%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC071+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n020.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 02:39:51 PM UTC 2026
% Result : Theorem 26.85s 4.37s
% Output : CNFRefutation 26.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 176
% Syntax : Number of formulae : 672 ( 35 unt; 125 def)
% Number of atoms : 3518 ( 523 equ)
% Maximal formula atoms : 25 ( 5 avg)
% Number of connectives : 5090 (2244 ~;2258 |; 279 &)
% ( 168 <=>; 141 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 144 ( 142 usr; 124 prp; 0-3 aty)
% Number of functors : 56 ( 56 usr; 8 con; 0-5 aty)
% Number of variables : 1226 (1139 !; 87 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( memberP(U,V)
<=> ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U] :
( ssList(U)
=> ( cyclefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ~ ( leq(W,V)
& leq(V,W) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [U] :
( ssList(U)
=> ( totalorderP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ( leq(W,V)
| leq(V,W) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [U] :
( ssList(U)
=> ( strictorderP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ( lt(W,V)
| lt(V,W) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [U] :
( ssList(U)
=> ( totalorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> leq(V,W) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [U] :
( ssList(U)
=> ( strictorderedP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> lt(V,W) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [U] :
( ssList(U)
=> ( duplicatefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> V != W ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [U] :
( ssList(U)
=> ( equalelemsP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ( app(X,cons(V,cons(W,Y))) = U
=> V = W ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssItem(X)
=> ( cons(W,U) = cons(X,V)
=> ( V = U
& W = X ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( frontsegP(V,W)
& frontsegP(U,V) )
=> frontsegP(U,W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( frontsegP(V,U)
& frontsegP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( frontsegP(cons(U,W),cons(V,X))
<=> ( frontsegP(W,X)
& U = V ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [U] :
( ssList(U)
=> ( frontsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( rearsegP(V,W)
& rearsegP(U,V) )
=> rearsegP(U,W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( rearsegP(V,U)
& rearsegP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [U] :
( ssList(U)
=> ( rearsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( segmentP(V,W)
& segmentP(U,V) )
=> segmentP(U,W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( segmentP(V,U)
& segmentP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( segmentP(U,V)
=> segmentP(app(app(W,U),X),V) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,axiom,
cyclefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f62,axiom,
totalorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f64,axiom,
strictorderP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f66,axiom,
totalorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f67,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ( totalorderedP(cons(U,V))
<=> ( ( leq(U,hd(V))
& totalorderedP(V)
& nil != V )
| nil = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f69,axiom,
strictorderedP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f70,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ( strictorderedP(cons(U,V))
<=> ( ( lt(U,hd(V))
& strictorderedP(V)
& nil != V )
| nil = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f72,axiom,
duplicatefreeP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f74,axiom,
equalelemsP(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f79,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(W,V) = app(U,V)
=> W = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(V,W) = app(V,U)
=> W = U ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) = app(cons(V,nil),U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ? [X4] :
( lt(X4,Z)
& memberP(X2,X4)
& ssItem(X4) )
| ? [X3] :
( lt(Z,X3)
& memberP(X1,X3)
& ssItem(X3) )
| app(app(X1,W),X2) != X
| cons(Z,nil) != W ) ) ) ) )
| ( nil = U
& nil = V )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [Z] :
( ssItem(Z)
=> ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> ( ? [X4] :
( lt(X4,Z)
& memberP(X2,X4)
& ssItem(X4) )
| ? [X3] :
( lt(Z,X3)
& memberP(X1,X3)
& ssItem(X3) )
| app(app(X1,W),X2) != X
| cons(Z,nil) != W ) ) ) ) )
| ( nil = U
& nil = V )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
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(f104,plain,
ssItem(sK1_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f106,plain,
! [U] :
( ! [V] :
( ( memberP(U,V)
<=> ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f107,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(W,cons(V,X)) != U
| ~ ssList(X) )
| ~ ssList(W) )
| memberP(U,V) )
& ( ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) )
| ~ memberP(U,V) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(W,cons(V,X)) != U
| ~ ssList(X) )
| ~ ssList(W) )
| memberP(U,V) )
& ( ( app(sK2_skl(V,U),cons(V,sK3_skl(V,U))) = U
& ssList(sK3_skl(V,U))
& ssList(sK2_skl(V,U)) )
| ~ memberP(U,V) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(W,sK2_skl(V,U)),skolemize(X,sK3_skl(V,U))],[f107]) ).
fof(f111,plain,
! [X0,X1] :
( app(sK2_skl(X1,X0),cons(X1,sK3_skl(X1,X0))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f113,plain,
! [U] :
( ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f114,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [V] :
( cons(V,nil) = U
& ssItem(V) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ( cons(sK4_skl(U),nil) = U
& ssItem(sK4_skl(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114]) ).
fof(f117,plain,
! [X0] :
( cons(sK4_skl(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f118,plain,
! [X0,X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f119,plain,
! [U] :
( ! [V] :
( ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f120,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ? [W] :
( app(V,W) = U
& ssList(W) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ( app(V,sK5_skl(V,U)) = U
& ssList(sK5_skl(V,U)) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( ssList(sK5_skl(X1,X0))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( app(X1,sK5_skl(X1,X0)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f124,plain,
! [X0,X1,X2] :
( app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f125,plain,
! [U] :
( ! [V] :
( ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f126,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ? [W] :
( app(W,V) = U
& ssList(W) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ( app(sK6_skl(V,U),V) = U
& ssList(sK6_skl(V,U)) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126]) ).
fof(f129,plain,
! [X0,X1] :
( app(sK6_skl(X1,X0),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f130,plain,
! [X0,X1,X2] :
( app(X2,X1) != X0
| ~ ssList(X2)
| rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f131,plain,
! [U] :
( ! [V] :
( ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f132,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ( app(app(sK7_skl(V,U),V),sK8_skl(V,U)) = U
& ssList(sK8_skl(V,U))
& ssList(sK7_skl(V,U)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132]) ).
fof(f136,plain,
! [X0,X1] :
( app(app(sK7_skl(X1,X0),X1),sK8_skl(X1,X0)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f138,plain,
! [U] :
( ( cyclefreeP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f139,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( leq(W,V)
& leq(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| cyclefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ cyclefreeP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
! [U] :
( ( ( ( leq(sK10_skl(U),sK9_skl(U))
& leq(sK9_skl(U),sK10_skl(U))
& app(app(sK11_skl(U),cons(sK9_skl(U),sK12_skl(U))),cons(sK10_skl(U),sK13_skl(U))) = U
& ssList(sK13_skl(U))
& ssList(sK12_skl(U))
& ssList(sK11_skl(U))
& ssItem(sK10_skl(U))
& ssItem(sK9_skl(U)) )
| cyclefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ cyclefreeP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl,sK12_skl,sK13_skl]),skolemize(V,sK9_skl(U)),skolemize(W,sK10_skl(U)),skolemize(X,sK11_skl(U)),skolemize(Y,sK12_skl(U)),skolemize(Z,sK13_skl(U))],[f139]) ).
fof(f141,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ cyclefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f150,plain,
! [U] :
( ( totalorderP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(W,V)
| leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f151,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ leq(W,V)
& ~ leq(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| totalorderP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(W,V)
| leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f150]) ).
fof(f152,plain,
! [U] :
( ( ( ( ~ leq(sK15_skl(U),sK14_skl(U))
& ~ leq(sK14_skl(U),sK15_skl(U))
& app(app(sK16_skl(U),cons(sK14_skl(U),sK17_skl(U))),cons(sK15_skl(U),sK18_skl(U))) = U
& ssList(sK18_skl(U))
& ssList(sK17_skl(U))
& ssList(sK16_skl(U))
& ssItem(sK15_skl(U))
& ssItem(sK14_skl(U)) )
| totalorderP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(W,V)
| leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl,sK17_skl,sK18_skl]),skolemize(V,sK14_skl(U)),skolemize(W,sK15_skl(U)),skolemize(X,sK16_skl(U)),skolemize(Y,sK17_skl(U)),skolemize(Z,sK18_skl(U))],[f151]) ).
fof(f153,plain,
! [X0,X1,X2,X3,X4,X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ totalorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(f162,plain,
! [U] :
( ( strictorderP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(W,V)
| lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f163,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ lt(W,V)
& ~ lt(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| strictorderP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(W,V)
| lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ strictorderP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f162]) ).
fof(f164,plain,
! [U] :
( ( ( ( ~ lt(sK20_skl(U),sK19_skl(U))
& ~ lt(sK19_skl(U),sK20_skl(U))
& app(app(sK21_skl(U),cons(sK19_skl(U),sK22_skl(U))),cons(sK20_skl(U),sK23_skl(U))) = U
& ssList(sK23_skl(U))
& ssList(sK22_skl(U))
& ssList(sK21_skl(U))
& ssItem(sK20_skl(U))
& ssItem(sK19_skl(U)) )
| strictorderP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(W,V)
| lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ strictorderP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK19_skl,sK20_skl,sK21_skl,sK22_skl,sK23_skl]),skolemize(V,sK19_skl(U)),skolemize(W,sK20_skl(U)),skolemize(X,sK21_skl(U)),skolemize(Y,sK22_skl(U)),skolemize(Z,sK23_skl(U))],[f163]) ).
fof(f165,plain,
! [X0,X1,X2,X3,X4,X5] :
( lt(X2,X1)
| lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ strictorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f164]) ).
fof(f174,plain,
! [U] :
( ( totalorderedP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f11]) ).
fof(f175,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ leq(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| totalorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderedP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f174]) ).
fof(f176,plain,
! [U] :
( ( ( ( ~ leq(sK24_skl(U),sK25_skl(U))
& app(app(sK26_skl(U),cons(sK24_skl(U),sK27_skl(U))),cons(sK25_skl(U),sK28_skl(U))) = U
& ssList(sK28_skl(U))
& ssList(sK27_skl(U))
& ssList(sK26_skl(U))
& ssItem(sK25_skl(U))
& ssItem(sK24_skl(U)) )
| totalorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderedP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK24_skl,sK25_skl,sK26_skl,sK27_skl,sK28_skl]),skolemize(V,sK24_skl(U)),skolemize(W,sK25_skl(U)),skolemize(X,sK26_skl(U)),skolemize(Y,sK27_skl(U)),skolemize(Z,sK28_skl(U))],[f175]) ).
fof(f177,plain,
! [X0,X1,X2,X3,X4,X5] :
( leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ totalorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f176]) ).
fof(f185,plain,
! [U] :
( ( strictorderedP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f186,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ lt(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| strictorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ strictorderedP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f185]) ).
fof(f187,plain,
! [U] :
( ( ( ( ~ lt(sK29_skl(U),sK30_skl(U))
& app(app(sK31_skl(U),cons(sK29_skl(U),sK32_skl(U))),cons(sK30_skl(U),sK33_skl(U))) = U
& ssList(sK33_skl(U))
& ssList(sK32_skl(U))
& ssList(sK31_skl(U))
& ssItem(sK30_skl(U))
& ssItem(sK29_skl(U)) )
| strictorderedP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( lt(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ strictorderedP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK29_skl,sK30_skl,sK31_skl,sK32_skl,sK33_skl]),skolemize(V,sK29_skl(U)),skolemize(W,sK30_skl(U)),skolemize(X,sK31_skl(U)),skolemize(Y,sK32_skl(U)),skolemize(Z,sK33_skl(U))],[f186]) ).
fof(f188,plain,
! [X0,X1,X2,X3,X4,X5] :
( lt(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ strictorderedP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f187]) ).
fof(f196,plain,
! [U] :
( ( duplicatefreeP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( V != W
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f197,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( V = W
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| duplicatefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( V != W
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ duplicatefreeP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f196]) ).
fof(f198,plain,
! [U] :
( ( ( ( sK34_skl(U) = sK35_skl(U)
& app(app(sK36_skl(U),cons(sK34_skl(U),sK37_skl(U))),cons(sK35_skl(U),sK38_skl(U))) = U
& ssList(sK38_skl(U))
& ssList(sK37_skl(U))
& ssList(sK36_skl(U))
& ssItem(sK35_skl(U))
& ssItem(sK34_skl(U)) )
| duplicatefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( V != W
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ duplicatefreeP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK34_skl,sK35_skl,sK36_skl,sK37_skl,sK38_skl]),skolemize(V,sK34_skl(U)),skolemize(W,sK35_skl(U)),skolemize(X,sK36_skl(U)),skolemize(Y,sK37_skl(U)),skolemize(Z,sK38_skl(U))],[f197]) ).
fof(f199,plain,
! [X0,X1,X2,X3,X4,X5] :
( X1 != X2
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f207,plain,
! [U] :
( ( equalelemsP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( V = W
| app(X,cons(V,cons(W,Y))) != U
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f14]) ).
fof(f208,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( V != W
& app(X,cons(V,cons(W,Y))) = U
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| equalelemsP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( V = W
| app(X,cons(V,cons(W,Y))) != U
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ equalelemsP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f207]) ).
fof(f209,plain,
! [U] :
( ( ( ( sK39_skl(U) != sK40_skl(U)
& app(sK41_skl(U),cons(sK39_skl(U),cons(sK40_skl(U),sK42_skl(U)))) = U
& ssList(sK42_skl(U))
& ssList(sK41_skl(U))
& ssItem(sK40_skl(U))
& ssItem(sK39_skl(U)) )
| equalelemsP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( V = W
| app(X,cons(V,cons(W,Y))) != U
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ equalelemsP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK39_skl,sK40_skl,sK41_skl,sK42_skl]),skolemize(V,sK39_skl(U)),skolemize(W,sK40_skl(U)),skolemize(X,sK41_skl(U)),skolemize(Y,sK42_skl(U))],[f208]) ).
fof(f210,plain,
! [X0,X1,X2,X3,X4] :
( X1 = X2
| app(X3,cons(X1,cons(X2,X4))) != X0
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ equalelemsP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f209]) ).
fof(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(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f224,plain,
! [U] :
( ! [V] :
( cons(V,U) != U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f225,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f226,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( V = U
& W = X )
| cons(W,U) != cons(X,V)
| ~ ssItem(X) )
| ~ ssItem(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f227,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f228,plain,
! [X0,X1,X2,X3] :
( X1 = X0
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f244,plain,
! [U] :
( ! [V] :
( ssList(app(U,V))
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(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(f273,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f274,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& U != V )
| memberP(cons(V,W),U) )
& ( memberP(W,U)
| U = V
| ~ memberP(cons(V,W),U) ) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f273]) ).
fof(f275,plain,
! [X0,X1,X2] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f278,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f279,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f281,plain,
! [U] :
( ! [V] :
( ! [W] :
( frontsegP(U,W)
| ~ frontsegP(V,W)
| ~ frontsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f282,plain,
! [X0,X1,X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f283,plain,
! [U] :
( ! [V] :
( U = V
| ~ frontsegP(V,U)
| ~ frontsegP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f284,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(f289,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( frontsegP(cons(U,W),cons(V,X))
<=> ( frontsegP(W,X)
& U = V ) )
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f290,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( ( ~ frontsegP(W,X)
| U != V
| frontsegP(cons(U,W),cons(V,X)) )
& ( ( frontsegP(W,X)
& U = V )
| ~ frontsegP(cons(U,W),cons(V,X)) ) )
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f289]) ).
fof(f291,plain,
! [X0,X1,X2,X3] :
( X0 = X1
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f292,plain,
! [X0,X1,X2,X3] :
( frontsegP(X2,X3)
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(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(f299,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(f308,plain,
! [U] :
( rearsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f309,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f310,plain,
! [U] :
( ( rearsegP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f311,plain,
! [U] :
( ( ( nil != U
| rearsegP(nil,U) )
& ( nil = U
| ~ rearsegP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f310]) ).
fof(f312,plain,
! [X0] :
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f311]) ).
fof(f314,plain,
! [U] :
( ! [V] :
( ! [W] :
( segmentP(U,W)
| ~ segmentP(V,W)
| ~ segmentP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f315,plain,
! [X0,X1,X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
fof(f316,plain,
! [U] :
( ! [V] :
( U = V
| ~ segmentP(V,U)
| ~ segmentP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f317,plain,
! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f316]) ).
fof(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(f320,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( segmentP(app(app(W,U),X),V)
| ~ segmentP(U,V)
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f321,plain,
! [X0,X1,X2,X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f322,plain,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f323,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f324,plain,
! [U] :
( ( segmentP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f325,plain,
! [U] :
( ( ( nil != U
| segmentP(nil,U) )
& ( nil = U
| ~ segmentP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f324]) ).
fof(f326,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f327,plain,
! [X0] :
( nil != X0
| segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(f330,plain,
cyclefreeP(nil),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f333,plain,
totalorderP(nil),
inference(cnf_transformation,[status(thm)],[f62]) ).
fof(f336,plain,
strictorderP(nil),
inference(cnf_transformation,[status(thm)],[f64]) ).
fof(f339,plain,
totalorderedP(nil),
inference(cnf_transformation,[status(thm)],[f66]) ).
fof(f340,plain,
! [U] :
( ! [V] :
( ( totalorderedP(cons(U,V))
<=> ( ( leq(U,hd(V))
& totalorderedP(V)
& nil != V )
| nil = V ) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f67]) ).
fof(f341,plain,
! [U] :
( ! [V] :
( ( ( ( ( ~ leq(U,hd(V))
| ~ totalorderedP(V)
| nil = V )
& nil != V )
| totalorderedP(cons(U,V)) )
& ( ( leq(U,hd(V))
& totalorderedP(V)
& nil != V )
| nil = V
| ~ totalorderedP(cons(U,V)) ) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f340]) ).
fof(f343,plain,
! [X0,X1] :
( totalorderedP(X1)
| nil = X1
| ~ totalorderedP(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f341]) ).
fof(f345,plain,
! [X0,X1] :
( nil != X1
| totalorderedP(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f341]) ).
fof(f349,plain,
strictorderedP(nil),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f350,plain,
! [U] :
( ! [V] :
( ( strictorderedP(cons(U,V))
<=> ( ( lt(U,hd(V))
& strictorderedP(V)
& nil != V )
| nil = V ) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f70]) ).
fof(f351,plain,
! [U] :
( ! [V] :
( ( ( ( ( ~ lt(U,hd(V))
| ~ strictorderedP(V)
| nil = V )
& nil != V )
| strictorderedP(cons(U,V)) )
& ( ( lt(U,hd(V))
& strictorderedP(V)
& nil != V )
| nil = V
| ~ strictorderedP(cons(U,V)) ) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f350]) ).
fof(f353,plain,
! [X0,X1] :
( strictorderedP(X1)
| nil = X1
| ~ strictorderedP(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f351]) ).
fof(f355,plain,
! [X0,X1] :
( nil != X1
| strictorderedP(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f351]) ).
fof(f359,plain,
duplicatefreeP(nil),
inference(cnf_transformation,[status(thm)],[f72]) ).
fof(f362,plain,
equalelemsP(nil),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f375,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(W,V) != app(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f79]) ).
fof(f376,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f375]) ).
fof(f377,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(V,W) != app(V,U)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f80]) ).
fof(f378,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f377]) ).
fof(f379,plain,
! [U] :
( ! [V] :
( cons(V,U) = app(cons(V,nil),U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f81]) ).
fof(f380,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f383,plain,
! [U] :
( ! [V] :
( ( nil = app(U,V)
<=> ( nil = U
& nil = V ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f384,plain,
! [U] :
( ! [V] :
( ( ( nil != U
| nil != V
| nil = app(U,V) )
& ( ( nil = U
& nil = V )
| nil != app(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f383]) ).
fof(f385,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f386,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f387,plain,
! [X0,X1] :
( nil != X0
| nil != X1
| 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(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Z] :
( ? [X1] :
( ? [X2] :
( ! [X4] :
( ~ lt(X4,Z)
| ~ memberP(X2,X4)
| ~ ssItem(X4) )
& ! [X3] :
( ~ lt(Z,X3)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& app(app(X1,W),X2) = X
& cons(Z,nil) = W
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) ) )
& ( nil != U
| nil != V )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [W,X,Z] :
( sP0_prd(Z,X,W)
<=> ( ? [X1] :
( ? [X2] :
( ! [X4] :
( ~ lt(X4,Z)
| ~ memberP(X2,X4)
| ~ ssItem(X4) )
& ! [X3] :
( ~ lt(Z,X3)
| ~ memberP(X1,X3)
| ~ ssItem(X3) )
& app(app(X1,W),X2) = X
& cons(Z,nil) = W
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [Z] : sP0_prd(Z,X,W) )
& ( nil != U
| nil != V )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( nil = sK49_skl
& nil = sK50_skl )
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) )
& ( nil != sK47_skl
| nil != sK48_skl )
& ! [Y] :
( ~ segmentP(sK47_skl,Y)
| ~ segmentP(sK48_skl,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Z,sK51_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,
! [X0] :
( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( nil != sK47_skl
| nil != sK48_skl ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
( nil = sK50_skl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
( nil = sK49_skl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,definition,
! [Z,X1,X3] :
( sP1_prd(X3,X1,Z)
<=> ( ~ lt(Z,X3)
| ~ memberP(X1,X3)
| ~ ssItem(X3) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f430,plain,
! [W,X,Z] :
( sP0_prd(Z,X,W)
<=> ( ? [X1] :
( ? [X2] :
( ! [X4] :
( ~ lt(X4,Z)
| ~ memberP(X2,X4)
| ~ ssItem(X4) )
& ! [X3] : sP1_prd(X3,X1,Z)
& app(app(X1,W),X2) = X
& cons(Z,nil) = W
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) ) ),
inference(formula_renaming,[status(thm)],[f416,f429]) ).
fof(f431,plain,
! [W,X,Z] :
( ( ! [X1] :
( ! [X2] :
( ? [X4] :
( lt(X4,Z)
& memberP(X2,X4)
& ssItem(X4) )
| ? [X3] : ~ sP1_prd(X3,X1,Z)
| app(app(X1,W),X2) != X
| cons(Z,nil) != W
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(Z)
| sP0_prd(Z,X,W) )
& ( ( ? [X1] :
( ? [X2] :
( ! [X4] :
( ~ lt(X4,Z)
| ~ memberP(X2,X4)
| ~ ssItem(X4) )
& ! [X3] : sP1_prd(X3,X1,Z)
& app(app(X1,W),X2) = X
& cons(Z,nil) = W
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
| ~ sP0_prd(Z,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f430]) ).
fof(f432,plain,
( ! [W,X,Z] :
( ! [X1] :
( ! [X2] :
( ? [X4] :
( lt(X4,Z)
& memberP(X2,X4)
& ssItem(X4) )
| ? [X3] : ~ sP1_prd(X3,X1,Z)
| app(app(X1,W),X2) != X
| cons(Z,nil) != W
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(Z)
| sP0_prd(Z,X,W) )
& ! [W,X,Z] :
( ( ? [X1] :
( ? [X2] :
( ! [X4] :
( ~ lt(X4,Z)
| ~ memberP(X2,X4)
| ~ ssItem(X4) )
& ! [X3] : sP1_prd(X3,X1,Z)
& app(app(X1,W),X2) = X
& cons(Z,nil) = W
& ssList(X2) )
& ssList(X1) )
& ssItem(Z) )
| ~ sP0_prd(Z,X,W) ) ),
inference(miniscoping,[status(thm)],[f431]) ).
fof(f433,plain,
( ! [W,X,Z] :
( ! [X1] :
( ! [X2] :
( ( lt(sK55_skl(X2,X1,Z,X,W),Z)
& memberP(X2,sK55_skl(X2,X1,Z,X,W))
& ssItem(sK55_skl(X2,X1,Z,X,W)) )
| ~ sP1_prd(sK54_skl(X2,X1,Z,X,W),X1,Z)
| app(app(X1,W),X2) != X
| cons(Z,nil) != W
| ~ ssList(X2) )
| ~ ssList(X1) )
| ~ ssItem(Z)
| sP0_prd(Z,X,W) )
& ! [W,X,Z] :
( ( ! [X4] :
( ~ lt(X4,Z)
| ~ memberP(sK53_skl(Z,X,W),X4)
| ~ ssItem(X4) )
& ! [X3] : sP1_prd(X3,sK52_skl(Z,X,W),Z)
& app(app(sK52_skl(Z,X,W),W),sK53_skl(Z,X,W)) = X
& cons(Z,nil) = W
& ssList(sK53_skl(Z,X,W))
& ssList(sK52_skl(Z,X,W))
& ssItem(Z) )
| ~ sP0_prd(Z,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK52_skl,sK53_skl,sK54_skl,sK55_skl]),skolemize(X1,sK52_skl(Z,X,W)),skolemize(X2,sK53_skl(Z,X,W)),skolemize(X3,sK54_skl(X2,X1,Z,X,W)),skolemize(X4,sK55_skl(X2,X1,Z,X,W))],[f432]) ).
fof(f434,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f435,plain,
! [X0,X1,X2] :
( ssList(sK52_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f436,plain,
! [X0,X1,X2] :
( ssList(sK53_skl(X0,X1,X2))
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f437,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f438,plain,
! [X0,X1,X2] :
( app(app(sK52_skl(X0,X1,X2),X2),sK53_skl(X0,X1,X2)) = X1
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f439,plain,
! [X0,X1,X2,X3] :
( sP1_prd(X3,sK52_skl(X0,X1,X2),X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f441,plain,
! [X0,X1,X2,X3,X4] :
( ssItem(sK55_skl(X4,X3,X0,X1,X2))
| ~ sP1_prd(sK54_skl(X4,X3,X0,X1,X2),X3,X0)
| app(app(X3,X2),X4) != X1
| cons(X0,nil) != X2
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f442,plain,
! [X0,X1,X2,X3,X4] :
( memberP(X4,sK55_skl(X4,X3,X0,X1,X2))
| ~ sP1_prd(sK54_skl(X4,X3,X0,X1,X2),X3,X0)
| app(app(X3,X2),X4) != X1
| cons(X0,nil) != X2
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f444,plain,
! [Z,X1,X3] :
( ( ( lt(Z,X3)
& memberP(X1,X3)
& ssItem(X3) )
| sP1_prd(X3,X1,Z) )
& ( ~ lt(Z,X3)
| ~ memberP(X1,X3)
| ~ ssItem(X3)
| ~ sP1_prd(X3,X1,Z) ) ),
inference(NNF_transformation,[status(thm)],[f429]) ).
fof(f445,plain,
( ! [Z,X1,X3] :
( ( lt(Z,X3)
& memberP(X1,X3)
& ssItem(X3) )
| sP1_prd(X3,X1,Z) )
& ! [Z,X1,X3] :
( ~ lt(Z,X3)
| ~ memberP(X1,X3)
| ~ ssItem(X3)
| ~ sP1_prd(X3,X1,Z) ) ),
inference(miniscoping,[status(thm)],[f444]) ).
fof(f447,plain,
! [X0,X1,X2] :
( ssItem(X0)
| sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f445]) ).
fof(f448,plain,
! [X0,X1,X2] :
( memberP(X1,X0)
| sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f445]) ).
fof(f450,definition,
( sQ0_spl
<=> nil = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f453,definition,
( sQ1_spl
<=> nil = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f454,plain,
( ~ sQ1_spl
| nil = sK47_skl ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f455,plain,
( sQ1_spl
| nil != sK47_skl ),
inference(component_clause,[status(thm)],[f453]) ).
fof(f456,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f450,f453]) ).
fof(f457,definition,
( sQ2_spl
<=> sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f458,plain,
( ~ sQ2_spl
| sP0_prd(sK51_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f457]) ).
fof(f460,definition,
( sQ3_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f461,plain,
( ~ sQ3_spl
| nil = sK50_skl ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f463,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f427,f457,f460]) ).
fof(f464,definition,
( sQ4_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( ~ sQ4_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f428,f457,f464]) ).
fof(f470,plain,
! [X0,X2,X3,X4,X5] :
( app(app(X3,cons(X2,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X2)
| ~ duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f199]) ).
fof(f471,plain,
! [X0,X1,X2,X3,X4] :
( app(app(X2,cons(X1,X3)),cons(X1,X4)) != X0
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ duplicatefreeP(X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f470]) ).
fof(f489,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| memberP(cons(sK4_skl(app(X0,cons(X1,X2))),nil),X1)
| ~ ssItem(X1)
| ~ ssList(cons(sK4_skl(app(X0,cons(X1,X2))),nil))
| ~ singletonP(app(X0,cons(X1,X2)))
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(resolution,[status(thm)],[f117,f112]) ).
fof(f495,plain,
( ~ segmentP(sK48_skl,sK47_skl)
| ~ neq(sK47_skl,nil)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f319,f425]) ).
fof(f497,definition,
( sQ5_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f499,plain,
( sQ5_spl
| ~ ssList(sK47_skl) ),
inference(component_clause,[status(thm)],[f497]) ).
fof(f500,definition,
( sQ6_spl
<=> neq(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f502,plain,
( sQ6_spl
| ~ neq(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f500]) ).
fof(f503,definition,
( sQ7_spl
<=> segmentP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f506,plain,
( ~ sQ7_spl
| ~ sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f495,f497,f500,f503]) ).
fof(f507,definition,
( sQ8_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f509,plain,
( sQ8_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f507]) ).
fof(f517,plain,
( sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f509,f420]) ).
fof(f518,plain,
sQ8_spl,
inference(contradiction_clause,[status(thm)],[f517]) ).
fof(f521,plain,
! [X0,X1,X2] :
( ~ ssList(sK5_skl(app(X1,X2),X0))
| ~ ssList(X1)
| segmentP(X0,X2)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ frontsegP(X0,app(X1,X2))
| ~ ssList(app(X1,X2))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f123,f137]) ).
fof(f525,plain,
! [X0,X1,X2] :
( ~ ssList(sK5_skl(app(X1,X2),X0))
| ~ ssList(X1)
| segmentP(X0,X2)
| ~ ssList(X2)
| ~ frontsegP(X0,app(X1,X2))
| ~ ssList(app(X1,X2))
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f521]) ).
fof(f526,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| segmentP(X0,X2)
| ~ ssList(X2)
| ~ frontsegP(X0,app(X1,X2))
| ~ ssList(app(X1,X2))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f525,f122]) ).
fof(f529,plain,
! [X0,X1] :
( ~ singletonP(app(X0,X1))
| ~ ssList(app(X0,X1))
| ~ ssList(X1)
| frontsegP(cons(sK4_skl(app(X0,X1)),nil),X0)
| ~ ssList(X0)
| ~ ssList(cons(sK4_skl(app(X0,X1)),nil)) ),
inference(resolution,[status(thm)],[f124,f117]) ).
fof(f537,definition,
( sQ11_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f539,plain,
( sQ11_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f548,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f539,f223]) ).
fof(f549,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f548]) ).
fof(f558,plain,
! [X0,X1] :
( ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| sK4_skl(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f227,f117]) ).
fof(f560,plain,
! [X0,X1] :
( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f227]) ).
fof(f561,definition,
! [X0,X1] :
( sQ16_spl
<=> ( ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| sK4_skl(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f564,plain,
( sQ16_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f558,f537,f561]) ).
fof(f566,definition,
! [X0] :
( sQ17_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f567,plain,
! [X0] :
( ~ sQ17_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f566]) ).
fof(f569,definition,
! [X1] :
( sQ18_spl
<=> ( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f572,plain,
( sQ18_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f560,f566,f569]) ).
fof(f574,plain,
! [X0] :
( ~ sQ17_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f567]) ).
fof(f576,plain,
( ~ sQ17_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f223,f574]) ).
fof(f579,plain,
~ sQ17_spl,
inference(contradiction_clause,[status(thm)],[f576]) ).
fof(f587,plain,
! [X0,X1] :
( X0 = X0
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f228]) ).
fof(f588,definition,
! [X0] :
( sQ19_spl
<=> ( X0 = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f591,definition,
! [X1] :
( sQ20_spl
<=> ( ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f592,plain,
! [X0] :
( ~ sQ20_spl
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f591]) ).
fof(f594,plain,
( sQ20_spl
| sQ19_spl ),
inference(split_clause,[status(thm)],[f587,f588,f591]) ).
fof(f595,plain,
! [X0] :
( ~ sQ20_spl
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f592]) ).
fof(f597,plain,
( ~ sQ20_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f104,f595]) ).
fof(f599,plain,
~ sQ20_spl,
inference(contradiction_clause,[status(thm)],[f597]) ).
fof(f615,plain,
! [X0] :
( ~ ssList(nil)
| rearsegP(X0,X0)
| ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f249,f130]) ).
fof(f618,definition,
! [X0] :
( sQ21_spl
<=> ( rearsegP(X0,X0)
| ~ ssList(X0)
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f621,plain,
( ~ sQ11_spl
| sQ21_spl ),
inference(split_clause,[status(thm)],[f615,f618,f537]) ).
fof(f667,definition,
( sQ22_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f669,plain,
( sQ22_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f667]) ).
fof(f703,plain,
( ~ sQ4_spl
| sK47_skl = nil ),
inference(backward_demodulation,[status(thm)],[f465,f424]) ).
fof(f704,plain,
( ~ sQ4_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f703,f455]) ).
fof(f705,plain,
( ~ sQ4_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f704]) ).
fof(f706,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP0_prd(X0,X3,X4)
| memberP(X5,sK55_skl(X5,sK52_skl(X0,X3,X4),X0,X1,X2))
| app(app(sK52_skl(X0,X3,X4),X2),X5) != X1
| cons(X0,nil) != X2
| ~ ssList(X5)
| ~ ssList(sK52_skl(X0,X3,X4))
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f442,f439]) ).
fof(f707,plain,
! [X0,X1,X2,X3,X4] :
( ssItem(sK54_skl(X4,X3,X0,X1,X2))
| memberP(X4,sK55_skl(X4,X3,X0,X1,X2))
| app(app(X3,X2),X4) != X1
| cons(X0,nil) != X2
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f442,f447]) ).
fof(f708,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP0_prd(X0,X3,X4)
| memberP(X5,sK55_skl(X5,sK52_skl(X0,X3,X4),X0,X1,X2))
| app(app(sK52_skl(X0,X3,X4),X2),X5) != X1
| cons(X0,nil) != X2
| ~ ssList(X5)
| ~ ssList(sK52_skl(X0,X3,X4))
| sP0_prd(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f706,f434]) ).
fof(f711,plain,
! [X0,X1] :
( ~ ssList(X1)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f315,f323]) ).
fof(f712,plain,
! [X0,X1,X2,X3] :
( ~ segmentP(X3,X2)
| ~ segmentP(X1,X3)
| ~ ssList(X2)
| ~ ssList(X3)
| ~ ssList(X1)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f315,f315]) ).
fof(f716,definition,
! [X0] :
( sQ30_spl
<=> ( segmentP(X0,nil)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f720,definition,
! [X0,X1] :
( sQ31_spl
<=> ( ~ ssList(X1)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f723,plain,
( ~ sQ11_spl
| sQ31_spl ),
inference(split_clause,[status(thm)],[f711,f720,f537]) ).
fof(f724,plain,
! [X0,X1,X2,X3] :
( ~ segmentP(X3,X2)
| ~ segmentP(X1,X3)
| ~ ssList(X3)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f712]) ).
fof(f730,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f499,f419]) ).
fof(f731,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f730]) ).
fof(f769,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f317,f323]) ).
fof(f770,plain,
! [X0,X1,X2] :
( ~ segmentP(X2,X0)
| ~ segmentP(X1,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f317,f315]) ).
fof(f776,definition,
! [X0] :
( sQ35_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f777,plain,
! [X0] :
( ~ sQ35_spl
| ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f776]) ).
fof(f779,plain,
( sQ35_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f769,f537,f776]) ).
fof(f780,plain,
! [X0,X1,X2] :
( ~ segmentP(X2,X0)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f770]) ).
fof(f781,plain,
! [X0] :
( ~ sQ35_spl
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f777]) ).
fof(f782,plain,
( ~ sQ2_spl
| sP0_prd(sK51_skl,sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f458]) ).
fof(f783,plain,
! [X0,X1,X2,X3] :
( X1 = app(app(X2,X0),X3)
| ~ segmentP(X1,app(app(X2,X0),X3))
| ~ ssList(app(app(X2,X0),X3))
| ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f321,f317]) ).
fof(f784,plain,
! [X0,X1,X2,X3,X4] :
( segmentP(X4,X1)
| ~ segmentP(X4,app(app(X2,X0),X3))
| ~ ssList(X1)
| ~ ssList(app(app(X2,X0),X3))
| ~ ssList(X4)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f321,f315]) ).
fof(f785,plain,
! [X0,X1,X2,X3] :
( X1 = app(app(X2,X0),X3)
| ~ segmentP(X1,app(app(X2,X0),X3))
| ~ ssList(app(app(X2,X0),X3))
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f783]) ).
fof(f786,plain,
! [X0,X1,X2,X3,X4] :
( segmentP(X4,X1)
| ~ segmentP(X4,app(app(X2,X0),X3))
| ~ ssList(app(app(X2,X0),X3))
| ~ ssList(X4)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f784]) ).
fof(f811,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f326,f323]) ).
fof(f812,plain,
! [X0,X1] :
( ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f326,f315]) ).
fof(f814,definition,
( sQ37_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f817,plain,
( sQ37_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f811,f537,f814]) ).
fof(f818,definition,
! [X0,X1] :
( sQ38_spl
<=> ( ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f819,plain,
! [X0,X1] :
( ~ sQ38_spl
| ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f818]) ).
fof(f821,plain,
( ~ sQ11_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f812,f818,f537]) ).
fof(f823,plain,
! [X0,X1] :
( ~ sQ38_spl
| ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f819]) ).
fof(f825,plain,
! [X0] :
( X0 = nil
| ~ segmentP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f327,f317]) ).
fof(f826,plain,
! [X0,X1] :
( segmentP(X1,X0)
| ~ segmentP(X1,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f327,f315]) ).
fof(f827,definition,
! [X0] :
( sQ39_spl
<=> ( X0 = nil
| ~ segmentP(X0,nil)
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f830,plain,
( ~ sQ11_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f825,f827,f537]) ).
fof(f831,definition,
! [X0,X1] :
( sQ40_spl
<=> ( segmentP(X1,X0)
| ~ segmentP(X1,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f832,plain,
! [X0,X1] :
( ~ sQ40_spl
| segmentP(X1,X0)
| ~ segmentP(X1,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f831]) ).
fof(f834,plain,
( ~ sQ11_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f826,f831,f537]) ).
fof(f835,plain,
! [X0,X1] :
( ~ sQ40_spl
| segmentP(X1,X0)
| ~ segmentP(X1,nil)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f832]) ).
fof(f836,plain,
! [X0,X1] :
( ~ sQ40_spl
| segmentP(X1,X0)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f835,f323]) ).
fof(f840,plain,
! [X0,X1,X2,X3,X4] :
( memberP(X1,sK55_skl(X1,X0,X2,X3,X4))
| app(app(X0,X4),X1) != X3
| cons(X2,nil) != X4
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| sP0_prd(X2,X3,X4)
| memberP(X0,sK54_skl(X1,X0,X2,X3,X4)) ),
inference(resolution,[status(thm)],[f448,f442]) ).
fof(f841,plain,
! [X0,X1,X2,X3,X4] :
( ssItem(sK55_skl(X1,X0,X2,X3,X4))
| app(app(X0,X4),X1) != X3
| cons(X2,nil) != X4
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(X2)
| sP0_prd(X2,X3,X4)
| memberP(X0,sK54_skl(X1,X0,X2,X3,X4)) ),
inference(resolution,[status(thm)],[f448,f441]) ).
fof(f854,plain,
! [X0] :
( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(app(nil,X0))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f378,f249]) ).
fof(f857,definition,
! [X0] :
( sQ42_spl
<=> ( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f860,plain,
( ~ sQ11_spl
| sQ42_spl ),
inference(split_clause,[status(thm)],[f854,f857,f537]) ).
fof(f938,definition,
( sQ43_spl
<=> neq(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f941,definition,
( sQ44_spl
<=> segmentP(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f942,plain,
( ~ sQ44_spl
| segmentP(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f941]) ).
fof(f943,plain,
( sQ44_spl
| ~ segmentP(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f941]) ).
fof(f950,definition,
( sQ46_spl
<=> segmentP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f951,plain,
( ~ sQ46_spl
| segmentP(nil,nil) ),
inference(component_clause,[status(thm)],[f950]) ).
fof(f952,plain,
( sQ46_spl
| ~ segmentP(nil,nil) ),
inference(component_clause,[status(thm)],[f950]) ).
fof(f965,plain,
! [X0] :
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = sK8_skl(X0,nil)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0)) ),
inference(resolution,[status(thm)],[f385,f136]) ).
fof(f966,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ),
inference(resolution,[status(thm)],[f385,f129]) ).
fof(f977,definition,
( sQ51_spl
<=> strictorderP(nil) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f979,plain,
( sQ51_spl
| ~ strictorderP(nil) ),
inference(component_clause,[status(thm)],[f977]) ).
fof(f990,definition,
( sQ55_spl
<=> totalorderP(nil) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f992,plain,
( sQ55_spl
| ~ totalorderP(nil) ),
inference(component_clause,[status(thm)],[f990]) ).
fof(f1003,definition,
( sQ59_spl
<=> cyclefreeP(nil) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1005,plain,
( sQ59_spl
| ~ cyclefreeP(nil) ),
inference(component_clause,[status(thm)],[f1003]) ).
fof(f1008,definition,
! [X0] :
( sQ60_spl
<=> ( ~ segmentP(nil,X0)
| ~ ssList(X0)
| nil = sK8_skl(X0,nil)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1011,plain,
( ~ sQ11_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f965,f1008,f537]) ).
fof(f1012,definition,
! [X0] :
( sQ61_spl
<=> ( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| nil = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1015,plain,
( ~ sQ11_spl
| sQ61_spl ),
inference(split_clause,[status(thm)],[f966,f1012,f537]) ).
fof(f1022,plain,
! [X0] :
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = app(sK7_skl(X0,nil),X0)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0)) ),
inference(resolution,[status(thm)],[f386,f136]) ).
fof(f1023,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ),
inference(resolution,[status(thm)],[f386,f129]) ).
fof(f1038,definition,
! [X0] :
( sQ65_spl
<=> ( ~ segmentP(nil,X0)
| ~ ssList(X0)
| nil = app(sK7_skl(X0,nil),X0)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1041,plain,
( ~ sQ11_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f1022,f1038,f537]) ).
fof(f1042,definition,
! [X0] :
( sQ66_spl
<=> ( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1045,plain,
( ~ sQ11_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f1023,f1042,f537]) ).
fof(f1058,plain,
! [X0,X1,X2,X3,X4] :
( leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ totalorderedP(nil)
| ~ ssList(nil)
| nil != app(X0,cons(X1,X2))
| nil != cons(X3,X4)
| ~ ssList(cons(X3,X4))
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(resolution,[status(thm)],[f387,f177]) ).
fof(f1059,plain,
! [X0,X1,X2,X3,X4] :
( lt(X3,X1)
| lt(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ strictorderP(nil)
| ~ ssList(nil)
| nil != app(X0,cons(X1,X2))
| nil != cons(X3,X4)
| ~ ssList(cons(X3,X4))
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(resolution,[status(thm)],[f387,f165]) ).
fof(f1060,plain,
! [X0,X1,X2,X3,X4] :
( leq(X3,X1)
| leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ totalorderP(nil)
| ~ ssList(nil)
| nil != app(X0,cons(X1,X2))
| nil != cons(X3,X4)
| ~ ssList(cons(X3,X4))
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(resolution,[status(thm)],[f387,f153]) ).
fof(f1061,plain,
! [X0,X1,X2,X3,X4] :
( ~ leq(X3,X1)
| ~ leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ cyclefreeP(nil)
| ~ ssList(nil)
| nil != app(X0,cons(X1,X2))
| nil != cons(X3,X4)
| ~ ssList(cons(X3,X4))
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(resolution,[status(thm)],[f387,f141]) ).
fof(f1062,plain,
! [X0,X1] :
( ~ ssList(X0)
| rearsegP(nil,X1)
| ~ ssList(X1)
| ~ ssList(nil)
| nil != X0
| nil != X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f387,f130]) ).
fof(f1063,definition,
! [X0] :
( sQ68_spl
<=> ( nil = X0
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1066,definition,
! [X1] :
( sQ69_spl
<=> ( ~ ssList(X1)
| nil != X1
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1067,plain,
! [X0] :
( ~ sQ69_spl
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1066]) ).
fof(f1071,definition,
! [X0,X1,X2,X3,X4] :
( sQ70_spl
<=> ( leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| nil != app(X0,cons(X1,X2))
| nil != cons(X3,X4)
| ~ ssList(cons(X3,X4))
| ~ ssList(app(X0,cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1074,definition,
( sQ71_spl
<=> totalorderedP(nil) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1076,plain,
( sQ71_spl
| ~ totalorderedP(nil) ),
inference(component_clause,[status(thm)],[f1074]) ).
fof(f1077,plain,
( ~ sQ71_spl
| ~ sQ11_spl
| sQ70_spl ),
inference(split_clause,[status(thm)],[f1058,f1071,f537,f1074]) ).
fof(f1078,definition,
! [X0,X1,X2,X3,X4] :
( sQ72_spl
<=> ( lt(X3,X1)
| lt(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| nil != app(X0,cons(X1,X2))
| nil != cons(X3,X4)
| ~ ssList(cons(X3,X4))
| ~ ssList(app(X0,cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1081,plain,
( ~ sQ51_spl
| ~ sQ11_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f1059,f1078,f537,f977]) ).
fof(f1082,definition,
! [X0,X1,X2,X3,X4] :
( sQ73_spl
<=> ( leq(X3,X1)
| leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| nil != app(X0,cons(X1,X2))
| nil != cons(X3,X4)
| ~ ssList(cons(X3,X4))
| ~ ssList(app(X0,cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1085,plain,
( ~ sQ55_spl
| ~ sQ11_spl
| sQ73_spl ),
inference(split_clause,[status(thm)],[f1060,f1082,f537,f990]) ).
fof(f1086,definition,
! [X0,X1,X2,X3,X4] :
( sQ74_spl
<=> ( ~ leq(X3,X1)
| ~ leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| nil != app(X0,cons(X1,X2))
| nil != cons(X3,X4)
| ~ ssList(cons(X3,X4))
| ~ ssList(app(X0,cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1089,plain,
( ~ sQ59_spl
| ~ sQ11_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f1061,f1086,f537,f1003]) ).
fof(f1090,definition,
! [X1] :
( sQ75_spl
<=> ( rearsegP(nil,X1)
| ~ ssList(X1)
| nil != X1
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1091,plain,
! [X0] :
( ~ sQ75_spl
| rearsegP(nil,X0)
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1090]) ).
fof(f1093,plain,
( ~ sQ11_spl
| sQ75_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f1062,f1066,f1090,f537]) ).
fof(f1094,plain,
! [X0] :
( ~ sQ69_spl
| nil != X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1067]) ).
fof(f1095,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(app(X0,nil))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(X0,nil)) ),
inference(resolution,[status(thm)],[f389,f376]) ).
fof(f1096,plain,
! [X0] :
( ~ ssList(X0)
| rearsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f389,f130]) ).
fof(f1105,definition,
! [X0] :
( sQ76_spl
<=> ( app(X0,nil) = X0
| ~ ssList(app(X0,nil))
| ~ ssList(X0)
| ~ ssList(app(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1108,plain,
( ~ sQ11_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f1095,f1105,f537]) ).
fof(f1109,definition,
! [X0] :
( sQ77_spl
<=> ( ~ ssList(X0)
| rearsegP(X0,nil)
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1112,plain,
( ~ sQ11_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f1096,f1109,f537]) ).
fof(f1158,plain,
! [X0,X1,X2,X3,X4] :
( nil != app(X2,cons(X0,X3))
| nil != cons(X1,X4)
| ~ ssList(cons(X1,X4))
| ~ ssList(app(X2,cons(X0,X3)))
| lt(X0,X1)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ strictorderedP(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f188,f387]) ).
fof(f1178,definition,
( sQ82_spl
<=> strictorderedP(nil) ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1180,plain,
( sQ82_spl
| ~ strictorderedP(nil) ),
inference(component_clause,[status(thm)],[f1178]) ).
fof(f1181,definition,
! [X0,X1,X2,X3,X4] :
( sQ83_spl
<=> ( nil != app(X2,cons(X0,X3))
| nil != cons(X1,X4)
| ~ ssList(cons(X1,X4))
| ~ ssList(app(X2,cons(X0,X3)))
| lt(X0,X1)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1184,plain,
( sQ83_spl
| ~ sQ82_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1158,f537,f1178,f1181]) ).
fof(f1185,plain,
( sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1180,f349]) ).
fof(f1186,plain,
sQ82_spl,
inference(contradiction_clause,[status(thm)],[f1185]) ).
fof(f1222,plain,
( ~ sQ69_spl
| nil != nil ),
inference(resolution,[status(thm)],[f1094,f223]) ).
fof(f1225,plain,
( ~ sQ69_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f1222]) ).
fof(f1226,plain,
~ sQ69_spl,
inference(contradiction_clause,[status(thm)],[f1225]) ).
fof(f1227,plain,
! [X0] :
( ~ sQ75_spl
| rearsegP(nil,X0)
| nil != X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1091]) ).
fof(f1306,plain,
( sQ6_spl
| sK47_skl = nil
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f220,f502]) ).
fof(f1310,plain,
( sQ6_spl
| sQ1_spl
| ~ sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1306,f497,f537,f453,f500]) ).
fof(f1355,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X2,X0,X1)
| ~ ssList(sK53_skl(X2,X0,X1))
| ~ ssList(sK52_skl(X2,X0,X1))
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f137,f438]) ).
fof(f1358,plain,
! [X0,X1] :
( ~ ssList(app(X0,X1))
| ~ ssList(nil)
| ~ ssList(X0)
| segmentP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(resolution,[status(thm)],[f137,f389]) ).
fof(f1381,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X2,X0,X1)
| ~ ssList(sK53_skl(X2,X0,X1))
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1355,f435]) ).
fof(f1383,definition,
! [X0,X1] :
( sQ94_spl
<=> ( ~ ssList(app(X0,X1))
| ~ ssList(X0)
| segmentP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1386,plain,
( ~ sQ11_spl
| sQ94_spl ),
inference(split_clause,[status(thm)],[f1358,f1383,f537]) ).
fof(f1390,plain,
! [X0,X1] :
( ~ ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssList(nil)
| memberP(cons(X0,X1),X0)
| ~ ssItem(X0)
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f112,f249]) ).
fof(f1412,definition,
! [X0,X1] :
( sQ95_spl
<=> ( ~ ssList(cons(X0,X1))
| ~ ssList(X1)
| memberP(cons(X0,X1),X0)
| ~ ssItem(X0)
| ~ ssList(cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1415,plain,
( ~ sQ11_spl
| sQ95_spl ),
inference(split_clause,[status(thm)],[f1390,f1412,f537]) ).
fof(f1544,plain,
! [X0,X1,X2,X3] :
( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ duplicatefreeP(nil)
| ~ ssList(nil)
| nil != app(X0,cons(X1,X2))
| nil != cons(X1,X3)
| ~ ssList(cons(X1,X3))
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(resolution,[status(thm)],[f387,f471]) ).
fof(f1551,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| memberP(nil,X1)
| ~ ssItem(X1)
| ~ ssList(nil)
| nil != X0
| nil != cons(X1,X2)
| ~ ssList(cons(X1,X2))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f387,f112]) ).
fof(f1553,definition,
! [X0,X1,X2,X3] :
( sQ108_spl
<=> ( ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| nil != app(X0,cons(X1,X2))
| nil != cons(X1,X3)
| ~ ssList(cons(X1,X3))
| ~ ssList(app(X0,cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1556,definition,
( sQ109_spl
<=> duplicatefreeP(nil) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1558,plain,
( sQ109_spl
| ~ duplicatefreeP(nil) ),
inference(component_clause,[status(thm)],[f1556]) ).
fof(f1559,plain,
( ~ sQ109_spl
| ~ sQ11_spl
| sQ108_spl ),
inference(split_clause,[status(thm)],[f1544,f1553,f537,f1556]) ).
fof(f1565,definition,
! [X0,X1] :
( sQ110_spl
<=> ( ~ ssList(X0)
| segmentP(nil,X1)
| ~ ssList(X1)
| nil != app(X0,X1)
| ~ ssList(app(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1566,plain,
! [X0,X1] :
( ~ sQ110_spl
| ~ ssList(X0)
| segmentP(nil,X1)
| ~ ssList(X1)
| nil != app(X0,X1)
| ~ ssList(app(X0,X1)) ),
inference(component_clause,[status(thm)],[f1565]) ).
fof(f1569,definition,
! [X1,X2] :
( sQ111_spl
<=> ( ~ ssList(X2)
| memberP(nil,X1)
| ~ ssItem(X1)
| nil != cons(X1,X2)
| ~ ssList(cons(X1,X2)) ) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1572,plain,
( ~ sQ11_spl
| sQ111_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f1551,f1066,f1569,f537]) ).
fof(f1574,plain,
! [X0,X1] :
( ~ sQ110_spl
| ~ ssList(X0)
| segmentP(nil,X1)
| ~ ssList(X1)
| nil != app(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f1566,f245]) ).
fof(f1661,plain,
( sQ46_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f952,f323]) ).
fof(f1665,plain,
( sQ46_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1661,f537,f950]) ).
fof(f1702,plain,
! [X0,X1] :
( ~ segmentP(X1,X0)
| ~ segmentP(sK48_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sK48_skl)
| ~ segmentP(sK47_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f425,f315]) ).
fof(f1704,plain,
( ~ ssList(sK47_skl)
| ~ segmentP(sK48_skl,nil)
| ~ neq(nil,nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f425,f323]) ).
fof(f1705,plain,
! [X0,X1] :
( ~ segmentP(X1,X0)
| ~ segmentP(sK47_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sK47_skl)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f425,f315]) ).
fof(f1708,definition,
! [X0,X1] :
( sQ123_spl
<=> ( ~ segmentP(X1,X0)
| ~ segmentP(sK48_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sK47_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1711,plain,
( ~ sQ8_spl
| sQ123_spl ),
inference(split_clause,[status(thm)],[f1702,f1708,f507]) ).
fof(f1713,definition,
( sQ124_spl
<=> segmentP(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1714,plain,
( ~ sQ124_spl
| segmentP(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f1713]) ).
fof(f1715,plain,
( sQ124_spl
| ~ segmentP(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f1713]) ).
fof(f1716,plain,
( ~ sQ5_spl
| ~ sQ124_spl
| ~ sQ43_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1704,f537,f938,f1713,f497]) ).
fof(f1717,definition,
! [X0,X1] :
( sQ125_spl
<=> ( ~ segmentP(X1,X0)
| ~ segmentP(sK47_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1720,plain,
( ~ sQ5_spl
| sQ125_spl ),
inference(split_clause,[status(thm)],[f1705,f1717,f497]) ).
fof(f1727,plain,
! [X0,X1,X2] :
( ~ ssList(cons(X0,cons(X1,X2)))
| X0 = X1
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ equalelemsP(cons(X0,cons(X1,X2)))
| ~ ssList(cons(X0,cons(X1,X2))) ),
inference(resolution,[status(thm)],[f210,f249]) ).
fof(f1730,plain,
! [X0,X1,X2,X3] :
( nil != X2
| nil != cons(X0,cons(X1,X3))
| ~ ssList(cons(X0,cons(X1,X3)))
| ~ ssList(X2)
| X0 = X1
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ equalelemsP(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f210,f387]) ).
fof(f1745,definition,
! [X0,X1,X2] :
( sQ126_spl
<=> ( ~ ssList(cons(X0,cons(X1,X2)))
| X0 = X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ equalelemsP(cons(X0,cons(X1,X2)))
| ~ ssList(cons(X0,cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1748,plain,
( ~ sQ11_spl
| sQ126_spl ),
inference(split_clause,[status(thm)],[f1727,f1745,f537]) ).
fof(f1752,definition,
( sQ127_spl
<=> equalelemsP(nil) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f1754,plain,
( sQ127_spl
| ~ equalelemsP(nil) ),
inference(component_clause,[status(thm)],[f1752]) ).
fof(f1755,definition,
! [X0,X1,X3] :
( sQ128_spl
<=> ( nil != cons(X0,cons(X1,X3))
| ~ ssList(cons(X0,cons(X1,X3)))
| X0 = X1
| ~ ssList(X3)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1758,plain,
( sQ69_spl
| sQ128_spl
| ~ sQ127_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1730,f537,f1752,f1755,f1066]) ).
fof(f1762,plain,
( sQ127_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1754,f362]) ).
fof(f1763,plain,
sQ127_spl,
inference(contradiction_clause,[status(thm)],[f1762]) ).
fof(f1764,plain,
( ~ sQ2_spl
| sP0_prd(sK51_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f782]) ).
fof(f1793,plain,
( ~ sQ2_spl
| ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1764,f434]) ).
fof(f1794,plain,
( ~ sQ2_spl
| cons(sK51_skl,nil) = sK47_skl ),
inference(resolution,[status(thm)],[f1764,f437]) ).
fof(f1853,definition,
! [X0] :
( sQ136_spl
<=> ( segmentP(X0,nil)
| ~ segmentP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1857,plain,
( sQ44_spl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f943,f323]) ).
fof(f1859,plain,
( sQ44_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1857,f497,f941]) ).
fof(f1864,plain,
( sQ124_spl
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1715,f323]) ).
fof(f1866,plain,
( sQ124_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f1864,f507,f1713]) ).
fof(f1933,plain,
! [X0] :
( ~ sQ44_spl
| segmentP(X0,nil)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(nil)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f942,f315]) ).
fof(f1936,plain,
( ~ sQ44_spl
| ~ sQ11_spl
| ~ sQ5_spl
| sQ30_spl ),
inference(split_clause,[status(thm)],[f1933,f716,f497,f537,f941]) ).
fof(f1970,plain,
! [X0] :
( ~ sQ124_spl
| segmentP(X0,nil)
| ~ segmentP(X0,sK48_skl)
| ~ ssList(nil)
| ~ ssList(sK48_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1714,f315]) ).
fof(f1973,definition,
! [X0] :
( sQ143_spl
<=> ( segmentP(X0,nil)
| ~ segmentP(X0,sK48_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1976,plain,
( ~ sQ124_spl
| ~ sQ11_spl
| ~ sQ8_spl
| sQ143_spl ),
inference(split_clause,[status(thm)],[f1970,f1973,f507,f537,f1713]) ).
fof(f2003,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| cons(sK51_skl,nil) = nil ),
inference(forward_demodulation,[status(thm)],[f454,f1794]) ).
fof(f2004,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2003,f225]) ).
fof(f2052,plain,
( ~ sQ2_spl
| ~ sQ1_spl
| ~ sQ22_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2004,f537,f667,f453,f457]) ).
fof(f2202,plain,
( sQ22_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f669,f1793]) ).
fof(f2203,plain,
( sQ22_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f2202]) ).
fof(f2204,plain,
( sQ71_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1076,f339]) ).
fof(f2205,plain,
sQ71_spl,
inference(contradiction_clause,[status(thm)],[f2204]) ).
fof(f2206,plain,
( sQ51_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f979,f336]) ).
fof(f2207,plain,
sQ51_spl,
inference(contradiction_clause,[status(thm)],[f2206]) ).
fof(f2208,plain,
( sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f992,f333]) ).
fof(f2209,plain,
sQ55_spl,
inference(contradiction_clause,[status(thm)],[f2208]) ).
fof(f2210,plain,
( sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1005,f330]) ).
fof(f2211,plain,
sQ59_spl,
inference(contradiction_clause,[status(thm)],[f2210]) ).
fof(f2212,plain,
( sQ109_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1558,f359]) ).
fof(f2213,plain,
sQ109_spl,
inference(contradiction_clause,[status(thm)],[f2212]) ).
fof(f2216,plain,
( ~ sQ3_spl
| sK48_skl = nil ),
inference(backward_demodulation,[status(thm)],[f461,f423]) ).
fof(f2217,plain,
( ~ sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f2216,f450,f460]) ).
fof(f2255,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f295]) ).
fof(f2259,definition,
! [X0,X1] :
( sQ178_spl
<=> ( ~ ssList(X1)
| frontsegP(X0,nil)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f2262,plain,
( ~ sQ11_spl
| sQ178_spl ),
inference(split_clause,[status(thm)],[f2255,f2259,f537]) ).
fof(f2278,plain,
! [X0,X1,X2] :
( memberP(nil,X1)
| X1 = sK4_skl(app(X0,cons(X1,X2)))
| ~ ssList(nil)
| ~ ssItem(sK4_skl(app(X0,cons(X1,X2))))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(cons(sK4_skl(app(X0,cons(X1,X2))),nil))
| ~ singletonP(app(X0,cons(X1,X2)))
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(resolution,[status(thm)],[f489,f275]) ).
fof(f2279,definition,
! [X0,X1,X2] :
( sQ179_spl
<=> ( memberP(nil,X1)
| X1 = sK4_skl(app(X0,cons(X1,X2)))
| ~ ssItem(sK4_skl(app(X0,cons(X1,X2))))
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssList(cons(sK4_skl(app(X0,cons(X1,X2))),nil))
| ~ singletonP(app(X0,cons(X1,X2)))
| ~ ssList(app(X0,cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f2282,plain,
( ~ sQ11_spl
| sQ179_spl ),
inference(split_clause,[status(thm)],[f2278,f2279,f537]) ).
fof(f2285,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| segmentP(X0,X2)
| ~ ssList(X2)
| ~ frontsegP(X0,app(X1,X2))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f526,f245]) ).
fof(f2296,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f284,f295]) ).
fof(f2299,definition,
! [X0] :
( sQ180_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f2302,plain,
( sQ180_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2296,f537,f2299]) ).
fof(f2556,plain,
! [X0,X1] :
( ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f298,f282]) ).
fof(f2559,definition,
! [X0,X1] :
( sQ202_spl
<=> ( ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f2562,plain,
( ~ sQ11_spl
| sQ202_spl ),
inference(split_clause,[status(thm)],[f2556,f2559,f537]) ).
fof(f2609,plain,
! [X0,X1] :
( ~ ssList(X0)
| segmentP(nil,X1)
| ~ ssList(X1)
| ~ ssList(nil)
| nil != app(X0,X1)
| ~ ssList(app(X0,X1)) ),
inference(resolution,[status(thm)],[f299,f2285]) ).
fof(f2610,plain,
! [X0] :
( X0 = nil
| ~ frontsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f299,f284]) ).
fof(f2611,plain,
! [X0,X1] :
( frontsegP(X1,X0)
| ~ frontsegP(X1,nil)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f299,f282]) ).
fof(f2612,plain,
( ~ sQ11_spl
| sQ110_spl ),
inference(split_clause,[status(thm)],[f2609,f1565,f537]) ).
fof(f2613,definition,
! [X0] :
( sQ203_spl
<=> ( X0 = nil
| ~ frontsegP(X0,nil)
| ~ ssList(X0)
| nil != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f2616,plain,
( ~ sQ11_spl
| sQ203_spl ),
inference(split_clause,[status(thm)],[f2610,f2613,f537]) ).
fof(f2617,definition,
! [X0,X1] :
( sQ204_spl
<=> ( frontsegP(X1,X0)
| ~ frontsegP(X1,nil)
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f2620,plain,
( ~ sQ11_spl
| sQ204_spl ),
inference(split_clause,[status(thm)],[f2611,f2617,f537]) ).
fof(f2624,plain,
! [X0,X1] :
( ~ sQ75_spl
| nil != X1
| ~ ssList(X1)
| rearsegP(X0,X1)
| ~ rearsegP(X0,nil)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f1227]) ).
fof(f2625,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f309]) ).
fof(f2630,definition,
! [X0,X1] :
( sQ205_spl
<=> ( nil != X1
| ~ ssList(X1)
| rearsegP(X0,X1)
| ~ rearsegP(X0,nil)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f2633,plain,
( ~ sQ75_spl
| ~ sQ11_spl
| sQ205_spl ),
inference(split_clause,[status(thm)],[f2624,f2630,f537,f1090]) ).
fof(f2634,definition,
! [X0,X1] :
( sQ206_spl
<=> ( ~ ssList(X1)
| rearsegP(X0,nil)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f2637,plain,
( ~ sQ11_spl
| sQ206_spl ),
inference(split_clause,[status(thm)],[f2625,f2634,f537]) ).
fof(f2644,plain,
! [X0] :
( ~ sQ75_spl
| nil != X0
| ~ ssList(X0)
| X0 = nil
| ~ rearsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f303,f1227]) ).
fof(f2645,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f303,f309]) ).
fof(f2649,definition,
! [X0] :
( sQ207_spl
<=> ( nil != X0
| ~ ssList(X0)
| X0 = nil
| ~ rearsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f2652,plain,
( ~ sQ75_spl
| ~ sQ11_spl
| sQ207_spl ),
inference(split_clause,[status(thm)],[f2644,f2649,f537,f1090]) ).
fof(f2653,definition,
! [X0] :
( sQ208_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f2656,plain,
( sQ208_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2645,f537,f2653]) ).
fof(f2674,plain,
! [X0,X1] :
( ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f312,f301]) ).
fof(f2677,definition,
! [X0,X1] :
( sQ209_spl
<=> ( ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f2680,plain,
( ~ sQ11_spl
| sQ209_spl ),
inference(split_clause,[status(thm)],[f2674,f2677,f537]) ).
fof(f2711,plain,
! [X0,X1] :
( totalorderedP(X1)
| nil = X1
| ~ ssList(X1)
| ~ ssItem(X0)
| nil != X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f345,f343]) ).
fof(f2713,definition,
! [X1] :
( sQ211_spl
<=> ( totalorderedP(X1)
| nil = X1
| ~ ssList(X1)
| nil != X1
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f2716,plain,
( sQ211_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f2711,f591,f2713]) ).
fof(f2859,plain,
! [X0,X1] :
( strictorderedP(X1)
| nil = X1
| ~ ssList(X1)
| ~ ssItem(X0)
| nil != X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f355,f353]) ).
fof(f2861,definition,
! [X1] :
( sQ220_spl
<=> ( strictorderedP(X1)
| nil = X1
| ~ ssList(X1)
| nil != X1
| ~ ssList(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f2864,plain,
( sQ220_spl
| sQ20_spl ),
inference(split_clause,[status(thm)],[f2859,f591,f2861]) ).
fof(f2923,plain,
! [X0,X1] :
( ~ sQ40_spl
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f836,f317]) ).
fof(f2940,plain,
! [X0,X1] :
( ~ sQ40_spl
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2923]) ).
fof(f3029,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ sP0_prd(X0,X4,X5)
| memberP(X3,sK55_skl(X3,sK52_skl(X0,X4,X5),X0,X1,X2))
| app(app(sK52_skl(X0,X4,X5),X2),X3) != X1
| cons(X0,nil) != X2
| ~ ssList(X3)
| sP0_prd(X0,X1,X2) ),
inference(forward_subsumption_resolution,[status(thm)],[f708,f435]) ).
fof(f3033,plain,
! [X0,X1,X2,X3,X4] :
( ~ ssItem(sK55_skl(nil,sK52_skl(X0,X3,X4),X0,X1,X2))
| ~ sP0_prd(X0,X3,X4)
| app(app(sK52_skl(X0,X3,X4),X2),nil) != X1
| cons(X0,nil) != X2
| ~ ssList(nil)
| sP0_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f3029,f279]) ).
fof(f3040,definition,
! [X0,X1,X2,X3,X4] :
( sQ238_spl
<=> ( ~ ssItem(sK55_skl(nil,sK52_skl(X0,X3,X4),X0,X1,X2))
| ~ sP0_prd(X0,X3,X4)
| app(app(sK52_skl(X0,X3,X4),X2),nil) != X1
| cons(X0,nil) != X2
| sP0_prd(X0,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f3043,plain,
( ~ sQ11_spl
| sQ238_spl ),
inference(split_clause,[status(thm)],[f3033,f3040,f537]) ).
fof(f3100,plain,
! [X0,X1,X2,X3] :
( ~ ssItem(sK55_skl(nil,X3,X0,X1,X2))
| ssItem(sK54_skl(nil,X3,X0,X1,X2))
| app(app(X3,X2),nil) != X1
| cons(X0,nil) != X2
| ~ ssList(nil)
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f707,f279]) ).
fof(f3108,definition,
! [X0,X1,X2,X3] :
( sQ243_spl
<=> ( ~ ssItem(sK55_skl(nil,X3,X0,X1,X2))
| ssItem(sK54_skl(nil,X3,X0,X1,X2))
| app(app(X3,X2),nil) != X1
| cons(X0,nil) != X2
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f3111,plain,
( ~ sQ11_spl
| sQ243_spl ),
inference(split_clause,[status(thm)],[f3100,f3108,f537]) ).
fof(f3385,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(X0)
| frontsegP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f124,f249]) ).
fof(f3396,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| frontsegP(X0,X0)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f124,f389]) ).
fof(f3399,plain,
! [X0,X1] :
( nil != X0
| nil != X1
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f124,f387]) ).
fof(f3421,definition,
! [X0] :
( sQ268_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0)
| frontsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f3424,plain,
( ~ sQ11_spl
| sQ268_spl ),
inference(split_clause,[status(thm)],[f3385,f3421,f537]) ).
fof(f3438,definition,
! [X0] :
( sQ269_spl
<=> ( ~ ssList(X0)
| frontsegP(X0,X0)
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f3441,plain,
( ~ sQ11_spl
| sQ269_spl ),
inference(split_clause,[status(thm)],[f3396,f3438,f537]) ).
fof(f3444,definition,
! [X0] :
( sQ270_spl
<=> ( nil != X0
| ~ ssList(X0)
| frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f3447,plain,
( sQ69_spl
| sQ270_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3399,f537,f3444,f1066]) ).
fof(f3480,plain,
! [X0] :
( nil = sK5_skl(X0,nil)
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f123,f385]) ).
fof(f3481,plain,
! [X0] :
( nil = X0
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f123,f386]) ).
fof(f3491,definition,
! [X0] :
( sQ272_spl
<=> ( nil = sK5_skl(X0,nil)
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f3494,plain,
( sQ272_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3480,f537,f3491]) ).
fof(f3495,definition,
! [X0] :
( sQ273_spl
<=> ( nil = X0
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f3498,plain,
( sQ273_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3481,f537,f3495]) ).
fof(f3575,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssItem(X0)
| singletonP(app(cons(X0,nil),nil))
| ~ ssList(app(cons(X0,nil),nil)) ),
inference(resolution,[status(thm)],[f118,f380]) ).
fof(f3595,definition,
( sQ280_spl
<=> ssList(app(sK47_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f3597,plain,
( sQ280_spl
| ~ ssList(app(sK47_skl,nil)) ),
inference(component_clause,[status(thm)],[f3595]) ).
fof(f3602,definition,
! [X0] :
( sQ282_spl
<=> ( ~ ssItem(X0)
| ~ ssItem(X0)
| singletonP(app(cons(X0,nil),nil))
| ~ ssList(app(cons(X0,nil),nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f3605,plain,
( ~ sQ11_spl
| sQ282_spl ),
inference(split_clause,[status(thm)],[f3575,f3602,f537]) ).
fof(f3616,plain,
! [X0,X1] :
( X1 = nil
| ~ ssItem(X0)
| ~ ssItem(sK4_skl(cons(X0,X1)))
| ~ ssList(X1)
| ~ ssList(nil)
| ~ singletonP(cons(X0,X1))
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f117,f228]) ).
fof(f3628,definition,
! [X0,X1] :
( sQ284_spl
<=> ( X1 = nil
| ~ ssItem(X0)
| ~ ssItem(sK4_skl(cons(X0,X1)))
| ~ ssList(X1)
| ~ singletonP(cons(X0,X1))
| ~ ssList(cons(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ284_spl])],[split_symbol_definition]) ).
fof(f3631,plain,
( ~ sQ11_spl
| sQ284_spl ),
inference(split_clause,[status(thm)],[f3616,f3628,f537]) ).
fof(f3647,plain,
! [X0] :
( nil = cons(X0,sK3_skl(X0,nil))
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil))
| ~ memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f111,f385]) ).
fof(f3648,plain,
! [X0] :
( nil = sK2_skl(X0,nil)
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil))
| ~ memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f111,f386]) ).
fof(f3655,definition,
! [X0] :
( sQ286_spl
<=> ( nil = cons(X0,sK3_skl(X0,nil))
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil))
| ~ memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f3658,plain,
( sQ286_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3647,f537,f3655]) ).
fof(f3659,definition,
! [X0] :
( sQ287_spl
<=> ( nil = sK2_skl(X0,nil)
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil))
| ~ memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ287_spl])],[split_symbol_definition]) ).
fof(f3662,plain,
( sQ287_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3648,f537,f3659]) ).
fof(f3733,plain,
( sQ280_spl
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f3597,f245]) ).
fof(f3734,plain,
( sQ280_spl
| ~ sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f3733,f497,f537,f3595]) ).
fof(f3832,plain,
! [X0,X1,X2,X3] :
( ~ ssItem(sK55_skl(nil,X0,X1,X2,X3))
| app(app(X0,X3),nil) != X2
| cons(X1,nil) != X3
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| sP0_prd(X1,X2,X3)
| memberP(X0,sK54_skl(nil,X0,X1,X2,X3)) ),
inference(resolution,[status(thm)],[f840,f279]) ).
fof(f3841,definition,
! [X0,X1,X2,X3] :
( sQ290_spl
<=> ( ~ ssItem(sK55_skl(nil,X0,X1,X2,X3))
| app(app(X0,X3),nil) != X2
| cons(X1,nil) != X3
| ~ ssList(X0)
| ~ ssItem(X1)
| sP0_prd(X1,X2,X3)
| memberP(X0,sK54_skl(nil,X0,X1,X2,X3)) ) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f3844,plain,
( ~ sQ11_spl
| sQ290_spl ),
inference(split_clause,[status(thm)],[f3832,f3841,f537]) ).
fof(f3895,plain,
! [X0,X1,X2,X3] :
( ~ ssItem(sK54_skl(X3,nil,X0,X1,X2))
| ssItem(sK55_skl(X3,nil,X0,X1,X2))
| app(app(nil,X2),X3) != X1
| cons(X0,nil) != X2
| ~ ssList(X3)
| ~ ssList(nil)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ),
inference(resolution,[status(thm)],[f841,f279]) ).
fof(f3904,definition,
! [X0,X1,X2,X3] :
( sQ294_spl
<=> ( ~ ssItem(sK54_skl(X3,nil,X0,X1,X2))
| ssItem(sK55_skl(X3,nil,X0,X1,X2))
| app(app(nil,X2),X3) != X1
| cons(X0,nil) != X2
| ~ ssList(X3)
| ~ ssItem(X0)
| sP0_prd(X0,X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ294_spl])],[split_symbol_definition]) ).
fof(f3907,plain,
( ~ sQ11_spl
| sQ294_spl ),
inference(split_clause,[status(thm)],[f3895,f3904,f537]) ).
fof(f3916,plain,
! [X0] :
( ~ sQ40_spl
| ~ ssList(X0)
| X0 = nil
| ~ ssList(nil)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2940,f323]) ).
fof(f3917,plain,
! [X0,X1] :
( ~ sQ40_spl
| ~ ssList(X0)
| nil != X1
| ~ ssList(X1)
| X0 = X1
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2940,f836]) ).
fof(f3929,plain,
( ~ sQ40_spl
| ~ sQ11_spl
| sQ68_spl ),
inference(split_clause,[status(thm)],[f3916,f1063,f537,f831]) ).
fof(f3930,plain,
! [X0,X1] :
( ~ sQ40_spl
| nil != X1
| X0 = X1
| ~ ssList(X1)
| nil != X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f3917]) ).
fof(f3965,plain,
! [X0] :
( ~ sQ40_spl
| nil != nil
| X0 = nil
| nil != X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3930,f223]) ).
fof(f3979,definition,
! [X0] :
( sQ298_spl
<=> ( X0 = nil
| nil != X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ298_spl])],[split_symbol_definition]) ).
fof(f3982,plain,
( ~ sQ40_spl
| ~ sQ37_spl
| sQ298_spl ),
inference(split_clause,[status(thm)],[f3965,f3979,f814,f831]) ).
fof(f3986,plain,
! [X0,X1,X2] :
( ~ sQ35_spl
| nil = X1
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X0,X2)
| ~ ssList(X2)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f724,f781]) ).
fof(f3995,plain,
! [X0,X1] :
( ~ sQ44_spl
| ~ segmentP(nil,X1)
| ~ ssList(nil)
| segmentP(X0,X1)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X1)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f724,f942]) ).
fof(f3998,plain,
! [X0,X1] :
( ~ sQ46_spl
| ~ segmentP(nil,X1)
| ~ ssList(nil)
| segmentP(X0,X1)
| ~ segmentP(X0,nil)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f724,f951]) ).
fof(f4000,plain,
! [X0,X1,X2] :
( nil != X2
| ~ ssList(X2)
| ~ segmentP(X2,X1)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ segmentP(X0,nil)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f724,f327]) ).
fof(f4006,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssList(nil)
| segmentP(X0,nil)
| ~ segmentP(X0,nil)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f724,f323]) ).
fof(f4007,plain,
! [X0,X1,X2] :
( ~ ssList(X1)
| ~ segmentP(nil,X2)
| ~ ssList(nil)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f724,f323]) ).
fof(f4016,plain,
! [X0,X1] :
( ~ sQ44_spl
| ~ segmentP(X1,sK47_skl)
| ~ ssList(sK47_skl)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f724,f942]) ).
fof(f4018,plain,
! [X0,X1] :
( ~ sQ46_spl
| ~ segmentP(X1,nil)
| ~ ssList(nil)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f724,f951]) ).
fof(f4019,plain,
! [X0,X1,X2] :
( nil != X2
| ~ ssList(X2)
| ~ segmentP(X1,nil)
| ~ ssList(nil)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f724,f327]) ).
fof(f4024,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f724,f323]) ).
fof(f4042,definition,
! [X0,X1,X2] :
( sQ302_spl
<=> ( nil = X1
| ~ ssList(X1)
| ~ segmentP(X2,X1)
| ~ segmentP(X0,X2)
| ~ ssList(X2)
| ~ segmentP(nil,X0)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ302_spl])],[split_symbol_definition]) ).
fof(f4045,plain,
( ~ sQ35_spl
| sQ302_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f3986,f537,f4042,f776]) ).
fof(f4055,definition,
! [X0,X1] :
( sQ304_spl
<=> ( ~ segmentP(nil,X1)
| segmentP(X0,X1)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ304_spl])],[split_symbol_definition]) ).
fof(f4058,plain,
( ~ sQ44_spl
| ~ sQ11_spl
| ~ sQ5_spl
| sQ304_spl ),
inference(split_clause,[status(thm)],[f3995,f4055,f497,f537,f941]) ).
fof(f4061,definition,
! [X0,X1] :
( sQ305_spl
<=> ( ~ segmentP(nil,X1)
| segmentP(X0,X1)
| ~ segmentP(X0,nil)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ305_spl])],[split_symbol_definition]) ).
fof(f4062,plain,
! [X0,X1] :
( ~ sQ305_spl
| ~ segmentP(nil,X1)
| segmentP(X0,X1)
| ~ segmentP(X0,nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f4061]) ).
fof(f4064,plain,
( ~ sQ46_spl
| ~ sQ11_spl
| sQ305_spl ),
inference(split_clause,[status(thm)],[f3998,f4061,f537,f950]) ).
fof(f4066,definition,
! [X0,X1,X2] :
( sQ306_spl
<=> ( nil != X2
| ~ ssList(X2)
| ~ segmentP(X2,X1)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ segmentP(X0,nil)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ306_spl])],[split_symbol_definition]) ).
fof(f4069,plain,
( ~ sQ11_spl
| sQ306_spl ),
inference(split_clause,[status(thm)],[f4000,f4066,f537]) ).
fof(f4075,plain,
( ~ sQ11_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f4006,f1853,f537]) ).
fof(f4076,definition,
! [X0,X1,X2] :
( sQ307_spl
<=> ( ~ ssList(X1)
| ~ segmentP(nil,X2)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ307_spl])],[split_symbol_definition]) ).
fof(f4079,plain,
( ~ sQ11_spl
| sQ307_spl ),
inference(split_clause,[status(thm)],[f4007,f4076,f537]) ).
fof(f4084,definition,
! [X0,X1] :
( sQ308_spl
<=> ( ~ segmentP(X1,sK47_skl)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ308_spl])],[split_symbol_definition]) ).
fof(f4087,plain,
( ~ sQ44_spl
| ~ sQ5_spl
| ~ sQ11_spl
| sQ308_spl ),
inference(split_clause,[status(thm)],[f4016,f4084,f537,f497,f941]) ).
fof(f4089,definition,
! [X0,X1] :
( sQ309_spl
<=> ( ~ segmentP(X1,nil)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ309_spl])],[split_symbol_definition]) ).
fof(f4092,plain,
( ~ sQ46_spl
| ~ sQ11_spl
| sQ309_spl ),
inference(split_clause,[status(thm)],[f4018,f4089,f537,f950]) ).
fof(f4093,definition,
! [X0,X1,X2] :
( sQ310_spl
<=> ( nil != X2
| ~ ssList(X2)
| ~ segmentP(X1,nil)
| segmentP(X0,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f4096,plain,
( ~ sQ11_spl
| sQ310_spl ),
inference(split_clause,[status(thm)],[f4019,f4093,f537]) ).
fof(f4102,definition,
! [X0,X1,X2] :
( sQ311_spl
<=> ( ~ ssList(X2)
| ~ segmentP(X1,X2)
| ~ ssList(X2)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ311_spl])],[split_symbol_definition]) ).
fof(f4105,plain,
( ~ sQ11_spl
| sQ311_spl ),
inference(split_clause,[status(thm)],[f4024,f4102,f537]) ).
fof(f4111,plain,
! [X0,X1] :
( ~ sQ305_spl
| ~ segmentP(nil,X1)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4062,f323]) ).
fof(f4318,plain,
! [X0] :
( ~ sQ44_spl
| ~ segmentP(nil,X0)
| ~ ssList(nil)
| X0 = sK47_skl
| ~ segmentP(X0,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f780,f942]) ).
fof(f4321,plain,
! [X0] :
( ~ sQ46_spl
| ~ segmentP(nil,X0)
| ~ ssList(nil)
| X0 = nil
| ~ segmentP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f780,f951]) ).
fof(f4323,plain,
! [X0,X1] :
( nil != X1
| ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ ssList(X1)
| X0 = nil
| ~ segmentP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f780,f327]) ).
fof(f4330,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ segmentP(nil,X0)
| ~ ssList(nil)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f780,f323]) ).
fof(f4339,plain,
! [X0] :
( ~ sQ44_spl
| ~ segmentP(X0,sK47_skl)
| ~ ssList(sK47_skl)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f780,f942]) ).
fof(f4342,plain,
! [X0,X1] :
( nil != X0
| ~ ssList(X0)
| ~ segmentP(X1,nil)
| ~ ssList(nil)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f780,f327]) ).
fof(f4347,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f780,f323]) ).
fof(f4353,definition,
! [X0] :
( sQ325_spl
<=> ( ~ segmentP(nil,X0)
| X0 = sK47_skl
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ325_spl])],[split_symbol_definition]) ).
fof(f4356,plain,
( ~ sQ44_spl
| ~ sQ11_spl
| ~ sQ5_spl
| sQ325_spl ),
inference(split_clause,[status(thm)],[f4318,f4353,f497,f537,f941]) ).
fof(f4359,definition,
! [X0] :
( sQ326_spl
<=> ( ~ segmentP(nil,X0)
| X0 = nil
| ~ segmentP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ326_spl])],[split_symbol_definition]) ).
fof(f4362,plain,
( ~ sQ46_spl
| ~ sQ11_spl
| sQ326_spl ),
inference(split_clause,[status(thm)],[f4321,f4359,f537,f950]) ).
fof(f4364,definition,
! [X0,X1] :
( sQ327_spl
<=> ( nil != X1
| ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ ssList(X1)
| X0 = nil
| ~ segmentP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ327_spl])],[split_symbol_definition]) ).
fof(f4367,plain,
( ~ sQ11_spl
| sQ327_spl ),
inference(split_clause,[status(thm)],[f4323,f4364,f537]) ).
fof(f4374,definition,
! [X0,X1] :
( sQ328_spl
<=> ( ~ ssList(X1)
| ~ segmentP(nil,X0)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ328_spl])],[split_symbol_definition]) ).
fof(f4377,plain,
( ~ sQ11_spl
| sQ328_spl ),
inference(split_clause,[status(thm)],[f4330,f4374,f537]) ).
fof(f4382,definition,
! [X0] :
( sQ329_spl
<=> ( ~ segmentP(X0,sK47_skl)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ329_spl])],[split_symbol_definition]) ).
fof(f4385,plain,
( ~ sQ44_spl
| ~ sQ5_spl
| sQ329_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4339,f537,f4382,f497,f941]) ).
fof(f4388,definition,
! [X0,X1] :
( sQ330_spl
<=> ( nil != X0
| ~ ssList(X0)
| ~ segmentP(X1,nil)
| X0 = X1
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ330_spl])],[split_symbol_definition]) ).
fof(f4391,plain,
( ~ sQ11_spl
| sQ330_spl ),
inference(split_clause,[status(thm)],[f4342,f4388,f537]) ).
fof(f4397,definition,
! [X0,X1] :
( sQ331_spl
<=> ( ~ ssList(X1)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ331_spl])],[split_symbol_definition]) ).
fof(f4400,plain,
( sQ331_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f4347,f537,f4397]) ).
fof(f4427,plain,
! [X0] :
( ~ sQ305_spl
| ~ ssList(nil)
| segmentP(X0,nil)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4111,f323]) ).
fof(f4428,plain,
! [X0,X1,X2,X3] :
( ~ sQ305_spl
| ~ segmentP(X3,X1)
| ~ segmentP(X2,X3)
| ~ ssList(X3)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(nil)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4111,f724]) ).
fof(f4429,plain,
! [X0,X1] :
( ~ sQ40_spl
| ~ sQ305_spl
| ~ ssList(nil)
| nil != X1
| ~ ssList(X1)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4111,f836]) ).
fof(f4430,plain,
! [X0,X1,X2] :
( ~ sQ305_spl
| ~ segmentP(X2,X1)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(nil)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f4111,f315]) ).
fof(f4432,definition,
! [X0] :
( sQ332_spl
<=> ( segmentP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ332_spl])],[split_symbol_definition]) ).
fof(f4437,plain,
( ~ sQ305_spl
| ~ sQ11_spl
| sQ332_spl ),
inference(split_clause,[status(thm)],[f4427,f4432,f537,f4061]) ).
fof(f4438,definition,
! [X0,X1,X2,X3] :
( sQ333_spl
<=> ( ~ segmentP(X3,X1)
| ~ segmentP(X2,X3)
| ~ ssList(X3)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ333_spl])],[split_symbol_definition]) ).
fof(f4441,plain,
( ~ sQ305_spl
| ~ sQ11_spl
| sQ333_spl ),
inference(split_clause,[status(thm)],[f4428,f4438,f537,f4061]) ).
fof(f4442,definition,
! [X0,X1] :
( sQ334_spl
<=> ( nil != X1
| ~ ssList(X1)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ334_spl])],[split_symbol_definition]) ).
fof(f4445,plain,
( ~ sQ40_spl
| ~ sQ305_spl
| ~ sQ11_spl
| sQ334_spl ),
inference(split_clause,[status(thm)],[f4429,f4442,f537,f4061,f831]) ).
fof(f4446,definition,
! [X0,X1,X2] :
( sQ335_spl
<=> ( ~ segmentP(X2,X1)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ335_spl])],[split_symbol_definition]) ).
fof(f4449,plain,
( ~ sQ305_spl
| ~ sQ11_spl
| sQ335_spl ),
inference(split_clause,[status(thm)],[f4430,f4446,f537,f4061]) ).
fof(f4603,plain,
! [X0,X1,X2] :
( nil != app(app(X1,X0),X2)
| ~ ssList(app(app(X1,X0),X2))
| nil = app(app(X1,X0),X2)
| ~ ssList(app(app(X1,X0),X2))
| ~ segmentP(X0,nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f785,f327]) ).
fof(f4613,definition,
! [X0,X1,X2] :
( sQ336_spl
<=> ( nil != app(app(X1,X0),X2)
| ~ ssList(app(app(X1,X0),X2))
| nil = app(app(X1,X0),X2)
| ~ ssList(app(app(X1,X0),X2))
| ~ segmentP(X0,nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ336_spl])],[split_symbol_definition]) ).
fof(f4616,plain,
( ~ sQ11_spl
| sQ336_spl ),
inference(split_clause,[status(thm)],[f4603,f4613,f537]) ).
fof(f4626,plain,
! [X0,X1,X2,X3] :
( nil != app(app(X2,X0),X3)
| ~ ssList(app(app(X2,X0),X3))
| segmentP(nil,X1)
| ~ ssList(app(app(X2,X0),X3))
| ~ ssList(nil)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f786,f327]) ).
fof(f4636,definition,
! [X0,X1,X2,X3] :
( sQ337_spl
<=> ( nil != app(app(X2,X0),X3)
| ~ ssList(app(app(X2,X0),X3))
| segmentP(nil,X1)
| ~ ssList(app(app(X2,X0),X3))
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ337_spl])],[split_symbol_definition]) ).
fof(f4639,plain,
( ~ sQ11_spl
| sQ337_spl ),
inference(split_clause,[status(thm)],[f4626,f4636,f537]) ).
fof(f4914,plain,
! [X0] :
( ~ sQ38_spl
| ~ ssList(nil)
| ~ segmentP(nil,X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f823,f323]) ).
fof(f4915,plain,
! [X0,X1,X2,X3] :
( ~ sQ38_spl
| ~ segmentP(X3,X1)
| ~ segmentP(X2,X3)
| ~ ssList(X3)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ segmentP(X1,X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f823,f724]) ).
fof(f4916,plain,
! [X0,X1] :
( ~ sQ40_spl
| ~ sQ38_spl
| ~ ssList(nil)
| nil != X1
| ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f823,f836]) ).
fof(f4917,plain,
! [X0,X1,X2] :
( ~ sQ38_spl
| ~ segmentP(X2,X1)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ segmentP(X1,X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f823,f315]) ).
fof(f4919,definition,
! [X0] :
( sQ350_spl
<=> ( ~ segmentP(nil,X0)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ350_spl])],[split_symbol_definition]) ).
fof(f4924,plain,
( ~ sQ38_spl
| ~ sQ11_spl
| sQ350_spl ),
inference(split_clause,[status(thm)],[f4914,f4919,f537,f818]) ).
fof(f4925,definition,
! [X0,X1,X2,X3] :
( sQ351_spl
<=> ( ~ segmentP(X3,X1)
| ~ segmentP(X2,X3)
| ~ ssList(X3)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ351_spl])],[split_symbol_definition]) ).
fof(f4928,plain,
( ~ sQ38_spl
| ~ sQ11_spl
| sQ351_spl ),
inference(split_clause,[status(thm)],[f4915,f4925,f537,f818]) ).
fof(f4929,definition,
! [X0,X1] :
( sQ352_spl
<=> ( nil != X1
| ~ ssList(X1)
| ~ segmentP(X1,X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ352_spl])],[split_symbol_definition]) ).
fof(f4932,plain,
( ~ sQ40_spl
| ~ sQ38_spl
| ~ sQ11_spl
| sQ352_spl ),
inference(split_clause,[status(thm)],[f4916,f4929,f537,f818,f831]) ).
fof(f4933,definition,
! [X0,X1,X2] :
( sQ353_spl
<=> ( ~ segmentP(X2,X1)
| ~ segmentP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ segmentP(X1,X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ353_spl])],[split_symbol_definition]) ).
fof(f4936,plain,
( ~ sQ38_spl
| ~ sQ11_spl
| sQ353_spl ),
inference(split_clause,[status(thm)],[f4917,f4933,f537,f818]) ).
fof(f5176,definition,
( sQ390_spl
<=> ssList(app(nil,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ390_spl])],[split_symbol_definition]) ).
fof(f5178,plain,
( sQ390_spl
| ~ ssList(app(nil,sK47_skl)) ),
inference(component_clause,[status(thm)],[f5176]) ).
fof(f5180,plain,
( sQ390_spl
| ~ ssList(sK47_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f5178,f245]) ).
fof(f5181,plain,
( sQ390_spl
| ~ sQ5_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f5180,f537,f497,f5176]) ).
fof(f5327,plain,
! [X0,X1] :
( ~ singletonP(app(X0,X1))
| ~ ssList(X1)
| frontsegP(cons(sK4_skl(app(X0,X1)),nil),X0)
| ~ ssList(X0)
| ~ ssList(cons(sK4_skl(app(X0,X1)),nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f529,f245]) ).
fof(f5328,plain,
! [X0,X1,X2] :
( sK4_skl(app(cons(X0,X1),X2)) = X0
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK4_skl(app(cons(X0,X1),X2)))
| ~ singletonP(app(cons(X0,X1),X2))
| ~ ssList(X2)
| ~ ssList(cons(X0,X1))
| ~ ssList(cons(sK4_skl(app(cons(X0,X1),X2)),nil)) ),
inference(resolution,[status(thm)],[f5327,f291]) ).
fof(f5329,plain,
! [X0,X1,X2] :
( frontsegP(nil,X1)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssItem(X0)
| ~ ssItem(sK4_skl(app(cons(X0,X1),X2)))
| ~ singletonP(app(cons(X0,X1),X2))
| ~ ssList(X2)
| ~ ssList(cons(X0,X1))
| ~ ssList(cons(sK4_skl(app(cons(X0,X1),X2)),nil)) ),
inference(resolution,[status(thm)],[f5327,f292]) ).
fof(f5334,definition,
! [X0,X1,X2] :
( sQ415_spl
<=> ( sK4_skl(app(cons(X0,X1),X2)) = X0
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(sK4_skl(app(cons(X0,X1),X2)))
| ~ singletonP(app(cons(X0,X1),X2))
| ~ ssList(X2)
| ~ ssList(cons(X0,X1))
| ~ ssList(cons(sK4_skl(app(cons(X0,X1),X2)),nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ415_spl])],[split_symbol_definition]) ).
fof(f5337,plain,
( ~ sQ11_spl
| sQ415_spl ),
inference(split_clause,[status(thm)],[f5328,f5334,f537]) ).
fof(f5338,definition,
! [X0,X1,X2] :
( sQ416_spl
<=> ( frontsegP(nil,X1)
| ~ ssList(X1)
| ~ ssItem(X0)
| ~ ssItem(sK4_skl(app(cons(X0,X1),X2)))
| ~ singletonP(app(cons(X0,X1),X2))
| ~ ssList(X2)
| ~ ssList(cons(X0,X1))
| ~ ssList(cons(sK4_skl(app(cons(X0,X1),X2)),nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ416_spl])],[split_symbol_definition]) ).
fof(f5341,plain,
( ~ sQ11_spl
| sQ416_spl ),
inference(split_clause,[status(thm)],[f5329,f5338,f537]) ).
fof(f5450,plain,
! [X0,X1] :
( ~ sQ110_spl
| nil != X1
| nil != X0
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(X1)
| segmentP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1574,f387]) ).
fof(f5451,plain,
! [X0] :
( ~ sQ110_spl
| ~ memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssList(sK2_skl(X0,nil))
| segmentP(nil,cons(X0,sK3_skl(X0,nil)))
| ~ ssList(cons(X0,sK3_skl(X0,nil))) ),
inference(resolution,[status(thm)],[f1574,f111]) ).
fof(f5461,plain,
! [X0] :
( ~ sQ110_spl
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(app(sK7_skl(X0,nil),X0))
| segmentP(nil,sK8_skl(X0,nil))
| ~ ssList(sK8_skl(X0,nil)) ),
inference(resolution,[status(thm)],[f1574,f136]) ).
fof(f5462,plain,
! [X0] :
( ~ sQ110_spl
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK6_skl(X0,nil))
| segmentP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1574,f129]) ).
fof(f5463,plain,
! [X0] :
( ~ sQ110_spl
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X0)
| segmentP(nil,sK5_skl(X0,nil))
| ~ ssList(sK5_skl(X0,nil)) ),
inference(resolution,[status(thm)],[f1574,f123]) ).
fof(f5465,definition,
! [X0] :
( sQ420_spl
<=> ( nil != X0
| ~ ssList(X0)
| segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ420_spl])],[split_symbol_definition]) ).
fof(f5468,plain,
( ~ sQ110_spl
| sQ69_spl
| sQ420_spl ),
inference(split_clause,[status(thm)],[f5450,f5465,f1066,f1565]) ).
fof(f5469,definition,
! [X0] :
( sQ421_spl
<=> ( ~ memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(sK2_skl(X0,nil))
| segmentP(nil,cons(X0,sK3_skl(X0,nil)))
| ~ ssList(cons(X0,sK3_skl(X0,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ421_spl])],[split_symbol_definition]) ).
fof(f5472,plain,
( ~ sQ110_spl
| ~ sQ11_spl
| sQ421_spl ),
inference(split_clause,[status(thm)],[f5451,f5469,f537,f1565]) ).
fof(f5503,definition,
! [X0] :
( sQ429_spl
<=> ( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(app(sK7_skl(X0,nil),X0))
| segmentP(nil,sK8_skl(X0,nil))
| ~ ssList(sK8_skl(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ429_spl])],[split_symbol_definition]) ).
fof(f5506,plain,
( ~ sQ110_spl
| ~ sQ11_spl
| sQ429_spl ),
inference(split_clause,[status(thm)],[f5461,f5503,f537,f1565]) ).
fof(f5507,definition,
! [X0] :
( sQ430_spl
<=> ( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil))
| segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ430_spl])],[split_symbol_definition]) ).
fof(f5510,plain,
( ~ sQ110_spl
| ~ sQ11_spl
| sQ430_spl ),
inference(split_clause,[status(thm)],[f5462,f5507,f537,f1565]) ).
fof(f5511,definition,
! [X0] :
( sQ431_spl
<=> ( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X0)
| segmentP(nil,sK5_skl(X0,nil))
| ~ ssList(sK5_skl(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ431_spl])],[split_symbol_definition]) ).
fof(f5514,plain,
( ~ sQ110_spl
| ~ sQ11_spl
| sQ431_spl ),
inference(split_clause,[status(thm)],[f5463,f5511,f537,f1565]) ).
fof(f5876,plain,
! [X0,X1,X2] :
( ~ sP0_prd(X2,X0,X1)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1381,f436]) ).
fof(f5884,plain,
( ~ sQ2_spl
| segmentP(sK48_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1764,f5876]) ).
fof(f5887,plain,
( ~ sQ2_spl
| sQ7_spl
| ~ sQ5_spl
| ~ sQ8_spl ),
inference(split_clause,[status(thm)],[f5884,f507,f497,f503,f457]) ).
fof(f5888,plain,
$false,
inference(sat_refutation,[status(thm)],[f456,f463,f467,f506,f518,f549,f564,f572,f579,f594,f599,f621,f705,f723,f731,f779,f817,f821,f830,f834,f860,f1011,f1015,f1041,f1045,f1077,f1081,f1085,f1089,f1093,f1108,f1112,f1184,f1186,f1226,f1310,f1386,f1415,f1559,f1572,f1665,f1711,f1716,f1720,f1748,f1758,f1763,f1859,f1866,f1936,f1976,f2052,f2203,f2205,f2207,f2209,f2211,f2213,f2217,f2262,f2282,f2302,f2562,f2612,f2616,f2620,f2633,f2637,f2652,f2656,f2680,f2716,f2864,f3043,f3111,f3424,f3441,f3447,f3494,f3498,f3605,f3631,f3658,f3662,f3734,f3844,f3907,f3929,f3982,f4045,f4058,f4064,f4069,f4075,f4079,f4087,f4092,f4096,f4105,f4356,f4362,f4367,f4377,f4385,f4391,f4400,f4437,f4441,f4445,f4449,f4616,f4639,f4924,f4928,f4932,f4936,f5181,f5337,f5341,f5468,f5472,f5506,f5510,f5514,f5887]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC071+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 07:54:32 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.41 % Drodi V4.1.1
% 26.85/4.37 % Refutation found
% 26.85/4.37 % SZS status Theorem for theBenchmark: Theorem is valid
% 26.85/4.37 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 26.85/4.43 % Elapsed time: 4.037136 seconds
% 26.85/4.43 % CPU time: 27.433085 seconds
% 26.85/4.43 % Total memory used: 232.292 MB
% 26.85/4.43 % Net memory used: 220.796 MB
%------------------------------------------------------------------------------