%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC416+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 : n003.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 02:41:09 PM UTC 2026
% Result : Theorem 19.60s 3.01s
% Output : CNFRefutation 19.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 335
% Syntax : Number of formulae : 1282 ( 47 unt; 278 def)
% Number of atoms : 4266 ( 689 equ)
% Maximal formula atoms : 24 ( 3 avg)
% Number of connectives : 4905 (1921 ~;2249 |; 252 &)
% ( 314 <=>; 169 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 4 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 298 ( 296 usr; 278 prp; 0-4 aty)
% Number of functors : 58 ( 58 usr; 7 con; 0-4 aty)
% Number of variables : 895 ( 812 !; 83 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
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(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
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(f22,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssItem(hd(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(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( leq(V,W)
& leq(U,V) )
=> leq(U,W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [U] :
( ssItem(U)
=> leq(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( geq(U,V)
<=> leq(V,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(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(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(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ? [V] :
( hd(U) = V
& ssItem(V) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ? [V] :
( tl(U) = V
& ssList(V) ) ) ),
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(f81,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) = app(cons(V,nil),U) ) ),
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(f87,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( ( geq(V,U)
& geq(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f88,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( geq(V,W)
& geq(U,V) )
=> geq(U,W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f91,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( lt(V,W)
& leq(U,V) )
=> lt(U,W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X2] :
( ssItem(X2)
=> app(cons(X2,nil),W) != X )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( neq(nil,V)
& hd(V) = X1
& cons(X1,nil) = Z
& ssItem(X1) )
& app(Z,U) = Y
& ssList(Z) )
& V = Y
& ssList(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ! [X2] :
( ssItem(X2)
=> app(cons(X2,nil),W) != X )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( neq(nil,V)
& hd(V) = X1
& cons(X1,nil) = Z
& ssItem(X1) )
& app(Z,U) = Y
& ssList(Z) )
& V = Y
& ssList(Y) )
| ~ neq(V,nil) ) )
| U != W
| V != 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(f102,plain,
( sK0_skl != sK1_skl
& ssItem(sK1_skl)
& ssItem(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2]) ).
fof(f103,plain,
ssItem(sK0_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
ssItem(sK1_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f105,plain,
sK0_skl != sK1_skl,
inference(cnf_transformation,[status(thm)],[f102]) ).
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(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(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(f134,plain,
! [X0,X1] :
( ssList(sK7_skl(X1,X0))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [X0,X1] :
( ssList(sK8_skl(X1,X0))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
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(f142,plain,
! [X0] :
( ssItem(sK9_skl(X0))
| cyclefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f143,plain,
! [X0] :
( ssItem(sK10_skl(X0))
| cyclefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f144,plain,
! [X0] :
( ssList(sK11_skl(X0))
| cyclefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f145,plain,
! [X0] :
( ssList(sK12_skl(X0))
| cyclefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f146,plain,
! [X0] :
( ssList(sK13_skl(X0))
| cyclefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f147,plain,
! [X0] :
( app(app(sK11_skl(X0),cons(sK9_skl(X0),sK12_skl(X0))),cons(sK10_skl(X0),sK13_skl(X0))) = X0
| cyclefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f148,plain,
! [X0] :
( leq(sK9_skl(X0),sK10_skl(X0))
| cyclefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f149,plain,
! [X0] :
( leq(sK10_skl(X0),sK9_skl(X0))
| 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(f154,plain,
! [X0] :
( ssItem(sK14_skl(X0))
| totalorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f155,plain,
! [X0] :
( ssItem(sK15_skl(X0))
| totalorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f156,plain,
! [X0] :
( ssList(sK16_skl(X0))
| totalorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f157,plain,
! [X0] :
( ssList(sK17_skl(X0))
| totalorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f158,plain,
! [X0] :
( ssList(sK18_skl(X0))
| totalorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f159,plain,
! [X0] :
( app(app(sK16_skl(X0),cons(sK14_skl(X0),sK17_skl(X0))),cons(sK15_skl(X0),sK18_skl(X0))) = X0
| 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(f166,plain,
! [X0] :
( ssItem(sK19_skl(X0))
| strictorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f167,plain,
! [X0] :
( ssItem(sK20_skl(X0))
| strictorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f168,plain,
! [X0] :
( ssList(sK21_skl(X0))
| strictorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f169,plain,
! [X0] :
( ssList(sK22_skl(X0))
| strictorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f170,plain,
! [X0] :
( ssList(sK23_skl(X0))
| strictorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f171,plain,
! [X0] :
( app(app(sK21_skl(X0),cons(sK19_skl(X0),sK22_skl(X0))),cons(sK20_skl(X0),sK23_skl(X0))) = X0
| 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(f178,plain,
! [X0] :
( ssItem(sK24_skl(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f179,plain,
! [X0] :
( ssItem(sK25_skl(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f180,plain,
! [X0] :
( ssList(sK26_skl(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f181,plain,
! [X0] :
( ssList(sK27_skl(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f182,plain,
! [X0] :
( ssList(sK28_skl(X0))
| totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f183,plain,
! [X0] :
( app(app(sK26_skl(X0),cons(sK24_skl(X0),sK27_skl(X0))),cons(sK25_skl(X0),sK28_skl(X0))) = X0
| 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(f189,plain,
! [X0] :
( ssItem(sK29_skl(X0))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f190,plain,
! [X0] :
( ssItem(sK30_skl(X0))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f191,plain,
! [X0] :
( ssList(sK31_skl(X0))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f192,plain,
! [X0] :
( ssList(sK32_skl(X0))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f193,plain,
! [X0] :
( ssList(sK33_skl(X0))
| strictorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f194,plain,
! [X0] :
( app(app(sK31_skl(X0),cons(sK29_skl(X0),sK32_skl(X0))),cons(sK30_skl(X0),sK33_skl(X0))) = X0
| 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(f200,plain,
! [X0] :
( ssItem(sK34_skl(X0))
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f201,plain,
! [X0] :
( ssItem(sK35_skl(X0))
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f202,plain,
! [X0] :
( ssList(sK36_skl(X0))
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f203,plain,
! [X0] :
( ssList(sK37_skl(X0))
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f204,plain,
! [X0] :
( ssList(sK38_skl(X0))
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f205,plain,
! [X0] :
( app(app(sK36_skl(X0),cons(sK34_skl(X0),sK37_skl(X0))),cons(sK35_skl(X0),sK38_skl(X0))) = X0
| duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f206,plain,
! [X0] :
( sK34_skl(X0) = sK35_skl(X0)
| 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(f211,plain,
! [X0] :
( ssItem(sK39_skl(X0))
| equalelemsP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f212,plain,
! [X0] :
( ssItem(sK40_skl(X0))
| equalelemsP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f213,plain,
! [X0] :
( ssList(sK41_skl(X0))
| equalelemsP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f214,plain,
! [X0] :
( ssList(sK42_skl(X0))
| equalelemsP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f215,plain,
! [X0] :
( app(sK41_skl(X0),cons(sK39_skl(X0),cons(sK40_skl(X0),sK42_skl(X0)))) = X0
| equalelemsP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f216,plain,
! [X0] :
( sK39_skl(X0) != sK40_skl(X0)
| equalelemsP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f219,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
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(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(f236,plain,
! [U] :
( ssItem(hd(U))
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f22]) ).
fof(f237,plain,
! [X0] :
( ssItem(hd(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f236]) ).
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(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(f252,plain,
! [U] :
( ! [V] :
( ! [W] :
( leq(U,W)
| ~ leq(V,W)
| ~ leq(U,V)
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f253,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f254,plain,
! [U] :
( leq(U,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f255,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f256,plain,
! [U] :
( ! [V] :
( ( geq(U,V)
<=> leq(V,U) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f257,plain,
! [U] :
( ! [V] :
( ( ( ~ leq(V,U)
| geq(U,V) )
& ( leq(V,U)
| ~ geq(U,V) ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f256]) ).
fof(f259,plain,
! [X0,X1] :
( ~ leq(X1,X0)
| geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f257]) ).
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(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(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(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(f318,plain,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f319,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f318]) ).
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(f363,plain,
! [U] :
( ? [V] :
( hd(U) = V
& ssItem(V) )
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f75]) ).
fof(f364,plain,
! [U] :
( ( hd(U) = sK45_skl(U)
& ssItem(sK45_skl(U)) )
| nil = U
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK45_skl]),skolemize(V,sK45_skl(U))],[f363]) ).
fof(f365,plain,
! [X0] :
( ssItem(sK45_skl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f364]) ).
fof(f366,plain,
! [X0] :
( hd(X0) = sK45_skl(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f364]) ).
fof(f367,plain,
! [U] :
( ? [V] :
( tl(U) = V
& ssList(V) )
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f76]) ).
fof(f368,plain,
! [U] :
( ( tl(U) = sK46_skl(U)
& ssList(sK46_skl(U)) )
| nil = U
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK46_skl]),skolemize(V,sK46_skl(U))],[f367]) ).
fof(f369,plain,
! [X0] :
( ssList(sK46_skl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f368]) ).
fof(f370,plain,
! [X0] :
( tl(X0) = sK46_skl(X0)
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f368]) ).
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(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(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(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(f394,plain,
! [U] :
( ! [V] :
( U = V
| ~ geq(V,U)
| ~ geq(U,V)
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f87]) ).
fof(f395,plain,
! [X0,X1] :
( X0 = X1
| ~ geq(X1,X0)
| ~ geq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f394]) ).
fof(f396,plain,
! [U] :
( ! [V] :
( ! [W] :
( geq(U,W)
| ~ geq(V,W)
| ~ geq(U,V)
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f88]) ).
fof(f397,plain,
! [X0,X1,X2] :
( geq(X0,X2)
| ~ geq(X1,X2)
| ~ geq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f396]) ).
fof(f402,plain,
! [U] :
( ! [V] :
( ! [W] :
( lt(U,W)
| ~ lt(V,W)
| ~ leq(U,V)
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f91]) ).
fof(f403,plain,
! [X0,X1,X2] :
( lt(X0,X2)
| ~ lt(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f402]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ? [X2] :
( app(cons(X2,nil),W) = X
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ~ neq(nil,V)
| hd(V) != X1
| cons(X1,nil) != Z
| ~ ssItem(X1) )
| app(Z,U) != Y
| ~ ssList(Z) )
| V != Y
| ~ ssList(Y) )
& neq(V,nil) ) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,V,W,X] :
( sP0_prd(X,W,V,U)
<=> ( ? [X2] :
( app(cons(X2,nil),W) = X
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ~ neq(nil,V)
| hd(V) != X1
| cons(X1,nil) != Z
| ~ ssItem(X1) )
| app(Z,U) != Y
| ~ ssList(Z) )
| V != Y
| ~ ssList(Y) )
& neq(V,nil) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| sP0_prd(X,W,V,U) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( ~ neq(sK50_skl,nil)
& neq(sK48_skl,nil) )
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_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]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f417]) ).
fof(f419,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f420,plain,
ssList(sK48_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
! [U,V,W,X] :
( ( ! [X2] :
( app(cons(X2,nil),W) != X
| ~ ssItem(X2) )
| ? [Y] :
( ? [Z] :
( ? [X1] :
( neq(nil,V)
& hd(V) = X1
& cons(X1,nil) = Z
& ssItem(X1) )
& app(Z,U) = Y
& ssList(Z) )
& V = Y
& ssList(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ( ( ? [X2] :
( app(cons(X2,nil),W) = X
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ! [X1] :
( ~ neq(nil,V)
| hd(V) != X1
| cons(X1,nil) != Z
| ~ ssItem(X1) )
| app(Z,U) != Y
| ~ ssList(Z) )
| V != Y
| ~ ssList(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ! [U,V,W,X] :
( ! [X2] :
( app(cons(X2,nil),W) != X
| ~ ssItem(X2) )
| ? [Y] :
( ? [Z] :
( neq(nil,V)
& ? [X1] :
( hd(V) = X1
& cons(X1,nil) = Z
& ssItem(X1) )
& app(Z,U) = Y
& ssList(Z) )
& V = Y
& ssList(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ? [X2] :
( app(cons(X2,nil),W) = X
& ssItem(X2) )
& ! [Y] :
( ! [Z] :
( ~ neq(nil,V)
| ! [X1] :
( hd(V) != X1
| cons(X1,nil) != Z
| ~ ssItem(X1) )
| app(Z,U) != Y
| ~ ssList(Z) )
| V != Y
| ~ ssList(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(miniscoping,[status(thm)],[f427]) ).
fof(f429,plain,
( ! [U,V,W,X] :
( ! [X2] :
( app(cons(X2,nil),W) != X
| ~ ssItem(X2) )
| ( neq(nil,V)
& hd(V) = sK54_skl(X,W,V,U)
& cons(sK54_skl(X,W,V,U),nil) = sK53_skl(X,W,V,U)
& ssItem(sK54_skl(X,W,V,U))
& app(sK53_skl(X,W,V,U),U) = sK52_skl(X,W,V,U)
& ssList(sK53_skl(X,W,V,U))
& V = sK52_skl(X,W,V,U)
& ssList(sK52_skl(X,W,V,U)) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( app(cons(sK51_skl(X,W,V,U),nil),W) = X
& ssItem(sK51_skl(X,W,V,U))
& ! [Y] :
( ! [Z] :
( ~ neq(nil,V)
| ! [X1] :
( hd(V) != X1
| cons(X1,nil) != Z
| ~ ssItem(X1) )
| app(Z,U) != Y
| ~ ssList(Z) )
| V != Y
| ~ ssList(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl,sK53_skl,sK54_skl]),skolemize(X2,sK51_skl(X,W,V,U)),skolemize(Y,sK52_skl(X,W,V,U)),skolemize(Z,sK53_skl(X,W,V,U)),skolemize(X1,sK54_skl(X,W,V,U))],[f428]) ).
fof(f430,plain,
! [X0,X1,X2,X3] :
( neq(X2,nil)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f431,plain,
! [X0,X1,X2,X3,X4,X5,X6] :
( ~ neq(nil,X2)
| hd(X2) != X6
| cons(X6,nil) != X5
| ~ ssItem(X6)
| app(X5,X3) != X4
| ~ ssList(X5)
| X2 != X4
| ~ ssList(X4)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f432,plain,
! [X0,X1,X2,X3] :
( ssItem(sK51_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f433,plain,
! [X0,X1,X2,X3] :
( app(cons(sK51_skl(X0,X1,X2,X3),nil),X1) = X0
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f442,definition,
( sQ0_spl
<=> sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f445,definition,
( sQ1_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( ~ sQ1_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f448,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f442,f445]) ).
fof(f449,definition,
( sQ2_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f451,plain,
( sQ2_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f449]) ).
fof(f452,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f442,f449]) ).
fof(f456,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f459,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(f468,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f469,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f468]) ).
fof(f474,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(f475,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)],[f474]) ).
fof(f487,plain,
! [X0,X1,X2,X3] :
( ~ neq(nil,app(cons(X2,nil),X3))
| hd(app(cons(X2,nil),X3)) != X2
| ~ ssItem(X2)
| ~ ssList(cons(X2,nil))
| ~ ssList(app(cons(X2,nil),X3))
| ~ sP0_prd(X0,X1,app(cons(X2,nil),X3),X3) ),
inference(destructive_equality_resolution,[status(thm)],[f431]) ).
fof(f496,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f443]) ).
fof(f497,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f496]) ).
fof(f498,plain,
! [X0] :
( nil = X0
| neq(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f220,f223]) ).
fof(f500,plain,
! [X0] :
( sK47_skl = X0
| neq(sK47_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f220,f419]) ).
fof(f501,plain,
! [X0] :
( sK0_skl = X0
| neq(sK0_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f103,f101]) ).
fof(f502,plain,
! [X0] :
( sK1_skl = X0
| neq(sK1_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f104,f101]) ).
fof(f504,plain,
( ssItem(sK4_skl(sK48_skl))
| ~ singletonP(sK48_skl) ),
inference(resolution,[status(thm)],[f116,f420]) ).
fof(f505,plain,
( ssItem(sK4_skl(sK47_skl))
| ~ singletonP(sK47_skl) ),
inference(resolution,[status(thm)],[f116,f419]) ).
fof(f513,definition,
( sQ5_spl
<=> singletonP(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f515,plain,
( sQ5_spl
| ~ singletonP(sK48_skl) ),
inference(component_clause,[status(thm)],[f513]) ).
fof(f516,definition,
( sQ6_spl
<=> ssItem(sK4_skl(sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f519,plain,
( sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f504,f513,f516]) ).
fof(f520,definition,
( sQ7_spl
<=> singletonP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f522,plain,
( sQ7_spl
| ~ singletonP(sK47_skl) ),
inference(component_clause,[status(thm)],[f520]) ).
fof(f523,definition,
( sQ8_spl
<=> ssItem(sK4_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f526,plain,
( sQ8_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f505,f520,f523]) ).
fof(f528,plain,
( cons(sK4_skl(sK48_skl),nil) = sK48_skl
| ~ singletonP(sK48_skl) ),
inference(resolution,[status(thm)],[f117,f420]) ).
fof(f529,plain,
( cons(sK4_skl(sK47_skl),nil) = sK47_skl
| ~ singletonP(sK47_skl) ),
inference(resolution,[status(thm)],[f117,f419]) ).
fof(f534,definition,
( sQ10_spl
<=> cons(sK4_skl(sK48_skl),nil) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f537,plain,
( sQ10_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f528,f513,f534]) ).
fof(f538,definition,
( sQ11_spl
<=> cons(sK4_skl(sK47_skl),nil) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f541,plain,
( sQ11_spl
| ~ sQ7_spl ),
inference(split_clause,[status(thm)],[f529,f520,f538]) ).
fof(f542,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f249,f223]) ).
fof(f543,plain,
app(nil,sK48_skl) = sK48_skl,
inference(resolution,[status(thm)],[f249,f420]) ).
fof(f544,plain,
app(nil,sK47_skl) = sK47_skl,
inference(resolution,[status(thm)],[f249,f419]) ).
fof(f545,plain,
! [X0] :
( ssList(cons(X0,nil))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f222,f223]) ).
fof(f548,plain,
! [X0,X1,X2,X3] :
( ~ neq(nil,app(cons(X2,nil),X3))
| hd(app(cons(X2,nil),X3)) != X2
| ~ ssItem(X2)
| ~ ssList(app(cons(X2,nil),X3))
| ~ sP0_prd(X0,X1,app(cons(X2,nil),X3),X3) ),
inference(backward_subsumption_resolution,[status(thm)],[f487,f545]) ).
fof(f549,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil)) ),
inference(backward_subsumption_resolution,[status(thm)],[f456,f545]) ).
fof(f552,plain,
! [X0] :
( cons(X0,sK47_skl) != sK47_skl
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f225,f419]) ).
fof(f556,plain,
! [X0,X1,X2] :
( X0 = nil
| cons(X1,nil) != cons(X2,X0)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f228,f223]) ).
fof(f558,plain,
! [X0,X1,X2] :
( X0 = sK47_skl
| cons(X1,sK47_skl) != cons(X2,X0)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f228,f419]) ).
fof(f563,plain,
( ssItem(hd(sK48_skl))
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f237,f420]) ).
fof(f564,plain,
( ssItem(hd(sK47_skl))
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f237,f419]) ).
fof(f565,definition,
( sQ12_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f572,definition,
( sQ14_spl
<=> nil = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f573,plain,
( ~ sQ14_spl
| nil = sK48_skl ),
inference(component_clause,[status(thm)],[f572]) ).
fof(f574,plain,
( sQ14_spl
| nil != sK48_skl ),
inference(component_clause,[status(thm)],[f572]) ).
fof(f575,definition,
( sQ15_spl
<=> ssItem(hd(sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f576,plain,
( ~ sQ15_spl
| ssItem(hd(sK48_skl)) ),
inference(component_clause,[status(thm)],[f575]) ).
fof(f578,plain,
( sQ15_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f563,f572,f575]) ).
fof(f579,definition,
( sQ16_spl
<=> nil = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f580,plain,
( ~ sQ16_spl
| nil = sK47_skl ),
inference(component_clause,[status(thm)],[f579]) ).
fof(f582,definition,
( sQ17_spl
<=> ssItem(hd(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f583,plain,
( ~ sQ17_spl
| ssItem(hd(sK47_skl)) ),
inference(component_clause,[status(thm)],[f582]) ).
fof(f585,plain,
( sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f564,f579,f582]) ).
fof(f586,plain,
! [X0] :
( ~ sQ16_spl
| ssItem(hd(X0))
| sK47_skl = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f237]) ).
fof(f597,plain,
! [X0] :
( ~ sQ16_spl
| cons(sK4_skl(X0),sK47_skl) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f117]) ).
fof(f616,plain,
! [X0,X1] :
( ~ sQ16_spl
| tl(app(X0,X1)) = app(tl(X0),X1)
| sK47_skl = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f393]) ).
fof(f617,plain,
! [X0,X1] :
( ~ sQ16_spl
| hd(app(X0,X1)) = hd(X0)
| sK47_skl = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f391]) ).
fof(f619,plain,
! [X0,X1] :
( ~ sQ16_spl
| sK47_skl = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f386]) ).
fof(f622,plain,
! [X0] :
( ~ sQ16_spl
| cons(hd(X0),tl(X0)) = X0
| sK47_skl = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f374]) ).
fof(f623,plain,
! [X0,X1] :
( ~ sQ16_spl
| X1 = X0
| tl(X1) != tl(X0)
| hd(X1) != hd(X0)
| sK47_skl = X0
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f372]) ).
fof(f624,plain,
! [X0] :
( ~ sQ16_spl
| tl(X0) = sK46_skl(X0)
| sK47_skl = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f370]) ).
fof(f625,plain,
! [X0] :
( ~ sQ16_spl
| ssList(sK46_skl(X0))
| sK47_skl = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f369]) ).
fof(f626,plain,
! [X0] :
( ~ sQ16_spl
| hd(X0) = sK45_skl(X0)
| sK47_skl = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f366]) ).
fof(f627,plain,
! [X0] :
( ~ sQ16_spl
| ssItem(sK45_skl(X0))
| sK47_skl = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f365]) ).
fof(f647,plain,
! [X0] :
( ~ sQ16_spl
| segmentP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f323]) ).
fof(f653,plain,
! [X0] :
( ~ sQ16_spl
| ssList(tl(X0))
| sK47_skl = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f241]) ).
fof(f654,plain,
! [X0] :
( ~ sQ16_spl
| cons(sK44_skl(X0),sK43_skl(X0)) = X0
| sK47_skl = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f233]) ).
fof(f655,plain,
! [X0] :
( ~ sQ16_spl
| ssItem(sK44_skl(X0))
| sK47_skl = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f232]) ).
fof(f656,plain,
! [X0] :
( ~ sQ16_spl
| ssList(sK43_skl(X0))
| sK47_skl = X0
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f580,f231]) ).
fof(f697,plain,
! [X0,X1] :
( ~ sQ16_spl
| sK47_skl = X0
| sK47_skl != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f580,f619]) ).
fof(f699,plain,
! [X0,X1] :
( ~ sQ16_spl
| X1 = X0
| tl(X1) != tl(X0)
| hd(X1) != hd(X0)
| sK47_skl = X0
| sK47_skl = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f580,f623]) ).
fof(f708,plain,
! [X0] :
( hd(cons(X0,sK47_skl)) = X0
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f239,f419]) ).
fof(f729,definition,
( sQ22_spl
<=> sK47_skl = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f793,plain,
! [X0,X1,X2,X3] :
( ~ sQ14_spl
| neq(X2,sK48_skl)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(backward_demodulation,[status(thm)],[f573,f430]) ).
fof(f922,plain,
( ~ sQ0_spl
| ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)) ),
inference(resolution,[status(thm)],[f497,f432]) ).
fof(f925,definition,
( sQ37_spl
<=> sK48_skl = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f928,definition,
( sQ38_spl
<=> ssList(sK43_skl(sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f932,definition,
( sQ39_spl
<=> sK48_skl = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f933,plain,
( ~ sQ39_spl
| sK48_skl = sK47_skl ),
inference(component_clause,[status(thm)],[f932]) ).
fof(f935,definition,
( sQ40_spl
<=> ssList(sK43_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f936,plain,
( ~ sQ40_spl
| ssList(sK43_skl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f935]) ).
fof(f1210,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| neq(sK48_skl,sK48_skl) ),
inference(resolution,[status(thm)],[f793,f497]) ).
fof(f1286,definition,
( sQ72_spl
<=> ssItem(hd(sK43_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1317,definition,
( sQ80_spl
<=> ssList(sK43_skl(sK43_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1391,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1210,f469]) ).
fof(f1400,plain,
( ~ sQ0_spl
| ~ sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1391,f420]) ).
fof(f1401,plain,
( ~ sQ0_spl
| ~ sQ14_spl ),
inference(contradiction_clause,[status(thm)],[f1400]) ).
fof(f1402,plain,
( sQ2_spl
| ~ neq(sK48_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f451]) ).
fof(f1403,plain,
( sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1402,f446]) ).
fof(f1404,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f1403]) ).
fof(f1660,plain,
! [X0] :
( cons(X0,sK47_skl) = app(cons(X0,nil),sK47_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f380,f419]) ).
fof(f1665,plain,
! [X0] :
( nil = sK48_skl
| nil != app(sK48_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f386,f420]) ).
fof(f1666,plain,
! [X0] :
( nil = sK47_skl
| nil != app(sK47_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f386,f419]) ).
fof(f1671,definition,
! [X0] :
( sQ144_spl
<=> ( nil != app(sK48_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1674,plain,
( sQ14_spl
| sQ144_spl ),
inference(split_clause,[status(thm)],[f1665,f1671,f572]) ).
fof(f1675,definition,
! [X0] :
( sQ145_spl
<=> ( nil != app(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1678,plain,
( sQ16_spl
| sQ145_spl ),
inference(split_clause,[status(thm)],[f1666,f1675,f579]) ).
fof(f1680,plain,
app(sK48_skl,nil) = sK48_skl,
inference(resolution,[status(thm)],[f389,f420]) ).
fof(f1681,plain,
app(sK47_skl,nil) = sK47_skl,
inference(resolution,[status(thm)],[f389,f419]) ).
fof(f1753,plain,
! [X0] :
( hd(app(sK48_skl,X0)) = hd(sK48_skl)
| nil = sK48_skl
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f391,f420]) ).
fof(f1754,plain,
! [X0] :
( hd(app(sK47_skl,X0)) = hd(sK47_skl)
| nil = sK47_skl
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f391,f419]) ).
fof(f1759,definition,
! [X0] :
( sQ162_spl
<=> ( hd(app(sK48_skl,X0)) = hd(sK48_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f1762,plain,
( sQ14_spl
| sQ162_spl ),
inference(split_clause,[status(thm)],[f1753,f1759,f572]) ).
fof(f1763,definition,
! [X0] :
( sQ163_spl
<=> ( hd(app(sK47_skl,X0)) = hd(sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f1766,plain,
( sQ16_spl
| sQ163_spl ),
inference(split_clause,[status(thm)],[f1754,f1763,f579]) ).
fof(f1779,plain,
( sQ14_spl
| ~ sQ16_spl
| sK47_skl != sK48_skl ),
inference(backward_demodulation,[status(thm)],[f580,f574]) ).
fof(f2257,plain,
! [X0] :
( tl(cons(X0,sK47_skl)) = sK47_skl
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f243,f419]) ).
fof(f2260,plain,
leq(sK1_skl,sK1_skl),
inference(resolution,[status(thm)],[f255,f104]) ).
fof(f2261,plain,
leq(sK0_skl,sK0_skl),
inference(resolution,[status(thm)],[f255,f103]) ).
fof(f2262,plain,
( ~ sQ0_spl
| app(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil),sK47_skl) = sK48_skl ),
inference(resolution,[status(thm)],[f433,f497]) ).
fof(f2264,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK47_skl)
| segmentP(app(app(sK47_skl,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f1681,f459]) ).
fof(f2265,definition,
! [X0] :
( sQ215_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK47_skl,nil),X0),nil)
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f2268,definition,
( sQ216_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f2270,plain,
( sQ216_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f2268]) ).
fof(f2271,definition,
( sQ217_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f2273,plain,
( sQ217_spl
| ~ ssList(sK47_skl) ),
inference(component_clause,[status(thm)],[f2271]) ).
fof(f2274,plain,
( ~ sQ217_spl
| ~ sQ216_spl
| sQ215_spl ),
inference(split_clause,[status(thm)],[f2264,f2265,f2268,f2271]) ).
fof(f2279,plain,
( sQ217_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2273,f419]) ).
fof(f2280,plain,
sQ217_spl,
inference(contradiction_clause,[status(thm)],[f2279]) ).
fof(f2294,plain,
( ~ sQ15_spl
| singletonP(cons(hd(sK48_skl),nil)) ),
inference(resolution,[status(thm)],[f549,f576]) ).
fof(f2297,plain,
singletonP(cons(sK0_skl,nil)),
inference(resolution,[status(thm)],[f549,f103]) ).
fof(f2298,plain,
( geq(sK1_skl,sK1_skl)
| ~ ssItem(sK1_skl)
| ~ ssItem(sK1_skl) ),
inference(resolution,[status(thm)],[f2260,f259]) ).
fof(f2299,plain,
! [X0] :
( leq(sK1_skl,X0)
| ~ leq(sK1_skl,X0)
| ~ ssItem(X0)
| ~ ssItem(sK1_skl)
| ~ ssItem(sK1_skl) ),
inference(resolution,[status(thm)],[f2260,f253]) ).
fof(f2301,definition,
( sQ218_spl
<=> ssItem(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f2303,plain,
( sQ218_spl
| ~ ssItem(sK1_skl) ),
inference(component_clause,[status(thm)],[f2301]) ).
fof(f2304,definition,
( sQ219_spl
<=> geq(sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f2305,plain,
( ~ sQ219_spl
| geq(sK1_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f2304]) ).
fof(f2307,plain,
( sQ219_spl
| ~ sQ218_spl ),
inference(split_clause,[status(thm)],[f2298,f2301,f2304]) ).
fof(f2308,definition,
! [X0] :
( sQ220_spl
<=> ( leq(sK1_skl,X0)
| ~ leq(sK1_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f2311,plain,
( sQ220_spl
| ~ sQ218_spl ),
inference(split_clause,[status(thm)],[f2299,f2301,f2308]) ).
fof(f2312,definition,
( sQ221_spl
<=> leq(sK1_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f2314,plain,
( sQ221_spl
| ~ leq(sK1_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f2312]) ).
fof(f2315,definition,
( sQ222_spl
<=> sK1_skl = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f2319,plain,
( sQ218_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2303,f104]) ).
fof(f2320,plain,
sQ218_spl,
inference(contradiction_clause,[status(thm)],[f2319]) ).
fof(f2321,plain,
( sQ221_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2314,f2260]) ).
fof(f2322,plain,
sQ221_spl,
inference(contradiction_clause,[status(thm)],[f2321]) ).
fof(f2323,plain,
( geq(sK0_skl,sK0_skl)
| ~ ssItem(sK0_skl)
| ~ ssItem(sK0_skl) ),
inference(resolution,[status(thm)],[f2261,f259]) ).
fof(f2324,plain,
! [X0] :
( leq(sK0_skl,X0)
| ~ leq(sK0_skl,X0)
| ~ ssItem(X0)
| ~ ssItem(sK0_skl)
| ~ ssItem(sK0_skl) ),
inference(resolution,[status(thm)],[f2261,f253]) ).
fof(f2326,definition,
( sQ223_spl
<=> ssItem(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f2328,plain,
( sQ223_spl
| ~ ssItem(sK0_skl) ),
inference(component_clause,[status(thm)],[f2326]) ).
fof(f2329,definition,
( sQ224_spl
<=> geq(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f2330,plain,
( ~ sQ224_spl
| geq(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f2329]) ).
fof(f2332,plain,
( sQ224_spl
| ~ sQ223_spl ),
inference(split_clause,[status(thm)],[f2323,f2326,f2329]) ).
fof(f2333,definition,
! [X0] :
( sQ225_spl
<=> ( leq(sK0_skl,X0)
| ~ leq(sK0_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f2336,plain,
( sQ225_spl
| ~ sQ223_spl ),
inference(split_clause,[status(thm)],[f2324,f2326,f2333]) ).
fof(f2337,definition,
( sQ226_spl
<=> leq(sK0_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f2339,plain,
( sQ226_spl
| ~ leq(sK0_skl,sK0_skl) ),
inference(component_clause,[status(thm)],[f2337]) ).
fof(f2340,definition,
( sQ227_spl
<=> sK0_skl = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2344,plain,
( sQ223_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2328,f103]) ).
fof(f2345,plain,
sQ223_spl,
inference(contradiction_clause,[status(thm)],[f2344]) ).
fof(f2346,plain,
( sQ226_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2339,f2261]) ).
fof(f2347,plain,
sQ226_spl,
inference(contradiction_clause,[status(thm)],[f2346]) ).
fof(f2348,plain,
! [X0] :
( memberP(nil,X0)
| memberP(sK47_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssList(sK47_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1681,f270]) ).
fof(f2349,definition,
! [X0] :
( sQ228_spl
<=> ( memberP(nil,X0)
| memberP(sK47_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f2352,plain,
( ~ sQ216_spl
| ~ sQ217_spl
| sQ228_spl ),
inference(split_clause,[status(thm)],[f2348,f2349,f2271,f2268]) ).
fof(f2353,plain,
( sQ216_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2270,f223]) ).
fof(f2354,plain,
sQ216_spl,
inference(contradiction_clause,[status(thm)],[f2353]) ).
fof(f2362,definition,
( sQ230_spl
<=> neq(nil,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f2363,plain,
( ~ sQ230_spl
| neq(nil,sK48_skl) ),
inference(component_clause,[status(thm)],[f2362]) ).
fof(f2376,plain,
( sK47_skl = nil
| neq(sK47_skl,nil) ),
inference(resolution,[status(thm)],[f500,f223]) ).
fof(f2377,plain,
( sK47_skl = sK48_skl
| neq(sK47_skl,sK48_skl) ),
inference(resolution,[status(thm)],[f500,f420]) ).
fof(f2379,definition,
( sQ231_spl
<=> neq(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f2382,plain,
( sQ16_spl
| sQ231_spl ),
inference(split_clause,[status(thm)],[f2376,f2379,f579]) ).
fof(f2383,definition,
( sQ232_spl
<=> neq(sK47_skl,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f2386,plain,
( sQ39_spl
| sQ232_spl ),
inference(split_clause,[status(thm)],[f2377,f2383,f932]) ).
fof(f2517,plain,
( ~ sQ16_spl
| app(nil,nil) = sK47_skl ),
inference(backward_demodulation,[status(thm)],[f580,f542]) ).
fof(f2530,plain,
( sQ14_spl
| ~ sQ16_spl
| ~ sQ39_spl
| sK47_skl != sK47_skl ),
inference(forward_demodulation,[status(thm)],[f933,f1779]) ).
fof(f2531,plain,
( sQ14_spl
| ~ sQ16_spl
| ~ sQ39_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2530]) ).
fof(f2532,plain,
( sQ14_spl
| ~ sQ16_spl
| ~ sQ39_spl ),
inference(contradiction_clause,[status(thm)],[f2531]) ).
fof(f2657,plain,
frontsegP(sK48_skl,sK48_skl),
inference(resolution,[status(thm)],[f286,f420]) ).
fof(f2658,plain,
frontsegP(sK47_skl,sK47_skl),
inference(resolution,[status(thm)],[f286,f419]) ).
fof(f2660,plain,
! [X0,X1] :
( frontsegP(app(X0,sK47_skl),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f288,f419]) ).
fof(f2662,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| frontsegP(cons(sK1_skl,X0),cons(sK1_skl,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f475,f104]) ).
fof(f2663,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| frontsegP(cons(sK0_skl,X0),cons(sK0_skl,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f475,f103]) ).
fof(f2666,plain,
! [X0,X1] :
( frontsegP(app(X0,nil),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f223,f288]) ).
fof(f2667,plain,
frontsegP(nil,nil),
inference(resolution,[status(thm)],[f223,f286]) ).
fof(f2790,plain,
rearsegP(nil,nil),
inference(resolution,[status(thm)],[f305,f223]) ).
fof(f2791,plain,
rearsegP(sK48_skl,sK48_skl),
inference(resolution,[status(thm)],[f305,f420]) ).
fof(f2792,plain,
rearsegP(sK47_skl,sK47_skl),
inference(resolution,[status(thm)],[f305,f419]) ).
fof(f2793,plain,
! [X0,X1] :
( rearsegP(app(nil,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f307,f223]) ).
fof(f2795,plain,
! [X0,X1] :
( rearsegP(app(sK47_skl,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f307,f419]) ).
fof(f2796,plain,
segmentP(nil,nil),
inference(resolution,[status(thm)],[f319,f223]) ).
fof(f2797,plain,
segmentP(sK48_skl,sK48_skl),
inference(resolution,[status(thm)],[f319,f420]) ).
fof(f2798,plain,
segmentP(sK47_skl,sK47_skl),
inference(resolution,[status(thm)],[f319,f419]) ).
fof(f2804,definition,
( sQ235_spl
<=> neq(nil,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f2932,plain,
( ~ sQ15_spl
| ~ sQ16_spl
| singletonP(cons(hd(sK48_skl),sK47_skl)) ),
inference(backward_demodulation,[status(thm)],[f2935,f2294]) ).
fof(f2935,plain,
( ~ sQ16_spl
| nil = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f542,f2517]) ).
fof(f3015,plain,
( ~ sQ16_spl
| cons(sK4_skl(sK48_skl),sK47_skl) = sK48_skl
| ~ singletonP(sK48_skl) ),
inference(resolution,[status(thm)],[f597,f420]) ).
fof(f3017,definition,
( sQ236_spl
<=> cons(sK4_skl(sK48_skl),sK47_skl) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f3020,plain,
( ~ sQ16_spl
| sQ236_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3015,f513,f3017,f579]) ).
fof(f3033,plain,
( sK48_skl = sK48_skl
| ~ frontsegP(sK48_skl,sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2657,f284]) ).
fof(f3034,plain,
! [X0] :
( frontsegP(sK48_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2657,f282]) ).
fof(f3035,plain,
( app(sK48_skl,sK5_skl(sK48_skl,sK48_skl)) = sK48_skl
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2657,f123]) ).
fof(f3036,plain,
( ssList(sK5_skl(sK48_skl,sK48_skl))
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2657,f122]) ).
fof(f3037,definition,
( sQ238_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f3039,plain,
( sQ238_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f3037]) ).
fof(f3040,definition,
( sQ239_spl
<=> frontsegP(sK48_skl,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f3042,plain,
( sQ239_spl
| ~ frontsegP(sK48_skl,sK48_skl) ),
inference(component_clause,[status(thm)],[f3040]) ).
fof(f3043,plain,
( sQ37_spl
| ~ sQ239_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f3033,f3037,f3040,f925]) ).
fof(f3044,definition,
! [X0] :
( sQ240_spl
<=> ( frontsegP(sK48_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f3047,plain,
( sQ240_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f3034,f3037,f3044]) ).
fof(f3048,definition,
( sQ241_spl
<=> app(sK48_skl,sK5_skl(sK48_skl,sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f3051,plain,
( sQ241_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f3035,f3037,f3048]) ).
fof(f3052,definition,
( sQ242_spl
<=> ssList(sK5_skl(sK48_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f3055,plain,
( sQ242_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f3036,f3037,f3052]) ).
fof(f3056,plain,
( sQ238_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3039,f420]) ).
fof(f3057,plain,
sQ238_spl,
inference(contradiction_clause,[status(thm)],[f3056]) ).
fof(f3058,plain,
( sQ239_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3042,f2657]) ).
fof(f3059,plain,
sQ239_spl,
inference(contradiction_clause,[status(thm)],[f3058]) ).
fof(f3062,plain,
( ~ sQ224_spl
| sK0_skl = sK0_skl
| ~ geq(sK0_skl,sK0_skl)
| ~ ssItem(sK0_skl)
| ~ ssItem(sK0_skl) ),
inference(resolution,[status(thm)],[f395,f2330]) ).
fof(f3063,plain,
( ~ sQ219_spl
| sK1_skl = sK1_skl
| ~ geq(sK1_skl,sK1_skl)
| ~ ssItem(sK1_skl)
| ~ ssItem(sK1_skl) ),
inference(resolution,[status(thm)],[f395,f2305]) ).
fof(f3064,plain,
( sQ227_spl
| ~ sQ224_spl
| ~ sQ223_spl ),
inference(split_clause,[status(thm)],[f3062,f2326,f2329,f2340]) ).
fof(f3065,plain,
( sQ222_spl
| ~ sQ219_spl
| ~ sQ218_spl ),
inference(split_clause,[status(thm)],[f3063,f2301,f2304,f2315]) ).
fof(f3066,plain,
! [X0] :
( ~ sQ224_spl
| geq(sK0_skl,X0)
| ~ geq(sK0_skl,X0)
| ~ ssItem(X0)
| ~ ssItem(sK0_skl)
| ~ ssItem(sK0_skl) ),
inference(resolution,[status(thm)],[f397,f2330]) ).
fof(f3067,plain,
! [X0] :
( ~ sQ219_spl
| geq(sK1_skl,X0)
| ~ geq(sK1_skl,X0)
| ~ ssItem(X0)
| ~ ssItem(sK1_skl)
| ~ ssItem(sK1_skl) ),
inference(resolution,[status(thm)],[f397,f2305]) ).
fof(f3068,definition,
! [X0] :
( sQ243_spl
<=> ( geq(sK0_skl,X0)
| ~ geq(sK0_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f3071,plain,
( ~ sQ224_spl
| sQ243_spl
| ~ sQ223_spl ),
inference(split_clause,[status(thm)],[f3066,f2326,f3068,f2329]) ).
fof(f3072,definition,
! [X0] :
( sQ244_spl
<=> ( geq(sK1_skl,X0)
| ~ geq(sK1_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f3075,plain,
( ~ sQ219_spl
| sQ244_spl
| ~ sQ218_spl ),
inference(split_clause,[status(thm)],[f3067,f2301,f3072,f2304]) ).
fof(f3080,plain,
! [X0] :
( lt(sK0_skl,X0)
| ~ lt(sK0_skl,X0)
| ~ ssItem(X0)
| ~ ssItem(sK0_skl)
| ~ ssItem(sK0_skl) ),
inference(resolution,[status(thm)],[f403,f2261]) ).
fof(f3081,plain,
! [X0] :
( lt(sK1_skl,X0)
| ~ lt(sK1_skl,X0)
| ~ ssItem(X0)
| ~ ssItem(sK1_skl)
| ~ ssItem(sK1_skl) ),
inference(resolution,[status(thm)],[f403,f2260]) ).
fof(f3082,definition,
! [X0] :
( sQ245_spl
<=> ( lt(sK0_skl,X0)
| ~ lt(sK0_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f3085,plain,
( sQ245_spl
| ~ sQ223_spl ),
inference(split_clause,[status(thm)],[f3080,f2326,f3082]) ).
fof(f3086,definition,
! [X0] :
( sQ246_spl
<=> ( lt(sK1_skl,X0)
| ~ lt(sK1_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f3089,plain,
( sQ246_spl
| ~ sQ218_spl ),
inference(split_clause,[status(thm)],[f3081,f2301,f3086]) ).
fof(f3090,plain,
( sK47_skl = sK47_skl
| ~ frontsegP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2658,f284]) ).
fof(f3091,plain,
! [X0] :
( frontsegP(sK47_skl,X0)
| ~ frontsegP(sK47_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2658,f282]) ).
fof(f3092,plain,
( app(sK47_skl,sK5_skl(sK47_skl,sK47_skl)) = sK47_skl
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2658,f123]) ).
fof(f3093,plain,
( ssList(sK5_skl(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2658,f122]) ).
fof(f3094,definition,
( sQ247_spl
<=> frontsegP(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f3096,plain,
( sQ247_spl
| ~ frontsegP(sK47_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f3094]) ).
fof(f3097,plain,
( sQ22_spl
| ~ sQ247_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f3090,f2271,f3094,f729]) ).
fof(f3098,definition,
! [X0] :
( sQ248_spl
<=> ( frontsegP(sK47_skl,X0)
| ~ frontsegP(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f3101,plain,
( sQ248_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f3091,f2271,f3098]) ).
fof(f3102,definition,
( sQ249_spl
<=> app(sK47_skl,sK5_skl(sK47_skl,sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f3105,plain,
( sQ249_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f3092,f2271,f3102]) ).
fof(f3106,definition,
( sQ250_spl
<=> ssList(sK5_skl(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f3109,plain,
( sQ250_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f3093,f2271,f3106]) ).
fof(f3110,plain,
( sQ247_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3096,f2658]) ).
fof(f3111,plain,
sQ247_spl,
inference(contradiction_clause,[status(thm)],[f3110]) ).
fof(f3113,plain,
! [X0] :
( rearsegP(sK48_skl,X0)
| ~ rearsegP(sK48_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2791,f301]) ).
fof(f3114,plain,
( app(sK6_skl(sK48_skl,sK48_skl),sK48_skl) = sK48_skl
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2791,f129]) ).
fof(f3115,plain,
( ssList(sK6_skl(sK48_skl,sK48_skl))
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2791,f128]) ).
fof(f3116,definition,
( sQ251_spl
<=> rearsegP(sK48_skl,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f3118,plain,
( sQ251_spl
| ~ rearsegP(sK48_skl,sK48_skl) ),
inference(component_clause,[status(thm)],[f3116]) ).
fof(f3120,definition,
! [X0] :
( sQ252_spl
<=> ( rearsegP(sK48_skl,X0)
| ~ rearsegP(sK48_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f3123,plain,
( sQ252_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f3113,f3037,f3120]) ).
fof(f3124,definition,
( sQ253_spl
<=> app(sK6_skl(sK48_skl,sK48_skl),sK48_skl) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f3127,plain,
( sQ253_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f3114,f3037,f3124]) ).
fof(f3128,definition,
( sQ254_spl
<=> ssList(sK6_skl(sK48_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f3131,plain,
( sQ254_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f3115,f3037,f3128]) ).
fof(f3132,plain,
( sQ251_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3118,f2791]) ).
fof(f3133,plain,
sQ251_spl,
inference(contradiction_clause,[status(thm)],[f3132]) ).
fof(f3135,plain,
! [X0] :
( rearsegP(sK47_skl,X0)
| ~ rearsegP(sK47_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2792,f301]) ).
fof(f3136,plain,
( app(sK6_skl(sK47_skl,sK47_skl),sK47_skl) = sK47_skl
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2792,f129]) ).
fof(f3137,plain,
( ssList(sK6_skl(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2792,f128]) ).
fof(f3138,definition,
( sQ255_spl
<=> rearsegP(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f3140,plain,
( sQ255_spl
| ~ rearsegP(sK47_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f3138]) ).
fof(f3142,definition,
! [X0] :
( sQ256_spl
<=> ( rearsegP(sK47_skl,X0)
| ~ rearsegP(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f3145,plain,
( sQ256_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f3135,f2271,f3142]) ).
fof(f3146,definition,
( sQ257_spl
<=> app(sK6_skl(sK47_skl,sK47_skl),sK47_skl) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f3149,plain,
( sQ257_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f3136,f2271,f3146]) ).
fof(f3150,definition,
( sQ258_spl
<=> ssList(sK6_skl(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f3153,plain,
( sQ258_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f3137,f2271,f3150]) ).
fof(f3154,plain,
( sQ255_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3140,f2792]) ).
fof(f3155,plain,
sQ255_spl,
inference(contradiction_clause,[status(thm)],[f3154]) ).
fof(f3157,plain,
! [X0] :
( segmentP(sK48_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2797,f315]) ).
fof(f3158,plain,
( app(app(sK7_skl(sK48_skl,sK48_skl),sK48_skl),sK8_skl(sK48_skl,sK48_skl)) = sK48_skl
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2797,f136]) ).
fof(f3159,plain,
( ssList(sK8_skl(sK48_skl,sK48_skl))
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2797,f135]) ).
fof(f3160,plain,
( ssList(sK7_skl(sK48_skl,sK48_skl))
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2797,f134]) ).
fof(f3161,definition,
( sQ259_spl
<=> segmentP(sK48_skl,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f3163,plain,
( sQ259_spl
| ~ segmentP(sK48_skl,sK48_skl) ),
inference(component_clause,[status(thm)],[f3161]) ).
fof(f3165,definition,
! [X0] :
( sQ260_spl
<=> ( segmentP(sK48_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f3168,plain,
( sQ260_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f3157,f3037,f3165]) ).
fof(f3169,definition,
( sQ261_spl
<=> app(app(sK7_skl(sK48_skl,sK48_skl),sK48_skl),sK8_skl(sK48_skl,sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f3172,plain,
( sQ261_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f3158,f3037,f3169]) ).
fof(f3173,definition,
( sQ262_spl
<=> ssList(sK8_skl(sK48_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f3176,plain,
( sQ262_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f3159,f3037,f3173]) ).
fof(f3177,definition,
( sQ263_spl
<=> ssList(sK7_skl(sK48_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f3180,plain,
( sQ263_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f3160,f3037,f3177]) ).
fof(f3181,plain,
( sQ259_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3163,f2797]) ).
fof(f3182,plain,
sQ259_spl,
inference(contradiction_clause,[status(thm)],[f3181]) ).
fof(f3184,plain,
! [X0] :
( segmentP(sK47_skl,X0)
| ~ segmentP(sK47_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2798,f315]) ).
fof(f3185,plain,
( app(app(sK7_skl(sK47_skl,sK47_skl),sK47_skl),sK8_skl(sK47_skl,sK47_skl)) = sK47_skl
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2798,f136]) ).
fof(f3186,plain,
( ssList(sK8_skl(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2798,f135]) ).
fof(f3187,plain,
( ssList(sK7_skl(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2798,f134]) ).
fof(f3188,definition,
( sQ264_spl
<=> segmentP(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f3190,plain,
( sQ264_spl
| ~ segmentP(sK47_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f3188]) ).
fof(f3192,definition,
! [X0] :
( sQ265_spl
<=> ( segmentP(sK47_skl,X0)
| ~ segmentP(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ265_spl])],[split_symbol_definition]) ).
fof(f3195,plain,
( sQ265_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f3184,f2271,f3192]) ).
fof(f3196,definition,
( sQ266_spl
<=> app(app(sK7_skl(sK47_skl,sK47_skl),sK47_skl),sK8_skl(sK47_skl,sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f3199,plain,
( sQ266_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f3185,f2271,f3196]) ).
fof(f3200,definition,
( sQ267_spl
<=> ssList(sK8_skl(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f3203,plain,
( sQ267_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f3186,f2271,f3200]) ).
fof(f3204,definition,
( sQ268_spl
<=> ssList(sK7_skl(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f3207,plain,
( sQ268_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f3187,f2271,f3204]) ).
fof(f3208,plain,
( sQ264_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3190,f2798]) ).
fof(f3209,plain,
sQ264_spl,
inference(contradiction_clause,[status(thm)],[f3208]) ).
fof(f3220,plain,
! [X0] :
( ~ sQ16_spl
| tl(app(sK48_skl,X0)) = app(tl(sK48_skl),X0)
| sK47_skl = sK48_skl
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f616,f420]) ).
fof(f3222,definition,
! [X0] :
( sQ271_spl
<=> ( tl(app(sK48_skl,X0)) = app(tl(sK48_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f3225,plain,
( ~ sQ16_spl
| sQ39_spl
| sQ271_spl ),
inference(split_clause,[status(thm)],[f3220,f3222,f932,f579]) ).
fof(f3226,definition,
! [X0] :
( sQ272_spl
<=> ( tl(app(sK47_skl,X0)) = app(tl(sK47_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f3474,plain,
! [X0] :
( tl(app(sK47_skl,X0)) = app(tl(sK47_skl),X0)
| nil = sK47_skl
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f393,f419]) ).
fof(f3479,plain,
( sQ16_spl
| sQ272_spl ),
inference(split_clause,[status(thm)],[f3474,f3226,f579]) ).
fof(f3487,plain,
( cons(hd(sK47_skl),tl(sK47_skl)) = sK47_skl
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f374,f419]) ).
fof(f3492,definition,
( sQ275_spl
<=> cons(hd(sK47_skl),tl(sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f3493,plain,
( ~ sQ275_spl
| cons(hd(sK47_skl),tl(sK47_skl)) = sK47_skl ),
inference(component_clause,[status(thm)],[f3492]) ).
fof(f3495,plain,
( sQ275_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f3487,f579,f3492]) ).
fof(f3771,plain,
! [X0] :
( ~ sQ16_spl
| hd(app(sK48_skl,X0)) = hd(sK48_skl)
| sK47_skl = sK48_skl
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f617,f420]) ).
fof(f3773,plain,
( ~ sQ16_spl
| sQ39_spl
| sQ162_spl ),
inference(split_clause,[status(thm)],[f3771,f1759,f932,f579]) ).
fof(f3777,plain,
! [X0] :
( ~ sQ16_spl
| sK47_skl = sK48_skl
| sK47_skl != app(sK48_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f697,f420]) ).
fof(f3779,definition,
! [X0] :
( sQ276_spl
<=> ( sK47_skl != app(sK48_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f3782,plain,
( ~ sQ16_spl
| sQ39_spl
| sQ276_spl ),
inference(split_clause,[status(thm)],[f3777,f3779,f932,f579]) ).
fof(f3791,plain,
( ~ sQ16_spl
| cons(hd(sK48_skl),tl(sK48_skl)) = sK48_skl
| sK47_skl = sK48_skl ),
inference(resolution,[status(thm)],[f622,f420]) ).
fof(f3793,definition,
( sQ278_spl
<=> cons(hd(sK48_skl),tl(sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f3794,plain,
( ~ sQ278_spl
| cons(hd(sK48_skl),tl(sK48_skl)) = sK48_skl ),
inference(component_clause,[status(thm)],[f3793]) ).
fof(f3796,plain,
( ~ sQ16_spl
| sQ278_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f3791,f932,f3793,f579]) ).
fof(f3798,plain,
! [X0] :
( ~ sQ16_spl
| X0 = sK48_skl
| tl(X0) != tl(sK48_skl)
| hd(X0) != hd(sK48_skl)
| sK47_skl = sK48_skl
| sK47_skl = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f699,f420]) ).
fof(f3800,definition,
! [X0] :
( sQ279_spl
<=> ( X0 = sK48_skl
| tl(X0) != tl(sK48_skl)
| hd(X0) != hd(sK48_skl)
| sK47_skl = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f3803,plain,
( ~ sQ16_spl
| sQ39_spl
| sQ279_spl ),
inference(split_clause,[status(thm)],[f3798,f3800,f932,f579]) ).
fof(f3809,plain,
( ~ sQ16_spl
| tl(sK48_skl) = sK46_skl(sK48_skl)
| sK47_skl = sK48_skl ),
inference(resolution,[status(thm)],[f624,f420]) ).
fof(f3811,definition,
( sQ281_spl
<=> tl(sK48_skl) = sK46_skl(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f3812,plain,
( ~ sQ281_spl
| tl(sK48_skl) = sK46_skl(sK48_skl) ),
inference(component_clause,[status(thm)],[f3811]) ).
fof(f3814,plain,
( ~ sQ16_spl
| sQ281_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f3809,f932,f3811,f579]) ).
fof(f3815,definition,
( sQ282_spl
<=> tl(sK47_skl) = sK46_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f3816,plain,
( ~ sQ282_spl
| tl(sK47_skl) = sK46_skl(sK47_skl) ),
inference(component_clause,[status(thm)],[f3815]) ).
fof(f3820,plain,
( ~ sQ278_spl
| ~ sQ281_spl
| cons(hd(sK48_skl),sK46_skl(sK48_skl)) = sK48_skl ),
inference(backward_demodulation,[status(thm)],[f3812,f3794]) ).
fof(f3823,plain,
( ~ sQ275_spl
| ~ sQ282_spl
| cons(hd(sK47_skl),sK46_skl(sK47_skl)) = sK47_skl ),
inference(backward_demodulation,[status(thm)],[f3816,f3493]) ).
fof(f3825,plain,
( ~ sQ16_spl
| ssList(sK46_skl(sK48_skl))
| sK47_skl = sK48_skl ),
inference(resolution,[status(thm)],[f625,f420]) ).
fof(f3827,definition,
( sQ283_spl
<=> ssList(sK46_skl(sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ283_spl])],[split_symbol_definition]) ).
fof(f3830,plain,
( ~ sQ16_spl
| sQ283_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f3825,f932,f3827,f579]) ).
fof(f3831,definition,
( sQ284_spl
<=> ssList(sK46_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f3832,plain,
( ~ sQ284_spl
| ssList(sK46_skl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f3831]) ).
fof(f3858,plain,
( ~ sQ16_spl
| hd(sK48_skl) = sK45_skl(sK48_skl)
| sK47_skl = sK48_skl ),
inference(resolution,[status(thm)],[f626,f420]) ).
fof(f3860,definition,
( sQ285_spl
<=> hd(sK48_skl) = sK45_skl(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f3861,plain,
( ~ sQ285_spl
| hd(sK48_skl) = sK45_skl(sK48_skl) ),
inference(component_clause,[status(thm)],[f3860]) ).
fof(f3863,plain,
( ~ sQ16_spl
| sQ285_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f3858,f932,f3860,f579]) ).
fof(f3864,definition,
( sQ286_spl
<=> hd(sK47_skl) = sK45_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f3865,plain,
( ~ sQ286_spl
| hd(sK47_skl) = sK45_skl(sK47_skl) ),
inference(component_clause,[status(thm)],[f3864]) ).
fof(f3868,plain,
( ~ sQ278_spl
| ~ sQ281_spl
| ~ sQ285_spl
| cons(sK45_skl(sK48_skl),sK46_skl(sK48_skl)) = sK48_skl ),
inference(backward_demodulation,[status(thm)],[f3861,f3820]) ).
fof(f3870,plain,
( ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ285_spl
| singletonP(cons(sK45_skl(sK48_skl),sK47_skl)) ),
inference(backward_demodulation,[status(thm)],[f3861,f2932]) ).
fof(f3900,plain,
( ~ sQ16_spl
| ssItem(sK45_skl(sK48_skl))
| sK47_skl = sK48_skl ),
inference(resolution,[status(thm)],[f627,f420]) ).
fof(f3902,definition,
( sQ287_spl
<=> ssItem(sK45_skl(sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f3903,plain,
( ~ sQ287_spl
| ssItem(sK45_skl(sK48_skl)) ),
inference(component_clause,[status(thm)],[f3902]) ).
fof(f3905,plain,
( ~ sQ16_spl
| sQ287_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f3900,f932,f3902,f579]) ).
fof(f3906,definition,
( sQ288_spl
<=> ssItem(sK45_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ288_spl])],[split_symbol_definition]) ).
fof(f3907,plain,
( ~ sQ288_spl
| ssItem(sK45_skl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f3906]) ).
fof(f3926,plain,
( ~ sQ16_spl
| segmentP(sK48_skl,sK47_skl) ),
inference(resolution,[status(thm)],[f647,f420]) ).
fof(f3962,plain,
( ~ sQ16_spl
| ssList(tl(sK48_skl))
| sK47_skl = sK48_skl ),
inference(resolution,[status(thm)],[f653,f420]) ).
fof(f3964,definition,
( sQ289_spl
<=> ssList(tl(sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f3967,plain,
( ~ sQ16_spl
| sQ289_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f3962,f932,f3964,f579]) ).
fof(f3968,definition,
( sQ290_spl
<=> ssList(tl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f4058,definition,
( sQ291_spl
<=> sK47_skl = sK46_skl(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f4059,plain,
( ~ sQ291_spl
| sK47_skl = sK46_skl(sK48_skl) ),
inference(component_clause,[status(thm)],[f4058]) ).
fof(f4060,plain,
( sQ291_spl
| sK47_skl != sK46_skl(sK48_skl) ),
inference(component_clause,[status(thm)],[f4058]) ).
fof(f4339,plain,
( ~ sQ278_spl
| ~ sQ281_spl
| ~ sQ285_spl
| ~ sQ291_spl
| cons(sK45_skl(sK48_skl),sK47_skl) = sK48_skl ),
inference(backward_demodulation,[status(thm)],[f4059,f3868]) ).
fof(f4475,plain,
( ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ285_spl
| ~ sQ278_spl
| ~ sQ281_spl
| ~ sQ291_spl
| singletonP(sK48_skl) ),
inference(backward_demodulation,[status(thm)],[f4339,f3870]) ).
fof(f4477,plain,
( ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ285_spl
| ~ sQ278_spl
| ~ sQ281_spl
| ~ sQ291_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f4475,f515]) ).
fof(f4478,plain,
( ~ sQ15_spl
| ~ sQ16_spl
| ~ sQ285_spl
| ~ sQ278_spl
| ~ sQ281_spl
| ~ sQ291_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f4477]) ).
fof(f4583,plain,
( ~ sQ16_spl
| cons(sK44_skl(sK48_skl),sK43_skl(sK48_skl)) = sK48_skl
| sK47_skl = sK48_skl ),
inference(resolution,[status(thm)],[f654,f420]) ).
fof(f4585,definition,
( sQ356_spl
<=> cons(sK44_skl(sK48_skl),sK43_skl(sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ356_spl])],[split_symbol_definition]) ).
fof(f4588,plain,
( ~ sQ16_spl
| sQ356_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f4583,f932,f4585,f579]) ).
fof(f4589,definition,
( sQ357_spl
<=> cons(sK44_skl(sK47_skl),sK43_skl(sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ357_spl])],[split_symbol_definition]) ).
fof(f4590,plain,
( ~ sQ357_spl
| cons(sK44_skl(sK47_skl),sK43_skl(sK47_skl)) = sK47_skl ),
inference(component_clause,[status(thm)],[f4589]) ).
fof(f4593,plain,
( ~ sQ16_spl
| ssItem(sK44_skl(sK48_skl))
| sK47_skl = sK48_skl ),
inference(resolution,[status(thm)],[f655,f420]) ).
fof(f4595,definition,
( sQ358_spl
<=> ssItem(sK44_skl(sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ358_spl])],[split_symbol_definition]) ).
fof(f4598,plain,
( ~ sQ16_spl
| sQ358_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f4593,f932,f4595,f579]) ).
fof(f4599,definition,
( sQ359_spl
<=> ssItem(sK44_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ359_spl])],[split_symbol_definition]) ).
fof(f4600,plain,
( ~ sQ359_spl
| ssItem(sK44_skl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f4599]) ).
fof(f4603,plain,
( ~ sQ16_spl
| ssList(sK43_skl(sK48_skl))
| sK47_skl = sK48_skl ),
inference(resolution,[status(thm)],[f656,f420]) ).
fof(f4605,plain,
( ~ sQ16_spl
| sQ38_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f4603,f932,f928,f579]) ).
fof(f4607,plain,
( ~ sQ16_spl
| ssItem(hd(sK48_skl))
| sK47_skl = sK48_skl ),
inference(resolution,[status(thm)],[f586,f420]) ).
fof(f4609,plain,
( ~ sQ16_spl
| sQ15_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f4607,f932,f575,f579]) ).
fof(f4653,plain,
( ~ sQ284_spl
| sK47_skl = sK46_skl(sK47_skl)
| neq(sK47_skl,sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f500]) ).
fof(f4656,plain,
( ~ sQ284_spl
| sK39_skl(sK46_skl(sK47_skl)) != sK40_skl(sK46_skl(sK47_skl))
| equalelemsP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f216]) ).
fof(f4657,plain,
( ~ sQ284_spl
| app(sK41_skl(sK46_skl(sK47_skl)),cons(sK39_skl(sK46_skl(sK47_skl)),cons(sK40_skl(sK46_skl(sK47_skl)),sK42_skl(sK46_skl(sK47_skl))))) = sK46_skl(sK47_skl)
| equalelemsP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f215]) ).
fof(f4658,plain,
( ~ sQ284_spl
| ssList(sK42_skl(sK46_skl(sK47_skl)))
| equalelemsP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f214]) ).
fof(f4659,plain,
( ~ sQ284_spl
| ssList(sK41_skl(sK46_skl(sK47_skl)))
| equalelemsP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f213]) ).
fof(f4660,plain,
( ~ sQ284_spl
| ssItem(sK40_skl(sK46_skl(sK47_skl)))
| equalelemsP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f212]) ).
fof(f4661,plain,
( ~ sQ284_spl
| ssItem(sK39_skl(sK46_skl(sK47_skl)))
| equalelemsP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f211]) ).
fof(f4662,plain,
( ~ sQ284_spl
| sK34_skl(sK46_skl(sK47_skl)) = sK35_skl(sK46_skl(sK47_skl))
| duplicatefreeP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f206]) ).
fof(f4663,plain,
( ~ sQ284_spl
| app(app(sK36_skl(sK46_skl(sK47_skl)),cons(sK34_skl(sK46_skl(sK47_skl)),sK37_skl(sK46_skl(sK47_skl)))),cons(sK35_skl(sK46_skl(sK47_skl)),sK38_skl(sK46_skl(sK47_skl)))) = sK46_skl(sK47_skl)
| duplicatefreeP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f205]) ).
fof(f4664,plain,
( ~ sQ284_spl
| ssList(sK38_skl(sK46_skl(sK47_skl)))
| duplicatefreeP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f204]) ).
fof(f4665,plain,
( ~ sQ284_spl
| ssList(sK37_skl(sK46_skl(sK47_skl)))
| duplicatefreeP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f203]) ).
fof(f4666,plain,
( ~ sQ284_spl
| ssList(sK36_skl(sK46_skl(sK47_skl)))
| duplicatefreeP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f202]) ).
fof(f4667,plain,
( ~ sQ284_spl
| ssItem(sK35_skl(sK46_skl(sK47_skl)))
| duplicatefreeP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f201]) ).
fof(f4668,plain,
( ~ sQ284_spl
| ssItem(sK34_skl(sK46_skl(sK47_skl)))
| duplicatefreeP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f200]) ).
fof(f4669,plain,
( ~ sQ284_spl
| app(app(sK31_skl(sK46_skl(sK47_skl)),cons(sK29_skl(sK46_skl(sK47_skl)),sK32_skl(sK46_skl(sK47_skl)))),cons(sK30_skl(sK46_skl(sK47_skl)),sK33_skl(sK46_skl(sK47_skl)))) = sK46_skl(sK47_skl)
| strictorderedP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f194]) ).
fof(f4670,plain,
( ~ sQ284_spl
| ssList(sK33_skl(sK46_skl(sK47_skl)))
| strictorderedP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f193]) ).
fof(f4671,plain,
( ~ sQ284_spl
| ssList(sK32_skl(sK46_skl(sK47_skl)))
| strictorderedP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f192]) ).
fof(f4672,plain,
( ~ sQ284_spl
| ssList(sK31_skl(sK46_skl(sK47_skl)))
| strictorderedP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f191]) ).
fof(f4673,plain,
( ~ sQ284_spl
| ssItem(sK30_skl(sK46_skl(sK47_skl)))
| strictorderedP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f190]) ).
fof(f4674,plain,
( ~ sQ284_spl
| ssItem(sK29_skl(sK46_skl(sK47_skl)))
| strictorderedP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f189]) ).
fof(f4675,plain,
( ~ sQ284_spl
| app(app(sK26_skl(sK46_skl(sK47_skl)),cons(sK24_skl(sK46_skl(sK47_skl)),sK27_skl(sK46_skl(sK47_skl)))),cons(sK25_skl(sK46_skl(sK47_skl)),sK28_skl(sK46_skl(sK47_skl)))) = sK46_skl(sK47_skl)
| totalorderedP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f183]) ).
fof(f4676,plain,
( ~ sQ284_spl
| ssList(sK28_skl(sK46_skl(sK47_skl)))
| totalorderedP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f182]) ).
fof(f4677,plain,
( ~ sQ284_spl
| ssList(sK27_skl(sK46_skl(sK47_skl)))
| totalorderedP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f181]) ).
fof(f4678,plain,
( ~ sQ284_spl
| ssList(sK26_skl(sK46_skl(sK47_skl)))
| totalorderedP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f180]) ).
fof(f4679,plain,
( ~ sQ284_spl
| ssItem(sK25_skl(sK46_skl(sK47_skl)))
| totalorderedP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f179]) ).
fof(f4680,plain,
( ~ sQ284_spl
| ssItem(sK24_skl(sK46_skl(sK47_skl)))
| totalorderedP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f178]) ).
fof(f4681,plain,
( ~ sQ284_spl
| app(app(sK21_skl(sK46_skl(sK47_skl)),cons(sK19_skl(sK46_skl(sK47_skl)),sK22_skl(sK46_skl(sK47_skl)))),cons(sK20_skl(sK46_skl(sK47_skl)),sK23_skl(sK46_skl(sK47_skl)))) = sK46_skl(sK47_skl)
| strictorderP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f171]) ).
fof(f4682,plain,
( ~ sQ284_spl
| ssList(sK23_skl(sK46_skl(sK47_skl)))
| strictorderP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f170]) ).
fof(f4683,plain,
( ~ sQ284_spl
| ssList(sK22_skl(sK46_skl(sK47_skl)))
| strictorderP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f169]) ).
fof(f4684,plain,
( ~ sQ284_spl
| ssList(sK21_skl(sK46_skl(sK47_skl)))
| strictorderP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f168]) ).
fof(f4685,plain,
( ~ sQ284_spl
| ssItem(sK20_skl(sK46_skl(sK47_skl)))
| strictorderP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f167]) ).
fof(f4686,plain,
( ~ sQ284_spl
| ssItem(sK19_skl(sK46_skl(sK47_skl)))
| strictorderP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f166]) ).
fof(f4687,plain,
( ~ sQ284_spl
| app(app(sK16_skl(sK46_skl(sK47_skl)),cons(sK14_skl(sK46_skl(sK47_skl)),sK17_skl(sK46_skl(sK47_skl)))),cons(sK15_skl(sK46_skl(sK47_skl)),sK18_skl(sK46_skl(sK47_skl)))) = sK46_skl(sK47_skl)
| totalorderP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f159]) ).
fof(f4688,plain,
( ~ sQ284_spl
| ssList(sK18_skl(sK46_skl(sK47_skl)))
| totalorderP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f158]) ).
fof(f4689,plain,
( ~ sQ284_spl
| ssList(sK17_skl(sK46_skl(sK47_skl)))
| totalorderP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f157]) ).
fof(f4690,plain,
( ~ sQ284_spl
| ssList(sK16_skl(sK46_skl(sK47_skl)))
| totalorderP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f156]) ).
fof(f4691,plain,
( ~ sQ284_spl
| ssItem(sK15_skl(sK46_skl(sK47_skl)))
| totalorderP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f155]) ).
fof(f4692,plain,
( ~ sQ284_spl
| ssItem(sK14_skl(sK46_skl(sK47_skl)))
| totalorderP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f154]) ).
fof(f4695,plain,
( ~ sQ284_spl
| leq(sK10_skl(sK46_skl(sK47_skl)),sK9_skl(sK46_skl(sK47_skl)))
| cyclefreeP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f149]) ).
fof(f4696,plain,
( ~ sQ284_spl
| leq(sK9_skl(sK46_skl(sK47_skl)),sK10_skl(sK46_skl(sK47_skl)))
| cyclefreeP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f148]) ).
fof(f4697,plain,
( ~ sQ284_spl
| app(app(sK11_skl(sK46_skl(sK47_skl)),cons(sK9_skl(sK46_skl(sK47_skl)),sK12_skl(sK46_skl(sK47_skl)))),cons(sK10_skl(sK46_skl(sK47_skl)),sK13_skl(sK46_skl(sK47_skl)))) = sK46_skl(sK47_skl)
| cyclefreeP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f147]) ).
fof(f4698,plain,
( ~ sQ284_spl
| ssList(sK13_skl(sK46_skl(sK47_skl)))
| cyclefreeP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f146]) ).
fof(f4699,plain,
( ~ sQ284_spl
| ssList(sK12_skl(sK46_skl(sK47_skl)))
| cyclefreeP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f145]) ).
fof(f4704,plain,
( ~ sQ284_spl
| ssList(sK11_skl(sK46_skl(sK47_skl)))
| cyclefreeP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f144]) ).
fof(f4705,plain,
( ~ sQ284_spl
| ssItem(sK10_skl(sK46_skl(sK47_skl)))
| cyclefreeP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f143]) ).
fof(f4706,plain,
( ~ sQ284_spl
| ssItem(sK9_skl(sK46_skl(sK47_skl)))
| cyclefreeP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f142]) ).
fof(f4713,plain,
( ~ sQ284_spl
| ssItem(sK4_skl(sK46_skl(sK47_skl)))
| ~ singletonP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f116]) ).
fof(f4715,definition,
( sQ360_spl
<=> sK47_skl = sK46_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ360_spl])],[split_symbol_definition]) ).
fof(f4716,plain,
( ~ sQ360_spl
| sK47_skl = sK46_skl(sK47_skl) ),
inference(component_clause,[status(thm)],[f4715]) ).
fof(f4718,definition,
( sQ361_spl
<=> ssItem(hd(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ361_spl])],[split_symbol_definition]) ).
fof(f4722,definition,
( sQ362_spl
<=> ssList(sK43_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ362_spl])],[split_symbol_definition]) ).
fof(f4726,definition,
( sQ363_spl
<=> ssItem(sK44_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ363_spl])],[split_symbol_definition]) ).
fof(f4730,definition,
( sQ364_spl
<=> cons(sK44_skl(sK46_skl(sK47_skl)),sK43_skl(sK46_skl(sK47_skl))) = sK46_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ364_spl])],[split_symbol_definition]) ).
fof(f4734,definition,
( sQ365_spl
<=> ssList(tl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ365_spl])],[split_symbol_definition]) ).
fof(f4738,definition,
( sQ366_spl
<=> ssItem(sK45_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ366_spl])],[split_symbol_definition]) ).
fof(f4742,definition,
( sQ367_spl
<=> hd(sK46_skl(sK47_skl)) = sK45_skl(sK46_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ367_spl])],[split_symbol_definition]) ).
fof(f4746,definition,
( sQ368_spl
<=> ssList(sK46_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ368_spl])],[split_symbol_definition]) ).
fof(f4750,definition,
( sQ369_spl
<=> tl(sK46_skl(sK47_skl)) = sK46_skl(sK46_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ369_spl])],[split_symbol_definition]) ).
fof(f4758,definition,
( sQ371_spl
<=> cons(hd(sK46_skl(sK47_skl)),tl(sK46_skl(sK47_skl))) = sK46_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ371_spl])],[split_symbol_definition]) ).
fof(f4766,definition,
! [X0] :
( sQ373_spl
<=> ( hd(app(sK46_skl(sK47_skl),X0)) = hd(sK46_skl(sK47_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ373_spl])],[split_symbol_definition]) ).
fof(f4770,definition,
( sQ374_spl
<=> neq(sK47_skl,sK46_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ374_spl])],[split_symbol_definition]) ).
fof(f4773,plain,
( ~ sQ284_spl
| sQ360_spl
| sQ374_spl ),
inference(split_clause,[status(thm)],[f4653,f4770,f4715,f3831]) ).
fof(f4774,definition,
( sQ375_spl
<=> equalelemsP(sK46_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ375_spl])],[split_symbol_definition]) ).
fof(f4777,definition,
( sQ376_spl
<=> sK39_skl(sK46_skl(sK47_skl)) = sK40_skl(sK46_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ376_spl])],[split_symbol_definition]) ).
fof(f4780,plain,
( ~ sQ284_spl
| ~ sQ376_spl
| sQ375_spl ),
inference(split_clause,[status(thm)],[f4656,f4774,f4777,f3831]) ).
fof(f4781,definition,
( sQ377_spl
<=> app(sK41_skl(sK46_skl(sK47_skl)),cons(sK39_skl(sK46_skl(sK47_skl)),cons(sK40_skl(sK46_skl(sK47_skl)),sK42_skl(sK46_skl(sK47_skl))))) = sK46_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ377_spl])],[split_symbol_definition]) ).
fof(f4784,plain,
( ~ sQ284_spl
| sQ377_spl
| sQ375_spl ),
inference(split_clause,[status(thm)],[f4657,f4774,f4781,f3831]) ).
fof(f4785,definition,
( sQ378_spl
<=> ssList(sK42_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ378_spl])],[split_symbol_definition]) ).
fof(f4788,plain,
( ~ sQ284_spl
| sQ378_spl
| sQ375_spl ),
inference(split_clause,[status(thm)],[f4658,f4774,f4785,f3831]) ).
fof(f4789,definition,
( sQ379_spl
<=> ssList(sK41_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ379_spl])],[split_symbol_definition]) ).
fof(f4792,plain,
( ~ sQ284_spl
| sQ379_spl
| sQ375_spl ),
inference(split_clause,[status(thm)],[f4659,f4774,f4789,f3831]) ).
fof(f4793,definition,
( sQ380_spl
<=> ssItem(sK40_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ380_spl])],[split_symbol_definition]) ).
fof(f4796,plain,
( ~ sQ284_spl
| sQ380_spl
| sQ375_spl ),
inference(split_clause,[status(thm)],[f4660,f4774,f4793,f3831]) ).
fof(f4797,definition,
( sQ381_spl
<=> ssItem(sK39_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ381_spl])],[split_symbol_definition]) ).
fof(f4800,plain,
( ~ sQ284_spl
| sQ381_spl
| sQ375_spl ),
inference(split_clause,[status(thm)],[f4661,f4774,f4797,f3831]) ).
fof(f4801,definition,
( sQ382_spl
<=> duplicatefreeP(sK46_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ382_spl])],[split_symbol_definition]) ).
fof(f4804,definition,
( sQ383_spl
<=> sK34_skl(sK46_skl(sK47_skl)) = sK35_skl(sK46_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ383_spl])],[split_symbol_definition]) ).
fof(f4807,plain,
( ~ sQ284_spl
| sQ383_spl
| sQ382_spl ),
inference(split_clause,[status(thm)],[f4662,f4801,f4804,f3831]) ).
fof(f4808,definition,
( sQ384_spl
<=> app(app(sK36_skl(sK46_skl(sK47_skl)),cons(sK34_skl(sK46_skl(sK47_skl)),sK37_skl(sK46_skl(sK47_skl)))),cons(sK35_skl(sK46_skl(sK47_skl)),sK38_skl(sK46_skl(sK47_skl)))) = sK46_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ384_spl])],[split_symbol_definition]) ).
fof(f4811,plain,
( ~ sQ284_spl
| sQ384_spl
| sQ382_spl ),
inference(split_clause,[status(thm)],[f4663,f4801,f4808,f3831]) ).
fof(f4812,definition,
( sQ385_spl
<=> ssList(sK38_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ385_spl])],[split_symbol_definition]) ).
fof(f4815,plain,
( ~ sQ284_spl
| sQ385_spl
| sQ382_spl ),
inference(split_clause,[status(thm)],[f4664,f4801,f4812,f3831]) ).
fof(f4816,definition,
( sQ386_spl
<=> ssList(sK37_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ386_spl])],[split_symbol_definition]) ).
fof(f4819,plain,
( ~ sQ284_spl
| sQ386_spl
| sQ382_spl ),
inference(split_clause,[status(thm)],[f4665,f4801,f4816,f3831]) ).
fof(f4820,definition,
( sQ387_spl
<=> ssList(sK36_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ387_spl])],[split_symbol_definition]) ).
fof(f4823,plain,
( ~ sQ284_spl
| sQ387_spl
| sQ382_spl ),
inference(split_clause,[status(thm)],[f4666,f4801,f4820,f3831]) ).
fof(f4824,definition,
( sQ388_spl
<=> ssItem(sK35_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ388_spl])],[split_symbol_definition]) ).
fof(f4827,plain,
( ~ sQ284_spl
| sQ388_spl
| sQ382_spl ),
inference(split_clause,[status(thm)],[f4667,f4801,f4824,f3831]) ).
fof(f4828,definition,
( sQ389_spl
<=> ssItem(sK34_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ389_spl])],[split_symbol_definition]) ).
fof(f4831,plain,
( ~ sQ284_spl
| sQ389_spl
| sQ382_spl ),
inference(split_clause,[status(thm)],[f4668,f4801,f4828,f3831]) ).
fof(f4832,definition,
( sQ390_spl
<=> strictorderedP(sK46_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ390_spl])],[split_symbol_definition]) ).
fof(f4835,definition,
( sQ391_spl
<=> app(app(sK31_skl(sK46_skl(sK47_skl)),cons(sK29_skl(sK46_skl(sK47_skl)),sK32_skl(sK46_skl(sK47_skl)))),cons(sK30_skl(sK46_skl(sK47_skl)),sK33_skl(sK46_skl(sK47_skl)))) = sK46_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ391_spl])],[split_symbol_definition]) ).
fof(f4838,plain,
( ~ sQ284_spl
| sQ391_spl
| sQ390_spl ),
inference(split_clause,[status(thm)],[f4669,f4832,f4835,f3831]) ).
fof(f4839,definition,
( sQ392_spl
<=> ssList(sK33_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ392_spl])],[split_symbol_definition]) ).
fof(f4842,plain,
( ~ sQ284_spl
| sQ392_spl
| sQ390_spl ),
inference(split_clause,[status(thm)],[f4670,f4832,f4839,f3831]) ).
fof(f4843,definition,
( sQ393_spl
<=> ssList(sK32_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ393_spl])],[split_symbol_definition]) ).
fof(f4846,plain,
( ~ sQ284_spl
| sQ393_spl
| sQ390_spl ),
inference(split_clause,[status(thm)],[f4671,f4832,f4843,f3831]) ).
fof(f4847,definition,
( sQ394_spl
<=> ssList(sK31_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ394_spl])],[split_symbol_definition]) ).
fof(f4850,plain,
( ~ sQ284_spl
| sQ394_spl
| sQ390_spl ),
inference(split_clause,[status(thm)],[f4672,f4832,f4847,f3831]) ).
fof(f4851,definition,
( sQ395_spl
<=> ssItem(sK30_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ395_spl])],[split_symbol_definition]) ).
fof(f4854,plain,
( ~ sQ284_spl
| sQ395_spl
| sQ390_spl ),
inference(split_clause,[status(thm)],[f4673,f4832,f4851,f3831]) ).
fof(f4855,definition,
( sQ396_spl
<=> ssItem(sK29_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ396_spl])],[split_symbol_definition]) ).
fof(f4858,plain,
( ~ sQ284_spl
| sQ396_spl
| sQ390_spl ),
inference(split_clause,[status(thm)],[f4674,f4832,f4855,f3831]) ).
fof(f4859,definition,
( sQ397_spl
<=> totalorderedP(sK46_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ397_spl])],[split_symbol_definition]) ).
fof(f4862,definition,
( sQ398_spl
<=> app(app(sK26_skl(sK46_skl(sK47_skl)),cons(sK24_skl(sK46_skl(sK47_skl)),sK27_skl(sK46_skl(sK47_skl)))),cons(sK25_skl(sK46_skl(sK47_skl)),sK28_skl(sK46_skl(sK47_skl)))) = sK46_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ398_spl])],[split_symbol_definition]) ).
fof(f4865,plain,
( ~ sQ284_spl
| sQ398_spl
| sQ397_spl ),
inference(split_clause,[status(thm)],[f4675,f4859,f4862,f3831]) ).
fof(f4866,definition,
( sQ399_spl
<=> ssList(sK28_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ399_spl])],[split_symbol_definition]) ).
fof(f4869,plain,
( ~ sQ284_spl
| sQ399_spl
| sQ397_spl ),
inference(split_clause,[status(thm)],[f4676,f4859,f4866,f3831]) ).
fof(f4870,definition,
( sQ400_spl
<=> ssList(sK27_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ400_spl])],[split_symbol_definition]) ).
fof(f4873,plain,
( ~ sQ284_spl
| sQ400_spl
| sQ397_spl ),
inference(split_clause,[status(thm)],[f4677,f4859,f4870,f3831]) ).
fof(f4874,definition,
( sQ401_spl
<=> ssList(sK26_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ401_spl])],[split_symbol_definition]) ).
fof(f4877,plain,
( ~ sQ284_spl
| sQ401_spl
| sQ397_spl ),
inference(split_clause,[status(thm)],[f4678,f4859,f4874,f3831]) ).
fof(f4878,definition,
( sQ402_spl
<=> ssItem(sK25_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ402_spl])],[split_symbol_definition]) ).
fof(f4881,plain,
( ~ sQ284_spl
| sQ402_spl
| sQ397_spl ),
inference(split_clause,[status(thm)],[f4679,f4859,f4878,f3831]) ).
fof(f4882,definition,
( sQ403_spl
<=> ssItem(sK24_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ403_spl])],[split_symbol_definition]) ).
fof(f4885,plain,
( ~ sQ284_spl
| sQ403_spl
| sQ397_spl ),
inference(split_clause,[status(thm)],[f4680,f4859,f4882,f3831]) ).
fof(f4886,definition,
( sQ404_spl
<=> strictorderP(sK46_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ404_spl])],[split_symbol_definition]) ).
fof(f4889,definition,
( sQ405_spl
<=> app(app(sK21_skl(sK46_skl(sK47_skl)),cons(sK19_skl(sK46_skl(sK47_skl)),sK22_skl(sK46_skl(sK47_skl)))),cons(sK20_skl(sK46_skl(sK47_skl)),sK23_skl(sK46_skl(sK47_skl)))) = sK46_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ405_spl])],[split_symbol_definition]) ).
fof(f4892,plain,
( ~ sQ284_spl
| sQ405_spl
| sQ404_spl ),
inference(split_clause,[status(thm)],[f4681,f4886,f4889,f3831]) ).
fof(f4893,definition,
( sQ406_spl
<=> ssList(sK23_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ406_spl])],[split_symbol_definition]) ).
fof(f4896,plain,
( ~ sQ284_spl
| sQ406_spl
| sQ404_spl ),
inference(split_clause,[status(thm)],[f4682,f4886,f4893,f3831]) ).
fof(f4897,definition,
( sQ407_spl
<=> ssList(sK22_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ407_spl])],[split_symbol_definition]) ).
fof(f4900,plain,
( ~ sQ284_spl
| sQ407_spl
| sQ404_spl ),
inference(split_clause,[status(thm)],[f4683,f4886,f4897,f3831]) ).
fof(f4901,definition,
( sQ408_spl
<=> ssList(sK21_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ408_spl])],[split_symbol_definition]) ).
fof(f4904,plain,
( ~ sQ284_spl
| sQ408_spl
| sQ404_spl ),
inference(split_clause,[status(thm)],[f4684,f4886,f4901,f3831]) ).
fof(f4905,definition,
( sQ409_spl
<=> ssItem(sK20_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ409_spl])],[split_symbol_definition]) ).
fof(f4908,plain,
( ~ sQ284_spl
| sQ409_spl
| sQ404_spl ),
inference(split_clause,[status(thm)],[f4685,f4886,f4905,f3831]) ).
fof(f4909,definition,
( sQ410_spl
<=> ssItem(sK19_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ410_spl])],[split_symbol_definition]) ).
fof(f4912,plain,
( ~ sQ284_spl
| sQ410_spl
| sQ404_spl ),
inference(split_clause,[status(thm)],[f4686,f4886,f4909,f3831]) ).
fof(f4913,definition,
( sQ411_spl
<=> totalorderP(sK46_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ411_spl])],[split_symbol_definition]) ).
fof(f4916,definition,
( sQ412_spl
<=> app(app(sK16_skl(sK46_skl(sK47_skl)),cons(sK14_skl(sK46_skl(sK47_skl)),sK17_skl(sK46_skl(sK47_skl)))),cons(sK15_skl(sK46_skl(sK47_skl)),sK18_skl(sK46_skl(sK47_skl)))) = sK46_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ412_spl])],[split_symbol_definition]) ).
fof(f4919,plain,
( ~ sQ284_spl
| sQ412_spl
| sQ411_spl ),
inference(split_clause,[status(thm)],[f4687,f4913,f4916,f3831]) ).
fof(f4920,definition,
( sQ413_spl
<=> ssList(sK18_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ413_spl])],[split_symbol_definition]) ).
fof(f4923,plain,
( ~ sQ284_spl
| sQ413_spl
| sQ411_spl ),
inference(split_clause,[status(thm)],[f4688,f4913,f4920,f3831]) ).
fof(f4924,definition,
( sQ414_spl
<=> ssList(sK17_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ414_spl])],[split_symbol_definition]) ).
fof(f4927,plain,
( ~ sQ284_spl
| sQ414_spl
| sQ411_spl ),
inference(split_clause,[status(thm)],[f4689,f4913,f4924,f3831]) ).
fof(f4928,definition,
( sQ415_spl
<=> ssList(sK16_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ415_spl])],[split_symbol_definition]) ).
fof(f4931,plain,
( ~ sQ284_spl
| sQ415_spl
| sQ411_spl ),
inference(split_clause,[status(thm)],[f4690,f4913,f4928,f3831]) ).
fof(f4932,definition,
( sQ416_spl
<=> ssItem(sK15_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ416_spl])],[split_symbol_definition]) ).
fof(f4935,plain,
( ~ sQ284_spl
| sQ416_spl
| sQ411_spl ),
inference(split_clause,[status(thm)],[f4691,f4913,f4932,f3831]) ).
fof(f4936,definition,
( sQ417_spl
<=> ssItem(sK14_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ417_spl])],[split_symbol_definition]) ).
fof(f4939,plain,
( ~ sQ284_spl
| sQ417_spl
| sQ411_spl ),
inference(split_clause,[status(thm)],[f4692,f4913,f4936,f3831]) ).
fof(f4940,definition,
( sQ418_spl
<=> cyclefreeP(sK46_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ418_spl])],[split_symbol_definition]) ).
fof(f4943,definition,
( sQ419_spl
<=> leq(sK10_skl(sK46_skl(sK47_skl)),sK9_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ419_spl])],[split_symbol_definition]) ).
fof(f4946,plain,
( ~ sQ284_spl
| sQ419_spl
| sQ418_spl ),
inference(split_clause,[status(thm)],[f4695,f4940,f4943,f3831]) ).
fof(f4947,definition,
( sQ420_spl
<=> leq(sK9_skl(sK46_skl(sK47_skl)),sK10_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f4950,plain,
( ~ sQ284_spl
| sQ420_spl
| sQ418_spl ),
inference(split_clause,[status(thm)],[f4696,f4940,f4947,f3831]) ).
fof(f4951,definition,
( sQ421_spl
<=> app(app(sK11_skl(sK46_skl(sK47_skl)),cons(sK9_skl(sK46_skl(sK47_skl)),sK12_skl(sK46_skl(sK47_skl)))),cons(sK10_skl(sK46_skl(sK47_skl)),sK13_skl(sK46_skl(sK47_skl)))) = sK46_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ421_spl])],[split_symbol_definition]) ).
fof(f4954,plain,
( ~ sQ284_spl
| sQ421_spl
| sQ418_spl ),
inference(split_clause,[status(thm)],[f4697,f4940,f4951,f3831]) ).
fof(f4955,definition,
( sQ422_spl
<=> ssList(sK13_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ422_spl])],[split_symbol_definition]) ).
fof(f4958,plain,
( ~ sQ284_spl
| sQ422_spl
| sQ418_spl ),
inference(split_clause,[status(thm)],[f4698,f4940,f4955,f3831]) ).
fof(f4959,definition,
( sQ423_spl
<=> ssList(sK12_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ423_spl])],[split_symbol_definition]) ).
fof(f4962,plain,
( ~ sQ284_spl
| sQ423_spl
| sQ418_spl ),
inference(split_clause,[status(thm)],[f4699,f4940,f4959,f3831]) ).
fof(f4963,definition,
( sQ424_spl
<=> ssList(sK11_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ424_spl])],[split_symbol_definition]) ).
fof(f4966,plain,
( ~ sQ284_spl
| sQ424_spl
| sQ418_spl ),
inference(split_clause,[status(thm)],[f4704,f4940,f4963,f3831]) ).
fof(f4967,definition,
( sQ425_spl
<=> ssItem(sK10_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ425_spl])],[split_symbol_definition]) ).
fof(f4970,plain,
( ~ sQ284_spl
| sQ425_spl
| sQ418_spl ),
inference(split_clause,[status(thm)],[f4705,f4940,f4967,f3831]) ).
fof(f4971,definition,
( sQ426_spl
<=> ssItem(sK9_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ426_spl])],[split_symbol_definition]) ).
fof(f4974,plain,
( ~ sQ284_spl
| sQ426_spl
| sQ418_spl ),
inference(split_clause,[status(thm)],[f4706,f4940,f4971,f3831]) ).
fof(f4975,definition,
( sQ427_spl
<=> singletonP(sK46_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ427_spl])],[split_symbol_definition]) ).
fof(f4978,definition,
( sQ428_spl
<=> ssItem(sK4_skl(sK46_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ428_spl])],[split_symbol_definition]) ).
fof(f4981,plain,
( ~ sQ284_spl
| sQ428_spl
| ~ sQ427_spl ),
inference(split_clause,[status(thm)],[f4713,f4975,f4978,f3831]) ).
fof(f5234,plain,
( ~ sQ275_spl
| ~ sQ282_spl
| ~ sQ360_spl
| cons(hd(sK47_skl),sK47_skl) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f4716,f3823]) ).
fof(f5268,plain,
( ~ sQ16_spl
| sK48_skl = sK47_skl
| ~ segmentP(sK47_skl,sK48_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f3926,f317]) ).
fof(f5269,plain,
! [X0] :
( ~ sQ16_spl
| segmentP(sK48_skl,X0)
| ~ segmentP(sK47_skl,X0)
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f3926,f315]) ).
fof(f5270,plain,
( ~ sQ16_spl
| app(app(sK7_skl(sK47_skl,sK48_skl),sK47_skl),sK8_skl(sK47_skl,sK48_skl)) = sK48_skl
| ~ ssList(sK47_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f3926,f136]) ).
fof(f5271,plain,
( ~ sQ16_spl
| ssList(sK8_skl(sK47_skl,sK48_skl))
| ~ ssList(sK47_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f3926,f135]) ).
fof(f5272,plain,
( ~ sQ16_spl
| ssList(sK7_skl(sK47_skl,sK48_skl))
| ~ ssList(sK47_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f3926,f134]) ).
fof(f5273,definition,
( sQ430_spl
<=> segmentP(sK47_skl,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ430_spl])],[split_symbol_definition]) ).
fof(f5276,plain,
( ~ sQ16_spl
| sQ39_spl
| ~ sQ430_spl
| ~ sQ217_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f5268,f3037,f2271,f5273,f932,f579]) ).
fof(f5277,definition,
! [X0] :
( sQ431_spl
<=> ( segmentP(sK48_skl,X0)
| ~ segmentP(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ431_spl])],[split_symbol_definition]) ).
fof(f5280,plain,
( ~ sQ16_spl
| sQ431_spl
| ~ sQ217_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f5269,f3037,f2271,f5277,f579]) ).
fof(f5281,definition,
( sQ432_spl
<=> app(app(sK7_skl(sK47_skl,sK48_skl),sK47_skl),sK8_skl(sK47_skl,sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ432_spl])],[split_symbol_definition]) ).
fof(f5284,plain,
( ~ sQ16_spl
| sQ432_spl
| ~ sQ217_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f5270,f3037,f2271,f5281,f579]) ).
fof(f5285,definition,
( sQ433_spl
<=> ssList(sK8_skl(sK47_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ433_spl])],[split_symbol_definition]) ).
fof(f5288,plain,
( ~ sQ16_spl
| sQ433_spl
| ~ sQ217_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f5271,f3037,f2271,f5285,f579]) ).
fof(f5289,definition,
( sQ434_spl
<=> ssList(sK7_skl(sK47_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ434_spl])],[split_symbol_definition]) ).
fof(f5292,plain,
( ~ sQ16_spl
| sQ434_spl
| ~ sQ217_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f5272,f3037,f2271,f5289,f579]) ).
fof(f5749,plain,
( ssList(sK43_skl(sK47_skl))
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f231,f419]) ).
fof(f5754,plain,
( sQ40_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f5749,f579,f935]) ).
fof(f5756,plain,
( ssItem(sK44_skl(sK47_skl))
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f232,f419]) ).
fof(f5761,plain,
( sQ359_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f5756,f579,f4599]) ).
fof(f5765,plain,
( ssItem(sK44_skl(sK48_skl))
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f420,f232]) ).
fof(f5766,plain,
( ssList(sK43_skl(sK48_skl))
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f420,f231]) ).
fof(f5774,plain,
! [X0] :
( tl(app(sK48_skl,X0)) = app(tl(sK48_skl),X0)
| nil = sK48_skl
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f420,f393]) ).
fof(f5777,plain,
( cons(hd(sK48_skl),tl(sK48_skl)) = sK48_skl
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f420,f374]) ).
fof(f5847,plain,
( sQ358_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f5765,f572,f4595]) ).
fof(f5848,plain,
( sQ38_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f5766,f572,f928]) ).
fof(f5852,plain,
( sQ14_spl
| sQ271_spl ),
inference(split_clause,[status(thm)],[f5774,f3222,f572]) ).
fof(f5854,plain,
( sQ278_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f5777,f572,f3793]) ).
fof(f5911,plain,
( sK0_skl = sK1_skl
| neq(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f501,f104]) ).
fof(f5913,definition,
( sQ437_spl
<=> neq(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ437_spl])],[split_symbol_definition]) ).
fof(f5916,definition,
( sQ438_spl
<=> sK0_skl = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ438_spl])],[split_symbol_definition]) ).
fof(f5917,plain,
( ~ sQ438_spl
| sK0_skl = sK1_skl ),
inference(component_clause,[status(thm)],[f5916]) ).
fof(f5919,plain,
( sQ438_spl
| sQ437_spl ),
inference(split_clause,[status(thm)],[f5911,f5913,f5916]) ).
fof(f5924,plain,
( ~ sQ438_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f5917,f105]) ).
fof(f5925,plain,
~ sQ438_spl,
inference(contradiction_clause,[status(thm)],[f5924]) ).
fof(f5927,plain,
( sK1_skl = sK0_skl
| neq(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f502,f103]) ).
fof(f5932,definition,
( sQ441_spl
<=> neq(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ441_spl])],[split_symbol_definition]) ).
fof(f5935,plain,
( sQ438_spl
| sQ441_spl ),
inference(split_clause,[status(thm)],[f5927,f5932,f5916]) ).
fof(f5936,plain,
( cons(sK44_skl(sK48_skl),sK43_skl(sK48_skl)) = sK48_skl
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f233,f420]) ).
fof(f5938,plain,
( cons(sK44_skl(sK47_skl),sK43_skl(sK47_skl)) = sK47_skl
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f233,f419]) ).
fof(f5939,plain,
( sQ356_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f5936,f572,f4585]) ).
fof(f5944,plain,
( sQ357_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f5938,f579,f4589]) ).
fof(f5945,plain,
( ssList(tl(sK48_skl))
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f241,f420]) ).
fof(f5947,plain,
( ssList(tl(sK47_skl))
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f241,f419]) ).
fof(f5948,plain,
( sQ289_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f5945,f572,f3964]) ).
fof(f5953,plain,
( sQ290_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f5947,f579,f3968]) ).
fof(f5954,plain,
frontsegP(sK48_skl,nil),
inference(resolution,[status(thm)],[f295,f420]) ).
fof(f5956,plain,
frontsegP(sK47_skl,nil),
inference(resolution,[status(thm)],[f295,f419]) ).
fof(f5957,plain,
rearsegP(sK48_skl,nil),
inference(resolution,[status(thm)],[f309,f420]) ).
fof(f5959,plain,
rearsegP(sK47_skl,nil),
inference(resolution,[status(thm)],[f309,f419]) ).
fof(f5967,plain,
! [X0,X1] :
( sK48_skl = sK47_skl
| cons(X0,sK47_skl) != cons(X1,sK48_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f558,f420]) ).
fof(f5968,plain,
! [X0,X1] :
( nil = sK47_skl
| cons(X0,sK47_skl) != cons(X1,nil)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f558,f223]) ).
fof(f5970,definition,
! [X0,X1] :
( sQ444_spl
<=> ( cons(X0,sK47_skl) != cons(X1,sK48_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ444_spl])],[split_symbol_definition]) ).
fof(f5973,plain,
( sQ39_spl
| sQ444_spl ),
inference(split_clause,[status(thm)],[f5967,f5970,f932]) ).
fof(f5974,definition,
! [X0,X1] :
( sQ445_spl
<=> ( cons(X0,sK47_skl) != cons(X1,nil)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ445_spl])],[split_symbol_definition]) ).
fof(f5977,plain,
( sQ16_spl
| sQ445_spl ),
inference(split_clause,[status(thm)],[f5968,f5974,f579]) ).
fof(f5988,plain,
( ~ sQ17_spl
| hd(cons(hd(sK47_skl),sK47_skl)) = hd(sK47_skl) ),
inference(resolution,[status(thm)],[f583,f708]) ).
fof(f5989,plain,
( ~ sQ17_spl
| cons(hd(sK47_skl),sK47_skl) != sK47_skl ),
inference(resolution,[status(thm)],[f583,f552]) ).
fof(f5991,plain,
( ~ sQ17_spl
| sK1_skl = hd(sK47_skl)
| neq(sK1_skl,hd(sK47_skl)) ),
inference(resolution,[status(thm)],[f583,f502]) ).
fof(f5992,plain,
( ~ sQ17_spl
| sK0_skl = hd(sK47_skl)
| neq(sK0_skl,hd(sK47_skl)) ),
inference(resolution,[status(thm)],[f583,f501]) ).
fof(f6000,plain,
( ~ sQ17_spl
| ~ sQ275_spl
| ~ sQ282_spl
| ~ sQ360_spl
| sK47_skl != sK47_skl ),
inference(forward_demodulation,[status(thm)],[f5234,f5989]) ).
fof(f6001,plain,
( ~ sQ17_spl
| ~ sQ275_spl
| ~ sQ282_spl
| ~ sQ360_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f6000]) ).
fof(f6002,plain,
( ~ sQ17_spl
| ~ sQ275_spl
| ~ sQ282_spl
| ~ sQ360_spl ),
inference(contradiction_clause,[status(thm)],[f6001]) ).
fof(f6003,definition,
( sQ447_spl
<=> neq(sK1_skl,hd(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ447_spl])],[split_symbol_definition]) ).
fof(f6006,definition,
( sQ448_spl
<=> sK1_skl = hd(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ448_spl])],[split_symbol_definition]) ).
fof(f6007,plain,
( ~ sQ448_spl
| sK1_skl = hd(sK47_skl) ),
inference(component_clause,[status(thm)],[f6006]) ).
fof(f6009,plain,
( ~ sQ17_spl
| sQ448_spl
| sQ447_spl ),
inference(split_clause,[status(thm)],[f5991,f6003,f6006,f582]) ).
fof(f6010,definition,
( sQ449_spl
<=> neq(sK0_skl,hd(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ449_spl])],[split_symbol_definition]) ).
fof(f6013,definition,
( sQ450_spl
<=> sK0_skl = hd(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ450_spl])],[split_symbol_definition]) ).
fof(f6014,plain,
( ~ sQ450_spl
| sK0_skl = hd(sK47_skl) ),
inference(component_clause,[status(thm)],[f6013]) ).
fof(f6015,plain,
( sQ450_spl
| sK0_skl != hd(sK47_skl) ),
inference(component_clause,[status(thm)],[f6013]) ).
fof(f6016,plain,
( ~ sQ17_spl
| sQ450_spl
| sQ449_spl ),
inference(split_clause,[status(thm)],[f5992,f6010,f6013,f582]) ).
fof(f6020,plain,
( ~ sQ17_spl
| ~ sQ450_spl
| hd(cons(hd(sK47_skl),sK47_skl)) = sK0_skl ),
inference(backward_demodulation,[status(thm)],[f6014,f5988]) ).
fof(f6023,plain,
( ~ sQ275_spl
| ~ sQ450_spl
| cons(sK0_skl,tl(sK47_skl)) = sK47_skl ),
inference(backward_demodulation,[status(thm)],[f6014,f3493]) ).
fof(f6032,plain,
( ~ sQ448_spl
| ~ sQ450_spl
| sK1_skl = sK0_skl ),
inference(forward_demodulation,[status(thm)],[f6014,f6007]) ).
fof(f6033,plain,
( ~ sQ448_spl
| ~ sQ450_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f6032,f105]) ).
fof(f6034,plain,
( ~ sQ448_spl
| ~ sQ450_spl ),
inference(contradiction_clause,[status(thm)],[f6033]) ).
fof(f6035,plain,
( nil = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2667,f298]) ).
fof(f6037,plain,
! [X0] :
( frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2667,f282]) ).
fof(f6038,plain,
( app(nil,sK5_skl(nil,nil)) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2667,f123]) ).
fof(f6039,plain,
( ssList(sK5_skl(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2667,f122]) ).
fof(f6040,plain,
( sQ12_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f6035,f2268,f565]) ).
fof(f6045,definition,
! [X0] :
( sQ452_spl
<=> ( frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ452_spl])],[split_symbol_definition]) ).
fof(f6048,plain,
( sQ452_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f6037,f2268,f6045]) ).
fof(f6049,definition,
( sQ453_spl
<=> app(nil,sK5_skl(nil,nil)) = nil ),
introduced(definition,[new_symbols(definition,[sQ453_spl])],[split_symbol_definition]) ).
fof(f6052,plain,
( sQ453_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f6038,f2268,f6049]) ).
fof(f6053,definition,
( sQ454_spl
<=> ssList(sK5_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ454_spl])],[split_symbol_definition]) ).
fof(f6056,plain,
( sQ454_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f6039,f2268,f6053]) ).
fof(f6058,plain,
! [X0] :
( rearsegP(nil,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2790,f301]) ).
fof(f6059,plain,
( app(sK6_skl(nil,nil),nil) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2790,f129]) ).
fof(f6060,plain,
( ssList(sK6_skl(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2790,f128]) ).
fof(f6065,definition,
! [X0] :
( sQ456_spl
<=> ( rearsegP(nil,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ456_spl])],[split_symbol_definition]) ).
fof(f6068,plain,
( sQ456_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f6058,f2268,f6065]) ).
fof(f6069,definition,
( sQ457_spl
<=> app(sK6_skl(nil,nil),nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ457_spl])],[split_symbol_definition]) ).
fof(f6072,plain,
( sQ457_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f6059,f2268,f6069]) ).
fof(f6073,definition,
( sQ458_spl
<=> ssList(sK6_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ458_spl])],[split_symbol_definition]) ).
fof(f6076,plain,
( sQ458_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f6060,f2268,f6073]) ).
fof(f6079,plain,
segmentP(sK48_skl,nil),
inference(resolution,[status(thm)],[f323,f420]) ).
fof(f6081,plain,
segmentP(sK47_skl,nil),
inference(resolution,[status(thm)],[f323,f419]) ).
fof(f6094,plain,
( ~ sQ40_spl
| ssList(tl(sK43_skl(sK47_skl)))
| nil = sK43_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f936,f241]) ).
fof(f6095,plain,
( ~ sQ40_spl
| cons(sK44_skl(sK43_skl(sK47_skl)),sK43_skl(sK43_skl(sK47_skl))) = sK43_skl(sK47_skl)
| nil = sK43_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f936,f233]) ).
fof(f6096,plain,
( ~ sQ40_spl
| ssItem(sK44_skl(sK43_skl(sK47_skl)))
| nil = sK43_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f936,f232]) ).
fof(f6097,plain,
( ~ sQ40_spl
| ssList(sK43_skl(sK43_skl(sK47_skl)))
| nil = sK43_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f936,f231]) ).
fof(f6098,plain,
! [X0] :
( ~ sQ40_spl
| nil = sK43_skl(sK47_skl)
| nil != app(sK43_skl(sK47_skl),X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f936,f386]) ).
fof(f6101,plain,
( ~ sQ40_spl
| ssItem(hd(sK43_skl(sK47_skl)))
| nil = sK43_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f936,f237]) ).
fof(f6105,plain,
! [X0] :
( ~ sQ40_spl
| tl(app(sK43_skl(sK47_skl),X0)) = app(tl(sK43_skl(sK47_skl)),X0)
| nil = sK43_skl(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f936,f393]) ).
fof(f6106,plain,
! [X0] :
( ~ sQ40_spl
| hd(app(sK43_skl(sK47_skl),X0)) = hd(sK43_skl(sK47_skl))
| nil = sK43_skl(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f936,f391]) ).
fof(f6108,plain,
( ~ sQ40_spl
| cons(hd(sK43_skl(sK47_skl)),tl(sK43_skl(sK47_skl))) = sK43_skl(sK47_skl)
| nil = sK43_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f936,f374]) ).
fof(f6185,definition,
( sQ461_spl
<=> nil = sK43_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ461_spl])],[split_symbol_definition]) ).
fof(f6186,plain,
( ~ sQ461_spl
| nil = sK43_skl(sK47_skl) ),
inference(component_clause,[status(thm)],[f6185]) ).
fof(f6188,definition,
( sQ462_spl
<=> ssList(tl(sK43_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ462_spl])],[split_symbol_definition]) ).
fof(f6191,plain,
( ~ sQ40_spl
| sQ462_spl
| sQ461_spl ),
inference(split_clause,[status(thm)],[f6094,f6185,f6188,f935]) ).
fof(f6192,definition,
( sQ463_spl
<=> cons(sK44_skl(sK43_skl(sK47_skl)),sK43_skl(sK43_skl(sK47_skl))) = sK43_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ463_spl])],[split_symbol_definition]) ).
fof(f6195,plain,
( ~ sQ40_spl
| sQ463_spl
| sQ461_spl ),
inference(split_clause,[status(thm)],[f6095,f6185,f6192,f935]) ).
fof(f6196,definition,
( sQ464_spl
<=> ssItem(sK44_skl(sK43_skl(sK47_skl))) ),
introduced(definition,[new_symbols(definition,[sQ464_spl])],[split_symbol_definition]) ).
fof(f6199,plain,
( ~ sQ40_spl
| sQ464_spl
| sQ461_spl ),
inference(split_clause,[status(thm)],[f6096,f6185,f6196,f935]) ).
fof(f6200,plain,
( ~ sQ40_spl
| sQ80_spl
| sQ461_spl ),
inference(split_clause,[status(thm)],[f6097,f6185,f1317,f935]) ).
fof(f6201,definition,
! [X0] :
( sQ465_spl
<=> ( nil != app(sK43_skl(sK47_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ465_spl])],[split_symbol_definition]) ).
fof(f6204,plain,
( ~ sQ40_spl
| sQ461_spl
| sQ465_spl ),
inference(split_clause,[status(thm)],[f6098,f6201,f6185,f935]) ).
fof(f6205,plain,
( ~ sQ40_spl
| sQ72_spl
| sQ461_spl ),
inference(split_clause,[status(thm)],[f6101,f6185,f1286,f935]) ).
fof(f6210,definition,
! [X0] :
( sQ467_spl
<=> ( tl(app(sK43_skl(sK47_skl),X0)) = app(tl(sK43_skl(sK47_skl)),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ467_spl])],[split_symbol_definition]) ).
fof(f6213,plain,
( ~ sQ40_spl
| sQ461_spl
| sQ467_spl ),
inference(split_clause,[status(thm)],[f6105,f6210,f6185,f935]) ).
fof(f6214,definition,
! [X0] :
( sQ468_spl
<=> ( hd(app(sK43_skl(sK47_skl),X0)) = hd(sK43_skl(sK47_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ468_spl])],[split_symbol_definition]) ).
fof(f6217,plain,
( ~ sQ40_spl
| sQ461_spl
| sQ468_spl ),
inference(split_clause,[status(thm)],[f6106,f6214,f6185,f935]) ).
fof(f6218,definition,
( sQ469_spl
<=> cons(hd(sK43_skl(sK47_skl)),tl(sK43_skl(sK47_skl))) = sK43_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ469_spl])],[split_symbol_definition]) ).
fof(f6221,plain,
( ~ sQ40_spl
| sQ469_spl
| sQ461_spl ),
inference(split_clause,[status(thm)],[f6108,f6185,f6218,f935]) ).
fof(f6391,plain,
( ~ sQ357_spl
| ~ sQ461_spl
| cons(sK44_skl(sK47_skl),nil) = sK47_skl ),
inference(backward_demodulation,[status(thm)],[f6186,f4590]) ).
fof(f6516,plain,
! [X0] :
( segmentP(nil,X0)
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2796,f315]) ).
fof(f6517,plain,
( app(app(sK7_skl(nil,nil),nil),sK8_skl(nil,nil)) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2796,f136]) ).
fof(f6518,plain,
( ssList(sK8_skl(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2796,f135]) ).
fof(f6519,plain,
( ssList(sK7_skl(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2796,f134]) ).
fof(f6525,definition,
! [X0] :
( sQ504_spl
<=> ( segmentP(nil,X0)
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ504_spl])],[split_symbol_definition]) ).
fof(f6528,plain,
( sQ504_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f6516,f2268,f6525]) ).
fof(f6529,definition,
( sQ505_spl
<=> app(app(sK7_skl(nil,nil),nil),sK8_skl(nil,nil)) = nil ),
introduced(definition,[new_symbols(definition,[sQ505_spl])],[split_symbol_definition]) ).
fof(f6532,plain,
( sQ505_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f6517,f2268,f6529]) ).
fof(f6533,definition,
( sQ506_spl
<=> ssList(sK8_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ506_spl])],[split_symbol_definition]) ).
fof(f6536,plain,
( sQ506_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f6518,f2268,f6533]) ).
fof(f6537,definition,
( sQ507_spl
<=> ssList(sK7_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ507_spl])],[split_symbol_definition]) ).
fof(f6540,plain,
( sQ507_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f6519,f2268,f6537]) ).
fof(f6593,plain,
( frontsegP(app(sK48_skl,sK47_skl),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2660,f2657]) ).
fof(f6594,plain,
( frontsegP(app(nil,sK47_skl),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2660,f2667]) ).
fof(f6595,plain,
( frontsegP(app(sK47_skl,sK47_skl),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2660,f2658]) ).
fof(f6596,definition,
( sQ508_spl
<=> frontsegP(app(sK48_skl,sK47_skl),sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ508_spl])],[split_symbol_definition]) ).
fof(f6599,plain,
( sQ508_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f6593,f3037,f6596]) ).
fof(f6600,definition,
( sQ509_spl
<=> frontsegP(app(nil,sK47_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ509_spl])],[split_symbol_definition]) ).
fof(f6603,plain,
( sQ509_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f6594,f2268,f6600]) ).
fof(f6604,definition,
( sQ510_spl
<=> frontsegP(app(sK47_skl,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ510_spl])],[split_symbol_definition]) ).
fof(f6607,plain,
( sQ510_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f6595,f2271,f6604]) ).
fof(f6609,plain,
( rearsegP(app(sK47_skl,sK48_skl),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2795,f2791]) ).
fof(f6610,plain,
( rearsegP(app(sK47_skl,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2795,f2790]) ).
fof(f6611,plain,
( rearsegP(app(sK47_skl,sK47_skl),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2795,f2792]) ).
fof(f6612,definition,
( sQ511_spl
<=> rearsegP(app(sK47_skl,sK48_skl),sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ511_spl])],[split_symbol_definition]) ).
fof(f6615,plain,
( sQ511_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f6609,f3037,f6612]) ).
fof(f6616,definition,
( sQ512_spl
<=> rearsegP(app(sK47_skl,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ512_spl])],[split_symbol_definition]) ).
fof(f6619,plain,
( sQ512_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f6610,f2268,f6616]) ).
fof(f6620,definition,
( sQ513_spl
<=> rearsegP(app(sK47_skl,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ513_spl])],[split_symbol_definition]) ).
fof(f6623,plain,
( sQ513_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f6611,f2271,f6620]) ).
fof(f6628,plain,
( ssItem(sK45_skl(sK48_skl))
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f365,f420]) ).
fof(f6630,plain,
( ssItem(sK45_skl(sK47_skl))
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f365,f419]) ).
fof(f6631,plain,
( sQ287_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f6628,f572,f3902]) ).
fof(f6636,plain,
( sQ288_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f6630,f579,f3906]) ).
fof(f6637,plain,
( hd(sK48_skl) = sK45_skl(sK48_skl)
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f366,f420]) ).
fof(f6639,plain,
( hd(sK47_skl) = sK45_skl(sK47_skl)
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f366,f419]) ).
fof(f6640,plain,
( sQ285_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f6637,f572,f3860]) ).
fof(f6645,plain,
( sQ286_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f6639,f579,f3864]) ).
fof(f6649,plain,
( sQ450_spl
| ~ sQ286_spl
| sK0_skl != sK45_skl(sK47_skl) ),
inference(backward_demodulation,[status(thm)],[f3865,f6015]) ).
fof(f6687,plain,
( ssList(sK46_skl(sK48_skl))
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f369,f420]) ).
fof(f6689,plain,
( ssList(sK46_skl(sK47_skl))
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f369,f419]) ).
fof(f6690,plain,
( sQ283_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f6687,f572,f3827]) ).
fof(f6695,plain,
( sQ284_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f6689,f579,f3831]) ).
fof(f6788,plain,
( tl(sK48_skl) = sK46_skl(sK48_skl)
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f370,f420]) ).
fof(f6790,plain,
( tl(sK47_skl) = sK46_skl(sK47_skl)
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f370,f419]) ).
fof(f6791,plain,
( sQ281_spl
| sQ14_spl ),
inference(split_clause,[status(thm)],[f6788,f572,f3811]) ).
fof(f6796,plain,
( sQ282_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f6790,f579,f3815]) ).
fof(f6806,plain,
( ~ sQ278_spl
| ~ sQ281_spl
| ~ sQ285_spl
| ~ sQ291_spl
| cons(sK45_skl(sK48_skl),sK47_skl) = sK48_skl ),
inference(forward_demodulation,[status(thm)],[f4059,f3868]) ).
fof(f6810,plain,
! [X0] :
( X0 = sK48_skl
| tl(X0) != tl(sK48_skl)
| hd(X0) != hd(sK48_skl)
| nil = sK48_skl
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f372,f420]) ).
fof(f6812,plain,
! [X0] :
( X0 = sK47_skl
| tl(X0) != tl(sK47_skl)
| hd(X0) != hd(sK47_skl)
| nil = sK47_skl
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f372,f419]) ).
fof(f6813,definition,
! [X0] :
( sQ518_spl
<=> ( X0 = sK48_skl
| tl(X0) != tl(sK48_skl)
| hd(X0) != hd(sK48_skl)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ518_spl])],[split_symbol_definition]) ).
fof(f6816,plain,
( sQ14_spl
| sQ518_spl ),
inference(split_clause,[status(thm)],[f6810,f6813,f572]) ).
fof(f6821,definition,
! [X0] :
( sQ520_spl
<=> ( X0 = sK47_skl
| tl(X0) != tl(sK47_skl)
| hd(X0) != hd(sK47_skl)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ520_spl])],[split_symbol_definition]) ).
fof(f6824,plain,
( sQ16_spl
| sQ520_spl ),
inference(split_clause,[status(thm)],[f6812,f6821,f579]) ).
fof(f7383,plain,
( ~ sQ359_spl
| singletonP(cons(sK44_skl(sK47_skl),nil)) ),
inference(resolution,[status(thm)],[f4600,f549]) ).
fof(f7411,plain,
( ~ sQ359_spl
| ~ sQ357_spl
| ~ sQ461_spl
| singletonP(sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f6391,f7383]) ).
fof(f7412,plain,
( ~ sQ359_spl
| ~ sQ357_spl
| ~ sQ461_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7411,f522]) ).
fof(f7413,plain,
( ~ sQ359_spl
| ~ sQ357_spl
| ~ sQ461_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f7412]) ).
fof(f7417,plain,
( frontsegP(cons(sK1_skl,sK48_skl),cons(sK1_skl,sK48_skl))
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2662,f2657]) ).
fof(f7418,plain,
( frontsegP(cons(sK1_skl,nil),cons(sK1_skl,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2662,f2667]) ).
fof(f7419,plain,
( frontsegP(cons(sK1_skl,sK47_skl),cons(sK1_skl,sK47_skl))
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2662,f2658]) ).
fof(f7420,definition,
( sQ606_spl
<=> frontsegP(cons(sK1_skl,sK48_skl),cons(sK1_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ606_spl])],[split_symbol_definition]) ).
fof(f7423,plain,
( sQ606_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7417,f3037,f7420]) ).
fof(f7424,definition,
( sQ607_spl
<=> frontsegP(cons(sK1_skl,nil),cons(sK1_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ607_spl])],[split_symbol_definition]) ).
fof(f7427,plain,
( sQ607_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f7418,f2268,f7424]) ).
fof(f7428,definition,
( sQ608_spl
<=> frontsegP(cons(sK1_skl,sK47_skl),cons(sK1_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ608_spl])],[split_symbol_definition]) ).
fof(f7431,plain,
( sQ608_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7419,f2271,f7428]) ).
fof(f7432,plain,
( frontsegP(cons(sK0_skl,sK48_skl),cons(sK0_skl,sK48_skl))
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2663,f2657]) ).
fof(f7433,plain,
( frontsegP(cons(sK0_skl,nil),cons(sK0_skl,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2663,f2667]) ).
fof(f7434,plain,
( frontsegP(cons(sK0_skl,sK47_skl),cons(sK0_skl,sK47_skl))
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2663,f2658]) ).
fof(f7435,definition,
( sQ609_spl
<=> frontsegP(cons(sK0_skl,sK48_skl),cons(sK0_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ609_spl])],[split_symbol_definition]) ).
fof(f7438,plain,
( sQ609_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7432,f3037,f7435]) ).
fof(f7439,definition,
( sQ610_spl
<=> frontsegP(cons(sK0_skl,nil),cons(sK0_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ610_spl])],[split_symbol_definition]) ).
fof(f7442,plain,
( sQ610_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f7433,f2268,f7439]) ).
fof(f7443,definition,
( sQ611_spl
<=> frontsegP(cons(sK0_skl,sK47_skl),cons(sK0_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ611_spl])],[split_symbol_definition]) ).
fof(f7446,plain,
( sQ611_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7434,f2271,f7443]) ).
fof(f7452,plain,
( frontsegP(cons(sK0_skl,sK48_skl),cons(sK0_skl,nil))
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f5954,f2663]) ).
fof(f7453,plain,
( frontsegP(cons(sK1_skl,sK48_skl),cons(sK1_skl,nil))
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f5954,f2662]) ).
fof(f7454,plain,
( frontsegP(app(sK48_skl,sK47_skl),nil)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f5954,f2660]) ).
fof(f7455,plain,
( sK48_skl = nil
| ~ frontsegP(nil,sK48_skl)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f5954,f284]) ).
fof(f7456,plain,
! [X0] :
( frontsegP(sK48_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f5954,f282]) ).
fof(f7457,plain,
( app(nil,sK5_skl(nil,sK48_skl)) = sK48_skl
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f5954,f123]) ).
fof(f7458,plain,
( ssList(sK5_skl(nil,sK48_skl))
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f5954,f122]) ).
fof(f7459,definition,
( sQ612_spl
<=> frontsegP(cons(sK0_skl,sK48_skl),cons(sK0_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ612_spl])],[split_symbol_definition]) ).
fof(f7462,plain,
( sQ612_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7452,f3037,f2268,f7459]) ).
fof(f7463,definition,
( sQ613_spl
<=> frontsegP(cons(sK1_skl,sK48_skl),cons(sK1_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ613_spl])],[split_symbol_definition]) ).
fof(f7466,plain,
( sQ613_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7453,f3037,f2268,f7463]) ).
fof(f7467,definition,
( sQ614_spl
<=> frontsegP(app(sK48_skl,sK47_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ614_spl])],[split_symbol_definition]) ).
fof(f7470,plain,
( sQ614_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7454,f3037,f2268,f7467]) ).
fof(f7471,definition,
( sQ615_spl
<=> frontsegP(nil,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ615_spl])],[split_symbol_definition]) ).
fof(f7474,plain,
( sQ14_spl
| ~ sQ615_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7455,f3037,f2268,f7471,f572]) ).
fof(f7475,definition,
! [X0] :
( sQ616_spl
<=> ( frontsegP(sK48_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ616_spl])],[split_symbol_definition]) ).
fof(f7478,plain,
( sQ616_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7456,f3037,f2268,f7475]) ).
fof(f7479,definition,
( sQ617_spl
<=> app(nil,sK5_skl(nil,sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ617_spl])],[split_symbol_definition]) ).
fof(f7482,plain,
( sQ617_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7457,f3037,f2268,f7479]) ).
fof(f7483,definition,
( sQ618_spl
<=> ssList(sK5_skl(nil,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ618_spl])],[split_symbol_definition]) ).
fof(f7486,plain,
( sQ618_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7458,f3037,f2268,f7483]) ).
fof(f7494,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK47_skl),X0),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f544,f459]) ).
fof(f7496,definition,
! [X0] :
( sQ619_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK47_skl),X0),sK47_skl)
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ619_spl])],[split_symbol_definition]) ).
fof(f7499,plain,
( ~ sQ216_spl
| ~ sQ217_spl
| sQ619_spl ),
inference(split_clause,[status(thm)],[f7494,f7496,f2271,f2268]) ).
fof(f7502,plain,
( frontsegP(cons(sK0_skl,sK47_skl),cons(sK0_skl,nil))
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5956,f2663]) ).
fof(f7503,plain,
( frontsegP(cons(sK1_skl,sK47_skl),cons(sK1_skl,nil))
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5956,f2662]) ).
fof(f7504,plain,
( frontsegP(app(sK47_skl,sK47_skl),nil)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5956,f2660]) ).
fof(f7505,plain,
( sK47_skl = nil
| ~ frontsegP(nil,sK47_skl)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5956,f284]) ).
fof(f7506,plain,
! [X0] :
( frontsegP(sK47_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5956,f282]) ).
fof(f7507,plain,
( app(nil,sK5_skl(nil,sK47_skl)) = sK47_skl
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5956,f123]) ).
fof(f7508,plain,
( ssList(sK5_skl(nil,sK47_skl))
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5956,f122]) ).
fof(f7509,definition,
( sQ620_spl
<=> frontsegP(cons(sK0_skl,sK47_skl),cons(sK0_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ620_spl])],[split_symbol_definition]) ).
fof(f7512,plain,
( sQ620_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7502,f2271,f2268,f7509]) ).
fof(f7513,definition,
( sQ621_spl
<=> frontsegP(cons(sK1_skl,sK47_skl),cons(sK1_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ621_spl])],[split_symbol_definition]) ).
fof(f7516,plain,
( sQ621_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7503,f2271,f2268,f7513]) ).
fof(f7517,definition,
( sQ622_spl
<=> frontsegP(app(sK47_skl,sK47_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ622_spl])],[split_symbol_definition]) ).
fof(f7520,plain,
( sQ622_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7504,f2271,f2268,f7517]) ).
fof(f7521,definition,
( sQ623_spl
<=> frontsegP(nil,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ623_spl])],[split_symbol_definition]) ).
fof(f7524,plain,
( sQ16_spl
| ~ sQ623_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7505,f2271,f2268,f7521,f579]) ).
fof(f7525,definition,
! [X0] :
( sQ624_spl
<=> ( frontsegP(sK47_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ624_spl])],[split_symbol_definition]) ).
fof(f7528,plain,
( sQ624_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7506,f2271,f2268,f7525]) ).
fof(f7529,definition,
( sQ625_spl
<=> app(nil,sK5_skl(nil,sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ625_spl])],[split_symbol_definition]) ).
fof(f7532,plain,
( sQ625_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7507,f2271,f2268,f7529]) ).
fof(f7533,definition,
( sQ626_spl
<=> ssList(sK5_skl(nil,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ626_spl])],[split_symbol_definition]) ).
fof(f7536,plain,
( sQ626_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7508,f2271,f2268,f7533]) ).
fof(f7537,plain,
( nil = sK48_skl
| neq(nil,sK48_skl) ),
inference(resolution,[status(thm)],[f498,f420]) ).
fof(f7539,plain,
( nil = sK47_skl
| neq(nil,sK47_skl) ),
inference(resolution,[status(thm)],[f498,f419]) ).
fof(f7540,plain,
( sQ14_spl
| sQ230_spl ),
inference(split_clause,[status(thm)],[f7537,f2362,f572]) ).
fof(f7545,plain,
( sQ16_spl
| sQ235_spl ),
inference(split_clause,[status(thm)],[f7539,f2804,f579]) ).
fof(f7563,plain,
( rearsegP(app(sK47_skl,sK48_skl),nil)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f5957,f2795]) ).
fof(f7564,plain,
( sK48_skl = nil
| ~ rearsegP(nil,sK48_skl)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f5957,f303]) ).
fof(f7565,plain,
! [X0] :
( rearsegP(sK48_skl,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f5957,f301]) ).
fof(f7566,plain,
( app(sK6_skl(nil,sK48_skl),nil) = sK48_skl
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f5957,f129]) ).
fof(f7567,plain,
( ssList(sK6_skl(nil,sK48_skl))
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f5957,f128]) ).
fof(f7568,definition,
( sQ628_spl
<=> rearsegP(app(sK47_skl,sK48_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ628_spl])],[split_symbol_definition]) ).
fof(f7571,plain,
( sQ628_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7563,f3037,f2268,f7568]) ).
fof(f7572,definition,
( sQ629_spl
<=> rearsegP(nil,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ629_spl])],[split_symbol_definition]) ).
fof(f7575,plain,
( sQ14_spl
| ~ sQ629_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7564,f3037,f2268,f7572,f572]) ).
fof(f7576,definition,
! [X0] :
( sQ630_spl
<=> ( rearsegP(sK48_skl,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ630_spl])],[split_symbol_definition]) ).
fof(f7579,plain,
( sQ630_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7565,f3037,f2268,f7576]) ).
fof(f7580,definition,
( sQ631_spl
<=> app(sK6_skl(nil,sK48_skl),nil) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ631_spl])],[split_symbol_definition]) ).
fof(f7583,plain,
( sQ631_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7566,f3037,f2268,f7580]) ).
fof(f7584,definition,
( sQ632_spl
<=> ssList(sK6_skl(nil,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ632_spl])],[split_symbol_definition]) ).
fof(f7587,plain,
( sQ632_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7567,f3037,f2268,f7584]) ).
fof(f7588,plain,
( rearsegP(app(sK47_skl,sK47_skl),nil)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5959,f2795]) ).
fof(f7589,plain,
( sK47_skl = nil
| ~ rearsegP(nil,sK47_skl)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5959,f303]) ).
fof(f7590,plain,
! [X0] :
( rearsegP(sK47_skl,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5959,f301]) ).
fof(f7591,plain,
( app(sK6_skl(nil,sK47_skl),nil) = sK47_skl
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5959,f129]) ).
fof(f7592,plain,
( ssList(sK6_skl(nil,sK47_skl))
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f5959,f128]) ).
fof(f7593,definition,
( sQ633_spl
<=> rearsegP(app(sK47_skl,sK47_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ633_spl])],[split_symbol_definition]) ).
fof(f7596,plain,
( sQ633_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7588,f2271,f2268,f7593]) ).
fof(f7597,definition,
( sQ634_spl
<=> rearsegP(nil,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ634_spl])],[split_symbol_definition]) ).
fof(f7600,plain,
( sQ16_spl
| ~ sQ634_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7589,f2271,f2268,f7597,f579]) ).
fof(f7601,definition,
! [X0] :
( sQ635_spl
<=> ( rearsegP(sK47_skl,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ635_spl])],[split_symbol_definition]) ).
fof(f7604,plain,
( sQ635_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7590,f2271,f2268,f7601]) ).
fof(f7605,definition,
( sQ636_spl
<=> app(sK6_skl(nil,sK47_skl),nil) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ636_spl])],[split_symbol_definition]) ).
fof(f7608,plain,
( sQ636_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7591,f2271,f2268,f7605]) ).
fof(f7609,definition,
( sQ637_spl
<=> ssList(sK6_skl(nil,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ637_spl])],[split_symbol_definition]) ).
fof(f7612,plain,
( sQ637_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7592,f2271,f2268,f7609]) ).
fof(f7613,plain,
( sK48_skl = nil
| ~ segmentP(nil,sK48_skl)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f6079,f317]) ).
fof(f7614,plain,
! [X0] :
( segmentP(sK48_skl,X0)
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f6079,f315]) ).
fof(f7615,plain,
( app(app(sK7_skl(nil,sK48_skl),nil),sK8_skl(nil,sK48_skl)) = sK48_skl
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f6079,f136]) ).
fof(f7616,plain,
( ssList(sK8_skl(nil,sK48_skl))
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f6079,f135]) ).
fof(f7617,plain,
( ssList(sK7_skl(nil,sK48_skl))
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f6079,f134]) ).
fof(f7618,definition,
( sQ638_spl
<=> segmentP(nil,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ638_spl])],[split_symbol_definition]) ).
fof(f7621,plain,
( sQ14_spl
| ~ sQ638_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7613,f3037,f2268,f7618,f572]) ).
fof(f7622,definition,
! [X0] :
( sQ639_spl
<=> ( segmentP(sK48_skl,X0)
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ639_spl])],[split_symbol_definition]) ).
fof(f7625,plain,
( sQ639_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7614,f3037,f2268,f7622]) ).
fof(f7626,definition,
( sQ640_spl
<=> app(app(sK7_skl(nil,sK48_skl),nil),sK8_skl(nil,sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ640_spl])],[split_symbol_definition]) ).
fof(f7629,plain,
( sQ640_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7615,f3037,f2268,f7626]) ).
fof(f7630,definition,
( sQ641_spl
<=> ssList(sK8_skl(nil,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ641_spl])],[split_symbol_definition]) ).
fof(f7633,plain,
( sQ641_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7616,f3037,f2268,f7630]) ).
fof(f7634,definition,
( sQ642_spl
<=> ssList(sK7_skl(nil,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ642_spl])],[split_symbol_definition]) ).
fof(f7637,plain,
( sQ642_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f7617,f3037,f2268,f7634]) ).
fof(f7638,plain,
! [X0,X1] :
( sK48_skl = nil
| cons(X0,nil) != cons(X1,sK48_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f556,f420]) ).
fof(f7641,definition,
! [X0,X1] :
( sQ643_spl
<=> ( cons(X0,nil) != cons(X1,sK48_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ643_spl])],[split_symbol_definition]) ).
fof(f7644,plain,
( sQ14_spl
| sQ643_spl ),
inference(split_clause,[status(thm)],[f7638,f7641,f572]) ).
fof(f7650,plain,
! [X0] :
( memberP(nil,X0)
| memberP(nil,X0)
| ~ memberP(nil,X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f542,f270]) ).
fof(f7651,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(nil,X0)) ),
inference(paramodulation,[status(thm)],[f542,f459]) ).
fof(f7652,definition,
! [X0] :
( sQ645_spl
<=> ( memberP(nil,X0)
| memberP(nil,X0)
| ~ memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ645_spl])],[split_symbol_definition]) ).
fof(f7655,plain,
( ~ sQ216_spl
| sQ645_spl ),
inference(split_clause,[status(thm)],[f7650,f7652,f2268]) ).
fof(f7656,definition,
! [X0] :
( sQ646_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ646_spl])],[split_symbol_definition]) ).
fof(f7659,plain,
( ~ sQ216_spl
| sQ646_spl ),
inference(split_clause,[status(thm)],[f7651,f7656,f2268]) ).
fof(f7685,plain,
( sK47_skl = nil
| ~ segmentP(nil,sK47_skl)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f6081,f317]) ).
fof(f7686,plain,
! [X0] :
( segmentP(sK47_skl,X0)
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f6081,f315]) ).
fof(f7687,plain,
( app(app(sK7_skl(nil,sK47_skl),nil),sK8_skl(nil,sK47_skl)) = sK47_skl
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f6081,f136]) ).
fof(f7688,plain,
( ssList(sK8_skl(nil,sK47_skl))
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f6081,f135]) ).
fof(f7689,plain,
( ssList(sK7_skl(nil,sK47_skl))
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f6081,f134]) ).
fof(f7690,definition,
( sQ647_spl
<=> segmentP(nil,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ647_spl])],[split_symbol_definition]) ).
fof(f7693,plain,
( sQ16_spl
| ~ sQ647_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7685,f2271,f2268,f7690,f579]) ).
fof(f7694,definition,
! [X0] :
( sQ648_spl
<=> ( segmentP(sK47_skl,X0)
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ648_spl])],[split_symbol_definition]) ).
fof(f7697,plain,
( sQ648_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7686,f2271,f2268,f7694]) ).
fof(f7698,definition,
( sQ649_spl
<=> app(app(sK7_skl(nil,sK47_skl),nil),sK8_skl(nil,sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ649_spl])],[split_symbol_definition]) ).
fof(f7701,plain,
( sQ649_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7687,f2271,f2268,f7698]) ).
fof(f7702,definition,
( sQ650_spl
<=> ssList(sK8_skl(nil,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ650_spl])],[split_symbol_definition]) ).
fof(f7705,plain,
( sQ650_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7688,f2271,f2268,f7702]) ).
fof(f7706,definition,
( sQ651_spl
<=> ssList(sK7_skl(nil,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ651_spl])],[split_symbol_definition]) ).
fof(f7709,plain,
( sQ651_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f7689,f2271,f2268,f7706]) ).
fof(f7710,plain,
( ~ sQ287_spl
| cons(sK45_skl(sK48_skl),sK47_skl) = app(cons(sK45_skl(sK48_skl),nil),sK47_skl) ),
inference(resolution,[status(thm)],[f1660,f3903]) ).
fof(f7715,plain,
( ~ sQ287_spl
| ~ sQ278_spl
| ~ sQ281_spl
| ~ sQ285_spl
| ~ sQ291_spl
| sK48_skl = app(cons(sK45_skl(sK48_skl),nil),sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f6806,f7710]) ).
fof(f7716,plain,
! [X0,X1] :
( ~ sQ0_spl
| ~ neq(nil,app(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil),sK47_skl))
| hd(app(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil),sK47_skl)) != sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)
| ~ ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))
| ~ ssList(app(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil),sK47_skl))
| ~ sP0_prd(X0,X1,sK48_skl,sK47_skl) ),
inference(paramodulation,[status(thm)],[f2262,f548]) ).
fof(f7719,definition,
! [X0,X1] :
( sQ652_spl
<=> ~ sP0_prd(X0,X1,sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ652_spl])],[split_symbol_definition]) ).
fof(f7720,plain,
! [X0,X1] :
( ~ sQ652_spl
| ~ sP0_prd(X0,X1,sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f7719]) ).
fof(f7722,definition,
( sQ653_spl
<=> ssList(app(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil),sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ653_spl])],[split_symbol_definition]) ).
fof(f7724,plain,
( sQ653_spl
| ~ ssList(app(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil),sK47_skl)) ),
inference(component_clause,[status(thm)],[f7722]) ).
fof(f7725,definition,
( sQ654_spl
<=> ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ654_spl])],[split_symbol_definition]) ).
fof(f7727,plain,
( sQ654_spl
| ~ ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f7725]) ).
fof(f7728,definition,
( sQ655_spl
<=> hd(app(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil),sK47_skl)) = sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ655_spl])],[split_symbol_definition]) ).
fof(f7730,plain,
( sQ655_spl
| hd(app(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil),sK47_skl)) != sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f7728]) ).
fof(f7731,definition,
( sQ656_spl
<=> neq(nil,app(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil),sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ656_spl])],[split_symbol_definition]) ).
fof(f7733,plain,
( sQ656_spl
| ~ neq(nil,app(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil),sK47_skl)) ),
inference(component_clause,[status(thm)],[f7731]) ).
fof(f7734,plain,
( ~ sQ0_spl
| ~ sQ656_spl
| ~ sQ655_spl
| ~ sQ654_spl
| ~ sQ653_spl
| sQ652_spl ),
inference(split_clause,[status(thm)],[f7716,f7719,f7722,f7725,f7728,f7731,f442]) ).
fof(f7748,plain,
( sQ656_spl
| ~ sQ0_spl
| ~ neq(nil,sK48_skl) ),
inference(forward_demodulation,[status(thm)],[f2262,f7733]) ).
fof(f7749,plain,
( sQ656_spl
| ~ sQ0_spl
| ~ sQ230_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7748,f2363]) ).
fof(f7750,plain,
( sQ656_spl
| ~ sQ0_spl
| ~ sQ230_spl ),
inference(contradiction_clause,[status(thm)],[f7749]) ).
fof(f7751,plain,
( sQ655_spl
| ~ sQ0_spl
| hd(sK48_skl) != sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f2262,f7730]) ).
fof(f7752,plain,
( sQ655_spl
| ~ sQ0_spl
| ~ sQ285_spl
| sK45_skl(sK48_skl) != sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f3861,f7751]) ).
fof(f7767,plain,
( ~ sQ288_spl
| hd(cons(sK45_skl(sK47_skl),sK47_skl)) = sK45_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f3907,f708]) ).
fof(f7770,plain,
( ~ sQ288_spl
| sK1_skl = sK45_skl(sK47_skl)
| neq(sK1_skl,sK45_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3907,f502]) ).
fof(f7771,plain,
( ~ sQ288_spl
| sK0_skl = sK45_skl(sK47_skl)
| neq(sK0_skl,sK45_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3907,f501]) ).
fof(f7779,definition,
( sQ660_spl
<=> neq(sK1_skl,sK45_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ660_spl])],[split_symbol_definition]) ).
fof(f7782,definition,
( sQ661_spl
<=> sK1_skl = sK45_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ661_spl])],[split_symbol_definition]) ).
fof(f7783,plain,
( ~ sQ661_spl
| sK1_skl = sK45_skl(sK47_skl) ),
inference(component_clause,[status(thm)],[f7782]) ).
fof(f7785,plain,
( ~ sQ288_spl
| sQ661_spl
| sQ660_spl ),
inference(split_clause,[status(thm)],[f7770,f7779,f7782,f3906]) ).
fof(f7786,definition,
( sQ662_spl
<=> neq(sK0_skl,sK45_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ662_spl])],[split_symbol_definition]) ).
fof(f7789,definition,
( sQ663_spl
<=> sK0_skl = sK45_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ663_spl])],[split_symbol_definition]) ).
fof(f7790,plain,
( ~ sQ663_spl
| sK0_skl = sK45_skl(sK47_skl) ),
inference(component_clause,[status(thm)],[f7789]) ).
fof(f7792,plain,
( ~ sQ288_spl
| sQ663_spl
| sQ662_spl ),
inference(split_clause,[status(thm)],[f7771,f7786,f7789,f3906]) ).
fof(f7793,plain,
( ~ sQ663_spl
| sQ450_spl
| ~ sQ286_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7790,f6649]) ).
fof(f7794,plain,
( ~ sQ663_spl
| sQ450_spl
| ~ sQ286_spl ),
inference(contradiction_clause,[status(thm)],[f7793]) ).
fof(f7826,plain,
( ~ sQ17_spl
| ~ sQ450_spl
| ~ sQ286_spl
| hd(cons(sK45_skl(sK47_skl),sK47_skl)) = sK0_skl ),
inference(forward_demodulation,[status(thm)],[f3865,f6020]) ).
fof(f7827,plain,
( ~ sQ17_spl
| ~ sQ450_spl
| ~ sQ286_spl
| ~ sQ288_spl
| sK45_skl(sK47_skl) = sK0_skl ),
inference(forward_demodulation,[status(thm)],[f7767,f7826]) ).
fof(f7828,plain,
( ~ sQ17_spl
| ~ sQ450_spl
| ~ sQ286_spl
| ~ sQ288_spl
| ~ sQ661_spl
| sK1_skl = sK0_skl ),
inference(forward_demodulation,[status(thm)],[f7783,f7827]) ).
fof(f7829,plain,
( ~ sQ17_spl
| ~ sQ450_spl
| ~ sQ286_spl
| ~ sQ288_spl
| ~ sQ661_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7828,f105]) ).
fof(f7830,plain,
( ~ sQ17_spl
| ~ sQ450_spl
| ~ sQ286_spl
| ~ sQ288_spl
| ~ sQ661_spl ),
inference(contradiction_clause,[status(thm)],[f7829]) ).
fof(f7831,plain,
( ~ sQ275_spl
| ~ sQ450_spl
| ~ sQ282_spl
| cons(sK0_skl,sK46_skl(sK47_skl)) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f3816,f6023]) ).
fof(f7907,plain,
! [X0,X1] :
( ~ sQ284_spl
| sK46_skl(sK47_skl) = nil
| cons(X0,nil) != cons(X1,sK46_skl(sK47_skl))
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f3832,f556]) ).
fof(f7909,plain,
( ~ sQ284_spl
| nil = sK46_skl(sK47_skl)
| neq(nil,sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f498]) ).
fof(f7914,plain,
! [X0] :
( ~ sQ284_spl
| X0 = sK46_skl(sK47_skl)
| tl(X0) != tl(sK46_skl(sK47_skl))
| hd(X0) != hd(sK46_skl(sK47_skl))
| nil = sK46_skl(sK47_skl)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3832,f372]) ).
fof(f7915,plain,
( ~ sQ284_spl
| tl(sK46_skl(sK47_skl)) = sK46_skl(sK46_skl(sK47_skl))
| nil = sK46_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f3832,f370]) ).
fof(f7916,plain,
( ~ sQ284_spl
| ssList(sK46_skl(sK46_skl(sK47_skl)))
| nil = sK46_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f3832,f369]) ).
fof(f7917,plain,
( ~ sQ284_spl
| hd(sK46_skl(sK47_skl)) = sK45_skl(sK46_skl(sK47_skl))
| nil = sK46_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f3832,f366]) ).
fof(f7918,plain,
( ~ sQ284_spl
| ssItem(sK45_skl(sK46_skl(sK47_skl)))
| nil = sK46_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f3832,f365]) ).
fof(f7928,plain,
! [X0,X1] :
( ~ sQ284_spl
| sK46_skl(sK47_skl) = sK47_skl
| cons(X0,sK47_skl) != cons(X1,sK46_skl(sK47_skl))
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f3832,f558]) ).
fof(f7932,plain,
( ~ sQ284_spl
| ssList(tl(sK46_skl(sK47_skl)))
| nil = sK46_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f3832,f241]) ).
fof(f7933,plain,
( ~ sQ284_spl
| cons(sK44_skl(sK46_skl(sK47_skl)),sK43_skl(sK46_skl(sK47_skl))) = sK46_skl(sK47_skl)
| nil = sK46_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f3832,f233]) ).
fof(f7934,plain,
( ~ sQ284_spl
| ssItem(sK44_skl(sK46_skl(sK47_skl)))
| nil = sK46_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f3832,f232]) ).
fof(f7935,plain,
( ~ sQ284_spl
| ssList(sK43_skl(sK46_skl(sK47_skl)))
| nil = sK46_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f3832,f231]) ).
fof(f7936,plain,
! [X0] :
( ~ sQ284_spl
| nil = sK46_skl(sK47_skl)
| nil != app(sK46_skl(sK47_skl),X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3832,f386]) ).
fof(f7939,plain,
( ~ sQ284_spl
| ssItem(hd(sK46_skl(sK47_skl)))
| nil = sK46_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f3832,f237]) ).
fof(f7942,plain,
( ~ sQ284_spl
| cons(sK4_skl(sK46_skl(sK47_skl)),nil) = sK46_skl(sK47_skl)
| ~ singletonP(sK46_skl(sK47_skl)) ),
inference(resolution,[status(thm)],[f3832,f117]) ).
fof(f7943,plain,
! [X0] :
( ~ sQ284_spl
| tl(app(sK46_skl(sK47_skl),X0)) = app(tl(sK46_skl(sK47_skl)),X0)
| nil = sK46_skl(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3832,f393]) ).
fof(f7944,plain,
! [X0] :
( ~ sQ284_spl
| hd(app(sK46_skl(sK47_skl),X0)) = hd(sK46_skl(sK47_skl))
| nil = sK46_skl(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3832,f391]) ).
fof(f7946,plain,
( ~ sQ284_spl
| cons(hd(sK46_skl(sK47_skl)),tl(sK46_skl(sK47_skl))) = sK46_skl(sK47_skl)
| nil = sK46_skl(sK47_skl) ),
inference(resolution,[status(thm)],[f3832,f374]) ).
fof(f8016,definition,
! [X0,X1] :
( sQ664_spl
<=> ( cons(X0,nil) != cons(X1,sK46_skl(sK47_skl))
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ664_spl])],[split_symbol_definition]) ).
fof(f8019,definition,
( sQ665_spl
<=> sK46_skl(sK47_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ665_spl])],[split_symbol_definition]) ).
fof(f8020,plain,
( ~ sQ665_spl
| sK46_skl(sK47_skl) = nil ),
inference(component_clause,[status(thm)],[f8019]) ).
fof(f8022,plain,
( ~ sQ284_spl
| sQ665_spl
| sQ664_spl ),
inference(split_clause,[status(thm)],[f7907,f8016,f8019,f3831]) ).
fof(f8023,definition,
( sQ666_spl
<=> neq(nil,sK46_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ666_spl])],[split_symbol_definition]) ).
fof(f8026,plain,
( ~ sQ284_spl
| sQ665_spl
| sQ666_spl ),
inference(split_clause,[status(thm)],[f7909,f8023,f8019,f3831]) ).
fof(f8028,definition,
! [X0] :
( sQ667_spl
<=> ( X0 = sK46_skl(sK47_skl)
| tl(X0) != tl(sK46_skl(sK47_skl))
| hd(X0) != hd(sK46_skl(sK47_skl))
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ667_spl])],[split_symbol_definition]) ).
fof(f8031,plain,
( ~ sQ284_spl
| sQ665_spl
| sQ667_spl ),
inference(split_clause,[status(thm)],[f7914,f8028,f8019,f3831]) ).
fof(f8032,plain,
( ~ sQ284_spl
| sQ369_spl
| sQ665_spl ),
inference(split_clause,[status(thm)],[f7915,f8019,f4750,f3831]) ).
fof(f8033,plain,
( ~ sQ284_spl
| sQ368_spl
| sQ665_spl ),
inference(split_clause,[status(thm)],[f7916,f8019,f4746,f3831]) ).
fof(f8034,plain,
( ~ sQ284_spl
| sQ367_spl
| sQ665_spl ),
inference(split_clause,[status(thm)],[f7917,f8019,f4742,f3831]) ).
fof(f8035,plain,
( ~ sQ284_spl
| sQ366_spl
| sQ665_spl ),
inference(split_clause,[status(thm)],[f7918,f8019,f4738,f3831]) ).
fof(f8036,definition,
! [X0,X1] :
( sQ668_spl
<=> ( cons(X0,sK47_skl) != cons(X1,sK46_skl(sK47_skl))
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ668_spl])],[split_symbol_definition]) ).
fof(f8039,plain,
( ~ sQ284_spl
| sQ360_spl
| sQ668_spl ),
inference(split_clause,[status(thm)],[f7928,f8036,f4715,f3831]) ).
fof(f8040,plain,
( ~ sQ284_spl
| sQ365_spl
| sQ665_spl ),
inference(split_clause,[status(thm)],[f7932,f8019,f4734,f3831]) ).
fof(f8041,plain,
( ~ sQ284_spl
| sQ364_spl
| sQ665_spl ),
inference(split_clause,[status(thm)],[f7933,f8019,f4730,f3831]) ).
fof(f8042,plain,
( ~ sQ284_spl
| sQ363_spl
| sQ665_spl ),
inference(split_clause,[status(thm)],[f7934,f8019,f4726,f3831]) ).
fof(f8043,plain,
( ~ sQ284_spl
| sQ362_spl
| sQ665_spl ),
inference(split_clause,[status(thm)],[f7935,f8019,f4722,f3831]) ).
fof(f8044,definition,
! [X0] :
( sQ669_spl
<=> ( nil != app(sK46_skl(sK47_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ669_spl])],[split_symbol_definition]) ).
fof(f8047,plain,
( ~ sQ284_spl
| sQ665_spl
| sQ669_spl ),
inference(split_clause,[status(thm)],[f7936,f8044,f8019,f3831]) ).
fof(f8048,plain,
( ~ sQ284_spl
| sQ361_spl
| sQ665_spl ),
inference(split_clause,[status(thm)],[f7939,f8019,f4718,f3831]) ).
fof(f8053,definition,
( sQ670_spl
<=> cons(sK4_skl(sK46_skl(sK47_skl)),nil) = sK46_skl(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ670_spl])],[split_symbol_definition]) ).
fof(f8056,plain,
( ~ sQ284_spl
| sQ670_spl
| ~ sQ427_spl ),
inference(split_clause,[status(thm)],[f7942,f4975,f8053,f3831]) ).
fof(f8057,definition,
! [X0] :
( sQ671_spl
<=> ( tl(app(sK46_skl(sK47_skl),X0)) = app(tl(sK46_skl(sK47_skl)),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ671_spl])],[split_symbol_definition]) ).
fof(f8060,plain,
( ~ sQ284_spl
| sQ665_spl
| sQ671_spl ),
inference(split_clause,[status(thm)],[f7943,f8057,f8019,f3831]) ).
fof(f8061,plain,
( ~ sQ284_spl
| sQ665_spl
| sQ373_spl ),
inference(split_clause,[status(thm)],[f7944,f4766,f8019,f3831]) ).
fof(f8065,plain,
( ~ sQ284_spl
| sQ371_spl
| sQ665_spl ),
inference(split_clause,[status(thm)],[f7946,f8019,f4758,f3831]) ).
fof(f8140,plain,
( ~ sQ275_spl
| ~ sQ450_spl
| ~ sQ282_spl
| ~ sQ665_spl
| cons(sK0_skl,nil) = sK47_skl ),
inference(backward_demodulation,[status(thm)],[f8020,f7831]) ).
fof(f8217,plain,
( ~ sQ275_spl
| ~ sQ450_spl
| ~ sQ282_spl
| ~ sQ665_spl
| singletonP(sK47_skl) ),
inference(backward_demodulation,[status(thm)],[f8140,f2297]) ).
fof(f8248,plain,
( ~ sQ275_spl
| ~ sQ450_spl
| ~ sQ282_spl
| ~ sQ665_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8217,f522]) ).
fof(f8249,plain,
( ~ sQ275_spl
| ~ sQ450_spl
| ~ sQ282_spl
| ~ sQ665_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f8248]) ).
fof(f8557,plain,
( frontsegP(app(sK48_skl,nil),nil)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2666,f5954]) ).
fof(f8558,plain,
( frontsegP(app(sK48_skl,nil),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2666,f2657]) ).
fof(f8559,plain,
( frontsegP(app(nil,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2666,f2667]) ).
fof(f8560,plain,
( frontsegP(app(sK47_skl,nil),nil)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2666,f5956]) ).
fof(f8561,plain,
( frontsegP(app(sK47_skl,nil),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2666,f2658]) ).
fof(f8562,definition,
( sQ672_spl
<=> frontsegP(app(sK48_skl,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ672_spl])],[split_symbol_definition]) ).
fof(f8565,plain,
( sQ672_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f8557,f3037,f2268,f8562]) ).
fof(f8566,definition,
( sQ673_spl
<=> frontsegP(app(sK48_skl,nil),sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ673_spl])],[split_symbol_definition]) ).
fof(f8569,plain,
( sQ673_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f8558,f3037,f8566]) ).
fof(f8570,definition,
( sQ674_spl
<=> frontsegP(app(nil,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ674_spl])],[split_symbol_definition]) ).
fof(f8573,plain,
( sQ674_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f8559,f2268,f8570]) ).
fof(f8574,definition,
( sQ675_spl
<=> frontsegP(app(sK47_skl,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ675_spl])],[split_symbol_definition]) ).
fof(f8577,plain,
( sQ675_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f8560,f2271,f2268,f8574]) ).
fof(f8578,definition,
( sQ676_spl
<=> frontsegP(app(sK47_skl,nil),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ676_spl])],[split_symbol_definition]) ).
fof(f8581,plain,
( sQ676_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f8561,f2271,f8578]) ).
fof(f8587,plain,
( rearsegP(app(nil,sK48_skl),nil)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2793,f5957]) ).
fof(f8588,plain,
( rearsegP(app(nil,sK48_skl),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2793,f2791]) ).
fof(f8589,plain,
( rearsegP(app(nil,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2793,f2790]) ).
fof(f8590,plain,
( rearsegP(app(nil,sK47_skl),nil)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2793,f5959]) ).
fof(f8591,plain,
( rearsegP(app(nil,sK47_skl),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2793,f2792]) ).
fof(f8592,definition,
( sQ677_spl
<=> rearsegP(app(nil,sK48_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ677_spl])],[split_symbol_definition]) ).
fof(f8595,plain,
( sQ677_spl
| ~ sQ216_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f8587,f3037,f2268,f8592]) ).
fof(f8596,definition,
( sQ678_spl
<=> rearsegP(app(nil,sK48_skl),sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ678_spl])],[split_symbol_definition]) ).
fof(f8599,plain,
( sQ678_spl
| ~ sQ238_spl ),
inference(split_clause,[status(thm)],[f8588,f3037,f8596]) ).
fof(f8600,definition,
( sQ679_spl
<=> rearsegP(app(nil,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ679_spl])],[split_symbol_definition]) ).
fof(f8603,plain,
( sQ679_spl
| ~ sQ216_spl ),
inference(split_clause,[status(thm)],[f8589,f2268,f8600]) ).
fof(f8604,definition,
( sQ680_spl
<=> rearsegP(app(nil,sK47_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ680_spl])],[split_symbol_definition]) ).
fof(f8607,plain,
( sQ680_spl
| ~ sQ216_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f8590,f2271,f2268,f8604]) ).
fof(f8608,definition,
( sQ681_spl
<=> rearsegP(app(nil,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ681_spl])],[split_symbol_definition]) ).
fof(f8611,plain,
( sQ681_spl
| ~ sQ217_spl ),
inference(split_clause,[status(thm)],[f8591,f2271,f8608]) ).
fof(f8620,plain,
! [X0] :
( memberP(sK48_skl,X0)
| memberP(nil,X0)
| ~ memberP(sK48_skl,X0)
| ~ ssList(sK48_skl)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f543,f270]) ).
fof(f8621,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK48_skl),X0),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f543,f459]) ).
fof(f8622,definition,
! [X0] :
( sQ682_spl
<=> ( memberP(sK48_skl,X0)
| memberP(nil,X0)
| ~ memberP(sK48_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ682_spl])],[split_symbol_definition]) ).
fof(f8625,plain,
( ~ sQ238_spl
| ~ sQ216_spl
| sQ682_spl ),
inference(split_clause,[status(thm)],[f8620,f8622,f2268,f3037]) ).
fof(f8626,definition,
! [X0] :
( sQ683_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK48_skl),X0),sK48_skl)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ683_spl])],[split_symbol_definition]) ).
fof(f8629,plain,
( ~ sQ216_spl
| ~ sQ238_spl
| sQ683_spl ),
inference(split_clause,[status(thm)],[f8621,f8626,f3037,f2268]) ).
fof(f8646,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK48_skl)
| segmentP(app(app(sK48_skl,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f1680,f459]) ).
fof(f8648,definition,
! [X0] :
( sQ684_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK48_skl,nil),X0),nil)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ684_spl])],[split_symbol_definition]) ).
fof(f8651,plain,
( ~ sQ238_spl
| ~ sQ216_spl
| sQ684_spl ),
inference(split_clause,[status(thm)],[f8646,f8648,f2268,f3037]) ).
fof(f8662,plain,
( ~ sQ0_spl
| cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),sK47_skl) = app(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil),sK47_skl) ),
inference(resolution,[status(thm)],[f922,f1660]) ).
fof(f8667,plain,
( ~ sQ0_spl
| tl(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),sK47_skl)) = sK47_skl ),
inference(resolution,[status(thm)],[f922,f2257]) ).
fof(f8675,plain,
( ~ sQ0_spl
| hd(cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),sK47_skl)) = sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(resolution,[status(thm)],[f922,f708]) ).
fof(f8687,plain,
( ~ sQ0_spl
| cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),sK47_skl) = sK48_skl ),
inference(forward_demodulation,[status(thm)],[f2262,f8662]) ).
fof(f8691,plain,
( ~ sQ0_spl
| tl(sK48_skl) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f8687,f8667]) ).
fof(f8692,plain,
( ~ sQ0_spl
| hd(sK48_skl) = sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f8687,f8675]) ).
fof(f8693,plain,
( ~ sQ0_spl
| ~ sQ285_spl
| sK45_skl(sK48_skl) = sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f3861,f8692]) ).
fof(f8694,plain,
( ~ sQ0_spl
| ~ sQ285_spl
| sQ655_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8693,f7752]) ).
fof(f8695,plain,
( ~ sQ0_spl
| ~ sQ285_spl
| sQ655_spl ),
inference(contradiction_clause,[status(thm)],[f8694]) ).
fof(f8712,plain,
( sQ654_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7727,f922]) ).
fof(f8713,plain,
( sQ654_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f8712]) ).
fof(f8742,plain,
( ~ sQ0_spl
| ~ sQ652_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f497,f7720]) ).
fof(f8756,plain,
( ~ sQ0_spl
| ~ sQ652_spl ),
inference(contradiction_clause,[status(thm)],[f8742]) ).
fof(f8757,plain,
( sQ653_spl
| ~ sQ0_spl
| ~ sQ285_spl
| ~ ssList(app(cons(sK45_skl(sK48_skl),nil),sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f8693,f7724]) ).
fof(f8758,plain,
( sQ653_spl
| ~ sQ0_spl
| ~ sQ285_spl
| ~ sQ287_spl
| ~ sQ278_spl
| ~ sQ281_spl
| ~ sQ291_spl
| ~ ssList(sK48_skl) ),
inference(forward_demodulation,[status(thm)],[f7715,f8757]) ).
fof(f8759,plain,
( sQ653_spl
| ~ sQ0_spl
| ~ sQ285_spl
| ~ sQ287_spl
| ~ sQ278_spl
| ~ sQ281_spl
| ~ sQ291_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8758,f420]) ).
fof(f8760,plain,
( sQ653_spl
| ~ sQ0_spl
| ~ sQ285_spl
| ~ sQ287_spl
| ~ sQ278_spl
| ~ sQ281_spl
| ~ sQ291_spl ),
inference(contradiction_clause,[status(thm)],[f8759]) ).
fof(f8886,plain,
( ~ sQ281_spl
| ~ sQ0_spl
| sK47_skl = sK46_skl(sK48_skl) ),
inference(forward_demodulation,[status(thm)],[f8691,f3812]) ).
fof(f8931,plain,
( sQ291_spl
| ~ sQ281_spl
| ~ sQ0_spl
| sK47_skl != sK47_skl ),
inference(forward_demodulation,[status(thm)],[f8886,f4060]) ).
fof(f8932,plain,
( sQ291_spl
| ~ sQ281_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f8931]) ).
fof(f8933,plain,
( sQ291_spl
| ~ sQ281_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f8932]) ).
fof(f8934,plain,
$false,
inference(sat_refutation,[status(thm)],[f448,f452,f519,f526,f537,f541,f578,f585,f1401,f1404,f1674,f1678,f1762,f1766,f2274,f2280,f2307,f2311,f2320,f2322,f2332,f2336,f2345,f2347,f2352,f2354,f2382,f2386,f2532,f3020,f3043,f3047,f3051,f3055,f3057,f3059,f3064,f3065,f3071,f3075,f3085,f3089,f3097,f3101,f3105,f3109,f3111,f3123,f3127,f3131,f3133,f3145,f3149,f3153,f3155,f3168,f3172,f3176,f3180,f3182,f3195,f3199,f3203,f3207,f3209,f3225,f3479,f3495,f3773,f3782,f3796,f3803,f3814,f3830,f3863,f3905,f3967,f4478,f4588,f4598,f4605,f4609,f4773,f4780,f4784,f4788,f4792,f4796,f4800,f4807,f4811,f4815,f4819,f4823,f4827,f4831,f4838,f4842,f4846,f4850,f4854,f4858,f4865,f4869,f4873,f4877,f4881,f4885,f4892,f4896,f4900,f4904,f4908,f4912,f4919,f4923,f4927,f4931,f4935,f4939,f4946,f4950,f4954,f4958,f4962,f4966,f4970,f4974,f4981,f5276,f5280,f5284,f5288,f5292,f5754,f5761,f5847,f5848,f5852,f5854,f5919,f5925,f5935,f5939,f5944,f5948,f5953,f5973,f5977,f6002,f6009,f6016,f6034,f6040,f6048,f6052,f6056,f6068,f6072,f6076,f6191,f6195,f6199,f6200,f6204,f6205,f6213,f6217,f6221,f6528,f6532,f6536,f6540,f6599,f6603,f6607,f6615,f6619,f6623,f6631,f6636,f6640,f6645,f6690,f6695,f6791,f6796,f6816,f6824,f7413,f7423,f7427,f7431,f7438,f7442,f7446,f7462,f7466,f7470,f7474,f7478,f7482,f7486,f7499,f7512,f7516,f7520,f7524,f7528,f7532,f7536,f7540,f7545,f7571,f7575,f7579,f7583,f7587,f7596,f7600,f7604,f7608,f7612,f7621,f7625,f7629,f7633,f7637,f7644,f7655,f7659,f7693,f7697,f7701,f7705,f7709,f7734,f7750,f7785,f7792,f7794,f7830,f8022,f8026,f8031,f8032,f8033,f8034,f8035,f8039,f8040,f8041,f8042,f8043,f8047,f8048,f8056,f8060,f8061,f8065,f8249,f8565,f8569,f8573,f8577,f8581,f8595,f8599,f8603,f8607,f8611,f8625,f8629,f8651,f8695,f8713,f8756,f8760,f8933]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC416+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.45 % Computer : n003.cluster.edu
% 0.17/0.45 % Model : x86_64 x86_64
% 0.17/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.45 % Memory : 8046.5625MB
% 0.17/0.45 % OS : Linux 6.8.0-71-generic
% 0.17/0.46 % CPULimit : 300
% 0.17/0.46 % WCLimit : 300
% 0.17/0.46 % DateTime : Mon Sep 21 08:24:16 UTC 2026
% 0.17/0.46 % CPUTime :
% 0.17/0.51 % Drodi V4.1.1
% 19.60/3.01 % Refutation found
% 19.60/3.01 % SZS status Theorem for theBenchmark: Theorem is valid
% 19.60/3.01 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 19.60/3.06 % Elapsed time: 2.572910 seconds
% 19.60/3.06 % CPU time: 19.802782 seconds
% 19.60/3.06 % Total memory used: 243.983 MB
% 19.60/3.06 % Net memory used: 229.562 MB
%------------------------------------------------------------------------------