%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC169+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 02:40:14 PM UTC 2026
% Result : Theorem 85.07s 11.28s
% Output : CNFRefutation 85.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 518
% Syntax : Number of formulae : 1973 ( 21 unt; 454 def)
% Number of atoms : 9412 ( 936 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 13875 (6436 ~;6525 |; 238 &)
% ( 494 <=>; 182 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 7 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 473 ( 471 usr; 454 prp; 0-3 aty)
% Number of functors : 57 ( 57 usr; 10 con; 0-2 aty)
% Number of variables : 2040 (1954 !; 86 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( memberP(U,V)
<=> ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U] :
( ssList(U)
=> ( cyclefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ~ ( leq(W,V)
& leq(V,W) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [U] :
( ssList(U)
=> ( totalorderP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ( leq(W,V)
| leq(V,W) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [U] :
( ssList(U)
=> ( strictorderP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ( lt(W,V)
| lt(V,W) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [U] :
( ssList(U)
=> ( totalorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> leq(V,W) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [U] :
( ssList(U)
=> ( strictorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> lt(V,W) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [U] :
( ssList(U)
=> ( duplicatefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> V != W ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [U] :
( ssList(U)
=> ( equalelemsP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ( app(X,cons(V,cons(W,Y))) = U
=> V = W ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssItem(X)
=> ( cons(W,U) = cons(X,V)
=> ( V = U
& W = X ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [U] :
( ssList(U)
=> ( ? [V] :
( ? [W] :
( cons(W,V) = U
& ssItem(W) )
& ssList(V) )
| nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> hd(cons(V,U)) = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssList(tl(U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> tl(cons(V,U)) = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> cons(W,app(V,U)) = app(cons(W,V),U) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( frontsegP(V,W)
& frontsegP(U,V) )
=> frontsegP(U,W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( frontsegP(V,U)
& frontsegP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( frontsegP(U,V)
=> frontsegP(app(U,W),V) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( frontsegP(cons(U,W),cons(V,X))
<=> ( frontsegP(W,X)
& U = V ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [U] :
( ssList(U)
=> ( frontsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( rearsegP(V,W)
& rearsegP(U,V) )
=> rearsegP(U,W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( rearsegP(V,U)
& rearsegP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( rearsegP(U,V)
=> rearsegP(app(W,U),V) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [U] :
( ssList(U)
=> ( rearsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( segmentP(V,W)
& segmentP(U,V) )
=> segmentP(U,W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( segmentP(V,U)
& segmentP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( segmentP(U,V)
=> segmentP(app(app(W,U),X),V) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [U] :
( ssItem(U)
=> cyclefreeP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [U] :
( ssItem(U)
=> totalorderP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f63,axiom,
! [U] :
( ssItem(U)
=> strictorderP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [U] :
( ssItem(U)
=> strictorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f71,axiom,
! [U] :
( ssItem(U)
=> duplicatefreeP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( ssItem(U)
=> equalelemsP(cons(U,nil)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f77,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( tl(V) = tl(U)
& hd(V) = hd(U)
& nil != U
& nil != V )
=> V = U ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> cons(hd(U),tl(U)) = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f79,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(W,V) = app(U,V)
=> W = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(V,W) = app(V,U)
=> W = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) = app(cons(V,nil),U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f82,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> app(app(U,V),W) = app(U,app(V,W)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil != U
=> hd(app(U,V)) = hd(U) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil != U
=> tl(app(U,V)) = app(tl(U),V) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( nil != W
| nil != X )
& ! [X3] :
( ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( neq(Y,Z)
| app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) != U
| ~ ssList(X2) ) ) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( nil != W
| nil != X )
& ! [X3] :
( ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( neq(Y,Z)
| app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) != U
| ~ ssList(X2) ) ) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f99,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f98]) ).
fof(f101,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f106,plain,
! [U] :
( ! [V] :
( ( memberP(U,V)
<=> ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f107,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(W,cons(V,X)) != U
| ~ ssList(X) )
| ~ ssList(W) )
| memberP(U,V) )
& ( ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) )
| ~ memberP(U,V) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(W,cons(V,X)) != U
| ~ ssList(X) )
| ~ ssList(W) )
| memberP(U,V) )
& ( ( app(sK2_skl(V,U),cons(V,sK3_skl(V,U))) = U
& ssList(sK3_skl(V,U))
& ssList(sK2_skl(V,U)) )
| ~ memberP(U,V) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(W,sK2_skl(V,U)),skolemize(X,sK3_skl(V,U))],[f107]) ).
fof(f111,plain,
! [X0,X1] :
( app(sK2_skl(X1,X0),cons(X1,sK3_skl(X1,X0))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f113,plain,
! [U] :
( ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f114,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [V] :
( cons(V,nil) = U
& ssItem(V) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ( cons(sK4_skl(U),nil) = U
& ssItem(sK4_skl(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114]) ).
fof(f116,plain,
! [X0] :
( ssItem(sK4_skl(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0] :
( cons(sK4_skl(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f118,plain,
! [X0,X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f119,plain,
! [U] :
( ! [V] :
( ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f120,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ? [W] :
( app(V,W) = U
& ssList(W) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ( app(V,sK5_skl(V,U)) = U
& ssList(sK5_skl(V,U)) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( ssList(sK5_skl(X1,X0))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( app(X1,sK5_skl(X1,X0)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f124,plain,
! [X0,X1,X2] :
( app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f125,plain,
! [U] :
( ! [V] :
( ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f126,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ? [W] :
( app(W,V) = U
& ssList(W) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ( app(sK6_skl(V,U),V) = U
& ssList(sK6_skl(V,U)) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ssList(sK6_skl(X1,X0))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( app(sK6_skl(X1,X0),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f130,plain,
! [X0,X1,X2] :
( app(X2,X1) != X0
| ~ ssList(X2)
| rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f131,plain,
! [U] :
( ! [V] :
( ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f132,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ( app(app(sK7_skl(V,U),V),sK8_skl(V,U)) = U
& ssList(sK8_skl(V,U))
& ssList(sK7_skl(V,U)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132]) ).
fof(f136,plain,
! [X0,X1] :
( app(app(sK7_skl(X1,X0),X1),sK8_skl(X1,X0)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f138,plain,
! [U] :
( ( cyclefreeP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f139,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( leq(W,V)
& leq(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| cyclefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ cyclefreeP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
! [U] :
( ( ( ( leq(sK10_skl(U),sK9_skl(U))
& leq(sK9_skl(U),sK10_skl(U))
& app(app(sK11_skl(U),cons(sK9_skl(U),sK12_skl(U))),cons(sK10_skl(U),sK13_skl(U))) = U
& ssList(sK13_skl(U))
& ssList(sK12_skl(U))
& ssList(sK11_skl(U))
& ssItem(sK10_skl(U))
& ssItem(sK9_skl(U)) )
| cyclefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ cyclefreeP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl,sK12_skl,sK13_skl]),skolemize(V,sK9_skl(U)),skolemize(W,sK10_skl(U)),skolemize(X,sK11_skl(U)),skolemize(Y,sK12_skl(U)),skolemize(Z,sK13_skl(U))],[f139]) ).
fof(f141,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ cyclefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f150,plain,
! [U] :
( ( totalorderP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(W,V)
| leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f151,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ leq(W,V)
& ~ leq(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| totalorderP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(W,V)
| leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f150]) ).
fof(f152,plain,
! [U] :
( ( ( ( ~ leq(sK15_skl(U),sK14_skl(U))
& ~ leq(sK14_skl(U),sK15_skl(U))
& app(app(sK16_skl(U),cons(sK14_skl(U),sK17_skl(U))),cons(sK15_skl(U),sK18_skl(U))) = U
& ssList(sK18_skl(U))
& ssList(sK17_skl(U))
& ssList(sK16_skl(U))
& ssItem(sK15_skl(U))
& ssItem(sK14_skl(U)) )
| totalorderP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(W,V)
| leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl,sK17_skl,sK18_skl]),skolemize(V,sK14_skl(U)),skolemize(W,sK15_skl(U)),skolemize(X,sK16_skl(U)),skolemize(Y,sK17_skl(U)),skolemize(Z,sK18_skl(U))],[f151]) ).
fof(f153,plain,
! [X0,X1,X2,X3,X4,X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ totalorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f162,plain,
! [U] :
( ( strictorderP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(W,V)
| lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f163,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ lt(W,V)
& ~ lt(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| strictorderP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(W,V)
| lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ strictorderP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f162]) ).
fof(f164,plain,
! [U] :
( ( ( ( ~ lt(sK20_skl(U),sK19_skl(U))
& ~ lt(sK19_skl(U),sK20_skl(U))
& app(app(sK21_skl(U),cons(sK19_skl(U),sK22_skl(U))),cons(sK20_skl(U),sK23_skl(U))) = U
& ssList(sK23_skl(U))
& ssList(sK22_skl(U))
& ssList(sK21_skl(U))
& ssItem(sK20_skl(U))
& ssItem(sK19_skl(U)) )
| strictorderP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(W,V)
| lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ strictorderP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl,sK21_skl,sK22_skl,sK23_skl]),skolemize(V,sK19_skl(U)),skolemize(W,sK20_skl(U)),skolemize(X,sK21_skl(U)),skolemize(Y,sK22_skl(U)),skolemize(Z,sK23_skl(U))],[f163]) ).
fof(f165,plain,
! [X0,X1,X2,X3,X4,X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ strictorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f174,plain,
! [U] :
( ( totalorderedP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f175,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ leq(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| totalorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderedP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f174]) ).
fof(f176,plain,
! [U] :
( ( ( ( ~ leq(sK24_skl(U),sK25_skl(U))
& app(app(sK26_skl(U),cons(sK24_skl(U),sK27_skl(U))),cons(sK25_skl(U),sK28_skl(U))) = U
& ssList(sK28_skl(U))
& ssList(sK27_skl(U))
& ssList(sK26_skl(U))
& ssItem(sK25_skl(U))
& ssItem(sK24_skl(U)) )
| totalorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderedP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl,sK25_skl,sK26_skl,sK27_skl,sK28_skl]),skolemize(V,sK24_skl(U)),skolemize(W,sK25_skl(U)),skolemize(X,sK26_skl(U)),skolemize(Y,sK27_skl(U)),skolemize(Z,sK28_skl(U))],[f175]) ).
fof(f177,plain,
! [X0,X1,X2,X3,X4,X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f185,plain,
! [U] :
( ( strictorderedP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f186,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ lt(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| strictorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ strictorderedP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
! [U] :
( ( ( ( ~ lt(sK29_skl(U),sK30_skl(U))
& app(app(sK31_skl(U),cons(sK29_skl(U),sK32_skl(U))),cons(sK30_skl(U),sK33_skl(U))) = U
& ssList(sK33_skl(U))
& ssList(sK32_skl(U))
& ssList(sK31_skl(U))
& ssItem(sK30_skl(U))
& ssItem(sK29_skl(U)) )
| strictorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ strictorderedP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29_skl,sK30_skl,sK31_skl,sK32_skl,sK33_skl]),skolemize(V,sK29_skl(U)),skolemize(W,sK30_skl(U)),skolemize(X,sK31_skl(U)),skolemize(Y,sK32_skl(U)),skolemize(Z,sK33_skl(U))],[f186]) ).
fof(f188,plain,
! [X0,X1,X2,X3,X4,X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ strictorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f196,plain,
! [U] :
( ( duplicatefreeP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( V != W
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f197,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( V = W
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| duplicatefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( V != W
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ duplicatefreeP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f196]) ).
fof(f198,plain,
! [U] :
( ( ( ( sK34_skl(U) = sK35_skl(U)
& app(app(sK36_skl(U),cons(sK34_skl(U),sK37_skl(U))),cons(sK35_skl(U),sK38_skl(U))) = U
& ssList(sK38_skl(U))
& ssList(sK37_skl(U))
& ssList(sK36_skl(U))
& ssItem(sK35_skl(U))
& ssItem(sK34_skl(U)) )
| duplicatefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( V != W
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ duplicatefreeP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34_skl,sK35_skl,sK36_skl,sK37_skl,sK38_skl]),skolemize(V,sK34_skl(U)),skolemize(W,sK35_skl(U)),skolemize(X,sK36_skl(U)),skolemize(Y,sK37_skl(U)),skolemize(Z,sK38_skl(U))],[f197]) ).
fof(f199,plain,
! [X0,X1,X2,X3,X4,X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f207,plain,
! [U] :
( ( equalelemsP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( V = W
| app(X,cons(V,cons(W,Y))) != U
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f208,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( V != W
& app(X,cons(V,cons(W,Y))) = U
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| equalelemsP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( V = W
| app(X,cons(V,cons(W,Y))) != U
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ equalelemsP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f207]) ).
fof(f209,plain,
! [U] :
( ( ( ( sK39_skl(U) != sK40_skl(U)
& app(sK41_skl(U),cons(sK39_skl(U),cons(sK40_skl(U),sK42_skl(U)))) = U
& ssList(sK42_skl(U))
& ssList(sK41_skl(U))
& ssItem(sK40_skl(U))
& ssItem(sK39_skl(U)) )
| equalelemsP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( V = W
| app(X,cons(V,cons(W,Y))) != U
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ equalelemsP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39_skl,sK40_skl,sK41_skl,sK42_skl]),skolemize(V,sK39_skl(U)),skolemize(W,sK40_skl(U)),skolemize(X,sK41_skl(U)),skolemize(Y,sK42_skl(U))],[f208]) ).
fof(f210,plain,
! [X0,X1,X2,X3,X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ equalelemsP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f221,plain,
! [U] :
( ! [V] :
( ssList(cons(V,U))
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f222,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f224,plain,
! [U] :
( ! [V] :
( cons(V,U) != U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f225,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f226,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( V = U
& W = X )
| cons(W,U) != cons(X,V)
| ~ ssItem(X) )
| ~ ssItem(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f227,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f228,plain,
! [X0,X1,X2,X3] :
( X1 = X0
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f229,plain,
! [U] :
( ? [V] :
( ? [W] :
( cons(W,V) = U
& ssItem(W) )
& ssList(V) )
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f230,plain,
! [U] :
( ( cons(sK44_skl(U),sK43_skl(U)) = U
& ssItem(sK44_skl(U))
& ssList(sK43_skl(U)) )
| nil = U
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl,sK44_skl]),skolemize(V,sK43_skl(U)),skolemize(W,sK44_skl(U))],[f229]) ).
fof(f231,plain,
! [X0] :
( ssList(sK43_skl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f232,plain,
! [X0] :
( ssItem(sK44_skl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f233,plain,
! [X0] :
( cons(sK44_skl(X0),sK43_skl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f234,plain,
! [U] :
( ! [V] :
( nil != cons(V,U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f235,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f238,plain,
! [U] :
( ! [V] :
( hd(cons(V,U)) = V
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f239,plain,
! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f240,plain,
! [U] :
( ssList(tl(U))
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f241,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f240]) ).
fof(f242,plain,
! [U] :
( ! [V] :
( tl(cons(V,U)) = U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f243,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f242]) ).
fof(f244,plain,
! [U] :
( ! [V] :
( ssList(app(U,V))
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f246,plain,
! [U] :
( ! [V] :
( ! [W] :
( cons(W,app(V,U)) = app(cons(W,V),U)
| ~ ssItem(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f247,plain,
! [X0,X1,X2] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f246]) ).
fof(f248,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f249,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f268,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f269,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& ~ memberP(V,U) )
| memberP(app(V,W),U) )
& ( memberP(W,U)
| memberP(V,U)
| ~ memberP(app(V,W),U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f268]) ).
fof(f270,plain,
! [X0,X1,X2] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f271,plain,
! [X0,X1,X2] :
( ~ memberP(X1,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f272,plain,
! [X0,X1,X2] :
( ~ memberP(X2,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f273,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f274,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& U != V )
| memberP(cons(V,W),U) )
& ( memberP(W,U)
| U = V
| ~ memberP(cons(V,W),U) ) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f273]) ).
fof(f275,plain,
! [X0,X1,X2] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f278,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f279,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f281,plain,
! [U] :
( ! [V] :
( ! [W] :
( frontsegP(U,W)
| ~ frontsegP(V,W)
| ~ frontsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f282,plain,
! [X0,X1,X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f283,plain,
! [U] :
( ! [V] :
( U = V
| ~ frontsegP(V,U)
| ~ frontsegP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f284,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(f285,plain,
! [U] :
( frontsegP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f286,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f285]) ).
fof(f287,plain,
! [U] :
( ! [V] :
( ! [W] :
( frontsegP(app(U,W),V)
| ~ frontsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f288,plain,
! [X0,X1,X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f287]) ).
fof(f289,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( frontsegP(cons(U,W),cons(V,X))
<=> ( frontsegP(W,X)
& U = V ) )
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f290,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( ( ~ frontsegP(W,X)
| U != V
| frontsegP(cons(U,W),cons(V,X)) )
& ( ( frontsegP(W,X)
& U = V )
| ~ frontsegP(cons(U,W),cons(V,X)) ) )
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f289]) ).
fof(f291,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f292,plain,
! [X0,X1,X2,X3] :
( frontsegP(X2,X3)
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f293,plain,
! [X0,X1,X2,X3] :
( ~ frontsegP(X2,X3)
| X0 != X1
| frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f294,plain,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f295,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f294]) ).
fof(f296,plain,
! [U] :
( ( frontsegP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f297,plain,
! [U] :
( ( ( nil != U
| frontsegP(nil,U) )
& ( nil = U
| ~ frontsegP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f296]) ).
fof(f298,plain,
! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f300,plain,
! [U] :
( ! [V] :
( ! [W] :
( rearsegP(U,W)
| ~ rearsegP(V,W)
| ~ rearsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f301,plain,
! [X0,X1,X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f300]) ).
fof(f302,plain,
! [U] :
( ! [V] :
( U = V
| ~ rearsegP(V,U)
| ~ rearsegP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f48]) ).
fof(f303,plain,
! [X0,X1] :
( X0 = X1
| ~ rearsegP(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f302]) ).
fof(f304,plain,
! [U] :
( rearsegP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f305,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f304]) ).
fof(f306,plain,
! [U] :
( ! [V] :
( ! [W] :
( rearsegP(app(W,U),V)
| ~ rearsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f307,plain,
! [X0,X1,X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f306]) ).
fof(f308,plain,
! [U] :
( rearsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f309,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f310,plain,
! [U] :
( ( rearsegP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f311,plain,
! [U] :
( ( ( nil != U
| rearsegP(nil,U) )
& ( nil = U
| ~ rearsegP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f310]) ).
fof(f312,plain,
! [X0] :
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f311]) ).
fof(f314,plain,
! [U] :
( ! [V] :
( ! [W] :
( segmentP(U,W)
| ~ segmentP(V,W)
| ~ segmentP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f315,plain,
! [X0,X1,X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
fof(f316,plain,
! [U] :
( ! [V] :
( U = V
| ~ segmentP(V,U)
| ~ segmentP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f317,plain,
! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f316]) ).
fof(f320,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( segmentP(app(app(W,U),X),V)
| ~ segmentP(U,V)
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f321,plain,
! [X0,X1,X2,X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f322,plain,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f323,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f324,plain,
! [U] :
( ( segmentP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f325,plain,
! [U] :
( ( ( nil != U
| segmentP(nil,U) )
& ( nil = U
| ~ segmentP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f324]) ).
fof(f326,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f328,plain,
! [U] :
( cyclefreeP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f59]) ).
fof(f329,plain,
! [X0] :
( cyclefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f328]) ).
fof(f331,plain,
! [U] :
( totalorderP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f61]) ).
fof(f332,plain,
! [X0] :
( totalorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f331]) ).
fof(f334,plain,
! [U] :
( strictorderP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f63]) ).
fof(f335,plain,
! [X0] :
( strictorderP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f334]) ).
fof(f337,plain,
! [U] :
( totalorderedP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f65]) ).
fof(f338,plain,
! [X0] :
( totalorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f337]) ).
fof(f347,plain,
! [U] :
( strictorderedP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f68]) ).
fof(f348,plain,
! [X0] :
( strictorderedP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f347]) ).
fof(f357,plain,
! [U] :
( duplicatefreeP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f71]) ).
fof(f358,plain,
! [X0] :
( duplicatefreeP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f357]) ).
fof(f360,plain,
! [U] :
( equalelemsP(cons(U,nil))
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f73]) ).
fof(f361,plain,
! [X0] :
( equalelemsP(cons(X0,nil))
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f360]) ).
fof(f371,plain,
! [U] :
( ! [V] :
( V = U
| tl(V) != tl(U)
| hd(V) != hd(U)
| nil = U
| nil = V
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f77]) ).
fof(f372,plain,
! [X0,X1] :
( X1 = X0
| tl(X1) != tl(X0)
| hd(X1) != hd(X0)
| nil = X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f371]) ).
fof(f373,plain,
! [U] :
( cons(hd(U),tl(U)) = U
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f78]) ).
fof(f374,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f373]) ).
fof(f375,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(W,V) != app(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f79]) ).
fof(f376,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f375]) ).
fof(f377,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(V,W) != app(V,U)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f80]) ).
fof(f378,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f377]) ).
fof(f379,plain,
! [U] :
( ! [V] :
( cons(V,U) = app(cons(V,nil),U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f81]) ).
fof(f380,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f381,plain,
! [U] :
( ! [V] :
( ! [W] :
( app(app(U,V),W) = app(U,app(V,W))
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f382,plain,
! [X0,X1,X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f381]) ).
fof(f383,plain,
! [U] :
( ! [V] :
( ( nil = app(U,V)
<=> ( nil = U
& nil = V ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f384,plain,
! [U] :
( ! [V] :
( ( ( nil != U
| nil != V
| nil = app(U,V) )
& ( ( nil = U
& nil = V )
| nil != app(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f383]) ).
fof(f385,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f386,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f388,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f389,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f390,plain,
! [U] :
( ! [V] :
( hd(app(U,V)) = hd(U)
| nil = U
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f85]) ).
fof(f391,plain,
! [X0,X1] :
( hd(app(X0,X1)) = hd(X0)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f390]) ).
fof(f392,plain,
! [U] :
( ! [V] :
( tl(app(U,V)) = app(tl(U),V)
| nil = U
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f86]) ).
fof(f393,plain,
! [X0,X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X3] :
( memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) ) )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ~ neq(Y,Z)
& app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) = U
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [W,X,X3] :
( sP0_prd(X3,X,W)
<=> ( memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X3] : sP0_prd(X3,X,W) )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ~ neq(Y,Z)
& app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) = U
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X3] : sP0_prd(X3,X,W) )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ~ neq(Y,Z)
& ? [X2] :
( app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) = U
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
& ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f417]) ).
fof(f419,plain,
( ( ( nil = sK49_skl
& nil = sK50_skl )
| sP0_prd(sK55_skl,sK50_skl,sK49_skl) )
& ~ neq(sK51_skl,sK52_skl)
& app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),sK54_skl) = sK47_skl
& ssList(sK54_skl)
& ssList(sK53_skl)
& ssItem(sK52_skl)
& ssItem(sK51_skl)
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl,sK52_skl,sK53_skl,sK54_skl,sK55_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl),skolemize(X1,sK53_skl),skolemize(X2,sK54_skl),skolemize(X3,sK55_skl)],[f418]) ).
fof(f422,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f425,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f426,plain,
ssItem(sK51_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f427,plain,
ssItem(sK52_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f428,plain,
ssList(sK53_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f429,plain,
ssList(sK54_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f430,plain,
app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),sK54_skl) = sK47_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f431,plain,
~ neq(sK51_skl,sK52_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f433,plain,
( nil = sK49_skl
| sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f434,plain,
! [W,X,X3] :
( ( ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ( ( memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) )
| ~ sP0_prd(X3,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f435,plain,
( ! [W,X,X3] :
( ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ! [W,X,X3] :
( ( memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) )
| ~ sP0_prd(X3,X,W) ) ),
inference(miniscoping,[status(thm)],[f434]) ).
fof(f436,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f437,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f438,plain,
! [X0,X1,X2] :
( memberP(X1,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f439,plain,
! [X0,X1,X2] :
( ~ memberP(X1,X0)
| cons(X0,nil) != X2
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f435]) ).
fof(f440,definition,
( sQ0_spl
<=> sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( ~ sQ0_spl
| sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( ~ sQ1_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f447,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f448,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f449,plain,
( sQ2_spl
| nil != sK49_skl ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f433,f440,f447]) ).
fof(f453,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| memberP(app(X0,cons(X1,X2)),X1)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(destructive_equality_resolution,[status(thm)],[f112]) ).
fof(f454,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f455,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f456,plain,
! [X0,X1] :
( ~ ssList(X0)
| rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f457,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f458,plain,
! [X0,X1,X2,X3,X4] :
( ~ leq(X3,X1)
| ~ leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
inference(destructive_equality_resolution,[status(thm)],[f141]) ).
fof(f459,plain,
! [X0,X1,X2,X3,X4] :
( leq(X3,X1)
| leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
inference(destructive_equality_resolution,[status(thm)],[f153]) ).
fof(f460,plain,
! [X0,X1,X2,X3,X4] :
( lt(X3,X1)
| lt(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
inference(destructive_equality_resolution,[status(thm)],[f165]) ).
fof(f461,plain,
! [X0,X1,X2,X3,X4] :
( leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
inference(destructive_equality_resolution,[status(thm)],[f177]) ).
fof(f462,plain,
! [X0,X1,X2,X3,X4] :
( lt(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
inference(destructive_equality_resolution,[status(thm)],[f188]) ).
fof(f463,plain,
! [X3,X2,X4,X5] :
( ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X2)
| ~ duplicatefreeP(app(app(X3,cons(X2,X4)),cons(X2,X5)))
| ~ ssList(app(app(X3,cons(X2,X4)),cons(X2,X5))) ),
inference(destructive_equality_resolution,[status(thm)],[f199]) ).
fof(f464,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ duplicatefreeP(app(app(X0,cons(X1,X2)),cons(X1,X3)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X1,X3))) ),
inference(duplicate_literals_removal,[status(thm)],[f463]) ).
fof(f465,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| ~ ssList(X3)
| ~ ssList(X0)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ equalelemsP(app(X0,cons(X1,cons(X2,X3))))
| ~ ssList(app(X0,cons(X1,cons(X2,X3)))) ),
inference(destructive_equality_resolution,[status(thm)],[f210]) ).
fof(f470,plain,
! [X1,X2,X3] :
( ~ frontsegP(X2,X3)
| frontsegP(cons(X1,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f293]) ).
fof(f471,plain,
! [X0,X1,X2] :
( ~ frontsegP(X1,X2)
| frontsegP(cons(X0,X1),cons(X0,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f470]) ).
fof(f481,plain,
! [X0,X1] :
( ~ memberP(X1,X0)
| ~ ssItem(X0)
| sP0_prd(X0,X1,cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f439]) ).
fof(f485,plain,
( sK51_skl = sK52_skl
| ~ ssItem(sK52_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f431,f101]) ).
fof(f486,definition,
( sQ3_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f488,plain,
( sQ3_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f486]) ).
fof(f489,definition,
( sQ4_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f491,plain,
( sQ4_spl
| ~ ssItem(sK52_skl) ),
inference(component_clause,[status(thm)],[f489]) ).
fof(f492,definition,
( sQ5_spl
<=> sK51_skl = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f493,plain,
( ~ sQ5_spl
| sK51_skl = sK52_skl ),
inference(component_clause,[status(thm)],[f492]) ).
fof(f495,plain,
( sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f485,f486,f489,f492]) ).
fof(f496,plain,
( ~ sQ5_spl
| ~ neq(sK51_skl,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f493,f431]) ).
fof(f498,plain,
( ~ sQ5_spl
| sK51_skl = sK51_skl
| ~ ssItem(sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f496,f101]) ).
fof(f499,definition,
( sQ6_spl
<=> sK51_skl = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f502,plain,
( ~ sQ5_spl
| sQ6_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f498,f486,f499,f492]) ).
fof(f503,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f488,f426]) ).
fof(f504,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f503]) ).
fof(f506,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f491,f427]) ).
fof(f507,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f506]) ).
fof(f509,plain,
( ~ sQ5_spl
| app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f493,f430]) ).
fof(f510,plain,
( ~ sQ5_spl
| app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl) = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f425,f509]) ).
fof(f521,plain,
( ~ sQ5_spl
| ~ ssList(sK54_skl)
| frontsegP(sK49_skl,app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| ~ ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl)) ),
inference(paramodulation,[status(thm)],[f510,f455]) ).
fof(f522,definition,
( sQ8_spl
<=> ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f524,plain,
( sQ8_spl
| ~ ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl)) ),
inference(component_clause,[status(thm)],[f522]) ).
fof(f525,definition,
( sQ9_spl
<=> ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f527,plain,
( sQ9_spl
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f525]) ).
fof(f528,definition,
( sQ10_spl
<=> frontsegP(sK49_skl,app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f529,plain,
( ~ sQ10_spl
| frontsegP(sK49_skl,app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f528]) ).
fof(f531,definition,
( sQ11_spl
<=> ssList(sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f533,plain,
( sQ11_spl
| ~ ssList(sK54_skl) ),
inference(component_clause,[status(thm)],[f531]) ).
fof(f534,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f521,f522,f525,f528,f531,f492]) ).
fof(f535,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f429]) ).
fof(f536,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f535]) ).
fof(f537,plain,
( ~ sQ0_spl
| ssItem(sK55_skl) ),
inference(resolution,[status(thm)],[f441,f436]) ).
fof(f538,plain,
( ~ sQ0_spl
| cons(sK55_skl,nil) = sK49_skl ),
inference(resolution,[status(thm)],[f437,f441]) ).
fof(f541,plain,
! [X0] :
( ~ sQ0_spl
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(app(X0,sK49_skl),sK55_skl)
| ~ ssItem(sK55_skl)
| ~ ssList(app(X0,cons(sK55_skl,nil))) ),
inference(paramodulation,[status(thm)],[f538,f453]) ).
fof(f542,definition,
( sQ12_spl
<=> ssList(cons(sK55_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f544,plain,
( sQ12_spl
| ~ ssList(cons(sK55_skl,nil)) ),
inference(component_clause,[status(thm)],[f542]) ).
fof(f545,definition,
( sQ13_spl
<=> singletonP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( ~ sQ13_spl
| singletonP(sK49_skl) ),
inference(component_clause,[status(thm)],[f545]) ).
fof(f548,definition,
( sQ14_spl
<=> ssItem(sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f550,plain,
( sQ14_spl
| ~ ssItem(sK55_skl) ),
inference(component_clause,[status(thm)],[f548]) ).
fof(f552,definition,
( sQ15_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f554,plain,
( sQ15_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f552]) ).
fof(f555,definition,
( sQ16_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f559,definition,
! [X0] :
( sQ17_spl
<=> ( ~ ssList(X0)
| memberP(app(X0,sK49_skl),sK55_skl)
| ~ ssList(app(X0,cons(sK55_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f562,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f541,f559,f548,f552,f440]) ).
fof(f563,plain,
( sQ14_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f550,f537]) ).
fof(f564,plain,
( sQ14_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f563]) ).
fof(f565,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f554,f223]) ).
fof(f566,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f565]) ).
fof(f583,plain,
! [X0,X1] :
( ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| sK4_skl(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f227,f117]) ).
fof(f585,plain,
! [X0,X1] :
( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f227]) ).
fof(f586,definition,
! [X0,X1] :
( sQ20_spl
<=> ( ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| sK4_skl(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f587,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| sK4_skl(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f586]) ).
fof(f589,plain,
( sQ20_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f583,f552,f586]) ).
fof(f591,definition,
! [X0] :
( sQ21_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f592,plain,
! [X0] :
( ~ sQ21_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f591]) ).
fof(f594,definition,
! [X1] :
( sQ22_spl
<=> ( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f597,plain,
( sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f585,f591,f594]) ).
fof(f598,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| sK4_skl(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f587,f116]) ).
fof(f599,plain,
! [X0] :
( ~ sQ21_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f592]) ).
fof(f600,plain,
( ~ sQ21_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f429,f599]) ).
fof(f603,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f600]) ).
fof(f605,plain,
! [X0,X1] :
( X0 = X0
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f228]) ).
fof(f606,definition,
! [X0] :
( sQ23_spl
<=> ( X0 = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f609,definition,
! [X1] :
( sQ24_spl
<=> ( ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f610,plain,
! [X0] :
( ~ sQ24_spl
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f609]) ).
fof(f612,plain,
( sQ24_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f605,f606,f609]) ).
fof(f613,plain,
! [X0] :
( ~ sQ24_spl
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f610]) ).
fof(f615,plain,
( ~ sQ0_spl
| ~ sQ24_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f537,f613]) ).
fof(f619,plain,
( ~ sQ0_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f615]) ).
fof(f627,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(app(X1,X0),X0)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f456,f245]) ).
fof(f634,definition,
( sQ25_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f636,plain,
( sQ25_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f634]) ).
fof(f637,definition,
( sQ26_spl
<=> segmentP(nil,cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f638,plain,
( ~ sQ26_spl
| segmentP(nil,cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f637]) ).
fof(f639,plain,
( sQ26_spl
| ~ segmentP(nil,cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f637]) ).
fof(f640,definition,
( sQ27_spl
<=> ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f641,plain,
( ~ sQ27_spl
| ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f640]) ).
fof(f642,plain,
( sQ27_spl
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f640]) ).
fof(f650,plain,
( ~ sQ0_spl
| memberP(sK50_skl,sK55_skl) ),
inference(resolution,[status(thm)],[f441,f438]) ).
fof(f651,plain,
( ~ sQ0_spl
| cons(sK55_skl,nil) = sK49_skl ),
inference(resolution,[status(thm)],[f441,f437]) ).
fof(f652,plain,
( ~ sQ5_spl
| ~ ssList(sK54_skl)
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil)))
| segmentP(sK49_skl,cons(sK51_skl,nil))
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl)) ),
inference(paramodulation,[status(thm)],[f510,f457]) ).
fof(f653,plain,
! [X0] :
( ~ sQ5_spl
| memberP(sK54_skl,X0)
| memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| ~ memberP(sK49_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f510,f270]) ).
fof(f654,plain,
! [X0] :
( ~ sQ5_spl
| ~ ssList(X0)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| segmentP(app(sK49_skl,X0),sK54_skl)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl),X0)) ),
inference(paramodulation,[status(thm)],[f510,f457]) ).
fof(f655,plain,
( ~ sQ5_spl
| ssList(sK49_skl)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f510,f245]) ).
fof(f656,definition,
( sQ29_spl
<=> segmentP(sK49_skl,cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f657,plain,
( ~ sQ29_spl
| segmentP(sK49_skl,cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f656]) ).
fof(f659,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ27_spl
| sQ29_spl
| ~ sQ25_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f652,f522,f634,f656,f640,f531,f492]) ).
fof(f660,definition,
! [X0] :
( sQ30_spl
<=> ( memberP(sK54_skl,X0)
| memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f661,plain,
! [X0] :
( ~ sQ30_spl
| memberP(sK54_skl,X0)
| memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f660]) ).
fof(f663,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f653,f660,f525,f531,f492]) ).
fof(f664,definition,
! [X0] :
( sQ31_spl
<=> ( ~ ssList(X0)
| segmentP(app(sK49_skl,X0),sK54_skl)
| ~ ssList(app(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f665,plain,
! [X0] :
( ~ sQ31_spl
| ~ ssList(X0)
| segmentP(app(sK49_skl,X0),sK54_skl)
| ~ ssList(app(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl),X0)) ),
inference(component_clause,[status(thm)],[f664]) ).
fof(f667,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ11_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f654,f664,f531,f525,f492]) ).
fof(f668,plain,
( ~ sQ5_spl
| sQ16_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f655,f525,f531,f555,f492]) ).
fof(f669,plain,
( sQ8_spl
| ~ sQ5_spl
| ~ ssList(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f510,f524]) ).
fof(f670,plain,
( sQ8_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f669,f422]) ).
fof(f671,plain,
( sQ8_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f670]) ).
fof(f673,plain,
( sQ12_spl
| ~ sQ0_spl
| ~ ssList(sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f538,f544]) ).
fof(f674,plain,
! [X0] :
( ~ sQ0_spl
| ~ memberP(X0,sK55_skl)
| ~ ssItem(sK55_skl)
| sP0_prd(sK55_skl,X0,sK49_skl) ),
inference(paramodulation,[status(thm)],[f538,f481]) ).
fof(f675,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ leq(sK55_skl,X1)
| ~ leq(X1,sK55_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil))) ),
inference(paramodulation,[status(thm)],[f538,f458]) ).
fof(f676,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ leq(X1,sK55_skl)
| ~ leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK55_skl)
| ~ cyclefreeP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f538,f458]) ).
fof(f677,plain,
! [X0] :
( ~ sQ0_spl
| cons(sK55_skl,app(nil,X0)) = app(sK49_skl,X0)
| ~ ssItem(sK55_skl)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f538,f247]) ).
fof(f678,plain,
( sQ12_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f673,f422]) ).
fof(f679,plain,
( sQ12_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f678]) ).
fof(f684,plain,
! [X0] :
( ~ sQ5_spl
| ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| memberP(sK49_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f510,f271]) ).
fof(f685,definition,
! [X0] :
( sQ32_spl
<=> ( ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f686,plain,
! [X0] :
( ~ sQ32_spl
| ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f685]) ).
fof(f688,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f684,f685,f525,f531,f492]) ).
fof(f689,definition,
! [X0] :
( sQ33_spl
<=> ( ~ memberP(X0,sK55_skl)
| sP0_prd(sK55_skl,X0,sK49_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f690,plain,
! [X0] :
( ~ sQ33_spl
| ~ memberP(X0,sK55_skl)
| sP0_prd(sK55_skl,X0,sK49_skl) ),
inference(component_clause,[status(thm)],[f689]) ).
fof(f692,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f674,f689,f548,f440]) ).
fof(f693,definition,
! [X0,X1,X2] :
( sQ34_spl
<=> ( ~ leq(sK55_skl,X1)
| ~ leq(X1,sK55_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f696,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f675,f693,f548,f552,f440]) ).
fof(f697,definition,
! [X0,X1,X2] :
( sQ35_spl
<=> ( ~ leq(X1,sK55_skl)
| ~ leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f700,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f676,f697,f548,f552,f440]) ).
fof(f701,definition,
! [X0] :
( sQ36_spl
<=> ( cons(sK55_skl,app(nil,X0)) = app(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f704,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f677,f701,f552,f548,f440]) ).
fof(f707,definition,
! [X0] :
( sQ37_spl
<=> ( ~ memberP(sK54_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f723,plain,
! [X0] :
( ~ sQ0_spl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK55_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f651,f275]) ).
fof(f724,definition,
! [X0] :
( sQ38_spl
<=> ( memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f725,plain,
! [X0] :
( ~ sQ38_spl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f724]) ).
fof(f727,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f723,f724,f548,f552,f440]) ).
fof(f728,plain,
! [X0] :
( ~ sQ38_spl
| X0 = sK55_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f725,f279]) ).
fof(f731,definition,
( sQ39_spl
<=> memberP(sK49_skl,sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f732,plain,
( ~ sQ39_spl
| memberP(sK49_skl,sK55_skl) ),
inference(component_clause,[status(thm)],[f731]) ).
fof(f733,plain,
( sQ39_spl
| ~ memberP(sK49_skl,sK55_skl) ),
inference(component_clause,[status(thm)],[f731]) ).
fof(f735,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| leq(X1,sK55_skl)
| leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK55_skl)
| ~ totalorderP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f651,f459]) ).
fof(f736,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| leq(sK55_skl,X1)
| leq(X1,sK55_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil))) ),
inference(paramodulation,[status(thm)],[f651,f459]) ).
fof(f737,definition,
! [X0,X1,X2] :
( sQ40_spl
<=> ( leq(X1,sK55_skl)
| leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f740,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f735,f737,f548,f552,f440]) ).
fof(f741,definition,
! [X0,X1,X2] :
( sQ41_spl
<=> ( leq(sK55_skl,X1)
| leq(X1,sK55_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f744,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f736,f741,f548,f552,f440]) ).
fof(f747,plain,
( ~ sQ39_spl
| ~ sQ38_spl
| sK55_skl = sK55_skl
| ~ ssItem(sK55_skl) ),
inference(resolution,[status(thm)],[f728,f732]) ).
fof(f748,definition,
( sQ42_spl
<=> sK55_skl = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f751,plain,
( ~ sQ39_spl
| ~ sQ38_spl
| sQ42_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f747,f548,f748,f724,f731]) ).
fof(f752,plain,
( sQ27_spl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f642,f245]) ).
fof(f753,definition,
( sQ43_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f755,plain,
( sQ43_spl
| ~ ssList(sK53_skl) ),
inference(component_clause,[status(thm)],[f753]) ).
fof(f756,plain,
( sQ27_spl
| ~ sQ25_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f752,f753,f634,f640]) ).
fof(f757,plain,
( sQ9_spl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(resolution,[status(thm)],[f527,f245]) ).
fof(f758,plain,
( sQ9_spl
| ~ sQ25_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f757,f640,f634,f525]) ).
fof(f761,plain,
( sQ25_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f222,f636]) ).
fof(f763,plain,
( sQ25_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f761,f552,f486,f634]) ).
fof(f765,plain,
( sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f755,f428]) ).
fof(f766,plain,
sQ43_spl,
inference(contradiction_clause,[status(thm)],[f765]) ).
fof(f767,plain,
! [X0] :
( ~ sQ31_spl
| ~ sQ5_spl
| ~ ssList(X0)
| segmentP(app(sK49_skl,X0),sK54_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f510,f665]) ).
fof(f770,definition,
! [X0] :
( sQ44_spl
<=> ( ~ memberP(nil,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f774,plain,
! [X0,X1] :
( ~ rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1))
| sK6_skl(X1,app(X0,X1)) = X0
| ~ ssList(sK6_skl(X1,app(X0,X1)))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f376,f129]) ).
fof(f775,plain,
! [X0] :
( ~ ssList(app(X0,nil))
| app(X0,nil) = X0
| ~ ssList(app(X0,nil))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f376,f389]) ).
fof(f778,plain,
! [X0] :
( ~ sQ5_spl
| app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)) = X0
| sK49_skl != app(X0,sK54_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| ~ ssList(sK54_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f510,f376]) ).
fof(f781,plain,
! [X0,X1] :
( ~ rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| sK6_skl(X1,app(X0,X1)) = X0
| ~ ssList(sK6_skl(X1,app(X0,X1)))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f774]) ).
fof(f782,plain,
! [X0,X1] :
( ~ rearsegP(app(X0,X1),X1)
| ~ ssList(app(X0,X1))
| sK6_skl(X1,app(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f781,f128]) ).
fof(f783,definition,
! [X0] :
( sQ45_spl
<=> ( ~ ssList(app(X0,nil))
| app(X0,nil) = X0
| ~ ssList(app(X0,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f786,plain,
( ~ sQ15_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f775,f783,f552]) ).
fof(f790,definition,
! [X0] :
( sQ46_spl
<=> ( app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)) = X0
| sK49_skl != app(X0,sK54_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f793,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ11_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f778,f790,f531,f525,f492]) ).
fof(f795,definition,
! [X1] :
( sQ47_spl
<=> ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f796,plain,
! [X0] :
( ~ sQ47_spl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f795]) ).
fof(f801,definition,
( sQ48_spl
<=> cyclefreeP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f806,definition,
( sQ49_spl
<=> totalorderP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f812,plain,
! [X0] :
( ~ sQ33_spl
| cons(sK55_skl,nil) = sK49_skl
| ~ memberP(X0,sK55_skl) ),
inference(resolution,[status(thm)],[f690,f437]) ).
fof(f813,definition,
! [X0] :
( sQ50_spl
<=> ~ memberP(X0,sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f814,plain,
! [X0] :
( ~ sQ50_spl
| ~ memberP(X0,sK55_skl) ),
inference(component_clause,[status(thm)],[f813]) ).
fof(f817,definition,
( sQ51_spl
<=> cons(sK55_skl,nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f818,plain,
( ~ sQ51_spl
| cons(sK55_skl,nil) = sK49_skl ),
inference(component_clause,[status(thm)],[f817]) ).
fof(f820,plain,
( ~ sQ33_spl
| sQ51_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f812,f813,f817,f689]) ).
fof(f821,plain,
( ~ sQ39_spl
| ~ sQ50_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f732,f814]) ).
fof(f827,plain,
( ~ sQ39_spl
| ~ sQ50_spl ),
inference(contradiction_clause,[status(thm)],[f821]) ).
fof(f834,plain,
! [X0] :
( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(app(nil,X0))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f378,f249]) ).
fof(f836,plain,
! [X0] :
( ~ sQ5_spl
| sK54_skl = X0
| sK49_skl != app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f510,f378]) ).
fof(f839,definition,
! [X0] :
( sQ52_spl
<=> ( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f842,plain,
( ~ sQ15_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f834,f839,f552]) ).
fof(f844,definition,
! [X0] :
( sQ53_spl
<=> ( sK54_skl = X0
| sK49_skl != app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f847,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f836,f844,f525,f531,f492]) ).
fof(f851,plain,
! [X0] :
( ~ sQ0_spl
| cons(sK55_skl,X0) = app(sK49_skl,X0)
| ~ ssItem(sK55_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f651,f380]) ).
fof(f852,definition,
! [X0] :
( sQ54_spl
<=> ( cons(sK55_skl,X0) = app(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f853,plain,
! [X0] :
( ~ sQ54_spl
| cons(sK55_skl,X0) = app(sK49_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f852]) ).
fof(f855,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f851,f852,f548,f440]) ).
fof(f857,definition,
( sQ55_spl
<=> strictorderP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f862,definition,
( sQ56_spl
<=> totalorderedP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f867,definition,
( sQ57_spl
<=> strictorderedP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f876,plain,
! [X0] :
( ~ sQ30_spl
| memberP(cons(sK51_skl,nil),X0)
| memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0)
| memberP(sK54_skl,X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f661,f270]) ).
fof(f877,definition,
! [X0] :
( sQ58_spl
<=> ( memberP(cons(sK51_skl,nil),X0)
| memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0)
| memberP(sK54_skl,X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f880,plain,
( ~ sQ30_spl
| ~ sQ25_spl
| ~ sQ27_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f876,f877,f640,f634,f660]) ).
fof(f889,definition,
( sQ59_spl
<=> rearsegP(sK49_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f890,plain,
( ~ sQ59_spl
| rearsegP(sK49_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f889]) ).
fof(f893,plain,
! [X0] :
( ~ sQ5_spl
| app(app(X0,app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))),sK54_skl) = app(X0,sK49_skl)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f510,f382]) ).
fof(f894,definition,
! [X0] :
( sQ60_spl
<=> ( app(app(X0,app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))),sK54_skl) = app(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f897,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f893,f894,f525,f531,f492]) ).
fof(f898,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f385,f249]) ).
fof(f901,plain,
! [X0] :
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = sK8_skl(X0,nil)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0)) ),
inference(resolution,[status(thm)],[f385,f136]) ).
fof(f902,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ),
inference(resolution,[status(thm)],[f385,f129]) ).
fof(f905,definition,
( sQ61_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f908,plain,
( sQ61_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f898,f552,f905]) ).
fof(f935,definition,
! [X0] :
( sQ70_spl
<=> ( ~ segmentP(nil,X0)
| ~ ssList(X0)
| nil = sK8_skl(X0,nil)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f938,plain,
( ~ sQ15_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f901,f935,f552]) ).
fof(f939,definition,
! [X0] :
( sQ71_spl
<=> ( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| nil = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f942,plain,
( ~ sQ15_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f902,f939,f552]) ).
fof(f944,definition,
( sQ72_spl
<=> nil = sK54_skl ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f945,plain,
( ~ sQ72_spl
| nil = sK54_skl ),
inference(component_clause,[status(thm)],[f944]) ).
fof(f951,plain,
( ~ sQ5_spl
| ~ sQ72_spl
| app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),nil) = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f945,f510]) ).
fof(f955,definition,
( sQ73_spl
<=> duplicatefreeP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f960,definition,
( sQ74_spl
<=> equalelemsP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f964,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| lt(X1,sK55_skl)
| lt(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK55_skl)
| ~ strictorderP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f651,f460]) ).
fof(f965,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| lt(sK55_skl,X1)
| lt(X1,sK55_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil))) ),
inference(paramodulation,[status(thm)],[f651,f460]) ).
fof(f966,definition,
! [X0,X1,X2] :
( sQ75_spl
<=> ( lt(X1,sK55_skl)
| lt(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f969,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f964,f966,f548,f552,f440]) ).
fof(f970,definition,
! [X0,X1,X2] :
( sQ76_spl
<=> ( lt(sK55_skl,X1)
| lt(X1,sK55_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f973,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f965,f970,f548,f552,f440]) ).
fof(f978,plain,
( ~ sQ5_spl
| ~ sQ72_spl
| sK49_skl = app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f951,f389]) ).
fof(f991,definition,
( sQ77_spl
<=> ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),nil)) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f993,plain,
( sQ77_spl
| ~ ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),nil)) ),
inference(component_clause,[status(thm)],[f991]) ).
fof(f995,definition,
( sQ78_spl
<=> sK49_skl = app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f996,plain,
( ~ sQ78_spl
| sK49_skl = app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f995]) ).
fof(f997,plain,
( sQ78_spl
| sK49_skl != app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f995]) ).
fof(f998,plain,
( ~ sQ5_spl
| ~ sQ72_spl
| sQ78_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f978,f525,f995,f944,f492]) ).
fof(f1004,definition,
( sQ80_spl
<=> rearsegP(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1005,plain,
( ~ sQ80_spl
| rearsegP(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f1004]) ).
fof(f1033,plain,
! [X0] :
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = app(sK7_skl(X0,nil),X0)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0)) ),
inference(resolution,[status(thm)],[f386,f136]) ).
fof(f1034,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ),
inference(resolution,[status(thm)],[f386,f129]) ).
fof(f1045,definition,
! [X0] :
( sQ87_spl
<=> ( ~ segmentP(nil,X0)
| ~ ssList(X0)
| nil = app(sK7_skl(X0,nil),X0)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1048,plain,
( ~ sQ15_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f1033,f1045,f552]) ).
fof(f1049,definition,
! [X0] :
( sQ88_spl
<=> ( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1050,plain,
! [X0] :
( ~ sQ88_spl
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ),
inference(component_clause,[status(thm)],[f1049]) ).
fof(f1052,plain,
( ~ sQ15_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f1034,f1049,f552]) ).
fof(f1054,plain,
! [X0] :
( ~ sQ88_spl
| ~ rearsegP(nil,X0)
| nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ),
inference(duplicate_literals_removal,[status(thm)],[f1050]) ).
fof(f1093,definition,
( sQ94_spl
<=> nil = app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1094,plain,
( ~ sQ94_spl
| nil = app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f1093]) ).
fof(f1122,plain,
( ~ sQ47_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f429,f796]) ).
fof(f1129,plain,
~ sQ47_spl,
inference(contradiction_clause,[status(thm)],[f1122]) ).
fof(f1130,plain,
! [X0,X1] :
( ~ sQ0_spl
| sK55_skl = X1
| sK49_skl != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssItem(sK55_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f651,f227]) ).
fof(f1133,definition,
! [X0,X1] :
( sQ97_spl
<=> ( sK55_skl = X1
| sK49_skl != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1136,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| sQ97_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1130,f552,f1133,f548,f440]) ).
fof(f1142,definition,
! [X0,X1] :
( sQ98_spl
<=> ( X0 = nil
| sK49_skl != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1148,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| memberP(nil,sK55_skl) ),
inference(backward_demodulation,[status(thm)],[f444,f650]) ).
fof(f1152,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK55_skl)
| ~ totalorderedP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f651,f461]) ).
fof(f1153,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| leq(X1,sK55_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil))) ),
inference(paramodulation,[status(thm)],[f651,f461]) ).
fof(f1154,definition,
! [X0,X1,X2] :
( sQ99_spl
<=> ( leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1157,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f1152,f1154,f548,f552,f440]) ).
fof(f1158,definition,
! [X0,X1,X2] :
( sQ100_spl
<=> ( leq(X1,sK55_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1161,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f1153,f1158,f548,f552,f440]) ).
fof(f1171,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ ssItem(sK55_skl) ),
inference(resolution,[status(thm)],[f1148,f279]) ).
fof(f1172,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1171,f548,f443,f440]) ).
fof(f1208,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| lt(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK55_skl)
| ~ strictorderedP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f651,f462]) ).
fof(f1209,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| lt(X1,sK55_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil))) ),
inference(paramodulation,[status(thm)],[f651,f462]) ).
fof(f1210,definition,
! [X0,X1,X2] :
( sQ106_spl
<=> ( lt(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1213,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f1208,f1210,f548,f552,f440]) ).
fof(f1214,definition,
! [X0,X1,X2] :
( sQ107_spl
<=> ( lt(X1,sK55_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1217,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ107_spl ),
inference(split_clause,[status(thm)],[f1209,f1214,f548,f552,f440]) ).
fof(f1220,plain,
( ~ sQ32_spl
| ~ ssList(nil)
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil)))
| ~ ssItem(sK51_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)))
| memberP(sK49_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f686,f453]) ).
fof(f1221,definition,
( sQ108_spl
<=> memberP(sK49_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1222,plain,
( ~ sQ108_spl
| memberP(sK49_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1221]) ).
fof(f1224,plain,
( ~ sQ32_spl
| ~ sQ15_spl
| ~ sQ27_spl
| ~ sQ9_spl
| sQ108_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1220,f486,f1221,f525,f640,f552,f685]) ).
fof(f1225,plain,
( ~ sQ38_spl
| ~ sQ108_spl
| sK51_skl = sK55_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1222,f728]) ).
fof(f1226,definition,
( sQ109_spl
<=> sK51_skl = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1227,plain,
( ~ sQ109_spl
| sK51_skl = sK55_skl ),
inference(component_clause,[status(thm)],[f1226]) ).
fof(f1229,plain,
( ~ sQ38_spl
| ~ sQ108_spl
| sQ109_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1225,f486,f1226,f1221,f724]) ).
fof(f1230,plain,
! [X0] :
( ~ sQ54_spl
| ~ sQ109_spl
| cons(sK51_skl,X0) = app(sK49_skl,X0)
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f1227,f853]) ).
fof(f1236,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| cons(sK51_skl,nil) = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f1227,f651]) ).
fof(f1245,plain,
( ~ sQ27_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ssList(app(sK53_skl,sK49_skl)) ),
inference(backward_demodulation,[status(thm)],[f1236,f641]) ).
fof(f1246,plain,
( ~ sQ26_spl
| ~ sQ0_spl
| ~ sQ109_spl
| segmentP(nil,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f1236,f638]) ).
fof(f1248,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| app(app(app(sK53_skl,cons(sK51_skl,nil)),sK49_skl),sK54_skl) = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f1236,f510]) ).
fof(f1250,plain,
( ~ sQ29_spl
| ~ sQ0_spl
| ~ sQ109_spl
| segmentP(sK49_skl,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f1236,f657]) ).
fof(f1251,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| equalelemsP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1236,f361]) ).
fof(f1252,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| duplicatefreeP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1236,f358]) ).
fof(f1253,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| strictorderedP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1236,f348]) ).
fof(f1254,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| totalorderedP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1236,f338]) ).
fof(f1255,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| strictorderP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1236,f335]) ).
fof(f1256,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| totalorderP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1236,f332]) ).
fof(f1257,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| cyclefreeP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1236,f329]) ).
fof(f1258,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ109_spl
| ~ memberP(X0,sK51_skl)
| ~ ssItem(sK51_skl)
| sP0_prd(sK51_skl,X0,sK49_skl) ),
inference(paramodulation,[status(thm)],[f1236,f481]) ).
fof(f1260,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ109_spl
| lt(X1,sK51_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f1236,f462]) ).
fof(f1261,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ109_spl
| lt(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ strictorderedP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f1236,f462]) ).
fof(f1262,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ109_spl
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(app(X0,sK49_skl),sK51_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(app(X0,cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f1236,f453]) ).
fof(f1263,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ109_spl
| leq(X1,sK51_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f1236,f461]) ).
fof(f1264,plain,
! [X0,X1,X2] :
( ~ sQ0_spl
| ~ sQ109_spl
| leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ totalorderedP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f1236,f461]) ).
fof(f1265,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ109_spl
| nil = X0
| cons(X1,X0) != sK49_skl
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1236,f228]) ).
fof(f1267,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ sQ109_spl
| X1 = sK51_skl
| cons(X1,X0) != sK49_skl
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1236,f227]) ).
fof(f1270,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl) = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f1236,f1248]) ).
fof(f1272,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| sQ74_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1251,f486,f960,f1226,f440]) ).
fof(f1273,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| sQ73_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1252,f486,f955,f1226,f440]) ).
fof(f1274,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| sQ57_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1253,f486,f867,f1226,f440]) ).
fof(f1275,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| sQ56_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1254,f486,f862,f1226,f440]) ).
fof(f1276,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| sQ55_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1255,f486,f857,f1226,f440]) ).
fof(f1277,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| sQ49_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1256,f486,f806,f1226,f440]) ).
fof(f1278,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| sQ48_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1257,f486,f801,f1226,f440]) ).
fof(f1279,definition,
! [X0] :
( sQ110_spl
<=> ( ~ memberP(X0,sK51_skl)
| sP0_prd(sK51_skl,X0,sK49_skl) ) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1282,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ3_spl
| sQ110_spl ),
inference(split_clause,[status(thm)],[f1258,f1279,f486,f1226,f440]) ).
fof(f1284,definition,
! [X0,X1,X2] :
( sQ111_spl
<=> ( lt(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1287,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ111_spl ),
inference(split_clause,[status(thm)],[f1260,f1284,f486,f552,f1226,f440]) ).
fof(f1288,definition,
! [X0,X1,X2] :
( sQ112_spl
<=> ( lt(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderedP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1291,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f1261,f1288,f486,f552,f1226,f440]) ).
fof(f1292,definition,
! [X0] :
( sQ113_spl
<=> ( ~ ssList(X0)
| memberP(app(X0,sK49_skl),sK51_skl)
| ~ ssList(app(X0,cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1295,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ113_spl ),
inference(split_clause,[status(thm)],[f1262,f1292,f486,f552,f1226,f440]) ).
fof(f1296,definition,
! [X0,X1,X2] :
( sQ114_spl
<=> ( leq(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1299,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ114_spl ),
inference(split_clause,[status(thm)],[f1263,f1296,f486,f552,f1226,f440]) ).
fof(f1300,definition,
! [X0,X1,X2] :
( sQ115_spl
<=> ( leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderedP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f1303,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ115_spl ),
inference(split_clause,[status(thm)],[f1264,f1300,f486,f552,f1226,f440]) ).
fof(f1304,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ3_spl
| ~ sQ15_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f1265,f1142,f552,f486,f1226,f440]) ).
fof(f1306,definition,
! [X0,X1] :
( sQ116_spl
<=> ( X1 = sK51_skl
| cons(X1,X0) != sK49_skl
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1309,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ3_spl
| ~ sQ15_spl
| sQ116_spl ),
inference(split_clause,[status(thm)],[f1267,f1306,f552,f486,f1226,f440]) ).
fof(f1325,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| cons(sK51_skl,nil) = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f1227,f818]) ).
fof(f1336,plain,
( sQ39_spl
| ~ sQ109_spl
| ~ memberP(sK49_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f1227,f733]) ).
fof(f1337,plain,
( sQ39_spl
| ~ sQ109_spl
| ~ sQ108_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1336,f1222]) ).
fof(f1338,plain,
( sQ39_spl
| ~ sQ109_spl
| ~ sQ108_spl ),
inference(contradiction_clause,[status(thm)],[f1337]) ).
fof(f1343,plain,
( ~ sQ108_spl
| ~ sQ2_spl
| memberP(nil,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f448,f1222]) ).
fof(f1369,definition,
( sQ117_spl
<=> rearsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1370,plain,
( ~ sQ117_spl
| rearsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f1369]) ).
fof(f1379,plain,
( ~ sQ108_spl
| ~ sQ2_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1343,f279]) ).
fof(f1380,plain,
( ~ sQ108_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1379,f486,f447,f1221]) ).
fof(f1432,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| X0 = app(app(sK53_skl,sK49_skl),sK49_skl)
| app(X0,sK54_skl) != sK49_skl
| ~ ssList(X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(paramodulation,[status(thm)],[f1270,f376]) ).
fof(f1434,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| X0 = sK54_skl
| app(app(app(sK53_skl,sK49_skl),sK49_skl),X0) != sK49_skl
| ~ ssList(X0)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f1270,f378]) ).
fof(f1436,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| rearsegP(sK49_skl,sK54_skl)
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f1270,f627]) ).
fof(f1437,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| app(app(X0,app(app(sK53_skl,sK49_skl),sK49_skl)),sK54_skl) = app(X0,sK49_skl)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1270,f382]) ).
fof(f1440,definition,
( sQ124_spl
<=> ssList(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1442,plain,
( sQ124_spl
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(component_clause,[status(thm)],[f1440]) ).
fof(f1443,definition,
! [X0] :
( sQ125_spl
<=> ( X0 = app(app(sK53_skl,sK49_skl),sK49_skl)
| app(X0,sK54_skl) != sK49_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1444,plain,
! [X0] :
( ~ sQ125_spl
| X0 = app(app(sK53_skl,sK49_skl),sK49_skl)
| app(X0,sK54_skl) != sK49_skl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1443]) ).
fof(f1446,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sQ125_spl
| ~ sQ11_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f1432,f1440,f531,f1443,f1226,f440,f492]) ).
fof(f1448,definition,
! [X0] :
( sQ126_spl
<=> ( X0 = sK54_skl
| app(app(app(sK53_skl,sK49_skl),sK49_skl),X0) != sK49_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1449,plain,
! [X0] :
( ~ sQ126_spl
| X0 = sK54_skl
| app(app(app(sK53_skl,sK49_skl),sK49_skl),X0) != sK49_skl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1448]) ).
fof(f1451,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sQ126_spl
| ~ sQ124_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1434,f531,f1440,f1448,f1226,f440,f492]) ).
fof(f1453,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| sQ59_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1436,f531,f889,f1440,f1226,f440,f492]) ).
fof(f1454,definition,
! [X0] :
( sQ127_spl
<=> ( app(app(X0,app(app(sK53_skl,sK49_skl),sK49_skl)),sK54_skl) = app(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f1457,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ11_spl
| ~ sQ124_spl
| sQ127_spl ),
inference(split_clause,[status(thm)],[f1437,f1454,f1440,f531,f1226,f440,f492]) ).
fof(f1459,definition,
( sQ128_spl
<=> nil = app(app(sK53_skl,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1460,plain,
( ~ sQ128_spl
| nil = app(app(sK53_skl,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f1459]) ).
fof(f1464,plain,
! [X0] :
( ~ sQ51_spl
| ~ sQ109_spl
| cons(sK51_skl,X0) = app(sK49_skl,X0)
| ~ ssItem(sK51_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1325,f380]) ).
fof(f1475,plain,
! [X0,X1] :
( ~ sQ51_spl
| ~ sQ109_spl
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ duplicatefreeP(app(app(X0,cons(sK51_skl,X1)),sK49_skl))
| ~ ssList(app(app(X0,cons(sK51_skl,X1)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f1325,f464]) ).
fof(f1476,plain,
! [X0,X1] :
( ~ sQ51_spl
| ~ sQ109_spl
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ duplicatefreeP(app(app(X0,sK49_skl),cons(sK51_skl,X1)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(sK51_skl,X1))) ),
inference(paramodulation,[status(thm)],[f1325,f464]) ).
fof(f1487,definition,
! [X0] :
( sQ129_spl
<=> ( cons(sK51_skl,X0) = app(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f1490,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ3_spl
| sQ129_spl ),
inference(split_clause,[status(thm)],[f1464,f1487,f486,f1226,f817]) ).
fof(f1501,definition,
! [X0,X1] :
( sQ130_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,cons(sK51_skl,X1)),sK49_skl))
| ~ ssList(app(app(X0,cons(sK51_skl,X1)),cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1504,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ130_spl ),
inference(split_clause,[status(thm)],[f1475,f1501,f486,f552,f1226,f817]) ).
fof(f1505,definition,
! [X0,X1] :
( sQ131_spl
<=> ( ~ ssList(X1)
| ~ ssList(X0)
| ~ duplicatefreeP(app(app(X0,sK49_skl),cons(sK51_skl,X1)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(sK51_skl,X1))) ) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1508,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ131_spl ),
inference(split_clause,[status(thm)],[f1476,f1505,f486,f552,f1226,f817]) ).
fof(f1561,plain,
! [X0] :
( ~ sQ51_spl
| ~ sQ109_spl
| memberP(nil,X0)
| X0 = sK51_skl
| ~ memberP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1325,f275]) ).
fof(f1562,definition,
! [X0] :
( sQ139_spl
<=> ( memberP(nil,X0)
| X0 = sK51_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f1565,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ139_spl ),
inference(split_clause,[status(thm)],[f1561,f1562,f486,f552,f1226,f817]) ).
fof(f1566,plain,
! [X0,X1] :
( ~ sQ51_spl
| ~ sQ109_spl
| X1 = sK51_skl
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ equalelemsP(app(X0,cons(X1,sK49_skl)))
| ~ ssList(app(X0,cons(X1,cons(sK51_skl,nil)))) ),
inference(paramodulation,[status(thm)],[f1325,f465]) ).
fof(f1567,definition,
! [X0,X1] :
( sQ140_spl
<=> ( X1 = sK51_skl
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ equalelemsP(app(X0,cons(X1,sK49_skl)))
| ~ ssList(app(X0,cons(X1,cons(sK51_skl,nil)))) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1570,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ140_spl ),
inference(split_clause,[status(thm)],[f1566,f1567,f486,f552,f1226,f817]) ).
fof(f1594,definition,
! [X0] :
( sQ146_spl
<=> ~ memberP(X0,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1595,plain,
! [X0] :
( ~ sQ146_spl
| ~ memberP(X0,sK51_skl) ),
inference(component_clause,[status(thm)],[f1594]) ).
fof(f1598,definition,
( sQ147_spl
<=> cons(sK51_skl,nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1602,plain,
( ~ sQ108_spl
| ~ sQ146_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1222,f1595]) ).
fof(f1607,plain,
( ~ sQ108_spl
| ~ sQ146_spl ),
inference(contradiction_clause,[status(thm)],[f1602]) ).
fof(f1623,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ memberP(sK54_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1270,f272]) ).
fof(f1624,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ11_spl
| ~ sQ124_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f1623,f707,f1440,f531,f1226,f440,f492]) ).
fof(f1625,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ memberP(app(app(sK53_skl,sK49_skl),sK49_skl),X0)
| memberP(sK49_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1270,f271]) ).
fof(f1626,definition,
! [X0] :
( sQ149_spl
<=> ( ~ memberP(app(app(sK53_skl,sK49_skl),sK49_skl),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1627,plain,
! [X0] :
( ~ sQ149_spl
| ~ memberP(app(app(sK53_skl,sK49_skl),sK49_skl),X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1626]) ).
fof(f1629,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ11_spl
| ~ sQ124_spl
| sQ149_spl ),
inference(split_clause,[status(thm)],[f1625,f1626,f1440,f531,f1226,f440,f492]) ).
fof(f1640,plain,
! [X0,X1] :
( X1 = sK43_skl(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssItem(sK44_skl(cons(X0,X1)))
| ~ ssList(X1)
| ~ ssList(sK43_skl(cons(X0,X1)))
| nil = cons(X0,X1)
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f233,f228]) ).
fof(f1641,plain,
! [X0,X1] :
( sK44_skl(cons(X0,X1)) = X0
| ~ ssItem(X0)
| ~ ssItem(sK44_skl(cons(X0,X1)))
| ~ ssList(X1)
| ~ ssList(sK43_skl(cons(X0,X1)))
| nil = cons(X0,X1)
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f233,f227]) ).
fof(f1645,plain,
! [X0,X1] :
( X1 = sK43_skl(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssItem(sK44_skl(cons(X0,X1)))
| ~ ssList(X1)
| ~ ssList(sK43_skl(cons(X0,X1)))
| nil = cons(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1640,f222]) ).
fof(f1646,plain,
! [X0,X1] :
( sK44_skl(cons(X0,X1)) = X0
| ~ ssItem(X0)
| ~ ssItem(sK44_skl(cons(X0,X1)))
| ~ ssList(X1)
| ~ ssList(sK43_skl(cons(X0,X1)))
| nil = cons(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1641,f222]) ).
fof(f1656,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| hd(sK49_skl) = sK51_skl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1325,f239]) ).
fof(f1657,definition,
( sQ152_spl
<=> hd(sK49_skl) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1658,plain,
( ~ sQ152_spl
| hd(sK49_skl) = sK51_skl ),
inference(component_clause,[status(thm)],[f1657]) ).
fof(f1660,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sQ152_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1656,f552,f486,f1657,f1226,f817]) ).
fof(f1673,definition,
! [X0] :
( sQ153_spl
<=> ( app(sK53_skl,sK49_skl) = X0
| ~ ssList(X0)
| sK49_skl != app(app(X0,sK49_skl),sK54_skl)
| ~ ssList(app(X0,sK49_skl)) ) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f1676,definition,
( sQ154_spl
<=> ssList(app(sK53_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f1678,plain,
( sQ154_spl
| ~ ssList(app(sK53_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1676]) ).
fof(f1680,definition,
! [X0] :
( sQ155_spl
<=> ( sK49_skl = X0
| ~ ssList(X0)
| sK49_skl != app(app(app(sK53_skl,sK49_skl),X0),sK54_skl)
| ~ ssList(app(app(sK53_skl,sK49_skl),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f1686,definition,
! [X0] :
( sQ156_spl
<=> ( ~ ssItem(X0)
| sK49_skl != app(cons(X0,app(app(sK53_skl,sK49_skl),sK49_skl)),sK54_skl)
| ~ ssList(cons(X0,app(app(sK53_skl,sK49_skl),sK49_skl))) ) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f1690,definition,
( sQ157_spl
<=> sK49_skl = app(nil,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f1692,plain,
( sQ157_spl
| sK49_skl != app(nil,sK54_skl) ),
inference(component_clause,[status(thm)],[f1690]) ).
fof(f1694,definition,
( sQ158_spl
<=> nil = app(sK53_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f1695,plain,
( ~ sQ158_spl
| nil = app(sK53_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f1694]) ).
fof(f1696,plain,
( sQ158_spl
| nil != app(sK53_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f1694]) ).
fof(f1698,plain,
( sQ154_spl
| ~ sQ27_spl
| ~ sQ0_spl
| ~ sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1678,f1245]) ).
fof(f1699,plain,
( sQ154_spl
| ~ sQ27_spl
| ~ sQ0_spl
| ~ sQ109_spl ),
inference(contradiction_clause,[status(thm)],[f1698]) ).
fof(f1712,plain,
( ~ sQ158_spl
| ~ ssList(sK53_skl)
| rearsegP(nil,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1695,f627]) ).
fof(f1717,definition,
( sQ159_spl
<=> nil = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f1718,plain,
( ~ sQ159_spl
| nil = sK53_skl ),
inference(component_clause,[status(thm)],[f1717]) ).
fof(f1719,plain,
( sQ159_spl
| nil != sK53_skl ),
inference(component_clause,[status(thm)],[f1717]) ).
fof(f1725,definition,
! [X0] :
( sQ161_spl
<=> ( ~ memberP(sK49_skl,X0)
| memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f1726,plain,
! [X0] :
( ~ sQ161_spl
| ~ memberP(sK49_skl,X0)
| memberP(nil,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1725]) ).
fof(f1739,definition,
( sQ164_spl
<=> rearsegP(nil,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f1741,plain,
( sQ164_spl
| ~ rearsegP(nil,sK49_skl) ),
inference(component_clause,[status(thm)],[f1739]) ).
fof(f1742,plain,
( ~ sQ158_spl
| ~ sQ43_spl
| sQ164_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1712,f555,f1739,f753,f1694]) ).
fof(f1749,plain,
! [X0] :
( ~ sQ161_spl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1726,f279]) ).
fof(f1758,plain,
! [X0] :
( ~ sQ51_spl
| ~ sQ109_spl
| cons(sK51_skl,app(nil,X0)) = app(sK49_skl,X0)
| ~ ssItem(sK51_skl)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1325,f247]) ).
fof(f1759,definition,
! [X0] :
( sQ166_spl
<=> ( cons(sK51_skl,app(nil,X0)) = app(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f1762,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ3_spl
| ~ sQ15_spl
| sQ166_spl ),
inference(split_clause,[status(thm)],[f1758,f1759,f552,f486,f1226,f817]) ).
fof(f1763,plain,
( ~ sQ108_spl
| ~ sQ161_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1749,f1222]) ).
fof(f1764,plain,
( ~ sQ108_spl
| ~ sQ161_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1763,f486,f1725,f1221]) ).
fof(f1768,plain,
( ~ sQ26_spl
| ~ sQ0_spl
| ~ sQ109_spl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f326,f1246]) ).
fof(f1771,plain,
( ~ sQ26_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1768,f555,f447,f1226,f440,f637]) ).
fof(f1774,plain,
( sQ26_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ segmentP(nil,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1325,f639]) ).
fof(f1775,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| tl(sK49_skl) = nil
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1325,f243]) ).
fof(f1776,definition,
( sQ167_spl
<=> tl(sK49_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f1777,plain,
( ~ sQ167_spl
| tl(sK49_skl) = nil ),
inference(component_clause,[status(thm)],[f1776]) ).
fof(f1779,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sQ167_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1775,f552,f486,f1776,f1226,f817]) ).
fof(f1805,definition,
( sQ168_spl
<=> ssList(app(nil,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f1807,plain,
( sQ168_spl
| ~ ssList(app(nil,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1805]) ).
fof(f1815,definition,
( sQ171_spl
<=> ssList(app(app(nil,sK49_skl),sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f1816,plain,
( ~ sQ171_spl
| ssList(app(app(nil,sK49_skl),sK49_skl)) ),
inference(component_clause,[status(thm)],[f1815]) ).
fof(f1817,plain,
( sQ171_spl
| ~ ssList(app(app(nil,sK49_skl),sK49_skl)) ),
inference(component_clause,[status(thm)],[f1815]) ).
fof(f1844,definition,
( sQ177_spl
<=> nil = app(app(nil,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f1845,plain,
( ~ sQ177_spl
| nil = app(app(nil,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f1844]) ).
fof(f1848,plain,
( sQ168_spl
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f245,f1807]) ).
fof(f1849,plain,
( sQ168_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1848,f552,f555,f1805]) ).
fof(f1851,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| memberP(sK54_skl,X0)
| memberP(app(app(sK53_skl,sK49_skl),sK49_skl),X0)
| ~ memberP(sK49_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1270,f270]) ).
fof(f1863,definition,
! [X0] :
( sQ178_spl
<=> ( memberP(sK54_skl,X0)
| memberP(app(app(sK53_skl,sK49_skl),sK49_skl),X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f1864,plain,
! [X0] :
( ~ sQ178_spl
| memberP(sK54_skl,X0)
| memberP(app(app(sK53_skl,sK49_skl),sK49_skl),X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1863]) ).
fof(f1866,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ11_spl
| ~ sQ124_spl
| sQ178_spl ),
inference(split_clause,[status(thm)],[f1851,f1863,f1440,f531,f1226,f440,f492]) ).
fof(f1893,definition,
( sQ179_spl
<=> sK54_skl = sK54_skl ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f1897,definition,
( sQ180_spl
<=> sK49_skl = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f2007,plain,
! [X0,X1] :
( ~ sQ20_spl
| ~ singletonP(cons(X1,X0))
| sK4_skl(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f598,f222]) ).
fof(f2008,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ20_spl
| ~ singletonP(cons(sK51_skl,nil))
| sK4_skl(sK49_skl) = sK51_skl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1325,f2007]) ).
fof(f2009,definition,
( sQ200_spl
<=> sK4_skl(sK49_skl) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f2010,plain,
( ~ sQ200_spl
| sK4_skl(sK49_skl) = sK51_skl ),
inference(component_clause,[status(thm)],[f2009]) ).
fof(f2012,definition,
( sQ201_spl
<=> singletonP(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f2014,plain,
( sQ201_spl
| ~ singletonP(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f2012]) ).
fof(f2015,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ20_spl
| ~ sQ201_spl
| sQ200_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2008,f552,f486,f2009,f2012,f586,f1226,f817]) ).
fof(f2016,plain,
( sQ201_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ singletonP(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1325,f2014]) ).
fof(f2017,plain,
( sQ201_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2016,f546]) ).
fof(f2018,plain,
( sQ201_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f2017]) ).
fof(f2020,plain,
! [X0,X1] :
( ~ rearsegP(app(X0,X1),X1)
| sK6_skl(X1,app(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f782,f245]) ).
fof(f2021,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ rearsegP(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),sK54_skl)
| sK6_skl(sK54_skl,sK49_skl) = app(app(sK53_skl,sK49_skl),sK49_skl)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(paramodulation,[status(thm)],[f1270,f2020]) ).
fof(f2022,definition,
( sQ202_spl
<=> sK6_skl(sK54_skl,sK49_skl) = app(app(sK53_skl,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f2025,definition,
( sQ203_spl
<=> rearsegP(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f2027,plain,
( sQ203_spl
| ~ rearsegP(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),sK54_skl) ),
inference(component_clause,[status(thm)],[f2025]) ).
fof(f2028,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ203_spl
| sQ202_spl
| ~ sQ11_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f2021,f1440,f531,f2022,f2025,f1226,f440,f492]) ).
fof(f2029,plain,
( sQ203_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ rearsegP(sK49_skl,sK54_skl) ),
inference(forward_demodulation,[status(thm)],[f1270,f2027]) ).
fof(f2030,plain,
( sQ203_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2029,f890]) ).
fof(f2031,plain,
( sQ203_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ59_spl ),
inference(contradiction_clause,[status(thm)],[f2030]) ).
fof(f2048,plain,
( sQ124_spl
| ~ ssList(sK49_skl)
| ~ ssList(app(sK53_skl,sK49_skl)) ),
inference(resolution,[status(thm)],[f1442,f245]) ).
fof(f2049,plain,
( sQ124_spl
| ~ sQ16_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f2048,f1676,f555,f1440]) ).
fof(f2051,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ128_spl
| app(nil,sK54_skl) = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f1460,f1270]) ).
fof(f2067,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ128_spl
| sQ157_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2051,f1692]) ).
fof(f2068,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ128_spl
| sQ157_spl ),
inference(contradiction_clause,[status(thm)],[f2067]) ).
fof(f2213,plain,
( ~ sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sK49_skl = app(app(sK53_skl,sK49_skl),cons(sK51_skl,nil)) ),
inference(forward_demodulation,[status(thm)],[f1325,f996]) ).
fof(f2214,plain,
( ~ sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sK49_skl = app(app(sK53_skl,sK49_skl),sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1325,f2213]) ).
fof(f2227,plain,
( sQ77_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ ssList(app(app(app(sK53_skl,sK49_skl),cons(sK51_skl,nil)),nil)) ),
inference(forward_demodulation,[status(thm)],[f1325,f993]) ).
fof(f2228,plain,
( sQ77_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ ssList(app(app(app(sK53_skl,sK49_skl),sK49_skl),nil)) ),
inference(forward_demodulation,[status(thm)],[f1325,f2227]) ).
fof(f2231,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f295]) ).
fof(f2232,plain,
! [X0,X1,X2,X3] :
( ~ frontsegP(X3,X2)
| ~ frontsegP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| frontsegP(X0,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f282]) ).
fof(f2234,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ frontsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f282,f298]) ).
fof(f2236,definition,
! [X0,X1] :
( sQ225_spl
<=> ( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f2239,plain,
( ~ sQ15_spl
| sQ225_spl ),
inference(split_clause,[status(thm)],[f2231,f2236,f552]) ).
fof(f2240,plain,
! [X0,X1,X2,X3] :
( ~ frontsegP(X3,X2)
| ~ frontsegP(X1,X3)
| ~ ssList(X3)
| frontsegP(X0,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2232]) ).
fof(f2241,definition,
! [X0,X1] :
( sQ226_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ frontsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f2242,plain,
! [X0,X1] :
( ~ sQ226_spl
| nil = X1
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ frontsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2241]) ).
fof(f2244,plain,
( sQ226_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2234,f552,f2241]) ).
fof(f2247,plain,
! [X0,X1] :
( ~ sQ226_spl
| nil = X1
| ~ frontsegP(X0,X1)
| ~ frontsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2242]) ).
fof(f2248,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f284,f295]) ).
fof(f2249,plain,
! [X0,X1,X2] :
( ~ frontsegP(X2,X0)
| ~ frontsegP(X1,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| X0 = X1
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f284,f282]) ).
fof(f2251,definition,
! [X0] :
( sQ227_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2254,plain,
( sQ227_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2248,f552,f2251]) ).
fof(f2255,plain,
! [X0,X1,X2] :
( ~ frontsegP(X2,X0)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| X0 = X1
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2249]) ).
fof(f2257,plain,
! [X0,X1,X2] :
( X1 = app(X0,X2)
| ~ frontsegP(X1,app(X0,X2))
| ~ ssList(app(X0,X2))
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f288,f284]) ).
fof(f2258,plain,
! [X0,X1,X2,X3] :
( frontsegP(X3,X1)
| ~ frontsegP(X3,app(X0,X2))
| ~ ssList(X1)
| ~ ssList(app(X0,X2))
| ~ ssList(X3)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f288,f282]) ).
fof(f2259,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| frontsegP(sK49_skl,X0)
| ~ frontsegP(app(app(sK53_skl,sK49_skl),sK49_skl),X0)
| ~ ssList(sK54_skl)
| ~ ssList(X0)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(paramodulation,[status(thm)],[f1270,f288]) ).
fof(f2260,plain,
! [X0,X1,X2] :
( X1 = app(X0,X2)
| ~ frontsegP(X1,app(X0,X2))
| ~ ssList(app(X0,X2))
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2257]) ).
fof(f2261,plain,
! [X0,X1,X2] :
( X1 = app(X0,X2)
| ~ frontsegP(X1,app(X0,X2))
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2260,f245]) ).
fof(f2262,plain,
! [X0,X1,X2,X3] :
( frontsegP(X3,X1)
| ~ frontsegP(X3,app(X0,X2))
| ~ ssList(app(X0,X2))
| ~ ssList(X3)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2258]) ).
fof(f2263,plain,
! [X0,X1,X2,X3] :
( frontsegP(X3,X1)
| ~ frontsegP(X3,app(X0,X2))
| ~ ssList(X3)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2262,f245]) ).
fof(f2264,definition,
! [X0] :
( sQ228_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(app(app(sK53_skl,sK49_skl),sK49_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f2265,plain,
! [X0] :
( ~ sQ228_spl
| frontsegP(sK49_skl,X0)
| ~ frontsegP(app(app(sK53_skl,sK49_skl),sK49_skl),X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2264]) ).
fof(f2267,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ11_spl
| sQ228_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f2259,f1440,f2264,f531,f1226,f440,f492]) ).
fof(f2271,definition,
! [X0] :
( sQ229_spl
<=> ( memberP(sK49_skl,X0)
| memberP(app(sK53_skl,sK49_skl),X0)
| ~ ssItem(X0)
| memberP(sK54_skl,X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f2303,plain,
! [X0,X1,X2,X3,X4] :
( ~ frontsegP(X4,cons(X1,X3))
| ~ frontsegP(cons(X0,X2),X4)
| ~ ssList(cons(X1,X3))
| ~ ssList(X4)
| ~ ssList(cons(X0,X2))
| X0 = X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f291,f282]) ).
fof(f2305,plain,
! [X0,X1] :
( ~ sQ51_spl
| ~ sQ109_spl
| sK51_skl = X0
| ~ frontsegP(sK49_skl,cons(X0,X1))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1325,f291]) ).
fof(f2306,plain,
! [X0,X1] :
( ~ sQ51_spl
| ~ sQ109_spl
| X0 = sK51_skl
| ~ frontsegP(cons(X0,X1),sK49_skl)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1325,f291]) ).
fof(f2307,plain,
! [X0,X1,X2,X3,X4] :
( ~ frontsegP(X4,cons(X1,X3))
| ~ frontsegP(cons(X0,X2),X4)
| ~ ssList(cons(X1,X3))
| ~ ssList(X4)
| X0 = X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2303,f222]) ).
fof(f2308,definition,
! [X0,X1] :
( sQ234_spl
<=> ( sK51_skl = X0
| ~ frontsegP(sK49_skl,cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f2311,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| sQ234_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2305,f486,f2308,f552,f1226,f817]) ).
fof(f2312,definition,
! [X0,X1] :
( sQ235_spl
<=> ( X0 = sK51_skl
| ~ frontsegP(cons(X0,X1),sK49_skl)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f2315,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ235_spl ),
inference(split_clause,[status(thm)],[f2306,f2312,f486,f552,f1226,f817]) ).
fof(f2316,plain,
! [X0,X1,X2,X3,X4] :
( ~ frontsegP(X4,cons(X1,X3))
| ~ frontsegP(cons(X0,X2),X4)
| ~ ssList(cons(X1,X3))
| ~ ssList(X4)
| ~ ssList(cons(X0,X2))
| frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f292,f282]) ).
fof(f2318,plain,
! [X0,X1] :
( ~ sQ51_spl
| ~ sQ109_spl
| frontsegP(nil,X1)
| ~ frontsegP(sK49_skl,cons(X0,X1))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1325,f292]) ).
fof(f2319,plain,
! [X0,X1] :
( ~ sQ51_spl
| ~ sQ109_spl
| frontsegP(X1,nil)
| ~ frontsegP(cons(X0,X1),sK49_skl)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1325,f292]) ).
fof(f2320,plain,
! [X0,X1,X2,X3,X4] :
( ~ frontsegP(X4,cons(X1,X3))
| ~ frontsegP(cons(X0,X2),X4)
| ~ ssList(cons(X1,X3))
| ~ ssList(X4)
| frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2316,f222]) ).
fof(f2322,definition,
! [X0,X1] :
( sQ236_spl
<=> ( frontsegP(nil,X1)
| ~ frontsegP(sK49_skl,cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f2325,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| sQ236_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2318,f486,f2322,f552,f1226,f817]) ).
fof(f2326,definition,
! [X0,X1] :
( sQ237_spl
<=> ( frontsegP(X1,nil)
| ~ frontsegP(cons(X0,X1),sK49_skl)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f2329,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ237_spl ),
inference(split_clause,[status(thm)],[f2319,f2326,f486,f552,f1226,f817]) ).
fof(f2331,plain,
! [X0,X1,X2] :
( X0 = X0
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(X0)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f471,f291]) ).
fof(f2332,plain,
! [X0,X1,X2] :
( cons(X0,X2) = cons(X0,X1)
| ~ frontsegP(cons(X0,X2),cons(X0,X1))
| ~ ssList(cons(X0,X1))
| ~ ssList(cons(X0,X2))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f471,f284]) ).
fof(f2333,plain,
! [X0,X1,X2,X3] :
( frontsegP(X3,cons(X0,X2))
| ~ frontsegP(X3,cons(X0,X1))
| ~ ssList(cons(X0,X2))
| ~ ssList(cons(X0,X1))
| ~ ssList(X3)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f471,f282]) ).
fof(f2334,plain,
! [X0] :
( ~ sQ51_spl
| ~ sQ109_spl
| ~ frontsegP(nil,X0)
| frontsegP(sK49_skl,cons(sK51_skl,X0))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1325,f471]) ).
fof(f2335,plain,
! [X0] :
( ~ sQ51_spl
| ~ sQ109_spl
| ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK49_skl)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1325,f471]) ).
fof(f2343,definition,
! [X0] :
( sQ240_spl
<=> ( X0 = X0
| ~ ssItem(X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f2346,definition,
! [X1,X2] :
( sQ241_spl
<=> ( ~ ssList(X2)
| ~ ssList(X1)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f2347,plain,
! [X0,X1] :
( ~ sQ241_spl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2346]) ).
fof(f2349,plain,
( sQ241_spl
| sQ240_spl ),
inference(split_clause,[status(thm)],[f2331,f2343,f2346]) ).
fof(f2350,plain,
! [X0,X1,X2] :
( cons(X0,X2) = cons(X0,X1)
| ~ frontsegP(cons(X0,X2),cons(X0,X1))
| ~ ssList(cons(X0,X1))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2332,f222]) ).
fof(f2351,plain,
! [X0,X1,X2,X3] :
( frontsegP(X3,cons(X0,X2))
| ~ frontsegP(X3,cons(X0,X1))
| ~ ssList(cons(X0,X2))
| ~ ssList(X3)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2333,f222]) ).
fof(f2352,definition,
! [X0] :
( sQ242_spl
<=> ( ~ frontsegP(nil,X0)
| frontsegP(sK49_skl,cons(sK51_skl,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f2355,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sQ242_spl
| ~ sQ15_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2334,f486,f552,f2352,f1226,f817]) ).
fof(f2356,definition,
! [X0] :
( sQ243_spl
<=> ( ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f2357,plain,
! [X0] :
( ~ sQ243_spl
| ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK49_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2356]) ).
fof(f2359,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| sQ243_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2335,f486,f2356,f552,f1226,f817]) ).
fof(f2360,plain,
! [X0] :
( ~ sQ243_spl
| frontsegP(cons(sK51_skl,X0),sK49_skl)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2357,f295]) ).
fof(f2362,plain,
! [X0,X1] :
( ~ sQ241_spl
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2347]) ).
fof(f2363,plain,
( sQ171_spl
| ~ ssList(sK49_skl)
| ~ ssList(app(nil,sK49_skl)) ),
inference(resolution,[status(thm)],[f1817,f245]) ).
fof(f2364,plain,
( sQ171_spl
| ~ sQ16_spl
| ~ sQ168_spl ),
inference(split_clause,[status(thm)],[f2363,f1805,f555,f1815]) ).
fof(f2365,plain,
( ~ sQ94_spl
| ~ sQ51_spl
| ~ sQ109_spl
| nil = app(app(sK53_skl,sK49_skl),cons(sK51_skl,nil)) ),
inference(forward_demodulation,[status(thm)],[f1325,f1094]) ).
fof(f2369,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ94_spl
| ~ sQ51_spl
| app(nil,sK54_skl) = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f2370,f1270]) ).
fof(f2370,plain,
( ~ sQ94_spl
| ~ sQ51_spl
| ~ sQ109_spl
| nil = app(app(sK53_skl,sK49_skl),sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1325,f2365]) ).
fof(f2388,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ94_spl
| ~ sQ51_spl
| sQ157_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2369,f1692]) ).
fof(f2389,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ94_spl
| ~ sQ51_spl
| sQ157_spl ),
inference(contradiction_clause,[status(thm)],[f2388]) ).
fof(f2394,plain,
( ~ sQ177_spl
| nil = app(nil,app(sK49_skl,sK49_skl))
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1845,f382]) ).
fof(f2411,definition,
( sQ244_spl
<=> nil = app(nil,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f2412,plain,
( ~ sQ244_spl
| nil = app(nil,sK49_skl) ),
inference(component_clause,[status(thm)],[f2411]) ).
fof(f2415,definition,
( sQ245_spl
<=> nil = app(nil,app(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f2416,plain,
( ~ sQ245_spl
| nil = app(nil,app(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f2415]) ).
fof(f2418,plain,
( ~ sQ177_spl
| sQ245_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2394,f552,f555,f2415,f1844]) ).
fof(f2423,definition,
( sQ247_spl
<=> sK6_skl(sK49_skl,nil) = app(nil,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f2424,plain,
( ~ sQ247_spl
| sK6_skl(sK49_skl,nil) = app(nil,sK49_skl) ),
inference(component_clause,[status(thm)],[f2423]) ).
fof(f2435,definition,
! [X0] :
( sQ250_spl
<=> ( ~ memberP(app(nil,sK49_skl),X0)
| memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f2436,plain,
! [X0] :
( ~ sQ250_spl
| ~ memberP(app(nil,sK49_skl),X0)
| memberP(nil,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f2435]) ).
fof(f2461,plain,
! [X0] :
( ~ sQ250_spl
| ~ memberP(app(nil,sK49_skl),X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2436,f279]) ).
fof(f2519,plain,
! [X0] :
( ~ sQ80_spl
| rearsegP(X0,nil)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(nil)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f1005]) ).
fof(f2520,plain,
! [X0] :
( ~ sQ59_spl
| rearsegP(X0,sK54_skl)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(sK54_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f890]) ).
fof(f2522,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f309]) ).
fof(f2523,plain,
! [X0,X1,X2,X3] :
( ~ rearsegP(X3,X2)
| ~ rearsegP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| rearsegP(X0,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f301]) ).
fof(f2525,plain,
! [X0] :
( sQ164_spl
| ~ rearsegP(X0,sK49_skl)
| ~ rearsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f301,f1741]) ).
fof(f2526,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f301,f312]) ).
fof(f2528,definition,
! [X0] :
( sQ257_spl
<=> ( rearsegP(X0,nil)
| ~ rearsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f2532,definition,
! [X0] :
( sQ258_spl
<=> ( rearsegP(X0,nil)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f2535,plain,
( ~ sQ80_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ258_spl ),
inference(split_clause,[status(thm)],[f2519,f2532,f555,f552,f1004]) ).
fof(f2536,definition,
! [X0] :
( sQ259_spl
<=> ( rearsegP(X0,sK54_skl)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f2539,plain,
( ~ sQ59_spl
| ~ sQ11_spl
| ~ sQ16_spl
| sQ259_spl ),
inference(split_clause,[status(thm)],[f2520,f2536,f555,f531,f889]) ).
fof(f2542,definition,
! [X0,X1] :
( sQ260_spl
<=> ( ~ ssList(X1)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f2545,plain,
( ~ sQ15_spl
| sQ260_spl ),
inference(split_clause,[status(thm)],[f2522,f2542,f552]) ).
fof(f2546,plain,
! [X0,X1,X2,X3] :
( ~ rearsegP(X3,X2)
| ~ rearsegP(X1,X3)
| ~ ssList(X3)
| rearsegP(X0,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2523]) ).
fof(f2547,definition,
! [X0] :
( sQ261_spl
<=> ( ~ rearsegP(X0,sK49_skl)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f2550,plain,
( sQ164_spl
| ~ sQ16_spl
| sQ261_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2525,f552,f2547,f555,f1739]) ).
fof(f2551,definition,
! [X0,X1] :
( sQ262_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f2552,plain,
! [X0,X1] :
( ~ sQ262_spl
| nil = X1
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2551]) ).
fof(f2554,plain,
( sQ262_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2526,f552,f2551]) ).
fof(f2557,plain,
! [X0,X1] :
( ~ sQ262_spl
| nil = X1
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2552]) ).
fof(f2559,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| X0 = app(X1,X0)
| ~ rearsegP(X0,app(X1,X0))
| ~ ssList(app(X1,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f303,f627]) ).
fof(f2560,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f303,f309]) ).
fof(f2561,plain,
! [X0,X1,X2] :
( ~ rearsegP(X2,X0)
| ~ rearsegP(X1,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| X0 = X1
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f303,f301]) ).
fof(f2563,definition,
( sQ263_spl
<=> rearsegP(sK54_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f2565,plain,
( sQ263_spl
| ~ rearsegP(sK54_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f2563]) ).
fof(f2566,definition,
( sQ264_spl
<=> sK54_skl = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f2567,plain,
( ~ sQ264_spl
| sK54_skl = sK49_skl ),
inference(component_clause,[status(thm)],[f2566]) ).
fof(f2568,plain,
( sQ264_spl
| sK54_skl != sK49_skl ),
inference(component_clause,[status(thm)],[f2566]) ).
fof(f2570,plain,
! [X0,X1] :
( ~ ssList(X1)
| X0 = app(X1,X0)
| ~ rearsegP(X0,app(X1,X0))
| ~ ssList(app(X1,X0))
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2559]) ).
fof(f2571,plain,
! [X0,X1] :
( ~ ssList(X1)
| X0 = app(X1,X0)
| ~ rearsegP(X0,app(X1,X0))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2570,f245]) ).
fof(f2572,definition,
! [X0] :
( sQ265_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f2575,plain,
( sQ265_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2560,f552,f2572]) ).
fof(f2576,plain,
! [X0,X1,X2] :
( ~ rearsegP(X2,X0)
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| X0 = X1
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2561]) ).
fof(f2578,plain,
! [X0,X1,X2] :
( X1 = app(X2,X0)
| ~ rearsegP(X1,app(X2,X0))
| ~ ssList(app(X2,X0))
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f307,f303]) ).
fof(f2580,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| rearsegP(sK49_skl,X0)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f1270,f307]) ).
fof(f2581,plain,
! [X0,X1,X2] :
( X1 = app(X2,X0)
| ~ rearsegP(X1,app(X2,X0))
| ~ ssList(app(X2,X0))
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2578]) ).
fof(f2582,plain,
! [X0,X1,X2] :
( X1 = app(X2,X0)
| ~ rearsegP(X1,app(X2,X0))
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2581,f245]) ).
fof(f2585,definition,
! [X0] :
( sQ266_spl
<=> ( rearsegP(sK49_skl,X0)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f2586,plain,
! [X0] :
( ~ sQ266_spl
| rearsegP(sK49_skl,X0)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2585]) ).
fof(f2588,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| sQ266_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2580,f531,f2585,f1440,f1226,f440,f492]) ).
fof(f2590,plain,
( sQ157_spl
| ~ sQ264_spl
| sK49_skl != app(nil,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f2567,f1692]) ).
fof(f2609,plain,
! [X0] :
( sQ263_spl
| ~ rearsegP(X0,sK49_skl)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f2565,f301]) ).
fof(f2610,definition,
! [X0] :
( sQ268_spl
<=> ( ~ rearsegP(X0,sK49_skl)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f2613,plain,
( sQ263_spl
| ~ sQ16_spl
| sQ268_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2609,f531,f2610,f555,f2563]) ).
fof(f2618,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ0_spl
| ~ sQ109_spl
| segmentP(X0,sK49_skl)
| ~ segmentP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f315,f1250]) ).
fof(f2619,plain,
! [X0,X1] :
( ~ ssList(X1)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f315,f323]) ).
fof(f2620,plain,
! [X0,X1,X2,X3] :
( ~ segmentP(X3,X2)
| ~ segmentP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f315,f315]) ).
fof(f2622,plain,
! [X0] :
( sQ26_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ segmentP(X0,sK49_skl)
| ~ segmentP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f315,f1774]) ).
fof(f2623,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f315,f326]) ).
fof(f2625,definition,
! [X0] :
( sQ269_spl
<=> ( segmentP(X0,sK49_skl)
| ~ segmentP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f2628,plain,
( ~ sQ29_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ16_spl
| sQ269_spl ),
inference(split_clause,[status(thm)],[f2618,f2625,f555,f1226,f440,f656]) ).
fof(f2629,definition,
! [X0,X1] :
( sQ270_spl
<=> ( ~ ssList(X1)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f2632,plain,
( ~ sQ15_spl
| sQ270_spl ),
inference(split_clause,[status(thm)],[f2619,f2629,f552]) ).
fof(f2633,plain,
! [X0,X1,X2,X3] :
( ~ segmentP(X3,X2)
| ~ segmentP(X1,X3)
| ~ ssList(X3)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2620]) ).
fof(f2634,definition,
! [X0] :
( sQ271_spl
<=> ( ~ segmentP(X0,sK49_skl)
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f2637,plain,
( sQ26_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ16_spl
| sQ271_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2622,f552,f2634,f555,f1226,f817,f637]) ).
fof(f2638,definition,
! [X0,X1] :
( sQ272_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f2639,plain,
! [X0,X1] :
( ~ sQ272_spl
| nil = X1
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2638]) ).
fof(f2641,plain,
( sQ272_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2623,f552,f2638]) ).
fof(f2644,plain,
! [X0,X1] :
( ~ sQ272_spl
| nil = X1
| ~ segmentP(X0,X1)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2639]) ).
fof(f2646,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f317,f323]) ).
fof(f2647,plain,
! [X0,X1,X2] :
( ~ segmentP(X2,X0)
| ~ segmentP(X1,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f317,f315]) ).
fof(f2649,definition,
( sQ273_spl
<=> segmentP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f2651,plain,
( sQ273_spl
| ~ segmentP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f2649]) ).
fof(f2653,definition,
! [X0] :
( sQ274_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f2656,plain,
( sQ274_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2646,f552,f2653]) ).
fof(f2657,plain,
! [X0,X1,X2] :
( ~ segmentP(X2,X0)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2647]) ).
fof(f2659,plain,
( sQ273_spl
| ~ sQ29_spl
| ~ sQ0_spl
| ~ sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2651,f1250]) ).
fof(f2660,plain,
( sQ273_spl
| ~ sQ29_spl
| ~ sQ0_spl
| ~ sQ109_spl ),
inference(contradiction_clause,[status(thm)],[f2659]) ).
fof(f2661,plain,
! [X0,X1,X2,X3] :
( X1 = app(app(X2,X0),X3)
| ~ segmentP(X1,app(app(X2,X0),X3))
| ~ ssList(app(app(X2,X0),X3))
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f321,f317]) ).
fof(f2662,plain,
! [X0,X1,X2,X3,X4] :
( segmentP(X4,X1)
| ~ segmentP(X4,app(app(X2,X0),X3))
| ~ ssList(X1)
| ~ ssList(app(app(X2,X0),X3))
| ~ ssList(X4)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f321,f315]) ).
fof(f2663,plain,
! [X0,X1,X2,X3] :
( X1 = app(app(X2,X0),X3)
| ~ segmentP(X1,app(app(X2,X0),X3))
| ~ ssList(app(app(X2,X0),X3))
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2661]) ).
fof(f2664,plain,
! [X0,X1,X2,X3,X4] :
( segmentP(X4,X1)
| ~ segmentP(X4,app(app(X2,X0),X3))
| ~ ssList(app(app(X2,X0),X3))
| ~ ssList(X4)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2662]) ).
fof(f2679,plain,
( ~ sQ244_spl
| ~ ssList(nil)
| rearsegP(nil,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f2412,f627]) ).
fof(f2699,definition,
! [X0] :
( sQ278_spl
<=> ( frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f2703,definition,
( sQ279_spl
<=> sK6_skl(sK49_skl,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f2704,plain,
( ~ sQ279_spl
| sK6_skl(sK49_skl,nil) = nil ),
inference(component_clause,[status(thm)],[f2703]) ).
fof(f2706,definition,
( sQ280_spl
<=> rearsegP(app(nil,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f2707,plain,
( ~ sQ280_spl
| rearsegP(app(nil,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f2706]) ).
fof(f2708,plain,
( sQ280_spl
| ~ rearsegP(app(nil,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f2706]) ).
fof(f2721,plain,
( ~ sQ244_spl
| ~ sQ15_spl
| sQ164_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2679,f555,f1739,f552,f2411]) ).
fof(f2739,plain,
! [X0] :
( ~ sQ241_spl
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2362,f295]) ).
fof(f2741,plain,
( ~ sQ241_spl
| ~ sQ15_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f2739,f591,f552,f2346]) ).
fof(f2764,plain,
( sQ280_spl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f2708,f627]) ).
fof(f2766,definition,
( sQ287_spl
<=> rearsegP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f2767,plain,
( ~ sQ287_spl
| rearsegP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f2766]) ).
fof(f2768,plain,
( sQ287_spl
| ~ rearsegP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f2766]) ).
fof(f2770,plain,
( sQ280_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2764,f555,f552,f2706]) ).
fof(f2775,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| segmentP(sK49_skl,X0)
| ~ segmentP(sK49_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(sK53_skl,sK49_skl))
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1270,f321]) ).
fof(f2778,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| segmentP(app(sK49_skl,X1),X0)
| ~ segmentP(sK54_skl,X0)
| ~ ssList(X1)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f1270,f321]) ).
fof(f2791,definition,
! [X0] :
( sQ289_spl
<=> ( segmentP(sK49_skl,X0)
| ~ segmentP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f2794,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ11_spl
| ~ sQ154_spl
| sQ289_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2775,f555,f2791,f1676,f531,f1226,f440,f492]) ).
fof(f2797,definition,
! [X0,X1] :
( sQ290_spl
<=> ( segmentP(app(sK49_skl,X1),X0)
| ~ segmentP(sK54_skl,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f2798,plain,
! [X0,X1] :
( ~ sQ290_spl
| segmentP(app(sK49_skl,X1),X0)
| ~ segmentP(sK54_skl,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2797]) ).
fof(f2800,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| sQ290_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2778,f531,f2797,f1440,f1226,f440,f492]) ).
fof(f2814,plain,
( sQ287_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f2768,f305]) ).
fof(f2816,plain,
( sQ287_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2814,f422]) ).
fof(f2817,plain,
sQ287_spl,
inference(contradiction_clause,[status(thm)],[f2816]) ).
fof(f2818,plain,
( ~ sQ287_spl
| sK49_skl = sK49_skl
| ~ rearsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f2767,f303]) ).
fof(f2819,plain,
! [X0] :
( ~ sQ287_spl
| rearsegP(X0,sK49_skl)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2767,f301]) ).
fof(f2820,plain,
( sQ180_spl
| ~ sQ287_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2818,f555,f2766,f1897]) ).
fof(f2821,definition,
! [X0] :
( sQ291_spl
<=> ( rearsegP(X0,sK49_skl)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f2824,plain,
( ~ sQ287_spl
| ~ sQ16_spl
| sQ291_spl ),
inference(split_clause,[status(thm)],[f2819,f2821,f555,f2766]) ).
fof(f2826,plain,
! [X0] :
( ~ sQ280_spl
| rearsegP(X0,sK49_skl)
| ~ rearsegP(X0,app(nil,sK49_skl))
| ~ ssList(sK49_skl)
| ~ ssList(app(nil,sK49_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2707,f301]) ).
fof(f2827,definition,
( sQ292_spl
<=> rearsegP(sK49_skl,app(nil,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f2829,plain,
( sQ292_spl
| ~ rearsegP(sK49_skl,app(nil,sK49_skl)) ),
inference(component_clause,[status(thm)],[f2827]) ).
fof(f2830,definition,
( sQ293_spl
<=> sK49_skl = app(nil,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f2831,plain,
( ~ sQ293_spl
| sK49_skl = app(nil,sK49_skl) ),
inference(component_clause,[status(thm)],[f2830]) ).
fof(f2832,plain,
( sQ293_spl
| sK49_skl != app(nil,sK49_skl) ),
inference(component_clause,[status(thm)],[f2830]) ).
fof(f2834,definition,
! [X0] :
( sQ294_spl
<=> ( rearsegP(X0,sK49_skl)
| ~ rearsegP(X0,app(nil,sK49_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f2837,plain,
( ~ sQ280_spl
| ~ sQ16_spl
| ~ sQ168_spl
| sQ294_spl ),
inference(split_clause,[status(thm)],[f2826,f2834,f1805,f555,f2706]) ).
fof(f2847,plain,
! [X0] :
( ~ sQ293_spl
| ~ memberP(sK49_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f2831,f272]) ).
fof(f2848,plain,
! [X0] :
( ~ sQ293_spl
| ~ memberP(nil,X0)
| memberP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f2831,f271]) ).
fof(f2849,plain,
! [X0,X1] :
( ~ sQ293_spl
| segmentP(app(sK49_skl,X1),X0)
| ~ segmentP(sK49_skl,X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f2831,f321]) ).
fof(f2850,plain,
! [X0] :
( ~ sQ293_spl
| memberP(sK49_skl,X0)
| memberP(nil,X0)
| ~ memberP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f2831,f270]) ).
fof(f2851,plain,
! [X0] :
( ~ sQ293_spl
| rearsegP(sK49_skl,X0)
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f2831,f307]) ).
fof(f2852,plain,
( ~ sQ293_spl
| ~ rearsegP(app(nil,sK49_skl),sK49_skl)
| sK6_skl(sK49_skl,sK49_skl) = nil
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2831,f2020]) ).
fof(f2854,plain,
! [X0] :
( ~ sQ293_spl
| X0 = nil
| app(X0,sK49_skl) != sK49_skl
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2831,f376]) ).
fof(f2856,plain,
! [X0] :
( ~ sQ293_spl
| X0 = sK49_skl
| app(nil,X0) != sK49_skl
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f2831,f378]) ).
fof(f2859,plain,
! [X0] :
( ~ sQ293_spl
| app(app(X0,nil),sK49_skl) = app(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f2831,f382]) ).
fof(f2860,plain,
! [X0] :
( ~ sQ293_spl
| app(sK49_skl,X0) = app(nil,app(sK49_skl,X0))
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2831,f382]) ).
fof(f2864,definition,
! [X0] :
( sQ295_spl
<=> ( ~ memberP(sK49_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ295_spl])],[split_symbol_definition]) ).
fof(f2867,plain,
( ~ sQ293_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ295_spl ),
inference(split_clause,[status(thm)],[f2847,f2864,f552,f555,f2830]) ).
fof(f2868,plain,
( ~ sQ293_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f2848,f770,f552,f555,f2830]) ).
fof(f2869,definition,
! [X0,X1] :
( sQ296_spl
<=> ( segmentP(app(sK49_skl,X1),X0)
| ~ segmentP(sK49_skl,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ296_spl])],[split_symbol_definition]) ).
fof(f2872,plain,
( ~ sQ293_spl
| ~ sQ15_spl
| sQ296_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2849,f555,f2869,f552,f2830]) ).
fof(f2873,definition,
! [X0] :
( sQ297_spl
<=> ( memberP(sK49_skl,X0)
| memberP(nil,X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ297_spl])],[split_symbol_definition]) ).
fof(f2876,plain,
( ~ sQ293_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ297_spl ),
inference(split_clause,[status(thm)],[f2850,f2873,f552,f555,f2830]) ).
fof(f2877,definition,
! [X0] :
( sQ298_spl
<=> ( rearsegP(sK49_skl,X0)
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f2880,plain,
( ~ sQ293_spl
| ~ sQ15_spl
| sQ298_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2851,f555,f2877,f552,f2830]) ).
fof(f2881,definition,
( sQ299_spl
<=> sK6_skl(sK49_skl,sK49_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f2882,plain,
( ~ sQ299_spl
| sK6_skl(sK49_skl,sK49_skl) = nil ),
inference(component_clause,[status(thm)],[f2881]) ).
fof(f2884,plain,
( ~ sQ293_spl
| ~ sQ280_spl
| sQ299_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2852,f552,f555,f2881,f2706,f2830]) ).
fof(f2886,definition,
! [X0] :
( sQ300_spl
<=> ( X0 = nil
| app(X0,sK49_skl) != sK49_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ300_spl])],[split_symbol_definition]) ).
fof(f2889,plain,
( ~ sQ293_spl
| sQ300_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2854,f552,f555,f2886,f2830]) ).
fof(f2891,definition,
! [X0] :
( sQ301_spl
<=> ( X0 = sK49_skl
| app(nil,X0) != sK49_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ301_spl])],[split_symbol_definition]) ).
fof(f2894,plain,
( ~ sQ293_spl
| sQ301_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2856,f555,f552,f2891,f2830]) ).
fof(f2897,definition,
! [X0] :
( sQ302_spl
<=> ( app(app(X0,nil),sK49_skl) = app(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f2900,plain,
( ~ sQ293_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ302_spl ),
inference(split_clause,[status(thm)],[f2859,f2897,f552,f555,f2830]) ).
fof(f2901,definition,
! [X0] :
( sQ303_spl
<=> ( app(sK49_skl,X0) = app(nil,app(sK49_skl,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ303_spl])],[split_symbol_definition]) ).
fof(f2904,plain,
( ~ sQ293_spl
| sQ303_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2860,f552,f555,f2901,f2830]) ).
fof(f2932,plain,
( sQ292_spl
| ~ sQ293_spl
| ~ rearsegP(sK49_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f2831,f2829]) ).
fof(f2933,plain,
( sQ292_spl
| ~ sQ293_spl
| ~ sQ287_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2932,f2767]) ).
fof(f2934,plain,
( sQ292_spl
| ~ sQ293_spl
| ~ sQ287_spl ),
inference(contradiction_clause,[status(thm)],[f2933]) ).
fof(f2940,definition,
! [X0] :
( sQ306_spl
<=> ( ~ memberP(sK49_skl,X0)
| ~ ssItem(X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f2944,definition,
! [X0] :
( sQ307_spl
<=> ( ~ memberP(app(sK53_skl,sK49_skl),X0)
| ~ ssItem(X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f3028,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ78_spl
| ~ sQ51_spl
| app(sK49_skl,sK54_skl) = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f2214,f1270]) ).
fof(f3059,definition,
( sQ320_spl
<=> sK6_skl(sK49_skl,sK49_skl) = app(sK53_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ320_spl])],[split_symbol_definition]) ).
fof(f3060,plain,
( ~ sQ320_spl
| sK6_skl(sK49_skl,sK49_skl) = app(sK53_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f3059]) ).
fof(f3084,plain,
( ~ sQ320_spl
| ~ sQ299_spl
| nil = app(sK53_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f2882,f3060]) ).
fof(f3085,plain,
( ~ sQ320_spl
| ~ sQ299_spl
| sQ158_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3084,f1696]) ).
fof(f3086,plain,
( ~ sQ320_spl
| ~ sQ299_spl
| sQ158_spl ),
inference(contradiction_clause,[status(thm)],[f3085]) ).
fof(f3087,plain,
( sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sK49_skl != app(app(sK53_skl,sK49_skl),cons(sK51_skl,nil)) ),
inference(forward_demodulation,[status(thm)],[f1325,f997]) ).
fof(f3088,plain,
( sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sK49_skl != app(app(sK53_skl,sK49_skl),sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1325,f3087]) ).
fof(f3121,plain,
( sQ293_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f2832,f249]) ).
fof(f3122,plain,
( sQ293_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3121,f422]) ).
fof(f3123,plain,
sQ293_spl,
inference(contradiction_clause,[status(thm)],[f3122]) ).
fof(f3177,plain,
! [X0] :
( ~ sQ167_spl
| sK49_skl = X0
| nil != tl(X0)
| hd(sK49_skl) != hd(X0)
| nil = X0
| nil = sK49_skl
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1777,f372]) ).
fof(f3180,definition,
! [X0] :
( sQ326_spl
<=> ( sK49_skl = X0
| nil != tl(X0)
| hd(sK49_skl) != hd(X0)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ326_spl])],[split_symbol_definition]) ).
fof(f3183,plain,
( ~ sQ167_spl
| sQ2_spl
| ~ sQ16_spl
| sQ326_spl ),
inference(split_clause,[status(thm)],[f3177,f3180,f555,f447,f1776]) ).
fof(f3187,plain,
( ~ sQ152_spl
| cons(sK51_skl,tl(sK49_skl)) = sK49_skl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1658,f374]) ).
fof(f3188,plain,
( ~ sQ167_spl
| cons(hd(sK49_skl),nil) = sK49_skl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1777,f374]) ).
fof(f3193,definition,
( sQ328_spl
<=> cons(sK51_skl,tl(sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f3196,plain,
( ~ sQ152_spl
| sQ328_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3187,f555,f447,f3193,f1657]) ).
fof(f3197,definition,
( sQ329_spl
<=> cons(hd(sK49_skl),nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f3200,plain,
( ~ sQ167_spl
| sQ329_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3188,f555,f447,f3197,f1776]) ).
fof(f3205,plain,
( ~ sQ10_spl
| ~ sQ51_spl
| ~ sQ109_spl
| frontsegP(sK49_skl,app(app(sK53_skl,sK49_skl),cons(sK51_skl,nil))) ),
inference(forward_demodulation,[status(thm)],[f1325,f529]) ).
fof(f3206,plain,
( ~ sQ10_spl
| ~ sQ51_spl
| ~ sQ109_spl
| frontsegP(sK49_skl,app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f1325,f3205]) ).
fof(f3336,plain,
! [X0,X1] :
( nil = cons(X0,X1)
| ~ ssList(cons(X0,X1))
| X1 = sK43_skl(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssItem(sK44_skl(cons(X0,X1)))
| ~ ssList(X1)
| ~ ssList(sK43_skl(cons(X0,X1))) ),
inference(resolution,[status(thm)],[f228,f233]) ).
fof(f3343,plain,
! [X0,X1] :
( nil = cons(X1,X0)
| ~ ssList(cons(X1,X0))
| X0 = sK43_skl(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssItem(sK44_skl(cons(X1,X0)))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3336,f231]) ).
fof(f3352,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| hd(sK49_skl) = hd(app(app(sK53_skl,sK49_skl),sK49_skl))
| nil = app(app(sK53_skl,sK49_skl),sK49_skl)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(paramodulation,[status(thm)],[f1270,f391]) ).
fof(f3357,definition,
( sQ351_spl
<=> hd(sK49_skl) = hd(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f3358,plain,
( ~ sQ351_spl
| hd(sK49_skl) = hd(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(component_clause,[status(thm)],[f3357]) ).
fof(f3360,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sQ351_spl
| sQ128_spl
| ~ sQ11_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f3352,f1440,f531,f1459,f3357,f1226,f440,f492]) ).
fof(f3361,plain,
( ~ sQ351_spl
| ~ sQ152_spl
| sK51_skl = hd(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f1658,f3358]) ).
fof(f3363,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| tl(sK49_skl) = app(tl(app(app(sK53_skl,sK49_skl),sK49_skl)),sK54_skl)
| nil = app(app(sK53_skl,sK49_skl),sK49_skl)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(paramodulation,[status(thm)],[f1270,f393]) ).
fof(f3368,definition,
( sQ353_spl
<=> tl(sK49_skl) = app(tl(app(app(sK53_skl,sK49_skl),sK49_skl)),sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ353_spl])],[split_symbol_definition]) ).
fof(f3371,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sQ353_spl
| sQ128_spl
| ~ sQ11_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f3363,f1440,f531,f1459,f3368,f1226,f440,f492]) ).
fof(f3375,definition,
( sQ354_spl
<=> frontsegP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f3376,plain,
( ~ sQ354_spl
| frontsegP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f3375]) ).
fof(f3452,plain,
! [X0,X1] :
( nil = cons(X0,X1)
| ~ ssList(cons(X0,X1))
| sK44_skl(cons(X0,X1)) = X0
| ~ ssItem(X0)
| ~ ssItem(sK44_skl(cons(X0,X1)))
| ~ ssList(X1)
| ~ ssList(sK43_skl(cons(X0,X1))) ),
inference(resolution,[status(thm)],[f227,f233]) ).
fof(f3459,plain,
! [X0,X1] :
( nil = cons(X1,X0)
| ~ ssList(cons(X1,X0))
| sK44_skl(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssItem(sK44_skl(cons(X1,X0)))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3452,f231]) ).
fof(f3498,plain,
( ~ sQ171_spl
| ~ sQ293_spl
| ssList(app(sK49_skl,sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f2831,f1816]) ).
fof(f3500,plain,
! [X0] :
( ~ sQ250_spl
| ~ sQ293_spl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f2831,f2461]) ).
fof(f3501,plain,
( ~ sQ108_spl
| ~ sQ250_spl
| ~ sQ293_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f3500,f1222]) ).
fof(f3502,plain,
( ~ sQ108_spl
| ~ sQ250_spl
| ~ sQ293_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3501,f486,f2830,f2435,f1221]) ).
fof(f3505,plain,
( ~ sQ293_spl
| ~ sQ247_spl
| ~ sQ279_spl
| sK49_skl = nil ),
inference(backward_demodulation,[status(thm)],[f3506,f2831]) ).
fof(f3506,plain,
( ~ sQ247_spl
| ~ sQ279_spl
| nil = app(nil,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f2704,f2424]) ).
fof(f3528,plain,
( ~ sQ293_spl
| ~ sQ247_spl
| ~ sQ279_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f3505,f447,f2703,f2423,f2830]) ).
fof(f3541,definition,
! [X0] :
( sQ369_spl
<=> ( ~ memberP(nil,X0)
| memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ369_spl])],[split_symbol_definition]) ).
fof(f3620,plain,
( ~ sQ245_spl
| ~ ssList(nil)
| rearsegP(nil,app(sK49_skl,sK49_skl))
| ~ ssList(app(sK49_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f2416,f627]) ).
fof(f3625,definition,
( sQ370_spl
<=> ssList(app(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ370_spl])],[split_symbol_definition]) ).
fof(f3627,plain,
( sQ370_spl
| ~ ssList(app(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f3625]) ).
fof(f3628,definition,
( sQ371_spl
<=> nil = app(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ371_spl])],[split_symbol_definition]) ).
fof(f3629,plain,
( ~ sQ371_spl
| nil = app(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f3628]) ).
fof(f3639,definition,
! [X0] :
( sQ373_spl
<=> ( ~ memberP(app(sK49_skl,sK49_skl),X0)
| memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ373_spl])],[split_symbol_definition]) ).
fof(f3640,plain,
! [X0] :
( ~ sQ373_spl
| ~ memberP(app(sK49_skl,sK49_skl),X0)
| memberP(nil,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f3639]) ).
fof(f3674,definition,
( sQ381_spl
<=> rearsegP(nil,app(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ381_spl])],[split_symbol_definition]) ).
fof(f3675,plain,
( ~ sQ381_spl
| rearsegP(nil,app(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f3674]) ).
fof(f3676,plain,
( sQ381_spl
| ~ rearsegP(nil,app(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f3674]) ).
fof(f3677,plain,
( ~ sQ245_spl
| ~ sQ15_spl
| sQ381_spl
| ~ sQ370_spl ),
inference(split_clause,[status(thm)],[f3620,f3625,f3674,f552,f2415]) ).
fof(f3688,plain,
( sQ370_spl
| ~ sQ171_spl
| ~ sQ293_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3627,f3498]) ).
fof(f3689,plain,
( sQ370_spl
| ~ sQ171_spl
| ~ sQ293_spl ),
inference(contradiction_clause,[status(thm)],[f3688]) ).
fof(f3690,plain,
! [X0] :
( ~ sQ373_spl
| ~ memberP(app(sK49_skl,sK49_skl),X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3640,f279]) ).
fof(f3707,plain,
( ~ sQ371_spl
| ~ ssList(sK49_skl)
| rearsegP(nil,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f3629,f627]) ).
fof(f3729,definition,
( sQ387_spl
<=> rearsegP(app(sK49_skl,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ387_spl])],[split_symbol_definition]) ).
fof(f3730,plain,
( ~ sQ387_spl
| rearsegP(app(sK49_skl,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f3729]) ).
fof(f3731,plain,
( sQ387_spl
| ~ rearsegP(app(sK49_skl,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f3729]) ).
fof(f3744,plain,
( ~ sQ371_spl
| sQ164_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3707,f555,f1739,f3628]) ).
fof(f3752,plain,
! [X0] :
( ~ sQ31_spl
| ~ sQ5_spl
| sK54_skl = app(sK49_skl,X0)
| ~ segmentP(sK54_skl,app(sK49_skl,X0))
| ~ ssList(app(sK49_skl,X0))
| ~ ssList(sK54_skl)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,X0)) ),
inference(resolution,[status(thm)],[f767,f317]) ).
fof(f3753,plain,
! [X0,X1] :
( ~ sQ31_spl
| ~ sQ5_spl
| segmentP(X1,sK54_skl)
| ~ segmentP(X1,app(sK49_skl,X0))
| ~ ssList(sK54_skl)
| ~ ssList(app(sK49_skl,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,X0)) ),
inference(resolution,[status(thm)],[f767,f315]) ).
fof(f3754,definition,
! [X0] :
( sQ391_spl
<=> ( sK54_skl = app(sK49_skl,X0)
| ~ segmentP(sK54_skl,app(sK49_skl,X0))
| ~ ssList(app(sK49_skl,X0))
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f3757,plain,
( ~ sQ31_spl
| ~ sQ5_spl
| ~ sQ11_spl
| sQ391_spl ),
inference(split_clause,[status(thm)],[f3752,f3754,f531,f492,f664]) ).
fof(f3758,definition,
! [X0,X1] :
( sQ392_spl
<=> ( segmentP(X1,sK54_skl)
| ~ segmentP(X1,app(sK49_skl,X0))
| ~ ssList(app(sK49_skl,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ392_spl])],[split_symbol_definition]) ).
fof(f3761,plain,
( ~ sQ31_spl
| ~ sQ5_spl
| ~ sQ11_spl
| sQ392_spl ),
inference(split_clause,[status(thm)],[f3753,f3758,f531,f492,f664]) ).
fof(f3789,plain,
! [X0] :
( ~ sQ381_spl
| rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ rearsegP(X0,nil)
| ~ ssList(app(sK49_skl,sK49_skl))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3675,f301]) ).
fof(f3795,definition,
! [X0] :
( sQ398_spl
<=> ( rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ rearsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ398_spl])],[split_symbol_definition]) ).
fof(f3796,plain,
! [X0] :
( ~ sQ398_spl
| rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3795]) ).
fof(f3798,plain,
( ~ sQ381_spl
| ~ sQ370_spl
| ~ sQ15_spl
| sQ398_spl ),
inference(split_clause,[status(thm)],[f3789,f3795,f552,f3625,f3674]) ).
fof(f3799,plain,
! [X0] :
( ~ sQ398_spl
| rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3796,f309]) ).
fof(f3801,plain,
( sQ387_spl
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f3731,f627]) ).
fof(f3804,plain,
( sQ387_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3801,f555,f3729]) ).
fof(f3809,plain,
! [X0] :
( sQ381_spl
| ~ rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ rearsegP(nil,X0)
| ~ ssList(app(sK49_skl,sK49_skl))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3676,f301]) ).
fof(f3810,definition,
! [X0] :
( sQ400_spl
<=> ( ~ rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ400_spl])],[split_symbol_definition]) ).
fof(f3813,plain,
( sQ381_spl
| ~ sQ370_spl
| sQ400_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f3809,f552,f3810,f3625,f3674]) ).
fof(f3814,plain,
( ~ sQ387_spl
| sK49_skl = app(sK49_skl,sK49_skl)
| ~ rearsegP(sK49_skl,app(sK49_skl,sK49_skl))
| ~ ssList(app(sK49_skl,sK49_skl))
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f3730,f303]) ).
fof(f3815,plain,
! [X0] :
( ~ sQ387_spl
| rearsegP(X0,sK49_skl)
| ~ rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ ssList(sK49_skl)
| ~ ssList(app(sK49_skl,sK49_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3730,f301]) ).
fof(f3816,definition,
( sQ401_spl
<=> rearsegP(sK49_skl,app(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ401_spl])],[split_symbol_definition]) ).
fof(f3818,plain,
( sQ401_spl
| ~ rearsegP(sK49_skl,app(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f3816]) ).
fof(f3819,definition,
( sQ402_spl
<=> sK49_skl = app(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ402_spl])],[split_symbol_definition]) ).
fof(f3820,plain,
( ~ sQ402_spl
| sK49_skl = app(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f3819]) ).
fof(f3821,plain,
( sQ402_spl
| sK49_skl != app(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f3819]) ).
fof(f3822,plain,
( ~ sQ387_spl
| sQ402_spl
| ~ sQ401_spl
| ~ sQ370_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3814,f555,f3625,f3816,f3819,f3729]) ).
fof(f3823,definition,
! [X0] :
( sQ403_spl
<=> ( rearsegP(X0,sK49_skl)
| ~ rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ403_spl])],[split_symbol_definition]) ).
fof(f3826,plain,
( ~ sQ387_spl
| ~ sQ16_spl
| ~ sQ370_spl
| sQ403_spl ),
inference(split_clause,[status(thm)],[f3815,f3823,f3625,f555,f3729]) ).
fof(f3833,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ ssItem(sK51_skl)
| singletonP(sK49_skl)
| ~ ssList(cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f1325,f454]) ).
fof(f3834,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ3_spl
| sQ13_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f3833,f634,f545,f486,f1226,f817]) ).
fof(f3835,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f455,f245]) ).
fof(f3836,plain,
( ~ sQ293_spl
| ~ ssList(sK49_skl)
| frontsegP(sK49_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2831,f3835]) ).
fof(f3838,definition,
( sQ404_spl
<=> frontsegP(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ404_spl])],[split_symbol_definition]) ).
fof(f3839,plain,
( ~ sQ404_spl
| frontsegP(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f3838]) ).
fof(f3841,plain,
( ~ sQ293_spl
| ~ sQ16_spl
| sQ404_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f3836,f552,f3838,f555,f2830]) ).
fof(f3842,definition,
( sQ405_spl
<=> frontsegP(sK49_skl,app(app(sK53_skl,sK49_skl),sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ405_spl])],[split_symbol_definition]) ).
fof(f3852,plain,
( ~ sQ402_spl
| tl(sK49_skl) = app(tl(sK49_skl),sK49_skl)
| nil = sK49_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f3820,f393]) ).
fof(f3869,definition,
( sQ406_spl
<=> segmentP(sK49_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ406_spl])],[split_symbol_definition]) ).
fof(f3870,plain,
( ~ sQ406_spl
| segmentP(sK49_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f3869]) ).
fof(f3874,definition,
( sQ407_spl
<=> tl(sK49_skl) = app(tl(sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ407_spl])],[split_symbol_definition]) ).
fof(f3875,plain,
( ~ sQ407_spl
| tl(sK49_skl) = app(tl(sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f3874]) ).
fof(f3877,plain,
( ~ sQ402_spl
| sQ407_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3852,f555,f447,f3874,f3819]) ).
fof(f3878,definition,
( sQ408_spl
<=> hd(sK49_skl) = hd(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ408_spl])],[split_symbol_definition]) ).
fof(f3890,definition,
( sQ410_spl
<=> sK6_skl(sK49_skl,sK49_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ410_spl])],[split_symbol_definition]) ).
fof(f3891,plain,
( ~ sQ410_spl
| sK6_skl(sK49_skl,sK49_skl) = sK49_skl ),
inference(component_clause,[status(thm)],[f3890]) ).
fof(f3912,plain,
( ~ sQ410_spl
| ~ sQ299_spl
| nil = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f2882,f3891]) ).
fof(f3913,plain,
( ~ sQ410_spl
| ~ sQ299_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3912,f449]) ).
fof(f3914,plain,
( ~ sQ410_spl
| ~ sQ299_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f3913]) ).
fof(f3915,plain,
( ~ sQ407_spl
| ~ sQ167_spl
| nil = app(tl(sK49_skl),sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1777,f3875]) ).
fof(f3916,plain,
( ~ sQ407_spl
| ~ sQ167_spl
| nil = app(nil,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1777,f3915]) ).
fof(f3918,plain,
( ~ sQ406_spl
| sK54_skl = sK49_skl
| ~ segmentP(sK54_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f3870,f317]) ).
fof(f3919,plain,
! [X0] :
( ~ sQ406_spl
| segmentP(X0,sK54_skl)
| ~ segmentP(X0,sK49_skl)
| ~ ssList(sK54_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3870,f315]) ).
fof(f3920,definition,
( sQ414_spl
<=> segmentP(sK54_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ414_spl])],[split_symbol_definition]) ).
fof(f3922,plain,
( sQ414_spl
| ~ segmentP(sK54_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f3920]) ).
fof(f3923,plain,
( ~ sQ406_spl
| sQ264_spl
| ~ sQ414_spl
| ~ sQ16_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3918,f531,f555,f3920,f2566,f3869]) ).
fof(f3924,definition,
! [X0] :
( sQ415_spl
<=> ( segmentP(X0,sK54_skl)
| ~ segmentP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ415_spl])],[split_symbol_definition]) ).
fof(f3927,plain,
( ~ sQ406_spl
| ~ sQ11_spl
| ~ sQ16_spl
| sQ415_spl ),
inference(split_clause,[status(thm)],[f3919,f3924,f555,f531,f3869]) ).
fof(f3928,plain,
! [X0] :
( sQ414_spl
| ~ segmentP(X0,sK49_skl)
| ~ segmentP(sK54_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f3922,f315]) ).
fof(f3929,definition,
! [X0] :
( sQ416_spl
<=> ( ~ segmentP(X0,sK49_skl)
| ~ segmentP(sK54_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ416_spl])],[split_symbol_definition]) ).
fof(f3932,plain,
( sQ414_spl
| ~ sQ16_spl
| sQ416_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3928,f531,f3929,f555,f3920]) ).
fof(f3960,plain,
( ~ sQ293_spl
| ~ sQ407_spl
| ~ sQ167_spl
| sK49_skl = nil ),
inference(backward_demodulation,[status(thm)],[f3916,f2831]) ).
fof(f3983,plain,
( ~ sQ293_spl
| ~ sQ407_spl
| ~ sQ167_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f3960,f447,f1776,f3874,f2830]) ).
fof(f3987,definition,
( sQ422_spl
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ422_spl])],[split_symbol_definition]) ).
fof(f3988,plain,
( ~ sQ422_spl
| frontsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f3987]) ).
fof(f4013,plain,
! [X0,X1] :
( sK5_skl(X0,app(X0,X1)) = X1
| ~ ssList(sK5_skl(X0,app(X0,X1)))
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(resolution,[status(thm)],[f123,f378]) ).
fof(f4015,plain,
! [X0] :
( nil = sK5_skl(X0,nil)
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f123,f385]) ).
fof(f4016,plain,
! [X0] :
( nil = X0
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f123,f386]) ).
fof(f4017,plain,
! [X0,X1] :
( sK5_skl(X0,app(X0,X1)) = X1
| ~ ssList(sK5_skl(X0,app(X0,X1)))
| ~ ssList(X1)
| ~ frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f4013]) ).
fof(f4018,plain,
! [X0,X1] :
( sK5_skl(X0,app(X0,X1)) = X1
| ~ ssList(sK5_skl(X0,app(X0,X1)))
| ~ ssList(X1)
| ~ frontsegP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4017,f245]) ).
fof(f4021,definition,
! [X0] :
( sQ423_spl
<=> ( nil = sK5_skl(X0,nil)
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ423_spl])],[split_symbol_definition]) ).
fof(f4022,plain,
! [X0] :
( ~ sQ423_spl
| nil = sK5_skl(X0,nil)
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f4021]) ).
fof(f4024,plain,
( sQ423_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4015,f552,f4021]) ).
fof(f4025,definition,
! [X0] :
( sQ424_spl
<=> ( nil = X0
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ424_spl])],[split_symbol_definition]) ).
fof(f4028,plain,
( sQ424_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4016,f552,f4025]) ).
fof(f4029,plain,
! [X0] :
( ~ sQ423_spl
| nil = sK5_skl(X0,nil)
| ~ ssList(sK5_skl(X0,nil))
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f4022]) ).
fof(f4032,plain,
! [X0,X1] :
( X1 = nil
| ~ ssItem(X0)
| ~ ssItem(sK4_skl(cons(X0,X1)))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ singletonP(cons(X0,X1))
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f117,f228]) ).
fof(f4039,definition,
! [X0,X1] :
( sQ425_spl
<=> ( X1 = nil
| ~ ssItem(X0)
| ~ ssItem(sK4_skl(cons(X0,X1)))
| ~ ssList(X1)
| ~ singletonP(cons(X0,X1))
| ~ ssList(cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ425_spl])],[split_symbol_definition]) ).
fof(f4042,plain,
( ~ sQ15_spl
| sQ425_spl ),
inference(split_clause,[status(thm)],[f4032,f4039,f552]) ).
fof(f4090,plain,
! [X0] :
( sQ401_spl
| ~ rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(app(sK49_skl,sK49_skl))
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f3818,f301]) ).
fof(f4091,definition,
! [X0] :
( sQ426_spl
<=> ( ~ rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ426_spl])],[split_symbol_definition]) ).
fof(f4094,plain,
( sQ401_spl
| ~ sQ370_spl
| sQ426_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4090,f555,f4091,f3625,f3816]) ).
fof(f4101,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ126_spl
| sK54_skl = sK54_skl
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f1449,f1270]) ).
fof(f4104,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ126_spl
| sQ179_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4101,f531,f1893,f1448,f1226,f440,f492]) ).
fof(f4113,plain,
! [X0] :
( ~ sQ125_spl
| ~ ssItem(X0)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| app(cons(X0,app(app(sK53_skl,sK49_skl),sK49_skl)),sK54_skl) != sK49_skl
| ~ ssList(cons(X0,app(app(sK53_skl,sK49_skl),sK49_skl))) ),
inference(resolution,[status(thm)],[f1444,f225]) ).
fof(f4114,plain,
! [X0] :
( ~ sQ125_spl
| X0 = app(sK53_skl,sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK53_skl,sK49_skl))
| app(app(X0,sK49_skl),sK54_skl) != sK49_skl
| ~ ssList(app(X0,sK49_skl)) ),
inference(resolution,[status(thm)],[f1444,f376]) ).
fof(f4115,plain,
! [X0] :
( ~ sQ125_spl
| X0 = sK49_skl
| ~ ssList(X0)
| ~ ssList(app(sK53_skl,sK49_skl))
| ~ ssList(sK49_skl)
| app(app(app(sK53_skl,sK49_skl),X0),sK54_skl) != sK49_skl
| ~ ssList(app(app(sK53_skl,sK49_skl),X0)) ),
inference(resolution,[status(thm)],[f1444,f378]) ).
fof(f4117,plain,
( ~ sQ125_spl
| nil = sK49_skl
| ~ ssList(sK49_skl)
| ~ ssList(app(sK53_skl,sK49_skl))
| app(nil,sK54_skl) != sK49_skl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1444,f385]) ).
fof(f4121,plain,
( ~ sQ125_spl
| ~ sQ124_spl
| sQ156_spl ),
inference(split_clause,[status(thm)],[f4113,f1686,f1440,f1443]) ).
fof(f4122,plain,
( ~ sQ125_spl
| ~ sQ16_spl
| ~ sQ154_spl
| sQ153_spl ),
inference(split_clause,[status(thm)],[f4114,f1673,f1676,f555,f1443]) ).
fof(f4123,plain,
( ~ sQ125_spl
| ~ sQ154_spl
| ~ sQ16_spl
| sQ155_spl ),
inference(split_clause,[status(thm)],[f4115,f1680,f555,f1676,f1443]) ).
fof(f4125,plain,
( ~ sQ125_spl
| sQ2_spl
| ~ sQ16_spl
| ~ sQ154_spl
| ~ sQ157_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4117,f552,f1690,f1676,f555,f447,f1443]) ).
fof(f4139,plain,
! [X0] :
( nil = cons(X0,sK3_skl(X0,nil))
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil))
| ~ memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f111,f385]) ).
fof(f4140,plain,
! [X0] :
( nil = sK2_skl(X0,nil)
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil))
| ~ memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f111,f386]) ).
fof(f4141,definition,
! [X0] :
( sQ429_spl
<=> ( nil = cons(X0,sK3_skl(X0,nil))
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil))
| ~ memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ429_spl])],[split_symbol_definition]) ).
fof(f4144,plain,
( sQ429_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4139,f552,f4141]) ).
fof(f4145,definition,
! [X0] :
( sQ430_spl
<=> ( nil = sK2_skl(X0,nil)
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil))
| ~ memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ430_spl])],[split_symbol_definition]) ).
fof(f4148,plain,
( sQ430_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4140,f552,f4145]) ).
fof(f4150,plain,
! [X0] :
( ~ sQ149_spl
| ~ memberP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK53_skl,sK49_skl))
| ~ ssItem(X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1627,f272]) ).
fof(f4151,plain,
! [X0] :
( ~ sQ149_spl
| ~ memberP(app(sK53_skl,sK49_skl),X0)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK53_skl,sK49_skl))
| ~ ssItem(X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1627,f271]) ).
fof(f4152,plain,
( ~ sQ149_spl
| ~ sQ16_spl
| ~ sQ154_spl
| sQ306_spl ),
inference(split_clause,[status(thm)],[f4150,f2940,f1676,f555,f1626]) ).
fof(f4153,plain,
( ~ sQ149_spl
| ~ sQ16_spl
| ~ sQ154_spl
| sQ307_spl ),
inference(split_clause,[status(thm)],[f4151,f2944,f1676,f555,f1626]) ).
fof(f4190,plain,
! [X0,X1,X2] :
( ~ sQ51_spl
| ~ sQ109_spl
| lt(X1,sK51_skl)
| lt(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ strictorderP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f1325,f460]) ).
fof(f4191,plain,
! [X0,X1,X2] :
( ~ sQ51_spl
| ~ sQ109_spl
| lt(sK51_skl,X1)
| lt(X1,sK51_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f1325,f460]) ).
fof(f4192,definition,
! [X0,X1,X2] :
( sQ437_spl
<=> ( lt(X1,sK51_skl)
| lt(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ437_spl])],[split_symbol_definition]) ).
fof(f4195,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ437_spl ),
inference(split_clause,[status(thm)],[f4190,f4192,f486,f552,f1226,f817]) ).
fof(f4196,definition,
! [X0,X1,X2] :
( sQ438_spl
<=> ( lt(sK51_skl,X1)
| lt(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ strictorderP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ438_spl])],[split_symbol_definition]) ).
fof(f4199,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ438_spl ),
inference(split_clause,[status(thm)],[f4191,f4196,f486,f552,f1226,f817]) ).
fof(f4202,plain,
! [X0,X1,X2] :
( ~ sQ51_spl
| ~ sQ109_spl
| leq(X1,sK51_skl)
| leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ totalorderP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f1325,f459]) ).
fof(f4203,plain,
! [X0,X1,X2] :
( ~ sQ51_spl
| ~ sQ109_spl
| leq(sK51_skl,X1)
| leq(X1,sK51_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f1325,f459]) ).
fof(f4204,definition,
! [X0,X1,X2] :
( sQ439_spl
<=> ( leq(X1,sK51_skl)
| leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ439_spl])],[split_symbol_definition]) ).
fof(f4207,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ439_spl ),
inference(split_clause,[status(thm)],[f4202,f4204,f486,f552,f1226,f817]) ).
fof(f4208,definition,
! [X0,X1,X2] :
( sQ440_spl
<=> ( leq(sK51_skl,X1)
| leq(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ440_spl])],[split_symbol_definition]) ).
fof(f4211,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ440_spl ),
inference(split_clause,[status(thm)],[f4203,f4208,f486,f552,f1226,f817]) ).
fof(f4214,plain,
! [X0,X1,X2] :
( ~ sQ51_spl
| ~ sQ109_spl
| ~ leq(X1,sK51_skl)
| ~ leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ cyclefreeP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f1325,f458]) ).
fof(f4215,plain,
! [X0,X1,X2] :
( ~ sQ51_spl
| ~ sQ109_spl
| ~ leq(sK51_skl,X1)
| ~ leq(X1,sK51_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f1325,f458]) ).
fof(f4216,definition,
! [X0,X1,X2] :
( sQ441_spl
<=> ( ~ leq(X1,sK51_skl)
| ~ leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,sK49_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ441_spl])],[split_symbol_definition]) ).
fof(f4219,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ441_spl ),
inference(split_clause,[status(thm)],[f4214,f4216,f486,f552,f1226,f817]) ).
fof(f4220,definition,
! [X0,X1,X2] :
( sQ442_spl
<=> ( ~ leq(sK51_skl,X1)
| ~ leq(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),sK49_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ442_spl])],[split_symbol_definition]) ).
fof(f4223,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ442_spl ),
inference(split_clause,[status(thm)],[f4215,f4220,f486,f552,f1226,f817]) ).
fof(f4243,plain,
! [X0,X1] :
( X1 = sK43_skl(cons(X0,X1))
| ~ ssItem(X0)
| ~ ssItem(sK44_skl(cons(X0,X1)))
| ~ ssList(X1)
| ~ ssList(sK43_skl(cons(X0,X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1645,f235]) ).
fof(f4245,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| nil = sK43_skl(cons(sK51_skl,nil))
| ~ ssItem(sK51_skl)
| ~ ssItem(sK44_skl(sK49_skl))
| ~ ssList(nil)
| ~ ssList(sK43_skl(cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f1325,f4243]) ).
fof(f4247,definition,
( sQ446_spl
<=> ssList(sK43_skl(cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ446_spl])],[split_symbol_definition]) ).
fof(f4249,plain,
( sQ446_spl
| ~ ssList(sK43_skl(cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f4247]) ).
fof(f4250,definition,
( sQ447_spl
<=> ssItem(sK44_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ447_spl])],[split_symbol_definition]) ).
fof(f4252,plain,
( sQ447_spl
| ~ ssItem(sK44_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f4250]) ).
fof(f4253,definition,
( sQ448_spl
<=> nil = sK43_skl(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f4254,plain,
( ~ sQ448_spl
| nil = sK43_skl(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f4253]) ).
fof(f4256,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sQ448_spl
| ~ sQ3_spl
| ~ sQ447_spl
| ~ sQ15_spl
| ~ sQ446_spl ),
inference(split_clause,[status(thm)],[f4245,f4247,f552,f4250,f486,f4253,f1226,f817]) ).
fof(f4257,plain,
( ~ sQ448_spl
| ~ sQ51_spl
| ~ sQ109_spl
| nil = sK43_skl(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1325,f4254]) ).
fof(f4258,plain,
( sQ446_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ ssList(sK43_skl(sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f1325,f4249]) ).
fof(f4259,plain,
! [X0,X1] :
( sK44_skl(cons(X0,X1)) = X0
| ~ ssItem(X0)
| ~ ssItem(sK44_skl(cons(X0,X1)))
| ~ ssList(X1)
| ~ ssList(sK43_skl(cons(X0,X1))) ),
inference(forward_subsumption_resolution,[status(thm)],[f1646,f235]) ).
fof(f4261,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sK44_skl(cons(sK51_skl,nil)) = sK51_skl
| ~ ssItem(sK51_skl)
| ~ ssItem(sK44_skl(sK49_skl))
| ~ ssList(nil)
| ~ ssList(sK43_skl(cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f1325,f4259]) ).
fof(f4263,definition,
( sQ449_spl
<=> sK44_skl(cons(sK51_skl,nil)) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ449_spl])],[split_symbol_definition]) ).
fof(f4264,plain,
( ~ sQ449_spl
| sK44_skl(cons(sK51_skl,nil)) = sK51_skl ),
inference(component_clause,[status(thm)],[f4263]) ).
fof(f4266,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sQ449_spl
| ~ sQ3_spl
| ~ sQ447_spl
| ~ sQ15_spl
| ~ sQ446_spl ),
inference(split_clause,[status(thm)],[f4261,f4247,f552,f4250,f486,f4263,f1226,f817]) ).
fof(f4267,plain,
( ~ sQ449_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sK44_skl(sK49_skl) = sK51_skl ),
inference(forward_demodulation,[status(thm)],[f1325,f4264]) ).
fof(f4268,plain,
( ~ sQ448_spl
| ~ sQ51_spl
| ~ sQ109_spl
| cons(sK44_skl(sK49_skl),nil) = sK49_skl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f4257,f233]) ).
fof(f4270,definition,
( sQ450_spl
<=> cons(sK44_skl(sK49_skl),nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ450_spl])],[split_symbol_definition]) ).
fof(f4273,plain,
( ~ sQ448_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sQ450_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4268,f555,f447,f4270,f1226,f817,f4253]) ).
fof(f4276,plain,
( sQ447_spl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f4252,f232]) ).
fof(f4277,plain,
( sQ447_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4276,f555,f447,f4250]) ).
fof(f4278,plain,
( sQ446_spl
| ~ sQ51_spl
| ~ sQ109_spl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f4258,f231]) ).
fof(f4279,plain,
( sQ446_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4278,f555,f447,f1226,f817,f4247]) ).
fof(f4282,plain,
( ~ sQ449_spl
| ~ sQ51_spl
| ~ sQ109_spl
| cons(sK51_skl,sK43_skl(sK49_skl)) = sK49_skl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f4267,f233]) ).
fof(f4284,definition,
( sQ451_spl
<=> cons(sK51_skl,sK43_skl(sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f4287,plain,
( ~ sQ449_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sQ451_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4282,f555,f447,f4284,f1226,f817,f4263]) ).
fof(f4289,plain,
! [X0,X1,X2] :
( X1 = app(app(X0,X1),X2)
| ~ segmentP(X1,app(app(X0,X1),X2))
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f457,f317]) ).
fof(f4290,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ segmentP(X3,app(app(X0,X1),X2))
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(resolution,[status(thm)],[f457,f315]) ).
fof(f4292,plain,
! [X0] :
( ~ sQ293_spl
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(sK49_skl,X0),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(app(app(nil,sK49_skl),X0)) ),
inference(paramodulation,[status(thm)],[f2831,f457]) ).
fof(f4293,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ ssList(X0)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| segmentP(app(sK49_skl,X0),sK54_skl)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),X0)) ),
inference(paramodulation,[status(thm)],[f1270,f457]) ).
fof(f4294,plain,
! [X0,X1,X2] :
( X1 = app(app(X0,X1),X2)
| ~ segmentP(X1,app(app(X0,X1),X2))
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(duplicate_literals_removal,[status(thm)],[f4289]) ).
fof(f4295,plain,
! [X0,X1,X2,X3] :
( segmentP(X3,X1)
| ~ segmentP(X3,app(app(X0,X1),X2))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(duplicate_literals_removal,[status(thm)],[f4290]) ).
fof(f4296,definition,
( sQ452_spl
<=> ssList(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ452_spl])],[split_symbol_definition]) ).
fof(f4298,plain,
( sQ452_spl
| ~ ssList(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl)) ),
inference(component_clause,[status(thm)],[f4296]) ).
fof(f4300,definition,
! [X0] :
( sQ453_spl
<=> ( ~ ssList(X0)
| segmentP(app(sK49_skl,X0),sK49_skl)
| ~ ssList(app(app(nil,sK49_skl),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ453_spl])],[split_symbol_definition]) ).
fof(f4303,plain,
( ~ sQ293_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ453_spl ),
inference(split_clause,[status(thm)],[f4292,f4300,f555,f552,f2830]) ).
fof(f4304,definition,
! [X0] :
( sQ454_spl
<=> ( ~ ssList(X0)
| segmentP(app(sK49_skl,X0),sK54_skl)
| ~ ssList(app(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ454_spl])],[split_symbol_definition]) ).
fof(f4307,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| ~ sQ11_spl
| sQ454_spl ),
inference(split_clause,[status(thm)],[f4293,f4304,f531,f1440,f1226,f440,f492]) ).
fof(f4310,plain,
( sQ452_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ ssList(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1270,f4298]) ).
fof(f4311,plain,
( sQ452_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4310,f422]) ).
fof(f4312,plain,
( sQ452_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl ),
inference(contradiction_clause,[status(thm)],[f4311]) ).
fof(f4329,plain,
! [X0] :
( ~ sQ178_spl
| memberP(sK49_skl,X0)
| memberP(app(sK53_skl,sK49_skl),X0)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK53_skl,sK49_skl))
| ~ ssItem(X0)
| memberP(sK54_skl,X0)
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1864,f270]) ).
fof(f4330,plain,
( ~ sQ178_spl
| ~ sQ16_spl
| ~ sQ154_spl
| sQ229_spl ),
inference(split_clause,[status(thm)],[f4329,f2271,f1676,f555,f1863]) ).
fof(f4344,plain,
! [X0] :
( ~ sQ373_spl
| ~ memberP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f3690,f272]) ).
fof(f4346,definition,
! [X0] :
( sQ455_spl
<=> ( ~ memberP(sK49_skl,X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ455_spl])],[split_symbol_definition]) ).
fof(f4347,plain,
! [X0] :
( ~ sQ455_spl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f4346]) ).
fof(f4349,plain,
( ~ sQ373_spl
| ~ sQ16_spl
| sQ455_spl ),
inference(split_clause,[status(thm)],[f4344,f4346,f555,f3639]) ).
fof(f4351,plain,
! [X0] :
( ~ sQ455_spl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f4347]) ).
fof(f4354,plain,
( ~ sQ108_spl
| ~ sQ455_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f4351,f1222]) ).
fof(f4355,plain,
( ~ sQ108_spl
| ~ sQ455_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4354,f486,f4346,f1221]) ).
fof(f4378,plain,
( sQ401_spl
| ~ sQ398_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f3799,f3818]) ).
fof(f4383,plain,
( sQ401_spl
| ~ sQ398_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4378,f422]) ).
fof(f4384,plain,
( sQ401_spl
| ~ sQ398_spl ),
inference(contradiction_clause,[status(thm)],[f4383]) ).
fof(f4491,definition,
( sQ468_spl
<=> ssList(app(sK49_skl,sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ468_spl])],[split_symbol_definition]) ).
fof(f4493,plain,
( sQ468_spl
| ~ ssList(app(sK49_skl,sK54_skl)) ),
inference(component_clause,[status(thm)],[f4491]) ).
fof(f4556,definition,
( sQ483_spl
<=> nil = app(sK49_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ483_spl])],[split_symbol_definition]) ).
fof(f4557,plain,
( ~ sQ483_spl
| nil = app(sK49_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f4556]) ).
fof(f4720,definition,
( sQ507_spl
<=> ssList(sK6_skl(sK54_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ507_spl])],[split_symbol_definition]) ).
fof(f4722,plain,
( sQ507_spl
| ~ ssList(sK6_skl(sK54_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f4720]) ).
fof(f4733,plain,
! [X0] :
( ~ sQ88_spl
| ~ rearsegP(nil,X0)
| nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f128,f1054]) ).
fof(f4736,definition,
! [X0] :
( sQ509_spl
<=> ( ~ rearsegP(nil,X0)
| nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ509_spl])],[split_symbol_definition]) ).
fof(f4739,plain,
( ~ sQ88_spl
| sQ509_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4733,f552,f4736,f1049]) ).
fof(f4743,plain,
( sQ468_spl
| ~ ssList(sK54_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f4493,f245]) ).
fof(f4744,plain,
( sQ468_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4743,f555,f531,f4491]) ).
fof(f4748,plain,
( ~ sQ483_spl
| nil = sK49_skl
| ~ ssList(sK54_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f4557,f386]) ).
fof(f4771,plain,
( ~ sQ483_spl
| sQ2_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4748,f555,f531,f447,f4556]) ).
fof(f4772,definition,
( sQ510_spl
<=> cons(sK51_skl,sK54_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ510_spl])],[split_symbol_definition]) ).
fof(f4773,plain,
( ~ sQ510_spl
| cons(sK51_skl,sK54_skl) = nil ),
inference(component_clause,[status(thm)],[f4772]) ).
fof(f4784,definition,
( sQ513_spl
<=> frontsegP(nil,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ513_spl])],[split_symbol_definition]) ).
fof(f4785,plain,
( ~ sQ513_spl
| frontsegP(nil,sK49_skl) ),
inference(component_clause,[status(thm)],[f4784]) ).
fof(f4786,plain,
( sQ513_spl
| ~ frontsegP(nil,sK49_skl) ),
inference(component_clause,[status(thm)],[f4784]) ).
fof(f4813,definition,
( sQ520_spl
<=> rearsegP(app(sK49_skl,sK54_skl),sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ520_spl])],[split_symbol_definition]) ).
fof(f4814,plain,
( ~ sQ520_spl
| rearsegP(app(sK49_skl,sK54_skl),sK54_skl) ),
inference(component_clause,[status(thm)],[f4813]) ).
fof(f4815,plain,
( sQ520_spl
| ~ rearsegP(app(sK49_skl,sK54_skl),sK54_skl) ),
inference(component_clause,[status(thm)],[f4813]) ).
fof(f4855,definition,
( sQ527_spl
<=> rearsegP(sK54_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ527_spl])],[split_symbol_definition]) ).
fof(f4856,plain,
( ~ sQ527_spl
| rearsegP(sK54_skl,nil) ),
inference(component_clause,[status(thm)],[f4855]) ).
fof(f4857,plain,
( sQ527_spl
| ~ rearsegP(sK54_skl,nil) ),
inference(component_clause,[status(thm)],[f4855]) ).
fof(f4864,plain,
( ~ sQ513_spl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f4785,f298]) ).
fof(f4865,plain,
( ~ sQ513_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4864,f555,f447,f4784]) ).
fof(f5175,plain,
( sQ507_spl
| ~ rearsegP(sK49_skl,sK54_skl)
| ~ ssList(sK54_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f4722,f128]) ).
fof(f5176,plain,
( sQ507_spl
| ~ sQ59_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5175,f555,f531,f889,f4720]) ).
fof(f5213,definition,
( sQ585_spl
<=> app(sK49_skl,nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ585_spl])],[split_symbol_definition]) ).
fof(f5214,plain,
( ~ sQ585_spl
| app(sK49_skl,nil) = sK49_skl ),
inference(component_clause,[status(thm)],[f5213]) ).
fof(f5215,plain,
( sQ585_spl
| app(sK49_skl,nil) != sK49_skl ),
inference(component_clause,[status(thm)],[f5213]) ).
fof(f5274,plain,
( ~ sQ510_spl
| ~ sQ243_spl
| frontsegP(nil,sK49_skl)
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f4773,f2360]) ).
fof(f5308,plain,
( ~ sQ510_spl
| ~ sQ243_spl
| sQ513_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5274,f531,f4784,f2356,f4772]) ).
fof(f5333,definition,
( sQ596_spl
<=> ssList(sK43_skl(cons(sK51_skl,sK54_skl))) ),
introduced(definition,[new_symbols(definition,[sQ596_spl])],[split_symbol_definition]) ).
fof(f5335,plain,
( sQ596_spl
| ~ ssList(sK43_skl(cons(sK51_skl,sK54_skl))) ),
inference(component_clause,[status(thm)],[f5333]) ).
fof(f5336,definition,
( sQ597_spl
<=> sK44_skl(cons(sK51_skl,sK54_skl)) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ597_spl])],[split_symbol_definition]) ).
fof(f5337,plain,
( ~ sQ597_spl
| sK44_skl(cons(sK51_skl,sK54_skl)) = sK51_skl ),
inference(component_clause,[status(thm)],[f5336]) ).
fof(f5338,plain,
( sQ597_spl
| sK44_skl(cons(sK51_skl,sK54_skl)) != sK51_skl ),
inference(component_clause,[status(thm)],[f5336]) ).
fof(f5340,definition,
( sQ598_spl
<=> sK54_skl = sK43_skl(cons(sK51_skl,sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ598_spl])],[split_symbol_definition]) ).
fof(f5341,plain,
( ~ sQ598_spl
| sK54_skl = sK43_skl(cons(sK51_skl,sK54_skl)) ),
inference(component_clause,[status(thm)],[f5340]) ).
fof(f5494,plain,
( sQ77_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ ssList(nil)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(resolution,[status(thm)],[f2228,f245]) ).
fof(f5495,plain,
( sQ77_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f5494,f1440,f552,f1226,f817,f991]) ).
fof(f5498,plain,
( sQ585_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f5215,f389]) ).
fof(f5499,plain,
( sQ585_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5498,f422]) ).
fof(f5500,plain,
sQ585_spl,
inference(contradiction_clause,[status(thm)],[f5499]) ).
fof(f5506,definition,
( sQ621_spl
<=> app(nil,sK54_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ621_spl])],[split_symbol_definition]) ).
fof(f5507,plain,
( ~ sQ621_spl
| app(nil,sK54_skl) = nil ),
inference(component_clause,[status(thm)],[f5506]) ).
fof(f5508,plain,
( sQ621_spl
| app(nil,sK54_skl) != nil ),
inference(component_clause,[status(thm)],[f5506]) ).
fof(f5836,plain,
( ~ sQ585_spl
| ~ sQ54_spl
| ~ sQ109_spl
| cons(sK51_skl,nil) = sK49_skl
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5214,f1230]) ).
fof(f5838,plain,
! [X0] :
( ~ sQ585_spl
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| segmentP(app(sK49_skl,X0),nil)
| ~ ssList(nil)
| ~ ssList(app(app(sK49_skl,nil),X0)) ),
inference(paramodulation,[status(thm)],[f5214,f457]) ).
fof(f5839,plain,
( ~ sQ585_spl
| ~ ssList(nil)
| frontsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f5214,f3835]) ).
fof(f5840,plain,
( ~ sQ585_spl
| tl(sK49_skl) = app(tl(sK49_skl),nil)
| nil = sK49_skl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f5214,f393]) ).
fof(f5841,plain,
( ~ sQ585_spl
| hd(sK49_skl) = hd(sK49_skl)
| nil = sK49_skl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f5214,f391]) ).
fof(f5844,plain,
! [X0,X1] :
( ~ sQ585_spl
| segmentP(app(sK49_skl,X1),X0)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5214,f321]) ).
fof(f5846,plain,
! [X0] :
( ~ sQ585_spl
| rearsegP(sK49_skl,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5214,f307]) ).
fof(f5847,plain,
( ~ sQ585_spl
| ~ rearsegP(app(sK49_skl,nil),nil)
| sK6_skl(nil,sK49_skl) = sK49_skl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f5214,f2020]) ).
fof(f5849,plain,
! [X0] :
( ~ sQ585_spl
| X0 = sK49_skl
| app(X0,nil) != sK49_skl
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f5214,f376]) ).
fof(f5851,plain,
! [X0] :
( ~ sQ585_spl
| X0 = nil
| app(sK49_skl,X0) != sK49_skl
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5214,f378]) ).
fof(f5853,plain,
( ~ sQ585_spl
| ~ ssList(sK49_skl)
| rearsegP(sK49_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5214,f627]) ).
fof(f5854,plain,
! [X0] :
( ~ sQ585_spl
| app(app(X0,sK49_skl),nil) = app(X0,sK49_skl)
| ~ ssList(nil)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f5214,f382]) ).
fof(f5857,plain,
( ~ sQ585_spl
| ~ sQ54_spl
| ~ sQ109_spl
| sQ147_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f5836,f552,f1598,f1226,f852,f5213]) ).
fof(f5859,definition,
! [X0] :
( sQ674_spl
<=> ( ~ ssList(X0)
| segmentP(app(sK49_skl,X0),nil)
| ~ ssList(app(app(sK49_skl,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ674_spl])],[split_symbol_definition]) ).
fof(f5862,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ674_spl ),
inference(split_clause,[status(thm)],[f5838,f5859,f552,f555,f5213]) ).
fof(f5863,plain,
( ~ sQ585_spl
| ~ sQ15_spl
| sQ354_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5839,f555,f3375,f552,f5213]) ).
fof(f5864,definition,
( sQ675_spl
<=> tl(sK49_skl) = app(tl(sK49_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ675_spl])],[split_symbol_definition]) ).
fof(f5865,plain,
( ~ sQ675_spl
| tl(sK49_skl) = app(tl(sK49_skl),nil) ),
inference(component_clause,[status(thm)],[f5864]) ).
fof(f5867,plain,
( ~ sQ585_spl
| sQ675_spl
| sQ2_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5840,f555,f552,f447,f5864,f5213]) ).
fof(f5868,plain,
( ~ sQ585_spl
| sQ408_spl
| sQ2_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5841,f555,f552,f447,f3878,f5213]) ).
fof(f5871,definition,
! [X0,X1] :
( sQ676_spl
<=> ( segmentP(app(sK49_skl,X1),X0)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ676_spl])],[split_symbol_definition]) ).
fof(f5874,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| sQ676_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f5844,f552,f5871,f555,f5213]) ).
fof(f5876,definition,
! [X0] :
( sQ677_spl
<=> ( rearsegP(sK49_skl,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ677_spl])],[split_symbol_definition]) ).
fof(f5879,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| sQ677_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f5846,f552,f5876,f555,f5213]) ).
fof(f5880,definition,
( sQ678_spl
<=> sK6_skl(nil,sK49_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ678_spl])],[split_symbol_definition]) ).
fof(f5883,definition,
( sQ679_spl
<=> rearsegP(app(sK49_skl,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ679_spl])],[split_symbol_definition]) ).
fof(f5885,plain,
( sQ679_spl
| ~ rearsegP(app(sK49_skl,nil),nil) ),
inference(component_clause,[status(thm)],[f5883]) ).
fof(f5886,plain,
( ~ sQ585_spl
| ~ sQ679_spl
| sQ678_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5847,f555,f552,f5880,f5883,f5213]) ).
fof(f5888,definition,
! [X0] :
( sQ680_spl
<=> ( X0 = sK49_skl
| app(X0,nil) != sK49_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ680_spl])],[split_symbol_definition]) ).
fof(f5891,plain,
( ~ sQ585_spl
| sQ680_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5849,f555,f552,f5888,f5213]) ).
fof(f5893,definition,
! [X0] :
( sQ681_spl
<=> ( X0 = nil
| app(sK49_skl,X0) != sK49_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ681_spl])],[split_symbol_definition]) ).
fof(f5896,plain,
( ~ sQ585_spl
| sQ681_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f5851,f552,f555,f5893,f5213]) ).
fof(f5898,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| sQ80_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f5853,f552,f1004,f555,f5213]) ).
fof(f5899,definition,
! [X0] :
( sQ682_spl
<=> ( app(app(X0,sK49_skl),nil) = app(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ682_spl])],[split_symbol_definition]) ).
fof(f5902,plain,
( ~ sQ585_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ682_spl ),
inference(split_clause,[status(thm)],[f5854,f5899,f555,f552,f5213]) ).
fof(f5906,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| nil = app(tl(sK49_skl),nil) ),
inference(forward_demodulation,[status(thm)],[f1777,f5865]) ).
fof(f5907,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| nil = app(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f1777,f5906]) ).
fof(f5908,plain,
( sQ679_spl
| ~ sQ585_spl
| ~ rearsegP(sK49_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f5214,f5885]) ).
fof(f5909,plain,
( ~ sQ228_spl
| ~ ssList(sK49_skl)
| ~ ssList(app(sK53_skl,sK49_skl))
| frontsegP(sK49_skl,app(sK53_skl,sK49_skl))
| ~ ssList(app(sK53_skl,sK49_skl)) ),
inference(resolution,[status(thm)],[f2265,f3835]) ).
fof(f5911,plain,
( ~ sQ228_spl
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| frontsegP(sK49_skl,app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(resolution,[status(thm)],[f2265,f286]) ).
fof(f5912,definition,
( sQ683_spl
<=> frontsegP(sK49_skl,app(sK53_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ683_spl])],[split_symbol_definition]) ).
fof(f5913,plain,
( ~ sQ683_spl
| frontsegP(sK49_skl,app(sK53_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f5912]) ).
fof(f5915,plain,
( ~ sQ228_spl
| ~ sQ16_spl
| sQ683_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f5909,f1676,f5912,f555,f2264]) ).
fof(f5917,plain,
( ~ sQ228_spl
| sQ405_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f5911,f1440,f3842,f2264]) ).
fof(f5918,plain,
( sQ679_spl
| ~ sQ585_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f5908,f309]) ).
fof(f5920,plain,
( sQ679_spl
| ~ sQ585_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5918,f422]) ).
fof(f5921,plain,
( sQ679_spl
| ~ sQ585_spl ),
inference(contradiction_clause,[status(thm)],[f5920]) ).
fof(f6200,plain,
( ~ sQ621_spl
| nil = sK54_skl
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f5507,f249]) ).
fof(f6223,plain,
( ~ sQ621_spl
| sQ72_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6200,f531,f944,f5506]) ).
fof(f6242,definition,
( sQ733_spl
<=> rearsegP(app(nil,sK54_skl),sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ733_spl])],[split_symbol_definition]) ).
fof(f6244,plain,
( sQ733_spl
| ~ rearsegP(app(nil,sK54_skl),sK54_skl) ),
inference(component_clause,[status(thm)],[f6242]) ).
fof(f6277,plain,
( ~ sQ10_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sK49_skl = app(app(sK53_skl,sK49_skl),sK49_skl)
| ~ frontsegP(app(sK53_skl,sK49_skl),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK53_skl,sK49_skl)) ),
inference(resolution,[status(thm)],[f2261,f3206]) ).
fof(f6279,plain,
! [X0] :
( ~ sQ585_spl
| X0 = app(sK49_skl,nil)
| ~ frontsegP(X0,sK49_skl)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f5214,f2261]) ).
fof(f6280,plain,
! [X0] :
( ~ sQ293_spl
| X0 = app(nil,sK49_skl)
| ~ frontsegP(X0,sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2831,f2261]) ).
fof(f6281,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| X0 = app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl)
| ~ frontsegP(X0,sK49_skl)
| ~ frontsegP(app(app(sK53_skl,sK49_skl),sK49_skl),X0)
| ~ ssList(sK54_skl)
| ~ ssList(X0)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(paramodulation,[status(thm)],[f1270,f2261]) ).
fof(f6283,definition,
( sQ739_spl
<=> frontsegP(app(sK53_skl,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ739_spl])],[split_symbol_definition]) ).
fof(f6285,plain,
( sQ739_spl
| ~ frontsegP(app(sK53_skl,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f6283]) ).
fof(f6286,definition,
( sQ740_spl
<=> sK49_skl = app(app(sK53_skl,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ740_spl])],[split_symbol_definition]) ).
fof(f6287,plain,
( ~ sQ740_spl
| sK49_skl = app(app(sK53_skl,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f6286]) ).
fof(f6289,plain,
( ~ sQ10_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sQ740_spl
| ~ sQ739_spl
| ~ sQ16_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f6277,f1676,f555,f6283,f6286,f1226,f817,f528]) ).
fof(f6290,definition,
! [X0] :
( sQ741_spl
<=> ( X0 = app(sK49_skl,nil)
| ~ frontsegP(X0,sK49_skl)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ741_spl])],[split_symbol_definition]) ).
fof(f6293,plain,
( ~ sQ585_spl
| ~ sQ15_spl
| sQ741_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f6279,f555,f6290,f552,f5213]) ).
fof(f6294,definition,
! [X0] :
( sQ742_spl
<=> ( X0 = app(nil,sK49_skl)
| ~ frontsegP(X0,sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ742_spl])],[split_symbol_definition]) ).
fof(f6297,plain,
( ~ sQ293_spl
| ~ sQ16_spl
| sQ742_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6280,f552,f6294,f555,f2830]) ).
fof(f6298,definition,
! [X0] :
( sQ743_spl
<=> ( X0 = app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl)
| ~ frontsegP(X0,sK49_skl)
| ~ frontsegP(app(app(sK53_skl,sK49_skl),sK49_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ743_spl])],[split_symbol_definition]) ).
fof(f6301,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ11_spl
| sQ743_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f6281,f1440,f6298,f531,f1226,f440,f492]) ).
fof(f6305,plain,
( ~ sQ740_spl
| sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6287,f3088]) ).
fof(f6306,plain,
( ~ sQ740_spl
| sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl ),
inference(contradiction_clause,[status(thm)],[f6305]) ).
fof(f6308,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ51_spl
| ~ sQ109_spl
| frontsegP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| ~ frontsegP(app(sK53_skl,sK49_skl),X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(app(sK53_skl,sK49_skl)) ),
inference(resolution,[status(thm)],[f2263,f3206]) ).
fof(f6312,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| frontsegP(X1,X0)
| ~ frontsegP(X1,sK49_skl)
| ~ ssList(X1)
| ~ frontsegP(app(app(sK53_skl,sK49_skl),sK49_skl),X0)
| ~ ssList(sK54_skl)
| ~ ssList(X0)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(paramodulation,[status(thm)],[f1270,f2263]) ).
fof(f6314,definition,
! [X0] :
( sQ744_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(app(sK53_skl,sK49_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ744_spl])],[split_symbol_definition]) ).
fof(f6317,plain,
( ~ sQ10_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ16_spl
| sQ744_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f6308,f1676,f6314,f555,f1226,f817,f528]) ).
fof(f6320,definition,
! [X0,X1] :
( sQ745_spl
<=> ( frontsegP(X1,X0)
| ~ frontsegP(X1,sK49_skl)
| ~ ssList(X1)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ745_spl])],[split_symbol_definition]) ).
fof(f6324,definition,
! [X0,X1] :
( sQ746_spl
<=> ( frontsegP(X1,X0)
| ~ frontsegP(X1,sK49_skl)
| ~ ssList(X1)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ746_spl])],[split_symbol_definition]) ).
fof(f6328,definition,
! [X0,X1] :
( sQ747_spl
<=> ( frontsegP(X1,X0)
| ~ frontsegP(X1,sK49_skl)
| ~ ssList(X1)
| ~ frontsegP(app(app(sK53_skl,sK49_skl),sK49_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ747_spl])],[split_symbol_definition]) ).
fof(f6331,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ11_spl
| sQ747_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f6312,f1440,f6328,f531,f1226,f440,f492]) ).
fof(f6356,plain,
! [X0] :
( ~ sQ228_spl
| frontsegP(sK49_skl,X0)
| ~ ssList(X0)
| ~ frontsegP(app(sK53_skl,sK49_skl),X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(app(sK53_skl,sK49_skl)) ),
inference(resolution,[status(thm)],[f288,f2265]) ).
fof(f6359,plain,
! [X0] :
( ~ sQ585_spl
| frontsegP(sK49_skl,X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f5214,f288]) ).
fof(f6360,plain,
! [X0] :
( ~ sQ293_spl
| frontsegP(sK49_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2831,f288]) ).
fof(f6362,definition,
! [X0] :
( sQ748_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ ssList(X0)
| ~ frontsegP(app(sK53_skl,sK49_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ748_spl])],[split_symbol_definition]) ).
fof(f6365,plain,
( ~ sQ228_spl
| ~ sQ16_spl
| sQ748_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f6356,f1676,f6362,f555,f2264]) ).
fof(f6368,definition,
! [X0] :
( sQ749_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ749_spl])],[split_symbol_definition]) ).
fof(f6371,plain,
( ~ sQ585_spl
| ~ sQ15_spl
| sQ749_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f6359,f555,f6368,f552,f5213]) ).
fof(f6372,definition,
! [X0] :
( sQ750_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ750_spl])],[split_symbol_definition]) ).
fof(f6375,plain,
( ~ sQ293_spl
| ~ sQ16_spl
| sQ750_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6360,f552,f6372,f555,f2830]) ).
fof(f6388,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5907,f288]) ).
fof(f6389,plain,
! [X0,X1] :
( ~ sQ675_spl
| ~ sQ167_spl
| frontsegP(X1,X0)
| ~ frontsegP(X1,nil)
| ~ ssList(X1)
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5907,f2263]) ).
fof(f6390,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| X0 = app(nil,nil)
| ~ frontsegP(X0,nil)
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5907,f2261]) ).
fof(f6391,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(nil,X0),nil)
| ~ ssList(nil)
| ~ ssList(app(app(nil,nil),X0)) ),
inference(paramodulation,[status(thm)],[f5907,f457]) ).
fof(f6392,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ ssList(nil)
| frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5907,f3835]) ).
fof(f6395,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| ~ memberP(nil,X0)
| memberP(nil,X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f5907,f272]) ).
fof(f6397,plain,
! [X0,X1] :
( ~ sQ675_spl
| ~ sQ167_spl
| segmentP(app(nil,X1),X0)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5907,f321]) ).
fof(f6398,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| memberP(nil,X0)
| memberP(nil,X0)
| ~ memberP(nil,X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f5907,f270]) ).
fof(f6399,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| rearsegP(nil,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5907,f307]) ).
fof(f6400,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ rearsegP(app(nil,nil),nil)
| sK6_skl(nil,nil) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5907,f2020]) ).
fof(f6402,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| X0 = nil
| app(X0,nil) != nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5907,f376]) ).
fof(f6404,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| X0 = nil
| app(nil,X0) != nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5907,f378]) ).
fof(f6406,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ ssList(nil)
| rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5907,f627]) ).
fof(f6407,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| app(app(X0,nil),nil) = app(X0,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f5907,f382]) ).
fof(f6408,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| app(nil,X0) = app(nil,app(nil,X0))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5907,f382]) ).
fof(f6415,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ278_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6388,f552,f2699,f1776,f5864]) ).
fof(f6416,definition,
! [X0,X1] :
( sQ752_spl
<=> ( frontsegP(X1,X0)
| ~ frontsegP(X1,nil)
| ~ ssList(X1)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ752_spl])],[split_symbol_definition]) ).
fof(f6419,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ752_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6389,f552,f6416,f1776,f5864]) ).
fof(f6420,definition,
! [X0] :
( sQ753_spl
<=> ( X0 = app(nil,nil)
| ~ frontsegP(X0,nil)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ753_spl])],[split_symbol_definition]) ).
fof(f6423,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ753_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6390,f552,f6420,f1776,f5864]) ).
fof(f6424,definition,
! [X0] :
( sQ754_spl
<=> ( ~ ssList(X0)
| segmentP(app(nil,X0),nil)
| ~ ssList(app(app(nil,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ754_spl])],[split_symbol_definition]) ).
fof(f6427,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ15_spl
| sQ754_spl ),
inference(split_clause,[status(thm)],[f6391,f6424,f552,f1776,f5864]) ).
fof(f6428,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ422_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6392,f552,f3987,f1776,f5864]) ).
fof(f6434,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ15_spl
| sQ369_spl ),
inference(split_clause,[status(thm)],[f6395,f3541,f552,f1776,f5864]) ).
fof(f6436,definition,
! [X0,X1] :
( sQ756_spl
<=> ( segmentP(app(nil,X1),X0)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ756_spl])],[split_symbol_definition]) ).
fof(f6439,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ756_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6397,f552,f6436,f1776,f5864]) ).
fof(f6440,definition,
! [X0] :
( sQ757_spl
<=> ( memberP(nil,X0)
| memberP(nil,X0)
| ~ memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ757_spl])],[split_symbol_definition]) ).
fof(f6443,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ15_spl
| sQ757_spl ),
inference(split_clause,[status(thm)],[f6398,f6440,f552,f1776,f5864]) ).
fof(f6444,definition,
! [X0] :
( sQ758_spl
<=> ( rearsegP(nil,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ758_spl])],[split_symbol_definition]) ).
fof(f6447,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ758_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6399,f552,f6444,f1776,f5864]) ).
fof(f6448,definition,
( sQ759_spl
<=> sK6_skl(nil,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ759_spl])],[split_symbol_definition]) ).
fof(f6449,plain,
( ~ sQ759_spl
| sK6_skl(nil,nil) = nil ),
inference(component_clause,[status(thm)],[f6448]) ).
fof(f6451,definition,
( sQ760_spl
<=> rearsegP(app(nil,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ760_spl])],[split_symbol_definition]) ).
fof(f6453,plain,
( sQ760_spl
| ~ rearsegP(app(nil,nil),nil) ),
inference(component_clause,[status(thm)],[f6451]) ).
fof(f6454,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ760_spl
| sQ759_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6400,f552,f6448,f6451,f1776,f5864]) ).
fof(f6456,definition,
! [X0] :
( sQ761_spl
<=> ( X0 = nil
| app(X0,nil) != nil
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ761_spl])],[split_symbol_definition]) ).
fof(f6459,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ761_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6402,f552,f6456,f1776,f5864]) ).
fof(f6461,definition,
! [X0] :
( sQ762_spl
<=> ( X0 = nil
| app(nil,X0) != nil
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ762_spl])],[split_symbol_definition]) ).
fof(f6464,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ762_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6404,f552,f6461,f1776,f5864]) ).
fof(f6466,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ117_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6406,f552,f1369,f1776,f5864]) ).
fof(f6467,definition,
! [X0] :
( sQ763_spl
<=> ( app(app(X0,nil),nil) = app(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ763_spl])],[split_symbol_definition]) ).
fof(f6470,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ15_spl
| sQ763_spl ),
inference(split_clause,[status(thm)],[f6407,f6467,f552,f1776,f5864]) ).
fof(f6471,definition,
! [X0] :
( sQ764_spl
<=> ( app(nil,X0) = app(nil,app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ764_spl])],[split_symbol_definition]) ).
fof(f6474,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ764_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6408,f552,f6471,f1776,f5864]) ).
fof(f6480,plain,
( sQ760_spl
| ~ sQ675_spl
| ~ sQ167_spl
| ~ rearsegP(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f5907,f6453]) ).
fof(f6481,plain,
( sQ760_spl
| ~ sQ675_spl
| ~ sQ167_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6480,f309]) ).
fof(f6484,plain,
( sQ760_spl
| ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6481,f552,f1776,f5864,f6451]) ).
fof(f6501,plain,
! [X0,X1,X2,X3,X4] :
( ~ frontsegP(X4,cons(X1,X3))
| ~ frontsegP(cons(X0,X2),X4)
| ~ ssList(X4)
| X0 = X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2307,f222]) ).
fof(f6504,plain,
! [X0,X1,X2,X3] :
( ~ ssList(cons(X0,X2))
| ~ frontsegP(nil,cons(X1,X3))
| ~ ssList(nil)
| X0 = X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f6501,f295]) ).
fof(f6506,plain,
! [X0,X1,X2] :
( ~ sQ51_spl
| ~ sQ109_spl
| ~ frontsegP(X2,cons(X0,X1))
| ~ frontsegP(sK49_skl,X2)
| ~ ssList(X2)
| sK51_skl = X0
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1325,f6501]) ).
fof(f6509,definition,
! [X0,X1,X2,X3] :
( sQ766_spl
<=> ( ~ ssList(cons(X0,X2))
| ~ frontsegP(nil,cons(X1,X3))
| X0 = X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ766_spl])],[split_symbol_definition]) ).
fof(f6512,plain,
( ~ sQ15_spl
| sQ766_spl ),
inference(split_clause,[status(thm)],[f6504,f6509,f552]) ).
fof(f6514,definition,
! [X0,X1,X2] :
( sQ767_spl
<=> ( ~ frontsegP(X2,cons(X0,X1))
| ~ frontsegP(sK49_skl,X2)
| ~ ssList(X2)
| sK51_skl = X0
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ767_spl])],[split_symbol_definition]) ).
fof(f6517,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| sQ767_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6506,f486,f6514,f552,f1226,f817]) ).
fof(f6519,plain,
! [X0,X1,X2,X3,X4] :
( ~ frontsegP(X4,cons(X1,X3))
| ~ frontsegP(cons(X0,X2),X4)
| ~ ssList(X4)
| frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2320,f222]) ).
fof(f6520,plain,
! [X0,X1,X2] :
( ~ sQ243_spl
| ~ ssList(X1)
| ~ frontsegP(sK49_skl,cons(X0,X2))
| ~ ssList(sK49_skl)
| frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f6519,f2360]) ).
fof(f6522,plain,
! [X0,X1,X2,X3] :
( ~ ssList(cons(X0,X2))
| ~ frontsegP(nil,cons(X1,X3))
| ~ ssList(nil)
| frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f6519,f295]) ).
fof(f6524,plain,
! [X0,X1,X2] :
( ~ sQ51_spl
| ~ sQ109_spl
| ~ frontsegP(X2,cons(X0,X1))
| ~ frontsegP(sK49_skl,X2)
| ~ ssList(X2)
| frontsegP(nil,X1)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1325,f6519]) ).
fof(f6525,definition,
! [X0,X1,X2] :
( sQ768_spl
<=> ( ~ ssList(X1)
| ~ frontsegP(sK49_skl,cons(X0,X2))
| frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ768_spl])],[split_symbol_definition]) ).
fof(f6528,plain,
( ~ sQ243_spl
| ~ sQ16_spl
| sQ768_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6520,f486,f6525,f555,f2356]) ).
fof(f6531,definition,
! [X0,X1,X2,X3] :
( sQ769_spl
<=> ( ~ ssList(cons(X0,X2))
| ~ frontsegP(nil,cons(X1,X3))
| frontsegP(X2,X3)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ769_spl])],[split_symbol_definition]) ).
fof(f6534,plain,
( ~ sQ15_spl
| sQ769_spl ),
inference(split_clause,[status(thm)],[f6522,f6531,f552]) ).
fof(f6536,definition,
! [X0,X1,X2] :
( sQ770_spl
<=> ( ~ frontsegP(X2,cons(X0,X1))
| ~ frontsegP(sK49_skl,X2)
| ~ ssList(X2)
| frontsegP(nil,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ770_spl])],[split_symbol_definition]) ).
fof(f6539,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| sQ770_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6524,f486,f6536,f552,f1226,f817]) ).
fof(f6563,plain,
! [X0] :
( ~ sQ243_spl
| ~ ssList(X0)
| sK49_skl = cons(sK51_skl,X0)
| ~ frontsegP(sK49_skl,cons(sK51_skl,X0))
| ~ ssList(cons(sK51_skl,X0))
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f284,f2360]) ).
fof(f6574,definition,
! [X0] :
( sQ771_spl
<=> ( ~ ssList(X0)
| sK49_skl = cons(sK51_skl,X0)
| ~ frontsegP(sK49_skl,cons(sK51_skl,X0))
| ~ ssList(cons(sK51_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ771_spl])],[split_symbol_definition]) ).
fof(f6577,plain,
( ~ sQ243_spl
| sQ771_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f6563,f555,f6574,f2356]) ).
fof(f6589,plain,
! [X0,X1] :
( ~ sQ243_spl
| ~ ssList(X1)
| frontsegP(X0,sK49_skl)
| ~ frontsegP(X0,cons(sK51_skl,X1))
| ~ ssList(sK49_skl)
| ~ ssList(cons(sK51_skl,X1))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f2360]) ).
fof(f6591,plain,
! [X0] :
( ~ sQ404_spl
| frontsegP(X0,nil)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(nil)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f3839]) ).
fof(f6592,plain,
! [X0] :
( ~ sQ354_spl
| frontsegP(X0,sK49_skl)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f3376]) ).
fof(f6593,plain,
! [X0] :
( ~ sQ10_spl
| ~ sQ51_spl
| ~ sQ109_spl
| frontsegP(X0,app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f3206]) ).
fof(f6597,plain,
! [X0,X1] :
( ~ sQ228_spl
| frontsegP(sK49_skl,X1)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ frontsegP(app(app(sK53_skl,sK49_skl),sK49_skl),X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(resolution,[status(thm)],[f282,f2265]) ).
fof(f6603,plain,
! [X0] :
( sQ513_spl
| ~ frontsegP(X0,sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f282,f4786]) ).
fof(f6609,definition,
! [X0] :
( sQ773_spl
<=> ( frontsegP(X0,nil)
| ~ frontsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ773_spl])],[split_symbol_definition]) ).
fof(f6616,definition,
! [X0,X1] :
( sQ774_spl
<=> ( ~ ssList(X1)
| frontsegP(X0,sK49_skl)
| ~ frontsegP(X0,cons(sK51_skl,X1))
| ~ ssList(cons(sK51_skl,X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ774_spl])],[split_symbol_definition]) ).
fof(f6619,plain,
( ~ sQ243_spl
| ~ sQ16_spl
| sQ774_spl ),
inference(split_clause,[status(thm)],[f6589,f6616,f555,f2356]) ).
fof(f6621,definition,
! [X0] :
( sQ775_spl
<=> ( frontsegP(X0,nil)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ775_spl])],[split_symbol_definition]) ).
fof(f6624,plain,
( ~ sQ404_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ775_spl ),
inference(split_clause,[status(thm)],[f6591,f6621,f555,f552,f3838]) ).
fof(f6625,definition,
! [X0] :
( sQ776_spl
<=> ( frontsegP(X0,sK49_skl)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ776_spl])],[split_symbol_definition]) ).
fof(f6628,plain,
( ~ sQ354_spl
| ~ sQ16_spl
| sQ776_spl ),
inference(split_clause,[status(thm)],[f6592,f6625,f555,f3375]) ).
fof(f6629,definition,
! [X0] :
( sQ777_spl
<=> ( frontsegP(X0,app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ777_spl])],[split_symbol_definition]) ).
fof(f6632,plain,
( ~ sQ10_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ124_spl
| ~ sQ16_spl
| sQ777_spl ),
inference(split_clause,[status(thm)],[f6593,f6629,f555,f1440,f1226,f817,f528]) ).
fof(f6635,definition,
! [X0,X1] :
( sQ778_spl
<=> ( frontsegP(sK49_skl,X1)
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ frontsegP(app(app(sK53_skl,sK49_skl),sK49_skl),X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ778_spl])],[split_symbol_definition]) ).
fof(f6638,plain,
( ~ sQ228_spl
| sQ778_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f6597,f1440,f6635,f2264]) ).
fof(f6647,definition,
! [X0] :
( sQ780_spl
<=> ( ~ frontsegP(X0,sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ780_spl])],[split_symbol_definition]) ).
fof(f6650,plain,
( sQ513_spl
| ~ sQ16_spl
| sQ780_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6603,f552,f6647,f555,f4784]) ).
fof(f6699,plain,
! [X0,X1] :
( ~ sQ266_spl
| ~ rearsegP(X1,X0)
| ~ rearsegP(sK54_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sK54_skl)
| rearsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2586,f301]) ).
fof(f6702,definition,
! [X0,X1] :
( sQ781_spl
<=> ( ~ rearsegP(X1,X0)
| ~ rearsegP(sK54_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| rearsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ781_spl])],[split_symbol_definition]) ).
fof(f6705,plain,
( ~ sQ266_spl
| ~ sQ11_spl
| sQ781_spl ),
inference(split_clause,[status(thm)],[f6699,f6702,f531,f2585]) ).
fof(f6734,definition,
( sQ784_spl
<=> app(nil,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ784_spl])],[split_symbol_definition]) ).
fof(f6738,plain,
! [X0,X1,X2] :
( cons(X0,X2) = cons(X0,X1)
| ~ frontsegP(cons(X0,X2),cons(X0,X1))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2350,f222]) ).
fof(f6742,plain,
! [X0] :
( ~ sQ51_spl
| ~ sQ109_spl
| cons(sK51_skl,nil) = cons(sK51_skl,X0)
| ~ frontsegP(sK49_skl,cons(sK51_skl,X0))
| ~ frontsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1325,f6738]) ).
fof(f6743,plain,
! [X0] :
( ~ sQ51_spl
| ~ sQ109_spl
| cons(sK51_skl,X0) = cons(sK51_skl,nil)
| ~ frontsegP(cons(sK51_skl,X0),sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1325,f6738]) ).
fof(f6746,definition,
! [X0] :
( sQ785_spl
<=> ( cons(sK51_skl,nil) = cons(sK51_skl,X0)
| ~ frontsegP(sK49_skl,cons(sK51_skl,X0))
| ~ frontsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ785_spl])],[split_symbol_definition]) ).
fof(f6749,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| sQ785_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6742,f486,f6746,f552,f1226,f817]) ).
fof(f6750,definition,
! [X0] :
( sQ786_spl
<=> ( cons(sK51_skl,X0) = cons(sK51_skl,nil)
| ~ frontsegP(cons(sK51_skl,X0),sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ786_spl])],[split_symbol_definition]) ).
fof(f6753,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sQ786_spl
| ~ sQ15_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6743,f486,f552,f6750,f1226,f817]) ).
fof(f6758,plain,
! [X0,X1,X2,X3] :
( frontsegP(X3,cons(X0,X2))
| ~ frontsegP(X3,cons(X0,X1))
| ~ ssList(X3)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2351,f222]) ).
fof(f6759,plain,
! [X0,X1,X2] :
( ~ sQ228_spl
| frontsegP(sK49_skl,cons(X0,X2))
| ~ ssList(cons(X0,X2))
| ~ frontsegP(app(app(sK53_skl,sK49_skl),sK49_skl),cons(X0,X1))
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f6758,f2265]) ).
fof(f6765,plain,
! [X0,X1,X2] :
( nil = cons(X0,X2)
| ~ ssList(cons(X0,X2))
| ~ frontsegP(nil,cons(X0,X1))
| ~ ssList(nil)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f6758,f298]) ).
fof(f6768,plain,
! [X0,X1] :
( ~ sQ51_spl
| ~ sQ109_spl
| frontsegP(X1,sK49_skl)
| ~ frontsegP(X1,cons(sK51_skl,X0))
| ~ ssList(X1)
| ~ frontsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1325,f6758]) ).
fof(f6769,definition,
! [X0,X1,X2] :
( sQ787_spl
<=> ( frontsegP(sK49_skl,cons(X0,X2))
| ~ ssList(cons(X0,X2))
| ~ frontsegP(app(app(sK53_skl,sK49_skl),sK49_skl),cons(X0,X1))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ787_spl])],[split_symbol_definition]) ).
fof(f6772,plain,
( ~ sQ228_spl
| ~ sQ124_spl
| sQ787_spl ),
inference(split_clause,[status(thm)],[f6759,f6769,f1440,f2264]) ).
fof(f6780,definition,
! [X0,X1,X2] :
( sQ788_spl
<=> ( nil = cons(X0,X2)
| ~ ssList(cons(X0,X2))
| ~ frontsegP(nil,cons(X0,X1))
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ788_spl])],[split_symbol_definition]) ).
fof(f6783,plain,
( ~ sQ15_spl
| sQ788_spl ),
inference(split_clause,[status(thm)],[f6765,f6780,f552]) ).
fof(f6788,definition,
! [X0,X1] :
( sQ789_spl
<=> ( frontsegP(X1,sK49_skl)
| ~ frontsegP(X1,cons(sK51_skl,X0))
| ~ ssList(X1)
| ~ frontsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ789_spl])],[split_symbol_definition]) ).
fof(f6791,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| sQ789_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6768,f486,f6788,f552,f1226,f817]) ).
fof(f6949,plain,
( sQ520_spl
| ~ ssList(sK49_skl)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f4815,f627]) ).
fof(f6951,definition,
( sQ807_spl
<=> rearsegP(sK54_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ807_spl])],[split_symbol_definition]) ).
fof(f6952,plain,
( ~ sQ807_spl
| rearsegP(sK54_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f6951]) ).
fof(f6953,plain,
( sQ807_spl
| ~ rearsegP(sK54_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f6951]) ).
fof(f6955,plain,
( sQ520_spl
| ~ sQ16_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6949,f531,f555,f4813]) ).
fof(f6961,plain,
( sQ807_spl
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f6953,f305]) ).
fof(f6966,plain,
( sQ807_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6961,f531,f6951]) ).
fof(f6969,plain,
! [X0] :
( ~ sQ585_spl
| ~ sQ290_spl
| segmentP(sK49_skl,X0)
| ~ segmentP(sK54_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f5214,f2798]) ).
fof(f6972,definition,
! [X0] :
( sQ810_spl
<=> ( segmentP(sK49_skl,X0)
| ~ segmentP(sK54_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ810_spl])],[split_symbol_definition]) ).
fof(f6975,plain,
( ~ sQ585_spl
| ~ sQ290_spl
| ~ sQ15_spl
| sQ810_spl ),
inference(split_clause,[status(thm)],[f6969,f6972,f552,f2797,f5213]) ).
fof(f6978,plain,
! [X0] :
( ~ sQ807_spl
| rearsegP(X0,sK54_skl)
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(sK54_skl)
| ~ ssList(sK54_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f6952,f301]) ).
fof(f6981,definition,
! [X0] :
( sQ811_spl
<=> ( rearsegP(X0,sK54_skl)
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ811_spl])],[split_symbol_definition]) ).
fof(f6984,plain,
( ~ sQ807_spl
| ~ sQ11_spl
| sQ811_spl ),
inference(split_clause,[status(thm)],[f6978,f6981,f531,f6951]) ).
fof(f7007,plain,
( sQ596_spl
| nil = cons(sK51_skl,sK54_skl)
| ~ ssList(cons(sK51_skl,sK54_skl)) ),
inference(resolution,[status(thm)],[f5335,f231]) ).
fof(f7008,definition,
( sQ812_spl
<=> ssList(cons(sK51_skl,sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ812_spl])],[split_symbol_definition]) ).
fof(f7010,plain,
( sQ812_spl
| ~ ssList(cons(sK51_skl,sK54_skl)) ),
inference(component_clause,[status(thm)],[f7008]) ).
fof(f7011,plain,
( sQ596_spl
| sQ510_spl
| ~ sQ812_spl ),
inference(split_clause,[status(thm)],[f7007,f7008,f4772,f5333]) ).
fof(f7012,plain,
( sQ812_spl
| ~ ssItem(sK51_skl)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f7010,f222]) ).
fof(f7013,plain,
( sQ812_spl
| ~ sQ3_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7012,f531,f486,f7008]) ).
fof(f7014,plain,
( ~ sQ598_spl
| cons(sK44_skl(cons(sK51_skl,sK54_skl)),sK54_skl) = cons(sK51_skl,sK54_skl)
| nil = cons(sK51_skl,sK54_skl)
| ~ ssList(cons(sK51_skl,sK54_skl)) ),
inference(paramodulation,[status(thm)],[f5341,f233]) ).
fof(f7016,definition,
( sQ813_spl
<=> cons(sK44_skl(cons(sK51_skl,sK54_skl)),sK54_skl) = cons(sK51_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ813_spl])],[split_symbol_definition]) ).
fof(f7019,plain,
( ~ sQ598_spl
| sQ813_spl
| sQ510_spl
| ~ sQ812_spl ),
inference(split_clause,[status(thm)],[f7014,f7008,f4772,f7016,f5340]) ).
fof(f7022,plain,
( ~ sQ597_spl
| sK54_skl = sK43_skl(cons(sK51_skl,sK54_skl))
| ~ ssItem(sK51_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(sK54_skl)
| ~ ssList(sK43_skl(cons(sK51_skl,sK54_skl))) ),
inference(paramodulation,[status(thm)],[f5337,f4243]) ).
fof(f7024,plain,
( ~ sQ597_spl
| cons(sK51_skl,sK43_skl(cons(sK51_skl,sK54_skl))) = cons(sK51_skl,sK54_skl)
| nil = cons(sK51_skl,sK54_skl)
| ~ ssList(cons(sK51_skl,sK54_skl)) ),
inference(paramodulation,[status(thm)],[f5337,f233]) ).
fof(f7026,plain,
( ~ sQ597_spl
| sQ598_spl
| ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ596_spl ),
inference(split_clause,[status(thm)],[f7022,f5333,f531,f486,f5340,f5336]) ).
fof(f7028,definition,
( sQ814_spl
<=> cons(sK51_skl,sK43_skl(cons(sK51_skl,sK54_skl))) = cons(sK51_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ814_spl])],[split_symbol_definition]) ).
fof(f7031,plain,
( ~ sQ597_spl
| sQ814_spl
| sQ510_spl
| ~ sQ812_spl ),
inference(split_clause,[status(thm)],[f7024,f7008,f4772,f7028,f5336]) ).
fof(f7088,plain,
! [X0] :
( ~ sQ683_spl
| frontsegP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| ~ frontsegP(sK53_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f5913,f2263]) ).
fof(f7089,plain,
( ~ sQ683_spl
| sK49_skl = app(sK53_skl,sK49_skl)
| ~ frontsegP(sK53_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f5913,f2261]) ).
fof(f7090,plain,
! [X0] :
( ~ sQ683_spl
| frontsegP(X0,app(sK53_skl,sK49_skl))
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(app(sK53_skl,sK49_skl))
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5913,f282]) ).
fof(f7092,definition,
! [X0] :
( sQ815_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(sK53_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ815_spl])],[split_symbol_definition]) ).
fof(f7095,plain,
( ~ sQ683_spl
| ~ sQ16_spl
| sQ815_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f7088,f753,f7092,f555,f5912]) ).
fof(f7096,definition,
( sQ816_spl
<=> frontsegP(sK53_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ816_spl])],[split_symbol_definition]) ).
fof(f7099,definition,
( sQ817_spl
<=> sK49_skl = app(sK53_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ817_spl])],[split_symbol_definition]) ).
fof(f7100,plain,
( ~ sQ817_spl
| sK49_skl = app(sK53_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f7099]) ).
fof(f7102,plain,
( ~ sQ683_spl
| sQ817_spl
| ~ sQ816_spl
| ~ sQ16_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f7089,f753,f555,f7096,f7099,f5912]) ).
fof(f7103,definition,
! [X0] :
( sQ818_spl
<=> ( frontsegP(X0,app(sK53_skl,sK49_skl))
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ818_spl])],[split_symbol_definition]) ).
fof(f7106,plain,
( ~ sQ683_spl
| ~ sQ154_spl
| ~ sQ16_spl
| sQ818_spl ),
inference(split_clause,[status(thm)],[f7090,f7103,f555,f1676,f5912]) ).
fof(f7146,plain,
( ~ sQ817_spl
| ~ rearsegP(app(sK53_skl,sK49_skl),sK49_skl)
| sK6_skl(sK49_skl,sK49_skl) = sK53_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f7100,f2020]) ).
fof(f7180,definition,
( sQ825_spl
<=> hd(sK49_skl) = hd(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ825_spl])],[split_symbol_definition]) ).
fof(f7181,plain,
( ~ sQ825_spl
| hd(sK49_skl) = hd(sK53_skl) ),
inference(component_clause,[status(thm)],[f7180]) ).
fof(f7182,plain,
( sQ825_spl
| hd(sK49_skl) != hd(sK53_skl) ),
inference(component_clause,[status(thm)],[f7180]) ).
fof(f7195,definition,
( sQ828_spl
<=> sK6_skl(sK49_skl,sK49_skl) = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ828_spl])],[split_symbol_definition]) ).
fof(f7196,plain,
( ~ sQ828_spl
| sK6_skl(sK49_skl,sK49_skl) = sK53_skl ),
inference(component_clause,[status(thm)],[f7195]) ).
fof(f7198,definition,
( sQ829_spl
<=> rearsegP(app(sK53_skl,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ829_spl])],[split_symbol_definition]) ).
fof(f7200,plain,
( sQ829_spl
| ~ rearsegP(app(sK53_skl,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f7198]) ).
fof(f7201,plain,
( ~ sQ817_spl
| ~ sQ829_spl
| sQ828_spl
| ~ sQ16_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f7146,f753,f555,f7195,f7198,f7099]) ).
fof(f7220,plain,
( ~ sQ828_spl
| ~ sQ299_spl
| nil = sK53_skl ),
inference(forward_demodulation,[status(thm)],[f2882,f7196]) ).
fof(f7221,plain,
( ~ sQ828_spl
| ~ sQ299_spl
| sQ159_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7220,f1719]) ).
fof(f7222,plain,
( ~ sQ828_spl
| ~ sQ299_spl
| sQ159_spl ),
inference(contradiction_clause,[status(thm)],[f7221]) ).
fof(f7223,plain,
( ~ sQ825_spl
| ~ sQ152_spl
| sK51_skl = hd(sK53_skl) ),
inference(forward_demodulation,[status(thm)],[f1658,f7181]) ).
fof(f7227,plain,
( ~ sQ825_spl
| ~ sQ152_spl
| cons(sK51_skl,tl(sK53_skl)) = sK53_skl
| nil = sK53_skl
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f7223,f374]) ).
fof(f7229,definition,
( sQ833_spl
<=> cons(sK51_skl,tl(sK53_skl)) = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ833_spl])],[split_symbol_definition]) ).
fof(f7230,plain,
( ~ sQ833_spl
| cons(sK51_skl,tl(sK53_skl)) = sK53_skl ),
inference(component_clause,[status(thm)],[f7229]) ).
fof(f7232,plain,
( ~ sQ825_spl
| ~ sQ152_spl
| sQ833_spl
| sQ159_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f7227,f753,f1717,f7229,f1657,f7180]) ).
fof(f7233,plain,
( sQ825_spl
| ~ sQ152_spl
| sK51_skl != hd(sK53_skl) ),
inference(forward_demodulation,[status(thm)],[f1658,f7182]) ).
fof(f7438,plain,
! [X0,X1] :
( sQ513_spl
| ~ frontsegP(X1,sK49_skl)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ frontsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2240,f4786]) ).
fof(f7439,plain,
! [X0,X1,X2] :
( nil = X1
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| ~ frontsegP(X0,X2)
| ~ ssList(X2)
| ~ frontsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2240,f298]) ).
fof(f7453,plain,
! [X0,X1,X2] :
( ~ sQ243_spl
| ~ ssList(X1)
| ~ frontsegP(sK49_skl,X2)
| ~ ssList(sK49_skl)
| frontsegP(X0,X2)
| ~ frontsegP(X0,cons(sK51_skl,X1))
| ~ ssList(X2)
| ~ ssList(cons(sK51_skl,X1))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2240,f2360]) ).
fof(f7456,plain,
! [X0,X1] :
( ~ sQ404_spl
| ~ frontsegP(nil,X1)
| ~ ssList(nil)
| frontsegP(X0,X1)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X1)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2240,f3839]) ).
fof(f7458,plain,
! [X0,X1] :
( ~ sQ354_spl
| ~ frontsegP(sK49_skl,X1)
| ~ ssList(sK49_skl)
| frontsegP(X0,X1)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X1)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2240,f3376]) ).
fof(f7461,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssList(nil)
| frontsegP(X0,nil)
| ~ frontsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2240,f295]) ).
fof(f7462,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ frontsegP(nil,X2)
| ~ ssList(nil)
| frontsegP(X0,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2240,f295]) ).
fof(f7469,plain,
! [X0,X1] :
( ~ sQ422_spl
| ~ frontsegP(X1,nil)
| ~ ssList(nil)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2240,f3988]) ).
fof(f7472,plain,
! [X0,X1,X2] :
( ~ sQ243_spl
| ~ ssList(X2)
| ~ frontsegP(X1,cons(sK51_skl,X2))
| ~ ssList(cons(sK51_skl,X2))
| frontsegP(X0,sK49_skl)
| ~ frontsegP(X0,X1)
| ~ ssList(sK49_skl)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2240,f2360]) ).
fof(f7474,plain,
! [X0,X1] :
( ~ sQ404_spl
| ~ frontsegP(X1,sK49_skl)
| ~ ssList(sK49_skl)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2240,f3839]) ).
fof(f7475,plain,
! [X0,X1] :
( ~ sQ354_spl
| ~ frontsegP(X1,sK49_skl)
| ~ ssList(sK49_skl)
| frontsegP(X0,sK49_skl)
| ~ frontsegP(X0,X1)
| ~ ssList(sK49_skl)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2240,f3376]) ).
fof(f7477,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2240,f295]) ).
fof(f7492,definition,
! [X0,X1] :
( sQ855_spl
<=> ( ~ frontsegP(X1,sK49_skl)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ855_spl])],[split_symbol_definition]) ).
fof(f7495,plain,
( sQ513_spl
| ~ sQ16_spl
| sQ855_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f7438,f552,f7492,f555,f4784]) ).
fof(f7496,definition,
! [X0,X1,X2] :
( sQ856_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ frontsegP(X2,X1)
| ~ frontsegP(X0,X2)
| ~ ssList(X2)
| ~ frontsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ856_spl])],[split_symbol_definition]) ).
fof(f7499,plain,
( sQ856_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f7439,f552,f7496]) ).
fof(f7513,definition,
! [X0,X1,X2] :
( sQ857_spl
<=> ( ~ ssList(X1)
| ~ frontsegP(sK49_skl,X2)
| frontsegP(X0,X2)
| ~ frontsegP(X0,cons(sK51_skl,X1))
| ~ ssList(X2)
| ~ ssList(cons(sK51_skl,X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ857_spl])],[split_symbol_definition]) ).
fof(f7516,plain,
( ~ sQ243_spl
| ~ sQ16_spl
| sQ857_spl ),
inference(split_clause,[status(thm)],[f7453,f7513,f555,f2356]) ).
fof(f7518,plain,
( ~ sQ404_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ746_spl ),
inference(split_clause,[status(thm)],[f7456,f6324,f555,f552,f3838]) ).
fof(f7520,plain,
( ~ sQ354_spl
| ~ sQ16_spl
| sQ745_spl ),
inference(split_clause,[status(thm)],[f7458,f6320,f555,f3375]) ).
fof(f7523,plain,
( ~ sQ15_spl
| sQ773_spl ),
inference(split_clause,[status(thm)],[f7461,f6609,f552]) ).
fof(f7524,definition,
! [X0,X1,X2] :
( sQ858_spl
<=> ( ~ ssList(X1)
| ~ frontsegP(nil,X2)
| frontsegP(X0,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ858_spl])],[split_symbol_definition]) ).
fof(f7527,plain,
( ~ sQ15_spl
| sQ858_spl ),
inference(split_clause,[status(thm)],[f7462,f7524,f552]) ).
fof(f7531,definition,
! [X0,X1] :
( sQ859_spl
<=> ( ~ frontsegP(X1,nil)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ859_spl])],[split_symbol_definition]) ).
fof(f7534,plain,
( ~ sQ422_spl
| ~ sQ15_spl
| sQ859_spl ),
inference(split_clause,[status(thm)],[f7469,f7531,f552,f3987]) ).
fof(f7539,definition,
! [X0,X1,X2] :
( sQ860_spl
<=> ( ~ ssList(X2)
| ~ frontsegP(X1,cons(sK51_skl,X2))
| ~ ssList(cons(sK51_skl,X2))
| frontsegP(X0,sK49_skl)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ860_spl])],[split_symbol_definition]) ).
fof(f7542,plain,
( ~ sQ243_spl
| ~ sQ16_spl
| sQ860_spl ),
inference(split_clause,[status(thm)],[f7472,f7539,f555,f2356]) ).
fof(f7544,definition,
! [X0,X1] :
( sQ861_spl
<=> ( ~ frontsegP(X1,sK49_skl)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ861_spl])],[split_symbol_definition]) ).
fof(f7547,plain,
( ~ sQ404_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ861_spl ),
inference(split_clause,[status(thm)],[f7474,f7544,f552,f555,f3838]) ).
fof(f7548,definition,
! [X0,X1] :
( sQ862_spl
<=> ( ~ frontsegP(X1,sK49_skl)
| frontsegP(X0,sK49_skl)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ862_spl])],[split_symbol_definition]) ).
fof(f7551,plain,
( ~ sQ354_spl
| ~ sQ16_spl
| sQ862_spl ),
inference(split_clause,[status(thm)],[f7475,f7548,f555,f3375]) ).
fof(f7554,definition,
! [X0,X1,X2] :
( sQ863_spl
<=> ( ~ ssList(X2)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ863_spl])],[split_symbol_definition]) ).
fof(f7557,plain,
( ~ sQ15_spl
| sQ863_spl ),
inference(split_clause,[status(thm)],[f7477,f7554,f552]) ).
fof(f7564,plain,
( ~ sQ351_spl
| ~ sQ152_spl
| sK51_skl = hd(app(sK53_skl,sK49_skl))
| nil = app(sK53_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK53_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f3361,f391]) ).
fof(f7566,plain,
( ~ sQ351_spl
| ~ sQ152_spl
| cons(sK51_skl,tl(app(app(sK53_skl,sK49_skl),sK49_skl))) = app(app(sK53_skl,sK49_skl),sK49_skl)
| nil = app(app(sK53_skl,sK49_skl),sK49_skl)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(paramodulation,[status(thm)],[f3361,f374]) ).
fof(f7567,definition,
( sQ864_spl
<=> sK51_skl = hd(app(sK53_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ864_spl])],[split_symbol_definition]) ).
fof(f7568,plain,
( ~ sQ864_spl
| sK51_skl = hd(app(sK53_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f7567]) ).
fof(f7570,plain,
( ~ sQ351_spl
| ~ sQ152_spl
| sQ864_spl
| sQ158_spl
| ~ sQ16_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f7564,f1676,f555,f1694,f7567,f1657,f3357]) ).
fof(f7572,definition,
( sQ865_spl
<=> cons(sK51_skl,tl(app(app(sK53_skl,sK49_skl),sK49_skl))) = app(app(sK53_skl,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ865_spl])],[split_symbol_definition]) ).
fof(f7575,plain,
( ~ sQ351_spl
| ~ sQ152_spl
| sQ865_spl
| sQ128_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f7566,f1440,f1459,f7572,f1657,f3357]) ).
fof(f7580,plain,
( ~ sQ585_spl
| ~ ssList(sK49_skl)
| nil = app(sK49_skl,nil)
| ~ rearsegP(nil,sK49_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5214,f2571]) ).
fof(f7583,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| sK54_skl = app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl)
| ~ rearsegP(sK54_skl,sK49_skl)
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f1270,f2571]) ).
fof(f7587,definition,
( sQ866_spl
<=> nil = app(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ866_spl])],[split_symbol_definition]) ).
fof(f7588,plain,
( ~ sQ866_spl
| nil = app(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f7587]) ).
fof(f7590,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| sQ866_spl
| ~ sQ164_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f7580,f552,f1739,f7587,f555,f5213]) ).
fof(f7593,definition,
( sQ867_spl
<=> sK54_skl = app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ867_spl])],[split_symbol_definition]) ).
fof(f7594,plain,
( ~ sQ867_spl
| sK54_skl = app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl) ),
inference(component_clause,[status(thm)],[f7593]) ).
fof(f7596,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| sQ867_spl
| ~ sQ263_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7583,f531,f2563,f7593,f1440,f1226,f440,f492]) ).
fof(f7597,plain,
( ~ sQ867_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sK54_skl = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f1270,f7594]) ).
fof(f7598,plain,
( ~ sQ867_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sQ264_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7597,f2568]) ).
fof(f7599,plain,
( ~ sQ867_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sQ264_spl ),
inference(contradiction_clause,[status(thm)],[f7598]) ).
fof(f7605,plain,
! [X0] :
( ~ sQ585_spl
| X0 = app(sK49_skl,nil)
| ~ rearsegP(X0,sK49_skl)
| ~ rearsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5214,f2582]) ).
fof(f7606,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| X0 = app(nil,nil)
| ~ rearsegP(X0,nil)
| ~ rearsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5907,f2582]) ).
fof(f7607,plain,
! [X0] :
( ~ sQ293_spl
| X0 = app(nil,sK49_skl)
| ~ rearsegP(X0,sK49_skl)
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f2831,f2582]) ).
fof(f7608,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| X0 = app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl)
| ~ rearsegP(X0,sK49_skl)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f1270,f2582]) ).
fof(f7613,definition,
! [X0] :
( sQ868_spl
<=> ( X0 = app(sK49_skl,nil)
| ~ rearsegP(X0,sK49_skl)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ868_spl])],[split_symbol_definition]) ).
fof(f7616,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| sQ868_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f7605,f552,f7613,f555,f5213]) ).
fof(f7617,definition,
! [X0] :
( sQ869_spl
<=> ( X0 = app(nil,nil)
| ~ rearsegP(X0,nil)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ869_spl])],[split_symbol_definition]) ).
fof(f7620,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ869_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f7606,f552,f7617,f1776,f5864]) ).
fof(f7621,definition,
! [X0] :
( sQ870_spl
<=> ( X0 = app(nil,sK49_skl)
| ~ rearsegP(X0,sK49_skl)
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ870_spl])],[split_symbol_definition]) ).
fof(f7624,plain,
( ~ sQ293_spl
| ~ sQ15_spl
| sQ870_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f7607,f555,f7621,f552,f2830]) ).
fof(f7625,definition,
! [X0] :
( sQ871_spl
<=> ( X0 = app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl)
| ~ rearsegP(X0,sK49_skl)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ871_spl])],[split_symbol_definition]) ).
fof(f7628,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| sQ871_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7608,f531,f7625,f1440,f1226,f440,f492]) ).
fof(f7637,plain,
( ~ sQ866_spl
| ~ sQ54_spl
| ~ sQ109_spl
| cons(sK51_skl,nil) = nil
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f7588,f1230]) ).
fof(f7671,definition,
( sQ873_spl
<=> cons(sK51_skl,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ873_spl])],[split_symbol_definition]) ).
fof(f7672,plain,
( ~ sQ873_spl
| cons(sK51_skl,nil) = nil ),
inference(component_clause,[status(thm)],[f7671]) ).
fof(f7674,plain,
( ~ sQ866_spl
| ~ sQ54_spl
| ~ sQ109_spl
| sQ873_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f7637,f552,f7671,f1226,f852,f7587]) ).
fof(f7709,definition,
( sQ880_spl
<=> sK6_skl(nil,nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ880_spl])],[split_symbol_definition]) ).
fof(f7710,plain,
( ~ sQ880_spl
| sK6_skl(nil,nil) = sK49_skl ),
inference(component_clause,[status(thm)],[f7709]) ).
fof(f7731,plain,
( ~ sQ880_spl
| ~ sQ759_spl
| nil = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f6449,f7710]) ).
fof(f7732,plain,
( ~ sQ880_spl
| ~ sQ759_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7731,f449]) ).
fof(f7733,plain,
( ~ sQ880_spl
| ~ sQ759_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f7732]) ).
fof(f7738,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ873_spl
| nil = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f7672,f1325]) ).
fof(f7799,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ873_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f7738,f447,f7671,f1226,f817]) ).
fof(f8016,plain,
! [X0,X1,X2,X3] :
( ~ sQ226_spl
| ~ frontsegP(nil,cons(X0,X3))
| ~ ssList(nil)
| ~ frontsegP(X3,X1)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X0)
| nil = X2
| ~ frontsegP(cons(X0,X1),X2)
| ~ ssList(X2)
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f2247,f6758]) ).
fof(f8017,plain,
! [X0] :
( ~ sQ226_spl
| ~ ssList(nil)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2247,f295]) ).
fof(f8018,plain,
! [X0,X1,X2,X3] :
( ~ sQ226_spl
| ~ frontsegP(X3,X0)
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ frontsegP(nil,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(nil)
| nil = X1
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2247,f2240]) ).
fof(f8019,plain,
! [X0,X1,X2] :
( ~ sQ226_spl
| ~ frontsegP(X2,X0)
| ~ frontsegP(nil,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(nil)
| nil = X1
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2247,f282]) ).
fof(f8021,definition,
! [X0] :
( sQ914_spl
<=> ( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ914_spl])],[split_symbol_definition]) ).
fof(f8025,definition,
! [X0,X1,X2,X3] :
( sQ915_spl
<=> ( ~ frontsegP(nil,cons(X0,X3))
| ~ frontsegP(X3,X1)
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X0)
| nil = X2
| ~ frontsegP(cons(X0,X1),X2)
| ~ ssList(X2)
| ~ ssList(cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ915_spl])],[split_symbol_definition]) ).
fof(f8028,plain,
( ~ sQ226_spl
| ~ sQ15_spl
| sQ915_spl ),
inference(split_clause,[status(thm)],[f8016,f8025,f552,f2241]) ).
fof(f8029,plain,
( ~ sQ226_spl
| sQ914_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8017,f552,f8021,f2241]) ).
fof(f8030,definition,
! [X0,X1,X2,X3] :
( sQ916_spl
<=> ( ~ frontsegP(X3,X0)
| ~ frontsegP(X2,X3)
| ~ ssList(X3)
| ~ frontsegP(nil,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| nil = X1
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ916_spl])],[split_symbol_definition]) ).
fof(f8033,plain,
( ~ sQ226_spl
| ~ sQ15_spl
| sQ916_spl ),
inference(split_clause,[status(thm)],[f8018,f8030,f552,f2241]) ).
fof(f8034,definition,
! [X0,X1,X2] :
( sQ917_spl
<=> ( ~ frontsegP(X2,X0)
| ~ frontsegP(nil,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| nil = X1
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ917_spl])],[split_symbol_definition]) ).
fof(f8037,plain,
( ~ sQ226_spl
| ~ sQ15_spl
| sQ917_spl ),
inference(split_clause,[status(thm)],[f8019,f8034,f552,f2241]) ).
fof(f8043,plain,
! [X0] :
( ~ sQ422_spl
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| X0 = nil
| ~ frontsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2255,f3988]) ).
fof(f8047,plain,
! [X0,X1] :
( ~ sQ243_spl
| ~ ssList(X1)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| X0 = cons(sK51_skl,X1)
| ~ frontsegP(X0,cons(sK51_skl,X1))
| ~ ssList(cons(sK51_skl,X1))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2255,f2360]) ).
fof(f8050,plain,
! [X0] :
( ~ sQ404_spl
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| X0 = sK49_skl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2255,f3839]) ).
fof(f8052,plain,
! [X0] :
( ~ sQ354_spl
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| X0 = sK49_skl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2255,f3376]) ).
fof(f8056,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| X0 = X1
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2255,f295]) ).
fof(f8066,plain,
! [X0,X1] :
( ~ sQ243_spl
| ~ ssList(X1)
| ~ frontsegP(X0,cons(sK51_skl,X1))
| ~ ssList(cons(sK51_skl,X1))
| sK49_skl = X0
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f2255,f2360]) ).
fof(f8068,plain,
! [X0] :
( ~ sQ404_spl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2255,f3839]) ).
fof(f8071,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2255,f295]) ).
fof(f8076,definition,
! [X0] :
( sQ918_spl
<=> ( ~ frontsegP(nil,X0)
| X0 = nil
| ~ frontsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ918_spl])],[split_symbol_definition]) ).
fof(f8079,plain,
( ~ sQ422_spl
| ~ sQ15_spl
| sQ918_spl ),
inference(split_clause,[status(thm)],[f8043,f8076,f552,f3987]) ).
fof(f8083,definition,
! [X0,X1] :
( sQ919_spl
<=> ( ~ ssList(X1)
| ~ frontsegP(sK49_skl,X0)
| X0 = cons(sK51_skl,X1)
| ~ frontsegP(X0,cons(sK51_skl,X1))
| ~ ssList(cons(sK51_skl,X1))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ919_spl])],[split_symbol_definition]) ).
fof(f8086,plain,
( ~ sQ243_spl
| ~ sQ16_spl
| sQ919_spl ),
inference(split_clause,[status(thm)],[f8047,f8083,f555,f2356]) ).
fof(f8088,definition,
! [X0] :
( sQ920_spl
<=> ( ~ frontsegP(nil,X0)
| X0 = sK49_skl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ920_spl])],[split_symbol_definition]) ).
fof(f8091,plain,
( ~ sQ404_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ920_spl ),
inference(split_clause,[status(thm)],[f8050,f8088,f555,f552,f3838]) ).
fof(f8093,definition,
! [X0] :
( sQ921_spl
<=> ( ~ frontsegP(sK49_skl,X0)
| X0 = sK49_skl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ921_spl])],[split_symbol_definition]) ).
fof(f8096,plain,
( ~ sQ354_spl
| ~ sQ16_spl
| sQ921_spl ),
inference(split_clause,[status(thm)],[f8052,f8093,f555,f3375]) ).
fof(f8100,definition,
! [X0,X1] :
( sQ922_spl
<=> ( ~ ssList(X1)
| ~ frontsegP(nil,X0)
| X0 = X1
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ922_spl])],[split_symbol_definition]) ).
fof(f8103,plain,
( ~ sQ15_spl
| sQ922_spl ),
inference(split_clause,[status(thm)],[f8056,f8100,f552]) ).
fof(f8112,definition,
! [X0,X1] :
( sQ923_spl
<=> ( ~ ssList(X1)
| ~ frontsegP(X0,cons(sK51_skl,X1))
| ~ ssList(cons(sK51_skl,X1))
| sK49_skl = X0
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ923_spl])],[split_symbol_definition]) ).
fof(f8115,plain,
( ~ sQ243_spl
| sQ923_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f8066,f555,f8112,f2356]) ).
fof(f8117,definition,
! [X0] :
( sQ924_spl
<=> ( ~ frontsegP(X0,sK49_skl)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ924_spl])],[split_symbol_definition]) ).
fof(f8120,plain,
( ~ sQ404_spl
| ~ sQ16_spl
| sQ924_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8068,f552,f8117,f555,f3838]) ).
fof(f8124,definition,
! [X0,X1] :
( sQ925_spl
<=> ( ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ925_spl])],[split_symbol_definition]) ).
fof(f8127,plain,
( sQ925_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8071,f552,f8124]) ).
fof(f8133,plain,
! [X0,X1] :
( sQ401_spl
| ~ rearsegP(X1,app(sK49_skl,sK49_skl))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(app(sK49_skl,sK49_skl))
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f2546,f3818]) ).
fof(f8134,plain,
! [X0,X1] :
( sQ263_spl
| ~ rearsegP(X1,sK49_skl)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f2546,f2565]) ).
fof(f8135,plain,
! [X0,X1,X2] :
( ~ sQ266_spl
| rearsegP(sK49_skl,X1)
| ~ ssList(X1)
| ~ rearsegP(X2,X1)
| ~ rearsegP(X0,X2)
| ~ ssList(X2)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f2546,f2586]) ).
fof(f8137,plain,
! [X0,X1] :
( sQ381_spl
| ~ rearsegP(X1,app(sK49_skl,sK49_skl))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ rearsegP(nil,X0)
| ~ ssList(app(sK49_skl,sK49_skl))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2546,f3676]) ).
fof(f8138,plain,
! [X0,X1] :
( sQ164_spl
| ~ rearsegP(X1,sK49_skl)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ rearsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2546,f1741]) ).
fof(f8139,plain,
! [X0,X1,X2] :
( nil = X1
| ~ ssList(X1)
| ~ rearsegP(X2,X1)
| ~ rearsegP(X0,X2)
| ~ ssList(X2)
| ~ rearsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2546,f312]) ).
fof(f8150,plain,
! [X0,X1] :
( ~ sQ807_spl
| ~ rearsegP(sK54_skl,X1)
| ~ ssList(sK54_skl)
| rearsegP(X0,X1)
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(X1)
| ~ ssList(sK54_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2546,f6952]) ).
fof(f8152,plain,
! [X0,X1] :
( ~ sQ117_spl
| ~ rearsegP(nil,X1)
| ~ ssList(nil)
| rearsegP(X0,X1)
| ~ rearsegP(X0,nil)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2546,f1370]) ).
fof(f8153,plain,
! [X0,X1] :
( ~ sQ80_spl
| ~ rearsegP(nil,X1)
| ~ ssList(nil)
| rearsegP(X0,X1)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X1)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2546,f1005]) ).
fof(f8155,plain,
! [X0,X1] :
( ~ sQ287_spl
| ~ rearsegP(sK49_skl,X1)
| ~ ssList(sK49_skl)
| rearsegP(X0,X1)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X1)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2546,f2767]) ).
fof(f8156,plain,
! [X0,X1] :
( ~ sQ59_spl
| ~ rearsegP(sK54_skl,X1)
| ~ ssList(sK54_skl)
| rearsegP(X0,X1)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X1)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2546,f890]) ).
fof(f8157,plain,
! [X0,X1] :
( ~ sQ387_spl
| ~ rearsegP(sK49_skl,X1)
| ~ ssList(sK49_skl)
| rearsegP(X0,X1)
| ~ rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ ssList(X1)
| ~ ssList(app(sK49_skl,sK49_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2546,f3730]) ).
fof(f8161,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssList(nil)
| rearsegP(X0,nil)
| ~ rearsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2546,f309]) ).
fof(f8162,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ rearsegP(nil,X2)
| ~ ssList(nil)
| rearsegP(X0,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2546,f309]) ).
fof(f8169,plain,
! [X0,X1] :
( ~ sQ807_spl
| ~ rearsegP(X1,sK54_skl)
| ~ ssList(sK54_skl)
| rearsegP(X0,sK54_skl)
| ~ rearsegP(X0,X1)
| ~ ssList(sK54_skl)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2546,f6952]) ).
fof(f8170,plain,
! [X0,X1] :
( ~ sQ117_spl
| ~ rearsegP(X1,nil)
| ~ ssList(nil)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2546,f1370]) ).
fof(f8171,plain,
! [X0,X1] :
( ~ sQ80_spl
| ~ rearsegP(X1,sK49_skl)
| ~ ssList(sK49_skl)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2546,f1005]) ).
fof(f8172,plain,
! [X0,X1] :
( ~ sQ287_spl
| ~ rearsegP(X1,sK49_skl)
| ~ ssList(sK49_skl)
| rearsegP(X0,sK49_skl)
| ~ rearsegP(X0,X1)
| ~ ssList(sK49_skl)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2546,f2767]) ).
fof(f8173,plain,
! [X0,X1] :
( ~ sQ59_spl
| ~ rearsegP(X1,sK49_skl)
| ~ ssList(sK49_skl)
| rearsegP(X0,sK54_skl)
| ~ rearsegP(X0,X1)
| ~ ssList(sK54_skl)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2546,f890]) ).
fof(f8174,plain,
! [X0,X1] :
( ~ sQ387_spl
| ~ rearsegP(X1,app(sK49_skl,sK49_skl))
| ~ ssList(app(sK49_skl,sK49_skl))
| rearsegP(X0,sK49_skl)
| ~ rearsegP(X0,X1)
| ~ ssList(sK49_skl)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2546,f3730]) ).
fof(f8177,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2546,f309]) ).
fof(f8181,definition,
! [X0,X1] :
( sQ926_spl
<=> ( ~ rearsegP(X1,app(sK49_skl,sK49_skl))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ926_spl])],[split_symbol_definition]) ).
fof(f8184,plain,
( sQ401_spl
| ~ sQ370_spl
| sQ926_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f8133,f555,f8181,f3625,f3816]) ).
fof(f8185,definition,
! [X0,X1] :
( sQ927_spl
<=> ( ~ rearsegP(X1,sK49_skl)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ927_spl])],[split_symbol_definition]) ).
fof(f8188,plain,
( sQ263_spl
| ~ sQ16_spl
| sQ927_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8134,f531,f8185,f555,f2563]) ).
fof(f8189,definition,
! [X0,X1,X2] :
( sQ928_spl
<=> ( rearsegP(sK49_skl,X1)
| ~ ssList(X1)
| ~ rearsegP(X2,X1)
| ~ rearsegP(X0,X2)
| ~ ssList(X2)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ928_spl])],[split_symbol_definition]) ).
fof(f8192,plain,
( ~ sQ266_spl
| sQ928_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8135,f531,f8189,f2585]) ).
fof(f8197,definition,
! [X0,X1] :
( sQ930_spl
<=> ( ~ rearsegP(X1,app(sK49_skl,sK49_skl))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ930_spl])],[split_symbol_definition]) ).
fof(f8200,plain,
( sQ381_spl
| ~ sQ370_spl
| sQ930_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8137,f552,f8197,f3625,f3674]) ).
fof(f8201,definition,
! [X0,X1] :
( sQ931_spl
<=> ( ~ rearsegP(X1,sK49_skl)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ931_spl])],[split_symbol_definition]) ).
fof(f8204,plain,
( sQ164_spl
| ~ sQ16_spl
| sQ931_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8138,f552,f8201,f555,f1739]) ).
fof(f8205,definition,
! [X0,X1,X2] :
( sQ932_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ rearsegP(X2,X1)
| ~ rearsegP(X0,X2)
| ~ ssList(X2)
| ~ rearsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ932_spl])],[split_symbol_definition]) ).
fof(f8208,plain,
( sQ932_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8139,f552,f8205]) ).
fof(f8220,definition,
! [X0,X1] :
( sQ933_spl
<=> ( ~ rearsegP(sK54_skl,X1)
| rearsegP(X0,X1)
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ933_spl])],[split_symbol_definition]) ).
fof(f8223,plain,
( ~ sQ807_spl
| ~ sQ11_spl
| sQ933_spl ),
inference(split_clause,[status(thm)],[f8150,f8220,f531,f6951]) ).
fof(f8225,definition,
! [X0,X1] :
( sQ934_spl
<=> ( ~ rearsegP(nil,X1)
| rearsegP(X0,X1)
| ~ rearsegP(X0,nil)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ934_spl])],[split_symbol_definition]) ).
fof(f8228,plain,
( ~ sQ117_spl
| ~ sQ15_spl
| sQ934_spl ),
inference(split_clause,[status(thm)],[f8152,f8225,f552,f1369]) ).
fof(f8229,definition,
! [X0,X1] :
( sQ935_spl
<=> ( ~ rearsegP(nil,X1)
| rearsegP(X0,X1)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ935_spl])],[split_symbol_definition]) ).
fof(f8232,plain,
( ~ sQ80_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ935_spl ),
inference(split_clause,[status(thm)],[f8153,f8229,f555,f552,f1004]) ).
fof(f8234,definition,
! [X0,X1] :
( sQ936_spl
<=> ( ~ rearsegP(sK49_skl,X1)
| rearsegP(X0,X1)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ936_spl])],[split_symbol_definition]) ).
fof(f8237,plain,
( ~ sQ287_spl
| ~ sQ16_spl
| sQ936_spl ),
inference(split_clause,[status(thm)],[f8155,f8234,f555,f2766]) ).
fof(f8238,definition,
! [X0,X1] :
( sQ937_spl
<=> ( ~ rearsegP(sK54_skl,X1)
| rearsegP(X0,X1)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ937_spl])],[split_symbol_definition]) ).
fof(f8241,plain,
( ~ sQ59_spl
| ~ sQ11_spl
| ~ sQ16_spl
| sQ937_spl ),
inference(split_clause,[status(thm)],[f8156,f8238,f555,f531,f889]) ).
fof(f8242,definition,
! [X0,X1] :
( sQ938_spl
<=> ( ~ rearsegP(sK49_skl,X1)
| rearsegP(X0,X1)
| ~ rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ938_spl])],[split_symbol_definition]) ).
fof(f8245,plain,
( ~ sQ387_spl
| ~ sQ16_spl
| ~ sQ370_spl
| sQ938_spl ),
inference(split_clause,[status(thm)],[f8157,f8242,f3625,f555,f3729]) ).
fof(f8250,plain,
( ~ sQ15_spl
| sQ257_spl ),
inference(split_clause,[status(thm)],[f8161,f2528,f552]) ).
fof(f8251,definition,
! [X0,X1,X2] :
( sQ939_spl
<=> ( ~ ssList(X1)
| ~ rearsegP(nil,X2)
| rearsegP(X0,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ939_spl])],[split_symbol_definition]) ).
fof(f8254,plain,
( ~ sQ15_spl
| sQ939_spl ),
inference(split_clause,[status(thm)],[f8162,f8251,f552]) ).
fof(f8258,definition,
! [X0,X1] :
( sQ940_spl
<=> ( ~ rearsegP(X1,sK54_skl)
| rearsegP(X0,sK54_skl)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ940_spl])],[split_symbol_definition]) ).
fof(f8261,plain,
( ~ sQ807_spl
| ~ sQ11_spl
| sQ940_spl ),
inference(split_clause,[status(thm)],[f8169,f8258,f531,f6951]) ).
fof(f8262,definition,
! [X0,X1] :
( sQ941_spl
<=> ( ~ rearsegP(X1,nil)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ941_spl])],[split_symbol_definition]) ).
fof(f8265,plain,
( ~ sQ117_spl
| ~ sQ15_spl
| sQ941_spl ),
inference(split_clause,[status(thm)],[f8170,f8262,f552,f1369]) ).
fof(f8266,definition,
! [X0,X1] :
( sQ942_spl
<=> ( ~ rearsegP(X1,sK49_skl)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ942_spl])],[split_symbol_definition]) ).
fof(f8269,plain,
( ~ sQ80_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ942_spl ),
inference(split_clause,[status(thm)],[f8171,f8266,f552,f555,f1004]) ).
fof(f8270,definition,
! [X0,X1] :
( sQ943_spl
<=> ( ~ rearsegP(X1,sK49_skl)
| rearsegP(X0,sK49_skl)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ943_spl])],[split_symbol_definition]) ).
fof(f8273,plain,
( ~ sQ287_spl
| ~ sQ16_spl
| sQ943_spl ),
inference(split_clause,[status(thm)],[f8172,f8270,f555,f2766]) ).
fof(f8274,definition,
! [X0,X1] :
( sQ944_spl
<=> ( ~ rearsegP(X1,sK49_skl)
| rearsegP(X0,sK54_skl)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ944_spl])],[split_symbol_definition]) ).
fof(f8277,plain,
( ~ sQ59_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sQ944_spl ),
inference(split_clause,[status(thm)],[f8173,f8274,f531,f555,f889]) ).
fof(f8278,definition,
! [X0,X1] :
( sQ945_spl
<=> ( ~ rearsegP(X1,app(sK49_skl,sK49_skl))
| rearsegP(X0,sK49_skl)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ945_spl])],[split_symbol_definition]) ).
fof(f8281,plain,
( ~ sQ387_spl
| ~ sQ370_spl
| ~ sQ16_spl
| sQ945_spl ),
inference(split_clause,[status(thm)],[f8174,f8278,f555,f3625,f3729]) ).
fof(f8286,definition,
! [X0,X1,X2] :
( sQ946_spl
<=> ( ~ ssList(X2)
| ~ rearsegP(X1,X2)
| ~ ssList(X2)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ946_spl])],[split_symbol_definition]) ).
fof(f8289,plain,
( ~ sQ15_spl
| sQ946_spl ),
inference(split_clause,[status(thm)],[f8177,f8286,f552]) ).
fof(f8535,plain,
( sQ527_spl
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f4857,f309]) ).
fof(f8538,plain,
( sQ527_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8535,f531,f4855]) ).
fof(f8548,plain,
! [X0,X1] :
( ~ sQ527_spl
| ~ rearsegP(X1,sK54_skl)
| ~ ssList(sK54_skl)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4856,f2546]) ).
fof(f8549,plain,
! [X0,X1] :
( ~ sQ527_spl
| ~ rearsegP(nil,X1)
| ~ ssList(nil)
| rearsegP(X0,X1)
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(X1)
| ~ ssList(sK54_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4856,f2546]) ).
fof(f8551,plain,
! [X0] :
( ~ sQ527_spl
| rearsegP(X0,nil)
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(nil)
| ~ ssList(sK54_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4856,f301]) ).
fof(f8553,definition,
! [X0,X1] :
( sQ967_spl
<=> ( ~ rearsegP(X1,sK54_skl)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ967_spl])],[split_symbol_definition]) ).
fof(f8556,plain,
( ~ sQ527_spl
| ~ sQ11_spl
| ~ sQ15_spl
| sQ967_spl ),
inference(split_clause,[status(thm)],[f8548,f8553,f552,f531,f4855]) ).
fof(f8557,definition,
! [X0,X1] :
( sQ968_spl
<=> ( ~ rearsegP(nil,X1)
| rearsegP(X0,X1)
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ968_spl])],[split_symbol_definition]) ).
fof(f8560,plain,
( ~ sQ527_spl
| ~ sQ15_spl
| ~ sQ11_spl
| sQ968_spl ),
inference(split_clause,[status(thm)],[f8549,f8557,f531,f552,f4855]) ).
fof(f8562,definition,
! [X0] :
( sQ969_spl
<=> ( rearsegP(X0,nil)
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ969_spl])],[split_symbol_definition]) ).
fof(f8565,plain,
( ~ sQ527_spl
| ~ sQ15_spl
| ~ sQ11_spl
| sQ969_spl ),
inference(split_clause,[status(thm)],[f8551,f8562,f531,f552,f4855]) ).
fof(f8602,plain,
( sQ733_spl
| ~ ssList(nil)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f6244,f627]) ).
fof(f8606,plain,
( sQ733_spl
| ~ sQ15_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8602,f531,f552,f6242]) ).
fof(f8607,definition,
( sQ971_spl
<=> ssList(app(nil,sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ971_spl])],[split_symbol_definition]) ).
fof(f8609,plain,
( sQ971_spl
| ~ ssList(app(nil,sK54_skl)) ),
inference(component_clause,[status(thm)],[f8607]) ).
fof(f8618,plain,
( sQ971_spl
| ~ ssList(sK54_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f8609,f245]) ).
fof(f8619,plain,
( sQ971_spl
| ~ sQ11_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8618,f552,f531,f8607]) ).
fof(f8620,plain,
( sQ739_spl
| ~ frontsegP(sK53_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f6285,f288]) ).
fof(f8623,plain,
( sQ739_spl
| ~ sQ816_spl
| ~ sQ16_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f8620,f753,f555,f7096,f6283]) ).
fof(f8633,plain,
! [X0] :
( ~ sQ262_spl
| ~ ssList(nil)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2557,f309]) ).
fof(f8634,plain,
! [X0,X1,X2,X3] :
( ~ sQ262_spl
| ~ rearsegP(X3,X0)
| ~ rearsegP(X2,X3)
| ~ ssList(X3)
| ~ rearsegP(nil,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(nil)
| nil = X1
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2557,f2546]) ).
fof(f8635,plain,
! [X0,X1,X2] :
( ~ sQ262_spl
| ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(nil)
| nil = X1
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2557,f301]) ).
fof(f8637,definition,
! [X0] :
( sQ976_spl
<=> ( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ976_spl])],[split_symbol_definition]) ).
fof(f8641,plain,
( ~ sQ262_spl
| sQ976_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8633,f552,f8637,f2551]) ).
fof(f8642,definition,
! [X0,X1,X2,X3] :
( sQ977_spl
<=> ( ~ rearsegP(X3,X0)
| ~ rearsegP(X2,X3)
| ~ ssList(X3)
| ~ rearsegP(nil,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| nil = X1
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ977_spl])],[split_symbol_definition]) ).
fof(f8645,plain,
( ~ sQ262_spl
| ~ sQ15_spl
| sQ977_spl ),
inference(split_clause,[status(thm)],[f8634,f8642,f552,f2551]) ).
fof(f8646,definition,
! [X0,X1,X2] :
( sQ978_spl
<=> ( ~ rearsegP(X2,X0)
| ~ rearsegP(nil,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| nil = X1
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ978_spl])],[split_symbol_definition]) ).
fof(f8649,plain,
( ~ sQ262_spl
| ~ sQ15_spl
| sQ978_spl ),
inference(split_clause,[status(thm)],[f8635,f8646,f552,f2551]) ).
fof(f8653,plain,
! [X0] :
( ~ sQ527_spl
| ~ rearsegP(nil,X0)
| ~ ssList(nil)
| X0 = sK54_skl
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(sK54_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2576,f4856]) ).
fof(f8655,plain,
! [X0] :
( ~ sQ807_spl
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(sK54_skl)
| X0 = sK54_skl
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(sK54_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2576,f6952]) ).
fof(f8657,plain,
! [X0] :
( ~ sQ117_spl
| ~ rearsegP(nil,X0)
| ~ ssList(nil)
| X0 = nil
| ~ rearsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2576,f1370]) ).
fof(f8658,plain,
! [X0] :
( ~ sQ80_spl
| ~ rearsegP(nil,X0)
| ~ ssList(nil)
| X0 = sK49_skl
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2576,f1005]) ).
fof(f8660,plain,
! [X0] :
( ~ sQ287_spl
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| X0 = sK49_skl
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2576,f2767]) ).
fof(f8661,plain,
! [X0] :
( ~ sQ59_spl
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(sK54_skl)
| X0 = sK49_skl
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2576,f890]) ).
fof(f8662,plain,
! [X0] :
( ~ sQ387_spl
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| X0 = app(sK49_skl,sK49_skl)
| ~ rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ ssList(app(sK49_skl,sK49_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2576,f3730]) ).
fof(f8667,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ rearsegP(nil,X0)
| ~ ssList(nil)
| X0 = X1
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2576,f309]) ).
fof(f8674,plain,
! [X0] :
( ~ sQ527_spl
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(sK54_skl)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2576,f4856]) ).
fof(f8677,plain,
! [X0] :
( ~ sQ80_spl
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2576,f1005]) ).
fof(f8679,plain,
! [X0] :
( ~ sQ59_spl
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| sK54_skl = X0
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f2576,f890]) ).
fof(f8680,plain,
! [X0] :
( ~ sQ387_spl
| ~ rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ ssList(app(sK49_skl,sK49_skl))
| sK49_skl = X0
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f2576,f3730]) ).
fof(f8683,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2576,f309]) ).
fof(f8687,definition,
! [X0] :
( sQ979_spl
<=> ( ~ rearsegP(nil,X0)
| X0 = sK54_skl
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ979_spl])],[split_symbol_definition]) ).
fof(f8690,plain,
( ~ sQ527_spl
| ~ sQ15_spl
| ~ sQ11_spl
| sQ979_spl ),
inference(split_clause,[status(thm)],[f8653,f8687,f531,f552,f4855]) ).
fof(f8692,definition,
! [X0] :
( sQ980_spl
<=> ( ~ rearsegP(sK54_skl,X0)
| X0 = sK54_skl
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ980_spl])],[split_symbol_definition]) ).
fof(f8695,plain,
( ~ sQ807_spl
| ~ sQ11_spl
| sQ980_spl ),
inference(split_clause,[status(thm)],[f8655,f8692,f531,f6951]) ).
fof(f8697,definition,
! [X0] :
( sQ981_spl
<=> ( ~ rearsegP(nil,X0)
| X0 = nil
| ~ rearsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ981_spl])],[split_symbol_definition]) ).
fof(f8700,plain,
( ~ sQ117_spl
| ~ sQ15_spl
| sQ981_spl ),
inference(split_clause,[status(thm)],[f8657,f8697,f552,f1369]) ).
fof(f8701,definition,
! [X0] :
( sQ982_spl
<=> ( ~ rearsegP(nil,X0)
| X0 = sK49_skl
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ982_spl])],[split_symbol_definition]) ).
fof(f8704,plain,
( ~ sQ80_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ982_spl ),
inference(split_clause,[status(thm)],[f8658,f8701,f555,f552,f1004]) ).
fof(f8706,definition,
! [X0] :
( sQ983_spl
<=> ( ~ rearsegP(sK49_skl,X0)
| X0 = sK49_skl
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ983_spl])],[split_symbol_definition]) ).
fof(f8709,plain,
( ~ sQ287_spl
| ~ sQ16_spl
| sQ983_spl ),
inference(split_clause,[status(thm)],[f8660,f8706,f555,f2766]) ).
fof(f8710,definition,
! [X0] :
( sQ984_spl
<=> ( ~ rearsegP(sK54_skl,X0)
| X0 = sK49_skl
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ984_spl])],[split_symbol_definition]) ).
fof(f8713,plain,
( ~ sQ59_spl
| ~ sQ11_spl
| ~ sQ16_spl
| sQ984_spl ),
inference(split_clause,[status(thm)],[f8661,f8710,f555,f531,f889]) ).
fof(f8714,definition,
! [X0] :
( sQ985_spl
<=> ( ~ rearsegP(sK49_skl,X0)
| X0 = app(sK49_skl,sK49_skl)
| ~ rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ985_spl])],[split_symbol_definition]) ).
fof(f8717,plain,
( ~ sQ387_spl
| ~ sQ16_spl
| ~ sQ370_spl
| sQ985_spl ),
inference(split_clause,[status(thm)],[f8662,f8714,f3625,f555,f3729]) ).
fof(f8722,definition,
! [X0,X1] :
( sQ986_spl
<=> ( ~ ssList(X1)
| ~ rearsegP(nil,X0)
| X0 = X1
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ986_spl])],[split_symbol_definition]) ).
fof(f8725,plain,
( ~ sQ15_spl
| sQ986_spl ),
inference(split_clause,[status(thm)],[f8667,f8722,f552]) ).
fof(f8729,definition,
! [X0] :
( sQ987_spl
<=> ( ~ rearsegP(X0,sK54_skl)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ987_spl])],[split_symbol_definition]) ).
fof(f8732,plain,
( ~ sQ527_spl
| ~ sQ11_spl
| sQ987_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8674,f552,f8729,f531,f4855]) ).
fof(f8735,definition,
! [X0] :
( sQ988_spl
<=> ( ~ rearsegP(X0,sK49_skl)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ988_spl])],[split_symbol_definition]) ).
fof(f8738,plain,
( ~ sQ80_spl
| ~ sQ16_spl
| sQ988_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8677,f552,f8735,f555,f1004]) ).
fof(f8740,definition,
! [X0] :
( sQ989_spl
<=> ( ~ rearsegP(X0,sK49_skl)
| sK54_skl = X0
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ989_spl])],[split_symbol_definition]) ).
fof(f8743,plain,
( ~ sQ59_spl
| ~ sQ16_spl
| sQ989_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8679,f531,f8740,f555,f889]) ).
fof(f8744,definition,
! [X0] :
( sQ990_spl
<=> ( ~ rearsegP(X0,app(sK49_skl,sK49_skl))
| sK49_skl = X0
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ990_spl])],[split_symbol_definition]) ).
fof(f8747,plain,
( ~ sQ387_spl
| ~ sQ370_spl
| sQ990_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f8680,f555,f8744,f3625,f3729]) ).
fof(f8752,definition,
! [X0,X1] :
( sQ991_spl
<=> ( ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ991_spl])],[split_symbol_definition]) ).
fof(f8755,plain,
( sQ991_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8683,f552,f8752]) ).
fof(f8794,plain,
! [X0,X1] :
( nil = cons(X1,X0)
| ~ ssList(cons(X1,X0))
| X0 = sK43_skl(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3343,f232]) ).
fof(f8795,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| nil = cons(sK51_skl,nil)
| ~ ssList(cons(sK51_skl,nil))
| nil = sK43_skl(sK49_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1325,f8794]) ).
fof(f8796,definition,
( sQ996_spl
<=> nil = sK43_skl(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ996_spl])],[split_symbol_definition]) ).
fof(f8799,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sQ873_spl
| ~ sQ25_spl
| sQ996_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8795,f552,f486,f8796,f634,f7671,f1226,f817]) ).
fof(f8848,plain,
! [X0] :
( ~ sQ520_spl
| ~ rearsegP(X0,app(sK49_skl,sK54_skl))
| ~ ssList(app(sK49_skl,sK54_skl))
| sK54_skl = X0
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f4814,f2576]) ).
fof(f8849,plain,
! [X0] :
( ~ sQ520_spl
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(sK54_skl)
| X0 = app(sK49_skl,sK54_skl)
| ~ rearsegP(X0,app(sK49_skl,sK54_skl))
| ~ ssList(app(sK49_skl,sK54_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4814,f2576]) ).
fof(f8850,plain,
! [X0,X1] :
( ~ sQ520_spl
| ~ rearsegP(X1,app(sK49_skl,sK54_skl))
| ~ ssList(app(sK49_skl,sK54_skl))
| rearsegP(X0,sK54_skl)
| ~ rearsegP(X0,X1)
| ~ ssList(sK54_skl)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4814,f2546]) ).
fof(f8851,plain,
! [X0,X1] :
( ~ sQ520_spl
| ~ rearsegP(sK54_skl,X1)
| ~ ssList(sK54_skl)
| rearsegP(X0,X1)
| ~ rearsegP(X0,app(sK49_skl,sK54_skl))
| ~ ssList(X1)
| ~ ssList(app(sK49_skl,sK54_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4814,f2546]) ).
fof(f8852,plain,
( ~ sQ520_spl
| sK54_skl = app(sK49_skl,sK54_skl)
| ~ rearsegP(sK54_skl,app(sK49_skl,sK54_skl))
| ~ ssList(app(sK49_skl,sK54_skl))
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f4814,f303]) ).
fof(f8853,plain,
! [X0] :
( ~ sQ520_spl
| rearsegP(X0,sK54_skl)
| ~ rearsegP(X0,app(sK49_skl,sK54_skl))
| ~ ssList(sK54_skl)
| ~ ssList(app(sK49_skl,sK54_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4814,f301]) ).
fof(f8854,definition,
! [X0] :
( sQ1005_spl
<=> ( ~ rearsegP(X0,app(sK49_skl,sK54_skl))
| sK54_skl = X0
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1005_spl])],[split_symbol_definition]) ).
fof(f8857,plain,
( ~ sQ520_spl
| ~ sQ468_spl
| sQ1005_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8848,f531,f8854,f4491,f4813]) ).
fof(f8858,definition,
! [X0] :
( sQ1006_spl
<=> ( ~ rearsegP(sK54_skl,X0)
| X0 = app(sK49_skl,sK54_skl)
| ~ rearsegP(X0,app(sK49_skl,sK54_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1006_spl])],[split_symbol_definition]) ).
fof(f8861,plain,
( ~ sQ520_spl
| ~ sQ11_spl
| ~ sQ468_spl
| sQ1006_spl ),
inference(split_clause,[status(thm)],[f8849,f8858,f4491,f531,f4813]) ).
fof(f8862,definition,
! [X0,X1] :
( sQ1007_spl
<=> ( ~ rearsegP(X1,app(sK49_skl,sK54_skl))
| rearsegP(X0,sK54_skl)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1007_spl])],[split_symbol_definition]) ).
fof(f8865,plain,
( ~ sQ520_spl
| ~ sQ468_spl
| ~ sQ11_spl
| sQ1007_spl ),
inference(split_clause,[status(thm)],[f8850,f8862,f531,f4491,f4813]) ).
fof(f8866,definition,
! [X0,X1] :
( sQ1008_spl
<=> ( ~ rearsegP(sK54_skl,X1)
| rearsegP(X0,X1)
| ~ rearsegP(X0,app(sK49_skl,sK54_skl))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1008_spl])],[split_symbol_definition]) ).
fof(f8869,plain,
( ~ sQ520_spl
| ~ sQ11_spl
| ~ sQ468_spl
| sQ1008_spl ),
inference(split_clause,[status(thm)],[f8851,f8866,f4491,f531,f4813]) ).
fof(f8870,definition,
( sQ1009_spl
<=> rearsegP(sK54_skl,app(sK49_skl,sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1009_spl])],[split_symbol_definition]) ).
fof(f8873,definition,
( sQ1010_spl
<=> sK54_skl = app(sK49_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ1010_spl])],[split_symbol_definition]) ).
fof(f8874,plain,
( ~ sQ1010_spl
| sK54_skl = app(sK49_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f8873]) ).
fof(f8876,plain,
( ~ sQ520_spl
| sQ1010_spl
| ~ sQ1009_spl
| ~ sQ468_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8852,f531,f4491,f8870,f8873,f4813]) ).
fof(f8877,definition,
! [X0] :
( sQ1011_spl
<=> ( rearsegP(X0,sK54_skl)
| ~ rearsegP(X0,app(sK49_skl,sK54_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1011_spl])],[split_symbol_definition]) ).
fof(f8880,plain,
( ~ sQ520_spl
| ~ sQ11_spl
| ~ sQ468_spl
| sQ1011_spl ),
inference(split_clause,[status(thm)],[f8853,f8877,f4491,f531,f4813]) ).
fof(f8887,plain,
( ~ sQ1010_spl
| ~ sQ54_spl
| ~ sQ109_spl
| cons(sK51_skl,sK54_skl) = sK54_skl
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f8874,f1230]) ).
fof(f8918,definition,
( sQ1013_spl
<=> cons(sK51_skl,sK54_skl) = sK54_skl ),
introduced(definition,[new_symbols(definition,[sQ1013_spl])],[split_symbol_definition]) ).
fof(f8919,plain,
( ~ sQ1013_spl
| cons(sK51_skl,sK54_skl) = sK54_skl ),
inference(component_clause,[status(thm)],[f8918]) ).
fof(f8921,plain,
( ~ sQ1010_spl
| ~ sQ54_spl
| ~ sQ109_spl
| sQ1013_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8887,f531,f8918,f1226,f852,f8873]) ).
fof(f8977,definition,
( sQ1027_spl
<=> sK6_skl(sK54_skl,sK54_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ1027_spl])],[split_symbol_definition]) ).
fof(f8978,plain,
( ~ sQ1027_spl
| sK6_skl(sK54_skl,sK54_skl) = sK49_skl ),
inference(component_clause,[status(thm)],[f8977]) ).
fof(f9039,plain,
! [X0,X1] :
( sQ26_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ segmentP(X1,sK49_skl)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ segmentP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2633,f1774]) ).
fof(f9040,plain,
! [X0,X1,X2] :
( nil = X1
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X0,X2)
| ~ ssList(X2)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2633,f326]) ).
fof(f9054,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssList(nil)
| segmentP(X0,nil)
| ~ segmentP(X0,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2633,f323]) ).
fof(f9055,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ segmentP(nil,X2)
| ~ ssList(nil)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2633,f323]) ).
fof(f9065,plain,
! [X0,X1] :
( ~ sQ29_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ segmentP(X1,sK49_skl)
| ~ ssList(sK49_skl)
| segmentP(X0,sK49_skl)
| ~ segmentP(X0,X1)
| ~ ssList(sK49_skl)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2633,f1250]) ).
fof(f9066,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2633,f323]) ).
fof(f9078,definition,
! [X0,X1] :
( sQ1039_spl
<=> ( ~ segmentP(X1,sK49_skl)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1039_spl])],[split_symbol_definition]) ).
fof(f9081,plain,
( sQ26_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ16_spl
| sQ1039_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9039,f552,f9078,f555,f1226,f817,f637]) ).
fof(f9082,definition,
! [X0,X1,X2] :
( sQ1040_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X0,X2)
| ~ ssList(X2)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1040_spl])],[split_symbol_definition]) ).
fof(f9085,plain,
( sQ1040_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9040,f552,f9082]) ).
fof(f9094,definition,
! [X0,X1] :
( sQ1041_spl
<=> ( ~ segmentP(sK49_skl,X1)
| segmentP(X0,X1)
| ~ segmentP(X0,sK49_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1041_spl])],[split_symbol_definition]) ).
fof(f9098,definition,
! [X0] :
( sQ1042_spl
<=> ( segmentP(X0,nil)
| ~ segmentP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1042_spl])],[split_symbol_definition]) ).
fof(f9101,plain,
( ~ sQ15_spl
| sQ1042_spl ),
inference(split_clause,[status(thm)],[f9054,f9098,f552]) ).
fof(f9102,definition,
! [X0,X1,X2] :
( sQ1043_spl
<=> ( ~ ssList(X1)
| ~ segmentP(nil,X2)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1043_spl])],[split_symbol_definition]) ).
fof(f9105,plain,
( ~ sQ15_spl
| sQ1043_spl ),
inference(split_clause,[status(thm)],[f9055,f9102,f552]) ).
fof(f9112,definition,
! [X0,X1] :
( sQ1044_spl
<=> ( ~ segmentP(X1,sK49_skl)
| segmentP(X0,sK49_skl)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1044_spl])],[split_symbol_definition]) ).
fof(f9115,plain,
( ~ sQ29_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ16_spl
| sQ1044_spl ),
inference(split_clause,[status(thm)],[f9065,f9112,f555,f1226,f440,f656]) ).
fof(f9116,definition,
! [X0,X1,X2] :
( sQ1045_spl
<=> ( ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1045_spl])],[split_symbol_definition]) ).
fof(f9119,plain,
( ~ sQ15_spl
| sQ1045_spl ),
inference(split_clause,[status(thm)],[f9066,f9116,f552]) ).
fof(f9126,plain,
! [X0] :
( ~ sQ272_spl
| ~ ssList(nil)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2644,f323]) ).
fof(f9127,plain,
! [X0,X1,X2,X3] :
( ~ sQ272_spl
| ~ segmentP(X3,X0)
| ~ segmentP(X2,X3)
| ~ ssList(X3)
| ~ segmentP(nil,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(nil)
| nil = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2644,f2633]) ).
fof(f9128,plain,
! [X0,X1,X2] :
( ~ sQ272_spl
| ~ segmentP(X2,X0)
| ~ segmentP(nil,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(nil)
| nil = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2644,f315]) ).
fof(f9130,definition,
! [X0] :
( sQ1046_spl
<=> ( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1046_spl])],[split_symbol_definition]) ).
fof(f9133,plain,
( ~ sQ272_spl
| sQ1046_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9126,f552,f9130,f2638]) ).
fof(f9134,definition,
! [X0,X1,X2,X3] :
( sQ1047_spl
<=> ( ~ segmentP(X3,X0)
| ~ segmentP(X2,X3)
| ~ ssList(X3)
| ~ segmentP(nil,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| nil = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1047_spl])],[split_symbol_definition]) ).
fof(f9137,plain,
( ~ sQ272_spl
| ~ sQ15_spl
| sQ1047_spl ),
inference(split_clause,[status(thm)],[f9127,f9134,f552,f2638]) ).
fof(f9138,definition,
! [X0,X1,X2] :
( sQ1048_spl
<=> ( ~ segmentP(X2,X0)
| ~ segmentP(nil,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| nil = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1048_spl])],[split_symbol_definition]) ).
fof(f9141,plain,
( ~ sQ272_spl
| ~ sQ15_spl
| sQ1048_spl ),
inference(split_clause,[status(thm)],[f9128,f9138,f552,f2638]) ).
fof(f9201,plain,
( ~ sQ1027_spl
| app(sK49_skl,sK54_skl) = sK54_skl
| ~ rearsegP(sK54_skl,sK54_skl)
| ~ ssList(sK54_skl)
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f8978,f129]) ).
fof(f9203,plain,
( ~ sQ1027_spl
| sQ1010_spl
| ~ sQ807_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f9201,f531,f6951,f8873,f8977]) ).
fof(f9225,plain,
( ~ sQ1013_spl
| ~ ssItem(sK51_skl)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f8919,f225]) ).
fof(f9275,plain,
( ~ sQ1013_spl
| ~ sQ3_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f9225,f531,f486,f8918]) ).
fof(f9445,plain,
! [X0] :
( ~ sQ29_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ segmentP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| X0 = sK49_skl
| ~ segmentP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2657,f1250]) ).
fof(f9447,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ segmentP(nil,X0)
| ~ ssList(nil)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2657,f323]) ).
fof(f9458,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2657,f323]) ).
fof(f9466,definition,
! [X0] :
( sQ1094_spl
<=> ( ~ segmentP(sK49_skl,X0)
| X0 = sK49_skl
| ~ segmentP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1094_spl])],[split_symbol_definition]) ).
fof(f9469,plain,
( ~ sQ29_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ16_spl
| sQ1094_spl ),
inference(split_clause,[status(thm)],[f9445,f9466,f555,f1226,f440,f656]) ).
fof(f9474,definition,
! [X0,X1] :
( sQ1096_spl
<=> ( ~ ssList(X1)
| ~ segmentP(nil,X0)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1096_spl])],[split_symbol_definition]) ).
fof(f9477,plain,
( ~ sQ15_spl
| sQ1096_spl ),
inference(split_clause,[status(thm)],[f9447,f9474,f552]) ).
fof(f9485,definition,
! [X0,X1] :
( sQ1097_spl
<=> ( ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1097_spl])],[split_symbol_definition]) ).
fof(f9488,plain,
( sQ1097_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9458,f552,f9485]) ).
fof(f9500,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| X0 = app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl)
| ~ segmentP(X0,sK49_skl)
| ~ ssList(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl))
| ~ segmentP(sK49_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(sK53_skl,sK49_skl))
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1270,f2663]) ).
fof(f9502,plain,
! [X0,X1] :
( ~ sQ585_spl
| X0 = app(app(sK49_skl,nil),X1)
| ~ segmentP(X0,app(sK49_skl,X1))
| ~ ssList(app(app(sK49_skl,nil),X1))
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5214,f2663]) ).
fof(f9503,plain,
! [X0,X1] :
( ~ sQ675_spl
| ~ sQ167_spl
| X0 = app(app(nil,nil),X1)
| ~ segmentP(X0,app(nil,X1))
| ~ ssList(app(app(nil,nil),X1))
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5907,f2663]) ).
fof(f9504,plain,
! [X0,X1] :
( ~ sQ293_spl
| X0 = app(app(nil,sK49_skl),X1)
| ~ segmentP(X0,app(sK49_skl,X1))
| ~ ssList(app(app(nil,sK49_skl),X1))
| ~ segmentP(sK49_skl,X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f2831,f2663]) ).
fof(f9505,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| X0 = app(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),X1)
| ~ segmentP(X0,app(sK49_skl,X1))
| ~ ssList(app(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),X1))
| ~ segmentP(sK54_skl,X0)
| ~ ssList(X1)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f1270,f2663]) ).
fof(f9511,definition,
! [X0] :
( sQ1098_spl
<=> ( X0 = app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl)
| ~ segmentP(X0,sK49_skl)
| ~ segmentP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1098_spl])],[split_symbol_definition]) ).
fof(f9514,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ452_spl
| ~ sQ11_spl
| ~ sQ154_spl
| sQ1098_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f9500,f555,f9511,f1676,f531,f4296,f1226,f440,f492]) ).
fof(f9519,definition,
! [X0,X1] :
( sQ1100_spl
<=> ( X0 = app(app(sK49_skl,nil),X1)
| ~ segmentP(X0,app(sK49_skl,X1))
| ~ ssList(app(app(sK49_skl,nil),X1))
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1100_spl])],[split_symbol_definition]) ).
fof(f9522,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| sQ1100_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9502,f552,f9519,f555,f5213]) ).
fof(f9523,definition,
! [X0,X1] :
( sQ1101_spl
<=> ( X0 = app(app(nil,nil),X1)
| ~ segmentP(X0,app(nil,X1))
| ~ ssList(app(app(nil,nil),X1))
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1101_spl])],[split_symbol_definition]) ).
fof(f9526,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ1101_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9503,f552,f9523,f1776,f5864]) ).
fof(f9527,definition,
! [X0,X1] :
( sQ1102_spl
<=> ( X0 = app(app(nil,sK49_skl),X1)
| ~ segmentP(X0,app(sK49_skl,X1))
| ~ ssList(app(app(nil,sK49_skl),X1))
| ~ segmentP(sK49_skl,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1102_spl])],[split_symbol_definition]) ).
fof(f9530,plain,
( ~ sQ293_spl
| ~ sQ15_spl
| sQ1102_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f9504,f555,f9527,f552,f2830]) ).
fof(f9531,definition,
! [X0,X1] :
( sQ1103_spl
<=> ( X0 = app(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),X1)
| ~ segmentP(X0,app(sK49_skl,X1))
| ~ ssList(app(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),X1))
| ~ segmentP(sK54_skl,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1103_spl])],[split_symbol_definition]) ).
fof(f9534,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| sQ1103_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f9505,f531,f9531,f1440,f1226,f440,f492]) ).
fof(f9552,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| segmentP(X1,X0)
| ~ segmentP(X1,sK49_skl)
| ~ ssList(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl))
| ~ ssList(X1)
| ~ segmentP(sK49_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(sK53_skl,sK49_skl))
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1270,f2664]) ).
fof(f9554,plain,
! [X0,X1,X2] :
( ~ sQ585_spl
| segmentP(X2,X0)
| ~ segmentP(X2,app(sK49_skl,X1))
| ~ ssList(app(app(sK49_skl,nil),X1))
| ~ ssList(X2)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5214,f2664]) ).
fof(f9555,plain,
! [X0,X1,X2] :
( ~ sQ675_spl
| ~ sQ167_spl
| segmentP(X2,X0)
| ~ segmentP(X2,app(nil,X1))
| ~ ssList(app(app(nil,nil),X1))
| ~ ssList(X2)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5907,f2664]) ).
fof(f9556,plain,
! [X0,X1,X2] :
( ~ sQ293_spl
| segmentP(X2,X0)
| ~ segmentP(X2,app(sK49_skl,X1))
| ~ ssList(app(app(nil,sK49_skl),X1))
| ~ ssList(X2)
| ~ segmentP(sK49_skl,X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f2831,f2664]) ).
fof(f9557,plain,
! [X0,X1,X2] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| segmentP(X2,X0)
| ~ segmentP(X2,app(sK49_skl,X1))
| ~ ssList(app(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),X1))
| ~ ssList(X2)
| ~ segmentP(sK54_skl,X0)
| ~ ssList(X1)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f1270,f2664]) ).
fof(f9564,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ452_spl
| ~ sQ11_spl
| ~ sQ154_spl
| sQ1041_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f9552,f555,f9094,f1676,f531,f4296,f1226,f440,f492]) ).
fof(f9569,definition,
! [X0,X1,X2] :
( sQ1105_spl
<=> ( segmentP(X2,X0)
| ~ segmentP(X2,app(sK49_skl,X1))
| ~ ssList(app(app(sK49_skl,nil),X1))
| ~ ssList(X2)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1105_spl])],[split_symbol_definition]) ).
fof(f9572,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| sQ1105_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9554,f552,f9569,f555,f5213]) ).
fof(f9573,definition,
! [X0,X1,X2] :
( sQ1106_spl
<=> ( segmentP(X2,X0)
| ~ segmentP(X2,app(nil,X1))
| ~ ssList(app(app(nil,nil),X1))
| ~ ssList(X2)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1106_spl])],[split_symbol_definition]) ).
fof(f9576,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ1106_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9555,f552,f9573,f1776,f5864]) ).
fof(f9577,definition,
! [X0,X1,X2] :
( sQ1107_spl
<=> ( segmentP(X2,X0)
| ~ segmentP(X2,app(sK49_skl,X1))
| ~ ssList(app(app(nil,sK49_skl),X1))
| ~ ssList(X2)
| ~ segmentP(sK49_skl,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1107_spl])],[split_symbol_definition]) ).
fof(f9580,plain,
( ~ sQ293_spl
| ~ sQ15_spl
| sQ1107_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f9556,f555,f9577,f552,f2830]) ).
fof(f9581,definition,
! [X0,X1,X2] :
( sQ1108_spl
<=> ( segmentP(X2,X0)
| ~ segmentP(X2,app(sK49_skl,X1))
| ~ ssList(app(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),X1))
| ~ ssList(X2)
| ~ segmentP(sK54_skl,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1108_spl])],[split_symbol_definition]) ).
fof(f9584,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| sQ1108_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f9557,f531,f9581,f1440,f1226,f440,f492]) ).
fof(f9594,plain,
! [X0,X1] :
( nil = cons(X1,X0)
| ~ ssList(cons(X1,X0))
| sK44_skl(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3459,f232]) ).
fof(f9595,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| nil = cons(sK51_skl,nil)
| ~ ssList(cons(sK51_skl,nil))
| sK44_skl(sK49_skl) = sK51_skl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1325,f9594]) ).
fof(f9596,definition,
( sQ1109_spl
<=> sK44_skl(sK49_skl) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ1109_spl])],[split_symbol_definition]) ).
fof(f9599,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sQ873_spl
| ~ sQ25_spl
| sQ1109_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9595,f552,f486,f9596,f634,f7671,f1226,f817]) ).
fof(f9600,plain,
( sQ597_spl
| nil = cons(sK51_skl,sK54_skl)
| ~ ssList(cons(sK51_skl,sK54_skl))
| ~ ssItem(sK51_skl)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f5338,f9594]) ).
fof(f9601,plain,
( sQ597_spl
| sQ510_spl
| ~ sQ812_spl
| ~ sQ3_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f9600,f531,f486,f7008,f4772,f5336]) ).
fof(f9635,plain,
( sQ829_spl
| ~ ssList(sK53_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f7200,f627]) ).
fof(f9639,plain,
( sQ829_spl
| ~ sQ43_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f9635,f555,f753,f7198]) ).
fof(f9678,definition,
( sQ1112_spl
<=> ssList(tl(sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1112_spl])],[split_symbol_definition]) ).
fof(f9680,plain,
( sQ1112_spl
| ~ ssList(tl(sK53_skl)) ),
inference(component_clause,[status(thm)],[f9678]) ).
fof(f9706,definition,
! [X0] :
( sQ1119_spl
<=> ( rearsegP(X0,sK49_skl)
| ~ rearsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1119_spl])],[split_symbol_definition]) ).
fof(f9707,plain,
! [X0] :
( ~ sQ1119_spl
| rearsegP(X0,sK49_skl)
| ~ rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f9706]) ).
fof(f9777,plain,
! [X0] :
( ~ sQ1119_spl
| rearsegP(X0,sK49_skl)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f9707,f309]) ).
fof(f9781,plain,
( sQ1112_spl
| nil = sK53_skl
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f9680,f241]) ).
fof(f9782,plain,
( sQ1112_spl
| sQ159_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f9781,f753,f1717,f9678]) ).
fof(f9787,plain,
( sQ157_spl
| ~ sQ264_spl
| ~ sQ293_spl ),
inference(split_clause,[status(thm)],[f2590,f2830,f2566,f1690]) ).
fof(f9790,plain,
( sQ739_spl
| ~ sQ159_spl
| ~ frontsegP(app(nil,sK49_skl),sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f1718,f6285]) ).
fof(f9801,plain,
( sQ739_spl
| ~ sQ159_spl
| ~ sQ293_spl
| ~ frontsegP(sK49_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f2831,f9790]) ).
fof(f9802,plain,
( sQ739_spl
| ~ sQ159_spl
| ~ sQ293_spl
| ~ sQ354_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9801,f3376]) ).
fof(f9803,plain,
( sQ739_spl
| ~ sQ159_spl
| ~ sQ293_spl
| ~ sQ354_spl ),
inference(contradiction_clause,[status(thm)],[f9802]) ).
fof(f9813,plain,
( ~ sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ159_spl
| sK49_skl = app(app(nil,sK49_skl),sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1718,f2214]) ).
fof(f9814,plain,
( ~ sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ159_spl
| ~ sQ293_spl
| sK49_skl = app(sK49_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f2831,f9813]) ).
fof(f9815,plain,
( ~ sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ159_spl
| ~ sQ293_spl
| sQ402_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9814,f3821]) ).
fof(f9816,plain,
( ~ sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ159_spl
| ~ sQ293_spl
| sQ402_spl ),
inference(contradiction_clause,[status(thm)],[f9815]) ).
fof(f9833,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ78_spl
| ~ sQ51_spl
| tl(sK49_skl) = app(tl(sK49_skl),sK54_skl)
| nil = sK49_skl
| ~ ssList(sK54_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f3028,f393]) ).
fof(f9881,definition,
( sQ1140_spl
<=> tl(sK49_skl) = app(tl(sK49_skl),sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ1140_spl])],[split_symbol_definition]) ).
fof(f9882,plain,
( ~ sQ1140_spl
| tl(sK49_skl) = app(tl(sK49_skl),sK54_skl) ),
inference(component_clause,[status(thm)],[f9881]) ).
fof(f9884,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ78_spl
| ~ sQ51_spl
| sQ1140_spl
| sQ2_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f9833,f555,f531,f447,f9881,f817,f995,f1226,f440,f492]) ).
fof(f9922,plain,
( ~ sQ1140_spl
| ~ sQ167_spl
| nil = app(tl(sK49_skl),sK54_skl) ),
inference(forward_demodulation,[status(thm)],[f1777,f9882]) ).
fof(f9923,plain,
( ~ sQ1140_spl
| ~ sQ167_spl
| nil = app(nil,sK54_skl) ),
inference(forward_demodulation,[status(thm)],[f1777,f9922]) ).
fof(f9924,plain,
( ~ sQ1140_spl
| ~ sQ167_spl
| sQ621_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9923,f5508]) ).
fof(f9925,plain,
( ~ sQ1140_spl
| ~ sQ167_spl
| sQ621_spl ),
inference(contradiction_clause,[status(thm)],[f9924]) ).
fof(f10088,plain,
! [X0,X1] :
( sQ414_spl
| ~ segmentP(X1,sK49_skl)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ segmentP(sK54_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f3922,f2633]) ).
fof(f10090,definition,
! [X0,X1] :
( sQ1148_spl
<=> ( ~ segmentP(X1,sK49_skl)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ segmentP(sK54_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1148_spl])],[split_symbol_definition]) ).
fof(f10093,plain,
( sQ414_spl
| ~ sQ16_spl
| sQ1148_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f10088,f531,f10090,f555,f3920]) ).
fof(f10095,plain,
! [X0,X1] :
( ~ sQ31_spl
| ~ sQ5_spl
| ~ segmentP(X1,app(sK49_skl,X0))
| ~ ssList(app(sK49_skl,X0))
| sK54_skl = X1
| ~ segmentP(sK54_skl,X1)
| ~ ssList(X1)
| ~ ssList(sK54_skl)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,X0)) ),
inference(resolution,[status(thm)],[f767,f2657]) ).
fof(f10096,plain,
! [X0,X1] :
( ~ sQ31_spl
| ~ sQ5_spl
| ~ segmentP(sK54_skl,X1)
| ~ ssList(sK54_skl)
| X1 = app(sK49_skl,X0)
| ~ segmentP(X1,app(sK49_skl,X0))
| ~ ssList(app(sK49_skl,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,X0)) ),
inference(resolution,[status(thm)],[f767,f2657]) ).
fof(f10097,plain,
! [X0,X1,X2] :
( ~ sQ31_spl
| ~ sQ5_spl
| ~ segmentP(X2,app(sK49_skl,X0))
| ~ ssList(app(sK49_skl,X0))
| segmentP(X1,sK54_skl)
| ~ segmentP(X1,X2)
| ~ ssList(sK54_skl)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,X0)) ),
inference(resolution,[status(thm)],[f767,f2633]) ).
fof(f10098,plain,
! [X0,X1,X2] :
( ~ sQ31_spl
| ~ sQ5_spl
| ~ segmentP(sK54_skl,X2)
| ~ ssList(sK54_skl)
| segmentP(X1,X2)
| ~ segmentP(X1,app(sK49_skl,X0))
| ~ ssList(X2)
| ~ ssList(app(sK49_skl,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,X0)) ),
inference(resolution,[status(thm)],[f767,f2633]) ).
fof(f10101,plain,
( ~ sQ585_spl
| ~ sQ31_spl
| ~ sQ5_spl
| ~ ssList(nil)
| segmentP(sK49_skl,sK54_skl)
| ~ ssList(app(sK49_skl,nil)) ),
inference(paramodulation,[status(thm)],[f5214,f767]) ).
fof(f10102,definition,
! [X0,X1] :
( sQ1149_spl
<=> ( ~ segmentP(X1,app(sK49_skl,X0))
| ~ ssList(app(sK49_skl,X0))
| sK54_skl = X1
| ~ segmentP(sK54_skl,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1149_spl])],[split_symbol_definition]) ).
fof(f10105,plain,
( ~ sQ31_spl
| ~ sQ5_spl
| ~ sQ11_spl
| sQ1149_spl ),
inference(split_clause,[status(thm)],[f10095,f10102,f531,f492,f664]) ).
fof(f10106,definition,
! [X0,X1] :
( sQ1150_spl
<=> ( ~ segmentP(sK54_skl,X1)
| X1 = app(sK49_skl,X0)
| ~ segmentP(X1,app(sK49_skl,X0))
| ~ ssList(app(sK49_skl,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1150_spl])],[split_symbol_definition]) ).
fof(f10109,plain,
( ~ sQ31_spl
| ~ sQ5_spl
| ~ sQ11_spl
| sQ1150_spl ),
inference(split_clause,[status(thm)],[f10096,f10106,f531,f492,f664]) ).
fof(f10110,definition,
! [X0,X1,X2] :
( sQ1151_spl
<=> ( ~ segmentP(X2,app(sK49_skl,X0))
| ~ ssList(app(sK49_skl,X0))
| segmentP(X1,sK54_skl)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1151_spl])],[split_symbol_definition]) ).
fof(f10113,plain,
( ~ sQ31_spl
| ~ sQ5_spl
| ~ sQ11_spl
| sQ1151_spl ),
inference(split_clause,[status(thm)],[f10097,f10110,f531,f492,f664]) ).
fof(f10114,definition,
! [X0,X1,X2] :
( sQ1152_spl
<=> ( ~ segmentP(sK54_skl,X2)
| segmentP(X1,X2)
| ~ segmentP(X1,app(sK49_skl,X0))
| ~ ssList(X2)
| ~ ssList(app(sK49_skl,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1152_spl])],[split_symbol_definition]) ).
fof(f10117,plain,
( ~ sQ31_spl
| ~ sQ5_spl
| ~ sQ11_spl
| sQ1152_spl ),
inference(split_clause,[status(thm)],[f10098,f10114,f531,f492,f664]) ).
fof(f10120,definition,
( sQ1153_spl
<=> ssList(app(sK49_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ1153_spl])],[split_symbol_definition]) ).
fof(f10122,plain,
( sQ1153_spl
| ~ ssList(app(sK49_skl,nil)) ),
inference(component_clause,[status(thm)],[f10120]) ).
fof(f10123,plain,
( ~ sQ585_spl
| ~ sQ31_spl
| ~ sQ5_spl
| ~ sQ15_spl
| sQ406_spl
| ~ sQ1153_spl ),
inference(split_clause,[status(thm)],[f10101,f10120,f3869,f552,f492,f664,f5213]) ).
fof(f10128,plain,
( sQ1153_spl
| ~ sQ585_spl
| ~ ssList(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f5214,f10122]) ).
fof(f10129,plain,
( sQ1153_spl
| ~ sQ585_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10128,f422]) ).
fof(f10130,plain,
( sQ1153_spl
| ~ sQ585_spl ),
inference(contradiction_clause,[status(thm)],[f10129]) ).
fof(f10136,plain,
! [X0] :
( ~ sQ406_spl
| ~ segmentP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| sK54_skl = X0
| ~ segmentP(sK54_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f3870,f2657]) ).
fof(f10137,plain,
! [X0] :
( ~ sQ406_spl
| ~ segmentP(sK54_skl,X0)
| ~ ssList(sK54_skl)
| X0 = sK49_skl
| ~ segmentP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3870,f2657]) ).
fof(f10138,plain,
! [X0,X1] :
( ~ sQ406_spl
| ~ segmentP(X1,sK49_skl)
| ~ ssList(sK49_skl)
| segmentP(X0,sK54_skl)
| ~ segmentP(X0,X1)
| ~ ssList(sK54_skl)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3870,f2633]) ).
fof(f10139,plain,
! [X0,X1] :
( ~ sQ406_spl
| ~ segmentP(sK54_skl,X1)
| ~ ssList(sK54_skl)
| segmentP(X0,X1)
| ~ segmentP(X0,sK49_skl)
| ~ ssList(X1)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3870,f2633]) ).
fof(f10142,definition,
! [X0] :
( sQ1154_spl
<=> ( ~ segmentP(X0,sK49_skl)
| sK54_skl = X0
| ~ segmentP(sK54_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1154_spl])],[split_symbol_definition]) ).
fof(f10145,plain,
( ~ sQ406_spl
| ~ sQ16_spl
| sQ1154_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f10136,f531,f10142,f555,f3869]) ).
fof(f10146,definition,
! [X0] :
( sQ1155_spl
<=> ( ~ segmentP(sK54_skl,X0)
| X0 = sK49_skl
| ~ segmentP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1155_spl])],[split_symbol_definition]) ).
fof(f10149,plain,
( ~ sQ406_spl
| ~ sQ11_spl
| ~ sQ16_spl
| sQ1155_spl ),
inference(split_clause,[status(thm)],[f10137,f10146,f555,f531,f3869]) ).
fof(f10150,definition,
! [X0,X1] :
( sQ1156_spl
<=> ( ~ segmentP(X1,sK49_skl)
| segmentP(X0,sK54_skl)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1156_spl])],[split_symbol_definition]) ).
fof(f10153,plain,
( ~ sQ406_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sQ1156_spl ),
inference(split_clause,[status(thm)],[f10138,f10150,f531,f555,f3869]) ).
fof(f10154,definition,
! [X0,X1] :
( sQ1157_spl
<=> ( ~ segmentP(sK54_skl,X1)
| segmentP(X0,X1)
| ~ segmentP(X0,sK49_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1157_spl])],[split_symbol_definition]) ).
fof(f10157,plain,
( ~ sQ406_spl
| ~ sQ11_spl
| ~ sQ16_spl
| sQ1157_spl ),
inference(split_clause,[status(thm)],[f10139,f10154,f555,f531,f3869]) ).
fof(f10160,plain,
! [X0,X1] :
( sK5_skl(X0,app(X0,X1)) = X1
| ~ ssList(sK5_skl(X0,app(X0,X1)))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4018,f3835]) ).
fof(f10162,plain,
( ~ sQ585_spl
| sK5_skl(sK49_skl,app(sK49_skl,nil)) = nil
| ~ ssList(sK5_skl(sK49_skl,sK49_skl))
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f5214,f10160]) ).
fof(f10163,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sK5_skl(nil,app(nil,nil)) = nil
| ~ ssList(sK5_skl(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5907,f10160]) ).
fof(f10164,plain,
( ~ sQ293_spl
| sK5_skl(nil,app(nil,sK49_skl)) = sK49_skl
| ~ ssList(sK5_skl(nil,sK49_skl))
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2831,f10160]) ).
fof(f10168,definition,
( sQ1158_spl
<=> ssList(sK5_skl(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1158_spl])],[split_symbol_definition]) ).
fof(f10170,plain,
( sQ1158_spl
| ~ ssList(sK5_skl(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f10168]) ).
fof(f10171,definition,
( sQ1159_spl
<=> sK5_skl(sK49_skl,app(sK49_skl,nil)) = nil ),
introduced(definition,[new_symbols(definition,[sQ1159_spl])],[split_symbol_definition]) ).
fof(f10174,plain,
( ~ sQ585_spl
| sQ1159_spl
| ~ sQ1158_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f10162,f555,f552,f10168,f10171,f5213]) ).
fof(f10175,definition,
( sQ1160_spl
<=> ssList(sK5_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ1160_spl])],[split_symbol_definition]) ).
fof(f10177,plain,
( sQ1160_spl
| ~ ssList(sK5_skl(nil,nil)) ),
inference(component_clause,[status(thm)],[f10175]) ).
fof(f10178,definition,
( sQ1161_spl
<=> sK5_skl(nil,app(nil,nil)) = nil ),
introduced(definition,[new_symbols(definition,[sQ1161_spl])],[split_symbol_definition]) ).
fof(f10179,plain,
( ~ sQ1161_spl
| sK5_skl(nil,app(nil,nil)) = nil ),
inference(component_clause,[status(thm)],[f10178]) ).
fof(f10181,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ1161_spl
| ~ sQ1160_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f10163,f552,f10175,f10178,f1776,f5864]) ).
fof(f10182,definition,
( sQ1162_spl
<=> ssList(sK5_skl(nil,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1162_spl])],[split_symbol_definition]) ).
fof(f10184,plain,
( sQ1162_spl
| ~ ssList(sK5_skl(nil,sK49_skl)) ),
inference(component_clause,[status(thm)],[f10182]) ).
fof(f10185,definition,
( sQ1163_spl
<=> sK5_skl(nil,app(nil,sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ1163_spl])],[split_symbol_definition]) ).
fof(f10188,plain,
( ~ sQ293_spl
| sQ1163_spl
| ~ sQ1162_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f10164,f552,f555,f10182,f10185,f2830]) ).
fof(f10195,plain,
( ~ sQ1161_spl
| ~ sQ675_spl
| ~ sQ167_spl
| sK5_skl(nil,nil) = nil ),
inference(forward_demodulation,[status(thm)],[f5907,f10179]) ).
fof(f10239,plain,
( sQ263_spl
| ~ sQ1119_spl
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f9777,f2565]) ).
fof(f10254,plain,
( sQ263_spl
| ~ sQ1119_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f10239,f531,f9706,f2563]) ).
fof(f10522,plain,
! [X0] :
( ~ sQ423_spl
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = sK5_skl(X0,nil)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4029,f122]) ).
fof(f10523,definition,
! [X0] :
( sQ1205_spl
<=> ( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| nil = sK5_skl(X0,nil)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1205_spl])],[split_symbol_definition]) ).
fof(f10526,plain,
( ~ sQ423_spl
| ~ sQ15_spl
| sQ1205_spl ),
inference(split_clause,[status(thm)],[f10522,f10523,f552,f4021]) ).
fof(f10532,definition,
( sQ1206_spl
<=> ssItem(sK4_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1206_spl])],[split_symbol_definition]) ).
fof(f10534,plain,
( sQ1206_spl
| ~ ssItem(sK4_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f10532]) ).
fof(f10536,plain,
( sQ1206_spl
| ~ sQ200_spl
| ~ ssItem(sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f2010,f10534]) ).
fof(f10537,plain,
( sQ1206_spl
| ~ sQ200_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10536,f426]) ).
fof(f10538,plain,
( sQ1206_spl
| ~ sQ200_spl ),
inference(contradiction_clause,[status(thm)],[f10537]) ).
fof(f10540,plain,
( sQ1160_spl
| ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f10177,f122]) ).
fof(f10541,plain,
( sQ1160_spl
| ~ sQ422_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f10540,f552,f3987,f10175]) ).
fof(f10542,plain,
( sQ1158_spl
| ~ frontsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f10170,f122]) ).
fof(f10543,plain,
( sQ1158_spl
| ~ sQ354_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f10542,f555,f3375,f10168]) ).
fof(f10544,plain,
( sQ1162_spl
| ~ frontsegP(sK49_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f10184,f122]) ).
fof(f10545,plain,
( sQ1162_spl
| ~ sQ404_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f10544,f555,f552,f3838,f10182]) ).
fof(f10550,plain,
( ~ sQ1161_spl
| ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ423_spl
| nil = sK5_skl(nil,nil)
| ~ ssList(nil)
| ~ frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f10195,f4029]) ).
fof(f10552,plain,
( ~ sQ1161_spl
| ~ sQ675_spl
| ~ sQ167_spl
| app(nil,nil) = nil
| ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f10195,f123]) ).
fof(f10553,definition,
( sQ1207_spl
<=> nil = sK5_skl(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ1207_spl])],[split_symbol_definition]) ).
fof(f10556,plain,
( ~ sQ1161_spl
| ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ423_spl
| sQ1207_spl
| ~ sQ422_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f10550,f552,f3987,f10553,f4021,f1776,f5864,f10178]) ).
fof(f10558,plain,
( ~ sQ1161_spl
| ~ sQ675_spl
| ~ sQ167_spl
| sQ784_spl
| ~ sQ422_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f10552,f552,f3987,f6734,f1776,f5864,f10178]) ).
fof(f10712,plain,
! [X0] :
( ~ sQ683_spl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| app(sK53_skl,sK49_skl) = X0
| ~ frontsegP(app(sK53_skl,sK49_skl),X0)
| ~ ssList(X0)
| ~ ssList(app(sK53_skl,sK49_skl)) ),
inference(resolution,[status(thm)],[f5913,f2255]) ).
fof(f10713,plain,
! [X0] :
( ~ sQ683_spl
| ~ frontsegP(app(sK53_skl,sK49_skl),X0)
| ~ ssList(app(sK53_skl,sK49_skl))
| X0 = sK49_skl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5913,f2255]) ).
fof(f10714,plain,
! [X0,X1] :
( ~ sQ683_spl
| ~ frontsegP(X1,sK49_skl)
| ~ ssList(sK49_skl)
| frontsegP(X0,app(sK53_skl,sK49_skl))
| ~ frontsegP(X0,X1)
| ~ ssList(app(sK53_skl,sK49_skl))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5913,f2240]) ).
fof(f10715,plain,
! [X0,X1] :
( ~ sQ683_spl
| ~ frontsegP(app(sK53_skl,sK49_skl),X1)
| ~ ssList(app(sK53_skl,sK49_skl))
| frontsegP(X0,X1)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X1)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f5913,f2240]) ).
fof(f10720,definition,
! [X0] :
( sQ1210_spl
<=> ( ~ frontsegP(X0,sK49_skl)
| app(sK53_skl,sK49_skl) = X0
| ~ frontsegP(app(sK53_skl,sK49_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1210_spl])],[split_symbol_definition]) ).
fof(f10723,plain,
( ~ sQ683_spl
| ~ sQ16_spl
| sQ1210_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f10712,f1676,f10720,f555,f5912]) ).
fof(f10724,definition,
! [X0] :
( sQ1211_spl
<=> ( ~ frontsegP(app(sK53_skl,sK49_skl),X0)
| X0 = sK49_skl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1211_spl])],[split_symbol_definition]) ).
fof(f10727,plain,
( ~ sQ683_spl
| ~ sQ154_spl
| ~ sQ16_spl
| sQ1211_spl ),
inference(split_clause,[status(thm)],[f10713,f10724,f555,f1676,f5912]) ).
fof(f10728,definition,
! [X0,X1] :
( sQ1212_spl
<=> ( ~ frontsegP(X1,sK49_skl)
| frontsegP(X0,app(sK53_skl,sK49_skl))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1212_spl])],[split_symbol_definition]) ).
fof(f10731,plain,
( ~ sQ683_spl
| ~ sQ16_spl
| ~ sQ154_spl
| sQ1212_spl ),
inference(split_clause,[status(thm)],[f10714,f10728,f1676,f555,f5912]) ).
fof(f10732,definition,
! [X0,X1] :
( sQ1213_spl
<=> ( ~ frontsegP(app(sK53_skl,sK49_skl),X1)
| frontsegP(X0,X1)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1213_spl])],[split_symbol_definition]) ).
fof(f10735,plain,
( ~ sQ683_spl
| ~ sQ154_spl
| ~ sQ16_spl
| sQ1213_spl ),
inference(split_clause,[status(thm)],[f10715,f10732,f555,f1676,f5912]) ).
fof(f10738,plain,
( ~ sQ833_spl
| ~ sQ243_spl
| frontsegP(sK53_skl,sK49_skl)
| ~ ssList(tl(sK53_skl)) ),
inference(paramodulation,[status(thm)],[f7230,f2360]) ).
fof(f10789,plain,
( ~ sQ833_spl
| ~ sQ243_spl
| sQ816_spl
| ~ sQ1112_spl ),
inference(split_clause,[status(thm)],[f10738,f9678,f7096,f2356,f7229]) ).
fof(f10863,definition,
( sQ1233_spl
<=> hd(sK53_skl) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ1233_spl])],[split_symbol_definition]) ).
fof(f10864,plain,
( ~ sQ1233_spl
| hd(sK53_skl) = sK51_skl ),
inference(component_clause,[status(thm)],[f10863]) ).
fof(f10994,plain,
( ~ sQ1233_spl
| sQ825_spl
| ~ sQ152_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10864,f7233]) ).
fof(f10995,plain,
( ~ sQ1233_spl
| sQ825_spl
| ~ sQ152_spl ),
inference(contradiction_clause,[status(thm)],[f10994]) ).
fof(f11000,plain,
! [X0,X1,X2] :
( ~ sQ228_spl
| ~ frontsegP(X2,X0)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ frontsegP(app(app(sK53_skl,sK49_skl),sK49_skl),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| frontsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2265,f2240]) ).
fof(f11007,definition,
! [X0,X1,X2] :
( sQ1265_spl
<=> ( ~ frontsegP(X2,X0)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| ~ frontsegP(app(app(sK53_skl,sK49_skl),sK49_skl),X1)
| ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1265_spl])],[split_symbol_definition]) ).
fof(f11010,plain,
( ~ sQ228_spl
| ~ sQ124_spl
| sQ1265_spl ),
inference(split_clause,[status(thm)],[f11000,f11007,f1440,f2264]) ).
fof(f11149,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sK49_skl = app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl)
| ~ segmentP(sK49_skl,sK49_skl)
| ~ ssList(sK54_skl)
| ~ ssList(app(sK53_skl,sK49_skl))
| ~ ssList(sK49_skl)
| ~ ssList(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl)) ),
inference(paramodulation,[status(thm)],[f1270,f4294]) ).
fof(f11150,plain,
! [X0] :
( ~ sQ585_spl
| nil = app(app(sK49_skl,nil),X0)
| ~ segmentP(nil,app(sK49_skl,X0))
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ ssList(nil)
| ~ ssList(app(app(sK49_skl,nil),X0)) ),
inference(paramodulation,[status(thm)],[f5214,f4294]) ).
fof(f11151,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| nil = app(app(nil,nil),X0)
| ~ segmentP(nil,app(nil,X0))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(app(app(nil,nil),X0)) ),
inference(paramodulation,[status(thm)],[f5907,f4294]) ).
fof(f11152,plain,
! [X0] :
( ~ sQ293_spl
| sK49_skl = app(app(nil,sK49_skl),X0)
| ~ segmentP(sK49_skl,app(sK49_skl,X0))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK49_skl)
| ~ ssList(app(app(nil,sK49_skl),X0)) ),
inference(paramodulation,[status(thm)],[f2831,f4294]) ).
fof(f11153,plain,
! [X0] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sK54_skl = app(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),X0)
| ~ segmentP(sK54_skl,app(sK49_skl,X0))
| ~ ssList(X0)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ ssList(sK54_skl)
| ~ ssList(app(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),X0)) ),
inference(paramodulation,[status(thm)],[f1270,f4294]) ).
fof(f11158,definition,
( sQ1269_spl
<=> sK49_skl = app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ1269_spl])],[split_symbol_definition]) ).
fof(f11161,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sQ1269_spl
| ~ sQ273_spl
| ~ sQ11_spl
| ~ sQ154_spl
| ~ sQ16_spl
| ~ sQ452_spl ),
inference(split_clause,[status(thm)],[f11149,f4296,f555,f1676,f531,f2649,f11158,f1226,f440,f492]) ).
fof(f11162,definition,
! [X0] :
( sQ1270_spl
<=> ( nil = app(app(sK49_skl,nil),X0)
| ~ segmentP(nil,app(sK49_skl,X0))
| ~ ssList(X0)
| ~ ssList(app(app(sK49_skl,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1270_spl])],[split_symbol_definition]) ).
fof(f11165,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ1270_spl ),
inference(split_clause,[status(thm)],[f11150,f11162,f552,f555,f5213]) ).
fof(f11166,definition,
! [X0] :
( sQ1271_spl
<=> ( nil = app(app(nil,nil),X0)
| ~ segmentP(nil,app(nil,X0))
| ~ ssList(X0)
| ~ ssList(app(app(nil,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1271_spl])],[split_symbol_definition]) ).
fof(f11169,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ15_spl
| sQ1271_spl ),
inference(split_clause,[status(thm)],[f11151,f11166,f552,f1776,f5864]) ).
fof(f11170,definition,
! [X0] :
( sQ1272_spl
<=> ( sK49_skl = app(app(nil,sK49_skl),X0)
| ~ segmentP(sK49_skl,app(sK49_skl,X0))
| ~ ssList(X0)
| ~ ssList(app(app(nil,sK49_skl),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1272_spl])],[split_symbol_definition]) ).
fof(f11173,plain,
( ~ sQ293_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ1272_spl ),
inference(split_clause,[status(thm)],[f11152,f11170,f555,f552,f2830]) ).
fof(f11174,definition,
! [X0] :
( sQ1273_spl
<=> ( sK54_skl = app(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),X0)
| ~ segmentP(sK54_skl,app(sK49_skl,X0))
| ~ ssList(X0)
| ~ ssList(app(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1273_spl])],[split_symbol_definition]) ).
fof(f11177,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| ~ sQ11_spl
| sQ1273_spl ),
inference(split_clause,[status(thm)],[f11153,f11174,f531,f1440,f1226,f440,f492]) ).
fof(f11193,plain,
! [X0,X1] :
( ~ sQ585_spl
| segmentP(X1,nil)
| ~ segmentP(X1,app(sK49_skl,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ ssList(nil)
| ~ ssList(app(app(sK49_skl,nil),X0)) ),
inference(paramodulation,[status(thm)],[f5214,f4295]) ).
fof(f11194,plain,
! [X0,X1] :
( ~ sQ675_spl
| ~ sQ167_spl
| segmentP(X1,nil)
| ~ segmentP(X1,app(nil,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(app(app(nil,nil),X0)) ),
inference(paramodulation,[status(thm)],[f5907,f4295]) ).
fof(f11195,plain,
! [X0,X1] :
( ~ sQ293_spl
| segmentP(X1,sK49_skl)
| ~ segmentP(X1,app(sK49_skl,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK49_skl)
| ~ ssList(app(app(nil,sK49_skl),X0)) ),
inference(paramodulation,[status(thm)],[f2831,f4295]) ).
fof(f11196,plain,
! [X0,X1] :
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| segmentP(X1,sK54_skl)
| ~ segmentP(X1,app(sK49_skl,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl))
| ~ ssList(sK54_skl)
| ~ ssList(app(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),X0)) ),
inference(paramodulation,[status(thm)],[f1270,f4295]) ).
fof(f11204,definition,
! [X0,X1] :
( sQ1274_spl
<=> ( segmentP(X1,nil)
| ~ segmentP(X1,app(sK49_skl,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(sK49_skl,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1274_spl])],[split_symbol_definition]) ).
fof(f11207,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ1274_spl ),
inference(split_clause,[status(thm)],[f11193,f11204,f552,f555,f5213]) ).
fof(f11208,definition,
! [X0,X1] :
( sQ1275_spl
<=> ( segmentP(X1,nil)
| ~ segmentP(X1,app(nil,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(nil,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1275_spl])],[split_symbol_definition]) ).
fof(f11211,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ15_spl
| sQ1275_spl ),
inference(split_clause,[status(thm)],[f11194,f11208,f552,f1776,f5864]) ).
fof(f11212,definition,
! [X0,X1] :
( sQ1276_spl
<=> ( segmentP(X1,sK49_skl)
| ~ segmentP(X1,app(sK49_skl,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(nil,sK49_skl),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1276_spl])],[split_symbol_definition]) ).
fof(f11215,plain,
( ~ sQ293_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ1276_spl ),
inference(split_clause,[status(thm)],[f11195,f11212,f555,f552,f2830]) ).
fof(f11216,definition,
! [X0,X1] :
( sQ1277_spl
<=> ( segmentP(X1,sK54_skl)
| ~ segmentP(X1,app(sK49_skl,X0))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(app(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ1277_spl])],[split_symbol_definition]) ).
fof(f11219,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| ~ sQ11_spl
| sQ1277_spl ),
inference(split_clause,[status(thm)],[f11196,f11216,f531,f1440,f1226,f440,f492]) ).
fof(f11256,plain,
( ~ sQ864_spl
| sK51_skl = hd(sK53_skl)
| nil = sK53_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f7568,f391]) ).
fof(f11258,plain,
( ~ sQ864_spl
| cons(sK51_skl,tl(app(sK53_skl,sK49_skl))) = app(sK53_skl,sK49_skl)
| nil = app(sK53_skl,sK49_skl)
| ~ ssList(app(sK53_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f7568,f374]) ).
fof(f11259,plain,
( ~ sQ864_spl
| sQ1233_spl
| sQ159_spl
| ~ sQ16_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f11256,f753,f555,f1717,f10863,f7567]) ).
fof(f11261,definition,
( sQ1279_spl
<=> cons(sK51_skl,tl(app(sK53_skl,sK49_skl))) = app(sK53_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ1279_spl])],[split_symbol_definition]) ).
fof(f11264,plain,
( ~ sQ864_spl
| sQ1279_spl
| sQ158_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f11258,f1676,f1694,f11261,f7567]) ).
fof(f11265,plain,
$false,
inference(sat_refutation,[status(thm)],[f450,f495,f502,f504,f507,f534,f536,f562,f564,f566,f589,f597,f603,f612,f619,f659,f663,f667,f668,f671,f679,f688,f692,f696,f700,f704,f727,f740,f744,f751,f756,f758,f763,f766,f786,f793,f820,f827,f842,f847,f855,f880,f897,f908,f938,f942,f969,f973,f998,f1048,f1052,f1129,f1136,f1157,f1161,f1172,f1213,f1217,f1224,f1229,f1272,f1273,f1274,f1275,f1276,f1277,f1278,f1282,f1287,f1291,f1295,f1299,f1303,f1304,f1309,f1338,f1380,f1446,f1451,f1453,f1457,f1490,f1504,f1508,f1565,f1570,f1607,f1624,f1629,f1660,f1699,f1742,f1762,f1764,f1771,f1779,f1849,f1866,f2015,f2018,f2028,f2031,f2049,f2068,f2239,f2244,f2254,f2267,f2311,f2315,f2325,f2329,f2349,f2355,f2359,f2364,f2389,f2418,f2535,f2539,f2545,f2550,f2554,f2575,f2588,f2613,f2628,f2632,f2637,f2641,f2656,f2660,f2721,f2741,f2770,f2794,f2800,f2817,f2820,f2824,f2837,f2867,f2868,f2872,f2876,f2880,f2884,f2889,f2894,f2900,f2904,f2934,f3086,f3123,f3183,f3196,f3200,f3360,f3371,f3502,f3528,f3677,f3689,f3744,f3757,f3761,f3798,f3804,f3813,f3822,f3826,f3834,f3841,f3877,f3914,f3923,f3927,f3932,f3983,f4024,f4028,f4042,f4094,f4104,f4121,f4122,f4123,f4125,f4144,f4148,f4152,f4153,f4195,f4199,f4207,f4211,f4219,f4223,f4256,f4266,f4273,f4277,f4279,f4287,f4303,f4307,f4312,f4330,f4349,f4355,f4384,f4739,f4744,f4771,f4865,f5176,f5308,f5495,f5500,f5857,f5862,f5863,f5867,f5868,f5874,f5879,f5886,f5891,f5896,f5898,f5902,f5915,f5917,f5921,f6223,f6289,f6293,f6297,f6301,f6306,f6317,f6331,f6365,f6371,f6375,f6415,f6419,f6423,f6427,f6428,f6434,f6439,f6443,f6447,f6454,f6459,f6464,f6466,f6470,f6474,f6484,f6512,f6517,f6528,f6534,f6539,f6577,f6619,f6624,f6628,f6632,f6638,f6650,f6705,f6749,f6753,f6772,f6783,f6791,f6955,f6966,f6975,f6984,f7011,f7013,f7019,f7026,f7031,f7095,f7102,f7106,f7201,f7222,f7232,f7495,f7499,f7516,f7518,f7520,f7523,f7527,f7534,f7542,f7547,f7551,f7557,f7570,f7575,f7590,f7596,f7599,f7616,f7620,f7624,f7628,f7674,f7733,f7799,f8028,f8029,f8033,f8037,f8079,f8086,f8091,f8096,f8103,f8115,f8120,f8127,f8184,f8188,f8192,f8200,f8204,f8208,f8223,f8228,f8232,f8237,f8241,f8245,f8250,f8254,f8261,f8265,f8269,f8273,f8277,f8281,f8289,f8538,f8556,f8560,f8565,f8606,f8619,f8623,f8641,f8645,f8649,f8690,f8695,f8700,f8704,f8709,f8713,f8717,f8725,f8732,f8738,f8743,f8747,f8755,f8799,f8857,f8861,f8865,f8869,f8876,f8880,f8921,f9081,f9085,f9101,f9105,f9115,f9119,f9133,f9137,f9141,f9203,f9275,f9469,f9477,f9488,f9514,f9522,f9526,f9530,f9534,f9564,f9572,f9576,f9580,f9584,f9599,f9601,f9639,f9782,f9787,f9803,f9816,f9884,f9925,f10093,f10105,f10109,f10113,f10117,f10123,f10130,f10145,f10149,f10153,f10157,f10174,f10181,f10188,f10254,f10526,f10538,f10541,f10543,f10545,f10556,f10558,f10723,f10727,f10731,f10735,f10789,f10995,f11010,f11161,f11165,f11169,f11173,f11177,f11207,f11211,f11215,f11219,f11259,f11264]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC169+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.45 % Computer : n026.cluster.edu
% 0.18/0.45 % Model : x86_64 x86_64
% 0.18/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.45 % Memory : 8046.5625MB
% 0.18/0.45 % OS : Linux 6.8.0-71-generic
% 0.18/0.45 % CPULimit : 300
% 0.18/0.45 % WCLimit : 300
% 0.18/0.45 % DateTime : Mon Sep 21 08:03:53 UTC 2026
% 0.18/0.45 % CPUTime :
% 0.18/0.48 % Drodi V4.1.1
% 85.07/11.28 % Refutation found
% 85.07/11.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 85.07/11.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 21.52/11.37 % Elapsed time: 10.902909 seconds
% 21.52/11.37 % CPU time: 85.787793 seconds
% 21.52/11.37 % Total memory used: 341.094 MB
% 21.52/11.37 % Net memory used: 318.305 MB
%------------------------------------------------------------------------------