%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC166-1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n012.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 02:40:13 PM UTC 2026
% Result : Unsatisfiable 9.42s 6.67s
% Output : CNFRefutation 9.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 106
% Syntax : Number of formulae : 387 ( 33 unt; 62 def)
% Number of atoms : 1282 ( 254 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 1690 ( 795 ~; 833 |; 0 &)
% ( 62 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 71 ( 69 usr; 63 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 289 ( 289 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [U] : ssList(skaf82(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(f61,axiom,
! [U] :
( frontsegP(U,U)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,axiom,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,axiom,
! [U,V] :
( ssItem(V)
| duplicatefreeP(U)
| ~ 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(f75,axiom,
! [U] :
( nil = U
| ssList(tl(U))
| ~ ssList(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(f86,axiom,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,axiom,
! [U,V] :
( tl(cons(U,V)) = V
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,axiom,
! [U,V] :
( hd(cons(U,V)) = U
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f98,axiom,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f101,axiom,
! [U] :
( cons(skaf44(U),nil) = U
| ~ ssList(U)
| ~ singletonP(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f102,axiom,
! [U,V] :
( V = U
| neq(V,U)
| ~ ssItem(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f104,axiom,
! [U] :
( nil = U
| cons(hd(U),tl(U)) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f109,axiom,
! [U] :
( nil = U
| cons(skaf83(U),skaf82(U)) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f116,axiom,
! [U,V] :
( singletonP(V)
| ~ ssList(V)
| ~ ssItem(U)
| cons(U,nil) != V ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f118,axiom,
! [U,V] :
( nil = U
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f119,axiom,
! [U,V] :
( nil = V
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f120,axiom,
! [U,V] :
( app(cons(U,nil),V) = cons(U,V)
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f123,axiom,
! [U,V] :
( hd(app(V,U)) = hd(V)
| nil = V
| ~ ssList(V)
| ~ ssList(U) ),
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(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(f140,axiom,
! [U,V,W] :
( memberP(app(U,W),V)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f149,axiom,
! [U,V,W] :
( app(app(W,V),U) = app(W,app(V,U))
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f150,axiom,
! [U,V,W] :
( V = W
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != app(U,W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f151,axiom,
! [U,V,W] :
( U = W
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U)
| app(U,V) != app(W,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f161,axiom,
! [U,V,W] :
( W = U
| memberP(V,W)
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f170,axiom,
! [U,V,W,X] :
( U = W
| ~ ssList(V)
| ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| cons(U,V) != cons(W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f171,axiom,
! [U,V,W,X] :
( X = V
| ~ ssList(V)
| ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| cons(U,V) != cons(W,X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f175,axiom,
! [U,V,W,X] :
( memberP(X,V)
| ~ ssList(X)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| app(U,cons(V,W)) != X ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f178,axiom,
! [U,V,W,X] :
( frontsegP(cons(W,U),cons(X,V))
| ~ ssItem(W)
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(V)
| W != X
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f179,axiom,
! [U,V,W,X,Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f186,negated_conjecture,
ssList(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
singletonP(sk3),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
ssItem(sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
ssList(sk8),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f197,negated_conjecture,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
~ neq(sk5,sk6),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f206,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f211,plain,
! [X0] : ssList(skaf82(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f258,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f259,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
fof(f269,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f270,plain,
( ! [V] : ssItem(V)
| ! [U] :
( duplicatefreeP(U)
| ~ ssList(U) ) ),
inference(miniscoping,[status(thm)],[f72]) ).
fof(f271,plain,
! [X0,X1] :
( ssItem(X1)
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f270]) ).
fof(f272,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f73]) ).
fof(f273,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f274,plain,
! [X0] :
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f284,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f285,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f295,plain,
! [X0,X1] :
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f296,plain,
! [X0,X1] :
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f297,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f298,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f302,plain,
! [X0] :
( cons(skaf44(X0),nil) = X0
| ~ ssList(X0)
| ~ singletonP(X0) ),
inference(cnf_transformation,[status(thm)],[f101]) ).
fof(f303,plain,
! [X0,X1] :
( X1 = X0
| neq(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f305,plain,
! [X0] :
( nil = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f310,plain,
! [X0] :
( nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f321,plain,
! [V] :
( singletonP(V)
| ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,nil) != V ) ),
inference(miniscoping,[status(thm)],[f116]) ).
fof(f322,plain,
! [X0,X1] :
( singletonP(X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,nil) != X1 ),
inference(cnf_transformation,[status(thm)],[f321]) ).
fof(f325,plain,
! [U] :
( nil = U
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f326,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f327,plain,
! [V] :
( nil = V
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f328,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f327]) ).
fof(f329,plain,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f332,plain,
! [X0,X1] :
( hd(app(X1,X0)) = hd(X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f340,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f350,plain,
! [X0,X1,X2] :
( frontsegP(app(X0,X2),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
fof(f353,plain,
! [X0,X1,X2] :
( memberP(app(X0,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f367,plain,
! [X0,X1,X2] :
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f368,plain,
! [V,W] :
( V = W
| ~ ssList(W)
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != app(U,W) ) ),
inference(miniscoping,[status(thm)],[f150]) ).
fof(f369,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != app(X0,X2) ),
inference(cnf_transformation,[status(thm)],[f368]) ).
fof(f370,plain,
! [U,W] :
( U = W
| ~ ssList(W)
| ! [V] :
( ~ ssList(V)
| ~ ssList(U)
| app(U,V) != app(W,V) ) ),
inference(miniscoping,[status(thm)],[f151]) ).
fof(f371,plain,
! [X0,X1,X2] :
( X0 = X2
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X0,X1) != app(X2,X1) ),
inference(cnf_transformation,[status(thm)],[f370]) ).
fof(f389,plain,
! [U,W] :
( W = U
| ! [V] :
( memberP(V,W)
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W) ) ),
inference(miniscoping,[status(thm)],[f161]) ).
fof(f390,plain,
! [X0,X1,X2] :
( X2 = X0
| memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f389]) ).
fof(f399,plain,
! [U,W] :
( U = W
| ! [V] :
( ~ ssList(V)
| ! [X] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| cons(U,V) != cons(W,X) ) ) ),
inference(miniscoping,[status(thm)],[f170]) ).
fof(f400,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| cons(X0,X1) != cons(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f399]) ).
fof(f401,plain,
! [V,X] :
( X = V
| ~ ssList(V)
| ~ ssList(X)
| ! [U] :
( ~ ssItem(U)
| ! [W] :
( ~ ssItem(W)
| cons(U,V) != cons(W,X) ) ) ),
inference(miniscoping,[status(thm)],[f171]) ).
fof(f402,plain,
! [X0,X1,X2,X3] :
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| cons(X0,X1) != cons(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f401]) ).
fof(f408,plain,
! [V,X] :
( memberP(X,V)
| ~ ssList(X)
| ~ ssItem(V)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| app(U,cons(V,W)) != X ) ) ),
inference(miniscoping,[status(thm)],[f175]) ).
fof(f409,plain,
! [X0,X1,X2,X3] :
( memberP(X3,X1)
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| app(X0,cons(X1,X2)) != X3 ),
inference(cnf_transformation,[status(thm)],[f408]) ).
fof(f414,plain,
! [X0,X1,X2,X3] :
( frontsegP(cons(X2,X0),cons(X3,X1))
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X1)
| X2 != X3
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f415,plain,
! [Y] :
( ~ ssList(Y)
| ~ duplicatefreeP(Y)
| ! [V] :
( ~ ssItem(V)
| ! [U] :
( ~ ssList(U)
| ! [W] :
( ~ ssList(W)
| ! [X] :
( ~ ssList(X)
| app(app(U,cons(V,W)),cons(V,X)) != Y ) ) ) ) ),
inference(miniscoping,[status(thm)],[f179]) ).
fof(f416,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssList(X4)
| ~ duplicatefreeP(X4)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X3)
| app(app(X0,cons(X1,X2)),cons(X1,X3)) != X4 ),
inference(cnf_transformation,[status(thm)],[f415]) ).
fof(f429,plain,
ssList(sk1),
inference(cnf_transformation,[status(thm)],[f186]) ).
fof(f434,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f435,plain,
singletonP(sk3),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f436,plain,
ssItem(sk5),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f437,plain,
ssItem(sk6),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f438,plain,
ssList(sk7),
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f439,plain,
ssList(sk8),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f440,plain,
app(app(app(sk7,cons(sk5,nil)),cons(sk6,nil)),sk8) = sk1,
inference(cnf_transformation,[status(thm)],[f197]) ).
fof(f441,plain,
~ neq(sk5,sk6),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f442,definition,
! [X0] :
( sQ0_spl
<=> ( duplicatefreeP(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f443,plain,
! [X0] :
( ~ sQ0_spl
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,definition,
! [X1] :
( sQ1_spl
<=> ssItem(X1) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f446,plain,
! [X0] :
( ~ sQ1_spl
| ssItem(X0) ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f448,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f271,f442,f445]) ).
fof(f458,plain,
! [X0] :
( singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f322]) ).
fof(f468,plain,
! [X0,X1,X2] :
( memberP(app(X1,cons(X2,X0)),X2)
| ~ ssList(app(X1,cons(X2,X0)))
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f409]) ).
fof(f469,plain,
! [X0,X1,X3] :
( frontsegP(cons(X3,X0),cons(X3,X1))
| ~ ssItem(X3)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f414]) ).
fof(f470,plain,
! [X0,X1,X2] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f469]) ).
fof(f471,plain,
! [X0,X1,X2,X3] :
( ~ ssList(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ duplicatefreeP(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f416]) ).
fof(f479,plain,
singletonP(sk1),
inference(backward_demodulation,[status(thm)],[f434,f435]) ).
fof(f482,definition,
( sQ2_spl
<=> ssList(sk8) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f484,plain,
( sQ2_spl
| ~ ssList(sk8) ),
inference(component_clause,[status(thm)],[f482]) ).
fof(f488,definition,
( sQ4_spl
<=> ssList(sk1) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f501,definition,
( sQ7_spl
<=> sk5 = sk6 ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f502,plain,
( ~ sQ7_spl
| sk5 = sk6 ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f505,plain,
( sk5 = sk6
| ~ ssItem(sk5)
| ~ ssItem(sk6) ),
inference(resolution,[status(thm)],[f303,f441]) ).
fof(f508,definition,
( sQ8_spl
<=> ssItem(sk6) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f510,plain,
( sQ8_spl
| ~ ssItem(sk6) ),
inference(component_clause,[status(thm)],[f508]) ).
fof(f511,definition,
( sQ9_spl
<=> ssItem(sk5) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f513,plain,
( sQ9_spl
| ~ ssItem(sk5) ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f514,plain,
( sQ7_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f505,f508,f511,f501]) ).
fof(f515,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f513,f436]) ).
fof(f516,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f515]) ).
fof(f517,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f437]) ).
fof(f518,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f517]) ).
fof(f520,plain,
( ~ sQ7_spl
| app(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)),sk8) = sk1 ),
inference(backward_demodulation,[status(thm)],[f502,f440]) ).
fof(f530,plain,
( ~ sQ7_spl
| ssList(sk1)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)))
| ~ ssList(sk8) ),
inference(paramodulation,[status(thm)],[f520,f284]) ).
fof(f531,definition,
( sQ11_spl
<=> ssList(app(app(sk7,cons(sk5,nil)),cons(sk5,nil))) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f532,plain,
( ~ sQ11_spl
| ssList(app(app(sk7,cons(sk5,nil)),cons(sk5,nil))) ),
inference(component_clause,[status(thm)],[f531]) ).
fof(f533,plain,
( sQ11_spl
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk5,nil))) ),
inference(component_clause,[status(thm)],[f531]) ).
fof(f534,plain,
( ~ sQ7_spl
| sQ4_spl
| ~ sQ11_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f530,f482,f531,f488,f501]) ).
fof(f537,plain,
( ~ sQ7_spl
| nil = app(app(sk7,cons(sk5,nil)),cons(sk5,nil))
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)))
| ~ ssList(sk8)
| sk1 != nil ),
inference(paramodulation,[status(thm)],[f520,f326]) ).
fof(f538,definition,
( sQ12_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( sQ12_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f538]) ).
fof(f546,definition,
( sQ14_spl
<=> sk1 = nil ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f549,definition,
( sQ15_spl
<=> nil = app(app(sk7,cons(sk5,nil)),cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f550,plain,
( ~ sQ15_spl
| nil = app(app(sk7,cons(sk5,nil)),cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f549]) ).
fof(f552,plain,
( ~ sQ7_spl
| sQ15_spl
| ~ sQ11_spl
| ~ sQ2_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f537,f546,f482,f531,f549,f501]) ).
fof(f553,plain,
( sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f484,f439]) ).
fof(f554,plain,
sQ2_spl,
inference(contradiction_clause,[status(thm)],[f553]) ).
fof(f555,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f540,f206]) ).
fof(f556,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f555]) ).
fof(f566,plain,
( sQ11_spl
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[f533,f284]) ).
fof(f567,definition,
( sQ17_spl
<=> ssList(cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f569,plain,
( sQ17_spl
| ~ ssList(cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f567]) ).
fof(f570,definition,
( sQ18_spl
<=> ssList(app(sk7,cons(sk5,nil))) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f572,plain,
( sQ18_spl
| ~ ssList(app(sk7,cons(sk5,nil))) ),
inference(component_clause,[status(thm)],[f570]) ).
fof(f573,plain,
( sQ11_spl
| ~ sQ18_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f566,f567,f570,f531]) ).
fof(f574,plain,
( sQ17_spl
| ~ ssList(nil)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f569,f285]) ).
fof(f575,plain,
( sQ17_spl
| ~ sQ12_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f574,f511,f538,f567]) ).
fof(f576,plain,
( ~ sQ7_spl
| sk1 = app(app(sk7,cons(sk5,nil)),app(cons(sk5,nil),sk8))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk8) ),
inference(paramodulation,[status(thm)],[f520,f367]) ).
fof(f578,definition,
( sQ19_spl
<=> sk1 = app(app(sk7,cons(sk5,nil)),app(cons(sk5,nil),sk8)) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f579,plain,
( ~ sQ19_spl
| sk1 = app(app(sk7,cons(sk5,nil)),app(cons(sk5,nil),sk8)) ),
inference(component_clause,[status(thm)],[f578]) ).
fof(f581,plain,
( ~ sQ7_spl
| sQ19_spl
| ~ sQ18_spl
| ~ sQ17_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f576,f482,f567,f570,f578,f501]) ).
fof(f586,plain,
( sQ18_spl
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[f572,f284]) ).
fof(f587,definition,
( sQ21_spl
<=> ssList(sk7) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f589,plain,
( sQ21_spl
| ~ ssList(sk7) ),
inference(component_clause,[status(thm)],[f587]) ).
fof(f590,plain,
( sQ18_spl
| ~ sQ21_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f586,f567,f587,f570]) ).
fof(f591,plain,
( sQ21_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f589,f438]) ).
fof(f592,plain,
sQ21_spl,
inference(contradiction_clause,[status(thm)],[f591]) ).
fof(f611,definition,
! [X1] :
( sQ25_spl
<=> ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f612,plain,
! [X0] :
( ~ sQ25_spl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f611]) ).
fof(f618,plain,
! [X0] :
( ~ sQ7_spl
| app(app(sk7,cons(sk5,nil)),cons(sk5,nil)) = X0
| ~ ssList(X0)
| ~ ssList(sk8)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)))
| sk1 != app(X0,sk8) ),
inference(paramodulation,[status(thm)],[f520,f371]) ).
fof(f626,definition,
! [X0] :
( sQ27_spl
<=> ( app(app(sk7,cons(sk5,nil)),cons(sk5,nil)) = X0
| ~ ssList(X0)
| sk1 != app(X0,sk8) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f627,plain,
! [X0] :
( ~ sQ27_spl
| app(app(sk7,cons(sk5,nil)),cons(sk5,nil)) = X0
| ~ ssList(X0)
| sk1 != app(X0,sk8) ),
inference(component_clause,[status(thm)],[f626]) ).
fof(f629,plain,
( ~ sQ7_spl
| ~ sQ2_spl
| ~ sQ11_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f618,f626,f531,f482,f501]) ).
fof(f646,plain,
( ~ sQ19_spl
| sk1 = app(sk7,app(cons(sk5,nil),app(cons(sk5,nil),sk8)))
| ~ ssList(sk7)
| ~ ssList(cons(sk5,nil))
| ~ ssList(app(cons(sk5,nil),sk8)) ),
inference(paramodulation,[status(thm)],[f579,f367]) ).
fof(f647,plain,
! [X0] :
( ~ sQ19_spl
| X0 = app(sk7,cons(sk5,nil))
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(app(cons(sk5,nil),sk8))
| ~ ssList(X0)
| app(X0,app(cons(sk5,nil),sk8)) != sk1 ),
inference(paramodulation,[status(thm)],[f579,f371]) ).
fof(f655,definition,
( sQ31_spl
<=> ssList(app(cons(sk5,nil),sk8)) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f657,plain,
( sQ31_spl
| ~ ssList(app(cons(sk5,nil),sk8)) ),
inference(component_clause,[status(thm)],[f655]) ).
fof(f658,definition,
( sQ32_spl
<=> sk1 = app(sk7,app(cons(sk5,nil),app(cons(sk5,nil),sk8))) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f659,plain,
( ~ sQ32_spl
| sk1 = app(sk7,app(cons(sk5,nil),app(cons(sk5,nil),sk8))) ),
inference(component_clause,[status(thm)],[f658]) ).
fof(f661,plain,
( ~ sQ19_spl
| sQ32_spl
| ~ sQ21_spl
| ~ sQ17_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f646,f655,f567,f587,f658,f578]) ).
fof(f662,definition,
! [X0] :
( sQ33_spl
<=> ( X0 = app(sk7,cons(sk5,nil))
| ~ ssList(X0)
| app(X0,app(cons(sk5,nil),sk8)) != sk1 ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f663,plain,
! [X0] :
( ~ sQ33_spl
| X0 = app(sk7,cons(sk5,nil))
| ~ ssList(X0)
| app(X0,app(cons(sk5,nil),sk8)) != sk1 ),
inference(component_clause,[status(thm)],[f662]) ).
fof(f665,plain,
( ~ sQ19_spl
| ~ sQ18_spl
| ~ sQ31_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f647,f662,f655,f570,f578]) ).
fof(f676,definition,
( sQ36_spl
<=> nil = app(cons(sk5,nil),sk8) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f677,plain,
( ~ sQ36_spl
| nil = app(cons(sk5,nil),sk8) ),
inference(component_clause,[status(thm)],[f676]) ).
fof(f685,plain,
( sQ31_spl
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk8) ),
inference(resolution,[status(thm)],[f657,f284]) ).
fof(f686,plain,
( sQ31_spl
| ~ sQ17_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f685,f482,f567,f655]) ).
fof(f737,plain,
! [X0] :
( ~ sQ32_spl
| X0 = app(cons(sk5,nil),app(cons(sk5,nil),sk8))
| ~ ssList(app(cons(sk5,nil),app(cons(sk5,nil),sk8)))
| ~ ssList(sk7)
| ~ ssList(X0)
| app(sk7,X0) != sk1 ),
inference(paramodulation,[status(thm)],[f659,f369]) ).
fof(f746,definition,
( sQ41_spl
<=> ssList(app(cons(sk5,nil),app(cons(sk5,nil),sk8))) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f748,plain,
( sQ41_spl
| ~ ssList(app(cons(sk5,nil),app(cons(sk5,nil),sk8))) ),
inference(component_clause,[status(thm)],[f746]) ).
fof(f751,definition,
! [X0] :
( sQ42_spl
<=> ( X0 = app(cons(sk5,nil),app(cons(sk5,nil),sk8))
| ~ ssList(X0)
| app(sk7,X0) != sk1 ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f752,plain,
! [X0] :
( ~ sQ42_spl
| X0 = app(cons(sk5,nil),app(cons(sk5,nil),sk8))
| ~ ssList(X0)
| app(sk7,X0) != sk1 ),
inference(component_clause,[status(thm)],[f751]) ).
fof(f754,plain,
( ~ sQ32_spl
| ~ sQ41_spl
| ~ sQ21_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f737,f751,f587,f746,f658]) ).
fof(f764,definition,
( sQ45_spl
<=> nil = sk7 ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f765,plain,
( ~ sQ45_spl
| nil = sk7 ),
inference(component_clause,[status(thm)],[f764]) ).
fof(f769,plain,
( sQ41_spl
| ~ ssList(cons(sk5,nil))
| ~ ssList(app(cons(sk5,nil),sk8)) ),
inference(resolution,[status(thm)],[f748,f284]) ).
fof(f770,plain,
( sQ41_spl
| ~ sQ17_spl
| ~ sQ31_spl ),
inference(split_clause,[status(thm)],[f769,f655,f567,f746]) ).
fof(f781,plain,
( ~ sQ27_spl
| nil = cons(sk5,nil)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(cons(sk5,nil))
| ~ ssList(nil)
| sk1 != app(nil,sk8) ),
inference(resolution,[status(thm)],[f627,f328]) ).
fof(f794,definition,
( sQ49_spl
<=> sk1 = app(nil,sk8) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f796,plain,
( sQ49_spl
| sk1 != app(nil,sk8) ),
inference(component_clause,[status(thm)],[f794]) ).
fof(f797,definition,
( sQ50_spl
<=> nil = cons(sk5,nil) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f798,plain,
( ~ sQ50_spl
| nil = cons(sk5,nil) ),
inference(component_clause,[status(thm)],[f797]) ).
fof(f800,plain,
( ~ sQ27_spl
| sQ50_spl
| ~ sQ18_spl
| ~ sQ17_spl
| ~ sQ12_spl
| ~ sQ49_spl ),
inference(split_clause,[status(thm)],[f781,f794,f538,f567,f570,f797,f626]) ).
fof(f1105,plain,
! [X0,X1] :
( ~ sQ1_spl
| hd(cons(X1,X0)) = X1
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f296,f446]) ).
fof(f1106,plain,
! [X0,X1] :
( ~ sQ1_spl
| tl(cons(X1,X0)) = X0
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f295,f446]) ).
fof(f1111,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| X3 = X1
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2)
| cons(X0,X1) != cons(X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f402,f446]) ).
fof(f1112,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| X0 = X2
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X2)
| cons(X0,X1) != cons(X2,X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f400,f446]) ).
fof(f1116,plain,
! [X0,X1] :
( ~ sQ1_spl
| ~ ssList(X1)
| cons(X0,X1) != nil ),
inference(backward_subsumption_resolution,[status(thm)],[f298,f446]) ).
fof(f1117,plain,
! [X0,X1] :
( ~ sQ1_spl
| ssList(cons(X1,X0))
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f285,f446]) ).
fof(f1122,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| X3 = X1
| ~ ssList(X1)
| ~ ssList(X3)
| cons(X0,X1) != cons(X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1111,f446]) ).
fof(f1123,plain,
! [X0,X1,X2,X3] :
( ~ sQ1_spl
| X0 = X2
| ~ ssList(X1)
| ~ ssList(X3)
| cons(X0,X1) != cons(X2,X3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1112,f446]) ).
fof(f1433,plain,
! [X0] :
( ~ sQ1_spl
| ~ memberP(nil,X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f269,f446]) ).
fof(f1639,plain,
( ~ sQ42_spl
| nil = cons(sk5,nil)
| ~ ssList(cons(sk5,nil))
| ~ ssList(app(cons(sk5,nil),sk8))
| ~ ssList(nil)
| app(sk7,nil) != sk1 ),
inference(resolution,[status(thm)],[f752,f326]) ).
fof(f1655,definition,
( sQ106_spl
<=> app(sk7,nil) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1657,plain,
( sQ106_spl
| app(sk7,nil) != sk1 ),
inference(component_clause,[status(thm)],[f1655]) ).
fof(f1658,plain,
( ~ sQ42_spl
| sQ50_spl
| ~ sQ17_spl
| ~ sQ31_spl
| ~ sQ12_spl
| ~ sQ106_spl ),
inference(split_clause,[status(thm)],[f1639,f1655,f538,f655,f567,f797,f751]) ).
fof(f1669,plain,
( ~ sQ42_spl
| ~ sQ33_spl
| ~ ssList(sk1)
| app(sk7,sk1) != sk1
| cons(sk5,nil) = app(sk7,cons(sk5,nil))
| ~ ssList(cons(sk5,nil)) ),
inference(resolution,[status(thm)],[f663,f752]) ).
fof(f1672,definition,
( sQ107_spl
<=> cons(sk5,nil) = app(sk7,cons(sk5,nil)) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1673,plain,
( ~ sQ107_spl
| cons(sk5,nil) = app(sk7,cons(sk5,nil)) ),
inference(component_clause,[status(thm)],[f1672]) ).
fof(f1675,definition,
( sQ108_spl
<=> app(sk7,sk1) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1677,plain,
( sQ108_spl
| app(sk7,sk1) != sk1 ),
inference(component_clause,[status(thm)],[f1675]) ).
fof(f1678,plain,
( ~ sQ42_spl
| ~ sQ33_spl
| ~ sQ4_spl
| ~ sQ108_spl
| sQ107_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1669,f567,f1672,f1675,f488,f662,f751]) ).
fof(f1690,plain,
( ~ sQ7_spl
| ~ sQ107_spl
| app(app(cons(sk5,nil),cons(sk5,nil)),sk8) = sk1 ),
inference(backward_demodulation,[status(thm)],[f1673,f520]) ).
fof(f1719,plain,
( ~ sQ7_spl
| ~ sQ107_spl
| sk1 = app(cons(sk5,nil),app(cons(sk5,nil),sk8))
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk8) ),
inference(paramodulation,[status(thm)],[f1690,f367]) ).
fof(f1728,definition,
( sQ112_spl
<=> sk1 = app(cons(sk5,nil),app(cons(sk5,nil),sk8)) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1729,plain,
( ~ sQ112_spl
| sk1 = app(cons(sk5,nil),app(cons(sk5,nil),sk8)) ),
inference(component_clause,[status(thm)],[f1728]) ).
fof(f1731,plain,
( ~ sQ7_spl
| ~ sQ107_spl
| sQ112_spl
| ~ sQ17_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1719,f482,f567,f1728,f1672,f501]) ).
fof(f1929,plain,
! [X0,X1] :
( ~ sQ1_spl
| X1 = nil
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(cons(X0,X1))
| ~ singletonP(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f302,f1122]) ).
fof(f1931,plain,
( ~ sQ1_spl
| ~ ssList(nil)
| ~ ssList(nil)
| ~ singletonP(nil) ),
inference(resolution,[status(thm)],[f302,f1116]) ).
fof(f1935,definition,
! [X0,X1] :
( sQ121_spl
<=> ( X1 = nil
| ~ ssList(X1)
| ~ ssList(cons(X0,X1))
| ~ singletonP(cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1936,plain,
! [X0,X1] :
( ~ sQ121_spl
| X1 = nil
| ~ ssList(X1)
| ~ ssList(cons(X0,X1))
| ~ singletonP(cons(X0,X1)) ),
inference(component_clause,[status(thm)],[f1935]) ).
fof(f1938,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f1929,f1935,f538,f445]) ).
fof(f1943,definition,
( sQ123_spl
<=> singletonP(nil) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1946,plain,
( ~ sQ1_spl
| ~ sQ12_spl
| ~ sQ123_spl ),
inference(split_clause,[status(thm)],[f1931,f1943,f538,f445]) ).
fof(f1950,plain,
! [X0,X1] :
( ~ sQ121_spl
| ~ sQ1_spl
| X1 = nil
| ~ ssList(X1)
| ~ singletonP(cons(X0,X1)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1936,f1117]) ).
fof(f1988,plain,
! [X0,X1] :
( ~ sQ1_spl
| skaf83(cons(X0,X1)) = X0
| ~ ssList(skaf82(cons(X0,X1)))
| ~ ssList(X1)
| nil = cons(X0,X1)
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f310,f1123]) ).
fof(f1993,plain,
! [X0,X1] :
( ~ sQ1_spl
| skaf83(cons(X0,X1)) = X0
| ~ ssList(skaf82(cons(X0,X1)))
| ~ ssList(X1)
| nil = cons(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1988,f1117]) ).
fof(f2013,plain,
! [X0,X1] :
( ~ sQ1_spl
| skaf83(cons(X1,X0)) = X1
| ~ ssList(skaf82(cons(X1,X0)))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1993,f1116]) ).
fof(f2014,plain,
! [X0,X1] :
( ~ sQ1_spl
| skaf83(cons(X1,X0)) = X1
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2013,f211]) ).
fof(f2037,plain,
( ~ sQ32_spl
| hd(sk1) = hd(sk7)
| nil = sk7
| ~ ssList(sk7)
| ~ ssList(app(cons(sk5,nil),app(cons(sk5,nil),sk8))) ),
inference(paramodulation,[status(thm)],[f659,f332]) ).
fof(f2041,definition,
( sQ127_spl
<=> hd(sk1) = hd(sk7) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f2042,plain,
( ~ sQ127_spl
| hd(sk1) = hd(sk7) ),
inference(component_clause,[status(thm)],[f2041]) ).
fof(f2044,plain,
( ~ sQ32_spl
| sQ127_spl
| sQ45_spl
| ~ sQ21_spl
| ~ sQ41_spl ),
inference(split_clause,[status(thm)],[f2037,f746,f587,f764,f2041,f658]) ).
fof(f2057,plain,
( ~ sQ127_spl
| nil = sk7
| cons(hd(sk1),tl(sk7)) = sk7
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f2042,f305]) ).
fof(f2058,definition,
( sQ131_spl
<=> cons(hd(sk1),tl(sk7)) = sk7 ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f2059,plain,
( ~ sQ131_spl
| cons(hd(sk1),tl(sk7)) = sk7 ),
inference(component_clause,[status(thm)],[f2058]) ).
fof(f2061,plain,
( ~ sQ127_spl
| sQ45_spl
| sQ131_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2057,f587,f2058,f764,f2041]) ).
fof(f2132,plain,
( ~ sQ131_spl
| ~ sQ1_spl
| skaf83(sk7) = hd(sk1)
| ~ ssList(tl(sk7)) ),
inference(paramodulation,[status(thm)],[f2059,f2014]) ).
fof(f2147,definition,
( sQ136_spl
<=> ssList(tl(sk7)) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f2149,plain,
( sQ136_spl
| ~ ssList(tl(sk7)) ),
inference(component_clause,[status(thm)],[f2147]) ).
fof(f2150,definition,
( sQ137_spl
<=> skaf83(sk7) = hd(sk1) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f2151,plain,
( ~ sQ137_spl
| skaf83(sk7) = hd(sk1) ),
inference(component_clause,[status(thm)],[f2150]) ).
fof(f2153,plain,
( ~ sQ131_spl
| ~ sQ1_spl
| sQ137_spl
| ~ sQ136_spl ),
inference(split_clause,[status(thm)],[f2132,f2147,f2150,f445,f2058]) ).
fof(f2154,definition,
( sQ138_spl
<=> tl(sk7) = skaf82(sk7) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f2155,plain,
( ~ sQ138_spl
| tl(sk7) = skaf82(sk7) ),
inference(component_clause,[status(thm)],[f2154]) ).
fof(f2201,plain,
( sQ136_spl
| nil = sk7
| ~ ssList(sk7) ),
inference(resolution,[status(thm)],[f2149,f274]) ).
fof(f2202,plain,
( sQ136_spl
| sQ45_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2201,f587,f764,f2147]) ).
fof(f2371,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| app(nil,sk8) = sk1 ),
inference(backward_demodulation,[status(thm)],[f550,f520]) ).
fof(f2385,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2371,f796]) ).
fof(f2386,plain,
( ~ sQ7_spl
| ~ sQ15_spl
| sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f2385]) ).
fof(f2493,plain,
( sQ108_spl
| ~ sQ45_spl
| app(nil,sk1) != sk1 ),
inference(forward_demodulation,[status(thm)],[f765,f1677]) ).
fof(f2547,plain,
( sQ108_spl
| ~ sQ45_spl
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f2493,f273]) ).
fof(f2548,plain,
( sQ108_spl
| ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2547,f429]) ).
fof(f2549,plain,
( sQ108_spl
| ~ sQ45_spl ),
inference(contradiction_clause,[status(thm)],[f2548]) ).
fof(f2791,plain,
! [X0] :
( ~ sQ32_spl
| frontsegP(sk1,X0)
| ~ ssList(sk7)
| ~ ssList(X0)
| ~ ssList(app(cons(sk5,nil),app(cons(sk5,nil),sk8)))
| ~ frontsegP(sk7,X0) ),
inference(paramodulation,[status(thm)],[f659,f350]) ).
fof(f2796,definition,
! [X0] :
( sQ198_spl
<=> ( frontsegP(sk1,X0)
| ~ ssList(X0)
| ~ frontsegP(sk7,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f2797,plain,
! [X0] :
( ~ sQ198_spl
| frontsegP(sk1,X0)
| ~ ssList(X0)
| ~ frontsegP(sk7,X0) ),
inference(component_clause,[status(thm)],[f2796]) ).
fof(f2799,plain,
( ~ sQ32_spl
| ~ sQ21_spl
| ~ sQ41_spl
| sQ198_spl ),
inference(split_clause,[status(thm)],[f2791,f2796,f746,f587,f658]) ).
fof(f2890,plain,
! [X0] :
( ~ sQ7_spl
| memberP(sk1,X0)
| ~ ssItem(X0)
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)))
| ~ ssList(sk8)
| ~ memberP(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)),X0) ),
inference(paramodulation,[status(thm)],[f520,f353]) ).
fof(f2900,definition,
! [X0] :
( sQ208_spl
<=> ( memberP(sk1,X0)
| ~ ssItem(X0)
| ~ memberP(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)),X0) ) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f2901,plain,
! [X0] :
( ~ sQ208_spl
| memberP(sk1,X0)
| ~ ssItem(X0)
| ~ memberP(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)),X0) ),
inference(component_clause,[status(thm)],[f2900]) ).
fof(f2903,plain,
( ~ sQ7_spl
| ~ sQ11_spl
| ~ sQ2_spl
| sQ208_spl ),
inference(split_clause,[status(thm)],[f2890,f2900,f482,f531,f501]) ).
fof(f3015,definition,
( sQ226_spl
<=> ssList(skaf82(sk7)) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f3017,plain,
( sQ226_spl
| ~ ssList(skaf82(sk7)) ),
inference(component_clause,[status(thm)],[f3015]) ).
fof(f3030,plain,
( sQ226_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3017,f211]) ).
fof(f3031,plain,
sQ226_spl,
inference(contradiction_clause,[status(thm)],[f3030]) ).
fof(f3055,plain,
( ~ sQ137_spl
| nil = sk1
| cons(skaf83(sk7),tl(sk1)) = sk1
| ~ ssList(sk1) ),
inference(paramodulation,[status(thm)],[f2151,f305]) ).
fof(f3064,definition,
( sQ234_spl
<=> cons(skaf83(sk7),tl(sk1)) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f3065,plain,
( ~ sQ234_spl
| cons(skaf83(sk7),tl(sk1)) = sk1 ),
inference(component_clause,[status(thm)],[f3064]) ).
fof(f3067,plain,
( ~ sQ137_spl
| sQ14_spl
| sQ234_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f3055,f488,f3064,f546,f2150]) ).
fof(f3077,plain,
( ~ sQ112_spl
| sk1 = cons(sk5,app(cons(sk5,nil),sk8))
| ~ ssList(app(cons(sk5,nil),sk8))
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f1729,f329]) ).
fof(f3093,definition,
( sQ235_spl
<=> sk1 = cons(sk5,app(cons(sk5,nil),sk8)) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f3094,plain,
( ~ sQ235_spl
| sk1 = cons(sk5,app(cons(sk5,nil),sk8)) ),
inference(component_clause,[status(thm)],[f3093]) ).
fof(f3096,plain,
( ~ sQ112_spl
| sQ235_spl
| ~ sQ31_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3077,f511,f655,f3093,f1728]) ).
fof(f3191,definition,
( sQ245_spl
<=> frontsegP(sk1,sk7) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f3192,plain,
( ~ sQ245_spl
| frontsegP(sk1,sk7) ),
inference(component_clause,[status(thm)],[f3191]) ).
fof(f3215,plain,
( ~ sQ245_spl
| sk1 = sk7
| ~ ssList(sk1)
| ~ ssList(sk7)
| ~ frontsegP(sk7,sk1) ),
inference(resolution,[status(thm)],[f3192,f340]) ).
fof(f3216,definition,
( sQ249_spl
<=> frontsegP(sk7,sk1) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f3219,definition,
( sQ250_spl
<=> sk1 = sk7 ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f3220,plain,
( ~ sQ250_spl
| sk1 = sk7 ),
inference(component_clause,[status(thm)],[f3219]) ).
fof(f3222,plain,
( ~ sQ245_spl
| sQ250_spl
| ~ sQ4_spl
| ~ sQ21_spl
| ~ sQ249_spl ),
inference(split_clause,[status(thm)],[f3215,f3216,f587,f488,f3219,f3191]) ).
fof(f3332,plain,
( sQ106_spl
| ~ sQ250_spl
| app(sk1,nil) != sk1 ),
inference(backward_demodulation,[status(thm)],[f3220,f1657]) ).
fof(f3432,plain,
( sQ106_spl
| ~ sQ250_spl
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f3332,f272]) ).
fof(f3433,plain,
( sQ106_spl
| ~ sQ250_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3432,f429]) ).
fof(f3434,plain,
( sQ106_spl
| ~ sQ250_spl ),
inference(contradiction_clause,[status(thm)],[f3433]) ).
fof(f3769,plain,
( ~ sQ50_spl
| singletonP(nil)
| ~ ssList(cons(sk5,nil))
| ~ ssItem(sk5) ),
inference(paramodulation,[status(thm)],[f798,f458]) ).
fof(f3796,plain,
( ~ sQ50_spl
| sQ123_spl
| ~ sQ17_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f3769,f511,f567,f1943,f797]) ).
fof(f3946,plain,
( ~ sQ36_spl
| nil = cons(sk5,nil)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk8) ),
inference(resolution,[status(thm)],[f677,f326]) ).
fof(f3966,plain,
( ~ sQ36_spl
| sQ50_spl
| ~ sQ17_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f3946,f482,f567,f797,f676]) ).
fof(f4752,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| X2 = X0
| memberP(X1,X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(backward_subsumption_resolution,[status(thm)],[f390,f446]) ).
fof(f4784,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| X2 = X0
| memberP(X1,X2)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f4752,f446]) ).
fof(f5241,plain,
! [X0,X1,X2,X3] :
( ~ sQ0_spl
| ~ ssList(app(app(X2,cons(X3,X1)),cons(X3,X0)))
| ~ ssItem(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f471,f443]) ).
fof(f5243,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ ssItem(sk5)
| ~ ssList(sk7)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f5241,f532]) ).
fof(f5246,plain,
( ~ sQ11_spl
| ~ sQ0_spl
| ~ sQ9_spl
| ~ sQ21_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f5243,f538,f587,f511,f442,f531]) ).
fof(f5266,plain,
( ~ sQ127_spl
| ~ sQ137_spl
| skaf83(sk7) = hd(sk7) ),
inference(backward_demodulation,[status(thm)],[f2151,f2042]) ).
fof(f5276,plain,
( ~ sQ208_spl
| ~ ssList(app(app(sk7,cons(sk5,nil)),cons(sk5,nil)))
| ~ ssItem(sk5)
| ~ ssList(app(sk7,cons(sk5,nil)))
| ~ ssList(nil)
| memberP(sk1,sk5)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f2901,f468]) ).
fof(f5277,definition,
( sQ439_spl
<=> memberP(sk1,sk5) ),
introduced(definition,[new_symbols(definition,[sQ439_spl])],[split_symbol_definition]) ).
fof(f5278,plain,
( ~ sQ439_spl
| memberP(sk1,sk5) ),
inference(component_clause,[status(thm)],[f5277]) ).
fof(f5280,plain,
( ~ sQ208_spl
| ~ sQ11_spl
| ~ sQ18_spl
| ~ sQ12_spl
| sQ439_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f5276,f511,f5277,f538,f570,f531,f2900]) ).
fof(f5319,plain,
! [X0,X1,X2] :
( ~ sQ1_spl
| frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f470,f446]) ).
fof(f5788,definition,
( sQ476_spl
<=> hd(sk1) = sk5 ),
introduced(definition,[new_symbols(definition,[sQ476_spl])],[split_symbol_definition]) ).
fof(f5789,plain,
( ~ sQ476_spl
| hd(sk1) = sk5 ),
inference(component_clause,[status(thm)],[f5788]) ).
fof(f5792,definition,
( sQ477_spl
<=> tl(sk1) = nil ),
introduced(definition,[new_symbols(definition,[sQ477_spl])],[split_symbol_definition]) ).
fof(f5793,plain,
( ~ sQ477_spl
| tl(sk1) = nil ),
inference(component_clause,[status(thm)],[f5792]) ).
fof(f5800,definition,
! [X0,X1] :
( sQ479_spl
<=> ( nil = X1
| ~ ssList(X1)
| cons(X0,X1) != sk1 ) ),
introduced(definition,[new_symbols(definition,[sQ479_spl])],[split_symbol_definition]) ).
fof(f5801,plain,
! [X0,X1] :
( ~ sQ479_spl
| nil = X1
| ~ ssList(X1)
| cons(X0,X1) != sk1 ),
inference(component_clause,[status(thm)],[f5800]) ).
fof(f5805,definition,
( sQ480_spl
<=> skaf83(sk1) = sk5 ),
introduced(definition,[new_symbols(definition,[sQ480_spl])],[split_symbol_definition]) ).
fof(f5806,plain,
( ~ sQ480_spl
| skaf83(sk1) = sk5 ),
inference(component_clause,[status(thm)],[f5805]) ).
fof(f5809,definition,
( sQ481_spl
<=> nil = skaf82(sk1) ),
introduced(definition,[new_symbols(definition,[sQ481_spl])],[split_symbol_definition]) ).
fof(f5810,plain,
( ~ sQ481_spl
| nil = skaf82(sk1) ),
inference(component_clause,[status(thm)],[f5809]) ).
fof(f5852,plain,
( ~ sQ476_spl
| ~ sQ137_spl
| skaf83(sk7) = sk5 ),
inference(forward_demodulation,[status(thm)],[f2151,f5789]) ).
fof(f5947,plain,
( ~ sQ137_spl
| ~ sQ476_spl
| sk5 = hd(sk1) ),
inference(backward_demodulation,[status(thm)],[f5852,f2151]) ).
fof(f5950,plain,
( ~ sQ476_spl
| ~ sQ137_spl
| nil = sk7
| cons(sk5,skaf82(sk7)) = sk7
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f5852,f310]) ).
fof(f5952,definition,
( sQ503_spl
<=> cons(sk5,skaf82(sk7)) = sk7 ),
introduced(definition,[new_symbols(definition,[sQ503_spl])],[split_symbol_definition]) ).
fof(f5953,plain,
( ~ sQ503_spl
| cons(sk5,skaf82(sk7)) = sk7 ),
inference(component_clause,[status(thm)],[f5952]) ).
fof(f5955,plain,
( ~ sQ476_spl
| ~ sQ137_spl
| sQ45_spl
| sQ503_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f5950,f587,f5952,f764,f2150,f5788]) ).
fof(f5958,plain,
( ~ sQ477_spl
| nil = sk1
| cons(hd(sk1),nil) = sk1
| ~ ssList(sk1) ),
inference(paramodulation,[status(thm)],[f5793,f305]) ).
fof(f5964,definition,
( sQ505_spl
<=> cons(hd(sk1),nil) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ505_spl])],[split_symbol_definition]) ).
fof(f5965,plain,
( ~ sQ505_spl
| cons(hd(sk1),nil) = sk1 ),
inference(component_clause,[status(thm)],[f5964]) ).
fof(f5967,plain,
( ~ sQ477_spl
| sQ14_spl
| sQ505_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5958,f488,f5964,f546,f5792]) ).
fof(f5969,plain,
( ~ sQ480_spl
| nil = sk1
| cons(sk5,skaf82(sk1)) = sk1
| ~ ssList(sk1) ),
inference(paramodulation,[status(thm)],[f5806,f310]) ).
fof(f5970,definition,
( sQ506_spl
<=> cons(sk5,skaf82(sk1)) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ506_spl])],[split_symbol_definition]) ).
fof(f5971,plain,
( ~ sQ506_spl
| cons(sk5,skaf82(sk1)) = sk1 ),
inference(component_clause,[status(thm)],[f5970]) ).
fof(f5973,plain,
( ~ sQ480_spl
| sQ14_spl
| sQ506_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5969,f488,f5970,f546,f5805]) ).
fof(f5974,plain,
( ~ sQ481_spl
| nil = sk1
| cons(skaf83(sk1),nil) = sk1
| ~ ssList(sk1) ),
inference(paramodulation,[status(thm)],[f5810,f310]) ).
fof(f5976,definition,
( sQ507_spl
<=> cons(skaf83(sk1),nil) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ507_spl])],[split_symbol_definition]) ).
fof(f5977,plain,
( ~ sQ507_spl
| cons(skaf83(sk1),nil) = sk1 ),
inference(component_clause,[status(thm)],[f5976]) ).
fof(f5979,plain,
( ~ sQ481_spl
| sQ14_spl
| sQ507_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5974,f488,f5976,f546,f5809]) ).
fof(f5983,plain,
( ~ sQ137_spl
| ~ sQ476_spl
| nil = sk1
| cons(sk5,tl(sk1)) = sk1
| ~ ssList(sk1) ),
inference(paramodulation,[status(thm)],[f5947,f305]) ).
fof(f5989,definition,
( sQ509_spl
<=> cons(sk5,tl(sk1)) = sk1 ),
introduced(definition,[new_symbols(definition,[sQ509_spl])],[split_symbol_definition]) ).
fof(f5990,plain,
( ~ sQ509_spl
| cons(sk5,tl(sk1)) = sk1 ),
inference(component_clause,[status(thm)],[f5989]) ).
fof(f5992,plain,
( ~ sQ137_spl
| ~ sQ476_spl
| sQ14_spl
| sQ509_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f5983,f488,f5989,f546,f5788,f2150]) ).
fof(f6126,plain,
( ~ sQ506_spl
| ~ sQ1_spl
| hd(sk1) = sk5
| ~ ssList(skaf82(sk1)) ),
inference(paramodulation,[status(thm)],[f5971,f1105]) ).
fof(f6143,definition,
( sQ510_spl
<=> ssList(skaf82(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ510_spl])],[split_symbol_definition]) ).
fof(f6145,plain,
( sQ510_spl
| ~ ssList(skaf82(sk1)) ),
inference(component_clause,[status(thm)],[f6143]) ).
fof(f6175,plain,
( ~ sQ506_spl
| ~ sQ1_spl
| sQ476_spl
| ~ sQ510_spl ),
inference(split_clause,[status(thm)],[f6126,f6143,f5788,f445,f5970]) ).
fof(f6222,plain,
( sQ510_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6145,f211]) ).
fof(f6223,plain,
sQ510_spl,
inference(contradiction_clause,[status(thm)],[f6222]) ).
fof(f6227,plain,
( ~ sQ505_spl
| ~ sQ137_spl
| cons(skaf83(sk7),nil) = sk1 ),
inference(forward_demodulation,[status(thm)],[f2151,f5965]) ).
fof(f6275,plain,
( ~ sQ127_spl
| ~ sQ137_spl
| ~ sQ476_spl
| sk5 = hd(sk7) ),
inference(forward_demodulation,[status(thm)],[f5852,f5266]) ).
fof(f6278,plain,
( ~ sQ127_spl
| ~ sQ137_spl
| ~ sQ476_spl
| nil = sk7
| cons(sk5,tl(sk7)) = sk7
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f6275,f305]) ).
fof(f6284,definition,
( sQ529_spl
<=> cons(sk5,tl(sk7)) = sk7 ),
introduced(definition,[new_symbols(definition,[sQ529_spl])],[split_symbol_definition]) ).
fof(f6285,plain,
( ~ sQ529_spl
| cons(sk5,tl(sk7)) = sk7 ),
inference(component_clause,[status(thm)],[f6284]) ).
fof(f6287,plain,
( ~ sQ127_spl
| ~ sQ137_spl
| ~ sQ476_spl
| sQ45_spl
| sQ529_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f6278,f587,f6284,f764,f5788,f2150,f2041]) ).
fof(f6307,definition,
( sQ530_spl
<=> ssList(tl(sk1)) ),
introduced(definition,[new_symbols(definition,[sQ530_spl])],[split_symbol_definition]) ).
fof(f6309,plain,
( sQ530_spl
| ~ ssList(tl(sk1)) ),
inference(component_clause,[status(thm)],[f6307]) ).
fof(f6314,definition,
( sQ532_spl
<=> singletonP(sk1) ),
introduced(definition,[new_symbols(definition,[sQ532_spl])],[split_symbol_definition]) ).
fof(f6316,plain,
( sQ532_spl
| ~ singletonP(sk1) ),
inference(component_clause,[status(thm)],[f6314]) ).
fof(f6507,plain,
( ~ sQ479_spl
| nil = sk1
| ~ ssList(sk1)
| nil = skaf82(sk1)
| ~ ssList(skaf82(sk1)) ),
inference(resolution,[status(thm)],[f5801,f310]) ).
fof(f6510,plain,
( ~ sQ479_spl
| sQ14_spl
| ~ sQ4_spl
| sQ481_spl
| ~ sQ510_spl ),
inference(split_clause,[status(thm)],[f6507,f6143,f5809,f488,f546,f5800]) ).
fof(f6513,plain,
( sQ530_spl
| nil = sk1
| ~ ssList(sk1) ),
inference(resolution,[status(thm)],[f6309,f274]) ).
fof(f6514,plain,
( sQ530_spl
| sQ14_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f6513,f488,f546,f6307]) ).
fof(f6531,plain,
( ~ sQ503_spl
| ~ sQ1_spl
| tl(sk7) = skaf82(sk7)
| ~ ssList(skaf82(sk7)) ),
inference(paramodulation,[status(thm)],[f5953,f1106]) ).
fof(f6583,plain,
( ~ sQ503_spl
| ~ sQ1_spl
| sQ138_spl
| ~ sQ226_spl ),
inference(split_clause,[status(thm)],[f6531,f3015,f2154,f445,f5952]) ).
fof(f6649,plain,
! [X0,X1] :
( ~ sQ505_spl
| ~ sQ137_spl
| ~ sQ1_spl
| nil = X1
| ~ ssList(X1)
| ~ ssList(nil)
| cons(X0,X1) != sk1 ),
inference(paramodulation,[status(thm)],[f6227,f1122]) ).
fof(f6699,plain,
( ~ sQ505_spl
| ~ sQ137_spl
| ~ sQ1_spl
| ~ sQ12_spl
| sQ479_spl ),
inference(split_clause,[status(thm)],[f6649,f5800,f538,f445,f2150,f5964]) ).
fof(f7071,plain,
( ~ sQ234_spl
| ~ sQ121_spl
| ~ sQ1_spl
| tl(sk1) = nil
| ~ ssList(tl(sk1))
| ~ singletonP(sk1) ),
inference(paramodulation,[status(thm)],[f3065,f1950]) ).
fof(f7100,plain,
( ~ sQ234_spl
| ~ sQ121_spl
| ~ sQ1_spl
| sQ477_spl
| ~ sQ530_spl
| ~ sQ532_spl ),
inference(split_clause,[status(thm)],[f7071,f6314,f6307,f5792,f445,f1935,f3064]) ).
fof(f7167,plain,
( sQ532_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6316,f479]) ).
fof(f7168,plain,
sQ532_spl,
inference(contradiction_clause,[status(thm)],[f7167]) ).
fof(f7343,plain,
( ~ sQ509_spl
| ~ sQ477_spl
| cons(sk5,nil) = sk1 ),
inference(forward_demodulation,[status(thm)],[f5793,f5990]) ).
fof(f7386,plain,
( ~ sQ25_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f439,f612]) ).
fof(f7431,plain,
~ sQ25_spl,
inference(contradiction_clause,[status(thm)],[f7386]) ).
fof(f7957,plain,
! [X0] :
( ~ sQ507_spl
| ~ sQ1_spl
| X0 = skaf83(sk1)
| memberP(nil,X0)
| ~ ssList(nil)
| ~ memberP(sk1,X0) ),
inference(paramodulation,[status(thm)],[f5977,f4784]) ).
fof(f7962,definition,
! [X0] :
( sQ682_spl
<=> ( X0 = skaf83(sk1)
| memberP(nil,X0)
| ~ memberP(sk1,X0) ) ),
introduced(definition,[new_symbols(definition,[sQ682_spl])],[split_symbol_definition]) ).
fof(f7963,plain,
! [X0] :
( ~ sQ682_spl
| X0 = skaf83(sk1)
| memberP(nil,X0)
| ~ memberP(sk1,X0) ),
inference(component_clause,[status(thm)],[f7962]) ).
fof(f7965,plain,
( ~ sQ507_spl
| ~ sQ1_spl
| ~ sQ12_spl
| sQ682_spl ),
inference(split_clause,[status(thm)],[f7957,f7962,f538,f445,f5976]) ).
fof(f7966,plain,
! [X0] :
( ~ sQ682_spl
| ~ sQ1_spl
| X0 = skaf83(sk1)
| ~ memberP(sk1,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f7963,f1433]) ).
fof(f7984,plain,
( ~ sQ439_spl
| ~ sQ682_spl
| ~ sQ1_spl
| sk5 = skaf83(sk1) ),
inference(resolution,[status(thm)],[f7966,f5278]) ).
fof(f7985,plain,
( ~ sQ439_spl
| ~ sQ682_spl
| ~ sQ1_spl
| sQ480_spl ),
inference(split_clause,[status(thm)],[f7984,f5805,f445,f7962,f5277]) ).
fof(f7987,plain,
( ~ sQ529_spl
| ~ sQ138_spl
| cons(sk5,skaf82(sk7)) = sk7 ),
inference(forward_demodulation,[status(thm)],[f2155,f6285]) ).
fof(f8478,plain,
( ~ sQ198_spl
| ~ ssList(sk7)
| frontsegP(sk1,sk7)
| ~ ssList(sk7) ),
inference(resolution,[status(thm)],[f2797,f259]) ).
fof(f8480,plain,
( ~ sQ198_spl
| sQ245_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f8478,f587,f3191,f2796]) ).
fof(f8690,plain,
! [X0] :
( ~ sQ509_spl
| ~ sQ477_spl
| ~ sQ1_spl
| frontsegP(cons(sk5,X0),sk1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(paramodulation,[status(thm)],[f7343,f5319]) ).
fof(f8703,definition,
! [X0] :
( sQ717_spl
<=> ( frontsegP(cons(sk5,X0),sk1)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ717_spl])],[split_symbol_definition]) ).
fof(f8704,plain,
! [X0] :
( ~ sQ717_spl
| frontsegP(cons(sk5,X0),sk1)
| ~ ssList(X0)
| ~ frontsegP(X0,nil) ),
inference(component_clause,[status(thm)],[f8703]) ).
fof(f8706,plain,
( ~ sQ509_spl
| ~ sQ477_spl
| ~ sQ1_spl
| ~ sQ12_spl
| sQ717_spl ),
inference(split_clause,[status(thm)],[f8690,f8703,f538,f445,f5792,f5989]) ).
fof(f8707,plain,
! [X0] :
( ~ sQ717_spl
| frontsegP(cons(sk5,X0),sk1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f8704,f258]) ).
fof(f8708,plain,
( ~ sQ529_spl
| ~ sQ138_spl
| ~ sQ717_spl
| frontsegP(sk7,sk1)
| ~ ssList(skaf82(sk7)) ),
inference(paramodulation,[status(thm)],[f7987,f8707]) ).
fof(f8710,plain,
( ~ sQ529_spl
| ~ sQ138_spl
| ~ sQ717_spl
| sQ249_spl
| ~ sQ226_spl ),
inference(split_clause,[status(thm)],[f8708,f3015,f3216,f8703,f2154,f6284]) ).
fof(f10484,plain,
( ~ sQ235_spl
| ~ sQ121_spl
| ~ sQ1_spl
| app(cons(sk5,nil),sk8) = nil
| ~ ssList(app(cons(sk5,nil),sk8))
| ~ singletonP(sk1) ),
inference(paramodulation,[status(thm)],[f3094,f1950]) ).
fof(f10586,plain,
( ~ sQ235_spl
| ~ sQ121_spl
| ~ sQ1_spl
| sQ36_spl
| ~ sQ31_spl
| ~ sQ532_spl ),
inference(split_clause,[status(thm)],[f10484,f6314,f655,f676,f445,f1935,f3093]) ).
fof(f10624,plain,
$false,
inference(sat_refutation,[status(thm)],[f448,f514,f516,f518,f534,f552,f554,f556,f573,f575,f581,f590,f592,f629,f661,f665,f686,f754,f770,f800,f1658,f1678,f1731,f1938,f1946,f2044,f2061,f2153,f2202,f2386,f2549,f2799,f2903,f3031,f3067,f3096,f3222,f3434,f3796,f3966,f5246,f5280,f5955,f5967,f5973,f5979,f5992,f6175,f6223,f6287,f6510,f6514,f6583,f6699,f7100,f7168,f7431,f7965,f7985,f8480,f8706,f8710,f10586]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC166-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/5.37 % Computer : n012.cluster.edu
% 0.08/5.37 % Model : x86_64 x86_64
% 0.08/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.37 % Memory : 8046.5625MB
% 0.08/5.37 % OS : Linux 6.8.0-71-generic
% 0.08/5.37 % CPULimit : 300
% 0.08/5.37 % WCLimit : 300
% 0.08/5.37 % DateTime : Mon Sep 21 08:01:37 UTC 2026
% 0.08/5.37 % CPUTime :
% 0.08/5.38 % Drodi V4.1.1
% 9.42/6.67 % Refutation found
% 9.42/6.67 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 9.42/6.67 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.45/6.72 % Elapsed time: 1.334098 seconds
% 1.45/6.72 % CPU time: 10.241536 seconds
% 1.45/6.72 % Total memory used: 223.214 MB
% 1.45/6.72 % Net memory used: 213.577 MB
%------------------------------------------------------------------------------