%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC057+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n026.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 02:39:47 PM UTC 2026
% Result : Theorem 3.92s 0.97s
% Output : CNFRefutation 0.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 264
% Syntax : Number of formulae : 985 ( 24 unt; 236 def)
% Number of atoms : 3616 ( 357 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 4862 (2231 ~;2226 |; 93 &)
% ( 254 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 245 ( 243 usr; 235 prp; 0-2 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 577 ( 550 !; 27 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
? [U] :
( ? [V] :
( U != V
& ssItem(V) )
& ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( frontsegP(V,W)
& frontsegP(U,V) )
=> frontsegP(U,W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( frontsegP(V,U)
& frontsegP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( frontsegP(U,V)
=> frontsegP(app(U,W),V) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( frontsegP(cons(U,W),cons(V,X))
<=> ( frontsegP(W,X)
& U = V ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f46,axiom,
! [U] :
( ssList(U)
=> ( frontsegP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f49,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f51,axiom,
! [U] :
( ssList(U)
=> rearsegP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f53,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( segmentP(V,W)
& segmentP(U,V) )
=> segmentP(U,W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( segmentP(V,U)
& segmentP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f55,axiom,
! [U] :
( ssList(U)
=> segmentP(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f56,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( segmentP(U,V)
=> segmentP(app(app(W,U),X),V) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f57,axiom,
! [U] :
( ssList(U)
=> segmentP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f58,axiom,
! [U] :
( ssList(U)
=> ( segmentP(nil,U)
<=> nil = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( ( ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( ~ frontsegP(X,W)
| ~ neq(W,nil) )
& ( nil != W
| nil != X ) )
| ( ( ? [Y] :
( segmentP(U,Y)
& segmentP(V,Y)
& neq(Y,nil)
& ssList(Y) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f99,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f98]) ).
fof(f101,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f102,plain,
( sK0_skl != sK1_skl
& ssItem(sK1_skl)
& ssItem(sK0_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(U,sK0_skl),skolemize(V,sK1_skl)],[f2]) ).
fof(f103,plain,
ssItem(sK0_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f104,plain,
ssItem(sK1_skl),
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f105,plain,
sK0_skl != sK1_skl,
inference(cnf_transformation,[status(thm)],[f102]) ).
fof(f113,plain,
! [U] :
( ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f114,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [V] :
( cons(V,nil) = U
& ssItem(V) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ( cons(sK4_skl(U),nil) = U
& ssItem(sK4_skl(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114]) ).
fof(f116,plain,
! [X0] :
( ssItem(sK4_skl(X0))
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f117,plain,
! [X0] :
( cons(sK4_skl(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f118,plain,
! [X0,X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f119,plain,
! [U] :
( ! [V] :
( ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f120,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ? [W] :
( app(V,W) = U
& ssList(W) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ( app(V,sK5_skl(V,U)) = U
& ssList(sK5_skl(V,U)) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( ssList(sK5_skl(X1,X0))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( app(X1,sK5_skl(X1,X0)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(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(f219,plain,
! [X0,X1] :
( X0 != X1
| ~ neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f221,plain,
! [U] :
( ! [V] :
( ssList(cons(V,U))
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f222,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f244,plain,
! [U] :
( ! [V] :
( ssList(app(U,V))
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f248,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f249,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(f281,plain,
! [U] :
( ! [V] :
( ! [W] :
( frontsegP(U,W)
| ~ frontsegP(V,W)
| ~ frontsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f282,plain,
! [X0,X1,X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f283,plain,
! [U] :
( ! [V] :
( U = V
| ~ frontsegP(V,U)
| ~ frontsegP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f284,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(f285,plain,
! [U] :
( frontsegP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f42]) ).
fof(f286,plain,
! [X0] :
( frontsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f285]) ).
fof(f287,plain,
! [U] :
( ! [V] :
( ! [W] :
( frontsegP(app(U,W),V)
| ~ frontsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f288,plain,
! [X0,X1,X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f287]) ).
fof(f289,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( frontsegP(cons(U,W),cons(V,X))
<=> ( frontsegP(W,X)
& U = V ) )
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f290,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( ( ~ frontsegP(W,X)
| U != V
| frontsegP(cons(U,W),cons(V,X)) )
& ( ( frontsegP(W,X)
& U = V )
| ~ frontsegP(cons(U,W),cons(V,X)) ) )
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f289]) ).
fof(f292,plain,
! [X0,X1,X2,X3] :
( frontsegP(X2,X3)
| ~ frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f293,plain,
! [X0,X1,X2,X3] :
( ~ frontsegP(X2,X3)
| X0 != X1
| frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f294,plain,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f295,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f294]) ).
fof(f296,plain,
! [U] :
( ( frontsegP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f297,plain,
! [U] :
( ( ( nil != U
| frontsegP(nil,U) )
& ( nil = U
| ~ frontsegP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f296]) ).
fof(f298,plain,
! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f304,plain,
! [U] :
( rearsegP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f49]) ).
fof(f305,plain,
! [X0] :
( rearsegP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f304]) ).
fof(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 ) )
& ( ( ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [U,V] :
( sP0_prd(V,U)
<=> ( nil != U
& nil = V ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,definition,
! [W,X] :
( sP1_prd(X,W)
<=> ( nil = W
& nil = X ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f418,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( frontsegP(X,W)
& neq(W,nil) )
| sP1_prd(X,W) )
& ( ( ! [Y] :
( ~ segmentP(U,Y)
| ~ segmentP(V,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(V,nil) )
| sP0_prd(V,U) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f417,f416]) ).
fof(f419,plain,
( ( ( frontsegP(sK50_skl,sK49_skl)
& neq(sK49_skl,nil) )
| sP1_prd(sK50_skl,sK49_skl) )
& ( ( ! [Y] :
( ~ segmentP(sK47_skl,Y)
| ~ segmentP(sK48_skl,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) )
& neq(sK48_skl,nil) )
| sP0_prd(sK48_skl,sK47_skl) )
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl)],[f418]) ).
fof(f422,plain,
ssList(sK49_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f423,plain,
ssList(sK50_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f424,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f425,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f426,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f427,plain,
! [X0] :
( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f428,plain,
( neq(sK49_skl,nil)
| sP1_prd(sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f429,plain,
( frontsegP(sK50_skl,sK49_skl)
| sP1_prd(sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f430,plain,
! [U,V] :
( ( nil = U
| nil != V
| sP0_prd(V,U) )
& ( ( nil != U
& nil = V )
| ~ sP0_prd(V,U) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f431,plain,
( ! [U,V] :
( nil = U
| nil != V
| sP0_prd(V,U) )
& ! [U,V] :
( ( nil != U
& nil = V )
| ~ sP0_prd(V,U) ) ),
inference(miniscoping,[status(thm)],[f430]) ).
fof(f432,plain,
! [X0,X1] :
( nil = X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f433,plain,
! [X0,X1] :
( nil != X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f434,plain,
! [X0,X1] :
( nil = X1
| nil != X0
| sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f431]) ).
fof(f435,plain,
! [W,X] :
( ( nil != W
| nil != X
| sP1_prd(X,W) )
& ( ( nil = W
& nil = X )
| ~ sP1_prd(X,W) ) ),
inference(NNF_transformation,[status(thm)],[f417]) ).
fof(f436,plain,
( ! [W,X] :
( nil != W
| nil != X
| sP1_prd(X,W) )
& ! [W,X] :
( ( nil = W
& nil = X )
| ~ sP1_prd(X,W) ) ),
inference(miniscoping,[status(thm)],[f435]) ).
fof(f437,plain,
! [X0,X1] :
( nil = X0
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f436]) ).
fof(f438,plain,
! [X0,X1] :
( nil = X1
| ~ sP1_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f436]) ).
fof(f440,definition,
( sQ0_spl
<=> sP0_prd(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f441,plain,
( ~ sQ0_spl
| sP0_prd(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f440]) ).
fof(f443,definition,
( sQ1_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f444,plain,
( ~ sQ1_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f443]) ).
fof(f446,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f440,f443]) ).
fof(f447,definition,
! [X0] :
( sQ2_spl
<=> ( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f448,plain,
! [X0] :
( ~ sQ2_spl
| ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f447]) ).
fof(f450,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f427,f440,f447]) ).
fof(f451,definition,
( sQ3_spl
<=> sP1_prd(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f452,plain,
( ~ sQ3_spl
| sP1_prd(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f451]) ).
fof(f454,definition,
( sQ4_spl
<=> neq(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( ~ sQ4_spl
| neq(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f457,plain,
( sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f428,f451,f454]) ).
fof(f458,definition,
( sQ5_spl
<=> frontsegP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f459,plain,
( ~ sQ5_spl
| frontsegP(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f458]) ).
fof(f461,plain,
( sQ5_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f429,f451,f458]) ).
fof(f465,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f466,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f467,plain,
! [X0,X1] :
( ~ ssList(X0)
| rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f468,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(f477,plain,
! [X1] :
( ~ neq(X1,X1)
| ~ ssList(X1)
| ~ ssList(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f219]) ).
fof(f478,plain,
! [X0] :
( ~ neq(X0,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f477]) ).
fof(f481,plain,
! [X1,X2,X3] :
( ~ frontsegP(X2,X3)
| frontsegP(cons(X1,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f293]) ).
fof(f482,plain,
! [X0,X1,X2] :
( ~ frontsegP(X1,X2)
| frontsegP(cons(X0,X1),cons(X0,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f481]) ).
fof(f492,plain,
! [X0] : ~ sP0_prd(X0,nil),
inference(destructive_equality_resolution,[status(thm)],[f433]) ).
fof(f493,plain,
! [X0] :
( nil = X0
| sP0_prd(nil,X0) ),
inference(destructive_equality_resolution,[status(thm)],[f434]) ).
fof(f497,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f441]) ).
fof(f498,plain,
( ~ sQ0_spl
| sP0_prd(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f497]) ).
fof(f499,plain,
! [X0] :
( X0 = sK0_skl
| neq(X0,sK0_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f103,f101]) ).
fof(f501,plain,
! [X0] :
( X0 = sK1_skl
| neq(X0,sK1_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f104,f101]) ).
fof(f503,plain,
( ~ sQ0_spl
| nil = sK50_skl ),
inference(resolution,[status(thm)],[f432,f498]) ).
fof(f504,plain,
( ~ sQ0_spl
| sP0_prd(nil,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f503,f498]) ).
fof(f505,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| sP1_prd(nil,sK49_skl) ),
inference(backward_demodulation,[status(thm)],[f503,f452]) ).
fof(f510,plain,
! [X0] :
( nil = nil
| nil = X0 ),
inference(resolution,[status(thm)],[f493,f432]) ).
fof(f511,definition,
! [X0] :
( sQ6_spl
<=> nil = X0 ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f512,plain,
! [X0] :
( ~ sQ6_spl
| nil = X0 ),
inference(component_clause,[status(thm)],[f511]) ).
fof(f514,definition,
( sQ7_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f517,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f510,f511,f514]) ).
fof(f518,plain,
! [X0,X1] :
( ~ sQ6_spl
| X0 = X1 ),
inference(paramodulation,[status(thm)],[f512,f512]) ).
fof(f532,plain,
( ~ sQ6_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f105,f518]) ).
fof(f533,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f532]) ).
fof(f553,plain,
( ~ sQ3_spl
| ~ sQ0_spl
| nil = sK49_skl ),
inference(resolution,[status(thm)],[f438,f505]) ).
fof(f557,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| sP0_prd(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f553,f504]) ).
fof(f559,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f557,f492]) ).
fof(f560,plain,
( ~ sQ0_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f559]) ).
fof(f561,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| frontsegP(nil,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f503,f459]) ).
fof(f567,plain,
! [X0] :
( ~ sQ2_spl
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f425,f448]) ).
fof(f569,plain,
( ~ sQ1_spl
| neq(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f424,f444]) ).
fof(f571,plain,
( ~ sQ3_spl
| nil = sK50_skl ),
inference(resolution,[status(thm)],[f452,f437]) ).
fof(f575,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(f577,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)],[f575]) ).
fof(f578,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| neq(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f571,f569]) ).
fof(f584,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f578,f478]) ).
fof(f585,plain,
( ~ sQ1_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f584,f223]) ).
fof(f586,plain,
( ~ sQ1_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f585]) ).
fof(f589,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(f591,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)],[f589]) ).
fof(f594,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| sK49_skl = nil
| ~ frontsegP(sK49_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f561,f284]) ).
fof(f595,definition,
( sQ12_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f597,plain,
( sQ12_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f595]) ).
fof(f598,definition,
( sQ13_spl
<=> ssList(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f600,plain,
( sQ13_spl
| ~ ssList(sK49_skl) ),
inference(component_clause,[status(thm)],[f598]) ).
fof(f605,definition,
( sQ15_spl
<=> frontsegP(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f607,plain,
( sQ15_spl
| ~ frontsegP(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f605]) ).
fof(f608,definition,
( sQ16_spl
<=> sK49_skl = nil ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f609,plain,
( ~ sQ16_spl
| sK49_skl = nil ),
inference(component_clause,[status(thm)],[f608]) ).
fof(f611,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| sQ16_spl
| ~ sQ15_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f594,f598,f595,f605,f608,f440,f458]) ).
fof(f612,plain,
( ~ sQ5_spl
| app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)) = sK50_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f459,f123]) ).
fof(f613,plain,
( ~ sQ5_spl
| sK49_skl = sK50_skl
| ~ frontsegP(sK49_skl,sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f459,f284]) ).
fof(f614,definition,
( sQ17_spl
<=> ssList(sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f616,plain,
( sQ17_spl
| ~ ssList(sK50_skl) ),
inference(component_clause,[status(thm)],[f614]) ).
fof(f617,definition,
( sQ18_spl
<=> app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f618,plain,
( ~ sQ18_spl
| app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)) = sK50_skl ),
inference(component_clause,[status(thm)],[f617]) ).
fof(f620,plain,
( ~ sQ5_spl
| sQ18_spl
| ~ sQ13_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f612,f614,f598,f617,f458]) ).
fof(f621,definition,
( sQ19_spl
<=> frontsegP(sK49_skl,sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f623,plain,
( sQ19_spl
| ~ frontsegP(sK49_skl,sK50_skl) ),
inference(component_clause,[status(thm)],[f621]) ).
fof(f624,definition,
( sQ20_spl
<=> sK49_skl = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f625,plain,
( ~ sQ20_spl
| sK49_skl = sK50_skl ),
inference(component_clause,[status(thm)],[f624]) ).
fof(f627,plain,
( ~ sQ5_spl
| sQ20_spl
| ~ sQ19_spl
| ~ sQ17_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f613,f598,f614,f621,f624,f458]) ).
fof(f628,plain,
( sQ13_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f600,f422]) ).
fof(f629,plain,
sQ13_spl,
inference(contradiction_clause,[status(thm)],[f628]) ).
fof(f631,plain,
( sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f616,f423]) ).
fof(f632,plain,
sQ17_spl,
inference(contradiction_clause,[status(thm)],[f631]) ).
fof(f633,plain,
! [X0] :
( ~ sQ2_spl
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f424,f567]) ).
fof(f635,plain,
! [X0] :
( sQ19_spl
| ~ frontsegP(X0,sK50_skl)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(sK50_skl)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f623,f282]) ).
fof(f636,definition,
! [X0] :
( sQ21_spl
<=> ( ~ frontsegP(X0,sK50_skl)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f637,plain,
! [X0] :
( ~ sQ21_spl
| ~ frontsegP(X0,sK50_skl)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f636]) ).
fof(f639,plain,
( sQ19_spl
| ~ sQ17_spl
| sQ21_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f635,f598,f636,f614,f621]) ).
fof(f643,plain,
( ~ sQ20_spl
| sK47_skl = sK50_skl ),
inference(backward_demodulation,[status(thm)],[f625,f425]) ).
fof(f648,definition,
( sQ22_spl
<=> app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f649,plain,
( ~ sQ22_spl
| app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)) = sK50_skl ),
inference(component_clause,[status(thm)],[f648]) ).
fof(f652,definition,
( sQ23_spl
<=> frontsegP(sK50_skl,sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f654,plain,
( sQ23_spl
| ~ frontsegP(sK50_skl,sK50_skl) ),
inference(component_clause,[status(thm)],[f652]) ).
fof(f655,definition,
( sQ24_spl
<=> sK50_skl = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f661,plain,
! [X0,X1,X2] :
( app(X1,sK5_skl(X1,app(X0,X2))) = app(X0,X2)
| ~ ssList(X1)
| ~ ssList(app(X0,X2))
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f288,f123]) ).
fof(f662,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(f663,plain,
! [X0,X1,X2] :
( app(X1,sK5_skl(X1,app(X0,X2))) = app(X0,X2)
| ~ ssList(app(X0,X2))
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f661]) ).
fof(f664,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)],[f662]) ).
fof(f667,plain,
! [X0] :
( app(nil,sK5_skl(nil,X0)) = X0
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f295,f123]) ).
fof(f668,plain,
! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f295,f284]) ).
fof(f669,definition,
! [X0] :
( sQ25_spl
<=> ( app(nil,sK5_skl(nil,X0)) = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f672,plain,
( ~ sQ12_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f667,f669,f595]) ).
fof(f673,definition,
! [X0] :
( sQ26_spl
<=> ( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f676,plain,
( ~ sQ12_spl
| sQ26_spl ),
inference(split_clause,[status(thm)],[f668,f673,f595]) ).
fof(f677,plain,
( sQ12_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f597,f223]) ).
fof(f678,plain,
sQ12_spl,
inference(contradiction_clause,[status(thm)],[f677]) ).
fof(f683,plain,
app(nil,sK50_skl) = sK50_skl,
inference(resolution,[status(thm)],[f249,f423]) ).
fof(f687,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f249,f223]) ).
fof(f688,plain,
! [X0] :
( frontsegP(sK50_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sK50_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f683,f288]) ).
fof(f689,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)],[f683,f468]) ).
fof(f690,plain,
( ~ ssList(sK50_skl)
| frontsegP(app(nil,sK50_skl),nil)
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f683,f466]) ).
fof(f691,definition,
! [X0] :
( sQ27_spl
<=> ( frontsegP(sK50_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f692,plain,
! [X0] :
( ~ sQ27_spl
| frontsegP(sK50_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f691]) ).
fof(f694,plain,
( ~ sQ17_spl
| sQ27_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f688,f595,f691,f614]) ).
fof(f695,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(f696,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)],[f695]) ).
fof(f698,plain,
( ~ sQ12_spl
| ~ sQ17_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f689,f695,f614,f595]) ).
fof(f699,definition,
( sQ29_spl
<=> frontsegP(app(nil,sK50_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f700,plain,
( ~ sQ29_spl
| frontsegP(app(nil,sK50_skl),nil) ),
inference(component_clause,[status(thm)],[f699]) ).
fof(f702,plain,
( sQ29_spl
| ~ sQ12_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f690,f614,f595,f699]) ).
fof(f703,plain,
! [X0] :
( ~ sQ28_spl
| ~ ssList(X0)
| segmentP(app(sK50_skl,X0),sK50_skl)
| ~ ssList(app(sK50_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f683,f696]) ).
fof(f704,plain,
( ~ sQ29_spl
| frontsegP(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f683,f700]) ).
fof(f705,plain,
( ~ sQ29_spl
| app(nil,sK5_skl(nil,sK50_skl)) = sK50_skl
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f704,f123]) ).
fof(f707,definition,
( sQ30_spl
<=> app(nil,sK5_skl(nil,sK50_skl)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f708,plain,
( ~ sQ30_spl
| app(nil,sK5_skl(nil,sK50_skl)) = sK50_skl ),
inference(component_clause,[status(thm)],[f707]) ).
fof(f710,plain,
( ~ sQ29_spl
| sQ30_spl
| ~ sQ12_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f705,f614,f595,f707,f699]) ).
fof(f711,definition,
( sQ31_spl
<=> frontsegP(nil,sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f713,plain,
( sQ31_spl
| ~ frontsegP(nil,sK50_skl) ),
inference(component_clause,[status(thm)],[f711]) ).
fof(f718,plain,
! [X0] :
( sQ31_spl
| ~ frontsegP(X0,sK50_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(sK50_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f713,f282]) ).
fof(f719,definition,
! [X0] :
( sQ33_spl
<=> ( ~ frontsegP(X0,sK50_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f720,plain,
! [X0] :
( ~ sQ33_spl
| ~ frontsegP(X0,sK50_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f719]) ).
fof(f722,plain,
( sQ31_spl
| ~ sQ17_spl
| sQ33_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f718,f595,f719,f614,f711]) ).
fof(f742,plain,
! [X0] :
( ~ ssList(X0)
| app(sK6_skl(nil,X0),nil) = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f129,f309]) ).
fof(f743,plain,
! [X0] :
( ~ ssList(X0)
| app(sK6_skl(X0,X0),X0) = X0
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f129,f305]) ).
fof(f744,definition,
! [X0] :
( sQ34_spl
<=> ( ~ ssList(X0)
| app(sK6_skl(nil,X0),nil) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f747,plain,
( ~ sQ12_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f742,f744,f595]) ).
fof(f748,plain,
! [X0] :
( app(sK6_skl(X0,X0),X0) = X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f743]) ).
fof(f750,plain,
app(nil,sK49_skl) = sK49_skl,
inference(resolution,[status(thm)],[f422,f249]) ).
fof(f774,plain,
! [X0,X1] :
( ~ frontsegP(X0,X1)
| frontsegP(cons(sK1_skl,X0),cons(sK1_skl,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f482,f104]) ).
fof(f780,plain,
( ~ ssList(nil)
| rearsegP(app(nil,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f687,f467]) ).
fof(f781,plain,
! [X0] :
( frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f687,f288]) ).
fof(f782,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(nil,X0)) ),
inference(paramodulation,[status(thm)],[f687,f468]) ).
fof(f783,plain,
( ~ ssList(nil)
| frontsegP(app(nil,nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f687,f466]) ).
fof(f784,definition,
( sQ36_spl
<=> rearsegP(app(nil,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f785,plain,
( ~ sQ36_spl
| rearsegP(app(nil,nil),nil) ),
inference(component_clause,[status(thm)],[f784]) ).
fof(f787,plain,
( sQ36_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f780,f595,f784]) ).
fof(f788,definition,
! [X0] :
( sQ37_spl
<=> ( frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f791,plain,
( sQ37_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f781,f595,f788]) ).
fof(f792,definition,
! [X0] :
( sQ38_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f795,plain,
( ~ sQ12_spl
| sQ38_spl ),
inference(split_clause,[status(thm)],[f782,f792,f595]) ).
fof(f796,definition,
( sQ39_spl
<=> frontsegP(app(nil,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f797,plain,
( ~ sQ39_spl
| frontsegP(app(nil,nil),nil) ),
inference(component_clause,[status(thm)],[f796]) ).
fof(f799,plain,
( sQ39_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f783,f595,f796]) ).
fof(f800,plain,
( ~ sQ36_spl
| rearsegP(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f687,f785]) ).
fof(f802,plain,
( ~ sQ39_spl
| frontsegP(nil,nil) ),
inference(forward_demodulation,[status(thm)],[f687,f797]) ).
fof(f803,plain,
( ~ sQ36_spl
| app(sK6_skl(nil,nil),nil) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f800,f129]) ).
fof(f804,definition,
( sQ40_spl
<=> app(sK6_skl(nil,nil),nil) = nil ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f805,plain,
( ~ sQ40_spl
| app(sK6_skl(nil,nil),nil) = nil ),
inference(component_clause,[status(thm)],[f804]) ).
fof(f807,plain,
( ~ sQ36_spl
| sQ40_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f803,f595,f804,f784]) ).
fof(f808,plain,
( ~ sQ39_spl
| app(nil,sK5_skl(nil,nil)) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f802,f123]) ).
fof(f810,definition,
( sQ41_spl
<=> app(nil,sK5_skl(nil,nil)) = nil ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f811,plain,
( ~ sQ41_spl
| app(nil,sK5_skl(nil,nil)) = nil ),
inference(component_clause,[status(thm)],[f810]) ).
fof(f813,plain,
( ~ sQ39_spl
| sQ41_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f808,f595,f810,f796]) ).
fof(f814,definition,
( sQ42_spl
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f816,plain,
( sQ42_spl
| ~ frontsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f814]) ).
fof(f818,plain,
( ~ ssList(nil)
| rearsegP(app(nil,sK50_skl),sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f683,f467]) ).
fof(f822,definition,
( sQ43_spl
<=> rearsegP(app(nil,sK50_skl),sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f823,plain,
( ~ sQ43_spl
| rearsegP(app(nil,sK50_skl),sK50_skl) ),
inference(component_clause,[status(thm)],[f822]) ).
fof(f825,plain,
( ~ sQ12_spl
| sQ43_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f818,f614,f822,f595]) ).
fof(f829,plain,
( ~ sQ43_spl
| rearsegP(sK50_skl,sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f683,f823]) ).
fof(f830,plain,
( ~ sQ43_spl
| app(sK6_skl(sK50_skl,sK50_skl),sK50_skl) = sK50_skl
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f829,f129]) ).
fof(f831,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(f832,plain,
( ~ sQ44_spl
| app(sK6_skl(sK50_skl,sK50_skl),sK50_skl) = sK50_skl ),
inference(component_clause,[status(thm)],[f831]) ).
fof(f834,plain,
( ~ sQ43_spl
| sQ44_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f830,f614,f831,f822]) ).
fof(f835,plain,
( ~ ssList(nil)
| rearsegP(app(nil,sK49_skl),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f750,f467]) ).
fof(f836,plain,
! [X0] :
( frontsegP(sK49_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f750,f288]) ).
fof(f837,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)],[f750,f468]) ).
fof(f838,plain,
( ~ ssList(sK49_skl)
| frontsegP(app(nil,sK49_skl),nil)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f750,f466]) ).
fof(f839,definition,
( sQ45_spl
<=> rearsegP(app(nil,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f840,plain,
( ~ sQ45_spl
| rearsegP(app(nil,sK49_skl),sK49_skl) ),
inference(component_clause,[status(thm)],[f839]) ).
fof(f842,plain,
( ~ sQ12_spl
| sQ45_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f835,f598,f839,f595]) ).
fof(f843,definition,
! [X0] :
( sQ46_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f844,plain,
! [X0] :
( ~ sQ46_spl
| frontsegP(sK49_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f843]) ).
fof(f846,plain,
( ~ sQ13_spl
| sQ46_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f836,f595,f843,f598]) ).
fof(f847,definition,
! [X0] :
( sQ47_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK49_skl),X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f848,plain,
! [X0] :
( ~ sQ47_spl
| ~ ssList(X0)
| segmentP(app(app(nil,sK49_skl),X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(component_clause,[status(thm)],[f847]) ).
fof(f850,plain,
( ~ sQ12_spl
| ~ sQ13_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f837,f847,f598,f595]) ).
fof(f851,definition,
( sQ48_spl
<=> frontsegP(app(nil,sK49_skl),nil) ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f852,plain,
( ~ sQ48_spl
| frontsegP(app(nil,sK49_skl),nil) ),
inference(component_clause,[status(thm)],[f851]) ).
fof(f854,plain,
( sQ48_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f838,f598,f595,f851]) ).
fof(f855,plain,
( ~ sQ45_spl
| rearsegP(sK49_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f750,f840]) ).
fof(f856,plain,
! [X0] :
( ~ sQ47_spl
| ~ ssList(X0)
| segmentP(app(sK49_skl,X0),sK49_skl)
| ~ ssList(app(sK49_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f750,f848]) ).
fof(f857,plain,
( ~ sQ48_spl
| frontsegP(sK49_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f750,f852]) ).
fof(f858,plain,
( ~ sQ45_spl
| app(sK6_skl(sK49_skl,sK49_skl),sK49_skl) = sK49_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f855,f129]) ).
fof(f859,definition,
( sQ49_spl
<=> app(sK6_skl(sK49_skl,sK49_skl),sK49_skl) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f860,plain,
( ~ sQ49_spl
| app(sK6_skl(sK49_skl,sK49_skl),sK49_skl) = sK49_skl ),
inference(component_clause,[status(thm)],[f859]) ).
fof(f862,plain,
( ~ sQ45_spl
| sQ49_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f858,f598,f859,f839]) ).
fof(f863,plain,
( ~ sQ48_spl
| app(nil,sK5_skl(nil,sK49_skl)) = sK49_skl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f857,f123]) ).
fof(f865,definition,
( sQ50_spl
<=> app(nil,sK5_skl(nil,sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f866,plain,
( ~ sQ50_spl
| app(nil,sK5_skl(nil,sK49_skl)) = sK49_skl ),
inference(component_clause,[status(thm)],[f865]) ).
fof(f868,plain,
( ~ sQ48_spl
| sQ50_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f863,f598,f595,f865,f851]) ).
fof(f875,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(f877,definition,
! [X0] :
( sQ52_spl
<=> ( ~ ssList(X0)
| app(app(sK7_skl(nil,X0),nil),sK8_skl(nil,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f880,plain,
( ~ sQ12_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f875,f877,f595]) ).
fof(f887,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| neq(nil,nil) ),
inference(backward_demodulation,[status(thm)],[f609,f455]) ).
fof(f896,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f887,f478]) ).
fof(f897,plain,
( ~ sQ4_spl
| ~ sQ16_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f896,f595,f608,f454]) ).
fof(f898,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ segmentP(sK49_skl,sK50_skl)
| ~ segmentP(sK50_skl,sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f633,f569]) ).
fof(f899,plain,
! [X0] :
( ~ sQ2_spl
| X0 = nil
| ~ ssList(nil)
| ~ ssList(X0)
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f633,f220]) ).
fof(f900,definition,
( sQ53_spl
<=> segmentP(sK50_skl,sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f901,plain,
( ~ sQ53_spl
| segmentP(sK50_skl,sK50_skl) ),
inference(component_clause,[status(thm)],[f900]) ).
fof(f902,plain,
( sQ53_spl
| ~ segmentP(sK50_skl,sK50_skl) ),
inference(component_clause,[status(thm)],[f900]) ).
fof(f903,definition,
( sQ54_spl
<=> segmentP(sK49_skl,sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f905,plain,
( sQ54_spl
| ~ segmentP(sK49_skl,sK50_skl) ),
inference(component_clause,[status(thm)],[f903]) ).
fof(f906,plain,
( ~ sQ1_spl
| ~ sQ2_spl
| ~ sQ54_spl
| ~ sQ53_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f898,f614,f900,f903,f447,f443]) ).
fof(f907,definition,
! [X0] :
( sQ55_spl
<=> ( X0 = nil
| ~ ssList(X0)
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f908,plain,
! [X0] :
( ~ sQ55_spl
| X0 = nil
| ~ ssList(X0)
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f907]) ).
fof(f910,plain,
( ~ sQ2_spl
| ~ sQ12_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f899,f907,f595,f447]) ).
fof(f911,plain,
! [X0] :
( ~ sQ55_spl
| X0 = nil
| ~ segmentP(sK49_skl,X0)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f908]) ).
fof(f918,plain,
( ~ sQ20_spl
| sK49_skl = sK50_skl ),
inference(forward_demodulation,[status(thm)],[f425,f643]) ).
fof(f927,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(f931,definition,
! [X0,X1] :
( sQ57_spl
<=> ( ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f932,plain,
! [X0,X1] :
( ~ sQ57_spl
| ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f931]) ).
fof(f934,plain,
( ~ sQ12_spl
| sQ57_spl ),
inference(split_clause,[status(thm)],[f927,f931,f595]) ).
fof(f936,plain,
! [X0,X1] :
( ~ sQ57_spl
| ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f932]) ).
fof(f948,plain,
( sQ53_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f902,f319]) ).
fof(f949,plain,
( sQ53_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f948,f614,f900]) ).
fof(f950,plain,
( sQ54_spl
| ~ sQ20_spl
| ~ segmentP(sK50_skl,sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f918,f905]) ).
fof(f951,plain,
( sQ54_spl
| ~ sQ20_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f950,f319]) ).
fof(f952,plain,
( sQ54_spl
| ~ sQ20_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f951,f614,f624,f903]) ).
fof(f954,plain,
( ~ sQ53_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)],[f901,f136]) ).
fof(f955,definition,
( sQ58_spl
<=> app(app(sK7_skl(sK50_skl,sK50_skl),sK50_skl),sK8_skl(sK50_skl,sK50_skl)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f958,plain,
( ~ sQ53_spl
| sQ58_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f954,f614,f955,f900]) ).
fof(f965,plain,
! [X0] :
( sQ54_spl
| ~ segmentP(X0,sK50_skl)
| ~ segmentP(sK49_skl,X0)
| ~ ssList(sK50_skl)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f315,f905]) ).
fof(f967,definition,
! [X0] :
( sQ59_spl
<=> ( ~ segmentP(X0,sK50_skl)
| ~ segmentP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f968,plain,
! [X0] :
( ~ sQ59_spl
| ~ segmentP(X0,sK50_skl)
| ~ segmentP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f967]) ).
fof(f970,plain,
( sQ54_spl
| ~ sQ17_spl
| sQ59_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f965,f598,f967,f614,f903]) ).
fof(f972,plain,
( ~ sQ53_spl
| sK50_skl = sK50_skl
| ~ segmentP(sK50_skl,sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f317,f901]) ).
fof(f973,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f317,f323]) ).
fof(f976,plain,
( sQ24_spl
| ~ sQ53_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f972,f614,f900,f655]) ).
fof(f977,definition,
! [X0] :
( sQ60_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ60_spl])],[split_symbol_definition]) ).
fof(f980,plain,
( sQ60_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f973,f595,f977]) ).
fof(f999,plain,
app(sK49_skl,nil) = sK49_skl,
inference(resolution,[status(thm)],[f389,f422]) ).
fof(f1002,plain,
app(sK50_skl,nil) = sK50_skl,
inference(resolution,[status(thm)],[f389,f423]) ).
fof(f1008,plain,
( ~ ssList(sK49_skl)
| rearsegP(app(sK49_skl,nil),nil)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f999,f467]) ).
fof(f1009,plain,
! [X0] :
( frontsegP(sK49_skl,X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f999,f288]) ).
fof(f1010,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)],[f999,f468]) ).
fof(f1011,plain,
( ~ ssList(nil)
| frontsegP(app(sK49_skl,nil),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f999,f466]) ).
fof(f1012,definition,
( sQ61_spl
<=> rearsegP(app(sK49_skl,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ61_spl])],[split_symbol_definition]) ).
fof(f1013,plain,
( ~ sQ61_spl
| rearsegP(app(sK49_skl,nil),nil) ),
inference(component_clause,[status(thm)],[f1012]) ).
fof(f1015,plain,
( sQ61_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1008,f598,f595,f1012]) ).
fof(f1016,definition,
! [X0] :
( sQ62_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1019,plain,
( ~ sQ12_spl
| sQ62_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1009,f598,f1016,f595]) ).
fof(f1020,definition,
! [X0] :
( sQ63_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK49_skl,nil),X0),nil)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1023,plain,
( ~ sQ13_spl
| ~ sQ12_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f1010,f1020,f595,f598]) ).
fof(f1024,definition,
( sQ64_spl
<=> frontsegP(app(sK49_skl,nil),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1025,plain,
( ~ sQ64_spl
| frontsegP(app(sK49_skl,nil),sK49_skl) ),
inference(component_clause,[status(thm)],[f1024]) ).
fof(f1027,plain,
( ~ sQ12_spl
| sQ64_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1011,f598,f1024,f595]) ).
fof(f1028,plain,
( ~ sQ61_spl
| rearsegP(sK49_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f999,f1013]) ).
fof(f1030,plain,
( ~ sQ64_spl
| frontsegP(sK49_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f999,f1025]) ).
fof(f1031,plain,
( ~ sQ61_spl
| app(sK6_skl(nil,sK49_skl),nil) = sK49_skl
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1028,f129]) ).
fof(f1032,definition,
( sQ65_spl
<=> app(sK6_skl(nil,sK49_skl),nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1033,plain,
( ~ sQ65_spl
| app(sK6_skl(nil,sK49_skl),nil) = sK49_skl ),
inference(component_clause,[status(thm)],[f1032]) ).
fof(f1035,plain,
( ~ sQ61_spl
| sQ65_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1031,f598,f595,f1032,f1012]) ).
fof(f1036,plain,
( ~ sQ64_spl
| app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)) = sK49_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1030,f123]) ).
fof(f1037,plain,
( ~ sQ64_spl
| sK49_skl = sK49_skl
| ~ frontsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1030,f284]) ).
fof(f1038,definition,
( sQ66_spl
<=> app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1039,plain,
( ~ sQ66_spl
| app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)) = sK49_skl ),
inference(component_clause,[status(thm)],[f1038]) ).
fof(f1041,plain,
( ~ sQ64_spl
| sQ66_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1036,f598,f1038,f1024]) ).
fof(f1042,definition,
( sQ67_spl
<=> frontsegP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1044,plain,
( sQ67_spl
| ~ frontsegP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f1042]) ).
fof(f1045,definition,
( sQ68_spl
<=> sK49_skl = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1048,plain,
( ~ sQ64_spl
| sQ68_spl
| ~ sQ67_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1037,f598,f1042,f1045,f1024]) ).
fof(f1049,plain,
( sQ67_spl
| ~ sQ64_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1044,f1030]) ).
fof(f1050,plain,
( sQ67_spl
| ~ sQ64_spl ),
inference(contradiction_clause,[status(thm)],[f1049]) ).
fof(f1051,plain,
( ~ ssList(sK50_skl)
| rearsegP(app(sK50_skl,nil),nil)
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f1002,f467]) ).
fof(f1052,plain,
! [X0] :
( frontsegP(sK50_skl,X0)
| ~ frontsegP(sK50_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f1002,f288]) ).
fof(f1053,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)],[f1002,f468]) ).
fof(f1054,plain,
( ~ ssList(nil)
| frontsegP(app(sK50_skl,nil),sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f1002,f466]) ).
fof(f1055,definition,
( sQ69_spl
<=> rearsegP(app(sK50_skl,nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1056,plain,
( ~ sQ69_spl
| rearsegP(app(sK50_skl,nil),nil) ),
inference(component_clause,[status(thm)],[f1055]) ).
fof(f1058,plain,
( sQ69_spl
| ~ sQ12_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1051,f614,f595,f1055]) ).
fof(f1059,definition,
! [X0] :
( sQ70_spl
<=> ( frontsegP(sK50_skl,X0)
| ~ frontsegP(sK50_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1062,plain,
( ~ sQ12_spl
| sQ70_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1052,f614,f1059,f595]) ).
fof(f1063,definition,
! [X0] :
( sQ71_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK50_skl,nil),X0),nil)
| ~ ssList(app(sK50_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1066,plain,
( ~ sQ17_spl
| ~ sQ12_spl
| sQ71_spl ),
inference(split_clause,[status(thm)],[f1053,f1063,f595,f614]) ).
fof(f1067,definition,
( sQ72_spl
<=> frontsegP(app(sK50_skl,nil),sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1068,plain,
( ~ sQ72_spl
| frontsegP(app(sK50_skl,nil),sK50_skl) ),
inference(component_clause,[status(thm)],[f1067]) ).
fof(f1070,plain,
( ~ sQ12_spl
| sQ72_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1054,f614,f1067,f595]) ).
fof(f1071,plain,
( ~ sQ69_spl
| rearsegP(sK50_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f1002,f1056]) ).
fof(f1073,plain,
( ~ sQ72_spl
| frontsegP(sK50_skl,sK50_skl) ),
inference(forward_demodulation,[status(thm)],[f1002,f1068]) ).
fof(f1074,plain,
( ~ sQ69_spl
| app(sK6_skl(nil,sK50_skl),nil) = sK50_skl
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1071,f129]) ).
fof(f1075,definition,
( sQ73_spl
<=> app(sK6_skl(nil,sK50_skl),nil) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1076,plain,
( ~ sQ73_spl
| app(sK6_skl(nil,sK50_skl),nil) = sK50_skl ),
inference(component_clause,[status(thm)],[f1075]) ).
fof(f1078,plain,
( ~ sQ69_spl
| sQ73_spl
| ~ sQ12_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1074,f614,f595,f1075,f1055]) ).
fof(f1079,plain,
( ~ sQ72_spl
| app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)) = sK50_skl
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1073,f123]) ).
fof(f1081,plain,
( ~ sQ72_spl
| sQ22_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1079,f614,f648,f1067]) ).
fof(f1083,plain,
( ~ sQ18_spl
| ~ ssList(sK49_skl)
| rearsegP(app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)),sK5_skl(sK49_skl,sK50_skl))
| ~ ssList(sK5_skl(sK49_skl,sK50_skl))
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f618,f467]) ).
fof(f1084,plain,
! [X0] :
( ~ sQ18_spl
| frontsegP(sK50_skl,X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(sK5_skl(sK49_skl,sK50_skl))
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f618,f288]) ).
fof(f1085,plain,
! [X0] :
( ~ sQ18_spl
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| segmentP(app(app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)),X0),sK5_skl(sK49_skl,sK50_skl))
| ~ ssList(sK5_skl(sK49_skl,sK50_skl))
| ~ ssList(app(sK50_skl,X0)) ),
inference(paramodulation,[status(thm)],[f618,f468]) ).
fof(f1086,plain,
( ~ sQ18_spl
| ~ ssList(sK5_skl(sK49_skl,sK50_skl))
| frontsegP(app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)),sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f618,f466]) ).
fof(f1087,definition,
( sQ74_spl
<=> ssList(sK5_skl(sK49_skl,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1088,plain,
( ~ sQ74_spl
| ssList(sK5_skl(sK49_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f1087]) ).
fof(f1089,plain,
( sQ74_spl
| ~ ssList(sK5_skl(sK49_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f1087]) ).
fof(f1090,definition,
( sQ75_spl
<=> rearsegP(app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)),sK5_skl(sK49_skl,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1091,plain,
( ~ sQ75_spl
| rearsegP(app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)),sK5_skl(sK49_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f1090]) ).
fof(f1093,plain,
( ~ sQ18_spl
| ~ sQ13_spl
| sQ75_spl
| ~ sQ74_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1083,f614,f1087,f1090,f598,f617]) ).
fof(f1094,definition,
! [X0] :
( sQ76_spl
<=> ( frontsegP(sK50_skl,X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1095,plain,
! [X0] :
( ~ sQ76_spl
| frontsegP(sK50_skl,X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1094]) ).
fof(f1097,plain,
( ~ sQ18_spl
| ~ sQ74_spl
| sQ76_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1084,f598,f1094,f1087,f617]) ).
fof(f1098,definition,
! [X0] :
( sQ77_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)),X0),sK5_skl(sK49_skl,sK50_skl))
| ~ ssList(app(sK50_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1101,plain,
( ~ sQ18_spl
| ~ sQ13_spl
| ~ sQ74_spl
| sQ77_spl ),
inference(split_clause,[status(thm)],[f1085,f1098,f1087,f598,f617]) ).
fof(f1102,definition,
( sQ78_spl
<=> frontsegP(app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1105,plain,
( ~ sQ18_spl
| ~ sQ74_spl
| sQ78_spl
| ~ sQ13_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1086,f614,f598,f1102,f1087,f617]) ).
fof(f1106,plain,
( sQ74_spl
| ~ frontsegP(sK50_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1089,f122]) ).
fof(f1107,plain,
( sQ74_spl
| ~ sQ5_spl
| ~ sQ13_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1106,f614,f598,f458,f1087]) ).
fof(f1108,plain,
( ~ sQ75_spl
| ~ sQ18_spl
| rearsegP(sK50_skl,sK5_skl(sK49_skl,sK50_skl)) ),
inference(forward_demodulation,[status(thm)],[f618,f1091]) ).
fof(f1114,definition,
( sQ79_spl
<=> segmentP(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1116,plain,
( sQ79_spl
| ~ segmentP(sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f1114]) ).
fof(f1117,definition,
( sQ80_spl
<=> segmentP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ80_spl])],[split_symbol_definition]) ).
fof(f1118,plain,
( ~ sQ80_spl
| segmentP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f1117]) ).
fof(f1119,plain,
( sQ80_spl
| ~ segmentP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f1117]) ).
fof(f1124,definition,
! [X0] :
( sQ81_spl
<=> ( ~ segmentP(X0,sK49_skl)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1125,plain,
! [X0] :
( ~ sQ81_spl
| ~ segmentP(X0,sK49_skl)
| ~ segmentP(sK50_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1124]) ).
fof(f1129,plain,
( sQ80_spl
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1119,f319]) ).
fof(f1134,plain,
( sQ80_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1129,f598,f1117]) ).
fof(f1136,plain,
( ~ sQ80_spl
| app(app(sK7_skl(sK49_skl,sK49_skl),sK49_skl),sK8_skl(sK49_skl,sK49_skl)) = sK49_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1118,f136]) ).
fof(f1138,definition,
( sQ83_spl
<=> app(app(sK7_skl(sK49_skl,sK49_skl),sK49_skl),sK8_skl(sK49_skl,sK49_skl)) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1141,plain,
( ~ sQ80_spl
| sQ83_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1136,f598,f1138,f1117]) ).
fof(f1146,plain,
( ~ sQ75_spl
| ~ sQ18_spl
| app(sK6_skl(sK5_skl(sK49_skl,sK50_skl),sK50_skl),sK5_skl(sK49_skl,sK50_skl)) = sK50_skl
| ~ ssList(sK5_skl(sK49_skl,sK50_skl))
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1108,f129]) ).
fof(f1147,definition,
( sQ84_spl
<=> app(sK6_skl(sK5_skl(sK49_skl,sK50_skl),sK50_skl),sK5_skl(sK49_skl,sK50_skl)) = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1150,plain,
( ~ sQ75_spl
| ~ sQ18_spl
| sQ84_spl
| ~ sQ74_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1146,f614,f1087,f1147,f617,f1090]) ).
fof(f1152,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(f1155,definition,
! [X0,X1] :
( sQ85_spl
<=> ( ~ segmentP(X1,X0)
| ~ segmentP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1158,plain,
( ~ sQ12_spl
| sQ85_spl ),
inference(split_clause,[status(thm)],[f1152,f1155,f595]) ).
fof(f1161,plain,
! [X0,X1] :
( ~ sQ80_spl
| segmentP(app(app(X0,sK49_skl),X1),sK49_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f321,f1118]) ).
fof(f1162,plain,
! [X0,X1] :
( ~ sQ53_spl
| segmentP(app(app(X0,sK50_skl),X1),sK50_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f321,f901]) ).
fof(f1163,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(f1166,definition,
! [X0,X1] :
( sQ86_spl
<=> ( segmentP(app(app(X0,sK49_skl),X1),sK49_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1169,plain,
( ~ sQ80_spl
| sQ86_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1161,f598,f1166,f1117]) ).
fof(f1170,definition,
! [X0,X1] :
( sQ87_spl
<=> ( segmentP(app(app(X0,sK50_skl),X1),sK50_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1173,plain,
( ~ sQ53_spl
| sQ87_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1162,f614,f1170,f900]) ).
fof(f1174,definition,
! [X0,X1,X2] :
( sQ88_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(X1,X0),X2),nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1177,plain,
( ~ sQ12_spl
| sQ88_spl ),
inference(split_clause,[status(thm)],[f1163,f1174,f595]) ).
fof(f1183,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)],[f708,f467]) ).
fof(f1185,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)],[f708,f468]) ).
fof(f1186,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)],[f708,f466]) ).
fof(f1187,definition,
( sQ89_spl
<=> ssList(sK5_skl(nil,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1189,plain,
( sQ89_spl
| ~ ssList(sK5_skl(nil,sK50_skl)) ),
inference(component_clause,[status(thm)],[f1187]) ).
fof(f1190,definition,
( sQ90_spl
<=> rearsegP(app(nil,sK5_skl(nil,sK50_skl)),sK5_skl(nil,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1193,plain,
( ~ sQ30_spl
| ~ sQ12_spl
| sQ90_spl
| ~ sQ89_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1183,f614,f1187,f1190,f595,f707]) ).
fof(f1195,definition,
! [X0] :
( sQ91_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,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1198,plain,
( ~ sQ30_spl
| ~ sQ12_spl
| ~ sQ89_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f1185,f1195,f1187,f595,f707]) ).
fof(f1199,definition,
( sQ92_spl
<=> frontsegP(app(nil,sK5_skl(nil,sK50_skl)),nil) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1202,plain,
( ~ sQ30_spl
| ~ sQ89_spl
| sQ92_spl
| ~ sQ12_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1186,f614,f595,f1199,f1187,f707]) ).
fof(f1203,plain,
( sQ89_spl
| ~ frontsegP(sK50_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1189,f122]) ).
fof(f1204,definition,
( sQ93_spl
<=> frontsegP(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1206,plain,
( sQ93_spl
| ~ frontsegP(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f1204]) ).
fof(f1207,plain,
( sQ89_spl
| ~ sQ93_spl
| ~ sQ12_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1203,f614,f595,f1204,f1187]) ).
fof(f1208,plain,
( sQ93_spl
| ~ sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1206,f704]) ).
fof(f1209,plain,
( sQ93_spl
| ~ sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f1208]) ).
fof(f1221,plain,
( sK1_skl = sK0_skl
| neq(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f499,f104]) ).
fof(f1223,definition,
( sQ94_spl
<=> neq(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1226,definition,
( sQ95_spl
<=> sK1_skl = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1227,plain,
( ~ sQ95_spl
| sK1_skl = sK0_skl ),
inference(component_clause,[status(thm)],[f1226]) ).
fof(f1229,plain,
( sQ95_spl
| sQ94_spl ),
inference(split_clause,[status(thm)],[f1221,f1223,f1226]) ).
fof(f1235,plain,
( sK0_skl = sK1_skl
| neq(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f501,f103]) ).
fof(f1240,definition,
( sQ98_spl
<=> neq(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ98_spl])],[split_symbol_definition]) ).
fof(f1243,plain,
( sQ95_spl
| sQ98_spl ),
inference(split_clause,[status(thm)],[f1235,f1240,f1226]) ).
fof(f1244,plain,
( ~ sQ95_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1227,f105]) ).
fof(f1245,plain,
~ sQ95_spl,
inference(contradiction_clause,[status(thm)],[f1244]) ).
fof(f1256,plain,
! [X0] :
( ~ frontsegP(sK49_skl,X0)
| ~ frontsegP(sK49_skl,sK49_skl)
| X0 = sK49_skl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f577,f422]) ).
fof(f1262,plain,
! [X0] :
( ~ frontsegP(sK50_skl,X0)
| ~ frontsegP(sK50_skl,sK50_skl)
| X0 = sK50_skl
| ~ frontsegP(X0,sK50_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f577,f423]) ).
fof(f1266,plain,
! [X0] :
( ~ sQ74_spl
| ~ frontsegP(sK5_skl(sK49_skl,sK50_skl),X0)
| ~ frontsegP(sK5_skl(sK49_skl,sK50_skl),sK5_skl(sK49_skl,sK50_skl))
| X0 = sK5_skl(sK49_skl,sK50_skl)
| ~ frontsegP(X0,sK5_skl(sK49_skl,sK50_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f577,f1088]) ).
fof(f1274,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| ~ frontsegP(nil,nil)
| X0 = nil
| ~ frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f577,f223]) ).
fof(f1286,definition,
! [X0] :
( sQ99_spl
<=> ( ~ frontsegP(sK49_skl,X0)
| X0 = sK49_skl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ99_spl])],[split_symbol_definition]) ).
fof(f1289,plain,
( ~ sQ67_spl
| sQ99_spl ),
inference(split_clause,[status(thm)],[f1256,f1286,f1042]) ).
fof(f1290,definition,
! [X0] :
( sQ100_spl
<=> ( ~ frontsegP(sK50_skl,X0)
| X0 = sK50_skl
| ~ frontsegP(X0,sK50_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ100_spl])],[split_symbol_definition]) ).
fof(f1293,plain,
( ~ sQ23_spl
| sQ100_spl ),
inference(split_clause,[status(thm)],[f1262,f1290,f652]) ).
fof(f1294,definition,
! [X0] :
( sQ101_spl
<=> ( ~ frontsegP(sK5_skl(sK49_skl,sK50_skl),X0)
| X0 = sK5_skl(sK49_skl,sK50_skl)
| ~ frontsegP(X0,sK5_skl(sK49_skl,sK50_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1297,definition,
( sQ102_spl
<=> frontsegP(sK5_skl(sK49_skl,sK50_skl),sK5_skl(sK49_skl,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1299,plain,
( sQ102_spl
| ~ frontsegP(sK5_skl(sK49_skl,sK50_skl),sK5_skl(sK49_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f1297]) ).
fof(f1300,plain,
( ~ sQ74_spl
| ~ sQ102_spl
| sQ101_spl ),
inference(split_clause,[status(thm)],[f1266,f1294,f1297,f1087]) ).
fof(f1301,definition,
! [X0] :
( sQ103_spl
<=> ( ~ frontsegP(nil,X0)
| X0 = nil
| ~ frontsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1304,plain,
( ~ sQ42_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f1274,f1301,f814]) ).
fof(f1307,plain,
( sQ42_spl
| ~ sQ39_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f816,f802]) ).
fof(f1308,plain,
( sQ42_spl
| ~ sQ39_spl ),
inference(contradiction_clause,[status(thm)],[f1307]) ).
fof(f1309,plain,
( sQ23_spl
| ~ sQ72_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f654,f1073]) ).
fof(f1310,plain,
( sQ23_spl
| ~ sQ72_spl ),
inference(contradiction_clause,[status(thm)],[f1309]) ).
fof(f1311,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)],[f591,f422]) ).
fof(f1317,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)],[f591,f423]) ).
fof(f1321,plain,
! [X0] :
( ~ sQ74_spl
| ~ frontsegP(sK5_skl(sK49_skl,sK50_skl),sK5_skl(sK49_skl,sK50_skl))
| ~ frontsegP(X0,sK5_skl(sK49_skl,sK50_skl))
| app(sK5_skl(sK49_skl,sK50_skl),sK5_skl(sK5_skl(sK49_skl,sK50_skl),X0)) = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f591,f1088]) ).
fof(f1329,plain,
! [X0] :
( ~ frontsegP(nil,nil)
| ~ frontsegP(X0,nil)
| app(nil,sK5_skl(nil,X0)) = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f591,f223]) ).
fof(f1341,definition,
! [X0] :
( sQ104_spl
<=> ( ~ frontsegP(X0,sK49_skl)
| app(sK49_skl,sK5_skl(sK49_skl,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1344,plain,
( ~ sQ67_spl
| sQ104_spl ),
inference(split_clause,[status(thm)],[f1311,f1341,f1042]) ).
fof(f1345,definition,
! [X0] :
( sQ105_spl
<=> ( ~ frontsegP(X0,sK50_skl)
| app(sK50_skl,sK5_skl(sK50_skl,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1348,plain,
( ~ sQ23_spl
| sQ105_spl ),
inference(split_clause,[status(thm)],[f1317,f1345,f652]) ).
fof(f1349,definition,
! [X0] :
( sQ106_spl
<=> ( ~ frontsegP(X0,sK5_skl(sK49_skl,sK50_skl))
| app(sK5_skl(sK49_skl,sK50_skl),sK5_skl(sK5_skl(sK49_skl,sK50_skl),X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ106_spl])],[split_symbol_definition]) ).
fof(f1352,plain,
( ~ sQ74_spl
| ~ sQ102_spl
| sQ106_spl ),
inference(split_clause,[status(thm)],[f1321,f1349,f1297,f1087]) ).
fof(f1353,definition,
! [X0] :
( sQ107_spl
<=> ( ~ frontsegP(X0,nil)
| app(nil,sK5_skl(nil,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1356,plain,
( ~ sQ42_spl
| sQ107_spl ),
inference(split_clause,[status(thm)],[f1329,f1353,f814]) ).
fof(f1364,definition,
( sQ108_spl
<=> rearsegP(app(sK6_skl(sK50_skl,sK50_skl),sK50_skl),sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1367,definition,
( sQ109_spl
<=> ssList(sK6_skl(sK50_skl,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1369,plain,
( sQ109_spl
| ~ ssList(sK6_skl(sK50_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f1367]) ).
fof(f1371,definition,
! [X0] :
( sQ110_spl
<=> ( frontsegP(sK50_skl,X0)
| ~ frontsegP(sK6_skl(sK50_skl,sK50_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1375,definition,
! [X0] :
( sQ111_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,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1379,definition,
( sQ112_spl
<=> frontsegP(app(sK6_skl(sK50_skl,sK50_skl),sK50_skl),sK6_skl(sK50_skl,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1380,plain,
( ~ sQ112_spl
| frontsegP(app(sK6_skl(sK50_skl,sK50_skl),sK50_skl),sK6_skl(sK50_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f1379]) ).
fof(f1383,plain,
( sQ109_spl
| ~ rearsegP(sK50_skl,sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1369,f128]) ).
fof(f1384,definition,
( sQ113_spl
<=> rearsegP(sK50_skl,sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1386,plain,
( sQ113_spl
| ~ rearsegP(sK50_skl,sK50_skl) ),
inference(component_clause,[status(thm)],[f1384]) ).
fof(f1387,plain,
( sQ109_spl
| ~ sQ113_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1383,f614,f1384,f1367]) ).
fof(f1388,plain,
( sQ113_spl
| ~ sQ43_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1386,f829]) ).
fof(f1389,plain,
( sQ113_spl
| ~ sQ43_spl ),
inference(contradiction_clause,[status(thm)],[f1388]) ).
fof(f1392,plain,
( ~ sQ112_spl
| ~ sQ44_spl
| frontsegP(sK50_skl,sK6_skl(sK50_skl,sK50_skl)) ),
inference(forward_demodulation,[status(thm)],[f832,f1380]) ).
fof(f1417,plain,
( ~ sQ112_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)],[f1392,f123]) ).
fof(f1419,definition,
( sQ117_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,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1422,plain,
( ~ sQ112_spl
| ~ sQ44_spl
| sQ117_spl
| ~ sQ109_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1417,f614,f1367,f1419,f831,f1379]) ).
fof(f1433,plain,
( ~ sQ55_spl
| ~ ssList(sK49_skl)
| sK49_skl = nil
| ~ segmentP(sK50_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f911,f319]) ).
fof(f1443,plain,
( ~ sQ55_spl
| sQ16_spl
| ~ sQ79_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1433,f598,f1114,f608,f907]) ).
fof(f1475,plain,
( ~ sQ40_spl
| ~ ssList(sK6_skl(nil,nil))
| rearsegP(app(sK6_skl(nil,nil),nil),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f805,f467]) ).
fof(f1476,plain,
! [X0] :
( ~ sQ40_spl
| frontsegP(nil,X0)
| ~ frontsegP(sK6_skl(nil,nil),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(nil,nil)) ),
inference(paramodulation,[status(thm)],[f805,f288]) ).
fof(f1477,plain,
! [X0] :
( ~ sQ40_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)],[f805,f468]) ).
fof(f1478,plain,
( ~ sQ40_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)],[f805,f466]) ).
fof(f1479,definition,
( sQ126_spl
<=> rearsegP(app(sK6_skl(nil,nil),nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f1482,definition,
( sQ127_spl
<=> ssList(sK6_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f1483,plain,
( ~ sQ127_spl
| ssList(sK6_skl(nil,nil)) ),
inference(component_clause,[status(thm)],[f1482]) ).
fof(f1484,plain,
( sQ127_spl
| ~ ssList(sK6_skl(nil,nil)) ),
inference(component_clause,[status(thm)],[f1482]) ).
fof(f1485,plain,
( ~ sQ40_spl
| ~ sQ127_spl
| sQ126_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1475,f595,f1479,f1482,f804]) ).
fof(f1486,definition,
! [X0] :
( sQ128_spl
<=> ( frontsegP(nil,X0)
| ~ frontsegP(sK6_skl(nil,nil),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1489,plain,
( ~ sQ40_spl
| ~ sQ12_spl
| sQ128_spl
| ~ sQ127_spl ),
inference(split_clause,[status(thm)],[f1476,f1482,f1486,f595,f804]) ).
fof(f1490,definition,
! [X0] :
( sQ129_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK6_skl(nil,nil),nil),X0),nil)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f1493,plain,
( ~ sQ40_spl
| ~ sQ127_spl
| ~ sQ12_spl
| sQ129_spl ),
inference(split_clause,[status(thm)],[f1477,f1490,f595,f1482,f804]) ).
fof(f1494,definition,
( sQ130_spl
<=> frontsegP(app(sK6_skl(nil,nil),nil),sK6_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f1497,plain,
( ~ sQ40_spl
| sQ130_spl
| ~ sQ127_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1478,f595,f1482,f1494,f804]) ).
fof(f1498,plain,
( sQ127_spl
| ~ rearsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1484,f128]) ).
fof(f1499,definition,
( sQ131_spl
<=> rearsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1501,plain,
( sQ131_spl
| ~ rearsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f1499]) ).
fof(f1502,plain,
( sQ127_spl
| ~ sQ131_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1498,f595,f1499,f1482]) ).
fof(f1503,plain,
( sQ131_spl
| ~ sQ36_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1501,f800]) ).
fof(f1504,plain,
( sQ131_spl
| ~ sQ36_spl ),
inference(contradiction_clause,[status(thm)],[f1503]) ).
fof(f1508,plain,
! [X0] :
( ~ sQ40_spl
| app(X0,sK5_skl(X0,app(sK6_skl(nil,nil),nil))) = app(sK6_skl(nil,nil),nil)
| ~ ssList(nil)
| ~ frontsegP(sK6_skl(nil,nil),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(nil,nil)) ),
inference(paramodulation,[status(thm)],[f805,f663]) ).
fof(f1510,plain,
! [X0] :
( app(X0,sK5_skl(X0,app(sK50_skl,nil))) = app(sK50_skl,nil)
| ~ ssList(sK50_skl)
| ~ frontsegP(sK50_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f1002,f663]) ).
fof(f1511,plain,
! [X0] :
( ~ sQ18_spl
| app(X0,sK5_skl(X0,app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)))) = app(sK49_skl,sK5_skl(sK49_skl,sK50_skl))
| ~ ssList(sK50_skl)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(sK5_skl(sK49_skl,sK50_skl))
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f618,f663]) ).
fof(f1512,plain,
! [X0] :
( app(X0,sK5_skl(X0,app(sK49_skl,nil))) = app(sK49_skl,nil)
| ~ ssList(sK49_skl)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f999,f663]) ).
fof(f1513,plain,
! [X0] :
( app(X0,sK5_skl(X0,app(nil,sK49_skl))) = app(nil,sK49_skl)
| ~ ssList(sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f750,f663]) ).
fof(f1514,plain,
! [X0] :
( app(X0,sK5_skl(X0,app(nil,sK50_skl))) = app(nil,sK50_skl)
| ~ ssList(sK50_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(sK50_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f683,f663]) ).
fof(f1515,plain,
! [X0] :
( app(X0,sK5_skl(X0,app(nil,nil))) = app(nil,nil)
| ~ ssList(nil)
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f687,f663]) ).
fof(f1516,definition,
! [X0] :
( sQ132_spl
<=> ( app(X0,sK5_skl(X0,app(sK6_skl(nil,nil),nil))) = app(sK6_skl(nil,nil),nil)
| ~ frontsegP(sK6_skl(nil,nil),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f1519,plain,
( ~ sQ40_spl
| ~ sQ12_spl
| sQ132_spl
| ~ sQ127_spl ),
inference(split_clause,[status(thm)],[f1508,f1482,f1516,f595,f804]) ).
fof(f1524,definition,
! [X0] :
( sQ134_spl
<=> ( app(X0,sK5_skl(X0,app(sK50_skl,nil))) = app(sK50_skl,nil)
| ~ frontsegP(sK50_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ134_spl])],[split_symbol_definition]) ).
fof(f1527,plain,
( ~ sQ12_spl
| sQ134_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1510,f614,f1524,f595]) ).
fof(f1528,definition,
! [X0] :
( sQ135_spl
<=> ( app(X0,sK5_skl(X0,app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)))) = app(sK49_skl,sK5_skl(sK49_skl,sK50_skl))
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ135_spl])],[split_symbol_definition]) ).
fof(f1531,plain,
( ~ sQ18_spl
| ~ sQ17_spl
| ~ sQ74_spl
| sQ135_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1511,f598,f1528,f1087,f614,f617]) ).
fof(f1532,definition,
! [X0] :
( sQ136_spl
<=> ( app(X0,sK5_skl(X0,app(sK49_skl,nil))) = app(sK49_skl,nil)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1535,plain,
( ~ sQ12_spl
| sQ136_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1512,f598,f1532,f595]) ).
fof(f1536,definition,
! [X0] :
( sQ137_spl
<=> ( app(X0,sK5_skl(X0,app(nil,sK49_skl))) = app(nil,sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ137_spl])],[split_symbol_definition]) ).
fof(f1539,plain,
( ~ sQ13_spl
| sQ137_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1513,f595,f1536,f598]) ).
fof(f1540,definition,
! [X0] :
( sQ138_spl
<=> ( app(X0,sK5_skl(X0,app(nil,sK50_skl))) = app(nil,sK50_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ138_spl])],[split_symbol_definition]) ).
fof(f1543,plain,
( ~ sQ17_spl
| sQ138_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1514,f595,f1540,f614]) ).
fof(f1544,definition,
! [X0] :
( sQ139_spl
<=> ( app(X0,sK5_skl(X0,app(nil,nil))) = app(nil,nil)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ139_spl])],[split_symbol_definition]) ).
fof(f1547,plain,
( sQ139_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1515,f595,f1544]) ).
fof(f1564,plain,
! [X0] :
( ~ sQ40_spl
| X0 = app(sK6_skl(nil,nil),nil)
| ~ frontsegP(X0,app(sK6_skl(nil,nil),nil))
| ~ ssList(nil)
| ~ frontsegP(sK6_skl(nil,nil),X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(nil,nil)) ),
inference(paramodulation,[status(thm)],[f805,f664]) ).
fof(f1566,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)],[f1002,f664]) ).
fof(f1567,plain,
! [X0] :
( ~ sQ18_spl
| X0 = app(sK49_skl,sK5_skl(sK49_skl,sK50_skl))
| ~ frontsegP(X0,app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)))
| ~ ssList(sK50_skl)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(sK5_skl(sK49_skl,sK50_skl))
| ~ ssList(X0)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f618,f664]) ).
fof(f1568,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)],[f999,f664]) ).
fof(f1569,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)],[f750,f664]) ).
fof(f1570,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)],[f683,f664]) ).
fof(f1571,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)],[f687,f664]) ).
fof(f1572,definition,
! [X0] :
( sQ140_spl
<=> ( X0 = app(sK6_skl(nil,nil),nil)
| ~ frontsegP(X0,app(sK6_skl(nil,nil),nil))
| ~ frontsegP(sK6_skl(nil,nil),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f1575,plain,
( ~ sQ40_spl
| ~ sQ12_spl
| sQ140_spl
| ~ sQ127_spl ),
inference(split_clause,[status(thm)],[f1564,f1482,f1572,f595,f804]) ).
fof(f1580,definition,
! [X0] :
( sQ142_spl
<=> ( X0 = app(sK50_skl,nil)
| ~ frontsegP(X0,app(sK50_skl,nil))
| ~ frontsegP(sK50_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f1583,plain,
( ~ sQ12_spl
| sQ142_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1566,f614,f1580,f595]) ).
fof(f1584,definition,
! [X0] :
( sQ143_spl
<=> ( X0 = app(sK49_skl,sK5_skl(sK49_skl,sK50_skl))
| ~ frontsegP(X0,app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)))
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f1587,plain,
( ~ sQ18_spl
| ~ sQ17_spl
| ~ sQ74_spl
| sQ143_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1567,f598,f1584,f1087,f614,f617]) ).
fof(f1588,definition,
! [X0] :
( sQ144_spl
<=> ( X0 = app(sK49_skl,nil)
| ~ frontsegP(X0,app(sK49_skl,nil))
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1591,plain,
( ~ sQ12_spl
| sQ144_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1568,f598,f1588,f595]) ).
fof(f1592,definition,
! [X0] :
( sQ145_spl
<=> ( X0 = app(nil,sK49_skl)
| ~ frontsegP(X0,app(nil,sK49_skl))
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1595,plain,
( ~ sQ13_spl
| sQ145_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1569,f595,f1592,f598]) ).
fof(f1596,definition,
! [X0] :
( sQ146_spl
<=> ( X0 = app(nil,sK50_skl)
| ~ frontsegP(X0,app(nil,sK50_skl))
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1599,plain,
( ~ sQ17_spl
| sQ146_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1570,f595,f1596,f614]) ).
fof(f1600,definition,
! [X0] :
( sQ147_spl
<=> ( X0 = app(nil,nil)
| ~ frontsegP(X0,app(nil,nil))
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1603,plain,
( sQ147_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1571,f595,f1600]) ).
fof(f1621,plain,
! [X0] :
( ~ sQ127_spl
| ~ frontsegP(sK6_skl(nil,nil),sK6_skl(nil,nil))
| ~ frontsegP(X0,sK6_skl(nil,nil))
| app(sK6_skl(nil,nil),sK5_skl(sK6_skl(nil,nil),X0)) = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1483,f591]) ).
fof(f1625,plain,
! [X0] :
( ~ sQ127_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)],[f1483,f577]) ).
fof(f1632,definition,
! [X0] :
( sQ148_spl
<=> ( ~ frontsegP(X0,sK6_skl(nil,nil))
| app(sK6_skl(nil,nil),sK5_skl(sK6_skl(nil,nil),X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1635,definition,
( sQ149_spl
<=> frontsegP(sK6_skl(nil,nil),sK6_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1638,plain,
( ~ sQ127_spl
| ~ sQ149_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1621,f1632,f1635,f1482]) ).
fof(f1640,definition,
! [X0] :
( sQ150_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,[sQ150_spl])],[split_symbol_definition]) ).
fof(f1643,plain,
( ~ sQ127_spl
| ~ sQ149_spl
| sQ150_spl ),
inference(split_clause,[status(thm)],[f1625,f1640,f1635,f1482]) ).
fof(f1651,plain,
! [X0] :
( ~ sQ49_spl
| X0 = app(sK6_skl(sK49_skl,sK49_skl),sK49_skl)
| ~ frontsegP(X0,app(sK6_skl(sK49_skl,sK49_skl),sK49_skl))
| ~ ssList(sK49_skl)
| ~ frontsegP(sK6_skl(sK49_skl,sK49_skl),X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK6_skl(sK49_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f860,f664]) ).
fof(f1652,plain,
! [X0] :
( ~ sQ49_spl
| app(X0,sK5_skl(X0,app(sK6_skl(sK49_skl,sK49_skl),sK49_skl))) = app(sK6_skl(sK49_skl,sK49_skl),sK49_skl)
| ~ ssList(sK49_skl)
| ~ frontsegP(sK6_skl(sK49_skl,sK49_skl),X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ ssList(sK6_skl(sK49_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f860,f663]) ).
fof(f1653,plain,
( ~ sQ49_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)],[f860,f467]) ).
fof(f1654,plain,
! [X0] :
( ~ sQ49_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)],[f860,f288]) ).
fof(f1655,plain,
! [X0] :
( ~ sQ49_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)],[f860,f468]) ).
fof(f1656,plain,
( ~ sQ49_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)],[f860,f466]) ).
fof(f1657,definition,
( sQ151_spl
<=> ssList(sK6_skl(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1659,plain,
( sQ151_spl
| ~ ssList(sK6_skl(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1657]) ).
fof(f1660,definition,
! [X0] :
( sQ152_spl
<=> ( X0 = app(sK6_skl(sK49_skl,sK49_skl),sK49_skl)
| ~ frontsegP(X0,app(sK6_skl(sK49_skl,sK49_skl),sK49_skl))
| ~ frontsegP(sK6_skl(sK49_skl,sK49_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f1663,plain,
( ~ sQ49_spl
| ~ sQ13_spl
| sQ152_spl
| ~ sQ151_spl ),
inference(split_clause,[status(thm)],[f1651,f1657,f1660,f598,f859]) ).
fof(f1664,definition,
! [X0] :
( sQ153_spl
<=> ( app(X0,sK5_skl(X0,app(sK6_skl(sK49_skl,sK49_skl),sK49_skl))) = app(sK6_skl(sK49_skl,sK49_skl),sK49_skl)
| ~ frontsegP(sK6_skl(sK49_skl,sK49_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f1667,plain,
( ~ sQ49_spl
| ~ sQ13_spl
| sQ153_spl
| ~ sQ151_spl ),
inference(split_clause,[status(thm)],[f1652,f1657,f1664,f598,f859]) ).
fof(f1668,definition,
( sQ154_spl
<=> rearsegP(app(sK6_skl(sK49_skl,sK49_skl),sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f1671,plain,
( ~ sQ49_spl
| ~ sQ151_spl
| sQ154_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1653,f598,f1668,f1657,f859]) ).
fof(f1672,definition,
! [X0] :
( sQ155_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(sK6_skl(sK49_skl,sK49_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f1675,plain,
( ~ sQ49_spl
| ~ sQ13_spl
| sQ155_spl
| ~ sQ151_spl ),
inference(split_clause,[status(thm)],[f1654,f1657,f1672,f598,f859]) ).
fof(f1676,definition,
! [X0] :
( sQ156_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,[sQ156_spl])],[split_symbol_definition]) ).
fof(f1679,plain,
( ~ sQ49_spl
| ~ sQ151_spl
| ~ sQ13_spl
| sQ156_spl ),
inference(split_clause,[status(thm)],[f1655,f1676,f598,f1657,f859]) ).
fof(f1680,definition,
( sQ157_spl
<=> frontsegP(app(sK6_skl(sK49_skl,sK49_skl),sK49_skl),sK6_skl(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f1681,plain,
( ~ sQ157_spl
| frontsegP(app(sK6_skl(sK49_skl,sK49_skl),sK49_skl),sK6_skl(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1680]) ).
fof(f1683,plain,
( ~ sQ49_spl
| sQ157_spl
| ~ sQ151_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1656,f598,f1657,f1680,f859]) ).
fof(f1684,plain,
( sQ151_spl
| ~ rearsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1659,f128]) ).
fof(f1685,definition,
( sQ158_spl
<=> rearsegP(sK49_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f1687,plain,
( sQ158_spl
| ~ rearsegP(sK49_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f1685]) ).
fof(f1688,plain,
( sQ151_spl
| ~ sQ158_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1684,f598,f1685,f1657]) ).
fof(f1689,plain,
( sQ158_spl
| ~ sQ45_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1687,f855]) ).
fof(f1690,plain,
( sQ158_spl
| ~ sQ45_spl ),
inference(contradiction_clause,[status(thm)],[f1689]) ).
fof(f1697,plain,
( ~ sQ157_spl
| ~ sQ49_spl
| frontsegP(sK49_skl,sK6_skl(sK49_skl,sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f860,f1681]) ).
fof(f1722,plain,
( ~ sQ157_spl
| ~ sQ49_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)],[f1697,f123]) ).
fof(f1724,definition,
( sQ162_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,[sQ162_spl])],[split_symbol_definition]) ).
fof(f1727,plain,
( ~ sQ157_spl
| ~ sQ49_spl
| sQ162_spl
| ~ sQ151_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1722,f598,f1657,f1724,f859,f1680]) ).
fof(f1735,plain,
! [X0] :
( ~ sQ22_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)],[f649,f664]) ).
fof(f1736,plain,
! [X0] :
( ~ sQ22_spl
| app(X0,sK5_skl(X0,app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)))) = 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)],[f649,f663]) ).
fof(f1737,plain,
( ~ sQ22_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)],[f649,f467]) ).
fof(f1739,plain,
! [X0] :
( ~ sQ22_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)],[f649,f468]) ).
fof(f1740,plain,
( ~ sQ22_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)],[f649,f466]) ).
fof(f1741,definition,
! [X0] :
( sQ165_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,[sQ165_spl])],[split_symbol_definition]) ).
fof(f1744,definition,
( sQ166_spl
<=> ssList(sK5_skl(sK50_skl,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f1746,plain,
( sQ166_spl
| ~ ssList(sK5_skl(sK50_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f1744]) ).
fof(f1747,plain,
( ~ sQ22_spl
| ~ sQ166_spl
| sQ165_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1735,f614,f1741,f1744,f648]) ).
fof(f1748,definition,
! [X0] :
( sQ167_spl
<=> ( app(X0,sK5_skl(X0,app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)))) = app(sK50_skl,sK5_skl(sK50_skl,sK50_skl))
| ~ frontsegP(sK50_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f1751,plain,
( ~ sQ22_spl
| ~ sQ166_spl
| sQ167_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1736,f614,f1748,f1744,f648]) ).
fof(f1752,definition,
( sQ168_spl
<=> rearsegP(app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)),sK5_skl(sK50_skl,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f1753,plain,
( ~ sQ168_spl
| rearsegP(app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)),sK5_skl(sK50_skl,sK50_skl)) ),
inference(component_clause,[status(thm)],[f1752]) ).
fof(f1755,plain,
( ~ sQ22_spl
| sQ168_spl
| ~ sQ166_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1737,f614,f1744,f1752,f648]) ).
fof(f1757,definition,
! [X0] :
( sQ169_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,[sQ169_spl])],[split_symbol_definition]) ).
fof(f1760,plain,
( ~ sQ22_spl
| ~ sQ17_spl
| ~ sQ166_spl
| sQ169_spl ),
inference(split_clause,[status(thm)],[f1739,f1757,f1744,f614,f648]) ).
fof(f1761,definition,
( sQ170_spl
<=> frontsegP(app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)),sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f1764,plain,
( ~ sQ22_spl
| ~ sQ166_spl
| sQ170_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1740,f614,f1761,f1744,f648]) ).
fof(f1765,plain,
( sQ166_spl
| ~ frontsegP(sK50_skl,sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f1746,f122]) ).
fof(f1766,plain,
( sQ166_spl
| ~ sQ23_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1765,f614,f652,f1744]) ).
fof(f1771,plain,
( ~ sQ168_spl
| ~ sQ22_spl
| rearsegP(sK50_skl,sK5_skl(sK50_skl,sK50_skl)) ),
inference(forward_demodulation,[status(thm)],[f649,f1753]) ).
fof(f1842,plain,
( ~ sQ168_spl
| ~ sQ22_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)],[f1771,f129]) ).
fof(f1843,definition,
( sQ180_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,[sQ180_spl])],[split_symbol_definition]) ).
fof(f1846,plain,
( ~ sQ168_spl
| ~ sQ22_spl
| sQ180_spl
| ~ sQ166_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f1842,f614,f1744,f1843,f648,f1752]) ).
fof(f1847,plain,
! [X0] :
( ~ sQ41_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)],[f811,f664]) ).
fof(f1848,plain,
! [X0] :
( ~ sQ41_spl
| app(X0,sK5_skl(X0,app(nil,sK5_skl(nil,nil)))) = app(nil,sK5_skl(nil,nil))
| ~ ssList(nil)
| ~ frontsegP(nil,X0)
| ~ ssList(sK5_skl(nil,nil))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f811,f663]) ).
fof(f1849,plain,
( ~ sQ41_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)],[f811,f467]) ).
fof(f1851,plain,
! [X0] :
( ~ sQ41_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)],[f811,f468]) ).
fof(f1852,plain,
( ~ sQ41_spl
| ~ ssList(sK5_skl(nil,nil))
| frontsegP(app(nil,sK5_skl(nil,nil)),nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f811,f466]) ).
fof(f1853,definition,
! [X0] :
( sQ181_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,[sQ181_spl])],[split_symbol_definition]) ).
fof(f1856,definition,
( sQ182_spl
<=> ssList(sK5_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f1857,plain,
( ~ sQ182_spl
| ssList(sK5_skl(nil,nil)) ),
inference(component_clause,[status(thm)],[f1856]) ).
fof(f1858,plain,
( sQ182_spl
| ~ ssList(sK5_skl(nil,nil)) ),
inference(component_clause,[status(thm)],[f1856]) ).
fof(f1859,plain,
( ~ sQ41_spl
| ~ sQ182_spl
| sQ181_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1847,f595,f1853,f1856,f810]) ).
fof(f1860,definition,
! [X0] :
( sQ183_spl
<=> ( app(X0,sK5_skl(X0,app(nil,sK5_skl(nil,nil)))) = app(nil,sK5_skl(nil,nil))
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f1863,plain,
( ~ sQ41_spl
| ~ sQ182_spl
| sQ183_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1848,f595,f1860,f1856,f810]) ).
fof(f1864,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(f1867,plain,
( ~ sQ41_spl
| sQ184_spl
| ~ sQ182_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1849,f595,f1856,f1864,f810]) ).
fof(f1869,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(f1872,plain,
( ~ sQ41_spl
| ~ sQ12_spl
| ~ sQ182_spl
| sQ185_spl ),
inference(split_clause,[status(thm)],[f1851,f1869,f1856,f595,f810]) ).
fof(f1873,definition,
( sQ186_spl
<=> frontsegP(app(nil,sK5_skl(nil,nil)),nil) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f1876,plain,
( ~ sQ41_spl
| ~ sQ182_spl
| sQ186_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1852,f595,f1873,f1856,f810]) ).
fof(f1877,plain,
( sQ182_spl
| ~ frontsegP(nil,nil)
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1858,f122]) ).
fof(f1878,plain,
( sQ182_spl
| ~ sQ42_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1877,f595,f814,f1856]) ).
fof(f1899,plain,
! [X0] :
( ~ sQ182_spl
| ~ frontsegP(sK5_skl(nil,nil),sK5_skl(nil,nil))
| ~ frontsegP(X0,sK5_skl(nil,nil))
| app(sK5_skl(nil,nil),sK5_skl(sK5_skl(nil,nil),X0)) = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1857,f591]) ).
fof(f1903,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)],[f1857,f577]) ).
fof(f1910,definition,
! [X0] :
( sQ187_spl
<=> ( ~ frontsegP(X0,sK5_skl(nil,nil))
| app(sK5_skl(nil,nil),sK5_skl(sK5_skl(nil,nil),X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f1913,definition,
( sQ188_spl
<=> frontsegP(sK5_skl(nil,nil),sK5_skl(nil,nil)) ),
introduced(definition,[new_symbols(definition,[sQ188_spl])],[split_symbol_definition]) ).
fof(f1916,plain,
( ~ sQ182_spl
| ~ sQ188_spl
| sQ187_spl ),
inference(split_clause,[status(thm)],[f1899,f1910,f1913,f1856]) ).
fof(f1918,definition,
! [X0] :
( sQ189_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,[sQ189_spl])],[split_symbol_definition]) ).
fof(f1921,plain,
( ~ sQ182_spl
| ~ sQ188_spl
| sQ189_spl ),
inference(split_clause,[status(thm)],[f1903,f1918,f1913,f1856]) ).
fof(f1942,plain,
! [X0] :
( ~ sQ50_spl
| X0 = app(nil,sK5_skl(nil,sK49_skl))
| ~ frontsegP(X0,app(nil,sK5_skl(nil,sK49_skl)))
| ~ ssList(sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(sK5_skl(nil,sK49_skl))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f866,f664]) ).
fof(f1943,plain,
! [X0] :
( ~ sQ50_spl
| app(X0,sK5_skl(X0,app(nil,sK5_skl(nil,sK49_skl)))) = app(nil,sK5_skl(nil,sK49_skl))
| ~ ssList(sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(sK5_skl(nil,sK49_skl))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f866,f663]) ).
fof(f1944,plain,
( ~ sQ50_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)],[f866,f467]) ).
fof(f1946,plain,
! [X0] :
( ~ sQ50_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)],[f866,f468]) ).
fof(f1947,plain,
( ~ sQ50_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)],[f866,f466]) ).
fof(f1948,definition,
! [X0] :
( sQ190_spl
<=> ( X0 = app(nil,sK5_skl(nil,sK49_skl))
| ~ frontsegP(X0,app(nil,sK5_skl(nil,sK49_skl)))
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ190_spl])],[split_symbol_definition]) ).
fof(f1951,definition,
( sQ191_spl
<=> ssList(sK5_skl(nil,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f1953,plain,
( sQ191_spl
| ~ ssList(sK5_skl(nil,sK49_skl)) ),
inference(component_clause,[status(thm)],[f1951]) ).
fof(f1954,plain,
( ~ sQ50_spl
| ~ sQ13_spl
| ~ sQ191_spl
| sQ190_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1942,f595,f1948,f1951,f598,f865]) ).
fof(f1955,definition,
! [X0] :
( sQ192_spl
<=> ( app(X0,sK5_skl(X0,app(nil,sK5_skl(nil,sK49_skl)))) = app(nil,sK5_skl(nil,sK49_skl))
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ192_spl])],[split_symbol_definition]) ).
fof(f1958,plain,
( ~ sQ50_spl
| ~ sQ13_spl
| ~ sQ191_spl
| sQ192_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f1943,f595,f1955,f1951,f598,f865]) ).
fof(f1959,definition,
( sQ193_spl
<=> rearsegP(app(nil,sK5_skl(nil,sK49_skl)),sK5_skl(nil,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ193_spl])],[split_symbol_definition]) ).
fof(f1962,plain,
( ~ sQ50_spl
| ~ sQ12_spl
| sQ193_spl
| ~ sQ191_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1944,f598,f1951,f1959,f595,f865]) ).
fof(f1964,definition,
! [X0] :
( sQ194_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,[sQ194_spl])],[split_symbol_definition]) ).
fof(f1967,plain,
( ~ sQ50_spl
| ~ sQ12_spl
| ~ sQ191_spl
| sQ194_spl ),
inference(split_clause,[status(thm)],[f1946,f1964,f1951,f595,f865]) ).
fof(f1968,definition,
( sQ195_spl
<=> frontsegP(app(nil,sK5_skl(nil,sK49_skl)),nil) ),
introduced(definition,[new_symbols(definition,[sQ195_spl])],[split_symbol_definition]) ).
fof(f1971,plain,
( ~ sQ50_spl
| ~ sQ191_spl
| sQ195_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1947,f598,f595,f1968,f1951,f865]) ).
fof(f1972,plain,
( sQ191_spl
| ~ frontsegP(sK49_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1953,f122]) ).
fof(f1973,plain,
( sQ191_spl
| ~ sQ15_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f1972,f598,f595,f605,f1951]) ).
fof(f1974,plain,
( sQ15_spl
| ~ sQ48_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f607,f857]) ).
fof(f1975,plain,
( sQ15_spl
| ~ sQ48_spl ),
inference(contradiction_clause,[status(thm)],[f1974]) ).
fof(f2015,plain,
! [X0,X1] :
( ~ sQ21_spl
| ~ frontsegP(X0,sK50_skl)
| ~ ssList(X1)
| ~ ssList(sK50_skl)
| ~ ssList(X0)
| ~ frontsegP(sK49_skl,app(X0,X1))
| ~ ssList(app(X0,X1)) ),
inference(resolution,[status(thm)],[f637,f288]) ).
fof(f2016,plain,
! [X0,X1] :
( ~ sQ21_spl
| ~ frontsegP(X1,sK50_skl)
| ~ frontsegP(X0,X1)
| ~ ssList(sK50_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f637,f282]) ).
fof(f2019,definition,
! [X0,X1] :
( sQ199_spl
<=> ( ~ frontsegP(X0,sK50_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(sK49_skl,app(X0,X1))
| ~ ssList(app(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f2022,plain,
( ~ sQ21_spl
| ~ sQ17_spl
| sQ199_spl ),
inference(split_clause,[status(thm)],[f2015,f2019,f614,f636]) ).
fof(f2023,definition,
! [X0,X1] :
( sQ200_spl
<=> ( ~ frontsegP(X1,sK50_skl)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f2026,plain,
( ~ sQ21_spl
| ~ sQ17_spl
| sQ200_spl ),
inference(split_clause,[status(thm)],[f2016,f2023,f614,f636]) ).
fof(f2030,plain,
! [X0] :
( ~ sQ65_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)],[f1033,f664]) ).
fof(f2031,plain,
! [X0] :
( ~ sQ65_spl
| app(X0,sK5_skl(X0,app(sK6_skl(nil,sK49_skl),nil))) = 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)],[f1033,f663]) ).
fof(f2032,plain,
( ~ sQ65_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)],[f1033,f467]) ).
fof(f2033,plain,
! [X0] :
( ~ sQ65_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)],[f1033,f288]) ).
fof(f2034,plain,
! [X0] :
( ~ sQ65_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)],[f1033,f468]) ).
fof(f2035,plain,
( ~ sQ65_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)],[f1033,f466]) ).
fof(f2036,definition,
( sQ201_spl
<=> ssList(sK6_skl(nil,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f2038,plain,
( sQ201_spl
| ~ ssList(sK6_skl(nil,sK49_skl)) ),
inference(component_clause,[status(thm)],[f2036]) ).
fof(f2039,definition,
! [X0] :
( sQ202_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,[sQ202_spl])],[split_symbol_definition]) ).
fof(f2042,plain,
( ~ sQ65_spl
| ~ sQ13_spl
| ~ sQ12_spl
| sQ202_spl
| ~ sQ201_spl ),
inference(split_clause,[status(thm)],[f2030,f2036,f2039,f595,f598,f1032]) ).
fof(f2043,definition,
! [X0] :
( sQ203_spl
<=> ( app(X0,sK5_skl(X0,app(sK6_skl(nil,sK49_skl),nil))) = app(sK6_skl(nil,sK49_skl),nil)
| ~ frontsegP(sK6_skl(nil,sK49_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f2046,plain,
( ~ sQ65_spl
| ~ sQ13_spl
| ~ sQ12_spl
| sQ203_spl
| ~ sQ201_spl ),
inference(split_clause,[status(thm)],[f2031,f2036,f2043,f595,f598,f1032]) ).
fof(f2047,definition,
( sQ204_spl
<=> rearsegP(app(sK6_skl(nil,sK49_skl),nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f2050,plain,
( ~ sQ65_spl
| ~ sQ201_spl
| sQ204_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2032,f598,f595,f2047,f2036,f1032]) ).
fof(f2051,definition,
! [X0] :
( sQ205_spl
<=> ( frontsegP(sK49_skl,X0)
| ~ frontsegP(sK6_skl(nil,sK49_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f2054,plain,
( ~ sQ65_spl
| ~ sQ12_spl
| sQ205_spl
| ~ sQ201_spl ),
inference(split_clause,[status(thm)],[f2033,f2036,f2051,f595,f1032]) ).
fof(f2055,definition,
! [X0] :
( sQ206_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK6_skl(nil,sK49_skl),nil),X0),nil)
| ~ ssList(app(sK49_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f2058,plain,
( ~ sQ65_spl
| ~ sQ201_spl
| ~ sQ12_spl
| sQ206_spl ),
inference(split_clause,[status(thm)],[f2034,f2055,f595,f2036,f1032]) ).
fof(f2059,definition,
( sQ207_spl
<=> frontsegP(app(sK6_skl(nil,sK49_skl),nil),sK6_skl(nil,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f2062,plain,
( ~ sQ65_spl
| ~ sQ12_spl
| sQ207_spl
| ~ sQ201_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2035,f598,f2036,f2059,f595,f1032]) ).
fof(f2063,plain,
( sQ201_spl
| ~ rearsegP(sK49_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f2038,f128]) ).
fof(f2064,definition,
( sQ208_spl
<=> rearsegP(sK49_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ208_spl])],[split_symbol_definition]) ).
fof(f2066,plain,
( sQ208_spl
| ~ rearsegP(sK49_skl,nil) ),
inference(component_clause,[status(thm)],[f2064]) ).
fof(f2067,plain,
( sQ201_spl
| ~ sQ208_spl
| ~ sQ12_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2063,f598,f595,f2064,f2036]) ).
fof(f2068,plain,
( sQ208_spl
| ~ sQ61_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2066,f1028]) ).
fof(f2069,plain,
( sQ208_spl
| ~ sQ61_spl ),
inference(contradiction_clause,[status(thm)],[f2068]) ).
fof(f2109,plain,
! [X0] :
( ~ sQ66_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)],[f1039,f664]) ).
fof(f2110,plain,
! [X0] :
( ~ sQ66_spl
| app(X0,sK5_skl(X0,app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)))) = 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)],[f1039,f663]) ).
fof(f2111,plain,
( ~ sQ66_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)],[f1039,f467]) ).
fof(f2113,plain,
! [X0] :
( ~ sQ66_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)],[f1039,f468]) ).
fof(f2114,plain,
( ~ sQ66_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)],[f1039,f466]) ).
fof(f2115,definition,
! [X0] :
( sQ212_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,[sQ212_spl])],[split_symbol_definition]) ).
fof(f2118,definition,
( sQ213_spl
<=> ssList(sK5_skl(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f2120,plain,
( sQ213_spl
| ~ ssList(sK5_skl(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f2118]) ).
fof(f2121,plain,
( ~ sQ66_spl
| ~ sQ213_spl
| sQ212_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2109,f598,f2115,f2118,f1038]) ).
fof(f2122,definition,
! [X0] :
( sQ214_spl
<=> ( app(X0,sK5_skl(X0,app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)))) = app(sK49_skl,sK5_skl(sK49_skl,sK49_skl))
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ214_spl])],[split_symbol_definition]) ).
fof(f2125,plain,
( ~ sQ66_spl
| ~ sQ213_spl
| sQ214_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2110,f598,f2122,f2118,f1038]) ).
fof(f2126,definition,
( sQ215_spl
<=> rearsegP(app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)),sK5_skl(sK49_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ215_spl])],[split_symbol_definition]) ).
fof(f2127,plain,
( ~ sQ215_spl
| rearsegP(app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)),sK5_skl(sK49_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f2126]) ).
fof(f2129,plain,
( ~ sQ66_spl
| sQ215_spl
| ~ sQ213_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2111,f598,f2118,f2126,f1038]) ).
fof(f2131,definition,
! [X0] :
( sQ216_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,[sQ216_spl])],[split_symbol_definition]) ).
fof(f2134,plain,
( ~ sQ66_spl
| ~ sQ13_spl
| ~ sQ213_spl
| sQ216_spl ),
inference(split_clause,[status(thm)],[f2113,f2131,f2118,f598,f1038]) ).
fof(f2135,definition,
( sQ217_spl
<=> frontsegP(app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ217_spl])],[split_symbol_definition]) ).
fof(f2138,plain,
( ~ sQ66_spl
| ~ sQ213_spl
| sQ217_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2114,f598,f2135,f2118,f1038]) ).
fof(f2139,plain,
( sQ213_spl
| ~ frontsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f2120,f122]) ).
fof(f2140,plain,
( sQ213_spl
| ~ sQ67_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2139,f598,f1042,f2118]) ).
fof(f2145,plain,
( ~ sQ215_spl
| ~ sQ66_spl
| rearsegP(sK49_skl,sK5_skl(sK49_skl,sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f1039,f2127]) ).
fof(f2148,plain,
! [X0,X1] :
( frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssItem(sK1_skl)
| ~ ssItem(sK1_skl)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f774,f292]) ).
fof(f2152,definition,
! [X0,X1] :
( sQ218_spl
<=> ( frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ218_spl])],[split_symbol_definition]) ).
fof(f2155,definition,
( sQ219_spl
<=> ssItem(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ219_spl])],[split_symbol_definition]) ).
fof(f2157,plain,
( sQ219_spl
| ~ ssItem(sK1_skl) ),
inference(component_clause,[status(thm)],[f2155]) ).
fof(f2158,plain,
( ~ sQ219_spl
| sQ218_spl ),
inference(split_clause,[status(thm)],[f2148,f2152,f2155]) ).
fof(f2163,plain,
( sQ219_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2157,f104]) ).
fof(f2164,plain,
sQ219_spl,
inference(contradiction_clause,[status(thm)],[f2163]) ).
fof(f2203,plain,
( ~ sQ215_spl
| ~ sQ66_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)],[f2145,f129]) ).
fof(f2204,definition,
( sQ224_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,[sQ224_spl])],[split_symbol_definition]) ).
fof(f2207,plain,
( ~ sQ215_spl
| ~ sQ66_spl
| sQ224_spl
| ~ sQ213_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2203,f598,f2118,f2204,f1038,f2126]) ).
fof(f2260,plain,
! [X0] :
( ~ sQ73_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)],[f1076,f664]) ).
fof(f2261,plain,
! [X0] :
( ~ sQ73_spl
| app(X0,sK5_skl(X0,app(sK6_skl(nil,sK50_skl),nil))) = 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)],[f1076,f663]) ).
fof(f2262,plain,
( ~ sQ73_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)],[f1076,f467]) ).
fof(f2263,plain,
! [X0] :
( ~ sQ73_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)],[f1076,f288]) ).
fof(f2264,plain,
! [X0] :
( ~ sQ73_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)],[f1076,f468]) ).
fof(f2265,plain,
( ~ sQ73_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)],[f1076,f466]) ).
fof(f2266,definition,
( sQ225_spl
<=> ssList(sK6_skl(nil,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ225_spl])],[split_symbol_definition]) ).
fof(f2268,plain,
( sQ225_spl
| ~ ssList(sK6_skl(nil,sK50_skl)) ),
inference(component_clause,[status(thm)],[f2266]) ).
fof(f2269,definition,
! [X0] :
( sQ226_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,[sQ226_spl])],[split_symbol_definition]) ).
fof(f2272,plain,
( ~ sQ73_spl
| ~ sQ17_spl
| ~ sQ12_spl
| sQ226_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f2260,f2266,f2269,f595,f614,f1075]) ).
fof(f2273,definition,
! [X0] :
( sQ227_spl
<=> ( app(X0,sK5_skl(X0,app(sK6_skl(nil,sK50_skl),nil))) = app(sK6_skl(nil,sK50_skl),nil)
| ~ frontsegP(sK6_skl(nil,sK50_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ227_spl])],[split_symbol_definition]) ).
fof(f2276,plain,
( ~ sQ73_spl
| ~ sQ17_spl
| ~ sQ12_spl
| sQ227_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f2261,f2266,f2273,f595,f614,f1075]) ).
fof(f2277,definition,
( sQ228_spl
<=> rearsegP(app(sK6_skl(nil,sK50_skl),nil),nil) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f2280,plain,
( ~ sQ73_spl
| ~ sQ225_spl
| sQ228_spl
| ~ sQ12_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2262,f614,f595,f2277,f2266,f1075]) ).
fof(f2281,definition,
! [X0] :
( sQ229_spl
<=> ( frontsegP(sK50_skl,X0)
| ~ frontsegP(sK6_skl(nil,sK50_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f2284,plain,
( ~ sQ73_spl
| ~ sQ12_spl
| sQ229_spl
| ~ sQ225_spl ),
inference(split_clause,[status(thm)],[f2263,f2266,f2281,f595,f1075]) ).
fof(f2285,definition,
! [X0] :
( sQ230_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK6_skl(nil,sK50_skl),nil),X0),nil)
| ~ ssList(app(sK50_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f2288,plain,
( ~ sQ73_spl
| ~ sQ225_spl
| ~ sQ12_spl
| sQ230_spl ),
inference(split_clause,[status(thm)],[f2264,f2285,f595,f2266,f1075]) ).
fof(f2289,definition,
( sQ231_spl
<=> frontsegP(app(sK6_skl(nil,sK50_skl),nil),sK6_skl(nil,sK50_skl)) ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f2292,plain,
( ~ sQ73_spl
| ~ sQ12_spl
| sQ231_spl
| ~ sQ225_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2265,f614,f2266,f2289,f595,f1075]) ).
fof(f2293,plain,
( sQ225_spl
| ~ rearsegP(sK50_skl,nil)
| ~ ssList(nil)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f2268,f128]) ).
fof(f2294,definition,
( sQ232_spl
<=> rearsegP(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f2296,plain,
( sQ232_spl
| ~ rearsegP(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f2294]) ).
fof(f2297,plain,
( sQ225_spl
| ~ sQ232_spl
| ~ sQ12_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2293,f614,f595,f2294,f2266]) ).
fof(f2298,plain,
( sQ232_spl
| ~ sQ69_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2296,f1071]) ).
fof(f2299,plain,
( sQ232_spl
| ~ sQ69_spl ),
inference(contradiction_clause,[status(thm)],[f2298]) ).
fof(f2340,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)],[f692,f123]) ).
fof(f2341,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)],[f692,f284]) ).
fof(f2343,definition,
! [X0] :
( sQ236_spl
<=> ( app(X0,sK5_skl(X0,sK50_skl)) = sK50_skl
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f2346,plain,
( ~ sQ27_spl
| ~ sQ17_spl
| sQ236_spl ),
inference(split_clause,[status(thm)],[f2340,f2343,f614,f691]) ).
fof(f2347,definition,
! [X0] :
( sQ237_spl
<=> ( X0 = sK50_skl
| ~ frontsegP(X0,sK50_skl)
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f2350,plain,
( ~ sQ27_spl
| ~ sQ17_spl
| sQ237_spl ),
inference(split_clause,[status(thm)],[f2341,f2347,f614,f691]) ).
fof(f2358,plain,
! [X0,X1] :
( ~ sQ33_spl
| ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(X0,sK50_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f720,f282]) ).
fof(f2362,definition,
! [X0,X1] :
( sQ238_spl
<=> ( ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sK50_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f2365,plain,
( ~ sQ33_spl
| ~ sQ12_spl
| sQ238_spl ),
inference(split_clause,[status(thm)],[f2358,f2362,f595,f719]) ).
fof(f2369,plain,
( ~ sQ21_spl
| ~ sQ46_spl
| ~ frontsegP(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ frontsegP(nil,sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f844,f637]) ).
fof(f2370,plain,
! [X0] :
( ~ sQ46_spl
| app(X0,sK5_skl(X0,sK49_skl)) = sK49_skl
| ~ ssList(X0)
| ~ ssList(sK49_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f844,f123]) ).
fof(f2371,plain,
! [X0] :
( ~ sQ46_spl
| X0 = sK49_skl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f844,f284]) ).
fof(f2373,plain,
( ~ sQ21_spl
| ~ sQ46_spl
| ~ sQ67_spl
| ~ sQ13_spl
| ~ sQ31_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2369,f614,f711,f598,f1042,f843,f636]) ).
fof(f2374,definition,
! [X0] :
( sQ239_spl
<=> ( app(X0,sK5_skl(X0,sK49_skl)) = sK49_skl
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f2377,plain,
( ~ sQ46_spl
| ~ sQ13_spl
| sQ239_spl ),
inference(split_clause,[status(thm)],[f2370,f2374,f598,f843]) ).
fof(f2378,definition,
! [X0] :
( sQ240_spl
<=> ( X0 = sK49_skl
| ~ frontsegP(X0,sK49_skl)
| ~ ssList(X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f2381,plain,
( ~ sQ46_spl
| ~ sQ13_spl
| sQ240_spl ),
inference(split_clause,[status(thm)],[f2371,f2378,f598,f843]) ).
fof(f2400,definition,
( sQ242_spl
<=> ssItem(sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ242_spl])],[split_symbol_definition]) ).
fof(f2402,plain,
( sQ242_spl
| ~ ssItem(sK0_skl) ),
inference(component_clause,[status(thm)],[f2400]) ).
fof(f2440,plain,
app(sK6_skl(sK50_skl,sK50_skl),sK50_skl) = sK50_skl,
inference(resolution,[status(thm)],[f748,f423]) ).
fof(f2457,plain,
! [X0] :
( ssList(cons(sK1_skl,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f222,f104]) ).
fof(f2458,plain,
! [X0] :
( ssList(cons(sK0_skl,X0))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f222,f103]) ).
fof(f2461,plain,
( ~ ssItem(sK1_skl)
| singletonP(cons(sK1_skl,nil))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2457,f465]) ).
fof(f2478,definition,
( sQ243_spl
<=> singletonP(cons(sK1_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f2479,plain,
( ~ sQ243_spl
| singletonP(cons(sK1_skl,nil)) ),
inference(component_clause,[status(thm)],[f2478]) ).
fof(f2481,plain,
( ~ sQ219_spl
| sQ243_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f2461,f595,f2478,f2155]) ).
fof(f2482,plain,
( ~ sQ243_spl
| cons(sK4_skl(cons(sK1_skl,nil)),nil) = cons(sK1_skl,nil)
| ~ ssList(cons(sK1_skl,nil)) ),
inference(resolution,[status(thm)],[f2479,f117]) ).
fof(f2483,plain,
( ~ sQ243_spl
| ssItem(sK4_skl(cons(sK1_skl,nil)))
| ~ ssList(cons(sK1_skl,nil)) ),
inference(resolution,[status(thm)],[f2479,f116]) ).
fof(f2484,definition,
( sQ244_spl
<=> ssList(cons(sK1_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ244_spl])],[split_symbol_definition]) ).
fof(f2485,plain,
( ~ sQ244_spl
| ssList(cons(sK1_skl,nil)) ),
inference(component_clause,[status(thm)],[f2484]) ).
fof(f2486,plain,
( sQ244_spl
| ~ ssList(cons(sK1_skl,nil)) ),
inference(component_clause,[status(thm)],[f2484]) ).
fof(f2487,definition,
( sQ245_spl
<=> cons(sK4_skl(cons(sK1_skl,nil)),nil) = cons(sK1_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ245_spl])],[split_symbol_definition]) ).
fof(f2490,plain,
( ~ sQ243_spl
| sQ245_spl
| ~ sQ244_spl ),
inference(split_clause,[status(thm)],[f2482,f2484,f2487,f2478]) ).
fof(f2491,definition,
( sQ246_spl
<=> ssItem(sK4_skl(cons(sK1_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ246_spl])],[split_symbol_definition]) ).
fof(f2492,plain,
( ~ sQ246_spl
| ssItem(sK4_skl(cons(sK1_skl,nil))) ),
inference(component_clause,[status(thm)],[f2491]) ).
fof(f2494,plain,
( ~ sQ243_spl
| sQ246_spl
| ~ sQ244_spl ),
inference(split_clause,[status(thm)],[f2483,f2484,f2491,f2478]) ).
fof(f2495,plain,
( sQ244_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2486,f2457]) ).
fof(f2496,plain,
( sQ244_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f2495,f595,f2484]) ).
fof(f2503,plain,
! [X0] :
( ~ sQ244_spl
| ~ frontsegP(cons(sK1_skl,nil),cons(sK1_skl,nil))
| ~ frontsegP(X0,cons(sK1_skl,nil))
| app(cons(sK1_skl,nil),sK5_skl(cons(sK1_skl,nil),X0)) = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2485,f591]) ).
fof(f2507,plain,
! [X0] :
( ~ sQ244_spl
| ~ frontsegP(cons(sK1_skl,nil),X0)
| ~ frontsegP(cons(sK1_skl,nil),cons(sK1_skl,nil))
| X0 = cons(sK1_skl,nil)
| ~ frontsegP(X0,cons(sK1_skl,nil))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2485,f577]) ).
fof(f2515,definition,
! [X0] :
( sQ247_spl
<=> ( ~ frontsegP(X0,cons(sK1_skl,nil))
| app(cons(sK1_skl,nil),sK5_skl(cons(sK1_skl,nil),X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ247_spl])],[split_symbol_definition]) ).
fof(f2518,definition,
( sQ248_spl
<=> frontsegP(cons(sK1_skl,nil),cons(sK1_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ248_spl])],[split_symbol_definition]) ).
fof(f2521,plain,
( ~ sQ244_spl
| ~ sQ248_spl
| sQ247_spl ),
inference(split_clause,[status(thm)],[f2503,f2515,f2518,f2484]) ).
fof(f2523,definition,
! [X0] :
( sQ249_spl
<=> ( ~ frontsegP(cons(sK1_skl,nil),X0)
| X0 = cons(sK1_skl,nil)
| ~ frontsegP(X0,cons(sK1_skl,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ249_spl])],[split_symbol_definition]) ).
fof(f2526,plain,
( ~ sQ244_spl
| ~ sQ248_spl
| sQ249_spl ),
inference(split_clause,[status(thm)],[f2507,f2523,f2518,f2484]) ).
fof(f2528,plain,
( ~ ssItem(sK0_skl)
| singletonP(cons(sK0_skl,nil))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2458,f465]) ).
fof(f2545,definition,
( sQ250_spl
<=> singletonP(cons(sK0_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ250_spl])],[split_symbol_definition]) ).
fof(f2546,plain,
( ~ sQ250_spl
| singletonP(cons(sK0_skl,nil)) ),
inference(component_clause,[status(thm)],[f2545]) ).
fof(f2548,plain,
( ~ sQ242_spl
| sQ250_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f2528,f595,f2545,f2400]) ).
fof(f2549,plain,
( sQ242_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2402,f103]) ).
fof(f2550,plain,
sQ242_spl,
inference(contradiction_clause,[status(thm)],[f2549]) ).
fof(f2551,plain,
( ~ sQ250_spl
| cons(sK4_skl(cons(sK0_skl,nil)),nil) = cons(sK0_skl,nil)
| ~ ssList(cons(sK0_skl,nil)) ),
inference(resolution,[status(thm)],[f2546,f117]) ).
fof(f2552,plain,
( ~ sQ250_spl
| ssItem(sK4_skl(cons(sK0_skl,nil)))
| ~ ssList(cons(sK0_skl,nil)) ),
inference(resolution,[status(thm)],[f2546,f116]) ).
fof(f2553,definition,
( sQ251_spl
<=> ssList(cons(sK0_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ251_spl])],[split_symbol_definition]) ).
fof(f2554,plain,
( ~ sQ251_spl
| ssList(cons(sK0_skl,nil)) ),
inference(component_clause,[status(thm)],[f2553]) ).
fof(f2555,plain,
( sQ251_spl
| ~ ssList(cons(sK0_skl,nil)) ),
inference(component_clause,[status(thm)],[f2553]) ).
fof(f2556,definition,
( sQ252_spl
<=> cons(sK4_skl(cons(sK0_skl,nil)),nil) = cons(sK0_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ252_spl])],[split_symbol_definition]) ).
fof(f2559,plain,
( ~ sQ250_spl
| sQ252_spl
| ~ sQ251_spl ),
inference(split_clause,[status(thm)],[f2551,f2553,f2556,f2545]) ).
fof(f2560,definition,
( sQ253_spl
<=> ssItem(sK4_skl(cons(sK0_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ253_spl])],[split_symbol_definition]) ).
fof(f2561,plain,
( ~ sQ253_spl
| ssItem(sK4_skl(cons(sK0_skl,nil))) ),
inference(component_clause,[status(thm)],[f2560]) ).
fof(f2563,plain,
( ~ sQ250_spl
| sQ253_spl
| ~ sQ251_spl ),
inference(split_clause,[status(thm)],[f2552,f2553,f2560,f2545]) ).
fof(f2564,plain,
( sQ251_spl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2555,f2458]) ).
fof(f2565,plain,
( sQ251_spl
| ~ sQ12_spl ),
inference(split_clause,[status(thm)],[f2564,f595,f2553]) ).
fof(f2567,plain,
! [X0,X1] :
( ~ sQ59_spl
| ~ segmentP(X1,sK50_skl)
| ~ segmentP(X0,X1)
| ~ ssList(sK50_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f968,f315]) ).
fof(f2568,plain,
( ~ sQ59_spl
| ~ ssList(sK50_skl)
| ~ segmentP(sK49_skl,sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f968,f319]) ).
fof(f2570,definition,
! [X0,X1] :
( sQ254_spl
<=> ( ~ segmentP(X1,sK50_skl)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ segmentP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ254_spl])],[split_symbol_definition]) ).
fof(f2573,plain,
( ~ sQ59_spl
| ~ sQ17_spl
| sQ254_spl ),
inference(split_clause,[status(thm)],[f2567,f2570,f614,f967]) ).
fof(f2574,plain,
( ~ sQ59_spl
| ~ sQ54_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2568,f614,f903,f967]) ).
fof(f2577,plain,
! [X0] :
( ~ sQ76_spl
| app(X0,sK5_skl(X0,sK50_skl)) = sK50_skl
| ~ ssList(X0)
| ~ ssList(sK50_skl)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1095,f123]) ).
fof(f2578,plain,
! [X0] :
( ~ sQ76_spl
| X0 = sK50_skl
| ~ frontsegP(X0,sK50_skl)
| ~ ssList(sK50_skl)
| ~ ssList(X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1095,f284]) ).
fof(f2580,definition,
! [X0] :
( sQ255_spl
<=> ( app(X0,sK5_skl(X0,sK50_skl)) = sK50_skl
| ~ ssList(X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ255_spl])],[split_symbol_definition]) ).
fof(f2583,plain,
( ~ sQ76_spl
| ~ sQ17_spl
| sQ255_spl ),
inference(split_clause,[status(thm)],[f2577,f2580,f614,f1094]) ).
fof(f2584,definition,
! [X0] :
( sQ256_spl
<=> ( X0 = sK50_skl
| ~ frontsegP(X0,sK50_skl)
| ~ ssList(X0)
| ~ frontsegP(sK49_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ256_spl])],[split_symbol_definition]) ).
fof(f2587,plain,
( ~ sQ76_spl
| ~ sQ17_spl
| sQ256_spl ),
inference(split_clause,[status(thm)],[f2578,f2584,f614,f1094]) ).
fof(f2592,plain,
( ~ sQ81_spl
| ~ ssList(sK49_skl)
| ~ segmentP(sK50_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1125,f319]) ).
fof(f2598,plain,
( ~ sQ81_spl
| ~ sQ79_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2592,f598,f1114,f1124]) ).
fof(f2601,plain,
( sQ102_spl
| ~ ssList(sK5_skl(sK49_skl,sK50_skl)) ),
inference(resolution,[status(thm)],[f1299,f286]) ).
fof(f2606,plain,
( sQ102_spl
| ~ sQ74_spl ),
inference(split_clause,[status(thm)],[f2601,f1087,f1297]) ).
fof(f2607,plain,
( ~ sQ22_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)],[f649,f703]) ).
fof(f2609,plain,
( ~ sQ28_spl
| ~ ssList(nil)
| segmentP(app(sK50_skl,nil),sK50_skl)
| ~ ssList(sK50_skl) ),
inference(paramodulation,[status(thm)],[f1002,f703]) ).
fof(f2610,definition,
( sQ259_spl
<=> segmentP(app(sK50_skl,sK5_skl(sK50_skl,sK50_skl)),sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f2613,plain,
( ~ sQ22_spl
| ~ sQ28_spl
| ~ sQ166_spl
| sQ259_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2607,f614,f2610,f1744,f695,f648]) ).
fof(f2614,definition,
( sQ260_spl
<=> segmentP(app(sK50_skl,sK50_skl),sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ260_spl])],[split_symbol_definition]) ).
fof(f2618,definition,
( sQ261_spl
<=> segmentP(app(sK50_skl,nil),sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ261_spl])],[split_symbol_definition]) ).
fof(f2621,plain,
( ~ sQ28_spl
| ~ sQ12_spl
| sQ261_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2609,f614,f2618,f595,f695]) ).
fof(f2655,plain,
! [X0] :
( X0 = app(sK6_skl(sK50_skl,sK50_skl),sK50_skl)
| ~ frontsegP(X0,app(sK6_skl(sK50_skl,sK50_skl),sK50_skl))
| ~ ssList(sK50_skl)
| ~ frontsegP(sK6_skl(sK50_skl,sK50_skl),X0)
| ~ ssList(sK50_skl)
| ~ ssList(X0)
| ~ ssList(sK6_skl(sK50_skl,sK50_skl)) ),
inference(paramodulation,[status(thm)],[f2440,f664]) ).
fof(f2656,plain,
! [X0] :
( app(X0,sK5_skl(X0,app(sK6_skl(sK50_skl,sK50_skl),sK50_skl))) = app(sK6_skl(sK50_skl,sK50_skl),sK50_skl)
| ~ ssList(sK50_skl)
| ~ frontsegP(sK6_skl(sK50_skl,sK50_skl),X0)
| ~ ssList(sK50_skl)
| ~ ssList(X0)
| ~ ssList(sK6_skl(sK50_skl,sK50_skl)) ),
inference(paramodulation,[status(thm)],[f2440,f663]) ).
fof(f2657,plain,
( ~ 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)],[f2440,f467]) ).
fof(f2658,plain,
! [X0] :
( 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)],[f2440,f288]) ).
fof(f2659,plain,
! [X0] :
( ~ 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)],[f2440,f468]) ).
fof(f2660,plain,
( ~ 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)],[f2440,f466]) ).
fof(f2661,definition,
! [X0] :
( sQ262_spl
<=> ( X0 = app(sK6_skl(sK50_skl,sK50_skl),sK50_skl)
| ~ frontsegP(X0,app(sK6_skl(sK50_skl,sK50_skl),sK50_skl))
| ~ frontsegP(sK6_skl(sK50_skl,sK50_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ262_spl])],[split_symbol_definition]) ).
fof(f2664,plain,
( ~ sQ17_spl
| sQ262_spl
| ~ sQ109_spl ),
inference(split_clause,[status(thm)],[f2655,f1367,f2661,f614]) ).
fof(f2665,definition,
! [X0] :
( sQ263_spl
<=> ( app(X0,sK5_skl(X0,app(sK6_skl(sK50_skl,sK50_skl),sK50_skl))) = app(sK6_skl(sK50_skl,sK50_skl),sK50_skl)
| ~ frontsegP(sK6_skl(sK50_skl,sK50_skl),X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ263_spl])],[split_symbol_definition]) ).
fof(f2668,plain,
( ~ sQ17_spl
| sQ263_spl
| ~ sQ109_spl ),
inference(split_clause,[status(thm)],[f2656,f1367,f2665,f614]) ).
fof(f2669,plain,
( ~ sQ109_spl
| sQ108_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2657,f614,f1364,f1367]) ).
fof(f2670,plain,
( ~ sQ17_spl
| sQ110_spl
| ~ sQ109_spl ),
inference(split_clause,[status(thm)],[f2658,f1367,f1371,f614]) ).
fof(f2671,plain,
( ~ sQ109_spl
| ~ sQ17_spl
| sQ111_spl ),
inference(split_clause,[status(thm)],[f2659,f1375,f614,f1367]) ).
fof(f2672,plain,
( sQ112_spl
| ~ sQ109_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2660,f614,f1367,f1379]) ).
fof(f2697,plain,
! [X0] :
( ~ sQ57_spl
| ~ ssList(nil)
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f936,f295]) ).
fof(f2698,plain,
! [X0,X1,X2] :
( ~ sQ57_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)],[f936,f282]) ).
fof(f2700,definition,
! [X0] :
( sQ264_spl
<=> ( ~ frontsegP(nil,X0)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ264_spl])],[split_symbol_definition]) ).
fof(f2704,plain,
( ~ sQ57_spl
| ~ sQ12_spl
| sQ264_spl ),
inference(split_clause,[status(thm)],[f2697,f2700,f595,f931]) ).
fof(f2705,definition,
! [X0,X1,X2] :
( sQ265_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,[sQ265_spl])],[split_symbol_definition]) ).
fof(f2708,plain,
( ~ sQ57_spl
| ~ sQ12_spl
| sQ265_spl ),
inference(split_clause,[status(thm)],[f2698,f2705,f595,f931]) ).
fof(f2718,plain,
! [X0] :
( ~ sQ251_spl
| ~ frontsegP(cons(sK0_skl,nil),cons(sK0_skl,nil))
| ~ frontsegP(X0,cons(sK0_skl,nil))
| app(cons(sK0_skl,nil),sK5_skl(cons(sK0_skl,nil),X0)) = X0
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2554,f591]) ).
fof(f2722,plain,
! [X0] :
( ~ sQ251_spl
| ~ frontsegP(cons(sK0_skl,nil),X0)
| ~ frontsegP(cons(sK0_skl,nil),cons(sK0_skl,nil))
| X0 = cons(sK0_skl,nil)
| ~ frontsegP(X0,cons(sK0_skl,nil))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2554,f577]) ).
fof(f2730,definition,
! [X0] :
( sQ266_spl
<=> ( ~ frontsegP(X0,cons(sK0_skl,nil))
| app(cons(sK0_skl,nil),sK5_skl(cons(sK0_skl,nil),X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ266_spl])],[split_symbol_definition]) ).
fof(f2733,definition,
( sQ267_spl
<=> frontsegP(cons(sK0_skl,nil),cons(sK0_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ267_spl])],[split_symbol_definition]) ).
fof(f2736,plain,
( ~ sQ251_spl
| ~ sQ267_spl
| sQ266_spl ),
inference(split_clause,[status(thm)],[f2718,f2730,f2733,f2553]) ).
fof(f2738,definition,
! [X0] :
( sQ268_spl
<=> ( ~ frontsegP(cons(sK0_skl,nil),X0)
| X0 = cons(sK0_skl,nil)
| ~ frontsegP(X0,cons(sK0_skl,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ268_spl])],[split_symbol_definition]) ).
fof(f2741,plain,
( ~ sQ251_spl
| ~ sQ267_spl
| sQ268_spl ),
inference(split_clause,[status(thm)],[f2722,f2738,f2733,f2553]) ).
fof(f2745,plain,
( ~ sQ246_spl
| sK4_skl(cons(sK1_skl,nil)) = sK1_skl
| neq(sK4_skl(cons(sK1_skl,nil)),sK1_skl) ),
inference(resolution,[status(thm)],[f2492,f501]) ).
fof(f2746,plain,
( ~ sQ246_spl
| sK4_skl(cons(sK1_skl,nil)) = sK0_skl
| neq(sK4_skl(cons(sK1_skl,nil)),sK0_skl) ),
inference(resolution,[status(thm)],[f2492,f499]) ).
fof(f2750,definition,
( sQ269_spl
<=> neq(sK4_skl(cons(sK1_skl,nil)),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ269_spl])],[split_symbol_definition]) ).
fof(f2753,definition,
( sQ270_spl
<=> sK4_skl(cons(sK1_skl,nil)) = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ270_spl])],[split_symbol_definition]) ).
fof(f2756,plain,
( ~ sQ246_spl
| sQ270_spl
| sQ269_spl ),
inference(split_clause,[status(thm)],[f2745,f2750,f2753,f2491]) ).
fof(f2757,definition,
( sQ271_spl
<=> neq(sK4_skl(cons(sK1_skl,nil)),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ271_spl])],[split_symbol_definition]) ).
fof(f2760,definition,
( sQ272_spl
<=> sK4_skl(cons(sK1_skl,nil)) = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ272_spl])],[split_symbol_definition]) ).
fof(f2763,plain,
( ~ sQ246_spl
| sQ272_spl
| sQ271_spl ),
inference(split_clause,[status(thm)],[f2746,f2757,f2760,f2491]) ).
fof(f2766,plain,
( ~ sQ253_spl
| sK4_skl(cons(sK0_skl,nil)) = sK1_skl
| neq(sK4_skl(cons(sK0_skl,nil)),sK1_skl) ),
inference(resolution,[status(thm)],[f2561,f501]) ).
fof(f2767,plain,
( ~ sQ253_spl
| sK4_skl(cons(sK0_skl,nil)) = sK0_skl
| neq(sK4_skl(cons(sK0_skl,nil)),sK0_skl) ),
inference(resolution,[status(thm)],[f2561,f499]) ).
fof(f2771,definition,
( sQ273_spl
<=> neq(sK4_skl(cons(sK0_skl,nil)),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ273_spl])],[split_symbol_definition]) ).
fof(f2774,definition,
( sQ274_spl
<=> sK4_skl(cons(sK0_skl,nil)) = sK1_skl ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f2777,plain,
( ~ sQ253_spl
| sQ274_spl
| sQ273_spl ),
inference(split_clause,[status(thm)],[f2766,f2771,f2774,f2560]) ).
fof(f2778,definition,
( sQ275_spl
<=> neq(sK4_skl(cons(sK0_skl,nil)),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ275_spl])],[split_symbol_definition]) ).
fof(f2781,definition,
( sQ276_spl
<=> sK4_skl(cons(sK0_skl,nil)) = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ276_spl])],[split_symbol_definition]) ).
fof(f2784,plain,
( ~ sQ253_spl
| sQ276_spl
| sQ275_spl ),
inference(split_clause,[status(thm)],[f2767,f2778,f2781,f2560]) ).
fof(f2843,plain,
! [X0] :
( ssList(app(X0,sK49_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f245,f422]) ).
fof(f2846,plain,
! [X0] :
( ssList(app(X0,sK50_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f245,f423]) ).
fof(f2856,plain,
( ~ sQ28_spl
| ~ ssList(sK49_skl)
| segmentP(app(sK50_skl,sK49_skl),sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f2843,f703]) ).
fof(f2857,plain,
! [X0,X1] :
( ~ ssList(sK49_skl)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),sK49_skl),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(resolution,[status(thm)],[f2843,f468]) ).
fof(f2880,definition,
( sQ277_spl
<=> segmentP(app(sK50_skl,sK49_skl),sK50_skl) ),
introduced(definition,[new_symbols(definition,[sQ277_spl])],[split_symbol_definition]) ).
fof(f2881,plain,
( ~ sQ277_spl
| segmentP(app(sK50_skl,sK49_skl),sK50_skl) ),
inference(component_clause,[status(thm)],[f2880]) ).
fof(f2883,plain,
( ~ sQ28_spl
| ~ sQ13_spl
| sQ277_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2856,f614,f2880,f598,f695]) ).
fof(f2884,definition,
! [X0,X1] :
( sQ278_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(X0,X1),sK49_skl),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f2887,plain,
( ~ sQ13_spl
| sQ278_spl ),
inference(split_clause,[status(thm)],[f2857,f2884,f598]) ).
fof(f2891,plain,
( ~ sQ28_spl
| ~ ssList(sK50_skl)
| segmentP(app(sK50_skl,sK50_skl),sK50_skl)
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f2846,f703]) ).
fof(f2892,plain,
! [X0,X1] :
( ~ ssList(sK50_skl)
| ~ ssList(X0)
| segmentP(app(app(X0,X1),sK50_skl),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(resolution,[status(thm)],[f2846,f468]) ).
fof(f2915,plain,
( ~ sQ28_spl
| sQ260_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2891,f614,f2614,f695]) ).
fof(f2916,definition,
! [X0,X1] :
( sQ279_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(X0,X1),sK50_skl),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f2919,plain,
( ~ sQ17_spl
| sQ279_spl ),
inference(split_clause,[status(thm)],[f2892,f2916,f614]) ).
fof(f2923,plain,
( ~ sQ59_spl
| ~ sQ277_spl
| ~ segmentP(sK49_skl,app(sK50_skl,sK49_skl))
| ~ ssList(app(sK50_skl,sK49_skl)) ),
inference(resolution,[status(thm)],[f2881,f968]) ).
fof(f2924,plain,
! [X0,X1] :
( ~ sQ277_spl
| segmentP(app(app(X0,app(sK50_skl,sK49_skl)),X1),sK50_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK50_skl)
| ~ ssList(app(sK50_skl,sK49_skl)) ),
inference(resolution,[status(thm)],[f2881,f321]) ).
fof(f2926,plain,
( ~ sQ277_spl
| app(app(sK7_skl(sK50_skl,app(sK50_skl,sK49_skl)),sK50_skl),sK8_skl(sK50_skl,app(sK50_skl,sK49_skl))) = app(sK50_skl,sK49_skl)
| ~ ssList(sK50_skl)
| ~ ssList(app(sK50_skl,sK49_skl)) ),
inference(resolution,[status(thm)],[f2881,f136]) ).
fof(f2927,definition,
( sQ280_spl
<=> ssList(app(sK50_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ280_spl])],[split_symbol_definition]) ).
fof(f2929,plain,
( sQ280_spl
| ~ ssList(app(sK50_skl,sK49_skl)) ),
inference(component_clause,[status(thm)],[f2927]) ).
fof(f2930,definition,
( sQ281_spl
<=> segmentP(sK49_skl,app(sK50_skl,sK49_skl)) ),
introduced(definition,[new_symbols(definition,[sQ281_spl])],[split_symbol_definition]) ).
fof(f2933,plain,
( ~ sQ59_spl
| ~ sQ277_spl
| ~ sQ281_spl
| ~ sQ280_spl ),
inference(split_clause,[status(thm)],[f2923,f2927,f2930,f2880,f967]) ).
fof(f2934,definition,
! [X0,X1] :
( sQ282_spl
<=> ( segmentP(app(app(X0,app(sK50_skl,sK49_skl)),X1),sK50_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ282_spl])],[split_symbol_definition]) ).
fof(f2937,plain,
( ~ sQ277_spl
| sQ282_spl
| ~ sQ17_spl
| ~ sQ280_spl ),
inference(split_clause,[status(thm)],[f2924,f2927,f614,f2934,f2880]) ).
fof(f2945,definition,
( sQ285_spl
<=> app(app(sK7_skl(sK50_skl,app(sK50_skl,sK49_skl)),sK50_skl),sK8_skl(sK50_skl,app(sK50_skl,sK49_skl))) = app(sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ285_spl])],[split_symbol_definition]) ).
fof(f2948,plain,
( ~ sQ277_spl
| sQ285_spl
| ~ sQ17_spl
| ~ sQ280_spl ),
inference(split_clause,[status(thm)],[f2926,f2927,f614,f2945,f2880]) ).
fof(f2949,plain,
( sQ280_spl
| ~ ssList(sK50_skl) ),
inference(resolution,[status(thm)],[f2929,f2843]) ).
fof(f2950,plain,
( sQ280_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2949,f614,f2927]) ).
fof(f2986,plain,
( ~ sQ47_spl
| ~ ssList(sK49_skl)
| ~ ssList(sK50_skl)
| segmentP(app(sK49_skl,sK50_skl),sK49_skl) ),
inference(resolution,[status(thm)],[f856,f2846]) ).
fof(f2987,plain,
( ~ sQ47_spl
| ~ ssList(sK49_skl)
| ~ ssList(sK49_skl)
| segmentP(app(sK49_skl,sK49_skl),sK49_skl) ),
inference(resolution,[status(thm)],[f856,f2843]) ).
fof(f2989,plain,
( ~ sQ66_spl
| ~ sQ47_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)],[f1039,f856]) ).
fof(f2990,plain,
( ~ sQ18_spl
| ~ sQ47_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)],[f618,f856]) ).
fof(f2991,plain,
( ~ sQ47_spl
| ~ ssList(nil)
| segmentP(app(sK49_skl,nil),sK49_skl)
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f999,f856]) ).
fof(f2992,definition,
( sQ289_spl
<=> segmentP(app(sK49_skl,sK50_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ289_spl])],[split_symbol_definition]) ).
fof(f2995,plain,
( ~ sQ47_spl
| ~ sQ13_spl
| ~ sQ17_spl
| sQ289_spl ),
inference(split_clause,[status(thm)],[f2986,f2992,f614,f598,f847]) ).
fof(f2996,definition,
( sQ290_spl
<=> segmentP(app(sK49_skl,sK49_skl),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ290_spl])],[split_symbol_definition]) ).
fof(f2999,plain,
( ~ sQ47_spl
| ~ sQ13_spl
| sQ290_spl ),
inference(split_clause,[status(thm)],[f2987,f2996,f598,f847]) ).
fof(f3001,definition,
( sQ291_spl
<=> segmentP(app(sK49_skl,sK5_skl(sK49_skl,sK49_skl)),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ291_spl])],[split_symbol_definition]) ).
fof(f3004,plain,
( ~ sQ66_spl
| ~ sQ47_spl
| ~ sQ213_spl
| sQ291_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2989,f598,f3001,f2118,f847,f1038]) ).
fof(f3005,definition,
( sQ292_spl
<=> segmentP(app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ292_spl])],[split_symbol_definition]) ).
fof(f3006,plain,
( ~ sQ292_spl
| segmentP(app(sK49_skl,sK5_skl(sK49_skl,sK50_skl)),sK49_skl) ),
inference(component_clause,[status(thm)],[f3005]) ).
fof(f3008,plain,
( ~ sQ18_spl
| ~ sQ47_spl
| ~ sQ74_spl
| sQ292_spl
| ~ sQ17_spl ),
inference(split_clause,[status(thm)],[f2990,f614,f3005,f1087,f847,f617]) ).
fof(f3009,definition,
( sQ293_spl
<=> segmentP(app(sK49_skl,nil),sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ293_spl])],[split_symbol_definition]) ).
fof(f3012,plain,
( ~ sQ47_spl
| ~ sQ12_spl
| sQ293_spl
| ~ sQ13_spl ),
inference(split_clause,[status(thm)],[f2991,f598,f3009,f595,f847]) ).
fof(f3016,plain,
( ~ sQ292_spl
| ~ sQ18_spl
| segmentP(sK50_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f618,f3006]) ).
fof(f3017,plain,
( ~ sQ292_spl
| ~ sQ18_spl
| sQ79_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3016,f1116]) ).
fof(f3018,plain,
( ~ sQ292_spl
| ~ sQ18_spl
| sQ79_spl ),
inference(contradiction_clause,[status(thm)],[f3017]) ).
fof(f3019,plain,
$false,
inference(sat_refutation,[status(thm)],[f446,f450,f457,f461,f517,f533,f560,f586,f611,f620,f627,f629,f632,f639,f672,f676,f678,f694,f698,f702,f710,f722,f747,f787,f791,f795,f799,f807,f813,f825,f834,f842,f846,f850,f854,f862,f868,f880,f897,f906,f910,f934,f949,f952,f958,f970,f976,f980,f1015,f1019,f1023,f1027,f1035,f1041,f1048,f1050,f1058,f1062,f1066,f1070,f1078,f1081,f1093,f1097,f1101,f1105,f1107,f1134,f1141,f1150,f1158,f1169,f1173,f1177,f1193,f1198,f1202,f1207,f1209,f1229,f1243,f1245,f1289,f1293,f1300,f1304,f1308,f1310,f1344,f1348,f1352,f1356,f1387,f1389,f1422,f1443,f1485,f1489,f1493,f1497,f1502,f1504,f1519,f1527,f1531,f1535,f1539,f1543,f1547,f1575,f1583,f1587,f1591,f1595,f1599,f1603,f1638,f1643,f1663,f1667,f1671,f1675,f1679,f1683,f1688,f1690,f1727,f1747,f1751,f1755,f1760,f1764,f1766,f1846,f1859,f1863,f1867,f1872,f1876,f1878,f1916,f1921,f1954,f1958,f1962,f1967,f1971,f1973,f1975,f2022,f2026,f2042,f2046,f2050,f2054,f2058,f2062,f2067,f2069,f2121,f2125,f2129,f2134,f2138,f2140,f2158,f2164,f2207,f2272,f2276,f2280,f2284,f2288,f2292,f2297,f2299,f2346,f2350,f2365,f2373,f2377,f2381,f2481,f2490,f2494,f2496,f2521,f2526,f2548,f2550,f2559,f2563,f2565,f2573,f2574,f2583,f2587,f2598,f2606,f2613,f2621,f2664,f2668,f2669,f2670,f2671,f2672,f2704,f2708,f2736,f2741,f2756,f2763,f2777,f2784,f2883,f2887,f2915,f2919,f2933,f2937,f2948,f2950,f2995,f2999,f3004,f3008,f3012,f3018]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC057+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n026.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 07:54:51 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 3.92/0.97 % Refutation found
% 3.92/0.97 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.92/0.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.43/1.02 % Elapsed time: 0.643195 seconds
% 0.43/1.02 % CPU time: 4.621451 seconds
% 0.43/1.02 % Total memory used: 148.935 MB
% 0.43/1.02 % Net memory used: 145.288 MB
%------------------------------------------------------------------------------