%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC106+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 02:39:59 PM UTC 2026
% Result : Theorem 4.65s 1.12s
% Output : CNFRefutation 4.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 189
% Syntax : Number of formulae : 719 ( 19 unt; 165 def)
% Number of atoms : 2483 ( 296 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 3171 (1407 ~;1425 |; 104 &)
% ( 181 <=>; 54 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 175 ( 173 usr; 165 prp; 0-4 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-4 aty)
% Number of variables : 487 ( 450 !; 37 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [U] :
( ssList(U)
=> ( ? [V] :
( ? [W] :
( cons(W,V) = U
& ssItem(W) )
& ssList(V) )
| nil = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( rearsegP(V,W)
& rearsegP(U,V) )
=> rearsegP(U,W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( rearsegP(V,U)
& rearsegP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( rearsegP(U,V)
=> rearsegP(app(W,U),V) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f52,axiom,
! [U] :
( ssList(U)
=> ( rearsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f79,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(W,V) = app(U,V)
=> W = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ( rearsegP(V,U)
& neq(U,nil) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,cons(Y,nil)) != X
| cons(Y,nil) != W ) ) )
| ~ neq(V,nil) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( neq(X,nil)
| ~ neq(V,nil) )
& ( ( rearsegP(V,U)
& neq(U,nil) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(Z,cons(Y,nil)) != X
| cons(Y,nil) != W ) ) )
| ~ neq(V,nil) ) )
| 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(f103,plain,
ssItem(sK0_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
ssItem(sK1_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f113,plain,
! [U] :
( ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f114,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [V] :
( cons(V,nil) = U
& ssItem(V) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ( cons(sK4_skl(U),nil) = U
& ssItem(sK4_skl(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114]) ).
fof(f116,plain,
! [X0] :
( ssItem(sK4_skl(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0] :
( cons(sK4_skl(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f118,plain,
! [X0,X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f119,plain,
! [U] :
( ! [V] :
( ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f120,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ? [W] :
( app(V,W) = U
& ssList(W) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ( app(V,sK5_skl(V,U)) = U
& ssList(sK5_skl(V,U)) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( ssList(sK5_skl(X1,X0))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( app(X1,sK5_skl(X1,X0)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f124,plain,
! [X0,X1,X2] :
( app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f125,plain,
! [U] :
( ! [V] :
( ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f126,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ? [W] :
( app(W,V) = U
& ssList(W) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ( app(sK6_skl(V,U),V) = U
& ssList(sK6_skl(V,U)) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ssList(sK6_skl(X1,X0))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( app(sK6_skl(X1,X0),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f130,plain,
! [X0,X1,X2] :
( app(X2,X1) != X0
| ~ ssList(X2)
| rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f131,plain,
! [U] :
( ! [V] :
( ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f132,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ( app(app(sK7_skl(V,U),V),sK8_skl(V,U)) = U
& ssList(sK8_skl(V,U))
& ssList(sK7_skl(V,U)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132]) ).
fof(f134,plain,
! [X0,X1] :
( ssList(sK7_skl(X1,X0))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
! [X0,X1] :
( ssList(sK8_skl(X1,X0))
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f136,plain,
! [X0,X1] :
( app(app(sK7_skl(X1,X0),X1),sK8_skl(X1,X0)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f219,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f221,plain,
! [U] :
( ! [V] :
( ssList(cons(V,U))
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f222,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f229,plain,
! [U] :
( ? [V] :
( ? [W] :
( cons(W,V) = U
& ssItem(W) )
& ssList(V) )
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f20]) ).
fof(f230,plain,
! [U] :
( ( cons(sK44_skl(U),sK43_skl(U)) = U
& ssItem(sK44_skl(U))
& ssList(sK43_skl(U)) )
| nil = U
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK43_skl,sK44_skl]),skolemize(V,sK43_skl(U)),skolemize(W,sK44_skl(U))],[f229]) ).
fof(f233,plain,
! [X0] :
( cons(sK44_skl(X0),sK43_skl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f230]) ).
fof(f234,plain,
! [U] :
( ! [V] :
( nil != cons(V,U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f235,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(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(f268,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f269,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& ~ memberP(V,U) )
| memberP(app(V,W),U) )
& ( memberP(W,U)
| memberP(V,U)
| ~ memberP(app(V,W),U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f268]) ).
fof(f270,plain,
! [X0,X1,X2] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(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(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(f306,plain,
! [U] :
( ! [V] :
( ! [W] :
( rearsegP(app(W,U),V)
| ~ rearsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f50]) ).
fof(f307,plain,
! [X0,X1,X2] :
( rearsegP(app(X2,X0),X1)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f306]) ).
fof(f308,plain,
! [U] :
( rearsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f309,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f310,plain,
! [U] :
( ( rearsegP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f52]) ).
fof(f311,plain,
! [U] :
( ( ( nil != U
| rearsegP(nil,U) )
& ( nil = U
| ~ rearsegP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f310]) ).
fof(f312,plain,
! [X0] :
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f311]) ).
fof(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(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(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(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] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| ( ( ~ rearsegP(V,U)
| ~ neq(U,nil) )
& ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& cons(Y,nil) = W
& ssList(Z) )
& ssItem(Y) )
& neq(V,nil) ) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,V,W,X] :
( sP0_prd(X,W,V,U)
<=> ( ( ~ rearsegP(V,U)
| ~ neq(U,nil) )
& ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& cons(Y,nil) = W
& ssList(Z) )
& ssItem(Y) )
& neq(V,nil) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ~ neq(X,nil)
& neq(V,nil) )
| sP0_prd(X,W,V,U) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( ~ neq(sK50_skl,nil)
& neq(sK48_skl,nil) )
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) )
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f417]) ).
fof(f419,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f420,plain,
ssList(sK48_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( ~ neq(sK50_skl,nil)
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
! [U,V,W,X] :
( ( ( rearsegP(V,U)
& neq(U,nil) )
| ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != X
| cons(Y,nil) != W
| ~ ssList(Z) )
| ~ ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ( ( ( ~ rearsegP(V,U)
| ~ neq(U,nil) )
& ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& cons(Y,nil) = W
& ssList(Z) )
& ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f428,plain,
( ! [U,V,W,X] :
( ( rearsegP(V,U)
& neq(U,nil) )
| ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != X
| cons(Y,nil) != W
| ~ ssList(Z) )
| ~ ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ( ~ rearsegP(V,U)
| ~ neq(U,nil) )
& ? [Y] :
( ? [Z] :
( app(Z,cons(Y,nil)) = X
& cons(Y,nil) = W
& ssList(Z) )
& ssItem(Y) )
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(miniscoping,[status(thm)],[f427]) ).
fof(f429,plain,
( ! [U,V,W,X] :
( ( rearsegP(V,U)
& neq(U,nil) )
| ! [Y] :
( ! [Z] :
( app(Z,cons(Y,nil)) != X
| cons(Y,nil) != W
| ~ ssList(Z) )
| ~ ssItem(Y) )
| ~ neq(V,nil)
| sP0_prd(X,W,V,U) )
& ! [U,V,W,X] :
( ( ( ~ rearsegP(V,U)
| ~ neq(U,nil) )
& app(sK52_skl(X,W,V,U),cons(sK51_skl(X,W,V,U),nil)) = X
& cons(sK51_skl(X,W,V,U),nil) = W
& ssList(sK52_skl(X,W,V,U))
& ssItem(sK51_skl(X,W,V,U))
& neq(V,nil) )
| ~ sP0_prd(X,W,V,U) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK51_skl,sK52_skl]),skolemize(Y,sK51_skl(X,W,V,U)),skolemize(Z,sK52_skl(X,W,V,U))],[f428]) ).
fof(f430,plain,
! [X0,X1,X2,X3] :
( neq(X2,nil)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f431,plain,
! [X0,X1,X2,X3] :
( ssItem(sK51_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f432,plain,
! [X0,X1,X2,X3] :
( ssList(sK52_skl(X0,X1,X2,X3))
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f433,plain,
! [X0,X1,X2,X3] :
( cons(sK51_skl(X0,X1,X2,X3),nil) = X1
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f434,plain,
! [X0,X1,X2,X3] :
( app(sK52_skl(X0,X1,X2,X3),cons(sK51_skl(X0,X1,X2,X3),nil)) = X0
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f435,plain,
! [X0,X1,X2,X3] :
( ~ rearsegP(X2,X3)
| ~ neq(X3,nil)
| ~ sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f436,plain,
! [X0,X1,X2,X3,X4,X5] :
( neq(X3,nil)
| app(X5,cons(X4,nil)) != X0
| cons(X4,nil) != X1
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ neq(X2,nil)
| sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f437,plain,
! [X0,X1,X2,X3,X4,X5] :
( rearsegP(X2,X3)
| app(X5,cons(X4,nil)) != X0
| cons(X4,nil) != X1
| ~ ssList(X5)
| ~ ssItem(X4)
| ~ neq(X2,nil)
| sP0_prd(X0,X1,X2,X3) ),
inference(cnf_transformation,[status(thm)],[f429]) ).
fof(f438,definition,
( sQ0_spl
<=> sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,definition,
( sQ1_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( ~ sQ1_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f443,plain,
( sQ1_spl
| ~ neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f425,f438,f441]) ).
fof(f445,definition,
( sQ2_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( sQ2_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f448,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f438,f445]) ).
fof(f452,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f453,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f454,plain,
! [X0,X1] :
( ~ ssList(X0)
| rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f455,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),X2),X1)
| ~ ssList(X1)
| ~ ssList(app(app(X0,X1),X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f137]) ).
fof(f464,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f465,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f464]) ).
fof(f479,plain,
! [X0,X1,X2,X3] :
( neq(X3,nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ neq(X2,nil)
| sP0_prd(app(X0,cons(X1,nil)),cons(X1,nil),X2,X3) ),
inference(destructive_equality_resolution,[status(thm)],[f436]) ).
fof(f480,plain,
! [X0,X1,X2,X3] :
( rearsegP(X2,X3)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ neq(X2,nil)
| sP0_prd(app(X0,cons(X1,nil)),cons(X1,nil),X2,X3) ),
inference(destructive_equality_resolution,[status(thm)],[f437]) ).
fof(f487,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK49_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f439]) ).
fof(f488,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f487]) ).
fof(f489,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ sP0_prd(X0,X1,nil,X2) ),
inference(resolution,[status(thm)],[f430,f465]) ).
fof(f490,definition,
! [X0,X1,X2] :
( sQ3_spl
<=> ~ sP0_prd(X0,X1,nil,X2) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f491,plain,
! [X0,X1,X2] :
( ~ sQ3_spl
| ~ sP0_prd(X0,X1,nil,X2) ),
inference(component_clause,[status(thm)],[f490]) ).
fof(f493,definition,
( sQ4_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f495,plain,
( sQ4_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f493]) ).
fof(f496,plain,
( ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f489,f490,f493]) ).
fof(f497,plain,
( ~ sQ0_spl
| ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)) ),
inference(resolution,[status(thm)],[f431,f488]) ).
fof(f500,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f249,f223]) ).
fof(f501,plain,
app(nil,sK48_skl) = sK48_skl,
inference(resolution,[status(thm)],[f249,f420]) ).
fof(f502,plain,
app(nil,sK47_skl) = sK47_skl,
inference(resolution,[status(thm)],[f249,f419]) ).
fof(f503,plain,
( ~ ssList(nil)
| rearsegP(app(nil,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f500,f454]) ).
fof(f504,definition,
( sQ5_spl
<=> rearsegP(app(nil,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( ~ sQ5_spl
| rearsegP(app(nil,nil),nil) ),
inference(component_clause,[status(thm)],[f504]) ).
fof(f507,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f503,f493,f504]) ).
fof(f508,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f495,f223]) ).
fof(f509,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f508]) ).
fof(f510,plain,
( ~ sQ5_spl
| rearsegP(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f500,f505]) ).
fof(f529,plain,
( ~ ssList(nil)
| rearsegP(app(nil,sK48_skl),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f501,f454]) ).
fof(f530,definition,
( sQ10_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f532,plain,
( sQ10_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f530]) ).
fof(f533,definition,
( sQ11_spl
<=> rearsegP(app(nil,sK48_skl),sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f534,plain,
( ~ sQ11_spl
| rearsegP(app(nil,sK48_skl),sK48_skl) ),
inference(component_clause,[status(thm)],[f533]) ).
fof(f536,plain,
( ~ sQ4_spl
| sQ11_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f529,f530,f533,f493]) ).
fof(f537,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f532,f420]) ).
fof(f538,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f537]) ).
fof(f539,plain,
( ~ sQ11_spl
| rearsegP(sK48_skl,sK48_skl) ),
inference(forward_demodulation,[status(thm)],[f501,f534]) ).
fof(f541,plain,
( ~ ssList(nil)
| rearsegP(app(nil,sK47_skl),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f502,f454]) ).
fof(f542,definition,
( sQ12_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f544,plain,
( sQ12_spl
| ~ ssList(sK47_skl) ),
inference(component_clause,[status(thm)],[f542]) ).
fof(f545,definition,
( sQ13_spl
<=> rearsegP(app(nil,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f546,plain,
( ~ sQ13_spl
| rearsegP(app(nil,sK47_skl),sK47_skl) ),
inference(component_clause,[status(thm)],[f545]) ).
fof(f548,plain,
( ~ sQ4_spl
| sQ13_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f541,f542,f545,f493]) ).
fof(f549,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f544,f419]) ).
fof(f550,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f549]) ).
fof(f551,plain,
( ~ sQ13_spl
| rearsegP(sK47_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f502,f546]) ).
fof(f557,plain,
app(sK48_skl,nil) = sK48_skl,
inference(resolution,[status(thm)],[f389,f420]) ).
fof(f558,plain,
app(sK47_skl,nil) = sK47_skl,
inference(resolution,[status(thm)],[f389,f419]) ).
fof(f559,plain,
( ~ ssList(sK48_skl)
| rearsegP(app(sK48_skl,nil),nil)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f557,f454]) ).
fof(f560,definition,
( sQ14_spl
<=> rearsegP(app(sK48_skl,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f561,plain,
( ~ sQ14_spl
| rearsegP(app(sK48_skl,nil),nil) ),
inference(component_clause,[status(thm)],[f560]) ).
fof(f563,plain,
( sQ14_spl
| ~ sQ4_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f559,f530,f493,f560]) ).
fof(f564,plain,
( ~ sQ14_spl
| rearsegP(sK48_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f557,f561]) ).
fof(f565,plain,
( ~ ssList(sK47_skl)
| rearsegP(app(sK47_skl,nil),nil)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f558,f454]) ).
fof(f566,definition,
( sQ15_spl
<=> rearsegP(app(sK47_skl,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f567,plain,
( ~ sQ15_spl
| rearsegP(app(sK47_skl,nil),nil) ),
inference(component_clause,[status(thm)],[f566]) ).
fof(f569,plain,
( sQ15_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f565,f542,f493,f566]) ).
fof(f570,plain,
( ~ sQ15_spl
| rearsegP(sK47_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f558,f567]) ).
fof(f582,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssList(nil)
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) ),
inference(resolution,[status(thm)],[f452,f222]) ).
fof(f583,definition,
! [X0] :
( sQ16_spl
<=> ( ~ ssItem(X0)
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f584,plain,
! [X0] :
( ~ sQ16_spl
| ~ ssItem(X0)
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) ),
inference(component_clause,[status(thm)],[f583]) ).
fof(f586,plain,
( ~ sQ4_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f582,f583,f493]) ).
fof(f587,plain,
! [X0] :
( ~ sQ16_spl
| ~ ssItem(X0)
| singletonP(cons(X0,nil)) ),
inference(duplicate_literals_removal,[status(thm)],[f584]) ).
fof(f588,plain,
! [X0] :
( ~ ssList(X0)
| ssList(sK5_skl(nil,X0))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f122,f295]) ).
fof(f590,definition,
! [X0] :
( sQ17_spl
<=> ( ~ ssList(X0)
| ssList(sK5_skl(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f593,plain,
( ~ sQ4_spl
| sQ17_spl ),
inference(split_clause,[status(thm)],[f588,f590,f493]) ).
fof(f596,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,sK5_skl(nil,X0)) = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f123,f295]) ).
fof(f598,definition,
! [X0] :
( sQ18_spl
<=> ( ~ ssList(X0)
| app(nil,sK5_skl(nil,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f601,plain,
( ~ sQ4_spl
| sQ18_spl ),
inference(split_clause,[status(thm)],[f596,f598,f493]) ).
fof(f608,plain,
( ~ sQ0_spl
| ~ rearsegP(sK48_skl,sK47_skl)
| ~ neq(sK47_skl,nil) ),
inference(resolution,[status(thm)],[f435,f488]) ).
fof(f609,definition,
( sQ19_spl
<=> neq(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f611,plain,
( sQ19_spl
| ~ neq(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f609]) ).
fof(f612,definition,
( sQ20_spl
<=> rearsegP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f615,plain,
( ~ sQ0_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f608,f609,f612,f438]) ).
fof(f617,plain,
( sQ19_spl
| sK47_skl = nil
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f611,f220]) ).
fof(f618,definition,
( sQ21_spl
<=> sK47_skl = nil ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f621,plain,
( sQ19_spl
| sQ21_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f617,f542,f493,f618,f609]) ).
fof(f622,plain,
( ~ sQ0_spl
| cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil) = sK47_skl ),
inference(resolution,[status(thm)],[f433,f488]) ).
fof(f641,plain,
( sQ2_spl
| ~ neq(sK48_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f447]) ).
fof(f650,plain,
( sQ2_spl
| ~ sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f641,f442]) ).
fof(f651,plain,
( sQ2_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f650]) ).
fof(f653,plain,
( sQ1_spl
| sK48_skl = nil
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f443,f220]) ).
fof(f654,definition,
( sQ22_spl
<=> sK48_skl = nil ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f655,plain,
( ~ sQ22_spl
| sK48_skl = nil ),
inference(component_clause,[status(thm)],[f654]) ).
fof(f657,plain,
( sQ1_spl
| sQ22_spl
| ~ sQ4_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f653,f530,f493,f654,f441]) ).
fof(f671,plain,
( ~ ssList(nil)
| frontsegP(app(nil,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f500,f453]) ).
fof(f672,definition,
( sQ23_spl
<=> frontsegP(app(nil,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f673,plain,
( ~ sQ23_spl
| frontsegP(app(nil,nil),nil) ),
inference(component_clause,[status(thm)],[f672]) ).
fof(f675,plain,
( sQ23_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f671,f493,f672]) ).
fof(f676,plain,
( ~ sQ23_spl
| frontsegP(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f500,f673]) ).
fof(f678,plain,
! [X0,X1] :
( app(sK6_skl(X1,X0),nil) = sK6_skl(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f128,f389]) ).
fof(f679,plain,
! [X0,X1] :
( app(nil,sK6_skl(X1,X0)) = sK6_skl(X1,X0)
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f128,f249]) ).
fof(f680,plain,
( ~ sQ13_spl
| app(sK6_skl(sK47_skl,sK47_skl),sK47_skl) = sK47_skl
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f129,f551]) ).
fof(f681,plain,
( ~ sQ15_spl
| app(sK6_skl(nil,sK47_skl),nil) = sK47_skl
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f129,f570]) ).
fof(f682,plain,
( ~ sQ5_spl
| app(sK6_skl(nil,nil),nil) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f129,f510]) ).
fof(f683,plain,
! [X0] :
( ~ ssList(X0)
| app(sK6_skl(nil,X0),nil) = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f129,f309]) ).
fof(f685,definition,
( sQ24_spl
<=> app(sK6_skl(sK47_skl,sK47_skl),sK47_skl) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f686,plain,
( ~ sQ24_spl
| app(sK6_skl(sK47_skl,sK47_skl),sK47_skl) = sK47_skl ),
inference(component_clause,[status(thm)],[f685]) ).
fof(f688,plain,
( ~ sQ13_spl
| sQ24_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f680,f542,f685,f545]) ).
fof(f689,definition,
( sQ25_spl
<=> app(sK6_skl(nil,sK47_skl),nil) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f690,plain,
( ~ sQ25_spl
| app(sK6_skl(nil,sK47_skl),nil) = sK47_skl ),
inference(component_clause,[status(thm)],[f689]) ).
fof(f692,plain,
( ~ sQ15_spl
| sQ25_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f681,f542,f493,f689,f566]) ).
fof(f693,definition,
( sQ26_spl
<=> app(sK6_skl(nil,nil),nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f694,plain,
( ~ sQ26_spl
| app(sK6_skl(nil,nil),nil) = nil ),
inference(component_clause,[status(thm)],[f693]) ).
fof(f696,plain,
( ~ sQ5_spl
| sQ26_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f682,f493,f693,f504]) ).
fof(f697,definition,
! [X0] :
( sQ27_spl
<=> ( ~ ssList(X0)
| app(sK6_skl(nil,X0),nil) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f700,plain,
( ~ sQ4_spl
| sQ27_spl ),
inference(split_clause,[status(thm)],[f683,f697,f493]) ).
fof(f705,definition,
( sQ28_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f710,plain,
( ~ sQ23_spl
| app(nil,sK5_skl(nil,nil)) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f676,f123]) ).
fof(f711,plain,
( ~ sQ23_spl
| ssList(sK5_skl(nil,nil))
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f676,f122]) ).
fof(f712,definition,
( sQ29_spl
<=> app(nil,sK5_skl(nil,nil)) = nil ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f713,plain,
( ~ sQ29_spl
| app(nil,sK5_skl(nil,nil)) = nil ),
inference(component_clause,[status(thm)],[f712]) ).
fof(f715,plain,
( ~ sQ23_spl
| sQ29_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f710,f493,f712,f672]) ).
fof(f716,definition,
( sQ30_spl
<=> ssList(sK5_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f719,plain,
( ~ sQ23_spl
| sQ30_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f711,f493,f716,f672]) ).
fof(f720,plain,
( ~ ssList(nil)
| frontsegP(app(sK47_skl,nil),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f558,f453]) ).
fof(f722,definition,
( sQ31_spl
<=> frontsegP(app(sK47_skl,nil),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f723,plain,
( ~ sQ31_spl
| frontsegP(app(sK47_skl,nil),sK47_skl) ),
inference(component_clause,[status(thm)],[f722]) ).
fof(f725,plain,
( ~ sQ4_spl
| sQ31_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f720,f542,f722,f493]) ).
fof(f727,plain,
( ~ sQ31_spl
| frontsegP(sK47_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f558,f723]) ).
fof(f728,plain,
( ~ sQ31_spl
| app(sK47_skl,sK5_skl(sK47_skl,sK47_skl)) = sK47_skl
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f727,f123]) ).
fof(f729,plain,
( ~ sQ31_spl
| ssList(sK5_skl(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f727,f122]) ).
fof(f730,definition,
( sQ32_spl
<=> app(sK47_skl,sK5_skl(sK47_skl,sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f731,plain,
( ~ sQ32_spl
| app(sK47_skl,sK5_skl(sK47_skl,sK47_skl)) = sK47_skl ),
inference(component_clause,[status(thm)],[f730]) ).
fof(f733,plain,
( ~ sQ31_spl
| sQ32_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f728,f542,f730,f722]) ).
fof(f734,definition,
( sQ33_spl
<=> ssList(sK5_skl(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f737,plain,
( ~ sQ31_spl
| sQ33_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f729,f542,f734,f722]) ).
fof(f738,plain,
( ~ ssList(sK47_skl)
| frontsegP(app(nil,sK47_skl),nil)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f502,f453]) ).
fof(f740,definition,
( sQ34_spl
<=> frontsegP(app(nil,sK47_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f741,plain,
( ~ sQ34_spl
| frontsegP(app(nil,sK47_skl),nil) ),
inference(component_clause,[status(thm)],[f740]) ).
fof(f743,plain,
( sQ34_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f738,f542,f493,f740]) ).
fof(f745,plain,
( ~ sQ34_spl
| frontsegP(sK47_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f502,f741]) ).
fof(f746,plain,
( ~ sQ34_spl
| app(nil,sK5_skl(nil,sK47_skl)) = sK47_skl
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f745,f123]) ).
fof(f747,plain,
( ~ sQ34_spl
| ssList(sK5_skl(nil,sK47_skl))
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f745,f122]) ).
fof(f748,definition,
( sQ35_spl
<=> app(nil,sK5_skl(nil,sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f749,plain,
( ~ sQ35_spl
| app(nil,sK5_skl(nil,sK47_skl)) = sK47_skl ),
inference(component_clause,[status(thm)],[f748]) ).
fof(f751,plain,
( ~ sQ34_spl
| sQ35_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f746,f542,f493,f748,f740]) ).
fof(f752,definition,
( sQ36_spl
<=> ssList(sK5_skl(nil,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f755,plain,
( ~ sQ34_spl
| sQ36_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f747,f542,f493,f752,f740]) ).
fof(f756,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f453,f245]) ).
fof(f757,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(app(X1,X0),X0)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f454,f245]) ).
fof(f758,plain,
! [X0,X1,X2] :
( ~ rearsegP(X2,X1)
| ~ ssList(X1)
| ~ ssList(X2)
| ssList(app(X0,sK6_skl(X1,X2)))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f245,f128]) ).
fof(f759,plain,
! [X0] :
( ssList(app(X0,sK47_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f245,f419]) ).
fof(f764,plain,
! [X0] :
( ssList(app(X0,nil))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f245,f223]) ).
fof(f789,plain,
! [X0] :
( ~ ssList(X0)
| ssList(sK7_skl(nil,X0))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f134,f323]) ).
fof(f791,definition,
! [X0] :
( sQ37_spl
<=> ( ~ ssList(X0)
| ssList(sK7_skl(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f794,plain,
( ~ sQ4_spl
| sQ37_spl ),
inference(split_clause,[status(thm)],[f789,f791,f493]) ).
fof(f797,plain,
! [X0] :
( ~ ssList(X0)
| ssList(sK8_skl(nil,X0))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f135,f323]) ).
fof(f799,definition,
! [X0] :
( sQ38_spl
<=> ( ~ ssList(X0)
| ssList(sK8_skl(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f802,plain,
( ~ sQ4_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f797,f799,f493]) ).
fof(f805,plain,
! [X0] :
( ~ ssList(X0)
| app(app(sK7_skl(nil,X0),nil),sK8_skl(nil,X0)) = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f136,f323]) ).
fof(f807,definition,
! [X0] :
( sQ39_spl
<=> ( ~ ssList(X0)
| app(app(sK7_skl(nil,X0),nil),sK8_skl(nil,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f810,plain,
( ~ sQ4_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f805,f807,f493]) ).
fof(f813,plain,
( ~ sQ0_spl
| ~ sQ22_spl
| sP0_prd(nil,sK47_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f655,f488]) ).
fof(f814,plain,
( ~ sQ0_spl
| ~ sQ22_spl
| sP0_prd(nil,sK47_skl,nil,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f655,f813]) ).
fof(f815,plain,
( ~ sQ0_spl
| ~ sQ22_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f814,f491]) ).
fof(f816,plain,
( ~ sQ0_spl
| ~ sQ22_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f815]) ).
fof(f818,plain,
! [X0] :
( ssList(app(X0,sK48_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f420,f245]) ).
fof(f822,plain,
! [X0,X1,X2] :
( ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ neq(X2,nil)
| sP0_prd(app(X0,cons(X1,nil)),cons(X1,nil),X2,nil) ),
inference(resolution,[status(thm)],[f479,f465]) ).
fof(f823,definition,
! [X0,X1,X2] :
( sQ40_spl
<=> ( ~ ssList(X0)
| ~ ssItem(X1)
| ~ neq(X2,nil)
| sP0_prd(app(X0,cons(X1,nil)),cons(X1,nil),X2,nil) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f826,plain,
( ~ sQ4_spl
| sQ40_spl ),
inference(split_clause,[status(thm)],[f822,f823,f493]) ).
fof(f827,plain,
( ~ sQ14_spl
| app(sK6_skl(nil,sK48_skl),nil) = sK48_skl
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f564,f129]) ).
fof(f828,definition,
( sQ41_spl
<=> app(sK6_skl(nil,sK48_skl),nil) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f829,plain,
( ~ sQ41_spl
| app(sK6_skl(nil,sK48_skl),nil) = sK48_skl ),
inference(component_clause,[status(thm)],[f828]) ).
fof(f831,plain,
( ~ sQ14_spl
| sQ41_spl
| ~ sQ4_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f827,f530,f493,f828,f560]) ).
fof(f832,plain,
( ~ sQ11_spl
| app(sK6_skl(sK48_skl,sK48_skl),sK48_skl) = sK48_skl
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f539,f129]) ).
fof(f833,definition,
( sQ42_spl
<=> app(sK6_skl(sK48_skl,sK48_skl),sK48_skl) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f834,plain,
( ~ sQ42_spl
| app(sK6_skl(sK48_skl,sK48_skl),sK48_skl) = sK48_skl ),
inference(component_clause,[status(thm)],[f833]) ).
fof(f836,plain,
( ~ sQ11_spl
| sQ42_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f832,f530,f833,f533]) ).
fof(f846,plain,
( ~ sQ11_spl
| sK48_skl = sK48_skl
| ~ rearsegP(sK48_skl,sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f303,f539]) ).
fof(f848,plain,
( ~ sQ13_spl
| sK47_skl = sK47_skl
| ~ rearsegP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f303,f551]) ).
fof(f851,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f303,f309]) ).
fof(f854,definition,
( sQ44_spl
<=> rearsegP(sK48_skl,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f856,plain,
( sQ44_spl
| ~ rearsegP(sK48_skl,sK48_skl) ),
inference(component_clause,[status(thm)],[f854]) ).
fof(f857,definition,
( sQ45_spl
<=> sK48_skl = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f860,plain,
( ~ sQ11_spl
| sQ45_spl
| ~ sQ44_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f846,f530,f854,f857,f533]) ).
fof(f865,definition,
( sQ47_spl
<=> rearsegP(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f867,plain,
( sQ47_spl
| ~ rearsegP(sK47_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f865]) ).
fof(f868,definition,
( sQ48_spl
<=> sK47_skl = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f871,plain,
( ~ sQ13_spl
| sQ48_spl
| ~ sQ47_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f848,f542,f865,f868,f545]) ).
fof(f876,definition,
( sQ50_spl
<=> rearsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f880,definition,
! [X0] :
( sQ51_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f883,plain,
( sQ51_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f851,f493,f880]) ).
fof(f886,plain,
( sQ47_spl
| ~ sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f867,f551]) ).
fof(f887,plain,
( sQ47_spl
| ~ sQ13_spl ),
inference(contradiction_clause,[status(thm)],[f886]) ).
fof(f888,plain,
( sQ44_spl
| ~ sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f856,f539]) ).
fof(f889,plain,
( sQ44_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f888]) ).
fof(f933,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(nil,X0)) ),
inference(paramodulation,[status(thm)],[f500,f455]) ).
fof(f934,definition,
! [X0] :
( sQ54_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f937,plain,
( ~ sQ4_spl
| sQ54_spl ),
inference(split_clause,[status(thm)],[f933,f934,f493]) ).
fof(f943,plain,
! [X0,X1,X2] :
( rearsegP(X1,X2)
| ~ ssList(X0)
| ~ neq(X1,nil)
| sP0_prd(app(X0,cons(sK1_skl,nil)),cons(sK1_skl,nil),X1,X2) ),
inference(resolution,[status(thm)],[f480,f104]) ).
fof(f944,plain,
! [X0,X1,X2] :
( rearsegP(X1,X2)
| ~ ssList(X0)
| ~ neq(X1,nil)
| sP0_prd(app(X0,cons(sK0_skl,nil)),cons(sK0_skl,nil),X1,X2) ),
inference(resolution,[status(thm)],[f480,f103]) ).
fof(f965,plain,
! [X0] :
( rearsegP(nil,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f500,f307]) ).
fof(f970,definition,
! [X0] :
( sQ55_spl
<=> ( rearsegP(nil,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f973,plain,
( sQ55_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f965,f493,f970]) ).
fof(f975,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f312,f309]) ).
fof(f976,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(f979,plain,
( sQ28_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f975,f493,f705]) ).
fof(f980,definition,
! [X0,X1] :
( sQ56_spl
<=> ( ~ rearsegP(X1,X0)
| ~ rearsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f983,plain,
( ~ sQ4_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f976,f980,f493]) ).
fof(f986,plain,
! [X0] :
( rearsegP(sK48_skl,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(sK48_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f557,f307]) ).
fof(f987,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK48_skl)
| segmentP(app(app(sK48_skl,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f557,f455]) ).
fof(f988,definition,
! [X0] :
( sQ57_spl
<=> ( rearsegP(sK48_skl,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f991,plain,
( ~ sQ10_spl
| sQ57_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f986,f493,f988,f530]) ).
fof(f992,definition,
! [X0] :
( sQ58_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK48_skl,nil),X0),nil)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f995,plain,
( ~ sQ10_spl
| ~ sQ4_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f987,f992,f493,f530]) ).
fof(f998,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK48_skl),X0),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f501,f455]) ).
fof(f999,definition,
! [X0] :
( sQ59_spl
<=> ( rearsegP(sK48_skl,X0)
| ~ rearsegP(sK48_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1003,definition,
! [X0] :
( sQ60_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK48_skl),X0),sK48_skl)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f1006,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| sQ60_spl ),
inference(split_clause,[status(thm)],[f998,f1003,f530,f493]) ).
fof(f1025,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK47_skl),X0),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f502,f455]) ).
fof(f1026,definition,
! [X0] :
( sQ61_spl
<=> ( rearsegP(sK47_skl,X0)
| ~ rearsegP(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1030,definition,
! [X0] :
( sQ62_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK47_skl),X0),sK47_skl)
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1033,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f1025,f1030,f542,f493]) ).
fof(f1036,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK47_skl)
| segmentP(app(app(sK47_skl,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f558,f455]) ).
fof(f1037,definition,
! [X0] :
( sQ63_spl
<=> ( rearsegP(sK47_skl,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1041,definition,
! [X0] :
( sQ64_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK47_skl,nil),X0),nil)
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1044,plain,
( ~ sQ12_spl
| ~ sQ4_spl
| sQ64_spl ),
inference(split_clause,[status(thm)],[f1036,f1041,f493,f542]) ).
fof(f1046,plain,
( ~ sQ0_spl
| app(sK52_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),cons(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),nil)) = sK48_skl ),
inference(resolution,[status(thm)],[f488,f434]) ).
fof(f1052,plain,
! [X0,X1] :
( X1 = X0
| app(X1,sK47_skl) != app(X0,sK47_skl)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f376,f419]) ).
fof(f1053,plain,
! [X0] :
( sK48_skl = X0
| app(sK48_skl,sK48_skl) != app(X0,sK48_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f376,f420]) ).
fof(f1054,plain,
! [X0,X1] :
( X1 = X0
| app(X1,sK48_skl) != app(X0,sK48_skl)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f376,f420]) ).
fof(f1162,plain,
! [X0,X1] :
( ~ ssList(sK47_skl)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),sK47_skl),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(resolution,[status(thm)],[f759,f455]) ).
fof(f1177,definition,
! [X0,X1] :
( sQ65_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(X0,X1),sK47_skl),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1180,plain,
( ~ sQ12_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f1162,f1177,f542]) ).
fof(f1183,plain,
! [X0,X1] :
( ~ ssList(sK48_skl)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),sK48_skl),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(resolution,[status(thm)],[f818,f455]) ).
fof(f1198,definition,
! [X0,X1] :
( sQ66_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(X0,X1),sK48_skl),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1201,plain,
( ~ sQ10_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f1183,f1198,f530]) ).
fof(f1309,plain,
! [X0,X1] :
( ~ ssList(nil)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),nil),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(resolution,[status(thm)],[f764,f455]) ).
fof(f1332,definition,
! [X0,X1] :
( sQ67_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(X0,X1),nil),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1335,plain,
( ~ sQ4_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f1309,f1332,f493]) ).
fof(f1388,plain,
! [X0] :
( ~ sQ24_spl
| rearsegP(sK47_skl,X0)
| ~ rearsegP(sK47_skl,X0)
| ~ ssList(sK6_skl(sK47_skl,sK47_skl))
| ~ ssList(X0)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f686,f307]) ).
fof(f1389,plain,
! [X0] :
( ~ sQ24_spl
| ~ ssList(X0)
| ~ ssList(sK6_skl(sK47_skl,sK47_skl))
| segmentP(app(app(sK6_skl(sK47_skl,sK47_skl),sK47_skl),X0),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f686,f455]) ).
fof(f1390,definition,
( sQ68_spl
<=> ssList(sK6_skl(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1392,plain,
( sQ68_spl
| ~ ssList(sK6_skl(sK47_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1390]) ).
fof(f1394,plain,
( ~ sQ24_spl
| ~ sQ68_spl
| sQ61_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1388,f542,f1026,f1390,f685]) ).
fof(f1395,definition,
! [X0] :
( sQ69_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK6_skl(sK47_skl,sK47_skl),sK47_skl),X0),sK47_skl)
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1398,plain,
( ~ sQ24_spl
| ~ sQ68_spl
| ~ sQ12_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f1389,f1395,f542,f1390,f685]) ).
fof(f1399,plain,
( sQ68_spl
| ~ rearsegP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1392,f128]) ).
fof(f1400,plain,
( sQ68_spl
| ~ sQ47_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1399,f542,f865,f1390]) ).
fof(f1503,definition,
( sQ79_spl
<=> nil = sK5_skl(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1586,plain,
! [X0] :
( ~ sQ25_spl
| rearsegP(sK47_skl,X0)
| ~ rearsegP(nil,X0)
| ~ ssList(sK6_skl(nil,sK47_skl))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f690,f307]) ).
fof(f1587,plain,
! [X0] :
( ~ sQ25_spl
| ~ ssList(X0)
| ~ ssList(sK6_skl(nil,sK47_skl))
| segmentP(app(app(sK6_skl(nil,sK47_skl),nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f690,f455]) ).
fof(f1588,definition,
( sQ83_spl
<=> ssList(sK6_skl(nil,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1590,plain,
( sQ83_spl
| ~ ssList(sK6_skl(nil,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1588]) ).
fof(f1592,plain,
( ~ sQ25_spl
| ~ sQ83_spl
| sQ63_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1586,f493,f1037,f1588,f689]) ).
fof(f1593,definition,
! [X0] :
( sQ84_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK6_skl(nil,sK47_skl),nil),X0),nil)
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1596,plain,
( ~ sQ25_spl
| ~ sQ83_spl
| ~ sQ4_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f1587,f1593,f493,f1588,f689]) ).
fof(f1597,plain,
( sQ83_spl
| ~ rearsegP(sK47_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1590,f128]) ).
fof(f1598,definition,
( sQ85_spl
<=> rearsegP(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1600,plain,
( sQ85_spl
| ~ rearsegP(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f1598]) ).
fof(f1601,plain,
( sQ83_spl
| ~ sQ85_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1597,f542,f493,f1598,f1588]) ).
fof(f1602,plain,
( sQ85_spl
| ~ sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1600,f570]) ).
fof(f1603,plain,
( sQ85_spl
| ~ sQ15_spl ),
inference(contradiction_clause,[status(thm)],[f1602]) ).
fof(f1640,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))
| singletonP(sK47_skl) ),
inference(paramodulation,[status(thm)],[f622,f587]) ).
fof(f1651,definition,
( sQ88_spl
<=> ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1653,plain,
( sQ88_spl
| ~ ssItem(sK51_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1651]) ).
fof(f1666,definition,
( sQ92_spl
<=> singletonP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1667,plain,
( ~ sQ92_spl
| singletonP(sK47_skl) ),
inference(component_clause,[status(thm)],[f1666]) ).
fof(f1669,plain,
( ~ sQ0_spl
| ~ sQ16_spl
| ~ sQ88_spl
| sQ92_spl ),
inference(split_clause,[status(thm)],[f1640,f1666,f1651,f583,f438]) ).
fof(f1707,plain,
( sQ88_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1653,f497]) ).
fof(f1708,plain,
( sQ88_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1707]) ).
fof(f1715,plain,
( ~ sQ92_spl
| cons(sK4_skl(sK47_skl),nil) = sK47_skl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1667,f117]) ).
fof(f1716,plain,
( ~ sQ92_spl
| ssItem(sK4_skl(sK47_skl))
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1667,f116]) ).
fof(f1717,definition,
( sQ102_spl
<=> cons(sK4_skl(sK47_skl),nil) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1718,plain,
( ~ sQ102_spl
| cons(sK4_skl(sK47_skl),nil) = sK47_skl ),
inference(component_clause,[status(thm)],[f1717]) ).
fof(f1720,plain,
( ~ sQ92_spl
| sQ102_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1715,f542,f1717,f1666]) ).
fof(f1721,definition,
( sQ103_spl
<=> ssItem(sK4_skl(sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1722,plain,
( ~ sQ103_spl
| ssItem(sK4_skl(sK47_skl)) ),
inference(component_clause,[status(thm)],[f1721]) ).
fof(f1724,plain,
( ~ sQ92_spl
| sQ103_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1716,f542,f1721,f1666]) ).
fof(f1727,plain,
( ~ sQ25_spl
| ~ ssList(nil)
| frontsegP(sK47_skl,sK6_skl(nil,sK47_skl))
| ~ ssList(sK6_skl(nil,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f690,f756]) ).
fof(f1728,plain,
( ~ sQ24_spl
| ~ ssList(sK47_skl)
| frontsegP(sK47_skl,sK6_skl(sK47_skl,sK47_skl))
| ~ ssList(sK6_skl(sK47_skl,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f686,f756]) ).
fof(f1730,plain,
( ~ ssList(nil)
| frontsegP(sK48_skl,sK48_skl)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f557,f756]) ).
fof(f1732,plain,
( ~ ssList(sK48_skl)
| frontsegP(sK48_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f501,f756]) ).
fof(f1733,plain,
( ~ ssList(nil)
| frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f500,f756]) ).
fof(f1738,definition,
( sQ104_spl
<=> frontsegP(sK47_skl,sK6_skl(nil,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1741,plain,
( ~ sQ25_spl
| ~ sQ4_spl
| sQ104_spl
| ~ sQ83_spl ),
inference(split_clause,[status(thm)],[f1727,f1588,f1738,f493,f689]) ).
fof(f1742,definition,
( sQ105_spl
<=> frontsegP(sK47_skl,sK6_skl(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1743,plain,
( ~ sQ105_spl
| frontsegP(sK47_skl,sK6_skl(sK47_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1742]) ).
fof(f1745,plain,
( ~ sQ24_spl
| ~ sQ12_spl
| sQ105_spl
| ~ sQ68_spl ),
inference(split_clause,[status(thm)],[f1728,f1390,f1742,f542,f685]) ).
fof(f1746,definition,
( sQ106_spl
<=> frontsegP(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1750,definition,
( sQ107_spl
<=> frontsegP(sK48_skl,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1751,plain,
( ~ sQ107_spl
| frontsegP(sK48_skl,sK48_skl) ),
inference(component_clause,[status(thm)],[f1750]) ).
fof(f1753,plain,
( ~ sQ4_spl
| sQ107_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1730,f530,f1750,f493]) ).
fof(f1754,definition,
( sQ108_spl
<=> frontsegP(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1758,definition,
( sQ109_spl
<=> frontsegP(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1759,plain,
( ~ sQ109_spl
| frontsegP(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f1758]) ).
fof(f1761,plain,
( ~ sQ10_spl
| sQ109_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1732,f493,f1758,f530]) ).
fof(f1762,definition,
( sQ110_spl
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1765,plain,
( sQ110_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1733,f493,f1762]) ).
fof(f1771,plain,
( ~ ssList(sK48_skl)
| rearsegP(sK48_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f557,f757]) ).
fof(f1774,plain,
( ~ ssList(nil)
| rearsegP(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f500,f757]) ).
fof(f1782,definition,
( sQ111_spl
<=> rearsegP(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1785,plain,
( ~ sQ10_spl
| sQ111_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1771,f493,f1782,f530]) ).
fof(f1788,plain,
( sQ50_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1774,f493,f876]) ).
fof(f1792,plain,
! [X0] :
( ~ sQ103_spl
| nil != cons(sK4_skl(sK47_skl),X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1722,f235]) ).
fof(f1798,plain,
( ~ sQ107_spl
| app(sK48_skl,sK5_skl(sK48_skl,sK48_skl)) = sK48_skl
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1751,f123]) ).
fof(f1799,plain,
( ~ sQ107_spl
| ssList(sK5_skl(sK48_skl,sK48_skl))
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1751,f122]) ).
fof(f1800,definition,
( sQ112_spl
<=> app(sK48_skl,sK5_skl(sK48_skl,sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1801,plain,
( ~ sQ112_spl
| app(sK48_skl,sK5_skl(sK48_skl,sK48_skl)) = sK48_skl ),
inference(component_clause,[status(thm)],[f1800]) ).
fof(f1803,plain,
( ~ sQ107_spl
| sQ112_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1798,f530,f1800,f1750]) ).
fof(f1804,definition,
( sQ113_spl
<=> ssList(sK5_skl(sK48_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1807,plain,
( ~ sQ107_spl
| sQ113_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1799,f530,f1804,f1750]) ).
fof(f1808,plain,
( ~ sQ109_spl
| app(nil,sK5_skl(nil,sK48_skl)) = sK48_skl
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1759,f123]) ).
fof(f1809,plain,
( ~ sQ109_spl
| ssList(sK5_skl(nil,sK48_skl))
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1759,f122]) ).
fof(f1810,definition,
( sQ114_spl
<=> app(nil,sK5_skl(nil,sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1811,plain,
( ~ sQ114_spl
| app(nil,sK5_skl(nil,sK48_skl)) = sK48_skl ),
inference(component_clause,[status(thm)],[f1810]) ).
fof(f1813,plain,
( ~ sQ109_spl
| sQ114_spl
| ~ sQ4_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1808,f530,f493,f1810,f1758]) ).
fof(f1814,definition,
( sQ115_spl
<=> ssList(sK5_skl(nil,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f1815,plain,
( ~ sQ115_spl
| ssList(sK5_skl(nil,sK48_skl)) ),
inference(component_clause,[status(thm)],[f1814]) ).
fof(f1817,plain,
( ~ sQ109_spl
| sQ115_spl
| ~ sQ4_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f1809,f530,f493,f1814,f1758]) ).
fof(f1856,plain,
! [X0] :
( ~ sQ115_spl
| nil = sK5_skl(nil,sK48_skl)
| nil != app(X0,sK5_skl(nil,sK48_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1815,f385]) ).
fof(f1877,definition,
! [X0] :
( sQ118_spl
<=> ( nil != app(X0,sK5_skl(nil,sK48_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1878,plain,
! [X0] :
( ~ sQ118_spl
| nil != app(X0,sK5_skl(nil,sK48_skl))
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1877]) ).
fof(f1880,definition,
( sQ119_spl
<=> nil = sK5_skl(nil,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f1881,plain,
( ~ sQ119_spl
| nil = sK5_skl(nil,sK48_skl) ),
inference(component_clause,[status(thm)],[f1880]) ).
fof(f1883,plain,
( ~ sQ115_spl
| sQ119_spl
| sQ118_spl ),
inference(split_clause,[status(thm)],[f1856,f1877,f1880,f1814]) ).
fof(f1936,plain,
( ~ sQ105_spl
| app(sK6_skl(sK47_skl,sK47_skl),sK5_skl(sK6_skl(sK47_skl,sK47_skl),sK47_skl)) = sK47_skl
| ~ ssList(sK6_skl(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1743,f123]) ).
fof(f1937,plain,
( ~ sQ105_spl
| ssList(sK5_skl(sK6_skl(sK47_skl,sK47_skl),sK47_skl))
| ~ ssList(sK6_skl(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1743,f122]) ).
fof(f1938,definition,
( sQ125_spl
<=> app(sK6_skl(sK47_skl,sK47_skl),sK5_skl(sK6_skl(sK47_skl,sK47_skl),sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1941,plain,
( ~ sQ105_spl
| sQ125_spl
| ~ sQ68_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1936,f542,f1390,f1938,f1742]) ).
fof(f1942,definition,
( sQ126_spl
<=> ssList(sK5_skl(sK6_skl(sK47_skl,sK47_skl),sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1945,plain,
( ~ sQ105_spl
| sQ126_spl
| ~ sQ68_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1937,f542,f1390,f1942,f1742]) ).
fof(f1982,plain,
( ~ sQ26_spl
| ~ ssList(nil)
| frontsegP(nil,sK6_skl(nil,nil))
| ~ ssList(sK6_skl(nil,nil)) ),
inference(paramodulation,[status(thm)],[f694,f756]) ).
fof(f1984,plain,
! [X0] :
( ~ sQ26_spl
| ~ ssList(X0)
| ~ ssList(sK6_skl(nil,nil))
| segmentP(app(app(sK6_skl(nil,nil),nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(nil,X0)) ),
inference(paramodulation,[status(thm)],[f694,f455]) ).
fof(f1985,definition,
( sQ129_spl
<=> ssList(sK6_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f1986,plain,
( ~ sQ129_spl
| ssList(sK6_skl(nil,nil)) ),
inference(component_clause,[status(thm)],[f1985]) ).
fof(f1987,plain,
( sQ129_spl
| ~ ssList(sK6_skl(nil,nil)) ),
inference(component_clause,[status(thm)],[f1985]) ).
fof(f1990,definition,
( sQ130_spl
<=> frontsegP(nil,sK6_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1993,plain,
( ~ sQ26_spl
| ~ sQ4_spl
| sQ130_spl
| ~ sQ129_spl ),
inference(split_clause,[status(thm)],[f1982,f1985,f1990,f493,f693]) ).
fof(f1995,definition,
! [X0] :
( sQ131_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK6_skl(nil,nil),nil),X0),nil)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1998,plain,
( ~ sQ26_spl
| ~ sQ129_spl
| ~ sQ4_spl
| sQ131_spl ),
inference(split_clause,[status(thm)],[f1984,f1995,f493,f1985,f693]) ).
fof(f1999,plain,
( sQ129_spl
| ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1987,f128]) ).
fof(f2000,plain,
( sQ129_spl
| ~ sQ50_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f1999,f493,f876,f1985]) ).
fof(f2006,plain,
! [X0] :
( ~ sQ129_spl
| nil = sK6_skl(nil,nil)
| nil != app(X0,sK6_skl(nil,nil))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1986,f385]) ).
fof(f2027,definition,
! [X0] :
( sQ132_spl
<=> ( nil != app(X0,sK6_skl(nil,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f2030,definition,
( sQ133_spl
<=> nil = sK6_skl(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f2033,plain,
( ~ sQ129_spl
| sQ133_spl
| sQ132_spl ),
inference(split_clause,[status(thm)],[f2006,f2027,f2030,f1985]) ).
fof(f2040,plain,
( ~ sQ32_spl
| ~ ssList(sK47_skl)
| rearsegP(sK47_skl,sK5_skl(sK47_skl,sK47_skl))
| ~ ssList(sK5_skl(sK47_skl,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f731,f757]) ).
fof(f2041,plain,
( ~ sQ32_spl
| ~ ssList(sK5_skl(sK47_skl,sK47_skl))
| frontsegP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f731,f756]) ).
fof(f2042,plain,
! [X0] :
( ~ sQ32_spl
| rearsegP(sK47_skl,X0)
| ~ rearsegP(sK5_skl(sK47_skl,sK47_skl),X0)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(sK5_skl(sK47_skl,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f731,f307]) ).
fof(f2043,plain,
! [X0] :
( ~ sQ32_spl
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| segmentP(app(app(sK47_skl,sK5_skl(sK47_skl,sK47_skl)),X0),sK5_skl(sK47_skl,sK47_skl))
| ~ ssList(sK5_skl(sK47_skl,sK47_skl))
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f731,f455]) ).
fof(f2044,definition,
( sQ134_spl
<=> rearsegP(sK47_skl,sK5_skl(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f2045,plain,
( ~ sQ134_spl
| rearsegP(sK47_skl,sK5_skl(sK47_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f2044]) ).
fof(f2047,plain,
( ~ sQ32_spl
| ~ sQ12_spl
| sQ134_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f2040,f734,f2044,f542,f730]) ).
fof(f2048,plain,
( ~ sQ32_spl
| ~ sQ33_spl
| sQ106_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f2041,f542,f1746,f734,f730]) ).
fof(f2049,definition,
! [X0] :
( sQ135_spl
<=> ( rearsegP(sK47_skl,X0)
| ~ rearsegP(sK5_skl(sK47_skl,sK47_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f2052,plain,
( ~ sQ32_spl
| ~ sQ12_spl
| sQ135_spl
| ~ sQ33_spl ),
inference(split_clause,[status(thm)],[f2042,f734,f2049,f542,f730]) ).
fof(f2053,definition,
! [X0] :
( sQ136_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK47_skl,sK5_skl(sK47_skl,sK47_skl)),X0),sK5_skl(sK47_skl,sK47_skl))
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f2056,plain,
( ~ sQ32_spl
| ~ sQ12_spl
| ~ sQ33_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f2043,f2053,f734,f542,f730]) ).
fof(f2059,plain,
( ~ sQ134_spl
| app(sK6_skl(sK5_skl(sK47_skl,sK47_skl),sK47_skl),sK5_skl(sK47_skl,sK47_skl)) = sK47_skl
| ~ ssList(sK5_skl(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2045,f129]) ).
fof(f2067,definition,
( sQ139_spl
<=> app(sK6_skl(sK5_skl(sK47_skl,sK47_skl),sK47_skl),sK5_skl(sK47_skl,sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f2070,plain,
( ~ sQ134_spl
| sQ139_spl
| ~ sQ33_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f2059,f542,f734,f2067,f2044]) ).
fof(f2104,plain,
( ~ sQ29_spl
| ~ ssList(nil)
| rearsegP(nil,sK5_skl(nil,nil))
| ~ ssList(sK5_skl(nil,nil)) ),
inference(paramodulation,[status(thm)],[f713,f757]) ).
fof(f2106,plain,
! [X0] :
( ~ sQ29_spl
| rearsegP(nil,X0)
| ~ rearsegP(sK5_skl(nil,nil),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK5_skl(nil,nil)) ),
inference(paramodulation,[status(thm)],[f713,f307]) ).
fof(f2107,plain,
! [X0] :
( ~ sQ29_spl
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK5_skl(nil,nil)),X0),sK5_skl(nil,nil))
| ~ ssList(sK5_skl(nil,nil))
| ~ ssList(app(nil,X0)) ),
inference(paramodulation,[status(thm)],[f713,f455]) ).
fof(f2108,definition,
( sQ142_spl
<=> rearsegP(nil,sK5_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f2109,plain,
( ~ sQ142_spl
| rearsegP(nil,sK5_skl(nil,nil)) ),
inference(component_clause,[status(thm)],[f2108]) ).
fof(f2111,plain,
( ~ sQ29_spl
| ~ sQ4_spl
| sQ142_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2104,f716,f2108,f493,f712]) ).
fof(f2113,definition,
! [X0] :
( sQ143_spl
<=> ( rearsegP(nil,X0)
| ~ rearsegP(sK5_skl(nil,nil),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f2116,plain,
( ~ sQ29_spl
| ~ sQ4_spl
| sQ143_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2106,f716,f2113,f493,f712]) ).
fof(f2117,definition,
! [X0] :
( sQ144_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK5_skl(nil,nil)),X0),sK5_skl(nil,nil))
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f2120,plain,
( ~ sQ29_spl
| ~ sQ4_spl
| ~ sQ30_spl
| sQ144_spl ),
inference(split_clause,[status(thm)],[f2107,f2117,f716,f493,f712]) ).
fof(f2122,plain,
( ~ sQ142_spl
| nil = sK5_skl(nil,nil)
| ~ ssList(sK5_skl(nil,nil)) ),
inference(resolution,[status(thm)],[f2109,f312]) ).
fof(f2124,plain,
( ~ sQ142_spl
| app(sK6_skl(sK5_skl(nil,nil),nil),sK5_skl(nil,nil)) = nil
| ~ ssList(sK5_skl(nil,nil))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2109,f129]) ).
fof(f2125,plain,
( ~ sQ142_spl
| sQ79_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2122,f716,f1503,f2108]) ).
fof(f2130,definition,
( sQ146_spl
<=> app(sK6_skl(sK5_skl(nil,nil),nil),sK5_skl(nil,nil)) = nil ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f2133,plain,
( ~ sQ142_spl
| sQ146_spl
| ~ sQ30_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f2124,f493,f716,f2130,f2108]) ).
fof(f2141,plain,
( ~ sQ35_spl
| ~ ssList(nil)
| rearsegP(sK47_skl,sK5_skl(nil,sK47_skl))
| ~ ssList(sK5_skl(nil,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f749,f757]) ).
fof(f2142,plain,
( ~ sQ35_spl
| ~ ssList(sK5_skl(nil,sK47_skl))
| frontsegP(sK47_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f749,f756]) ).
fof(f2143,plain,
! [X0] :
( ~ sQ35_spl
| rearsegP(sK47_skl,X0)
| ~ rearsegP(sK5_skl(nil,sK47_skl),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK5_skl(nil,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f749,f307]) ).
fof(f2144,plain,
! [X0] :
( ~ sQ35_spl
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK5_skl(nil,sK47_skl)),X0),sK5_skl(nil,sK47_skl))
| ~ ssList(sK5_skl(nil,sK47_skl))
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f749,f455]) ).
fof(f2145,definition,
( sQ147_spl
<=> rearsegP(sK47_skl,sK5_skl(nil,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f2146,plain,
( ~ sQ147_spl
| rearsegP(sK47_skl,sK5_skl(nil,sK47_skl)) ),
inference(component_clause,[status(thm)],[f2145]) ).
fof(f2148,plain,
( ~ sQ35_spl
| ~ sQ4_spl
| sQ147_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f2141,f752,f2145,f493,f748]) ).
fof(f2149,plain,
( ~ sQ35_spl
| ~ sQ36_spl
| sQ108_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f2142,f493,f1754,f752,f748]) ).
fof(f2150,definition,
! [X0] :
( sQ148_spl
<=> ( rearsegP(sK47_skl,X0)
| ~ rearsegP(sK5_skl(nil,sK47_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f2153,plain,
( ~ sQ35_spl
| ~ sQ4_spl
| sQ148_spl
| ~ sQ36_spl ),
inference(split_clause,[status(thm)],[f2143,f752,f2150,f493,f748]) ).
fof(f2154,definition,
! [X0] :
( sQ149_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK5_skl(nil,sK47_skl)),X0),sK5_skl(nil,sK47_skl))
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f2157,plain,
( ~ sQ35_spl
| ~ sQ4_spl
| ~ sQ36_spl
| sQ149_spl ),
inference(split_clause,[status(thm)],[f2144,f2154,f752,f493,f748]) ).
fof(f2168,plain,
( ~ sQ147_spl
| app(sK6_skl(sK5_skl(nil,sK47_skl),sK47_skl),sK5_skl(nil,sK47_skl)) = sK47_skl
| ~ ssList(sK5_skl(nil,sK47_skl))
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2146,f129]) ).
fof(f2176,definition,
( sQ152_spl
<=> app(sK6_skl(sK5_skl(nil,sK47_skl),sK47_skl),sK5_skl(nil,sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f2179,plain,
( ~ sQ147_spl
| sQ152_spl
| ~ sQ36_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f2168,f542,f752,f2176,f2145]) ).
fof(f2196,plain,
( ~ sQ41_spl
| ~ ssList(nil)
| frontsegP(sK48_skl,sK6_skl(nil,sK48_skl))
| ~ ssList(sK6_skl(nil,sK48_skl)) ),
inference(paramodulation,[status(thm)],[f829,f756]) ).
fof(f2198,plain,
! [X0] :
( ~ sQ41_spl
| ~ ssList(X0)
| ~ ssList(sK6_skl(nil,sK48_skl))
| segmentP(app(app(sK6_skl(nil,sK48_skl),nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f829,f455]) ).
fof(f2199,definition,
( sQ154_spl
<=> ssList(sK6_skl(nil,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f2200,plain,
( ~ sQ154_spl
| ssList(sK6_skl(nil,sK48_skl)) ),
inference(component_clause,[status(thm)],[f2199]) ).
fof(f2201,plain,
( sQ154_spl
| ~ ssList(sK6_skl(nil,sK48_skl)) ),
inference(component_clause,[status(thm)],[f2199]) ).
fof(f2204,definition,
( sQ155_spl
<=> frontsegP(sK48_skl,sK6_skl(nil,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f2207,plain,
( ~ sQ41_spl
| ~ sQ4_spl
| sQ155_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f2196,f2199,f2204,f493,f828]) ).
fof(f2209,definition,
! [X0] :
( sQ156_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK6_skl(nil,sK48_skl),nil),X0),nil)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f2212,plain,
( ~ sQ41_spl
| ~ sQ154_spl
| ~ sQ4_spl
| sQ156_spl ),
inference(split_clause,[status(thm)],[f2198,f2209,f493,f2199,f828]) ).
fof(f2213,plain,
( sQ154_spl
| ~ rearsegP(sK48_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2201,f128]) ).
fof(f2214,plain,
( sQ154_spl
| ~ sQ111_spl
| ~ sQ4_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2213,f530,f493,f1782,f2199]) ).
fof(f2220,plain,
! [X0] :
( ~ sQ154_spl
| nil = sK6_skl(nil,sK48_skl)
| nil != app(X0,sK6_skl(nil,sK48_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2200,f385]) ).
fof(f2241,definition,
! [X0] :
( sQ157_spl
<=> ( nil != app(X0,sK6_skl(nil,sK48_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f2244,definition,
( sQ158_spl
<=> nil = sK6_skl(nil,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f2247,plain,
( ~ sQ154_spl
| sQ158_spl
| sQ157_spl ),
inference(split_clause,[status(thm)],[f2220,f2241,f2244,f2199]) ).
fof(f2253,plain,
! [X0,X1,X2] :
( X1 = nil
| ~ ssList(nil)
| ~ ssList(X1)
| rearsegP(X1,X2)
| ~ ssList(X0)
| sP0_prd(app(X0,cons(sK1_skl,nil)),cons(sK1_skl,nil),X1,X2) ),
inference(resolution,[status(thm)],[f943,f220]) ).
fof(f2254,definition,
! [X0,X1,X2] :
( sQ159_spl
<=> ( X1 = nil
| ~ ssList(X1)
| rearsegP(X1,X2)
| ~ ssList(X0)
| sP0_prd(app(X0,cons(sK1_skl,nil)),cons(sK1_skl,nil),X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f2257,plain,
( ~ sQ4_spl
| sQ159_spl ),
inference(split_clause,[status(thm)],[f2253,f2254,f493]) ).
fof(f2265,plain,
( ~ sQ42_spl
| ~ ssList(sK48_skl)
| frontsegP(sK48_skl,sK6_skl(sK48_skl,sK48_skl))
| ~ ssList(sK6_skl(sK48_skl,sK48_skl)) ),
inference(paramodulation,[status(thm)],[f834,f756]) ).
fof(f2266,plain,
! [X0] :
( ~ sQ42_spl
| rearsegP(sK48_skl,X0)
| ~ rearsegP(sK48_skl,X0)
| ~ ssList(sK6_skl(sK48_skl,sK48_skl))
| ~ ssList(X0)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f834,f307]) ).
fof(f2267,plain,
! [X0] :
( ~ sQ42_spl
| ~ ssList(X0)
| ~ ssList(sK6_skl(sK48_skl,sK48_skl))
| segmentP(app(app(sK6_skl(sK48_skl,sK48_skl),sK48_skl),X0),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f834,f455]) ).
fof(f2268,definition,
( sQ160_spl
<=> ssList(sK6_skl(sK48_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f2270,plain,
( sQ160_spl
| ~ ssList(sK6_skl(sK48_skl,sK48_skl)) ),
inference(component_clause,[status(thm)],[f2268]) ).
fof(f2273,definition,
( sQ161_spl
<=> frontsegP(sK48_skl,sK6_skl(sK48_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f2274,plain,
( ~ sQ161_spl
| frontsegP(sK48_skl,sK6_skl(sK48_skl,sK48_skl)) ),
inference(component_clause,[status(thm)],[f2273]) ).
fof(f2276,plain,
( ~ sQ42_spl
| ~ sQ10_spl
| sQ161_spl
| ~ sQ160_spl ),
inference(split_clause,[status(thm)],[f2265,f2268,f2273,f530,f833]) ).
fof(f2277,plain,
( ~ sQ42_spl
| ~ sQ160_spl
| sQ59_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2266,f530,f999,f2268,f833]) ).
fof(f2278,definition,
! [X0] :
( sQ162_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK6_skl(sK48_skl,sK48_skl),sK48_skl),X0),sK48_skl)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f2281,plain,
( ~ sQ42_spl
| ~ sQ160_spl
| ~ sQ10_spl
| sQ162_spl ),
inference(split_clause,[status(thm)],[f2267,f2278,f530,f2268,f833]) ).
fof(f2282,plain,
( sQ160_spl
| ~ rearsegP(sK48_skl,sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2270,f128]) ).
fof(f2283,plain,
( sQ160_spl
| ~ sQ44_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2282,f530,f854,f2268]) ).
fof(f2318,plain,
( ~ sQ161_spl
| app(sK6_skl(sK48_skl,sK48_skl),sK5_skl(sK6_skl(sK48_skl,sK48_skl),sK48_skl)) = sK48_skl
| ~ ssList(sK6_skl(sK48_skl,sK48_skl))
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2274,f123]) ).
fof(f2319,plain,
( ~ sQ161_spl
| ssList(sK5_skl(sK6_skl(sK48_skl,sK48_skl),sK48_skl))
| ~ ssList(sK6_skl(sK48_skl,sK48_skl))
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f2274,f122]) ).
fof(f2320,definition,
( sQ165_spl
<=> app(sK6_skl(sK48_skl,sK48_skl),sK5_skl(sK6_skl(sK48_skl,sK48_skl),sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f2323,plain,
( ~ sQ161_spl
| sQ165_spl
| ~ sQ160_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2318,f530,f2268,f2320,f2273]) ).
fof(f2324,definition,
( sQ166_spl
<=> ssList(sK5_skl(sK6_skl(sK48_skl,sK48_skl),sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f2327,plain,
( ~ sQ161_spl
| sQ166_spl
| ~ sQ160_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2319,f530,f2268,f2324,f2273]) ).
fof(f2336,plain,
! [X0,X1,X2] :
( X1 = nil
| ~ ssList(nil)
| ~ ssList(X1)
| rearsegP(X1,X2)
| ~ ssList(X0)
| sP0_prd(app(X0,cons(sK0_skl,nil)),cons(sK0_skl,nil),X1,X2) ),
inference(resolution,[status(thm)],[f944,f220]) ).
fof(f2337,definition,
! [X0,X1,X2] :
( sQ167_spl
<=> ( X1 = nil
| ~ ssList(X1)
| rearsegP(X1,X2)
| ~ ssList(X0)
| sP0_prd(app(X0,cons(sK0_skl,nil)),cons(sK0_skl,nil),X1,X2) ) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f2340,plain,
( ~ sQ4_spl
| sQ167_spl ),
inference(split_clause,[status(thm)],[f2336,f2337,f493]) ).
fof(f2552,plain,
( ~ sQ0_spl
| app(sK52_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl),sK47_skl) = sK48_skl ),
inference(forward_demodulation,[status(thm)],[f622,f1046]) ).
fof(f2554,plain,
( ~ sQ0_spl
| ~ ssList(sK52_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl))
| rearsegP(sK48_skl,sK47_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f2552,f757]) ).
fof(f2558,definition,
( sQ184_spl
<=> ssList(sK52_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f2560,plain,
( sQ184_spl
| ~ ssList(sK52_skl(sK48_skl,sK47_skl,sK48_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f2558]) ).
fof(f2562,plain,
( ~ sQ0_spl
| ~ sQ184_spl
| sQ20_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f2554,f542,f612,f2558,f438]) ).
fof(f2650,plain,
( ~ sQ103_spl
| nil != cons(sK4_skl(sK47_skl),nil) ),
inference(resolution,[status(thm)],[f1792,f223]) ).
fof(f2651,plain,
( ~ sQ103_spl
| ~ sQ102_spl
| nil != sK47_skl ),
inference(forward_demodulation,[status(thm)],[f1718,f2650]) ).
fof(f2677,plain,
( ~ sQ115_spl
| cons(sK44_skl(sK5_skl(nil,sK48_skl)),sK43_skl(sK5_skl(nil,sK48_skl))) = sK5_skl(nil,sK48_skl)
| nil = sK5_skl(nil,sK48_skl) ),
inference(resolution,[status(thm)],[f233,f1815]) ).
fof(f2702,definition,
( sQ193_spl
<=> cons(sK44_skl(sK5_skl(nil,sK48_skl)),sK43_skl(sK5_skl(nil,sK48_skl))) = sK5_skl(nil,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f2705,plain,
( ~ sQ115_spl
| sQ193_spl
| sQ119_spl ),
inference(split_clause,[status(thm)],[f2677,f1880,f2702,f1814]) ).
fof(f2722,plain,
! [X0] :
( ~ sQ118_spl
| ~ sQ119_spl
| nil != app(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f1881,f1878]) ).
fof(f2762,plain,
( ~ sQ118_spl
| ~ sQ119_spl
| nil != app(nil,nil) ),
inference(resolution,[status(thm)],[f2722,f223]) ).
fof(f2765,plain,
( ~ sQ118_spl
| ~ sQ119_spl
| nil != nil ),
inference(forward_demodulation,[status(thm)],[f500,f2762]) ).
fof(f2766,plain,
( ~ sQ118_spl
| ~ sQ119_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f2765]) ).
fof(f2767,plain,
( ~ sQ118_spl
| ~ sQ119_spl ),
inference(contradiction_clause,[status(thm)],[f2766]) ).
fof(f2800,plain,
( ~ sQ15_spl
| app(sK6_skl(nil,sK47_skl),nil) = sK6_skl(nil,sK47_skl)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f678,f570]) ).
fof(f2801,plain,
( ~ sQ13_spl
| app(sK6_skl(sK47_skl,sK47_skl),nil) = sK6_skl(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f678,f551]) ).
fof(f2802,plain,
( ~ sQ11_spl
| app(sK6_skl(sK48_skl,sK48_skl),nil) = sK6_skl(sK48_skl,sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f678,f539]) ).
fof(f2803,plain,
( ~ sQ14_spl
| app(sK6_skl(nil,sK48_skl),nil) = sK6_skl(nil,sK48_skl)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f678,f564]) ).
fof(f2804,plain,
( ~ sQ5_spl
| app(sK6_skl(nil,nil),nil) = sK6_skl(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f678,f510]) ).
fof(f2805,plain,
! [X0] :
( ~ ssList(X0)
| app(sK6_skl(nil,X0),nil) = sK6_skl(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f678,f309]) ).
fof(f2812,definition,
( sQ197_spl
<=> app(sK6_skl(nil,sK47_skl),nil) = sK6_skl(nil,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f2815,plain,
( ~ sQ15_spl
| sQ197_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f2800,f542,f493,f2812,f566]) ).
fof(f2816,definition,
( sQ198_spl
<=> app(sK6_skl(sK47_skl,sK47_skl),nil) = sK6_skl(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f2819,plain,
( ~ sQ13_spl
| sQ198_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f2801,f542,f2816,f545]) ).
fof(f2820,definition,
( sQ199_spl
<=> app(sK6_skl(sK48_skl,sK48_skl),nil) = sK6_skl(sK48_skl,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f2823,plain,
( ~ sQ11_spl
| sQ199_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2802,f530,f2820,f533]) ).
fof(f2824,definition,
( sQ200_spl
<=> app(sK6_skl(nil,sK48_skl),nil) = sK6_skl(nil,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f2827,plain,
( ~ sQ14_spl
| sQ200_spl
| ~ sQ4_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2803,f530,f493,f2824,f560]) ).
fof(f2828,definition,
( sQ201_spl
<=> app(sK6_skl(nil,nil),nil) = sK6_skl(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f2831,plain,
( ~ sQ5_spl
| sQ201_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f2804,f493,f2828,f504]) ).
fof(f2832,definition,
! [X0] :
( sQ202_spl
<=> ( ~ ssList(X0)
| app(sK6_skl(nil,X0),nil) = sK6_skl(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f2835,plain,
( ~ sQ4_spl
| sQ202_spl ),
inference(split_clause,[status(thm)],[f2805,f2832,f493]) ).
fof(f2851,plain,
( ~ sQ15_spl
| app(nil,sK6_skl(nil,sK47_skl)) = sK6_skl(nil,sK47_skl)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f679,f570]) ).
fof(f2852,plain,
( ~ sQ13_spl
| app(nil,sK6_skl(sK47_skl,sK47_skl)) = sK6_skl(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f679,f551]) ).
fof(f2853,plain,
( ~ sQ11_spl
| app(nil,sK6_skl(sK48_skl,sK48_skl)) = sK6_skl(sK48_skl,sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f679,f539]) ).
fof(f2854,plain,
( ~ sQ14_spl
| app(nil,sK6_skl(nil,sK48_skl)) = sK6_skl(nil,sK48_skl)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f679,f564]) ).
fof(f2855,plain,
( ~ sQ5_spl
| app(nil,sK6_skl(nil,nil)) = sK6_skl(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f679,f510]) ).
fof(f2856,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,sK6_skl(nil,X0)) = sK6_skl(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f679,f309]) ).
fof(f2863,definition,
( sQ203_spl
<=> app(nil,sK6_skl(nil,sK47_skl)) = sK6_skl(nil,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f2866,plain,
( ~ sQ15_spl
| sQ203_spl
| ~ sQ4_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f2851,f542,f493,f2863,f566]) ).
fof(f2867,definition,
( sQ204_spl
<=> app(nil,sK6_skl(sK47_skl,sK47_skl)) = sK6_skl(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f2870,plain,
( ~ sQ13_spl
| sQ204_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f2852,f542,f2867,f545]) ).
fof(f2871,definition,
( sQ205_spl
<=> app(nil,sK6_skl(sK48_skl,sK48_skl)) = sK6_skl(sK48_skl,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f2874,plain,
( ~ sQ11_spl
| sQ205_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2853,f530,f2871,f533]) ).
fof(f2875,definition,
( sQ206_spl
<=> app(nil,sK6_skl(nil,sK48_skl)) = sK6_skl(nil,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f2878,plain,
( ~ sQ14_spl
| sQ206_spl
| ~ sQ4_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f2854,f530,f493,f2875,f560]) ).
fof(f2879,definition,
( sQ207_spl
<=> app(nil,sK6_skl(nil,nil)) = sK6_skl(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f2882,plain,
( ~ sQ5_spl
| sQ207_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f2855,f493,f2879,f504]) ).
fof(f2883,definition,
! [X0] :
( sQ208_spl
<=> ( ~ ssList(X0)
| app(nil,sK6_skl(nil,X0)) = sK6_skl(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f2886,plain,
( ~ sQ4_spl
| sQ208_spl ),
inference(split_clause,[status(thm)],[f2856,f2883,f493]) ).
fof(f3100,plain,
( ~ sQ112_spl
| ~ ssList(sK48_skl)
| rearsegP(sK48_skl,sK5_skl(sK48_skl,sK48_skl))
| ~ ssList(sK5_skl(sK48_skl,sK48_skl)) ),
inference(paramodulation,[status(thm)],[f1801,f757]) ).
fof(f3102,plain,
! [X0] :
( ~ sQ112_spl
| rearsegP(sK48_skl,X0)
| ~ rearsegP(sK5_skl(sK48_skl,sK48_skl),X0)
| ~ ssList(sK48_skl)
| ~ ssList(X0)
| ~ ssList(sK5_skl(sK48_skl,sK48_skl)) ),
inference(paramodulation,[status(thm)],[f1801,f307]) ).
fof(f3103,plain,
! [X0] :
( ~ sQ112_spl
| ~ ssList(X0)
| ~ ssList(sK48_skl)
| segmentP(app(app(sK48_skl,sK5_skl(sK48_skl,sK48_skl)),X0),sK5_skl(sK48_skl,sK48_skl))
| ~ ssList(sK5_skl(sK48_skl,sK48_skl))
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f1801,f455]) ).
fof(f3104,definition,
( sQ209_spl
<=> rearsegP(sK48_skl,sK5_skl(sK48_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f3105,plain,
( ~ sQ209_spl
| rearsegP(sK48_skl,sK5_skl(sK48_skl,sK48_skl)) ),
inference(component_clause,[status(thm)],[f3104]) ).
fof(f3107,plain,
( ~ sQ112_spl
| ~ sQ10_spl
| sQ209_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f3100,f1804,f3104,f530,f1800]) ).
fof(f3109,definition,
! [X0] :
( sQ210_spl
<=> ( rearsegP(sK48_skl,X0)
| ~ rearsegP(sK5_skl(sK48_skl,sK48_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f3112,plain,
( ~ sQ112_spl
| ~ sQ10_spl
| sQ210_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f3102,f1804,f3109,f530,f1800]) ).
fof(f3113,definition,
! [X0] :
( sQ211_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK48_skl,sK5_skl(sK48_skl,sK48_skl)),X0),sK5_skl(sK48_skl,sK48_skl))
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f3116,plain,
( ~ sQ112_spl
| ~ sQ10_spl
| ~ sQ113_spl
| sQ211_spl ),
inference(split_clause,[status(thm)],[f3103,f3113,f1804,f530,f1800]) ).
fof(f3179,definition,
( sQ222_spl
<=> sK47_skl = app(nil,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f3181,plain,
( sQ222_spl
| sK47_skl != app(nil,sK47_skl) ),
inference(component_clause,[status(thm)],[f3179]) ).
fof(f3183,plain,
( ~ sQ103_spl
| ~ sQ102_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f2651,f618,f1717,f1721]) ).
fof(f3186,plain,
( sQ222_spl
| sK47_skl != sK47_skl ),
inference(forward_demodulation,[status(thm)],[f502,f3181]) ).
fof(f3187,plain,
( sQ222_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3186]) ).
fof(f3188,plain,
sQ222_spl,
inference(contradiction_clause,[status(thm)],[f3187]) ).
fof(f3223,plain,
! [X0] :
( ~ sQ15_spl
| ~ ssList(nil)
| ~ ssList(sK47_skl)
| ssList(app(X0,sK6_skl(nil,sK47_skl)))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f758,f570]) ).
fof(f3224,plain,
! [X0] :
( ~ sQ13_spl
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl)
| ssList(app(X0,sK6_skl(sK47_skl,sK47_skl)))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f758,f551]) ).
fof(f3225,plain,
! [X0] :
( ~ sQ11_spl
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl)
| ssList(app(X0,sK6_skl(sK48_skl,sK48_skl)))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f758,f539]) ).
fof(f3226,plain,
! [X0] :
( ~ sQ14_spl
| ~ ssList(nil)
| ~ ssList(sK48_skl)
| ssList(app(X0,sK6_skl(nil,sK48_skl)))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f758,f564]) ).
fof(f3227,plain,
! [X0] :
( ~ sQ5_spl
| ~ ssList(nil)
| ~ ssList(nil)
| ssList(app(X0,sK6_skl(nil,nil)))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f758,f510]) ).
fof(f3228,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ssList(app(X0,sK6_skl(nil,X1)))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f758,f309]) ).
fof(f3235,definition,
! [X0] :
( sQ223_spl
<=> ( ssList(app(X0,sK6_skl(nil,sK47_skl)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f3238,plain,
( ~ sQ15_spl
| ~ sQ4_spl
| ~ sQ12_spl
| sQ223_spl ),
inference(split_clause,[status(thm)],[f3223,f3235,f542,f493,f566]) ).
fof(f3239,definition,
! [X0] :
( sQ224_spl
<=> ( ssList(app(X0,sK6_skl(sK47_skl,sK47_skl)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f3242,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| sQ224_spl ),
inference(split_clause,[status(thm)],[f3224,f3239,f542,f545]) ).
fof(f3243,definition,
! [X0] :
( sQ225_spl
<=> ( ssList(app(X0,sK6_skl(sK48_skl,sK48_skl)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f3246,plain,
( ~ sQ11_spl
| ~ sQ10_spl
| sQ225_spl ),
inference(split_clause,[status(thm)],[f3225,f3243,f530,f533]) ).
fof(f3247,definition,
! [X0] :
( sQ226_spl
<=> ( ssList(app(X0,sK6_skl(nil,sK48_skl)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f3250,plain,
( ~ sQ14_spl
| ~ sQ4_spl
| ~ sQ10_spl
| sQ226_spl ),
inference(split_clause,[status(thm)],[f3226,f3247,f530,f493,f560]) ).
fof(f3251,definition,
! [X0] :
( sQ227_spl
<=> ( ssList(app(X0,sK6_skl(nil,nil)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f3254,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sQ227_spl ),
inference(split_clause,[status(thm)],[f3227,f3251,f493,f504]) ).
fof(f3255,definition,
! [X0,X1] :
( sQ228_spl
<=> ( ~ ssList(X1)
| ~ ssList(X1)
| ssList(app(X0,sK6_skl(nil,X1)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f3258,plain,
( ~ sQ4_spl
| sQ228_spl ),
inference(split_clause,[status(thm)],[f3228,f3255,f493]) ).
fof(f3316,plain,
! [X0] :
( ~ sQ209_spl
| ~ ssList(sK5_skl(sK48_skl,sK48_skl))
| ~ ssList(sK48_skl)
| ssList(app(X0,sK6_skl(sK5_skl(sK48_skl,sK48_skl),sK48_skl)))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3105,f758]) ).
fof(f3317,plain,
( ~ sQ209_spl
| app(nil,sK6_skl(sK5_skl(sK48_skl,sK48_skl),sK48_skl)) = sK6_skl(sK5_skl(sK48_skl,sK48_skl),sK48_skl)
| ~ ssList(sK5_skl(sK48_skl,sK48_skl))
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f3105,f679]) ).
fof(f3318,plain,
( ~ sQ209_spl
| app(sK6_skl(sK5_skl(sK48_skl,sK48_skl),sK48_skl),nil) = sK6_skl(sK5_skl(sK48_skl,sK48_skl),sK48_skl)
| ~ ssList(sK5_skl(sK48_skl,sK48_skl))
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f3105,f678]) ).
fof(f3319,plain,
( ~ sQ209_spl
| sK5_skl(sK48_skl,sK48_skl) = sK48_skl
| ~ rearsegP(sK5_skl(sK48_skl,sK48_skl),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK5_skl(sK48_skl,sK48_skl)) ),
inference(resolution,[status(thm)],[f3105,f303]) ).
fof(f3320,plain,
( ~ sQ209_spl
| app(sK6_skl(sK5_skl(sK48_skl,sK48_skl),sK48_skl),sK5_skl(sK48_skl,sK48_skl)) = sK48_skl
| ~ ssList(sK5_skl(sK48_skl,sK48_skl))
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f3105,f129]) ).
fof(f3321,definition,
! [X0] :
( sQ230_spl
<=> ( ssList(app(X0,sK6_skl(sK5_skl(sK48_skl,sK48_skl),sK48_skl)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f3324,plain,
( ~ sQ209_spl
| ~ sQ113_spl
| ~ sQ10_spl
| sQ230_spl ),
inference(split_clause,[status(thm)],[f3316,f3321,f530,f1804,f3104]) ).
fof(f3325,definition,
( sQ231_spl
<=> app(nil,sK6_skl(sK5_skl(sK48_skl,sK48_skl),sK48_skl)) = sK6_skl(sK5_skl(sK48_skl,sK48_skl),sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f3328,plain,
( ~ sQ209_spl
| sQ231_spl
| ~ sQ113_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f3317,f530,f1804,f3325,f3104]) ).
fof(f3329,definition,
( sQ232_spl
<=> app(sK6_skl(sK5_skl(sK48_skl,sK48_skl),sK48_skl),nil) = sK6_skl(sK5_skl(sK48_skl,sK48_skl),sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f3332,plain,
( ~ sQ209_spl
| sQ232_spl
| ~ sQ113_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f3318,f530,f1804,f3329,f3104]) ).
fof(f3333,definition,
( sQ233_spl
<=> rearsegP(sK5_skl(sK48_skl,sK48_skl),sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f3335,plain,
( sQ233_spl
| ~ rearsegP(sK5_skl(sK48_skl,sK48_skl),sK48_skl) ),
inference(component_clause,[status(thm)],[f3333]) ).
fof(f3336,definition,
( sQ234_spl
<=> sK5_skl(sK48_skl,sK48_skl) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f3337,plain,
( ~ sQ234_spl
| sK5_skl(sK48_skl,sK48_skl) = sK48_skl ),
inference(component_clause,[status(thm)],[f3336]) ).
fof(f3339,plain,
( ~ sQ209_spl
| sQ234_spl
| ~ sQ233_spl
| ~ sQ10_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f3319,f1804,f530,f3333,f3336,f3104]) ).
fof(f3340,definition,
( sQ235_spl
<=> app(sK6_skl(sK5_skl(sK48_skl,sK48_skl),sK48_skl),sK5_skl(sK48_skl,sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f3343,plain,
( ~ sQ209_spl
| sQ235_spl
| ~ sQ113_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f3320,f530,f1804,f3340,f3104]) ).
fof(f3370,plain,
! [X0] :
( nil = X0
| sK47_skl != app(X0,sK47_skl)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f502,f1052]) ).
fof(f3378,definition,
! [X0] :
( sQ237_spl
<=> ( nil = X0
| sK47_skl != app(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f3381,plain,
( ~ sQ4_spl
| sQ237_spl ),
inference(split_clause,[status(thm)],[f3370,f3378,f493]) ).
fof(f3461,plain,
! [X0] :
( sQ233_spl
| ~ rearsegP(X0,sK48_skl)
| ~ rearsegP(sK5_skl(sK48_skl,sK48_skl),X0)
| ~ ssList(sK48_skl)
| ~ ssList(X0)
| ~ ssList(sK5_skl(sK48_skl,sK48_skl)) ),
inference(resolution,[status(thm)],[f3335,f301]) ).
fof(f3462,definition,
! [X0] :
( sQ238_spl
<=> ( ~ rearsegP(X0,sK48_skl)
| ~ rearsegP(sK5_skl(sK48_skl,sK48_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f3465,plain,
( sQ233_spl
| ~ sQ10_spl
| sQ238_spl
| ~ sQ113_spl ),
inference(split_clause,[status(thm)],[f3461,f1804,f3462,f530,f3333]) ).
fof(f3467,plain,
( ~ sQ112_spl
| ~ sQ234_spl
| app(sK48_skl,sK48_skl) = sK48_skl ),
inference(backward_demodulation,[status(thm)],[f3337,f1801]) ).
fof(f3489,plain,
! [X0] :
( ~ sQ134_spl
| ~ ssList(sK5_skl(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl)
| ssList(app(X0,sK6_skl(sK5_skl(sK47_skl,sK47_skl),sK47_skl)))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2045,f758]) ).
fof(f3490,plain,
( ~ sQ134_spl
| app(nil,sK6_skl(sK5_skl(sK47_skl,sK47_skl),sK47_skl)) = sK6_skl(sK5_skl(sK47_skl,sK47_skl),sK47_skl)
| ~ ssList(sK5_skl(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2045,f679]) ).
fof(f3491,plain,
( ~ sQ134_spl
| app(sK6_skl(sK5_skl(sK47_skl,sK47_skl),sK47_skl),nil) = sK6_skl(sK5_skl(sK47_skl,sK47_skl),sK47_skl)
| ~ ssList(sK5_skl(sK47_skl,sK47_skl))
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2045,f678]) ).
fof(f3494,definition,
! [X0] :
( sQ240_spl
<=> ( ssList(app(X0,sK6_skl(sK5_skl(sK47_skl,sK47_skl),sK47_skl)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f3497,plain,
( ~ sQ134_spl
| ~ sQ33_spl
| ~ sQ12_spl
| sQ240_spl ),
inference(split_clause,[status(thm)],[f3489,f3494,f542,f734,f2044]) ).
fof(f3498,definition,
( sQ241_spl
<=> app(nil,sK6_skl(sK5_skl(sK47_skl,sK47_skl),sK47_skl)) = sK6_skl(sK5_skl(sK47_skl,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ241_spl])],[split_symbol_definition]) ).
fof(f3501,plain,
( ~ sQ134_spl
| sQ241_spl
| ~ sQ33_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f3490,f542,f734,f3498,f2044]) ).
fof(f3502,definition,
( sQ242_spl
<=> app(sK6_skl(sK5_skl(sK47_skl,sK47_skl),sK47_skl),nil) = sK6_skl(sK5_skl(sK47_skl,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f3505,plain,
( ~ sQ134_spl
| sQ242_spl
| ~ sQ33_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f3491,f542,f734,f3502,f2044]) ).
fof(f3571,plain,
( ~ sQ114_spl
| ~ ssList(nil)
| rearsegP(sK48_skl,sK5_skl(nil,sK48_skl))
| ~ ssList(sK5_skl(nil,sK48_skl)) ),
inference(paramodulation,[status(thm)],[f1811,f757]) ).
fof(f3573,plain,
! [X0] :
( ~ sQ114_spl
| rearsegP(sK48_skl,X0)
| ~ rearsegP(sK5_skl(nil,sK48_skl),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK5_skl(nil,sK48_skl)) ),
inference(paramodulation,[status(thm)],[f1811,f307]) ).
fof(f3574,plain,
! [X0] :
( ~ sQ114_spl
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK5_skl(nil,sK48_skl)),X0),sK5_skl(nil,sK48_skl))
| ~ ssList(sK5_skl(nil,sK48_skl))
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f1811,f455]) ).
fof(f3575,definition,
( sQ249_spl
<=> rearsegP(sK48_skl,sK5_skl(nil,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f3576,plain,
( ~ sQ249_spl
| rearsegP(sK48_skl,sK5_skl(nil,sK48_skl)) ),
inference(component_clause,[status(thm)],[f3575]) ).
fof(f3578,plain,
( ~ sQ114_spl
| ~ sQ4_spl
| sQ249_spl
| ~ sQ115_spl ),
inference(split_clause,[status(thm)],[f3571,f1814,f3575,f493,f1810]) ).
fof(f3580,definition,
! [X0] :
( sQ250_spl
<=> ( rearsegP(sK48_skl,X0)
| ~ rearsegP(sK5_skl(nil,sK48_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f3583,plain,
( ~ sQ114_spl
| ~ sQ4_spl
| sQ250_spl
| ~ sQ115_spl ),
inference(split_clause,[status(thm)],[f3573,f1814,f3580,f493,f1810]) ).
fof(f3584,definition,
! [X0] :
( sQ251_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK5_skl(nil,sK48_skl)),X0),sK5_skl(nil,sK48_skl))
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f3587,plain,
( ~ sQ114_spl
| ~ sQ4_spl
| ~ sQ115_spl
| sQ251_spl ),
inference(split_clause,[status(thm)],[f3574,f3584,f1814,f493,f1810]) ).
fof(f3589,plain,
! [X0] :
( ~ sQ249_spl
| ~ ssList(sK5_skl(nil,sK48_skl))
| ~ ssList(sK48_skl)
| ssList(app(X0,sK6_skl(sK5_skl(nil,sK48_skl),sK48_skl)))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3576,f758]) ).
fof(f3590,plain,
( ~ sQ249_spl
| app(nil,sK6_skl(sK5_skl(nil,sK48_skl),sK48_skl)) = sK6_skl(sK5_skl(nil,sK48_skl),sK48_skl)
| ~ ssList(sK5_skl(nil,sK48_skl))
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f3576,f679]) ).
fof(f3591,plain,
( ~ sQ249_spl
| app(sK6_skl(sK5_skl(nil,sK48_skl),sK48_skl),nil) = sK6_skl(sK5_skl(nil,sK48_skl),sK48_skl)
| ~ ssList(sK5_skl(nil,sK48_skl))
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f3576,f678]) ).
fof(f3592,plain,
( ~ sQ249_spl
| sK5_skl(nil,sK48_skl) = sK48_skl
| ~ rearsegP(sK5_skl(nil,sK48_skl),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK5_skl(nil,sK48_skl)) ),
inference(resolution,[status(thm)],[f3576,f303]) ).
fof(f3593,plain,
( ~ sQ249_spl
| app(sK6_skl(sK5_skl(nil,sK48_skl),sK48_skl),sK5_skl(nil,sK48_skl)) = sK48_skl
| ~ ssList(sK5_skl(nil,sK48_skl))
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f3576,f129]) ).
fof(f3594,definition,
! [X0] :
( sQ252_spl
<=> ( ssList(app(X0,sK6_skl(sK5_skl(nil,sK48_skl),sK48_skl)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f3597,plain,
( ~ sQ249_spl
| ~ sQ115_spl
| ~ sQ10_spl
| sQ252_spl ),
inference(split_clause,[status(thm)],[f3589,f3594,f530,f1814,f3575]) ).
fof(f3598,definition,
( sQ253_spl
<=> app(nil,sK6_skl(sK5_skl(nil,sK48_skl),sK48_skl)) = sK6_skl(sK5_skl(nil,sK48_skl),sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f3601,plain,
( ~ sQ249_spl
| sQ253_spl
| ~ sQ115_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f3590,f530,f1814,f3598,f3575]) ).
fof(f3602,definition,
( sQ254_spl
<=> app(sK6_skl(sK5_skl(nil,sK48_skl),sK48_skl),nil) = sK6_skl(sK5_skl(nil,sK48_skl),sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f3605,plain,
( ~ sQ249_spl
| sQ254_spl
| ~ sQ115_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f3591,f530,f1814,f3602,f3575]) ).
fof(f3606,definition,
( sQ255_spl
<=> rearsegP(sK5_skl(nil,sK48_skl),sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f3608,plain,
( sQ255_spl
| ~ rearsegP(sK5_skl(nil,sK48_skl),sK48_skl) ),
inference(component_clause,[status(thm)],[f3606]) ).
fof(f3609,definition,
( sQ256_spl
<=> sK5_skl(nil,sK48_skl) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f3612,plain,
( ~ sQ249_spl
| sQ256_spl
| ~ sQ255_spl
| ~ sQ10_spl
| ~ sQ115_spl ),
inference(split_clause,[status(thm)],[f3592,f1814,f530,f3606,f3609,f3575]) ).
fof(f3613,definition,
( sQ257_spl
<=> app(sK6_skl(sK5_skl(nil,sK48_skl),sK48_skl),sK5_skl(nil,sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ257_spl])],[split_symbol_definition]) ).
fof(f3616,plain,
( ~ sQ249_spl
| sQ257_spl
| ~ sQ115_spl
| ~ sQ10_spl ),
inference(split_clause,[status(thm)],[f3593,f530,f1814,f3613,f3575]) ).
fof(f3617,plain,
! [X0] :
( sQ255_spl
| ~ rearsegP(X0,sK48_skl)
| ~ rearsegP(sK5_skl(nil,sK48_skl),X0)
| ~ ssList(sK48_skl)
| ~ ssList(X0)
| ~ ssList(sK5_skl(nil,sK48_skl)) ),
inference(resolution,[status(thm)],[f3608,f301]) ).
fof(f3618,definition,
! [X0] :
( sQ258_spl
<=> ( ~ rearsegP(X0,sK48_skl)
| ~ rearsegP(sK5_skl(nil,sK48_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ258_spl])],[split_symbol_definition]) ).
fof(f3621,plain,
( sQ255_spl
| ~ sQ10_spl
| sQ258_spl
| ~ sQ115_spl ),
inference(split_clause,[status(thm)],[f3617,f1814,f3618,f530,f3606]) ).
fof(f3622,plain,
! [X0] :
( ~ sQ112_spl
| ~ sQ234_spl
| sK48_skl = X0
| sK48_skl != app(X0,sK48_skl)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f3467,f1053]) ).
fof(f3646,plain,
( ~ sQ112_spl
| ~ sQ234_spl
| sK48_skl = nil
| sK48_skl != app(nil,sK48_skl) ),
inference(resolution,[status(thm)],[f3622,f223]) ).
fof(f3677,definition,
( sQ267_spl
<=> sK48_skl = app(nil,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f3679,plain,
( sQ267_spl
| sK48_skl != app(nil,sK48_skl) ),
inference(component_clause,[status(thm)],[f3677]) ).
fof(f3680,plain,
( ~ sQ112_spl
| ~ sQ234_spl
| sQ22_spl
| ~ sQ267_spl ),
inference(split_clause,[status(thm)],[f3646,f3677,f654,f3336,f1800]) ).
fof(f3681,plain,
( sQ267_spl
| sK48_skl != sK48_skl ),
inference(forward_demodulation,[status(thm)],[f501,f3679]) ).
fof(f3682,plain,
( sQ267_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f3681]) ).
fof(f3683,plain,
sQ267_spl,
inference(contradiction_clause,[status(thm)],[f3682]) ).
fof(f3785,plain,
! [X0] :
( memberP(nil,X0)
| memberP(sK47_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssList(sK47_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f558,f270]) ).
fof(f3786,plain,
! [X0] :
( memberP(nil,X0)
| memberP(sK48_skl,X0)
| ~ memberP(sK48_skl,X0)
| ~ ssList(nil)
| ~ ssList(sK48_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f557,f270]) ).
fof(f3789,plain,
! [X0] :
( memberP(nil,X0)
| memberP(nil,X0)
| ~ memberP(nil,X0)
| ~ ssList(nil)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f500,f270]) ).
fof(f3794,definition,
! [X0] :
( sQ275_spl
<=> ( memberP(nil,X0)
| memberP(sK47_skl,X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f3797,plain,
( ~ sQ4_spl
| ~ sQ12_spl
| sQ275_spl ),
inference(split_clause,[status(thm)],[f3785,f3794,f542,f493]) ).
fof(f3798,definition,
! [X0] :
( sQ276_spl
<=> ( memberP(nil,X0)
| memberP(sK48_skl,X0)
| ~ memberP(sK48_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f3801,plain,
( ~ sQ4_spl
| ~ sQ10_spl
| sQ276_spl ),
inference(split_clause,[status(thm)],[f3786,f3798,f530,f493]) ).
fof(f3804,definition,
! [X0] :
( sQ277_spl
<=> ( memberP(nil,X0)
| memberP(nil,X0)
| ~ memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f3807,plain,
( ~ sQ4_spl
| sQ277_spl ),
inference(split_clause,[status(thm)],[f3789,f3804,f493]) ).
fof(f3852,plain,
! [X0] :
( nil = X0
| sK48_skl != app(X0,sK48_skl)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f501,f1054]) ).
fof(f3855,definition,
! [X0] :
( sQ281_spl
<=> ( nil = X0
| sK48_skl != app(X0,sK48_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f3858,plain,
( ~ sQ4_spl
| sQ281_spl ),
inference(split_clause,[status(thm)],[f3852,f3855,f493]) ).
fof(f3961,plain,
( sQ184_spl
| ~ sP0_prd(sK48_skl,sK47_skl,sK48_skl,sK47_skl) ),
inference(resolution,[status(thm)],[f2560,f432]) ).
fof(f3962,plain,
( sQ184_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3961,f488]) ).
fof(f3963,plain,
( sQ184_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f3962]) ).
fof(f3964,plain,
$false,
inference(sat_refutation,[status(thm)],[f444,f448,f496,f507,f509,f536,f538,f548,f550,f563,f569,f586,f593,f601,f615,f621,f651,f657,f675,f688,f692,f696,f700,f715,f719,f725,f733,f737,f743,f751,f755,f794,f802,f810,f816,f826,f831,f836,f860,f871,f883,f887,f889,f937,f973,f979,f983,f991,f995,f1006,f1033,f1044,f1180,f1201,f1335,f1394,f1398,f1400,f1592,f1596,f1601,f1603,f1669,f1708,f1720,f1724,f1741,f1745,f1753,f1761,f1765,f1785,f1788,f1803,f1807,f1813,f1817,f1883,f1941,f1945,f1993,f1998,f2000,f2033,f2047,f2048,f2052,f2056,f2070,f2111,f2116,f2120,f2125,f2133,f2148,f2149,f2153,f2157,f2179,f2207,f2212,f2214,f2247,f2257,f2276,f2277,f2281,f2283,f2323,f2327,f2340,f2562,f2705,f2767,f2815,f2819,f2823,f2827,f2831,f2835,f2866,f2870,f2874,f2878,f2882,f2886,f3107,f3112,f3116,f3183,f3188,f3238,f3242,f3246,f3250,f3254,f3258,f3324,f3328,f3332,f3339,f3343,f3381,f3465,f3497,f3501,f3505,f3578,f3583,f3587,f3597,f3601,f3605,f3612,f3616,f3621,f3680,f3683,f3797,f3801,f3807,f3858,f3963]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC106+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n010.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 07:56:25 UTC 2026
% 0.08/0.37 % CPUTime :
% 0.14/0.39 % Drodi V4.1.1
% 4.65/1.12 % Refutation found
% 4.65/1.12 % SZS status Theorem for theBenchmark: Theorem is valid
% 4.65/1.12 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 4.84/1.15 % Elapsed time: 0.774392 seconds
% 4.84/1.15 % CPU time: 5.640721 seconds
% 4.84/1.15 % Total memory used: 154.787 MB
% 4.84/1.15 % Net memory used: 150.789 MB
%------------------------------------------------------------------------------