%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC177+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:40:16 PM UTC 2026
% Result : Theorem 96.76s 22.71s
% Output : CNFRefutation 94.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 518
% Syntax : Number of formulae : 1972 ( 21 unt; 454 def)
% Number of atoms : 9397 ( 931 equ)
% Maximal formula atoms : 19 ( 4 avg)
% Number of connectives : 13860 (6435 ~;6524 |; 225 &)
% ( 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 : 2031 (1954 !; 77 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [U] :
( ssList(U)
=> ( ? [V] :
( ? [W] :
( cons(W,V) = U
& ssItem(W) )
& ssList(V) )
| nil = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> hd(cons(V,U)) = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssList(tl(U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> tl(cons(V,U)) = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( frontsegP(V,U)
& frontsegP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,U) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [U] :
( ssList(U)
=> ( frontsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( rearsegP(V,U)
& rearsegP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,U) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [U] :
( ssList(U)
=> ( rearsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( segmentP(V,U)
& segmentP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [U] :
( ssItem(U)
=> cyclefreeP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f61,axiom,
! [U] :
( ssItem(U)
=> totalorderP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f63,axiom,
! [U] :
( ssItem(U)
=> strictorderP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,axiom,
! [U] :
( ssItem(U)
=> totalorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f68,axiom,
! [U] :
( ssItem(U)
=> strictorderedP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,axiom,
! [U] :
( ssItem(U)
=> duplicatefreeP(cons(U,nil)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f73,axiom,
! [U] :
( ssItem(U)
=> equalelemsP(cons(U,nil)) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> cons(hd(U),tl(U)) = U ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) = app(cons(V,nil),U) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil != U
=> hd(app(U,V)) = hd(U) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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] :
( neq(Y,Z)
| ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) != U ) )
| ~ ssItem(Z) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox/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] :
( neq(Y,Z)
| ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) != U ) )
| ~ ssItem(Z) ) )
| 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] :
( ~ neq(Y,Z)
& ? [X1] :
( ? [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(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] :
( ~ neq(Y,Z)
& ? [X1] :
( ? [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(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,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)],[f417]) ).
fof(f421,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
ssItem(sK51_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
ssItem(sK52_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
ssList(sK53_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
ssList(sK54_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),sK54_skl) = sK47_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f430,plain,
~ neq(sK51_skl,sK52_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f432,plain,
( nil = sK49_skl
| sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f433,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(f434,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)],[f433]) ).
fof(f435,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f436,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f437,plain,
! [X0,X1,X2] :
( memberP(X1,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f438,plain,
! [X0,X1,X2] :
( ~ memberP(X1,X0)
| cons(X0,nil) != X2
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f439,definition,
( sQ0_spl
<=> sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f440,plain,
( ~ sQ0_spl
| sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ1_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f446,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f448,plain,
( sQ2_spl
| nil != sK49_skl ),
inference(component_clause,[status(thm)],[f446]) ).
fof(f449,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f432,f439,f446]) ).
fof(f452,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(f453,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f454,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f455,plain,
! [X0,X1] :
( ~ ssList(X0)
| rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f456,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(f457,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(f458,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(f459,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(f460,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(f461,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(f462,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(f463,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)],[f462]) ).
fof(f464,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(f469,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(f470,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)],[f469]) ).
fof(f480,plain,
! [X0,X1] :
( ~ memberP(X1,X0)
| ~ ssItem(X0)
| sP0_prd(X0,X1,cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f438]) ).
fof(f484,plain,
( sK51_skl = sK52_skl
| ~ ssItem(sK52_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f430,f101]) ).
fof(f485,definition,
( sQ3_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f487,plain,
( sQ3_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f485]) ).
fof(f488,definition,
( sQ4_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f490,plain,
( sQ4_spl
| ~ ssItem(sK52_skl) ),
inference(component_clause,[status(thm)],[f488]) ).
fof(f491,definition,
( sQ5_spl
<=> sK51_skl = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f492,plain,
( ~ sQ5_spl
| sK51_skl = sK52_skl ),
inference(component_clause,[status(thm)],[f491]) ).
fof(f494,plain,
( sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f484,f485,f488,f491]) ).
fof(f495,plain,
( ~ sQ5_spl
| ~ neq(sK51_skl,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f492,f430]) ).
fof(f497,plain,
( ~ sQ5_spl
| sK51_skl = sK51_skl
| ~ ssItem(sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f495,f101]) ).
fof(f498,definition,
( sQ6_spl
<=> sK51_skl = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f501,plain,
( ~ sQ5_spl
| sQ6_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f497,f485,f498,f491]) ).
fof(f502,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f487,f425]) ).
fof(f503,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f502]) ).
fof(f505,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f490,f426]) ).
fof(f506,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f505]) ).
fof(f508,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)],[f492,f429]) ).
fof(f509,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)],[f424,f508]) ).
fof(f520,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)],[f509,f454]) ).
fof(f521,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(f523,plain,
( sQ8_spl
| ~ ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl)) ),
inference(component_clause,[status(thm)],[f521]) ).
fof(f524,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(f526,plain,
( sQ9_spl
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f524]) ).
fof(f527,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(f528,plain,
( ~ sQ10_spl
| frontsegP(sK49_skl,app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f527]) ).
fof(f530,definition,
( sQ11_spl
<=> ssList(sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f532,plain,
( sQ11_spl
| ~ ssList(sK54_skl) ),
inference(component_clause,[status(thm)],[f530]) ).
fof(f533,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| sQ10_spl
| ~ sQ9_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f520,f521,f524,f527,f530,f491]) ).
fof(f534,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f532,f428]) ).
fof(f535,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f534]) ).
fof(f536,plain,
( ~ sQ0_spl
| ssItem(sK55_skl) ),
inference(resolution,[status(thm)],[f440,f435]) ).
fof(f537,plain,
( ~ sQ0_spl
| cons(sK55_skl,nil) = sK49_skl ),
inference(resolution,[status(thm)],[f436,f440]) ).
fof(f540,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)],[f537,f452]) ).
fof(f541,definition,
( sQ12_spl
<=> ssList(cons(sK55_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f543,plain,
( sQ12_spl
| ~ ssList(cons(sK55_skl,nil)) ),
inference(component_clause,[status(thm)],[f541]) ).
fof(f544,definition,
( sQ13_spl
<=> singletonP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f545,plain,
( ~ sQ13_spl
| singletonP(sK49_skl) ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f547,definition,
( sQ14_spl
<=> ssItem(sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f549,plain,
( sQ14_spl
| ~ ssItem(sK55_skl) ),
inference(component_clause,[status(thm)],[f547]) ).
fof(f551,definition,
( sQ15_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f553,plain,
( sQ15_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f551]) ).
fof(f554,definition,
( sQ16_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f558,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(f561,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f540,f558,f547,f551,f439]) ).
fof(f562,plain,
( sQ14_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f549,f536]) ).
fof(f563,plain,
( sQ14_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f562]) ).
fof(f564,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f553,f223]) ).
fof(f565,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f564]) ).
fof(f582,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(f584,plain,
! [X0,X1] :
( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f227]) ).
fof(f585,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(f586,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)],[f585]) ).
fof(f588,plain,
( sQ20_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f582,f551,f585]) ).
fof(f590,definition,
! [X0] :
( sQ21_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f591,plain,
! [X0] :
( ~ sQ21_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f590]) ).
fof(f593,definition,
! [X1] :
( sQ22_spl
<=> ( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f596,plain,
( sQ22_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f584,f590,f593]) ).
fof(f597,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)],[f586,f116]) ).
fof(f598,plain,
! [X0] :
( ~ sQ21_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f591]) ).
fof(f599,plain,
( ~ sQ21_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f428,f598]) ).
fof(f602,plain,
~ sQ21_spl,
inference(contradiction_clause,[status(thm)],[f599]) ).
fof(f604,plain,
! [X0,X1] :
( X0 = X0
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f228]) ).
fof(f605,definition,
! [X0] :
( sQ23_spl
<=> ( X0 = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f608,definition,
! [X1] :
( sQ24_spl
<=> ( ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f609,plain,
! [X0] :
( ~ sQ24_spl
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f608]) ).
fof(f611,plain,
( sQ24_spl
| sQ23_spl ),
inference(split_clause,[status(thm)],[f604,f605,f608]) ).
fof(f612,plain,
! [X0] :
( ~ sQ24_spl
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f609]) ).
fof(f614,plain,
( ~ sQ0_spl
| ~ sQ24_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f536,f612]) ).
fof(f618,plain,
( ~ sQ0_spl
| ~ sQ24_spl ),
inference(contradiction_clause,[status(thm)],[f614]) ).
fof(f626,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(app(X1,X0),X0)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f455,f245]) ).
fof(f633,definition,
( sQ25_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f635,plain,
( sQ25_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f633]) ).
fof(f636,definition,
( sQ26_spl
<=> segmentP(nil,cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f637,plain,
( ~ sQ26_spl
| segmentP(nil,cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f636]) ).
fof(f638,plain,
( sQ26_spl
| ~ segmentP(nil,cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f636]) ).
fof(f639,definition,
( sQ27_spl
<=> ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f640,plain,
( ~ sQ27_spl
| ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f639]) ).
fof(f641,plain,
( sQ27_spl
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f639]) ).
fof(f649,plain,
( ~ sQ0_spl
| memberP(sK50_skl,sK55_skl) ),
inference(resolution,[status(thm)],[f440,f437]) ).
fof(f650,plain,
( ~ sQ0_spl
| cons(sK55_skl,nil) = sK49_skl ),
inference(resolution,[status(thm)],[f440,f436]) ).
fof(f651,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)],[f509,f456]) ).
fof(f652,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)],[f509,f270]) ).
fof(f653,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)],[f509,f456]) ).
fof(f654,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)],[f509,f245]) ).
fof(f655,definition,
( sQ29_spl
<=> segmentP(sK49_skl,cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f656,plain,
( ~ sQ29_spl
| segmentP(sK49_skl,cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f655]) ).
fof(f658,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ27_spl
| sQ29_spl
| ~ sQ25_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f651,f521,f633,f655,f639,f530,f491]) ).
fof(f659,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(f660,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)],[f659]) ).
fof(f662,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f652,f659,f524,f530,f491]) ).
fof(f663,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(f664,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)],[f663]) ).
fof(f666,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ11_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f653,f663,f530,f524,f491]) ).
fof(f667,plain,
( ~ sQ5_spl
| sQ16_spl
| ~ sQ11_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f654,f524,f530,f554,f491]) ).
fof(f668,plain,
( sQ8_spl
| ~ sQ5_spl
| ~ ssList(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f509,f523]) ).
fof(f669,plain,
( sQ8_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f668,f421]) ).
fof(f670,plain,
( sQ8_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f669]) ).
fof(f672,plain,
( sQ12_spl
| ~ sQ0_spl
| ~ ssList(sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f537,f543]) ).
fof(f673,plain,
! [X0] :
( ~ sQ0_spl
| ~ memberP(X0,sK55_skl)
| ~ ssItem(sK55_skl)
| sP0_prd(sK55_skl,X0,sK49_skl) ),
inference(paramodulation,[status(thm)],[f537,f480]) ).
fof(f674,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)],[f537,f457]) ).
fof(f675,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)],[f537,f457]) ).
fof(f676,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)],[f537,f247]) ).
fof(f677,plain,
( sQ12_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f672,f421]) ).
fof(f678,plain,
( sQ12_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f677]) ).
fof(f683,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)],[f509,f271]) ).
fof(f684,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(f685,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)],[f684]) ).
fof(f687,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ32_spl ),
inference(split_clause,[status(thm)],[f683,f684,f524,f530,f491]) ).
fof(f688,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(f689,plain,
! [X0] :
( ~ sQ33_spl
| ~ memberP(X0,sK55_skl)
| sP0_prd(sK55_skl,X0,sK49_skl) ),
inference(component_clause,[status(thm)],[f688]) ).
fof(f691,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| sQ33_spl ),
inference(split_clause,[status(thm)],[f673,f688,f547,f439]) ).
fof(f692,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(f695,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f674,f692,f547,f551,f439]) ).
fof(f696,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(f699,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f675,f696,f547,f551,f439]) ).
fof(f700,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(f703,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ sQ15_spl
| sQ36_spl ),
inference(split_clause,[status(thm)],[f676,f700,f551,f547,f439]) ).
fof(f706,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(f722,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)],[f650,f275]) ).
fof(f723,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(f724,plain,
! [X0] :
( ~ sQ38_spl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f723]) ).
fof(f726,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f722,f723,f547,f551,f439]) ).
fof(f727,plain,
! [X0] :
( ~ sQ38_spl
| X0 = sK55_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f724,f279]) ).
fof(f730,definition,
( sQ39_spl
<=> memberP(sK49_skl,sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f731,plain,
( ~ sQ39_spl
| memberP(sK49_skl,sK55_skl) ),
inference(component_clause,[status(thm)],[f730]) ).
fof(f732,plain,
( sQ39_spl
| ~ memberP(sK49_skl,sK55_skl) ),
inference(component_clause,[status(thm)],[f730]) ).
fof(f734,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)],[f650,f458]) ).
fof(f735,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)],[f650,f458]) ).
fof(f736,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(f739,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f734,f736,f547,f551,f439]) ).
fof(f740,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(f743,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f735,f740,f547,f551,f439]) ).
fof(f746,plain,
( ~ sQ39_spl
| ~ sQ38_spl
| sK55_skl = sK55_skl
| ~ ssItem(sK55_skl) ),
inference(resolution,[status(thm)],[f727,f731]) ).
fof(f747,definition,
( sQ42_spl
<=> sK55_skl = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f750,plain,
( ~ sQ39_spl
| ~ sQ38_spl
| sQ42_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f746,f547,f747,f723,f730]) ).
fof(f751,plain,
( sQ27_spl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f641,f245]) ).
fof(f752,definition,
( sQ43_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f754,plain,
( sQ43_spl
| ~ ssList(sK53_skl) ),
inference(component_clause,[status(thm)],[f752]) ).
fof(f755,plain,
( sQ27_spl
| ~ sQ25_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f751,f752,f633,f639]) ).
fof(f756,plain,
( sQ9_spl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(resolution,[status(thm)],[f526,f245]) ).
fof(f757,plain,
( sQ9_spl
| ~ sQ25_spl
| ~ sQ27_spl ),
inference(split_clause,[status(thm)],[f756,f639,f633,f524]) ).
fof(f760,plain,
( sQ25_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f222,f635]) ).
fof(f762,plain,
( sQ25_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f760,f551,f485,f633]) ).
fof(f764,plain,
( sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f754,f427]) ).
fof(f765,plain,
sQ43_spl,
inference(contradiction_clause,[status(thm)],[f764]) ).
fof(f766,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)],[f509,f664]) ).
fof(f769,definition,
! [X0] :
( sQ44_spl
<=> ( ~ memberP(nil,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f773,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(f774,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(f777,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)],[f509,f376]) ).
fof(f780,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)],[f773]) ).
fof(f781,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)],[f780,f128]) ).
fof(f782,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(f785,plain,
( ~ sQ15_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f774,f782,f551]) ).
fof(f789,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(f792,plain,
( ~ sQ5_spl
| ~ sQ9_spl
| ~ sQ11_spl
| sQ46_spl ),
inference(split_clause,[status(thm)],[f777,f789,f530,f524,f491]) ).
fof(f794,definition,
! [X1] :
( sQ47_spl
<=> ~ ssList(X1) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f795,plain,
! [X0] :
( ~ sQ47_spl
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f794]) ).
fof(f800,definition,
( sQ48_spl
<=> cyclefreeP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f805,definition,
( sQ49_spl
<=> totalorderP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f811,plain,
! [X0] :
( ~ sQ33_spl
| cons(sK55_skl,nil) = sK49_skl
| ~ memberP(X0,sK55_skl) ),
inference(resolution,[status(thm)],[f689,f436]) ).
fof(f812,definition,
! [X0] :
( sQ50_spl
<=> ~ memberP(X0,sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f813,plain,
! [X0] :
( ~ sQ50_spl
| ~ memberP(X0,sK55_skl) ),
inference(component_clause,[status(thm)],[f812]) ).
fof(f816,definition,
( sQ51_spl
<=> cons(sK55_skl,nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f817,plain,
( ~ sQ51_spl
| cons(sK55_skl,nil) = sK49_skl ),
inference(component_clause,[status(thm)],[f816]) ).
fof(f819,plain,
( ~ sQ33_spl
| sQ51_spl
| sQ50_spl ),
inference(split_clause,[status(thm)],[f811,f812,f816,f688]) ).
fof(f820,plain,
( ~ sQ39_spl
| ~ sQ50_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f731,f813]) ).
fof(f826,plain,
( ~ sQ39_spl
| ~ sQ50_spl ),
inference(contradiction_clause,[status(thm)],[f820]) ).
fof(f833,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(f835,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)],[f509,f378]) ).
fof(f838,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(f841,plain,
( ~ sQ15_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f833,f838,f551]) ).
fof(f843,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(f846,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ53_spl ),
inference(split_clause,[status(thm)],[f835,f843,f524,f530,f491]) ).
fof(f850,plain,
! [X0] :
( ~ sQ0_spl
| cons(sK55_skl,X0) = app(sK49_skl,X0)
| ~ ssItem(sK55_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f650,f380]) ).
fof(f851,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(f852,plain,
! [X0] :
( ~ sQ54_spl
| cons(sK55_skl,X0) = app(sK49_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f851]) ).
fof(f854,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f850,f851,f547,f439]) ).
fof(f856,definition,
( sQ55_spl
<=> strictorderP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f861,definition,
( sQ56_spl
<=> totalorderedP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f866,definition,
( sQ57_spl
<=> strictorderedP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f875,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)],[f660,f270]) ).
fof(f876,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(f879,plain,
( ~ sQ30_spl
| ~ sQ25_spl
| ~ sQ27_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f875,f876,f639,f633,f659]) ).
fof(f888,definition,
( sQ59_spl
<=> rearsegP(sK49_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f889,plain,
( ~ sQ59_spl
| rearsegP(sK49_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f888]) ).
fof(f892,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)],[f509,f382]) ).
fof(f893,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(f896,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| ~ sQ9_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f892,f893,f524,f530,f491]) ).
fof(f897,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f385,f249]) ).
fof(f900,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(f901,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(f904,definition,
( sQ61_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f907,plain,
( sQ61_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f897,f551,f904]) ).
fof(f934,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(f937,plain,
( ~ sQ15_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f900,f934,f551]) ).
fof(f938,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(f941,plain,
( ~ sQ15_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f901,f938,f551]) ).
fof(f943,definition,
( sQ72_spl
<=> nil = sK54_skl ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f944,plain,
( ~ sQ72_spl
| nil = sK54_skl ),
inference(component_clause,[status(thm)],[f943]) ).
fof(f950,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)],[f944,f509]) ).
fof(f954,definition,
( sQ73_spl
<=> duplicatefreeP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f959,definition,
( sQ74_spl
<=> equalelemsP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f963,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)],[f650,f459]) ).
fof(f964,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)],[f650,f459]) ).
fof(f965,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(f968,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ75_spl ),
inference(split_clause,[status(thm)],[f963,f965,f547,f551,f439]) ).
fof(f969,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(f972,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f964,f969,f547,f551,f439]) ).
fof(f977,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)],[f950,f389]) ).
fof(f990,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(f992,plain,
( sQ77_spl
| ~ ssList(app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),nil)) ),
inference(component_clause,[status(thm)],[f990]) ).
fof(f994,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(f995,plain,
( ~ sQ78_spl
| sK49_skl = app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f994]) ).
fof(f996,plain,
( sQ78_spl
| sK49_skl != app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f994]) ).
fof(f997,plain,
( ~ sQ5_spl
| ~ sQ72_spl
| sQ78_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f977,f524,f994,f943,f491]) ).
fof(f1003,definition,
( sQ80_spl
<=> rearsegP(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1004,plain,
( ~ sQ80_spl
| rearsegP(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f1003]) ).
fof(f1032,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(f1033,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(f1044,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(f1047,plain,
( ~ sQ15_spl
| sQ87_spl ),
inference(split_clause,[status(thm)],[f1032,f1044,f551]) ).
fof(f1048,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(f1049,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)],[f1048]) ).
fof(f1051,plain,
( ~ sQ15_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f1033,f1048,f551]) ).
fof(f1053,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)],[f1049]) ).
fof(f1092,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(f1093,plain,
( ~ sQ94_spl
| nil = app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f1092]) ).
fof(f1121,plain,
( ~ sQ47_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f428,f795]) ).
fof(f1128,plain,
~ sQ47_spl,
inference(contradiction_clause,[status(thm)],[f1121]) ).
fof(f1129,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)],[f650,f227]) ).
fof(f1132,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(f1135,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| sQ97_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1129,f551,f1132,f547,f439]) ).
fof(f1141,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(f1147,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| memberP(nil,sK55_skl) ),
inference(backward_demodulation,[status(thm)],[f443,f649]) ).
fof(f1151,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)],[f650,f460]) ).
fof(f1152,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)],[f650,f460]) ).
fof(f1153,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(f1156,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f1151,f1153,f547,f551,f439]) ).
fof(f1157,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(f1160,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f1152,f1157,f547,f551,f439]) ).
fof(f1170,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ ssItem(sK55_skl) ),
inference(resolution,[status(thm)],[f1147,f279]) ).
fof(f1171,plain,
( ~ sQ0_spl
| ~ sQ1_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1170,f547,f442,f439]) ).
fof(f1207,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)],[f650,f461]) ).
fof(f1208,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)],[f650,f461]) ).
fof(f1209,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(f1212,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f1207,f1209,f547,f551,f439]) ).
fof(f1213,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(f1216,plain,
( ~ sQ0_spl
| ~ sQ15_spl
| ~ sQ14_spl
| sQ107_spl ),
inference(split_clause,[status(thm)],[f1208,f1213,f547,f551,f439]) ).
fof(f1219,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)],[f685,f452]) ).
fof(f1220,definition,
( sQ108_spl
<=> memberP(sK49_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1221,plain,
( ~ sQ108_spl
| memberP(sK49_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1220]) ).
fof(f1223,plain,
( ~ sQ32_spl
| ~ sQ15_spl
| ~ sQ27_spl
| ~ sQ9_spl
| sQ108_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1219,f485,f1220,f524,f639,f551,f684]) ).
fof(f1224,plain,
( ~ sQ38_spl
| ~ sQ108_spl
| sK51_skl = sK55_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1221,f727]) ).
fof(f1225,definition,
( sQ109_spl
<=> sK51_skl = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1226,plain,
( ~ sQ109_spl
| sK51_skl = sK55_skl ),
inference(component_clause,[status(thm)],[f1225]) ).
fof(f1228,plain,
( ~ sQ38_spl
| ~ sQ108_spl
| sQ109_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1224,f485,f1225,f1220,f723]) ).
fof(f1229,plain,
! [X0] :
( ~ sQ54_spl
| ~ sQ109_spl
| cons(sK51_skl,X0) = app(sK49_skl,X0)
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f1226,f852]) ).
fof(f1235,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| cons(sK51_skl,nil) = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f1226,f650]) ).
fof(f1244,plain,
( ~ sQ27_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ssList(app(sK53_skl,sK49_skl)) ),
inference(backward_demodulation,[status(thm)],[f1235,f640]) ).
fof(f1245,plain,
( ~ sQ26_spl
| ~ sQ0_spl
| ~ sQ109_spl
| segmentP(nil,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f1235,f637]) ).
fof(f1247,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)],[f1235,f509]) ).
fof(f1249,plain,
( ~ sQ29_spl
| ~ sQ0_spl
| ~ sQ109_spl
| segmentP(sK49_skl,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f1235,f656]) ).
fof(f1250,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| equalelemsP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1235,f361]) ).
fof(f1251,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| duplicatefreeP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1235,f358]) ).
fof(f1252,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| strictorderedP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1235,f348]) ).
fof(f1253,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| totalorderedP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1235,f338]) ).
fof(f1254,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| strictorderP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1235,f335]) ).
fof(f1255,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| totalorderP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1235,f332]) ).
fof(f1256,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| cyclefreeP(sK49_skl)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1235,f329]) ).
fof(f1257,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ109_spl
| ~ memberP(X0,sK51_skl)
| ~ ssItem(sK51_skl)
| sP0_prd(sK51_skl,X0,sK49_skl) ),
inference(paramodulation,[status(thm)],[f1235,f480]) ).
fof(f1259,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)],[f1235,f461]) ).
fof(f1260,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)],[f1235,f461]) ).
fof(f1261,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)],[f1235,f452]) ).
fof(f1262,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)],[f1235,f460]) ).
fof(f1263,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)],[f1235,f460]) ).
fof(f1264,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)],[f1235,f228]) ).
fof(f1266,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)],[f1235,f227]) ).
fof(f1269,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)],[f1235,f1247]) ).
fof(f1271,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| sQ74_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1250,f485,f959,f1225,f439]) ).
fof(f1272,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| sQ73_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1251,f485,f954,f1225,f439]) ).
fof(f1273,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| sQ57_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1252,f485,f866,f1225,f439]) ).
fof(f1274,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| sQ56_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1253,f485,f861,f1225,f439]) ).
fof(f1275,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| sQ55_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1254,f485,f856,f1225,f439]) ).
fof(f1276,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| sQ49_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1255,f485,f805,f1225,f439]) ).
fof(f1277,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| sQ48_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1256,f485,f800,f1225,f439]) ).
fof(f1278,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(f1281,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ3_spl
| sQ110_spl ),
inference(split_clause,[status(thm)],[f1257,f1278,f485,f1225,f439]) ).
fof(f1283,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(f1286,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ111_spl ),
inference(split_clause,[status(thm)],[f1259,f1283,f485,f551,f1225,f439]) ).
fof(f1287,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(f1290,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f1260,f1287,f485,f551,f1225,f439]) ).
fof(f1291,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(f1294,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ113_spl ),
inference(split_clause,[status(thm)],[f1261,f1291,f485,f551,f1225,f439]) ).
fof(f1295,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(f1298,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ114_spl ),
inference(split_clause,[status(thm)],[f1262,f1295,f485,f551,f1225,f439]) ).
fof(f1299,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(f1302,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ115_spl ),
inference(split_clause,[status(thm)],[f1263,f1299,f485,f551,f1225,f439]) ).
fof(f1303,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ3_spl
| ~ sQ15_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f1264,f1141,f551,f485,f1225,f439]) ).
fof(f1305,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(f1308,plain,
( ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ3_spl
| ~ sQ15_spl
| sQ116_spl ),
inference(split_clause,[status(thm)],[f1266,f1305,f551,f485,f1225,f439]) ).
fof(f1324,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| cons(sK51_skl,nil) = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f1226,f817]) ).
fof(f1335,plain,
( sQ39_spl
| ~ sQ109_spl
| ~ memberP(sK49_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f1226,f732]) ).
fof(f1336,plain,
( sQ39_spl
| ~ sQ109_spl
| ~ sQ108_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1335,f1221]) ).
fof(f1337,plain,
( sQ39_spl
| ~ sQ109_spl
| ~ sQ108_spl ),
inference(contradiction_clause,[status(thm)],[f1336]) ).
fof(f1342,plain,
( ~ sQ108_spl
| ~ sQ2_spl
| memberP(nil,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f447,f1221]) ).
fof(f1368,definition,
( sQ117_spl
<=> rearsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1369,plain,
( ~ sQ117_spl
| rearsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f1368]) ).
fof(f1378,plain,
( ~ sQ108_spl
| ~ sQ2_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1342,f279]) ).
fof(f1379,plain,
( ~ sQ108_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1378,f485,f446,f1220]) ).
fof(f1431,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)],[f1269,f376]) ).
fof(f1433,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)],[f1269,f378]) ).
fof(f1435,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)],[f1269,f626]) ).
fof(f1436,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)],[f1269,f382]) ).
fof(f1439,definition,
( sQ124_spl
<=> ssList(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1441,plain,
( sQ124_spl
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(component_clause,[status(thm)],[f1439]) ).
fof(f1442,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(f1443,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)],[f1442]) ).
fof(f1445,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sQ125_spl
| ~ sQ11_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f1431,f1439,f530,f1442,f1225,f439,f491]) ).
fof(f1447,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(f1448,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)],[f1447]) ).
fof(f1450,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sQ126_spl
| ~ sQ124_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1433,f530,f1439,f1447,f1225,f439,f491]) ).
fof(f1452,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| sQ59_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1435,f530,f888,f1439,f1225,f439,f491]) ).
fof(f1453,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(f1456,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ11_spl
| ~ sQ124_spl
| sQ127_spl ),
inference(split_clause,[status(thm)],[f1436,f1453,f1439,f530,f1225,f439,f491]) ).
fof(f1458,definition,
( sQ128_spl
<=> nil = app(app(sK53_skl,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1459,plain,
( ~ sQ128_spl
| nil = app(app(sK53_skl,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f1458]) ).
fof(f1463,plain,
! [X0] :
( ~ sQ51_spl
| ~ sQ109_spl
| cons(sK51_skl,X0) = app(sK49_skl,X0)
| ~ ssItem(sK51_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1324,f380]) ).
fof(f1474,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)],[f1324,f463]) ).
fof(f1475,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)],[f1324,f463]) ).
fof(f1486,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(f1489,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ3_spl
| sQ129_spl ),
inference(split_clause,[status(thm)],[f1463,f1486,f485,f1225,f816]) ).
fof(f1500,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(f1503,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ130_spl ),
inference(split_clause,[status(thm)],[f1474,f1500,f485,f551,f1225,f816]) ).
fof(f1504,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(f1507,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ131_spl ),
inference(split_clause,[status(thm)],[f1475,f1504,f485,f551,f1225,f816]) ).
fof(f1560,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)],[f1324,f275]) ).
fof(f1561,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(f1564,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ139_spl ),
inference(split_clause,[status(thm)],[f1560,f1561,f485,f551,f1225,f816]) ).
fof(f1565,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)],[f1324,f464]) ).
fof(f1566,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(f1569,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ140_spl ),
inference(split_clause,[status(thm)],[f1565,f1566,f485,f551,f1225,f816]) ).
fof(f1593,definition,
! [X0] :
( sQ146_spl
<=> ~ memberP(X0,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1594,plain,
! [X0] :
( ~ sQ146_spl
| ~ memberP(X0,sK51_skl) ),
inference(component_clause,[status(thm)],[f1593]) ).
fof(f1597,definition,
( sQ147_spl
<=> cons(sK51_skl,nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1601,plain,
( ~ sQ108_spl
| ~ sQ146_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f1221,f1594]) ).
fof(f1606,plain,
( ~ sQ108_spl
| ~ sQ146_spl ),
inference(contradiction_clause,[status(thm)],[f1601]) ).
fof(f1622,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)],[f1269,f272]) ).
fof(f1623,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ11_spl
| ~ sQ124_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f1622,f706,f1439,f530,f1225,f439,f491]) ).
fof(f1624,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)],[f1269,f271]) ).
fof(f1625,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(f1626,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)],[f1625]) ).
fof(f1628,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ11_spl
| ~ sQ124_spl
| sQ149_spl ),
inference(split_clause,[status(thm)],[f1624,f1625,f1439,f530,f1225,f439,f491]) ).
fof(f1639,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(f1640,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(f1644,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)],[f1639,f222]) ).
fof(f1645,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)],[f1640,f222]) ).
fof(f1655,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| hd(sK49_skl) = sK51_skl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1324,f239]) ).
fof(f1656,definition,
( sQ152_spl
<=> hd(sK49_skl) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1657,plain,
( ~ sQ152_spl
| hd(sK49_skl) = sK51_skl ),
inference(component_clause,[status(thm)],[f1656]) ).
fof(f1659,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sQ152_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1655,f551,f485,f1656,f1225,f816]) ).
fof(f1672,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(f1675,definition,
( sQ154_spl
<=> ssList(app(sK53_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f1677,plain,
( sQ154_spl
| ~ ssList(app(sK53_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1675]) ).
fof(f1679,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(f1685,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(f1689,definition,
( sQ157_spl
<=> sK49_skl = app(nil,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f1691,plain,
( sQ157_spl
| sK49_skl != app(nil,sK54_skl) ),
inference(component_clause,[status(thm)],[f1689]) ).
fof(f1693,definition,
( sQ158_spl
<=> nil = app(sK53_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f1694,plain,
( ~ sQ158_spl
| nil = app(sK53_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f1693]) ).
fof(f1695,plain,
( sQ158_spl
| nil != app(sK53_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f1693]) ).
fof(f1697,plain,
( sQ154_spl
| ~ sQ27_spl
| ~ sQ0_spl
| ~ sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1677,f1244]) ).
fof(f1698,plain,
( sQ154_spl
| ~ sQ27_spl
| ~ sQ0_spl
| ~ sQ109_spl ),
inference(contradiction_clause,[status(thm)],[f1697]) ).
fof(f1711,plain,
( ~ sQ158_spl
| ~ ssList(sK53_skl)
| rearsegP(nil,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1694,f626]) ).
fof(f1716,definition,
( sQ159_spl
<=> nil = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f1717,plain,
( ~ sQ159_spl
| nil = sK53_skl ),
inference(component_clause,[status(thm)],[f1716]) ).
fof(f1718,plain,
( sQ159_spl
| nil != sK53_skl ),
inference(component_clause,[status(thm)],[f1716]) ).
fof(f1724,definition,
! [X0] :
( sQ161_spl
<=> ( ~ memberP(sK49_skl,X0)
| memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f1725,plain,
! [X0] :
( ~ sQ161_spl
| ~ memberP(sK49_skl,X0)
| memberP(nil,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1724]) ).
fof(f1738,definition,
( sQ164_spl
<=> rearsegP(nil,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f1740,plain,
( sQ164_spl
| ~ rearsegP(nil,sK49_skl) ),
inference(component_clause,[status(thm)],[f1738]) ).
fof(f1741,plain,
( ~ sQ158_spl
| ~ sQ43_spl
| sQ164_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1711,f554,f1738,f752,f1693]) ).
fof(f1748,plain,
! [X0] :
( ~ sQ161_spl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1725,f279]) ).
fof(f1757,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)],[f1324,f247]) ).
fof(f1758,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(f1761,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ3_spl
| ~ sQ15_spl
| sQ166_spl ),
inference(split_clause,[status(thm)],[f1757,f1758,f551,f485,f1225,f816]) ).
fof(f1762,plain,
( ~ sQ108_spl
| ~ sQ161_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1748,f1221]) ).
fof(f1763,plain,
( ~ sQ108_spl
| ~ sQ161_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1762,f485,f1724,f1220]) ).
fof(f1767,plain,
( ~ sQ26_spl
| ~ sQ0_spl
| ~ sQ109_spl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f326,f1245]) ).
fof(f1770,plain,
( ~ sQ26_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1767,f554,f446,f1225,f439,f636]) ).
fof(f1773,plain,
( sQ26_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ segmentP(nil,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1324,f638]) ).
fof(f1774,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| tl(sK49_skl) = nil
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1324,f243]) ).
fof(f1775,definition,
( sQ167_spl
<=> tl(sK49_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f1776,plain,
( ~ sQ167_spl
| tl(sK49_skl) = nil ),
inference(component_clause,[status(thm)],[f1775]) ).
fof(f1778,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sQ167_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1774,f551,f485,f1775,f1225,f816]) ).
fof(f1804,definition,
( sQ168_spl
<=> ssList(app(nil,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f1806,plain,
( sQ168_spl
| ~ ssList(app(nil,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1804]) ).
fof(f1814,definition,
( sQ171_spl
<=> ssList(app(app(nil,sK49_skl),sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f1815,plain,
( ~ sQ171_spl
| ssList(app(app(nil,sK49_skl),sK49_skl)) ),
inference(component_clause,[status(thm)],[f1814]) ).
fof(f1816,plain,
( sQ171_spl
| ~ ssList(app(app(nil,sK49_skl),sK49_skl)) ),
inference(component_clause,[status(thm)],[f1814]) ).
fof(f1843,definition,
( sQ177_spl
<=> nil = app(app(nil,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f1844,plain,
( ~ sQ177_spl
| nil = app(app(nil,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f1843]) ).
fof(f1847,plain,
( sQ168_spl
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f245,f1806]) ).
fof(f1848,plain,
( sQ168_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f1847,f551,f554,f1804]) ).
fof(f1850,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)],[f1269,f270]) ).
fof(f1862,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(f1863,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)],[f1862]) ).
fof(f1865,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ11_spl
| ~ sQ124_spl
| sQ178_spl ),
inference(split_clause,[status(thm)],[f1850,f1862,f1439,f530,f1225,f439,f491]) ).
fof(f1892,definition,
( sQ179_spl
<=> sK54_skl = sK54_skl ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f1896,definition,
( sQ180_spl
<=> sK49_skl = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f2006,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)],[f597,f222]) ).
fof(f2007,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)],[f1324,f2006]) ).
fof(f2008,definition,
( sQ200_spl
<=> sK4_skl(sK49_skl) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f2009,plain,
( ~ sQ200_spl
| sK4_skl(sK49_skl) = sK51_skl ),
inference(component_clause,[status(thm)],[f2008]) ).
fof(f2011,definition,
( sQ201_spl
<=> singletonP(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f2013,plain,
( sQ201_spl
| ~ singletonP(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f2011]) ).
fof(f2014,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ20_spl
| ~ sQ201_spl
| sQ200_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2007,f551,f485,f2008,f2011,f585,f1225,f816]) ).
fof(f2015,plain,
( sQ201_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ singletonP(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1324,f2013]) ).
fof(f2016,plain,
( sQ201_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2015,f545]) ).
fof(f2017,plain,
( sQ201_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f2016]) ).
fof(f2019,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)],[f781,f245]) ).
fof(f2020,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)],[f1269,f2019]) ).
fof(f2021,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(f2024,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(f2026,plain,
( sQ203_spl
| ~ rearsegP(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl),sK54_skl) ),
inference(component_clause,[status(thm)],[f2024]) ).
fof(f2027,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ203_spl
| sQ202_spl
| ~ sQ11_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f2020,f1439,f530,f2021,f2024,f1225,f439,f491]) ).
fof(f2028,plain,
( sQ203_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ rearsegP(sK49_skl,sK54_skl) ),
inference(forward_demodulation,[status(thm)],[f1269,f2026]) ).
fof(f2029,plain,
( sQ203_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2028,f889]) ).
fof(f2030,plain,
( sQ203_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ59_spl ),
inference(contradiction_clause,[status(thm)],[f2029]) ).
fof(f2047,plain,
( sQ124_spl
| ~ ssList(sK49_skl)
| ~ ssList(app(sK53_skl,sK49_skl)) ),
inference(resolution,[status(thm)],[f1441,f245]) ).
fof(f2048,plain,
( sQ124_spl
| ~ sQ16_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f2047,f1675,f554,f1439]) ).
fof(f2050,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ128_spl
| app(nil,sK54_skl) = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f1459,f1269]) ).
fof(f2066,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ128_spl
| sQ157_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2050,f1691]) ).
fof(f2067,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ128_spl
| sQ157_spl ),
inference(contradiction_clause,[status(thm)],[f2066]) ).
fof(f2212,plain,
( ~ sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sK49_skl = app(app(sK53_skl,sK49_skl),cons(sK51_skl,nil)) ),
inference(forward_demodulation,[status(thm)],[f1324,f995]) ).
fof(f2213,plain,
( ~ sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sK49_skl = app(app(sK53_skl,sK49_skl),sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1324,f2212]) ).
fof(f2226,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)],[f1324,f992]) ).
fof(f2227,plain,
( sQ77_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ ssList(app(app(app(sK53_skl,sK49_skl),sK49_skl),nil)) ),
inference(forward_demodulation,[status(thm)],[f1324,f2226]) ).
fof(f2230,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f295]) ).
fof(f2231,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(f2233,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(f2235,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(f2238,plain,
( ~ sQ15_spl
| sQ225_spl ),
inference(split_clause,[status(thm)],[f2230,f2235,f551]) ).
fof(f2239,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)],[f2231]) ).
fof(f2240,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(f2241,plain,
! [X0,X1] :
( ~ sQ226_spl
| nil = X1
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ frontsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2240]) ).
fof(f2243,plain,
( sQ226_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2233,f551,f2240]) ).
fof(f2246,plain,
! [X0,X1] :
( ~ sQ226_spl
| nil = X1
| ~ frontsegP(X0,X1)
| ~ frontsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2241]) ).
fof(f2247,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f284,f295]) ).
fof(f2248,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(f2250,definition,
! [X0] :
( sQ227_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2253,plain,
( sQ227_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2247,f551,f2250]) ).
fof(f2254,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)],[f2248]) ).
fof(f2256,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(f2257,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(f2258,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)],[f1269,f288]) ).
fof(f2259,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)],[f2256]) ).
fof(f2260,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)],[f2259,f245]) ).
fof(f2261,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)],[f2257]) ).
fof(f2262,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)],[f2261,f245]) ).
fof(f2263,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(f2264,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)],[f2263]) ).
fof(f2266,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ11_spl
| sQ228_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f2258,f1439,f2263,f530,f1225,f439,f491]) ).
fof(f2270,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(f2302,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(f2304,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)],[f1324,f291]) ).
fof(f2305,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)],[f1324,f291]) ).
fof(f2306,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)],[f2302,f222]) ).
fof(f2307,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(f2310,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| sQ234_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2304,f485,f2307,f551,f1225,f816]) ).
fof(f2311,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(f2314,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ235_spl ),
inference(split_clause,[status(thm)],[f2305,f2311,f485,f551,f1225,f816]) ).
fof(f2315,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(f2317,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)],[f1324,f292]) ).
fof(f2318,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)],[f1324,f292]) ).
fof(f2319,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)],[f2315,f222]) ).
fof(f2321,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(f2324,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| sQ236_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2317,f485,f2321,f551,f1225,f816]) ).
fof(f2325,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(f2328,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ237_spl ),
inference(split_clause,[status(thm)],[f2318,f2325,f485,f551,f1225,f816]) ).
fof(f2330,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)],[f470,f291]) ).
fof(f2331,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)],[f470,f284]) ).
fof(f2332,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)],[f470,f282]) ).
fof(f2333,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)],[f1324,f470]) ).
fof(f2334,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)],[f1324,f470]) ).
fof(f2342,definition,
! [X0] :
( sQ240_spl
<=> ( X0 = X0
| ~ ssItem(X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f2345,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(f2346,plain,
! [X0,X1] :
( ~ sQ241_spl
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2345]) ).
fof(f2348,plain,
( sQ241_spl
| sQ240_spl ),
inference(split_clause,[status(thm)],[f2330,f2342,f2345]) ).
fof(f2349,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)],[f2331,f222]) ).
fof(f2350,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)],[f2332,f222]) ).
fof(f2351,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(f2354,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sQ242_spl
| ~ sQ15_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2333,f485,f551,f2351,f1225,f816]) ).
fof(f2355,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(f2356,plain,
! [X0] :
( ~ sQ243_spl
| ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK49_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2355]) ).
fof(f2358,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| sQ243_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2334,f485,f2355,f551,f1225,f816]) ).
fof(f2359,plain,
! [X0] :
( ~ sQ243_spl
| frontsegP(cons(sK51_skl,X0),sK49_skl)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2356,f295]) ).
fof(f2361,plain,
! [X0,X1] :
( ~ sQ241_spl
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2346]) ).
fof(f2362,plain,
( sQ171_spl
| ~ ssList(sK49_skl)
| ~ ssList(app(nil,sK49_skl)) ),
inference(resolution,[status(thm)],[f1816,f245]) ).
fof(f2363,plain,
( sQ171_spl
| ~ sQ16_spl
| ~ sQ168_spl ),
inference(split_clause,[status(thm)],[f2362,f1804,f554,f1814]) ).
fof(f2364,plain,
( ~ sQ94_spl
| ~ sQ51_spl
| ~ sQ109_spl
| nil = app(app(sK53_skl,sK49_skl),cons(sK51_skl,nil)) ),
inference(forward_demodulation,[status(thm)],[f1324,f1093]) ).
fof(f2368,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ94_spl
| ~ sQ51_spl
| app(nil,sK54_skl) = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f2369,f1269]) ).
fof(f2369,plain,
( ~ sQ94_spl
| ~ sQ51_spl
| ~ sQ109_spl
| nil = app(app(sK53_skl,sK49_skl),sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1324,f2364]) ).
fof(f2387,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ94_spl
| ~ sQ51_spl
| sQ157_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2368,f1691]) ).
fof(f2388,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ94_spl
| ~ sQ51_spl
| sQ157_spl ),
inference(contradiction_clause,[status(thm)],[f2387]) ).
fof(f2393,plain,
( ~ sQ177_spl
| nil = app(nil,app(sK49_skl,sK49_skl))
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1844,f382]) ).
fof(f2410,definition,
( sQ244_spl
<=> nil = app(nil,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f2411,plain,
( ~ sQ244_spl
| nil = app(nil,sK49_skl) ),
inference(component_clause,[status(thm)],[f2410]) ).
fof(f2414,definition,
( sQ245_spl
<=> nil = app(nil,app(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f2415,plain,
( ~ sQ245_spl
| nil = app(nil,app(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f2414]) ).
fof(f2417,plain,
( ~ sQ177_spl
| sQ245_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2393,f551,f554,f2414,f1843]) ).
fof(f2422,definition,
( sQ247_spl
<=> sK6_skl(sK49_skl,nil) = app(nil,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f2423,plain,
( ~ sQ247_spl
| sK6_skl(sK49_skl,nil) = app(nil,sK49_skl) ),
inference(component_clause,[status(thm)],[f2422]) ).
fof(f2434,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(f2435,plain,
! [X0] :
( ~ sQ250_spl
| ~ memberP(app(nil,sK49_skl),X0)
| memberP(nil,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f2434]) ).
fof(f2460,plain,
! [X0] :
( ~ sQ250_spl
| ~ memberP(app(nil,sK49_skl),X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2435,f279]) ).
fof(f2518,plain,
! [X0] :
( ~ sQ80_spl
| rearsegP(X0,nil)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(nil)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f1004]) ).
fof(f2519,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,f889]) ).
fof(f2521,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f309]) ).
fof(f2522,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(f2524,plain,
! [X0] :
( sQ164_spl
| ~ rearsegP(X0,sK49_skl)
| ~ rearsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f301,f1740]) ).
fof(f2525,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(f2527,definition,
! [X0] :
( sQ257_spl
<=> ( rearsegP(X0,nil)
| ~ rearsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f2531,definition,
! [X0] :
( sQ258_spl
<=> ( rearsegP(X0,nil)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f2534,plain,
( ~ sQ80_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ258_spl ),
inference(split_clause,[status(thm)],[f2518,f2531,f554,f551,f1003]) ).
fof(f2535,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(f2538,plain,
( ~ sQ59_spl
| ~ sQ11_spl
| ~ sQ16_spl
| sQ259_spl ),
inference(split_clause,[status(thm)],[f2519,f2535,f554,f530,f888]) ).
fof(f2541,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(f2544,plain,
( ~ sQ15_spl
| sQ260_spl ),
inference(split_clause,[status(thm)],[f2521,f2541,f551]) ).
fof(f2545,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)],[f2522]) ).
fof(f2546,definition,
! [X0] :
( sQ261_spl
<=> ( ~ rearsegP(X0,sK49_skl)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f2549,plain,
( sQ164_spl
| ~ sQ16_spl
| sQ261_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2524,f551,f2546,f554,f1738]) ).
fof(f2550,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(f2551,plain,
! [X0,X1] :
( ~ sQ262_spl
| nil = X1
| ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2550]) ).
fof(f2553,plain,
( sQ262_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2525,f551,f2550]) ).
fof(f2556,plain,
! [X0,X1] :
( ~ sQ262_spl
| nil = X1
| ~ rearsegP(X0,X1)
| ~ rearsegP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2551]) ).
fof(f2558,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,f626]) ).
fof(f2559,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f303,f309]) ).
fof(f2560,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(f2562,definition,
( sQ263_spl
<=> rearsegP(sK54_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f2564,plain,
( sQ263_spl
| ~ rearsegP(sK54_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f2562]) ).
fof(f2565,definition,
( sQ264_spl
<=> sK54_skl = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f2566,plain,
( ~ sQ264_spl
| sK54_skl = sK49_skl ),
inference(component_clause,[status(thm)],[f2565]) ).
fof(f2567,plain,
( sQ264_spl
| sK54_skl != sK49_skl ),
inference(component_clause,[status(thm)],[f2565]) ).
fof(f2569,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)],[f2558]) ).
fof(f2570,plain,
! [X0,X1] :
( ~ ssList(X1)
| X0 = app(X1,X0)
| ~ rearsegP(X0,app(X1,X0))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2569,f245]) ).
fof(f2571,definition,
! [X0] :
( sQ265_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f2574,plain,
( sQ265_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2559,f551,f2571]) ).
fof(f2575,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)],[f2560]) ).
fof(f2577,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(f2579,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)],[f1269,f307]) ).
fof(f2580,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)],[f2577]) ).
fof(f2581,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)],[f2580,f245]) ).
fof(f2584,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(f2585,plain,
! [X0] :
( ~ sQ266_spl
| rearsegP(sK49_skl,X0)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2584]) ).
fof(f2587,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| sQ266_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2579,f530,f2584,f1439,f1225,f439,f491]) ).
fof(f2589,plain,
( sQ157_spl
| ~ sQ264_spl
| sK49_skl != app(nil,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f2566,f1691]) ).
fof(f2608,plain,
! [X0] :
( sQ263_spl
| ~ rearsegP(X0,sK49_skl)
| ~ rearsegP(sK54_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f2564,f301]) ).
fof(f2609,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(f2612,plain,
( sQ263_spl
| ~ sQ16_spl
| sQ268_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2608,f530,f2609,f554,f2562]) ).
fof(f2617,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,f1249]) ).
fof(f2618,plain,
! [X0,X1] :
( ~ ssList(X1)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f315,f323]) ).
fof(f2619,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(f2621,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,f1773]) ).
fof(f2622,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(f2624,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(f2627,plain,
( ~ sQ29_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ16_spl
| sQ269_spl ),
inference(split_clause,[status(thm)],[f2617,f2624,f554,f1225,f439,f655]) ).
fof(f2628,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(f2631,plain,
( ~ sQ15_spl
| sQ270_spl ),
inference(split_clause,[status(thm)],[f2618,f2628,f551]) ).
fof(f2632,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)],[f2619]) ).
fof(f2633,definition,
! [X0] :
( sQ271_spl
<=> ( ~ segmentP(X0,sK49_skl)
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f2636,plain,
( sQ26_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ16_spl
| sQ271_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2621,f551,f2633,f554,f1225,f816,f636]) ).
fof(f2637,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(f2638,plain,
! [X0,X1] :
( ~ sQ272_spl
| nil = X1
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2637]) ).
fof(f2640,plain,
( sQ272_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2622,f551,f2637]) ).
fof(f2643,plain,
! [X0,X1] :
( ~ sQ272_spl
| nil = X1
| ~ segmentP(X0,X1)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2638]) ).
fof(f2645,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f317,f323]) ).
fof(f2646,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(f2648,definition,
( sQ273_spl
<=> segmentP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f2650,plain,
( sQ273_spl
| ~ segmentP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f2648]) ).
fof(f2652,definition,
! [X0] :
( sQ274_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f2655,plain,
( sQ274_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2645,f551,f2652]) ).
fof(f2656,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)],[f2646]) ).
fof(f2658,plain,
( sQ273_spl
| ~ sQ29_spl
| ~ sQ0_spl
| ~ sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2650,f1249]) ).
fof(f2659,plain,
( sQ273_spl
| ~ sQ29_spl
| ~ sQ0_spl
| ~ sQ109_spl ),
inference(contradiction_clause,[status(thm)],[f2658]) ).
fof(f2660,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(f2661,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(f2662,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)],[f2660]) ).
fof(f2663,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)],[f2661]) ).
fof(f2678,plain,
( ~ sQ244_spl
| ~ ssList(nil)
| rearsegP(nil,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f2411,f626]) ).
fof(f2698,definition,
! [X0] :
( sQ278_spl
<=> ( frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f2702,definition,
( sQ279_spl
<=> sK6_skl(sK49_skl,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f2703,plain,
( ~ sQ279_spl
| sK6_skl(sK49_skl,nil) = nil ),
inference(component_clause,[status(thm)],[f2702]) ).
fof(f2705,definition,
( sQ280_spl
<=> rearsegP(app(nil,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f2706,plain,
( ~ sQ280_spl
| rearsegP(app(nil,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f2705]) ).
fof(f2707,plain,
( sQ280_spl
| ~ rearsegP(app(nil,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f2705]) ).
fof(f2720,plain,
( ~ sQ244_spl
| ~ sQ15_spl
| sQ164_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2678,f554,f1738,f551,f2410]) ).
fof(f2738,plain,
! [X0] :
( ~ sQ241_spl
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2361,f295]) ).
fof(f2740,plain,
( ~ sQ241_spl
| ~ sQ15_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f2738,f590,f551,f2345]) ).
fof(f2763,plain,
( sQ280_spl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f2707,f626]) ).
fof(f2765,definition,
( sQ287_spl
<=> rearsegP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f2766,plain,
( ~ sQ287_spl
| rearsegP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f2765]) ).
fof(f2767,plain,
( sQ287_spl
| ~ rearsegP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f2765]) ).
fof(f2769,plain,
( sQ280_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2763,f554,f551,f2705]) ).
fof(f2774,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)],[f1269,f321]) ).
fof(f2777,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)],[f1269,f321]) ).
fof(f2790,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(f2793,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ11_spl
| ~ sQ154_spl
| sQ289_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2774,f554,f2790,f1675,f530,f1225,f439,f491]) ).
fof(f2796,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(f2797,plain,
! [X0,X1] :
( ~ sQ290_spl
| segmentP(app(sK49_skl,X1),X0)
| ~ segmentP(sK54_skl,X0)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2796]) ).
fof(f2799,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| sQ290_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2777,f530,f2796,f1439,f1225,f439,f491]) ).
fof(f2813,plain,
( sQ287_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f2767,f305]) ).
fof(f2815,plain,
( sQ287_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2813,f421]) ).
fof(f2816,plain,
sQ287_spl,
inference(contradiction_clause,[status(thm)],[f2815]) ).
fof(f2817,plain,
( ~ sQ287_spl
| sK49_skl = sK49_skl
| ~ rearsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f2766,f303]) ).
fof(f2818,plain,
! [X0] :
( ~ sQ287_spl
| rearsegP(X0,sK49_skl)
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2766,f301]) ).
fof(f2819,plain,
( sQ180_spl
| ~ sQ287_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2817,f554,f2765,f1896]) ).
fof(f2820,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(f2823,plain,
( ~ sQ287_spl
| ~ sQ16_spl
| sQ291_spl ),
inference(split_clause,[status(thm)],[f2818,f2820,f554,f2765]) ).
fof(f2825,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)],[f2706,f301]) ).
fof(f2826,definition,
( sQ292_spl
<=> rearsegP(sK49_skl,app(nil,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f2828,plain,
( sQ292_spl
| ~ rearsegP(sK49_skl,app(nil,sK49_skl)) ),
inference(component_clause,[status(thm)],[f2826]) ).
fof(f2829,definition,
( sQ293_spl
<=> sK49_skl = app(nil,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f2830,plain,
( ~ sQ293_spl
| sK49_skl = app(nil,sK49_skl) ),
inference(component_clause,[status(thm)],[f2829]) ).
fof(f2831,plain,
( sQ293_spl
| sK49_skl != app(nil,sK49_skl) ),
inference(component_clause,[status(thm)],[f2829]) ).
fof(f2833,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(f2836,plain,
( ~ sQ280_spl
| ~ sQ16_spl
| ~ sQ168_spl
| sQ294_spl ),
inference(split_clause,[status(thm)],[f2825,f2833,f1804,f554,f2705]) ).
fof(f2846,plain,
! [X0] :
( ~ sQ293_spl
| ~ memberP(sK49_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f2830,f272]) ).
fof(f2847,plain,
! [X0] :
( ~ sQ293_spl
| ~ memberP(nil,X0)
| memberP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f2830,f271]) ).
fof(f2848,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)],[f2830,f321]) ).
fof(f2849,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)],[f2830,f270]) ).
fof(f2850,plain,
! [X0] :
( ~ sQ293_spl
| rearsegP(sK49_skl,X0)
| ~ rearsegP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f2830,f307]) ).
fof(f2851,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)],[f2830,f2019]) ).
fof(f2853,plain,
! [X0] :
( ~ sQ293_spl
| X0 = nil
| app(X0,sK49_skl) != sK49_skl
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2830,f376]) ).
fof(f2855,plain,
! [X0] :
( ~ sQ293_spl
| X0 = sK49_skl
| app(nil,X0) != sK49_skl
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f2830,f378]) ).
fof(f2858,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)],[f2830,f382]) ).
fof(f2859,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)],[f2830,f382]) ).
fof(f2863,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(f2866,plain,
( ~ sQ293_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ295_spl ),
inference(split_clause,[status(thm)],[f2846,f2863,f551,f554,f2829]) ).
fof(f2867,plain,
( ~ sQ293_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ44_spl ),
inference(split_clause,[status(thm)],[f2847,f769,f551,f554,f2829]) ).
fof(f2868,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(f2871,plain,
( ~ sQ293_spl
| ~ sQ15_spl
| sQ296_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2848,f554,f2868,f551,f2829]) ).
fof(f2872,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(f2875,plain,
( ~ sQ293_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ297_spl ),
inference(split_clause,[status(thm)],[f2849,f2872,f551,f554,f2829]) ).
fof(f2876,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(f2879,plain,
( ~ sQ293_spl
| ~ sQ15_spl
| sQ298_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2850,f554,f2876,f551,f2829]) ).
fof(f2880,definition,
( sQ299_spl
<=> sK6_skl(sK49_skl,sK49_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f2881,plain,
( ~ sQ299_spl
| sK6_skl(sK49_skl,sK49_skl) = nil ),
inference(component_clause,[status(thm)],[f2880]) ).
fof(f2883,plain,
( ~ sQ293_spl
| ~ sQ280_spl
| sQ299_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2851,f551,f554,f2880,f2705,f2829]) ).
fof(f2885,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(f2888,plain,
( ~ sQ293_spl
| sQ300_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2853,f551,f554,f2885,f2829]) ).
fof(f2890,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(f2893,plain,
( ~ sQ293_spl
| sQ301_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2855,f554,f551,f2890,f2829]) ).
fof(f2896,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(f2899,plain,
( ~ sQ293_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ302_spl ),
inference(split_clause,[status(thm)],[f2858,f2896,f551,f554,f2829]) ).
fof(f2900,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(f2903,plain,
( ~ sQ293_spl
| sQ303_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f2859,f551,f554,f2900,f2829]) ).
fof(f2931,plain,
( sQ292_spl
| ~ sQ293_spl
| ~ rearsegP(sK49_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f2830,f2828]) ).
fof(f2932,plain,
( sQ292_spl
| ~ sQ293_spl
| ~ sQ287_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2931,f2766]) ).
fof(f2933,plain,
( sQ292_spl
| ~ sQ293_spl
| ~ sQ287_spl ),
inference(contradiction_clause,[status(thm)],[f2932]) ).
fof(f2939,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(f2943,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(f3027,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ78_spl
| ~ sQ51_spl
| app(sK49_skl,sK54_skl) = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f2213,f1269]) ).
fof(f3058,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(f3059,plain,
( ~ sQ320_spl
| sK6_skl(sK49_skl,sK49_skl) = app(sK53_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f3058]) ).
fof(f3083,plain,
( ~ sQ320_spl
| ~ sQ299_spl
| nil = app(sK53_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f2881,f3059]) ).
fof(f3084,plain,
( ~ sQ320_spl
| ~ sQ299_spl
| sQ158_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3083,f1695]) ).
fof(f3085,plain,
( ~ sQ320_spl
| ~ sQ299_spl
| sQ158_spl ),
inference(contradiction_clause,[status(thm)],[f3084]) ).
fof(f3086,plain,
( sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sK49_skl != app(app(sK53_skl,sK49_skl),cons(sK51_skl,nil)) ),
inference(forward_demodulation,[status(thm)],[f1324,f996]) ).
fof(f3087,plain,
( sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sK49_skl != app(app(sK53_skl,sK49_skl),sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1324,f3086]) ).
fof(f3120,plain,
( sQ293_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f2831,f249]) ).
fof(f3121,plain,
( sQ293_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3120,f421]) ).
fof(f3122,plain,
sQ293_spl,
inference(contradiction_clause,[status(thm)],[f3121]) ).
fof(f3176,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)],[f1776,f372]) ).
fof(f3179,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(f3182,plain,
( ~ sQ167_spl
| sQ2_spl
| ~ sQ16_spl
| sQ326_spl ),
inference(split_clause,[status(thm)],[f3176,f3179,f554,f446,f1775]) ).
fof(f3186,plain,
( ~ sQ152_spl
| cons(sK51_skl,tl(sK49_skl)) = sK49_skl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1657,f374]) ).
fof(f3187,plain,
( ~ sQ167_spl
| cons(hd(sK49_skl),nil) = sK49_skl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f1776,f374]) ).
fof(f3192,definition,
( sQ328_spl
<=> cons(sK51_skl,tl(sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f3195,plain,
( ~ sQ152_spl
| sQ328_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3186,f554,f446,f3192,f1656]) ).
fof(f3196,definition,
( sQ329_spl
<=> cons(hd(sK49_skl),nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f3199,plain,
( ~ sQ167_spl
| sQ329_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3187,f554,f446,f3196,f1775]) ).
fof(f3204,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)],[f1324,f528]) ).
fof(f3205,plain,
( ~ sQ10_spl
| ~ sQ51_spl
| ~ sQ109_spl
| frontsegP(sK49_skl,app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f1324,f3204]) ).
fof(f3335,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(f3342,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)],[f3335,f231]) ).
fof(f3351,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)],[f1269,f391]) ).
fof(f3356,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(f3357,plain,
( ~ sQ351_spl
| hd(sK49_skl) = hd(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(component_clause,[status(thm)],[f3356]) ).
fof(f3359,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sQ351_spl
| sQ128_spl
| ~ sQ11_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f3351,f1439,f530,f1458,f3356,f1225,f439,f491]) ).
fof(f3360,plain,
( ~ sQ351_spl
| ~ sQ152_spl
| sK51_skl = hd(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f1657,f3357]) ).
fof(f3362,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)],[f1269,f393]) ).
fof(f3367,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(f3370,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sQ353_spl
| sQ128_spl
| ~ sQ11_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f3362,f1439,f530,f1458,f3367,f1225,f439,f491]) ).
fof(f3374,definition,
( sQ354_spl
<=> frontsegP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ354_spl])],[split_symbol_definition]) ).
fof(f3375,plain,
( ~ sQ354_spl
| frontsegP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f3374]) ).
fof(f3451,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(f3458,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)],[f3451,f231]) ).
fof(f3497,plain,
( ~ sQ171_spl
| ~ sQ293_spl
| ssList(app(sK49_skl,sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f2830,f1815]) ).
fof(f3499,plain,
! [X0] :
( ~ sQ250_spl
| ~ sQ293_spl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f2830,f2460]) ).
fof(f3500,plain,
( ~ sQ108_spl
| ~ sQ250_spl
| ~ sQ293_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f3499,f1221]) ).
fof(f3501,plain,
( ~ sQ108_spl
| ~ sQ250_spl
| ~ sQ293_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3500,f485,f2829,f2434,f1220]) ).
fof(f3504,plain,
( ~ sQ293_spl
| ~ sQ247_spl
| ~ sQ279_spl
| sK49_skl = nil ),
inference(backward_demodulation,[status(thm)],[f3505,f2830]) ).
fof(f3505,plain,
( ~ sQ247_spl
| ~ sQ279_spl
| nil = app(nil,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f2703,f2423]) ).
fof(f3527,plain,
( ~ sQ293_spl
| ~ sQ247_spl
| ~ sQ279_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f3504,f446,f2702,f2422,f2829]) ).
fof(f3540,definition,
! [X0] :
( sQ369_spl
<=> ( ~ memberP(nil,X0)
| memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ369_spl])],[split_symbol_definition]) ).
fof(f3619,plain,
( ~ sQ245_spl
| ~ ssList(nil)
| rearsegP(nil,app(sK49_skl,sK49_skl))
| ~ ssList(app(sK49_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f2415,f626]) ).
fof(f3624,definition,
( sQ370_spl
<=> ssList(app(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ370_spl])],[split_symbol_definition]) ).
fof(f3626,plain,
( sQ370_spl
| ~ ssList(app(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f3624]) ).
fof(f3627,definition,
( sQ371_spl
<=> nil = app(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ371_spl])],[split_symbol_definition]) ).
fof(f3628,plain,
( ~ sQ371_spl
| nil = app(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f3627]) ).
fof(f3638,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(f3639,plain,
! [X0] :
( ~ sQ373_spl
| ~ memberP(app(sK49_skl,sK49_skl),X0)
| memberP(nil,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f3638]) ).
fof(f3673,definition,
( sQ381_spl
<=> rearsegP(nil,app(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ381_spl])],[split_symbol_definition]) ).
fof(f3674,plain,
( ~ sQ381_spl
| rearsegP(nil,app(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f3673]) ).
fof(f3675,plain,
( sQ381_spl
| ~ rearsegP(nil,app(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f3673]) ).
fof(f3676,plain,
( ~ sQ245_spl
| ~ sQ15_spl
| sQ381_spl
| ~ sQ370_spl ),
inference(split_clause,[status(thm)],[f3619,f3624,f3673,f551,f2414]) ).
fof(f3687,plain,
( sQ370_spl
| ~ sQ171_spl
| ~ sQ293_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3626,f3497]) ).
fof(f3688,plain,
( sQ370_spl
| ~ sQ171_spl
| ~ sQ293_spl ),
inference(contradiction_clause,[status(thm)],[f3687]) ).
fof(f3689,plain,
! [X0] :
( ~ sQ373_spl
| ~ memberP(app(sK49_skl,sK49_skl),X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3639,f279]) ).
fof(f3706,plain,
( ~ sQ371_spl
| ~ ssList(sK49_skl)
| rearsegP(nil,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f3628,f626]) ).
fof(f3728,definition,
( sQ387_spl
<=> rearsegP(app(sK49_skl,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ387_spl])],[split_symbol_definition]) ).
fof(f3729,plain,
( ~ sQ387_spl
| rearsegP(app(sK49_skl,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f3728]) ).
fof(f3730,plain,
( sQ387_spl
| ~ rearsegP(app(sK49_skl,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f3728]) ).
fof(f3743,plain,
( ~ sQ371_spl
| sQ164_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3706,f554,f1738,f3627]) ).
fof(f3751,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)],[f766,f317]) ).
fof(f3752,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)],[f766,f315]) ).
fof(f3753,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(f3756,plain,
( ~ sQ31_spl
| ~ sQ5_spl
| ~ sQ11_spl
| sQ391_spl ),
inference(split_clause,[status(thm)],[f3751,f3753,f530,f491,f663]) ).
fof(f3757,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(f3760,plain,
( ~ sQ31_spl
| ~ sQ5_spl
| ~ sQ11_spl
| sQ392_spl ),
inference(split_clause,[status(thm)],[f3752,f3757,f530,f491,f663]) ).
fof(f3788,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)],[f3674,f301]) ).
fof(f3794,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(f3795,plain,
! [X0] :
( ~ sQ398_spl
| rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3794]) ).
fof(f3797,plain,
( ~ sQ381_spl
| ~ sQ370_spl
| ~ sQ15_spl
| sQ398_spl ),
inference(split_clause,[status(thm)],[f3788,f3794,f551,f3624,f3673]) ).
fof(f3798,plain,
! [X0] :
( ~ sQ398_spl
| rearsegP(X0,app(sK49_skl,sK49_skl))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3795,f309]) ).
fof(f3800,plain,
( sQ387_spl
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f3730,f626]) ).
fof(f3803,plain,
( sQ387_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3800,f554,f3728]) ).
fof(f3808,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)],[f3675,f301]) ).
fof(f3809,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(f3812,plain,
( sQ381_spl
| ~ sQ370_spl
| sQ400_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f3808,f551,f3809,f3624,f3673]) ).
fof(f3813,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)],[f3729,f303]) ).
fof(f3814,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)],[f3729,f301]) ).
fof(f3815,definition,
( sQ401_spl
<=> rearsegP(sK49_skl,app(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ401_spl])],[split_symbol_definition]) ).
fof(f3817,plain,
( sQ401_spl
| ~ rearsegP(sK49_skl,app(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f3815]) ).
fof(f3818,definition,
( sQ402_spl
<=> sK49_skl = app(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ402_spl])],[split_symbol_definition]) ).
fof(f3819,plain,
( ~ sQ402_spl
| sK49_skl = app(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f3818]) ).
fof(f3820,plain,
( sQ402_spl
| sK49_skl != app(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f3818]) ).
fof(f3821,plain,
( ~ sQ387_spl
| sQ402_spl
| ~ sQ401_spl
| ~ sQ370_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3813,f554,f3624,f3815,f3818,f3728]) ).
fof(f3822,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(f3825,plain,
( ~ sQ387_spl
| ~ sQ16_spl
| ~ sQ370_spl
| sQ403_spl ),
inference(split_clause,[status(thm)],[f3814,f3822,f3624,f554,f3728]) ).
fof(f3832,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ ssItem(sK51_skl)
| singletonP(sK49_skl)
| ~ ssList(cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f1324,f453]) ).
fof(f3833,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ3_spl
| sQ13_spl
| ~ sQ25_spl ),
inference(split_clause,[status(thm)],[f3832,f633,f544,f485,f1225,f816]) ).
fof(f3834,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f454,f245]) ).
fof(f3835,plain,
( ~ sQ293_spl
| ~ ssList(sK49_skl)
| frontsegP(sK49_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2830,f3834]) ).
fof(f3837,definition,
( sQ404_spl
<=> frontsegP(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ404_spl])],[split_symbol_definition]) ).
fof(f3838,plain,
( ~ sQ404_spl
| frontsegP(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f3837]) ).
fof(f3840,plain,
( ~ sQ293_spl
| ~ sQ16_spl
| sQ404_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f3835,f551,f3837,f554,f2829]) ).
fof(f3841,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(f3851,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)],[f3819,f393]) ).
fof(f3868,definition,
( sQ406_spl
<=> segmentP(sK49_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ406_spl])],[split_symbol_definition]) ).
fof(f3869,plain,
( ~ sQ406_spl
| segmentP(sK49_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f3868]) ).
fof(f3873,definition,
( sQ407_spl
<=> tl(sK49_skl) = app(tl(sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ407_spl])],[split_symbol_definition]) ).
fof(f3874,plain,
( ~ sQ407_spl
| tl(sK49_skl) = app(tl(sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f3873]) ).
fof(f3876,plain,
( ~ sQ402_spl
| sQ407_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f3851,f554,f446,f3873,f3818]) ).
fof(f3877,definition,
( sQ408_spl
<=> hd(sK49_skl) = hd(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ408_spl])],[split_symbol_definition]) ).
fof(f3889,definition,
( sQ410_spl
<=> sK6_skl(sK49_skl,sK49_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ410_spl])],[split_symbol_definition]) ).
fof(f3890,plain,
( ~ sQ410_spl
| sK6_skl(sK49_skl,sK49_skl) = sK49_skl ),
inference(component_clause,[status(thm)],[f3889]) ).
fof(f3911,plain,
( ~ sQ410_spl
| ~ sQ299_spl
| nil = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f2881,f3890]) ).
fof(f3912,plain,
( ~ sQ410_spl
| ~ sQ299_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3911,f448]) ).
fof(f3913,plain,
( ~ sQ410_spl
| ~ sQ299_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f3912]) ).
fof(f3914,plain,
( ~ sQ407_spl
| ~ sQ167_spl
| nil = app(tl(sK49_skl),sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1776,f3874]) ).
fof(f3915,plain,
( ~ sQ407_spl
| ~ sQ167_spl
| nil = app(nil,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1776,f3914]) ).
fof(f3917,plain,
( ~ sQ406_spl
| sK54_skl = sK49_skl
| ~ segmentP(sK54_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f3869,f317]) ).
fof(f3918,plain,
! [X0] :
( ~ sQ406_spl
| segmentP(X0,sK54_skl)
| ~ segmentP(X0,sK49_skl)
| ~ ssList(sK54_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3869,f315]) ).
fof(f3919,definition,
( sQ414_spl
<=> segmentP(sK54_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ414_spl])],[split_symbol_definition]) ).
fof(f3921,plain,
( sQ414_spl
| ~ segmentP(sK54_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f3919]) ).
fof(f3922,plain,
( ~ sQ406_spl
| sQ264_spl
| ~ sQ414_spl
| ~ sQ16_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3917,f530,f554,f3919,f2565,f3868]) ).
fof(f3923,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(f3926,plain,
( ~ sQ406_spl
| ~ sQ11_spl
| ~ sQ16_spl
| sQ415_spl ),
inference(split_clause,[status(thm)],[f3918,f3923,f554,f530,f3868]) ).
fof(f3927,plain,
! [X0] :
( sQ414_spl
| ~ segmentP(X0,sK49_skl)
| ~ segmentP(sK54_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f3921,f315]) ).
fof(f3928,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(f3931,plain,
( sQ414_spl
| ~ sQ16_spl
| sQ416_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3927,f530,f3928,f554,f3919]) ).
fof(f3959,plain,
( ~ sQ293_spl
| ~ sQ407_spl
| ~ sQ167_spl
| sK49_skl = nil ),
inference(backward_demodulation,[status(thm)],[f3915,f2830]) ).
fof(f3982,plain,
( ~ sQ293_spl
| ~ sQ407_spl
| ~ sQ167_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f3959,f446,f1775,f3873,f2829]) ).
fof(f3986,definition,
( sQ422_spl
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ422_spl])],[split_symbol_definition]) ).
fof(f3987,plain,
( ~ sQ422_spl
| frontsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f3986]) ).
fof(f4012,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(f4014,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(f4015,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(f4016,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)],[f4012]) ).
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) ),
inference(forward_subsumption_resolution,[status(thm)],[f4016,f245]) ).
fof(f4020,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(f4021,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)],[f4020]) ).
fof(f4023,plain,
( sQ423_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4014,f551,f4020]) ).
fof(f4024,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(f4027,plain,
( sQ424_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4015,f551,f4024]) ).
fof(f4028,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)],[f4021]) ).
fof(f4031,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(f4038,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(f4041,plain,
( ~ sQ15_spl
| sQ425_spl ),
inference(split_clause,[status(thm)],[f4031,f4038,f551]) ).
fof(f4089,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)],[f3817,f301]) ).
fof(f4090,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(f4093,plain,
( sQ401_spl
| ~ sQ370_spl
| sQ426_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4089,f554,f4090,f3624,f3815]) ).
fof(f4100,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ126_spl
| sK54_skl = sK54_skl
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f1448,f1269]) ).
fof(f4103,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ126_spl
| sQ179_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4100,f530,f1892,f1447,f1225,f439,f491]) ).
fof(f4112,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)],[f1443,f225]) ).
fof(f4113,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)],[f1443,f376]) ).
fof(f4114,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)],[f1443,f378]) ).
fof(f4116,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)],[f1443,f385]) ).
fof(f4120,plain,
( ~ sQ125_spl
| ~ sQ124_spl
| sQ156_spl ),
inference(split_clause,[status(thm)],[f4112,f1685,f1439,f1442]) ).
fof(f4121,plain,
( ~ sQ125_spl
| ~ sQ16_spl
| ~ sQ154_spl
| sQ153_spl ),
inference(split_clause,[status(thm)],[f4113,f1672,f1675,f554,f1442]) ).
fof(f4122,plain,
( ~ sQ125_spl
| ~ sQ154_spl
| ~ sQ16_spl
| sQ155_spl ),
inference(split_clause,[status(thm)],[f4114,f1679,f554,f1675,f1442]) ).
fof(f4124,plain,
( ~ sQ125_spl
| sQ2_spl
| ~ sQ16_spl
| ~ sQ154_spl
| ~ sQ157_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4116,f551,f1689,f1675,f554,f446,f1442]) ).
fof(f4138,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(f4139,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(f4140,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(f4143,plain,
( sQ429_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4138,f551,f4140]) ).
fof(f4144,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(f4147,plain,
( sQ430_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4139,f551,f4144]) ).
fof(f4149,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)],[f1626,f272]) ).
fof(f4150,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)],[f1626,f271]) ).
fof(f4151,plain,
( ~ sQ149_spl
| ~ sQ16_spl
| ~ sQ154_spl
| sQ306_spl ),
inference(split_clause,[status(thm)],[f4149,f2939,f1675,f554,f1625]) ).
fof(f4152,plain,
( ~ sQ149_spl
| ~ sQ16_spl
| ~ sQ154_spl
| sQ307_spl ),
inference(split_clause,[status(thm)],[f4150,f2943,f1675,f554,f1625]) ).
fof(f4189,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)],[f1324,f459]) ).
fof(f4190,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)],[f1324,f459]) ).
fof(f4191,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(f4194,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ437_spl ),
inference(split_clause,[status(thm)],[f4189,f4191,f485,f551,f1225,f816]) ).
fof(f4195,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(f4198,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ438_spl ),
inference(split_clause,[status(thm)],[f4190,f4195,f485,f551,f1225,f816]) ).
fof(f4201,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)],[f1324,f458]) ).
fof(f4202,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)],[f1324,f458]) ).
fof(f4203,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(f4206,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ439_spl ),
inference(split_clause,[status(thm)],[f4201,f4203,f485,f551,f1225,f816]) ).
fof(f4207,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(f4210,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ440_spl ),
inference(split_clause,[status(thm)],[f4202,f4207,f485,f551,f1225,f816]) ).
fof(f4213,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)],[f1324,f457]) ).
fof(f4214,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)],[f1324,f457]) ).
fof(f4215,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(f4218,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ441_spl ),
inference(split_clause,[status(thm)],[f4213,f4215,f485,f551,f1225,f816]) ).
fof(f4219,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(f4222,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ3_spl
| sQ442_spl ),
inference(split_clause,[status(thm)],[f4214,f4219,f485,f551,f1225,f816]) ).
fof(f4242,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)],[f1644,f235]) ).
fof(f4244,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)],[f1324,f4242]) ).
fof(f4246,definition,
( sQ446_spl
<=> ssList(sK43_skl(cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ446_spl])],[split_symbol_definition]) ).
fof(f4248,plain,
( sQ446_spl
| ~ ssList(sK43_skl(cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f4246]) ).
fof(f4249,definition,
( sQ447_spl
<=> ssItem(sK44_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ447_spl])],[split_symbol_definition]) ).
fof(f4251,plain,
( sQ447_spl
| ~ ssItem(sK44_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f4249]) ).
fof(f4252,definition,
( sQ448_spl
<=> nil = sK43_skl(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f4253,plain,
( ~ sQ448_spl
| nil = sK43_skl(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f4252]) ).
fof(f4255,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sQ448_spl
| ~ sQ3_spl
| ~ sQ447_spl
| ~ sQ15_spl
| ~ sQ446_spl ),
inference(split_clause,[status(thm)],[f4244,f4246,f551,f4249,f485,f4252,f1225,f816]) ).
fof(f4256,plain,
( ~ sQ448_spl
| ~ sQ51_spl
| ~ sQ109_spl
| nil = sK43_skl(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1324,f4253]) ).
fof(f4257,plain,
( sQ446_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ ssList(sK43_skl(sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f1324,f4248]) ).
fof(f4258,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)],[f1645,f235]) ).
fof(f4260,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)],[f1324,f4258]) ).
fof(f4262,definition,
( sQ449_spl
<=> sK44_skl(cons(sK51_skl,nil)) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ449_spl])],[split_symbol_definition]) ).
fof(f4263,plain,
( ~ sQ449_spl
| sK44_skl(cons(sK51_skl,nil)) = sK51_skl ),
inference(component_clause,[status(thm)],[f4262]) ).
fof(f4265,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sQ449_spl
| ~ sQ3_spl
| ~ sQ447_spl
| ~ sQ15_spl
| ~ sQ446_spl ),
inference(split_clause,[status(thm)],[f4260,f4246,f551,f4249,f485,f4262,f1225,f816]) ).
fof(f4266,plain,
( ~ sQ449_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sK44_skl(sK49_skl) = sK51_skl ),
inference(forward_demodulation,[status(thm)],[f1324,f4263]) ).
fof(f4267,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)],[f4256,f233]) ).
fof(f4269,definition,
( sQ450_spl
<=> cons(sK44_skl(sK49_skl),nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ450_spl])],[split_symbol_definition]) ).
fof(f4272,plain,
( ~ sQ448_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sQ450_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4267,f554,f446,f4269,f1225,f816,f4252]) ).
fof(f4275,plain,
( sQ447_spl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f4251,f232]) ).
fof(f4276,plain,
( sQ447_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4275,f554,f446,f4249]) ).
fof(f4277,plain,
( sQ446_spl
| ~ sQ51_spl
| ~ sQ109_spl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f4257,f231]) ).
fof(f4278,plain,
( sQ446_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4277,f554,f446,f1225,f816,f4246]) ).
fof(f4281,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)],[f4266,f233]) ).
fof(f4283,definition,
( sQ451_spl
<=> cons(sK51_skl,sK43_skl(sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ451_spl])],[split_symbol_definition]) ).
fof(f4286,plain,
( ~ sQ449_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sQ451_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4281,f554,f446,f4283,f1225,f816,f4262]) ).
fof(f4288,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)],[f456,f317]) ).
fof(f4289,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)],[f456,f315]) ).
fof(f4291,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)],[f2830,f456]) ).
fof(f4292,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)],[f1269,f456]) ).
fof(f4293,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)],[f4288]) ).
fof(f4294,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)],[f4289]) ).
fof(f4295,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(f4297,plain,
( sQ452_spl
| ~ ssList(app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl)) ),
inference(component_clause,[status(thm)],[f4295]) ).
fof(f4299,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(f4302,plain,
( ~ sQ293_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ453_spl ),
inference(split_clause,[status(thm)],[f4291,f4299,f554,f551,f2829]) ).
fof(f4303,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(f4306,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| ~ sQ11_spl
| sQ454_spl ),
inference(split_clause,[status(thm)],[f4292,f4303,f530,f1439,f1225,f439,f491]) ).
fof(f4309,plain,
( sQ452_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ ssList(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1269,f4297]) ).
fof(f4310,plain,
( sQ452_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4309,f421]) ).
fof(f4311,plain,
( sQ452_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl ),
inference(contradiction_clause,[status(thm)],[f4310]) ).
fof(f4328,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)],[f1863,f270]) ).
fof(f4329,plain,
( ~ sQ178_spl
| ~ sQ16_spl
| ~ sQ154_spl
| sQ229_spl ),
inference(split_clause,[status(thm)],[f4328,f2270,f1675,f554,f1862]) ).
fof(f4343,plain,
! [X0] :
( ~ sQ373_spl
| ~ memberP(sK49_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f3689,f272]) ).
fof(f4345,definition,
! [X0] :
( sQ455_spl
<=> ( ~ memberP(sK49_skl,X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ455_spl])],[split_symbol_definition]) ).
fof(f4346,plain,
! [X0] :
( ~ sQ455_spl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f4345]) ).
fof(f4348,plain,
( ~ sQ373_spl
| ~ sQ16_spl
| sQ455_spl ),
inference(split_clause,[status(thm)],[f4343,f4345,f554,f3638]) ).
fof(f4350,plain,
! [X0] :
( ~ sQ455_spl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f4346]) ).
fof(f4353,plain,
( ~ sQ108_spl
| ~ sQ455_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f4350,f1221]) ).
fof(f4354,plain,
( ~ sQ108_spl
| ~ sQ455_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f4353,f485,f4345,f1220]) ).
fof(f4377,plain,
( sQ401_spl
| ~ sQ398_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f3798,f3817]) ).
fof(f4382,plain,
( sQ401_spl
| ~ sQ398_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4377,f421]) ).
fof(f4383,plain,
( sQ401_spl
| ~ sQ398_spl ),
inference(contradiction_clause,[status(thm)],[f4382]) ).
fof(f4490,definition,
( sQ468_spl
<=> ssList(app(sK49_skl,sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ468_spl])],[split_symbol_definition]) ).
fof(f4492,plain,
( sQ468_spl
| ~ ssList(app(sK49_skl,sK54_skl)) ),
inference(component_clause,[status(thm)],[f4490]) ).
fof(f4555,definition,
( sQ483_spl
<=> nil = app(sK49_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ483_spl])],[split_symbol_definition]) ).
fof(f4556,plain,
( ~ sQ483_spl
| nil = app(sK49_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f4555]) ).
fof(f4719,definition,
( sQ507_spl
<=> ssList(sK6_skl(sK54_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ507_spl])],[split_symbol_definition]) ).
fof(f4721,plain,
( sQ507_spl
| ~ ssList(sK6_skl(sK54_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f4719]) ).
fof(f4732,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,f1053]) ).
fof(f4735,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(f4738,plain,
( ~ sQ88_spl
| sQ509_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f4732,f551,f4735,f1048]) ).
fof(f4742,plain,
( sQ468_spl
| ~ ssList(sK54_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f4492,f245]) ).
fof(f4743,plain,
( sQ468_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4742,f554,f530,f4490]) ).
fof(f4747,plain,
( ~ sQ483_spl
| nil = sK49_skl
| ~ ssList(sK54_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f4556,f386]) ).
fof(f4770,plain,
( ~ sQ483_spl
| sQ2_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4747,f554,f530,f446,f4555]) ).
fof(f4771,definition,
( sQ510_spl
<=> cons(sK51_skl,sK54_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ510_spl])],[split_symbol_definition]) ).
fof(f4772,plain,
( ~ sQ510_spl
| cons(sK51_skl,sK54_skl) = nil ),
inference(component_clause,[status(thm)],[f4771]) ).
fof(f4783,definition,
( sQ513_spl
<=> frontsegP(nil,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ513_spl])],[split_symbol_definition]) ).
fof(f4784,plain,
( ~ sQ513_spl
| frontsegP(nil,sK49_skl) ),
inference(component_clause,[status(thm)],[f4783]) ).
fof(f4785,plain,
( sQ513_spl
| ~ frontsegP(nil,sK49_skl) ),
inference(component_clause,[status(thm)],[f4783]) ).
fof(f4812,definition,
( sQ520_spl
<=> rearsegP(app(sK49_skl,sK54_skl),sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ520_spl])],[split_symbol_definition]) ).
fof(f4813,plain,
( ~ sQ520_spl
| rearsegP(app(sK49_skl,sK54_skl),sK54_skl) ),
inference(component_clause,[status(thm)],[f4812]) ).
fof(f4814,plain,
( sQ520_spl
| ~ rearsegP(app(sK49_skl,sK54_skl),sK54_skl) ),
inference(component_clause,[status(thm)],[f4812]) ).
fof(f4854,definition,
( sQ527_spl
<=> rearsegP(sK54_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ527_spl])],[split_symbol_definition]) ).
fof(f4855,plain,
( ~ sQ527_spl
| rearsegP(sK54_skl,nil) ),
inference(component_clause,[status(thm)],[f4854]) ).
fof(f4856,plain,
( sQ527_spl
| ~ rearsegP(sK54_skl,nil) ),
inference(component_clause,[status(thm)],[f4854]) ).
fof(f4863,plain,
( ~ sQ513_spl
| nil = sK49_skl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f4784,f298]) ).
fof(f4864,plain,
( ~ sQ513_spl
| sQ2_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f4863,f554,f446,f4783]) ).
fof(f5174,plain,
( sQ507_spl
| ~ rearsegP(sK49_skl,sK54_skl)
| ~ ssList(sK54_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f4721,f128]) ).
fof(f5175,plain,
( sQ507_spl
| ~ sQ59_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5174,f554,f530,f888,f4719]) ).
fof(f5212,definition,
( sQ585_spl
<=> app(sK49_skl,nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ585_spl])],[split_symbol_definition]) ).
fof(f5213,plain,
( ~ sQ585_spl
| app(sK49_skl,nil) = sK49_skl ),
inference(component_clause,[status(thm)],[f5212]) ).
fof(f5214,plain,
( sQ585_spl
| app(sK49_skl,nil) != sK49_skl ),
inference(component_clause,[status(thm)],[f5212]) ).
fof(f5273,plain,
( ~ sQ510_spl
| ~ sQ243_spl
| frontsegP(nil,sK49_skl)
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f4772,f2359]) ).
fof(f5307,plain,
( ~ sQ510_spl
| ~ sQ243_spl
| sQ513_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5273,f530,f4783,f2355,f4771]) ).
fof(f5332,definition,
( sQ596_spl
<=> ssList(sK43_skl(cons(sK51_skl,sK54_skl))) ),
introduced(definition,[new_symbols(definition,[sQ596_spl])],[split_symbol_definition]) ).
fof(f5334,plain,
( sQ596_spl
| ~ ssList(sK43_skl(cons(sK51_skl,sK54_skl))) ),
inference(component_clause,[status(thm)],[f5332]) ).
fof(f5335,definition,
( sQ597_spl
<=> sK44_skl(cons(sK51_skl,sK54_skl)) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ597_spl])],[split_symbol_definition]) ).
fof(f5336,plain,
( ~ sQ597_spl
| sK44_skl(cons(sK51_skl,sK54_skl)) = sK51_skl ),
inference(component_clause,[status(thm)],[f5335]) ).
fof(f5337,plain,
( sQ597_spl
| sK44_skl(cons(sK51_skl,sK54_skl)) != sK51_skl ),
inference(component_clause,[status(thm)],[f5335]) ).
fof(f5339,definition,
( sQ598_spl
<=> sK54_skl = sK43_skl(cons(sK51_skl,sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ598_spl])],[split_symbol_definition]) ).
fof(f5340,plain,
( ~ sQ598_spl
| sK54_skl = sK43_skl(cons(sK51_skl,sK54_skl)) ),
inference(component_clause,[status(thm)],[f5339]) ).
fof(f5493,plain,
( sQ77_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ ssList(nil)
| ~ ssList(app(app(sK53_skl,sK49_skl),sK49_skl)) ),
inference(resolution,[status(thm)],[f2227,f245]) ).
fof(f5494,plain,
( sQ77_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f5493,f1439,f551,f1225,f816,f990]) ).
fof(f5497,plain,
( sQ585_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f5214,f389]) ).
fof(f5498,plain,
( sQ585_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5497,f421]) ).
fof(f5499,plain,
sQ585_spl,
inference(contradiction_clause,[status(thm)],[f5498]) ).
fof(f5505,definition,
( sQ621_spl
<=> app(nil,sK54_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ621_spl])],[split_symbol_definition]) ).
fof(f5506,plain,
( ~ sQ621_spl
| app(nil,sK54_skl) = nil ),
inference(component_clause,[status(thm)],[f5505]) ).
fof(f5507,plain,
( sQ621_spl
| app(nil,sK54_skl) != nil ),
inference(component_clause,[status(thm)],[f5505]) ).
fof(f5835,plain,
( ~ sQ585_spl
| ~ sQ54_spl
| ~ sQ109_spl
| cons(sK51_skl,nil) = sK49_skl
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5213,f1229]) ).
fof(f5837,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)],[f5213,f456]) ).
fof(f5838,plain,
( ~ sQ585_spl
| ~ ssList(nil)
| frontsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f5213,f3834]) ).
fof(f5839,plain,
( ~ sQ585_spl
| tl(sK49_skl) = app(tl(sK49_skl),nil)
| nil = sK49_skl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f5213,f393]) ).
fof(f5840,plain,
( ~ sQ585_spl
| hd(sK49_skl) = hd(sK49_skl)
| nil = sK49_skl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f5213,f391]) ).
fof(f5843,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)],[f5213,f321]) ).
fof(f5845,plain,
! [X0] :
( ~ sQ585_spl
| rearsegP(sK49_skl,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5213,f307]) ).
fof(f5846,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)],[f5213,f2019]) ).
fof(f5848,plain,
! [X0] :
( ~ sQ585_spl
| X0 = sK49_skl
| app(X0,nil) != sK49_skl
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f5213,f376]) ).
fof(f5850,plain,
! [X0] :
( ~ sQ585_spl
| X0 = nil
| app(sK49_skl,X0) != sK49_skl
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5213,f378]) ).
fof(f5852,plain,
( ~ sQ585_spl
| ~ ssList(sK49_skl)
| rearsegP(sK49_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5213,f626]) ).
fof(f5853,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)],[f5213,f382]) ).
fof(f5856,plain,
( ~ sQ585_spl
| ~ sQ54_spl
| ~ sQ109_spl
| sQ147_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f5835,f551,f1597,f1225,f851,f5212]) ).
fof(f5858,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(f5861,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ674_spl ),
inference(split_clause,[status(thm)],[f5837,f5858,f551,f554,f5212]) ).
fof(f5862,plain,
( ~ sQ585_spl
| ~ sQ15_spl
| sQ354_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5838,f554,f3374,f551,f5212]) ).
fof(f5863,definition,
( sQ675_spl
<=> tl(sK49_skl) = app(tl(sK49_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ675_spl])],[split_symbol_definition]) ).
fof(f5864,plain,
( ~ sQ675_spl
| tl(sK49_skl) = app(tl(sK49_skl),nil) ),
inference(component_clause,[status(thm)],[f5863]) ).
fof(f5866,plain,
( ~ sQ585_spl
| sQ675_spl
| sQ2_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5839,f554,f551,f446,f5863,f5212]) ).
fof(f5867,plain,
( ~ sQ585_spl
| sQ408_spl
| sQ2_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5840,f554,f551,f446,f3877,f5212]) ).
fof(f5870,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(f5873,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| sQ676_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f5843,f551,f5870,f554,f5212]) ).
fof(f5875,definition,
! [X0] :
( sQ677_spl
<=> ( rearsegP(sK49_skl,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ677_spl])],[split_symbol_definition]) ).
fof(f5878,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| sQ677_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f5845,f551,f5875,f554,f5212]) ).
fof(f5879,definition,
( sQ678_spl
<=> sK6_skl(nil,sK49_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ678_spl])],[split_symbol_definition]) ).
fof(f5882,definition,
( sQ679_spl
<=> rearsegP(app(sK49_skl,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ679_spl])],[split_symbol_definition]) ).
fof(f5884,plain,
( sQ679_spl
| ~ rearsegP(app(sK49_skl,nil),nil) ),
inference(component_clause,[status(thm)],[f5882]) ).
fof(f5885,plain,
( ~ sQ585_spl
| ~ sQ679_spl
| sQ678_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5846,f554,f551,f5879,f5882,f5212]) ).
fof(f5887,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(f5890,plain,
( ~ sQ585_spl
| sQ680_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f5848,f554,f551,f5887,f5212]) ).
fof(f5892,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(f5895,plain,
( ~ sQ585_spl
| sQ681_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f5850,f551,f554,f5892,f5212]) ).
fof(f5897,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| sQ80_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f5852,f551,f1003,f554,f5212]) ).
fof(f5898,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(f5901,plain,
( ~ sQ585_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ682_spl ),
inference(split_clause,[status(thm)],[f5853,f5898,f554,f551,f5212]) ).
fof(f5905,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| nil = app(tl(sK49_skl),nil) ),
inference(forward_demodulation,[status(thm)],[f1776,f5864]) ).
fof(f5906,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| nil = app(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f1776,f5905]) ).
fof(f5907,plain,
( sQ679_spl
| ~ sQ585_spl
| ~ rearsegP(sK49_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f5213,f5884]) ).
fof(f5908,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)],[f2264,f3834]) ).
fof(f5910,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)],[f2264,f286]) ).
fof(f5911,definition,
( sQ683_spl
<=> frontsegP(sK49_skl,app(sK53_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ683_spl])],[split_symbol_definition]) ).
fof(f5912,plain,
( ~ sQ683_spl
| frontsegP(sK49_skl,app(sK53_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f5911]) ).
fof(f5914,plain,
( ~ sQ228_spl
| ~ sQ16_spl
| sQ683_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f5908,f1675,f5911,f554,f2263]) ).
fof(f5916,plain,
( ~ sQ228_spl
| sQ405_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f5910,f1439,f3841,f2263]) ).
fof(f5917,plain,
( sQ679_spl
| ~ sQ585_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f5907,f309]) ).
fof(f5919,plain,
( sQ679_spl
| ~ sQ585_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5917,f421]) ).
fof(f5920,plain,
( sQ679_spl
| ~ sQ585_spl ),
inference(contradiction_clause,[status(thm)],[f5919]) ).
fof(f6199,plain,
( ~ sQ621_spl
| nil = sK54_skl
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f5506,f249]) ).
fof(f6222,plain,
( ~ sQ621_spl
| sQ72_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6199,f530,f943,f5505]) ).
fof(f6241,definition,
( sQ733_spl
<=> rearsegP(app(nil,sK54_skl),sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ733_spl])],[split_symbol_definition]) ).
fof(f6243,plain,
( sQ733_spl
| ~ rearsegP(app(nil,sK54_skl),sK54_skl) ),
inference(component_clause,[status(thm)],[f6241]) ).
fof(f6276,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)],[f2260,f3205]) ).
fof(f6278,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)],[f5213,f2260]) ).
fof(f6279,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)],[f2830,f2260]) ).
fof(f6280,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)],[f1269,f2260]) ).
fof(f6282,definition,
( sQ739_spl
<=> frontsegP(app(sK53_skl,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ739_spl])],[split_symbol_definition]) ).
fof(f6284,plain,
( sQ739_spl
| ~ frontsegP(app(sK53_skl,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f6282]) ).
fof(f6285,definition,
( sQ740_spl
<=> sK49_skl = app(app(sK53_skl,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ740_spl])],[split_symbol_definition]) ).
fof(f6286,plain,
( ~ sQ740_spl
| sK49_skl = app(app(sK53_skl,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f6285]) ).
fof(f6288,plain,
( ~ sQ10_spl
| ~ sQ51_spl
| ~ sQ109_spl
| sQ740_spl
| ~ sQ739_spl
| ~ sQ16_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f6276,f1675,f554,f6282,f6285,f1225,f816,f527]) ).
fof(f6289,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(f6292,plain,
( ~ sQ585_spl
| ~ sQ15_spl
| sQ741_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f6278,f554,f6289,f551,f5212]) ).
fof(f6293,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(f6296,plain,
( ~ sQ293_spl
| ~ sQ16_spl
| sQ742_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6279,f551,f6293,f554,f2829]) ).
fof(f6297,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(f6300,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ11_spl
| sQ743_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f6280,f1439,f6297,f530,f1225,f439,f491]) ).
fof(f6304,plain,
( ~ sQ740_spl
| sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6286,f3087]) ).
fof(f6305,plain,
( ~ sQ740_spl
| sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl ),
inference(contradiction_clause,[status(thm)],[f6304]) ).
fof(f6307,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)],[f2262,f3205]) ).
fof(f6311,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)],[f1269,f2262]) ).
fof(f6313,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(f6316,plain,
( ~ sQ10_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ16_spl
| sQ744_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f6307,f1675,f6313,f554,f1225,f816,f527]) ).
fof(f6319,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(f6323,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(f6327,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(f6330,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ11_spl
| sQ747_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f6311,f1439,f6327,f530,f1225,f439,f491]) ).
fof(f6355,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,f2264]) ).
fof(f6358,plain,
! [X0] :
( ~ sQ585_spl
| frontsegP(sK49_skl,X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f5213,f288]) ).
fof(f6359,plain,
! [X0] :
( ~ sQ293_spl
| frontsegP(sK49_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2830,f288]) ).
fof(f6361,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(f6364,plain,
( ~ sQ228_spl
| ~ sQ16_spl
| sQ748_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f6355,f1675,f6361,f554,f2263]) ).
fof(f6367,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(f6370,plain,
( ~ sQ585_spl
| ~ sQ15_spl
| sQ749_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f6358,f554,f6367,f551,f5212]) ).
fof(f6371,definition,
! [X0] :
( sQ750_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ750_spl])],[split_symbol_definition]) ).
fof(f6374,plain,
( ~ sQ293_spl
| ~ sQ16_spl
| sQ750_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6359,f551,f6371,f554,f2829]) ).
fof(f6387,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5906,f288]) ).
fof(f6388,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)],[f5906,f2262]) ).
fof(f6389,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)],[f5906,f2260]) ).
fof(f6390,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)],[f5906,f456]) ).
fof(f6391,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ ssList(nil)
| frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5906,f3834]) ).
fof(f6394,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| ~ memberP(nil,X0)
| memberP(nil,X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f5906,f272]) ).
fof(f6396,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)],[f5906,f321]) ).
fof(f6397,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)],[f5906,f270]) ).
fof(f6398,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| rearsegP(nil,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5906,f307]) ).
fof(f6399,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ rearsegP(app(nil,nil),nil)
| sK6_skl(nil,nil) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5906,f2019]) ).
fof(f6401,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| X0 = nil
| app(X0,nil) != nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5906,f376]) ).
fof(f6403,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| X0 = nil
| app(nil,X0) != nil
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5906,f378]) ).
fof(f6405,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ ssList(nil)
| rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5906,f626]) ).
fof(f6406,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| app(app(X0,nil),nil) = app(X0,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f5906,f382]) ).
fof(f6407,plain,
! [X0] :
( ~ sQ675_spl
| ~ sQ167_spl
| app(nil,X0) = app(nil,app(nil,X0))
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5906,f382]) ).
fof(f6414,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ278_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6387,f551,f2698,f1775,f5863]) ).
fof(f6415,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(f6418,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ752_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6388,f551,f6415,f1775,f5863]) ).
fof(f6419,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(f6422,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ753_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6389,f551,f6419,f1775,f5863]) ).
fof(f6423,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(f6426,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ15_spl
| sQ754_spl ),
inference(split_clause,[status(thm)],[f6390,f6423,f551,f1775,f5863]) ).
fof(f6427,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ422_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6391,f551,f3986,f1775,f5863]) ).
fof(f6433,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ15_spl
| sQ369_spl ),
inference(split_clause,[status(thm)],[f6394,f3540,f551,f1775,f5863]) ).
fof(f6435,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(f6438,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ756_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6396,f551,f6435,f1775,f5863]) ).
fof(f6439,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(f6442,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ15_spl
| sQ757_spl ),
inference(split_clause,[status(thm)],[f6397,f6439,f551,f1775,f5863]) ).
fof(f6443,definition,
! [X0] :
( sQ758_spl
<=> ( rearsegP(nil,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ758_spl])],[split_symbol_definition]) ).
fof(f6446,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ758_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6398,f551,f6443,f1775,f5863]) ).
fof(f6447,definition,
( sQ759_spl
<=> sK6_skl(nil,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ759_spl])],[split_symbol_definition]) ).
fof(f6448,plain,
( ~ sQ759_spl
| sK6_skl(nil,nil) = nil ),
inference(component_clause,[status(thm)],[f6447]) ).
fof(f6450,definition,
( sQ760_spl
<=> rearsegP(app(nil,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ760_spl])],[split_symbol_definition]) ).
fof(f6452,plain,
( sQ760_spl
| ~ rearsegP(app(nil,nil),nil) ),
inference(component_clause,[status(thm)],[f6450]) ).
fof(f6453,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ760_spl
| sQ759_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6399,f551,f6447,f6450,f1775,f5863]) ).
fof(f6455,definition,
! [X0] :
( sQ761_spl
<=> ( X0 = nil
| app(X0,nil) != nil
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ761_spl])],[split_symbol_definition]) ).
fof(f6458,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ761_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6401,f551,f6455,f1775,f5863]) ).
fof(f6460,definition,
! [X0] :
( sQ762_spl
<=> ( X0 = nil
| app(nil,X0) != nil
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ762_spl])],[split_symbol_definition]) ).
fof(f6463,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ762_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6403,f551,f6460,f1775,f5863]) ).
fof(f6465,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ117_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6405,f551,f1368,f1775,f5863]) ).
fof(f6466,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(f6469,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ15_spl
| sQ763_spl ),
inference(split_clause,[status(thm)],[f6406,f6466,f551,f1775,f5863]) ).
fof(f6470,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(f6473,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ764_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6407,f551,f6470,f1775,f5863]) ).
fof(f6479,plain,
( sQ760_spl
| ~ sQ675_spl
| ~ sQ167_spl
| ~ rearsegP(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f5906,f6452]) ).
fof(f6480,plain,
( sQ760_spl
| ~ sQ675_spl
| ~ sQ167_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f6479,f309]) ).
fof(f6483,plain,
( sQ760_spl
| ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6480,f551,f1775,f5863,f6450]) ).
fof(f6500,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)],[f2306,f222]) ).
fof(f6503,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)],[f6500,f295]) ).
fof(f6505,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)],[f1324,f6500]) ).
fof(f6508,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(f6511,plain,
( ~ sQ15_spl
| sQ766_spl ),
inference(split_clause,[status(thm)],[f6503,f6508,f551]) ).
fof(f6513,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(f6516,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| sQ767_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6505,f485,f6513,f551,f1225,f816]) ).
fof(f6518,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)],[f2319,f222]) ).
fof(f6519,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)],[f6518,f2359]) ).
fof(f6521,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)],[f6518,f295]) ).
fof(f6523,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)],[f1324,f6518]) ).
fof(f6524,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(f6527,plain,
( ~ sQ243_spl
| ~ sQ16_spl
| sQ768_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6519,f485,f6524,f554,f2355]) ).
fof(f6530,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(f6533,plain,
( ~ sQ15_spl
| sQ769_spl ),
inference(split_clause,[status(thm)],[f6521,f6530,f551]) ).
fof(f6535,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(f6538,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| sQ770_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6523,f485,f6535,f551,f1225,f816]) ).
fof(f6562,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,f2359]) ).
fof(f6573,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(f6576,plain,
( ~ sQ243_spl
| sQ771_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f6562,f554,f6573,f2355]) ).
fof(f6588,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,f2359]) ).
fof(f6590,plain,
! [X0] :
( ~ sQ404_spl
| frontsegP(X0,nil)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(nil)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f3838]) ).
fof(f6591,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,f3375]) ).
fof(f6592,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,f3205]) ).
fof(f6596,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,f2264]) ).
fof(f6602,plain,
! [X0] :
( sQ513_spl
| ~ frontsegP(X0,sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f282,f4785]) ).
fof(f6608,definition,
! [X0] :
( sQ773_spl
<=> ( frontsegP(X0,nil)
| ~ frontsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ773_spl])],[split_symbol_definition]) ).
fof(f6615,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(f6618,plain,
( ~ sQ243_spl
| ~ sQ16_spl
| sQ774_spl ),
inference(split_clause,[status(thm)],[f6588,f6615,f554,f2355]) ).
fof(f6620,definition,
! [X0] :
( sQ775_spl
<=> ( frontsegP(X0,nil)
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ775_spl])],[split_symbol_definition]) ).
fof(f6623,plain,
( ~ sQ404_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ775_spl ),
inference(split_clause,[status(thm)],[f6590,f6620,f554,f551,f3837]) ).
fof(f6624,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(f6627,plain,
( ~ sQ354_spl
| ~ sQ16_spl
| sQ776_spl ),
inference(split_clause,[status(thm)],[f6591,f6624,f554,f3374]) ).
fof(f6628,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(f6631,plain,
( ~ sQ10_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ124_spl
| ~ sQ16_spl
| sQ777_spl ),
inference(split_clause,[status(thm)],[f6592,f6628,f554,f1439,f1225,f816,f527]) ).
fof(f6634,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(f6637,plain,
( ~ sQ228_spl
| sQ778_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f6596,f1439,f6634,f2263]) ).
fof(f6646,definition,
! [X0] :
( sQ780_spl
<=> ( ~ frontsegP(X0,sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ780_spl])],[split_symbol_definition]) ).
fof(f6649,plain,
( sQ513_spl
| ~ sQ16_spl
| sQ780_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f6602,f551,f6646,f554,f4783]) ).
fof(f6698,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)],[f2585,f301]) ).
fof(f6701,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(f6704,plain,
( ~ sQ266_spl
| ~ sQ11_spl
| sQ781_spl ),
inference(split_clause,[status(thm)],[f6698,f6701,f530,f2584]) ).
fof(f6733,definition,
( sQ784_spl
<=> app(nil,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ784_spl])],[split_symbol_definition]) ).
fof(f6737,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)],[f2349,f222]) ).
fof(f6741,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)],[f1324,f6737]) ).
fof(f6742,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)],[f1324,f6737]) ).
fof(f6745,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(f6748,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| sQ785_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6741,f485,f6745,f551,f1225,f816]) ).
fof(f6749,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(f6752,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sQ786_spl
| ~ sQ15_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6742,f485,f551,f6749,f1225,f816]) ).
fof(f6757,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)],[f2350,f222]) ).
fof(f6758,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)],[f6757,f2264]) ).
fof(f6764,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)],[f6757,f298]) ).
fof(f6767,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)],[f1324,f6757]) ).
fof(f6768,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(f6771,plain,
( ~ sQ228_spl
| ~ sQ124_spl
| sQ787_spl ),
inference(split_clause,[status(thm)],[f6758,f6768,f1439,f2263]) ).
fof(f6779,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(f6782,plain,
( ~ sQ15_spl
| sQ788_spl ),
inference(split_clause,[status(thm)],[f6764,f6779,f551]) ).
fof(f6787,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(f6790,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ15_spl
| sQ789_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f6767,f485,f6787,f551,f1225,f816]) ).
fof(f6948,plain,
( sQ520_spl
| ~ ssList(sK49_skl)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f4814,f626]) ).
fof(f6950,definition,
( sQ807_spl
<=> rearsegP(sK54_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ807_spl])],[split_symbol_definition]) ).
fof(f6951,plain,
( ~ sQ807_spl
| rearsegP(sK54_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f6950]) ).
fof(f6952,plain,
( sQ807_spl
| ~ rearsegP(sK54_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f6950]) ).
fof(f6954,plain,
( sQ520_spl
| ~ sQ16_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6948,f530,f554,f4812]) ).
fof(f6960,plain,
( sQ807_spl
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f6952,f305]) ).
fof(f6965,plain,
( sQ807_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f6960,f530,f6950]) ).
fof(f6968,plain,
! [X0] :
( ~ sQ585_spl
| ~ sQ290_spl
| segmentP(sK49_skl,X0)
| ~ segmentP(sK54_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f5213,f2797]) ).
fof(f6971,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(f6974,plain,
( ~ sQ585_spl
| ~ sQ290_spl
| ~ sQ15_spl
| sQ810_spl ),
inference(split_clause,[status(thm)],[f6968,f6971,f551,f2796,f5212]) ).
fof(f6977,plain,
! [X0] :
( ~ sQ807_spl
| rearsegP(X0,sK54_skl)
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(sK54_skl)
| ~ ssList(sK54_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f6951,f301]) ).
fof(f6980,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(f6983,plain,
( ~ sQ807_spl
| ~ sQ11_spl
| sQ811_spl ),
inference(split_clause,[status(thm)],[f6977,f6980,f530,f6950]) ).
fof(f7006,plain,
( sQ596_spl
| nil = cons(sK51_skl,sK54_skl)
| ~ ssList(cons(sK51_skl,sK54_skl)) ),
inference(resolution,[status(thm)],[f5334,f231]) ).
fof(f7007,definition,
( sQ812_spl
<=> ssList(cons(sK51_skl,sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ812_spl])],[split_symbol_definition]) ).
fof(f7009,plain,
( sQ812_spl
| ~ ssList(cons(sK51_skl,sK54_skl)) ),
inference(component_clause,[status(thm)],[f7007]) ).
fof(f7010,plain,
( sQ596_spl
| sQ510_spl
| ~ sQ812_spl ),
inference(split_clause,[status(thm)],[f7006,f7007,f4771,f5332]) ).
fof(f7011,plain,
( sQ812_spl
| ~ ssItem(sK51_skl)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f7009,f222]) ).
fof(f7012,plain,
( sQ812_spl
| ~ sQ3_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7011,f530,f485,f7007]) ).
fof(f7013,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)],[f5340,f233]) ).
fof(f7015,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(f7018,plain,
( ~ sQ598_spl
| sQ813_spl
| sQ510_spl
| ~ sQ812_spl ),
inference(split_clause,[status(thm)],[f7013,f7007,f4771,f7015,f5339]) ).
fof(f7021,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)],[f5336,f4242]) ).
fof(f7023,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)],[f5336,f233]) ).
fof(f7025,plain,
( ~ sQ597_spl
| sQ598_spl
| ~ sQ3_spl
| ~ sQ11_spl
| ~ sQ596_spl ),
inference(split_clause,[status(thm)],[f7021,f5332,f530,f485,f5339,f5335]) ).
fof(f7027,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(f7030,plain,
( ~ sQ597_spl
| sQ814_spl
| sQ510_spl
| ~ sQ812_spl ),
inference(split_clause,[status(thm)],[f7023,f7007,f4771,f7027,f5335]) ).
fof(f7087,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)],[f5912,f2262]) ).
fof(f7088,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)],[f5912,f2260]) ).
fof(f7089,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)],[f5912,f282]) ).
fof(f7091,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(f7094,plain,
( ~ sQ683_spl
| ~ sQ16_spl
| sQ815_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f7087,f752,f7091,f554,f5911]) ).
fof(f7095,definition,
( sQ816_spl
<=> frontsegP(sK53_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ816_spl])],[split_symbol_definition]) ).
fof(f7098,definition,
( sQ817_spl
<=> sK49_skl = app(sK53_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ817_spl])],[split_symbol_definition]) ).
fof(f7099,plain,
( ~ sQ817_spl
| sK49_skl = app(sK53_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f7098]) ).
fof(f7101,plain,
( ~ sQ683_spl
| sQ817_spl
| ~ sQ816_spl
| ~ sQ16_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f7088,f752,f554,f7095,f7098,f5911]) ).
fof(f7102,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(f7105,plain,
( ~ sQ683_spl
| ~ sQ154_spl
| ~ sQ16_spl
| sQ818_spl ),
inference(split_clause,[status(thm)],[f7089,f7102,f554,f1675,f5911]) ).
fof(f7145,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)],[f7099,f2019]) ).
fof(f7179,definition,
( sQ825_spl
<=> hd(sK49_skl) = hd(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ825_spl])],[split_symbol_definition]) ).
fof(f7180,plain,
( ~ sQ825_spl
| hd(sK49_skl) = hd(sK53_skl) ),
inference(component_clause,[status(thm)],[f7179]) ).
fof(f7181,plain,
( sQ825_spl
| hd(sK49_skl) != hd(sK53_skl) ),
inference(component_clause,[status(thm)],[f7179]) ).
fof(f7194,definition,
( sQ828_spl
<=> sK6_skl(sK49_skl,sK49_skl) = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ828_spl])],[split_symbol_definition]) ).
fof(f7195,plain,
( ~ sQ828_spl
| sK6_skl(sK49_skl,sK49_skl) = sK53_skl ),
inference(component_clause,[status(thm)],[f7194]) ).
fof(f7197,definition,
( sQ829_spl
<=> rearsegP(app(sK53_skl,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ829_spl])],[split_symbol_definition]) ).
fof(f7199,plain,
( sQ829_spl
| ~ rearsegP(app(sK53_skl,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f7197]) ).
fof(f7200,plain,
( ~ sQ817_spl
| ~ sQ829_spl
| sQ828_spl
| ~ sQ16_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f7145,f752,f554,f7194,f7197,f7098]) ).
fof(f7219,plain,
( ~ sQ828_spl
| ~ sQ299_spl
| nil = sK53_skl ),
inference(forward_demodulation,[status(thm)],[f2881,f7195]) ).
fof(f7220,plain,
( ~ sQ828_spl
| ~ sQ299_spl
| sQ159_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7219,f1718]) ).
fof(f7221,plain,
( ~ sQ828_spl
| ~ sQ299_spl
| sQ159_spl ),
inference(contradiction_clause,[status(thm)],[f7220]) ).
fof(f7222,plain,
( ~ sQ825_spl
| ~ sQ152_spl
| sK51_skl = hd(sK53_skl) ),
inference(forward_demodulation,[status(thm)],[f1657,f7180]) ).
fof(f7226,plain,
( ~ sQ825_spl
| ~ sQ152_spl
| cons(sK51_skl,tl(sK53_skl)) = sK53_skl
| nil = sK53_skl
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f7222,f374]) ).
fof(f7228,definition,
( sQ833_spl
<=> cons(sK51_skl,tl(sK53_skl)) = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ833_spl])],[split_symbol_definition]) ).
fof(f7229,plain,
( ~ sQ833_spl
| cons(sK51_skl,tl(sK53_skl)) = sK53_skl ),
inference(component_clause,[status(thm)],[f7228]) ).
fof(f7231,plain,
( ~ sQ825_spl
| ~ sQ152_spl
| sQ833_spl
| sQ159_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f7226,f752,f1716,f7228,f1656,f7179]) ).
fof(f7232,plain,
( sQ825_spl
| ~ sQ152_spl
| sK51_skl != hd(sK53_skl) ),
inference(forward_demodulation,[status(thm)],[f1657,f7181]) ).
fof(f7437,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)],[f2239,f4785]) ).
fof(f7438,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)],[f2239,f298]) ).
fof(f7452,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)],[f2239,f2359]) ).
fof(f7455,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)],[f2239,f3838]) ).
fof(f7457,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)],[f2239,f3375]) ).
fof(f7460,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssList(nil)
| frontsegP(X0,nil)
| ~ frontsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2239,f295]) ).
fof(f7461,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)],[f2239,f295]) ).
fof(f7468,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)],[f2239,f3987]) ).
fof(f7471,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)],[f2239,f2359]) ).
fof(f7473,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)],[f2239,f3838]) ).
fof(f7474,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)],[f2239,f3375]) ).
fof(f7476,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)],[f2239,f295]) ).
fof(f7491,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(f7494,plain,
( sQ513_spl
| ~ sQ16_spl
| sQ855_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f7437,f551,f7491,f554,f4783]) ).
fof(f7495,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(f7498,plain,
( sQ856_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f7438,f551,f7495]) ).
fof(f7512,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(f7515,plain,
( ~ sQ243_spl
| ~ sQ16_spl
| sQ857_spl ),
inference(split_clause,[status(thm)],[f7452,f7512,f554,f2355]) ).
fof(f7517,plain,
( ~ sQ404_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ746_spl ),
inference(split_clause,[status(thm)],[f7455,f6323,f554,f551,f3837]) ).
fof(f7519,plain,
( ~ sQ354_spl
| ~ sQ16_spl
| sQ745_spl ),
inference(split_clause,[status(thm)],[f7457,f6319,f554,f3374]) ).
fof(f7522,plain,
( ~ sQ15_spl
| sQ773_spl ),
inference(split_clause,[status(thm)],[f7460,f6608,f551]) ).
fof(f7523,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(f7526,plain,
( ~ sQ15_spl
| sQ858_spl ),
inference(split_clause,[status(thm)],[f7461,f7523,f551]) ).
fof(f7530,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(f7533,plain,
( ~ sQ422_spl
| ~ sQ15_spl
| sQ859_spl ),
inference(split_clause,[status(thm)],[f7468,f7530,f551,f3986]) ).
fof(f7538,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(f7541,plain,
( ~ sQ243_spl
| ~ sQ16_spl
| sQ860_spl ),
inference(split_clause,[status(thm)],[f7471,f7538,f554,f2355]) ).
fof(f7543,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(f7546,plain,
( ~ sQ404_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ861_spl ),
inference(split_clause,[status(thm)],[f7473,f7543,f551,f554,f3837]) ).
fof(f7547,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(f7550,plain,
( ~ sQ354_spl
| ~ sQ16_spl
| sQ862_spl ),
inference(split_clause,[status(thm)],[f7474,f7547,f554,f3374]) ).
fof(f7553,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(f7556,plain,
( ~ sQ15_spl
| sQ863_spl ),
inference(split_clause,[status(thm)],[f7476,f7553,f551]) ).
fof(f7563,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)],[f3360,f391]) ).
fof(f7565,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)],[f3360,f374]) ).
fof(f7566,definition,
( sQ864_spl
<=> sK51_skl = hd(app(sK53_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ864_spl])],[split_symbol_definition]) ).
fof(f7567,plain,
( ~ sQ864_spl
| sK51_skl = hd(app(sK53_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f7566]) ).
fof(f7569,plain,
( ~ sQ351_spl
| ~ sQ152_spl
| sQ864_spl
| sQ158_spl
| ~ sQ16_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f7563,f1675,f554,f1693,f7566,f1656,f3356]) ).
fof(f7571,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(f7574,plain,
( ~ sQ351_spl
| ~ sQ152_spl
| sQ865_spl
| sQ128_spl
| ~ sQ124_spl ),
inference(split_clause,[status(thm)],[f7565,f1439,f1458,f7571,f1656,f3356]) ).
fof(f7579,plain,
( ~ sQ585_spl
| ~ ssList(sK49_skl)
| nil = app(sK49_skl,nil)
| ~ rearsegP(nil,sK49_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f5213,f2570]) ).
fof(f7582,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)],[f1269,f2570]) ).
fof(f7586,definition,
( sQ866_spl
<=> nil = app(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ866_spl])],[split_symbol_definition]) ).
fof(f7587,plain,
( ~ sQ866_spl
| nil = app(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f7586]) ).
fof(f7589,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| sQ866_spl
| ~ sQ164_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f7579,f551,f1738,f7586,f554,f5212]) ).
fof(f7592,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(f7593,plain,
( ~ sQ867_spl
| sK54_skl = app(app(app(sK53_skl,sK49_skl),sK49_skl),sK54_skl) ),
inference(component_clause,[status(thm)],[f7592]) ).
fof(f7595,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| sQ867_spl
| ~ sQ263_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7582,f530,f2562,f7592,f1439,f1225,f439,f491]) ).
fof(f7596,plain,
( ~ sQ867_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sK54_skl = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f1269,f7593]) ).
fof(f7597,plain,
( ~ sQ867_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sQ264_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7596,f2567]) ).
fof(f7598,plain,
( ~ sQ867_spl
| ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sQ264_spl ),
inference(contradiction_clause,[status(thm)],[f7597]) ).
fof(f7604,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)],[f5213,f2581]) ).
fof(f7605,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)],[f5906,f2581]) ).
fof(f7606,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)],[f2830,f2581]) ).
fof(f7607,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)],[f1269,f2581]) ).
fof(f7612,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(f7615,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| sQ868_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f7604,f551,f7612,f554,f5212]) ).
fof(f7616,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(f7619,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ869_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f7605,f551,f7616,f1775,f5863]) ).
fof(f7620,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(f7623,plain,
( ~ sQ293_spl
| ~ sQ15_spl
| sQ870_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f7606,f554,f7620,f551,f2829]) ).
fof(f7624,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(f7627,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| sQ871_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7607,f530,f7624,f1439,f1225,f439,f491]) ).
fof(f7636,plain,
( ~ sQ866_spl
| ~ sQ54_spl
| ~ sQ109_spl
| cons(sK51_skl,nil) = nil
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f7587,f1229]) ).
fof(f7670,definition,
( sQ873_spl
<=> cons(sK51_skl,nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ873_spl])],[split_symbol_definition]) ).
fof(f7671,plain,
( ~ sQ873_spl
| cons(sK51_skl,nil) = nil ),
inference(component_clause,[status(thm)],[f7670]) ).
fof(f7673,plain,
( ~ sQ866_spl
| ~ sQ54_spl
| ~ sQ109_spl
| sQ873_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f7636,f551,f7670,f1225,f851,f7586]) ).
fof(f7708,definition,
( sQ880_spl
<=> sK6_skl(nil,nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ880_spl])],[split_symbol_definition]) ).
fof(f7709,plain,
( ~ sQ880_spl
| sK6_skl(nil,nil) = sK49_skl ),
inference(component_clause,[status(thm)],[f7708]) ).
fof(f7730,plain,
( ~ sQ880_spl
| ~ sQ759_spl
| nil = sK49_skl ),
inference(forward_demodulation,[status(thm)],[f6448,f7709]) ).
fof(f7731,plain,
( ~ sQ880_spl
| ~ sQ759_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7730,f448]) ).
fof(f7732,plain,
( ~ sQ880_spl
| ~ sQ759_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f7731]) ).
fof(f7737,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ873_spl
| nil = sK49_skl ),
inference(backward_demodulation,[status(thm)],[f7671,f1324]) ).
fof(f7798,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ873_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f7737,f446,f7670,f1225,f816]) ).
fof(f8015,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)],[f2246,f6757]) ).
fof(f8016,plain,
! [X0] :
( ~ sQ226_spl
| ~ ssList(nil)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2246,f295]) ).
fof(f8017,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)],[f2246,f2239]) ).
fof(f8018,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)],[f2246,f282]) ).
fof(f8020,definition,
! [X0] :
( sQ914_spl
<=> ( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ914_spl])],[split_symbol_definition]) ).
fof(f8024,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(f8027,plain,
( ~ sQ226_spl
| ~ sQ15_spl
| sQ915_spl ),
inference(split_clause,[status(thm)],[f8015,f8024,f551,f2240]) ).
fof(f8028,plain,
( ~ sQ226_spl
| sQ914_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8016,f551,f8020,f2240]) ).
fof(f8029,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(f8032,plain,
( ~ sQ226_spl
| ~ sQ15_spl
| sQ916_spl ),
inference(split_clause,[status(thm)],[f8017,f8029,f551,f2240]) ).
fof(f8033,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(f8036,plain,
( ~ sQ226_spl
| ~ sQ15_spl
| sQ917_spl ),
inference(split_clause,[status(thm)],[f8018,f8033,f551,f2240]) ).
fof(f8042,plain,
! [X0] :
( ~ sQ422_spl
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| X0 = nil
| ~ frontsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2254,f3987]) ).
fof(f8046,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)],[f2254,f2359]) ).
fof(f8049,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)],[f2254,f3838]) ).
fof(f8051,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)],[f2254,f3375]) ).
fof(f8055,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| X0 = X1
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2254,f295]) ).
fof(f8065,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)],[f2254,f2359]) ).
fof(f8067,plain,
! [X0] :
( ~ sQ404_spl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2254,f3838]) ).
fof(f8070,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2254,f295]) ).
fof(f8075,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(f8078,plain,
( ~ sQ422_spl
| ~ sQ15_spl
| sQ918_spl ),
inference(split_clause,[status(thm)],[f8042,f8075,f551,f3986]) ).
fof(f8082,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(f8085,plain,
( ~ sQ243_spl
| ~ sQ16_spl
| sQ919_spl ),
inference(split_clause,[status(thm)],[f8046,f8082,f554,f2355]) ).
fof(f8087,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(f8090,plain,
( ~ sQ404_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ920_spl ),
inference(split_clause,[status(thm)],[f8049,f8087,f554,f551,f3837]) ).
fof(f8092,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(f8095,plain,
( ~ sQ354_spl
| ~ sQ16_spl
| sQ921_spl ),
inference(split_clause,[status(thm)],[f8051,f8092,f554,f3374]) ).
fof(f8099,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(f8102,plain,
( ~ sQ15_spl
| sQ922_spl ),
inference(split_clause,[status(thm)],[f8055,f8099,f551]) ).
fof(f8111,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(f8114,plain,
( ~ sQ243_spl
| sQ923_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f8065,f554,f8111,f2355]) ).
fof(f8116,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(f8119,plain,
( ~ sQ404_spl
| ~ sQ16_spl
| sQ924_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8067,f551,f8116,f554,f3837]) ).
fof(f8123,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(f8126,plain,
( sQ925_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8070,f551,f8123]) ).
fof(f8132,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)],[f2545,f3817]) ).
fof(f8133,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)],[f2545,f2564]) ).
fof(f8134,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)],[f2545,f2585]) ).
fof(f8136,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)],[f2545,f3675]) ).
fof(f8137,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)],[f2545,f1740]) ).
fof(f8138,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)],[f2545,f312]) ).
fof(f8149,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)],[f2545,f6951]) ).
fof(f8151,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)],[f2545,f1369]) ).
fof(f8152,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)],[f2545,f1004]) ).
fof(f8154,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)],[f2545,f2766]) ).
fof(f8155,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)],[f2545,f889]) ).
fof(f8156,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)],[f2545,f3729]) ).
fof(f8160,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssList(nil)
| rearsegP(X0,nil)
| ~ rearsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2545,f309]) ).
fof(f8161,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)],[f2545,f309]) ).
fof(f8168,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)],[f2545,f6951]) ).
fof(f8169,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)],[f2545,f1369]) ).
fof(f8170,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)],[f2545,f1004]) ).
fof(f8171,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)],[f2545,f2766]) ).
fof(f8172,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)],[f2545,f889]) ).
fof(f8173,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)],[f2545,f3729]) ).
fof(f8176,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)],[f2545,f309]) ).
fof(f8180,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(f8183,plain,
( sQ401_spl
| ~ sQ370_spl
| sQ926_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f8132,f554,f8180,f3624,f3815]) ).
fof(f8184,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(f8187,plain,
( sQ263_spl
| ~ sQ16_spl
| sQ927_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8133,f530,f8184,f554,f2562]) ).
fof(f8188,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(f8191,plain,
( ~ sQ266_spl
| sQ928_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8134,f530,f8188,f2584]) ).
fof(f8196,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(f8199,plain,
( sQ381_spl
| ~ sQ370_spl
| sQ930_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8136,f551,f8196,f3624,f3673]) ).
fof(f8200,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(f8203,plain,
( sQ164_spl
| ~ sQ16_spl
| sQ931_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8137,f551,f8200,f554,f1738]) ).
fof(f8204,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(f8207,plain,
( sQ932_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8138,f551,f8204]) ).
fof(f8219,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(f8222,plain,
( ~ sQ807_spl
| ~ sQ11_spl
| sQ933_spl ),
inference(split_clause,[status(thm)],[f8149,f8219,f530,f6950]) ).
fof(f8224,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(f8227,plain,
( ~ sQ117_spl
| ~ sQ15_spl
| sQ934_spl ),
inference(split_clause,[status(thm)],[f8151,f8224,f551,f1368]) ).
fof(f8228,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(f8231,plain,
( ~ sQ80_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ935_spl ),
inference(split_clause,[status(thm)],[f8152,f8228,f554,f551,f1003]) ).
fof(f8233,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(f8236,plain,
( ~ sQ287_spl
| ~ sQ16_spl
| sQ936_spl ),
inference(split_clause,[status(thm)],[f8154,f8233,f554,f2765]) ).
fof(f8237,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(f8240,plain,
( ~ sQ59_spl
| ~ sQ11_spl
| ~ sQ16_spl
| sQ937_spl ),
inference(split_clause,[status(thm)],[f8155,f8237,f554,f530,f888]) ).
fof(f8241,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(f8244,plain,
( ~ sQ387_spl
| ~ sQ16_spl
| ~ sQ370_spl
| sQ938_spl ),
inference(split_clause,[status(thm)],[f8156,f8241,f3624,f554,f3728]) ).
fof(f8249,plain,
( ~ sQ15_spl
| sQ257_spl ),
inference(split_clause,[status(thm)],[f8160,f2527,f551]) ).
fof(f8250,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(f8253,plain,
( ~ sQ15_spl
| sQ939_spl ),
inference(split_clause,[status(thm)],[f8161,f8250,f551]) ).
fof(f8257,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(f8260,plain,
( ~ sQ807_spl
| ~ sQ11_spl
| sQ940_spl ),
inference(split_clause,[status(thm)],[f8168,f8257,f530,f6950]) ).
fof(f8261,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(f8264,plain,
( ~ sQ117_spl
| ~ sQ15_spl
| sQ941_spl ),
inference(split_clause,[status(thm)],[f8169,f8261,f551,f1368]) ).
fof(f8265,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(f8268,plain,
( ~ sQ80_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ942_spl ),
inference(split_clause,[status(thm)],[f8170,f8265,f551,f554,f1003]) ).
fof(f8269,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(f8272,plain,
( ~ sQ287_spl
| ~ sQ16_spl
| sQ943_spl ),
inference(split_clause,[status(thm)],[f8171,f8269,f554,f2765]) ).
fof(f8273,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(f8276,plain,
( ~ sQ59_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sQ944_spl ),
inference(split_clause,[status(thm)],[f8172,f8273,f530,f554,f888]) ).
fof(f8277,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(f8280,plain,
( ~ sQ387_spl
| ~ sQ370_spl
| ~ sQ16_spl
| sQ945_spl ),
inference(split_clause,[status(thm)],[f8173,f8277,f554,f3624,f3728]) ).
fof(f8285,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(f8288,plain,
( ~ sQ15_spl
| sQ946_spl ),
inference(split_clause,[status(thm)],[f8176,f8285,f551]) ).
fof(f8534,plain,
( sQ527_spl
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f4856,f309]) ).
fof(f8537,plain,
( sQ527_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8534,f530,f4854]) ).
fof(f8547,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)],[f4855,f2545]) ).
fof(f8548,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)],[f4855,f2545]) ).
fof(f8550,plain,
! [X0] :
( ~ sQ527_spl
| rearsegP(X0,nil)
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(nil)
| ~ ssList(sK54_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4855,f301]) ).
fof(f8552,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(f8555,plain,
( ~ sQ527_spl
| ~ sQ11_spl
| ~ sQ15_spl
| sQ967_spl ),
inference(split_clause,[status(thm)],[f8547,f8552,f551,f530,f4854]) ).
fof(f8556,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(f8559,plain,
( ~ sQ527_spl
| ~ sQ15_spl
| ~ sQ11_spl
| sQ968_spl ),
inference(split_clause,[status(thm)],[f8548,f8556,f530,f551,f4854]) ).
fof(f8561,definition,
! [X0] :
( sQ969_spl
<=> ( rearsegP(X0,nil)
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ969_spl])],[split_symbol_definition]) ).
fof(f8564,plain,
( ~ sQ527_spl
| ~ sQ15_spl
| ~ sQ11_spl
| sQ969_spl ),
inference(split_clause,[status(thm)],[f8550,f8561,f530,f551,f4854]) ).
fof(f8601,plain,
( sQ733_spl
| ~ ssList(nil)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f6243,f626]) ).
fof(f8605,plain,
( sQ733_spl
| ~ sQ15_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8601,f530,f551,f6241]) ).
fof(f8606,definition,
( sQ971_spl
<=> ssList(app(nil,sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ971_spl])],[split_symbol_definition]) ).
fof(f8608,plain,
( sQ971_spl
| ~ ssList(app(nil,sK54_skl)) ),
inference(component_clause,[status(thm)],[f8606]) ).
fof(f8617,plain,
( sQ971_spl
| ~ ssList(sK54_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f8608,f245]) ).
fof(f8618,plain,
( sQ971_spl
| ~ sQ11_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8617,f551,f530,f8606]) ).
fof(f8619,plain,
( sQ739_spl
| ~ frontsegP(sK53_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f6284,f288]) ).
fof(f8622,plain,
( sQ739_spl
| ~ sQ816_spl
| ~ sQ16_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f8619,f752,f554,f7095,f6282]) ).
fof(f8632,plain,
! [X0] :
( ~ sQ262_spl
| ~ ssList(nil)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2556,f309]) ).
fof(f8633,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)],[f2556,f2545]) ).
fof(f8634,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)],[f2556,f301]) ).
fof(f8636,definition,
! [X0] :
( sQ976_spl
<=> ( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ976_spl])],[split_symbol_definition]) ).
fof(f8640,plain,
( ~ sQ262_spl
| sQ976_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8632,f551,f8636,f2550]) ).
fof(f8641,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(f8644,plain,
( ~ sQ262_spl
| ~ sQ15_spl
| sQ977_spl ),
inference(split_clause,[status(thm)],[f8633,f8641,f551,f2550]) ).
fof(f8645,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(f8648,plain,
( ~ sQ262_spl
| ~ sQ15_spl
| sQ978_spl ),
inference(split_clause,[status(thm)],[f8634,f8645,f551,f2550]) ).
fof(f8652,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)],[f2575,f4855]) ).
fof(f8654,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)],[f2575,f6951]) ).
fof(f8656,plain,
! [X0] :
( ~ sQ117_spl
| ~ rearsegP(nil,X0)
| ~ ssList(nil)
| X0 = nil
| ~ rearsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2575,f1369]) ).
fof(f8657,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)],[f2575,f1004]) ).
fof(f8659,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)],[f2575,f2766]) ).
fof(f8660,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)],[f2575,f889]) ).
fof(f8661,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)],[f2575,f3729]) ).
fof(f8666,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ rearsegP(nil,X0)
| ~ ssList(nil)
| X0 = X1
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2575,f309]) ).
fof(f8673,plain,
! [X0] :
( ~ sQ527_spl
| ~ rearsegP(X0,sK54_skl)
| ~ ssList(sK54_skl)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2575,f4855]) ).
fof(f8676,plain,
! [X0] :
( ~ sQ80_spl
| ~ rearsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2575,f1004]) ).
fof(f8678,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)],[f2575,f889]) ).
fof(f8679,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)],[f2575,f3729]) ).
fof(f8682,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2575,f309]) ).
fof(f8686,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(f8689,plain,
( ~ sQ527_spl
| ~ sQ15_spl
| ~ sQ11_spl
| sQ979_spl ),
inference(split_clause,[status(thm)],[f8652,f8686,f530,f551,f4854]) ).
fof(f8691,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(f8694,plain,
( ~ sQ807_spl
| ~ sQ11_spl
| sQ980_spl ),
inference(split_clause,[status(thm)],[f8654,f8691,f530,f6950]) ).
fof(f8696,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(f8699,plain,
( ~ sQ117_spl
| ~ sQ15_spl
| sQ981_spl ),
inference(split_clause,[status(thm)],[f8656,f8696,f551,f1368]) ).
fof(f8700,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(f8703,plain,
( ~ sQ80_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ982_spl ),
inference(split_clause,[status(thm)],[f8657,f8700,f554,f551,f1003]) ).
fof(f8705,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(f8708,plain,
( ~ sQ287_spl
| ~ sQ16_spl
| sQ983_spl ),
inference(split_clause,[status(thm)],[f8659,f8705,f554,f2765]) ).
fof(f8709,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(f8712,plain,
( ~ sQ59_spl
| ~ sQ11_spl
| ~ sQ16_spl
| sQ984_spl ),
inference(split_clause,[status(thm)],[f8660,f8709,f554,f530,f888]) ).
fof(f8713,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(f8716,plain,
( ~ sQ387_spl
| ~ sQ16_spl
| ~ sQ370_spl
| sQ985_spl ),
inference(split_clause,[status(thm)],[f8661,f8713,f3624,f554,f3728]) ).
fof(f8721,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(f8724,plain,
( ~ sQ15_spl
| sQ986_spl ),
inference(split_clause,[status(thm)],[f8666,f8721,f551]) ).
fof(f8728,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(f8731,plain,
( ~ sQ527_spl
| ~ sQ11_spl
| sQ987_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8673,f551,f8728,f530,f4854]) ).
fof(f8734,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(f8737,plain,
( ~ sQ80_spl
| ~ sQ16_spl
| sQ988_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8676,f551,f8734,f554,f1003]) ).
fof(f8739,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(f8742,plain,
( ~ sQ59_spl
| ~ sQ16_spl
| sQ989_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8678,f530,f8739,f554,f888]) ).
fof(f8743,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(f8746,plain,
( ~ sQ387_spl
| ~ sQ370_spl
| sQ990_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f8679,f554,f8743,f3624,f3728]) ).
fof(f8751,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(f8754,plain,
( sQ991_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8682,f551,f8751]) ).
fof(f8793,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)],[f3342,f232]) ).
fof(f8794,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)],[f1324,f8793]) ).
fof(f8795,definition,
( sQ996_spl
<=> nil = sK43_skl(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ996_spl])],[split_symbol_definition]) ).
fof(f8798,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sQ873_spl
| ~ sQ25_spl
| sQ996_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f8794,f551,f485,f8795,f633,f7670,f1225,f816]) ).
fof(f8847,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)],[f4813,f2575]) ).
fof(f8848,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)],[f4813,f2575]) ).
fof(f8849,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)],[f4813,f2545]) ).
fof(f8850,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)],[f4813,f2545]) ).
fof(f8851,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)],[f4813,f303]) ).
fof(f8852,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)],[f4813,f301]) ).
fof(f8853,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(f8856,plain,
( ~ sQ520_spl
| ~ sQ468_spl
| sQ1005_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8847,f530,f8853,f4490,f4812]) ).
fof(f8857,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(f8860,plain,
( ~ sQ520_spl
| ~ sQ11_spl
| ~ sQ468_spl
| sQ1006_spl ),
inference(split_clause,[status(thm)],[f8848,f8857,f4490,f530,f4812]) ).
fof(f8861,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(f8864,plain,
( ~ sQ520_spl
| ~ sQ468_spl
| ~ sQ11_spl
| sQ1007_spl ),
inference(split_clause,[status(thm)],[f8849,f8861,f530,f4490,f4812]) ).
fof(f8865,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(f8868,plain,
( ~ sQ520_spl
| ~ sQ11_spl
| ~ sQ468_spl
| sQ1008_spl ),
inference(split_clause,[status(thm)],[f8850,f8865,f4490,f530,f4812]) ).
fof(f8869,definition,
( sQ1009_spl
<=> rearsegP(sK54_skl,app(sK49_skl,sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1009_spl])],[split_symbol_definition]) ).
fof(f8872,definition,
( sQ1010_spl
<=> sK54_skl = app(sK49_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ1010_spl])],[split_symbol_definition]) ).
fof(f8873,plain,
( ~ sQ1010_spl
| sK54_skl = app(sK49_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f8872]) ).
fof(f8875,plain,
( ~ sQ520_spl
| sQ1010_spl
| ~ sQ1009_spl
| ~ sQ468_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8851,f530,f4490,f8869,f8872,f4812]) ).
fof(f8876,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(f8879,plain,
( ~ sQ520_spl
| ~ sQ11_spl
| ~ sQ468_spl
| sQ1011_spl ),
inference(split_clause,[status(thm)],[f8852,f8876,f4490,f530,f4812]) ).
fof(f8886,plain,
( ~ sQ1010_spl
| ~ sQ54_spl
| ~ sQ109_spl
| cons(sK51_skl,sK54_skl) = sK54_skl
| ~ ssList(sK54_skl) ),
inference(paramodulation,[status(thm)],[f8873,f1229]) ).
fof(f8917,definition,
( sQ1013_spl
<=> cons(sK51_skl,sK54_skl) = sK54_skl ),
introduced(definition,[new_symbols(definition,[sQ1013_spl])],[split_symbol_definition]) ).
fof(f8918,plain,
( ~ sQ1013_spl
| cons(sK51_skl,sK54_skl) = sK54_skl ),
inference(component_clause,[status(thm)],[f8917]) ).
fof(f8920,plain,
( ~ sQ1010_spl
| ~ sQ54_spl
| ~ sQ109_spl
| sQ1013_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8886,f530,f8917,f1225,f851,f8872]) ).
fof(f8976,definition,
( sQ1027_spl
<=> sK6_skl(sK54_skl,sK54_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ1027_spl])],[split_symbol_definition]) ).
fof(f8977,plain,
( ~ sQ1027_spl
| sK6_skl(sK54_skl,sK54_skl) = sK49_skl ),
inference(component_clause,[status(thm)],[f8976]) ).
fof(f9038,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)],[f2632,f1773]) ).
fof(f9039,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)],[f2632,f326]) ).
fof(f9053,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssList(nil)
| segmentP(X0,nil)
| ~ segmentP(X0,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2632,f323]) ).
fof(f9054,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)],[f2632,f323]) ).
fof(f9064,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)],[f2632,f1249]) ).
fof(f9065,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)],[f2632,f323]) ).
fof(f9077,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(f9080,plain,
( sQ26_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ16_spl
| sQ1039_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9038,f551,f9077,f554,f1225,f816,f636]) ).
fof(f9081,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(f9084,plain,
( sQ1040_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9039,f551,f9081]) ).
fof(f9093,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(f9097,definition,
! [X0] :
( sQ1042_spl
<=> ( segmentP(X0,nil)
| ~ segmentP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1042_spl])],[split_symbol_definition]) ).
fof(f9100,plain,
( ~ sQ15_spl
| sQ1042_spl ),
inference(split_clause,[status(thm)],[f9053,f9097,f551]) ).
fof(f9101,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(f9104,plain,
( ~ sQ15_spl
| sQ1043_spl ),
inference(split_clause,[status(thm)],[f9054,f9101,f551]) ).
fof(f9111,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(f9114,plain,
( ~ sQ29_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ16_spl
| sQ1044_spl ),
inference(split_clause,[status(thm)],[f9064,f9111,f554,f1225,f439,f655]) ).
fof(f9115,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(f9118,plain,
( ~ sQ15_spl
| sQ1045_spl ),
inference(split_clause,[status(thm)],[f9065,f9115,f551]) ).
fof(f9125,plain,
! [X0] :
( ~ sQ272_spl
| ~ ssList(nil)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2643,f323]) ).
fof(f9126,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)],[f2643,f2632]) ).
fof(f9127,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)],[f2643,f315]) ).
fof(f9129,definition,
! [X0] :
( sQ1046_spl
<=> ( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1046_spl])],[split_symbol_definition]) ).
fof(f9132,plain,
( ~ sQ272_spl
| sQ1046_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9125,f551,f9129,f2637]) ).
fof(f9133,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(f9136,plain,
( ~ sQ272_spl
| ~ sQ15_spl
| sQ1047_spl ),
inference(split_clause,[status(thm)],[f9126,f9133,f551,f2637]) ).
fof(f9137,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(f9140,plain,
( ~ sQ272_spl
| ~ sQ15_spl
| sQ1048_spl ),
inference(split_clause,[status(thm)],[f9127,f9137,f551,f2637]) ).
fof(f9200,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)],[f8977,f129]) ).
fof(f9202,plain,
( ~ sQ1027_spl
| sQ1010_spl
| ~ sQ807_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f9200,f530,f6950,f8872,f8976]) ).
fof(f9224,plain,
( ~ sQ1013_spl
| ~ ssItem(sK51_skl)
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f8918,f225]) ).
fof(f9274,plain,
( ~ sQ1013_spl
| ~ sQ3_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f9224,f530,f485,f8917]) ).
fof(f9444,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)],[f2656,f1249]) ).
fof(f9446,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ segmentP(nil,X0)
| ~ ssList(nil)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2656,f323]) ).
fof(f9457,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2656,f323]) ).
fof(f9465,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(f9468,plain,
( ~ sQ29_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ16_spl
| sQ1094_spl ),
inference(split_clause,[status(thm)],[f9444,f9465,f554,f1225,f439,f655]) ).
fof(f9473,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(f9476,plain,
( ~ sQ15_spl
| sQ1096_spl ),
inference(split_clause,[status(thm)],[f9446,f9473,f551]) ).
fof(f9484,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(f9487,plain,
( sQ1097_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9457,f551,f9484]) ).
fof(f9499,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)],[f1269,f2662]) ).
fof(f9501,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)],[f5213,f2662]) ).
fof(f9502,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)],[f5906,f2662]) ).
fof(f9503,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)],[f2830,f2662]) ).
fof(f9504,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)],[f1269,f2662]) ).
fof(f9510,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(f9513,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ452_spl
| ~ sQ11_spl
| ~ sQ154_spl
| sQ1098_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f9499,f554,f9510,f1675,f530,f4295,f1225,f439,f491]) ).
fof(f9518,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(f9521,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| sQ1100_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9501,f551,f9518,f554,f5212]) ).
fof(f9522,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(f9525,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ1101_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9502,f551,f9522,f1775,f5863]) ).
fof(f9526,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(f9529,plain,
( ~ sQ293_spl
| ~ sQ15_spl
| sQ1102_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f9503,f554,f9526,f551,f2829]) ).
fof(f9530,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(f9533,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| sQ1103_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f9504,f530,f9530,f1439,f1225,f439,f491]) ).
fof(f9551,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)],[f1269,f2663]) ).
fof(f9553,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)],[f5213,f2663]) ).
fof(f9554,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)],[f5906,f2663]) ).
fof(f9555,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)],[f2830,f2663]) ).
fof(f9556,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)],[f1269,f2663]) ).
fof(f9563,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ452_spl
| ~ sQ11_spl
| ~ sQ154_spl
| sQ1041_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f9551,f554,f9093,f1675,f530,f4295,f1225,f439,f491]) ).
fof(f9568,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(f9571,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| sQ1105_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9553,f551,f9568,f554,f5212]) ).
fof(f9572,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(f9575,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ1106_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9554,f551,f9572,f1775,f5863]) ).
fof(f9576,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(f9579,plain,
( ~ sQ293_spl
| ~ sQ15_spl
| sQ1107_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f9555,f554,f9576,f551,f2829]) ).
fof(f9580,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(f9583,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| sQ1108_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f9556,f530,f9580,f1439,f1225,f439,f491]) ).
fof(f9593,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)],[f3458,f232]) ).
fof(f9594,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)],[f1324,f9593]) ).
fof(f9595,definition,
( sQ1109_spl
<=> sK44_skl(sK49_skl) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ1109_spl])],[split_symbol_definition]) ).
fof(f9598,plain,
( ~ sQ51_spl
| ~ sQ109_spl
| sQ873_spl
| ~ sQ25_spl
| sQ1109_spl
| ~ sQ3_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f9594,f551,f485,f9595,f633,f7670,f1225,f816]) ).
fof(f9599,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)],[f5337,f9593]) ).
fof(f9600,plain,
( sQ597_spl
| sQ510_spl
| ~ sQ812_spl
| ~ sQ3_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f9599,f530,f485,f7007,f4771,f5335]) ).
fof(f9634,plain,
( sQ829_spl
| ~ ssList(sK53_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f7199,f626]) ).
fof(f9638,plain,
( sQ829_spl
| ~ sQ43_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f9634,f554,f752,f7197]) ).
fof(f9677,definition,
( sQ1112_spl
<=> ssList(tl(sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1112_spl])],[split_symbol_definition]) ).
fof(f9679,plain,
( sQ1112_spl
| ~ ssList(tl(sK53_skl)) ),
inference(component_clause,[status(thm)],[f9677]) ).
fof(f9705,definition,
! [X0] :
( sQ1119_spl
<=> ( rearsegP(X0,sK49_skl)
| ~ rearsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ1119_spl])],[split_symbol_definition]) ).
fof(f9706,plain,
! [X0] :
( ~ sQ1119_spl
| rearsegP(X0,sK49_skl)
| ~ rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f9705]) ).
fof(f9776,plain,
! [X0] :
( ~ sQ1119_spl
| rearsegP(X0,sK49_skl)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f9706,f309]) ).
fof(f9780,plain,
( sQ1112_spl
| nil = sK53_skl
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f9679,f241]) ).
fof(f9781,plain,
( sQ1112_spl
| sQ159_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f9780,f752,f1716,f9677]) ).
fof(f9786,plain,
( sQ157_spl
| ~ sQ264_spl
| ~ sQ293_spl ),
inference(split_clause,[status(thm)],[f2589,f2829,f2565,f1689]) ).
fof(f9789,plain,
( sQ739_spl
| ~ sQ159_spl
| ~ frontsegP(app(nil,sK49_skl),sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f1717,f6284]) ).
fof(f9800,plain,
( sQ739_spl
| ~ sQ159_spl
| ~ sQ293_spl
| ~ frontsegP(sK49_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f2830,f9789]) ).
fof(f9801,plain,
( sQ739_spl
| ~ sQ159_spl
| ~ sQ293_spl
| ~ sQ354_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9800,f3375]) ).
fof(f9802,plain,
( sQ739_spl
| ~ sQ159_spl
| ~ sQ293_spl
| ~ sQ354_spl ),
inference(contradiction_clause,[status(thm)],[f9801]) ).
fof(f9812,plain,
( ~ sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ159_spl
| sK49_skl = app(app(nil,sK49_skl),sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f1717,f2213]) ).
fof(f9813,plain,
( ~ sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ159_spl
| ~ sQ293_spl
| sK49_skl = app(sK49_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f2830,f9812]) ).
fof(f9814,plain,
( ~ sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ159_spl
| ~ sQ293_spl
| sQ402_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9813,f3820]) ).
fof(f9815,plain,
( ~ sQ78_spl
| ~ sQ51_spl
| ~ sQ109_spl
| ~ sQ159_spl
| ~ sQ293_spl
| sQ402_spl ),
inference(contradiction_clause,[status(thm)],[f9814]) ).
fof(f9832,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)],[f3027,f393]) ).
fof(f9880,definition,
( sQ1140_spl
<=> tl(sK49_skl) = app(tl(sK49_skl),sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ1140_spl])],[split_symbol_definition]) ).
fof(f9881,plain,
( ~ sQ1140_spl
| tl(sK49_skl) = app(tl(sK49_skl),sK54_skl) ),
inference(component_clause,[status(thm)],[f9880]) ).
fof(f9883,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ78_spl
| ~ sQ51_spl
| sQ1140_spl
| sQ2_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f9832,f554,f530,f446,f9880,f816,f994,f1225,f439,f491]) ).
fof(f9921,plain,
( ~ sQ1140_spl
| ~ sQ167_spl
| nil = app(tl(sK49_skl),sK54_skl) ),
inference(forward_demodulation,[status(thm)],[f1776,f9881]) ).
fof(f9922,plain,
( ~ sQ1140_spl
| ~ sQ167_spl
| nil = app(nil,sK54_skl) ),
inference(forward_demodulation,[status(thm)],[f1776,f9921]) ).
fof(f9923,plain,
( ~ sQ1140_spl
| ~ sQ167_spl
| sQ621_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f9922,f5507]) ).
fof(f9924,plain,
( ~ sQ1140_spl
| ~ sQ167_spl
| sQ621_spl ),
inference(contradiction_clause,[status(thm)],[f9923]) ).
fof(f10087,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)],[f3921,f2632]) ).
fof(f10089,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(f10092,plain,
( sQ414_spl
| ~ sQ16_spl
| sQ1148_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f10087,f530,f10089,f554,f3919]) ).
fof(f10094,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)],[f766,f2656]) ).
fof(f10095,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)],[f766,f2656]) ).
fof(f10096,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)],[f766,f2632]) ).
fof(f10097,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)],[f766,f2632]) ).
fof(f10100,plain,
( ~ sQ585_spl
| ~ sQ31_spl
| ~ sQ5_spl
| ~ ssList(nil)
| segmentP(sK49_skl,sK54_skl)
| ~ ssList(app(sK49_skl,nil)) ),
inference(paramodulation,[status(thm)],[f5213,f766]) ).
fof(f10101,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(f10104,plain,
( ~ sQ31_spl
| ~ sQ5_spl
| ~ sQ11_spl
| sQ1149_spl ),
inference(split_clause,[status(thm)],[f10094,f10101,f530,f491,f663]) ).
fof(f10105,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(f10108,plain,
( ~ sQ31_spl
| ~ sQ5_spl
| ~ sQ11_spl
| sQ1150_spl ),
inference(split_clause,[status(thm)],[f10095,f10105,f530,f491,f663]) ).
fof(f10109,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(f10112,plain,
( ~ sQ31_spl
| ~ sQ5_spl
| ~ sQ11_spl
| sQ1151_spl ),
inference(split_clause,[status(thm)],[f10096,f10109,f530,f491,f663]) ).
fof(f10113,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(f10116,plain,
( ~ sQ31_spl
| ~ sQ5_spl
| ~ sQ11_spl
| sQ1152_spl ),
inference(split_clause,[status(thm)],[f10097,f10113,f530,f491,f663]) ).
fof(f10119,definition,
( sQ1153_spl
<=> ssList(app(sK49_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ1153_spl])],[split_symbol_definition]) ).
fof(f10121,plain,
( sQ1153_spl
| ~ ssList(app(sK49_skl,nil)) ),
inference(component_clause,[status(thm)],[f10119]) ).
fof(f10122,plain,
( ~ sQ585_spl
| ~ sQ31_spl
| ~ sQ5_spl
| ~ sQ15_spl
| sQ406_spl
| ~ sQ1153_spl ),
inference(split_clause,[status(thm)],[f10100,f10119,f3868,f551,f491,f663,f5212]) ).
fof(f10127,plain,
( sQ1153_spl
| ~ sQ585_spl
| ~ ssList(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f5213,f10121]) ).
fof(f10128,plain,
( sQ1153_spl
| ~ sQ585_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10127,f421]) ).
fof(f10129,plain,
( sQ1153_spl
| ~ sQ585_spl ),
inference(contradiction_clause,[status(thm)],[f10128]) ).
fof(f10135,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)],[f3869,f2656]) ).
fof(f10136,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)],[f3869,f2656]) ).
fof(f10137,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)],[f3869,f2632]) ).
fof(f10138,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)],[f3869,f2632]) ).
fof(f10141,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(f10144,plain,
( ~ sQ406_spl
| ~ sQ16_spl
| sQ1154_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f10135,f530,f10141,f554,f3868]) ).
fof(f10145,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(f10148,plain,
( ~ sQ406_spl
| ~ sQ11_spl
| ~ sQ16_spl
| sQ1155_spl ),
inference(split_clause,[status(thm)],[f10136,f10145,f554,f530,f3868]) ).
fof(f10149,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(f10152,plain,
( ~ sQ406_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sQ1156_spl ),
inference(split_clause,[status(thm)],[f10137,f10149,f530,f554,f3868]) ).
fof(f10153,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(f10156,plain,
( ~ sQ406_spl
| ~ sQ11_spl
| ~ sQ16_spl
| sQ1157_spl ),
inference(split_clause,[status(thm)],[f10138,f10153,f554,f530,f3868]) ).
fof(f10159,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)],[f4017,f3834]) ).
fof(f10161,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)],[f5213,f10159]) ).
fof(f10162,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)],[f5906,f10159]) ).
fof(f10163,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)],[f2830,f10159]) ).
fof(f10167,definition,
( sQ1158_spl
<=> ssList(sK5_skl(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1158_spl])],[split_symbol_definition]) ).
fof(f10169,plain,
( sQ1158_spl
| ~ ssList(sK5_skl(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f10167]) ).
fof(f10170,definition,
( sQ1159_spl
<=> sK5_skl(sK49_skl,app(sK49_skl,nil)) = nil ),
introduced(definition,[new_symbols(definition,[sQ1159_spl])],[split_symbol_definition]) ).
fof(f10173,plain,
( ~ sQ585_spl
| sQ1159_spl
| ~ sQ1158_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f10161,f554,f551,f10167,f10170,f5212]) ).
fof(f10174,definition,
( sQ1160_spl
<=> ssList(sK5_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ1160_spl])],[split_symbol_definition]) ).
fof(f10176,plain,
( sQ1160_spl
| ~ ssList(sK5_skl(nil,nil)) ),
inference(component_clause,[status(thm)],[f10174]) ).
fof(f10177,definition,
( sQ1161_spl
<=> sK5_skl(nil,app(nil,nil)) = nil ),
introduced(definition,[new_symbols(definition,[sQ1161_spl])],[split_symbol_definition]) ).
fof(f10178,plain,
( ~ sQ1161_spl
| sK5_skl(nil,app(nil,nil)) = nil ),
inference(component_clause,[status(thm)],[f10177]) ).
fof(f10180,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| sQ1161_spl
| ~ sQ1160_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f10162,f551,f10174,f10177,f1775,f5863]) ).
fof(f10181,definition,
( sQ1162_spl
<=> ssList(sK5_skl(nil,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1162_spl])],[split_symbol_definition]) ).
fof(f10183,plain,
( sQ1162_spl
| ~ ssList(sK5_skl(nil,sK49_skl)) ),
inference(component_clause,[status(thm)],[f10181]) ).
fof(f10184,definition,
( sQ1163_spl
<=> sK5_skl(nil,app(nil,sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ1163_spl])],[split_symbol_definition]) ).
fof(f10187,plain,
( ~ sQ293_spl
| sQ1163_spl
| ~ sQ1162_spl
| ~ sQ16_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f10163,f551,f554,f10181,f10184,f2829]) ).
fof(f10194,plain,
( ~ sQ1161_spl
| ~ sQ675_spl
| ~ sQ167_spl
| sK5_skl(nil,nil) = nil ),
inference(forward_demodulation,[status(thm)],[f5906,f10178]) ).
fof(f10238,plain,
( sQ263_spl
| ~ sQ1119_spl
| ~ ssList(sK54_skl) ),
inference(resolution,[status(thm)],[f9776,f2564]) ).
fof(f10253,plain,
( sQ263_spl
| ~ sQ1119_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f10238,f530,f9705,f2562]) ).
fof(f10521,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)],[f4028,f122]) ).
fof(f10522,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(f10525,plain,
( ~ sQ423_spl
| ~ sQ15_spl
| sQ1205_spl ),
inference(split_clause,[status(thm)],[f10521,f10522,f551,f4020]) ).
fof(f10531,definition,
( sQ1206_spl
<=> ssItem(sK4_skl(sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1206_spl])],[split_symbol_definition]) ).
fof(f10533,plain,
( sQ1206_spl
| ~ ssItem(sK4_skl(sK49_skl)) ),
inference(component_clause,[status(thm)],[f10531]) ).
fof(f10535,plain,
( sQ1206_spl
| ~ sQ200_spl
| ~ ssItem(sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f2009,f10533]) ).
fof(f10536,plain,
( sQ1206_spl
| ~ sQ200_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10535,f425]) ).
fof(f10537,plain,
( sQ1206_spl
| ~ sQ200_spl ),
inference(contradiction_clause,[status(thm)],[f10536]) ).
fof(f10539,plain,
( sQ1160_spl
| ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f10176,f122]) ).
fof(f10540,plain,
( sQ1160_spl
| ~ sQ422_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f10539,f551,f3986,f10174]) ).
fof(f10541,plain,
( sQ1158_spl
| ~ frontsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f10169,f122]) ).
fof(f10542,plain,
( sQ1158_spl
| ~ sQ354_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f10541,f554,f3374,f10167]) ).
fof(f10543,plain,
( sQ1162_spl
| ~ frontsegP(sK49_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f10183,f122]) ).
fof(f10544,plain,
( sQ1162_spl
| ~ sQ404_spl
| ~ sQ15_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f10543,f554,f551,f3837,f10181]) ).
fof(f10549,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)],[f10194,f4028]) ).
fof(f10551,plain,
( ~ sQ1161_spl
| ~ sQ675_spl
| ~ sQ167_spl
| app(nil,nil) = nil
| ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f10194,f123]) ).
fof(f10552,definition,
( sQ1207_spl
<=> nil = sK5_skl(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ1207_spl])],[split_symbol_definition]) ).
fof(f10555,plain,
( ~ sQ1161_spl
| ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ423_spl
| sQ1207_spl
| ~ sQ422_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f10549,f551,f3986,f10552,f4020,f1775,f5863,f10177]) ).
fof(f10557,plain,
( ~ sQ1161_spl
| ~ sQ675_spl
| ~ sQ167_spl
| sQ784_spl
| ~ sQ422_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f10551,f551,f3986,f6733,f1775,f5863,f10177]) ).
fof(f10711,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)],[f5912,f2254]) ).
fof(f10712,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)],[f5912,f2254]) ).
fof(f10713,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)],[f5912,f2239]) ).
fof(f10714,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)],[f5912,f2239]) ).
fof(f10719,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(f10722,plain,
( ~ sQ683_spl
| ~ sQ16_spl
| sQ1210_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f10711,f1675,f10719,f554,f5911]) ).
fof(f10723,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(f10726,plain,
( ~ sQ683_spl
| ~ sQ154_spl
| ~ sQ16_spl
| sQ1211_spl ),
inference(split_clause,[status(thm)],[f10712,f10723,f554,f1675,f5911]) ).
fof(f10727,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(f10730,plain,
( ~ sQ683_spl
| ~ sQ16_spl
| ~ sQ154_spl
| sQ1212_spl ),
inference(split_clause,[status(thm)],[f10713,f10727,f1675,f554,f5911]) ).
fof(f10731,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(f10734,plain,
( ~ sQ683_spl
| ~ sQ154_spl
| ~ sQ16_spl
| sQ1213_spl ),
inference(split_clause,[status(thm)],[f10714,f10731,f554,f1675,f5911]) ).
fof(f10737,plain,
( ~ sQ833_spl
| ~ sQ243_spl
| frontsegP(sK53_skl,sK49_skl)
| ~ ssList(tl(sK53_skl)) ),
inference(paramodulation,[status(thm)],[f7229,f2359]) ).
fof(f10788,plain,
( ~ sQ833_spl
| ~ sQ243_spl
| sQ816_spl
| ~ sQ1112_spl ),
inference(split_clause,[status(thm)],[f10737,f9677,f7095,f2355,f7228]) ).
fof(f10862,definition,
( sQ1233_spl
<=> hd(sK53_skl) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ1233_spl])],[split_symbol_definition]) ).
fof(f10863,plain,
( ~ sQ1233_spl
| hd(sK53_skl) = sK51_skl ),
inference(component_clause,[status(thm)],[f10862]) ).
fof(f10993,plain,
( ~ sQ1233_spl
| sQ825_spl
| ~ sQ152_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f10863,f7232]) ).
fof(f10994,plain,
( ~ sQ1233_spl
| sQ825_spl
| ~ sQ152_spl ),
inference(contradiction_clause,[status(thm)],[f10993]) ).
fof(f10999,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)],[f2264,f2239]) ).
fof(f11006,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(f11009,plain,
( ~ sQ228_spl
| ~ sQ124_spl
| sQ1265_spl ),
inference(split_clause,[status(thm)],[f10999,f11006,f1439,f2263]) ).
fof(f11148,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)],[f1269,f4293]) ).
fof(f11149,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)],[f5213,f4293]) ).
fof(f11150,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)],[f5906,f4293]) ).
fof(f11151,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)],[f2830,f4293]) ).
fof(f11152,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)],[f1269,f4293]) ).
fof(f11157,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(f11160,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| sQ1269_spl
| ~ sQ273_spl
| ~ sQ11_spl
| ~ sQ154_spl
| ~ sQ16_spl
| ~ sQ452_spl ),
inference(split_clause,[status(thm)],[f11148,f4295,f554,f1675,f530,f2648,f11157,f1225,f439,f491]) ).
fof(f11161,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(f11164,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ1270_spl ),
inference(split_clause,[status(thm)],[f11149,f11161,f551,f554,f5212]) ).
fof(f11165,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(f11168,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ15_spl
| sQ1271_spl ),
inference(split_clause,[status(thm)],[f11150,f11165,f551,f1775,f5863]) ).
fof(f11169,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(f11172,plain,
( ~ sQ293_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ1272_spl ),
inference(split_clause,[status(thm)],[f11151,f11169,f554,f551,f2829]) ).
fof(f11173,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(f11176,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| ~ sQ11_spl
| sQ1273_spl ),
inference(split_clause,[status(thm)],[f11152,f11173,f530,f1439,f1225,f439,f491]) ).
fof(f11192,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)],[f5213,f4294]) ).
fof(f11193,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)],[f5906,f4294]) ).
fof(f11194,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)],[f2830,f4294]) ).
fof(f11195,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)],[f1269,f4294]) ).
fof(f11203,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(f11206,plain,
( ~ sQ585_spl
| ~ sQ16_spl
| ~ sQ15_spl
| sQ1274_spl ),
inference(split_clause,[status(thm)],[f11192,f11203,f551,f554,f5212]) ).
fof(f11207,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(f11210,plain,
( ~ sQ675_spl
| ~ sQ167_spl
| ~ sQ15_spl
| sQ1275_spl ),
inference(split_clause,[status(thm)],[f11193,f11207,f551,f1775,f5863]) ).
fof(f11211,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(f11214,plain,
( ~ sQ293_spl
| ~ sQ15_spl
| ~ sQ16_spl
| sQ1276_spl ),
inference(split_clause,[status(thm)],[f11194,f11211,f554,f551,f2829]) ).
fof(f11215,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(f11218,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ109_spl
| ~ sQ124_spl
| ~ sQ11_spl
| sQ1277_spl ),
inference(split_clause,[status(thm)],[f11195,f11215,f530,f1439,f1225,f439,f491]) ).
fof(f11255,plain,
( ~ sQ864_spl
| sK51_skl = hd(sK53_skl)
| nil = sK53_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f7567,f391]) ).
fof(f11257,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)],[f7567,f374]) ).
fof(f11258,plain,
( ~ sQ864_spl
| sQ1233_spl
| sQ159_spl
| ~ sQ16_spl
| ~ sQ43_spl ),
inference(split_clause,[status(thm)],[f11255,f752,f554,f1716,f10862,f7566]) ).
fof(f11260,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(f11263,plain,
( ~ sQ864_spl
| sQ1279_spl
| sQ158_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f11257,f1675,f1693,f11260,f7566]) ).
fof(f11264,plain,
$false,
inference(sat_refutation,[status(thm)],[f449,f494,f501,f503,f506,f533,f535,f561,f563,f565,f588,f596,f602,f611,f618,f658,f662,f666,f667,f670,f678,f687,f691,f695,f699,f703,f726,f739,f743,f750,f755,f757,f762,f765,f785,f792,f819,f826,f841,f846,f854,f879,f896,f907,f937,f941,f968,f972,f997,f1047,f1051,f1128,f1135,f1156,f1160,f1171,f1212,f1216,f1223,f1228,f1271,f1272,f1273,f1274,f1275,f1276,f1277,f1281,f1286,f1290,f1294,f1298,f1302,f1303,f1308,f1337,f1379,f1445,f1450,f1452,f1456,f1489,f1503,f1507,f1564,f1569,f1606,f1623,f1628,f1659,f1698,f1741,f1761,f1763,f1770,f1778,f1848,f1865,f2014,f2017,f2027,f2030,f2048,f2067,f2238,f2243,f2253,f2266,f2310,f2314,f2324,f2328,f2348,f2354,f2358,f2363,f2388,f2417,f2534,f2538,f2544,f2549,f2553,f2574,f2587,f2612,f2627,f2631,f2636,f2640,f2655,f2659,f2720,f2740,f2769,f2793,f2799,f2816,f2819,f2823,f2836,f2866,f2867,f2871,f2875,f2879,f2883,f2888,f2893,f2899,f2903,f2933,f3085,f3122,f3182,f3195,f3199,f3359,f3370,f3501,f3527,f3676,f3688,f3743,f3756,f3760,f3797,f3803,f3812,f3821,f3825,f3833,f3840,f3876,f3913,f3922,f3926,f3931,f3982,f4023,f4027,f4041,f4093,f4103,f4120,f4121,f4122,f4124,f4143,f4147,f4151,f4152,f4194,f4198,f4206,f4210,f4218,f4222,f4255,f4265,f4272,f4276,f4278,f4286,f4302,f4306,f4311,f4329,f4348,f4354,f4383,f4738,f4743,f4770,f4864,f5175,f5307,f5494,f5499,f5856,f5861,f5862,f5866,f5867,f5873,f5878,f5885,f5890,f5895,f5897,f5901,f5914,f5916,f5920,f6222,f6288,f6292,f6296,f6300,f6305,f6316,f6330,f6364,f6370,f6374,f6414,f6418,f6422,f6426,f6427,f6433,f6438,f6442,f6446,f6453,f6458,f6463,f6465,f6469,f6473,f6483,f6511,f6516,f6527,f6533,f6538,f6576,f6618,f6623,f6627,f6631,f6637,f6649,f6704,f6748,f6752,f6771,f6782,f6790,f6954,f6965,f6974,f6983,f7010,f7012,f7018,f7025,f7030,f7094,f7101,f7105,f7200,f7221,f7231,f7494,f7498,f7515,f7517,f7519,f7522,f7526,f7533,f7541,f7546,f7550,f7556,f7569,f7574,f7589,f7595,f7598,f7615,f7619,f7623,f7627,f7673,f7732,f7798,f8027,f8028,f8032,f8036,f8078,f8085,f8090,f8095,f8102,f8114,f8119,f8126,f8183,f8187,f8191,f8199,f8203,f8207,f8222,f8227,f8231,f8236,f8240,f8244,f8249,f8253,f8260,f8264,f8268,f8272,f8276,f8280,f8288,f8537,f8555,f8559,f8564,f8605,f8618,f8622,f8640,f8644,f8648,f8689,f8694,f8699,f8703,f8708,f8712,f8716,f8724,f8731,f8737,f8742,f8746,f8754,f8798,f8856,f8860,f8864,f8868,f8875,f8879,f8920,f9080,f9084,f9100,f9104,f9114,f9118,f9132,f9136,f9140,f9202,f9274,f9468,f9476,f9487,f9513,f9521,f9525,f9529,f9533,f9563,f9571,f9575,f9579,f9583,f9598,f9600,f9638,f9781,f9786,f9802,f9815,f9883,f9924,f10092,f10104,f10108,f10112,f10116,f10122,f10129,f10144,f10148,f10152,f10156,f10173,f10180,f10187,f10253,f10525,f10537,f10540,f10542,f10544,f10555,f10557,f10722,f10726,f10730,f10734,f10788,f10994,f11009,f11160,f11164,f11168,f11172,f11176,f11206,f11210,f11214,f11218,f11258,f11263]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC177+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/10.37 % Computer : n015.cluster.edu
% 0.09/10.37 % Model : x86_64 x86_64
% 0.09/10.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/10.37 % Memory : 8046.5625MB
% 0.09/10.37 % OS : Linux 6.8.0-71-generic
% 0.09/10.37 % CPULimit : 300
% 0.09/10.37 % WCLimit : 300
% 0.09/10.37 % DateTime : Mon Sep 21 08:05:02 UTC 2026
% 0.09/10.37 % CPUTime :
% 0.09/10.39 % Drodi V4.1.1
% 96.76/22.71 % Refutation found
% 96.76/22.71 % SZS status Theorem for theBenchmark: Theorem is valid
% 96.76/22.71 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 94.65/22.78 % Elapsed time: 12.392736 seconds
% 94.65/22.78 % CPU time: 98.016883 seconds
% 94.65/22.78 % Total memory used: 441.894 MB
% 94.65/22.78 % Net memory used: 407.926 MB
%------------------------------------------------------------------------------