%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC070+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n011.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 02:39:50 PM UTC 2026
% Result : Theorem 0.13s 0.55s
% Output : CNFRefutation 1.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 197
% Syntax : Number of formulae : 731 ( 20 unt; 175 def)
% Number of atoms : 2697 ( 282 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 3608 (1642 ~;1651 |; 77 &)
% ( 189 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 183 ( 181 usr; 175 prp; 0-2 aty)
% Number of functors : 12 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 412 ( 388 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( frontsegP(V,W)
& frontsegP(U,V) )
=> frontsegP(U,W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( frontsegP(V,U)
& frontsegP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( frontsegP(U,V)
=> frontsegP(app(U,W),V) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [U] :
( ssList(U)
=> ( frontsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( segmentP(V,W)
& segmentP(U,V) )
=> segmentP(U,W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( segmentP(V,U)
& segmentP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( segmentP(U,V)
=> segmentP(app(app(W,U),X),V) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( nil = U
& nil = V )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( nil = U
& nil = V )
| ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f99,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f98]) ).
fof(f101,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f102,plain,
( sK0_skl != sK1_skl
& ssItem(sK1_skl)
& ssItem(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2]) ).
fof(f103,plain,
ssItem(sK0_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
ssItem(sK1_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f105,plain,
sK0_skl != sK1_skl,
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f119,plain,
! [U] :
( ! [V] :
( ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f120,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ? [W] :
( app(V,W) = U
& ssList(W) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ( app(V,sK5_skl(V,U)) = U
& ssList(sK5_skl(V,U)) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( ssList(sK5_skl(X1,X0))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( app(X1,sK5_skl(X1,X0)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f124,plain,
! [X0,X1,X2] :
( app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f125,plain,
! [U] :
( ! [V] :
( ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f126,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ? [W] :
( app(W,V) = U
& ssList(W) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ( app(sK6_skl(V,U),V) = U
& ssList(sK6_skl(V,U)) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ssList(sK6_skl(X1,X0))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( app(sK6_skl(X1,X0),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f130,plain,
! [X0,X1,X2] :
( app(X2,X1) != X0
| ~ ssList(X2)
| rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f131,plain,
! [U] :
( ! [V] :
( ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f132,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ( app(app(sK7_skl(V,U),V),sK8_skl(V,U)) = U
& ssList(sK8_skl(V,U))
& ssList(sK7_skl(V,U)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132]) ).
fof(f136,plain,
! [X0,X1] :
( app(app(sK7_skl(X1,X0),X1),sK8_skl(X1,X0)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(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(f281,plain,
! [U] :
( ! [V] :
( ! [W] :
( frontsegP(U,W)
| ~ frontsegP(V,W)
| ~ frontsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f282,plain,
! [X0,X1,X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f283,plain,
! [U] :
( ! [V] :
( U = V
| ~ frontsegP(V,U)
| ~ frontsegP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f284,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(f287,plain,
! [U] :
( ! [V] :
( ! [W] :
( frontsegP(app(U,W),V)
| ~ frontsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f288,plain,
! [X0,X1,X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f287]) ).
fof(f294,plain,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f295,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f294]) ).
fof(f296,plain,
! [U] :
( ( frontsegP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f297,plain,
! [U] :
( ( ( nil != U
| frontsegP(nil,U) )
& ( nil = U
| ~ frontsegP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f296]) ).
fof(f298,plain,
! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f308,plain,
! [U] :
( rearsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f309,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f314,plain,
! [U] :
( ! [V] :
( ! [W] :
( segmentP(U,W)
| ~ segmentP(V,W)
| ~ segmentP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f315,plain,
! [X0,X1,X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
fof(f316,plain,
! [U] :
( ! [V] :
( U = V
| ~ segmentP(V,U)
| ~ segmentP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f317,plain,
! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f316]) ).
fof(f318,plain,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f319,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f320,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( segmentP(app(app(W,U),X),V)
| ~ segmentP(U,V)
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f321,plain,
! [X0,X1,X2,X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f322,plain,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f323,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(f324,plain,
! [U] :
( ( segmentP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f58]) ).
fof(f325,plain,
! [U] :
( ( ( nil != U
| segmentP(nil,U) )
& ( nil = U
| ~ segmentP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f324]) ).
fof(f326,plain,
! [X0] :
( nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f325]) ).
fof(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] :
( ( ( frontsegP(X,W)
& neq(W,nil) )
| ( nil = W
& nil = X ) )
& ( nil != U
| nil != V )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [W,X] :
( sP0_prd(X,W)
<=> ( nil = W
& nil = X ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( frontsegP(X,W)
& neq(W,nil) )
| sP0_prd(X,W) )
& ( nil != U
| nil != V )
& ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ( frontsegP(sK50_skl,sK49_skl)
& neq(sK49_skl,nil) )
| sP0_prd(sK50_skl,sK49_skl) )
& ( nil != sK47_skl
| nil != sK48_skl )
& ! [Y] :
( ~ segmentP(sK47_skl,Y)
| ~ segmentP(sK48_skl,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f417]) ).
fof(f421,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f422,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
! [X0] :
( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
( nil != sK47_skl
| nil != sK48_skl ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
( neq(sK49_skl,nil)
| sP0_prd(sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
( frontsegP(sK50_skl,sK49_skl)
| sP0_prd(sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
! [W,X] :
( ( nil != W
| nil != X
| sP0_prd(X,W) )
& ( ( nil = W
& nil = X )
| ~ sP0_prd(X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f430,plain,
( ! [W,X] :
( nil != W
| nil != X
| sP0_prd(X,W) )
& ! [W,X] :
( ( nil = W
& nil = X )
| ~ sP0_prd(X,W) ) ),
inference(miniscoping,[status(thm)],[f429]) ).
fof(f431,plain,
! [X0,X1] :
( nil = X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f432,plain,
! [X0,X1] :
( nil = X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f430]) ).
fof(f434,definition,
( sQ0_spl
<=> nil = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f436,plain,
( sQ0_spl
| nil != sK48_skl ),
inference(component_clause,[status(thm)],[f434]) ).
fof(f437,definition,
( sQ1_spl
<=> nil = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( sQ1_spl
| nil != sK47_skl ),
inference(component_clause,[status(thm)],[f437]) ).
fof(f440,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f434,f437]) ).
fof(f441,definition,
( sQ2_spl
<=> sP0_prd(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( ~ sQ2_spl
| sP0_prd(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,definition,
( sQ3_spl
<=> neq(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f447,plain,
( sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f427,f441,f444]) ).
fof(f448,definition,
( sQ4_spl
<=> frontsegP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f449,plain,
( ~ sQ4_spl
| frontsegP(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f451,plain,
( sQ4_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f428,f441,f448]) ).
fof(f456,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f457,plain,
! [X0,X1] :
( ~ ssList(X0)
| rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f458,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(f485,plain,
( sQ0_spl
| nil != sK50_skl ),
inference(forward_demodulation,[status(thm)],[f423,f436]) ).
fof(f486,plain,
! [X0] :
( X0 = sK0_skl
| neq(X0,sK0_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f103,f101]) ).
fof(f488,plain,
! [X0] :
( X0 = sK1_skl
| neq(X0,sK1_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f104,f101]) ).
fof(f490,plain,
( ~ sQ2_spl
| nil = sK50_skl ),
inference(resolution,[status(thm)],[f431,f442]) ).
fof(f492,plain,
( ~ sQ2_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f490,f485]) ).
fof(f493,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f492]) ).
fof(f494,plain,
( sQ1_spl
| nil != sK49_skl ),
inference(forward_demodulation,[status(thm)],[f424,f439]) ).
fof(f495,plain,
! [X0] :
( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f423,f425]) ).
fof(f496,plain,
! [X0] :
( ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f424,f495]) ).
fof(f497,plain,
( ~ segmentP(sK50_skl,sK49_skl)
| ~ neq(sK49_skl,nil)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f319,f496]) ).
fof(f498,definition,
( sQ5_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f500,plain,
( sQ5_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f498]) ).
fof(f501,definition,
( sQ6_spl
<=> segmentP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f503,plain,
( sQ6_spl
| ~ segmentP(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f501]) ).
fof(f504,plain,
( ~ sQ6_spl
| ~ sQ3_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f497,f498,f444,f501]) ).
fof(f510,plain,
( ~ sQ2_spl
| sP0_prd(nil,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f490,f442]) ).
fof(f529,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(resolution,[status(thm)],[f432,f510]) ).
fof(f531,plain,
( ~ sQ2_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f529,f494]) ).
fof(f532,plain,
( ~ sQ2_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f531]) ).
fof(f533,plain,
( sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f500,f421]) ).
fof(f534,plain,
sQ5_spl,
inference(contradiction_clause,[status(thm)],[f533]) ).
fof(f537,plain,
( ~ segmentP(sK50_skl,nil)
| ~ neq(nil,nil)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f323,f496]) ).
fof(f538,definition,
( sQ11_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( sQ11_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f538]) ).
fof(f541,definition,
( sQ12_spl
<=> neq(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f544,definition,
( sQ13_spl
<=> segmentP(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f545,plain,
( ~ sQ13_spl
| segmentP(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f546,plain,
( sQ13_spl
| ~ segmentP(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f547,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| ~ sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f537,f498,f538,f541,f544]) ).
fof(f548,plain,
( sQ13_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f546,f323]) ).
fof(f549,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f548,f422]) ).
fof(f550,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f549]) ).
fof(f551,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f540,f223]) ).
fof(f552,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f551]) ).
fof(f554,definition,
( sQ14_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f558,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f298,f295]) ).
fof(f559,plain,
! [X0,X1] :
( ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f298,f282]) ).
fof(f561,plain,
( sQ14_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f558,f538,f554]) ).
fof(f562,definition,
! [X0,X1] :
( sQ15_spl
<=> ( ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f563,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f562]) ).
fof(f565,plain,
( ~ sQ11_spl
| sQ15_spl ),
inference(split_clause,[status(thm)],[f559,f562,f538]) ).
fof(f567,plain,
! [X0,X1] :
( ~ sQ15_spl
| ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f563]) ).
fof(f569,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f284,f295]) ).
fof(f570,plain,
! [X0,X1,X2] :
( ~ frontsegP(X2,X0)
| ~ frontsegP(X1,X2)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ ssList(X1)
| X0 = X1
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f284,f282]) ).
fof(f572,definition,
( sQ16_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f574,plain,
( sQ16_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f572]) ).
fof(f578,definition,
( sQ18_spl
<=> sK49_skl = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f579,plain,
( ~ sQ18_spl
| sK49_skl = sK50_skl ),
inference(component_clause,[status(thm)],[f578]) ).
fof(f582,definition,
! [X0] :
( sQ19_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f585,plain,
( sQ19_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f569,f538,f582]) ).
fof(f586,plain,
! [X0,X1,X2] :
( ~ frontsegP(X2,X0)
| ~ frontsegP(X1,X2)
| ~ ssList(X2)
| X0 = X1
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f570]) ).
fof(f588,plain,
! [X0,X1,X2] :
( X1 = app(X0,X2)
| ~ frontsegP(X1,app(X0,X2))
| ~ ssList(app(X0,X2))
| ~ ssList(X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f288,f284]) ).
fof(f589,plain,
! [X0,X1,X2] :
( X1 = app(X0,X2)
| ~ frontsegP(X1,app(X0,X2))
| ~ ssList(app(X0,X2))
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f588]) ).
fof(f591,plain,
( sQ6_spl
| ~ sQ18_spl
| ~ segmentP(sK50_skl,sK50_skl) ),
inference(backward_demodulation,[status(thm)],[f579,f503]) ).
fof(f598,plain,
( sQ6_spl
| ~ sQ18_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f591,f319]) ).
fof(f599,plain,
( sQ6_spl
| ~ sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f598,f422]) ).
fof(f600,plain,
( sQ6_spl
| ~ sQ18_spl ),
inference(contradiction_clause,[status(thm)],[f599]) ).
fof(f601,plain,
( sQ16_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f574,f422]) ).
fof(f602,plain,
sQ16_spl,
inference(contradiction_clause,[status(thm)],[f601]) ).
fof(f610,plain,
( ~ sQ4_spl
| app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)) = sK50_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f123,f449]) ).
fof(f611,plain,
! [X0,X1,X2] :
( ~ frontsegP(X0,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| app(X2,sK5_skl(X2,app(X0,X1))) = app(X0,X1)
| ~ ssList(X2)
| ~ ssList(app(X0,X1)) ),
inference(resolution,[status(thm)],[f123,f288]) ).
fof(f612,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,sK5_skl(nil,X0)) = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f123,f295]) ).
fof(f613,plain,
! [X0,X1,X2] :
( ~ frontsegP(X2,X1)
| ~ frontsegP(X0,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| app(X1,sK5_skl(X1,X0)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f123,f282]) ).
fof(f615,definition,
( sQ21_spl
<=> app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f616,plain,
( ~ sQ21_spl
| app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)) = sK50_skl ),
inference(component_clause,[status(thm)],[f615]) ).
fof(f618,plain,
( ~ sQ4_spl
| sQ21_spl
| ~ sQ5_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f610,f572,f498,f615,f448]) ).
fof(f619,plain,
! [X0,X1,X2] :
( ~ frontsegP(X0,X2)
| ~ ssList(X1)
| ~ ssList(X0)
| app(X2,sK5_skl(X2,app(X0,X1))) = app(X0,X1)
| ~ ssList(X2)
| ~ ssList(app(X0,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f611]) ).
fof(f620,definition,
! [X0] :
( sQ22_spl
<=> ( ~ ssList(X0)
| app(nil,sK5_skl(nil,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f623,plain,
( ~ sQ11_spl
| sQ22_spl ),
inference(split_clause,[status(thm)],[f612,f620,f538]) ).
fof(f624,plain,
! [X0,X1,X2] :
( ~ frontsegP(X2,X1)
| ~ frontsegP(X0,X2)
| ~ ssList(X2)
| app(X1,sK5_skl(X1,X0)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f613]) ).
fof(f668,plain,
app(nil,sK50_skl) = sK50_skl,
inference(resolution,[status(thm)],[f249,f422]) ).
fof(f670,plain,
app(nil,sK49_skl) = sK49_skl,
inference(resolution,[status(thm)],[f249,f421]) ).
fof(f673,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f249,f223]) ).
fof(f674,plain,
! [X0] :
( frontsegP(sK50_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sK50_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f668,f288]) ).
fof(f675,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK50_skl),X0),sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(app(sK50_skl,X0)) ),
inference(paramodulation,[status(thm)],[f668,f458]) ).
fof(f676,plain,
( ~ ssList(sK50_skl)
| frontsegP(app(nil,sK50_skl),nil)
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f668,f456]) ).
fof(f677,definition,
! [X0] :
( sQ27_spl
<=> ( frontsegP(sK50_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f678,plain,
! [X0] :
( ~ sQ27_spl
| frontsegP(sK50_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f677]) ).
fof(f680,plain,
( ~ sQ16_spl
| sQ27_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f674,f538,f677,f572]) ).
fof(f681,definition,
! [X0] :
( sQ28_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK50_skl),X0),sK50_skl)
| ~ ssList(app(sK50_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f682,plain,
! [X0] :
( ~ sQ28_spl
| ~ ssList(X0)
| segmentP(app(app(nil,sK50_skl),X0),sK50_skl)
| ~ ssList(app(sK50_skl,X0)) ),
inference(component_clause,[status(thm)],[f681]) ).
fof(f684,plain,
( ~ sQ11_spl
| ~ sQ16_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f675,f681,f572,f538]) ).
fof(f685,definition,
( sQ29_spl
<=> frontsegP(app(nil,sK50_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f686,plain,
( ~ sQ29_spl
| frontsegP(app(nil,sK50_skl),nil) ),
inference(component_clause,[status(thm)],[f685]) ).
fof(f688,plain,
( sQ29_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f676,f572,f538,f685]) ).
fof(f689,plain,
! [X0] :
( ~ sQ28_spl
| ~ ssList(X0)
| segmentP(app(sK50_skl,X0),sK50_skl)
| ~ ssList(app(sK50_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f668,f682]) ).
fof(f690,plain,
( ~ sQ29_spl
| frontsegP(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f668,f686]) ).
fof(f691,plain,
( ~ sQ29_spl
| app(nil,sK5_skl(nil,sK50_skl)) = sK50_skl
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f690,f123]) ).
fof(f693,definition,
( sQ30_spl
<=> app(nil,sK5_skl(nil,sK50_skl)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f694,plain,
( ~ sQ30_spl
| app(nil,sK5_skl(nil,sK50_skl)) = sK50_skl ),
inference(component_clause,[status(thm)],[f693]) ).
fof(f696,plain,
( ~ sQ29_spl
| sQ30_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f691,f572,f538,f693,f685]) ).
fof(f713,plain,
! [X0] :
( frontsegP(sK49_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f670,f288]) ).
fof(f714,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK49_skl),X0),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(paramodulation,[status(thm)],[f670,f458]) ).
fof(f715,plain,
( ~ ssList(sK49_skl)
| frontsegP(app(nil,sK49_skl),nil)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f670,f456]) ).
fof(f716,definition,
! [X0] :
( sQ34_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f717,plain,
! [X0] :
( ~ sQ34_spl
| frontsegP(sK49_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f716]) ).
fof(f719,plain,
( ~ sQ5_spl
| sQ34_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f713,f538,f716,f498]) ).
fof(f720,definition,
! [X0] :
( sQ35_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK49_skl),X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f721,plain,
! [X0] :
( ~ sQ35_spl
| ~ ssList(X0)
| segmentP(app(app(nil,sK49_skl),X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(component_clause,[status(thm)],[f720]) ).
fof(f723,plain,
( ~ sQ11_spl
| ~ sQ5_spl
| sQ35_spl ),
inference(split_clause,[status(thm)],[f714,f720,f498,f538]) ).
fof(f724,definition,
( sQ36_spl
<=> frontsegP(app(nil,sK49_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f725,plain,
( ~ sQ36_spl
| frontsegP(app(nil,sK49_skl),nil) ),
inference(component_clause,[status(thm)],[f724]) ).
fof(f727,plain,
( sQ36_spl
| ~ sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f715,f498,f538,f724]) ).
fof(f728,plain,
! [X0] :
( ~ sQ35_spl
| ~ ssList(X0)
| segmentP(app(sK49_skl,X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f670,f721]) ).
fof(f729,plain,
( ~ sQ36_spl
| frontsegP(sK49_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f670,f725]) ).
fof(f730,plain,
( ~ sQ36_spl
| app(nil,sK5_skl(nil,sK49_skl)) = sK49_skl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f729,f123]) ).
fof(f731,plain,
( ~ sQ36_spl
| nil = sK49_skl
| ~ frontsegP(nil,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f729,f284]) ).
fof(f732,definition,
( sQ37_spl
<=> app(nil,sK5_skl(nil,sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f733,plain,
( ~ sQ37_spl
| app(nil,sK5_skl(nil,sK49_skl)) = sK49_skl ),
inference(component_clause,[status(thm)],[f732]) ).
fof(f735,plain,
( ~ sQ36_spl
| sQ37_spl
| ~ sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f730,f498,f538,f732,f724]) ).
fof(f736,definition,
( sQ38_spl
<=> frontsegP(nil,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f738,plain,
( sQ38_spl
| ~ frontsegP(nil,sK49_skl) ),
inference(component_clause,[status(thm)],[f736]) ).
fof(f739,definition,
( sQ39_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f740,plain,
( ~ sQ39_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f739]) ).
fof(f742,plain,
( ~ sQ36_spl
| sQ39_spl
| ~ sQ38_spl
| ~ sQ5_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f731,f538,f498,f736,f739,f724]) ).
fof(f743,plain,
! [X0] :
( sQ38_spl
| ~ frontsegP(X0,sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f738,f282]) ).
fof(f744,definition,
! [X0] :
( sQ40_spl
<=> ( ~ frontsegP(X0,sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f747,plain,
( sQ38_spl
| ~ sQ5_spl
| sQ40_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f743,f538,f744,f498,f736]) ).
fof(f750,plain,
( sQ6_spl
| ~ sQ39_spl
| ~ segmentP(sK50_skl,nil) ),
inference(backward_demodulation,[status(thm)],[f740,f503]) ).
fof(f759,plain,
( sQ6_spl
| ~ sQ39_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f750,f544,f739,f501]) ).
fof(f763,plain,
! [X0] :
( ~ ssList(X0)
| app(sK6_skl(nil,X0),nil) = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f129,f309]) ).
fof(f765,definition,
! [X0] :
( sQ41_spl
<=> ( ~ ssList(X0)
| app(sK6_skl(nil,X0),nil) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f768,plain,
( ~ sQ11_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f763,f765,f538]) ).
fof(f771,plain,
( ~ ssList(nil)
| rearsegP(app(nil,sK50_skl),sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f668,f457]) ).
fof(f772,definition,
( sQ42_spl
<=> rearsegP(app(nil,sK50_skl),sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f773,plain,
( ~ sQ42_spl
| rearsegP(app(nil,sK50_skl),sK50_skl) ),
inference(component_clause,[status(thm)],[f772]) ).
fof(f775,plain,
( ~ sQ11_spl
| sQ42_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f771,f572,f772,f538]) ).
fof(f776,plain,
( ~ sQ42_spl
| rearsegP(sK50_skl,sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f668,f773]) ).
fof(f778,plain,
! [X0] :
( X0 = nil
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f496,f220]) ).
fof(f779,definition,
! [X0] :
( sQ43_spl
<=> ( X0 = nil
| ~ ssList(X0)
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f780,plain,
! [X0] :
( ~ sQ43_spl
| X0 = nil
| ~ ssList(X0)
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f779]) ).
fof(f782,plain,
( ~ sQ11_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f778,f779,f538]) ).
fof(f783,plain,
! [X0] :
( ~ sQ43_spl
| X0 = nil
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f780]) ).
fof(f798,plain,
( ~ sQ42_spl
| app(sK6_skl(sK50_skl,sK50_skl),sK50_skl) = sK50_skl
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f776,f129]) ).
fof(f799,definition,
( sQ44_spl
<=> app(sK6_skl(sK50_skl,sK50_skl),sK50_skl) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f800,plain,
( ~ sQ44_spl
| app(sK6_skl(sK50_skl,sK50_skl),sK50_skl) = sK50_skl ),
inference(component_clause,[status(thm)],[f799]) ).
fof(f802,plain,
( ~ sQ42_spl
| sQ44_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f798,f572,f799,f772]) ).
fof(f805,plain,
! [X0] :
( sQ6_spl
| ~ segmentP(X0,sK49_skl)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f315,f503]) ).
fof(f806,definition,
! [X0] :
( sQ45_spl
<=> ( ~ segmentP(X0,sK49_skl)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f809,plain,
( sQ6_spl
| ~ sQ5_spl
| sQ45_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f805,f572,f806,f498,f501]) ).
fof(f810,plain,
( ~ ssList(nil)
| rearsegP(app(nil,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f673,f457]) ).
fof(f811,plain,
! [X0] :
( frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f673,f288]) ).
fof(f812,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(nil,X0)) ),
inference(paramodulation,[status(thm)],[f673,f458]) ).
fof(f813,plain,
( ~ ssList(nil)
| frontsegP(app(nil,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f673,f456]) ).
fof(f814,definition,
( sQ46_spl
<=> rearsegP(app(nil,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f815,plain,
( ~ sQ46_spl
| rearsegP(app(nil,nil),nil) ),
inference(component_clause,[status(thm)],[f814]) ).
fof(f817,plain,
( sQ46_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f810,f538,f814]) ).
fof(f818,definition,
! [X0] :
( sQ47_spl
<=> ( frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f821,plain,
( sQ47_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f811,f538,f818]) ).
fof(f822,definition,
! [X0] :
( sQ48_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f825,plain,
( ~ sQ11_spl
| sQ48_spl ),
inference(split_clause,[status(thm)],[f812,f822,f538]) ).
fof(f826,definition,
( sQ49_spl
<=> frontsegP(app(nil,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f827,plain,
( ~ sQ49_spl
| frontsegP(app(nil,nil),nil) ),
inference(component_clause,[status(thm)],[f826]) ).
fof(f829,plain,
( sQ49_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f813,f538,f826]) ).
fof(f830,plain,
( ~ sQ46_spl
| rearsegP(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f673,f815]) ).
fof(f832,plain,
( ~ sQ49_spl
| frontsegP(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f673,f827]) ).
fof(f833,plain,
( ~ sQ46_spl
| app(sK6_skl(nil,nil),nil) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f830,f129]) ).
fof(f834,definition,
( sQ50_spl
<=> app(sK6_skl(nil,nil),nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f835,plain,
( ~ sQ50_spl
| app(sK6_skl(nil,nil),nil) = nil ),
inference(component_clause,[status(thm)],[f834]) ).
fof(f837,plain,
( ~ sQ46_spl
| sQ50_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f833,f538,f834,f814]) ).
fof(f839,plain,
( ~ sQ49_spl
| app(nil,sK5_skl(nil,nil)) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f832,f123]) ).
fof(f842,definition,
( sQ51_spl
<=> app(nil,sK5_skl(nil,nil)) = nil ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f843,plain,
( ~ sQ51_spl
| app(nil,sK5_skl(nil,nil)) = nil ),
inference(component_clause,[status(thm)],[f842]) ).
fof(f845,plain,
( ~ sQ49_spl
| sQ51_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f839,f538,f842,f826]) ).
fof(f846,definition,
( sQ52_spl
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f848,plain,
( sQ52_spl
| ~ frontsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f846]) ).
fof(f850,plain,
( ~ ssList(nil)
| rearsegP(app(nil,sK49_skl),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f670,f457]) ).
fof(f854,definition,
( sQ53_spl
<=> rearsegP(app(nil,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f855,plain,
( ~ sQ53_spl
| rearsegP(app(nil,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f854]) ).
fof(f857,plain,
( ~ sQ11_spl
| sQ53_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f850,f498,f854,f538]) ).
fof(f861,plain,
( ~ sQ53_spl
| rearsegP(sK49_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f670,f855]) ).
fof(f862,plain,
( ~ sQ53_spl
| app(sK6_skl(sK49_skl,sK49_skl),sK49_skl) = sK49_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f861,f129]) ).
fof(f863,definition,
( sQ54_spl
<=> app(sK6_skl(sK49_skl,sK49_skl),sK49_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f864,plain,
( ~ sQ54_spl
| app(sK6_skl(sK49_skl,sK49_skl),sK49_skl) = sK49_skl ),
inference(component_clause,[status(thm)],[f863]) ).
fof(f866,plain,
( ~ sQ53_spl
| sQ54_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f862,f498,f863,f854]) ).
fof(f867,plain,
app(sK49_skl,nil) = sK49_skl,
inference(resolution,[status(thm)],[f389,f421]) ).
fof(f869,plain,
app(sK50_skl,nil) = sK50_skl,
inference(resolution,[status(thm)],[f389,f422]) ).
fof(f874,plain,
( ~ ssList(sK49_skl)
| rearsegP(app(sK49_skl,nil),nil)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f867,f457]) ).
fof(f875,plain,
! [X0] :
( frontsegP(sK49_skl,X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f867,f288]) ).
fof(f876,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK49_skl)
| segmentP(app(app(sK49_skl,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK49_skl,X0)) ),
inference(paramodulation,[status(thm)],[f867,f458]) ).
fof(f877,plain,
( ~ ssList(nil)
| frontsegP(app(sK49_skl,nil),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f867,f456]) ).
fof(f878,definition,
( sQ55_spl
<=> rearsegP(app(sK49_skl,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f879,plain,
( ~ sQ55_spl
| rearsegP(app(sK49_skl,nil),nil) ),
inference(component_clause,[status(thm)],[f878]) ).
fof(f881,plain,
( sQ55_spl
| ~ sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f874,f498,f538,f878]) ).
fof(f882,definition,
! [X0] :
( sQ56_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f885,plain,
( ~ sQ11_spl
| sQ56_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f875,f498,f882,f538]) ).
fof(f886,definition,
! [X0] :
( sQ57_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK49_skl,nil),X0),nil)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f889,plain,
( ~ sQ5_spl
| ~ sQ11_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f876,f886,f538,f498]) ).
fof(f890,definition,
( sQ58_spl
<=> frontsegP(app(sK49_skl,nil),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f891,plain,
( ~ sQ58_spl
| frontsegP(app(sK49_skl,nil),sK49_skl) ),
inference(component_clause,[status(thm)],[f890]) ).
fof(f893,plain,
( ~ sQ11_spl
| sQ58_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f877,f498,f890,f538]) ).
fof(f894,plain,
( ~ sQ55_spl
| rearsegP(sK49_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f867,f879]) ).
fof(f896,plain,
( ~ sQ58_spl
| frontsegP(sK49_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f867,f891]) ).
fof(f897,plain,
( ~ sQ55_spl
| app(sK6_skl(nil,sK49_skl),nil) = sK49_skl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f894,f129]) ).
fof(f898,definition,
( sQ59_spl
<=> app(sK6_skl(nil,sK49_skl),nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f899,plain,
( ~ sQ59_spl
| app(sK6_skl(nil,sK49_skl),nil) = sK49_skl ),
inference(component_clause,[status(thm)],[f898]) ).
fof(f901,plain,
( ~ sQ55_spl
| sQ59_spl
| ~ sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f897,f498,f538,f898,f878]) ).
fof(f902,plain,
( ~ sQ58_spl
| app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)) = sK49_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f896,f123]) ).
fof(f903,plain,
( ~ sQ58_spl
| sK49_skl = sK49_skl
| ~ frontsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f896,f284]) ).
fof(f904,definition,
( sQ60_spl
<=> app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f905,plain,
( ~ sQ60_spl
| app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)) = sK49_skl ),
inference(component_clause,[status(thm)],[f904]) ).
fof(f907,plain,
( ~ sQ58_spl
| sQ60_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f902,f498,f904,f890]) ).
fof(f908,definition,
( sQ61_spl
<=> frontsegP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f910,plain,
( sQ61_spl
| ~ frontsegP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f908]) ).
fof(f911,definition,
( sQ62_spl
<=> sK49_skl = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f914,plain,
( ~ sQ58_spl
| sQ62_spl
| ~ sQ61_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f903,f498,f908,f911,f890]) ).
fof(f915,plain,
( sQ61_spl
| ~ sQ58_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f910,f896]) ).
fof(f916,plain,
( sQ61_spl
| ~ sQ58_spl ),
inference(contradiction_clause,[status(thm)],[f915]) ).
fof(f917,plain,
( ~ ssList(sK50_skl)
| rearsegP(app(sK50_skl,nil),nil)
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f869,f457]) ).
fof(f918,plain,
! [X0] :
( frontsegP(sK50_skl,X0)
| ~ frontsegP(sK50_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f869,f288]) ).
fof(f919,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK50_skl)
| segmentP(app(app(sK50_skl,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK50_skl,X0)) ),
inference(paramodulation,[status(thm)],[f869,f458]) ).
fof(f920,plain,
( ~ ssList(nil)
| frontsegP(app(sK50_skl,nil),sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f869,f456]) ).
fof(f921,definition,
( sQ63_spl
<=> rearsegP(app(sK50_skl,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f922,plain,
( ~ sQ63_spl
| rearsegP(app(sK50_skl,nil),nil) ),
inference(component_clause,[status(thm)],[f921]) ).
fof(f924,plain,
( sQ63_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f917,f572,f538,f921]) ).
fof(f925,definition,
! [X0] :
( sQ64_spl
<=> ( frontsegP(sK50_skl,X0)
| ~ frontsegP(sK50_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f928,plain,
( ~ sQ11_spl
| sQ64_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f918,f572,f925,f538]) ).
fof(f929,definition,
! [X0] :
( sQ65_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK50_skl,nil),X0),nil)
| ~ ssList(app(sK50_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f932,plain,
( ~ sQ16_spl
| ~ sQ11_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f919,f929,f538,f572]) ).
fof(f933,definition,
( sQ66_spl
<=> frontsegP(app(sK50_skl,nil),sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f934,plain,
( ~ sQ66_spl
| frontsegP(app(sK50_skl,nil),sK50_skl) ),
inference(component_clause,[status(thm)],[f933]) ).
fof(f936,plain,
( ~ sQ11_spl
| sQ66_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f920,f572,f933,f538]) ).
fof(f937,plain,
( ~ sQ63_spl
| rearsegP(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f869,f922]) ).
fof(f939,plain,
( ~ sQ66_spl
| frontsegP(sK50_skl,sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f869,f934]) ).
fof(f940,plain,
( ~ sQ63_spl
| app(sK6_skl(nil,sK50_skl),nil) = sK50_skl
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f937,f129]) ).
fof(f941,definition,
( sQ67_spl
<=> app(sK6_skl(nil,sK50_skl),nil) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f942,plain,
( ~ sQ67_spl
| app(sK6_skl(nil,sK50_skl),nil) = sK50_skl ),
inference(component_clause,[status(thm)],[f941]) ).
fof(f944,plain,
( ~ sQ63_spl
| sQ67_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f940,f572,f538,f941,f921]) ).
fof(f949,plain,
( ~ sQ13_spl
| app(app(sK7_skl(nil,sK50_skl),nil),sK8_skl(nil,sK50_skl)) = sK50_skl
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f136,f545]) ).
fof(f950,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(f953,definition,
( sQ68_spl
<=> app(app(sK7_skl(nil,sK50_skl),nil),sK8_skl(nil,sK50_skl)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f956,plain,
( ~ sQ13_spl
| sQ68_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f949,f572,f538,f953,f544]) ).
fof(f957,definition,
! [X0] :
( sQ69_spl
<=> ( ~ ssList(X0)
| app(app(sK7_skl(nil,X0),nil),sK8_skl(nil,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f960,plain,
( ~ sQ11_spl
| sQ69_spl ),
inference(split_clause,[status(thm)],[f950,f957,f538]) ).
fof(f964,plain,
( ~ sQ66_spl
| app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)) = sK50_skl
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f939,f123]) ).
fof(f965,plain,
( ~ sQ66_spl
| sK50_skl = sK50_skl
| ~ frontsegP(sK50_skl,sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f939,f284]) ).
fof(f966,definition,
( sQ70_spl
<=> app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f967,plain,
( ~ sQ70_spl
| app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)) = sK50_skl ),
inference(component_clause,[status(thm)],[f966]) ).
fof(f969,plain,
( ~ sQ66_spl
| sQ70_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f964,f572,f966,f933]) ).
fof(f970,definition,
( sQ71_spl
<=> frontsegP(sK50_skl,sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f972,plain,
( sQ71_spl
| ~ frontsegP(sK50_skl,sK50_skl) ),
inference(component_clause,[status(thm)],[f970]) ).
fof(f973,definition,
( sQ72_spl
<=> sK50_skl = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f976,plain,
( ~ sQ66_spl
| sQ72_spl
| ~ sQ71_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f965,f572,f970,f973,f933]) ).
fof(f977,plain,
( sQ71_spl
| ~ sQ66_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f972,f939]) ).
fof(f978,plain,
( sQ71_spl
| ~ sQ66_spl ),
inference(contradiction_clause,[status(thm)],[f977]) ).
fof(f983,definition,
( sQ73_spl
<=> ssList(sK5_skl(sK49_skl,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f985,plain,
( sQ73_spl
| ~ ssList(sK5_skl(sK49_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f983]) ).
fof(f1002,plain,
( sQ73_spl
| ~ frontsegP(sK50_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f985,f122]) ).
fof(f1003,plain,
( sQ73_spl
| ~ sQ4_spl
| ~ sQ5_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1002,f572,f498,f448,f983]) ).
fof(f1010,plain,
! [X0,X1] :
( ~ sQ43_spl
| ~ segmentP(X1,X0)
| ~ segmentP(sK49_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sK49_skl)
| X0 = nil
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f783,f315]) ).
fof(f1013,definition,
! [X0,X1] :
( sQ78_spl
<=> ( ~ segmentP(X1,X0)
| ~ segmentP(sK49_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| X0 = nil
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1016,plain,
( ~ sQ43_spl
| ~ sQ5_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f1010,f1013,f498,f779]) ).
fof(f1025,plain,
! [X0,X1] :
( ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f326,f315]) ).
fof(f1028,definition,
! [X0,X1] :
( sQ80_spl
<=> ( ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1031,plain,
( ~ sQ11_spl
| sQ80_spl ),
inference(split_clause,[status(thm)],[f1025,f1028,f538]) ).
fof(f1034,plain,
( sK1_skl = sK0_skl
| neq(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f486,f104]) ).
fof(f1036,definition,
( sQ81_spl
<=> neq(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1039,definition,
( sQ82_spl
<=> sK1_skl = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1040,plain,
( ~ sQ82_spl
| sK1_skl = sK0_skl ),
inference(component_clause,[status(thm)],[f1039]) ).
fof(f1042,plain,
( sQ82_spl
| sQ81_spl ),
inference(split_clause,[status(thm)],[f1034,f1036,f1039]) ).
fof(f1048,plain,
( sK0_skl = sK1_skl
| neq(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f488,f103]) ).
fof(f1053,definition,
( sQ85_spl
<=> neq(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1056,plain,
( sQ82_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f1048,f1053,f1039]) ).
fof(f1057,plain,
( ~ sQ82_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1040,f105]) ).
fof(f1058,plain,
~ sQ82_spl,
inference(contradiction_clause,[status(thm)],[f1057]) ).
fof(f1070,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f317,f323]) ).
fof(f1077,definition,
! [X0] :
( sQ87_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1080,plain,
( sQ87_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1070,f538,f1077]) ).
fof(f1083,plain,
! [X0,X1] :
( ~ sQ13_spl
| segmentP(app(app(X0,sK50_skl),X1),nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f321,f545]) ).
fof(f1084,plain,
! [X0,X1,X2] :
( ~ ssList(X0)
| segmentP(app(app(X1,X0),X2),nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f321,f323]) ).
fof(f1087,definition,
! [X0,X1] :
( sQ88_spl
<=> ( segmentP(app(app(X0,sK50_skl),X1),nil)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1090,plain,
( ~ sQ13_spl
| sQ88_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1083,f572,f538,f1087,f544]) ).
fof(f1091,definition,
! [X0,X1,X2] :
( sQ89_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(X1,X0),X2),nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1094,plain,
( ~ sQ11_spl
| sQ89_spl ),
inference(split_clause,[status(thm)],[f1084,f1091,f538]) ).
fof(f1103,plain,
( ~ sQ30_spl
| ~ ssList(nil)
| rearsegP(app(nil,sK5_skl(nil,sK50_skl)),sK5_skl(nil,sK50_skl))
| ~ ssList(sK5_skl(nil,sK50_skl))
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f694,f457]) ).
fof(f1105,plain,
! [X0] :
( ~ sQ30_spl
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK5_skl(nil,sK50_skl)),X0),sK5_skl(nil,sK50_skl))
| ~ ssList(sK5_skl(nil,sK50_skl))
| ~ ssList(app(sK50_skl,X0)) ),
inference(paramodulation,[status(thm)],[f694,f458]) ).
fof(f1106,plain,
( ~ sQ30_spl
| ~ ssList(sK5_skl(nil,sK50_skl))
| frontsegP(app(nil,sK5_skl(nil,sK50_skl)),nil)
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f694,f456]) ).
fof(f1107,definition,
( sQ91_spl
<=> ssList(sK5_skl(nil,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1109,plain,
( sQ91_spl
| ~ ssList(sK5_skl(nil,sK50_skl)) ),
inference(component_clause,[status(thm)],[f1107]) ).
fof(f1110,definition,
( sQ92_spl
<=> rearsegP(app(nil,sK5_skl(nil,sK50_skl)),sK5_skl(nil,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1113,plain,
( ~ sQ30_spl
| ~ sQ11_spl
| sQ92_spl
| ~ sQ91_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1103,f572,f1107,f1110,f538,f693]) ).
fof(f1115,definition,
! [X0] :
( sQ93_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK5_skl(nil,sK50_skl)),X0),sK5_skl(nil,sK50_skl))
| ~ ssList(app(sK50_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1118,plain,
( ~ sQ30_spl
| ~ sQ11_spl
| ~ sQ91_spl
| sQ93_spl ),
inference(split_clause,[status(thm)],[f1105,f1115,f1107,f538,f693]) ).
fof(f1119,definition,
( sQ94_spl
<=> frontsegP(app(nil,sK5_skl(nil,sK50_skl)),nil) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1122,plain,
( ~ sQ30_spl
| ~ sQ91_spl
| sQ94_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1106,f572,f538,f1119,f1107,f693]) ).
fof(f1123,plain,
( sQ91_spl
| ~ frontsegP(sK50_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1109,f122]) ).
fof(f1124,definition,
( sQ95_spl
<=> frontsegP(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1126,plain,
( sQ95_spl
| ~ frontsegP(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f1124]) ).
fof(f1127,plain,
( sQ91_spl
| ~ sQ95_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1123,f572,f538,f1124,f1107]) ).
fof(f1128,plain,
( sQ95_spl
| ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1126,f690]) ).
fof(f1129,plain,
( sQ95_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f1128]) ).
fof(f1157,plain,
( ~ sQ37_spl
| ~ ssList(nil)
| rearsegP(app(nil,sK5_skl(nil,sK49_skl)),sK5_skl(nil,sK49_skl))
| ~ ssList(sK5_skl(nil,sK49_skl))
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f733,f457]) ).
fof(f1159,plain,
! [X0] :
( ~ sQ37_spl
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK5_skl(nil,sK49_skl)),X0),sK5_skl(nil,sK49_skl))
| ~ ssList(sK5_skl(nil,sK49_skl))
| ~ ssList(app(sK49_skl,X0)) ),
inference(paramodulation,[status(thm)],[f733,f458]) ).
fof(f1160,plain,
( ~ sQ37_spl
| ~ ssList(sK5_skl(nil,sK49_skl))
| frontsegP(app(nil,sK5_skl(nil,sK49_skl)),nil)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f733,f456]) ).
fof(f1161,definition,
( sQ98_spl
<=> ssList(sK5_skl(nil,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1163,plain,
( sQ98_spl
| ~ ssList(sK5_skl(nil,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1161]) ).
fof(f1164,definition,
( sQ99_spl
<=> rearsegP(app(nil,sK5_skl(nil,sK49_skl)),sK5_skl(nil,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1167,plain,
( ~ sQ37_spl
| ~ sQ11_spl
| sQ99_spl
| ~ sQ98_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1157,f498,f1161,f1164,f538,f732]) ).
fof(f1169,definition,
! [X0] :
( sQ100_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK5_skl(nil,sK49_skl)),X0),sK5_skl(nil,sK49_skl))
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1172,plain,
( ~ sQ37_spl
| ~ sQ11_spl
| ~ sQ98_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f1159,f1169,f1161,f538,f732]) ).
fof(f1173,definition,
( sQ101_spl
<=> frontsegP(app(nil,sK5_skl(nil,sK49_skl)),nil) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1176,plain,
( ~ sQ37_spl
| ~ sQ98_spl
| sQ101_spl
| ~ sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1160,f498,f538,f1173,f1161,f732]) ).
fof(f1177,plain,
( sQ98_spl
| ~ frontsegP(sK49_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1163,f122]) ).
fof(f1178,definition,
( sQ102_spl
<=> frontsegP(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1180,plain,
( sQ102_spl
| ~ frontsegP(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f1178]) ).
fof(f1181,plain,
( sQ98_spl
| ~ sQ102_spl
| ~ sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1177,f498,f538,f1178,f1161]) ).
fof(f1182,plain,
( sQ102_spl
| ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1180,f729]) ).
fof(f1183,plain,
( sQ102_spl
| ~ sQ36_spl ),
inference(contradiction_clause,[status(thm)],[f1182]) ).
fof(f1196,plain,
( ~ sQ44_spl
| ~ ssList(sK6_skl(sK50_skl,sK50_skl))
| rearsegP(app(sK6_skl(sK50_skl,sK50_skl),sK50_skl),sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f800,f457]) ).
fof(f1197,plain,
! [X0] :
( ~ sQ44_spl
| frontsegP(sK50_skl,X0)
| ~ frontsegP(sK6_skl(sK50_skl,sK50_skl),X0)
| ~ ssList(sK50_skl)
| ~ ssList(X0)
| ~ ssList(sK6_skl(sK50_skl,sK50_skl)) ),
inference(paramodulation,[status(thm)],[f800,f288]) ).
fof(f1198,plain,
! [X0] :
( ~ sQ44_spl
| ~ ssList(X0)
| ~ ssList(sK6_skl(sK50_skl,sK50_skl))
| segmentP(app(app(sK6_skl(sK50_skl,sK50_skl),sK50_skl),X0),sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(app(sK50_skl,X0)) ),
inference(paramodulation,[status(thm)],[f800,f458]) ).
fof(f1199,plain,
( ~ sQ44_spl
| ~ ssList(sK50_skl)
| frontsegP(app(sK6_skl(sK50_skl,sK50_skl),sK50_skl),sK6_skl(sK50_skl,sK50_skl))
| ~ ssList(sK6_skl(sK50_skl,sK50_skl))
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f800,f456]) ).
fof(f1200,definition,
( sQ103_spl
<=> rearsegP(app(sK6_skl(sK50_skl,sK50_skl),sK50_skl),sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1203,definition,
( sQ104_spl
<=> ssList(sK6_skl(sK50_skl,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1205,plain,
( sQ104_spl
| ~ ssList(sK6_skl(sK50_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f1203]) ).
fof(f1206,plain,
( ~ sQ44_spl
| ~ sQ104_spl
| sQ103_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1196,f572,f1200,f1203,f799]) ).
fof(f1207,definition,
! [X0] :
( sQ105_spl
<=> ( frontsegP(sK50_skl,X0)
| ~ frontsegP(sK6_skl(sK50_skl,sK50_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1210,plain,
( ~ sQ44_spl
| ~ sQ16_spl
| sQ105_spl
| ~ sQ104_spl ),
inference(split_clause,[status(thm)],[f1197,f1203,f1207,f572,f799]) ).
fof(f1211,definition,
! [X0] :
( sQ106_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK6_skl(sK50_skl,sK50_skl),sK50_skl),X0),sK50_skl)
| ~ ssList(app(sK50_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1214,plain,
( ~ sQ44_spl
| ~ sQ104_spl
| ~ sQ16_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f1198,f1211,f572,f1203,f799]) ).
fof(f1215,definition,
( sQ107_spl
<=> frontsegP(app(sK6_skl(sK50_skl,sK50_skl),sK50_skl),sK6_skl(sK50_skl,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1216,plain,
( ~ sQ107_spl
| frontsegP(app(sK6_skl(sK50_skl,sK50_skl),sK50_skl),sK6_skl(sK50_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f1215]) ).
fof(f1218,plain,
( ~ sQ44_spl
| sQ107_spl
| ~ sQ104_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1199,f572,f1203,f1215,f799]) ).
fof(f1219,plain,
( sQ104_spl
| ~ rearsegP(sK50_skl,sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1205,f128]) ).
fof(f1220,definition,
( sQ108_spl
<=> rearsegP(sK50_skl,sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1222,plain,
( sQ108_spl
| ~ rearsegP(sK50_skl,sK50_skl) ),
inference(component_clause,[status(thm)],[f1220]) ).
fof(f1223,plain,
( sQ104_spl
| ~ sQ108_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1219,f572,f1220,f1203]) ).
fof(f1224,plain,
( sQ108_spl
| ~ sQ42_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1222,f776]) ).
fof(f1225,plain,
( sQ108_spl
| ~ sQ42_spl ),
inference(contradiction_clause,[status(thm)],[f1224]) ).
fof(f1228,plain,
( ~ sQ107_spl
| ~ sQ44_spl
| frontsegP(sK50_skl,sK6_skl(sK50_skl,sK50_skl)) ),
inference(forward_demodulation,[status(thm)],[f800,f1216]) ).
fof(f1230,plain,
! [X0] :
( ~ sQ15_spl
| ~ ssList(nil)
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f567,f295]) ).
fof(f1231,plain,
! [X0,X1,X2] :
( ~ sQ15_spl
| ~ frontsegP(X2,X1)
| ~ frontsegP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ frontsegP(X1,X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f567,f282]) ).
fof(f1233,definition,
! [X0] :
( sQ109_spl
<=> ( ~ frontsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1237,plain,
( ~ sQ15_spl
| ~ sQ11_spl
| sQ109_spl ),
inference(split_clause,[status(thm)],[f1230,f1233,f538,f562]) ).
fof(f1238,definition,
! [X0,X1,X2] :
( sQ110_spl
<=> ( ~ frontsegP(X2,X1)
| ~ frontsegP(nil,X2)
| ~ ssList(X1)
| ~ ssList(X2)
| ~ frontsegP(X1,X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1241,plain,
( ~ sQ15_spl
| ~ sQ11_spl
| sQ110_spl ),
inference(split_clause,[status(thm)],[f1231,f1238,f538,f562]) ).
fof(f1248,plain,
! [X0] :
( ~ frontsegP(sK49_skl,X0)
| ~ frontsegP(sK49_skl,sK49_skl)
| X0 = sK49_skl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f586,f421]) ).
fof(f1252,plain,
! [X0] :
( ~ frontsegP(sK50_skl,X0)
| ~ frontsegP(sK50_skl,sK50_skl)
| X0 = sK50_skl
| ~ frontsegP(X0,sK50_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f586,f422]) ).
fof(f1262,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| ~ frontsegP(nil,nil)
| X0 = nil
| ~ frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f586,f223]) ).
fof(f1274,definition,
! [X0] :
( sQ111_spl
<=> ( ~ frontsegP(sK49_skl,X0)
| X0 = sK49_skl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1277,plain,
( ~ sQ61_spl
| sQ111_spl ),
inference(split_clause,[status(thm)],[f1248,f1274,f908]) ).
fof(f1278,definition,
! [X0] :
( sQ112_spl
<=> ( ~ frontsegP(sK50_skl,X0)
| X0 = sK50_skl
| ~ frontsegP(X0,sK50_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1281,plain,
( ~ sQ71_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f1252,f1278,f970]) ).
fof(f1289,definition,
! [X0] :
( sQ115_spl
<=> ( ~ frontsegP(nil,X0)
| X0 = nil
| ~ frontsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f1292,plain,
( ~ sQ52_spl
| sQ115_spl ),
inference(split_clause,[status(thm)],[f1262,f1289,f846]) ).
fof(f1309,plain,
( ~ sQ107_spl
| ~ sQ44_spl
| app(sK6_skl(sK50_skl,sK50_skl),sK5_skl(sK6_skl(sK50_skl,sK50_skl),sK50_skl)) = sK50_skl
| ~ ssList(sK6_skl(sK50_skl,sK50_skl))
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1228,f123]) ).
fof(f1311,definition,
( sQ118_spl
<=> app(sK6_skl(sK50_skl,sK50_skl),sK5_skl(sK6_skl(sK50_skl,sK50_skl),sK50_skl)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1314,plain,
( ~ sQ107_spl
| ~ sQ44_spl
| sQ118_spl
| ~ sQ104_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1309,f572,f1203,f1311,f799,f1215]) ).
fof(f1352,plain,
( ~ sQ54_spl
| ~ ssList(sK6_skl(sK49_skl,sK49_skl))
| rearsegP(app(sK6_skl(sK49_skl,sK49_skl),sK49_skl),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f864,f457]) ).
fof(f1353,plain,
! [X0] :
( ~ sQ54_spl
| frontsegP(sK49_skl,X0)
| ~ frontsegP(sK6_skl(sK49_skl,sK49_skl),X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK6_skl(sK49_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f864,f288]) ).
fof(f1354,plain,
! [X0] :
( ~ sQ54_spl
| ~ ssList(X0)
| ~ ssList(sK6_skl(sK49_skl,sK49_skl))
| segmentP(app(app(sK6_skl(sK49_skl,sK49_skl),sK49_skl),X0),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(paramodulation,[status(thm)],[f864,f458]) ).
fof(f1355,plain,
( ~ sQ54_spl
| ~ ssList(sK49_skl)
| frontsegP(app(sK6_skl(sK49_skl,sK49_skl),sK49_skl),sK6_skl(sK49_skl,sK49_skl))
| ~ ssList(sK6_skl(sK49_skl,sK49_skl))
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f864,f456]) ).
fof(f1356,definition,
( sQ125_spl
<=> rearsegP(app(sK6_skl(sK49_skl,sK49_skl),sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f1359,definition,
( sQ126_spl
<=> ssList(sK6_skl(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1361,plain,
( sQ126_spl
| ~ ssList(sK6_skl(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1359]) ).
fof(f1362,plain,
( ~ sQ54_spl
| ~ sQ126_spl
| sQ125_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1352,f498,f1356,f1359,f863]) ).
fof(f1363,definition,
! [X0] :
( sQ127_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(sK6_skl(sK49_skl,sK49_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f1366,plain,
( ~ sQ54_spl
| ~ sQ5_spl
| sQ127_spl
| ~ sQ126_spl ),
inference(split_clause,[status(thm)],[f1353,f1359,f1363,f498,f863]) ).
fof(f1367,definition,
! [X0] :
( sQ128_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK6_skl(sK49_skl,sK49_skl),sK49_skl),X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1370,plain,
( ~ sQ54_spl
| ~ sQ126_spl
| ~ sQ5_spl
| sQ128_spl ),
inference(split_clause,[status(thm)],[f1354,f1367,f498,f1359,f863]) ).
fof(f1371,definition,
( sQ129_spl
<=> frontsegP(app(sK6_skl(sK49_skl,sK49_skl),sK49_skl),sK6_skl(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f1372,plain,
( ~ sQ129_spl
| frontsegP(app(sK6_skl(sK49_skl,sK49_skl),sK49_skl),sK6_skl(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1371]) ).
fof(f1374,plain,
( ~ sQ54_spl
| sQ129_spl
| ~ sQ126_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1355,f498,f1359,f1371,f863]) ).
fof(f1375,plain,
( sQ126_spl
| ~ rearsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1361,f128]) ).
fof(f1376,definition,
( sQ130_spl
<=> rearsegP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1378,plain,
( sQ130_spl
| ~ rearsegP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f1376]) ).
fof(f1379,plain,
( sQ126_spl
| ~ sQ130_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1375,f498,f1376,f1359]) ).
fof(f1380,plain,
( sQ130_spl
| ~ sQ53_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1378,f861]) ).
fof(f1381,plain,
( sQ130_spl
| ~ sQ53_spl ),
inference(contradiction_clause,[status(thm)],[f1380]) ).
fof(f1384,plain,
( ~ sQ129_spl
| ~ sQ54_spl
| frontsegP(sK49_skl,sK6_skl(sK49_skl,sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f864,f1372]) ).
fof(f1400,plain,
( ~ sQ129_spl
| ~ sQ54_spl
| app(sK6_skl(sK49_skl,sK49_skl),sK5_skl(sK6_skl(sK49_skl,sK49_skl),sK49_skl)) = sK49_skl
| ~ ssList(sK6_skl(sK49_skl,sK49_skl))
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1384,f123]) ).
fof(f1402,definition,
( sQ133_spl
<=> app(sK6_skl(sK49_skl,sK49_skl),sK5_skl(sK6_skl(sK49_skl,sK49_skl),sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f1405,plain,
( ~ sQ129_spl
| ~ sQ54_spl
| sQ133_spl
| ~ sQ126_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1400,f498,f1359,f1402,f863,f1371]) ).
fof(f1414,plain,
! [X0] :
( ~ sQ27_spl
| app(X0,sK5_skl(X0,sK50_skl)) = sK50_skl
| ~ ssList(X0)
| ~ ssList(sK50_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f678,f123]) ).
fof(f1415,plain,
! [X0] :
( ~ sQ27_spl
| X0 = sK50_skl
| ~ frontsegP(X0,sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f678,f284]) ).
fof(f1417,definition,
! [X0] :
( sQ136_spl
<=> ( app(X0,sK5_skl(X0,sK50_skl)) = sK50_skl
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1420,plain,
( ~ sQ27_spl
| ~ sQ16_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f1414,f1417,f572,f677]) ).
fof(f1421,definition,
! [X0] :
( sQ137_spl
<=> ( X0 = sK50_skl
| ~ frontsegP(X0,sK50_skl)
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1424,plain,
( ~ sQ27_spl
| ~ sQ16_spl
| sQ137_spl ),
inference(split_clause,[status(thm)],[f1415,f1421,f572,f677]) ).
fof(f1457,plain,
( ~ sQ50_spl
| ~ ssList(sK6_skl(nil,nil))
| rearsegP(app(sK6_skl(nil,nil),nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f835,f457]) ).
fof(f1458,plain,
! [X0] :
( ~ sQ50_spl
| frontsegP(nil,X0)
| ~ frontsegP(sK6_skl(nil,nil),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(nil,nil)) ),
inference(paramodulation,[status(thm)],[f835,f288]) ).
fof(f1459,plain,
! [X0] :
( ~ sQ50_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)],[f835,f458]) ).
fof(f1460,plain,
( ~ sQ50_spl
| ~ ssList(nil)
| frontsegP(app(sK6_skl(nil,nil),nil),sK6_skl(nil,nil))
| ~ ssList(sK6_skl(nil,nil))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f835,f456]) ).
fof(f1461,definition,
( sQ142_spl
<=> rearsegP(app(sK6_skl(nil,nil),nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f1464,definition,
( sQ143_spl
<=> ssList(sK6_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1465,plain,
( ~ sQ143_spl
| ssList(sK6_skl(nil,nil)) ),
inference(component_clause,[status(thm)],[f1464]) ).
fof(f1466,plain,
( sQ143_spl
| ~ ssList(sK6_skl(nil,nil)) ),
inference(component_clause,[status(thm)],[f1464]) ).
fof(f1467,plain,
( ~ sQ50_spl
| ~ sQ143_spl
| sQ142_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1457,f538,f1461,f1464,f834]) ).
fof(f1468,definition,
! [X0] :
( sQ144_spl
<=> ( frontsegP(nil,X0)
| ~ frontsegP(sK6_skl(nil,nil),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1471,plain,
( ~ sQ50_spl
| ~ sQ11_spl
| sQ144_spl
| ~ sQ143_spl ),
inference(split_clause,[status(thm)],[f1458,f1464,f1468,f538,f834]) ).
fof(f1472,definition,
! [X0] :
( sQ145_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK6_skl(nil,nil),nil),X0),nil)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1475,plain,
( ~ sQ50_spl
| ~ sQ143_spl
| ~ sQ11_spl
| sQ145_spl ),
inference(split_clause,[status(thm)],[f1459,f1472,f538,f1464,f834]) ).
fof(f1476,definition,
( sQ146_spl
<=> frontsegP(app(sK6_skl(nil,nil),nil),sK6_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1479,plain,
( ~ sQ50_spl
| sQ146_spl
| ~ sQ143_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1460,f538,f1464,f1476,f834]) ).
fof(f1480,plain,
( sQ143_spl
| ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1466,f128]) ).
fof(f1481,definition,
( sQ147_spl
<=> rearsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1483,plain,
( sQ147_spl
| ~ rearsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f1481]) ).
fof(f1484,plain,
( sQ143_spl
| ~ sQ147_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1480,f538,f1481,f1464]) ).
fof(f1485,plain,
( sQ147_spl
| ~ sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1483,f830]) ).
fof(f1486,plain,
( sQ147_spl
| ~ sQ46_spl ),
inference(contradiction_clause,[status(thm)],[f1485]) ).
fof(f1490,plain,
! [X0] :
( ~ sQ143_spl
| ~ frontsegP(sK6_skl(nil,nil),X0)
| ~ frontsegP(sK6_skl(nil,nil),sK6_skl(nil,nil))
| X0 = sK6_skl(nil,nil)
| ~ frontsegP(X0,sK6_skl(nil,nil))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1465,f586]) ).
fof(f1497,definition,
! [X0] :
( sQ148_spl
<=> ( ~ frontsegP(sK6_skl(nil,nil),X0)
| X0 = sK6_skl(nil,nil)
| ~ frontsegP(X0,sK6_skl(nil,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1500,definition,
( sQ149_spl
<=> frontsegP(sK6_skl(nil,nil),sK6_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1503,plain,
( ~ sQ143_spl
| ~ sQ149_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1490,f1497,f1500,f1464]) ).
fof(f1512,plain,
! [X0] :
( X0 = app(sK50_skl,nil)
| ~ frontsegP(X0,app(sK50_skl,nil))
| ~ ssList(sK50_skl)
| ~ frontsegP(sK50_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f869,f589]) ).
fof(f1515,plain,
! [X0] :
( X0 = app(sK49_skl,nil)
| ~ frontsegP(X0,app(sK49_skl,nil))
| ~ ssList(sK49_skl)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f867,f589]) ).
fof(f1516,plain,
! [X0] :
( X0 = app(nil,sK49_skl)
| ~ frontsegP(X0,app(nil,sK49_skl))
| ~ ssList(sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f670,f589]) ).
fof(f1517,plain,
! [X0] :
( X0 = app(nil,nil)
| ~ frontsegP(X0,app(nil,nil))
| ~ ssList(nil)
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f673,f589]) ).
fof(f1518,plain,
! [X0] :
( X0 = app(nil,sK50_skl)
| ~ frontsegP(X0,app(nil,sK50_skl))
| ~ ssList(sK50_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(sK50_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f668,f589]) ).
fof(f1523,definition,
! [X0] :
( sQ151_spl
<=> ( X0 = app(sK50_skl,nil)
| ~ frontsegP(X0,app(sK50_skl,nil))
| ~ frontsegP(sK50_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1526,plain,
( ~ sQ11_spl
| sQ151_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1512,f572,f1523,f538]) ).
fof(f1535,definition,
! [X0] :
( sQ154_spl
<=> ( X0 = app(sK49_skl,nil)
| ~ frontsegP(X0,app(sK49_skl,nil))
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f1538,plain,
( ~ sQ11_spl
| sQ154_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1515,f498,f1535,f538]) ).
fof(f1539,definition,
! [X0] :
( sQ155_spl
<=> ( X0 = app(nil,sK49_skl)
| ~ frontsegP(X0,app(nil,sK49_skl))
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f1542,plain,
( ~ sQ5_spl
| sQ155_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1516,f538,f1539,f498]) ).
fof(f1543,definition,
! [X0] :
( sQ156_spl
<=> ( X0 = app(nil,nil)
| ~ frontsegP(X0,app(nil,nil))
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f1546,plain,
( sQ156_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1517,f538,f1543]) ).
fof(f1547,definition,
! [X0] :
( sQ157_spl
<=> ( X0 = app(nil,sK50_skl)
| ~ frontsegP(X0,app(nil,sK50_skl))
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f1550,plain,
( ~ sQ16_spl
| sQ157_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1518,f538,f1547,f572]) ).
fof(f1568,plain,
! [X0] :
( ~ frontsegP(sK50_skl,X0)
| ~ ssList(nil)
| ~ ssList(sK50_skl)
| app(X0,sK5_skl(X0,app(sK50_skl,nil))) = app(sK50_skl,nil)
| ~ ssList(X0)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f869,f619]) ).
fof(f1571,plain,
! [X0] :
( ~ frontsegP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssList(sK49_skl)
| app(X0,sK5_skl(X0,app(sK49_skl,nil))) = app(sK49_skl,nil)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f867,f619]) ).
fof(f1572,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(nil)
| app(X0,sK5_skl(X0,app(nil,sK49_skl))) = app(nil,sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f670,f619]) ).
fof(f1573,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(nil)
| app(X0,sK5_skl(X0,app(nil,nil))) = app(nil,nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f673,f619]) ).
fof(f1574,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| ~ ssList(sK50_skl)
| ~ ssList(nil)
| app(X0,sK5_skl(X0,app(nil,sK50_skl))) = app(nil,sK50_skl)
| ~ ssList(X0)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f668,f619]) ).
fof(f1579,definition,
! [X0] :
( sQ159_spl
<=> ( ~ frontsegP(sK50_skl,X0)
| app(X0,sK5_skl(X0,app(sK50_skl,nil))) = app(sK50_skl,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f1582,plain,
( ~ sQ11_spl
| sQ159_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1568,f572,f1579,f538]) ).
fof(f1591,definition,
! [X0] :
( sQ162_spl
<=> ( ~ frontsegP(sK49_skl,X0)
| app(X0,sK5_skl(X0,app(sK49_skl,nil))) = app(sK49_skl,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f1594,plain,
( ~ sQ11_spl
| sQ162_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1571,f498,f1591,f538]) ).
fof(f1595,definition,
! [X0] :
( sQ163_spl
<=> ( ~ frontsegP(nil,X0)
| app(X0,sK5_skl(X0,app(nil,sK49_skl))) = app(nil,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f1598,plain,
( ~ sQ11_spl
| sQ163_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1572,f498,f1595,f538]) ).
fof(f1599,definition,
! [X0] :
( sQ164_spl
<=> ( ~ frontsegP(nil,X0)
| app(X0,sK5_skl(X0,app(nil,nil))) = app(nil,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f1602,plain,
( sQ164_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1573,f538,f1599]) ).
fof(f1603,definition,
! [X0] :
( sQ165_spl
<=> ( ~ frontsegP(nil,X0)
| app(X0,sK5_skl(X0,app(nil,sK50_skl))) = app(nil,sK50_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f1606,plain,
( ~ sQ11_spl
| sQ165_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1574,f572,f1603,f538]) ).
fof(f1623,plain,
! [X0] :
( ~ sQ59_spl
| ~ frontsegP(sK6_skl(nil,sK49_skl),X0)
| ~ ssList(nil)
| ~ ssList(sK6_skl(nil,sK49_skl))
| app(X0,sK5_skl(X0,app(sK6_skl(nil,sK49_skl),nil))) = app(sK6_skl(nil,sK49_skl),nil)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f899,f619]) ).
fof(f1624,plain,
! [X0] :
( ~ sQ59_spl
| X0 = app(sK6_skl(nil,sK49_skl),nil)
| ~ frontsegP(X0,app(sK6_skl(nil,sK49_skl),nil))
| ~ ssList(sK49_skl)
| ~ frontsegP(sK6_skl(nil,sK49_skl),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(nil,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f899,f589]) ).
fof(f1625,plain,
( ~ sQ59_spl
| ~ ssList(sK6_skl(nil,sK49_skl))
| rearsegP(app(sK6_skl(nil,sK49_skl),nil),nil)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f899,f457]) ).
fof(f1626,plain,
! [X0] :
( ~ sQ59_spl
| frontsegP(sK49_skl,X0)
| ~ frontsegP(sK6_skl(nil,sK49_skl),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(nil,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f899,f288]) ).
fof(f1627,plain,
! [X0] :
( ~ sQ59_spl
| ~ ssList(X0)
| ~ ssList(sK6_skl(nil,sK49_skl))
| segmentP(app(app(sK6_skl(nil,sK49_skl),nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK49_skl,X0)) ),
inference(paramodulation,[status(thm)],[f899,f458]) ).
fof(f1628,plain,
( ~ sQ59_spl
| ~ ssList(nil)
| frontsegP(app(sK6_skl(nil,sK49_skl),nil),sK6_skl(nil,sK49_skl))
| ~ ssList(sK6_skl(nil,sK49_skl))
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f899,f456]) ).
fof(f1629,definition,
! [X0] :
( sQ166_spl
<=> ( ~ frontsegP(sK6_skl(nil,sK49_skl),X0)
| app(X0,sK5_skl(X0,app(sK6_skl(nil,sK49_skl),nil))) = app(sK6_skl(nil,sK49_skl),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f1632,definition,
( sQ167_spl
<=> ssList(sK6_skl(nil,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f1634,plain,
( sQ167_spl
| ~ ssList(sK6_skl(nil,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1632]) ).
fof(f1635,plain,
( ~ sQ59_spl
| ~ sQ11_spl
| ~ sQ167_spl
| sQ166_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1623,f498,f1629,f1632,f538,f898]) ).
fof(f1636,definition,
! [X0] :
( sQ168_spl
<=> ( X0 = app(sK6_skl(nil,sK49_skl),nil)
| ~ frontsegP(X0,app(sK6_skl(nil,sK49_skl),nil))
| ~ frontsegP(sK6_skl(nil,sK49_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f1639,plain,
( ~ sQ59_spl
| ~ sQ5_spl
| ~ sQ11_spl
| sQ168_spl
| ~ sQ167_spl ),
inference(split_clause,[status(thm)],[f1624,f1632,f1636,f538,f498,f898]) ).
fof(f1640,definition,
( sQ169_spl
<=> rearsegP(app(sK6_skl(nil,sK49_skl),nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f1643,plain,
( ~ sQ59_spl
| ~ sQ167_spl
| sQ169_spl
| ~ sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1625,f498,f538,f1640,f1632,f898]) ).
fof(f1644,definition,
! [X0] :
( sQ170_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(sK6_skl(nil,sK49_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f1647,plain,
( ~ sQ59_spl
| ~ sQ11_spl
| sQ170_spl
| ~ sQ167_spl ),
inference(split_clause,[status(thm)],[f1626,f1632,f1644,f538,f898]) ).
fof(f1648,definition,
! [X0] :
( sQ171_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK6_skl(nil,sK49_skl),nil),X0),nil)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f1651,plain,
( ~ sQ59_spl
| ~ sQ167_spl
| ~ sQ11_spl
| sQ171_spl ),
inference(split_clause,[status(thm)],[f1627,f1648,f538,f1632,f898]) ).
fof(f1652,definition,
( sQ172_spl
<=> frontsegP(app(sK6_skl(nil,sK49_skl),nil),sK6_skl(nil,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f1655,plain,
( ~ sQ59_spl
| ~ sQ11_spl
| sQ172_spl
| ~ sQ167_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1628,f498,f1632,f1652,f538,f898]) ).
fof(f1656,plain,
( sQ167_spl
| ~ rearsegP(sK49_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1634,f128]) ).
fof(f1657,definition,
( sQ173_spl
<=> rearsegP(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ173_spl])],[split_symbol_definition]) ).
fof(f1659,plain,
( sQ173_spl
| ~ rearsegP(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f1657]) ).
fof(f1660,plain,
( sQ167_spl
| ~ sQ173_spl
| ~ sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1656,f498,f538,f1657,f1632]) ).
fof(f1661,plain,
( sQ173_spl
| ~ sQ55_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1659,f894]) ).
fof(f1662,plain,
( sQ173_spl
| ~ sQ55_spl ),
inference(contradiction_clause,[status(thm)],[f1661]) ).
fof(f1691,plain,
( ~ sQ28_spl
| ~ ssList(nil)
| segmentP(app(sK50_skl,nil),sK50_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f869,f689]) ).
fof(f1696,definition,
( sQ177_spl
<=> segmentP(app(sK50_skl,nil),sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f1697,plain,
( ~ sQ177_spl
| segmentP(app(sK50_skl,nil),sK50_skl) ),
inference(component_clause,[status(thm)],[f1696]) ).
fof(f1699,plain,
( ~ sQ28_spl
| ~ sQ11_spl
| sQ177_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1691,f572,f1696,f538,f681]) ).
fof(f1700,plain,
( ~ sQ177_spl
| segmentP(sK50_skl,sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f869,f1697]) ).
fof(f1702,plain,
! [X0,X1] :
( ~ sQ177_spl
| segmentP(app(app(X0,sK50_skl),X1),sK50_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1700,f321]) ).
fof(f1704,plain,
( ~ sQ177_spl
| app(app(sK7_skl(sK50_skl,sK50_skl),sK50_skl),sK8_skl(sK50_skl,sK50_skl)) = sK50_skl
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1700,f136]) ).
fof(f1705,definition,
! [X0,X1] :
( sQ178_spl
<=> ( segmentP(app(app(X0,sK50_skl),X1),sK50_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f1708,plain,
( ~ sQ177_spl
| sQ178_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1702,f572,f1705,f1696]) ).
fof(f1713,definition,
( sQ180_spl
<=> app(app(sK7_skl(sK50_skl,sK50_skl),sK50_skl),sK8_skl(sK50_skl,sK50_skl)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f1716,plain,
( ~ sQ177_spl
| sQ180_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1704,f572,f1713,f1696]) ).
fof(f1718,plain,
! [X0] :
( ~ sQ51_spl
| ~ frontsegP(nil,X0)
| ~ ssList(sK5_skl(nil,nil))
| ~ ssList(nil)
| app(X0,sK5_skl(X0,app(nil,sK5_skl(nil,nil)))) = app(nil,sK5_skl(nil,nil))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f843,f619]) ).
fof(f1719,plain,
! [X0] :
( ~ sQ51_spl
| X0 = app(nil,sK5_skl(nil,nil))
| ~ frontsegP(X0,app(nil,sK5_skl(nil,nil)))
| ~ ssList(nil)
| ~ frontsegP(nil,X0)
| ~ ssList(sK5_skl(nil,nil))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f843,f589]) ).
fof(f1720,plain,
( ~ sQ51_spl
| ~ ssList(nil)
| rearsegP(app(nil,sK5_skl(nil,nil)),sK5_skl(nil,nil))
| ~ ssList(sK5_skl(nil,nil))
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f843,f457]) ).
fof(f1722,plain,
! [X0] :
( ~ sQ51_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)],[f843,f458]) ).
fof(f1723,plain,
( ~ sQ51_spl
| ~ ssList(sK5_skl(nil,nil))
| frontsegP(app(nil,sK5_skl(nil,nil)),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f843,f456]) ).
fof(f1724,definition,
! [X0] :
( sQ181_spl
<=> ( ~ frontsegP(nil,X0)
| app(X0,sK5_skl(X0,app(nil,sK5_skl(nil,nil)))) = app(nil,sK5_skl(nil,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f1727,definition,
( sQ182_spl
<=> ssList(sK5_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f1728,plain,
( ~ sQ182_spl
| ssList(sK5_skl(nil,nil)) ),
inference(component_clause,[status(thm)],[f1727]) ).
fof(f1729,plain,
( sQ182_spl
| ~ ssList(sK5_skl(nil,nil)) ),
inference(component_clause,[status(thm)],[f1727]) ).
fof(f1730,plain,
( ~ sQ51_spl
| ~ sQ182_spl
| sQ181_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1718,f538,f1724,f1727,f842]) ).
fof(f1731,definition,
! [X0] :
( sQ183_spl
<=> ( X0 = app(nil,sK5_skl(nil,nil))
| ~ frontsegP(X0,app(nil,sK5_skl(nil,nil)))
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f1734,plain,
( ~ sQ51_spl
| ~ sQ182_spl
| sQ183_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1719,f538,f1731,f1727,f842]) ).
fof(f1735,definition,
( sQ184_spl
<=> rearsegP(app(nil,sK5_skl(nil,nil)),sK5_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f1738,plain,
( ~ sQ51_spl
| sQ184_spl
| ~ sQ182_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1720,f538,f1727,f1735,f842]) ).
fof(f1740,definition,
! [X0] :
( sQ185_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,[sQ185_spl])],[split_symbol_definition]) ).
fof(f1743,plain,
( ~ sQ51_spl
| ~ sQ11_spl
| ~ sQ182_spl
| sQ185_spl ),
inference(split_clause,[status(thm)],[f1722,f1740,f1727,f538,f842]) ).
fof(f1744,definition,
( sQ186_spl
<=> frontsegP(app(nil,sK5_skl(nil,nil)),nil) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f1747,plain,
( ~ sQ51_spl
| ~ sQ182_spl
| sQ186_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1723,f538,f1744,f1727,f842]) ).
fof(f1748,plain,
( sQ182_spl
| ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1729,f122]) ).
fof(f1749,plain,
( sQ182_spl
| ~ sQ52_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f1748,f538,f846,f1727]) ).
fof(f1750,plain,
( sQ52_spl
| ~ sQ49_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f848,f832]) ).
fof(f1751,plain,
( sQ52_spl
| ~ sQ49_spl ),
inference(contradiction_clause,[status(thm)],[f1750]) ).
fof(f1759,plain,
! [X0] :
( ~ sQ182_spl
| ~ frontsegP(sK5_skl(nil,nil),X0)
| ~ frontsegP(sK5_skl(nil,nil),sK5_skl(nil,nil))
| X0 = sK5_skl(nil,nil)
| ~ frontsegP(X0,sK5_skl(nil,nil))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1728,f586]) ).
fof(f1766,definition,
! [X0] :
( sQ187_spl
<=> ( ~ frontsegP(sK5_skl(nil,nil),X0)
| X0 = sK5_skl(nil,nil)
| ~ frontsegP(X0,sK5_skl(nil,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f1769,definition,
( sQ188_spl
<=> frontsegP(sK5_skl(nil,nil),sK5_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f1772,plain,
( ~ sQ182_spl
| ~ sQ188_spl
| sQ187_spl ),
inference(split_clause,[status(thm)],[f1759,f1766,f1769,f1727]) ).
fof(f1784,plain,
! [X0] :
( ~ frontsegP(sK49_skl,sK49_skl)
| ~ frontsegP(X0,sK49_skl)
| app(sK49_skl,sK5_skl(sK49_skl,X0)) = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f624,f421]) ).
fof(f1788,plain,
! [X0] :
( ~ frontsegP(sK50_skl,sK50_skl)
| ~ frontsegP(X0,sK50_skl)
| app(sK50_skl,sK5_skl(sK50_skl,X0)) = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f624,f422]) ).
fof(f1798,plain,
! [X0] :
( ~ frontsegP(nil,nil)
| ~ frontsegP(X0,nil)
| app(nil,sK5_skl(nil,X0)) = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f624,f223]) ).
fof(f1810,definition,
! [X0] :
( sQ189_spl
<=> ( ~ frontsegP(X0,sK49_skl)
| app(sK49_skl,sK5_skl(sK49_skl,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ189_spl])],[split_symbol_definition]) ).
fof(f1813,plain,
( ~ sQ61_spl
| sQ189_spl ),
inference(split_clause,[status(thm)],[f1784,f1810,f908]) ).
fof(f1814,definition,
! [X0] :
( sQ190_spl
<=> ( ~ frontsegP(X0,sK50_skl)
| app(sK50_skl,sK5_skl(sK50_skl,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f1817,plain,
( ~ sQ71_spl
| sQ190_spl ),
inference(split_clause,[status(thm)],[f1788,f1814,f970]) ).
fof(f1822,definition,
! [X0] :
( sQ192_spl
<=> ( ~ frontsegP(X0,nil)
| app(nil,sK5_skl(nil,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f1825,plain,
( ~ sQ52_spl
| sQ192_spl ),
inference(split_clause,[status(thm)],[f1798,f1822,f846]) ).
fof(f1854,plain,
! [X0] :
( ~ sQ60_spl
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(sK5_skl(sK49_skl,sK49_skl))
| ~ ssList(sK49_skl)
| app(X0,sK5_skl(X0,app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)))) = app(sK49_skl,sK5_skl(sK49_skl,sK49_skl))
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f905,f619]) ).
fof(f1855,plain,
! [X0] :
( ~ sQ60_spl
| X0 = app(sK49_skl,sK5_skl(sK49_skl,sK49_skl))
| ~ frontsegP(X0,app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)))
| ~ ssList(sK49_skl)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(sK5_skl(sK49_skl,sK49_skl))
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f905,f589]) ).
fof(f1856,plain,
( ~ sQ60_spl
| ~ ssList(sK49_skl)
| rearsegP(app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)),sK5_skl(sK49_skl,sK49_skl))
| ~ ssList(sK5_skl(sK49_skl,sK49_skl))
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f905,f457]) ).
fof(f1858,plain,
! [X0] :
( ~ sQ60_spl
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| segmentP(app(app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)),X0),sK5_skl(sK49_skl,sK49_skl))
| ~ ssList(sK5_skl(sK49_skl,sK49_skl))
| ~ ssList(app(sK49_skl,X0)) ),
inference(paramodulation,[status(thm)],[f905,f458]) ).
fof(f1859,plain,
( ~ sQ60_spl
| ~ ssList(sK5_skl(sK49_skl,sK49_skl))
| frontsegP(app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f905,f456]) ).
fof(f1860,definition,
! [X0] :
( sQ193_spl
<=> ( ~ frontsegP(sK49_skl,X0)
| app(X0,sK5_skl(X0,app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)))) = app(sK49_skl,sK5_skl(sK49_skl,sK49_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f1863,definition,
( sQ194_spl
<=> ssList(sK5_skl(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ194_spl])],[split_symbol_definition]) ).
fof(f1865,plain,
( sQ194_spl
| ~ ssList(sK5_skl(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1863]) ).
fof(f1866,plain,
( ~ sQ60_spl
| ~ sQ194_spl
| sQ193_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1854,f498,f1860,f1863,f904]) ).
fof(f1867,definition,
! [X0] :
( sQ195_spl
<=> ( X0 = app(sK49_skl,sK5_skl(sK49_skl,sK49_skl))
| ~ frontsegP(X0,app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)))
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f1870,plain,
( ~ sQ60_spl
| ~ sQ194_spl
| sQ195_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1855,f498,f1867,f1863,f904]) ).
fof(f1871,definition,
( sQ196_spl
<=> rearsegP(app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)),sK5_skl(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f1872,plain,
( ~ sQ196_spl
| rearsegP(app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)),sK5_skl(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1871]) ).
fof(f1874,plain,
( ~ sQ60_spl
| sQ196_spl
| ~ sQ194_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1856,f498,f1863,f1871,f904]) ).
fof(f1876,definition,
! [X0] :
( sQ197_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)),X0),sK5_skl(sK49_skl,sK49_skl))
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f1879,plain,
( ~ sQ60_spl
| ~ sQ5_spl
| ~ sQ194_spl
| sQ197_spl ),
inference(split_clause,[status(thm)],[f1858,f1876,f1863,f498,f904]) ).
fof(f1880,definition,
( sQ198_spl
<=> frontsegP(app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ198_spl])],[split_symbol_definition]) ).
fof(f1883,plain,
( ~ sQ60_spl
| ~ sQ194_spl
| sQ198_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1859,f498,f1880,f1863,f904]) ).
fof(f1884,plain,
( sQ194_spl
| ~ frontsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1865,f122]) ).
fof(f1885,plain,
( sQ194_spl
| ~ sQ61_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1884,f498,f908,f1863]) ).
fof(f1890,plain,
( ~ sQ196_spl
| ~ sQ60_spl
| rearsegP(sK49_skl,sK5_skl(sK49_skl,sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f905,f1872]) ).
fof(f1895,plain,
! [X0] :
( ~ sQ34_spl
| app(X0,sK5_skl(X0,sK49_skl)) = sK49_skl
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f717,f123]) ).
fof(f1896,plain,
! [X0] :
( ~ sQ34_spl
| X0 = sK49_skl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f717,f284]) ).
fof(f1899,definition,
! [X0] :
( sQ199_spl
<=> ( app(X0,sK5_skl(X0,sK49_skl)) = sK49_skl
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f1902,plain,
( ~ sQ34_spl
| ~ sQ5_spl
| sQ199_spl ),
inference(split_clause,[status(thm)],[f1895,f1899,f498,f716]) ).
fof(f1903,definition,
! [X0] :
( sQ200_spl
<=> ( X0 = sK49_skl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f1906,plain,
( ~ sQ34_spl
| ~ sQ5_spl
| sQ200_spl ),
inference(split_clause,[status(thm)],[f1896,f1903,f498,f716]) ).
fof(f1935,plain,
( ~ sQ196_spl
| ~ sQ60_spl
| app(sK6_skl(sK5_skl(sK49_skl,sK49_skl),sK49_skl),sK5_skl(sK49_skl,sK49_skl)) = sK49_skl
| ~ ssList(sK5_skl(sK49_skl,sK49_skl))
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1890,f129]) ).
fof(f1936,definition,
( sQ204_spl
<=> app(sK6_skl(sK5_skl(sK49_skl,sK49_skl),sK49_skl),sK5_skl(sK49_skl,sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f1939,plain,
( ~ sQ196_spl
| ~ sQ60_spl
| sQ204_spl
| ~ sQ194_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1935,f498,f1863,f1936,f904,f1871]) ).
fof(f1940,plain,
! [X0] :
( ~ sQ67_spl
| ~ frontsegP(sK6_skl(nil,sK50_skl),X0)
| ~ ssList(nil)
| ~ ssList(sK6_skl(nil,sK50_skl))
| app(X0,sK5_skl(X0,app(sK6_skl(nil,sK50_skl),nil))) = app(sK6_skl(nil,sK50_skl),nil)
| ~ ssList(X0)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f942,f619]) ).
fof(f1941,plain,
! [X0] :
( ~ sQ67_spl
| X0 = app(sK6_skl(nil,sK50_skl),nil)
| ~ frontsegP(X0,app(sK6_skl(nil,sK50_skl),nil))
| ~ ssList(sK50_skl)
| ~ frontsegP(sK6_skl(nil,sK50_skl),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(nil,sK50_skl)) ),
inference(paramodulation,[status(thm)],[f942,f589]) ).
fof(f1942,plain,
( ~ sQ67_spl
| ~ ssList(sK6_skl(nil,sK50_skl))
| rearsegP(app(sK6_skl(nil,sK50_skl),nil),nil)
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f942,f457]) ).
fof(f1943,plain,
! [X0] :
( ~ sQ67_spl
| frontsegP(sK50_skl,X0)
| ~ frontsegP(sK6_skl(nil,sK50_skl),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(nil,sK50_skl)) ),
inference(paramodulation,[status(thm)],[f942,f288]) ).
fof(f1944,plain,
! [X0] :
( ~ sQ67_spl
| ~ ssList(X0)
| ~ ssList(sK6_skl(nil,sK50_skl))
| segmentP(app(app(sK6_skl(nil,sK50_skl),nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK50_skl,X0)) ),
inference(paramodulation,[status(thm)],[f942,f458]) ).
fof(f1945,plain,
( ~ sQ67_spl
| ~ ssList(nil)
| frontsegP(app(sK6_skl(nil,sK50_skl),nil),sK6_skl(nil,sK50_skl))
| ~ ssList(sK6_skl(nil,sK50_skl))
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f942,f456]) ).
fof(f1946,definition,
! [X0] :
( sQ205_spl
<=> ( ~ frontsegP(sK6_skl(nil,sK50_skl),X0)
| app(X0,sK5_skl(X0,app(sK6_skl(nil,sK50_skl),nil))) = app(sK6_skl(nil,sK50_skl),nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f1949,definition,
( sQ206_spl
<=> ssList(sK6_skl(nil,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f1950,plain,
( ~ sQ206_spl
| ssList(sK6_skl(nil,sK50_skl)) ),
inference(component_clause,[status(thm)],[f1949]) ).
fof(f1951,plain,
( sQ206_spl
| ~ ssList(sK6_skl(nil,sK50_skl)) ),
inference(component_clause,[status(thm)],[f1949]) ).
fof(f1952,plain,
( ~ sQ67_spl
| ~ sQ11_spl
| ~ sQ206_spl
| sQ205_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1940,f572,f1946,f1949,f538,f941]) ).
fof(f1953,definition,
! [X0] :
( sQ207_spl
<=> ( X0 = app(sK6_skl(nil,sK50_skl),nil)
| ~ frontsegP(X0,app(sK6_skl(nil,sK50_skl),nil))
| ~ frontsegP(sK6_skl(nil,sK50_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f1956,plain,
( ~ sQ67_spl
| ~ sQ16_spl
| ~ sQ11_spl
| sQ207_spl
| ~ sQ206_spl ),
inference(split_clause,[status(thm)],[f1941,f1949,f1953,f538,f572,f941]) ).
fof(f1957,definition,
( sQ208_spl
<=> rearsegP(app(sK6_skl(nil,sK50_skl),nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f1960,plain,
( ~ sQ67_spl
| ~ sQ206_spl
| sQ208_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1942,f572,f538,f1957,f1949,f941]) ).
fof(f1961,definition,
! [X0] :
( sQ209_spl
<=> ( frontsegP(sK50_skl,X0)
| ~ frontsegP(sK6_skl(nil,sK50_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f1964,plain,
( ~ sQ67_spl
| ~ sQ11_spl
| sQ209_spl
| ~ sQ206_spl ),
inference(split_clause,[status(thm)],[f1943,f1949,f1961,f538,f941]) ).
fof(f1965,definition,
! [X0] :
( sQ210_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK6_skl(nil,sK50_skl),nil),X0),nil)
| ~ ssList(app(sK50_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ210_spl])],[split_symbol_definition]) ).
fof(f1968,plain,
( ~ sQ67_spl
| ~ sQ206_spl
| ~ sQ11_spl
| sQ210_spl ),
inference(split_clause,[status(thm)],[f1944,f1965,f538,f1949,f941]) ).
fof(f1969,definition,
( sQ211_spl
<=> frontsegP(app(sK6_skl(nil,sK50_skl),nil),sK6_skl(nil,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f1972,plain,
( ~ sQ67_spl
| ~ sQ11_spl
| sQ211_spl
| ~ sQ206_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1945,f572,f1949,f1969,f538,f941]) ).
fof(f1973,plain,
( sQ206_spl
| ~ rearsegP(sK50_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1951,f128]) ).
fof(f1974,definition,
( sQ212_spl
<=> rearsegP(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f1976,plain,
( sQ212_spl
| ~ rearsegP(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f1974]) ).
fof(f1977,plain,
( sQ206_spl
| ~ sQ212_spl
| ~ sQ11_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f1973,f572,f538,f1974,f1949]) ).
fof(f1978,plain,
( sQ212_spl
| ~ sQ63_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1976,f937]) ).
fof(f1979,plain,
( sQ212_spl
| ~ sQ63_spl ),
inference(contradiction_clause,[status(thm)],[f1978]) ).
fof(f1989,plain,
! [X0] :
( ~ sQ206_spl
| ~ frontsegP(sK6_skl(nil,sK50_skl),sK6_skl(nil,sK50_skl))
| ~ frontsegP(X0,sK6_skl(nil,sK50_skl))
| app(sK6_skl(nil,sK50_skl),sK5_skl(sK6_skl(nil,sK50_skl),X0)) = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1950,f624]) ).
fof(f1993,plain,
! [X0] :
( ~ sQ206_spl
| ~ frontsegP(sK6_skl(nil,sK50_skl),X0)
| ~ frontsegP(sK6_skl(nil,sK50_skl),sK6_skl(nil,sK50_skl))
| X0 = sK6_skl(nil,sK50_skl)
| ~ frontsegP(X0,sK6_skl(nil,sK50_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1950,f586]) ).
fof(f2000,definition,
! [X0] :
( sQ213_spl
<=> ( ~ frontsegP(X0,sK6_skl(nil,sK50_skl))
| app(sK6_skl(nil,sK50_skl),sK5_skl(sK6_skl(nil,sK50_skl),X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f2003,definition,
( sQ214_spl
<=> frontsegP(sK6_skl(nil,sK50_skl),sK6_skl(nil,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f2006,plain,
( ~ sQ206_spl
| ~ sQ214_spl
| sQ213_spl ),
inference(split_clause,[status(thm)],[f1989,f2000,f2003,f1949]) ).
fof(f2008,definition,
! [X0] :
( sQ215_spl
<=> ( ~ frontsegP(sK6_skl(nil,sK50_skl),X0)
| X0 = sK6_skl(nil,sK50_skl)
| ~ frontsegP(X0,sK6_skl(nil,sK50_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f2011,plain,
( ~ sQ206_spl
| ~ sQ214_spl
| sQ215_spl ),
inference(split_clause,[status(thm)],[f1993,f2008,f2003,f1949]) ).
fof(f2113,plain,
( ~ sQ70_spl
| ~ sQ28_spl
| ~ ssList(sK5_skl(sK50_skl,sK50_skl))
| segmentP(app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)),sK50_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f967,f689]) ).
fof(f2114,plain,
! [X0] :
( ~ sQ70_spl
| ~ frontsegP(sK50_skl,X0)
| ~ ssList(sK5_skl(sK50_skl,sK50_skl))
| ~ ssList(sK50_skl)
| app(X0,sK5_skl(X0,app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)))) = app(sK50_skl,sK5_skl(sK50_skl,sK50_skl))
| ~ ssList(X0)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f967,f619]) ).
fof(f2115,plain,
! [X0] :
( ~ sQ70_spl
| X0 = app(sK50_skl,sK5_skl(sK50_skl,sK50_skl))
| ~ frontsegP(X0,app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)))
| ~ ssList(sK50_skl)
| ~ frontsegP(sK50_skl,X0)
| ~ ssList(sK5_skl(sK50_skl,sK50_skl))
| ~ ssList(X0)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f967,f589]) ).
fof(f2116,plain,
( ~ sQ70_spl
| ~ ssList(sK50_skl)
| rearsegP(app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)),sK5_skl(sK50_skl,sK50_skl))
| ~ ssList(sK5_skl(sK50_skl,sK50_skl))
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f967,f457]) ).
fof(f2118,plain,
! [X0] :
( ~ sQ70_spl
| ~ ssList(X0)
| ~ ssList(sK50_skl)
| segmentP(app(app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)),X0),sK5_skl(sK50_skl,sK50_skl))
| ~ ssList(sK5_skl(sK50_skl,sK50_skl))
| ~ ssList(app(sK50_skl,X0)) ),
inference(paramodulation,[status(thm)],[f967,f458]) ).
fof(f2119,plain,
( ~ sQ70_spl
| ~ ssList(sK5_skl(sK50_skl,sK50_skl))
| frontsegP(app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)),sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f967,f456]) ).
fof(f2120,definition,
( sQ216_spl
<=> segmentP(app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)),sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ216_spl])],[split_symbol_definition]) ).
fof(f2123,definition,
( sQ217_spl
<=> ssList(sK5_skl(sK50_skl,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f2124,plain,
( ~ sQ217_spl
| ssList(sK5_skl(sK50_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f2123]) ).
fof(f2125,plain,
( sQ217_spl
| ~ ssList(sK5_skl(sK50_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f2123]) ).
fof(f2126,plain,
( ~ sQ70_spl
| ~ sQ28_spl
| ~ sQ217_spl
| sQ216_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2113,f572,f2120,f2123,f681,f966]) ).
fof(f2127,definition,
! [X0] :
( sQ218_spl
<=> ( ~ frontsegP(sK50_skl,X0)
| app(X0,sK5_skl(X0,app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)))) = app(sK50_skl,sK5_skl(sK50_skl,sK50_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f2130,plain,
( ~ sQ70_spl
| ~ sQ217_spl
| sQ218_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2114,f572,f2127,f2123,f966]) ).
fof(f2131,definition,
! [X0] :
( sQ219_spl
<=> ( X0 = app(sK50_skl,sK5_skl(sK50_skl,sK50_skl))
| ~ frontsegP(X0,app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)))
| ~ frontsegP(sK50_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f2134,plain,
( ~ sQ70_spl
| ~ sQ217_spl
| sQ219_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2115,f572,f2131,f2123,f966]) ).
fof(f2135,definition,
( sQ220_spl
<=> rearsegP(app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)),sK5_skl(sK50_skl,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f2136,plain,
( ~ sQ220_spl
| rearsegP(app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)),sK5_skl(sK50_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f2135]) ).
fof(f2138,plain,
( ~ sQ70_spl
| sQ220_spl
| ~ sQ217_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2116,f572,f2123,f2135,f966]) ).
fof(f2140,definition,
! [X0] :
( sQ221_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)),X0),sK5_skl(sK50_skl,sK50_skl))
| ~ ssList(app(sK50_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f2143,plain,
( ~ sQ70_spl
| ~ sQ16_spl
| ~ sQ217_spl
| sQ221_spl ),
inference(split_clause,[status(thm)],[f2118,f2140,f2123,f572,f966]) ).
fof(f2144,definition,
( sQ222_spl
<=> frontsegP(app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)),sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f2147,plain,
( ~ sQ70_spl
| ~ sQ217_spl
| sQ222_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2119,f572,f2144,f2123,f966]) ).
fof(f2148,plain,
( sQ217_spl
| ~ frontsegP(sK50_skl,sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f2125,f122]) ).
fof(f2149,plain,
( sQ217_spl
| ~ sQ71_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2148,f572,f970,f2123]) ).
fof(f2155,plain,
( ~ sQ220_spl
| ~ sQ70_spl
| rearsegP(sK50_skl,sK5_skl(sK50_skl,sK50_skl)) ),
inference(forward_demodulation,[status(thm)],[f967,f2136]) ).
fof(f2162,plain,
! [X0] :
( ~ sQ217_spl
| ~ frontsegP(sK5_skl(sK50_skl,sK50_skl),sK5_skl(sK50_skl,sK50_skl))
| ~ frontsegP(X0,sK5_skl(sK50_skl,sK50_skl))
| app(sK5_skl(sK50_skl,sK50_skl),sK5_skl(sK5_skl(sK50_skl,sK50_skl),X0)) = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2124,f624]) ).
fof(f2166,plain,
! [X0] :
( ~ sQ217_spl
| ~ frontsegP(sK5_skl(sK50_skl,sK50_skl),X0)
| ~ frontsegP(sK5_skl(sK50_skl,sK50_skl),sK5_skl(sK50_skl,sK50_skl))
| X0 = sK5_skl(sK50_skl,sK50_skl)
| ~ frontsegP(X0,sK5_skl(sK50_skl,sK50_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2124,f586]) ).
fof(f2173,definition,
! [X0] :
( sQ223_spl
<=> ( ~ frontsegP(X0,sK5_skl(sK50_skl,sK50_skl))
| app(sK5_skl(sK50_skl,sK50_skl),sK5_skl(sK5_skl(sK50_skl,sK50_skl),X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ223_spl])],[split_symbol_definition]) ).
fof(f2176,definition,
( sQ224_spl
<=> frontsegP(sK5_skl(sK50_skl,sK50_skl),sK5_skl(sK50_skl,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ224_spl])],[split_symbol_definition]) ).
fof(f2179,plain,
( ~ sQ217_spl
| ~ sQ224_spl
| sQ223_spl ),
inference(split_clause,[status(thm)],[f2162,f2173,f2176,f2123]) ).
fof(f2181,definition,
! [X0] :
( sQ225_spl
<=> ( ~ frontsegP(sK5_skl(sK50_skl,sK50_skl),X0)
| X0 = sK5_skl(sK50_skl,sK50_skl)
| ~ frontsegP(X0,sK5_skl(sK50_skl,sK50_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f2184,plain,
( ~ sQ217_spl
| ~ sQ224_spl
| sQ225_spl ),
inference(split_clause,[status(thm)],[f2166,f2181,f2176,f2123]) ).
fof(f2186,plain,
( ~ sQ220_spl
| ~ sQ70_spl
| app(sK6_skl(sK5_skl(sK50_skl,sK50_skl),sK50_skl),sK5_skl(sK50_skl,sK50_skl)) = sK50_skl
| ~ ssList(sK5_skl(sK50_skl,sK50_skl))
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f2155,f129]) ).
fof(f2187,definition,
( sQ226_spl
<=> app(sK6_skl(sK5_skl(sK50_skl,sK50_skl),sK50_skl),sK5_skl(sK50_skl,sK50_skl)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ226_spl])],[split_symbol_definition]) ).
fof(f2190,plain,
( ~ sQ220_spl
| ~ sQ70_spl
| sQ226_spl
| ~ sQ217_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2186,f572,f2123,f2187,f966,f2135]) ).
fof(f2192,plain,
( ~ sQ60_spl
| ~ sQ35_spl
| ~ ssList(sK5_skl(sK49_skl,sK49_skl))
| segmentP(app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)),sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f905,f728]) ).
fof(f2193,plain,
( ~ sQ21_spl
| ~ sQ35_spl
| ~ ssList(sK5_skl(sK49_skl,sK50_skl))
| segmentP(app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)),sK49_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f616,f728]) ).
fof(f2194,plain,
( ~ sQ35_spl
| ~ ssList(nil)
| segmentP(app(sK49_skl,nil),sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f867,f728]) ).
fof(f2199,definition,
( sQ228_spl
<=> segmentP(app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f2202,plain,
( ~ sQ60_spl
| ~ sQ35_spl
| ~ sQ194_spl
| sQ228_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2192,f498,f2199,f1863,f720,f904]) ).
fof(f2203,definition,
( sQ229_spl
<=> segmentP(app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f2204,plain,
( ~ sQ229_spl
| segmentP(app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)),sK49_skl) ),
inference(component_clause,[status(thm)],[f2203]) ).
fof(f2206,plain,
( ~ sQ21_spl
| ~ sQ35_spl
| ~ sQ73_spl
| sQ229_spl
| ~ sQ16_spl ),
inference(split_clause,[status(thm)],[f2193,f572,f2203,f983,f720,f615]) ).
fof(f2207,definition,
( sQ230_spl
<=> segmentP(app(sK49_skl,nil),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f2210,plain,
( ~ sQ35_spl
| ~ sQ11_spl
| sQ230_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f2194,f498,f2207,f538,f720]) ).
fof(f2213,plain,
( ~ sQ229_spl
| ~ sQ21_spl
| segmentP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f616,f2204]) ).
fof(f2214,plain,
( ~ sQ229_spl
| ~ sQ21_spl
| sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2213,f503]) ).
fof(f2215,plain,
( ~ sQ229_spl
| ~ sQ21_spl
| sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f2214]) ).
fof(f2216,plain,
$false,
inference(sat_refutation,[status(thm)],[f440,f447,f451,f493,f504,f532,f534,f547,f550,f552,f561,f565,f585,f600,f602,f618,f623,f680,f684,f688,f696,f719,f723,f727,f735,f742,f747,f759,f768,f775,f782,f802,f809,f817,f821,f825,f829,f837,f845,f857,f866,f881,f885,f889,f893,f901,f907,f914,f916,f924,f928,f932,f936,f944,f956,f960,f969,f976,f978,f1003,f1016,f1031,f1042,f1056,f1058,f1080,f1090,f1094,f1113,f1118,f1122,f1127,f1129,f1167,f1172,f1176,f1181,f1183,f1206,f1210,f1214,f1218,f1223,f1225,f1237,f1241,f1277,f1281,f1292,f1314,f1362,f1366,f1370,f1374,f1379,f1381,f1405,f1420,f1424,f1467,f1471,f1475,f1479,f1484,f1486,f1503,f1526,f1538,f1542,f1546,f1550,f1582,f1594,f1598,f1602,f1606,f1635,f1639,f1643,f1647,f1651,f1655,f1660,f1662,f1699,f1708,f1716,f1730,f1734,f1738,f1743,f1747,f1749,f1751,f1772,f1813,f1817,f1825,f1866,f1870,f1874,f1879,f1883,f1885,f1902,f1906,f1939,f1952,f1956,f1960,f1964,f1968,f1972,f1977,f1979,f2006,f2011,f2126,f2130,f2134,f2138,f2143,f2147,f2149,f2179,f2184,f2190,f2202,f2206,f2210,f2215]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC070+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n011.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 07:53:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.13/0.55 % Refutation found
% 0.13/0.55 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.55 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.08/0.57 % Elapsed time: 0.211031 seconds
% 1.08/0.57 % CPU time: 1.304888 seconds
% 1.08/0.57 % Total memory used: 127.952 MB
% 1.08/0.57 % Net memory used: 126.233 MB
%------------------------------------------------------------------------------