0)
| ~ rearsegP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1458,plain,
! [X0] :
( ~ sQ109_spl
| app(nil,sk1) = X0
| ~ rearsegP(X0,app(nil,sk1))
| ~ ssList(X0)
| ~ rearsegP(sk1,X0) ),
inference(component_clause,[status(thm)],[f1457]) ).
fof(f1460,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| sQ109_spl ),
inference(split_clause,[status(thm)],[f1440,f1457,f545,f558]) ).
fof(f1461,definition,
! [X0] :
( sQ110_spl
<=> ( segmentP(app(app(nil,sk1),X0),sk1)
| ~ ssList(app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1462,plain,
! [X0] :
( ~ sQ110_spl
| segmentP(app(app(nil,sk1),X0),sk1)
| ~ ssList(app(sk1,X0))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1461]) ).
fof(f1464,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| sQ110_spl ),
inference(split_clause,[status(thm)],[f1441,f1461,f545,f558]) ).
fof(f1465,definition,
! [X0,X1] :
( sQ111_spl
<=> ( segmentP(app(sk1,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1466,plain,
! [X0,X1] :
( ~ sQ111_spl
| segmentP(app(sk1,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ),
inference(component_clause,[status(thm)],[f1465]) ).
fof(f1468,plain,
( ~ sQ13_spl
| ~ sQ11_spl
| sQ111_spl ),
inference(split_clause,[status(thm)],[f1442,f1465,f545,f558]) ).
fof(f1469,definition,
( sQ112_spl
<=> rearsegP(app(nil,sk1),sk1) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1470,plain,
( ~ sQ112_spl
| rearsegP(app(nil,sk1),sk1) ),
inference(component_clause,[status(thm)],[f1469]) ).
fof(f1472,plain,
( sQ112_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1443,f545,f558,f1469]) ).
fof(f1473,definition,
! [X0] :
( sQ113_spl
<=> ( rearsegP(sk1,X0)
| ~ ssList(X0)
| ~ rearsegP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1477,plain,
! [X0,X1] :
( ~ sQ106_spl
| ~ rearsegP(sk1,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sk1) ),
inference(forward_demodulation,[status(thm)],[f1407,f1446]) ).
fof(f1478,plain,
! [X0,X1] :
( ~ sQ107_spl
| app(app(nil,sk1),X1) = X0
| ~ ssList(app(sk1,X1))
| ~ segmentP(X0,app(sk1,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ),
inference(forward_demodulation,[status(thm)],[f1407,f1450]) ).
fof(f1479,plain,
! [X0,X1] :
( ~ sQ107_spl
| app(sk1,X1) = X0
| ~ ssList(app(sk1,X1))
| ~ segmentP(X0,app(sk1,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ),
inference(forward_demodulation,[status(thm)],[f1407,f1478]) ).
fof(f1480,plain,
! [X0,X1,X2] :
( ~ sQ108_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk1,X1))
| ~ segmentP(X2,app(sk1,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ),
inference(forward_demodulation,[status(thm)],[f1407,f1454]) ).
fof(f1481,plain,
! [X0] :
( ~ sQ109_spl
| app(nil,sk1) = X0
| ~ rearsegP(X0,sk1)
| ~ ssList(X0)
| ~ rearsegP(sk1,X0) ),
inference(forward_demodulation,[status(thm)],[f1407,f1458]) ).
fof(f1482,plain,
! [X0] :
( ~ sQ109_spl
| sk1 = X0
| ~ rearsegP(X0,sk1)
| ~ ssList(X0)
| ~ rearsegP(sk1,X0) ),
inference(forward_demodulation,[status(thm)],[f1407,f1481]) ).
fof(f1483,plain,
! [X0] :
( ~ sQ110_spl
| segmentP(app(sk1,X0),sk1)
| ~ ssList(app(sk1,X0))
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f1407,f1462]) ).
fof(f1484,plain,
( ~ sQ112_spl
| rearsegP(sk1,sk1) ),
inference(forward_demodulation,[status(thm)],[f1407,f1470]) ).
fof(f1489,plain,
! [X0,X1] :
( ~ sQ112_spl
| ~ ssList(sk1)
| ~ rearsegP(X1,sk1)
| sk1 = X1
| ~ ssList(sk1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(sk1,X0) ),
inference(resolution,[status(thm)],[f1484,f764]) ).
fof(f1491,plain,
! [X0,X1] :
( ~ sQ112_spl
| ~ ssList(sk1)
| ~ rearsegP(sk1,X0)
| X0 = sk1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sk1)
| ~ rearsegP(X1,sk1)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f1484,f764]) ).
fof(f1497,plain,
! [X0,X1] :
( ~ sQ112_spl
| ~ ssList(sk1)
| ~ rearsegP(sk1,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(X1)
| ~ rearsegP(X0,sk1) ),
inference(resolution,[status(thm)],[f1484,f759]) ).
fof(f1508,definition,
( sQ114_spl
<=> rearsegP(sk1,sk1) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1512,definition,
! [X0,X1] :
( sQ115_spl
<=> ( ~ rearsegP(X1,sk1)
| sk1 = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f1515,plain,
( ~ sQ112_spl
| ~ sQ13_spl
| sQ115_spl ),
inference(split_clause,[status(thm)],[f1489,f1512,f558,f1469]) ).
fof(f1517,definition,
! [X0,X1] :
( sQ116_spl
<=> ( ~ rearsegP(sk1,X0)
| X0 = sk1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,sk1)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1520,plain,
( ~ sQ112_spl
| ~ sQ13_spl
| sQ116_spl ),
inference(split_clause,[status(thm)],[f1491,f1517,f558,f1469]) ).
fof(f1526,definition,
! [X0,X1] :
( sQ117_spl
<=> ( ~ rearsegP(sk1,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1529,plain,
( ~ sQ112_spl
| ~ sQ13_spl
| sQ117_spl ),
inference(split_clause,[status(thm)],[f1497,f1526,f558,f1469]) ).
fof(f1541,definition,
! [X0] :
( sQ120_spl
<=> ( X0 = sk1
| ~ rearsegP(sk1,X0)
| ~ ssList(X0)
| ~ rearsegP(X0,sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1546,plain,
! [X0,X1] :
( ~ ssList(sk2)
| ~ ssList(nil)
| ~ rearsegP(sk2,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ rearsegP(X0,app(nil,sk2)) ),
inference(paramodulation,[status(thm)],[f1423,f750]) ).
fof(f1547,plain,
! [X0,X1] :
( app(app(nil,sk2),X1) = X0
| ~ ssList(app(sk2,X1))
| ~ segmentP(X0,app(app(nil,sk2),X1))
| ~ ssList(sk2)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ),
inference(paramodulation,[status(thm)],[f1423,f666]) ).
fof(f1548,plain,
! [X0,X1,X2] :
( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk2,X1))
| ~ segmentP(X2,app(app(nil,sk2),X1))
| ~ ssList(sk2)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ),
inference(paramodulation,[status(thm)],[f1423,f665]) ).
fof(f1549,plain,
! [X0] :
( app(nil,sk2) = X0
| ~ ssList(sk2)
| ~ rearsegP(X0,app(nil,sk2))
| ~ ssList(sk2)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ rearsegP(sk2,X0) ),
inference(paramodulation,[status(thm)],[f1423,f608]) ).
fof(f1550,plain,
! [X0] :
( segmentP(app(app(nil,sk2),X0),sk2)
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1423,f504]) ).
fof(f1551,plain,
! [X0,X1] :
( segmentP(app(sk2,X1),X0)
| ~ ssList(sk2)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ),
inference(paramodulation,[status(thm)],[f1423,f404]) ).
fof(f1552,plain,
( rearsegP(app(nil,sk2),sk2)
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1423,f500]) ).
fof(f1554,definition,
! [X0,X1] :
( sQ121_spl
<=> ( ~ rearsegP(sk2,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,app(nil,sk2)) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1557,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f1546,f1554,f587,f545]) ).
fof(f1558,definition,
! [X0,X1] :
( sQ122_spl
<=> ( app(app(nil,sk2),X1) = X0
| ~ ssList(app(sk2,X1))
| ~ segmentP(X0,app(app(nil,sk2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1559,plain,
! [X0,X1] :
( ~ sQ122_spl
| app(app(nil,sk2),X1) = X0
| ~ ssList(app(sk2,X1))
| ~ segmentP(X0,app(app(nil,sk2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ),
inference(component_clause,[status(thm)],[f1558]) ).
fof(f1561,plain,
( ~ sQ16_spl
| ~ sQ11_spl
| sQ122_spl ),
inference(split_clause,[status(thm)],[f1547,f1558,f545,f587]) ).
fof(f1562,definition,
! [X0,X1,X2] :
( sQ123_spl
<=> ( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk2,X1))
| ~ segmentP(X2,app(app(nil,sk2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1563,plain,
! [X0,X1,X2] :
( ~ sQ123_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk2,X1))
| ~ segmentP(X2,app(app(nil,sk2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ),
inference(component_clause,[status(thm)],[f1562]) ).
fof(f1565,plain,
( ~ sQ16_spl
| ~ sQ11_spl
| sQ123_spl ),
inference(split_clause,[status(thm)],[f1548,f1562,f545,f587]) ).
fof(f1566,definition,
! [X0] :
( sQ124_spl
<=> ( app(nil,sk2) = X0
| ~ rearsegP(X0,app(nil,sk2))
| ~ ssList(X0)
| ~ rearsegP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1567,plain,
! [X0] :
( ~ sQ124_spl
| app(nil,sk2) = X0
| ~ rearsegP(X0,app(nil,sk2))
| ~ ssList(X0)
| ~ rearsegP(sk2,X0) ),
inference(component_clause,[status(thm)],[f1566]) ).
fof(f1569,plain,
( ~ sQ16_spl
| ~ sQ11_spl
| sQ124_spl ),
inference(split_clause,[status(thm)],[f1549,f1566,f545,f587]) ).
fof(f1570,definition,
! [X0] :
( sQ125_spl
<=> ( segmentP(app(app(nil,sk2),X0),sk2)
| ~ ssList(app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1573,plain,
( ~ sQ16_spl
| ~ sQ11_spl
| sQ125_spl ),
inference(split_clause,[status(thm)],[f1550,f1570,f545,f587]) ).
fof(f1574,definition,
! [X0,X1] :
( sQ126_spl
<=> ( segmentP(app(sk2,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1575,plain,
! [X0,X1] :
( ~ sQ126_spl
| segmentP(app(sk2,X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ),
inference(component_clause,[status(thm)],[f1574]) ).
fof(f1577,plain,
( ~ sQ16_spl
| ~ sQ11_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f1551,f1574,f545,f587]) ).
fof(f1578,definition,
( sQ127_spl
<=> rearsegP(app(nil,sk2),sk2) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f1579,plain,
( ~ sQ127_spl
| rearsegP(app(nil,sk2),sk2) ),
inference(component_clause,[status(thm)],[f1578]) ).
fof(f1581,plain,
( sQ127_spl
| ~ sQ16_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1552,f545,f587,f1578]) ).
fof(f1582,definition,
! [X0] :
( sQ128_spl
<=> ( rearsegP(sk2,X0)
| ~ ssList(X0)
| ~ rearsegP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1587,plain,
! [X0,X1] :
( ~ sQ122_spl
| app(app(nil,sk2),X1) = X0
| ~ ssList(app(sk2,X1))
| ~ segmentP(X0,app(sk2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ),
inference(forward_demodulation,[status(thm)],[f1423,f1559]) ).
fof(f1588,plain,
! [X0,X1] :
( ~ sQ122_spl
| app(sk2,X1) = X0
| ~ ssList(app(sk2,X1))
| ~ segmentP(X0,app(sk2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ),
inference(forward_demodulation,[status(thm)],[f1423,f1587]) ).
fof(f1589,plain,
! [X0,X1,X2] :
( ~ sQ123_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk2,X1))
| ~ segmentP(X2,app(sk2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ),
inference(forward_demodulation,[status(thm)],[f1423,f1563]) ).
fof(f1590,plain,
! [X0] :
( ~ sQ124_spl
| app(nil,sk2) = X0
| ~ rearsegP(X0,sk2)
| ~ ssList(X0)
| ~ rearsegP(sk2,X0) ),
inference(forward_demodulation,[status(thm)],[f1423,f1567]) ).
fof(f1591,plain,
! [X0] :
( ~ sQ124_spl
| sk2 = X0
| ~ rearsegP(X0,sk2)
| ~ ssList(X0)
| ~ rearsegP(sk2,X0) ),
inference(forward_demodulation,[status(thm)],[f1423,f1590]) ).
fof(f1593,plain,
( ~ sQ127_spl
| rearsegP(sk2,sk2) ),
inference(forward_demodulation,[status(thm)],[f1423,f1579]) ).
fof(f1595,plain,
! [X0,X1] :
( ~ sQ127_spl
| ~ ssList(sk2)
| ~ rearsegP(X1,sk2)
| sk2 = X1
| ~ ssList(sk2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(sk2,X0) ),
inference(resolution,[status(thm)],[f1593,f764]) ).
fof(f1597,plain,
! [X0,X1] :
( ~ sQ127_spl
| ~ ssList(sk2)
| ~ rearsegP(sk2,X0)
| X0 = sk2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sk2)
| ~ rearsegP(X1,sk2)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f1593,f764]) ).
fof(f1603,plain,
! [X0,X1] :
( ~ sQ127_spl
| ~ ssList(sk2)
| ~ rearsegP(sk2,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ rearsegP(X0,sk2) ),
inference(resolution,[status(thm)],[f1593,f759]) ).
fof(f1609,plain,
! [X0] :
( ~ sQ127_spl
| X0 = sk2
| ~ rearsegP(sk2,X0)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ rearsegP(X0,sk2) ),
inference(resolution,[status(thm)],[f1593,f629]) ).
fof(f1611,definition,
( sQ129_spl
<=> rearsegP(sk2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f1614,definition,
( sQ130_spl
<=> sk2 = sk2 ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1618,definition,
! [X0,X1] :
( sQ131_spl
<=> ( ~ rearsegP(X1,sk2)
| sk2 = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1621,plain,
( ~ sQ127_spl
| ~ sQ16_spl
| sQ131_spl ),
inference(split_clause,[status(thm)],[f1595,f1618,f587,f1578]) ).
fof(f1623,definition,
! [X0,X1] :
( sQ132_spl
<=> ( ~ rearsegP(sk2,X0)
| X0 = sk2
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,sk2)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f1626,plain,
( ~ sQ127_spl
| ~ sQ16_spl
| sQ132_spl ),
inference(split_clause,[status(thm)],[f1597,f1623,f587,f1578]) ).
fof(f1632,definition,
! [X0,X1] :
( sQ133_spl
<=> ( ~ rearsegP(sk2,X1)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f1635,plain,
( ~ sQ127_spl
| ~ sQ16_spl
| sQ133_spl ),
inference(split_clause,[status(thm)],[f1603,f1632,f587,f1578]) ).
fof(f1647,definition,
! [X0] :
( sQ136_spl
<=> ( X0 = sk2
| ~ rearsegP(sk2,X0)
| ~ ssList(X0)
| ~ rearsegP(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1650,plain,
( ~ sQ127_spl
| ~ sQ16_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f1609,f1647,f587,f1578]) ).
fof(f1654,plain,
! [X0,X1] :
( ~ sQ99_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(sk1,X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(sk1,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1364,f374]) ).
fof(f1655,plain,
! [X0] :
( ~ sQ99_spl
| app(sk1,X0) = nil
| ~ ssList(app(sk1,X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(sk1,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1364,f339]) ).
fof(f1656,plain,
( ~ sQ99_spl
| segmentP(sk1,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1013,f1364]) ).
fof(f1657,definition,
! [X0,X1] :
( sQ137_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(sk1,X0))
| ~ segmentP(X1,app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1660,plain,
( ~ sQ99_spl
| ~ sQ11_spl
| sQ137_spl ),
inference(split_clause,[status(thm)],[f1654,f1657,f545,f1363]) ).
fof(f1661,definition,
! [X0] :
( sQ138_spl
<=> ( app(sk1,X0) = nil
| ~ ssList(app(sk1,X0))
| ~ segmentP(nil,app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1664,plain,
( ~ sQ99_spl
| ~ sQ11_spl
| sQ138_spl ),
inference(split_clause,[status(thm)],[f1655,f1661,f545,f1363]) ).
fof(f1665,definition,
( sQ139_spl
<=> segmentP(sk1,nil) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f1668,plain,
( ~ sQ99_spl
| sQ139_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1656,f545,f1665,f1363]) ).
fof(f1671,definition,
! [X0] :
( sQ140_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ segmentP(X0,sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1679,plain,
! [X0,X1] :
( ~ sQ74_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(sk2)
| ~ segmentP(X1,app(sk2,nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1029,f1166]) ).
fof(f1680,definition,
! [X0,X1] :
( sQ142_spl
<=> ( segmentP(X1,X0)
| ~ ssList(X1)
| ~ segmentP(X1,app(sk2,nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f1681,plain,
! [X0,X1] :
( ~ sQ142_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| ~ segmentP(X1,app(sk2,nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1680]) ).
fof(f1683,plain,
( ~ sQ74_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sQ142_spl ),
inference(split_clause,[status(thm)],[f1679,f1680,f545,f587,f1142]) ).
fof(f1684,plain,
! [X0,X1] :
( ~ sQ142_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| ~ segmentP(X1,sk2)
| ~ ssList(X0)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1029,f1681]) ).
fof(f1688,plain,
! [X0,X1] :
( ~ sQ109_spl
| ~ ssList(sk1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(sk1,X1)
| sk1 = X0
| ~ rearsegP(X0,sk1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1482,f376]) ).
fof(f1693,definition,
! [X0,X1] :
( sQ143_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,X0)
| ~ rearsegP(sk1,X1)
| sk1 = X0
| ~ rearsegP(X0,sk1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1696,plain,
( ~ sQ109_spl
| ~ sQ13_spl
| sQ143_spl ),
inference(split_clause,[status(thm)],[f1688,f1693,f558,f1457]) ).
fof(f1700,plain,
! [X0,X1] :
( ~ sQ124_spl
| ~ ssList(X1)
| ~ ssList(sk2)
| ~ ssList(X0)
| ~ rearsegP(X1,sk2)
| sk2 = app(X0,X1)
| ~ ssList(app(X0,X1))
| ~ rearsegP(sk2,app(X0,X1)) ),
inference(resolution,[status(thm)],[f1591,f350]) ).
fof(f1701,plain,
! [X0,X1] :
( ~ sQ124_spl
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sk2)
| ~ rearsegP(X1,sk2)
| ~ rearsegP(X0,X1)
| sk2 = X0
| ~ ssList(X0)
| ~ rearsegP(sk2,X0) ),
inference(resolution,[status(thm)],[f1591,f376]) ).
fof(f1704,definition,
! [X0,X1] :
( sQ144_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ rearsegP(X1,sk2)
| sk2 = app(X0,X1)
| ~ ssList(app(X0,X1))
| ~ rearsegP(sk2,app(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1707,plain,
( ~ sQ124_spl
| ~ sQ16_spl
| sQ144_spl ),
inference(split_clause,[status(thm)],[f1700,f1704,f587,f1566]) ).
fof(f1708,definition,
! [X0,X1] :
( sQ145_spl
<=> ( ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,sk2)
| ~ rearsegP(X0,X1)
| sk2 = X0
| ~ ssList(X0)
| ~ rearsegP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1711,plain,
( ~ sQ124_spl
| ~ sQ16_spl
| sQ145_spl ),
inference(split_clause,[status(thm)],[f1701,f1708,f587,f1566]) ).
fof(f1714,plain,
! [X0] :
( ~ sQ77_spl
| ~ ssList(nil)
| segmentP(app(sk2,X0),nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1155,f255]) ).
fof(f1716,definition,
! [X0] :
( sQ146_spl
<=> ( segmentP(app(sk2,X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1717,plain,
! [X0] :
( ~ sQ146_spl
| segmentP(app(sk2,X0),nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1716]) ).
fof(f1719,plain,
( ~ sQ77_spl
| ~ sQ11_spl
| sQ146_spl ),
inference(split_clause,[status(thm)],[f1714,f1716,f545,f1154]) ).
fof(f1721,plain,
! [X0,X1] :
( ~ sQ146_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(sk2,X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(sk2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1717,f374]) ).
fof(f1722,plain,
! [X0] :
( ~ sQ146_spl
| app(sk2,X0) = nil
| ~ ssList(app(sk2,X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(sk2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1717,f339]) ).
fof(f1723,plain,
( ~ sQ146_spl
| segmentP(sk2,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1029,f1717]) ).
fof(f1724,definition,
! [X0,X1] :
( sQ147_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(sk2,X0))
| ~ segmentP(X1,app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1727,plain,
( ~ sQ146_spl
| ~ sQ11_spl
| sQ147_spl ),
inference(split_clause,[status(thm)],[f1721,f1724,f545,f1716]) ).
fof(f1728,definition,
! [X0] :
( sQ148_spl
<=> ( app(sk2,X0) = nil
| ~ ssList(app(sk2,X0))
| ~ segmentP(nil,app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1731,plain,
( ~ sQ146_spl
| ~ sQ11_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1722,f1728,f545,f1716]) ).
fof(f1732,definition,
( sQ149_spl
<=> segmentP(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1735,plain,
( ~ sQ146_spl
| sQ149_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1723,f545,f1732,f1716]) ).
fof(f1736,plain,
! [X0,X1] :
( ~ ssList(sk2)
| ~ ssList(nil)
| ~ rearsegP(sk2,X0)
| X0 = app(nil,sk2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sk2)
| ~ rearsegP(X1,app(nil,sk2))
| ~ rearsegP(X0,X1) ),
inference(paramodulation,[status(thm)],[f1423,f762]) ).
fof(f1737,plain,
! [X0,X1] :
( ~ ssList(sk1)
| ~ ssList(nil)
| ~ rearsegP(sk1,X0)
| X0 = app(nil,sk1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sk1)
| ~ rearsegP(X1,app(nil,sk1))
| ~ rearsegP(X0,X1) ),
inference(paramodulation,[status(thm)],[f1407,f762]) ).
fof(f1738,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(nil)
| ~ rearsegP(nil,X0)
| X0 = app(nil,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(X1,app(nil,nil))
| ~ rearsegP(X0,X1) ),
inference(paramodulation,[status(thm)],[f1042,f762]) ).
fof(f1739,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(sk2)
| ~ rearsegP(nil,X0)
| X0 = app(sk2,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sk2)
| ~ rearsegP(X1,app(sk2,nil))
| ~ rearsegP(X0,X1) ),
inference(paramodulation,[status(thm)],[f1029,f762]) ).
fof(f1740,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(sk1)
| ~ rearsegP(nil,X0)
| X0 = app(sk1,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sk1)
| ~ rearsegP(X1,app(sk1,nil))
| ~ rearsegP(X0,X1) ),
inference(paramodulation,[status(thm)],[f1013,f762]) ).
fof(f1741,definition,
! [X0,X1] :
( sQ150_spl
<=> ( ~ rearsegP(sk2,X0)
| X0 = app(nil,sk2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,app(nil,sk2))
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f1744,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| sQ150_spl ),
inference(split_clause,[status(thm)],[f1736,f1741,f587,f545]) ).
fof(f1745,definition,
! [X0,X1] :
( sQ151_spl
<=> ( ~ rearsegP(sk1,X0)
| X0 = app(nil,sk1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,app(nil,sk1))
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1748,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| sQ151_spl ),
inference(split_clause,[status(thm)],[f1737,f1745,f558,f545]) ).
fof(f1749,definition,
! [X0,X1] :
( sQ152_spl
<=> ( ~ rearsegP(nil,X0)
| X0 = app(nil,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,app(nil,nil))
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1752,plain,
( ~ sQ11_spl
| sQ152_spl ),
inference(split_clause,[status(thm)],[f1738,f1749,f545]) ).
fof(f1753,definition,
! [X0,X1] :
( sQ153_spl
<=> ( ~ rearsegP(nil,X0)
| X0 = app(sk2,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,app(sk2,nil))
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f1756,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| sQ153_spl ),
inference(split_clause,[status(thm)],[f1739,f1753,f587,f545]) ).
fof(f1757,definition,
! [X0,X1] :
( sQ154_spl
<=> ( ~ rearsegP(nil,X0)
| X0 = app(sk1,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X1,app(sk1,nil))
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f1760,plain,
( ~ sQ11_spl
| ~ sQ13_spl
| sQ154_spl ),
inference(split_clause,[status(thm)],[f1740,f1757,f558,f545]) ).
fof(f1771,plain,
! [X0,X1] :
( ~ sQ86_spl
| ~ ssList(nil)
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(nil,X0))
| ~ segmentP(X1,app(nil,X0))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1262,f255]) ).
fof(f1773,definition,
! [X0,X1] :
( sQ155_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(nil,X0))
| ~ segmentP(X1,app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f1776,plain,
( ~ sQ86_spl
| ~ sQ11_spl
| sQ155_spl ),
inference(split_clause,[status(thm)],[f1771,f1773,f545,f1238]) ).
fof(f1780,definition,
! [X0] :
( sQ156_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ segmentP(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f1788,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ ssList(skaf51(X2))
| ~ rearsegP(nil,X0)
| X0 = app(skaf51(X2),nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf51(X2))
| ~ rearsegP(X1,app(skaf51(X2),nil))
| ~ rearsegP(X0,X1) ),
inference(paramodulation,[status(thm)],[f1020,f762]) ).
fof(f1789,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ ssList(skaf51(X1))
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,app(skaf51(X1),nil)) ),
inference(paramodulation,[status(thm)],[f1020,f750]) ).
fof(f1790,plain,
! [X0,X1,X2] :
( app(app(skaf51(X2),nil),X1) = X0
| ~ ssList(app(skaf51(X2),X1))
| ~ segmentP(X0,app(app(skaf51(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf51(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1020,f666]) ).
fof(f1791,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf51(X2),X1))
| ~ segmentP(X3,app(app(skaf51(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf51(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1020,f665]) ).
fof(f1792,plain,
! [X0,X1] :
( app(skaf51(X1),nil) = X0
| ~ ssList(skaf51(X1))
| ~ rearsegP(X0,app(skaf51(X1),nil))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1020,f608]) ).
fof(f1793,plain,
! [X0,X1] :
( segmentP(app(app(skaf51(X1),nil),X0),nil)
| ~ ssList(app(skaf51(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf51(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1020,f504]) ).
fof(f1794,plain,
! [X0,X1,X2] :
( segmentP(app(skaf51(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf51(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1020,f404]) ).
fof(f1795,plain,
! [X0] :
( rearsegP(app(skaf51(X0),nil),nil)
| ~ ssList(skaf51(X0))
| ~ ssList(nil)
| ~ ssList(skaf51(X0)) ),
inference(paramodulation,[status(thm)],[f1020,f500]) ).
fof(f1796,plain,
! [X0,X1] :
( rearsegP(skaf51(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1020,f350]) ).
fof(f1797,definition,
! [X0,X1,X2] :
( sQ158_spl
<=> ( ~ ssList(skaf51(X2))
| ~ rearsegP(nil,X0)
| X0 = app(skaf51(X2),nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf51(X2))
| ~ rearsegP(X1,app(skaf51(X2),nil))
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f1800,plain,
( ~ sQ11_spl
| sQ158_spl ),
inference(split_clause,[status(thm)],[f1788,f1797,f545]) ).
fof(f1801,definition,
! [X0,X1,X2] :
( sQ159_spl
<=> ( ~ ssList(skaf51(X1))
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,app(skaf51(X1),nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f1804,plain,
( ~ sQ11_spl
| sQ159_spl ),
inference(split_clause,[status(thm)],[f1789,f1801,f545]) ).
fof(f1805,definition,
! [X0,X1,X2] :
( sQ160_spl
<=> ( app(app(skaf51(X2),nil),X1) = X0
| ~ ssList(app(skaf51(X2),X1))
| ~ segmentP(X0,app(app(skaf51(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf51(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f1806,plain,
! [X0,X1,X2] :
( ~ sQ160_spl
| app(app(skaf51(X2),nil),X1) = X0
| ~ ssList(app(skaf51(X2),X1))
| ~ segmentP(X0,app(app(skaf51(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf51(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1805]) ).
fof(f1808,plain,
( ~ sQ11_spl
| sQ160_spl ),
inference(split_clause,[status(thm)],[f1790,f1805,f545]) ).
fof(f1809,definition,
! [X0,X1,X2,X3] :
( sQ161_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf51(X2),X1))
| ~ segmentP(X3,app(app(skaf51(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf51(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f1810,plain,
! [X0,X1,X2,X3] :
( ~ sQ161_spl
| segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf51(X2),X1))
| ~ segmentP(X3,app(app(skaf51(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf51(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1809]) ).
fof(f1812,plain,
( ~ sQ11_spl
| sQ161_spl ),
inference(split_clause,[status(thm)],[f1791,f1809,f545]) ).
fof(f1813,definition,
! [X0,X1] :
( sQ162_spl
<=> ( app(skaf51(X1),nil) = X0
| ~ ssList(skaf51(X1))
| ~ rearsegP(X0,app(skaf51(X1),nil))
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f1816,plain,
( ~ sQ11_spl
| sQ162_spl ),
inference(split_clause,[status(thm)],[f1792,f1813,f545]) ).
fof(f1817,definition,
! [X0,X1] :
( sQ163_spl
<=> ( segmentP(app(app(skaf51(X1),nil),X0),nil)
| ~ ssList(app(skaf51(X1),X0))
| ~ ssList(skaf51(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f1820,plain,
( ~ sQ11_spl
| sQ163_spl ),
inference(split_clause,[status(thm)],[f1793,f1817,f545]) ).
fof(f1821,definition,
! [X0,X1,X2] :
( sQ164_spl
<=> ( segmentP(app(skaf51(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf51(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f1822,plain,
! [X0,X1,X2] :
( ~ sQ164_spl
| segmentP(app(skaf51(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf51(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1821]) ).
fof(f1824,plain,
( ~ sQ11_spl
| sQ164_spl ),
inference(split_clause,[status(thm)],[f1794,f1821,f545]) ).
fof(f1825,definition,
! [X0] :
( sQ165_spl
<=> ( rearsegP(app(skaf51(X0),nil),nil)
| ~ ssList(skaf51(X0))
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f1828,plain,
( ~ sQ11_spl
| sQ165_spl ),
inference(split_clause,[status(thm)],[f1795,f1825,f545]) ).
fof(f1829,definition,
! [X0,X1] :
( sQ166_spl
<=> ( rearsegP(skaf51(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f1830,plain,
! [X0,X1] :
( ~ sQ166_spl
| rearsegP(skaf51(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ rearsegP(nil,X0) ),
inference(component_clause,[status(thm)],[f1829]) ).
fof(f1832,plain,
( ~ sQ11_spl
| sQ166_spl ),
inference(split_clause,[status(thm)],[f1796,f1829,f545]) ).
fof(f1838,plain,
! [X0,X1,X2] :
( ~ sQ160_spl
| app(app(skaf51(X2),nil),X1) = X0
| ~ ssList(app(skaf51(X2),X1))
| ~ segmentP(X0,app(skaf51(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf51(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1020,f1806]) ).
fof(f1839,plain,
! [X0,X1,X2] :
( ~ sQ160_spl
| app(skaf51(X2),X1) = X0
| ~ ssList(app(skaf51(X2),X1))
| ~ segmentP(X0,app(skaf51(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf51(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1020,f1838]) ).
fof(f1840,plain,
! [X0,X1,X2] :
( ~ sQ160_spl
| app(skaf51(X2),X1) = X0
| ~ ssList(app(skaf51(X2),X1))
| ~ segmentP(X0,app(skaf51(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1839,f243]) ).
fof(f1841,plain,
! [X0,X1,X2,X3] :
( ~ sQ161_spl
| segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf51(X2),X1))
| ~ segmentP(X3,app(skaf51(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf51(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1020,f1810]) ).
fof(f1842,plain,
! [X0,X1,X2,X3] :
( ~ sQ161_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(skaf51(X3),X1))
| ~ segmentP(X2,app(skaf51(X3),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1841,f243]) ).
fof(f1847,plain,
! [X0,X1,X2] :
( ~ sQ164_spl
| segmentP(app(skaf51(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1822,f243]) ).
fof(f1850,plain,
! [X0,X1] :
( ~ sQ166_spl
| rearsegP(skaf51(X1),X0)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1830,f243]) ).
fof(f1851,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ ssList(skaf52(X2))
| ~ rearsegP(nil,X0)
| X0 = app(skaf52(X2),nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf52(X2))
| ~ rearsegP(X1,app(skaf52(X2),nil))
| ~ rearsegP(X0,X1) ),
inference(paramodulation,[status(thm)],[f1021,f762]) ).
fof(f1852,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ ssList(skaf52(X1))
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,app(skaf52(X1),nil)) ),
inference(paramodulation,[status(thm)],[f1021,f750]) ).
fof(f1853,plain,
! [X0,X1,X2] :
( app(app(skaf52(X2),nil),X1) = X0
| ~ ssList(app(skaf52(X2),X1))
| ~ segmentP(X0,app(app(skaf52(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf52(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1021,f666]) ).
fof(f1854,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf52(X2),X1))
| ~ segmentP(X3,app(app(skaf52(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf52(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1021,f665]) ).
fof(f1855,plain,
! [X0,X1] :
( app(skaf52(X1),nil) = X0
| ~ ssList(skaf52(X1))
| ~ rearsegP(X0,app(skaf52(X1),nil))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1021,f608]) ).
fof(f1856,plain,
! [X0,X1] :
( segmentP(app(app(skaf52(X1),nil),X0),nil)
| ~ ssList(app(skaf52(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf52(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1021,f504]) ).
fof(f1857,plain,
! [X0,X1,X2] :
( segmentP(app(skaf52(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf52(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1021,f404]) ).
fof(f1858,plain,
! [X0] :
( rearsegP(app(skaf52(X0),nil),nil)
| ~ ssList(skaf52(X0))
| ~ ssList(nil)
| ~ ssList(skaf52(X0)) ),
inference(paramodulation,[status(thm)],[f1021,f500]) ).
fof(f1859,plain,
! [X0,X1] :
( rearsegP(skaf52(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1021,f350]) ).
fof(f1860,definition,
! [X0,X1,X2] :
( sQ167_spl
<=> ( ~ ssList(skaf52(X2))
| ~ rearsegP(nil,X0)
| X0 = app(skaf52(X2),nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf52(X2))
| ~ rearsegP(X1,app(skaf52(X2),nil))
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f1863,plain,
( ~ sQ11_spl
| sQ167_spl ),
inference(split_clause,[status(thm)],[f1851,f1860,f545]) ).
fof(f1864,definition,
! [X0,X1,X2] :
( sQ168_spl
<=> ( ~ ssList(skaf52(X1))
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,app(skaf52(X1),nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f1867,plain,
( ~ sQ11_spl
| sQ168_spl ),
inference(split_clause,[status(thm)],[f1852,f1864,f545]) ).
fof(f1868,definition,
! [X0,X1,X2] :
( sQ169_spl
<=> ( app(app(skaf52(X2),nil),X1) = X0
| ~ ssList(app(skaf52(X2),X1))
| ~ segmentP(X0,app(app(skaf52(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf52(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f1869,plain,
! [X0,X1,X2] :
( ~ sQ169_spl
| app(app(skaf52(X2),nil),X1) = X0
| ~ ssList(app(skaf52(X2),X1))
| ~ segmentP(X0,app(app(skaf52(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf52(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1868]) ).
fof(f1871,plain,
( ~ sQ11_spl
| sQ169_spl ),
inference(split_clause,[status(thm)],[f1853,f1868,f545]) ).
fof(f1872,definition,
! [X0,X1,X2,X3] :
( sQ170_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf52(X2),X1))
| ~ segmentP(X3,app(app(skaf52(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf52(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f1873,plain,
! [X0,X1,X2,X3] :
( ~ sQ170_spl
| segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf52(X2),X1))
| ~ segmentP(X3,app(app(skaf52(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf52(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1872]) ).
fof(f1875,plain,
( ~ sQ11_spl
| sQ170_spl ),
inference(split_clause,[status(thm)],[f1854,f1872,f545]) ).
fof(f1876,definition,
! [X0,X1] :
( sQ171_spl
<=> ( app(skaf52(X1),nil) = X0
| ~ ssList(skaf52(X1))
| ~ rearsegP(X0,app(skaf52(X1),nil))
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f1879,plain,
( ~ sQ11_spl
| sQ171_spl ),
inference(split_clause,[status(thm)],[f1855,f1876,f545]) ).
fof(f1880,definition,
! [X0,X1] :
( sQ172_spl
<=> ( segmentP(app(app(skaf52(X1),nil),X0),nil)
| ~ ssList(app(skaf52(X1),X0))
| ~ ssList(skaf52(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f1883,plain,
( ~ sQ11_spl
| sQ172_spl ),
inference(split_clause,[status(thm)],[f1856,f1880,f545]) ).
fof(f1884,definition,
! [X0,X1,X2] :
( sQ173_spl
<=> ( segmentP(app(skaf52(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf52(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f1885,plain,
! [X0,X1,X2] :
( ~ sQ173_spl
| segmentP(app(skaf52(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf52(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1884]) ).
fof(f1887,plain,
( ~ sQ11_spl
| sQ173_spl ),
inference(split_clause,[status(thm)],[f1857,f1884,f545]) ).
fof(f1888,definition,
! [X0] :
( sQ174_spl
<=> ( rearsegP(app(skaf52(X0),nil),nil)
| ~ ssList(skaf52(X0))
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f1891,plain,
( ~ sQ11_spl
| sQ174_spl ),
inference(split_clause,[status(thm)],[f1858,f1888,f545]) ).
fof(f1892,definition,
! [X0,X1] :
( sQ175_spl
<=> ( rearsegP(skaf52(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f1893,plain,
! [X0,X1] :
( ~ sQ175_spl
| rearsegP(skaf52(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ rearsegP(nil,X0) ),
inference(component_clause,[status(thm)],[f1892]) ).
fof(f1895,plain,
( ~ sQ11_spl
| sQ175_spl ),
inference(split_clause,[status(thm)],[f1859,f1892,f545]) ).
fof(f1901,plain,
! [X0,X1,X2] :
( ~ sQ169_spl
| app(app(skaf52(X2),nil),X1) = X0
| ~ ssList(app(skaf52(X2),X1))
| ~ segmentP(X0,app(skaf52(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf52(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1021,f1869]) ).
fof(f1902,plain,
! [X0,X1,X2] :
( ~ sQ169_spl
| app(skaf52(X2),X1) = X0
| ~ ssList(app(skaf52(X2),X1))
| ~ segmentP(X0,app(skaf52(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf52(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1021,f1901]) ).
fof(f1903,plain,
! [X0,X1,X2] :
( ~ sQ169_spl
| app(skaf52(X2),X1) = X0
| ~ ssList(app(skaf52(X2),X1))
| ~ segmentP(X0,app(skaf52(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1902,f242]) ).
fof(f1904,plain,
! [X0,X1,X2,X3] :
( ~ sQ170_spl
| segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf52(X2),X1))
| ~ segmentP(X3,app(skaf52(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf52(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1021,f1873]) ).
fof(f1905,plain,
! [X0,X1,X2,X3] :
( ~ sQ170_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(skaf52(X3),X1))
| ~ segmentP(X2,app(skaf52(X3),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1904,f242]) ).
fof(f1910,plain,
! [X0,X1,X2] :
( ~ sQ173_spl
| segmentP(app(skaf52(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1885,f242]) ).
fof(f1913,plain,
! [X0,X1] :
( ~ sQ175_spl
| rearsegP(skaf52(X1),X0)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1893,f242]) ).
fof(f1914,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ ssList(skaf53(X2))
| ~ rearsegP(nil,X0)
| X0 = app(skaf53(X2),nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf53(X2))
| ~ rearsegP(X1,app(skaf53(X2),nil))
| ~ rearsegP(X0,X1) ),
inference(paramodulation,[status(thm)],[f1022,f762]) ).
fof(f1915,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ ssList(skaf53(X1))
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,app(skaf53(X1),nil)) ),
inference(paramodulation,[status(thm)],[f1022,f750]) ).
fof(f1916,plain,
! [X0,X1,X2] :
( app(app(skaf53(X2),nil),X1) = X0
| ~ ssList(app(skaf53(X2),X1))
| ~ segmentP(X0,app(app(skaf53(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf53(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1022,f666]) ).
fof(f1917,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf53(X2),X1))
| ~ segmentP(X3,app(app(skaf53(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf53(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1022,f665]) ).
fof(f1918,plain,
! [X0,X1] :
( app(skaf53(X1),nil) = X0
| ~ ssList(skaf53(X1))
| ~ rearsegP(X0,app(skaf53(X1),nil))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1022,f608]) ).
fof(f1919,plain,
! [X0,X1] :
( segmentP(app(app(skaf53(X1),nil),X0),nil)
| ~ ssList(app(skaf53(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf53(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1022,f504]) ).
fof(f1920,plain,
! [X0,X1,X2] :
( segmentP(app(skaf53(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf53(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1022,f404]) ).
fof(f1921,plain,
! [X0] :
( rearsegP(app(skaf53(X0),nil),nil)
| ~ ssList(skaf53(X0))
| ~ ssList(nil)
| ~ ssList(skaf53(X0)) ),
inference(paramodulation,[status(thm)],[f1022,f500]) ).
fof(f1922,plain,
! [X0,X1] :
( rearsegP(skaf53(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1022,f350]) ).
fof(f1923,definition,
! [X0,X1,X2] :
( sQ176_spl
<=> ( ~ ssList(skaf53(X2))
| ~ rearsegP(nil,X0)
| X0 = app(skaf53(X2),nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf53(X2))
| ~ rearsegP(X1,app(skaf53(X2),nil))
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f1926,plain,
( ~ sQ11_spl
| sQ176_spl ),
inference(split_clause,[status(thm)],[f1914,f1923,f545]) ).
fof(f1927,definition,
! [X0,X1,X2] :
( sQ177_spl
<=> ( ~ ssList(skaf53(X1))
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,app(skaf53(X1),nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f1930,plain,
( ~ sQ11_spl
| sQ177_spl ),
inference(split_clause,[status(thm)],[f1915,f1927,f545]) ).
fof(f1931,definition,
! [X0,X1,X2] :
( sQ178_spl
<=> ( app(app(skaf53(X2),nil),X1) = X0
| ~ ssList(app(skaf53(X2),X1))
| ~ segmentP(X0,app(app(skaf53(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf53(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f1932,plain,
! [X0,X1,X2] :
( ~ sQ178_spl
| app(app(skaf53(X2),nil),X1) = X0
| ~ ssList(app(skaf53(X2),X1))
| ~ segmentP(X0,app(app(skaf53(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf53(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1931]) ).
fof(f1934,plain,
( ~ sQ11_spl
| sQ178_spl ),
inference(split_clause,[status(thm)],[f1916,f1931,f545]) ).
fof(f1935,definition,
! [X0,X1,X2,X3] :
( sQ179_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf53(X2),X1))
| ~ segmentP(X3,app(app(skaf53(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf53(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f1936,plain,
! [X0,X1,X2,X3] :
( ~ sQ179_spl
| segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf53(X2),X1))
| ~ segmentP(X3,app(app(skaf53(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf53(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1935]) ).
fof(f1938,plain,
( ~ sQ11_spl
| sQ179_spl ),
inference(split_clause,[status(thm)],[f1917,f1935,f545]) ).
fof(f1939,definition,
! [X0,X1] :
( sQ180_spl
<=> ( app(skaf53(X1),nil) = X0
| ~ ssList(skaf53(X1))
| ~ rearsegP(X0,app(skaf53(X1),nil))
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f1942,plain,
( ~ sQ11_spl
| sQ180_spl ),
inference(split_clause,[status(thm)],[f1918,f1939,f545]) ).
fof(f1943,definition,
! [X0,X1] :
( sQ181_spl
<=> ( segmentP(app(app(skaf53(X1),nil),X0),nil)
| ~ ssList(app(skaf53(X1),X0))
| ~ ssList(skaf53(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f1946,plain,
( ~ sQ11_spl
| sQ181_spl ),
inference(split_clause,[status(thm)],[f1919,f1943,f545]) ).
fof(f1947,definition,
! [X0,X1,X2] :
( sQ182_spl
<=> ( segmentP(app(skaf53(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf53(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f1948,plain,
! [X0,X1,X2] :
( ~ sQ182_spl
| segmentP(app(skaf53(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf53(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1947]) ).
fof(f1950,plain,
( ~ sQ11_spl
| sQ182_spl ),
inference(split_clause,[status(thm)],[f1920,f1947,f545]) ).
fof(f1951,definition,
! [X0] :
( sQ183_spl
<=> ( rearsegP(app(skaf53(X0),nil),nil)
| ~ ssList(skaf53(X0))
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f1954,plain,
( ~ sQ11_spl
| sQ183_spl ),
inference(split_clause,[status(thm)],[f1921,f1951,f545]) ).
fof(f1955,definition,
! [X0,X1] :
( sQ184_spl
<=> ( rearsegP(skaf53(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f1956,plain,
! [X0,X1] :
( ~ sQ184_spl
| rearsegP(skaf53(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ rearsegP(nil,X0) ),
inference(component_clause,[status(thm)],[f1955]) ).
fof(f1958,plain,
( ~ sQ11_spl
| sQ184_spl ),
inference(split_clause,[status(thm)],[f1922,f1955,f545]) ).
fof(f1964,plain,
! [X0,X1,X2] :
( ~ sQ178_spl
| app(app(skaf53(X2),nil),X1) = X0
| ~ ssList(app(skaf53(X2),X1))
| ~ segmentP(X0,app(skaf53(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf53(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1022,f1932]) ).
fof(f1965,plain,
! [X0,X1,X2] :
( ~ sQ178_spl
| app(skaf53(X2),X1) = X0
| ~ ssList(app(skaf53(X2),X1))
| ~ segmentP(X0,app(skaf53(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf53(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1022,f1964]) ).
fof(f1966,plain,
! [X0,X1,X2] :
( ~ sQ178_spl
| app(skaf53(X2),X1) = X0
| ~ ssList(app(skaf53(X2),X1))
| ~ segmentP(X0,app(skaf53(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1965,f241]) ).
fof(f1967,plain,
! [X0,X1,X2,X3] :
( ~ sQ179_spl
| segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf53(X2),X1))
| ~ segmentP(X3,app(skaf53(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf53(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1022,f1936]) ).
fof(f1968,plain,
! [X0,X1,X2,X3] :
( ~ sQ179_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(skaf53(X3),X1))
| ~ segmentP(X2,app(skaf53(X3),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1967,f241]) ).
fof(f1973,plain,
! [X0,X1,X2] :
( ~ sQ182_spl
| segmentP(app(skaf53(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1948,f241]) ).
fof(f1976,plain,
! [X0,X1] :
( ~ sQ184_spl
| rearsegP(skaf53(X1),X0)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1956,f241]) ).
fof(f1977,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ ssList(skaf56(X2))
| ~ rearsegP(nil,X0)
| X0 = app(skaf56(X2),nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf56(X2))
| ~ rearsegP(X1,app(skaf56(X2),nil))
| ~ rearsegP(X0,X1) ),
inference(paramodulation,[status(thm)],[f1023,f762]) ).
fof(f1978,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ ssList(skaf56(X1))
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,app(skaf56(X1),nil)) ),
inference(paramodulation,[status(thm)],[f1023,f750]) ).
fof(f1979,plain,
! [X0,X1,X2] :
( app(app(skaf56(X2),nil),X1) = X0
| ~ ssList(app(skaf56(X2),X1))
| ~ segmentP(X0,app(app(skaf56(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf56(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1023,f666]) ).
fof(f1980,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf56(X2),X1))
| ~ segmentP(X3,app(app(skaf56(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf56(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1023,f665]) ).
fof(f1981,plain,
! [X0,X1] :
( app(skaf56(X1),nil) = X0
| ~ ssList(skaf56(X1))
| ~ rearsegP(X0,app(skaf56(X1),nil))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1023,f608]) ).
fof(f1982,plain,
! [X0,X1] :
( segmentP(app(app(skaf56(X1),nil),X0),nil)
| ~ ssList(app(skaf56(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf56(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1023,f504]) ).
fof(f1983,plain,
! [X0,X1,X2] :
( segmentP(app(skaf56(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf56(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1023,f404]) ).
fof(f1984,plain,
! [X0] :
( rearsegP(app(skaf56(X0),nil),nil)
| ~ ssList(skaf56(X0))
| ~ ssList(nil)
| ~ ssList(skaf56(X0)) ),
inference(paramodulation,[status(thm)],[f1023,f500]) ).
fof(f1985,plain,
! [X0,X1] :
( rearsegP(skaf56(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1023,f350]) ).
fof(f1986,definition,
! [X0,X1,X2] :
( sQ185_spl
<=> ( ~ ssList(skaf56(X2))
| ~ rearsegP(nil,X0)
| X0 = app(skaf56(X2),nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf56(X2))
| ~ rearsegP(X1,app(skaf56(X2),nil))
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f1989,plain,
( ~ sQ11_spl
| sQ185_spl ),
inference(split_clause,[status(thm)],[f1977,f1986,f545]) ).
fof(f1990,definition,
! [X0,X1,X2] :
( sQ186_spl
<=> ( ~ ssList(skaf56(X1))
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,app(skaf56(X1),nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f1993,plain,
( ~ sQ11_spl
| sQ186_spl ),
inference(split_clause,[status(thm)],[f1978,f1990,f545]) ).
fof(f1994,definition,
! [X0,X1,X2] :
( sQ187_spl
<=> ( app(app(skaf56(X2),nil),X1) = X0
| ~ ssList(app(skaf56(X2),X1))
| ~ segmentP(X0,app(app(skaf56(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf56(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f1995,plain,
! [X0,X1,X2] :
( ~ sQ187_spl
| app(app(skaf56(X2),nil),X1) = X0
| ~ ssList(app(skaf56(X2),X1))
| ~ segmentP(X0,app(app(skaf56(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf56(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1994]) ).
fof(f1997,plain,
( ~ sQ11_spl
| sQ187_spl ),
inference(split_clause,[status(thm)],[f1979,f1994,f545]) ).
fof(f1998,definition,
! [X0,X1,X2,X3] :
( sQ188_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf56(X2),X1))
| ~ segmentP(X3,app(app(skaf56(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf56(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f1999,plain,
! [X0,X1,X2,X3] :
( ~ sQ188_spl
| segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf56(X2),X1))
| ~ segmentP(X3,app(app(skaf56(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf56(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f1998]) ).
fof(f2001,plain,
( ~ sQ11_spl
| sQ188_spl ),
inference(split_clause,[status(thm)],[f1980,f1998,f545]) ).
fof(f2002,definition,
! [X0,X1] :
( sQ189_spl
<=> ( app(skaf56(X1),nil) = X0
| ~ ssList(skaf56(X1))
| ~ rearsegP(X0,app(skaf56(X1),nil))
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f2005,plain,
( ~ sQ11_spl
| sQ189_spl ),
inference(split_clause,[status(thm)],[f1981,f2002,f545]) ).
fof(f2006,definition,
! [X0,X1] :
( sQ190_spl
<=> ( segmentP(app(app(skaf56(X1),nil),X0),nil)
| ~ ssList(app(skaf56(X1),X0))
| ~ ssList(skaf56(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f2009,plain,
( ~ sQ11_spl
| sQ190_spl ),
inference(split_clause,[status(thm)],[f1982,f2006,f545]) ).
fof(f2010,definition,
! [X0,X1,X2] :
( sQ191_spl
<=> ( segmentP(app(skaf56(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf56(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f2011,plain,
! [X0,X1,X2] :
( ~ sQ191_spl
| segmentP(app(skaf56(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf56(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f2010]) ).
fof(f2013,plain,
( ~ sQ11_spl
| sQ191_spl ),
inference(split_clause,[status(thm)],[f1983,f2010,f545]) ).
fof(f2014,definition,
! [X0] :
( sQ192_spl
<=> ( rearsegP(app(skaf56(X0),nil),nil)
| ~ ssList(skaf56(X0))
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f2017,plain,
( ~ sQ11_spl
| sQ192_spl ),
inference(split_clause,[status(thm)],[f1984,f2014,f545]) ).
fof(f2018,definition,
! [X0,X1] :
( sQ193_spl
<=> ( rearsegP(skaf56(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f2019,plain,
! [X0,X1] :
( ~ sQ193_spl
| rearsegP(skaf56(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ rearsegP(nil,X0) ),
inference(component_clause,[status(thm)],[f2018]) ).
fof(f2021,plain,
( ~ sQ11_spl
| sQ193_spl ),
inference(split_clause,[status(thm)],[f1985,f2018,f545]) ).
fof(f2027,plain,
! [X0,X1,X2] :
( ~ sQ187_spl
| app(app(skaf56(X2),nil),X1) = X0
| ~ ssList(app(skaf56(X2),X1))
| ~ segmentP(X0,app(skaf56(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf56(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1023,f1995]) ).
fof(f2028,plain,
! [X0,X1,X2] :
( ~ sQ187_spl
| app(skaf56(X2),X1) = X0
| ~ ssList(app(skaf56(X2),X1))
| ~ segmentP(X0,app(skaf56(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf56(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1023,f2027]) ).
fof(f2029,plain,
! [X0,X1,X2] :
( ~ sQ187_spl
| app(skaf56(X2),X1) = X0
| ~ ssList(app(skaf56(X2),X1))
| ~ segmentP(X0,app(skaf56(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2028,f238]) ).
fof(f2030,plain,
! [X0,X1,X2,X3] :
( ~ sQ188_spl
| segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf56(X2),X1))
| ~ segmentP(X3,app(skaf56(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf56(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1023,f1999]) ).
fof(f2031,plain,
! [X0,X1,X2,X3] :
( ~ sQ188_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(skaf56(X3),X1))
| ~ segmentP(X2,app(skaf56(X3),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2030,f238]) ).
fof(f2036,plain,
! [X0,X1,X2] :
( ~ sQ191_spl
| segmentP(app(skaf56(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2011,f238]) ).
fof(f2039,plain,
! [X0,X1] :
( ~ sQ193_spl
| rearsegP(skaf56(X1),X0)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2019,f238]) ).
fof(f2040,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ ssList(skaf57(X2))
| ~ rearsegP(nil,X0)
| X0 = app(skaf57(X2),nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf57(X2))
| ~ rearsegP(X1,app(skaf57(X2),nil))
| ~ rearsegP(X0,X1) ),
inference(paramodulation,[status(thm)],[f1024,f762]) ).
fof(f2041,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ ssList(skaf57(X1))
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,app(skaf57(X1),nil)) ),
inference(paramodulation,[status(thm)],[f1024,f750]) ).
fof(f2042,plain,
! [X0,X1,X2] :
( app(app(skaf57(X2),nil),X1) = X0
| ~ ssList(app(skaf57(X2),X1))
| ~ segmentP(X0,app(app(skaf57(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf57(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1024,f666]) ).
fof(f2043,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf57(X2),X1))
| ~ segmentP(X3,app(app(skaf57(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf57(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1024,f665]) ).
fof(f2044,plain,
! [X0,X1] :
( app(skaf57(X1),nil) = X0
| ~ ssList(skaf57(X1))
| ~ rearsegP(X0,app(skaf57(X1),nil))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1024,f608]) ).
fof(f2045,plain,
! [X0,X1] :
( segmentP(app(app(skaf57(X1),nil),X0),nil)
| ~ ssList(app(skaf57(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf57(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1024,f504]) ).
fof(f2046,plain,
! [X0,X1,X2] :
( segmentP(app(skaf57(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf57(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1024,f404]) ).
fof(f2047,plain,
! [X0] :
( rearsegP(app(skaf57(X0),nil),nil)
| ~ ssList(skaf57(X0))
| ~ ssList(nil)
| ~ ssList(skaf57(X0)) ),
inference(paramodulation,[status(thm)],[f1024,f500]) ).
fof(f2048,plain,
! [X0,X1] :
( rearsegP(skaf57(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1024,f350]) ).
fof(f2049,definition,
! [X0,X1,X2] :
( sQ194_spl
<=> ( ~ ssList(skaf57(X2))
| ~ rearsegP(nil,X0)
| X0 = app(skaf57(X2),nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf57(X2))
| ~ rearsegP(X1,app(skaf57(X2),nil))
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f2052,plain,
( ~ sQ11_spl
| sQ194_spl ),
inference(split_clause,[status(thm)],[f2040,f2049,f545]) ).
fof(f2053,definition,
! [X0,X1,X2] :
( sQ195_spl
<=> ( ~ ssList(skaf57(X1))
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,app(skaf57(X1),nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f2056,plain,
( ~ sQ11_spl
| sQ195_spl ),
inference(split_clause,[status(thm)],[f2041,f2053,f545]) ).
fof(f2057,definition,
! [X0,X1,X2] :
( sQ196_spl
<=> ( app(app(skaf57(X2),nil),X1) = X0
| ~ ssList(app(skaf57(X2),X1))
| ~ segmentP(X0,app(app(skaf57(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf57(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f2058,plain,
! [X0,X1,X2] :
( ~ sQ196_spl
| app(app(skaf57(X2),nil),X1) = X0
| ~ ssList(app(skaf57(X2),X1))
| ~ segmentP(X0,app(app(skaf57(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf57(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f2057]) ).
fof(f2060,plain,
( ~ sQ11_spl
| sQ196_spl ),
inference(split_clause,[status(thm)],[f2042,f2057,f545]) ).
fof(f2061,definition,
! [X0,X1,X2,X3] :
( sQ197_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf57(X2),X1))
| ~ segmentP(X3,app(app(skaf57(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf57(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f2062,plain,
! [X0,X1,X2,X3] :
( ~ sQ197_spl
| segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf57(X2),X1))
| ~ segmentP(X3,app(app(skaf57(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf57(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f2061]) ).
fof(f2064,plain,
( ~ sQ11_spl
| sQ197_spl ),
inference(split_clause,[status(thm)],[f2043,f2061,f545]) ).
fof(f2065,definition,
! [X0,X1] :
( sQ198_spl
<=> ( app(skaf57(X1),nil) = X0
| ~ ssList(skaf57(X1))
| ~ rearsegP(X0,app(skaf57(X1),nil))
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f2068,plain,
( ~ sQ11_spl
| sQ198_spl ),
inference(split_clause,[status(thm)],[f2044,f2065,f545]) ).
fof(f2069,definition,
! [X0,X1] :
( sQ199_spl
<=> ( segmentP(app(app(skaf57(X1),nil),X0),nil)
| ~ ssList(app(skaf57(X1),X0))
| ~ ssList(skaf57(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f2072,plain,
( ~ sQ11_spl
| sQ199_spl ),
inference(split_clause,[status(thm)],[f2045,f2069,f545]) ).
fof(f2073,definition,
! [X0,X1,X2] :
( sQ200_spl
<=> ( segmentP(app(skaf57(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf57(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f2074,plain,
! [X0,X1,X2] :
( ~ sQ200_spl
| segmentP(app(skaf57(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf57(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f2073]) ).
fof(f2076,plain,
( ~ sQ11_spl
| sQ200_spl ),
inference(split_clause,[status(thm)],[f2046,f2073,f545]) ).
fof(f2077,definition,
! [X0] :
( sQ201_spl
<=> ( rearsegP(app(skaf57(X0),nil),nil)
| ~ ssList(skaf57(X0))
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f2080,plain,
( ~ sQ11_spl
| sQ201_spl ),
inference(split_clause,[status(thm)],[f2047,f2077,f545]) ).
fof(f2081,definition,
! [X0,X1] :
( sQ202_spl
<=> ( rearsegP(skaf57(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f2082,plain,
! [X0,X1] :
( ~ sQ202_spl
| rearsegP(skaf57(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ rearsegP(nil,X0) ),
inference(component_clause,[status(thm)],[f2081]) ).
fof(f2084,plain,
( ~ sQ11_spl
| sQ202_spl ),
inference(split_clause,[status(thm)],[f2048,f2081,f545]) ).
fof(f2090,plain,
! [X0,X1,X2] :
( ~ sQ196_spl
| app(app(skaf57(X2),nil),X1) = X0
| ~ ssList(app(skaf57(X2),X1))
| ~ segmentP(X0,app(skaf57(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf57(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1024,f2058]) ).
fof(f2091,plain,
! [X0,X1,X2] :
( ~ sQ196_spl
| app(skaf57(X2),X1) = X0
| ~ ssList(app(skaf57(X2),X1))
| ~ segmentP(X0,app(skaf57(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf57(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1024,f2090]) ).
fof(f2092,plain,
! [X0,X1,X2] :
( ~ sQ196_spl
| app(skaf57(X2),X1) = X0
| ~ ssList(app(skaf57(X2),X1))
| ~ segmentP(X0,app(skaf57(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2091,f237]) ).
fof(f2093,plain,
! [X0,X1,X2,X3] :
( ~ sQ197_spl
| segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf57(X2),X1))
| ~ segmentP(X3,app(skaf57(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf57(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1024,f2062]) ).
fof(f2094,plain,
! [X0,X1,X2,X3] :
( ~ sQ197_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(skaf57(X3),X1))
| ~ segmentP(X2,app(skaf57(X3),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2093,f237]) ).
fof(f2099,plain,
! [X0,X1,X2] :
( ~ sQ200_spl
| segmentP(app(skaf57(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2074,f237]) ).
fof(f2102,plain,
! [X0,X1] :
( ~ sQ202_spl
| rearsegP(skaf57(X1),X0)
| ~ ssList(X0)
| ~ rearsegP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2082,f237]) ).
fof(f2103,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ ssList(skaf58(X2))
| ~ rearsegP(nil,X0)
| X0 = app(skaf58(X2),nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf58(X2))
| ~ rearsegP(X1,app(skaf58(X2),nil))
| ~ rearsegP(X0,X1) ),
inference(paramodulation,[status(thm)],[f1025,f762]) ).
fof(f2104,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ ssList(skaf58(X1))
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf58(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,app(skaf58(X1),nil)) ),
inference(paramodulation,[status(thm)],[f1025,f750]) ).
fof(f2105,plain,
! [X0,X1,X2] :
( app(app(skaf58(X2),nil),X1) = X0
| ~ ssList(app(skaf58(X2),X1))
| ~ segmentP(X0,app(app(skaf58(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf58(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1025,f666]) ).
fof(f2106,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf58(X2),X1))
| ~ segmentP(X3,app(app(skaf58(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf58(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1025,f665]) ).
fof(f2107,plain,
! [X0,X1] :
( app(skaf58(X1),nil) = X0
| ~ ssList(skaf58(X1))
| ~ rearsegP(X0,app(skaf58(X1),nil))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf58(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1025,f608]) ).
fof(f2108,plain,
! [X0,X1] :
( segmentP(app(app(skaf58(X1),nil),X0),nil)
| ~ ssList(app(skaf58(X1),X0))
| ~ ssList(nil)
| ~ ssList(skaf58(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1025,f504]) ).
fof(f2109,plain,
! [X0,X1,X2] :
( segmentP(app(skaf58(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf58(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1025,f404]) ).
fof(f2110,plain,
! [X0] :
( rearsegP(app(skaf58(X0),nil),nil)
| ~ ssList(skaf58(X0))
| ~ ssList(nil)
| ~ ssList(skaf58(X0)) ),
inference(paramodulation,[status(thm)],[f1025,f500]) ).
fof(f2111,plain,
! [X0,X1] :
( rearsegP(skaf58(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf58(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1025,f350]) ).
fof(f2112,definition,
! [X0,X1,X2] :
( sQ203_spl
<=> ( ~ ssList(skaf58(X2))
| ~ rearsegP(nil,X0)
| X0 = app(skaf58(X2),nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf58(X2))
| ~ rearsegP(X1,app(skaf58(X2),nil))
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f2115,plain,
( ~ sQ11_spl
| sQ203_spl ),
inference(split_clause,[status(thm)],[f2103,f2112,f545]) ).
fof(f2116,definition,
! [X0,X1,X2] :
( sQ204_spl
<=> ( ~ ssList(skaf58(X1))
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf58(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,app(skaf58(X1),nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f2119,plain,
( ~ sQ11_spl
| sQ204_spl ),
inference(split_clause,[status(thm)],[f2104,f2116,f545]) ).
fof(f2120,definition,
! [X0,X1,X2] :
( sQ205_spl
<=> ( app(app(skaf58(X2),nil),X1) = X0
| ~ ssList(app(skaf58(X2),X1))
| ~ segmentP(X0,app(app(skaf58(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf58(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f2121,plain,
! [X0,X1,X2] :
( ~ sQ205_spl
| app(app(skaf58(X2),nil),X1) = X0
| ~ ssList(app(skaf58(X2),X1))
| ~ segmentP(X0,app(app(skaf58(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf58(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f2120]) ).
fof(f2123,plain,
( ~ sQ11_spl
| sQ205_spl ),
inference(split_clause,[status(thm)],[f2105,f2120,f545]) ).
fof(f2124,definition,
! [X0,X1,X2,X3] :
( sQ206_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf58(X2),X1))
| ~ segmentP(X3,app(app(skaf58(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf58(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f2125,plain,
! [X0,X1,X2,X3] :
( ~ sQ206_spl
| segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf58(X2),X1))
| ~ segmentP(X3,app(app(skaf58(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf58(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f2124]) ).
fof(f2127,plain,
( ~ sQ11_spl
| sQ206_spl ),
inference(split_clause,[status(thm)],[f2106,f2124,f545]) ).
fof(f2128,definition,
! [X0,X1] :
( sQ207_spl
<=> ( app(skaf58(X1),nil) = X0
| ~ ssList(skaf58(X1))
| ~ rearsegP(X0,app(skaf58(X1),nil))
| ~ ssList(X0)
| ~ ssList(skaf58(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f2131,plain,
( ~ sQ11_spl
| sQ207_spl ),
inference(split_clause,[status(thm)],[f2107,f2128,f545]) ).
fof(f2132,definition,
! [X0,X1] :
( sQ208_spl
<=> ( segmentP(app(app(skaf58(X1),nil),X0),nil)
| ~ ssList(app(skaf58(X1),X0))
| ~ ssList(skaf58(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f2135,plain,
( ~ sQ11_spl
| sQ208_spl ),
inference(split_clause,[status(thm)],[f2108,f2132,f545]) ).
fof(f2136,definition,
! [X0,X1,X2] :
( sQ209_spl
<=> ( segmentP(app(skaf58(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf58(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f2137,plain,
! [X0,X1,X2] :
( ~ sQ209_spl
| segmentP(app(skaf58(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf58(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(component_clause,[status(thm)],[f2136]) ).
fof(f2139,plain,
( ~ sQ11_spl
| sQ209_spl ),
inference(split_clause,[status(thm)],[f2109,f2136,f545]) ).
fof(f2140,definition,
! [X0] :
( sQ210_spl
<=> ( rearsegP(app(skaf58(X0),nil),nil)
| ~ ssList(skaf58(X0))
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f2143,plain,
( ~ sQ11_spl
| sQ210_spl ),
inference(split_clause,[status(thm)],[f2110,f2140,f545]) ).
fof(f2144,definition,
! [X0,X1] :
( sQ211_spl
<=> ( rearsegP(skaf58(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf58(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f2147,plain,
( ~ sQ11_spl
| sQ211_spl ),
inference(split_clause,[status(thm)],[f2111,f2144,f545]) ).
fof(f2153,plain,
! [X0,X1,X2] :
( ~ sQ205_spl
| app(app(skaf58(X2),nil),X1) = X0
| ~ ssList(app(skaf58(X2),X1))
| ~ segmentP(X0,app(skaf58(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf58(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1025,f2121]) ).
fof(f2154,plain,
! [X0,X1,X2] :
( ~ sQ205_spl
| app(skaf58(X2),X1) = X0
| ~ ssList(app(skaf58(X2),X1))
| ~ segmentP(X0,app(skaf58(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf58(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1025,f2153]) ).
fof(f2155,plain,
! [X0,X1,X2] :
( ~ sQ205_spl
| app(skaf58(X2),X1) = X0
| ~ ssList(app(skaf58(X2),X1))
| ~ segmentP(X0,app(skaf58(X2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2154,f236]) ).
fof(f2156,plain,
! [X0,X1,X2,X3] :
( ~ sQ206_spl
| segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf58(X2),X1))
| ~ segmentP(X3,app(skaf58(X2),X1))
| ~ ssList(X0)
| ~ ssList(skaf58(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_demodulation,[status(thm)],[f1025,f2125]) ).
fof(f2157,plain,
! [X0,X1,X2,X3] :
( ~ sQ206_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(skaf58(X3),X1))
| ~ segmentP(X2,app(skaf58(X3),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2156,f236]) ).
fof(f2162,plain,
! [X0,X1,X2] :
( ~ sQ209_spl
| segmentP(app(skaf58(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2137,f236]) ).
fof(f2172,plain,
! [X0,X1,X2] :
( app(X2,X0) = X1
| ~ rearsegP(X1,app(X2,X0))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ rearsegP(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f608,f285]) ).
fof(f2173,plain,
! [X0,X1] :
( rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f500,f285]) ).
fof(f2174,plain,
! [X0,X1,X2] :
( ~ sQ74_spl
| segmentP(X2,X1)
| ~ ssList(X2)
| ~ segmentP(X2,app(sk2,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(nil,X1)
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f285,f1166]) ).
fof(f2175,plain,
! [X0,X1,X2] :
( ~ sQ60_spl
| segmentP(X2,X1)
| ~ ssList(X2)
| ~ segmentP(X2,app(sk1,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(nil,X1)
| ~ ssList(sk1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f285,f1073]) ).
fof(f2178,plain,
! [X0,X1,X2] :
( segmentP(app(app(X1,X2),X0),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(X1,X2))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f285,f504]) ).
fof(f2181,plain,
! [X0] :
( ssList(skaf58(X0))
| ~ ssList(skaf58(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1025,f285]) ).
fof(f2182,plain,
! [X0] :
( ssList(skaf57(X0))
| ~ ssList(skaf57(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1024,f285]) ).
fof(f2183,plain,
! [X0] :
( ssList(skaf56(X0))
| ~ ssList(skaf56(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1023,f285]) ).
fof(f2184,plain,
! [X0] :
( ssList(skaf53(X0))
| ~ ssList(skaf53(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1022,f285]) ).
fof(f2185,plain,
! [X0] :
( ssList(skaf52(X0))
| ~ ssList(skaf52(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1021,f285]) ).
fof(f2186,plain,
! [X0] :
( ssList(skaf51(X0))
| ~ ssList(skaf51(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1020,f285]) ).
fof(f2192,definition,
! [X0,X1,X2] :
( sQ212_spl
<=> ( segmentP(X2,X1)
| ~ ssList(X2)
| ~ segmentP(X2,app(sk2,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(nil,X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f2195,plain,
( ~ sQ74_spl
| ~ sQ16_spl
| sQ212_spl ),
inference(split_clause,[status(thm)],[f2174,f2192,f587,f1142]) ).
fof(f2196,definition,
! [X0,X1,X2] :
( sQ213_spl
<=> ( segmentP(X2,X1)
| ~ ssList(X2)
| ~ segmentP(X2,app(sk1,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(nil,X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f2199,plain,
( ~ sQ60_spl
| ~ sQ13_spl
| sQ213_spl ),
inference(split_clause,[status(thm)],[f2175,f2196,f558,f1049]) ).
fof(f2204,plain,
! [X0,X1,X2] :
( segmentP(app(app(X1,X2),X0),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(app(X1,X2))
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2178]) ).
fof(f2205,plain,
! [X0,X1,X2] :
( segmentP(app(app(X1,X2),X0),X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2204,f285]) ).
fof(f2206,definition,
! [X0] :
( sQ214_spl
<=> ( ssList(skaf58(X0))
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f2209,plain,
( sQ214_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2181,f545,f2206]) ).
fof(f2210,definition,
! [X0] :
( sQ215_spl
<=> ( ssList(skaf57(X0))
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f2213,plain,
( sQ215_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2182,f545,f2210]) ).
fof(f2214,definition,
! [X0] :
( sQ216_spl
<=> ( ssList(skaf56(X0))
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f2217,plain,
( sQ216_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2183,f545,f2214]) ).
fof(f2218,definition,
! [X0] :
( sQ217_spl
<=> ( ssList(skaf53(X0))
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f2221,plain,
( sQ217_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2184,f545,f2218]) ).
fof(f2222,definition,
! [X0] :
( sQ218_spl
<=> ( ssList(skaf52(X0))
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f2225,plain,
( sQ218_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2185,f545,f2222]) ).
fof(f2226,definition,
! [X0] :
( sQ219_spl
<=> ( ssList(skaf51(X0))
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f2229,plain,
( sQ219_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2186,f545,f2226]) ).
fof(f2237,plain,
! [X0] :
( ~ sQ110_spl
| ~ ssList(sk1)
| ~ ssList(X0)
| segmentP(app(sk1,X0),sk1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1483,f285]) ).
fof(f2238,plain,
( ~ sQ110_spl
| segmentP(app(sk1,nil),sk1)
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1013,f1483]) ).
fof(f2239,definition,
! [X0] :
( sQ220_spl
<=> ( ~ ssList(X0)
| segmentP(app(sk1,X0),sk1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f2240,plain,
! [X0] :
( ~ sQ220_spl
| ~ ssList(X0)
| segmentP(app(sk1,X0),sk1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2239]) ).
fof(f2242,plain,
( ~ sQ110_spl
| ~ sQ13_spl
| sQ220_spl ),
inference(split_clause,[status(thm)],[f2237,f2239,f558,f1461]) ).
fof(f2243,definition,
( sQ221_spl
<=> segmentP(app(sk1,nil),sk1) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f2244,plain,
( ~ sQ221_spl
| segmentP(app(sk1,nil),sk1) ),
inference(component_clause,[status(thm)],[f2243]) ).
fof(f2246,plain,
( ~ sQ110_spl
| sQ221_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2238,f545,f558,f2243,f1461]) ).
fof(f2247,plain,
! [X0] :
( ~ sQ220_spl
| segmentP(app(sk1,X0),sk1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2240]) ).
fof(f2248,plain,
( ~ sQ221_spl
| segmentP(sk1,sk1) ),
inference(forward_demodulation,[status(thm)],[f1013,f2244]) ).
fof(f2249,plain,
! [X0] :
( ~ sQ221_spl
| segmentP(X0,sk1)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(sk1)
| ~ segmentP(X0,sk1) ),
inference(resolution,[status(thm)],[f2248,f374]) ).
fof(f2251,definition,
! [X0] :
( sQ222_spl
<=> ( segmentP(X0,sk1)
| ~ ssList(X0)
| ~ segmentP(X0,sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f2254,plain,
( ~ sQ221_spl
| ~ sQ13_spl
| sQ222_spl ),
inference(split_clause,[status(thm)],[f2249,f2251,f558,f2243]) ).
fof(f2255,definition,
( sQ223_spl
<=> segmentP(sk1,sk1) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f2259,plain,
! [X0,X1] :
( ~ sQ220_spl
| segmentP(X1,sk1)
| ~ ssList(X1)
| ~ ssList(app(sk1,X0))
| ~ ssList(sk1)
| ~ segmentP(X1,app(sk1,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2247,f374]) ).
fof(f2260,plain,
! [X0] :
( ~ sQ220_spl
| app(sk1,X0) = sk1
| ~ ssList(app(sk1,X0))
| ~ ssList(sk1)
| ~ segmentP(sk1,app(sk1,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2247,f339]) ).
fof(f2261,plain,
( ~ sQ220_spl
| segmentP(sk1,sk1)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1013,f2247]) ).
fof(f2262,definition,
! [X0,X1] :
( sQ224_spl
<=> ( segmentP(X1,sk1)
| ~ ssList(X1)
| ~ ssList(app(sk1,X0))
| ~ segmentP(X1,app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f2265,plain,
( ~ sQ220_spl
| ~ sQ13_spl
| sQ224_spl ),
inference(split_clause,[status(thm)],[f2259,f2262,f558,f2239]) ).
fof(f2266,definition,
! [X0] :
( sQ225_spl
<=> ( app(sk1,X0) = sk1
| ~ ssList(app(sk1,X0))
| ~ segmentP(sk1,app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f2269,plain,
( ~ sQ220_spl
| ~ sQ13_spl
| sQ225_spl ),
inference(split_clause,[status(thm)],[f2260,f2266,f558,f2239]) ).
fof(f2270,plain,
( ~ sQ220_spl
| sQ223_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2261,f545,f2255,f2239]) ).
fof(f2271,plain,
! [X0,X1] :
( ~ sQ101_spl
| ~ ssList(sk2)
| ~ ssList(X1)
| app(sk2,X1) = X0
| ~ segmentP(X0,app(sk2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(resolution,[status(thm)],[f1386,f285]) ).
fof(f2272,plain,
! [X0] :
( ~ sQ101_spl
| app(sk2,nil) = X0
| ~ ssList(sk2)
| ~ segmentP(X0,app(sk2,nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1029,f1386]) ).
fof(f2273,definition,
! [X0,X1] :
( sQ226_spl
<=> ( ~ ssList(X1)
| app(sk2,X1) = X0
| ~ segmentP(X0,app(sk2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f2276,plain,
( ~ sQ101_spl
| ~ sQ16_spl
| sQ226_spl ),
inference(split_clause,[status(thm)],[f2271,f2273,f587,f1375]) ).
fof(f2277,definition,
! [X0] :
( sQ227_spl
<=> ( app(sk2,nil) = X0
| ~ segmentP(X0,app(sk2,nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2280,plain,
( ~ sQ101_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sQ227_spl ),
inference(split_clause,[status(thm)],[f2272,f2277,f545,f587,f1375]) ).
fof(f2284,plain,
! [X0] :
( ~ sQ124_spl
| sk2 = app(X0,sk2)
| ~ ssList(app(X0,sk2))
| ~ rearsegP(sk2,app(X0,sk2))
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2173,f1591]) ).
fof(f2297,plain,
! [X0,X1] :
( app(X0,X1) = X1
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| ~ rearsegP(X1,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2173,f340]) ).
fof(f2298,plain,
! [X0] :
( rearsegP(skaf58(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf58(X0)) ),
inference(paramodulation,[status(thm)],[f1025,f2173]) ).
fof(f2299,plain,
! [X0] :
( rearsegP(skaf57(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf57(X0)) ),
inference(paramodulation,[status(thm)],[f1024,f2173]) ).
fof(f2300,plain,
! [X0] :
( rearsegP(skaf56(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf56(X0)) ),
inference(paramodulation,[status(thm)],[f1023,f2173]) ).
fof(f2301,plain,
! [X0] :
( rearsegP(skaf53(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf53(X0)) ),
inference(paramodulation,[status(thm)],[f1022,f2173]) ).
fof(f2302,plain,
! [X0] :
( rearsegP(skaf52(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf52(X0)) ),
inference(paramodulation,[status(thm)],[f1021,f2173]) ).
fof(f2303,plain,
! [X0] :
( rearsegP(skaf51(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf51(X0)) ),
inference(paramodulation,[status(thm)],[f1020,f2173]) ).
fof(f2309,definition,
! [X0] :
( sQ228_spl
<=> ( sk2 = app(X0,sk2)
| ~ ssList(app(X0,sk2))
| ~ rearsegP(sk2,app(X0,sk2))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f2312,plain,
( ~ sQ124_spl
| ~ sQ16_spl
| sQ228_spl ),
inference(split_clause,[status(thm)],[f2284,f2309,f587,f1566]) ).
fof(f2333,plain,
! [X0,X1] :
( app(X0,X1) = X1
| ~ ssList(app(X0,X1))
| ~ rearsegP(X1,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2297]) ).
fof(f2334,plain,
! [X0,X1] :
( app(X0,X1) = X1
| ~ rearsegP(X1,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2333,f285]) ).
fof(f2335,definition,
! [X0] :
( sQ229_spl
<=> ( rearsegP(skaf58(X0),nil)
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f2338,plain,
( ~ sQ11_spl
| sQ229_spl ),
inference(split_clause,[status(thm)],[f2298,f2335,f545]) ).
fof(f2339,definition,
! [X0] :
( sQ230_spl
<=> ( rearsegP(skaf57(X0),nil)
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f2342,plain,
( ~ sQ11_spl
| sQ230_spl ),
inference(split_clause,[status(thm)],[f2299,f2339,f545]) ).
fof(f2343,definition,
! [X0] :
( sQ231_spl
<=> ( rearsegP(skaf56(X0),nil)
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f2346,plain,
( ~ sQ11_spl
| sQ231_spl ),
inference(split_clause,[status(thm)],[f2300,f2343,f545]) ).
fof(f2347,definition,
! [X0] :
( sQ232_spl
<=> ( rearsegP(skaf53(X0),nil)
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f2350,plain,
( ~ sQ11_spl
| sQ232_spl ),
inference(split_clause,[status(thm)],[f2301,f2347,f545]) ).
fof(f2351,definition,
! [X0] :
( sQ233_spl
<=> ( rearsegP(skaf52(X0),nil)
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f2354,plain,
( ~ sQ11_spl
| sQ233_spl ),
inference(split_clause,[status(thm)],[f2302,f2351,f545]) ).
fof(f2355,definition,
! [X0] :
( sQ234_spl
<=> ( rearsegP(skaf51(X0),nil)
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f2358,plain,
( ~ sQ11_spl
| sQ234_spl ),
inference(split_clause,[status(thm)],[f2303,f2355,f545]) ).
fof(f2365,plain,
! [X0] :
( ~ sQ166_spl
| ~ ssList(nil)
| rearsegP(skaf51(X0),nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1850,f257]) ).
fof(f2366,plain,
! [X0,X1,X2] :
( ~ sQ166_spl
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| rearsegP(skaf51(X1),X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1850,f376]) ).
fof(f2368,definition,
! [X0] :
( sQ235_spl
<=> rearsegP(skaf51(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f2369,plain,
! [X0] :
( ~ sQ235_spl
| rearsegP(skaf51(X0),nil) ),
inference(component_clause,[status(thm)],[f2368]) ).
fof(f2372,plain,
( ~ sQ166_spl
| sQ235_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2365,f545,f2368,f1829]) ).
fof(f2373,definition,
! [X0,X1,X2] :
( sQ236_spl
<=> ( ~ ssList(X2)
| ~ ssList(X0)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| rearsegP(skaf51(X1),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f2376,plain,
( ~ sQ166_spl
| ~ sQ11_spl
| sQ236_spl ),
inference(split_clause,[status(thm)],[f2366,f2373,f545,f1829]) ).
fof(f2380,plain,
! [X0,X1,X2] :
( ~ sQ235_spl
| ~ ssList(skaf51(X2))
| ~ rearsegP(X1,skaf51(X2))
| nil = X1
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f2369,f764]) ).
fof(f2381,plain,
! [X0,X1,X2] :
( ~ sQ235_spl
| ~ ssList(nil)
| ~ rearsegP(nil,X0)
| X0 = skaf51(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf51(X2))
| ~ rearsegP(X1,skaf51(X2))
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f2369,f764]) ).
fof(f2384,plain,
! [X0,X1,X2] :
( ~ sQ235_spl
| ~ ssList(skaf51(X2))
| ~ rearsegP(X1,skaf51(X2))
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f2369,f759]) ).
fof(f2385,plain,
! [X0] :
( ~ sQ235_spl
| ~ ssList(nil)
| ~ rearsegP(nil,skaf51(X0))
| nil = skaf51(X0)
| ~ ssList(nil)
| ~ ssList(skaf51(X0))
| ~ ssList(skaf51(X0))
| ~ rearsegP(nil,skaf51(X0)) ),
inference(resolution,[status(thm)],[f2369,f759]) ).
fof(f2386,plain,
! [X0,X1,X2] :
( ~ sQ235_spl
| ~ ssList(nil)
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,skaf51(X1)) ),
inference(resolution,[status(thm)],[f2369,f759]) ).
fof(f2388,plain,
! [X0,X1,X2] :
( ~ sQ235_spl
| ~ ssList(X2)
| ~ rearsegP(X2,skaf51(X1))
| ~ rearsegP(X0,X2)
| nil = skaf51(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f2369,f759]) ).
fof(f2389,plain,
! [X0,X1] :
( ~ sQ235_spl
| nil = skaf51(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ rearsegP(X0,skaf51(X1))
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f2369,f629]) ).
fof(f2390,plain,
! [X0,X1] :
( ~ sQ235_spl
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ ssList(nil)
| ~ rearsegP(X0,skaf51(X1)) ),
inference(resolution,[status(thm)],[f2369,f629]) ).
fof(f2391,plain,
! [X0] :
( ~ sQ235_spl
| skaf51(X0) = nil
| ~ ssList(skaf51(X0))
| ~ ssList(nil)
| ~ rearsegP(nil,skaf51(X0)) ),
inference(resolution,[status(thm)],[f2369,f340]) ).
fof(f2396,definition,
! [X0,X1,X2] :
( sQ238_spl
<=> ( ~ ssList(skaf51(X2))
| ~ rearsegP(X1,skaf51(X2))
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f2399,plain,
( ~ sQ235_spl
| ~ sQ11_spl
| sQ238_spl ),
inference(split_clause,[status(thm)],[f2380,f2396,f545,f2368]) ).
fof(f2400,definition,
! [X0,X1,X2] :
( sQ239_spl
<=> ( ~ rearsegP(nil,X0)
| X0 = skaf51(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf51(X2))
| ~ rearsegP(X1,skaf51(X2))
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f2403,plain,
( ~ sQ235_spl
| ~ sQ11_spl
| sQ239_spl ),
inference(split_clause,[status(thm)],[f2381,f2400,f545,f2368]) ).
fof(f2406,definition,
! [X0,X1,X2] :
( sQ240_spl
<=> ( ~ ssList(skaf51(X2))
| ~ rearsegP(X1,skaf51(X2))
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f2409,plain,
( ~ sQ235_spl
| ~ sQ11_spl
| sQ240_spl ),
inference(split_clause,[status(thm)],[f2384,f2406,f545,f2368]) ).
fof(f2410,definition,
! [X0] :
( sQ241_spl
<=> ( ~ rearsegP(nil,skaf51(X0))
| nil = skaf51(X0)
| ~ ssList(skaf51(X0))
| ~ ssList(skaf51(X0))
| ~ rearsegP(nil,skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f2413,plain,
( ~ sQ235_spl
| ~ sQ11_spl
| sQ241_spl ),
inference(split_clause,[status(thm)],[f2385,f2410,f545,f2368]) ).
fof(f2414,definition,
! [X0,X1,X2] :
( sQ242_spl
<=> ( ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,skaf51(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f2417,plain,
( ~ sQ235_spl
| ~ sQ11_spl
| sQ242_spl ),
inference(split_clause,[status(thm)],[f2386,f2414,f545,f2368]) ).
fof(f2419,definition,
! [X0,X1,X2] :
( sQ243_spl
<=> ( ~ ssList(X2)
| ~ rearsegP(X2,skaf51(X1))
| ~ rearsegP(X0,X2)
| nil = skaf51(X1)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f2422,plain,
( ~ sQ235_spl
| ~ sQ11_spl
| sQ243_spl ),
inference(split_clause,[status(thm)],[f2388,f2419,f545,f2368]) ).
fof(f2423,definition,
! [X0,X1] :
( sQ244_spl
<=> ( nil = skaf51(X1)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ rearsegP(X0,skaf51(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f2426,plain,
( ~ sQ235_spl
| ~ sQ11_spl
| sQ244_spl ),
inference(split_clause,[status(thm)],[f2389,f2423,f545,f2368]) ).
fof(f2427,definition,
! [X0,X1] :
( sQ245_spl
<=> ( X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ rearsegP(X0,skaf51(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f2430,plain,
( ~ sQ235_spl
| ~ sQ11_spl
| sQ245_spl ),
inference(split_clause,[status(thm)],[f2390,f2427,f545,f2368]) ).
fof(f2431,definition,
! [X0] :
( sQ246_spl
<=> ( skaf51(X0) = nil
| ~ ssList(skaf51(X0))
| ~ rearsegP(nil,skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f2434,plain,
( ~ sQ235_spl
| ~ sQ11_spl
| sQ246_spl ),
inference(split_clause,[status(thm)],[f2391,f2431,f545,f2368]) ).
fof(f2437,plain,
! [X0] :
( ~ sQ175_spl
| ~ ssList(nil)
| rearsegP(skaf52(X0),nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1913,f257]) ).
fof(f2438,plain,
! [X0,X1,X2] :
( ~ sQ175_spl
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| rearsegP(skaf52(X1),X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1913,f376]) ).
fof(f2440,definition,
! [X0] :
( sQ247_spl
<=> rearsegP(skaf52(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f2441,plain,
! [X0] :
( ~ sQ247_spl
| rearsegP(skaf52(X0),nil) ),
inference(component_clause,[status(thm)],[f2440]) ).
fof(f2444,plain,
( ~ sQ175_spl
| sQ247_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2437,f545,f2440,f1892]) ).
fof(f2445,definition,
! [X0,X1,X2] :
( sQ248_spl
<=> ( ~ ssList(X2)
| ~ ssList(X0)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| rearsegP(skaf52(X1),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f2448,plain,
( ~ sQ175_spl
| ~ sQ11_spl
| sQ248_spl ),
inference(split_clause,[status(thm)],[f2438,f2445,f545,f1892]) ).
fof(f2452,plain,
! [X0,X1,X2] :
( ~ sQ247_spl
| ~ ssList(skaf52(X2))
| ~ rearsegP(X1,skaf52(X2))
| nil = X1
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f2441,f764]) ).
fof(f2453,plain,
! [X0,X1,X2] :
( ~ sQ247_spl
| ~ ssList(nil)
| ~ rearsegP(nil,X0)
| X0 = skaf52(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf52(X2))
| ~ rearsegP(X1,skaf52(X2))
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f2441,f764]) ).
fof(f2456,plain,
! [X0,X1,X2] :
( ~ sQ247_spl
| ~ ssList(skaf52(X2))
| ~ rearsegP(X1,skaf52(X2))
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f2441,f759]) ).
fof(f2457,plain,
! [X0] :
( ~ sQ247_spl
| ~ ssList(nil)
| ~ rearsegP(nil,skaf52(X0))
| nil = skaf52(X0)
| ~ ssList(nil)
| ~ ssList(skaf52(X0))
| ~ ssList(skaf52(X0))
| ~ rearsegP(nil,skaf52(X0)) ),
inference(resolution,[status(thm)],[f2441,f759]) ).
fof(f2458,plain,
! [X0,X1,X2] :
( ~ sQ247_spl
| ~ ssList(nil)
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,skaf52(X1)) ),
inference(resolution,[status(thm)],[f2441,f759]) ).
fof(f2460,plain,
! [X0,X1,X2] :
( ~ sQ247_spl
| ~ ssList(X2)
| ~ rearsegP(X2,skaf52(X1))
| ~ rearsegP(X0,X2)
| nil = skaf52(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f2441,f759]) ).
fof(f2461,plain,
! [X0,X1] :
( ~ sQ247_spl
| nil = skaf52(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ rearsegP(X0,skaf52(X1))
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f2441,f629]) ).
fof(f2462,plain,
! [X0,X1] :
( ~ sQ247_spl
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ ssList(nil)
| ~ rearsegP(X0,skaf52(X1)) ),
inference(resolution,[status(thm)],[f2441,f629]) ).
fof(f2463,plain,
! [X0] :
( ~ sQ247_spl
| skaf52(X0) = nil
| ~ ssList(skaf52(X0))
| ~ ssList(nil)
| ~ rearsegP(nil,skaf52(X0)) ),
inference(resolution,[status(thm)],[f2441,f340]) ).
fof(f2468,definition,
! [X0,X1,X2] :
( sQ250_spl
<=> ( ~ ssList(skaf52(X2))
| ~ rearsegP(X1,skaf52(X2))
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f2471,plain,
( ~ sQ247_spl
| ~ sQ11_spl
| sQ250_spl ),
inference(split_clause,[status(thm)],[f2452,f2468,f545,f2440]) ).
fof(f2472,definition,
! [X0,X1,X2] :
( sQ251_spl
<=> ( ~ rearsegP(nil,X0)
| X0 = skaf52(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf52(X2))
| ~ rearsegP(X1,skaf52(X2))
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f2475,plain,
( ~ sQ247_spl
| ~ sQ11_spl
| sQ251_spl ),
inference(split_clause,[status(thm)],[f2453,f2472,f545,f2440]) ).
fof(f2478,definition,
! [X0,X1,X2] :
( sQ252_spl
<=> ( ~ ssList(skaf52(X2))
| ~ rearsegP(X1,skaf52(X2))
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f2481,plain,
( ~ sQ247_spl
| ~ sQ11_spl
| sQ252_spl ),
inference(split_clause,[status(thm)],[f2456,f2478,f545,f2440]) ).
fof(f2482,definition,
! [X0] :
( sQ253_spl
<=> ( ~ rearsegP(nil,skaf52(X0))
| nil = skaf52(X0)
| ~ ssList(skaf52(X0))
| ~ ssList(skaf52(X0))
| ~ rearsegP(nil,skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f2485,plain,
( ~ sQ247_spl
| ~ sQ11_spl
| sQ253_spl ),
inference(split_clause,[status(thm)],[f2457,f2482,f545,f2440]) ).
fof(f2486,definition,
! [X0,X1,X2] :
( sQ254_spl
<=> ( ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,skaf52(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f2489,plain,
( ~ sQ247_spl
| ~ sQ11_spl
| sQ254_spl ),
inference(split_clause,[status(thm)],[f2458,f2486,f545,f2440]) ).
fof(f2491,definition,
! [X0,X1,X2] :
( sQ255_spl
<=> ( ~ ssList(X2)
| ~ rearsegP(X2,skaf52(X1))
| ~ rearsegP(X0,X2)
| nil = skaf52(X1)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f2494,plain,
( ~ sQ247_spl
| ~ sQ11_spl
| sQ255_spl ),
inference(split_clause,[status(thm)],[f2460,f2491,f545,f2440]) ).
fof(f2495,definition,
! [X0,X1] :
( sQ256_spl
<=> ( nil = skaf52(X1)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ rearsegP(X0,skaf52(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f2498,plain,
( ~ sQ247_spl
| ~ sQ11_spl
| sQ256_spl ),
inference(split_clause,[status(thm)],[f2461,f2495,f545,f2440]) ).
fof(f2499,definition,
! [X0,X1] :
( sQ257_spl
<=> ( X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ rearsegP(X0,skaf52(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f2502,plain,
( ~ sQ247_spl
| ~ sQ11_spl
| sQ257_spl ),
inference(split_clause,[status(thm)],[f2462,f2499,f545,f2440]) ).
fof(f2503,definition,
! [X0] :
( sQ258_spl
<=> ( skaf52(X0) = nil
| ~ ssList(skaf52(X0))
| ~ rearsegP(nil,skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f2506,plain,
( ~ sQ247_spl
| ~ sQ11_spl
| sQ258_spl ),
inference(split_clause,[status(thm)],[f2463,f2503,f545,f2440]) ).
fof(f2509,plain,
! [X0] :
( ~ sQ184_spl
| ~ ssList(nil)
| rearsegP(skaf53(X0),nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1976,f257]) ).
fof(f2510,plain,
! [X0,X1,X2] :
( ~ sQ184_spl
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| rearsegP(skaf53(X1),X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1976,f376]) ).
fof(f2512,definition,
! [X0] :
( sQ259_spl
<=> rearsegP(skaf53(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f2513,plain,
! [X0] :
( ~ sQ259_spl
| rearsegP(skaf53(X0),nil) ),
inference(component_clause,[status(thm)],[f2512]) ).
fof(f2516,plain,
( ~ sQ184_spl
| sQ259_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2509,f545,f2512,f1955]) ).
fof(f2517,definition,
! [X0,X1,X2] :
( sQ260_spl
<=> ( ~ ssList(X2)
| ~ ssList(X0)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| rearsegP(skaf53(X1),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f2520,plain,
( ~ sQ184_spl
| ~ sQ11_spl
| sQ260_spl ),
inference(split_clause,[status(thm)],[f2510,f2517,f545,f1955]) ).
fof(f2523,plain,
! [X0,X1] :
( ~ sQ247_spl
| app(X0,skaf52(X1)) = nil
| ~ rearsegP(nil,app(X0,skaf52(X1)))
| ~ ssList(skaf52(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2172,f2441]) ).
fof(f2524,plain,
! [X0,X1] :
( ~ sQ235_spl
| app(X0,skaf51(X1)) = nil
| ~ rearsegP(nil,app(X0,skaf51(X1)))
| ~ ssList(skaf51(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2172,f2369]) ).
fof(f2525,plain,
! [X0] :
( ~ sQ90_spl
| app(X0,nil) = nil
| ~ rearsegP(nil,app(X0,nil))
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2172,f1266]) ).
fof(f2526,plain,
! [X0] :
( ~ sQ112_spl
| app(X0,sk1) = sk1
| ~ rearsegP(sk1,app(X0,sk1))
| ~ ssList(sk1)
| ~ ssList(sk1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2172,f1484]) ).
fof(f2527,plain,
! [X0] :
( ~ sQ64_spl
| app(X0,sk1) = nil
| ~ rearsegP(nil,app(X0,sk1))
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2172,f1077]) ).
fof(f2528,plain,
! [X0] :
( ~ sQ127_spl
| app(X0,sk2) = sk2
| ~ rearsegP(sk2,app(X0,sk2))
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2172,f1593]) ).
fof(f2529,plain,
! [X0] :
( ~ sQ78_spl
| app(X0,sk2) = nil
| ~ rearsegP(nil,app(X0,sk2))
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2172,f1170]) ).
fof(f2533,plain,
! [X0,X1] :
( ~ ssList(X1)
| app(X0,X1) = nil
| ~ rearsegP(nil,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2172,f257]) ).
fof(f2536,definition,
! [X0,X1] :
( sQ261_spl
<=> ( app(X0,skaf52(X1)) = nil
| ~ rearsegP(nil,app(X0,skaf52(X1)))
| ~ ssList(skaf52(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f2539,plain,
( ~ sQ247_spl
| ~ sQ11_spl
| sQ261_spl ),
inference(split_clause,[status(thm)],[f2523,f2536,f545,f2440]) ).
fof(f2540,definition,
! [X0,X1] :
( sQ262_spl
<=> ( app(X0,skaf51(X1)) = nil
| ~ rearsegP(nil,app(X0,skaf51(X1)))
| ~ ssList(skaf51(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f2543,plain,
( ~ sQ235_spl
| ~ sQ11_spl
| sQ262_spl ),
inference(split_clause,[status(thm)],[f2524,f2540,f545,f2368]) ).
fof(f2544,definition,
! [X0] :
( sQ263_spl
<=> ( app(X0,nil) = nil
| ~ rearsegP(nil,app(X0,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f2547,plain,
( ~ sQ90_spl
| ~ sQ11_spl
| sQ263_spl ),
inference(split_clause,[status(thm)],[f2525,f2544,f545,f1254]) ).
fof(f2548,definition,
! [X0] :
( sQ264_spl
<=> ( app(X0,sk1) = sk1
| ~ rearsegP(sk1,app(X0,sk1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f2549,plain,
! [X0] :
( ~ sQ264_spl
| app(X0,sk1) = sk1
| ~ rearsegP(sk1,app(X0,sk1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2548]) ).
fof(f2551,plain,
( ~ sQ112_spl
| ~ sQ13_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f2526,f2548,f558,f1469]) ).
fof(f2552,definition,
! [X0] :
( sQ265_spl
<=> ( app(X0,sk1) = nil
| ~ rearsegP(nil,app(X0,sk1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f2553,plain,
! [X0] :
( ~ sQ265_spl
| app(X0,sk1) = nil
| ~ rearsegP(nil,app(X0,sk1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2552]) ).
fof(f2555,plain,
( ~ sQ64_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sQ265_spl ),
inference(split_clause,[status(thm)],[f2527,f2552,f545,f558,f1065]) ).
fof(f2556,definition,
! [X0] :
( sQ266_spl
<=> ( app(X0,sk2) = sk2
| ~ rearsegP(sk2,app(X0,sk2))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f2557,plain,
! [X0] :
( ~ sQ266_spl
| app(X0,sk2) = sk2
| ~ rearsegP(sk2,app(X0,sk2))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2556]) ).
fof(f2559,plain,
( ~ sQ127_spl
| ~ sQ16_spl
| sQ266_spl ),
inference(split_clause,[status(thm)],[f2528,f2556,f587,f1578]) ).
fof(f2560,definition,
! [X0] :
( sQ267_spl
<=> ( app(X0,sk2) = nil
| ~ rearsegP(nil,app(X0,sk2))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f2561,plain,
! [X0] :
( ~ sQ267_spl
| app(X0,sk2) = nil
| ~ rearsegP(nil,app(X0,sk2))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2560]) ).
fof(f2563,plain,
( ~ sQ78_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sQ267_spl ),
inference(split_clause,[status(thm)],[f2529,f2560,f545,f587,f1158]) ).
fof(f2572,definition,
! [X0,X1] :
( sQ269_spl
<=> ( ~ ssList(X1)
| app(X0,X1) = nil
| ~ rearsegP(nil,app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f2575,plain,
( ~ sQ11_spl
| sQ269_spl ),
inference(split_clause,[status(thm)],[f2533,f2572,f545]) ).
fof(f2583,plain,
! [X0,X1] :
( segmentP(app(skaf58(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf58(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1025,f2205]) ).
fof(f2584,plain,
! [X0,X1] :
( segmentP(app(skaf57(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf57(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1024,f2205]) ).
fof(f2585,plain,
! [X0,X1] :
( segmentP(app(skaf56(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf56(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1023,f2205]) ).
fof(f2586,plain,
! [X0,X1] :
( segmentP(app(skaf53(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf53(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1022,f2205]) ).
fof(f2587,plain,
! [X0,X1] :
( segmentP(app(skaf52(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf52(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1021,f2205]) ).
fof(f2588,plain,
! [X0,X1] :
( segmentP(app(skaf51(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf51(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1020,f2205]) ).
fof(f2591,plain,
! [X0] :
( segmentP(app(nil,X0),nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1042,f2205]) ).
fof(f2596,definition,
! [X0,X1] :
( sQ270_spl
<=> ( segmentP(app(skaf58(X1),X0),nil)
| ~ ssList(skaf58(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f2597,plain,
! [X0,X1] :
( ~ sQ270_spl
| segmentP(app(skaf58(X1),X0),nil)
| ~ ssList(skaf58(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2596]) ).
fof(f2599,plain,
( ~ sQ11_spl
| sQ270_spl ),
inference(split_clause,[status(thm)],[f2583,f2596,f545]) ).
fof(f2600,definition,
! [X0,X1] :
( sQ271_spl
<=> ( segmentP(app(skaf57(X1),X0),nil)
| ~ ssList(skaf57(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f2601,plain,
! [X0,X1] :
( ~ sQ271_spl
| segmentP(app(skaf57(X1),X0),nil)
| ~ ssList(skaf57(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2600]) ).
fof(f2603,plain,
( ~ sQ11_spl
| sQ271_spl ),
inference(split_clause,[status(thm)],[f2584,f2600,f545]) ).
fof(f2604,definition,
! [X0,X1] :
( sQ272_spl
<=> ( segmentP(app(skaf56(X1),X0),nil)
| ~ ssList(skaf56(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f2605,plain,
! [X0,X1] :
( ~ sQ272_spl
| segmentP(app(skaf56(X1),X0),nil)
| ~ ssList(skaf56(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2604]) ).
fof(f2607,plain,
( ~ sQ11_spl
| sQ272_spl ),
inference(split_clause,[status(thm)],[f2585,f2604,f545]) ).
fof(f2608,definition,
! [X0,X1] :
( sQ273_spl
<=> ( segmentP(app(skaf53(X1),X0),nil)
| ~ ssList(skaf53(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f2609,plain,
! [X0,X1] :
( ~ sQ273_spl
| segmentP(app(skaf53(X1),X0),nil)
| ~ ssList(skaf53(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2608]) ).
fof(f2611,plain,
( ~ sQ11_spl
| sQ273_spl ),
inference(split_clause,[status(thm)],[f2586,f2608,f545]) ).
fof(f2612,definition,
! [X0,X1] :
( sQ274_spl
<=> ( segmentP(app(skaf52(X1),X0),nil)
| ~ ssList(skaf52(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f2613,plain,
! [X0,X1] :
( ~ sQ274_spl
| segmentP(app(skaf52(X1),X0),nil)
| ~ ssList(skaf52(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2612]) ).
fof(f2615,plain,
( ~ sQ11_spl
| sQ274_spl ),
inference(split_clause,[status(thm)],[f2587,f2612,f545]) ).
fof(f2616,definition,
! [X0,X1] :
( sQ275_spl
<=> ( segmentP(app(skaf51(X1),X0),nil)
| ~ ssList(skaf51(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f2617,plain,
! [X0,X1] :
( ~ sQ275_spl
| segmentP(app(skaf51(X1),X0),nil)
| ~ ssList(skaf51(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2616]) ).
fof(f2619,plain,
( ~ sQ11_spl
| sQ275_spl ),
inference(split_clause,[status(thm)],[f2588,f2616,f545]) ).
fof(f2620,definition,
! [X0] :
( sQ276_spl
<=> ( segmentP(app(sk2,X0),sk2)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f2621,plain,
! [X0] :
( ~ sQ276_spl
| segmentP(app(sk2,X0),sk2)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2620]) ).
fof(f2624,definition,
! [X0] :
( sQ277_spl
<=> ( segmentP(app(sk1,X0),sk1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f2628,definition,
! [X0] :
( sQ278_spl
<=> ( segmentP(app(nil,X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f2629,plain,
! [X0] :
( ~ sQ278_spl
| segmentP(app(nil,X0),nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2628]) ).
fof(f2631,plain,
( ~ sQ11_spl
| sQ278_spl ),
inference(split_clause,[status(thm)],[f2591,f2628,f545]) ).
fof(f2634,plain,
! [X0,X1] :
( ~ sQ270_spl
| segmentP(app(skaf58(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2597,f236]) ).
fof(f2635,plain,
! [X0,X1] :
( ~ sQ271_spl
| segmentP(app(skaf57(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2601,f237]) ).
fof(f2636,plain,
! [X0,X1] :
( ~ sQ272_spl
| segmentP(app(skaf56(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2605,f238]) ).
fof(f2637,plain,
! [X0,X1] :
( ~ sQ273_spl
| segmentP(app(skaf53(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2609,f241]) ).
fof(f2638,plain,
! [X0,X1] :
( ~ sQ274_spl
| segmentP(app(skaf52(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2613,f242]) ).
fof(f2639,plain,
! [X0,X1] :
( ~ sQ275_spl
| segmentP(app(skaf51(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2617,f243]) ).
fof(f2640,plain,
! [X0,X1] :
( ~ sQ259_spl
| app(X0,skaf53(X1)) = nil
| ~ rearsegP(nil,app(X0,skaf53(X1)))
| ~ ssList(skaf53(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2513,f2172]) ).
fof(f2642,plain,
! [X0,X1,X2] :
( ~ sQ259_spl
| ~ ssList(skaf53(X2))
| ~ rearsegP(X1,skaf53(X2))
| nil = X1
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f2513,f764]) ).
fof(f2643,plain,
! [X0,X1,X2] :
( ~ sQ259_spl
| ~ ssList(nil)
| ~ rearsegP(nil,X0)
| X0 = skaf53(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf53(X2))
| ~ rearsegP(X1,skaf53(X2))
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f2513,f764]) ).
fof(f2646,plain,
! [X0,X1,X2] :
( ~ sQ259_spl
| ~ ssList(skaf53(X2))
| ~ rearsegP(X1,skaf53(X2))
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f2513,f759]) ).
fof(f2647,plain,
! [X0] :
( ~ sQ259_spl
| ~ ssList(nil)
| ~ rearsegP(nil,skaf53(X0))
| nil = skaf53(X0)
| ~ ssList(nil)
| ~ ssList(skaf53(X0))
| ~ ssList(skaf53(X0))
| ~ rearsegP(nil,skaf53(X0)) ),
inference(resolution,[status(thm)],[f2513,f759]) ).
fof(f2648,plain,
! [X0,X1,X2] :
( ~ sQ259_spl
| ~ ssList(nil)
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,skaf53(X1)) ),
inference(resolution,[status(thm)],[f2513,f759]) ).
fof(f2650,plain,
! [X0,X1,X2] :
( ~ sQ259_spl
| ~ ssList(X2)
| ~ rearsegP(X2,skaf53(X1))
| ~ rearsegP(X0,X2)
| nil = skaf53(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f2513,f759]) ).
fof(f2651,plain,
! [X0,X1] :
( ~ sQ259_spl
| nil = skaf53(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ rearsegP(X0,skaf53(X1))
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f2513,f629]) ).
fof(f2652,plain,
! [X0,X1] :
( ~ sQ259_spl
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ ssList(nil)
| ~ rearsegP(X0,skaf53(X1)) ),
inference(resolution,[status(thm)],[f2513,f629]) ).
fof(f2653,plain,
! [X0] :
( ~ sQ259_spl
| skaf53(X0) = nil
| ~ ssList(skaf53(X0))
| ~ ssList(nil)
| ~ rearsegP(nil,skaf53(X0)) ),
inference(resolution,[status(thm)],[f2513,f340]) ).
fof(f2654,definition,
! [X0,X1] :
( sQ279_spl
<=> ( app(X0,skaf53(X1)) = nil
| ~ rearsegP(nil,app(X0,skaf53(X1)))
| ~ ssList(skaf53(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f2657,plain,
( ~ sQ259_spl
| ~ sQ11_spl
| sQ279_spl ),
inference(split_clause,[status(thm)],[f2640,f2654,f545,f2512]) ).
fof(f2662,definition,
! [X0,X1,X2] :
( sQ281_spl
<=> ( ~ ssList(skaf53(X2))
| ~ rearsegP(X1,skaf53(X2))
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f2665,plain,
( ~ sQ259_spl
| ~ sQ11_spl
| sQ281_spl ),
inference(split_clause,[status(thm)],[f2642,f2662,f545,f2512]) ).
fof(f2666,definition,
! [X0,X1,X2] :
( sQ282_spl
<=> ( ~ rearsegP(nil,X0)
| X0 = skaf53(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf53(X2))
| ~ rearsegP(X1,skaf53(X2))
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f2669,plain,
( ~ sQ259_spl
| ~ sQ11_spl
| sQ282_spl ),
inference(split_clause,[status(thm)],[f2643,f2666,f545,f2512]) ).
fof(f2672,definition,
! [X0,X1,X2] :
( sQ283_spl
<=> ( ~ ssList(skaf53(X2))
| ~ rearsegP(X1,skaf53(X2))
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f2675,plain,
( ~ sQ259_spl
| ~ sQ11_spl
| sQ283_spl ),
inference(split_clause,[status(thm)],[f2646,f2672,f545,f2512]) ).
fof(f2676,definition,
! [X0] :
( sQ284_spl
<=> ( ~ rearsegP(nil,skaf53(X0))
| nil = skaf53(X0)
| ~ ssList(skaf53(X0))
| ~ ssList(skaf53(X0))
| ~ rearsegP(nil,skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f2679,plain,
( ~ sQ259_spl
| ~ sQ11_spl
| sQ284_spl ),
inference(split_clause,[status(thm)],[f2647,f2676,f545,f2512]) ).
fof(f2680,definition,
! [X0,X1,X2] :
( sQ285_spl
<=> ( ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,skaf53(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f2683,plain,
( ~ sQ259_spl
| ~ sQ11_spl
| sQ285_spl ),
inference(split_clause,[status(thm)],[f2648,f2680,f545,f2512]) ).
fof(f2685,definition,
! [X0,X1,X2] :
( sQ286_spl
<=> ( ~ ssList(X2)
| ~ rearsegP(X2,skaf53(X1))
| ~ rearsegP(X0,X2)
| nil = skaf53(X1)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f2688,plain,
( ~ sQ259_spl
| ~ sQ11_spl
| sQ286_spl ),
inference(split_clause,[status(thm)],[f2650,f2685,f545,f2512]) ).
fof(f2689,definition,
! [X0,X1] :
( sQ287_spl
<=> ( nil = skaf53(X1)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ rearsegP(X0,skaf53(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f2692,plain,
( ~ sQ259_spl
| ~ sQ11_spl
| sQ287_spl ),
inference(split_clause,[status(thm)],[f2651,f2689,f545,f2512]) ).
fof(f2693,definition,
! [X0,X1] :
( sQ288_spl
<=> ( X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ rearsegP(X0,skaf53(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f2696,plain,
( ~ sQ259_spl
| ~ sQ11_spl
| sQ288_spl ),
inference(split_clause,[status(thm)],[f2652,f2693,f545,f2512]) ).
fof(f2697,definition,
! [X0] :
( sQ289_spl
<=> ( skaf53(X0) = nil
| ~ ssList(skaf53(X0))
| ~ rearsegP(nil,skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f2700,plain,
( ~ sQ259_spl
| ~ sQ11_spl
| sQ289_spl ),
inference(split_clause,[status(thm)],[f2653,f2697,f545,f2512]) ).
fof(f2703,plain,
! [X0,X1] :
( segmentP(app(skaf61(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf61(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1026,f2205]) ).
fof(f2704,plain,
! [X0] :
( rearsegP(skaf61(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf61(X0)) ),
inference(paramodulation,[status(thm)],[f1026,f2173]) ).
fof(f2705,plain,
! [X0] :
( ssList(skaf61(X0))
| ~ ssList(skaf61(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1026,f285]) ).
fof(f2706,plain,
! [X0,X1,X2] :
( app(app(skaf61(X2),nil),X1) = X0
| ~ ssList(app(skaf61(X2),X1))
| ~ segmentP(X0,app(app(skaf61(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf61(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1026,f666]) ).
fof(f2707,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf61(X2),X1))
| ~ segmentP(X3,app(app(skaf61(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf61(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1026,f665]) ).
fof(f2708,plain,
! [X0,X1,X2] :
( segmentP(app(skaf61(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf61(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1026,f404]) ).
fof(f2709,plain,
! [X0,X1] :
( rearsegP(skaf61(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf61(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1026,f350]) ).
fof(f2710,definition,
! [X0,X1] :
( sQ290_spl
<=> ( segmentP(app(skaf61(X1),X0),nil)
| ~ ssList(skaf61(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f2711,plain,
! [X0,X1] :
( ~ sQ290_spl
| segmentP(app(skaf61(X1),X0),nil)
| ~ ssList(skaf61(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2710]) ).
fof(f2713,plain,
( ~ sQ11_spl
| sQ290_spl ),
inference(split_clause,[status(thm)],[f2703,f2710,f545]) ).
fof(f2714,definition,
! [X0] :
( sQ291_spl
<=> ( rearsegP(skaf61(X0),nil)
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f2717,plain,
( ~ sQ11_spl
| sQ291_spl ),
inference(split_clause,[status(thm)],[f2704,f2714,f545]) ).
fof(f2718,definition,
! [X0] :
( sQ292_spl
<=> ( ssList(skaf61(X0))
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f2721,plain,
( sQ292_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2705,f545,f2718]) ).
fof(f2722,definition,
! [X0,X1,X2] :
( sQ293_spl
<=> ( app(app(skaf61(X2),nil),X1) = X0
| ~ ssList(app(skaf61(X2),X1))
| ~ segmentP(X0,app(app(skaf61(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf61(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f2725,plain,
( ~ sQ11_spl
| sQ293_spl ),
inference(split_clause,[status(thm)],[f2706,f2722,f545]) ).
fof(f2726,definition,
! [X0,X1,X2,X3] :
( sQ294_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf61(X2),X1))
| ~ segmentP(X3,app(app(skaf61(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf61(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f2729,plain,
( ~ sQ11_spl
| sQ294_spl ),
inference(split_clause,[status(thm)],[f2707,f2726,f545]) ).
fof(f2730,definition,
! [X0,X1,X2] :
( sQ295_spl
<=> ( segmentP(app(skaf61(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf61(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f2733,plain,
( ~ sQ11_spl
| sQ295_spl ),
inference(split_clause,[status(thm)],[f2708,f2730,f545]) ).
fof(f2734,definition,
! [X0,X1] :
( sQ296_spl
<=> ( rearsegP(skaf61(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf61(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f2737,plain,
( ~ sQ11_spl
| sQ296_spl ),
inference(split_clause,[status(thm)],[f2709,f2734,f545]) ).
fof(f2738,plain,
! [X0,X1] :
( ~ sQ290_spl
| segmentP(app(skaf61(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2711,f233]) ).
fof(f2746,plain,
! [X0,X1] :
( segmentP(app(skaf62(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf62(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1027,f2205]) ).
fof(f2747,plain,
! [X0] :
( rearsegP(skaf62(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf62(X0)) ),
inference(paramodulation,[status(thm)],[f1027,f2173]) ).
fof(f2748,plain,
! [X0] :
( ssList(skaf62(X0))
| ~ ssList(skaf62(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1027,f285]) ).
fof(f2749,plain,
! [X0,X1,X2] :
( app(app(skaf62(X2),nil),X1) = X0
| ~ ssList(app(skaf62(X2),X1))
| ~ segmentP(X0,app(app(skaf62(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf62(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1027,f666]) ).
fof(f2750,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf62(X2),X1))
| ~ segmentP(X3,app(app(skaf62(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf62(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1027,f665]) ).
fof(f2751,plain,
! [X0,X1,X2] :
( segmentP(app(skaf62(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf62(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1027,f404]) ).
fof(f2752,plain,
! [X0,X1] :
( rearsegP(skaf62(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf62(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1027,f350]) ).
fof(f2753,definition,
! [X0,X1] :
( sQ297_spl
<=> ( segmentP(app(skaf62(X1),X0),nil)
| ~ ssList(skaf62(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f2754,plain,
! [X0,X1] :
( ~ sQ297_spl
| segmentP(app(skaf62(X1),X0),nil)
| ~ ssList(skaf62(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2753]) ).
fof(f2756,plain,
( ~ sQ11_spl
| sQ297_spl ),
inference(split_clause,[status(thm)],[f2746,f2753,f545]) ).
fof(f2757,definition,
! [X0] :
( sQ298_spl
<=> ( rearsegP(skaf62(X0),nil)
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f2760,plain,
( ~ sQ11_spl
| sQ298_spl ),
inference(split_clause,[status(thm)],[f2747,f2757,f545]) ).
fof(f2761,definition,
! [X0] :
( sQ299_spl
<=> ( ssList(skaf62(X0))
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f2764,plain,
( sQ299_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2748,f545,f2761]) ).
fof(f2765,definition,
! [X0,X1,X2] :
( sQ300_spl
<=> ( app(app(skaf62(X2),nil),X1) = X0
| ~ ssList(app(skaf62(X2),X1))
| ~ segmentP(X0,app(app(skaf62(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf62(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f2768,plain,
( ~ sQ11_spl
| sQ300_spl ),
inference(split_clause,[status(thm)],[f2749,f2765,f545]) ).
fof(f2769,definition,
! [X0,X1,X2,X3] :
( sQ301_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf62(X2),X1))
| ~ segmentP(X3,app(app(skaf62(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf62(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ301_spl])],[split_symbol_definition]) ).
fof(f2772,plain,
( ~ sQ11_spl
| sQ301_spl ),
inference(split_clause,[status(thm)],[f2750,f2769,f545]) ).
fof(f2773,definition,
! [X0,X1,X2] :
( sQ302_spl
<=> ( segmentP(app(skaf62(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf62(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f2776,plain,
( ~ sQ11_spl
| sQ302_spl ),
inference(split_clause,[status(thm)],[f2751,f2773,f545]) ).
fof(f2777,definition,
! [X0,X1] :
( sQ303_spl
<=> ( rearsegP(skaf62(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf62(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f2780,plain,
( ~ sQ11_spl
| sQ303_spl ),
inference(split_clause,[status(thm)],[f2752,f2777,f545]) ).
fof(f2781,plain,
! [X0,X1] :
( ~ sQ297_spl
| segmentP(app(skaf62(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2754,f232]) ).
fof(f2789,plain,
! [X0,X1] :
( segmentP(app(skaf63(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf63(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1028,f2205]) ).
fof(f2790,plain,
! [X0] :
( rearsegP(skaf63(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf63(X0)) ),
inference(paramodulation,[status(thm)],[f1028,f2173]) ).
fof(f2791,plain,
! [X0] :
( ssList(skaf63(X0))
| ~ ssList(skaf63(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1028,f285]) ).
fof(f2792,plain,
! [X0,X1,X2] :
( app(app(skaf63(X2),nil),X1) = X0
| ~ ssList(app(skaf63(X2),X1))
| ~ segmentP(X0,app(app(skaf63(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf63(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1028,f666]) ).
fof(f2793,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf63(X2),X1))
| ~ segmentP(X3,app(app(skaf63(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf63(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1028,f665]) ).
fof(f2794,plain,
! [X0,X1,X2] :
( segmentP(app(skaf63(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf63(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1028,f404]) ).
fof(f2795,plain,
! [X0,X1] :
( rearsegP(skaf63(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf63(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1028,f350]) ).
fof(f2796,definition,
! [X0,X1] :
( sQ304_spl
<=> ( segmentP(app(skaf63(X1),X0),nil)
| ~ ssList(skaf63(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f2797,plain,
! [X0,X1] :
( ~ sQ304_spl
| segmentP(app(skaf63(X1),X0),nil)
| ~ ssList(skaf63(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2796]) ).
fof(f2799,plain,
( ~ sQ11_spl
| sQ304_spl ),
inference(split_clause,[status(thm)],[f2789,f2796,f545]) ).
fof(f2800,definition,
! [X0] :
( sQ305_spl
<=> ( rearsegP(skaf63(X0),nil)
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f2803,plain,
( ~ sQ11_spl
| sQ305_spl ),
inference(split_clause,[status(thm)],[f2790,f2800,f545]) ).
fof(f2804,definition,
! [X0] :
( sQ306_spl
<=> ( ssList(skaf63(X0))
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f2807,plain,
( sQ306_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2791,f545,f2804]) ).
fof(f2808,definition,
! [X0,X1,X2] :
( sQ307_spl
<=> ( app(app(skaf63(X2),nil),X1) = X0
| ~ ssList(app(skaf63(X2),X1))
| ~ segmentP(X0,app(app(skaf63(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf63(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f2811,plain,
( ~ sQ11_spl
| sQ307_spl ),
inference(split_clause,[status(thm)],[f2792,f2808,f545]) ).
fof(f2812,definition,
! [X0,X1,X2,X3] :
( sQ308_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf63(X2),X1))
| ~ segmentP(X3,app(app(skaf63(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf63(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ308_spl])],[split_symbol_definition]) ).
fof(f2815,plain,
( ~ sQ11_spl
| sQ308_spl ),
inference(split_clause,[status(thm)],[f2793,f2812,f545]) ).
fof(f2816,definition,
! [X0,X1,X2] :
( sQ309_spl
<=> ( segmentP(app(skaf63(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf63(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ309_spl])],[split_symbol_definition]) ).
fof(f2819,plain,
( ~ sQ11_spl
| sQ309_spl ),
inference(split_clause,[status(thm)],[f2794,f2816,f545]) ).
fof(f2820,definition,
! [X0,X1] :
( sQ310_spl
<=> ( rearsegP(skaf63(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf63(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f2823,plain,
( ~ sQ11_spl
| sQ310_spl ),
inference(split_clause,[status(thm)],[f2795,f2820,f545]) ).
fof(f2824,plain,
! [X0,X1] :
( ~ sQ304_spl
| segmentP(app(skaf63(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2797,f231]) ).
fof(f2832,plain,
! [X0,X1] :
( segmentP(app(skaf66(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf66(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1030,f2205]) ).
fof(f2833,plain,
! [X0] :
( rearsegP(skaf66(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf66(X0)) ),
inference(paramodulation,[status(thm)],[f1030,f2173]) ).
fof(f2834,plain,
! [X0] :
( ssList(skaf66(X0))
| ~ ssList(skaf66(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1030,f285]) ).
fof(f2835,plain,
! [X0,X1,X2] :
( app(app(skaf66(X2),nil),X1) = X0
| ~ ssList(app(skaf66(X2),X1))
| ~ segmentP(X0,app(app(skaf66(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf66(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1030,f666]) ).
fof(f2836,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf66(X2),X1))
| ~ segmentP(X3,app(app(skaf66(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf66(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1030,f665]) ).
fof(f2837,plain,
! [X0,X1,X2] :
( segmentP(app(skaf66(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf66(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1030,f404]) ).
fof(f2838,plain,
! [X0,X1] :
( rearsegP(skaf66(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf66(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1030,f350]) ).
fof(f2839,definition,
! [X0,X1] :
( sQ311_spl
<=> ( segmentP(app(skaf66(X1),X0),nil)
| ~ ssList(skaf66(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f2840,plain,
! [X0,X1] :
( ~ sQ311_spl
| segmentP(app(skaf66(X1),X0),nil)
| ~ ssList(skaf66(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2839]) ).
fof(f2842,plain,
( ~ sQ11_spl
| sQ311_spl ),
inference(split_clause,[status(thm)],[f2832,f2839,f545]) ).
fof(f2843,definition,
! [X0] :
( sQ312_spl
<=> ( rearsegP(skaf66(X0),nil)
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ312_spl])],[split_symbol_definition]) ).
fof(f2846,plain,
( ~ sQ11_spl
| sQ312_spl ),
inference(split_clause,[status(thm)],[f2833,f2843,f545]) ).
fof(f2847,definition,
! [X0] :
( sQ313_spl
<=> ( ssList(skaf66(X0))
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ313_spl])],[split_symbol_definition]) ).
fof(f2850,plain,
( sQ313_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2834,f545,f2847]) ).
fof(f2851,definition,
! [X0,X1,X2] :
( sQ314_spl
<=> ( app(app(skaf66(X2),nil),X1) = X0
| ~ ssList(app(skaf66(X2),X1))
| ~ segmentP(X0,app(app(skaf66(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf66(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ314_spl])],[split_symbol_definition]) ).
fof(f2854,plain,
( ~ sQ11_spl
| sQ314_spl ),
inference(split_clause,[status(thm)],[f2835,f2851,f545]) ).
fof(f2855,definition,
! [X0,X1,X2,X3] :
( sQ315_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf66(X2),X1))
| ~ segmentP(X3,app(app(skaf66(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf66(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ315_spl])],[split_symbol_definition]) ).
fof(f2858,plain,
( ~ sQ11_spl
| sQ315_spl ),
inference(split_clause,[status(thm)],[f2836,f2855,f545]) ).
fof(f2859,definition,
! [X0,X1,X2] :
( sQ316_spl
<=> ( segmentP(app(skaf66(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf66(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ316_spl])],[split_symbol_definition]) ).
fof(f2862,plain,
( ~ sQ11_spl
| sQ316_spl ),
inference(split_clause,[status(thm)],[f2837,f2859,f545]) ).
fof(f2863,definition,
! [X0,X1] :
( sQ317_spl
<=> ( rearsegP(skaf66(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf66(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ317_spl])],[split_symbol_definition]) ).
fof(f2866,plain,
( ~ sQ11_spl
| sQ317_spl ),
inference(split_clause,[status(thm)],[f2838,f2863,f545]) ).
fof(f2867,plain,
! [X0,X1] :
( ~ sQ311_spl
| segmentP(app(skaf66(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2840,f228]) ).
fof(f2875,plain,
! [X0,X1] :
( segmentP(app(skaf67(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf67(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1031,f2205]) ).
fof(f2876,plain,
! [X0] :
( rearsegP(skaf67(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf67(X0)) ),
inference(paramodulation,[status(thm)],[f1031,f2173]) ).
fof(f2877,plain,
! [X0] :
( ssList(skaf67(X0))
| ~ ssList(skaf67(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1031,f285]) ).
fof(f2878,plain,
! [X0,X1,X2] :
( app(app(skaf67(X2),nil),X1) = X0
| ~ ssList(app(skaf67(X2),X1))
| ~ segmentP(X0,app(app(skaf67(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf67(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1031,f666]) ).
fof(f2879,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf67(X2),X1))
| ~ segmentP(X3,app(app(skaf67(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf67(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1031,f665]) ).
fof(f2880,plain,
! [X0,X1,X2] :
( segmentP(app(skaf67(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf67(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1031,f404]) ).
fof(f2881,plain,
! [X0,X1] :
( rearsegP(skaf67(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf67(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1031,f350]) ).
fof(f2882,definition,
! [X0,X1] :
( sQ318_spl
<=> ( segmentP(app(skaf67(X1),X0),nil)
| ~ ssList(skaf67(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ318_spl])],[split_symbol_definition]) ).
fof(f2883,plain,
! [X0,X1] :
( ~ sQ318_spl
| segmentP(app(skaf67(X1),X0),nil)
| ~ ssList(skaf67(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2882]) ).
fof(f2885,plain,
( ~ sQ11_spl
| sQ318_spl ),
inference(split_clause,[status(thm)],[f2875,f2882,f545]) ).
fof(f2886,definition,
! [X0] :
( sQ319_spl
<=> ( rearsegP(skaf67(X0),nil)
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ319_spl])],[split_symbol_definition]) ).
fof(f2889,plain,
( ~ sQ11_spl
| sQ319_spl ),
inference(split_clause,[status(thm)],[f2876,f2886,f545]) ).
fof(f2890,definition,
! [X0] :
( sQ320_spl
<=> ( ssList(skaf67(X0))
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f2893,plain,
( sQ320_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2877,f545,f2890]) ).
fof(f2894,definition,
! [X0,X1,X2] :
( sQ321_spl
<=> ( app(app(skaf67(X2),nil),X1) = X0
| ~ ssList(app(skaf67(X2),X1))
| ~ segmentP(X0,app(app(skaf67(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf67(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ321_spl])],[split_symbol_definition]) ).
fof(f2897,plain,
( ~ sQ11_spl
| sQ321_spl ),
inference(split_clause,[status(thm)],[f2878,f2894,f545]) ).
fof(f2898,definition,
! [X0,X1,X2,X3] :
( sQ322_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf67(X2),X1))
| ~ segmentP(X3,app(app(skaf67(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf67(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ322_spl])],[split_symbol_definition]) ).
fof(f2901,plain,
( ~ sQ11_spl
| sQ322_spl ),
inference(split_clause,[status(thm)],[f2879,f2898,f545]) ).
fof(f2902,definition,
! [X0,X1,X2] :
( sQ323_spl
<=> ( segmentP(app(skaf67(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf67(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ323_spl])],[split_symbol_definition]) ).
fof(f2905,plain,
( ~ sQ11_spl
| sQ323_spl ),
inference(split_clause,[status(thm)],[f2880,f2902,f545]) ).
fof(f2906,definition,
! [X0,X1] :
( sQ324_spl
<=> ( rearsegP(skaf67(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf67(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ324_spl])],[split_symbol_definition]) ).
fof(f2909,plain,
( ~ sQ11_spl
| sQ324_spl ),
inference(split_clause,[status(thm)],[f2881,f2906,f545]) ).
fof(f2910,plain,
! [X0,X1] :
( ~ sQ318_spl
| segmentP(app(skaf67(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2883,f227]) ).
fof(f2918,plain,
! [X0,X1] :
( segmentP(app(skaf68(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf68(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1032,f2205]) ).
fof(f2919,plain,
! [X0] :
( rearsegP(skaf68(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf68(X0)) ),
inference(paramodulation,[status(thm)],[f1032,f2173]) ).
fof(f2920,plain,
! [X0] :
( ssList(skaf68(X0))
| ~ ssList(skaf68(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1032,f285]) ).
fof(f2921,plain,
! [X0,X1,X2] :
( app(app(skaf68(X2),nil),X1) = X0
| ~ ssList(app(skaf68(X2),X1))
| ~ segmentP(X0,app(app(skaf68(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf68(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1032,f666]) ).
fof(f2922,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf68(X2),X1))
| ~ segmentP(X3,app(app(skaf68(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf68(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1032,f665]) ).
fof(f2923,plain,
! [X0,X1,X2] :
( segmentP(app(skaf68(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf68(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1032,f404]) ).
fof(f2924,plain,
! [X0,X1] :
( rearsegP(skaf68(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf68(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1032,f350]) ).
fof(f2925,definition,
! [X0,X1] :
( sQ325_spl
<=> ( segmentP(app(skaf68(X1),X0),nil)
| ~ ssList(skaf68(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ325_spl])],[split_symbol_definition]) ).
fof(f2926,plain,
! [X0,X1] :
( ~ sQ325_spl
| segmentP(app(skaf68(X1),X0),nil)
| ~ ssList(skaf68(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2925]) ).
fof(f2928,plain,
( ~ sQ11_spl
| sQ325_spl ),
inference(split_clause,[status(thm)],[f2918,f2925,f545]) ).
fof(f2929,definition,
! [X0] :
( sQ326_spl
<=> ( rearsegP(skaf68(X0),nil)
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ326_spl])],[split_symbol_definition]) ).
fof(f2932,plain,
( ~ sQ11_spl
| sQ326_spl ),
inference(split_clause,[status(thm)],[f2919,f2929,f545]) ).
fof(f2933,definition,
! [X0] :
( sQ327_spl
<=> ( ssList(skaf68(X0))
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition]) ).
fof(f2936,plain,
( sQ327_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2920,f545,f2933]) ).
fof(f2937,definition,
! [X0,X1,X2] :
( sQ328_spl
<=> ( app(app(skaf68(X2),nil),X1) = X0
| ~ ssList(app(skaf68(X2),X1))
| ~ segmentP(X0,app(app(skaf68(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf68(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f2940,plain,
( ~ sQ11_spl
| sQ328_spl ),
inference(split_clause,[status(thm)],[f2921,f2937,f545]) ).
fof(f2941,definition,
! [X0,X1,X2,X3] :
( sQ329_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf68(X2),X1))
| ~ segmentP(X3,app(app(skaf68(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf68(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f2944,plain,
( ~ sQ11_spl
| sQ329_spl ),
inference(split_clause,[status(thm)],[f2922,f2941,f545]) ).
fof(f2945,definition,
! [X0,X1,X2] :
( sQ330_spl
<=> ( segmentP(app(skaf68(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf68(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f2948,plain,
( ~ sQ11_spl
| sQ330_spl ),
inference(split_clause,[status(thm)],[f2923,f2945,f545]) ).
fof(f2949,definition,
! [X0,X1] :
( sQ331_spl
<=> ( rearsegP(skaf68(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf68(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f2952,plain,
( ~ sQ11_spl
| sQ331_spl ),
inference(split_clause,[status(thm)],[f2924,f2949,f545]) ).
fof(f2953,plain,
! [X0,X1] :
( ~ sQ325_spl
| segmentP(app(skaf68(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2926,f226]) ).
fof(f2961,plain,
! [X0,X1] :
( segmentP(app(skaf71(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf71(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1033,f2205]) ).
fof(f2962,plain,
! [X0] :
( rearsegP(skaf71(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf71(X0)) ),
inference(paramodulation,[status(thm)],[f1033,f2173]) ).
fof(f2963,plain,
! [X0] :
( ssList(skaf71(X0))
| ~ ssList(skaf71(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1033,f285]) ).
fof(f2964,plain,
! [X0,X1,X2] :
( app(app(skaf71(X2),nil),X1) = X0
| ~ ssList(app(skaf71(X2),X1))
| ~ segmentP(X0,app(app(skaf71(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf71(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1033,f666]) ).
fof(f2965,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf71(X2),X1))
| ~ segmentP(X3,app(app(skaf71(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf71(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1033,f665]) ).
fof(f2966,plain,
! [X0,X1,X2] :
( segmentP(app(skaf71(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf71(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1033,f404]) ).
fof(f2967,plain,
! [X0,X1] :
( rearsegP(skaf71(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf71(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1033,f350]) ).
fof(f2968,definition,
! [X0,X1] :
( sQ332_spl
<=> ( segmentP(app(skaf71(X1),X0),nil)
| ~ ssList(skaf71(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f2969,plain,
! [X0,X1] :
( ~ sQ332_spl
| segmentP(app(skaf71(X1),X0),nil)
| ~ ssList(skaf71(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2968]) ).
fof(f2971,plain,
( ~ sQ11_spl
| sQ332_spl ),
inference(split_clause,[status(thm)],[f2961,f2968,f545]) ).
fof(f2972,definition,
! [X0] :
( sQ333_spl
<=> ( rearsegP(skaf71(X0),nil)
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f2975,plain,
( ~ sQ11_spl
| sQ333_spl ),
inference(split_clause,[status(thm)],[f2962,f2972,f545]) ).
fof(f2976,definition,
! [X0] :
( sQ334_spl
<=> ( ssList(skaf71(X0))
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f2979,plain,
( sQ334_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2963,f545,f2976]) ).
fof(f2980,definition,
! [X0,X1,X2] :
( sQ335_spl
<=> ( app(app(skaf71(X2),nil),X1) = X0
| ~ ssList(app(skaf71(X2),X1))
| ~ segmentP(X0,app(app(skaf71(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf71(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f2983,plain,
( ~ sQ11_spl
| sQ335_spl ),
inference(split_clause,[status(thm)],[f2964,f2980,f545]) ).
fof(f2984,definition,
! [X0,X1,X2,X3] :
( sQ336_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf71(X2),X1))
| ~ segmentP(X3,app(app(skaf71(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf71(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f2987,plain,
( ~ sQ11_spl
| sQ336_spl ),
inference(split_clause,[status(thm)],[f2965,f2984,f545]) ).
fof(f2988,definition,
! [X0,X1,X2] :
( sQ337_spl
<=> ( segmentP(app(skaf71(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf71(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f2991,plain,
( ~ sQ11_spl
| sQ337_spl ),
inference(split_clause,[status(thm)],[f2966,f2988,f545]) ).
fof(f2992,definition,
! [X0,X1] :
( sQ338_spl
<=> ( rearsegP(skaf71(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf71(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ338_spl])],[split_symbol_definition]) ).
fof(f2995,plain,
( ~ sQ11_spl
| sQ338_spl ),
inference(split_clause,[status(thm)],[f2967,f2992,f545]) ).
fof(f2996,plain,
! [X0,X1] :
( ~ sQ332_spl
| segmentP(app(skaf71(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2969,f223]) ).
fof(f3004,plain,
! [X0,X1] :
( segmentP(app(skaf72(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf72(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1034,f2205]) ).
fof(f3005,plain,
! [X0] :
( rearsegP(skaf72(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf72(X0)) ),
inference(paramodulation,[status(thm)],[f1034,f2173]) ).
fof(f3006,plain,
! [X0] :
( ssList(skaf72(X0))
| ~ ssList(skaf72(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1034,f285]) ).
fof(f3007,plain,
! [X0,X1,X2] :
( app(app(skaf72(X2),nil),X1) = X0
| ~ ssList(app(skaf72(X2),X1))
| ~ segmentP(X0,app(app(skaf72(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf72(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1034,f666]) ).
fof(f3008,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf72(X2),X1))
| ~ segmentP(X3,app(app(skaf72(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf72(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1034,f665]) ).
fof(f3009,plain,
! [X0,X1,X2] :
( segmentP(app(skaf72(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf72(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1034,f404]) ).
fof(f3010,plain,
! [X0,X1] :
( rearsegP(skaf72(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf72(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1034,f350]) ).
fof(f3011,definition,
! [X0,X1] :
( sQ339_spl
<=> ( segmentP(app(skaf72(X1),X0),nil)
| ~ ssList(skaf72(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ339_spl])],[split_symbol_definition]) ).
fof(f3012,plain,
! [X0,X1] :
( ~ sQ339_spl
| segmentP(app(skaf72(X1),X0),nil)
| ~ ssList(skaf72(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3011]) ).
fof(f3014,plain,
( ~ sQ11_spl
| sQ339_spl ),
inference(split_clause,[status(thm)],[f3004,f3011,f545]) ).
fof(f3015,definition,
! [X0] :
( sQ340_spl
<=> ( rearsegP(skaf72(X0),nil)
| ~ ssList(skaf72(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ340_spl])],[split_symbol_definition]) ).
fof(f3018,plain,
( ~ sQ11_spl
| sQ340_spl ),
inference(split_clause,[status(thm)],[f3005,f3015,f545]) ).
fof(f3019,definition,
! [X0] :
( sQ341_spl
<=> ( ssList(skaf72(X0))
| ~ ssList(skaf72(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ341_spl])],[split_symbol_definition]) ).
fof(f3022,plain,
( sQ341_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3006,f545,f3019]) ).
fof(f3023,definition,
! [X0,X1,X2] :
( sQ342_spl
<=> ( app(app(skaf72(X2),nil),X1) = X0
| ~ ssList(app(skaf72(X2),X1))
| ~ segmentP(X0,app(app(skaf72(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf72(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ342_spl])],[split_symbol_definition]) ).
fof(f3026,plain,
( ~ sQ11_spl
| sQ342_spl ),
inference(split_clause,[status(thm)],[f3007,f3023,f545]) ).
fof(f3027,definition,
! [X0,X1,X2,X3] :
( sQ343_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf72(X2),X1))
| ~ segmentP(X3,app(app(skaf72(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf72(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ343_spl])],[split_symbol_definition]) ).
fof(f3030,plain,
( ~ sQ11_spl
| sQ343_spl ),
inference(split_clause,[status(thm)],[f3008,f3027,f545]) ).
fof(f3031,definition,
! [X0,X1,X2] :
( sQ344_spl
<=> ( segmentP(app(skaf72(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf72(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ344_spl])],[split_symbol_definition]) ).
fof(f3034,plain,
( ~ sQ11_spl
| sQ344_spl ),
inference(split_clause,[status(thm)],[f3009,f3031,f545]) ).
fof(f3035,definition,
! [X0,X1] :
( sQ345_spl
<=> ( rearsegP(skaf72(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf72(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ345_spl])],[split_symbol_definition]) ).
fof(f3038,plain,
( ~ sQ11_spl
| sQ345_spl ),
inference(split_clause,[status(thm)],[f3010,f3035,f545]) ).
fof(f3039,plain,
! [X0,X1] :
( ~ sQ339_spl
| segmentP(app(skaf72(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3012,f222]) ).
fof(f3049,plain,
! [X0,X1] :
( ~ sQ276_spl
| segmentP(X1,sk2)
| ~ ssList(X1)
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ segmentP(X1,app(sk2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2621,f374]) ).
fof(f3050,plain,
! [X0] :
( ~ sQ276_spl
| app(sk2,X0) = sk2
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ segmentP(sk2,app(sk2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2621,f339]) ).
fof(f3051,plain,
( ~ sQ276_spl
| segmentP(sk2,sk2)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1029,f2621]) ).
fof(f3052,definition,
! [X0,X1] :
( sQ346_spl
<=> ( segmentP(X1,sk2)
| ~ ssList(X1)
| ~ ssList(app(sk2,X0))
| ~ segmentP(X1,app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ346_spl])],[split_symbol_definition]) ).
fof(f3055,plain,
( ~ sQ276_spl
| ~ sQ16_spl
| sQ346_spl ),
inference(split_clause,[status(thm)],[f3049,f3052,f587,f2620]) ).
fof(f3056,definition,
! [X0] :
( sQ347_spl
<=> ( app(sk2,X0) = sk2
| ~ ssList(app(sk2,X0))
| ~ segmentP(sk2,app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ347_spl])],[split_symbol_definition]) ).
fof(f3059,plain,
( ~ sQ276_spl
| ~ sQ16_spl
| sQ347_spl ),
inference(split_clause,[status(thm)],[f3050,f3056,f587,f2620]) ).
fof(f3060,definition,
( sQ348_spl
<=> segmentP(sk2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ348_spl])],[split_symbol_definition]) ).
fof(f3061,plain,
( ~ sQ348_spl
| segmentP(sk2,sk2) ),
inference(component_clause,[status(thm)],[f3060]) ).
fof(f3063,plain,
( ~ sQ276_spl
| sQ348_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3051,f545,f3060,f2620]) ).
fof(f3064,plain,
! [X0] :
( ~ sQ348_spl
| segmentP(X0,sk2)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ segmentP(X0,sk2) ),
inference(resolution,[status(thm)],[f3061,f374]) ).
fof(f3065,plain,
( ~ sQ348_spl
| sk2 = sk2
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ segmentP(sk2,sk2) ),
inference(resolution,[status(thm)],[f3061,f339]) ).
fof(f3066,definition,
! [X0] :
( sQ349_spl
<=> ( segmentP(X0,sk2)
| ~ ssList(X0)
| ~ segmentP(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ349_spl])],[split_symbol_definition]) ).
fof(f3069,plain,
( ~ sQ348_spl
| ~ sQ16_spl
| sQ349_spl ),
inference(split_clause,[status(thm)],[f3064,f3066,f587,f3060]) ).
fof(f3070,plain,
( sQ130_spl
| ~ sQ16_spl
| ~ sQ348_spl ),
inference(split_clause,[status(thm)],[f3065,f3060,f587,f1614]) ).
fof(f3075,plain,
! [X0,X1] :
( ~ sQ102_spl
| ~ ssList(sk1)
| ~ ssList(X1)
| app(sk1,X1) = X0
| ~ segmentP(X0,app(sk1,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(resolution,[status(thm)],[f1388,f285]) ).
fof(f3076,plain,
! [X0] :
( ~ sQ102_spl
| app(sk1,nil) = X0
| ~ ssList(sk1)
| ~ segmentP(X0,app(sk1,nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1013,f1388]) ).
fof(f3077,definition,
! [X0,X1] :
( sQ350_spl
<=> ( ~ ssList(X1)
| app(sk1,X1) = X0
| ~ segmentP(X0,app(sk1,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f3080,plain,
( ~ sQ102_spl
| ~ sQ13_spl
| sQ350_spl ),
inference(split_clause,[status(thm)],[f3075,f3077,f558,f1379]) ).
fof(f3081,definition,
! [X0] :
( sQ351_spl
<=> ( app(sk1,nil) = X0
| ~ segmentP(X0,app(sk1,nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f3084,plain,
( ~ sQ102_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sQ351_spl ),
inference(split_clause,[status(thm)],[f3076,f3081,f545,f558,f1379]) ).
fof(f3092,plain,
( ~ sQ278_spl
| segmentP(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1042,f2629]) ).
fof(f3094,definition,
! [X0] :
( sQ352_spl
<=> ( app(nil,X0) = nil
| ~ ssList(app(nil,X0))
| ~ segmentP(nil,app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition]) ).
fof(f3100,definition,
( sQ353_spl
<=> segmentP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ353_spl])],[split_symbol_definition]) ).
fof(f3101,plain,
( ~ sQ353_spl
| segmentP(nil,nil) ),
inference(component_clause,[status(thm)],[f3100]) ).
fof(f3103,plain,
( ~ sQ278_spl
| sQ353_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3092,f545,f3100,f2628]) ).
fof(f3109,plain,
! [X0] :
( ~ sQ353_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ segmentP(X0,nil) ),
inference(resolution,[status(thm)],[f3101,f374]) ).
fof(f3116,definition,
! [X0] :
( sQ354_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ segmentP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f3119,plain,
( ~ sQ353_spl
| ~ sQ11_spl
| sQ354_spl ),
inference(split_clause,[status(thm)],[f3109,f3116,f545,f3100]) ).
fof(f3121,plain,
! [X0,X1,X2] :
( ~ sQ270_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf58(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf58(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2634,f374]) ).
fof(f3122,plain,
! [X0,X1] :
( ~ sQ270_spl
| app(skaf58(X1),X0) = nil
| ~ ssList(app(skaf58(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf58(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2634,f339]) ).
fof(f3123,plain,
! [X0] :
( ~ sQ270_spl
| segmentP(skaf58(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1025,f2634]) ).
fof(f3124,definition,
! [X0,X1,X2] :
( sQ355_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf58(X2),X0))
| ~ segmentP(X1,app(skaf58(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ355_spl])],[split_symbol_definition]) ).
fof(f3127,plain,
( ~ sQ270_spl
| ~ sQ11_spl
| sQ355_spl ),
inference(split_clause,[status(thm)],[f3121,f3124,f545,f2596]) ).
fof(f3128,definition,
! [X0,X1] :
( sQ356_spl
<=> ( app(skaf58(X1),X0) = nil
| ~ ssList(app(skaf58(X1),X0))
| ~ segmentP(nil,app(skaf58(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ356_spl])],[split_symbol_definition]) ).
fof(f3131,plain,
( ~ sQ270_spl
| ~ sQ11_spl
| sQ356_spl ),
inference(split_clause,[status(thm)],[f3122,f3128,f545,f2596]) ).
fof(f3132,definition,
! [X0] :
( sQ357_spl
<=> segmentP(skaf58(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition]) ).
fof(f3133,plain,
! [X0] :
( ~ sQ357_spl
| segmentP(skaf58(X0),nil) ),
inference(component_clause,[status(thm)],[f3132]) ).
fof(f3135,plain,
( ~ sQ270_spl
| sQ357_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3123,f545,f3132,f2596]) ).
fof(f3136,plain,
! [X0,X1] :
( ~ sQ357_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf58(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf58(X1)) ),
inference(resolution,[status(thm)],[f3133,f374]) ).
fof(f3137,plain,
! [X0] :
( ~ sQ357_spl
| skaf58(X0) = nil
| ~ ssList(skaf58(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf58(X0)) ),
inference(resolution,[status(thm)],[f3133,f339]) ).
fof(f3138,definition,
! [X0,X1] :
( sQ358_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf58(X1))
| ~ segmentP(X0,skaf58(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ358_spl])],[split_symbol_definition]) ).
fof(f3141,plain,
( ~ sQ357_spl
| ~ sQ11_spl
| sQ358_spl ),
inference(split_clause,[status(thm)],[f3136,f3138,f545,f3132]) ).
fof(f3142,definition,
! [X0] :
( sQ359_spl
<=> ( skaf58(X0) = nil
| ~ ssList(skaf58(X0))
| ~ segmentP(nil,skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f3145,plain,
( ~ sQ357_spl
| ~ sQ11_spl
| sQ359_spl ),
inference(split_clause,[status(thm)],[f3137,f3142,f545,f3132]) ).
fof(f3146,plain,
! [X0,X1,X2] :
( ~ sQ271_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf57(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf57(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2635,f374]) ).
fof(f3147,plain,
! [X0,X1] :
( ~ sQ271_spl
| app(skaf57(X1),X0) = nil
| ~ ssList(app(skaf57(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf57(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2635,f339]) ).
fof(f3148,plain,
! [X0] :
( ~ sQ271_spl
| segmentP(skaf57(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1024,f2635]) ).
fof(f3149,definition,
! [X0,X1,X2] :
( sQ360_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf57(X2),X0))
| ~ segmentP(X1,app(skaf57(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ360_spl])],[split_symbol_definition]) ).
fof(f3152,plain,
( ~ sQ271_spl
| ~ sQ11_spl
| sQ360_spl ),
inference(split_clause,[status(thm)],[f3146,f3149,f545,f2600]) ).
fof(f3153,definition,
! [X0,X1] :
( sQ361_spl
<=> ( app(skaf57(X1),X0) = nil
| ~ ssList(app(skaf57(X1),X0))
| ~ segmentP(nil,app(skaf57(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition]) ).
fof(f3156,plain,
( ~ sQ271_spl
| ~ sQ11_spl
| sQ361_spl ),
inference(split_clause,[status(thm)],[f3147,f3153,f545,f2600]) ).
fof(f3157,definition,
! [X0] :
( sQ362_spl
<=> segmentP(skaf57(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ362_spl])],[split_symbol_definition]) ).
fof(f3158,plain,
! [X0] :
( ~ sQ362_spl
| segmentP(skaf57(X0),nil) ),
inference(component_clause,[status(thm)],[f3157]) ).
fof(f3160,plain,
( ~ sQ271_spl
| sQ362_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3148,f545,f3157,f2600]) ).
fof(f3161,plain,
! [X0,X1] :
( ~ sQ362_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf57(X1)) ),
inference(resolution,[status(thm)],[f3158,f374]) ).
fof(f3162,plain,
! [X0] :
( ~ sQ362_spl
| skaf57(X0) = nil
| ~ ssList(skaf57(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf57(X0)) ),
inference(resolution,[status(thm)],[f3158,f339]) ).
fof(f3163,definition,
! [X0,X1] :
( sQ363_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ segmentP(X0,skaf57(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition]) ).
fof(f3166,plain,
( ~ sQ362_spl
| ~ sQ11_spl
| sQ363_spl ),
inference(split_clause,[status(thm)],[f3161,f3163,f545,f3157]) ).
fof(f3167,definition,
! [X0] :
( sQ364_spl
<=> ( skaf57(X0) = nil
| ~ ssList(skaf57(X0))
| ~ segmentP(nil,skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition]) ).
fof(f3170,plain,
( ~ sQ362_spl
| ~ sQ11_spl
| sQ364_spl ),
inference(split_clause,[status(thm)],[f3162,f3167,f545,f3157]) ).
fof(f3173,plain,
! [X0] :
( app(skaf72(X0),nil) = nil
| ~ rearsegP(nil,skaf72(X0))
| ~ ssList(nil)
| ~ ssList(skaf72(X0)) ),
inference(paramodulation,[status(thm)],[f1034,f2334]) ).
fof(f3174,plain,
! [X0] :
( app(skaf71(X0),nil) = nil
| ~ rearsegP(nil,skaf71(X0))
| ~ ssList(nil)
| ~ ssList(skaf71(X0)) ),
inference(paramodulation,[status(thm)],[f1033,f2334]) ).
fof(f3175,plain,
! [X0] :
( app(skaf68(X0),nil) = nil
| ~ rearsegP(nil,skaf68(X0))
| ~ ssList(nil)
| ~ ssList(skaf68(X0)) ),
inference(paramodulation,[status(thm)],[f1032,f2334]) ).
fof(f3176,plain,
! [X0] :
( app(skaf67(X0),nil) = nil
| ~ rearsegP(nil,skaf67(X0))
| ~ ssList(nil)
| ~ ssList(skaf67(X0)) ),
inference(paramodulation,[status(thm)],[f1031,f2334]) ).
fof(f3177,plain,
! [X0] :
( app(skaf66(X0),nil) = nil
| ~ rearsegP(nil,skaf66(X0))
| ~ ssList(nil)
| ~ ssList(skaf66(X0)) ),
inference(paramodulation,[status(thm)],[f1030,f2334]) ).
fof(f3178,plain,
! [X0] :
( app(skaf63(X0),nil) = nil
| ~ rearsegP(nil,skaf63(X0))
| ~ ssList(nil)
| ~ ssList(skaf63(X0)) ),
inference(paramodulation,[status(thm)],[f1028,f2334]) ).
fof(f3179,plain,
! [X0] :
( app(skaf62(X0),nil) = nil
| ~ rearsegP(nil,skaf62(X0))
| ~ ssList(nil)
| ~ ssList(skaf62(X0)) ),
inference(paramodulation,[status(thm)],[f1027,f2334]) ).
fof(f3180,plain,
! [X0] :
( app(skaf61(X0),nil) = nil
| ~ rearsegP(nil,skaf61(X0))
| ~ ssList(nil)
| ~ ssList(skaf61(X0)) ),
inference(paramodulation,[status(thm)],[f1026,f2334]) ).
fof(f3181,plain,
! [X0] :
( app(skaf58(X0),nil) = nil
| ~ rearsegP(nil,skaf58(X0))
| ~ ssList(nil)
| ~ ssList(skaf58(X0)) ),
inference(paramodulation,[status(thm)],[f1025,f2334]) ).
fof(f3182,plain,
! [X0] :
( app(skaf57(X0),nil) = nil
| ~ rearsegP(nil,skaf57(X0))
| ~ ssList(nil)
| ~ ssList(skaf57(X0)) ),
inference(paramodulation,[status(thm)],[f1024,f2334]) ).
fof(f3183,plain,
! [X0] :
( app(skaf56(X0),nil) = nil
| ~ rearsegP(nil,skaf56(X0))
| ~ ssList(nil)
| ~ ssList(skaf56(X0)) ),
inference(paramodulation,[status(thm)],[f1023,f2334]) ).
fof(f3184,plain,
! [X0] :
( app(skaf53(X0),nil) = nil
| ~ rearsegP(nil,skaf53(X0))
| ~ ssList(nil)
| ~ ssList(skaf53(X0)) ),
inference(paramodulation,[status(thm)],[f1022,f2334]) ).
fof(f3185,plain,
! [X0] :
( app(skaf52(X0),nil) = nil
| ~ rearsegP(nil,skaf52(X0))
| ~ ssList(nil)
| ~ ssList(skaf52(X0)) ),
inference(paramodulation,[status(thm)],[f1021,f2334]) ).
fof(f3186,plain,
! [X0] :
( app(skaf51(X0),nil) = nil
| ~ rearsegP(nil,skaf51(X0))
| ~ ssList(nil)
| ~ ssList(skaf51(X0)) ),
inference(paramodulation,[status(thm)],[f1020,f2334]) ).
fof(f3187,plain,
( app(nil,sk2) = sk2
| ~ rearsegP(sk2,sk2)
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1423,f2334]) ).
fof(f3188,plain,
( app(nil,sk1) = sk1
| ~ rearsegP(sk1,sk1)
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1407,f2334]) ).
fof(f3189,plain,
( app(nil,nil) = nil
| ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1042,f2334]) ).
fof(f3195,definition,
! [X0] :
( sQ365_spl
<=> ( app(skaf72(X0),nil) = nil
| ~ rearsegP(nil,skaf72(X0))
| ~ ssList(skaf72(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f3198,plain,
( ~ sQ11_spl
| sQ365_spl ),
inference(split_clause,[status(thm)],[f3173,f3195,f545]) ).
fof(f3199,definition,
! [X0] :
( sQ366_spl
<=> ( app(skaf71(X0),nil) = nil
| ~ rearsegP(nil,skaf71(X0))
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f3202,plain,
( ~ sQ11_spl
| sQ366_spl ),
inference(split_clause,[status(thm)],[f3174,f3199,f545]) ).
fof(f3203,definition,
! [X0] :
( sQ367_spl
<=> ( app(skaf68(X0),nil) = nil
| ~ rearsegP(nil,skaf68(X0))
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f3206,plain,
( ~ sQ11_spl
| sQ367_spl ),
inference(split_clause,[status(thm)],[f3175,f3203,f545]) ).
fof(f3207,definition,
! [X0] :
( sQ368_spl
<=> ( app(skaf67(X0),nil) = nil
| ~ rearsegP(nil,skaf67(X0))
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ368_spl])],[split_symbol_definition]) ).
fof(f3210,plain,
( ~ sQ11_spl
| sQ368_spl ),
inference(split_clause,[status(thm)],[f3176,f3207,f545]) ).
fof(f3211,definition,
! [X0] :
( sQ369_spl
<=> ( app(skaf66(X0),nil) = nil
| ~ rearsegP(nil,skaf66(X0))
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ369_spl])],[split_symbol_definition]) ).
fof(f3214,plain,
( ~ sQ11_spl
| sQ369_spl ),
inference(split_clause,[status(thm)],[f3177,f3211,f545]) ).
fof(f3215,definition,
! [X0] :
( sQ370_spl
<=> ( app(skaf63(X0),nil) = nil
| ~ rearsegP(nil,skaf63(X0))
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ370_spl])],[split_symbol_definition]) ).
fof(f3218,plain,
( ~ sQ11_spl
| sQ370_spl ),
inference(split_clause,[status(thm)],[f3178,f3215,f545]) ).
fof(f3219,definition,
! [X0] :
( sQ371_spl
<=> ( app(skaf62(X0),nil) = nil
| ~ rearsegP(nil,skaf62(X0))
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ371_spl])],[split_symbol_definition]) ).
fof(f3222,plain,
( ~ sQ11_spl
| sQ371_spl ),
inference(split_clause,[status(thm)],[f3179,f3219,f545]) ).
fof(f3223,definition,
! [X0] :
( sQ372_spl
<=> ( app(skaf61(X0),nil) = nil
| ~ rearsegP(nil,skaf61(X0))
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ372_spl])],[split_symbol_definition]) ).
fof(f3226,plain,
( ~ sQ11_spl
| sQ372_spl ),
inference(split_clause,[status(thm)],[f3180,f3223,f545]) ).
fof(f3227,definition,
! [X0] :
( sQ373_spl
<=> ( app(skaf58(X0),nil) = nil
| ~ rearsegP(nil,skaf58(X0))
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ373_spl])],[split_symbol_definition]) ).
fof(f3230,plain,
( ~ sQ11_spl
| sQ373_spl ),
inference(split_clause,[status(thm)],[f3181,f3227,f545]) ).
fof(f3231,definition,
! [X0] :
( sQ374_spl
<=> ( app(skaf57(X0),nil) = nil
| ~ rearsegP(nil,skaf57(X0))
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f3234,plain,
( ~ sQ11_spl
| sQ374_spl ),
inference(split_clause,[status(thm)],[f3182,f3231,f545]) ).
fof(f3235,definition,
! [X0] :
( sQ375_spl
<=> ( app(skaf56(X0),nil) = nil
| ~ rearsegP(nil,skaf56(X0))
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f3238,plain,
( ~ sQ11_spl
| sQ375_spl ),
inference(split_clause,[status(thm)],[f3183,f3235,f545]) ).
fof(f3239,definition,
! [X0] :
( sQ376_spl
<=> ( app(skaf53(X0),nil) = nil
| ~ rearsegP(nil,skaf53(X0))
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ376_spl])],[split_symbol_definition]) ).
fof(f3242,plain,
( ~ sQ11_spl
| sQ376_spl ),
inference(split_clause,[status(thm)],[f3184,f3239,f545]) ).
fof(f3243,definition,
! [X0] :
( sQ377_spl
<=> ( app(skaf52(X0),nil) = nil
| ~ rearsegP(nil,skaf52(X0))
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ377_spl])],[split_symbol_definition]) ).
fof(f3246,plain,
( ~ sQ11_spl
| sQ377_spl ),
inference(split_clause,[status(thm)],[f3185,f3243,f545]) ).
fof(f3247,definition,
! [X0] :
( sQ378_spl
<=> ( app(skaf51(X0),nil) = nil
| ~ rearsegP(nil,skaf51(X0))
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ378_spl])],[split_symbol_definition]) ).
fof(f3250,plain,
( ~ sQ11_spl
| sQ378_spl ),
inference(split_clause,[status(thm)],[f3186,f3247,f545]) ).
fof(f3251,definition,
( sQ379_spl
<=> app(nil,sk2) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ379_spl])],[split_symbol_definition]) ).
fof(f3254,plain,
( sQ379_spl
| ~ sQ129_spl
| ~ sQ16_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3187,f545,f587,f1611,f3251]) ).
fof(f3255,definition,
( sQ380_spl
<=> app(nil,sk1) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ380_spl])],[split_symbol_definition]) ).
fof(f3258,plain,
( sQ380_spl
| ~ sQ114_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3188,f545,f558,f1508,f3255]) ).
fof(f3259,definition,
( sQ381_spl
<=> app(nil,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ381_spl])],[split_symbol_definition]) ).
fof(f3262,plain,
( sQ381_spl
| ~ sQ37_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3189,f545,f751,f3259]) ).
fof(f3291,plain,
! [X0] :
( app(skaf73(X0),nil) = nil
| ~ rearsegP(nil,skaf73(X0))
| ~ ssList(nil)
| ~ ssList(skaf73(X0)) ),
inference(paramodulation,[status(thm)],[f1035,f2334]) ).
fof(f3292,plain,
! [X0,X1] :
( segmentP(app(skaf73(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf73(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1035,f2205]) ).
fof(f3293,plain,
! [X0] :
( rearsegP(skaf73(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf73(X0)) ),
inference(paramodulation,[status(thm)],[f1035,f2173]) ).
fof(f3294,plain,
! [X0] :
( ssList(skaf73(X0))
| ~ ssList(skaf73(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1035,f285]) ).
fof(f3295,plain,
! [X0,X1,X2] :
( app(app(skaf73(X2),nil),X1) = X0
| ~ ssList(app(skaf73(X2),X1))
| ~ segmentP(X0,app(app(skaf73(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf73(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1035,f666]) ).
fof(f3296,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf73(X2),X1))
| ~ segmentP(X3,app(app(skaf73(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf73(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1035,f665]) ).
fof(f3297,plain,
! [X0,X1,X2] :
( segmentP(app(skaf73(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf73(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1035,f404]) ).
fof(f3298,plain,
! [X0,X1] :
( rearsegP(skaf73(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf73(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1035,f350]) ).
fof(f3299,definition,
! [X0] :
( sQ384_spl
<=> ( app(skaf73(X0),nil) = nil
| ~ rearsegP(nil,skaf73(X0))
| ~ ssList(skaf73(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ384_spl])],[split_symbol_definition]) ).
fof(f3302,plain,
( ~ sQ11_spl
| sQ384_spl ),
inference(split_clause,[status(thm)],[f3291,f3299,f545]) ).
fof(f3303,definition,
! [X0,X1] :
( sQ385_spl
<=> ( segmentP(app(skaf73(X1),X0),nil)
| ~ ssList(skaf73(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ385_spl])],[split_symbol_definition]) ).
fof(f3304,plain,
! [X0,X1] :
( ~ sQ385_spl
| segmentP(app(skaf73(X1),X0),nil)
| ~ ssList(skaf73(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3303]) ).
fof(f3306,plain,
( ~ sQ11_spl
| sQ385_spl ),
inference(split_clause,[status(thm)],[f3292,f3303,f545]) ).
fof(f3307,definition,
! [X0] :
( sQ386_spl
<=> ( rearsegP(skaf73(X0),nil)
| ~ ssList(skaf73(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ386_spl])],[split_symbol_definition]) ).
fof(f3310,plain,
( ~ sQ11_spl
| sQ386_spl ),
inference(split_clause,[status(thm)],[f3293,f3307,f545]) ).
fof(f3311,definition,
! [X0] :
( sQ387_spl
<=> ( ssList(skaf73(X0))
| ~ ssList(skaf73(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ387_spl])],[split_symbol_definition]) ).
fof(f3314,plain,
( sQ387_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3294,f545,f3311]) ).
fof(f3315,definition,
! [X0,X1,X2] :
( sQ388_spl
<=> ( app(app(skaf73(X2),nil),X1) = X0
| ~ ssList(app(skaf73(X2),X1))
| ~ segmentP(X0,app(app(skaf73(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf73(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ388_spl])],[split_symbol_definition]) ).
fof(f3318,plain,
( ~ sQ11_spl
| sQ388_spl ),
inference(split_clause,[status(thm)],[f3295,f3315,f545]) ).
fof(f3319,definition,
! [X0,X1,X2,X3] :
( sQ389_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf73(X2),X1))
| ~ segmentP(X3,app(app(skaf73(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf73(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f3322,plain,
( ~ sQ11_spl
| sQ389_spl ),
inference(split_clause,[status(thm)],[f3296,f3319,f545]) ).
fof(f3323,definition,
! [X0,X1,X2] :
( sQ390_spl
<=> ( segmentP(app(skaf73(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf73(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ390_spl])],[split_symbol_definition]) ).
fof(f3326,plain,
( ~ sQ11_spl
| sQ390_spl ),
inference(split_clause,[status(thm)],[f3297,f3323,f545]) ).
fof(f3327,definition,
! [X0,X1] :
( sQ391_spl
<=> ( rearsegP(skaf73(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf73(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f3330,plain,
( ~ sQ11_spl
| sQ391_spl ),
inference(split_clause,[status(thm)],[f3298,f3327,f545]) ).
fof(f3332,plain,
! [X0,X1] :
( ~ sQ385_spl
| segmentP(app(skaf73(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3304,f221]) ).
fof(f3340,plain,
! [X0] :
( app(skaf75(X0),nil) = nil
| ~ rearsegP(nil,skaf75(X0))
| ~ ssList(nil)
| ~ ssList(skaf75(X0)) ),
inference(paramodulation,[status(thm)],[f1036,f2334]) ).
fof(f3341,plain,
! [X0,X1] :
( segmentP(app(skaf75(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf75(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1036,f2205]) ).
fof(f3342,plain,
! [X0] :
( rearsegP(skaf75(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf75(X0)) ),
inference(paramodulation,[status(thm)],[f1036,f2173]) ).
fof(f3343,plain,
! [X0] :
( ssList(skaf75(X0))
| ~ ssList(skaf75(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1036,f285]) ).
fof(f3344,plain,
! [X0,X1,X2] :
( app(app(skaf75(X2),nil),X1) = X0
| ~ ssList(app(skaf75(X2),X1))
| ~ segmentP(X0,app(app(skaf75(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf75(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1036,f666]) ).
fof(f3345,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf75(X2),X1))
| ~ segmentP(X3,app(app(skaf75(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf75(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1036,f665]) ).
fof(f3346,plain,
! [X0,X1,X2] :
( segmentP(app(skaf75(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf75(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1036,f404]) ).
fof(f3347,plain,
! [X0,X1] :
( rearsegP(skaf75(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf75(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1036,f350]) ).
fof(f3348,definition,
! [X0] :
( sQ392_spl
<=> ( app(skaf75(X0),nil) = nil
| ~ rearsegP(nil,skaf75(X0))
| ~ ssList(skaf75(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ392_spl])],[split_symbol_definition]) ).
fof(f3351,plain,
( ~ sQ11_spl
| sQ392_spl ),
inference(split_clause,[status(thm)],[f3340,f3348,f545]) ).
fof(f3352,definition,
! [X0,X1] :
( sQ393_spl
<=> ( segmentP(app(skaf75(X1),X0),nil)
| ~ ssList(skaf75(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ393_spl])],[split_symbol_definition]) ).
fof(f3353,plain,
! [X0,X1] :
( ~ sQ393_spl
| segmentP(app(skaf75(X1),X0),nil)
| ~ ssList(skaf75(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3352]) ).
fof(f3355,plain,
( ~ sQ11_spl
| sQ393_spl ),
inference(split_clause,[status(thm)],[f3341,f3352,f545]) ).
fof(f3356,definition,
! [X0] :
( sQ394_spl
<=> ( rearsegP(skaf75(X0),nil)
| ~ ssList(skaf75(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ394_spl])],[split_symbol_definition]) ).
fof(f3359,plain,
( ~ sQ11_spl
| sQ394_spl ),
inference(split_clause,[status(thm)],[f3342,f3356,f545]) ).
fof(f3360,definition,
! [X0] :
( sQ395_spl
<=> ( ssList(skaf75(X0))
| ~ ssList(skaf75(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ395_spl])],[split_symbol_definition]) ).
fof(f3363,plain,
( sQ395_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3343,f545,f3360]) ).
fof(f3364,definition,
! [X0,X1,X2] :
( sQ396_spl
<=> ( app(app(skaf75(X2),nil),X1) = X0
| ~ ssList(app(skaf75(X2),X1))
| ~ segmentP(X0,app(app(skaf75(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf75(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ396_spl])],[split_symbol_definition]) ).
fof(f3367,plain,
( ~ sQ11_spl
| sQ396_spl ),
inference(split_clause,[status(thm)],[f3344,f3364,f545]) ).
fof(f3368,definition,
! [X0,X1,X2,X3] :
( sQ397_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf75(X2),X1))
| ~ segmentP(X3,app(app(skaf75(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf75(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ397_spl])],[split_symbol_definition]) ).
fof(f3371,plain,
( ~ sQ11_spl
| sQ397_spl ),
inference(split_clause,[status(thm)],[f3345,f3368,f545]) ).
fof(f3372,definition,
! [X0,X1,X2] :
( sQ398_spl
<=> ( segmentP(app(skaf75(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf75(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ398_spl])],[split_symbol_definition]) ).
fof(f3375,plain,
( ~ sQ11_spl
| sQ398_spl ),
inference(split_clause,[status(thm)],[f3346,f3372,f545]) ).
fof(f3376,definition,
! [X0,X1] :
( sQ399_spl
<=> ( rearsegP(skaf75(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf75(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ399_spl])],[split_symbol_definition]) ).
fof(f3379,plain,
( ~ sQ11_spl
| sQ399_spl ),
inference(split_clause,[status(thm)],[f3347,f3376,f545]) ).
fof(f3381,plain,
! [X0,X1] :
( ~ sQ393_spl
| segmentP(app(skaf75(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3353,f219]) ).
fof(f3389,plain,
! [X0] :
( app(skaf76(X0),nil) = nil
| ~ rearsegP(nil,skaf76(X0))
| ~ ssList(nil)
| ~ ssList(skaf76(X0)) ),
inference(paramodulation,[status(thm)],[f1037,f2334]) ).
fof(f3390,plain,
! [X0,X1] :
( segmentP(app(skaf76(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf76(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1037,f2205]) ).
fof(f3391,plain,
! [X0] :
( rearsegP(skaf76(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf76(X0)) ),
inference(paramodulation,[status(thm)],[f1037,f2173]) ).
fof(f3392,plain,
! [X0] :
( ssList(skaf76(X0))
| ~ ssList(skaf76(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1037,f285]) ).
fof(f3393,plain,
! [X0,X1,X2] :
( app(app(skaf76(X2),nil),X1) = X0
| ~ ssList(app(skaf76(X2),X1))
| ~ segmentP(X0,app(app(skaf76(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf76(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1037,f666]) ).
fof(f3394,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf76(X2),X1))
| ~ segmentP(X3,app(app(skaf76(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf76(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1037,f665]) ).
fof(f3395,plain,
! [X0,X1,X2] :
( segmentP(app(skaf76(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf76(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1037,f404]) ).
fof(f3396,plain,
! [X0,X1] :
( rearsegP(skaf76(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf76(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1037,f350]) ).
fof(f3397,definition,
! [X0] :
( sQ400_spl
<=> ( app(skaf76(X0),nil) = nil
| ~ rearsegP(nil,skaf76(X0))
| ~ ssList(skaf76(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ400_spl])],[split_symbol_definition]) ).
fof(f3400,plain,
( ~ sQ11_spl
| sQ400_spl ),
inference(split_clause,[status(thm)],[f3389,f3397,f545]) ).
fof(f3401,definition,
! [X0,X1] :
( sQ401_spl
<=> ( segmentP(app(skaf76(X1),X0),nil)
| ~ ssList(skaf76(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ401_spl])],[split_symbol_definition]) ).
fof(f3402,plain,
! [X0,X1] :
( ~ sQ401_spl
| segmentP(app(skaf76(X1),X0),nil)
| ~ ssList(skaf76(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3401]) ).
fof(f3404,plain,
( ~ sQ11_spl
| sQ401_spl ),
inference(split_clause,[status(thm)],[f3390,f3401,f545]) ).
fof(f3405,definition,
! [X0] :
( sQ402_spl
<=> ( rearsegP(skaf76(X0),nil)
| ~ ssList(skaf76(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ402_spl])],[split_symbol_definition]) ).
fof(f3408,plain,
( ~ sQ11_spl
| sQ402_spl ),
inference(split_clause,[status(thm)],[f3391,f3405,f545]) ).
fof(f3409,definition,
! [X0] :
( sQ403_spl
<=> ( ssList(skaf76(X0))
| ~ ssList(skaf76(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ403_spl])],[split_symbol_definition]) ).
fof(f3412,plain,
( sQ403_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3392,f545,f3409]) ).
fof(f3413,definition,
! [X0,X1,X2] :
( sQ404_spl
<=> ( app(app(skaf76(X2),nil),X1) = X0
| ~ ssList(app(skaf76(X2),X1))
| ~ segmentP(X0,app(app(skaf76(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf76(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ404_spl])],[split_symbol_definition]) ).
fof(f3416,plain,
( ~ sQ11_spl
| sQ404_spl ),
inference(split_clause,[status(thm)],[f3393,f3413,f545]) ).
fof(f3417,definition,
! [X0,X1,X2,X3] :
( sQ405_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf76(X2),X1))
| ~ segmentP(X3,app(app(skaf76(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf76(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ405_spl])],[split_symbol_definition]) ).
fof(f3420,plain,
( ~ sQ11_spl
| sQ405_spl ),
inference(split_clause,[status(thm)],[f3394,f3417,f545]) ).
fof(f3421,definition,
! [X0,X1,X2] :
( sQ406_spl
<=> ( segmentP(app(skaf76(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf76(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ406_spl])],[split_symbol_definition]) ).
fof(f3424,plain,
( ~ sQ11_spl
| sQ406_spl ),
inference(split_clause,[status(thm)],[f3395,f3421,f545]) ).
fof(f3425,definition,
! [X0,X1] :
( sQ407_spl
<=> ( rearsegP(skaf76(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf76(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ407_spl])],[split_symbol_definition]) ).
fof(f3428,plain,
( ~ sQ11_spl
| sQ407_spl ),
inference(split_clause,[status(thm)],[f3396,f3425,f545]) ).
fof(f3430,plain,
! [X0,X1] :
( ~ sQ401_spl
| segmentP(app(skaf76(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3402,f218]) ).
fof(f3438,plain,
! [X0] :
( app(skaf77(X0),nil) = nil
| ~ rearsegP(nil,skaf77(X0))
| ~ ssList(nil)
| ~ ssList(skaf77(X0)) ),
inference(paramodulation,[status(thm)],[f1038,f2334]) ).
fof(f3439,plain,
! [X0,X1] :
( segmentP(app(skaf77(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf77(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1038,f2205]) ).
fof(f3440,plain,
! [X0] :
( rearsegP(skaf77(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf77(X0)) ),
inference(paramodulation,[status(thm)],[f1038,f2173]) ).
fof(f3441,plain,
! [X0] :
( ssList(skaf77(X0))
| ~ ssList(skaf77(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1038,f285]) ).
fof(f3442,plain,
! [X0,X1,X2] :
( app(app(skaf77(X2),nil),X1) = X0
| ~ ssList(app(skaf77(X2),X1))
| ~ segmentP(X0,app(app(skaf77(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf77(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1038,f666]) ).
fof(f3443,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf77(X2),X1))
| ~ segmentP(X3,app(app(skaf77(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf77(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1038,f665]) ).
fof(f3444,plain,
! [X0,X1,X2] :
( segmentP(app(skaf77(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf77(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1038,f404]) ).
fof(f3445,plain,
! [X0,X1] :
( rearsegP(skaf77(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf77(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1038,f350]) ).
fof(f3446,definition,
! [X0] :
( sQ408_spl
<=> ( app(skaf77(X0),nil) = nil
| ~ rearsegP(nil,skaf77(X0))
| ~ ssList(skaf77(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ408_spl])],[split_symbol_definition]) ).
fof(f3449,plain,
( ~ sQ11_spl
| sQ408_spl ),
inference(split_clause,[status(thm)],[f3438,f3446,f545]) ).
fof(f3450,definition,
! [X0,X1] :
( sQ409_spl
<=> ( segmentP(app(skaf77(X1),X0),nil)
| ~ ssList(skaf77(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ409_spl])],[split_symbol_definition]) ).
fof(f3451,plain,
! [X0,X1] :
( ~ sQ409_spl
| segmentP(app(skaf77(X1),X0),nil)
| ~ ssList(skaf77(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3450]) ).
fof(f3453,plain,
( ~ sQ11_spl
| sQ409_spl ),
inference(split_clause,[status(thm)],[f3439,f3450,f545]) ).
fof(f3454,definition,
! [X0] :
( sQ410_spl
<=> ( rearsegP(skaf77(X0),nil)
| ~ ssList(skaf77(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ410_spl])],[split_symbol_definition]) ).
fof(f3457,plain,
( ~ sQ11_spl
| sQ410_spl ),
inference(split_clause,[status(thm)],[f3440,f3454,f545]) ).
fof(f3458,definition,
! [X0] :
( sQ411_spl
<=> ( ssList(skaf77(X0))
| ~ ssList(skaf77(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ411_spl])],[split_symbol_definition]) ).
fof(f3461,plain,
( sQ411_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3441,f545,f3458]) ).
fof(f3462,definition,
! [X0,X1,X2] :
( sQ412_spl
<=> ( app(app(skaf77(X2),nil),X1) = X0
| ~ ssList(app(skaf77(X2),X1))
| ~ segmentP(X0,app(app(skaf77(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf77(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ412_spl])],[split_symbol_definition]) ).
fof(f3465,plain,
( ~ sQ11_spl
| sQ412_spl ),
inference(split_clause,[status(thm)],[f3442,f3462,f545]) ).
fof(f3466,definition,
! [X0,X1,X2,X3] :
( sQ413_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf77(X2),X1))
| ~ segmentP(X3,app(app(skaf77(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf77(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ413_spl])],[split_symbol_definition]) ).
fof(f3469,plain,
( ~ sQ11_spl
| sQ413_spl ),
inference(split_clause,[status(thm)],[f3443,f3466,f545]) ).
fof(f3470,definition,
! [X0,X1,X2] :
( sQ414_spl
<=> ( segmentP(app(skaf77(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf77(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ414_spl])],[split_symbol_definition]) ).
fof(f3473,plain,
( ~ sQ11_spl
| sQ414_spl ),
inference(split_clause,[status(thm)],[f3444,f3470,f545]) ).
fof(f3474,definition,
! [X0,X1] :
( sQ415_spl
<=> ( rearsegP(skaf77(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf77(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ415_spl])],[split_symbol_definition]) ).
fof(f3477,plain,
( ~ sQ11_spl
| sQ415_spl ),
inference(split_clause,[status(thm)],[f3445,f3474,f545]) ).
fof(f3479,plain,
! [X0,X1] :
( ~ sQ409_spl
| segmentP(app(skaf77(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3451,f217]) ).
fof(f3487,plain,
! [X0] :
( app(skaf80(X0),nil) = nil
| ~ rearsegP(nil,skaf80(X0))
| ~ ssList(nil)
| ~ ssList(skaf80(X0)) ),
inference(paramodulation,[status(thm)],[f1039,f2334]) ).
fof(f3488,plain,
! [X0,X1] :
( segmentP(app(skaf80(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf80(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1039,f2205]) ).
fof(f3489,plain,
! [X0] :
( rearsegP(skaf80(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf80(X0)) ),
inference(paramodulation,[status(thm)],[f1039,f2173]) ).
fof(f3490,plain,
! [X0] :
( ssList(skaf80(X0))
| ~ ssList(skaf80(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1039,f285]) ).
fof(f3491,plain,
! [X0,X1,X2] :
( app(app(skaf80(X2),nil),X1) = X0
| ~ ssList(app(skaf80(X2),X1))
| ~ segmentP(X0,app(app(skaf80(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf80(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1039,f666]) ).
fof(f3492,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf80(X2),X1))
| ~ segmentP(X3,app(app(skaf80(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf80(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1039,f665]) ).
fof(f3493,plain,
! [X0,X1,X2] :
( segmentP(app(skaf80(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf80(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1039,f404]) ).
fof(f3494,plain,
! [X0,X1] :
( rearsegP(skaf80(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf80(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1039,f350]) ).
fof(f3495,definition,
! [X0] :
( sQ416_spl
<=> ( app(skaf80(X0),nil) = nil
| ~ rearsegP(nil,skaf80(X0))
| ~ ssList(skaf80(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ416_spl])],[split_symbol_definition]) ).
fof(f3498,plain,
( ~ sQ11_spl
| sQ416_spl ),
inference(split_clause,[status(thm)],[f3487,f3495,f545]) ).
fof(f3499,definition,
! [X0,X1] :
( sQ417_spl
<=> ( segmentP(app(skaf80(X1),X0),nil)
| ~ ssList(skaf80(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ417_spl])],[split_symbol_definition]) ).
fof(f3500,plain,
! [X0,X1] :
( ~ sQ417_spl
| segmentP(app(skaf80(X1),X0),nil)
| ~ ssList(skaf80(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3499]) ).
fof(f3502,plain,
( ~ sQ11_spl
| sQ417_spl ),
inference(split_clause,[status(thm)],[f3488,f3499,f545]) ).
fof(f3503,definition,
! [X0] :
( sQ418_spl
<=> ( rearsegP(skaf80(X0),nil)
| ~ ssList(skaf80(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ418_spl])],[split_symbol_definition]) ).
fof(f3506,plain,
( ~ sQ11_spl
| sQ418_spl ),
inference(split_clause,[status(thm)],[f3489,f3503,f545]) ).
fof(f3507,definition,
! [X0] :
( sQ419_spl
<=> ( ssList(skaf80(X0))
| ~ ssList(skaf80(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ419_spl])],[split_symbol_definition]) ).
fof(f3510,plain,
( sQ419_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3490,f545,f3507]) ).
fof(f3511,definition,
! [X0,X1,X2] :
( sQ420_spl
<=> ( app(app(skaf80(X2),nil),X1) = X0
| ~ ssList(app(skaf80(X2),X1))
| ~ segmentP(X0,app(app(skaf80(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf80(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f3514,plain,
( ~ sQ11_spl
| sQ420_spl ),
inference(split_clause,[status(thm)],[f3491,f3511,f545]) ).
fof(f3515,definition,
! [X0,X1,X2,X3] :
( sQ421_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf80(X2),X1))
| ~ segmentP(X3,app(app(skaf80(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf80(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ421_spl])],[split_symbol_definition]) ).
fof(f3518,plain,
( ~ sQ11_spl
| sQ421_spl ),
inference(split_clause,[status(thm)],[f3492,f3515,f545]) ).
fof(f3519,definition,
! [X0,X1,X2] :
( sQ422_spl
<=> ( segmentP(app(skaf80(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf80(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ422_spl])],[split_symbol_definition]) ).
fof(f3522,plain,
( ~ sQ11_spl
| sQ422_spl ),
inference(split_clause,[status(thm)],[f3493,f3519,f545]) ).
fof(f3523,definition,
! [X0,X1] :
( sQ423_spl
<=> ( rearsegP(skaf80(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf80(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ423_spl])],[split_symbol_definition]) ).
fof(f3526,plain,
( ~ sQ11_spl
| sQ423_spl ),
inference(split_clause,[status(thm)],[f3494,f3523,f545]) ).
fof(f3528,plain,
! [X0,X1] :
( ~ sQ417_spl
| segmentP(app(skaf80(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3500,f214]) ).
fof(f3536,plain,
! [X0] :
( app(skaf81(X0),nil) = nil
| ~ rearsegP(nil,skaf81(X0))
| ~ ssList(nil)
| ~ ssList(skaf81(X0)) ),
inference(paramodulation,[status(thm)],[f1040,f2334]) ).
fof(f3537,plain,
! [X0,X1] :
( segmentP(app(skaf81(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf81(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1040,f2205]) ).
fof(f3538,plain,
! [X0] :
( rearsegP(skaf81(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf81(X0)) ),
inference(paramodulation,[status(thm)],[f1040,f2173]) ).
fof(f3539,plain,
! [X0] :
( ssList(skaf81(X0))
| ~ ssList(skaf81(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1040,f285]) ).
fof(f3540,plain,
! [X0,X1,X2] :
( app(app(skaf81(X2),nil),X1) = X0
| ~ ssList(app(skaf81(X2),X1))
| ~ segmentP(X0,app(app(skaf81(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf81(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1040,f666]) ).
fof(f3541,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf81(X2),X1))
| ~ segmentP(X3,app(app(skaf81(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf81(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1040,f665]) ).
fof(f3542,plain,
! [X0,X1,X2] :
( segmentP(app(skaf81(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf81(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1040,f404]) ).
fof(f3543,plain,
! [X0,X1] :
( rearsegP(skaf81(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf81(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1040,f350]) ).
fof(f3544,definition,
! [X0] :
( sQ424_spl
<=> ( app(skaf81(X0),nil) = nil
| ~ rearsegP(nil,skaf81(X0))
| ~ ssList(skaf81(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ424_spl])],[split_symbol_definition]) ).
fof(f3547,plain,
( ~ sQ11_spl
| sQ424_spl ),
inference(split_clause,[status(thm)],[f3536,f3544,f545]) ).
fof(f3548,definition,
! [X0,X1] :
( sQ425_spl
<=> ( segmentP(app(skaf81(X1),X0),nil)
| ~ ssList(skaf81(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ425_spl])],[split_symbol_definition]) ).
fof(f3549,plain,
! [X0,X1] :
( ~ sQ425_spl
| segmentP(app(skaf81(X1),X0),nil)
| ~ ssList(skaf81(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3548]) ).
fof(f3551,plain,
( ~ sQ11_spl
| sQ425_spl ),
inference(split_clause,[status(thm)],[f3537,f3548,f545]) ).
fof(f3552,definition,
! [X0] :
( sQ426_spl
<=> ( rearsegP(skaf81(X0),nil)
| ~ ssList(skaf81(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ426_spl])],[split_symbol_definition]) ).
fof(f3555,plain,
( ~ sQ11_spl
| sQ426_spl ),
inference(split_clause,[status(thm)],[f3538,f3552,f545]) ).
fof(f3556,definition,
! [X0] :
( sQ427_spl
<=> ( ssList(skaf81(X0))
| ~ ssList(skaf81(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ427_spl])],[split_symbol_definition]) ).
fof(f3559,plain,
( sQ427_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3539,f545,f3556]) ).
fof(f3560,definition,
! [X0,X1,X2] :
( sQ428_spl
<=> ( app(app(skaf81(X2),nil),X1) = X0
| ~ ssList(app(skaf81(X2),X1))
| ~ segmentP(X0,app(app(skaf81(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf81(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ428_spl])],[split_symbol_definition]) ).
fof(f3563,plain,
( ~ sQ11_spl
| sQ428_spl ),
inference(split_clause,[status(thm)],[f3540,f3560,f545]) ).
fof(f3564,definition,
! [X0,X1,X2,X3] :
( sQ429_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf81(X2),X1))
| ~ segmentP(X3,app(app(skaf81(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf81(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ429_spl])],[split_symbol_definition]) ).
fof(f3567,plain,
( ~ sQ11_spl
| sQ429_spl ),
inference(split_clause,[status(thm)],[f3541,f3564,f545]) ).
fof(f3568,definition,
! [X0,X1,X2] :
( sQ430_spl
<=> ( segmentP(app(skaf81(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf81(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ430_spl])],[split_symbol_definition]) ).
fof(f3571,plain,
( ~ sQ11_spl
| sQ430_spl ),
inference(split_clause,[status(thm)],[f3542,f3568,f545]) ).
fof(f3572,definition,
! [X0,X1] :
( sQ431_spl
<=> ( rearsegP(skaf81(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf81(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ431_spl])],[split_symbol_definition]) ).
fof(f3575,plain,
( ~ sQ11_spl
| sQ431_spl ),
inference(split_clause,[status(thm)],[f3543,f3572,f545]) ).
fof(f3577,plain,
! [X0,X1] :
( ~ sQ425_spl
| segmentP(app(skaf81(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3549,f213]) ).
fof(f3585,plain,
! [X0] :
( app(skaf82(X0),nil) = nil
| ~ rearsegP(nil,skaf82(X0))
| ~ ssList(nil)
| ~ ssList(skaf82(X0)) ),
inference(paramodulation,[status(thm)],[f1041,f2334]) ).
fof(f3586,plain,
! [X0,X1] :
( segmentP(app(skaf82(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf82(X1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1041,f2205]) ).
fof(f3587,plain,
! [X0] :
( rearsegP(skaf82(X0),nil)
| ~ ssList(nil)
| ~ ssList(skaf82(X0)) ),
inference(paramodulation,[status(thm)],[f1041,f2173]) ).
fof(f3588,plain,
! [X0] :
( ssList(skaf82(X0))
| ~ ssList(skaf82(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1041,f285]) ).
fof(f3589,plain,
! [X0,X1,X2] :
( app(app(skaf82(X2),nil),X1) = X0
| ~ ssList(app(skaf82(X2),X1))
| ~ segmentP(X0,app(app(skaf82(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf82(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1041,f666]) ).
fof(f3590,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf82(X2),X1))
| ~ segmentP(X3,app(app(skaf82(X2),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf82(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1041,f665]) ).
fof(f3591,plain,
! [X0,X1,X2] :
( segmentP(app(skaf82(X2),X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf82(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1041,f404]) ).
fof(f3592,plain,
! [X0,X1] :
( rearsegP(skaf82(X1),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf82(X1))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1041,f350]) ).
fof(f3593,definition,
! [X0] :
( sQ432_spl
<=> ( app(skaf82(X0),nil) = nil
| ~ rearsegP(nil,skaf82(X0))
| ~ ssList(skaf82(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ432_spl])],[split_symbol_definition]) ).
fof(f3596,plain,
( ~ sQ11_spl
| sQ432_spl ),
inference(split_clause,[status(thm)],[f3585,f3593,f545]) ).
fof(f3597,definition,
! [X0,X1] :
( sQ433_spl
<=> ( segmentP(app(skaf82(X1),X0),nil)
| ~ ssList(skaf82(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ433_spl])],[split_symbol_definition]) ).
fof(f3598,plain,
! [X0,X1] :
( ~ sQ433_spl
| segmentP(app(skaf82(X1),X0),nil)
| ~ ssList(skaf82(X1))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3597]) ).
fof(f3600,plain,
( ~ sQ11_spl
| sQ433_spl ),
inference(split_clause,[status(thm)],[f3586,f3597,f545]) ).
fof(f3601,definition,
! [X0] :
( sQ434_spl
<=> ( rearsegP(skaf82(X0),nil)
| ~ ssList(skaf82(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ434_spl])],[split_symbol_definition]) ).
fof(f3604,plain,
( ~ sQ11_spl
| sQ434_spl ),
inference(split_clause,[status(thm)],[f3587,f3601,f545]) ).
fof(f3605,definition,
! [X0] :
( sQ435_spl
<=> ( ssList(skaf82(X0))
| ~ ssList(skaf82(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ435_spl])],[split_symbol_definition]) ).
fof(f3608,plain,
( sQ435_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3588,f545,f3605]) ).
fof(f3609,definition,
! [X0,X1,X2] :
( sQ436_spl
<=> ( app(app(skaf82(X2),nil),X1) = X0
| ~ ssList(app(skaf82(X2),X1))
| ~ segmentP(X0,app(app(skaf82(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf82(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ436_spl])],[split_symbol_definition]) ).
fof(f3612,plain,
( ~ sQ11_spl
| sQ436_spl ),
inference(split_clause,[status(thm)],[f3589,f3609,f545]) ).
fof(f3613,definition,
! [X0,X1,X2,X3] :
( sQ437_spl
<=> ( segmentP(X3,X0)
| ~ ssList(X3)
| ~ ssList(app(skaf82(X2),X1))
| ~ segmentP(X3,app(app(skaf82(X2),nil),X1))
| ~ ssList(X0)
| ~ ssList(skaf82(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ437_spl])],[split_symbol_definition]) ).
fof(f3616,plain,
( ~ sQ11_spl
| sQ437_spl ),
inference(split_clause,[status(thm)],[f3590,f3613,f545]) ).
fof(f3617,definition,
! [X0,X1,X2] :
( sQ438_spl
<=> ( segmentP(app(skaf82(X2),X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf82(X2))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ438_spl])],[split_symbol_definition]) ).
fof(f3620,plain,
( ~ sQ11_spl
| sQ438_spl ),
inference(split_clause,[status(thm)],[f3591,f3617,f545]) ).
fof(f3621,definition,
! [X0,X1] :
( sQ439_spl
<=> ( rearsegP(skaf82(X1),X0)
| ~ ssList(X0)
| ~ ssList(skaf82(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ439_spl])],[split_symbol_definition]) ).
fof(f3624,plain,
( ~ sQ11_spl
| sQ439_spl ),
inference(split_clause,[status(thm)],[f3592,f3621,f545]) ).
fof(f3626,plain,
! [X0,X1] :
( ~ sQ433_spl
| segmentP(app(skaf82(X1),X0),nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3598,f212]) ).
fof(f3635,plain,
! [X0] :
( app(nil,skaf51(X0)) = skaf51(X0)
| ~ rearsegP(skaf51(X0),skaf51(X0))
| ~ ssList(skaf51(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1414,f2334]) ).
fof(f3636,plain,
! [X0,X1] :
( segmentP(app(skaf51(X1),X0),skaf51(X1))
| ~ ssList(skaf51(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1414,f2205]) ).
fof(f3637,plain,
! [X0] :
( rearsegP(skaf51(X0),skaf51(X0))
| ~ ssList(skaf51(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1414,f2173]) ).
fof(f3639,plain,
! [X0,X1,X2] :
( app(app(nil,skaf51(X0)),X2) = X1
| ~ ssList(app(skaf51(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf51(X0)),X2))
| ~ ssList(skaf51(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf51(X0),X1) ),
inference(paramodulation,[status(thm)],[f1414,f666]) ).
fof(f3640,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf51(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf51(X0)),X2))
| ~ ssList(skaf51(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf51(X0),X1) ),
inference(paramodulation,[status(thm)],[f1414,f665]) ).
fof(f3641,plain,
! [X0,X1,X2] :
( segmentP(app(skaf51(X0),X2),X1)
| ~ ssList(skaf51(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf51(X0),X1) ),
inference(paramodulation,[status(thm)],[f1414,f404]) ).
fof(f3642,plain,
! [X0,X1] :
( rearsegP(skaf51(X0),X1)
| ~ ssList(skaf51(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf51(X0),X1) ),
inference(paramodulation,[status(thm)],[f1414,f350]) ).
fof(f3643,definition,
! [X0] :
( sQ440_spl
<=> ( app(nil,skaf51(X0)) = skaf51(X0)
| ~ rearsegP(skaf51(X0),skaf51(X0))
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ440_spl])],[split_symbol_definition]) ).
fof(f3646,plain,
( sQ440_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3635,f545,f3643]) ).
fof(f3647,definition,
! [X0,X1] :
( sQ441_spl
<=> ( segmentP(app(skaf51(X1),X0),skaf51(X1))
| ~ ssList(skaf51(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ441_spl])],[split_symbol_definition]) ).
fof(f3650,plain,
( ~ sQ11_spl
| sQ441_spl ),
inference(split_clause,[status(thm)],[f3636,f3647,f545]) ).
fof(f3651,definition,
! [X0] :
( sQ442_spl
<=> ( rearsegP(skaf51(X0),skaf51(X0))
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ442_spl])],[split_symbol_definition]) ).
fof(f3654,plain,
( sQ442_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3637,f545,f3651]) ).
fof(f3656,definition,
! [X0,X1,X2] :
( sQ443_spl
<=> ( app(app(nil,skaf51(X0)),X2) = X1
| ~ ssList(app(skaf51(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf51(X0)),X2))
| ~ ssList(skaf51(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf51(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ443_spl])],[split_symbol_definition]) ).
fof(f3659,plain,
( ~ sQ11_spl
| sQ443_spl ),
inference(split_clause,[status(thm)],[f3639,f3656,f545]) ).
fof(f3660,definition,
! [X0,X1,X2,X3] :
( sQ444_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf51(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf51(X0)),X2))
| ~ ssList(skaf51(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf51(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ444_spl])],[split_symbol_definition]) ).
fof(f3663,plain,
( ~ sQ11_spl
| sQ444_spl ),
inference(split_clause,[status(thm)],[f3640,f3660,f545]) ).
fof(f3664,definition,
! [X0,X1,X2] :
( sQ445_spl
<=> ( segmentP(app(skaf51(X0),X2),X1)
| ~ ssList(skaf51(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf51(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ445_spl])],[split_symbol_definition]) ).
fof(f3667,plain,
( ~ sQ11_spl
| sQ445_spl ),
inference(split_clause,[status(thm)],[f3641,f3664,f545]) ).
fof(f3668,definition,
! [X0,X1] :
( sQ446_spl
<=> ( rearsegP(skaf51(X0),X1)
| ~ ssList(skaf51(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf51(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ446_spl])],[split_symbol_definition]) ).
fof(f3671,plain,
( ~ sQ11_spl
| sQ446_spl ),
inference(split_clause,[status(thm)],[f3642,f3668,f545]) ).
fof(f3680,plain,
! [X0] :
( app(nil,skaf52(X0)) = skaf52(X0)
| ~ rearsegP(skaf52(X0),skaf52(X0))
| ~ ssList(skaf52(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1415,f2334]) ).
fof(f3681,plain,
! [X0,X1] :
( segmentP(app(skaf52(X1),X0),skaf52(X1))
| ~ ssList(skaf52(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1415,f2205]) ).
fof(f3682,plain,
! [X0] :
( rearsegP(skaf52(X0),skaf52(X0))
| ~ ssList(skaf52(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1415,f2173]) ).
fof(f3684,plain,
! [X0,X1,X2] :
( app(app(nil,skaf52(X0)),X2) = X1
| ~ ssList(app(skaf52(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf52(X0)),X2))
| ~ ssList(skaf52(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf52(X0),X1) ),
inference(paramodulation,[status(thm)],[f1415,f666]) ).
fof(f3685,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf52(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf52(X0)),X2))
| ~ ssList(skaf52(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf52(X0),X1) ),
inference(paramodulation,[status(thm)],[f1415,f665]) ).
fof(f3686,plain,
! [X0,X1,X2] :
( segmentP(app(skaf52(X0),X2),X1)
| ~ ssList(skaf52(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf52(X0),X1) ),
inference(paramodulation,[status(thm)],[f1415,f404]) ).
fof(f3687,plain,
! [X0,X1] :
( rearsegP(skaf52(X0),X1)
| ~ ssList(skaf52(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf52(X0),X1) ),
inference(paramodulation,[status(thm)],[f1415,f350]) ).
fof(f3688,definition,
! [X0] :
( sQ447_spl
<=> ( app(nil,skaf52(X0)) = skaf52(X0)
| ~ rearsegP(skaf52(X0),skaf52(X0))
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ447_spl])],[split_symbol_definition]) ).
fof(f3691,plain,
( sQ447_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3680,f545,f3688]) ).
fof(f3692,definition,
! [X0,X1] :
( sQ448_spl
<=> ( segmentP(app(skaf52(X1),X0),skaf52(X1))
| ~ ssList(skaf52(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f3695,plain,
( ~ sQ11_spl
| sQ448_spl ),
inference(split_clause,[status(thm)],[f3681,f3692,f545]) ).
fof(f3696,definition,
! [X0] :
( sQ449_spl
<=> ( rearsegP(skaf52(X0),skaf52(X0))
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ449_spl])],[split_symbol_definition]) ).
fof(f3699,plain,
( sQ449_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3682,f545,f3696]) ).
fof(f3701,definition,
! [X0,X1,X2] :
( sQ450_spl
<=> ( app(app(nil,skaf52(X0)),X2) = X1
| ~ ssList(app(skaf52(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf52(X0)),X2))
| ~ ssList(skaf52(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf52(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ450_spl])],[split_symbol_definition]) ).
fof(f3704,plain,
( ~ sQ11_spl
| sQ450_spl ),
inference(split_clause,[status(thm)],[f3684,f3701,f545]) ).
fof(f3705,definition,
! [X0,X1,X2,X3] :
( sQ451_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf52(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf52(X0)),X2))
| ~ ssList(skaf52(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf52(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f3708,plain,
( ~ sQ11_spl
| sQ451_spl ),
inference(split_clause,[status(thm)],[f3685,f3705,f545]) ).
fof(f3709,definition,
! [X0,X1,X2] :
( sQ452_spl
<=> ( segmentP(app(skaf52(X0),X2),X1)
| ~ ssList(skaf52(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf52(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ452_spl])],[split_symbol_definition]) ).
fof(f3712,plain,
( ~ sQ11_spl
| sQ452_spl ),
inference(split_clause,[status(thm)],[f3686,f3709,f545]) ).
fof(f3713,definition,
! [X0,X1] :
( sQ453_spl
<=> ( rearsegP(skaf52(X0),X1)
| ~ ssList(skaf52(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf52(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ453_spl])],[split_symbol_definition]) ).
fof(f3716,plain,
( ~ sQ11_spl
| sQ453_spl ),
inference(split_clause,[status(thm)],[f3687,f3713,f545]) ).
fof(f3732,plain,
! [X0] :
( ~ sQ111_spl
| segmentP(sk1,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(sk1,X0) ),
inference(paramodulation,[status(thm)],[f1013,f1466]) ).
fof(f3735,definition,
! [X0] :
( sQ454_spl
<=> ( segmentP(sk1,X0)
| ~ ssList(X0)
| ~ segmentP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ454_spl])],[split_symbol_definition]) ).
fof(f3738,plain,
( ~ sQ111_spl
| ~ sQ11_spl
| sQ454_spl ),
inference(split_clause,[status(thm)],[f3732,f3735,f545,f1465]) ).
fof(f3739,plain,
! [X0,X1] :
( ~ sQ107_spl
| ~ ssList(sk1)
| ~ ssList(X1)
| app(sk1,X1) = X0
| ~ segmentP(X0,app(sk1,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ),
inference(resolution,[status(thm)],[f1479,f285]) ).
fof(f3740,plain,
! [X0] :
( ~ sQ107_spl
| app(sk1,nil) = X0
| ~ ssList(sk1)
| ~ segmentP(X0,app(sk1,nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(sk1,X0) ),
inference(paramodulation,[status(thm)],[f1013,f1479]) ).
fof(f3741,definition,
! [X0,X1] :
( sQ455_spl
<=> ( ~ ssList(X1)
| app(sk1,X1) = X0
| ~ segmentP(X0,app(sk1,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ455_spl])],[split_symbol_definition]) ).
fof(f3744,plain,
( ~ sQ107_spl
| ~ sQ13_spl
| sQ455_spl ),
inference(split_clause,[status(thm)],[f3739,f3741,f558,f1449]) ).
fof(f3745,definition,
! [X0] :
( sQ456_spl
<=> ( app(sk1,nil) = X0
| ~ segmentP(X0,app(sk1,nil))
| ~ ssList(X0)
| ~ segmentP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ456_spl])],[split_symbol_definition]) ).
fof(f3746,plain,
! [X0] :
( ~ sQ456_spl
| app(sk1,nil) = X0
| ~ segmentP(X0,app(sk1,nil))
| ~ ssList(X0)
| ~ segmentP(sk1,X0) ),
inference(component_clause,[status(thm)],[f3745]) ).
fof(f3748,plain,
( ~ sQ107_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sQ456_spl ),
inference(split_clause,[status(thm)],[f3740,f3745,f545,f558,f1449]) ).
fof(f3750,plain,
! [X0] :
( ~ sQ456_spl
| app(sk1,nil) = X0
| ~ segmentP(X0,sk1)
| ~ ssList(X0)
| ~ segmentP(sk1,X0) ),
inference(forward_demodulation,[status(thm)],[f1013,f3746]) ).
fof(f3751,plain,
! [X0] :
( ~ sQ456_spl
| sk1 = X0
| ~ segmentP(X0,sk1)
| ~ ssList(X0)
| ~ segmentP(sk1,X0) ),
inference(forward_demodulation,[status(thm)],[f1013,f3750]) ).
fof(f3752,plain,
! [X0,X1,X2] :
( ~ sQ272_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf56(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf56(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2636,f374]) ).
fof(f3753,plain,
! [X0,X1] :
( ~ sQ272_spl
| app(skaf56(X1),X0) = nil
| ~ ssList(app(skaf56(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf56(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2636,f339]) ).
fof(f3754,plain,
! [X0] :
( ~ sQ272_spl
| segmentP(skaf56(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1023,f2636]) ).
fof(f3755,definition,
! [X0,X1,X2] :
( sQ457_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf56(X2),X0))
| ~ segmentP(X1,app(skaf56(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ457_spl])],[split_symbol_definition]) ).
fof(f3758,plain,
( ~ sQ272_spl
| ~ sQ11_spl
| sQ457_spl ),
inference(split_clause,[status(thm)],[f3752,f3755,f545,f2604]) ).
fof(f3759,definition,
! [X0,X1] :
( sQ458_spl
<=> ( app(skaf56(X1),X0) = nil
| ~ ssList(app(skaf56(X1),X0))
| ~ segmentP(nil,app(skaf56(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ458_spl])],[split_symbol_definition]) ).
fof(f3762,plain,
( ~ sQ272_spl
| ~ sQ11_spl
| sQ458_spl ),
inference(split_clause,[status(thm)],[f3753,f3759,f545,f2604]) ).
fof(f3763,definition,
! [X0] :
( sQ459_spl
<=> segmentP(skaf56(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ459_spl])],[split_symbol_definition]) ).
fof(f3764,plain,
! [X0] :
( ~ sQ459_spl
| segmentP(skaf56(X0),nil) ),
inference(component_clause,[status(thm)],[f3763]) ).
fof(f3766,plain,
( ~ sQ272_spl
| sQ459_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3754,f545,f3763,f2604]) ).
fof(f3767,plain,
! [X0,X1] :
( ~ sQ459_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf56(X1)) ),
inference(resolution,[status(thm)],[f3764,f374]) ).
fof(f3768,plain,
! [X0] :
( ~ sQ459_spl
| skaf56(X0) = nil
| ~ ssList(skaf56(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf56(X0)) ),
inference(resolution,[status(thm)],[f3764,f339]) ).
fof(f3769,definition,
! [X0,X1] :
( sQ460_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ segmentP(X0,skaf56(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ460_spl])],[split_symbol_definition]) ).
fof(f3772,plain,
( ~ sQ459_spl
| ~ sQ11_spl
| sQ460_spl ),
inference(split_clause,[status(thm)],[f3767,f3769,f545,f3763]) ).
fof(f3773,definition,
! [X0] :
( sQ461_spl
<=> ( skaf56(X0) = nil
| ~ ssList(skaf56(X0))
| ~ segmentP(nil,skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ461_spl])],[split_symbol_definition]) ).
fof(f3776,plain,
( ~ sQ459_spl
| ~ sQ11_spl
| sQ461_spl ),
inference(split_clause,[status(thm)],[f3768,f3773,f545,f3763]) ).
fof(f3777,plain,
! [X0,X1,X2] :
( ~ sQ273_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf53(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf53(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2637,f374]) ).
fof(f3778,plain,
! [X0,X1] :
( ~ sQ273_spl
| app(skaf53(X1),X0) = nil
| ~ ssList(app(skaf53(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf53(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2637,f339]) ).
fof(f3779,plain,
! [X0] :
( ~ sQ273_spl
| segmentP(skaf53(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1022,f2637]) ).
fof(f3780,definition,
! [X0,X1,X2] :
( sQ462_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf53(X2),X0))
| ~ segmentP(X1,app(skaf53(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ462_spl])],[split_symbol_definition]) ).
fof(f3783,plain,
( ~ sQ273_spl
| ~ sQ11_spl
| sQ462_spl ),
inference(split_clause,[status(thm)],[f3777,f3780,f545,f2608]) ).
fof(f3784,definition,
! [X0,X1] :
( sQ463_spl
<=> ( app(skaf53(X1),X0) = nil
| ~ ssList(app(skaf53(X1),X0))
| ~ segmentP(nil,app(skaf53(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ463_spl])],[split_symbol_definition]) ).
fof(f3787,plain,
( ~ sQ273_spl
| ~ sQ11_spl
| sQ463_spl ),
inference(split_clause,[status(thm)],[f3778,f3784,f545,f2608]) ).
fof(f3788,definition,
! [X0] :
( sQ464_spl
<=> segmentP(skaf53(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ464_spl])],[split_symbol_definition]) ).
fof(f3789,plain,
! [X0] :
( ~ sQ464_spl
| segmentP(skaf53(X0),nil) ),
inference(component_clause,[status(thm)],[f3788]) ).
fof(f3791,plain,
( ~ sQ273_spl
| sQ464_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3779,f545,f3788,f2608]) ).
fof(f3792,plain,
! [X0,X1] :
( ~ sQ464_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf53(X1)) ),
inference(resolution,[status(thm)],[f3789,f374]) ).
fof(f3793,plain,
! [X0] :
( ~ sQ464_spl
| skaf53(X0) = nil
| ~ ssList(skaf53(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf53(X0)) ),
inference(resolution,[status(thm)],[f3789,f339]) ).
fof(f3794,definition,
! [X0,X1] :
( sQ465_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf53(X1))
| ~ segmentP(X0,skaf53(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ465_spl])],[split_symbol_definition]) ).
fof(f3797,plain,
( ~ sQ464_spl
| ~ sQ11_spl
| sQ465_spl ),
inference(split_clause,[status(thm)],[f3792,f3794,f545,f3788]) ).
fof(f3798,definition,
! [X0] :
( sQ466_spl
<=> ( skaf53(X0) = nil
| ~ ssList(skaf53(X0))
| ~ segmentP(nil,skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ466_spl])],[split_symbol_definition]) ).
fof(f3801,plain,
( ~ sQ464_spl
| ~ sQ11_spl
| sQ466_spl ),
inference(split_clause,[status(thm)],[f3793,f3798,f545,f3788]) ).
fof(f3802,plain,
! [X0,X1,X2] :
( ~ sQ274_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf52(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf52(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2638,f374]) ).
fof(f3803,plain,
! [X0,X1] :
( ~ sQ274_spl
| app(skaf52(X1),X0) = nil
| ~ ssList(app(skaf52(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf52(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2638,f339]) ).
fof(f3804,plain,
! [X0] :
( ~ sQ274_spl
| segmentP(skaf52(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1021,f2638]) ).
fof(f3805,definition,
! [X0,X1,X2] :
( sQ467_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf52(X2),X0))
| ~ segmentP(X1,app(skaf52(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ467_spl])],[split_symbol_definition]) ).
fof(f3808,plain,
( ~ sQ274_spl
| ~ sQ11_spl
| sQ467_spl ),
inference(split_clause,[status(thm)],[f3802,f3805,f545,f2612]) ).
fof(f3809,definition,
! [X0,X1] :
( sQ468_spl
<=> ( app(skaf52(X1),X0) = nil
| ~ ssList(app(skaf52(X1),X0))
| ~ segmentP(nil,app(skaf52(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ468_spl])],[split_symbol_definition]) ).
fof(f3812,plain,
( ~ sQ274_spl
| ~ sQ11_spl
| sQ468_spl ),
inference(split_clause,[status(thm)],[f3803,f3809,f545,f2612]) ).
fof(f3813,definition,
! [X0] :
( sQ469_spl
<=> segmentP(skaf52(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ469_spl])],[split_symbol_definition]) ).
fof(f3814,plain,
! [X0] :
( ~ sQ469_spl
| segmentP(skaf52(X0),nil) ),
inference(component_clause,[status(thm)],[f3813]) ).
fof(f3816,plain,
( ~ sQ274_spl
| sQ469_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3804,f545,f3813,f2612]) ).
fof(f3817,plain,
! [X0,X1] :
( ~ sQ469_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf52(X1)) ),
inference(resolution,[status(thm)],[f3814,f374]) ).
fof(f3818,plain,
! [X0] :
( ~ sQ469_spl
| skaf52(X0) = nil
| ~ ssList(skaf52(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf52(X0)) ),
inference(resolution,[status(thm)],[f3814,f339]) ).
fof(f3819,definition,
! [X0,X1] :
( sQ470_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf52(X1))
| ~ segmentP(X0,skaf52(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ470_spl])],[split_symbol_definition]) ).
fof(f3822,plain,
( ~ sQ469_spl
| ~ sQ11_spl
| sQ470_spl ),
inference(split_clause,[status(thm)],[f3817,f3819,f545,f3813]) ).
fof(f3823,definition,
! [X0] :
( sQ471_spl
<=> ( skaf52(X0) = nil
| ~ ssList(skaf52(X0))
| ~ segmentP(nil,skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ471_spl])],[split_symbol_definition]) ).
fof(f3826,plain,
( ~ sQ469_spl
| ~ sQ11_spl
| sQ471_spl ),
inference(split_clause,[status(thm)],[f3818,f3823,f545,f3813]) ).
fof(f3828,plain,
! [X0] :
( ~ sQ100_spl
| ~ ssList(nil)
| app(nil,X0) = nil
| ~ ssList(app(nil,X0))
| ~ segmentP(nil,app(nil,X0))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1384,f255]) ).
fof(f3831,plain,
( ~ sQ100_spl
| ~ sQ11_spl
| sQ352_spl ),
inference(split_clause,[status(thm)],[f3828,f3094,f545,f1371]) ).
fof(f3833,plain,
! [X0,X1,X2] :
( ~ sQ108_spl
| ~ ssList(sk1)
| ~ ssList(X1)
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ segmentP(X2,app(sk1,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ),
inference(resolution,[status(thm)],[f1480,f285]) ).
fof(f3834,plain,
! [X0,X1] :
( ~ sQ108_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(sk1)
| ~ segmentP(X1,app(sk1,nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(sk1,X0) ),
inference(paramodulation,[status(thm)],[f1013,f1480]) ).
fof(f3835,definition,
! [X0,X1,X2] :
( sQ472_spl
<=> ( ~ ssList(X1)
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ segmentP(X2,app(sk1,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ472_spl])],[split_symbol_definition]) ).
fof(f3838,plain,
( ~ sQ108_spl
| ~ sQ13_spl
| sQ472_spl ),
inference(split_clause,[status(thm)],[f3833,f3835,f558,f1453]) ).
fof(f3839,definition,
! [X0,X1] :
( sQ473_spl
<=> ( segmentP(X1,X0)
| ~ ssList(X1)
| ~ segmentP(X1,app(sk1,nil))
| ~ ssList(X0)
| ~ segmentP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ473_spl])],[split_symbol_definition]) ).
fof(f3842,plain,
( ~ sQ108_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sQ473_spl ),
inference(split_clause,[status(thm)],[f3834,f3839,f545,f558,f1453]) ).
fof(f3846,plain,
! [X0] :
( app(nil,skaf53(X0)) = skaf53(X0)
| ~ rearsegP(skaf53(X0),skaf53(X0))
| ~ ssList(skaf53(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1416,f2334]) ).
fof(f3847,plain,
! [X0,X1] :
( segmentP(app(skaf53(X1),X0),skaf53(X1))
| ~ ssList(skaf53(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1416,f2205]) ).
fof(f3848,plain,
! [X0] :
( rearsegP(skaf53(X0),skaf53(X0))
| ~ ssList(skaf53(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1416,f2173]) ).
fof(f3850,plain,
! [X0,X1,X2] :
( app(app(nil,skaf53(X0)),X2) = X1
| ~ ssList(app(skaf53(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf53(X0)),X2))
| ~ ssList(skaf53(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf53(X0),X1) ),
inference(paramodulation,[status(thm)],[f1416,f666]) ).
fof(f3851,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf53(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf53(X0)),X2))
| ~ ssList(skaf53(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf53(X0),X1) ),
inference(paramodulation,[status(thm)],[f1416,f665]) ).
fof(f3852,plain,
! [X0,X1,X2] :
( segmentP(app(skaf53(X0),X2),X1)
| ~ ssList(skaf53(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf53(X0),X1) ),
inference(paramodulation,[status(thm)],[f1416,f404]) ).
fof(f3853,plain,
! [X0,X1] :
( rearsegP(skaf53(X0),X1)
| ~ ssList(skaf53(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf53(X0),X1) ),
inference(paramodulation,[status(thm)],[f1416,f350]) ).
fof(f3854,definition,
! [X0] :
( sQ474_spl
<=> ( app(nil,skaf53(X0)) = skaf53(X0)
| ~ rearsegP(skaf53(X0),skaf53(X0))
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ474_spl])],[split_symbol_definition]) ).
fof(f3857,plain,
( sQ474_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3846,f545,f3854]) ).
fof(f3858,definition,
! [X0,X1] :
( sQ475_spl
<=> ( segmentP(app(skaf53(X1),X0),skaf53(X1))
| ~ ssList(skaf53(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ475_spl])],[split_symbol_definition]) ).
fof(f3861,plain,
( ~ sQ11_spl
| sQ475_spl ),
inference(split_clause,[status(thm)],[f3847,f3858,f545]) ).
fof(f3862,definition,
! [X0] :
( sQ476_spl
<=> ( rearsegP(skaf53(X0),skaf53(X0))
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ476_spl])],[split_symbol_definition]) ).
fof(f3865,plain,
( sQ476_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3848,f545,f3862]) ).
fof(f3867,definition,
! [X0,X1,X2] :
( sQ477_spl
<=> ( app(app(nil,skaf53(X0)),X2) = X1
| ~ ssList(app(skaf53(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf53(X0)),X2))
| ~ ssList(skaf53(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf53(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ477_spl])],[split_symbol_definition]) ).
fof(f3870,plain,
( ~ sQ11_spl
| sQ477_spl ),
inference(split_clause,[status(thm)],[f3850,f3867,f545]) ).
fof(f3871,definition,
! [X0,X1,X2,X3] :
( sQ478_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf53(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf53(X0)),X2))
| ~ ssList(skaf53(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf53(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ478_spl])],[split_symbol_definition]) ).
fof(f3874,plain,
( ~ sQ11_spl
| sQ478_spl ),
inference(split_clause,[status(thm)],[f3851,f3871,f545]) ).
fof(f3875,definition,
! [X0,X1,X2] :
( sQ479_spl
<=> ( segmentP(app(skaf53(X0),X2),X1)
| ~ ssList(skaf53(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf53(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ479_spl])],[split_symbol_definition]) ).
fof(f3878,plain,
( ~ sQ11_spl
| sQ479_spl ),
inference(split_clause,[status(thm)],[f3852,f3875,f545]) ).
fof(f3879,definition,
! [X0,X1] :
( sQ480_spl
<=> ( rearsegP(skaf53(X0),X1)
| ~ ssList(skaf53(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf53(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ480_spl])],[split_symbol_definition]) ).
fof(f3882,plain,
( ~ sQ11_spl
| sQ480_spl ),
inference(split_clause,[status(thm)],[f3853,f3879,f545]) ).
fof(f3891,plain,
! [X0] :
( app(nil,skaf56(X0)) = skaf56(X0)
| ~ rearsegP(skaf56(X0),skaf56(X0))
| ~ ssList(skaf56(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1417,f2334]) ).
fof(f3892,plain,
! [X0,X1] :
( segmentP(app(skaf56(X1),X0),skaf56(X1))
| ~ ssList(skaf56(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1417,f2205]) ).
fof(f3893,plain,
! [X0] :
( rearsegP(skaf56(X0),skaf56(X0))
| ~ ssList(skaf56(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1417,f2173]) ).
fof(f3895,plain,
! [X0,X1,X2] :
( app(app(nil,skaf56(X0)),X2) = X1
| ~ ssList(app(skaf56(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf56(X0)),X2))
| ~ ssList(skaf56(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf56(X0),X1) ),
inference(paramodulation,[status(thm)],[f1417,f666]) ).
fof(f3896,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf56(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf56(X0)),X2))
| ~ ssList(skaf56(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf56(X0),X1) ),
inference(paramodulation,[status(thm)],[f1417,f665]) ).
fof(f3897,plain,
! [X0,X1,X2] :
( segmentP(app(skaf56(X0),X2),X1)
| ~ ssList(skaf56(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf56(X0),X1) ),
inference(paramodulation,[status(thm)],[f1417,f404]) ).
fof(f3898,plain,
! [X0,X1] :
( rearsegP(skaf56(X0),X1)
| ~ ssList(skaf56(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf56(X0),X1) ),
inference(paramodulation,[status(thm)],[f1417,f350]) ).
fof(f3899,definition,
! [X0] :
( sQ481_spl
<=> ( app(nil,skaf56(X0)) = skaf56(X0)
| ~ rearsegP(skaf56(X0),skaf56(X0))
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ481_spl])],[split_symbol_definition]) ).
fof(f3902,plain,
( sQ481_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3891,f545,f3899]) ).
fof(f3903,definition,
! [X0,X1] :
( sQ482_spl
<=> ( segmentP(app(skaf56(X1),X0),skaf56(X1))
| ~ ssList(skaf56(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ482_spl])],[split_symbol_definition]) ).
fof(f3906,plain,
( ~ sQ11_spl
| sQ482_spl ),
inference(split_clause,[status(thm)],[f3892,f3903,f545]) ).
fof(f3907,definition,
! [X0] :
( sQ483_spl
<=> ( rearsegP(skaf56(X0),skaf56(X0))
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ483_spl])],[split_symbol_definition]) ).
fof(f3910,plain,
( sQ483_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3893,f545,f3907]) ).
fof(f3912,definition,
! [X0,X1,X2] :
( sQ484_spl
<=> ( app(app(nil,skaf56(X0)),X2) = X1
| ~ ssList(app(skaf56(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf56(X0)),X2))
| ~ ssList(skaf56(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf56(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ484_spl])],[split_symbol_definition]) ).
fof(f3915,plain,
( ~ sQ11_spl
| sQ484_spl ),
inference(split_clause,[status(thm)],[f3895,f3912,f545]) ).
fof(f3916,definition,
! [X0,X1,X2,X3] :
( sQ485_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf56(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf56(X0)),X2))
| ~ ssList(skaf56(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf56(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ485_spl])],[split_symbol_definition]) ).
fof(f3919,plain,
( ~ sQ11_spl
| sQ485_spl ),
inference(split_clause,[status(thm)],[f3896,f3916,f545]) ).
fof(f3920,definition,
! [X0,X1,X2] :
( sQ486_spl
<=> ( segmentP(app(skaf56(X0),X2),X1)
| ~ ssList(skaf56(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf56(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ486_spl])],[split_symbol_definition]) ).
fof(f3923,plain,
( ~ sQ11_spl
| sQ486_spl ),
inference(split_clause,[status(thm)],[f3897,f3920,f545]) ).
fof(f3924,definition,
! [X0,X1] :
( sQ487_spl
<=> ( rearsegP(skaf56(X0),X1)
| ~ ssList(skaf56(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf56(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ487_spl])],[split_symbol_definition]) ).
fof(f3927,plain,
( ~ sQ11_spl
| sQ487_spl ),
inference(split_clause,[status(thm)],[f3898,f3924,f545]) ).
fof(f3936,plain,
! [X0] :
( app(nil,skaf57(X0)) = skaf57(X0)
| ~ rearsegP(skaf57(X0),skaf57(X0))
| ~ ssList(skaf57(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1418,f2334]) ).
fof(f3937,plain,
! [X0,X1] :
( segmentP(app(skaf57(X1),X0),skaf57(X1))
| ~ ssList(skaf57(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1418,f2205]) ).
fof(f3938,plain,
! [X0] :
( rearsegP(skaf57(X0),skaf57(X0))
| ~ ssList(skaf57(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1418,f2173]) ).
fof(f3940,plain,
! [X0,X1,X2] :
( app(app(nil,skaf57(X0)),X2) = X1
| ~ ssList(app(skaf57(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf57(X0)),X2))
| ~ ssList(skaf57(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf57(X0),X1) ),
inference(paramodulation,[status(thm)],[f1418,f666]) ).
fof(f3941,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf57(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf57(X0)),X2))
| ~ ssList(skaf57(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf57(X0),X1) ),
inference(paramodulation,[status(thm)],[f1418,f665]) ).
fof(f3942,plain,
! [X0,X1,X2] :
( segmentP(app(skaf57(X0),X2),X1)
| ~ ssList(skaf57(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf57(X0),X1) ),
inference(paramodulation,[status(thm)],[f1418,f404]) ).
fof(f3943,plain,
! [X0,X1] :
( rearsegP(skaf57(X0),X1)
| ~ ssList(skaf57(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf57(X0),X1) ),
inference(paramodulation,[status(thm)],[f1418,f350]) ).
fof(f3944,definition,
! [X0] :
( sQ488_spl
<=> ( app(nil,skaf57(X0)) = skaf57(X0)
| ~ rearsegP(skaf57(X0),skaf57(X0))
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ488_spl])],[split_symbol_definition]) ).
fof(f3947,plain,
( sQ488_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3936,f545,f3944]) ).
fof(f3948,definition,
! [X0,X1] :
( sQ489_spl
<=> ( segmentP(app(skaf57(X1),X0),skaf57(X1))
| ~ ssList(skaf57(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ489_spl])],[split_symbol_definition]) ).
fof(f3951,plain,
( ~ sQ11_spl
| sQ489_spl ),
inference(split_clause,[status(thm)],[f3937,f3948,f545]) ).
fof(f3952,definition,
! [X0] :
( sQ490_spl
<=> ( rearsegP(skaf57(X0),skaf57(X0))
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ490_spl])],[split_symbol_definition]) ).
fof(f3955,plain,
( sQ490_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3938,f545,f3952]) ).
fof(f3957,definition,
! [X0,X1,X2] :
( sQ491_spl
<=> ( app(app(nil,skaf57(X0)),X2) = X1
| ~ ssList(app(skaf57(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf57(X0)),X2))
| ~ ssList(skaf57(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf57(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ491_spl])],[split_symbol_definition]) ).
fof(f3960,plain,
( ~ sQ11_spl
| sQ491_spl ),
inference(split_clause,[status(thm)],[f3940,f3957,f545]) ).
fof(f3961,definition,
! [X0,X1,X2,X3] :
( sQ492_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf57(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf57(X0)),X2))
| ~ ssList(skaf57(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf57(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ492_spl])],[split_symbol_definition]) ).
fof(f3964,plain,
( ~ sQ11_spl
| sQ492_spl ),
inference(split_clause,[status(thm)],[f3941,f3961,f545]) ).
fof(f3965,definition,
! [X0,X1,X2] :
( sQ493_spl
<=> ( segmentP(app(skaf57(X0),X2),X1)
| ~ ssList(skaf57(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf57(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ493_spl])],[split_symbol_definition]) ).
fof(f3968,plain,
( ~ sQ11_spl
| sQ493_spl ),
inference(split_clause,[status(thm)],[f3942,f3965,f545]) ).
fof(f3969,definition,
! [X0,X1] :
( sQ494_spl
<=> ( rearsegP(skaf57(X0),X1)
| ~ ssList(skaf57(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf57(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ494_spl])],[split_symbol_definition]) ).
fof(f3972,plain,
( ~ sQ11_spl
| sQ494_spl ),
inference(split_clause,[status(thm)],[f3943,f3969,f545]) ).
fof(f3981,plain,
! [X0] :
( app(nil,skaf58(X0)) = skaf58(X0)
| ~ rearsegP(skaf58(X0),skaf58(X0))
| ~ ssList(skaf58(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1419,f2334]) ).
fof(f3982,plain,
! [X0,X1] :
( segmentP(app(skaf58(X1),X0),skaf58(X1))
| ~ ssList(skaf58(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1419,f2205]) ).
fof(f3983,plain,
! [X0] :
( rearsegP(skaf58(X0),skaf58(X0))
| ~ ssList(skaf58(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1419,f2173]) ).
fof(f3985,plain,
! [X0,X1,X2] :
( app(app(nil,skaf58(X0)),X2) = X1
| ~ ssList(app(skaf58(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf58(X0)),X2))
| ~ ssList(skaf58(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf58(X0),X1) ),
inference(paramodulation,[status(thm)],[f1419,f666]) ).
fof(f3986,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf58(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf58(X0)),X2))
| ~ ssList(skaf58(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf58(X0),X1) ),
inference(paramodulation,[status(thm)],[f1419,f665]) ).
fof(f3987,plain,
! [X0,X1,X2] :
( segmentP(app(skaf58(X0),X2),X1)
| ~ ssList(skaf58(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf58(X0),X1) ),
inference(paramodulation,[status(thm)],[f1419,f404]) ).
fof(f3988,plain,
! [X0,X1] :
( rearsegP(skaf58(X0),X1)
| ~ ssList(skaf58(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf58(X0),X1) ),
inference(paramodulation,[status(thm)],[f1419,f350]) ).
fof(f3989,definition,
! [X0] :
( sQ495_spl
<=> ( app(nil,skaf58(X0)) = skaf58(X0)
| ~ rearsegP(skaf58(X0),skaf58(X0))
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ495_spl])],[split_symbol_definition]) ).
fof(f3992,plain,
( sQ495_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3981,f545,f3989]) ).
fof(f3993,definition,
! [X0,X1] :
( sQ496_spl
<=> ( segmentP(app(skaf58(X1),X0),skaf58(X1))
| ~ ssList(skaf58(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ496_spl])],[split_symbol_definition]) ).
fof(f3996,plain,
( ~ sQ11_spl
| sQ496_spl ),
inference(split_clause,[status(thm)],[f3982,f3993,f545]) ).
fof(f3997,definition,
! [X0] :
( sQ497_spl
<=> ( rearsegP(skaf58(X0),skaf58(X0))
| ~ ssList(skaf58(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ497_spl])],[split_symbol_definition]) ).
fof(f4000,plain,
( sQ497_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3983,f545,f3997]) ).
fof(f4002,definition,
! [X0,X1,X2] :
( sQ498_spl
<=> ( app(app(nil,skaf58(X0)),X2) = X1
| ~ ssList(app(skaf58(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf58(X0)),X2))
| ~ ssList(skaf58(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf58(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ498_spl])],[split_symbol_definition]) ).
fof(f4005,plain,
( ~ sQ11_spl
| sQ498_spl ),
inference(split_clause,[status(thm)],[f3985,f4002,f545]) ).
fof(f4006,definition,
! [X0,X1,X2,X3] :
( sQ499_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf58(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf58(X0)),X2))
| ~ ssList(skaf58(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf58(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ499_spl])],[split_symbol_definition]) ).
fof(f4009,plain,
( ~ sQ11_spl
| sQ499_spl ),
inference(split_clause,[status(thm)],[f3986,f4006,f545]) ).
fof(f4010,definition,
! [X0,X1,X2] :
( sQ500_spl
<=> ( segmentP(app(skaf58(X0),X2),X1)
| ~ ssList(skaf58(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf58(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ500_spl])],[split_symbol_definition]) ).
fof(f4013,plain,
( ~ sQ11_spl
| sQ500_spl ),
inference(split_clause,[status(thm)],[f3987,f4010,f545]) ).
fof(f4014,definition,
! [X0,X1] :
( sQ501_spl
<=> ( rearsegP(skaf58(X0),X1)
| ~ ssList(skaf58(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf58(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ501_spl])],[split_symbol_definition]) ).
fof(f4017,plain,
( ~ sQ11_spl
| sQ501_spl ),
inference(split_clause,[status(thm)],[f3988,f4014,f545]) ).
fof(f4026,plain,
! [X0] :
( app(nil,skaf61(X0)) = skaf61(X0)
| ~ rearsegP(skaf61(X0),skaf61(X0))
| ~ ssList(skaf61(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1420,f2334]) ).
fof(f4027,plain,
! [X0,X1] :
( segmentP(app(skaf61(X1),X0),skaf61(X1))
| ~ ssList(skaf61(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1420,f2205]) ).
fof(f4028,plain,
! [X0] :
( rearsegP(skaf61(X0),skaf61(X0))
| ~ ssList(skaf61(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1420,f2173]) ).
fof(f4030,plain,
! [X0,X1,X2] :
( app(app(nil,skaf61(X0)),X2) = X1
| ~ ssList(app(skaf61(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf61(X0)),X2))
| ~ ssList(skaf61(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf61(X0),X1) ),
inference(paramodulation,[status(thm)],[f1420,f666]) ).
fof(f4031,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf61(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf61(X0)),X2))
| ~ ssList(skaf61(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf61(X0),X1) ),
inference(paramodulation,[status(thm)],[f1420,f665]) ).
fof(f4032,plain,
! [X0,X1,X2] :
( segmentP(app(skaf61(X0),X2),X1)
| ~ ssList(skaf61(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf61(X0),X1) ),
inference(paramodulation,[status(thm)],[f1420,f404]) ).
fof(f4033,plain,
! [X0,X1] :
( rearsegP(skaf61(X0),X1)
| ~ ssList(skaf61(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf61(X0),X1) ),
inference(paramodulation,[status(thm)],[f1420,f350]) ).
fof(f4034,definition,
! [X0] :
( sQ502_spl
<=> ( app(nil,skaf61(X0)) = skaf61(X0)
| ~ rearsegP(skaf61(X0),skaf61(X0))
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ502_spl])],[split_symbol_definition]) ).
fof(f4037,plain,
( sQ502_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4026,f545,f4034]) ).
fof(f4038,definition,
! [X0,X1] :
( sQ503_spl
<=> ( segmentP(app(skaf61(X1),X0),skaf61(X1))
| ~ ssList(skaf61(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ503_spl])],[split_symbol_definition]) ).
fof(f4041,plain,
( ~ sQ11_spl
| sQ503_spl ),
inference(split_clause,[status(thm)],[f4027,f4038,f545]) ).
fof(f4042,definition,
! [X0] :
( sQ504_spl
<=> ( rearsegP(skaf61(X0),skaf61(X0))
| ~ ssList(skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ504_spl])],[split_symbol_definition]) ).
fof(f4045,plain,
( sQ504_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4028,f545,f4042]) ).
fof(f4047,definition,
! [X0,X1,X2] :
( sQ505_spl
<=> ( app(app(nil,skaf61(X0)),X2) = X1
| ~ ssList(app(skaf61(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf61(X0)),X2))
| ~ ssList(skaf61(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf61(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ505_spl])],[split_symbol_definition]) ).
fof(f4050,plain,
( ~ sQ11_spl
| sQ505_spl ),
inference(split_clause,[status(thm)],[f4030,f4047,f545]) ).
fof(f4051,definition,
! [X0,X1,X2,X3] :
( sQ506_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf61(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf61(X0)),X2))
| ~ ssList(skaf61(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf61(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ506_spl])],[split_symbol_definition]) ).
fof(f4054,plain,
( ~ sQ11_spl
| sQ506_spl ),
inference(split_clause,[status(thm)],[f4031,f4051,f545]) ).
fof(f4055,definition,
! [X0,X1,X2] :
( sQ507_spl
<=> ( segmentP(app(skaf61(X0),X2),X1)
| ~ ssList(skaf61(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf61(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ507_spl])],[split_symbol_definition]) ).
fof(f4058,plain,
( ~ sQ11_spl
| sQ507_spl ),
inference(split_clause,[status(thm)],[f4032,f4055,f545]) ).
fof(f4059,definition,
! [X0,X1] :
( sQ508_spl
<=> ( rearsegP(skaf61(X0),X1)
| ~ ssList(skaf61(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf61(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ508_spl])],[split_symbol_definition]) ).
fof(f4062,plain,
( ~ sQ11_spl
| sQ508_spl ),
inference(split_clause,[status(thm)],[f4033,f4059,f545]) ).
fof(f4071,plain,
! [X0] :
( app(nil,skaf62(X0)) = skaf62(X0)
| ~ rearsegP(skaf62(X0),skaf62(X0))
| ~ ssList(skaf62(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1421,f2334]) ).
fof(f4072,plain,
! [X0,X1] :
( segmentP(app(skaf62(X1),X0),skaf62(X1))
| ~ ssList(skaf62(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1421,f2205]) ).
fof(f4073,plain,
! [X0] :
( rearsegP(skaf62(X0),skaf62(X0))
| ~ ssList(skaf62(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1421,f2173]) ).
fof(f4075,plain,
! [X0,X1,X2] :
( app(app(nil,skaf62(X0)),X2) = X1
| ~ ssList(app(skaf62(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf62(X0)),X2))
| ~ ssList(skaf62(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf62(X0),X1) ),
inference(paramodulation,[status(thm)],[f1421,f666]) ).
fof(f4076,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf62(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf62(X0)),X2))
| ~ ssList(skaf62(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf62(X0),X1) ),
inference(paramodulation,[status(thm)],[f1421,f665]) ).
fof(f4077,plain,
! [X0,X1,X2] :
( segmentP(app(skaf62(X0),X2),X1)
| ~ ssList(skaf62(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf62(X0),X1) ),
inference(paramodulation,[status(thm)],[f1421,f404]) ).
fof(f4078,plain,
! [X0,X1] :
( rearsegP(skaf62(X0),X1)
| ~ ssList(skaf62(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf62(X0),X1) ),
inference(paramodulation,[status(thm)],[f1421,f350]) ).
fof(f4079,definition,
! [X0] :
( sQ509_spl
<=> ( app(nil,skaf62(X0)) = skaf62(X0)
| ~ rearsegP(skaf62(X0),skaf62(X0))
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ509_spl])],[split_symbol_definition]) ).
fof(f4082,plain,
( sQ509_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4071,f545,f4079]) ).
fof(f4083,definition,
! [X0,X1] :
( sQ510_spl
<=> ( segmentP(app(skaf62(X1),X0),skaf62(X1))
| ~ ssList(skaf62(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ510_spl])],[split_symbol_definition]) ).
fof(f4086,plain,
( ~ sQ11_spl
| sQ510_spl ),
inference(split_clause,[status(thm)],[f4072,f4083,f545]) ).
fof(f4087,definition,
! [X0] :
( sQ511_spl
<=> ( rearsegP(skaf62(X0),skaf62(X0))
| ~ ssList(skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ511_spl])],[split_symbol_definition]) ).
fof(f4090,plain,
( sQ511_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4073,f545,f4087]) ).
fof(f4092,definition,
! [X0,X1,X2] :
( sQ512_spl
<=> ( app(app(nil,skaf62(X0)),X2) = X1
| ~ ssList(app(skaf62(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf62(X0)),X2))
| ~ ssList(skaf62(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf62(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ512_spl])],[split_symbol_definition]) ).
fof(f4095,plain,
( ~ sQ11_spl
| sQ512_spl ),
inference(split_clause,[status(thm)],[f4075,f4092,f545]) ).
fof(f4096,definition,
! [X0,X1,X2,X3] :
( sQ513_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf62(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf62(X0)),X2))
| ~ ssList(skaf62(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf62(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ513_spl])],[split_symbol_definition]) ).
fof(f4099,plain,
( ~ sQ11_spl
| sQ513_spl ),
inference(split_clause,[status(thm)],[f4076,f4096,f545]) ).
fof(f4100,definition,
! [X0,X1,X2] :
( sQ514_spl
<=> ( segmentP(app(skaf62(X0),X2),X1)
| ~ ssList(skaf62(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf62(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ514_spl])],[split_symbol_definition]) ).
fof(f4103,plain,
( ~ sQ11_spl
| sQ514_spl ),
inference(split_clause,[status(thm)],[f4077,f4100,f545]) ).
fof(f4104,definition,
! [X0,X1] :
( sQ515_spl
<=> ( rearsegP(skaf62(X0),X1)
| ~ ssList(skaf62(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf62(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ515_spl])],[split_symbol_definition]) ).
fof(f4107,plain,
( ~ sQ11_spl
| sQ515_spl ),
inference(split_clause,[status(thm)],[f4078,f4104,f545]) ).
fof(f4116,plain,
! [X0] :
( app(nil,skaf63(X0)) = skaf63(X0)
| ~ rearsegP(skaf63(X0),skaf63(X0))
| ~ ssList(skaf63(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1422,f2334]) ).
fof(f4117,plain,
! [X0,X1] :
( segmentP(app(skaf63(X1),X0),skaf63(X1))
| ~ ssList(skaf63(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1422,f2205]) ).
fof(f4118,plain,
! [X0] :
( rearsegP(skaf63(X0),skaf63(X0))
| ~ ssList(skaf63(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1422,f2173]) ).
fof(f4120,plain,
! [X0,X1,X2] :
( app(app(nil,skaf63(X0)),X2) = X1
| ~ ssList(app(skaf63(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf63(X0)),X2))
| ~ ssList(skaf63(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf63(X0),X1) ),
inference(paramodulation,[status(thm)],[f1422,f666]) ).
fof(f4121,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf63(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf63(X0)),X2))
| ~ ssList(skaf63(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf63(X0),X1) ),
inference(paramodulation,[status(thm)],[f1422,f665]) ).
fof(f4122,plain,
! [X0,X1,X2] :
( segmentP(app(skaf63(X0),X2),X1)
| ~ ssList(skaf63(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf63(X0),X1) ),
inference(paramodulation,[status(thm)],[f1422,f404]) ).
fof(f4123,plain,
! [X0,X1] :
( rearsegP(skaf63(X0),X1)
| ~ ssList(skaf63(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf63(X0),X1) ),
inference(paramodulation,[status(thm)],[f1422,f350]) ).
fof(f4124,definition,
! [X0] :
( sQ516_spl
<=> ( app(nil,skaf63(X0)) = skaf63(X0)
| ~ rearsegP(skaf63(X0),skaf63(X0))
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ516_spl])],[split_symbol_definition]) ).
fof(f4127,plain,
( sQ516_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4116,f545,f4124]) ).
fof(f4128,definition,
! [X0,X1] :
( sQ517_spl
<=> ( segmentP(app(skaf63(X1),X0),skaf63(X1))
| ~ ssList(skaf63(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ517_spl])],[split_symbol_definition]) ).
fof(f4131,plain,
( ~ sQ11_spl
| sQ517_spl ),
inference(split_clause,[status(thm)],[f4117,f4128,f545]) ).
fof(f4132,definition,
! [X0] :
( sQ518_spl
<=> ( rearsegP(skaf63(X0),skaf63(X0))
| ~ ssList(skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ518_spl])],[split_symbol_definition]) ).
fof(f4135,plain,
( sQ518_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4118,f545,f4132]) ).
fof(f4137,definition,
! [X0,X1,X2] :
( sQ519_spl
<=> ( app(app(nil,skaf63(X0)),X2) = X1
| ~ ssList(app(skaf63(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf63(X0)),X2))
| ~ ssList(skaf63(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf63(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ519_spl])],[split_symbol_definition]) ).
fof(f4140,plain,
( ~ sQ11_spl
| sQ519_spl ),
inference(split_clause,[status(thm)],[f4120,f4137,f545]) ).
fof(f4141,definition,
! [X0,X1,X2,X3] :
( sQ520_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf63(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf63(X0)),X2))
| ~ ssList(skaf63(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf63(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ520_spl])],[split_symbol_definition]) ).
fof(f4144,plain,
( ~ sQ11_spl
| sQ520_spl ),
inference(split_clause,[status(thm)],[f4121,f4141,f545]) ).
fof(f4145,definition,
! [X0,X1,X2] :
( sQ521_spl
<=> ( segmentP(app(skaf63(X0),X2),X1)
| ~ ssList(skaf63(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf63(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ521_spl])],[split_symbol_definition]) ).
fof(f4148,plain,
( ~ sQ11_spl
| sQ521_spl ),
inference(split_clause,[status(thm)],[f4122,f4145,f545]) ).
fof(f4149,definition,
! [X0,X1] :
( sQ522_spl
<=> ( rearsegP(skaf63(X0),X1)
| ~ ssList(skaf63(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf63(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ522_spl])],[split_symbol_definition]) ).
fof(f4152,plain,
( ~ sQ11_spl
| sQ522_spl ),
inference(split_clause,[status(thm)],[f4123,f4149,f545]) ).
fof(f4161,plain,
! [X0] :
( app(nil,skaf66(X0)) = skaf66(X0)
| ~ rearsegP(skaf66(X0),skaf66(X0))
| ~ ssList(skaf66(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1424,f2334]) ).
fof(f4162,plain,
! [X0,X1] :
( segmentP(app(skaf66(X1),X0),skaf66(X1))
| ~ ssList(skaf66(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1424,f2205]) ).
fof(f4163,plain,
! [X0] :
( rearsegP(skaf66(X0),skaf66(X0))
| ~ ssList(skaf66(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1424,f2173]) ).
fof(f4165,plain,
! [X0,X1,X2] :
( app(app(nil,skaf66(X0)),X2) = X1
| ~ ssList(app(skaf66(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf66(X0)),X2))
| ~ ssList(skaf66(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf66(X0),X1) ),
inference(paramodulation,[status(thm)],[f1424,f666]) ).
fof(f4166,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf66(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf66(X0)),X2))
| ~ ssList(skaf66(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf66(X0),X1) ),
inference(paramodulation,[status(thm)],[f1424,f665]) ).
fof(f4167,plain,
! [X0,X1,X2] :
( segmentP(app(skaf66(X0),X2),X1)
| ~ ssList(skaf66(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf66(X0),X1) ),
inference(paramodulation,[status(thm)],[f1424,f404]) ).
fof(f4168,plain,
! [X0,X1] :
( rearsegP(skaf66(X0),X1)
| ~ ssList(skaf66(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf66(X0),X1) ),
inference(paramodulation,[status(thm)],[f1424,f350]) ).
fof(f4169,definition,
! [X0] :
( sQ523_spl
<=> ( app(nil,skaf66(X0)) = skaf66(X0)
| ~ rearsegP(skaf66(X0),skaf66(X0))
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ523_spl])],[split_symbol_definition]) ).
fof(f4172,plain,
( sQ523_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4161,f545,f4169]) ).
fof(f4173,definition,
! [X0,X1] :
( sQ524_spl
<=> ( segmentP(app(skaf66(X1),X0),skaf66(X1))
| ~ ssList(skaf66(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ524_spl])],[split_symbol_definition]) ).
fof(f4176,plain,
( ~ sQ11_spl
| sQ524_spl ),
inference(split_clause,[status(thm)],[f4162,f4173,f545]) ).
fof(f4177,definition,
! [X0] :
( sQ525_spl
<=> ( rearsegP(skaf66(X0),skaf66(X0))
| ~ ssList(skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ525_spl])],[split_symbol_definition]) ).
fof(f4180,plain,
( sQ525_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4163,f545,f4177]) ).
fof(f4182,definition,
! [X0,X1,X2] :
( sQ526_spl
<=> ( app(app(nil,skaf66(X0)),X2) = X1
| ~ ssList(app(skaf66(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf66(X0)),X2))
| ~ ssList(skaf66(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf66(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ526_spl])],[split_symbol_definition]) ).
fof(f4185,plain,
( ~ sQ11_spl
| sQ526_spl ),
inference(split_clause,[status(thm)],[f4165,f4182,f545]) ).
fof(f4186,definition,
! [X0,X1,X2,X3] :
( sQ527_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf66(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf66(X0)),X2))
| ~ ssList(skaf66(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf66(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ527_spl])],[split_symbol_definition]) ).
fof(f4189,plain,
( ~ sQ11_spl
| sQ527_spl ),
inference(split_clause,[status(thm)],[f4166,f4186,f545]) ).
fof(f4190,definition,
! [X0,X1,X2] :
( sQ528_spl
<=> ( segmentP(app(skaf66(X0),X2),X1)
| ~ ssList(skaf66(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf66(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ528_spl])],[split_symbol_definition]) ).
fof(f4193,plain,
( ~ sQ11_spl
| sQ528_spl ),
inference(split_clause,[status(thm)],[f4167,f4190,f545]) ).
fof(f4194,definition,
! [X0,X1] :
( sQ529_spl
<=> ( rearsegP(skaf66(X0),X1)
| ~ ssList(skaf66(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf66(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ529_spl])],[split_symbol_definition]) ).
fof(f4197,plain,
( ~ sQ11_spl
| sQ529_spl ),
inference(split_clause,[status(thm)],[f4168,f4194,f545]) ).
fof(f4206,plain,
! [X0] :
( app(nil,skaf67(X0)) = skaf67(X0)
| ~ rearsegP(skaf67(X0),skaf67(X0))
| ~ ssList(skaf67(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1425,f2334]) ).
fof(f4207,plain,
! [X0,X1] :
( segmentP(app(skaf67(X1),X0),skaf67(X1))
| ~ ssList(skaf67(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1425,f2205]) ).
fof(f4208,plain,
! [X0] :
( rearsegP(skaf67(X0),skaf67(X0))
| ~ ssList(skaf67(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1425,f2173]) ).
fof(f4210,plain,
! [X0,X1,X2] :
( app(app(nil,skaf67(X0)),X2) = X1
| ~ ssList(app(skaf67(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf67(X0)),X2))
| ~ ssList(skaf67(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf67(X0),X1) ),
inference(paramodulation,[status(thm)],[f1425,f666]) ).
fof(f4211,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf67(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf67(X0)),X2))
| ~ ssList(skaf67(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf67(X0),X1) ),
inference(paramodulation,[status(thm)],[f1425,f665]) ).
fof(f4212,plain,
! [X0,X1,X2] :
( segmentP(app(skaf67(X0),X2),X1)
| ~ ssList(skaf67(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf67(X0),X1) ),
inference(paramodulation,[status(thm)],[f1425,f404]) ).
fof(f4213,plain,
! [X0,X1] :
( rearsegP(skaf67(X0),X1)
| ~ ssList(skaf67(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf67(X0),X1) ),
inference(paramodulation,[status(thm)],[f1425,f350]) ).
fof(f4214,definition,
! [X0] :
( sQ530_spl
<=> ( app(nil,skaf67(X0)) = skaf67(X0)
| ~ rearsegP(skaf67(X0),skaf67(X0))
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ530_spl])],[split_symbol_definition]) ).
fof(f4217,plain,
( sQ530_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4206,f545,f4214]) ).
fof(f4218,definition,
! [X0,X1] :
( sQ531_spl
<=> ( segmentP(app(skaf67(X1),X0),skaf67(X1))
| ~ ssList(skaf67(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ531_spl])],[split_symbol_definition]) ).
fof(f4221,plain,
( ~ sQ11_spl
| sQ531_spl ),
inference(split_clause,[status(thm)],[f4207,f4218,f545]) ).
fof(f4222,definition,
! [X0] :
( sQ532_spl
<=> ( rearsegP(skaf67(X0),skaf67(X0))
| ~ ssList(skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ532_spl])],[split_symbol_definition]) ).
fof(f4225,plain,
( sQ532_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4208,f545,f4222]) ).
fof(f4227,definition,
! [X0,X1,X2] :
( sQ533_spl
<=> ( app(app(nil,skaf67(X0)),X2) = X1
| ~ ssList(app(skaf67(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf67(X0)),X2))
| ~ ssList(skaf67(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf67(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ533_spl])],[split_symbol_definition]) ).
fof(f4230,plain,
( ~ sQ11_spl
| sQ533_spl ),
inference(split_clause,[status(thm)],[f4210,f4227,f545]) ).
fof(f4231,definition,
! [X0,X1,X2,X3] :
( sQ534_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf67(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf67(X0)),X2))
| ~ ssList(skaf67(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf67(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ534_spl])],[split_symbol_definition]) ).
fof(f4234,plain,
( ~ sQ11_spl
| sQ534_spl ),
inference(split_clause,[status(thm)],[f4211,f4231,f545]) ).
fof(f4235,definition,
! [X0,X1,X2] :
( sQ535_spl
<=> ( segmentP(app(skaf67(X0),X2),X1)
| ~ ssList(skaf67(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf67(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ535_spl])],[split_symbol_definition]) ).
fof(f4238,plain,
( ~ sQ11_spl
| sQ535_spl ),
inference(split_clause,[status(thm)],[f4212,f4235,f545]) ).
fof(f4239,definition,
! [X0,X1] :
( sQ536_spl
<=> ( rearsegP(skaf67(X0),X1)
| ~ ssList(skaf67(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf67(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ536_spl])],[split_symbol_definition]) ).
fof(f4242,plain,
( ~ sQ11_spl
| sQ536_spl ),
inference(split_clause,[status(thm)],[f4213,f4239,f545]) ).
fof(f4253,plain,
( ~ sQ456_spl
| ~ ssList(sk1)
| sk1 = sk1
| ~ segmentP(sk1,sk1)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f3751,f256]) ).
fof(f4257,plain,
( ~ sQ456_spl
| sQ53_spl
| ~ sQ223_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f4253,f558,f2255,f965,f3745]) ).
fof(f4260,plain,
! [X0] :
( ~ sQ126_spl
| segmentP(sk2,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(sk2,X0) ),
inference(paramodulation,[status(thm)],[f1029,f1575]) ).
fof(f4263,definition,
! [X0] :
( sQ537_spl
<=> ( segmentP(sk2,X0)
| ~ ssList(X0)
| ~ segmentP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ537_spl])],[split_symbol_definition]) ).
fof(f4266,plain,
( ~ sQ126_spl
| ~ sQ11_spl
| sQ537_spl ),
inference(split_clause,[status(thm)],[f4260,f4263,f545,f1574]) ).
fof(f4267,plain,
! [X0,X1] :
( ~ sQ265_spl
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(app(X0,sk1))
| ~ rearsegP(X1,app(X0,sk1))
| ~ rearsegP(nil,X1)
| app(X0,sk1) = nil
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2553,f376]) ).
fof(f4269,definition,
! [X0,X1] :
( sQ538_spl
<=> ( ~ ssList(X1)
| ~ ssList(app(X0,sk1))
| ~ rearsegP(X1,app(X0,sk1))
| ~ rearsegP(nil,X1)
| app(X0,sk1) = nil
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ538_spl])],[split_symbol_definition]) ).
fof(f4272,plain,
( ~ sQ265_spl
| ~ sQ11_spl
| sQ538_spl ),
inference(split_clause,[status(thm)],[f4267,f4269,f545,f2552]) ).
fof(f4277,plain,
! [X0,X1] :
( ~ sQ122_spl
| ~ ssList(sk2)
| ~ ssList(X1)
| app(sk2,X1) = X0
| ~ segmentP(X0,app(sk2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ),
inference(resolution,[status(thm)],[f1588,f285]) ).
fof(f4278,plain,
! [X0] :
( ~ sQ122_spl
| app(sk2,nil) = X0
| ~ ssList(sk2)
| ~ segmentP(X0,app(sk2,nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(sk2,X0) ),
inference(paramodulation,[status(thm)],[f1029,f1588]) ).
fof(f4279,definition,
! [X0,X1] :
( sQ540_spl
<=> ( ~ ssList(X1)
| app(sk2,X1) = X0
| ~ segmentP(X0,app(sk2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ540_spl])],[split_symbol_definition]) ).
fof(f4282,plain,
( ~ sQ122_spl
| ~ sQ16_spl
| sQ540_spl ),
inference(split_clause,[status(thm)],[f4277,f4279,f587,f1558]) ).
fof(f4283,definition,
! [X0] :
( sQ541_spl
<=> ( app(sk2,nil) = X0
| ~ segmentP(X0,app(sk2,nil))
| ~ ssList(X0)
| ~ segmentP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ541_spl])],[split_symbol_definition]) ).
fof(f4286,plain,
( ~ sQ122_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sQ541_spl ),
inference(split_clause,[status(thm)],[f4278,f4283,f545,f587,f1558]) ).
fof(f4290,plain,
! [X0,X1,X2] :
( ~ sQ275_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf51(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf51(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2639,f374]) ).
fof(f4291,plain,
! [X0,X1] :
( ~ sQ275_spl
| app(skaf51(X1),X0) = nil
| ~ ssList(app(skaf51(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf51(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2639,f339]) ).
fof(f4292,plain,
! [X0] :
( ~ sQ275_spl
| segmentP(skaf51(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1020,f2639]) ).
fof(f4293,definition,
! [X0,X1,X2] :
( sQ542_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf51(X2),X0))
| ~ segmentP(X1,app(skaf51(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ542_spl])],[split_symbol_definition]) ).
fof(f4296,plain,
( ~ sQ275_spl
| ~ sQ11_spl
| sQ542_spl ),
inference(split_clause,[status(thm)],[f4290,f4293,f545,f2616]) ).
fof(f4297,definition,
! [X0,X1] :
( sQ543_spl
<=> ( app(skaf51(X1),X0) = nil
| ~ ssList(app(skaf51(X1),X0))
| ~ segmentP(nil,app(skaf51(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ543_spl])],[split_symbol_definition]) ).
fof(f4300,plain,
( ~ sQ275_spl
| ~ sQ11_spl
| sQ543_spl ),
inference(split_clause,[status(thm)],[f4291,f4297,f545,f2616]) ).
fof(f4301,definition,
! [X0] :
( sQ544_spl
<=> segmentP(skaf51(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ544_spl])],[split_symbol_definition]) ).
fof(f4302,plain,
! [X0] :
( ~ sQ544_spl
| segmentP(skaf51(X0),nil) ),
inference(component_clause,[status(thm)],[f4301]) ).
fof(f4304,plain,
( ~ sQ275_spl
| sQ544_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4292,f545,f4301,f2616]) ).
fof(f4305,plain,
! [X0,X1] :
( ~ sQ544_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf51(X1)) ),
inference(resolution,[status(thm)],[f4302,f374]) ).
fof(f4306,plain,
! [X0] :
( ~ sQ544_spl
| skaf51(X0) = nil
| ~ ssList(skaf51(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf51(X0)) ),
inference(resolution,[status(thm)],[f4302,f339]) ).
fof(f4307,definition,
! [X0,X1] :
( sQ545_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf51(X1))
| ~ segmentP(X0,skaf51(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ545_spl])],[split_symbol_definition]) ).
fof(f4310,plain,
( ~ sQ544_spl
| ~ sQ11_spl
| sQ545_spl ),
inference(split_clause,[status(thm)],[f4305,f4307,f545,f4301]) ).
fof(f4311,definition,
! [X0] :
( sQ546_spl
<=> ( skaf51(X0) = nil
| ~ ssList(skaf51(X0))
| ~ segmentP(nil,skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ546_spl])],[split_symbol_definition]) ).
fof(f4314,plain,
( ~ sQ544_spl
| ~ sQ11_spl
| sQ546_spl ),
inference(split_clause,[status(thm)],[f4306,f4311,f545,f4301]) ).
fof(f4315,plain,
! [X0,X1,X2] :
( ~ sQ290_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf61(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf61(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2738,f374]) ).
fof(f4316,plain,
! [X0,X1] :
( ~ sQ290_spl
| app(skaf61(X1),X0) = nil
| ~ ssList(app(skaf61(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf61(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2738,f339]) ).
fof(f4317,plain,
! [X0] :
( ~ sQ290_spl
| segmentP(skaf61(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1026,f2738]) ).
fof(f4318,definition,
! [X0,X1,X2] :
( sQ547_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf61(X2),X0))
| ~ segmentP(X1,app(skaf61(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ547_spl])],[split_symbol_definition]) ).
fof(f4321,plain,
( ~ sQ290_spl
| ~ sQ11_spl
| sQ547_spl ),
inference(split_clause,[status(thm)],[f4315,f4318,f545,f2710]) ).
fof(f4322,definition,
! [X0,X1] :
( sQ548_spl
<=> ( app(skaf61(X1),X0) = nil
| ~ ssList(app(skaf61(X1),X0))
| ~ segmentP(nil,app(skaf61(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ548_spl])],[split_symbol_definition]) ).
fof(f4325,plain,
( ~ sQ290_spl
| ~ sQ11_spl
| sQ548_spl ),
inference(split_clause,[status(thm)],[f4316,f4322,f545,f2710]) ).
fof(f4326,definition,
! [X0] :
( sQ549_spl
<=> segmentP(skaf61(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ549_spl])],[split_symbol_definition]) ).
fof(f4327,plain,
! [X0] :
( ~ sQ549_spl
| segmentP(skaf61(X0),nil) ),
inference(component_clause,[status(thm)],[f4326]) ).
fof(f4329,plain,
( ~ sQ290_spl
| sQ549_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4317,f545,f4326,f2710]) ).
fof(f4330,plain,
! [X0,X1] :
( ~ sQ549_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf61(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf61(X1)) ),
inference(resolution,[status(thm)],[f4327,f374]) ).
fof(f4331,plain,
! [X0] :
( ~ sQ549_spl
| skaf61(X0) = nil
| ~ ssList(skaf61(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf61(X0)) ),
inference(resolution,[status(thm)],[f4327,f339]) ).
fof(f4332,definition,
! [X0,X1] :
( sQ550_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf61(X1))
| ~ segmentP(X0,skaf61(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ550_spl])],[split_symbol_definition]) ).
fof(f4335,plain,
( ~ sQ549_spl
| ~ sQ11_spl
| sQ550_spl ),
inference(split_clause,[status(thm)],[f4330,f4332,f545,f4326]) ).
fof(f4336,definition,
! [X0] :
( sQ551_spl
<=> ( skaf61(X0) = nil
| ~ ssList(skaf61(X0))
| ~ segmentP(nil,skaf61(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ551_spl])],[split_symbol_definition]) ).
fof(f4339,plain,
( ~ sQ549_spl
| ~ sQ11_spl
| sQ551_spl ),
inference(split_clause,[status(thm)],[f4331,f4336,f545,f4326]) ).
fof(f4340,plain,
! [X0,X1,X2] :
( ~ sQ297_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf62(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf62(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2781,f374]) ).
fof(f4341,plain,
! [X0,X1] :
( ~ sQ297_spl
| app(skaf62(X1),X0) = nil
| ~ ssList(app(skaf62(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf62(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2781,f339]) ).
fof(f4342,plain,
! [X0] :
( ~ sQ297_spl
| segmentP(skaf62(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1027,f2781]) ).
fof(f4343,definition,
! [X0,X1,X2] :
( sQ552_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf62(X2),X0))
| ~ segmentP(X1,app(skaf62(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ552_spl])],[split_symbol_definition]) ).
fof(f4346,plain,
( ~ sQ297_spl
| ~ sQ11_spl
| sQ552_spl ),
inference(split_clause,[status(thm)],[f4340,f4343,f545,f2753]) ).
fof(f4347,definition,
! [X0,X1] :
( sQ553_spl
<=> ( app(skaf62(X1),X0) = nil
| ~ ssList(app(skaf62(X1),X0))
| ~ segmentP(nil,app(skaf62(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ553_spl])],[split_symbol_definition]) ).
fof(f4350,plain,
( ~ sQ297_spl
| ~ sQ11_spl
| sQ553_spl ),
inference(split_clause,[status(thm)],[f4341,f4347,f545,f2753]) ).
fof(f4351,definition,
! [X0] :
( sQ554_spl
<=> segmentP(skaf62(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ554_spl])],[split_symbol_definition]) ).
fof(f4352,plain,
! [X0] :
( ~ sQ554_spl
| segmentP(skaf62(X0),nil) ),
inference(component_clause,[status(thm)],[f4351]) ).
fof(f4354,plain,
( ~ sQ297_spl
| sQ554_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4342,f545,f4351,f2753]) ).
fof(f4355,plain,
! [X0,X1] :
( ~ sQ554_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf62(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf62(X1)) ),
inference(resolution,[status(thm)],[f4352,f374]) ).
fof(f4356,plain,
! [X0] :
( ~ sQ554_spl
| skaf62(X0) = nil
| ~ ssList(skaf62(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf62(X0)) ),
inference(resolution,[status(thm)],[f4352,f339]) ).
fof(f4357,definition,
! [X0,X1] :
( sQ555_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf62(X1))
| ~ segmentP(X0,skaf62(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ555_spl])],[split_symbol_definition]) ).
fof(f4360,plain,
( ~ sQ554_spl
| ~ sQ11_spl
| sQ555_spl ),
inference(split_clause,[status(thm)],[f4355,f4357,f545,f4351]) ).
fof(f4361,definition,
! [X0] :
( sQ556_spl
<=> ( skaf62(X0) = nil
| ~ ssList(skaf62(X0))
| ~ segmentP(nil,skaf62(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ556_spl])],[split_symbol_definition]) ).
fof(f4364,plain,
( ~ sQ554_spl
| ~ sQ11_spl
| sQ556_spl ),
inference(split_clause,[status(thm)],[f4356,f4361,f545,f4351]) ).
fof(f4365,plain,
! [X0,X1,X2] :
( ~ sQ123_spl
| ~ ssList(sk2)
| ~ ssList(X1)
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ segmentP(X2,app(sk2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ),
inference(resolution,[status(thm)],[f1589,f285]) ).
fof(f4366,plain,
! [X0,X1] :
( ~ sQ123_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(sk2)
| ~ segmentP(X1,app(sk2,nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(sk2,X0) ),
inference(paramodulation,[status(thm)],[f1029,f1589]) ).
fof(f4367,definition,
! [X0,X1,X2] :
( sQ557_spl
<=> ( ~ ssList(X1)
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ segmentP(X2,app(sk2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ557_spl])],[split_symbol_definition]) ).
fof(f4370,plain,
( ~ sQ123_spl
| ~ sQ16_spl
| sQ557_spl ),
inference(split_clause,[status(thm)],[f4365,f4367,f587,f1562]) ).
fof(f4371,definition,
! [X0,X1] :
( sQ558_spl
<=> ( segmentP(X1,X0)
| ~ ssList(X1)
| ~ segmentP(X1,app(sk2,nil))
| ~ ssList(X0)
| ~ segmentP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ558_spl])],[split_symbol_definition]) ).
fof(f4374,plain,
( ~ sQ123_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sQ558_spl ),
inference(split_clause,[status(thm)],[f4366,f4371,f545,f587,f1562]) ).
fof(f4378,plain,
! [X0,X1] :
( ~ sQ160_spl
| app(skaf51(X1),nil) = X0
| ~ ssList(skaf51(X1))
| ~ segmentP(X0,app(skaf51(X1),nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1020,f1840]) ).
fof(f4381,definition,
! [X0,X1] :
( sQ559_spl
<=> ( app(skaf51(X1),nil) = X0
| ~ ssList(skaf51(X1))
| ~ segmentP(X0,app(skaf51(X1),nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ559_spl])],[split_symbol_definition]) ).
fof(f4384,plain,
( ~ sQ160_spl
| ~ sQ11_spl
| sQ559_spl ),
inference(split_clause,[status(thm)],[f4378,f4381,f545,f1805]) ).
fof(f4389,plain,
! [X0] :
( app(nil,skaf68(X0)) = skaf68(X0)
| ~ rearsegP(skaf68(X0),skaf68(X0))
| ~ ssList(skaf68(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1426,f2334]) ).
fof(f4390,plain,
! [X0,X1] :
( segmentP(app(skaf68(X1),X0),skaf68(X1))
| ~ ssList(skaf68(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1426,f2205]) ).
fof(f4391,plain,
! [X0] :
( rearsegP(skaf68(X0),skaf68(X0))
| ~ ssList(skaf68(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1426,f2173]) ).
fof(f4393,plain,
! [X0,X1,X2] :
( app(app(nil,skaf68(X0)),X2) = X1
| ~ ssList(app(skaf68(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf68(X0)),X2))
| ~ ssList(skaf68(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf68(X0),X1) ),
inference(paramodulation,[status(thm)],[f1426,f666]) ).
fof(f4394,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf68(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf68(X0)),X2))
| ~ ssList(skaf68(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf68(X0),X1) ),
inference(paramodulation,[status(thm)],[f1426,f665]) ).
fof(f4395,plain,
! [X0,X1,X2] :
( segmentP(app(skaf68(X0),X2),X1)
| ~ ssList(skaf68(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf68(X0),X1) ),
inference(paramodulation,[status(thm)],[f1426,f404]) ).
fof(f4396,plain,
! [X0,X1] :
( rearsegP(skaf68(X0),X1)
| ~ ssList(skaf68(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf68(X0),X1) ),
inference(paramodulation,[status(thm)],[f1426,f350]) ).
fof(f4397,definition,
! [X0] :
( sQ560_spl
<=> ( app(nil,skaf68(X0)) = skaf68(X0)
| ~ rearsegP(skaf68(X0),skaf68(X0))
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ560_spl])],[split_symbol_definition]) ).
fof(f4400,plain,
( sQ560_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4389,f545,f4397]) ).
fof(f4401,definition,
! [X0,X1] :
( sQ561_spl
<=> ( segmentP(app(skaf68(X1),X0),skaf68(X1))
| ~ ssList(skaf68(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ561_spl])],[split_symbol_definition]) ).
fof(f4404,plain,
( ~ sQ11_spl
| sQ561_spl ),
inference(split_clause,[status(thm)],[f4390,f4401,f545]) ).
fof(f4405,definition,
! [X0] :
( sQ562_spl
<=> ( rearsegP(skaf68(X0),skaf68(X0))
| ~ ssList(skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ562_spl])],[split_symbol_definition]) ).
fof(f4408,plain,
( sQ562_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4391,f545,f4405]) ).
fof(f4410,definition,
! [X0,X1,X2] :
( sQ563_spl
<=> ( app(app(nil,skaf68(X0)),X2) = X1
| ~ ssList(app(skaf68(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf68(X0)),X2))
| ~ ssList(skaf68(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf68(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ563_spl])],[split_symbol_definition]) ).
fof(f4413,plain,
( ~ sQ11_spl
| sQ563_spl ),
inference(split_clause,[status(thm)],[f4393,f4410,f545]) ).
fof(f4414,definition,
! [X0,X1,X2,X3] :
( sQ564_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf68(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf68(X0)),X2))
| ~ ssList(skaf68(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf68(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ564_spl])],[split_symbol_definition]) ).
fof(f4417,plain,
( ~ sQ11_spl
| sQ564_spl ),
inference(split_clause,[status(thm)],[f4394,f4414,f545]) ).
fof(f4418,definition,
! [X0,X1,X2] :
( sQ565_spl
<=> ( segmentP(app(skaf68(X0),X2),X1)
| ~ ssList(skaf68(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf68(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ565_spl])],[split_symbol_definition]) ).
fof(f4421,plain,
( ~ sQ11_spl
| sQ565_spl ),
inference(split_clause,[status(thm)],[f4395,f4418,f545]) ).
fof(f4422,definition,
! [X0,X1] :
( sQ566_spl
<=> ( rearsegP(skaf68(X0),X1)
| ~ ssList(skaf68(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf68(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ566_spl])],[split_symbol_definition]) ).
fof(f4425,plain,
( ~ sQ11_spl
| sQ566_spl ),
inference(split_clause,[status(thm)],[f4396,f4422,f545]) ).
fof(f4434,plain,
! [X0] :
( app(nil,skaf71(X0)) = skaf71(X0)
| ~ rearsegP(skaf71(X0),skaf71(X0))
| ~ ssList(skaf71(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1427,f2334]) ).
fof(f4435,plain,
! [X0,X1] :
( segmentP(app(skaf71(X1),X0),skaf71(X1))
| ~ ssList(skaf71(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1427,f2205]) ).
fof(f4436,plain,
! [X0] :
( rearsegP(skaf71(X0),skaf71(X0))
| ~ ssList(skaf71(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1427,f2173]) ).
fof(f4438,plain,
! [X0,X1,X2] :
( app(app(nil,skaf71(X0)),X2) = X1
| ~ ssList(app(skaf71(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf71(X0)),X2))
| ~ ssList(skaf71(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf71(X0),X1) ),
inference(paramodulation,[status(thm)],[f1427,f666]) ).
fof(f4439,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf71(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf71(X0)),X2))
| ~ ssList(skaf71(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf71(X0),X1) ),
inference(paramodulation,[status(thm)],[f1427,f665]) ).
fof(f4440,plain,
! [X0,X1,X2] :
( segmentP(app(skaf71(X0),X2),X1)
| ~ ssList(skaf71(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf71(X0),X1) ),
inference(paramodulation,[status(thm)],[f1427,f404]) ).
fof(f4441,plain,
! [X0,X1] :
( rearsegP(skaf71(X0),X1)
| ~ ssList(skaf71(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf71(X0),X1) ),
inference(paramodulation,[status(thm)],[f1427,f350]) ).
fof(f4442,definition,
! [X0] :
( sQ567_spl
<=> ( app(nil,skaf71(X0)) = skaf71(X0)
| ~ rearsegP(skaf71(X0),skaf71(X0))
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ567_spl])],[split_symbol_definition]) ).
fof(f4445,plain,
( sQ567_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4434,f545,f4442]) ).
fof(f4446,definition,
! [X0,X1] :
( sQ568_spl
<=> ( segmentP(app(skaf71(X1),X0),skaf71(X1))
| ~ ssList(skaf71(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ568_spl])],[split_symbol_definition]) ).
fof(f4449,plain,
( ~ sQ11_spl
| sQ568_spl ),
inference(split_clause,[status(thm)],[f4435,f4446,f545]) ).
fof(f4450,definition,
! [X0] :
( sQ569_spl
<=> ( rearsegP(skaf71(X0),skaf71(X0))
| ~ ssList(skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ569_spl])],[split_symbol_definition]) ).
fof(f4453,plain,
( sQ569_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4436,f545,f4450]) ).
fof(f4455,definition,
! [X0,X1,X2] :
( sQ570_spl
<=> ( app(app(nil,skaf71(X0)),X2) = X1
| ~ ssList(app(skaf71(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf71(X0)),X2))
| ~ ssList(skaf71(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf71(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ570_spl])],[split_symbol_definition]) ).
fof(f4458,plain,
( ~ sQ11_spl
| sQ570_spl ),
inference(split_clause,[status(thm)],[f4438,f4455,f545]) ).
fof(f4459,definition,
! [X0,X1,X2,X3] :
( sQ571_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf71(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf71(X0)),X2))
| ~ ssList(skaf71(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf71(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ571_spl])],[split_symbol_definition]) ).
fof(f4462,plain,
( ~ sQ11_spl
| sQ571_spl ),
inference(split_clause,[status(thm)],[f4439,f4459,f545]) ).
fof(f4463,definition,
! [X0,X1,X2] :
( sQ572_spl
<=> ( segmentP(app(skaf71(X0),X2),X1)
| ~ ssList(skaf71(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf71(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ572_spl])],[split_symbol_definition]) ).
fof(f4466,plain,
( ~ sQ11_spl
| sQ572_spl ),
inference(split_clause,[status(thm)],[f4440,f4463,f545]) ).
fof(f4467,definition,
! [X0,X1] :
( sQ573_spl
<=> ( rearsegP(skaf71(X0),X1)
| ~ ssList(skaf71(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf71(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ573_spl])],[split_symbol_definition]) ).
fof(f4470,plain,
( ~ sQ11_spl
| sQ573_spl ),
inference(split_clause,[status(thm)],[f4441,f4467,f545]) ).
fof(f4479,plain,
! [X0] :
( app(nil,skaf72(X0)) = skaf72(X0)
| ~ rearsegP(skaf72(X0),skaf72(X0))
| ~ ssList(skaf72(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1428,f2334]) ).
fof(f4480,plain,
! [X0,X1] :
( segmentP(app(skaf72(X1),X0),skaf72(X1))
| ~ ssList(skaf72(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1428,f2205]) ).
fof(f4481,plain,
! [X0] :
( rearsegP(skaf72(X0),skaf72(X0))
| ~ ssList(skaf72(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1428,f2173]) ).
fof(f4483,plain,
! [X0,X1,X2] :
( app(app(nil,skaf72(X0)),X2) = X1
| ~ ssList(app(skaf72(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf72(X0)),X2))
| ~ ssList(skaf72(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf72(X0),X1) ),
inference(paramodulation,[status(thm)],[f1428,f666]) ).
fof(f4484,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf72(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf72(X0)),X2))
| ~ ssList(skaf72(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf72(X0),X1) ),
inference(paramodulation,[status(thm)],[f1428,f665]) ).
fof(f4485,plain,
! [X0,X1,X2] :
( segmentP(app(skaf72(X0),X2),X1)
| ~ ssList(skaf72(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf72(X0),X1) ),
inference(paramodulation,[status(thm)],[f1428,f404]) ).
fof(f4486,plain,
! [X0,X1] :
( rearsegP(skaf72(X0),X1)
| ~ ssList(skaf72(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf72(X0),X1) ),
inference(paramodulation,[status(thm)],[f1428,f350]) ).
fof(f4487,definition,
! [X0] :
( sQ574_spl
<=> ( app(nil,skaf72(X0)) = skaf72(X0)
| ~ rearsegP(skaf72(X0),skaf72(X0))
| ~ ssList(skaf72(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ574_spl])],[split_symbol_definition]) ).
fof(f4490,plain,
( sQ574_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4479,f545,f4487]) ).
fof(f4491,definition,
! [X0,X1] :
( sQ575_spl
<=> ( segmentP(app(skaf72(X1),X0),skaf72(X1))
| ~ ssList(skaf72(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ575_spl])],[split_symbol_definition]) ).
fof(f4494,plain,
( ~ sQ11_spl
| sQ575_spl ),
inference(split_clause,[status(thm)],[f4480,f4491,f545]) ).
fof(f4495,definition,
! [X0] :
( sQ576_spl
<=> ( rearsegP(skaf72(X0),skaf72(X0))
| ~ ssList(skaf72(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ576_spl])],[split_symbol_definition]) ).
fof(f4498,plain,
( sQ576_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4481,f545,f4495]) ).
fof(f4500,definition,
! [X0,X1,X2] :
( sQ577_spl
<=> ( app(app(nil,skaf72(X0)),X2) = X1
| ~ ssList(app(skaf72(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf72(X0)),X2))
| ~ ssList(skaf72(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf72(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ577_spl])],[split_symbol_definition]) ).
fof(f4503,plain,
( ~ sQ11_spl
| sQ577_spl ),
inference(split_clause,[status(thm)],[f4483,f4500,f545]) ).
fof(f4504,definition,
! [X0,X1,X2,X3] :
( sQ578_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf72(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf72(X0)),X2))
| ~ ssList(skaf72(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf72(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ578_spl])],[split_symbol_definition]) ).
fof(f4507,plain,
( ~ sQ11_spl
| sQ578_spl ),
inference(split_clause,[status(thm)],[f4484,f4504,f545]) ).
fof(f4508,definition,
! [X0,X1,X2] :
( sQ579_spl
<=> ( segmentP(app(skaf72(X0),X2),X1)
| ~ ssList(skaf72(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf72(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ579_spl])],[split_symbol_definition]) ).
fof(f4511,plain,
( ~ sQ11_spl
| sQ579_spl ),
inference(split_clause,[status(thm)],[f4485,f4508,f545]) ).
fof(f4512,definition,
! [X0,X1] :
( sQ580_spl
<=> ( rearsegP(skaf72(X0),X1)
| ~ ssList(skaf72(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf72(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ580_spl])],[split_symbol_definition]) ).
fof(f4515,plain,
( ~ sQ11_spl
| sQ580_spl ),
inference(split_clause,[status(thm)],[f4486,f4512,f545]) ).
fof(f4524,plain,
! [X0] :
( app(nil,skaf73(X0)) = skaf73(X0)
| ~ rearsegP(skaf73(X0),skaf73(X0))
| ~ ssList(skaf73(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1429,f2334]) ).
fof(f4525,plain,
! [X0,X1] :
( segmentP(app(skaf73(X1),X0),skaf73(X1))
| ~ ssList(skaf73(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1429,f2205]) ).
fof(f4526,plain,
! [X0] :
( rearsegP(skaf73(X0),skaf73(X0))
| ~ ssList(skaf73(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1429,f2173]) ).
fof(f4528,plain,
! [X0,X1,X2] :
( app(app(nil,skaf73(X0)),X2) = X1
| ~ ssList(app(skaf73(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf73(X0)),X2))
| ~ ssList(skaf73(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf73(X0),X1) ),
inference(paramodulation,[status(thm)],[f1429,f666]) ).
fof(f4529,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf73(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf73(X0)),X2))
| ~ ssList(skaf73(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf73(X0),X1) ),
inference(paramodulation,[status(thm)],[f1429,f665]) ).
fof(f4530,plain,
! [X0,X1,X2] :
( segmentP(app(skaf73(X0),X2),X1)
| ~ ssList(skaf73(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf73(X0),X1) ),
inference(paramodulation,[status(thm)],[f1429,f404]) ).
fof(f4531,plain,
! [X0,X1] :
( rearsegP(skaf73(X0),X1)
| ~ ssList(skaf73(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf73(X0),X1) ),
inference(paramodulation,[status(thm)],[f1429,f350]) ).
fof(f4532,definition,
! [X0] :
( sQ581_spl
<=> ( app(nil,skaf73(X0)) = skaf73(X0)
| ~ rearsegP(skaf73(X0),skaf73(X0))
| ~ ssList(skaf73(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ581_spl])],[split_symbol_definition]) ).
fof(f4535,plain,
( sQ581_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4524,f545,f4532]) ).
fof(f4536,definition,
! [X0,X1] :
( sQ582_spl
<=> ( segmentP(app(skaf73(X1),X0),skaf73(X1))
| ~ ssList(skaf73(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ582_spl])],[split_symbol_definition]) ).
fof(f4539,plain,
( ~ sQ11_spl
| sQ582_spl ),
inference(split_clause,[status(thm)],[f4525,f4536,f545]) ).
fof(f4540,definition,
! [X0] :
( sQ583_spl
<=> ( rearsegP(skaf73(X0),skaf73(X0))
| ~ ssList(skaf73(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ583_spl])],[split_symbol_definition]) ).
fof(f4543,plain,
( sQ583_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4526,f545,f4540]) ).
fof(f4545,definition,
! [X0,X1,X2] :
( sQ584_spl
<=> ( app(app(nil,skaf73(X0)),X2) = X1
| ~ ssList(app(skaf73(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf73(X0)),X2))
| ~ ssList(skaf73(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf73(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ584_spl])],[split_symbol_definition]) ).
fof(f4548,plain,
( ~ sQ11_spl
| sQ584_spl ),
inference(split_clause,[status(thm)],[f4528,f4545,f545]) ).
fof(f4549,definition,
! [X0,X1,X2,X3] :
( sQ585_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf73(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf73(X0)),X2))
| ~ ssList(skaf73(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf73(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ585_spl])],[split_symbol_definition]) ).
fof(f4552,plain,
( ~ sQ11_spl
| sQ585_spl ),
inference(split_clause,[status(thm)],[f4529,f4549,f545]) ).
fof(f4553,definition,
! [X0,X1,X2] :
( sQ586_spl
<=> ( segmentP(app(skaf73(X0),X2),X1)
| ~ ssList(skaf73(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf73(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ586_spl])],[split_symbol_definition]) ).
fof(f4556,plain,
( ~ sQ11_spl
| sQ586_spl ),
inference(split_clause,[status(thm)],[f4530,f4553,f545]) ).
fof(f4557,definition,
! [X0,X1] :
( sQ587_spl
<=> ( rearsegP(skaf73(X0),X1)
| ~ ssList(skaf73(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf73(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ587_spl])],[split_symbol_definition]) ).
fof(f4560,plain,
( ~ sQ11_spl
| sQ587_spl ),
inference(split_clause,[status(thm)],[f4531,f4557,f545]) ).
fof(f4569,plain,
! [X0] :
( app(nil,skaf75(X0)) = skaf75(X0)
| ~ rearsegP(skaf75(X0),skaf75(X0))
| ~ ssList(skaf75(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1430,f2334]) ).
fof(f4570,plain,
! [X0,X1] :
( segmentP(app(skaf75(X1),X0),skaf75(X1))
| ~ ssList(skaf75(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1430,f2205]) ).
fof(f4571,plain,
! [X0] :
( rearsegP(skaf75(X0),skaf75(X0))
| ~ ssList(skaf75(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1430,f2173]) ).
fof(f4573,plain,
! [X0,X1,X2] :
( app(app(nil,skaf75(X0)),X2) = X1
| ~ ssList(app(skaf75(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf75(X0)),X2))
| ~ ssList(skaf75(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf75(X0),X1) ),
inference(paramodulation,[status(thm)],[f1430,f666]) ).
fof(f4574,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf75(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf75(X0)),X2))
| ~ ssList(skaf75(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf75(X0),X1) ),
inference(paramodulation,[status(thm)],[f1430,f665]) ).
fof(f4575,plain,
! [X0,X1,X2] :
( segmentP(app(skaf75(X0),X2),X1)
| ~ ssList(skaf75(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf75(X0),X1) ),
inference(paramodulation,[status(thm)],[f1430,f404]) ).
fof(f4576,plain,
! [X0,X1] :
( rearsegP(skaf75(X0),X1)
| ~ ssList(skaf75(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf75(X0),X1) ),
inference(paramodulation,[status(thm)],[f1430,f350]) ).
fof(f4577,definition,
! [X0] :
( sQ588_spl
<=> ( app(nil,skaf75(X0)) = skaf75(X0)
| ~ rearsegP(skaf75(X0),skaf75(X0))
| ~ ssList(skaf75(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ588_spl])],[split_symbol_definition]) ).
fof(f4580,plain,
( sQ588_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4569,f545,f4577]) ).
fof(f4581,definition,
! [X0,X1] :
( sQ589_spl
<=> ( segmentP(app(skaf75(X1),X0),skaf75(X1))
| ~ ssList(skaf75(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ589_spl])],[split_symbol_definition]) ).
fof(f4584,plain,
( ~ sQ11_spl
| sQ589_spl ),
inference(split_clause,[status(thm)],[f4570,f4581,f545]) ).
fof(f4585,definition,
! [X0] :
( sQ590_spl
<=> ( rearsegP(skaf75(X0),skaf75(X0))
| ~ ssList(skaf75(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ590_spl])],[split_symbol_definition]) ).
fof(f4588,plain,
( sQ590_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4571,f545,f4585]) ).
fof(f4590,definition,
! [X0,X1,X2] :
( sQ591_spl
<=> ( app(app(nil,skaf75(X0)),X2) = X1
| ~ ssList(app(skaf75(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf75(X0)),X2))
| ~ ssList(skaf75(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf75(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ591_spl])],[split_symbol_definition]) ).
fof(f4593,plain,
( ~ sQ11_spl
| sQ591_spl ),
inference(split_clause,[status(thm)],[f4573,f4590,f545]) ).
fof(f4594,definition,
! [X0,X1,X2,X3] :
( sQ592_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf75(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf75(X0)),X2))
| ~ ssList(skaf75(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf75(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ592_spl])],[split_symbol_definition]) ).
fof(f4597,plain,
( ~ sQ11_spl
| sQ592_spl ),
inference(split_clause,[status(thm)],[f4574,f4594,f545]) ).
fof(f4598,definition,
! [X0,X1,X2] :
( sQ593_spl
<=> ( segmentP(app(skaf75(X0),X2),X1)
| ~ ssList(skaf75(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf75(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ593_spl])],[split_symbol_definition]) ).
fof(f4601,plain,
( ~ sQ11_spl
| sQ593_spl ),
inference(split_clause,[status(thm)],[f4575,f4598,f545]) ).
fof(f4602,definition,
! [X0,X1] :
( sQ594_spl
<=> ( rearsegP(skaf75(X0),X1)
| ~ ssList(skaf75(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf75(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ594_spl])],[split_symbol_definition]) ).
fof(f4605,plain,
( ~ sQ11_spl
| sQ594_spl ),
inference(split_clause,[status(thm)],[f4576,f4602,f545]) ).
fof(f4614,plain,
! [X0] :
( app(nil,skaf76(X0)) = skaf76(X0)
| ~ rearsegP(skaf76(X0),skaf76(X0))
| ~ ssList(skaf76(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1431,f2334]) ).
fof(f4615,plain,
! [X0,X1] :
( segmentP(app(skaf76(X1),X0),skaf76(X1))
| ~ ssList(skaf76(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1431,f2205]) ).
fof(f4616,plain,
! [X0] :
( rearsegP(skaf76(X0),skaf76(X0))
| ~ ssList(skaf76(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1431,f2173]) ).
fof(f4618,plain,
! [X0,X1,X2] :
( app(app(nil,skaf76(X0)),X2) = X1
| ~ ssList(app(skaf76(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf76(X0)),X2))
| ~ ssList(skaf76(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf76(X0),X1) ),
inference(paramodulation,[status(thm)],[f1431,f666]) ).
fof(f4619,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf76(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf76(X0)),X2))
| ~ ssList(skaf76(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf76(X0),X1) ),
inference(paramodulation,[status(thm)],[f1431,f665]) ).
fof(f4620,plain,
! [X0,X1,X2] :
( segmentP(app(skaf76(X0),X2),X1)
| ~ ssList(skaf76(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf76(X0),X1) ),
inference(paramodulation,[status(thm)],[f1431,f404]) ).
fof(f4621,plain,
! [X0,X1] :
( rearsegP(skaf76(X0),X1)
| ~ ssList(skaf76(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf76(X0),X1) ),
inference(paramodulation,[status(thm)],[f1431,f350]) ).
fof(f4622,definition,
! [X0] :
( sQ595_spl
<=> ( app(nil,skaf76(X0)) = skaf76(X0)
| ~ rearsegP(skaf76(X0),skaf76(X0))
| ~ ssList(skaf76(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ595_spl])],[split_symbol_definition]) ).
fof(f4625,plain,
( sQ595_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4614,f545,f4622]) ).
fof(f4626,definition,
! [X0,X1] :
( sQ596_spl
<=> ( segmentP(app(skaf76(X1),X0),skaf76(X1))
| ~ ssList(skaf76(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ596_spl])],[split_symbol_definition]) ).
fof(f4629,plain,
( ~ sQ11_spl
| sQ596_spl ),
inference(split_clause,[status(thm)],[f4615,f4626,f545]) ).
fof(f4630,definition,
! [X0] :
( sQ597_spl
<=> ( rearsegP(skaf76(X0),skaf76(X0))
| ~ ssList(skaf76(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ597_spl])],[split_symbol_definition]) ).
fof(f4633,plain,
( sQ597_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4616,f545,f4630]) ).
fof(f4635,definition,
! [X0,X1,X2] :
( sQ598_spl
<=> ( app(app(nil,skaf76(X0)),X2) = X1
| ~ ssList(app(skaf76(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf76(X0)),X2))
| ~ ssList(skaf76(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf76(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ598_spl])],[split_symbol_definition]) ).
fof(f4638,plain,
( ~ sQ11_spl
| sQ598_spl ),
inference(split_clause,[status(thm)],[f4618,f4635,f545]) ).
fof(f4639,definition,
! [X0,X1,X2,X3] :
( sQ599_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf76(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf76(X0)),X2))
| ~ ssList(skaf76(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf76(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ599_spl])],[split_symbol_definition]) ).
fof(f4642,plain,
( ~ sQ11_spl
| sQ599_spl ),
inference(split_clause,[status(thm)],[f4619,f4639,f545]) ).
fof(f4643,definition,
! [X0,X1,X2] :
( sQ600_spl
<=> ( segmentP(app(skaf76(X0),X2),X1)
| ~ ssList(skaf76(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf76(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ600_spl])],[split_symbol_definition]) ).
fof(f4646,plain,
( ~ sQ11_spl
| sQ600_spl ),
inference(split_clause,[status(thm)],[f4620,f4643,f545]) ).
fof(f4647,definition,
! [X0,X1] :
( sQ601_spl
<=> ( rearsegP(skaf76(X0),X1)
| ~ ssList(skaf76(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf76(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ601_spl])],[split_symbol_definition]) ).
fof(f4650,plain,
( ~ sQ11_spl
| sQ601_spl ),
inference(split_clause,[status(thm)],[f4621,f4647,f545]) ).
fof(f4659,plain,
! [X0] :
( app(nil,skaf77(X0)) = skaf77(X0)
| ~ rearsegP(skaf77(X0),skaf77(X0))
| ~ ssList(skaf77(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1432,f2334]) ).
fof(f4660,plain,
! [X0,X1] :
( segmentP(app(skaf77(X1),X0),skaf77(X1))
| ~ ssList(skaf77(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1432,f2205]) ).
fof(f4661,plain,
! [X0] :
( rearsegP(skaf77(X0),skaf77(X0))
| ~ ssList(skaf77(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1432,f2173]) ).
fof(f4663,plain,
! [X0,X1,X2] :
( app(app(nil,skaf77(X0)),X2) = X1
| ~ ssList(app(skaf77(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf77(X0)),X2))
| ~ ssList(skaf77(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf77(X0),X1) ),
inference(paramodulation,[status(thm)],[f1432,f666]) ).
fof(f4664,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf77(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf77(X0)),X2))
| ~ ssList(skaf77(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf77(X0),X1) ),
inference(paramodulation,[status(thm)],[f1432,f665]) ).
fof(f4665,plain,
! [X0,X1,X2] :
( segmentP(app(skaf77(X0),X2),X1)
| ~ ssList(skaf77(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf77(X0),X1) ),
inference(paramodulation,[status(thm)],[f1432,f404]) ).
fof(f4666,plain,
! [X0,X1] :
( rearsegP(skaf77(X0),X1)
| ~ ssList(skaf77(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf77(X0),X1) ),
inference(paramodulation,[status(thm)],[f1432,f350]) ).
fof(f4667,definition,
! [X0] :
( sQ602_spl
<=> ( app(nil,skaf77(X0)) = skaf77(X0)
| ~ rearsegP(skaf77(X0),skaf77(X0))
| ~ ssList(skaf77(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ602_spl])],[split_symbol_definition]) ).
fof(f4670,plain,
( sQ602_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4659,f545,f4667]) ).
fof(f4671,definition,
! [X0,X1] :
( sQ603_spl
<=> ( segmentP(app(skaf77(X1),X0),skaf77(X1))
| ~ ssList(skaf77(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ603_spl])],[split_symbol_definition]) ).
fof(f4674,plain,
( ~ sQ11_spl
| sQ603_spl ),
inference(split_clause,[status(thm)],[f4660,f4671,f545]) ).
fof(f4675,definition,
! [X0] :
( sQ604_spl
<=> ( rearsegP(skaf77(X0),skaf77(X0))
| ~ ssList(skaf77(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ604_spl])],[split_symbol_definition]) ).
fof(f4678,plain,
( sQ604_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4661,f545,f4675]) ).
fof(f4680,definition,
! [X0,X1,X2] :
( sQ605_spl
<=> ( app(app(nil,skaf77(X0)),X2) = X1
| ~ ssList(app(skaf77(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf77(X0)),X2))
| ~ ssList(skaf77(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf77(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ605_spl])],[split_symbol_definition]) ).
fof(f4683,plain,
( ~ sQ11_spl
| sQ605_spl ),
inference(split_clause,[status(thm)],[f4663,f4680,f545]) ).
fof(f4684,definition,
! [X0,X1,X2,X3] :
( sQ606_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf77(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf77(X0)),X2))
| ~ ssList(skaf77(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf77(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ606_spl])],[split_symbol_definition]) ).
fof(f4687,plain,
( ~ sQ11_spl
| sQ606_spl ),
inference(split_clause,[status(thm)],[f4664,f4684,f545]) ).
fof(f4688,definition,
! [X0,X1,X2] :
( sQ607_spl
<=> ( segmentP(app(skaf77(X0),X2),X1)
| ~ ssList(skaf77(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf77(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ607_spl])],[split_symbol_definition]) ).
fof(f4691,plain,
( ~ sQ11_spl
| sQ607_spl ),
inference(split_clause,[status(thm)],[f4665,f4688,f545]) ).
fof(f4692,definition,
! [X0,X1] :
( sQ608_spl
<=> ( rearsegP(skaf77(X0),X1)
| ~ ssList(skaf77(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf77(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ608_spl])],[split_symbol_definition]) ).
fof(f4695,plain,
( ~ sQ11_spl
| sQ608_spl ),
inference(split_clause,[status(thm)],[f4666,f4692,f545]) ).
fof(f4704,plain,
! [X0] :
( app(nil,skaf80(X0)) = skaf80(X0)
| ~ rearsegP(skaf80(X0),skaf80(X0))
| ~ ssList(skaf80(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1433,f2334]) ).
fof(f4705,plain,
! [X0,X1] :
( segmentP(app(skaf80(X1),X0),skaf80(X1))
| ~ ssList(skaf80(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1433,f2205]) ).
fof(f4706,plain,
! [X0] :
( rearsegP(skaf80(X0),skaf80(X0))
| ~ ssList(skaf80(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1433,f2173]) ).
fof(f4708,plain,
! [X0,X1,X2] :
( app(app(nil,skaf80(X0)),X2) = X1
| ~ ssList(app(skaf80(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf80(X0)),X2))
| ~ ssList(skaf80(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf80(X0),X1) ),
inference(paramodulation,[status(thm)],[f1433,f666]) ).
fof(f4709,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf80(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf80(X0)),X2))
| ~ ssList(skaf80(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf80(X0),X1) ),
inference(paramodulation,[status(thm)],[f1433,f665]) ).
fof(f4710,plain,
! [X0,X1,X2] :
( segmentP(app(skaf80(X0),X2),X1)
| ~ ssList(skaf80(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf80(X0),X1) ),
inference(paramodulation,[status(thm)],[f1433,f404]) ).
fof(f4711,plain,
! [X0,X1] :
( rearsegP(skaf80(X0),X1)
| ~ ssList(skaf80(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf80(X0),X1) ),
inference(paramodulation,[status(thm)],[f1433,f350]) ).
fof(f4712,definition,
! [X0] :
( sQ609_spl
<=> ( app(nil,skaf80(X0)) = skaf80(X0)
| ~ rearsegP(skaf80(X0),skaf80(X0))
| ~ ssList(skaf80(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ609_spl])],[split_symbol_definition]) ).
fof(f4715,plain,
( sQ609_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4704,f545,f4712]) ).
fof(f4716,definition,
! [X0,X1] :
( sQ610_spl
<=> ( segmentP(app(skaf80(X1),X0),skaf80(X1))
| ~ ssList(skaf80(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ610_spl])],[split_symbol_definition]) ).
fof(f4719,plain,
( ~ sQ11_spl
| sQ610_spl ),
inference(split_clause,[status(thm)],[f4705,f4716,f545]) ).
fof(f4720,definition,
! [X0] :
( sQ611_spl
<=> ( rearsegP(skaf80(X0),skaf80(X0))
| ~ ssList(skaf80(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ611_spl])],[split_symbol_definition]) ).
fof(f4723,plain,
( sQ611_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4706,f545,f4720]) ).
fof(f4725,definition,
! [X0,X1,X2] :
( sQ612_spl
<=> ( app(app(nil,skaf80(X0)),X2) = X1
| ~ ssList(app(skaf80(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf80(X0)),X2))
| ~ ssList(skaf80(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf80(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ612_spl])],[split_symbol_definition]) ).
fof(f4728,plain,
( ~ sQ11_spl
| sQ612_spl ),
inference(split_clause,[status(thm)],[f4708,f4725,f545]) ).
fof(f4729,definition,
! [X0,X1,X2,X3] :
( sQ613_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf80(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf80(X0)),X2))
| ~ ssList(skaf80(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf80(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ613_spl])],[split_symbol_definition]) ).
fof(f4732,plain,
( ~ sQ11_spl
| sQ613_spl ),
inference(split_clause,[status(thm)],[f4709,f4729,f545]) ).
fof(f4733,definition,
! [X0,X1,X2] :
( sQ614_spl
<=> ( segmentP(app(skaf80(X0),X2),X1)
| ~ ssList(skaf80(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf80(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ614_spl])],[split_symbol_definition]) ).
fof(f4736,plain,
( ~ sQ11_spl
| sQ614_spl ),
inference(split_clause,[status(thm)],[f4710,f4733,f545]) ).
fof(f4737,definition,
! [X0,X1] :
( sQ615_spl
<=> ( rearsegP(skaf80(X0),X1)
| ~ ssList(skaf80(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf80(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ615_spl])],[split_symbol_definition]) ).
fof(f4740,plain,
( ~ sQ11_spl
| sQ615_spl ),
inference(split_clause,[status(thm)],[f4711,f4737,f545]) ).
fof(f4749,plain,
! [X0] :
( app(nil,skaf81(X0)) = skaf81(X0)
| ~ rearsegP(skaf81(X0),skaf81(X0))
| ~ ssList(skaf81(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1434,f2334]) ).
fof(f4750,plain,
! [X0,X1] :
( segmentP(app(skaf81(X1),X0),skaf81(X1))
| ~ ssList(skaf81(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1434,f2205]) ).
fof(f4751,plain,
! [X0] :
( rearsegP(skaf81(X0),skaf81(X0))
| ~ ssList(skaf81(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1434,f2173]) ).
fof(f4753,plain,
! [X0,X1,X2] :
( app(app(nil,skaf81(X0)),X2) = X1
| ~ ssList(app(skaf81(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf81(X0)),X2))
| ~ ssList(skaf81(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf81(X0),X1) ),
inference(paramodulation,[status(thm)],[f1434,f666]) ).
fof(f4754,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf81(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf81(X0)),X2))
| ~ ssList(skaf81(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf81(X0),X1) ),
inference(paramodulation,[status(thm)],[f1434,f665]) ).
fof(f4755,plain,
! [X0,X1,X2] :
( segmentP(app(skaf81(X0),X2),X1)
| ~ ssList(skaf81(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf81(X0),X1) ),
inference(paramodulation,[status(thm)],[f1434,f404]) ).
fof(f4756,plain,
! [X0,X1] :
( rearsegP(skaf81(X0),X1)
| ~ ssList(skaf81(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf81(X0),X1) ),
inference(paramodulation,[status(thm)],[f1434,f350]) ).
fof(f4757,definition,
! [X0] :
( sQ616_spl
<=> ( app(nil,skaf81(X0)) = skaf81(X0)
| ~ rearsegP(skaf81(X0),skaf81(X0))
| ~ ssList(skaf81(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ616_spl])],[split_symbol_definition]) ).
fof(f4760,plain,
( sQ616_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4749,f545,f4757]) ).
fof(f4761,definition,
! [X0,X1] :
( sQ617_spl
<=> ( segmentP(app(skaf81(X1),X0),skaf81(X1))
| ~ ssList(skaf81(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ617_spl])],[split_symbol_definition]) ).
fof(f4764,plain,
( ~ sQ11_spl
| sQ617_spl ),
inference(split_clause,[status(thm)],[f4750,f4761,f545]) ).
fof(f4765,definition,
! [X0] :
( sQ618_spl
<=> ( rearsegP(skaf81(X0),skaf81(X0))
| ~ ssList(skaf81(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ618_spl])],[split_symbol_definition]) ).
fof(f4768,plain,
( sQ618_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4751,f545,f4765]) ).
fof(f4770,definition,
! [X0,X1,X2] :
( sQ619_spl
<=> ( app(app(nil,skaf81(X0)),X2) = X1
| ~ ssList(app(skaf81(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf81(X0)),X2))
| ~ ssList(skaf81(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf81(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ619_spl])],[split_symbol_definition]) ).
fof(f4773,plain,
( ~ sQ11_spl
| sQ619_spl ),
inference(split_clause,[status(thm)],[f4753,f4770,f545]) ).
fof(f4774,definition,
! [X0,X1,X2,X3] :
( sQ620_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf81(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf81(X0)),X2))
| ~ ssList(skaf81(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf81(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ620_spl])],[split_symbol_definition]) ).
fof(f4777,plain,
( ~ sQ11_spl
| sQ620_spl ),
inference(split_clause,[status(thm)],[f4754,f4774,f545]) ).
fof(f4778,definition,
! [X0,X1,X2] :
( sQ621_spl
<=> ( segmentP(app(skaf81(X0),X2),X1)
| ~ ssList(skaf81(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf81(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ621_spl])],[split_symbol_definition]) ).
fof(f4781,plain,
( ~ sQ11_spl
| sQ621_spl ),
inference(split_clause,[status(thm)],[f4755,f4778,f545]) ).
fof(f4782,definition,
! [X0,X1] :
( sQ622_spl
<=> ( rearsegP(skaf81(X0),X1)
| ~ ssList(skaf81(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf81(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ622_spl])],[split_symbol_definition]) ).
fof(f4785,plain,
( ~ sQ11_spl
| sQ622_spl ),
inference(split_clause,[status(thm)],[f4756,f4782,f545]) ).
fof(f4837,plain,
! [X0,X1] :
( ~ sQ267_spl
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(app(X0,sk2))
| ~ rearsegP(X1,app(X0,sk2))
| ~ rearsegP(nil,X1)
| app(X0,sk2) = nil
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2561,f376]) ).
fof(f4839,definition,
! [X0,X1] :
( sQ623_spl
<=> ( ~ ssList(X1)
| ~ ssList(app(X0,sk2))
| ~ rearsegP(X1,app(X0,sk2))
| ~ rearsegP(nil,X1)
| app(X0,sk2) = nil
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ623_spl])],[split_symbol_definition]) ).
fof(f4842,plain,
( ~ sQ267_spl
| ~ sQ11_spl
| sQ623_spl ),
inference(split_clause,[status(thm)],[f4837,f4839,f545,f2560]) ).
fof(f4847,plain,
! [X0,X1] :
( ~ sQ264_spl
| ~ ssList(sk1)
| ~ ssList(X1)
| ~ ssList(app(X0,sk1))
| ~ rearsegP(X1,app(X0,sk1))
| ~ rearsegP(sk1,X1)
| app(X0,sk1) = sk1
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2549,f376]) ).
fof(f4849,definition,
! [X0,X1] :
( sQ625_spl
<=> ( ~ ssList(X1)
| ~ ssList(app(X0,sk1))
| ~ rearsegP(X1,app(X0,sk1))
| ~ rearsegP(sk1,X1)
| app(X0,sk1) = sk1
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ625_spl])],[split_symbol_definition]) ).
fof(f4852,plain,
( ~ sQ264_spl
| ~ sQ13_spl
| sQ625_spl ),
inference(split_clause,[status(thm)],[f4847,f4849,f558,f2548]) ).
fof(f4864,plain,
! [X0,X1,X2] :
( ~ sQ304_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf63(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf63(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2824,f374]) ).
fof(f4865,plain,
! [X0,X1] :
( ~ sQ304_spl
| app(skaf63(X1),X0) = nil
| ~ ssList(app(skaf63(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf63(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2824,f339]) ).
fof(f4866,plain,
! [X0] :
( ~ sQ304_spl
| segmentP(skaf63(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1028,f2824]) ).
fof(f4867,definition,
! [X0,X1,X2] :
( sQ628_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf63(X2),X0))
| ~ segmentP(X1,app(skaf63(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ628_spl])],[split_symbol_definition]) ).
fof(f4870,plain,
( ~ sQ304_spl
| ~ sQ11_spl
| sQ628_spl ),
inference(split_clause,[status(thm)],[f4864,f4867,f545,f2796]) ).
fof(f4871,definition,
! [X0,X1] :
( sQ629_spl
<=> ( app(skaf63(X1),X0) = nil
| ~ ssList(app(skaf63(X1),X0))
| ~ segmentP(nil,app(skaf63(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ629_spl])],[split_symbol_definition]) ).
fof(f4874,plain,
( ~ sQ304_spl
| ~ sQ11_spl
| sQ629_spl ),
inference(split_clause,[status(thm)],[f4865,f4871,f545,f2796]) ).
fof(f4875,definition,
! [X0] :
( sQ630_spl
<=> segmentP(skaf63(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ630_spl])],[split_symbol_definition]) ).
fof(f4876,plain,
! [X0] :
( ~ sQ630_spl
| segmentP(skaf63(X0),nil) ),
inference(component_clause,[status(thm)],[f4875]) ).
fof(f4878,plain,
( ~ sQ304_spl
| sQ630_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4866,f545,f4875,f2796]) ).
fof(f4879,plain,
! [X0,X1] :
( ~ sQ630_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf63(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf63(X1)) ),
inference(resolution,[status(thm)],[f4876,f374]) ).
fof(f4880,plain,
! [X0] :
( ~ sQ630_spl
| skaf63(X0) = nil
| ~ ssList(skaf63(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf63(X0)) ),
inference(resolution,[status(thm)],[f4876,f339]) ).
fof(f4881,definition,
! [X0,X1] :
( sQ631_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf63(X1))
| ~ segmentP(X0,skaf63(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ631_spl])],[split_symbol_definition]) ).
fof(f4884,plain,
( ~ sQ630_spl
| ~ sQ11_spl
| sQ631_spl ),
inference(split_clause,[status(thm)],[f4879,f4881,f545,f4875]) ).
fof(f4885,definition,
! [X0] :
( sQ632_spl
<=> ( skaf63(X0) = nil
| ~ ssList(skaf63(X0))
| ~ segmentP(nil,skaf63(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ632_spl])],[split_symbol_definition]) ).
fof(f4888,plain,
( ~ sQ630_spl
| ~ sQ11_spl
| sQ632_spl ),
inference(split_clause,[status(thm)],[f4880,f4885,f545,f4875]) ).
fof(f4889,plain,
! [X0,X1,X2] :
( ~ sQ311_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf66(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf66(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2867,f374]) ).
fof(f4890,plain,
! [X0,X1] :
( ~ sQ311_spl
| app(skaf66(X1),X0) = nil
| ~ ssList(app(skaf66(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf66(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2867,f339]) ).
fof(f4891,plain,
! [X0] :
( ~ sQ311_spl
| segmentP(skaf66(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1030,f2867]) ).
fof(f4892,definition,
! [X0,X1,X2] :
( sQ633_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf66(X2),X0))
| ~ segmentP(X1,app(skaf66(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ633_spl])],[split_symbol_definition]) ).
fof(f4895,plain,
( ~ sQ311_spl
| ~ sQ11_spl
| sQ633_spl ),
inference(split_clause,[status(thm)],[f4889,f4892,f545,f2839]) ).
fof(f4896,definition,
! [X0,X1] :
( sQ634_spl
<=> ( app(skaf66(X1),X0) = nil
| ~ ssList(app(skaf66(X1),X0))
| ~ segmentP(nil,app(skaf66(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ634_spl])],[split_symbol_definition]) ).
fof(f4899,plain,
( ~ sQ311_spl
| ~ sQ11_spl
| sQ634_spl ),
inference(split_clause,[status(thm)],[f4890,f4896,f545,f2839]) ).
fof(f4900,definition,
! [X0] :
( sQ635_spl
<=> segmentP(skaf66(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ635_spl])],[split_symbol_definition]) ).
fof(f4901,plain,
! [X0] :
( ~ sQ635_spl
| segmentP(skaf66(X0),nil) ),
inference(component_clause,[status(thm)],[f4900]) ).
fof(f4903,plain,
( ~ sQ311_spl
| sQ635_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4891,f545,f4900,f2839]) ).
fof(f4904,plain,
! [X0,X1] :
( ~ sQ635_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf66(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf66(X1)) ),
inference(resolution,[status(thm)],[f4901,f374]) ).
fof(f4905,plain,
! [X0] :
( ~ sQ635_spl
| skaf66(X0) = nil
| ~ ssList(skaf66(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf66(X0)) ),
inference(resolution,[status(thm)],[f4901,f339]) ).
fof(f4906,definition,
! [X0,X1] :
( sQ636_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf66(X1))
| ~ segmentP(X0,skaf66(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ636_spl])],[split_symbol_definition]) ).
fof(f4909,plain,
( ~ sQ635_spl
| ~ sQ11_spl
| sQ636_spl ),
inference(split_clause,[status(thm)],[f4904,f4906,f545,f4900]) ).
fof(f4910,definition,
! [X0] :
( sQ637_spl
<=> ( skaf66(X0) = nil
| ~ ssList(skaf66(X0))
| ~ segmentP(nil,skaf66(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ637_spl])],[split_symbol_definition]) ).
fof(f4913,plain,
( ~ sQ635_spl
| ~ sQ11_spl
| sQ637_spl ),
inference(split_clause,[status(thm)],[f4905,f4910,f545,f4900]) ).
fof(f4914,plain,
! [X0,X1,X2] :
( ~ sQ318_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf67(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf67(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2910,f374]) ).
fof(f4915,plain,
! [X0,X1] :
( ~ sQ318_spl
| app(skaf67(X1),X0) = nil
| ~ ssList(app(skaf67(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf67(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2910,f339]) ).
fof(f4916,plain,
! [X0] :
( ~ sQ318_spl
| segmentP(skaf67(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1031,f2910]) ).
fof(f4917,definition,
! [X0,X1,X2] :
( sQ638_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf67(X2),X0))
| ~ segmentP(X1,app(skaf67(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ638_spl])],[split_symbol_definition]) ).
fof(f4920,plain,
( ~ sQ318_spl
| ~ sQ11_spl
| sQ638_spl ),
inference(split_clause,[status(thm)],[f4914,f4917,f545,f2882]) ).
fof(f4921,definition,
! [X0,X1] :
( sQ639_spl
<=> ( app(skaf67(X1),X0) = nil
| ~ ssList(app(skaf67(X1),X0))
| ~ segmentP(nil,app(skaf67(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ639_spl])],[split_symbol_definition]) ).
fof(f4924,plain,
( ~ sQ318_spl
| ~ sQ11_spl
| sQ639_spl ),
inference(split_clause,[status(thm)],[f4915,f4921,f545,f2882]) ).
fof(f4925,definition,
! [X0] :
( sQ640_spl
<=> segmentP(skaf67(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ640_spl])],[split_symbol_definition]) ).
fof(f4926,plain,
! [X0] :
( ~ sQ640_spl
| segmentP(skaf67(X0),nil) ),
inference(component_clause,[status(thm)],[f4925]) ).
fof(f4928,plain,
( ~ sQ318_spl
| sQ640_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4916,f545,f4925,f2882]) ).
fof(f4929,plain,
! [X0,X1] :
( ~ sQ640_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf67(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf67(X1)) ),
inference(resolution,[status(thm)],[f4926,f374]) ).
fof(f4930,plain,
! [X0] :
( ~ sQ640_spl
| skaf67(X0) = nil
| ~ ssList(skaf67(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf67(X0)) ),
inference(resolution,[status(thm)],[f4926,f339]) ).
fof(f4931,definition,
! [X0,X1] :
( sQ641_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf67(X1))
| ~ segmentP(X0,skaf67(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ641_spl])],[split_symbol_definition]) ).
fof(f4934,plain,
( ~ sQ640_spl
| ~ sQ11_spl
| sQ641_spl ),
inference(split_clause,[status(thm)],[f4929,f4931,f545,f4925]) ).
fof(f4935,definition,
! [X0] :
( sQ642_spl
<=> ( skaf67(X0) = nil
| ~ ssList(skaf67(X0))
| ~ segmentP(nil,skaf67(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ642_spl])],[split_symbol_definition]) ).
fof(f4938,plain,
( ~ sQ640_spl
| ~ sQ11_spl
| sQ642_spl ),
inference(split_clause,[status(thm)],[f4930,f4935,f545,f4925]) ).
fof(f4940,plain,
! [X0,X1,X2] :
( ~ sQ161_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(skaf51(X2))
| ~ segmentP(X1,app(skaf51(X2),nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1020,f1842]) ).
fof(f4943,definition,
! [X0,X1,X2] :
( sQ643_spl
<=> ( segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(skaf51(X2))
| ~ segmentP(X1,app(skaf51(X2),nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ643_spl])],[split_symbol_definition]) ).
fof(f4946,plain,
( ~ sQ161_spl
| ~ sQ11_spl
| sQ643_spl ),
inference(split_clause,[status(thm)],[f4940,f4943,f545,f1809]) ).
fof(f4950,plain,
! [X0,X1] :
( ~ sQ164_spl
| ~ ssList(nil)
| segmentP(app(skaf51(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1847,f255]) ).
fof(f4952,definition,
! [X0,X1] :
( sQ644_spl
<=> ( segmentP(app(skaf51(X1),X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ644_spl])],[split_symbol_definition]) ).
fof(f4956,plain,
( ~ sQ164_spl
| ~ sQ11_spl
| sQ644_spl ),
inference(split_clause,[status(thm)],[f4950,f4952,f545,f1821]) ).
fof(f4959,plain,
! [X0] :
( app(nil,skaf82(X0)) = skaf82(X0)
| ~ rearsegP(skaf82(X0),skaf82(X0))
| ~ ssList(skaf82(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1435,f2334]) ).
fof(f4960,plain,
! [X0,X1] :
( segmentP(app(skaf82(X1),X0),skaf82(X1))
| ~ ssList(skaf82(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1435,f2205]) ).
fof(f4961,plain,
! [X0] :
( rearsegP(skaf82(X0),skaf82(X0))
| ~ ssList(skaf82(X0))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1435,f2173]) ).
fof(f4963,plain,
! [X0,X1,X2] :
( app(app(nil,skaf82(X0)),X2) = X1
| ~ ssList(app(skaf82(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf82(X0)),X2))
| ~ ssList(skaf82(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf82(X0),X1) ),
inference(paramodulation,[status(thm)],[f1435,f666]) ).
fof(f4964,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf82(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf82(X0)),X2))
| ~ ssList(skaf82(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf82(X0),X1) ),
inference(paramodulation,[status(thm)],[f1435,f665]) ).
fof(f4965,plain,
! [X0,X1,X2] :
( segmentP(app(skaf82(X0),X2),X1)
| ~ ssList(skaf82(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ segmentP(skaf82(X0),X1) ),
inference(paramodulation,[status(thm)],[f1435,f404]) ).
fof(f4966,plain,
! [X0,X1] :
( rearsegP(skaf82(X0),X1)
| ~ ssList(skaf82(X0))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(skaf82(X0),X1) ),
inference(paramodulation,[status(thm)],[f1435,f350]) ).
fof(f4967,definition,
! [X0] :
( sQ645_spl
<=> ( app(nil,skaf82(X0)) = skaf82(X0)
| ~ rearsegP(skaf82(X0),skaf82(X0))
| ~ ssList(skaf82(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ645_spl])],[split_symbol_definition]) ).
fof(f4970,plain,
( sQ645_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4959,f545,f4967]) ).
fof(f4971,definition,
! [X0,X1] :
( sQ646_spl
<=> ( segmentP(app(skaf82(X1),X0),skaf82(X1))
| ~ ssList(skaf82(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ646_spl])],[split_symbol_definition]) ).
fof(f4974,plain,
( ~ sQ11_spl
| sQ646_spl ),
inference(split_clause,[status(thm)],[f4960,f4971,f545]) ).
fof(f4975,definition,
! [X0] :
( sQ647_spl
<=> ( rearsegP(skaf82(X0),skaf82(X0))
| ~ ssList(skaf82(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ647_spl])],[split_symbol_definition]) ).
fof(f4978,plain,
( sQ647_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4961,f545,f4975]) ).
fof(f4980,definition,
! [X0,X1,X2] :
( sQ648_spl
<=> ( app(app(nil,skaf82(X0)),X2) = X1
| ~ ssList(app(skaf82(X0),X2))
| ~ segmentP(X1,app(app(nil,skaf82(X0)),X2))
| ~ ssList(skaf82(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf82(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ648_spl])],[split_symbol_definition]) ).
fof(f4983,plain,
( ~ sQ11_spl
| sQ648_spl ),
inference(split_clause,[status(thm)],[f4963,f4980,f545]) ).
fof(f4984,definition,
! [X0,X1,X2,X3] :
( sQ649_spl
<=> ( segmentP(X3,X1)
| ~ ssList(X3)
| ~ ssList(app(skaf82(X0),X2))
| ~ segmentP(X3,app(app(nil,skaf82(X0)),X2))
| ~ ssList(skaf82(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf82(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ649_spl])],[split_symbol_definition]) ).
fof(f4987,plain,
( ~ sQ11_spl
| sQ649_spl ),
inference(split_clause,[status(thm)],[f4964,f4984,f545]) ).
fof(f4988,definition,
! [X0,X1,X2] :
( sQ650_spl
<=> ( segmentP(app(skaf82(X0),X2),X1)
| ~ ssList(skaf82(X0))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(skaf82(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ650_spl])],[split_symbol_definition]) ).
fof(f4991,plain,
( ~ sQ11_spl
| sQ650_spl ),
inference(split_clause,[status(thm)],[f4965,f4988,f545]) ).
fof(f4992,definition,
! [X0,X1] :
( sQ651_spl
<=> ( rearsegP(skaf82(X0),X1)
| ~ ssList(skaf82(X0))
| ~ ssList(X1)
| ~ rearsegP(skaf82(X0),X1) ) ),
introduced(definition,[new_symbols(definition,[sQ651_spl])],[split_symbol_definition]) ).
fof(f4995,plain,
( ~ sQ11_spl
| sQ651_spl ),
inference(split_clause,[status(thm)],[f4966,f4992,f545]) ).
fof(f5105,plain,
! [X0,X1] :
( ~ sQ266_spl
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ ssList(app(X0,sk2))
| ~ rearsegP(X1,app(X0,sk2))
| ~ rearsegP(sk2,X1)
| app(X0,sk2) = sk2
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2557,f376]) ).
fof(f5107,definition,
! [X0,X1] :
( sQ652_spl
<=> ( ~ ssList(X1)
| ~ ssList(app(X0,sk2))
| ~ rearsegP(X1,app(X0,sk2))
| ~ rearsegP(sk2,X1)
| app(X0,sk2) = sk2
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ652_spl])],[split_symbol_definition]) ).
fof(f5110,plain,
( ~ sQ266_spl
| ~ sQ16_spl
| sQ652_spl ),
inference(split_clause,[status(thm)],[f5105,f5107,f587,f2556]) ).
fof(f5126,plain,
! [X0,X1,X2] :
( ~ sQ83_spl
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ rearsegP(X2,X1)
| ~ rearsegP(nil,X2)
| ~ ssList(X1)
| ~ rearsegP(X1,X0)
| rearsegP(sk1,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1215,f376]) ).
fof(f5130,definition,
! [X0,X1,X2] :
( sQ654_spl
<=> ( ~ ssList(X2)
| ~ ssList(X1)
| ~ rearsegP(X2,X1)
| ~ rearsegP(nil,X2)
| ~ ssList(X1)
| ~ rearsegP(X1,X0)
| rearsegP(sk1,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ654_spl])],[split_symbol_definition]) ).
fof(f5133,plain,
( ~ sQ83_spl
| ~ sQ11_spl
| sQ654_spl ),
inference(split_clause,[status(thm)],[f5126,f5130,f545,f1210]) ).
fof(f5136,plain,
! [X0,X1,X2] :
( ~ sQ325_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf68(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf68(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2953,f374]) ).
fof(f5137,plain,
! [X0,X1] :
( ~ sQ325_spl
| app(skaf68(X1),X0) = nil
| ~ ssList(app(skaf68(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf68(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2953,f339]) ).
fof(f5138,plain,
! [X0] :
( ~ sQ325_spl
| segmentP(skaf68(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1032,f2953]) ).
fof(f5139,definition,
! [X0,X1,X2] :
( sQ655_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf68(X2),X0))
| ~ segmentP(X1,app(skaf68(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ655_spl])],[split_symbol_definition]) ).
fof(f5142,plain,
( ~ sQ325_spl
| ~ sQ11_spl
| sQ655_spl ),
inference(split_clause,[status(thm)],[f5136,f5139,f545,f2925]) ).
fof(f5143,definition,
! [X0,X1] :
( sQ656_spl
<=> ( app(skaf68(X1),X0) = nil
| ~ ssList(app(skaf68(X1),X0))
| ~ segmentP(nil,app(skaf68(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ656_spl])],[split_symbol_definition]) ).
fof(f5146,plain,
( ~ sQ325_spl
| ~ sQ11_spl
| sQ656_spl ),
inference(split_clause,[status(thm)],[f5137,f5143,f545,f2925]) ).
fof(f5147,definition,
! [X0] :
( sQ657_spl
<=> segmentP(skaf68(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ657_spl])],[split_symbol_definition]) ).
fof(f5148,plain,
! [X0] :
( ~ sQ657_spl
| segmentP(skaf68(X0),nil) ),
inference(component_clause,[status(thm)],[f5147]) ).
fof(f5150,plain,
( ~ sQ325_spl
| sQ657_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5138,f545,f5147,f2925]) ).
fof(f5151,plain,
! [X0,X1] :
( ~ sQ657_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf68(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf68(X1)) ),
inference(resolution,[status(thm)],[f5148,f374]) ).
fof(f5152,plain,
! [X0] :
( ~ sQ657_spl
| skaf68(X0) = nil
| ~ ssList(skaf68(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf68(X0)) ),
inference(resolution,[status(thm)],[f5148,f339]) ).
fof(f5153,definition,
! [X0,X1] :
( sQ658_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf68(X1))
| ~ segmentP(X0,skaf68(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ658_spl])],[split_symbol_definition]) ).
fof(f5156,plain,
( ~ sQ657_spl
| ~ sQ11_spl
| sQ658_spl ),
inference(split_clause,[status(thm)],[f5151,f5153,f545,f5147]) ).
fof(f5157,definition,
! [X0] :
( sQ659_spl
<=> ( skaf68(X0) = nil
| ~ ssList(skaf68(X0))
| ~ segmentP(nil,skaf68(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ659_spl])],[split_symbol_definition]) ).
fof(f5160,plain,
( ~ sQ657_spl
| ~ sQ11_spl
| sQ659_spl ),
inference(split_clause,[status(thm)],[f5152,f5157,f545,f5147]) ).
fof(f5161,plain,
! [X0,X1,X2] :
( ~ sQ332_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf71(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf71(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2996,f374]) ).
fof(f5162,plain,
! [X0,X1] :
( ~ sQ332_spl
| app(skaf71(X1),X0) = nil
| ~ ssList(app(skaf71(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf71(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2996,f339]) ).
fof(f5163,plain,
! [X0] :
( ~ sQ332_spl
| segmentP(skaf71(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1033,f2996]) ).
fof(f5164,definition,
! [X0,X1,X2] :
( sQ660_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf71(X2),X0))
| ~ segmentP(X1,app(skaf71(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ660_spl])],[split_symbol_definition]) ).
fof(f5167,plain,
( ~ sQ332_spl
| ~ sQ11_spl
| sQ660_spl ),
inference(split_clause,[status(thm)],[f5161,f5164,f545,f2968]) ).
fof(f5168,definition,
! [X0,X1] :
( sQ661_spl
<=> ( app(skaf71(X1),X0) = nil
| ~ ssList(app(skaf71(X1),X0))
| ~ segmentP(nil,app(skaf71(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ661_spl])],[split_symbol_definition]) ).
fof(f5171,plain,
( ~ sQ332_spl
| ~ sQ11_spl
| sQ661_spl ),
inference(split_clause,[status(thm)],[f5162,f5168,f545,f2968]) ).
fof(f5172,definition,
! [X0] :
( sQ662_spl
<=> segmentP(skaf71(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ662_spl])],[split_symbol_definition]) ).
fof(f5173,plain,
! [X0] :
( ~ sQ662_spl
| segmentP(skaf71(X0),nil) ),
inference(component_clause,[status(thm)],[f5172]) ).
fof(f5175,plain,
( ~ sQ332_spl
| sQ662_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5163,f545,f5172,f2968]) ).
fof(f5176,plain,
! [X0,X1] :
( ~ sQ662_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf71(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf71(X1)) ),
inference(resolution,[status(thm)],[f5173,f374]) ).
fof(f5177,plain,
! [X0] :
( ~ sQ662_spl
| skaf71(X0) = nil
| ~ ssList(skaf71(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf71(X0)) ),
inference(resolution,[status(thm)],[f5173,f339]) ).
fof(f5178,definition,
! [X0,X1] :
( sQ663_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf71(X1))
| ~ segmentP(X0,skaf71(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ663_spl])],[split_symbol_definition]) ).
fof(f5181,plain,
( ~ sQ662_spl
| ~ sQ11_spl
| sQ663_spl ),
inference(split_clause,[status(thm)],[f5176,f5178,f545,f5172]) ).
fof(f5182,definition,
! [X0] :
( sQ664_spl
<=> ( skaf71(X0) = nil
| ~ ssList(skaf71(X0))
| ~ segmentP(nil,skaf71(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ664_spl])],[split_symbol_definition]) ).
fof(f5185,plain,
( ~ sQ662_spl
| ~ sQ11_spl
| sQ664_spl ),
inference(split_clause,[status(thm)],[f5177,f5182,f545,f5172]) ).
fof(f5186,plain,
! [X0,X1,X2] :
( ~ sQ339_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf72(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf72(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3039,f374]) ).
fof(f5187,plain,
! [X0,X1] :
( ~ sQ339_spl
| app(skaf72(X1),X0) = nil
| ~ ssList(app(skaf72(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf72(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3039,f339]) ).
fof(f5188,plain,
! [X0] :
( ~ sQ339_spl
| segmentP(skaf72(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1034,f3039]) ).
fof(f5189,definition,
! [X0,X1,X2] :
( sQ665_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf72(X2),X0))
| ~ segmentP(X1,app(skaf72(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ665_spl])],[split_symbol_definition]) ).
fof(f5192,plain,
( ~ sQ339_spl
| ~ sQ11_spl
| sQ665_spl ),
inference(split_clause,[status(thm)],[f5186,f5189,f545,f3011]) ).
fof(f5193,definition,
! [X0,X1] :
( sQ666_spl
<=> ( app(skaf72(X1),X0) = nil
| ~ ssList(app(skaf72(X1),X0))
| ~ segmentP(nil,app(skaf72(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ666_spl])],[split_symbol_definition]) ).
fof(f5196,plain,
( ~ sQ339_spl
| ~ sQ11_spl
| sQ666_spl ),
inference(split_clause,[status(thm)],[f5187,f5193,f545,f3011]) ).
fof(f5197,definition,
! [X0] :
( sQ667_spl
<=> segmentP(skaf72(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ667_spl])],[split_symbol_definition]) ).
fof(f5198,plain,
! [X0] :
( ~ sQ667_spl
| segmentP(skaf72(X0),nil) ),
inference(component_clause,[status(thm)],[f5197]) ).
fof(f5200,plain,
( ~ sQ339_spl
| sQ667_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5188,f545,f5197,f3011]) ).
fof(f5202,plain,
! [X0,X1] :
( ~ sQ169_spl
| app(skaf52(X1),nil) = X0
| ~ ssList(skaf52(X1))
| ~ segmentP(X0,app(skaf52(X1),nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1021,f1903]) ).
fof(f5205,definition,
! [X0,X1] :
( sQ668_spl
<=> ( app(skaf52(X1),nil) = X0
| ~ ssList(skaf52(X1))
| ~ segmentP(X0,app(skaf52(X1),nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ668_spl])],[split_symbol_definition]) ).
fof(f5208,plain,
( ~ sQ169_spl
| ~ sQ11_spl
| sQ668_spl ),
inference(split_clause,[status(thm)],[f5202,f5205,f545,f1868]) ).
fof(f5213,plain,
! [X0,X1,X2] :
( ~ sQ170_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(skaf52(X2))
| ~ segmentP(X1,app(skaf52(X2),nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1021,f1905]) ).
fof(f5216,definition,
! [X0,X1,X2] :
( sQ669_spl
<=> ( segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(skaf52(X2))
| ~ segmentP(X1,app(skaf52(X2),nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ669_spl])],[split_symbol_definition]) ).
fof(f5219,plain,
( ~ sQ170_spl
| ~ sQ11_spl
| sQ669_spl ),
inference(split_clause,[status(thm)],[f5213,f5216,f545,f1872]) ).
fof(f5222,plain,
! [X0,X1] :
( ~ sQ667_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf72(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf72(X1)) ),
inference(resolution,[status(thm)],[f5198,f374]) ).
fof(f5223,plain,
! [X0] :
( ~ sQ667_spl
| skaf72(X0) = nil
| ~ ssList(skaf72(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf72(X0)) ),
inference(resolution,[status(thm)],[f5198,f339]) ).
fof(f5224,definition,
! [X0,X1] :
( sQ670_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf72(X1))
| ~ segmentP(X0,skaf72(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ670_spl])],[split_symbol_definition]) ).
fof(f5227,plain,
( ~ sQ667_spl
| ~ sQ11_spl
| sQ670_spl ),
inference(split_clause,[status(thm)],[f5222,f5224,f545,f5197]) ).
fof(f5228,definition,
! [X0] :
( sQ671_spl
<=> ( skaf72(X0) = nil
| ~ ssList(skaf72(X0))
| ~ segmentP(nil,skaf72(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ671_spl])],[split_symbol_definition]) ).
fof(f5231,plain,
( ~ sQ667_spl
| ~ sQ11_spl
| sQ671_spl ),
inference(split_clause,[status(thm)],[f5223,f5228,f545,f5197]) ).
fof(f5360,plain,
! [X0,X1,X2] :
( ~ sQ385_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf73(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf73(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3332,f374]) ).
fof(f5361,plain,
! [X0,X1] :
( ~ sQ385_spl
| app(skaf73(X1),X0) = nil
| ~ ssList(app(skaf73(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf73(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3332,f339]) ).
fof(f5362,plain,
! [X0] :
( ~ sQ385_spl
| segmentP(skaf73(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1035,f3332]) ).
fof(f5363,definition,
! [X0,X1,X2] :
( sQ679_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf73(X2),X0))
| ~ segmentP(X1,app(skaf73(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ679_spl])],[split_symbol_definition]) ).
fof(f5366,plain,
( ~ sQ385_spl
| ~ sQ11_spl
| sQ679_spl ),
inference(split_clause,[status(thm)],[f5360,f5363,f545,f3303]) ).
fof(f5367,definition,
! [X0,X1] :
( sQ680_spl
<=> ( app(skaf73(X1),X0) = nil
| ~ ssList(app(skaf73(X1),X0))
| ~ segmentP(nil,app(skaf73(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ680_spl])],[split_symbol_definition]) ).
fof(f5370,plain,
( ~ sQ385_spl
| ~ sQ11_spl
| sQ680_spl ),
inference(split_clause,[status(thm)],[f5361,f5367,f545,f3303]) ).
fof(f5371,definition,
! [X0] :
( sQ681_spl
<=> segmentP(skaf73(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ681_spl])],[split_symbol_definition]) ).
fof(f5372,plain,
! [X0] :
( ~ sQ681_spl
| segmentP(skaf73(X0),nil) ),
inference(component_clause,[status(thm)],[f5371]) ).
fof(f5374,plain,
( ~ sQ385_spl
| sQ681_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5362,f545,f5371,f3303]) ).
fof(f5375,plain,
! [X0,X1] :
( ~ sQ681_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf73(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf73(X1)) ),
inference(resolution,[status(thm)],[f5372,f374]) ).
fof(f5376,plain,
! [X0] :
( ~ sQ681_spl
| skaf73(X0) = nil
| ~ ssList(skaf73(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf73(X0)) ),
inference(resolution,[status(thm)],[f5372,f339]) ).
fof(f5377,definition,
! [X0,X1] :
( sQ682_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf73(X1))
| ~ segmentP(X0,skaf73(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ682_spl])],[split_symbol_definition]) ).
fof(f5380,plain,
( ~ sQ681_spl
| ~ sQ11_spl
| sQ682_spl ),
inference(split_clause,[status(thm)],[f5375,f5377,f545,f5371]) ).
fof(f5381,definition,
! [X0] :
( sQ683_spl
<=> ( skaf73(X0) = nil
| ~ ssList(skaf73(X0))
| ~ segmentP(nil,skaf73(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ683_spl])],[split_symbol_definition]) ).
fof(f5384,plain,
( ~ sQ681_spl
| ~ sQ11_spl
| sQ683_spl ),
inference(split_clause,[status(thm)],[f5376,f5381,f545,f5371]) ).
fof(f5385,plain,
! [X0,X1,X2] :
( ~ sQ393_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf75(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf75(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3381,f374]) ).
fof(f5386,plain,
! [X0,X1] :
( ~ sQ393_spl
| app(skaf75(X1),X0) = nil
| ~ ssList(app(skaf75(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf75(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3381,f339]) ).
fof(f5387,plain,
! [X0] :
( ~ sQ393_spl
| segmentP(skaf75(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1036,f3381]) ).
fof(f5388,definition,
! [X0,X1,X2] :
( sQ684_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf75(X2),X0))
| ~ segmentP(X1,app(skaf75(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ684_spl])],[split_symbol_definition]) ).
fof(f5391,plain,
( ~ sQ393_spl
| ~ sQ11_spl
| sQ684_spl ),
inference(split_clause,[status(thm)],[f5385,f5388,f545,f3352]) ).
fof(f5392,definition,
! [X0,X1] :
( sQ685_spl
<=> ( app(skaf75(X1),X0) = nil
| ~ ssList(app(skaf75(X1),X0))
| ~ segmentP(nil,app(skaf75(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ685_spl])],[split_symbol_definition]) ).
fof(f5395,plain,
( ~ sQ393_spl
| ~ sQ11_spl
| sQ685_spl ),
inference(split_clause,[status(thm)],[f5386,f5392,f545,f3352]) ).
fof(f5396,definition,
! [X0] :
( sQ686_spl
<=> segmentP(skaf75(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ686_spl])],[split_symbol_definition]) ).
fof(f5397,plain,
! [X0] :
( ~ sQ686_spl
| segmentP(skaf75(X0),nil) ),
inference(component_clause,[status(thm)],[f5396]) ).
fof(f5399,plain,
( ~ sQ393_spl
| sQ686_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5387,f545,f5396,f3352]) ).
fof(f5400,plain,
! [X0,X1] :
( ~ sQ686_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf75(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf75(X1)) ),
inference(resolution,[status(thm)],[f5397,f374]) ).
fof(f5401,plain,
! [X0] :
( ~ sQ686_spl
| skaf75(X0) = nil
| ~ ssList(skaf75(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf75(X0)) ),
inference(resolution,[status(thm)],[f5397,f339]) ).
fof(f5402,definition,
! [X0,X1] :
( sQ687_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf75(X1))
| ~ segmentP(X0,skaf75(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ687_spl])],[split_symbol_definition]) ).
fof(f5405,plain,
( ~ sQ686_spl
| ~ sQ11_spl
| sQ687_spl ),
inference(split_clause,[status(thm)],[f5400,f5402,f545,f5396]) ).
fof(f5406,definition,
! [X0] :
( sQ688_spl
<=> ( skaf75(X0) = nil
| ~ ssList(skaf75(X0))
| ~ segmentP(nil,skaf75(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ688_spl])],[split_symbol_definition]) ).
fof(f5409,plain,
( ~ sQ686_spl
| ~ sQ11_spl
| sQ688_spl ),
inference(split_clause,[status(thm)],[f5401,f5406,f545,f5396]) ).
fof(f5410,plain,
! [X0,X1,X2] :
( ~ sQ401_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf76(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf76(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3430,f374]) ).
fof(f5411,plain,
! [X0,X1] :
( ~ sQ401_spl
| app(skaf76(X1),X0) = nil
| ~ ssList(app(skaf76(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf76(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3430,f339]) ).
fof(f5412,plain,
! [X0] :
( ~ sQ401_spl
| segmentP(skaf76(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1037,f3430]) ).
fof(f5413,definition,
! [X0,X1,X2] :
( sQ689_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf76(X2),X0))
| ~ segmentP(X1,app(skaf76(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ689_spl])],[split_symbol_definition]) ).
fof(f5416,plain,
( ~ sQ401_spl
| ~ sQ11_spl
| sQ689_spl ),
inference(split_clause,[status(thm)],[f5410,f5413,f545,f3401]) ).
fof(f5417,definition,
! [X0,X1] :
( sQ690_spl
<=> ( app(skaf76(X1),X0) = nil
| ~ ssList(app(skaf76(X1),X0))
| ~ segmentP(nil,app(skaf76(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ690_spl])],[split_symbol_definition]) ).
fof(f5420,plain,
( ~ sQ401_spl
| ~ sQ11_spl
| sQ690_spl ),
inference(split_clause,[status(thm)],[f5411,f5417,f545,f3401]) ).
fof(f5421,definition,
! [X0] :
( sQ691_spl
<=> segmentP(skaf76(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ691_spl])],[split_symbol_definition]) ).
fof(f5422,plain,
! [X0] :
( ~ sQ691_spl
| segmentP(skaf76(X0),nil) ),
inference(component_clause,[status(thm)],[f5421]) ).
fof(f5424,plain,
( ~ sQ401_spl
| sQ691_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5412,f545,f5421,f3401]) ).
fof(f5425,plain,
! [X0,X1] :
( ~ sQ691_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf76(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf76(X1)) ),
inference(resolution,[status(thm)],[f5422,f374]) ).
fof(f5426,plain,
! [X0] :
( ~ sQ691_spl
| skaf76(X0) = nil
| ~ ssList(skaf76(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf76(X0)) ),
inference(resolution,[status(thm)],[f5422,f339]) ).
fof(f5427,definition,
! [X0,X1] :
( sQ692_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf76(X1))
| ~ segmentP(X0,skaf76(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ692_spl])],[split_symbol_definition]) ).
fof(f5430,plain,
( ~ sQ691_spl
| ~ sQ11_spl
| sQ692_spl ),
inference(split_clause,[status(thm)],[f5425,f5427,f545,f5421]) ).
fof(f5431,definition,
! [X0] :
( sQ693_spl
<=> ( skaf76(X0) = nil
| ~ ssList(skaf76(X0))
| ~ segmentP(nil,skaf76(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ693_spl])],[split_symbol_definition]) ).
fof(f5434,plain,
( ~ sQ691_spl
| ~ sQ11_spl
| sQ693_spl ),
inference(split_clause,[status(thm)],[f5426,f5431,f545,f5421]) ).
fof(f5436,plain,
! [X0,X1] :
( ~ sQ173_spl
| ~ ssList(nil)
| segmentP(app(skaf52(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1910,f255]) ).
fof(f5438,definition,
! [X0,X1] :
( sQ694_spl
<=> ( segmentP(app(skaf52(X1),X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ694_spl])],[split_symbol_definition]) ).
fof(f5442,plain,
( ~ sQ173_spl
| ~ sQ11_spl
| sQ694_spl ),
inference(split_clause,[status(thm)],[f5436,f5438,f545,f1884]) ).
fof(f5445,plain,
! [X0,X1] :
( ~ sQ178_spl
| app(skaf53(X1),nil) = X0
| ~ ssList(skaf53(X1))
| ~ segmentP(X0,app(skaf53(X1),nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1022,f1966]) ).
fof(f5448,definition,
! [X0,X1] :
( sQ695_spl
<=> ( app(skaf53(X1),nil) = X0
| ~ ssList(skaf53(X1))
| ~ segmentP(X0,app(skaf53(X1),nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ695_spl])],[split_symbol_definition]) ).
fof(f5451,plain,
( ~ sQ178_spl
| ~ sQ11_spl
| sQ695_spl ),
inference(split_clause,[status(thm)],[f5445,f5448,f545,f1931]) ).
fof(f5604,definition,
( sQ699_spl
<=> ssItem(skaf83(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ699_spl])],[split_symbol_definition]) ).
fof(f5606,plain,
( sQ699_spl
| ~ ssItem(skaf83(sk1)) ),
inference(component_clause,[status(thm)],[f5604]) ).
fof(f5607,definition,
( sQ700_spl
<=> ssList(skaf82(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ700_spl])],[split_symbol_definition]) ).
fof(f5609,plain,
( sQ700_spl
| ~ ssList(skaf82(sk1)) ),
inference(component_clause,[status(thm)],[f5607]) ).
fof(f5612,definition,
( sQ701_spl
<=> ssItem(skaf83(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ701_spl])],[split_symbol_definition]) ).
fof(f5614,plain,
( sQ701_spl
| ~ ssItem(skaf83(sk2)) ),
inference(component_clause,[status(thm)],[f5612]) ).
fof(f5615,definition,
( sQ702_spl
<=> ssList(skaf82(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ702_spl])],[split_symbol_definition]) ).
fof(f5617,plain,
( sQ702_spl
| ~ ssList(skaf82(sk2)) ),
inference(component_clause,[status(thm)],[f5615]) ).
fof(f5619,plain,
! [X0,X1,X2] :
( ~ sQ409_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf77(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf77(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3479,f374]) ).
fof(f5620,plain,
! [X0,X1] :
( ~ sQ409_spl
| app(skaf77(X1),X0) = nil
| ~ ssList(app(skaf77(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf77(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3479,f339]) ).
fof(f5621,plain,
! [X0] :
( ~ sQ409_spl
| segmentP(skaf77(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1038,f3479]) ).
fof(f5622,definition,
! [X0,X1,X2] :
( sQ703_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf77(X2),X0))
| ~ segmentP(X1,app(skaf77(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ703_spl])],[split_symbol_definition]) ).
fof(f5625,plain,
( ~ sQ409_spl
| ~ sQ11_spl
| sQ703_spl ),
inference(split_clause,[status(thm)],[f5619,f5622,f545,f3450]) ).
fof(f5626,definition,
! [X0,X1] :
( sQ704_spl
<=> ( app(skaf77(X1),X0) = nil
| ~ ssList(app(skaf77(X1),X0))
| ~ segmentP(nil,app(skaf77(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ704_spl])],[split_symbol_definition]) ).
fof(f5629,plain,
( ~ sQ409_spl
| ~ sQ11_spl
| sQ704_spl ),
inference(split_clause,[status(thm)],[f5620,f5626,f545,f3450]) ).
fof(f5630,definition,
! [X0] :
( sQ705_spl
<=> segmentP(skaf77(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ705_spl])],[split_symbol_definition]) ).
fof(f5631,plain,
! [X0] :
( ~ sQ705_spl
| segmentP(skaf77(X0),nil) ),
inference(component_clause,[status(thm)],[f5630]) ).
fof(f5633,plain,
( ~ sQ409_spl
| sQ705_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5621,f545,f5630,f3450]) ).
fof(f5634,plain,
! [X0,X1] :
( ~ sQ705_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf77(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf77(X1)) ),
inference(resolution,[status(thm)],[f5631,f374]) ).
fof(f5635,plain,
! [X0] :
( ~ sQ705_spl
| skaf77(X0) = nil
| ~ ssList(skaf77(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf77(X0)) ),
inference(resolution,[status(thm)],[f5631,f339]) ).
fof(f5636,definition,
! [X0,X1] :
( sQ706_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf77(X1))
| ~ segmentP(X0,skaf77(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ706_spl])],[split_symbol_definition]) ).
fof(f5639,plain,
( ~ sQ705_spl
| ~ sQ11_spl
| sQ706_spl ),
inference(split_clause,[status(thm)],[f5634,f5636,f545,f5630]) ).
fof(f5640,definition,
! [X0] :
( sQ707_spl
<=> ( skaf77(X0) = nil
| ~ ssList(skaf77(X0))
| ~ segmentP(nil,skaf77(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ707_spl])],[split_symbol_definition]) ).
fof(f5643,plain,
( ~ sQ705_spl
| ~ sQ11_spl
| sQ707_spl ),
inference(split_clause,[status(thm)],[f5635,f5640,f545,f5630]) ).
fof(f5644,plain,
! [X0,X1,X2] :
( ~ sQ417_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf80(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf80(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3528,f374]) ).
fof(f5645,plain,
! [X0,X1] :
( ~ sQ417_spl
| app(skaf80(X1),X0) = nil
| ~ ssList(app(skaf80(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf80(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3528,f339]) ).
fof(f5646,plain,
! [X0] :
( ~ sQ417_spl
| segmentP(skaf80(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1039,f3528]) ).
fof(f5647,definition,
! [X0,X1,X2] :
( sQ708_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf80(X2),X0))
| ~ segmentP(X1,app(skaf80(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ708_spl])],[split_symbol_definition]) ).
fof(f5650,plain,
( ~ sQ417_spl
| ~ sQ11_spl
| sQ708_spl ),
inference(split_clause,[status(thm)],[f5644,f5647,f545,f3499]) ).
fof(f5651,definition,
! [X0,X1] :
( sQ709_spl
<=> ( app(skaf80(X1),X0) = nil
| ~ ssList(app(skaf80(X1),X0))
| ~ segmentP(nil,app(skaf80(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ709_spl])],[split_symbol_definition]) ).
fof(f5654,plain,
( ~ sQ417_spl
| ~ sQ11_spl
| sQ709_spl ),
inference(split_clause,[status(thm)],[f5645,f5651,f545,f3499]) ).
fof(f5655,definition,
! [X0] :
( sQ710_spl
<=> segmentP(skaf80(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ710_spl])],[split_symbol_definition]) ).
fof(f5656,plain,
! [X0] :
( ~ sQ710_spl
| segmentP(skaf80(X0),nil) ),
inference(component_clause,[status(thm)],[f5655]) ).
fof(f5658,plain,
( ~ sQ417_spl
| sQ710_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5646,f545,f5655,f3499]) ).
fof(f5659,plain,
! [X0,X1] :
( ~ sQ710_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf80(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf80(X1)) ),
inference(resolution,[status(thm)],[f5656,f374]) ).
fof(f5660,plain,
! [X0] :
( ~ sQ710_spl
| skaf80(X0) = nil
| ~ ssList(skaf80(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf80(X0)) ),
inference(resolution,[status(thm)],[f5656,f339]) ).
fof(f5661,definition,
! [X0,X1] :
( sQ711_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf80(X1))
| ~ segmentP(X0,skaf80(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ711_spl])],[split_symbol_definition]) ).
fof(f5664,plain,
( ~ sQ710_spl
| ~ sQ11_spl
| sQ711_spl ),
inference(split_clause,[status(thm)],[f5659,f5661,f545,f5655]) ).
fof(f5665,definition,
! [X0] :
( sQ712_spl
<=> ( skaf80(X0) = nil
| ~ ssList(skaf80(X0))
| ~ segmentP(nil,skaf80(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ712_spl])],[split_symbol_definition]) ).
fof(f5668,plain,
( ~ sQ710_spl
| ~ sQ11_spl
| sQ712_spl ),
inference(split_clause,[status(thm)],[f5660,f5665,f545,f5655]) ).
fof(f5669,plain,
! [X0,X1,X2] :
( ~ sQ425_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf81(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf81(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3577,f374]) ).
fof(f5670,plain,
! [X0,X1] :
( ~ sQ425_spl
| app(skaf81(X1),X0) = nil
| ~ ssList(app(skaf81(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf81(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3577,f339]) ).
fof(f5671,plain,
! [X0] :
( ~ sQ425_spl
| segmentP(skaf81(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1040,f3577]) ).
fof(f5672,definition,
! [X0,X1,X2] :
( sQ713_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf81(X2),X0))
| ~ segmentP(X1,app(skaf81(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ713_spl])],[split_symbol_definition]) ).
fof(f5675,plain,
( ~ sQ425_spl
| ~ sQ11_spl
| sQ713_spl ),
inference(split_clause,[status(thm)],[f5669,f5672,f545,f3548]) ).
fof(f5676,definition,
! [X0,X1] :
( sQ714_spl
<=> ( app(skaf81(X1),X0) = nil
| ~ ssList(app(skaf81(X1),X0))
| ~ segmentP(nil,app(skaf81(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ714_spl])],[split_symbol_definition]) ).
fof(f5679,plain,
( ~ sQ425_spl
| ~ sQ11_spl
| sQ714_spl ),
inference(split_clause,[status(thm)],[f5670,f5676,f545,f3548]) ).
fof(f5680,definition,
! [X0] :
( sQ715_spl
<=> segmentP(skaf81(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ715_spl])],[split_symbol_definition]) ).
fof(f5681,plain,
! [X0] :
( ~ sQ715_spl
| segmentP(skaf81(X0),nil) ),
inference(component_clause,[status(thm)],[f5680]) ).
fof(f5683,plain,
( ~ sQ425_spl
| sQ715_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5671,f545,f5680,f3548]) ).
fof(f5685,plain,
! [X0,X1,X2] :
( ~ sQ179_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(skaf53(X2))
| ~ segmentP(X1,app(skaf53(X2),nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1022,f1968]) ).
fof(f5688,definition,
! [X0,X1,X2] :
( sQ716_spl
<=> ( segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(skaf53(X2))
| ~ segmentP(X1,app(skaf53(X2),nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ716_spl])],[split_symbol_definition]) ).
fof(f5691,plain,
( ~ sQ179_spl
| ~ sQ11_spl
| sQ716_spl ),
inference(split_clause,[status(thm)],[f5685,f5688,f545,f1935]) ).
fof(f5695,plain,
! [X0,X1] :
( ~ sQ182_spl
| ~ ssList(nil)
| segmentP(app(skaf53(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1973,f255]) ).
fof(f5697,definition,
! [X0,X1] :
( sQ717_spl
<=> ( segmentP(app(skaf53(X1),X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ717_spl])],[split_symbol_definition]) ).
fof(f5701,plain,
( ~ sQ182_spl
| ~ sQ11_spl
| sQ717_spl ),
inference(split_clause,[status(thm)],[f5695,f5697,f545,f1947]) ).
fof(f5703,plain,
! [X0,X1] :
( ~ sQ715_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf81(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf81(X1)) ),
inference(resolution,[status(thm)],[f5681,f374]) ).
fof(f5704,plain,
! [X0] :
( ~ sQ715_spl
| skaf81(X0) = nil
| ~ ssList(skaf81(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf81(X0)) ),
inference(resolution,[status(thm)],[f5681,f339]) ).
fof(f5705,definition,
! [X0,X1] :
( sQ718_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf81(X1))
| ~ segmentP(X0,skaf81(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ718_spl])],[split_symbol_definition]) ).
fof(f5708,plain,
( ~ sQ715_spl
| ~ sQ11_spl
| sQ718_spl ),
inference(split_clause,[status(thm)],[f5703,f5705,f545,f5680]) ).
fof(f5709,definition,
! [X0] :
( sQ719_spl
<=> ( skaf81(X0) = nil
| ~ ssList(skaf81(X0))
| ~ segmentP(nil,skaf81(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ719_spl])],[split_symbol_definition]) ).
fof(f5712,plain,
( ~ sQ715_spl
| ~ sQ11_spl
| sQ719_spl ),
inference(split_clause,[status(thm)],[f5704,f5709,f545,f5680]) ).
fof(f5780,plain,
! [X0] :
( ~ sQ85_spl
| ~ ssList(nil)
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ segmentP(X0,sk1)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1231,f255]) ).
fof(f5783,plain,
( ~ sQ85_spl
| sQ140_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5780,f545,f1671,f1227]) ).
fof(f5787,plain,
! [X0,X1,X2] :
( ~ sQ97_spl
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ rearsegP(X2,X1)
| ~ rearsegP(nil,X2)
| ~ ssList(X1)
| ~ rearsegP(X1,X0)
| rearsegP(sk2,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1348,f376]) ).
fof(f5791,definition,
! [X0,X1,X2] :
( sQ720_spl
<=> ( ~ ssList(X2)
| ~ ssList(X1)
| ~ rearsegP(X2,X1)
| ~ rearsegP(nil,X2)
| ~ ssList(X1)
| ~ rearsegP(X1,X0)
| rearsegP(sk2,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ720_spl])],[split_symbol_definition]) ).
fof(f5794,plain,
( ~ sQ97_spl
| ~ sQ11_spl
| sQ720_spl ),
inference(split_clause,[status(thm)],[f5787,f5791,f545,f1343]) ).
fof(f5798,plain,
! [X0] :
( ~ sQ142_spl
| ~ ssList(nil)
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ segmentP(X0,sk2)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1684,f255]) ).
fof(f5801,plain,
( ~ sQ142_spl
| sQ156_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5798,f545,f1780,f1680]) ).
fof(f5806,plain,
! [X0,X1,X2] :
( ~ sQ106_spl
| ~ ssList(sk1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ rearsegP(X2,X1)
| ~ rearsegP(sk1,X2)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sk1) ),
inference(resolution,[status(thm)],[f1477,f376]) ).
fof(f5807,plain,
! [X0] :
( ~ sQ106_spl
| ~ ssList(sk1)
| X0 = sk1
| ~ rearsegP(sk1,X0)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ rearsegP(X0,sk1) ),
inference(resolution,[status(thm)],[f1477,f258]) ).
fof(f5811,definition,
! [X0,X1,X2] :
( sQ721_spl
<=> ( ~ ssList(X2)
| ~ ssList(X1)
| ~ rearsegP(X2,X1)
| ~ rearsegP(sk1,X2)
| X0 = X1
| ~ rearsegP(X1,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ721_spl])],[split_symbol_definition]) ).
fof(f5814,plain,
( ~ sQ106_spl
| ~ sQ13_spl
| sQ721_spl ),
inference(split_clause,[status(thm)],[f5806,f5811,f558,f1445]) ).
fof(f5815,plain,
( ~ sQ106_spl
| ~ sQ13_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f5807,f1541,f558,f1445]) ).
fof(f5817,plain,
! [X0,X1,X2] :
( ~ sQ433_spl
| segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf82(X2),X0))
| ~ ssList(nil)
| ~ segmentP(X1,app(skaf82(X2),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3626,f374]) ).
fof(f5818,plain,
! [X0,X1] :
( ~ sQ433_spl
| app(skaf82(X1),X0) = nil
| ~ ssList(app(skaf82(X1),X0))
| ~ ssList(nil)
| ~ segmentP(nil,app(skaf82(X1),X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3626,f339]) ).
fof(f5819,plain,
! [X0] :
( ~ sQ433_spl
| segmentP(skaf82(X0),nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1041,f3626]) ).
fof(f5820,definition,
! [X0,X1,X2] :
( sQ722_spl
<=> ( segmentP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(skaf82(X2),X0))
| ~ segmentP(X1,app(skaf82(X2),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ722_spl])],[split_symbol_definition]) ).
fof(f5823,plain,
( ~ sQ433_spl
| ~ sQ11_spl
| sQ722_spl ),
inference(split_clause,[status(thm)],[f5817,f5820,f545,f3597]) ).
fof(f5824,definition,
! [X0,X1] :
( sQ723_spl
<=> ( app(skaf82(X1),X0) = nil
| ~ ssList(app(skaf82(X1),X0))
| ~ segmentP(nil,app(skaf82(X1),X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ723_spl])],[split_symbol_definition]) ).
fof(f5827,plain,
( ~ sQ433_spl
| ~ sQ11_spl
| sQ723_spl ),
inference(split_clause,[status(thm)],[f5818,f5824,f545,f3597]) ).
fof(f5828,definition,
! [X0] :
( sQ724_spl
<=> segmentP(skaf82(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ724_spl])],[split_symbol_definition]) ).
fof(f5829,plain,
! [X0] :
( ~ sQ724_spl
| segmentP(skaf82(X0),nil) ),
inference(component_clause,[status(thm)],[f5828]) ).
fof(f5831,plain,
( ~ sQ433_spl
| sQ724_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5819,f545,f5828,f3597]) ).
fof(f5832,plain,
! [X0,X1] :
( ~ sQ724_spl
| segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf82(X1))
| ~ ssList(nil)
| ~ segmentP(X0,skaf82(X1)) ),
inference(resolution,[status(thm)],[f5829,f374]) ).
fof(f5833,plain,
! [X0] :
( ~ sQ724_spl
| skaf82(X0) = nil
| ~ ssList(skaf82(X0))
| ~ ssList(nil)
| ~ segmentP(nil,skaf82(X0)) ),
inference(resolution,[status(thm)],[f5829,f339]) ).
fof(f5834,definition,
! [X0,X1] :
( sQ725_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0)
| ~ ssList(skaf82(X1))
| ~ segmentP(X0,skaf82(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ725_spl])],[split_symbol_definition]) ).
fof(f5837,plain,
( ~ sQ724_spl
| ~ sQ11_spl
| sQ725_spl ),
inference(split_clause,[status(thm)],[f5832,f5834,f545,f5828]) ).
fof(f5838,definition,
! [X0] :
( sQ726_spl
<=> ( skaf82(X0) = nil
| ~ ssList(skaf82(X0))
| ~ segmentP(nil,skaf82(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ726_spl])],[split_symbol_definition]) ).
fof(f5841,plain,
( ~ sQ724_spl
| ~ sQ11_spl
| sQ726_spl ),
inference(split_clause,[status(thm)],[f5833,f5838,f545,f5828]) ).
fof(f5843,plain,
! [X0] :
( ~ sQ193_spl
| ~ ssList(nil)
| rearsegP(skaf56(X0),nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2039,f257]) ).
fof(f5844,plain,
! [X0,X1,X2] :
( ~ sQ193_spl
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| rearsegP(skaf56(X1),X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2039,f376]) ).
fof(f5846,definition,
! [X0] :
( sQ727_spl
<=> rearsegP(skaf56(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ727_spl])],[split_symbol_definition]) ).
fof(f5847,plain,
! [X0] :
( ~ sQ727_spl
| rearsegP(skaf56(X0),nil) ),
inference(component_clause,[status(thm)],[f5846]) ).
fof(f5850,plain,
( ~ sQ193_spl
| sQ727_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5843,f545,f5846,f2018]) ).
fof(f5851,definition,
! [X0,X1,X2] :
( sQ728_spl
<=> ( ~ ssList(X2)
| ~ ssList(X0)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| rearsegP(skaf56(X1),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ728_spl])],[split_symbol_definition]) ).
fof(f5854,plain,
( ~ sQ193_spl
| ~ sQ11_spl
| sQ728_spl ),
inference(split_clause,[status(thm)],[f5844,f5851,f545,f2018]) ).
fof(f5857,plain,
! [X0,X1] :
( ~ sQ727_spl
| app(X0,skaf56(X1)) = nil
| ~ rearsegP(nil,app(X0,skaf56(X1)))
| ~ ssList(skaf56(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5847,f2172]) ).
fof(f5859,plain,
! [X0,X1,X2] :
( ~ sQ727_spl
| ~ ssList(skaf56(X2))
| ~ rearsegP(X1,skaf56(X2))
| nil = X1
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f5847,f764]) ).
fof(f5860,plain,
! [X0,X1,X2] :
( ~ sQ727_spl
| ~ ssList(nil)
| ~ rearsegP(nil,X0)
| X0 = skaf56(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf56(X2))
| ~ rearsegP(X1,skaf56(X2))
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f5847,f764]) ).
fof(f5863,plain,
! [X0,X1,X2] :
( ~ sQ727_spl
| ~ ssList(skaf56(X2))
| ~ rearsegP(X1,skaf56(X2))
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f5847,f759]) ).
fof(f5864,plain,
! [X0] :
( ~ sQ727_spl
| ~ ssList(nil)
| ~ rearsegP(nil,skaf56(X0))
| nil = skaf56(X0)
| ~ ssList(nil)
| ~ ssList(skaf56(X0))
| ~ ssList(skaf56(X0))
| ~ rearsegP(nil,skaf56(X0)) ),
inference(resolution,[status(thm)],[f5847,f759]) ).
fof(f5865,plain,
! [X0,X1,X2] :
( ~ sQ727_spl
| ~ ssList(nil)
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,skaf56(X1)) ),
inference(resolution,[status(thm)],[f5847,f759]) ).
fof(f5867,plain,
! [X0,X1,X2] :
( ~ sQ727_spl
| ~ ssList(X2)
| ~ rearsegP(X2,skaf56(X1))
| ~ rearsegP(X0,X2)
| nil = skaf56(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f5847,f759]) ).
fof(f5868,plain,
! [X0,X1] :
( ~ sQ727_spl
| nil = skaf56(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ rearsegP(X0,skaf56(X1))
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f5847,f629]) ).
fof(f5869,plain,
! [X0,X1] :
( ~ sQ727_spl
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ ssList(nil)
| ~ rearsegP(X0,skaf56(X1)) ),
inference(resolution,[status(thm)],[f5847,f629]) ).
fof(f5870,plain,
! [X0] :
( ~ sQ727_spl
| skaf56(X0) = nil
| ~ ssList(skaf56(X0))
| ~ ssList(nil)
| ~ rearsegP(nil,skaf56(X0)) ),
inference(resolution,[status(thm)],[f5847,f340]) ).
fof(f5871,definition,
! [X0,X1] :
( sQ729_spl
<=> ( app(X0,skaf56(X1)) = nil
| ~ rearsegP(nil,app(X0,skaf56(X1)))
| ~ ssList(skaf56(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ729_spl])],[split_symbol_definition]) ).
fof(f5874,plain,
( ~ sQ727_spl
| ~ sQ11_spl
| sQ729_spl ),
inference(split_clause,[status(thm)],[f5857,f5871,f545,f5846]) ).
fof(f5879,definition,
! [X0,X1,X2] :
( sQ731_spl
<=> ( ~ ssList(skaf56(X2))
| ~ rearsegP(X1,skaf56(X2))
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ731_spl])],[split_symbol_definition]) ).
fof(f5882,plain,
( ~ sQ727_spl
| ~ sQ11_spl
| sQ731_spl ),
inference(split_clause,[status(thm)],[f5859,f5879,f545,f5846]) ).
fof(f5883,definition,
! [X0,X1,X2] :
( sQ732_spl
<=> ( ~ rearsegP(nil,X0)
| X0 = skaf56(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf56(X2))
| ~ rearsegP(X1,skaf56(X2))
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ732_spl])],[split_symbol_definition]) ).
fof(f5886,plain,
( ~ sQ727_spl
| ~ sQ11_spl
| sQ732_spl ),
inference(split_clause,[status(thm)],[f5860,f5883,f545,f5846]) ).
fof(f5889,definition,
! [X0,X1,X2] :
( sQ733_spl
<=> ( ~ ssList(skaf56(X2))
| ~ rearsegP(X1,skaf56(X2))
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ733_spl])],[split_symbol_definition]) ).
fof(f5892,plain,
( ~ sQ727_spl
| ~ sQ11_spl
| sQ733_spl ),
inference(split_clause,[status(thm)],[f5863,f5889,f545,f5846]) ).
fof(f5893,definition,
! [X0] :
( sQ734_spl
<=> ( ~ rearsegP(nil,skaf56(X0))
| nil = skaf56(X0)
| ~ ssList(skaf56(X0))
| ~ ssList(skaf56(X0))
| ~ rearsegP(nil,skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ734_spl])],[split_symbol_definition]) ).
fof(f5896,plain,
( ~ sQ727_spl
| ~ sQ11_spl
| sQ734_spl ),
inference(split_clause,[status(thm)],[f5864,f5893,f545,f5846]) ).
fof(f5897,definition,
! [X0,X1,X2] :
( sQ735_spl
<=> ( ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,skaf56(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ735_spl])],[split_symbol_definition]) ).
fof(f5900,plain,
( ~ sQ727_spl
| ~ sQ11_spl
| sQ735_spl ),
inference(split_clause,[status(thm)],[f5865,f5897,f545,f5846]) ).
fof(f5902,definition,
! [X0,X1,X2] :
( sQ736_spl
<=> ( ~ ssList(X2)
| ~ rearsegP(X2,skaf56(X1))
| ~ rearsegP(X0,X2)
| nil = skaf56(X1)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ736_spl])],[split_symbol_definition]) ).
fof(f5905,plain,
( ~ sQ727_spl
| ~ sQ11_spl
| sQ736_spl ),
inference(split_clause,[status(thm)],[f5867,f5902,f545,f5846]) ).
fof(f5906,definition,
! [X0,X1] :
( sQ737_spl
<=> ( nil = skaf56(X1)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ rearsegP(X0,skaf56(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ737_spl])],[split_symbol_definition]) ).
fof(f5909,plain,
( ~ sQ727_spl
| ~ sQ11_spl
| sQ737_spl ),
inference(split_clause,[status(thm)],[f5868,f5906,f545,f5846]) ).
fof(f5910,definition,
! [X0,X1] :
( sQ738_spl
<=> ( X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(skaf56(X1))
| ~ rearsegP(X0,skaf56(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ738_spl])],[split_symbol_definition]) ).
fof(f5913,plain,
( ~ sQ727_spl
| ~ sQ11_spl
| sQ738_spl ),
inference(split_clause,[status(thm)],[f5869,f5910,f545,f5846]) ).
fof(f5914,definition,
! [X0] :
( sQ739_spl
<=> ( skaf56(X0) = nil
| ~ ssList(skaf56(X0))
| ~ rearsegP(nil,skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ739_spl])],[split_symbol_definition]) ).
fof(f5917,plain,
( ~ sQ727_spl
| ~ sQ11_spl
| sQ739_spl ),
inference(split_clause,[status(thm)],[f5870,f5914,f545,f5846]) ).
fof(f5921,plain,
! [X0] :
( ~ sQ202_spl
| ~ ssList(nil)
| rearsegP(skaf57(X0),nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2102,f257]) ).
fof(f5922,plain,
! [X0,X1,X2] :
( ~ sQ202_spl
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| rearsegP(skaf57(X1),X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2102,f376]) ).
fof(f5924,definition,
! [X0] :
( sQ740_spl
<=> rearsegP(skaf57(X0),nil) ),
introduced(definition,[new_symbols(definition,[sQ740_spl])],[split_symbol_definition]) ).
fof(f5925,plain,
! [X0] :
( ~ sQ740_spl
| rearsegP(skaf57(X0),nil) ),
inference(component_clause,[status(thm)],[f5924]) ).
fof(f5928,plain,
( ~ sQ202_spl
| sQ740_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5921,f545,f5924,f2081]) ).
fof(f5929,definition,
! [X0,X1,X2] :
( sQ741_spl
<=> ( ~ ssList(X2)
| ~ ssList(X0)
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| rearsegP(skaf57(X1),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ741_spl])],[split_symbol_definition]) ).
fof(f5932,plain,
( ~ sQ202_spl
| ~ sQ11_spl
| sQ741_spl ),
inference(split_clause,[status(thm)],[f5922,f5929,f545,f2081]) ).
fof(f5935,plain,
! [X0,X1] :
( ~ sQ740_spl
| app(X0,skaf57(X1)) = nil
| ~ rearsegP(nil,app(X0,skaf57(X1)))
| ~ ssList(skaf57(X1))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5925,f2172]) ).
fof(f5937,plain,
! [X0,X1,X2] :
( ~ sQ740_spl
| ~ ssList(skaf57(X2))
| ~ rearsegP(X1,skaf57(X2))
| nil = X1
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f5925,f764]) ).
fof(f5938,plain,
! [X0,X1,X2] :
( ~ sQ740_spl
| ~ ssList(nil)
| ~ rearsegP(nil,X0)
| X0 = skaf57(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf57(X2))
| ~ rearsegP(X1,skaf57(X2))
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f5925,f764]) ).
fof(f5941,plain,
! [X0,X1,X2] :
( ~ sQ740_spl
| ~ ssList(skaf57(X2))
| ~ rearsegP(X1,skaf57(X2))
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ rearsegP(X0,X1) ),
inference(resolution,[status(thm)],[f5925,f759]) ).
fof(f5942,plain,
! [X0] :
( ~ sQ740_spl
| ~ ssList(nil)
| ~ rearsegP(nil,skaf57(X0))
| nil = skaf57(X0)
| ~ ssList(nil)
| ~ ssList(skaf57(X0))
| ~ ssList(skaf57(X0))
| ~ rearsegP(nil,skaf57(X0)) ),
inference(resolution,[status(thm)],[f5925,f759]) ).
fof(f5943,plain,
! [X0,X1,X2] :
( ~ sQ740_spl
| ~ ssList(nil)
| ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,skaf57(X1)) ),
inference(resolution,[status(thm)],[f5925,f759]) ).
fof(f5945,plain,
! [X0,X1,X2] :
( ~ sQ740_spl
| ~ ssList(X2)
| ~ rearsegP(X2,skaf57(X1))
| ~ rearsegP(X0,X2)
| nil = skaf57(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f5925,f759]) ).
fof(f5946,plain,
! [X0,X1] :
( ~ sQ740_spl
| nil = skaf57(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ rearsegP(X0,skaf57(X1))
| ~ rearsegP(nil,X0) ),
inference(resolution,[status(thm)],[f5925,f629]) ).
fof(f5947,plain,
! [X0,X1] :
( ~ sQ740_spl
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ ssList(nil)
| ~ rearsegP(X0,skaf57(X1)) ),
inference(resolution,[status(thm)],[f5925,f629]) ).
fof(f5948,plain,
! [X0] :
( ~ sQ740_spl
| skaf57(X0) = nil
| ~ ssList(skaf57(X0))
| ~ ssList(nil)
| ~ rearsegP(nil,skaf57(X0)) ),
inference(resolution,[status(thm)],[f5925,f340]) ).
fof(f5949,definition,
! [X0,X1] :
( sQ742_spl
<=> ( app(X0,skaf57(X1)) = nil
| ~ rearsegP(nil,app(X0,skaf57(X1)))
| ~ ssList(skaf57(X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ742_spl])],[split_symbol_definition]) ).
fof(f5952,plain,
( ~ sQ740_spl
| ~ sQ11_spl
| sQ742_spl ),
inference(split_clause,[status(thm)],[f5935,f5949,f545,f5924]) ).
fof(f5957,definition,
! [X0,X1,X2] :
( sQ744_spl
<=> ( ~ ssList(skaf57(X2))
| ~ rearsegP(X1,skaf57(X2))
| nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ744_spl])],[split_symbol_definition]) ).
fof(f5960,plain,
( ~ sQ740_spl
| ~ sQ11_spl
| sQ744_spl ),
inference(split_clause,[status(thm)],[f5937,f5957,f545,f5924]) ).
fof(f5961,definition,
! [X0,X1,X2] :
( sQ745_spl
<=> ( ~ rearsegP(nil,X0)
| X0 = skaf57(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(skaf57(X2))
| ~ rearsegP(X1,skaf57(X2))
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ745_spl])],[split_symbol_definition]) ).
fof(f5964,plain,
( ~ sQ740_spl
| ~ sQ11_spl
| sQ745_spl ),
inference(split_clause,[status(thm)],[f5938,f5961,f545,f5924]) ).
fof(f5967,definition,
! [X0,X1,X2] :
( sQ746_spl
<=> ( ~ ssList(skaf57(X2))
| ~ rearsegP(X1,skaf57(X2))
| X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ746_spl])],[split_symbol_definition]) ).
fof(f5970,plain,
( ~ sQ740_spl
| ~ sQ11_spl
| sQ746_spl ),
inference(split_clause,[status(thm)],[f5941,f5967,f545,f5924]) ).
fof(f5971,definition,
! [X0] :
( sQ747_spl
<=> ( ~ rearsegP(nil,skaf57(X0))
| nil = skaf57(X0)
| ~ ssList(skaf57(X0))
| ~ ssList(skaf57(X0))
| ~ rearsegP(nil,skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ747_spl])],[split_symbol_definition]) ).
fof(f5974,plain,
( ~ sQ740_spl
| ~ sQ11_spl
| sQ747_spl ),
inference(split_clause,[status(thm)],[f5942,f5971,f545,f5924]) ).
fof(f5975,definition,
! [X0,X1,X2] :
( sQ748_spl
<=> ( ~ rearsegP(nil,X2)
| X0 = X2
| ~ rearsegP(X2,X0)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ ssList(X2)
| ~ rearsegP(X0,skaf57(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ748_spl])],[split_symbol_definition]) ).
fof(f5978,plain,
( ~ sQ740_spl
| ~ sQ11_spl
| sQ748_spl ),
inference(split_clause,[status(thm)],[f5943,f5975,f545,f5924]) ).
fof(f5980,definition,
! [X0,X1,X2] :
( sQ749_spl
<=> ( ~ ssList(X2)
| ~ rearsegP(X2,skaf57(X1))
| ~ rearsegP(X0,X2)
| nil = skaf57(X1)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ749_spl])],[split_symbol_definition]) ).
fof(f5983,plain,
( ~ sQ740_spl
| ~ sQ11_spl
| sQ749_spl ),
inference(split_clause,[status(thm)],[f5945,f5980,f545,f5924]) ).
fof(f5984,definition,
! [X0,X1] :
( sQ750_spl
<=> ( nil = skaf57(X1)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ rearsegP(X0,skaf57(X1))
| ~ rearsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ750_spl])],[split_symbol_definition]) ).
fof(f5987,plain,
( ~ sQ740_spl
| ~ sQ11_spl
| sQ750_spl ),
inference(split_clause,[status(thm)],[f5946,f5984,f545,f5924]) ).
fof(f5988,definition,
! [X0,X1] :
( sQ751_spl
<=> ( X0 = nil
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(skaf57(X1))
| ~ rearsegP(X0,skaf57(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ751_spl])],[split_symbol_definition]) ).
fof(f5991,plain,
( ~ sQ740_spl
| ~ sQ11_spl
| sQ751_spl ),
inference(split_clause,[status(thm)],[f5947,f5988,f545,f5924]) ).
fof(f5992,definition,
! [X0] :
( sQ752_spl
<=> ( skaf57(X0) = nil
| ~ ssList(skaf57(X0))
| ~ rearsegP(nil,skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ752_spl])],[split_symbol_definition]) ).
fof(f5995,plain,
( ~ sQ740_spl
| ~ sQ11_spl
| sQ752_spl ),
inference(split_clause,[status(thm)],[f5948,f5992,f545,f5924]) ).
fof(f5999,plain,
! [X0,X1] :
( ~ sQ187_spl
| app(skaf56(X1),nil) = X0
| ~ ssList(skaf56(X1))
| ~ segmentP(X0,app(skaf56(X1),nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1023,f2029]) ).
fof(f6002,definition,
! [X0,X1] :
( sQ753_spl
<=> ( app(skaf56(X1),nil) = X0
| ~ ssList(skaf56(X1))
| ~ segmentP(X0,app(skaf56(X1),nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ753_spl])],[split_symbol_definition]) ).
fof(f6005,plain,
( ~ sQ187_spl
| ~ sQ11_spl
| sQ753_spl ),
inference(split_clause,[status(thm)],[f5999,f6002,f545,f1994]) ).
fof(f6010,plain,
! [X0,X1,X2] :
( ~ sQ188_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(skaf56(X2))
| ~ segmentP(X1,app(skaf56(X2),nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1023,f2031]) ).
fof(f6013,definition,
! [X0,X1,X2] :
( sQ754_spl
<=> ( segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(skaf56(X2))
| ~ segmentP(X1,app(skaf56(X2),nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ754_spl])],[split_symbol_definition]) ).
fof(f6016,plain,
( ~ sQ188_spl
| ~ sQ11_spl
| sQ754_spl ),
inference(split_clause,[status(thm)],[f6010,f6013,f545,f1998]) ).
fof(f6279,plain,
! [X0,X1] :
( ~ sQ191_spl
| ~ ssList(nil)
| segmentP(app(skaf56(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2036,f255]) ).
fof(f6281,definition,
! [X0,X1] :
( sQ759_spl
<=> ( segmentP(app(skaf56(X1),X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ759_spl])],[split_symbol_definition]) ).
fof(f6285,plain,
( ~ sQ191_spl
| ~ sQ11_spl
| sQ759_spl ),
inference(split_clause,[status(thm)],[f6279,f6281,f545,f2010]) ).
fof(f6288,plain,
! [X0,X1] :
( ~ sQ196_spl
| app(skaf57(X1),nil) = X0
| ~ ssList(skaf57(X1))
| ~ segmentP(X0,app(skaf57(X1),nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1024,f2092]) ).
fof(f6291,definition,
! [X0,X1] :
( sQ760_spl
<=> ( app(skaf57(X1),nil) = X0
| ~ ssList(skaf57(X1))
| ~ segmentP(X0,app(skaf57(X1),nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ760_spl])],[split_symbol_definition]) ).
fof(f6294,plain,
( ~ sQ196_spl
| ~ sQ11_spl
| sQ760_spl ),
inference(split_clause,[status(thm)],[f6288,f6291,f545,f2057]) ).
fof(f6537,plain,
! [X0,X1,X2] :
( ~ sQ197_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(skaf57(X2))
| ~ segmentP(X1,app(skaf57(X2),nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1024,f2094]) ).
fof(f6540,definition,
! [X0,X1,X2] :
( sQ764_spl
<=> ( segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(skaf57(X2))
| ~ segmentP(X1,app(skaf57(X2),nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ764_spl])],[split_symbol_definition]) ).
fof(f6543,plain,
( ~ sQ197_spl
| ~ sQ11_spl
| sQ764_spl ),
inference(split_clause,[status(thm)],[f6537,f6540,f545,f2061]) ).
fof(f6547,plain,
! [X0,X1] :
( ~ sQ200_spl
| ~ ssList(nil)
| segmentP(app(skaf57(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2099,f255]) ).
fof(f6549,definition,
! [X0,X1] :
( sQ765_spl
<=> ( segmentP(app(skaf57(X1),X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ765_spl])],[split_symbol_definition]) ).
fof(f6553,plain,
( ~ sQ200_spl
| ~ sQ11_spl
| sQ765_spl ),
inference(split_clause,[status(thm)],[f6547,f6549,f545,f2073]) ).
fof(f6612,plain,
! [X0,X1] :
( ~ sQ205_spl
| app(skaf58(X1),nil) = X0
| ~ ssList(skaf58(X1))
| ~ segmentP(X0,app(skaf58(X1),nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1025,f2155]) ).
fof(f6615,definition,
! [X0,X1] :
( sQ771_spl
<=> ( app(skaf58(X1),nil) = X0
| ~ ssList(skaf58(X1))
| ~ segmentP(X0,app(skaf58(X1),nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ771_spl])],[split_symbol_definition]) ).
fof(f6618,plain,
( ~ sQ205_spl
| ~ sQ11_spl
| sQ771_spl ),
inference(split_clause,[status(thm)],[f6612,f6615,f545,f2120]) ).
fof(f6625,plain,
! [X0] :
( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(nil,X0) ),
inference(resolution,[status(thm)],[f341,f259]) ).
fof(f6627,definition,
! [X0] :
( sQ772_spl
<=> ( ~ ssList(X0)
| X0 = nil
| ~ ssList(X0)
| ~ frontsegP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ772_spl])],[split_symbol_definition]) ).
fof(f6630,plain,
( ~ sQ11_spl
| sQ772_spl ),
inference(split_clause,[status(thm)],[f6625,f6627,f545]) ).
fof(f6651,plain,
! [X0,X1,X2] :
( ~ sQ206_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(skaf58(X2))
| ~ segmentP(X1,app(skaf58(X2),nil))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f1025,f2157]) ).
fof(f6654,definition,
! [X0,X1,X2] :
( sQ773_spl
<=> ( segmentP(X1,X0)
| ~ ssList(X1)
| ~ ssList(skaf58(X2))
| ~ segmentP(X1,app(skaf58(X2),nil))
| ~ ssList(X0)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ773_spl])],[split_symbol_definition]) ).
fof(f6657,plain,
( ~ sQ206_spl
| ~ sQ11_spl
| sQ773_spl ),
inference(split_clause,[status(thm)],[f6651,f6654,f545,f2124]) ).
fof(f6661,plain,
! [X0,X1] :
( ~ sQ209_spl
| ~ ssList(nil)
| segmentP(app(skaf58(X1),X0),nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2162,f255]) ).
fof(f6663,definition,
! [X0,X1] :
( sQ774_spl
<=> ( segmentP(app(skaf58(X1),X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ774_spl])],[split_symbol_definition]) ).
fof(f6667,plain,
( ~ sQ209_spl
| ~ sQ11_spl
| sQ774_spl ),
inference(split_clause,[status(thm)],[f6661,f6663,f545,f2136]) ).
fof(f6740,plain,
! [X0] :
( ~ sQ740_spl
| app(skaf46(skaf57(X0),nil),nil) = skaf57(X0)
| ~ ssList(skaf57(X0))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f343,f5925]) ).
fof(f6741,plain,
! [X0] :
( ~ sQ727_spl
| app(skaf46(skaf56(X0),nil),nil) = skaf56(X0)
| ~ ssList(skaf56(X0))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f343,f5847]) ).
fof(f6742,plain,
! [X0] :
( ~ sQ259_spl
| app(skaf46(skaf53(X0),nil),nil) = skaf53(X0)
| ~ ssList(skaf53(X0))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f343,f2513]) ).
fof(f6743,plain,
! [X0] :
( ~ sQ247_spl
| app(skaf46(skaf52(X0),nil),nil) = skaf52(X0)
| ~ ssList(skaf52(X0))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f343,f2441]) ).
fof(f6744,plain,
! [X0] :
( ~ sQ235_spl
| app(skaf46(skaf51(X0),nil),nil) = skaf51(X0)
| ~ ssList(skaf51(X0))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f343,f2369]) ).
fof(f6745,plain,
( ~ sQ90_spl
| app(skaf46(nil,nil),nil) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f343,f1266]) ).
fof(f6746,plain,
( ~ sQ112_spl
| app(skaf46(sk1,sk1),sk1) = sk1
| ~ ssList(sk1)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f343,f1484]) ).
fof(f6747,plain,
( ~ sQ64_spl
| app(skaf46(sk1,nil),nil) = sk1
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f343,f1077]) ).
fof(f6748,plain,
( ~ sQ127_spl
| app(skaf46(sk2,sk2),sk2) = sk2
| ~ ssList(sk2)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f343,f1593]) ).
fof(f6749,plain,
( ~ sQ78_spl
| app(skaf46(sk2,nil),nil) = sk2
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f343,f1170]) ).
fof(f6750,plain,
( ~ sQ9_spl
| app(skaf46(sk2,sk1),sk1) = sk2
| ~ ssList(sk2)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f343,f571]) ).
fof(f6752,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ rearsegP(X2,X0)
| app(skaf46(app(X1,X2),X0),X0) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f343,f350]) ).
fof(f6753,plain,
! [X0] :
( ~ ssList(X0)
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f343,f257]) ).
fof(f6754,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ rearsegP(X2,X0)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X0),X0) = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f343,f376]) ).
fof(f6756,definition,
! [X0] :
( sQ775_spl
<=> ( app(skaf46(skaf57(X0),nil),nil) = skaf57(X0)
| ~ ssList(skaf57(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ775_spl])],[split_symbol_definition]) ).
fof(f6759,plain,
( ~ sQ740_spl
| sQ775_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6740,f545,f6756,f5924]) ).
fof(f6760,definition,
! [X0] :
( sQ776_spl
<=> ( app(skaf46(skaf56(X0),nil),nil) = skaf56(X0)
| ~ ssList(skaf56(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ776_spl])],[split_symbol_definition]) ).
fof(f6763,plain,
( ~ sQ727_spl
| sQ776_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6741,f545,f6760,f5846]) ).
fof(f6764,definition,
! [X0] :
( sQ777_spl
<=> ( app(skaf46(skaf53(X0),nil),nil) = skaf53(X0)
| ~ ssList(skaf53(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ777_spl])],[split_symbol_definition]) ).
fof(f6767,plain,
( ~ sQ259_spl
| sQ777_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6742,f545,f6764,f2512]) ).
fof(f6768,definition,
! [X0] :
( sQ778_spl
<=> ( app(skaf46(skaf52(X0),nil),nil) = skaf52(X0)
| ~ ssList(skaf52(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ778_spl])],[split_symbol_definition]) ).
fof(f6771,plain,
( ~ sQ247_spl
| sQ778_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6743,f545,f6768,f2440]) ).
fof(f6772,definition,
! [X0] :
( sQ779_spl
<=> ( app(skaf46(skaf51(X0),nil),nil) = skaf51(X0)
| ~ ssList(skaf51(X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ779_spl])],[split_symbol_definition]) ).
fof(f6775,plain,
( ~ sQ235_spl
| sQ779_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6744,f545,f6772,f2368]) ).
fof(f6776,definition,
( sQ780_spl
<=> app(skaf46(nil,nil),nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ780_spl])],[split_symbol_definition]) ).
fof(f6777,plain,
( ~ sQ780_spl
| app(skaf46(nil,nil),nil) = nil ),
inference(component_clause,[status(thm)],[f6776]) ).
fof(f6779,plain,
( ~ sQ90_spl
| sQ780_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6745,f545,f6776,f1254]) ).
fof(f6780,definition,
( sQ781_spl
<=> app(skaf46(sk1,sk1),sk1) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ781_spl])],[split_symbol_definition]) ).
fof(f6781,plain,
( ~ sQ781_spl
| app(skaf46(sk1,sk1),sk1) = sk1 ),
inference(component_clause,[status(thm)],[f6780]) ).
fof(f6783,plain,
( ~ sQ112_spl
| sQ781_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6746,f558,f6780,f1469]) ).
fof(f6784,definition,
( sQ782_spl
<=> app(skaf46(sk1,nil),nil) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ782_spl])],[split_symbol_definition]) ).
fof(f6785,plain,
( ~ sQ782_spl
| app(skaf46(sk1,nil),nil) = sk1 ),
inference(component_clause,[status(thm)],[f6784]) ).
fof(f6787,plain,
( ~ sQ64_spl
| sQ782_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6747,f545,f558,f6784,f1065]) ).
fof(f6788,definition,
( sQ783_spl
<=> app(skaf46(sk2,sk2),sk2) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ783_spl])],[split_symbol_definition]) ).
fof(f6789,plain,
( ~ sQ783_spl
| app(skaf46(sk2,sk2),sk2) = sk2 ),
inference(component_clause,[status(thm)],[f6788]) ).
fof(f6791,plain,
( ~ sQ127_spl
| sQ783_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f6748,f587,f6788,f1578]) ).
fof(f6792,definition,
( sQ784_spl
<=> app(skaf46(sk2,nil),nil) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ784_spl])],[split_symbol_definition]) ).
fof(f6793,plain,
( ~ sQ784_spl
| app(skaf46(sk2,nil),nil) = sk2 ),
inference(component_clause,[status(thm)],[f6792]) ).
fof(f6795,plain,
( ~ sQ78_spl
| sQ784_spl
| ~ sQ16_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6749,f545,f587,f6792,f1158]) ).
fof(f6796,definition,
( sQ785_spl
<=> app(skaf46(sk2,sk1),sk1) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ785_spl])],[split_symbol_definition]) ).
fof(f6797,plain,
( ~ sQ785_spl
| app(skaf46(sk2,sk1),sk1) = sk2 ),
inference(component_clause,[status(thm)],[f6796]) ).
fof(f6799,plain,
( ~ sQ9_spl
| sQ785_spl
| ~ sQ16_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6750,f558,f587,f6796,f477]) ).
fof(f6802,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ rearsegP(X2,X0)
| app(skaf46(app(X1,X2),X0),X0) = app(X1,X2)
| ~ ssList(app(X1,X2))
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f6752]) ).
fof(f6803,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X1)
| ~ rearsegP(X2,X0)
| app(skaf46(app(X1,X2),X0),X0) = app(X1,X2)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f6802,f285]) ).
fof(f6804,definition,
! [X0] :
( sQ786_spl
<=> ( ~ ssList(X0)
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ786_spl])],[split_symbol_definition]) ).
fof(f6807,plain,
( sQ786_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6753,f545,f6804]) ).
fof(f6808,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ rearsegP(X2,X0)
| ~ rearsegP(X1,X2)
| app(skaf46(X1,X0),X0) = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f6754]) ).
fof(f6816,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f344,f259]) ).
fof(f6818,definition,
! [X0] :
( sQ787_spl
<=> ( ~ ssList(X0)
| app(nil,skaf45(X0,nil)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ787_spl])],[split_symbol_definition]) ).
fof(f6821,plain,
( sQ787_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6816,f545,f6818]) ).
fof(f6826,plain,
! [X0] :
( ~ sQ785_spl
| segmentP(app(sk2,X0),sk1)
| ~ ssList(sk1)
| ~ ssList(skaf46(sk2,sk1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f6797,f2205]) ).
fof(f6833,definition,
( sQ788_spl
<=> ssList(skaf46(sk2,sk1)) ),
introduced(definition,[new_symbols(definition,[sQ788_spl])],[split_symbol_definition]) ).
fof(f6835,plain,
( sQ788_spl
| ~ ssList(skaf46(sk2,sk1)) ),
inference(component_clause,[status(thm)],[f6833]) ).
fof(f6841,definition,
! [X0] :
( sQ790_spl
<=> ( segmentP(app(sk2,X0),sk1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ790_spl])],[split_symbol_definition]) ).
fof(f6842,plain,
! [X0] :
( ~ sQ790_spl
| segmentP(app(sk2,X0),sk1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f6841]) ).
fof(f6844,plain,
( ~ sQ785_spl
| ~ sQ13_spl
| ~ sQ788_spl
| sQ790_spl ),
inference(split_clause,[status(thm)],[f6826,f6841,f6833,f558,f6796]) ).
fof(f6866,plain,
( sQ788_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6835,f249]) ).
fof(f6867,plain,
sQ788_spl,
inference(contradiction_clause,[status(thm)],[f6866]) ).
fof(f6905,plain,
! [X0,X1] :
( ~ sQ740_spl
| ~ ssList(skaf57(X1))
| ~ ssList(X0)
| app(skaf46(app(X0,skaf57(X1)),nil),nil) = app(X0,skaf57(X1))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6803,f5925]) ).
fof(f6906,plain,
! [X0,X1] :
( ~ sQ727_spl
| ~ ssList(skaf56(X1))
| ~ ssList(X0)
| app(skaf46(app(X0,skaf56(X1)),nil),nil) = app(X0,skaf56(X1))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6803,f5847]) ).
fof(f6907,plain,
! [X0,X1] :
( ~ sQ259_spl
| ~ ssList(skaf53(X1))
| ~ ssList(X0)
| app(skaf46(app(X0,skaf53(X1)),nil),nil) = app(X0,skaf53(X1))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6803,f2513]) ).
fof(f6908,plain,
! [X0,X1] :
( ~ sQ247_spl
| ~ ssList(skaf52(X1))
| ~ ssList(X0)
| app(skaf46(app(X0,skaf52(X1)),nil),nil) = app(X0,skaf52(X1))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6803,f2441]) ).
fof(f6909,plain,
! [X0,X1] :
( ~ sQ235_spl
| ~ ssList(skaf51(X1))
| ~ ssList(X0)
| app(skaf46(app(X0,skaf51(X1)),nil),nil) = app(X0,skaf51(X1))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6803,f2369]) ).
fof(f6910,plain,
! [X0] :
( ~ sQ90_spl
| ~ ssList(nil)
| ~ ssList(X0)
| app(skaf46(app(X0,nil),nil),nil) = app(X0,nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6803,f1266]) ).
fof(f6911,plain,
! [X0] :
( ~ sQ112_spl
| ~ ssList(sk1)
| ~ ssList(X0)
| app(skaf46(app(X0,sk1),sk1),sk1) = app(X0,sk1)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f6803,f1484]) ).
fof(f6912,plain,
! [X0] :
( ~ sQ64_spl
| ~ ssList(sk1)
| ~ ssList(X0)
| app(skaf46(app(X0,sk1),nil),nil) = app(X0,sk1)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6803,f1077]) ).
fof(f6913,plain,
! [X0] :
( ~ sQ127_spl
| ~ ssList(sk2)
| ~ ssList(X0)
| app(skaf46(app(X0,sk2),sk2),sk2) = app(X0,sk2)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f6803,f1593]) ).
fof(f6914,plain,
! [X0] :
( ~ sQ78_spl
| ~ ssList(sk2)
| ~ ssList(X0)
| app(skaf46(app(X0,sk2),nil),nil) = app(X0,sk2)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6803,f1170]) ).
fof(f6918,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ ssList(X0)
| app(skaf46(app(X0,X1),nil),nil) = app(X0,X1)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6803,f257]) ).
fof(f6921,definition,
! [X0,X1] :
( sQ796_spl
<=> ( ~ ssList(skaf57(X1))
| ~ ssList(X0)
| app(skaf46(app(X0,skaf57(X1)),nil),nil) = app(X0,skaf57(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ796_spl])],[split_symbol_definition]) ).
fof(f6924,plain,
( ~ sQ740_spl
| sQ796_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6905,f545,f6921,f5924]) ).
fof(f6925,definition,
! [X0,X1] :
( sQ797_spl
<=> ( ~ ssList(skaf56(X1))
| ~ ssList(X0)
| app(skaf46(app(X0,skaf56(X1)),nil),nil) = app(X0,skaf56(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ797_spl])],[split_symbol_definition]) ).
fof(f6928,plain,
( ~ sQ727_spl
| sQ797_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6906,f545,f6925,f5846]) ).
fof(f6929,definition,
! [X0,X1] :
( sQ798_spl
<=> ( ~ ssList(skaf53(X1))
| ~ ssList(X0)
| app(skaf46(app(X0,skaf53(X1)),nil),nil) = app(X0,skaf53(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ798_spl])],[split_symbol_definition]) ).
fof(f6932,plain,
( ~ sQ259_spl
| sQ798_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6907,f545,f6929,f2512]) ).
fof(f6933,definition,
! [X0,X1] :
( sQ799_spl
<=> ( ~ ssList(skaf52(X1))
| ~ ssList(X0)
| app(skaf46(app(X0,skaf52(X1)),nil),nil) = app(X0,skaf52(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ799_spl])],[split_symbol_definition]) ).
fof(f6936,plain,
( ~ sQ247_spl
| sQ799_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6908,f545,f6933,f2440]) ).
fof(f6937,definition,
! [X0,X1] :
( sQ800_spl
<=> ( ~ ssList(skaf51(X1))
| ~ ssList(X0)
| app(skaf46(app(X0,skaf51(X1)),nil),nil) = app(X0,skaf51(X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ800_spl])],[split_symbol_definition]) ).
fof(f6940,plain,
( ~ sQ235_spl
| sQ800_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6909,f545,f6937,f2368]) ).
fof(f6941,definition,
! [X0] :
( sQ801_spl
<=> ( ~ ssList(X0)
| app(skaf46(app(X0,nil),nil),nil) = app(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ801_spl])],[split_symbol_definition]) ).
fof(f6944,plain,
( ~ sQ90_spl
| sQ801_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6910,f545,f6941,f1254]) ).
fof(f6945,definition,
! [X0] :
( sQ802_spl
<=> ( ~ ssList(X0)
| app(skaf46(app(X0,sk1),sk1),sk1) = app(X0,sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ802_spl])],[split_symbol_definition]) ).
fof(f6948,plain,
( ~ sQ112_spl
| sQ802_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f6911,f558,f6945,f1469]) ).
fof(f6949,definition,
! [X0] :
( sQ803_spl
<=> ( ~ ssList(X0)
| app(skaf46(app(X0,sk1),nil),nil) = app(X0,sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ803_spl])],[split_symbol_definition]) ).
fof(f6952,plain,
( ~ sQ64_spl
| ~ sQ13_spl
| sQ803_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6912,f545,f6949,f558,f1065]) ).
fof(f6953,definition,
! [X0] :
( sQ804_spl
<=> ( ~ ssList(X0)
| app(skaf46(app(X0,sk2),sk2),sk2) = app(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ804_spl])],[split_symbol_definition]) ).
fof(f6956,plain,
( ~ sQ127_spl
| sQ804_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f6913,f587,f6953,f1578]) ).
fof(f6957,definition,
! [X0] :
( sQ805_spl
<=> ( ~ ssList(X0)
| app(skaf46(app(X0,sk2),nil),nil) = app(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ805_spl])],[split_symbol_definition]) ).
fof(f6960,plain,
( ~ sQ78_spl
| ~ sQ16_spl
| sQ805_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6914,f545,f6957,f587,f1158]) ).
fof(f6969,definition,
! [X0,X1] :
( sQ807_spl
<=> ( ~ ssList(X1)
| ~ ssList(X1)
| ~ ssList(X0)
| app(skaf46(app(X0,X1),nil),nil) = app(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ807_spl])],[split_symbol_definition]) ).
fof(f6972,plain,
( sQ807_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6918,f545,f6969]) ).
fof(f7083,plain,
( sQ699_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5606,f211]) ).
fof(f7084,plain,
sQ699_spl,
inference(contradiction_clause,[status(thm)],[f7083]) ).
fof(f7085,plain,
( sQ700_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5609,f212]) ).
fof(f7086,plain,
sQ700_spl,
inference(contradiction_clause,[status(thm)],[f7085]) ).
fof(f7087,plain,
( sQ701_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5614,f211]) ).
fof(f7088,plain,
sQ701_spl,
inference(contradiction_clause,[status(thm)],[f7087]) ).
fof(f7089,plain,
( sQ702_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5617,f212]) ).
fof(f7090,plain,
sQ702_spl,
inference(contradiction_clause,[status(thm)],[f7089]) ).
fof(f7132,plain,
! [X0,X1] :
( ~ sQ740_spl
| ~ ssList(skaf57(X1))
| ~ rearsegP(X0,skaf57(X1))
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6808,f5925]) ).
fof(f7133,plain,
! [X0,X1] :
( ~ sQ727_spl
| ~ ssList(skaf56(X1))
| ~ rearsegP(X0,skaf56(X1))
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6808,f5847]) ).
fof(f7134,plain,
! [X0,X1] :
( ~ sQ259_spl
| ~ ssList(skaf53(X1))
| ~ rearsegP(X0,skaf53(X1))
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6808,f2513]) ).
fof(f7135,plain,
! [X0,X1] :
( ~ sQ247_spl
| ~ ssList(skaf52(X1))
| ~ rearsegP(X0,skaf52(X1))
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6808,f2441]) ).
fof(f7136,plain,
! [X0,X1] :
( ~ sQ235_spl
| ~ ssList(skaf51(X1))
| ~ rearsegP(X0,skaf51(X1))
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6808,f2369]) ).
fof(f7137,plain,
! [X0] :
( ~ sQ90_spl
| ~ ssList(nil)
| ~ rearsegP(X0,nil)
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6808,f1266]) ).
fof(f7138,plain,
! [X0] :
( ~ sQ112_spl
| ~ ssList(sk1)
| ~ rearsegP(X0,sk1)
| app(skaf46(X0,sk1),sk1) = X0
| ~ ssList(X0)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f6808,f1484]) ).
fof(f7139,plain,
! [X0] :
( ~ sQ64_spl
| ~ ssList(sk1)
| ~ rearsegP(X0,sk1)
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6808,f1077]) ).
fof(f7140,plain,
! [X0] :
( ~ sQ127_spl
| ~ ssList(sk2)
| ~ rearsegP(X0,sk2)
| app(skaf46(X0,sk2),sk2) = X0
| ~ ssList(X0)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f6808,f1593]) ).
fof(f7141,plain,
! [X0] :
( ~ sQ78_spl
| ~ ssList(sk2)
| ~ rearsegP(X0,sk2)
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6808,f1170]) ).
fof(f7145,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6808,f257]) ).
fof(f7148,definition,
! [X0,X1] :
( sQ825_spl
<=> ( ~ ssList(skaf57(X1))
| ~ rearsegP(X0,skaf57(X1))
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ825_spl])],[split_symbol_definition]) ).
fof(f7151,plain,
( ~ sQ740_spl
| sQ825_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7132,f545,f7148,f5924]) ).
fof(f7152,definition,
! [X0,X1] :
( sQ826_spl
<=> ( ~ ssList(skaf56(X1))
| ~ rearsegP(X0,skaf56(X1))
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ826_spl])],[split_symbol_definition]) ).
fof(f7155,plain,
( ~ sQ727_spl
| sQ826_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7133,f545,f7152,f5846]) ).
fof(f7156,definition,
! [X0,X1] :
( sQ827_spl
<=> ( ~ ssList(skaf53(X1))
| ~ rearsegP(X0,skaf53(X1))
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ827_spl])],[split_symbol_definition]) ).
fof(f7159,plain,
( ~ sQ259_spl
| sQ827_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7134,f545,f7156,f2512]) ).
fof(f7160,definition,
! [X0,X1] :
( sQ828_spl
<=> ( ~ ssList(skaf52(X1))
| ~ rearsegP(X0,skaf52(X1))
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ828_spl])],[split_symbol_definition]) ).
fof(f7163,plain,
( ~ sQ247_spl
| sQ828_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7135,f545,f7160,f2440]) ).
fof(f7164,definition,
! [X0,X1] :
( sQ829_spl
<=> ( ~ ssList(skaf51(X1))
| ~ rearsegP(X0,skaf51(X1))
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ829_spl])],[split_symbol_definition]) ).
fof(f7167,plain,
( ~ sQ235_spl
| sQ829_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7136,f545,f7164,f2368]) ).
fof(f7168,definition,
! [X0] :
( sQ830_spl
<=> ( ~ rearsegP(X0,nil)
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ830_spl])],[split_symbol_definition]) ).
fof(f7171,plain,
( ~ sQ90_spl
| sQ830_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7137,f545,f7168,f1254]) ).
fof(f7172,definition,
! [X0] :
( sQ831_spl
<=> ( ~ rearsegP(X0,sk1)
| app(skaf46(X0,sk1),sk1) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ831_spl])],[split_symbol_definition]) ).
fof(f7175,plain,
( ~ sQ112_spl
| sQ831_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f7138,f558,f7172,f1469]) ).
fof(f7176,definition,
! [X0] :
( sQ832_spl
<=> ( ~ rearsegP(X0,sk1)
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ832_spl])],[split_symbol_definition]) ).
fof(f7179,plain,
( ~ sQ64_spl
| ~ sQ13_spl
| sQ832_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7139,f545,f7176,f558,f1065]) ).
fof(f7180,definition,
! [X0] :
( sQ833_spl
<=> ( ~ rearsegP(X0,sk2)
| app(skaf46(X0,sk2),sk2) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ833_spl])],[split_symbol_definition]) ).
fof(f7183,plain,
( ~ sQ127_spl
| sQ833_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f7140,f587,f7180,f1578]) ).
fof(f7184,definition,
! [X0] :
( sQ834_spl
<=> ( ~ rearsegP(X0,sk2)
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ834_spl])],[split_symbol_definition]) ).
fof(f7187,plain,
( ~ sQ78_spl
| ~ sQ16_spl
| sQ834_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7141,f545,f7184,f587,f1158]) ).
fof(f7196,definition,
! [X0,X1] :
( sQ836_spl
<=> ( ~ ssList(X1)
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| app(skaf46(X0,nil),nil) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ836_spl])],[split_symbol_definition]) ).
fof(f7199,plain,
( sQ836_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7145,f545,f7196]) ).
fof(f7380,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X1,X0),nil)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f351,f259]) ).
fof(f7382,definition,
! [X0,X1] :
( sQ849_spl
<=> ( ~ ssList(X1)
| frontsegP(app(X1,X0),nil)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ849_spl])],[split_symbol_definition]) ).
fof(f7385,plain,
( ~ sQ11_spl
| sQ849_spl ),
inference(split_clause,[status(thm)],[f7380,f7382,f545]) ).
fof(f7766,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f501,f285]) ).
fof(f7770,plain,
! [X0] :
( frontsegP(app(sk1,X0),sk1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f7766,f430]) ).
fof(f7786,plain,
! [X0] :
( frontsegP(app(sk2,X0),sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f7766,f431]) ).
fof(f7799,plain,
! [X0] :
( frontsegP(app(nil,X0),nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f7766,f207]) ).
fof(f8069,definition,
( sQ892_spl
<=> ssItem(skaf44(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ892_spl])],[split_symbol_definition]) ).
fof(f8071,plain,
( sQ892_spl
| ~ ssItem(skaf44(sk1)) ),
inference(component_clause,[status(thm)],[f8069]) ).
fof(f8093,plain,
( sQ892_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8071,f246]) ).
fof(f8094,plain,
sQ892_spl,
inference(contradiction_clause,[status(thm)],[f8093]) ).
fof(f8238,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(X0,X1) ),
inference(resolution,[status(thm)],[f378,f259]) ).
fof(f8240,definition,
! [X0,X1] :
( sQ898_spl
<=> ( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ) ),
introduced(definition,[new_symbols(definition,[sQ898_spl])],[split_symbol_definition]) ).
fof(f8243,plain,
( ~ sQ11_spl
| sQ898_spl ),
inference(split_clause,[status(thm)],[f8238,f8240,f545]) ).
fof(f8258,definition,
( sQ899_spl
<=> ssItem(skaf44(sk2)) ),
introduced(definition,[new_symbols(definition,[sQ899_spl])],[split_symbol_definition]) ).
fof(f8260,plain,
( sQ899_spl
| ~ ssItem(skaf44(sk2)) ),
inference(component_clause,[status(thm)],[f8258]) ).
fof(f8282,plain,
( sQ899_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8260,f246]) ).
fof(f8283,plain,
sQ899_spl,
inference(contradiction_clause,[status(thm)],[f8282]) ).
fof(f8328,plain,
! [X0,X1] :
( frontsegP(X1,sk1)
| ~ ssList(X1)
| ~ ssList(app(sk1,X0))
| ~ ssList(sk1)
| ~ frontsegP(X1,app(sk1,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f7770,f378]) ).
fof(f8329,plain,
! [X0,X1] :
( frontsegP(app(app(sk1,X0),X1),sk1)
| ~ ssList(app(sk1,X0))
| ~ ssList(sk1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f7770,f351]) ).
fof(f8330,plain,
! [X0] :
( app(sk1,skaf45(app(sk1,X0),sk1)) = app(sk1,X0)
| ~ ssList(app(sk1,X0))
| ~ ssList(sk1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f7770,f344]) ).
fof(f8331,plain,
! [X0] :
( app(sk1,X0) = sk1
| ~ ssList(app(sk1,X0))
| ~ ssList(sk1)
| ~ frontsegP(sk1,app(sk1,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f7770,f341]) ).
fof(f8332,plain,
( frontsegP(sk1,sk1)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1013,f7770]) ).
fof(f8333,definition,
! [X0,X1] :
( sQ905_spl
<=> ( frontsegP(X1,sk1)
| ~ ssList(X1)
| ~ ssList(app(sk1,X0))
| ~ frontsegP(X1,app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ905_spl])],[split_symbol_definition]) ).
fof(f8336,plain,
( ~ sQ13_spl
| sQ905_spl ),
inference(split_clause,[status(thm)],[f8328,f8333,f558]) ).
fof(f8337,definition,
! [X0,X1] :
( sQ906_spl
<=> ( frontsegP(app(app(sk1,X0),X1),sk1)
| ~ ssList(app(sk1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ906_spl])],[split_symbol_definition]) ).
fof(f8340,plain,
( ~ sQ13_spl
| sQ906_spl ),
inference(split_clause,[status(thm)],[f8329,f8337,f558]) ).
fof(f8341,definition,
! [X0] :
( sQ907_spl
<=> ( app(sk1,skaf45(app(sk1,X0),sk1)) = app(sk1,X0)
| ~ ssList(app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ907_spl])],[split_symbol_definition]) ).
fof(f8344,plain,
( ~ sQ13_spl
| sQ907_spl ),
inference(split_clause,[status(thm)],[f8330,f8341,f558]) ).
fof(f8345,definition,
! [X0] :
( sQ908_spl
<=> ( app(sk1,X0) = sk1
| ~ ssList(app(sk1,X0))
| ~ frontsegP(sk1,app(sk1,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ908_spl])],[split_symbol_definition]) ).
fof(f8348,plain,
( ~ sQ13_spl
| sQ908_spl ),
inference(split_clause,[status(thm)],[f8331,f8345,f558]) ).
fof(f8349,definition,
( sQ909_spl
<=> frontsegP(sk1,sk1) ),
introduced(definition,[new_symbols(definition,[sQ909_spl])],[split_symbol_definition]) ).
fof(f8350,plain,
( ~ sQ909_spl
| frontsegP(sk1,sk1) ),
inference(component_clause,[status(thm)],[f8349]) ).
fof(f8352,plain,
( sQ909_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8332,f545,f8349]) ).
fof(f8353,plain,
! [X0] :
( ~ sQ909_spl
| frontsegP(X0,sk1)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(sk1)
| ~ frontsegP(X0,sk1) ),
inference(resolution,[status(thm)],[f8350,f378]) ).
fof(f8354,plain,
! [X0] :
( ~ sQ909_spl
| frontsegP(app(sk1,X0),sk1)
| ~ ssList(sk1)
| ~ ssList(sk1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f8350,f351]) ).
fof(f8355,plain,
( ~ sQ909_spl
| app(sk1,skaf45(sk1,sk1)) = sk1
| ~ ssList(sk1)
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f8350,f344]) ).
fof(f8357,definition,
! [X0] :
( sQ910_spl
<=> ( frontsegP(X0,sk1)
| ~ ssList(X0)
| ~ frontsegP(X0,sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ910_spl])],[split_symbol_definition]) ).
fof(f8360,plain,
( ~ sQ909_spl
| ~ sQ13_spl
| sQ910_spl ),
inference(split_clause,[status(thm)],[f8353,f8357,f558,f8349]) ).
fof(f8361,definition,
! [X0] :
( sQ911_spl
<=> ( frontsegP(app(sk1,X0),sk1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ911_spl])],[split_symbol_definition]) ).
fof(f8364,plain,
( ~ sQ909_spl
| ~ sQ13_spl
| sQ911_spl ),
inference(split_clause,[status(thm)],[f8354,f8361,f558,f8349]) ).
fof(f8365,definition,
( sQ912_spl
<=> app(sk1,skaf45(sk1,sk1)) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ912_spl])],[split_symbol_definition]) ).
fof(f8368,plain,
( ~ sQ909_spl
| sQ912_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f8355,f558,f8365,f8349]) ).
fof(f8404,plain,
! [X0,X1] :
( frontsegP(X1,sk2)
| ~ ssList(X1)
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ frontsegP(X1,app(sk2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f7786,f378]) ).
fof(f8405,plain,
! [X0,X1] :
( frontsegP(app(app(sk2,X0),X1),sk2)
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f7786,f351]) ).
fof(f8406,plain,
! [X0] :
( app(sk2,skaf45(app(sk2,X0),sk2)) = app(sk2,X0)
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f7786,f344]) ).
fof(f8407,plain,
! [X0] :
( app(sk2,X0) = sk2
| ~ ssList(app(sk2,X0))
| ~ ssList(sk2)
| ~ frontsegP(sk2,app(sk2,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f7786,f341]) ).
fof(f8408,plain,
( frontsegP(sk2,sk2)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1029,f7786]) ).
fof(f8409,definition,
! [X0,X1] :
( sQ913_spl
<=> ( frontsegP(X1,sk2)
| ~ ssList(X1)
| ~ ssList(app(sk2,X0))
| ~ frontsegP(X1,app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ913_spl])],[split_symbol_definition]) ).
fof(f8412,plain,
( ~ sQ16_spl
| sQ913_spl ),
inference(split_clause,[status(thm)],[f8404,f8409,f587]) ).
fof(f8413,definition,
! [X0,X1] :
( sQ914_spl
<=> ( frontsegP(app(app(sk2,X0),X1),sk2)
| ~ ssList(app(sk2,X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ914_spl])],[split_symbol_definition]) ).
fof(f8416,plain,
( ~ sQ16_spl
| sQ914_spl ),
inference(split_clause,[status(thm)],[f8405,f8413,f587]) ).
fof(f8417,definition,
! [X0] :
( sQ915_spl
<=> ( app(sk2,skaf45(app(sk2,X0),sk2)) = app(sk2,X0)
| ~ ssList(app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ915_spl])],[split_symbol_definition]) ).
fof(f8420,plain,
( ~ sQ16_spl
| sQ915_spl ),
inference(split_clause,[status(thm)],[f8406,f8417,f587]) ).
fof(f8421,definition,
! [X0] :
( sQ916_spl
<=> ( app(sk2,X0) = sk2
| ~ ssList(app(sk2,X0))
| ~ frontsegP(sk2,app(sk2,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ916_spl])],[split_symbol_definition]) ).
fof(f8424,plain,
( ~ sQ16_spl
| sQ916_spl ),
inference(split_clause,[status(thm)],[f8407,f8421,f587]) ).
fof(f8425,definition,
( sQ917_spl
<=> frontsegP(sk2,sk2) ),
introduced(definition,[new_symbols(definition,[sQ917_spl])],[split_symbol_definition]) ).
fof(f8426,plain,
( ~ sQ917_spl
| frontsegP(sk2,sk2) ),
inference(component_clause,[status(thm)],[f8425]) ).
fof(f8428,plain,
( sQ917_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8408,f545,f8425]) ).
fof(f8429,plain,
! [X0,X1] :
( frontsegP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(nil,X0))
| ~ ssList(nil)
| ~ frontsegP(X1,app(nil,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f7799,f378]) ).
fof(f8430,plain,
! [X0,X1] :
( frontsegP(app(app(nil,X0),X1),nil)
| ~ ssList(app(nil,X0))
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f7799,f351]) ).
fof(f8431,plain,
! [X0] :
( app(nil,skaf45(app(nil,X0),nil)) = app(nil,X0)
| ~ ssList(app(nil,X0))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f7799,f344]) ).
fof(f8432,plain,
! [X0] :
( app(nil,X0) = nil
| ~ ssList(app(nil,X0))
| ~ ssList(nil)
| ~ frontsegP(nil,app(nil,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f7799,f341]) ).
fof(f8454,plain,
( frontsegP(sk2,nil)
| ~ ssList(sk2) ),
inference(paramodulation,[status(thm)],[f1423,f7799]) ).
fof(f8455,plain,
( frontsegP(sk1,nil)
| ~ ssList(sk1) ),
inference(paramodulation,[status(thm)],[f1407,f7799]) ).
fof(f8456,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1042,f7799]) ).
fof(f8457,definition,
! [X0,X1] :
( sQ918_spl
<=> ( frontsegP(X1,nil)
| ~ ssList(X1)
| ~ ssList(app(nil,X0))
| ~ frontsegP(X1,app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ918_spl])],[split_symbol_definition]) ).
fof(f8460,plain,
( ~ sQ11_spl
| sQ918_spl ),
inference(split_clause,[status(thm)],[f8429,f8457,f545]) ).
fof(f8461,definition,
! [X0,X1] :
( sQ919_spl
<=> ( frontsegP(app(app(nil,X0),X1),nil)
| ~ ssList(app(nil,X0))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ919_spl])],[split_symbol_definition]) ).
fof(f8464,plain,
( ~ sQ11_spl
| sQ919_spl ),
inference(split_clause,[status(thm)],[f8430,f8461,f545]) ).
fof(f8465,definition,
! [X0] :
( sQ920_spl
<=> ( app(nil,skaf45(app(nil,X0),nil)) = app(nil,X0)
| ~ ssList(app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ920_spl])],[split_symbol_definition]) ).
fof(f8468,plain,
( ~ sQ11_spl
| sQ920_spl ),
inference(split_clause,[status(thm)],[f8431,f8465,f545]) ).
fof(f8469,definition,
! [X0] :
( sQ921_spl
<=> ( app(nil,X0) = nil
| ~ ssList(app(nil,X0))
| ~ frontsegP(nil,app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ921_spl])],[split_symbol_definition]) ).
fof(f8472,plain,
( ~ sQ11_spl
| sQ921_spl ),
inference(split_clause,[status(thm)],[f8432,f8469,f545]) ).
fof(f8473,definition,
( sQ922_spl
<=> frontsegP(sk2,nil) ),
introduced(definition,[new_symbols(definition,[sQ922_spl])],[split_symbol_definition]) ).
fof(f8474,plain,
( ~ sQ922_spl
| frontsegP(sk2,nil) ),
inference(component_clause,[status(thm)],[f8473]) ).
fof(f8476,plain,
( sQ922_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f8454,f587,f8473]) ).
fof(f8477,definition,
( sQ923_spl
<=> frontsegP(sk1,nil) ),
introduced(definition,[new_symbols(definition,[sQ923_spl])],[split_symbol_definition]) ).
fof(f8478,plain,
( ~ sQ923_spl
| frontsegP(sk1,nil) ),
inference(component_clause,[status(thm)],[f8477]) ).
fof(f8480,plain,
( sQ923_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f8455,f558,f8477]) ).
fof(f8481,definition,
( sQ924_spl
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ924_spl])],[split_symbol_definition]) ).
fof(f8482,plain,
( ~ sQ924_spl
| frontsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f8481]) ).
fof(f8484,plain,
( sQ924_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8456,f545,f8481]) ).
fof(f8485,plain,
! [X0] :
( ~ sQ917_spl
| frontsegP(X0,sk2)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ frontsegP(X0,sk2) ),
inference(resolution,[status(thm)],[f8426,f378]) ).
fof(f8486,plain,
! [X0] :
( ~ sQ917_spl
| frontsegP(app(sk2,X0),sk2)
| ~ ssList(sk2)
| ~ ssList(sk2)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f8426,f351]) ).
fof(f8487,plain,
( ~ sQ917_spl
| app(sk2,skaf45(sk2,sk2)) = sk2
| ~ ssList(sk2)
| ~ ssList(sk2) ),
inference(resolution,[status(thm)],[f8426,f344]) ).
fof(f8489,definition,
! [X0] :
( sQ925_spl
<=> ( frontsegP(X0,sk2)
| ~ ssList(X0)
| ~ frontsegP(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ925_spl])],[split_symbol_definition]) ).
fof(f8492,plain,
( ~ sQ917_spl
| ~ sQ16_spl
| sQ925_spl ),
inference(split_clause,[status(thm)],[f8485,f8489,f587,f8425]) ).
fof(f8493,definition,
! [X0] :
( sQ926_spl
<=> ( frontsegP(app(sk2,X0),sk2)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ926_spl])],[split_symbol_definition]) ).
fof(f8496,plain,
( ~ sQ917_spl
| ~ sQ16_spl
| sQ926_spl ),
inference(split_clause,[status(thm)],[f8486,f8493,f587,f8425]) ).
fof(f8497,definition,
( sQ927_spl
<=> app(sk2,skaf45(sk2,sk2)) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ927_spl])],[split_symbol_definition]) ).
fof(f8500,plain,
( ~ sQ917_spl
| sQ927_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f8487,f587,f8497,f8425]) ).
fof(f8503,plain,
! [X0] :
( ~ sQ924_spl
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(resolution,[status(thm)],[f8482,f378]) ).
fof(f8504,plain,
! [X0] :
( ~ sQ924_spl
| frontsegP(app(nil,X0),nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f8482,f351]) ).
fof(f8505,plain,
( ~ sQ924_spl
| app(nil,skaf45(nil,nil)) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f8482,f344]) ).
fof(f8508,definition,
! [X0] :
( sQ928_spl
<=> ( frontsegP(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ928_spl])],[split_symbol_definition]) ).
fof(f8511,plain,
( ~ sQ924_spl
| ~ sQ11_spl
| sQ928_spl ),
inference(split_clause,[status(thm)],[f8503,f8508,f545,f8481]) ).
fof(f8512,definition,
! [X0] :
( sQ929_spl
<=> ( frontsegP(app(nil,X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ929_spl])],[split_symbol_definition]) ).
fof(f8515,plain,
( ~ sQ924_spl
| ~ sQ11_spl
| sQ929_spl ),
inference(split_clause,[status(thm)],[f8504,f8512,f545,f8481]) ).
fof(f8516,definition,
( sQ930_spl
<=> app(nil,skaf45(nil,nil)) = nil ),
introduced(definition,[new_symbols(definition,[sQ930_spl])],[split_symbol_definition]) ).
fof(f8519,plain,
( ~ sQ924_spl
| sQ930_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8505,f545,f8516,f8481]) ).
fof(f8521,plain,
! [X0] :
( ~ sQ923_spl
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ frontsegP(X0,sk1) ),
inference(resolution,[status(thm)],[f8478,f378]) ).
fof(f8522,plain,
! [X0] :
( ~ sQ923_spl
| frontsegP(app(sk1,X0),nil)
| ~ ssList(sk1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f8478,f351]) ).
fof(f8523,plain,
( ~ sQ923_spl
| app(nil,skaf45(sk1,nil)) = sk1
| ~ ssList(sk1)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f8478,f344]) ).
fof(f8525,definition,
! [X0] :
( sQ931_spl
<=> ( frontsegP(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(X0,sk1) ) ),
introduced(definition,[new_symbols(definition,[sQ931_spl])],[split_symbol_definition]) ).
fof(f8528,plain,
( ~ sQ923_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sQ931_spl ),
inference(split_clause,[status(thm)],[f8521,f8525,f545,f558,f8477]) ).
fof(f8529,definition,
! [X0] :
( sQ932_spl
<=> ( frontsegP(app(sk1,X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ932_spl])],[split_symbol_definition]) ).
fof(f8532,plain,
( ~ sQ923_spl
| ~ sQ13_spl
| ~ sQ11_spl
| sQ932_spl ),
inference(split_clause,[status(thm)],[f8522,f8529,f545,f558,f8477]) ).
fof(f8533,definition,
( sQ933_spl
<=> app(nil,skaf45(sk1,nil)) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ933_spl])],[split_symbol_definition]) ).
fof(f8536,plain,
( ~ sQ923_spl
| sQ933_spl
| ~ sQ13_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8523,f545,f558,f8533,f8477]) ).
fof(f8541,plain,
! [X0] :
( ~ sQ922_spl
| frontsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ frontsegP(X0,sk2) ),
inference(resolution,[status(thm)],[f8474,f378]) ).
fof(f8542,plain,
! [X0] :
( ~ sQ922_spl
| frontsegP(app(sk2,X0),nil)
| ~ ssList(sk2)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f8474,f351]) ).
fof(f8543,plain,
( ~ sQ922_spl
| app(nil,skaf45(sk2,nil)) = sk2
| ~ ssList(sk2)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f8474,f344]) ).
fof(f8545,definition,
! [X0] :
( sQ935_spl
<=> ( frontsegP(X0,nil)
| ~ ssList(X0)
| ~ frontsegP(X0,sk2) ) ),
introduced(definition,[new_symbols(definition,[sQ935_spl])],[split_symbol_definition]) ).
fof(f8548,plain,
( ~ sQ922_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sQ935_spl ),
inference(split_clause,[status(thm)],[f8541,f8545,f545,f587,f8473]) ).
fof(f8549,definition,
! [X0] :
( sQ936_spl
<=> ( frontsegP(app(sk2,X0),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ936_spl])],[split_symbol_definition]) ).
fof(f8552,plain,
( ~ sQ922_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sQ936_spl ),
inference(split_clause,[status(thm)],[f8542,f8549,f545,f587,f8473]) ).
fof(f8553,definition,
( sQ937_spl
<=> app(nil,skaf45(sk2,nil)) = sk2 ),
introduced(definition,[new_symbols(definition,[sQ937_spl])],[split_symbol_definition]) ).
fof(f8556,plain,
( ~ sQ922_spl
| sQ937_spl
| ~ sQ16_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8543,f545,f587,f8553,f8473]) ).
fof(f8607,plain,
( ~ sQ782_spl
| rearsegP(sk1,nil)
| ~ ssList(nil)
| ~ ssList(skaf46(sk1,nil)) ),
inference(paramodulation,[status(thm)],[f6785,f2173]) ).
fof(f8609,plain,
! [X0,X1] :
( ~ sQ782_spl
| app(app(skaf46(sk1,nil),nil),X1) = X0
| ~ ssList(app(sk1,X1))
| ~ segmentP(X0,app(app(skaf46(sk1,nil),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf46(sk1,nil))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f6785,f666]) ).
fof(f8610,plain,
! [X0,X1,X2] :
( ~ sQ782_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk1,X1))
| ~ segmentP(X2,app(app(skaf46(sk1,nil),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf46(sk1,nil))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f6785,f665]) ).
fof(f8612,plain,
! [X0] :
( ~ sQ782_spl
| rearsegP(sk1,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf46(sk1,nil))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f6785,f350]) ).
fof(f8613,definition,
( sQ941_spl
<=> ssList(skaf46(sk1,nil)) ),
introduced(definition,[new_symbols(definition,[sQ941_spl])],[split_symbol_definition]) ).
fof(f8615,plain,
( sQ941_spl
| ~ ssList(skaf46(sk1,nil)) ),
inference(component_clause,[status(thm)],[f8613]) ).
fof(f8621,plain,
( ~ sQ782_spl
| sQ82_spl
| ~ sQ11_spl
| ~ sQ941_spl ),
inference(split_clause,[status(thm)],[f8607,f8613,f545,f1206,f6784]) ).
fof(f8623,definition,
! [X0,X1] :
( sQ943_spl
<=> ( app(app(skaf46(sk1,nil),nil),X1) = X0
| ~ ssList(app(sk1,X1))
| ~ segmentP(X0,app(app(skaf46(sk1,nil),nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ943_spl])],[split_symbol_definition]) ).
fof(f8626,plain,
( ~ sQ782_spl
| ~ sQ11_spl
| ~ sQ941_spl
| sQ943_spl ),
inference(split_clause,[status(thm)],[f8609,f8623,f8613,f545,f6784]) ).
fof(f8627,definition,
! [X0,X1,X2] :
( sQ944_spl
<=> ( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk1,X1))
| ~ segmentP(X2,app(app(skaf46(sk1,nil),nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ944_spl])],[split_symbol_definition]) ).
fof(f8630,plain,
( ~ sQ782_spl
| ~ sQ11_spl
| ~ sQ941_spl
| sQ944_spl ),
inference(split_clause,[status(thm)],[f8610,f8627,f8613,f545,f6784]) ).
fof(f8632,plain,
( ~ sQ782_spl
| ~ sQ11_spl
| ~ sQ941_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f8612,f1069,f8613,f545,f6784]) ).
fof(f8633,plain,
( sQ941_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8615,f249]) ).
fof(f8634,plain,
sQ941_spl,
inference(contradiction_clause,[status(thm)],[f8633]) ).
fof(f8674,plain,
( ~ sQ784_spl
| rearsegP(sk2,nil)
| ~ ssList(nil)
| ~ ssList(skaf46(sk2,nil)) ),
inference(paramodulation,[status(thm)],[f6793,f2173]) ).
fof(f8676,plain,
! [X0,X1] :
( ~ sQ784_spl
| app(app(skaf46(sk2,nil),nil),X1) = X0
| ~ ssList(app(sk2,X1))
| ~ segmentP(X0,app(app(skaf46(sk2,nil),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf46(sk2,nil))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f6793,f666]) ).
fof(f8677,plain,
! [X0,X1,X2] :
( ~ sQ784_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk2,X1))
| ~ segmentP(X2,app(app(skaf46(sk2,nil),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf46(sk2,nil))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f6793,f665]) ).
fof(f8679,plain,
! [X0] :
( ~ sQ784_spl
| rearsegP(sk2,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf46(sk2,nil))
| ~ rearsegP(nil,X0) ),
inference(paramodulation,[status(thm)],[f6793,f350]) ).
fof(f8680,definition,
( sQ945_spl
<=> ssList(skaf46(sk2,nil)) ),
introduced(definition,[new_symbols(definition,[sQ945_spl])],[split_symbol_definition]) ).
fof(f8682,plain,
( sQ945_spl
| ~ ssList(skaf46(sk2,nil)) ),
inference(component_clause,[status(thm)],[f8680]) ).
fof(f8688,plain,
( ~ sQ784_spl
| sQ96_spl
| ~ sQ11_spl
| ~ sQ945_spl ),
inference(split_clause,[status(thm)],[f8674,f8680,f545,f1338,f6792]) ).
fof(f8690,definition,
! [X0,X1] :
( sQ947_spl
<=> ( app(app(skaf46(sk2,nil),nil),X1) = X0
| ~ ssList(app(sk2,X1))
| ~ segmentP(X0,app(app(skaf46(sk2,nil),nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ947_spl])],[split_symbol_definition]) ).
fof(f8693,plain,
( ~ sQ784_spl
| ~ sQ11_spl
| ~ sQ945_spl
| sQ947_spl ),
inference(split_clause,[status(thm)],[f8676,f8690,f8680,f545,f6792]) ).
fof(f8694,definition,
! [X0,X1,X2] :
( sQ948_spl
<=> ( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk2,X1))
| ~ segmentP(X2,app(app(skaf46(sk2,nil),nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ948_spl])],[split_symbol_definition]) ).
fof(f8697,plain,
( ~ sQ784_spl
| ~ sQ11_spl
| ~ sQ945_spl
| sQ948_spl ),
inference(split_clause,[status(thm)],[f8677,f8694,f8680,f545,f6792]) ).
fof(f8699,plain,
( ~ sQ784_spl
| ~ sQ11_spl
| ~ sQ945_spl
| sQ79_spl ),
inference(split_clause,[status(thm)],[f8679,f1162,f8680,f545,f6792]) ).
fof(f8700,plain,
( sQ945_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8682,f249]) ).
fof(f8701,plain,
sQ945_spl,
inference(contradiction_clause,[status(thm)],[f8700]) ).
fof(f8707,plain,
( ~ sQ780_spl
| rearsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(skaf46(nil,nil)) ),
inference(paramodulation,[status(thm)],[f6777,f2173]) ).
fof(f8709,plain,
! [X0,X1] :
( ~ sQ780_spl
| app(app(skaf46(nil,nil),nil),X1) = X0
| ~ ssList(app(nil,X1))
| ~ segmentP(X0,app(app(skaf46(nil,nil),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf46(nil,nil))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f6777,f666]) ).
fof(f8710,plain,
! [X0,X1,X2] :
( ~ sQ780_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(nil,X1))
| ~ segmentP(X2,app(app(skaf46(nil,nil),nil),X1))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(skaf46(nil,nil))
| ~ ssList(X1)
| ~ segmentP(nil,X0) ),
inference(paramodulation,[status(thm)],[f6777,f665]) ).
fof(f8713,definition,
( sQ949_spl
<=> ssList(skaf46(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ949_spl])],[split_symbol_definition]) ).
fof(f8715,plain,
( sQ949_spl
| ~ ssList(skaf46(nil,nil)) ),
inference(component_clause,[status(thm)],[f8713]) ).
fof(f8718,plain,
( ~ sQ780_spl
| sQ37_spl
| ~ sQ11_spl
| ~ sQ949_spl ),
inference(split_clause,[status(thm)],[f8707,f8713,f545,f751,f6776]) ).
fof(f8720,definition,
! [X0,X1] :
( sQ950_spl
<=> ( app(app(skaf46(nil,nil),nil),X1) = X0
| ~ ssList(app(nil,X1))
| ~ segmentP(X0,app(app(skaf46(nil,nil),nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ950_spl])],[split_symbol_definition]) ).
fof(f8723,plain,
( ~ sQ780_spl
| ~ sQ11_spl
| ~ sQ949_spl
| sQ950_spl ),
inference(split_clause,[status(thm)],[f8709,f8720,f8713,f545,f6776]) ).
fof(f8724,definition,
! [X0,X1,X2] :
( sQ951_spl
<=> ( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(nil,X1))
| ~ segmentP(X2,app(app(skaf46(nil,nil),nil),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(nil,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ951_spl])],[split_symbol_definition]) ).
fof(f8727,plain,
( ~ sQ780_spl
| ~ sQ11_spl
| ~ sQ949_spl
| sQ951_spl ),
inference(split_clause,[status(thm)],[f8710,f8724,f8713,f545,f6776]) ).
fof(f8730,plain,
( sQ949_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8715,f249]) ).
fof(f8731,plain,
sQ949_spl,
inference(contradiction_clause,[status(thm)],[f8730]) ).
fof(f8739,plain,
! [X0] :
( ~ sQ781_spl
| segmentP(app(sk1,X0),sk1)
| ~ ssList(sk1)
| ~ ssList(skaf46(sk1,sk1))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f6781,f2205]) ).
fof(f8740,plain,
( ~ sQ781_spl
| rearsegP(sk1,sk1)
| ~ ssList(sk1)
| ~ ssList(skaf46(sk1,sk1)) ),
inference(paramodulation,[status(thm)],[f6781,f2173]) ).
fof(f8742,plain,
! [X0,X1] :
( ~ sQ781_spl
| app(app(skaf46(sk1,sk1),sk1),X1) = X0
| ~ ssList(app(sk1,X1))
| ~ segmentP(X0,app(app(skaf46(sk1,sk1),sk1),X1))
| ~ ssList(sk1)
| ~ ssList(X0)
| ~ ssList(skaf46(sk1,sk1))
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ),
inference(paramodulation,[status(thm)],[f6781,f666]) ).
fof(f8743,plain,
! [X0,X1,X2] :
( ~ sQ781_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk1,X1))
| ~ segmentP(X2,app(app(skaf46(sk1,sk1),sk1),X1))
| ~ ssList(sk1)
| ~ ssList(X0)
| ~ ssList(skaf46(sk1,sk1))
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ),
inference(paramodulation,[status(thm)],[f6781,f665]) ).
fof(f8745,plain,
! [X0] :
( ~ sQ781_spl
| rearsegP(sk1,X0)
| ~ ssList(sk1)
| ~ ssList(X0)
| ~ ssList(skaf46(sk1,sk1))
| ~ rearsegP(sk1,X0) ),
inference(paramodulation,[status(thm)],[f6781,f350]) ).
fof(f8746,definition,
( sQ952_spl
<=> ssList(skaf46(sk1,sk1)) ),
introduced(definition,[new_symbols(definition,[sQ952_spl])],[split_symbol_definition]) ).
fof(f8748,plain,
( sQ952_spl
| ~ ssList(skaf46(sk1,sk1)) ),
inference(component_clause,[status(thm)],[f8746]) ).
fof(f8752,plain,
( ~ sQ781_spl
| ~ sQ13_spl
| ~ sQ952_spl
| sQ277_spl ),
inference(split_clause,[status(thm)],[f8739,f2624,f8746,f558,f6780]) ).
fof(f8753,plain,
( ~ sQ781_spl
| sQ114_spl
| ~ sQ13_spl
| ~ sQ952_spl ),
inference(split_clause,[status(thm)],[f8740,f8746,f558,f1508,f6780]) ).
fof(f8755,definition,
! [X0,X1] :
( sQ953_spl
<=> ( app(app(skaf46(sk1,sk1),sk1),X1) = X0
| ~ ssList(app(sk1,X1))
| ~ segmentP(X0,app(app(skaf46(sk1,sk1),sk1),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ953_spl])],[split_symbol_definition]) ).
fof(f8758,plain,
( ~ sQ781_spl
| ~ sQ13_spl
| ~ sQ952_spl
| sQ953_spl ),
inference(split_clause,[status(thm)],[f8742,f8755,f8746,f558,f6780]) ).
fof(f8759,definition,
! [X0,X1,X2] :
( sQ954_spl
<=> ( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk1,X1))
| ~ segmentP(X2,app(app(skaf46(sk1,sk1),sk1),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ954_spl])],[split_symbol_definition]) ).
fof(f8762,plain,
( ~ sQ781_spl
| ~ sQ13_spl
| ~ sQ952_spl
| sQ954_spl ),
inference(split_clause,[status(thm)],[f8743,f8759,f8746,f558,f6780]) ).
fof(f8764,plain,
( ~ sQ781_spl
| ~ sQ13_spl
| ~ sQ952_spl
| sQ113_spl ),
inference(split_clause,[status(thm)],[f8745,f1473,f8746,f558,f6780]) ).
fof(f8765,plain,
( sQ952_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8748,f249]) ).
fof(f8766,plain,
sQ952_spl,
inference(contradiction_clause,[status(thm)],[f8765]) ).
fof(f8775,plain,
! [X0] :
( ~ sQ783_spl
| segmentP(app(sk2,X0),sk2)
| ~ ssList(sk2)
| ~ ssList(skaf46(sk2,sk2))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f6789,f2205]) ).
fof(f8776,plain,
( ~ sQ783_spl
| rearsegP(sk2,sk2)
| ~ ssList(sk2)
| ~ ssList(skaf46(sk2,sk2)) ),
inference(paramodulation,[status(thm)],[f6789,f2173]) ).
fof(f8778,plain,
! [X0,X1] :
( ~ sQ783_spl
| app(app(skaf46(sk2,sk2),sk2),X1) = X0
| ~ ssList(app(sk2,X1))
| ~ segmentP(X0,app(app(skaf46(sk2,sk2),sk2),X1))
| ~ ssList(sk2)
| ~ ssList(X0)
| ~ ssList(skaf46(sk2,sk2))
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ),
inference(paramodulation,[status(thm)],[f6789,f666]) ).
fof(f8779,plain,
! [X0,X1,X2] :
( ~ sQ783_spl
| segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk2,X1))
| ~ segmentP(X2,app(app(skaf46(sk2,sk2),sk2),X1))
| ~ ssList(sk2)
| ~ ssList(X0)
| ~ ssList(skaf46(sk2,sk2))
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ),
inference(paramodulation,[status(thm)],[f6789,f665]) ).
fof(f8781,plain,
! [X0] :
( ~ sQ783_spl
| rearsegP(sk2,X0)
| ~ ssList(sk2)
| ~ ssList(X0)
| ~ ssList(skaf46(sk2,sk2))
| ~ rearsegP(sk2,X0) ),
inference(paramodulation,[status(thm)],[f6789,f350]) ).
fof(f8782,definition,
( sQ955_spl
<=> ssList(skaf46(sk2,sk2)) ),
introduced(definition,[new_symbols(definition,[sQ955_spl])],[split_symbol_definition]) ).
fof(f8784,plain,
( sQ955_spl
| ~ ssList(skaf46(sk2,sk2)) ),
inference(component_clause,[status(thm)],[f8782]) ).
fof(f8792,plain,
( ~ sQ783_spl
| ~ sQ16_spl
| ~ sQ955_spl
| sQ276_spl ),
inference(split_clause,[status(thm)],[f8775,f2620,f8782,f587,f6788]) ).
fof(f8793,plain,
( ~ sQ783_spl
| sQ129_spl
| ~ sQ16_spl
| ~ sQ955_spl ),
inference(split_clause,[status(thm)],[f8776,f8782,f587,f1611,f6788]) ).
fof(f8795,definition,
! [X0,X1] :
( sQ957_spl
<=> ( app(app(skaf46(sk2,sk2),sk2),X1) = X0
| ~ ssList(app(sk2,X1))
| ~ segmentP(X0,app(app(skaf46(sk2,sk2),sk2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ957_spl])],[split_symbol_definition]) ).
fof(f8798,plain,
( ~ sQ783_spl
| ~ sQ16_spl
| ~ sQ955_spl
| sQ957_spl ),
inference(split_clause,[status(thm)],[f8778,f8795,f8782,f587,f6788]) ).
fof(f8799,definition,
! [X0,X1,X2] :
( sQ958_spl
<=> ( segmentP(X2,X0)
| ~ ssList(X2)
| ~ ssList(app(sk2,X1))
| ~ segmentP(X2,app(app(skaf46(sk2,sk2),sk2),X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sk2,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ958_spl])],[split_symbol_definition]) ).
fof(f8802,plain,
( ~ sQ783_spl
| ~ sQ16_spl
| ~ sQ955_spl
| sQ958_spl ),
inference(split_clause,[status(thm)],[f8779,f8799,f8782,f587,f6788]) ).
fof(f8804,plain,
( ~ sQ783_spl
| ~ sQ16_spl
| ~ sQ955_spl
| sQ128_spl ),
inference(split_clause,[status(thm)],[f8781,f1582,f8782,f587,f6788]) ).
fof(f8805,plain,
( sQ955_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8784,f249]) ).
fof(f8806,plain,
sQ955_spl,
inference(contradiction_clause,[status(thm)],[f8805]) ).
fof(f8812,plain,
( ~ sQ790_spl
| segmentP(sk2,sk1)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1029,f6842]) ).
fof(f8821,plain,
( ~ sQ790_spl
| sQ5_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8812,f545,f461,f6841]) ).
fof(f8822,plain,
$false,
inference(sat_refutation,[status(thm)],[f457,f464,f468,f476,f485,f525,f534,f541,f551,f554,f561,f565,f567,f579,f597,f616,f628,f631,f725,f729,f758,f772,f776,f820,f831,f835,f848,f891,f928,f932,f978,f993,f1010,f1052,f1056,f1060,f1064,f1068,f1104,f1108,f1114,f1119,f1132,f1145,f1149,f1153,f1157,f1161,f1188,f1192,f1195,f1197,f1201,f1213,f1230,f1241,f1245,f1249,f1253,f1257,f1261,f1308,f1313,f1322,f1346,f1358,f1366,f1374,f1378,f1382,f1395,f1399,f1403,f1448,f1452,f1456,f1460,f1464,f1468,f1472,f1515,f1520,f1529,f1557,f1561,f1565,f1569,f1573,f1577,f1581,f1621,f1626,f1635,f1650,f1660,f1664,f1668,f1683,f1696,f1707,f1711,f1719,f1727,f1731,f1735,f1744,f1748,f1752,f1756,f1760,f1776,f1800,f1804,f1808,f1812,f1816,f1820,f1824,f1828,f1832,f1863,f1867,f1871,f1875,f1879,f1883,f1887,f1891,f1895,f1926,f1930,f1934,f1938,f1942,f1946,f1950,f1954,f1958,f1989,f1993,f1997,f2001,f2005,f2009,f2013,f2017,f2021,f2052,f2056,f2060,f2064,f2068,f2072,f2076,f2080,f2084,f2115,f2119,f2123,f2127,f2131,f2135,f2139,f2143,f2147,f2195,f2199,f2209,f2213,f2217,f2221,f2225,f2229,f2242,f2246,f2254,f2265,f2269,f2270,f2276,f2280,f2312,f2338,f2342,f2346,f2350,f2354,f2358,f2372,f2376,f2399,f2403,f2409,f2413,f2417,f2422,f2426,f2430,f2434,f2444,f2448,f2471,f2475,f2481,f2485,f2489,f2494,f2498,f2502,f2506,f2516,f2520,f2539,f2543,f2547,f2551,f2555,f2559,f2563,f2575,f2599,f2603,f2607,f2611,f2615,f2619,f2631,f2657,f2665,f2669,f2675,f2679,f2683,f2688,f2692,f2696,f2700,f2713,f2717,f2721,f2725,f2729,f2733,f2737,f2756,f2760,f2764,f2768,f2772,f2776,f2780,f2799,f2803,f2807,f2811,f2815,f2819,f2823,f2842,f2846,f2850,f2854,f2858,f2862,f2866,f2885,f2889,f2893,f2897,f2901,f2905,f2909,f2928,f2932,f2936,f2940,f2944,f2948,f2952,f2971,f2975,f2979,f2983,f2987,f2991,f2995,f3014,f3018,f3022,f3026,f3030,f3034,f3038,f3055,f3059,f3063,f3069,f3070,f3080,f3084,f3103,f3119,f3127,f3131,f3135,f3141,f3145,f3152,f3156,f3160,f3166,f3170,f3198,f3202,f3206,f3210,f3214,f3218,f3222,f3226,f3230,f3234,f3238,f3242,f3246,f3250,f3254,f3258,f3262,f3302,f3306,f3310,f3314,f3318,f3322,f3326,f3330,f3351,f3355,f3359,f3363,f3367,f3371,f3375,f3379,f3400,f3404,f3408,f3412,f3416,f3420,f3424,f3428,f3449,f3453,f3457,f3461,f3465,f3469,f3473,f3477,f3498,f3502,f3506,f3510,f3514,f3518,f3522,f3526,f3547,f3551,f3555,f3559,f3563,f3567,f3571,f3575,f3596,f3600,f3604,f3608,f3612,f3616,f3620,f3624,f3646,f3650,f3654,f3659,f3663,f3667,f3671,f3691,f3695,f3699,f3704,f3708,f3712,f3716,f3738,f3744,f3748,f3758,f3762,f3766,f3772,f3776,f3783,f3787,f3791,f3797,f3801,f3808,f3812,f3816,f3822,f3826,f3831,f3838,f3842,f3857,f3861,f3865,f3870,f3874,f3878,f3882,f3902,f3906,f3910,f3915,f3919,f3923,f3927,f3947,f3951,f3955,f3960,f3964,f3968,f3972,f3992,f3996,f4000,f4005,f4009,f4013,f4017,f4037,f4041,f4045,f4050,f4054,f4058,f4062,f4082,f4086,f4090,f4095,f4099,f4103,f4107,f4127,f4131,f4135,f4140,f4144,f4148,f4152,f4172,f4176,f4180,f4185,f4189,f4193,f4197,f4217,f4221,f4225,f4230,f4234,f4238,f4242,f4257,f4266,f4272,f4282,f4286,f4296,f4300,f4304,f4310,f4314,f4321,f4325,f4329,f4335,f4339,f4346,f4350,f4354,f4360,f4364,f4370,f4374,f4384,f4400,f4404,f4408,f4413,f4417,f4421,f4425,f4445,f4449,f4453,f4458,f4462,f4466,f4470,f4490,f4494,f4498,f4503,f4507,f4511,f4515,f4535,f4539,f4543,f4548,f4552,f4556,f4560,f4580,f4584,f4588,f4593,f4597,f4601,f4605,f4625,f4629,f4633,f4638,f4642,f4646,f4650,f4670,f4674,f4678,f4683,f4687,f4691,f4695,f4715,f4719,f4723,f4728,f4732,f4736,f4740,f4760,f4764,f4768,f4773,f4777,f4781,f4785,f4842,f4852,f4870,f4874,f4878,f4884,f4888,f4895,f4899,f4903,f4909,f4913,f4920,f4924,f4928,f4934,f4938,f4946,f4956,f4970,f4974,f4978,f4983,f4987,f4991,f4995,f5110,f5133,f5142,f5146,f5150,f5156,f5160,f5167,f5171,f5175,f5181,f5185,f5192,f5196,f5200,f5208,f5219,f5227,f5231,f5366,f5370,f5374,f5380,f5384,f5391,f5395,f5399,f5405,f5409,f5416,f5420,f5424,f5430,f5434,f5442,f5451,f5625,f5629,f5633,f5639,f5643,f5650,f5654,f5658,f5664,f5668,f5675,f5679,f5683,f5691,f5701,f5708,f5712,f5783,f5794,f5801,f5814,f5815,f5823,f5827,f5831,f5837,f5841,f5850,f5854,f5874,f5882,f5886,f5892,f5896,f5900,f5905,f5909,f5913,f5917,f5928,f5932,f5952,f5960,f5964,f5970,f5974,f5978,f5983,f5987,f5991,f5995,f6005,f6016,f6285,f6294,f6543,f6553,f6618,f6630,f6657,f6667,f6759,f6763,f6767,f6771,f6775,f6779,f6783,f6787,f6791,f6795,f6799,f6807,f6821,f6844,f6867,f6924,f6928,f6932,f6936,f6940,f6944,f6948,f6952,f6956,f6960,f6972,f7084,f7086,f7088,f7090,f7151,f7155,f7159,f7163,f7167,f7171,f7175,f7179,f7183,f7187,f7199,f7385,f8094,f8243,f8283,f8336,f8340,f8344,f8348,f8352,f8360,f8364,f8368,f8412,f8416,f8420,f8424,f8428,f8460,f8464,f8468,f8472,f8476,f8480,f8484,f8492,f8496,f8500,f8511,f8515,f8519,f8528,f8532,f8536,f8548,f8552,f8556,f8621,f8626,f8630,f8632,f8634,f8688,f8693,f8697,f8699,f8701,f8718,f8723,f8727,f8731,f8752,f8753,f8758,f8762,f8764,f8766,f8792,f8793,f8798,f8802,f8804,f8806,f8821]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC108-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n026.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 07:58:37 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 3.44/1.29 % Refutation found
% 3.44/1.29 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 3.44/1.29 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.62/1.34 % Elapsed time: 0.963922 seconds
% 0.62/1.34 % CPU time: 7.132529 seconds
% 0.62/1.34 % Total memory used: 159.974 MB
% 0.62/1.34 % Net memory used: 155.732 MB
%------------------------------------------------------------------------------