%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC052+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 : n007.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 02:39:45 PM UTC 2026
% Result : Theorem 9.40s 1.88s
% Output : CNFRefutation 9.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 181
% Syntax : Number of formulae : 713 ( 22 unt; 158 def)
% Number of atoms : 2625 ( 238 equ)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 3535 (1623 ~;1594 |; 99 &)
% ( 170 <=>; 49 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 166 ( 164 usr; 158 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 421 ( 390 !; 31 ?)
% 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(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(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(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(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(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] :
( ( ( ? [Z] :
( segmentP(U,Z)
& segmentP(V,Z)
& neq(Z,nil)
& ssList(Z) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( neq(X,nil)
& ! [Y] :
( ~ frontsegP(W,Y)
| ~ frontsegP(X,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) ) )
| ( nil = X
& nil != W )
| 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] :
( ( ( ? [Z] :
( segmentP(U,Z)
& segmentP(V,Z)
& neq(Z,nil)
& ssList(Z) )
| ~ neq(V,nil) )
& ( nil = U
| nil != V ) )
| ( neq(X,nil)
& ! [Y] :
( ~ frontsegP(W,Y)
| ~ frontsegP(X,Y)
| ~ neq(Y,nil)
| ~ ssList(Y) ) )
| ( nil = X
& nil != W )
| 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(f119,plain,
! [U] :
( ! [V] :
( ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f120,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ? [W] :
( app(V,W) = U
& ssList(W) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ( app(V,sK5_skl(V,U)) = U
& ssList(sK5_skl(V,U)) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( ssList(sK5_skl(X1,X0))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( app(X1,sK5_skl(X1,X0)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f124,plain,
! [X0,X1,X2] :
( app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f125,plain,
! [U] :
( ! [V] :
( ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f126,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ? [W] :
( app(W,V) = U
& ssList(W) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ( app(sK6_skl(V,U),V) = U
& ssList(sK6_skl(V,U)) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126]) ).
fof(f129,plain,
! [X0,X1] :
( app(sK6_skl(X1,X0),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f131,plain,
! [U] :
( ! [V] :
( ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f132,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ( app(app(sK7_skl(V,U),V),sK8_skl(V,U)) = U
& ssList(sK8_skl(V,U))
& ssList(sK7_skl(V,U)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132]) ).
fof(f136,plain,
! [X0,X1] :
( app(app(sK7_skl(X1,X0),X1),sK8_skl(X1,X0)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f217,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f15]) ).
fof(f218,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f217]) ).
fof(f220,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f218]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(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(f294,plain,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f295,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f294]) ).
fof(f296,plain,
! [U] :
( ( frontsegP(nil,U)
<=> nil = U )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f46]) ).
fof(f297,plain,
! [U] :
( ( ( nil != U
| frontsegP(nil,U) )
& ( nil = U
| ~ frontsegP(nil,U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f296]) ).
fof(f298,plain,
! [X0] :
( nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f297]) ).
fof(f308,plain,
! [U] :
( rearsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f51]) ).
fof(f309,plain,
! [X0] :
( rearsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f314,plain,
! [U] :
( ! [V] :
( ! [W] :
( segmentP(U,W)
| ~ segmentP(V,W)
| ~ segmentP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f53]) ).
fof(f315,plain,
! [X0,X1,X2] :
( segmentP(X0,X2)
| ~ segmentP(X1,X2)
| ~ segmentP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f314]) ).
fof(f316,plain,
! [U] :
( ! [V] :
( U = V
| ~ segmentP(V,U)
| ~ segmentP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f54]) ).
fof(f317,plain,
! [X0,X1] :
( X0 = X1
| ~ segmentP(X1,X0)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f316]) ).
fof(f318,plain,
! [U] :
( segmentP(U,U)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f55]) ).
fof(f319,plain,
! [X0] :
( segmentP(X0,X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f318]) ).
fof(f320,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( segmentP(app(app(W,U),X),V)
| ~ segmentP(U,V)
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f56]) ).
fof(f321,plain,
! [X0,X1,X2,X3] :
( segmentP(app(app(X2,X0),X3),X1)
| ~ segmentP(X0,X1)
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f320]) ).
fof(f322,plain,
! [U] :
( segmentP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f57]) ).
fof(f323,plain,
! [X0] :
( segmentP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f322]) ).
fof(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] :
( ( ( ! [Z] :
( ~ segmentP(U,Z)
| ~ segmentP(V,Z)
| ~ neq(Z,nil)
| ~ ssList(Z) )
& neq(V,nil) )
| ( nil != U
& nil = V ) )
& ( ~ neq(X,nil)
| ? [Y] :
( frontsegP(W,Y)
& frontsegP(X,Y)
& neq(Y,nil)
& ssList(Y) ) )
& ( nil != X
| nil = W )
& 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,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( ! [Z] :
( ~ segmentP(U,Z)
| ~ segmentP(V,Z)
| ~ neq(Z,nil)
| ~ ssList(Z) )
& neq(V,nil) )
| sP0_prd(V,U) )
& ( ~ neq(X,nil)
| ? [Y] :
( frontsegP(W,Y)
& frontsegP(X,Y)
& neq(Y,nil)
& ssList(Y) ) )
& ( nil != X
| nil = W )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
? [U] :
( ? [V] :
( ? [W] :
( ( ( ! [Z] :
( ~ segmentP(U,Z)
| ~ segmentP(V,Z)
| ~ neq(Z,nil)
| ~ ssList(Z) )
& neq(V,nil) )
| sP0_prd(V,U) )
& ? [X] :
( ( ~ neq(X,nil)
| ? [Y] :
( frontsegP(W,Y)
& frontsegP(X,Y)
& neq(Y,nil)
& ssList(Y) ) )
& ( nil != X
| nil = W )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(miniscoping,[status(thm)],[f417]) ).
fof(f419,plain,
( ( ( ! [Z] :
( ~ segmentP(sK47_skl,Z)
| ~ segmentP(sK48_skl,Z)
| ~ neq(Z,nil)
| ~ ssList(Z) )
& neq(sK48_skl,nil) )
| sP0_prd(sK48_skl,sK47_skl) )
& ( ~ neq(sK50_skl,nil)
| ( frontsegP(sK49_skl,sK51_skl)
& frontsegP(sK50_skl,sK51_skl)
& neq(sK51_skl,nil)
& ssList(sK51_skl) ) )
& ( nil != sK50_skl
| nil = sK49_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,sK51_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl)],[f418]) ).
fof(f420,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f421,plain,
ssList(sK48_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,
( nil != sK50_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f427,plain,
( ~ neq(sK50_skl,nil)
| ssList(sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f428,plain,
( ~ neq(sK50_skl,nil)
| neq(sK51_skl,nil) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f429,plain,
( ~ neq(sK50_skl,nil)
| frontsegP(sK50_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f430,plain,
( ~ neq(sK50_skl,nil)
| frontsegP(sK49_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f431,plain,
( neq(sK48_skl,nil)
| sP0_prd(sK48_skl,sK47_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f432,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(f433,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(f434,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)],[f433]) ).
fof(f435,plain,
! [X0,X1] :
( nil = X0
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f436,plain,
! [X0,X1] :
( nil != X1
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f438,definition,
( sQ0_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f439,plain,
( ~ sQ0_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f440,plain,
( sQ0_spl
| nil != sK49_skl ),
inference(component_clause,[status(thm)],[f438]) ).
fof(f441,definition,
( sQ1_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f443,plain,
( sQ1_spl
| nil != sK50_skl ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f426,f438,f441]) ).
fof(f445,definition,
( sQ2_spl
<=> ssList(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f446,plain,
( ~ sQ2_spl
| ssList(sK51_skl) ),
inference(component_clause,[status(thm)],[f445]) ).
fof(f448,definition,
( sQ3_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( sQ3_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f451,plain,
( ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f427,f445,f448]) ).
fof(f452,definition,
( sQ4_spl
<=> neq(sK51_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( ~ sQ4_spl
| neq(sK51_skl,nil) ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,plain,
( ~ sQ3_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f428,f452,f448]) ).
fof(f456,definition,
( sQ5_spl
<=> frontsegP(sK50_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( ~ sQ5_spl
| frontsegP(sK50_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f456]) ).
fof(f459,plain,
( ~ sQ3_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f429,f456,f448]) ).
fof(f460,definition,
( sQ6_spl
<=> frontsegP(sK49_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f461,plain,
( ~ sQ6_spl
| frontsegP(sK49_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f460]) ).
fof(f463,plain,
( ~ sQ3_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f430,f460,f448]) ).
fof(f464,definition,
( sQ7_spl
<=> sP0_prd(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f465,plain,
( ~ sQ7_spl
| sP0_prd(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f464]) ).
fof(f467,definition,
( sQ8_spl
<=> neq(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f468,plain,
( ~ sQ8_spl
| neq(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f467]) ).
fof(f470,plain,
( sQ8_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f431,f464,f467]) ).
fof(f471,definition,
! [X0] :
( sQ9_spl
<=> ( ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f472,plain,
! [X0] :
( ~ sQ9_spl
| ~ segmentP(sK47_skl,X0)
| ~ segmentP(sK48_skl,X0)
| ~ neq(X0,nil)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f471]) ).
fof(f474,plain,
( sQ9_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f432,f464,f471]) ).
fof(f479,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f481,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(f493,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f479,f245]) ).
fof(f509,plain,
! [X0] : ~ sP0_prd(X0,nil),
inference(destructive_equality_resolution,[status(thm)],[f436]) ).
fof(f511,plain,
( sQ3_spl
| ~ neq(sK48_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f424,f450]) ).
fof(f514,plain,
! [X0] :
( ~ sQ0_spl
| ~ sP0_prd(X0,sK47_skl) ),
inference(backward_demodulation,[status(thm)],[f566,f509]) ).
fof(f566,plain,
( ~ sQ0_spl
| nil = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f425,f439]) ).
fof(f568,plain,
( ~ sQ7_spl
| ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f465,f514]) ).
fof(f576,plain,
( ~ sQ7_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f568]) ).
fof(f577,plain,
( sQ1_spl
| nil != sK48_skl ),
inference(forward_demodulation,[status(thm)],[f424,f443]) ).
fof(f578,plain,
( sQ3_spl
| ~ sQ8_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f511,f468]) ).
fof(f579,plain,
( sQ3_spl
| ~ sQ8_spl ),
inference(contradiction_clause,[status(thm)],[f578]) ).
fof(f580,plain,
( ~ sQ5_spl
| frontsegP(sK48_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f457]) ).
fof(f581,plain,
( ~ sQ6_spl
| frontsegP(sK47_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f461]) ).
fof(f583,plain,
( sQ0_spl
| nil != sK47_skl ),
inference(forward_demodulation,[status(thm)],[f425,f440]) ).
fof(f585,plain,
! [X0] :
( X0 = sK0_skl
| neq(X0,sK0_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f103,f101]) ).
fof(f587,plain,
! [X0] :
( X0 = sK1_skl
| neq(X0,sK1_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f104,f101]) ).
fof(f589,plain,
( ~ sQ7_spl
| nil = sK48_skl ),
inference(resolution,[status(thm)],[f435,f465]) ).
fof(f591,plain,
( ~ sQ7_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f589,f577]) ).
fof(f592,plain,
( ~ sQ7_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f591]) ).
fof(f593,definition,
( sQ10_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f812,definition,
( sQ16_spl
<=> sK47_skl = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f815,definition,
! [X0] :
( sQ17_spl
<=> sK47_skl = X0 ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f816,plain,
! [X0] :
( ~ sQ17_spl
| sK47_skl = X0 ),
inference(component_clause,[status(thm)],[f815]) ).
fof(f828,definition,
( sQ19_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f830,plain,
( sQ19_spl
| ~ ssList(sK47_skl) ),
inference(component_clause,[status(thm)],[f828]) ).
fof(f831,definition,
( sQ20_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ20_spl])],[split_symbol_definition]) ).
fof(f833,plain,
( sQ20_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f831]) ).
fof(f835,plain,
( sQ20_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f833,f421]) ).
fof(f836,plain,
sQ20_spl,
inference(contradiction_clause,[status(thm)],[f835]) ).
fof(f844,plain,
( sQ19_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f830,f420]) ).
fof(f845,plain,
sQ19_spl,
inference(contradiction_clause,[status(thm)],[f844]) ).
fof(f846,plain,
( ~ sQ9_spl
| ~ ssList(sK48_skl)
| ~ segmentP(sK47_skl,sK48_skl)
| ~ neq(sK48_skl,nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f472,f319]) ).
fof(f847,definition,
( sQ22_spl
<=> segmentP(sK47_skl,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f849,plain,
( sQ22_spl
| ~ segmentP(sK47_skl,sK48_skl) ),
inference(component_clause,[status(thm)],[f847]) ).
fof(f850,plain,
( ~ sQ9_spl
| ~ sQ22_spl
| ~ sQ8_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f846,f831,f467,f847,f471]) ).
fof(f851,plain,
( ~ sQ9_spl
| ~ segmentP(sK47_skl,nil)
| ~ neq(nil,nil)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f323,f472]) ).
fof(f852,definition,
( sQ23_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f854,plain,
( sQ23_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f852]) ).
fof(f855,definition,
( sQ24_spl
<=> neq(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f857,plain,
( sQ24_spl
| ~ neq(nil,nil) ),
inference(component_clause,[status(thm)],[f855]) ).
fof(f858,definition,
( sQ25_spl
<=> segmentP(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f859,plain,
( ~ sQ25_spl
| segmentP(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f858]) ).
fof(f860,plain,
( sQ25_spl
| ~ segmentP(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f858]) ).
fof(f861,plain,
( ~ sQ9_spl
| ~ sQ25_spl
| ~ sQ24_spl
| ~ sQ23_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f851,f831,f852,f855,f858,f471]) ).
fof(f862,plain,
( sQ25_spl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f860,f323]) ).
fof(f863,plain,
( sQ25_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f862,f828,f858]) ).
fof(f864,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f854,f223]) ).
fof(f865,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f864]) ).
fof(f868,plain,
( ~ sQ5_spl
| sK51_skl = sK48_skl
| ~ frontsegP(sK51_skl,sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f284,f580]) ).
fof(f870,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f284,f295]) ).
fof(f872,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(f873,definition,
( sQ26_spl
<=> frontsegP(sK51_skl,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ26_spl])],[split_symbol_definition]) ).
fof(f875,plain,
( sQ26_spl
| ~ frontsegP(sK51_skl,sK48_skl) ),
inference(component_clause,[status(thm)],[f873]) ).
fof(f876,definition,
( sQ27_spl
<=> sK51_skl = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ27_spl])],[split_symbol_definition]) ).
fof(f877,plain,
( ~ sQ27_spl
| sK51_skl = sK48_skl ),
inference(component_clause,[status(thm)],[f876]) ).
fof(f879,plain,
( ~ sQ5_spl
| sQ27_spl
| ~ sQ26_spl
| ~ sQ20_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f868,f445,f831,f873,f876,f456]) ).
fof(f880,definition,
( sQ28_spl
<=> frontsegP(sK51_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f882,plain,
( sQ28_spl
| ~ frontsegP(sK51_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f880]) ).
fof(f883,definition,
( sQ29_spl
<=> sK51_skl = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f884,plain,
( ~ sQ29_spl
| sK51_skl = sK47_skl ),
inference(component_clause,[status(thm)],[f883]) ).
fof(f887,definition,
! [X0] :
( sQ30_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f890,plain,
( sQ30_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f870,f852,f887]) ).
fof(f891,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)],[f872]) ).
fof(f896,plain,
! [X0] :
( sQ28_spl
| ~ frontsegP(X0,sK47_skl)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f882,f282]) ).
fof(f897,definition,
! [X0] :
( sQ31_spl
<=> ( ~ frontsegP(X0,sK47_skl)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f898,plain,
! [X0] :
( ~ sQ31_spl
| ~ frontsegP(X0,sK47_skl)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f897]) ).
fof(f900,plain,
( sQ28_spl
| ~ sQ19_spl
| sQ31_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f896,f445,f897,f828,f880]) ).
fof(f902,plain,
( ~ sQ5_spl
| ~ sQ29_spl
| frontsegP(sK48_skl,sK47_skl) ),
inference(backward_demodulation,[status(thm)],[f884,f580]) ).
fof(f903,plain,
( ~ sQ6_spl
| ~ sQ29_spl
| frontsegP(sK47_skl,sK47_skl) ),
inference(backward_demodulation,[status(thm)],[f884,f581]) ).
fof(f907,plain,
( ~ sQ5_spl
| ~ sQ29_spl
| sK47_skl = sK48_skl
| ~ frontsegP(sK47_skl,sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f902,f284]) ).
fof(f908,definition,
( sQ32_spl
<=> frontsegP(sK47_skl,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f909,plain,
( ~ sQ32_spl
| frontsegP(sK47_skl,sK48_skl) ),
inference(component_clause,[status(thm)],[f908]) ).
fof(f910,plain,
( sQ32_spl
| ~ frontsegP(sK47_skl,sK48_skl) ),
inference(component_clause,[status(thm)],[f908]) ).
fof(f911,definition,
( sQ33_spl
<=> sK47_skl = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ33_spl])],[split_symbol_definition]) ).
fof(f912,plain,
( ~ sQ33_spl
| sK47_skl = sK48_skl ),
inference(component_clause,[status(thm)],[f911]) ).
fof(f913,plain,
( sQ33_spl
| sK47_skl != sK48_skl ),
inference(component_clause,[status(thm)],[f911]) ).
fof(f914,plain,
( ~ sQ5_spl
| ~ sQ29_spl
| sQ33_spl
| ~ sQ32_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f907,f828,f831,f908,f911,f883,f456]) ).
fof(f915,plain,
( sQ22_spl
| ~ sQ33_spl
| ~ segmentP(sK47_skl,sK47_skl) ),
inference(backward_demodulation,[status(thm)],[f912,f849]) ).
fof(f926,plain,
! [X0] :
( ~ ssList(X0)
| app(nil,sK5_skl(nil,X0)) = X0
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f123,f295]) ).
fof(f927,plain,
! [X0] :
( ~ ssList(X0)
| app(X0,sK5_skl(X0,X0)) = X0
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f123,f286]) ).
fof(f931,definition,
! [X0] :
( sQ34_spl
<=> ( ~ ssList(X0)
| app(nil,sK5_skl(nil,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f934,plain,
( ~ sQ23_spl
| sQ34_spl ),
inference(split_clause,[status(thm)],[f926,f931,f852]) ).
fof(f935,plain,
! [X0] :
( app(X0,sK5_skl(X0,X0)) = X0
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f927]) ).
fof(f944,definition,
( sQ35_spl
<=> app(sK51_skl,sK5_skl(sK51_skl,sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ35_spl])],[split_symbol_definition]) ).
fof(f945,plain,
( ~ sQ35_spl
| app(sK51_skl,sK5_skl(sK51_skl,sK47_skl)) = sK47_skl ),
inference(component_clause,[status(thm)],[f944]) ).
fof(f952,plain,
! [X0] :
( sQ32_spl
| ~ frontsegP(X0,sK48_skl)
| ~ frontsegP(sK47_skl,X0)
| ~ ssList(sK48_skl)
| ~ ssList(X0)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f910,f282]) ).
fof(f953,definition,
! [X0] :
( sQ36_spl
<=> ( ~ frontsegP(X0,sK48_skl)
| ~ frontsegP(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f954,plain,
! [X0] :
( ~ sQ36_spl
| ~ frontsegP(X0,sK48_skl)
| ~ frontsegP(sK47_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f953]) ).
fof(f956,plain,
( sQ32_spl
| ~ sQ20_spl
| sQ36_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f952,f828,f953,f831,f908]) ).
fof(f960,plain,
( ~ sQ5_spl
| ~ sQ27_spl
| frontsegP(sK48_skl,sK48_skl) ),
inference(backward_demodulation,[status(thm)],[f877,f580]) ).
fof(f962,plain,
( sQ26_spl
| ~ sQ27_spl
| ~ frontsegP(sK48_skl,sK48_skl) ),
inference(backward_demodulation,[status(thm)],[f877,f875]) ).
fof(f970,plain,
( sQ33_spl
| ~ sQ17_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f913,f816]) ).
fof(f971,plain,
( sQ33_spl
| ~ sQ17_spl ),
inference(contradiction_clause,[status(thm)],[f970]) ).
fof(f972,plain,
( sQ26_spl
| ~ sQ27_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f962,f960]) ).
fof(f973,plain,
( sQ26_spl
| ~ sQ27_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f972]) ).
fof(f976,plain,
( sQ28_spl
| ~ sQ29_spl
| ~ frontsegP(sK47_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f884,f882]) ).
fof(f977,plain,
( sQ28_spl
| ~ sQ29_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f976,f903]) ).
fof(f978,plain,
( sQ28_spl
| ~ sQ29_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f977]) ).
fof(f986,plain,
( ~ sQ5_spl
| app(sK51_skl,sK5_skl(sK51_skl,sK48_skl)) = sK48_skl
| ~ ssList(sK51_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f580,f123]) ).
fof(f988,definition,
( sQ37_spl
<=> app(sK51_skl,sK5_skl(sK51_skl,sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ37_spl])],[split_symbol_definition]) ).
fof(f989,plain,
( ~ sQ37_spl
| app(sK51_skl,sK5_skl(sK51_skl,sK48_skl)) = sK48_skl ),
inference(component_clause,[status(thm)],[f988]) ).
fof(f991,plain,
( ~ sQ5_spl
| sQ37_spl
| ~ sQ2_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f986,f831,f445,f988,f456]) ).
fof(f993,plain,
( ~ sQ6_spl
| app(sK51_skl,sK5_skl(sK51_skl,sK47_skl)) = sK47_skl
| ~ ssList(sK51_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f581,f123]) ).
fof(f995,plain,
( ~ sQ6_spl
| sQ35_spl
| ~ sQ2_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f993,f828,f445,f944,f460]) ).
fof(f997,plain,
! [X0] :
( sQ26_spl
| ~ frontsegP(X0,sK48_skl)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(sK48_skl)
| ~ ssList(X0)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f875,f282]) ).
fof(f998,definition,
! [X0] :
( sQ38_spl
<=> ( ~ frontsegP(X0,sK48_skl)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ38_spl])],[split_symbol_definition]) ).
fof(f999,plain,
! [X0] :
( ~ sQ38_spl
| ~ frontsegP(X0,sK48_skl)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f998]) ).
fof(f1001,plain,
( sQ26_spl
| ~ sQ20_spl
| sQ38_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f997,f445,f998,f831,f873]) ).
fof(f1004,plain,
! [X0] :
( app(sK6_skl(nil,X0),nil) = X0
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f309,f129]) ).
fof(f1005,definition,
! [X0] :
( sQ39_spl
<=> ( app(sK6_skl(nil,X0),nil) = X0
| ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f1008,plain,
( ~ sQ23_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f1004,f1005,f852]) ).
fof(f1013,plain,
( ~ sQ2_spl
| app(sK51_skl,nil) = sK51_skl ),
inference(resolution,[status(thm)],[f389,f446]) ).
fof(f1014,plain,
app(sK48_skl,nil) = sK48_skl,
inference(resolution,[status(thm)],[f389,f421]) ).
fof(f1016,plain,
app(nil,nil) = nil,
inference(resolution,[status(thm)],[f389,f223]) ).
fof(f1020,plain,
app(sK47_skl,nil) = sK47_skl,
inference(resolution,[status(thm)],[f389,f420]) ).
fof(f1021,plain,
! [X0] :
( ~ sQ2_spl
| frontsegP(sK51_skl,X0)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1013,f288]) ).
fof(f1022,plain,
! [X0] :
( ~ sQ2_spl
| ~ ssList(X0)
| ~ ssList(sK51_skl)
| segmentP(app(app(sK51_skl,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK51_skl,X0)) ),
inference(paramodulation,[status(thm)],[f1013,f481]) ).
fof(f1023,definition,
! [X0] :
( sQ40_spl
<=> ( frontsegP(sK51_skl,X0)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ40_spl])],[split_symbol_definition]) ).
fof(f1026,plain,
( ~ sQ23_spl
| sQ40_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1021,f445,f1023,f852]) ).
fof(f1027,definition,
! [X0] :
( sQ41_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK51_skl,nil),X0),nil)
| ~ ssList(app(sK51_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ41_spl])],[split_symbol_definition]) ).
fof(f1030,plain,
( ~ sQ2_spl
| ~ sQ23_spl
| sQ41_spl ),
inference(split_clause,[status(thm)],[f1022,f1027,f852,f445]) ).
fof(f1032,plain,
! [X0] :
( frontsegP(sK48_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f1014,f288]) ).
fof(f1033,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK48_skl)
| segmentP(app(app(sK48_skl,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f1014,f481]) ).
fof(f1034,definition,
! [X0] :
( sQ42_spl
<=> ( frontsegP(sK48_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f1037,plain,
( ~ sQ23_spl
| sQ42_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1032,f831,f1034,f852]) ).
fof(f1038,definition,
! [X0] :
( sQ43_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK48_skl,nil),X0),nil)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ43_spl])],[split_symbol_definition]) ).
fof(f1041,plain,
( ~ sQ20_spl
| ~ sQ23_spl
| sQ43_spl ),
inference(split_clause,[status(thm)],[f1033,f1038,f852,f831]) ).
fof(f1043,plain,
! [X0] :
( frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1016,f288]) ).
fof(f1044,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(nil,X0)) ),
inference(paramodulation,[status(thm)],[f1016,f481]) ).
fof(f1045,definition,
! [X0] :
( sQ44_spl
<=> ( frontsegP(nil,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f1048,plain,
( sQ44_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1043,f852,f1045]) ).
fof(f1049,definition,
! [X0] :
( sQ45_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,nil),X0),nil)
| ~ ssList(app(nil,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f1052,plain,
( ~ sQ23_spl
| sQ45_spl ),
inference(split_clause,[status(thm)],[f1044,f1049,f852]) ).
fof(f1054,plain,
! [X0] :
( frontsegP(sK47_skl,X0)
| ~ frontsegP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f1020,f288]) ).
fof(f1055,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK47_skl)
| segmentP(app(app(sK47_skl,nil),X0),nil)
| ~ ssList(nil)
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f1020,f481]) ).
fof(f1056,definition,
! [X0] :
( sQ46_spl
<=> ( frontsegP(sK47_skl,X0)
| ~ frontsegP(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f1059,plain,
( ~ sQ23_spl
| sQ46_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1054,f828,f1056,f852]) ).
fof(f1060,definition,
! [X0] :
( sQ47_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK47_skl,nil),X0),nil)
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ47_spl])],[split_symbol_definition]) ).
fof(f1063,plain,
( ~ sQ19_spl
| ~ sQ23_spl
| sQ47_spl ),
inference(split_clause,[status(thm)],[f1055,f1060,f852,f828]) ).
fof(f1067,plain,
( ~ sQ25_spl
| app(app(sK7_skl(nil,sK47_skl),nil),sK8_skl(nil,sK47_skl)) = sK47_skl
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f136,f859]) ).
fof(f1068,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(f1070,definition,
( sQ48_spl
<=> app(app(sK7_skl(nil,sK47_skl),nil),sK8_skl(nil,sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ48_spl])],[split_symbol_definition]) ).
fof(f1073,plain,
( ~ sQ25_spl
| sQ48_spl
| ~ sQ23_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1067,f828,f852,f1070,f858]) ).
fof(f1074,definition,
! [X0] :
( sQ49_spl
<=> ( ~ ssList(X0)
| app(app(sK7_skl(nil,X0),nil),sK8_skl(nil,X0)) = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ49_spl])],[split_symbol_definition]) ).
fof(f1077,plain,
( ~ sQ23_spl
| sQ49_spl ),
inference(split_clause,[status(thm)],[f1068,f1074,f852]) ).
fof(f1080,plain,
! [X0] :
( ~ sQ35_spl
| frontsegP(sK47_skl,X0)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(sK5_skl(sK51_skl,sK47_skl))
| ~ ssList(X0)
| ~ ssList(sK51_skl) ),
inference(paramodulation,[status(thm)],[f945,f288]) ).
fof(f1081,plain,
! [X0] :
( ~ sQ35_spl
| ~ ssList(X0)
| ~ ssList(sK51_skl)
| segmentP(app(app(sK51_skl,sK5_skl(sK51_skl,sK47_skl)),X0),sK5_skl(sK51_skl,sK47_skl))
| ~ ssList(sK5_skl(sK51_skl,sK47_skl))
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f945,f481]) ).
fof(f1082,definition,
! [X0] :
( sQ50_spl
<=> ( frontsegP(sK47_skl,X0)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ50_spl])],[split_symbol_definition]) ).
fof(f1083,plain,
! [X0] :
( ~ sQ50_spl
| frontsegP(sK47_skl,X0)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1082]) ).
fof(f1085,definition,
( sQ51_spl
<=> ssList(sK5_skl(sK51_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ51_spl])],[split_symbol_definition]) ).
fof(f1086,plain,
( ~ sQ51_spl
| ssList(sK5_skl(sK51_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1085]) ).
fof(f1087,plain,
( sQ51_spl
| ~ ssList(sK5_skl(sK51_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1085]) ).
fof(f1088,plain,
( ~ sQ35_spl
| ~ sQ51_spl
| sQ50_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1080,f445,f1082,f1085,f944]) ).
fof(f1089,definition,
! [X0] :
( sQ52_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK51_skl,sK5_skl(sK51_skl,sK47_skl)),X0),sK5_skl(sK51_skl,sK47_skl))
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ52_spl])],[split_symbol_definition]) ).
fof(f1090,plain,
! [X0] :
( ~ sQ52_spl
| ~ ssList(X0)
| segmentP(app(app(sK51_skl,sK5_skl(sK51_skl,sK47_skl)),X0),sK5_skl(sK51_skl,sK47_skl))
| ~ ssList(app(sK47_skl,X0)) ),
inference(component_clause,[status(thm)],[f1089]) ).
fof(f1092,plain,
( ~ sQ35_spl
| ~ sQ2_spl
| ~ sQ51_spl
| sQ52_spl ),
inference(split_clause,[status(thm)],[f1081,f1089,f1085,f445,f944]) ).
fof(f1093,plain,
( sQ51_spl
| ~ frontsegP(sK47_skl,sK51_skl)
| ~ ssList(sK51_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1087,f122]) ).
fof(f1094,definition,
( sQ53_spl
<=> frontsegP(sK47_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ53_spl])],[split_symbol_definition]) ).
fof(f1096,plain,
( sQ53_spl
| ~ frontsegP(sK47_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1094]) ).
fof(f1097,plain,
( sQ51_spl
| ~ sQ53_spl
| ~ sQ2_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1093,f828,f445,f1094,f1085]) ).
fof(f1098,plain,
! [X0] :
( ~ sQ52_spl
| ~ sQ35_spl
| ~ ssList(X0)
| segmentP(app(sK47_skl,X0),sK5_skl(sK51_skl,sK47_skl))
| ~ ssList(app(sK47_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f945,f1090]) ).
fof(f1099,plain,
( sQ53_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1096,f581]) ).
fof(f1100,plain,
( sQ53_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f1099]) ).
fof(f1102,plain,
! [X0] :
( ~ sQ37_spl
| frontsegP(sK48_skl,X0)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(sK5_skl(sK51_skl,sK48_skl))
| ~ ssList(X0)
| ~ ssList(sK51_skl) ),
inference(paramodulation,[status(thm)],[f989,f288]) ).
fof(f1103,plain,
! [X0] :
( ~ sQ37_spl
| ~ ssList(X0)
| ~ ssList(sK51_skl)
| segmentP(app(app(sK51_skl,sK5_skl(sK51_skl,sK48_skl)),X0),sK5_skl(sK51_skl,sK48_skl))
| ~ ssList(sK5_skl(sK51_skl,sK48_skl))
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f989,f481]) ).
fof(f1104,definition,
! [X0] :
( sQ54_spl
<=> ( frontsegP(sK48_skl,X0)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ54_spl])],[split_symbol_definition]) ).
fof(f1105,plain,
! [X0] :
( ~ sQ54_spl
| frontsegP(sK48_skl,X0)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1104]) ).
fof(f1107,definition,
( sQ55_spl
<=> ssList(sK5_skl(sK51_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1109,plain,
( sQ55_spl
| ~ ssList(sK5_skl(sK51_skl,sK48_skl)) ),
inference(component_clause,[status(thm)],[f1107]) ).
fof(f1110,plain,
( ~ sQ37_spl
| ~ sQ55_spl
| sQ54_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1102,f445,f1104,f1107,f988]) ).
fof(f1111,definition,
! [X0] :
( sQ56_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK51_skl,sK5_skl(sK51_skl,sK48_skl)),X0),sK5_skl(sK51_skl,sK48_skl))
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ56_spl])],[split_symbol_definition]) ).
fof(f1114,plain,
( ~ sQ37_spl
| ~ sQ2_spl
| ~ sQ55_spl
| sQ56_spl ),
inference(split_clause,[status(thm)],[f1103,f1111,f1107,f445,f988]) ).
fof(f1115,plain,
( sQ55_spl
| ~ frontsegP(sK48_skl,sK51_skl)
| ~ ssList(sK51_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1109,f122]) ).
fof(f1116,definition,
( sQ57_spl
<=> frontsegP(sK48_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ57_spl])],[split_symbol_definition]) ).
fof(f1118,plain,
( sQ57_spl
| ~ frontsegP(sK48_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1116]) ).
fof(f1119,plain,
( sQ55_spl
| ~ sQ57_spl
| ~ sQ2_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1115,f831,f445,f1116,f1107]) ).
fof(f1121,plain,
( sQ57_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1118,f580]) ).
fof(f1122,plain,
( sQ57_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f1121]) ).
fof(f1128,plain,
( sK1_skl = sK0_skl
| neq(sK1_skl,sK0_skl) ),
inference(resolution,[status(thm)],[f585,f104]) ).
fof(f1130,definition,
( sQ58_spl
<=> neq(sK1_skl,sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ58_spl])],[split_symbol_definition]) ).
fof(f1133,definition,
( sQ59_spl
<=> sK1_skl = sK0_skl ),
introduced(definition,[new_symbols(definition,[sQ59_spl])],[split_symbol_definition]) ).
fof(f1134,plain,
( ~ sQ59_spl
| sK1_skl = sK0_skl ),
inference(component_clause,[status(thm)],[f1133]) ).
fof(f1136,plain,
( sQ59_spl
| sQ58_spl ),
inference(split_clause,[status(thm)],[f1128,f1130,f1133]) ).
fof(f1142,plain,
( sK0_skl = sK1_skl
| neq(sK0_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f587,f103]) ).
fof(f1147,definition,
( sQ62_spl
<=> neq(sK0_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ62_spl])],[split_symbol_definition]) ).
fof(f1150,plain,
( sQ59_spl
| sQ62_spl ),
inference(split_clause,[status(thm)],[f1142,f1147,f1133]) ).
fof(f1151,plain,
( ~ sQ59_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1134,f105]) ).
fof(f1152,plain,
~ sQ59_spl,
inference(contradiction_clause,[status(thm)],[f1151]) ).
fof(f1155,plain,
( ~ sQ2_spl
| app(sK51_skl,sK5_skl(sK51_skl,sK51_skl)) = sK51_skl ),
inference(resolution,[status(thm)],[f935,f446]) ).
fof(f1156,plain,
app(sK48_skl,sK5_skl(sK48_skl,sK48_skl)) = sK48_skl,
inference(resolution,[status(thm)],[f935,f421]) ).
fof(f1164,plain,
app(sK47_skl,sK5_skl(sK47_skl,sK47_skl)) = sK47_skl,
inference(resolution,[status(thm)],[f935,f420]) ).
fof(f1165,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f298,f295]) ).
fof(f1167,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(f1168,plain,
( sQ10_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1165,f852,f593]) ).
fof(f1170,definition,
! [X0,X1] :
( sQ63_spl
<=> ( ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| nil = X0
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ63_spl])],[split_symbol_definition]) ).
fof(f1173,plain,
( ~ sQ23_spl
| sQ63_spl ),
inference(split_clause,[status(thm)],[f1167,f1170,f852]) ).
fof(f1180,plain,
! [X0] :
( ~ sQ2_spl
| ~ ssList(X0)
| ~ ssList(sK51_skl)
| segmentP(app(app(sK51_skl,sK5_skl(sK51_skl,sK51_skl)),X0),sK5_skl(sK51_skl,sK51_skl))
| ~ ssList(sK5_skl(sK51_skl,sK51_skl))
| ~ ssList(app(sK51_skl,X0)) ),
inference(paramodulation,[status(thm)],[f1155,f481]) ).
fof(f1181,definition,
( sQ64_spl
<=> ssList(sK5_skl(sK51_skl,sK51_skl)) ),
introduced(definition,[new_symbols(definition,[sQ64_spl])],[split_symbol_definition]) ).
fof(f1183,plain,
( sQ64_spl
| ~ ssList(sK5_skl(sK51_skl,sK51_skl)) ),
inference(component_clause,[status(thm)],[f1181]) ).
fof(f1185,definition,
! [X0] :
( sQ65_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK51_skl,sK5_skl(sK51_skl,sK51_skl)),X0),sK5_skl(sK51_skl,sK51_skl))
| ~ ssList(app(sK51_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ65_spl])],[split_symbol_definition]) ).
fof(f1188,plain,
( ~ sQ2_spl
| ~ sQ64_spl
| sQ65_spl ),
inference(split_clause,[status(thm)],[f1180,f1185,f1181,f445]) ).
fof(f1191,plain,
! [X0] :
( ~ sQ25_spl
| segmentP(X0,nil)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(nil)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f315,f859]) ).
fof(f1192,plain,
! [X0,X1] :
( ~ ssList(X1)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f315,f323]) ).
fof(f1194,definition,
! [X0] :
( sQ66_spl
<=> ( segmentP(X0,nil)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ66_spl])],[split_symbol_definition]) ).
fof(f1197,plain,
( ~ sQ25_spl
| ~ sQ23_spl
| ~ sQ19_spl
| sQ66_spl ),
inference(split_clause,[status(thm)],[f1191,f1194,f828,f852,f858]) ).
fof(f1198,definition,
! [X0,X1] :
( sQ67_spl
<=> ( ~ ssList(X1)
| segmentP(X0,nil)
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ67_spl])],[split_symbol_definition]) ).
fof(f1201,plain,
( ~ sQ23_spl
| sQ67_spl ),
inference(split_clause,[status(thm)],[f1192,f1198,f852]) ).
fof(f1203,plain,
( sQ64_spl
| ~ frontsegP(sK51_skl,sK51_skl)
| ~ ssList(sK51_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f1183,f122]) ).
fof(f1204,definition,
( sQ68_spl
<=> frontsegP(sK51_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ68_spl])],[split_symbol_definition]) ).
fof(f1205,plain,
( ~ sQ68_spl
| frontsegP(sK51_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1204]) ).
fof(f1206,plain,
( sQ68_spl
| ~ frontsegP(sK51_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1204]) ).
fof(f1207,plain,
( sQ64_spl
| ~ sQ68_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1203,f445,f1204,f1181]) ).
fof(f1209,plain,
( sQ68_spl
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f1206,f286]) ).
fof(f1211,plain,
( sQ68_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1209,f446]) ).
fof(f1212,plain,
( sQ68_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f1211]) ).
fof(f1213,plain,
( ~ sQ68_spl
| app(sK51_skl,sK5_skl(sK51_skl,sK51_skl)) = sK51_skl
| ~ ssList(sK51_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f1205,f123]) ).
fof(f1214,plain,
( ~ sQ68_spl
| sK51_skl = sK51_skl
| ~ frontsegP(sK51_skl,sK51_skl)
| ~ ssList(sK51_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f1205,f284]) ).
fof(f1215,definition,
( sQ69_spl
<=> app(sK51_skl,sK5_skl(sK51_skl,sK51_skl)) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ69_spl])],[split_symbol_definition]) ).
fof(f1218,plain,
( ~ sQ68_spl
| sQ69_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1213,f445,f1215,f1204]) ).
fof(f1219,definition,
( sQ70_spl
<=> sK51_skl = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ70_spl])],[split_symbol_definition]) ).
fof(f1222,plain,
( sQ70_spl
| ~ sQ68_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1214,f445,f1204,f1219]) ).
fof(f1227,plain,
( ~ sQ2_spl
| app(nil,sK51_skl) = sK51_skl ),
inference(resolution,[status(thm)],[f249,f446]) ).
fof(f1228,plain,
app(nil,sK48_skl) = sK48_skl,
inference(resolution,[status(thm)],[f249,f421]) ).
fof(f1237,plain,
app(nil,sK47_skl) = sK47_skl,
inference(resolution,[status(thm)],[f249,f420]) ).
fof(f1238,plain,
! [X0] :
( ~ sQ2_spl
| frontsegP(sK51_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sK51_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1227,f288]) ).
fof(f1239,plain,
! [X0] :
( ~ sQ2_spl
| ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK51_skl),X0),sK51_skl)
| ~ ssList(sK51_skl)
| ~ ssList(app(sK51_skl,X0)) ),
inference(paramodulation,[status(thm)],[f1227,f481]) ).
fof(f1240,definition,
! [X0] :
( sQ71_spl
<=> ( frontsegP(sK51_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ71_spl])],[split_symbol_definition]) ).
fof(f1241,plain,
! [X0] :
( ~ sQ71_spl
| frontsegP(sK51_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1240]) ).
fof(f1243,plain,
( ~ sQ2_spl
| sQ71_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1238,f852,f1240,f445]) ).
fof(f1244,definition,
! [X0] :
( sQ72_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK51_skl),X0),sK51_skl)
| ~ ssList(app(sK51_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ72_spl])],[split_symbol_definition]) ).
fof(f1245,plain,
! [X0] :
( ~ sQ72_spl
| ~ ssList(X0)
| segmentP(app(app(nil,sK51_skl),X0),sK51_skl)
| ~ ssList(app(sK51_skl,X0)) ),
inference(component_clause,[status(thm)],[f1244]) ).
fof(f1247,plain,
( ~ sQ23_spl
| ~ sQ2_spl
| sQ72_spl ),
inference(split_clause,[status(thm)],[f1239,f1244,f445,f852]) ).
fof(f1248,plain,
! [X0] :
( ~ sQ72_spl
| ~ sQ2_spl
| ~ ssList(X0)
| segmentP(app(sK51_skl,X0),sK51_skl)
| ~ ssList(app(sK51_skl,X0)) ),
inference(forward_demodulation,[status(thm)],[f1227,f1245]) ).
fof(f1249,plain,
! [X0] :
( frontsegP(sK48_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sK48_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1228,f288]) ).
fof(f1250,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK48_skl),X0),sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f1228,f481]) ).
fof(f1251,definition,
! [X0] :
( sQ73_spl
<=> ( frontsegP(sK48_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ73_spl])],[split_symbol_definition]) ).
fof(f1254,plain,
( ~ sQ20_spl
| sQ73_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1249,f852,f1251,f831]) ).
fof(f1255,definition,
! [X0] :
( sQ74_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK48_skl),X0),sK48_skl)
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ74_spl])],[split_symbol_definition]) ).
fof(f1258,plain,
( ~ sQ23_spl
| ~ sQ20_spl
| sQ74_spl ),
inference(split_clause,[status(thm)],[f1250,f1255,f831,f852]) ).
fof(f1260,plain,
! [X0] :
( frontsegP(sK47_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1237,f288]) ).
fof(f1261,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(nil)
| segmentP(app(app(nil,sK47_skl),X0),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK47_skl,X0)) ),
inference(paramodulation,[status(thm)],[f1237,f481]) ).
fof(f1262,definition,
! [X0] :
( sQ75_spl
<=> ( frontsegP(sK47_skl,X0)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ75_spl])],[split_symbol_definition]) ).
fof(f1265,plain,
( ~ sQ19_spl
| sQ75_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1260,f852,f1262,f828]) ).
fof(f1266,definition,
! [X0] :
( sQ76_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(nil,sK47_skl),X0),sK47_skl)
| ~ ssList(app(sK47_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ76_spl])],[split_symbol_definition]) ).
fof(f1269,plain,
( ~ sQ23_spl
| ~ sQ19_spl
| sQ76_spl ),
inference(split_clause,[status(thm)],[f1261,f1266,f828,f852]) ).
fof(f1276,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK48_skl)
| segmentP(app(app(sK48_skl,sK5_skl(sK48_skl,sK48_skl)),X0),sK5_skl(sK48_skl,sK48_skl))
| ~ ssList(sK5_skl(sK48_skl,sK48_skl))
| ~ ssList(app(sK48_skl,X0)) ),
inference(paramodulation,[status(thm)],[f1156,f481]) ).
fof(f1277,definition,
( sQ77_spl
<=> ssList(sK5_skl(sK48_skl,sK48_skl)) ),
introduced(definition,[new_symbols(definition,[sQ77_spl])],[split_symbol_definition]) ).
fof(f1279,plain,
( sQ77_spl
| ~ ssList(sK5_skl(sK48_skl,sK48_skl)) ),
inference(component_clause,[status(thm)],[f1277]) ).
fof(f1281,definition,
! [X0] :
( sQ78_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(sK48_skl,sK5_skl(sK48_skl,sK48_skl)),X0),sK5_skl(sK48_skl,sK48_skl))
| ~ ssList(app(sK48_skl,X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ78_spl])],[split_symbol_definition]) ).
fof(f1284,plain,
( ~ sQ20_spl
| ~ sQ77_spl
| sQ78_spl ),
inference(split_clause,[status(thm)],[f1276,f1281,f1277,f831]) ).
fof(f1285,plain,
( sQ77_spl
| ~ frontsegP(sK48_skl,sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1279,f122]) ).
fof(f1286,definition,
( sQ79_spl
<=> frontsegP(sK48_skl,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ79_spl])],[split_symbol_definition]) ).
fof(f1287,plain,
( ~ sQ79_spl
| frontsegP(sK48_skl,sK48_skl) ),
inference(component_clause,[status(thm)],[f1286]) ).
fof(f1288,plain,
( sQ79_spl
| ~ frontsegP(sK48_skl,sK48_skl) ),
inference(component_clause,[status(thm)],[f1286]) ).
fof(f1289,plain,
( sQ77_spl
| ~ sQ79_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1285,f831,f1286,f1277]) ).
fof(f1291,plain,
( sQ79_spl
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1288,f286]) ).
fof(f1293,plain,
( sQ79_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1291,f831,f1286]) ).
fof(f1298,plain,
( ~ sQ79_spl
| app(sK48_skl,sK5_skl(sK48_skl,sK48_skl)) = sK48_skl
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1287,f123]) ).
fof(f1299,plain,
( ~ sQ79_spl
| sK48_skl = sK48_skl
| ~ frontsegP(sK48_skl,sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1287,f284]) ).
fof(f1300,definition,
( sQ81_spl
<=> app(sK48_skl,sK5_skl(sK48_skl,sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ81_spl])],[split_symbol_definition]) ).
fof(f1303,plain,
( ~ sQ79_spl
| sQ81_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1298,f831,f1300,f1286]) ).
fof(f1304,definition,
( sQ82_spl
<=> sK48_skl = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ82_spl])],[split_symbol_definition]) ).
fof(f1307,plain,
( sQ82_spl
| ~ sQ79_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1299,f831,f1286,f1304]) ).
fof(f1312,plain,
( ~ sQ36_spl
| ~ ssList(sK47_skl)
| ~ frontsegP(nil,sK48_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f954,f295]) ).
fof(f1313,plain,
( ~ sQ36_spl
| ~ ssList(sK47_skl)
| ~ frontsegP(sK47_skl,sK48_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f954,f286]) ).
fof(f1314,plain,
! [X0,X1] :
( ~ sQ36_spl
| ~ frontsegP(X1,X0)
| ~ frontsegP(sK47_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sK47_skl)
| ~ frontsegP(X0,sK48_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f954,f282]) ).
fof(f1316,definition,
( sQ83_spl
<=> frontsegP(nil,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ83_spl])],[split_symbol_definition]) ).
fof(f1318,plain,
( sQ83_spl
| ~ frontsegP(nil,sK48_skl) ),
inference(component_clause,[status(thm)],[f1316]) ).
fof(f1319,plain,
( ~ sQ36_spl
| ~ sQ19_spl
| ~ sQ83_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1312,f852,f1316,f828,f953]) ).
fof(f1320,plain,
( ~ sQ36_spl
| ~ sQ32_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1313,f828,f908,f953]) ).
fof(f1321,definition,
! [X0,X1] :
( sQ84_spl
<=> ( ~ frontsegP(X1,X0)
| ~ frontsegP(sK47_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sK48_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ84_spl])],[split_symbol_definition]) ).
fof(f1324,plain,
( ~ sQ36_spl
| ~ sQ19_spl
| sQ84_spl ),
inference(split_clause,[status(thm)],[f1314,f1321,f828,f953]) ).
fof(f1325,plain,
( ~ sQ32_spl
| app(sK48_skl,sK5_skl(sK48_skl,sK47_skl)) = sK47_skl
| ~ ssList(sK48_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f909,f123]) ).
fof(f1326,plain,
( ~ sQ32_spl
| sK48_skl = sK47_skl
| ~ frontsegP(sK48_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f909,f284]) ).
fof(f1327,definition,
( sQ85_spl
<=> app(sK48_skl,sK5_skl(sK48_skl,sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ85_spl])],[split_symbol_definition]) ).
fof(f1328,plain,
( ~ sQ85_spl
| app(sK48_skl,sK5_skl(sK48_skl,sK47_skl)) = sK47_skl ),
inference(component_clause,[status(thm)],[f1327]) ).
fof(f1330,plain,
( ~ sQ32_spl
| sQ85_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1325,f828,f831,f1327,f908]) ).
fof(f1331,definition,
( sQ86_spl
<=> frontsegP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ86_spl])],[split_symbol_definition]) ).
fof(f1333,plain,
( sQ86_spl
| ~ frontsegP(sK48_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f1331]) ).
fof(f1334,plain,
( ~ sQ32_spl
| sQ33_spl
| ~ sQ86_spl
| ~ sQ19_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1326,f831,f828,f1331,f911,f908]) ).
fof(f1335,plain,
( ~ sQ32_spl
| ~ sQ33_spl
| frontsegP(sK47_skl,sK47_skl) ),
inference(backward_demodulation,[status(thm)],[f912,f909]) ).
fof(f1352,plain,
( sQ86_spl
| ~ sQ33_spl
| ~ frontsegP(sK47_skl,sK47_skl) ),
inference(backward_demodulation,[status(thm)],[f912,f1333]) ).
fof(f1374,plain,
( sQ86_spl
| ~ sQ33_spl
| ~ sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1352,f1335]) ).
fof(f1375,plain,
( sQ86_spl
| ~ sQ33_spl
| ~ sQ32_spl ),
inference(contradiction_clause,[status(thm)],[f1374]) ).
fof(f1393,plain,
( ~ sQ25_spl
| nil = sK47_skl
| ~ segmentP(nil,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f317,f859]) ).
fof(f1394,plain,
! [X0] :
( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f317,f323]) ).
fof(f1396,definition,
( sQ87_spl
<=> segmentP(nil,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ87_spl])],[split_symbol_definition]) ).
fof(f1399,definition,
( sQ88_spl
<=> nil = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ88_spl])],[split_symbol_definition]) ).
fof(f1400,plain,
( ~ sQ88_spl
| nil = sK47_skl ),
inference(component_clause,[status(thm)],[f1399]) ).
fof(f1402,plain,
( ~ sQ25_spl
| sQ88_spl
| ~ sQ87_spl
| ~ sQ19_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1393,f852,f828,f1396,f1399,f858]) ).
fof(f1403,definition,
! [X0] :
( sQ89_spl
<=> ( ~ ssList(X0)
| nil = X0
| ~ segmentP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1406,plain,
( sQ89_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1394,f852,f1403]) ).
fof(f1408,plain,
! [X0,X1] :
( ~ sQ25_spl
| segmentP(app(app(X0,sK47_skl),X1),nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f321,f859]) ).
fof(f1409,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(f1411,definition,
! [X0,X1] :
( sQ90_spl
<=> ( segmentP(app(app(X0,sK47_skl),X1),nil)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1414,plain,
( ~ sQ25_spl
| sQ90_spl
| ~ sQ23_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1408,f828,f852,f1411,f858]) ).
fof(f1415,definition,
! [X0,X1,X2] :
( sQ91_spl
<=> ( ~ ssList(X0)
| segmentP(app(app(X1,X0),X2),nil)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ91_spl])],[split_symbol_definition]) ).
fof(f1418,plain,
( ~ sQ23_spl
| sQ91_spl ),
inference(split_clause,[status(thm)],[f1409,f1415,f852]) ).
fof(f1421,plain,
! [X0] :
( sQ86_spl
| ~ frontsegP(X0,sK47_skl)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1333,f282]) ).
fof(f1422,definition,
! [X0] :
( sQ92_spl
<=> ( ~ frontsegP(X0,sK47_skl)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ92_spl])],[split_symbol_definition]) ).
fof(f1423,plain,
! [X0] :
( ~ sQ92_spl
| ~ frontsegP(X0,sK47_skl)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1422]) ).
fof(f1425,plain,
( sQ86_spl
| ~ sQ19_spl
| sQ92_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1421,f831,f1422,f828,f1331]) ).
fof(f1445,definition,
( sQ93_spl
<=> ssList(sK5_skl(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ93_spl])],[split_symbol_definition]) ).
fof(f1446,plain,
( ~ sQ93_spl
| ssList(sK5_skl(sK47_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1445]) ).
fof(f1447,plain,
( sQ93_spl
| ~ ssList(sK5_skl(sK47_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1445]) ).
fof(f1453,plain,
! [X0] :
( ~ sQ85_spl
| frontsegP(sK47_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(sK5_skl(sK48_skl,sK47_skl))
| ~ ssList(X0)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f1328,f288]) ).
fof(f1454,definition,
! [X0] :
( sQ94_spl
<=> ( frontsegP(sK47_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ94_spl])],[split_symbol_definition]) ).
fof(f1455,plain,
! [X0] :
( ~ sQ94_spl
| frontsegP(sK47_skl,X0)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1454]) ).
fof(f1457,definition,
( sQ95_spl
<=> ssList(sK5_skl(sK48_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ95_spl])],[split_symbol_definition]) ).
fof(f1458,plain,
( ~ sQ95_spl
| ssList(sK5_skl(sK48_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1457]) ).
fof(f1459,plain,
( sQ95_spl
| ~ ssList(sK5_skl(sK48_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1457]) ).
fof(f1460,plain,
( ~ sQ85_spl
| ~ sQ95_spl
| sQ94_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1453,f831,f1454,f1457,f1327]) ).
fof(f1461,plain,
! [X0,X1] :
( ~ sQ31_spl
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X1)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ frontsegP(sK51_skl,app(X0,X1))
| ~ ssList(app(X0,X1)) ),
inference(resolution,[status(thm)],[f898,f288]) ).
fof(f1462,plain,
( ~ sQ31_spl
| ~ ssList(sK47_skl)
| ~ frontsegP(sK51_skl,sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f898,f286]) ).
fof(f1463,plain,
! [X0,X1] :
( ~ sQ31_spl
| ~ frontsegP(X1,sK47_skl)
| ~ frontsegP(X0,X1)
| ~ ssList(sK47_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f898,f282]) ).
fof(f1464,definition,
! [X0,X1] :
( sQ96_spl
<=> ( ~ frontsegP(X0,sK47_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(sK51_skl,app(X0,X1))
| ~ ssList(app(X0,X1)) ) ),
introduced(definition,[new_symbols(definition,[sQ96_spl])],[split_symbol_definition]) ).
fof(f1467,plain,
( ~ sQ31_spl
| ~ sQ19_spl
| sQ96_spl ),
inference(split_clause,[status(thm)],[f1461,f1464,f828,f897]) ).
fof(f1468,plain,
( ~ sQ31_spl
| ~ sQ28_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1462,f828,f880,f897]) ).
fof(f1469,definition,
! [X0,X1] :
( sQ97_spl
<=> ( ~ frontsegP(X1,sK47_skl)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ97_spl])],[split_symbol_definition]) ).
fof(f1472,plain,
( ~ sQ31_spl
| ~ sQ19_spl
| sQ97_spl ),
inference(split_clause,[status(thm)],[f1463,f1469,f828,f897]) ).
fof(f1484,plain,
! [X0] :
( frontsegP(app(X0,sK48_skl),X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f493,f421]) ).
fof(f1489,plain,
! [X0] :
( frontsegP(app(X0,nil),X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f493,f223]) ).
fof(f1497,plain,
! [X0] :
( frontsegP(app(X0,sK47_skl),X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f493,f420]) ).
fof(f1501,plain,
( frontsegP(sK48_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1228,f1484]) ).
fof(f1511,definition,
( sQ101_spl
<=> frontsegP(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ101_spl])],[split_symbol_definition]) ).
fof(f1512,plain,
( ~ sQ101_spl
| frontsegP(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f1511]) ).
fof(f1514,plain,
( sQ101_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1501,f852,f1511]) ).
fof(f1515,plain,
( ~ sQ101_spl
| app(nil,sK5_skl(nil,sK48_skl)) = sK48_skl
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1512,f123]) ).
fof(f1516,plain,
( ~ sQ101_spl
| nil = sK48_skl
| ~ frontsegP(nil,sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1512,f284]) ).
fof(f1517,definition,
( sQ102_spl
<=> app(nil,sK5_skl(nil,sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ102_spl])],[split_symbol_definition]) ).
fof(f1520,plain,
( ~ sQ101_spl
| sQ102_spl
| ~ sQ23_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f1515,f831,f852,f1517,f1511]) ).
fof(f1521,definition,
( sQ103_spl
<=> nil = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1522,plain,
( ~ sQ103_spl
| nil = sK48_skl ),
inference(component_clause,[status(thm)],[f1521]) ).
fof(f1524,plain,
( ~ sQ101_spl
| sQ103_spl
| ~ sQ83_spl
| ~ sQ20_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1516,f852,f831,f1316,f1521,f1511]) ).
fof(f1525,plain,
! [X0] :
( sQ83_spl
| ~ frontsegP(X0,sK48_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(sK48_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1318,f282]) ).
fof(f1526,definition,
! [X0] :
( sQ104_spl
<=> ( ~ frontsegP(X0,sK48_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1529,plain,
( sQ83_spl
| ~ sQ20_spl
| sQ104_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1525,f852,f1526,f831,f1316]) ).
fof(f1543,definition,
( sQ107_spl
<=> frontsegP(sK51_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ107_spl])],[split_symbol_definition]) ).
fof(f1544,plain,
( ~ sQ107_spl
| frontsegP(sK51_skl,nil) ),
inference(component_clause,[status(thm)],[f1543]) ).
fof(f1547,plain,
( ~ sQ107_spl
| app(nil,sK5_skl(nil,sK51_skl)) = sK51_skl
| ~ ssList(nil)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f1544,f123]) ).
fof(f1548,plain,
( ~ sQ107_spl
| nil = sK51_skl
| ~ frontsegP(nil,sK51_skl)
| ~ ssList(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1544,f284]) ).
fof(f1549,definition,
( sQ108_spl
<=> app(nil,sK5_skl(nil,sK51_skl)) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ108_spl])],[split_symbol_definition]) ).
fof(f1552,plain,
( ~ sQ107_spl
| sQ108_spl
| ~ sQ23_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f1547,f445,f852,f1549,f1543]) ).
fof(f1553,definition,
( sQ109_spl
<=> frontsegP(nil,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1555,plain,
( sQ109_spl
| ~ frontsegP(nil,sK51_skl) ),
inference(component_clause,[status(thm)],[f1553]) ).
fof(f1556,definition,
( sQ110_spl
<=> nil = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1557,plain,
( ~ sQ110_spl
| nil = sK51_skl ),
inference(component_clause,[status(thm)],[f1556]) ).
fof(f1559,plain,
( ~ sQ107_spl
| sQ110_spl
| ~ sQ109_spl
| ~ sQ2_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1548,f852,f445,f1553,f1556,f1543]) ).
fof(f1560,plain,
! [X0] :
( sQ109_spl
| ~ frontsegP(X0,sK51_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(sK51_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1555,f282]) ).
fof(f1561,definition,
! [X0] :
( sQ111_spl
<=> ( ~ frontsegP(X0,sK51_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1562,plain,
! [X0] :
( ~ sQ111_spl
| ~ frontsegP(X0,sK51_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f1561]) ).
fof(f1564,plain,
( sQ109_spl
| ~ sQ2_spl
| sQ111_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1560,f852,f1561,f445,f1553]) ).
fof(f1595,plain,
( ~ sQ4_spl
| ~ sQ110_spl
| neq(sK51_skl,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f1557,f453]) ).
fof(f1606,plain,
( sQ24_spl
| ~ sQ110_spl
| ~ neq(nil,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f1557,f857]) ).
fof(f1682,plain,
( sQ24_spl
| ~ sQ110_spl
| ~ neq(sK51_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f1557,f1606]) ).
fof(f1683,plain,
( sQ24_spl
| ~ sQ110_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1682,f1595]) ).
fof(f1684,plain,
( sQ24_spl
| ~ sQ110_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f1683]) ).
fof(f1686,plain,
( ~ sQ9_spl
| ~ ssList(sK47_skl)
| ~ segmentP(sK48_skl,sK47_skl)
| ~ neq(sK47_skl,nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f472,f319]) ).
fof(f1688,definition,
( sQ112_spl
<=> neq(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1690,plain,
( sQ112_spl
| ~ neq(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f1688]) ).
fof(f1691,definition,
( sQ113_spl
<=> segmentP(sK48_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1694,plain,
( ~ sQ9_spl
| ~ sQ113_spl
| ~ sQ112_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1686,f828,f1688,f1691,f471]) ).
fof(f1714,definition,
( sQ114_spl
<=> segmentP(sK48_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1715,plain,
( ~ sQ114_spl
| segmentP(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f1714]) ).
fof(f1716,plain,
( sQ114_spl
| ~ segmentP(sK48_skl,nil) ),
inference(component_clause,[status(thm)],[f1714]) ).
fof(f1725,plain,
( sQ112_spl
| sK47_skl = nil
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1690,f220]) ).
fof(f1726,plain,
( sQ112_spl
| sQ88_spl
| ~ sQ23_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1725,f828,f852,f1399,f1688]) ).
fof(f1727,plain,
( ~ sQ88_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1400,f583]) ).
fof(f1728,plain,
( ~ sQ88_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f1727]) ).
fof(f1808,plain,
( frontsegP(sK47_skl,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1237,f1497]) ).
fof(f1818,definition,
( sQ117_spl
<=> frontsegP(sK47_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1819,plain,
( ~ sQ117_spl
| frontsegP(sK47_skl,nil) ),
inference(component_clause,[status(thm)],[f1818]) ).
fof(f1821,plain,
( sQ117_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1808,f852,f1818]) ).
fof(f1822,plain,
( ~ sQ117_spl
| app(nil,sK5_skl(nil,sK47_skl)) = sK47_skl
| ~ ssList(nil)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1819,f123]) ).
fof(f1823,plain,
( ~ sQ117_spl
| nil = sK47_skl
| ~ frontsegP(nil,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1819,f284]) ).
fof(f1824,definition,
( sQ118_spl
<=> app(nil,sK5_skl(nil,sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1827,plain,
( ~ sQ117_spl
| sQ118_spl
| ~ sQ23_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f1822,f828,f852,f1824,f1818]) ).
fof(f1828,definition,
( sQ119_spl
<=> frontsegP(nil,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f1830,plain,
( sQ119_spl
| ~ frontsegP(nil,sK47_skl) ),
inference(component_clause,[status(thm)],[f1828]) ).
fof(f1831,plain,
( ~ sQ117_spl
| sQ88_spl
| ~ sQ119_spl
| ~ sQ19_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1823,f852,f828,f1828,f1399,f1818]) ).
fof(f1856,plain,
( sQ109_spl
| ~ sQ88_spl
| ~ frontsegP(sK47_skl,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f1400,f1555]) ).
fof(f2053,plain,
! [X0] :
( sQ119_spl
| ~ frontsegP(X0,sK47_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1830,f282]) ).
fof(f2054,definition,
! [X0] :
( sQ120_spl
<=> ( ~ frontsegP(X0,sK47_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f2055,plain,
! [X0] :
( ~ sQ120_spl
| ~ frontsegP(X0,sK47_skl)
| ~ frontsegP(nil,X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f2054]) ).
fof(f2057,plain,
( sQ119_spl
| ~ sQ19_spl
| sQ120_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f2053,f852,f2054,f828,f1828]) ).
fof(f2181,plain,
( sQ109_spl
| ~ sQ88_spl
| ~ sQ53_spl ),
inference(split_clause,[status(thm)],[f1856,f1094,f1399,f1553]) ).
fof(f2319,plain,
( frontsegP(nil,nil)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1016,f1489]) ).
fof(f2320,plain,
( frontsegP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f1020,f1489]) ).
fof(f2325,definition,
( sQ124_spl
<=> frontsegP(nil,nil) ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f2326,plain,
( ~ sQ124_spl
| frontsegP(nil,nil) ),
inference(component_clause,[status(thm)],[f2325]) ).
fof(f2328,plain,
( sQ124_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f2319,f852,f2325]) ).
fof(f2329,definition,
( sQ125_spl
<=> frontsegP(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ125_spl])],[split_symbol_definition]) ).
fof(f2330,plain,
( ~ sQ125_spl
| frontsegP(sK47_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f2329]) ).
fof(f2332,plain,
( sQ125_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2320,f828,f2329]) ).
fof(f2334,plain,
( ~ sQ125_spl
| app(sK47_skl,sK5_skl(sK47_skl,sK47_skl)) = sK47_skl
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2330,f123]) ).
fof(f2335,plain,
( ~ sQ125_spl
| sK47_skl = sK47_skl
| ~ frontsegP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2330,f284]) ).
fof(f2336,definition,
( sQ126_spl
<=> app(sK47_skl,sK5_skl(sK47_skl,sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ126_spl])],[split_symbol_definition]) ).
fof(f2339,plain,
( ~ sQ125_spl
| sQ126_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2334,f828,f2336,f2329]) ).
fof(f2340,plain,
( sQ16_spl
| ~ sQ125_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2335,f828,f2329,f812]) ).
fof(f2342,plain,
( ~ sQ124_spl
| app(nil,sK5_skl(nil,nil)) = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f2326,f123]) ).
fof(f2345,definition,
( sQ127_spl
<=> app(nil,sK5_skl(nil,nil)) = nil ),
introduced(definition,[new_symbols(definition,[sQ127_spl])],[split_symbol_definition]) ).
fof(f2348,plain,
( ~ sQ124_spl
| sQ127_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f2342,f852,f2345,f2325]) ).
fof(f2367,plain,
( ~ sQ92_spl
| ~ ssList(sK48_skl)
| ~ frontsegP(sK48_skl,sK47_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1423,f286]) ).
fof(f2368,plain,
! [X0,X1] :
( ~ sQ92_spl
| ~ frontsegP(X1,X0)
| ~ frontsegP(sK48_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sK48_skl)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1423,f282]) ).
fof(f2373,plain,
( ~ sQ92_spl
| ~ sQ86_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f2367,f831,f1331,f1422]) ).
fof(f2374,definition,
! [X0,X1] :
( sQ129_spl
<=> ( ~ frontsegP(X1,X0)
| ~ frontsegP(sK48_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ129_spl])],[split_symbol_definition]) ).
fof(f2377,plain,
( ~ sQ92_spl
| ~ sQ20_spl
| sQ129_spl ),
inference(split_clause,[status(thm)],[f2368,f2374,f831,f1422]) ).
fof(f2383,plain,
! [X0,X1] :
( ~ sQ31_spl
| ~ frontsegP(X1,X0)
| ~ frontsegP(sK51_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sK51_skl)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f898,f282]) ).
fof(f2388,definition,
! [X0,X1] :
( sQ130_spl
<=> ( ~ frontsegP(X1,X0)
| ~ frontsegP(sK51_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ130_spl])],[split_symbol_definition]) ).
fof(f2391,plain,
( ~ sQ31_spl
| ~ sQ2_spl
| sQ130_spl ),
inference(split_clause,[status(thm)],[f2383,f2388,f445,f897]) ).
fof(f2393,plain,
! [X0] :
( ~ frontsegP(sK48_skl,X0)
| ~ frontsegP(sK48_skl,sK48_skl)
| X0 = sK48_skl
| ~ frontsegP(X0,sK48_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f891,f421]) ).
fof(f2395,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| ~ frontsegP(nil,nil)
| X0 = nil
| ~ frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f891,f223]) ).
fof(f2401,plain,
! [X0] :
( ~ sQ2_spl
| ~ frontsegP(sK51_skl,X0)
| ~ frontsegP(sK51_skl,sK51_skl)
| X0 = sK51_skl
| ~ frontsegP(X0,sK51_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f891,f446]) ).
fof(f2411,plain,
! [X0] :
( ~ sQ51_spl
| ~ frontsegP(sK5_skl(sK51_skl,sK47_skl),X0)
| ~ frontsegP(sK5_skl(sK51_skl,sK47_skl),sK5_skl(sK51_skl,sK47_skl))
| X0 = sK5_skl(sK51_skl,sK47_skl)
| ~ frontsegP(X0,sK5_skl(sK51_skl,sK47_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f891,f1086]) ).
fof(f2419,plain,
! [X0] :
( ~ frontsegP(sK47_skl,X0)
| ~ frontsegP(sK47_skl,sK47_skl)
| X0 = sK47_skl
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f891,f420]) ).
fof(f2435,definition,
! [X0] :
( sQ131_spl
<=> ( ~ frontsegP(sK48_skl,X0)
| X0 = sK48_skl
| ~ frontsegP(X0,sK48_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f2438,plain,
( ~ sQ79_spl
| sQ131_spl ),
inference(split_clause,[status(thm)],[f2393,f2435,f1286]) ).
fof(f2439,definition,
! [X0] :
( sQ132_spl
<=> ( ~ frontsegP(nil,X0)
| X0 = nil
| ~ frontsegP(X0,nil)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f2442,plain,
( ~ sQ124_spl
| sQ132_spl ),
inference(split_clause,[status(thm)],[f2395,f2439,f2325]) ).
fof(f2443,definition,
! [X0] :
( sQ133_spl
<=> ( ~ frontsegP(sK51_skl,X0)
| X0 = sK51_skl
| ~ frontsegP(X0,sK51_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f2446,plain,
( ~ sQ2_spl
| ~ sQ68_spl
| sQ133_spl ),
inference(split_clause,[status(thm)],[f2401,f2443,f1204,f445]) ).
fof(f2468,definition,
! [X0] :
( sQ140_spl
<=> ( ~ frontsegP(sK5_skl(sK51_skl,sK47_skl),X0)
| X0 = sK5_skl(sK51_skl,sK47_skl)
| ~ frontsegP(X0,sK5_skl(sK51_skl,sK47_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ140_spl])],[split_symbol_definition]) ).
fof(f2471,definition,
( sQ141_spl
<=> frontsegP(sK5_skl(sK51_skl,sK47_skl),sK5_skl(sK51_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f2473,plain,
( sQ141_spl
| ~ frontsegP(sK5_skl(sK51_skl,sK47_skl),sK5_skl(sK51_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f2471]) ).
fof(f2474,plain,
( ~ sQ51_spl
| ~ sQ141_spl
| sQ140_spl ),
inference(split_clause,[status(thm)],[f2411,f2468,f2471,f1085]) ).
fof(f2475,definition,
! [X0] :
( sQ142_spl
<=> ( ~ frontsegP(sK47_skl,X0)
| X0 = sK47_skl
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f2478,plain,
( ~ sQ125_spl
| sQ142_spl ),
inference(split_clause,[status(thm)],[f2419,f2475,f2329]) ).
fof(f2554,plain,
! [X0] :
( ~ sQ50_spl
| app(X0,sK5_skl(X0,sK47_skl)) = sK47_skl
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1083,f123]) ).
fof(f2555,plain,
! [X0] :
( ~ sQ50_spl
| X0 = sK47_skl
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1083,f284]) ).
fof(f2556,definition,
! [X0] :
( sQ143_spl
<=> ( app(X0,sK5_skl(X0,sK47_skl)) = sK47_skl
| ~ ssList(X0)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ143_spl])],[split_symbol_definition]) ).
fof(f2559,plain,
( ~ sQ50_spl
| ~ sQ19_spl
| sQ143_spl ),
inference(split_clause,[status(thm)],[f2554,f2556,f828,f1082]) ).
fof(f2560,definition,
! [X0] :
( sQ144_spl
<=> ( X0 = sK47_skl
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f2563,plain,
( ~ sQ50_spl
| ~ sQ19_spl
| sQ144_spl ),
inference(split_clause,[status(thm)],[f2555,f2560,f828,f1082]) ).
fof(f2567,plain,
( ~ sQ71_spl
| ~ ssList(nil)
| frontsegP(sK51_skl,nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1241,f295]) ).
fof(f2569,plain,
! [X0,X1] :
( ~ sQ71_spl
| ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| frontsegP(sK51_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1241,f282]) ).
fof(f2571,plain,
( ~ sQ71_spl
| sQ107_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f2567,f852,f1543,f1240]) ).
fof(f2573,definition,
! [X0,X1] :
( sQ145_spl
<=> ( ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| frontsegP(sK51_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f2576,plain,
( ~ sQ71_spl
| ~ sQ23_spl
| sQ145_spl ),
inference(split_clause,[status(thm)],[f2569,f2573,f852,f1240]) ).
fof(f2579,plain,
( ~ sQ111_spl
| ~ ssList(nil)
| ~ frontsegP(nil,sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1562,f295]) ).
fof(f2581,plain,
! [X0,X1] :
( ~ sQ111_spl
| ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(X0,sK51_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1562,f282]) ).
fof(f2583,plain,
( ~ sQ111_spl
| ~ sQ109_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f2579,f852,f1553,f1561]) ).
fof(f2585,definition,
! [X0,X1] :
( sQ146_spl
<=> ( ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sK51_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f2588,plain,
( ~ sQ111_spl
| ~ sQ23_spl
| sQ146_spl ),
inference(split_clause,[status(thm)],[f2581,f2585,f852,f1561]) ).
fof(f2593,plain,
! [X0,X1] :
( ~ sQ120_spl
| ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(nil)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2055,f282]) ).
fof(f2597,definition,
! [X0,X1] :
( sQ147_spl
<=> ( ~ frontsegP(X1,X0)
| ~ frontsegP(nil,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f2600,plain,
( ~ sQ120_spl
| ~ sQ23_spl
| sQ147_spl ),
inference(split_clause,[status(thm)],[f2593,f2597,f852,f2054]) ).
fof(f2602,plain,
! [X0] :
( ~ sQ94_spl
| app(X0,sK5_skl(X0,sK47_skl)) = sK47_skl
| ~ ssList(X0)
| ~ ssList(sK47_skl)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1455,f123]) ).
fof(f2603,plain,
! [X0] :
( ~ sQ94_spl
| X0 = sK47_skl
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(X0)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1455,f284]) ).
fof(f2604,definition,
! [X0] :
( sQ148_spl
<=> ( app(X0,sK5_skl(X0,sK47_skl)) = sK47_skl
| ~ ssList(X0)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f2607,plain,
( ~ sQ94_spl
| ~ sQ19_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f2602,f2604,f828,f1454]) ).
fof(f2608,definition,
! [X0] :
( sQ149_spl
<=> ( X0 = sK47_skl
| ~ frontsegP(X0,sK47_skl)
| ~ ssList(X0)
| ~ frontsegP(sK48_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f2611,plain,
( ~ sQ94_spl
| ~ sQ19_spl
| sQ149_spl ),
inference(split_clause,[status(thm)],[f2603,f2608,f828,f1454]) ).
fof(f2614,plain,
( ~ sQ52_spl
| ~ sQ35_spl
| ~ ssList(nil)
| segmentP(app(sK47_skl,nil),sK5_skl(sK51_skl,sK47_skl))
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f1020,f1098]) ).
fof(f2615,plain,
( ~ sQ52_spl
| ~ sQ35_spl
| ~ ssList(sK5_skl(sK47_skl,sK47_skl))
| segmentP(app(sK47_skl,sK5_skl(sK47_skl,sK47_skl)),sK5_skl(sK51_skl,sK47_skl))
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f1164,f1098]) ).
fof(f2616,definition,
( sQ150_spl
<=> segmentP(app(sK47_skl,nil),sK5_skl(sK51_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f2617,plain,
( ~ sQ150_spl
| segmentP(app(sK47_skl,nil),sK5_skl(sK51_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f2616]) ).
fof(f2619,plain,
( ~ sQ52_spl
| ~ sQ35_spl
| ~ sQ23_spl
| sQ150_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2614,f828,f2616,f852,f944,f1089]) ).
fof(f2620,definition,
( sQ151_spl
<=> segmentP(app(sK47_skl,sK5_skl(sK47_skl,sK47_skl)),sK5_skl(sK51_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f2623,plain,
( ~ sQ52_spl
| ~ sQ35_spl
| ~ sQ93_spl
| sQ151_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2615,f828,f2620,f1445,f944,f1089]) ).
fof(f2624,plain,
( ~ sQ150_spl
| segmentP(sK47_skl,sK5_skl(sK51_skl,sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f1020,f2617]) ).
fof(f2625,plain,
( sQ93_spl
| ~ frontsegP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1447,f122]) ).
fof(f2626,plain,
( sQ93_spl
| ~ sQ125_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2625,f828,f2329,f1445]) ).
fof(f2634,plain,
! [X0] :
( ~ sQ93_spl
| ~ frontsegP(sK5_skl(sK47_skl,sK47_skl),X0)
| ~ frontsegP(sK5_skl(sK47_skl,sK47_skl),sK5_skl(sK47_skl,sK47_skl))
| X0 = sK5_skl(sK47_skl,sK47_skl)
| ~ frontsegP(X0,sK5_skl(sK47_skl,sK47_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1446,f891]) ).
fof(f2640,definition,
! [X0] :
( sQ152_spl
<=> ( ~ frontsegP(sK5_skl(sK47_skl,sK47_skl),X0)
| X0 = sK5_skl(sK47_skl,sK47_skl)
| ~ frontsegP(X0,sK5_skl(sK47_skl,sK47_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ152_spl])],[split_symbol_definition]) ).
fof(f2643,definition,
( sQ153_spl
<=> frontsegP(sK5_skl(sK47_skl,sK47_skl),sK5_skl(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ153_spl])],[split_symbol_definition]) ).
fof(f2646,plain,
( ~ sQ93_spl
| ~ sQ153_spl
| sQ152_spl ),
inference(split_clause,[status(thm)],[f2634,f2640,f2643,f1445]) ).
fof(f2648,plain,
! [X0,X1] :
( ~ sQ150_spl
| segmentP(app(app(X0,sK47_skl),X1),sK5_skl(sK51_skl,sK47_skl))
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK5_skl(sK51_skl,sK47_skl))
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2624,f321]) ).
fof(f2649,plain,
( ~ sQ150_spl
| sK5_skl(sK51_skl,sK47_skl) = sK47_skl
| ~ segmentP(sK5_skl(sK51_skl,sK47_skl),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK5_skl(sK51_skl,sK47_skl)) ),
inference(resolution,[status(thm)],[f2624,f317]) ).
fof(f2650,plain,
! [X0] :
( ~ sQ150_spl
| segmentP(X0,sK5_skl(sK51_skl,sK47_skl))
| ~ segmentP(X0,sK47_skl)
| ~ ssList(sK5_skl(sK51_skl,sK47_skl))
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f2624,f315]) ).
fof(f2651,plain,
( ~ sQ150_spl
| app(app(sK7_skl(sK5_skl(sK51_skl,sK47_skl),sK47_skl),sK5_skl(sK51_skl,sK47_skl)),sK8_skl(sK5_skl(sK51_skl,sK47_skl),sK47_skl)) = sK47_skl
| ~ ssList(sK5_skl(sK51_skl,sK47_skl))
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2624,f136]) ).
fof(f2652,definition,
! [X0,X1] :
( sQ154_spl
<=> ( segmentP(app(app(X0,sK47_skl),X1),sK5_skl(sK51_skl,sK47_skl))
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f2655,plain,
( ~ sQ150_spl
| sQ154_spl
| ~ sQ51_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2648,f828,f1085,f2652,f2616]) ).
fof(f2656,definition,
( sQ155_spl
<=> segmentP(sK5_skl(sK51_skl,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f2659,definition,
( sQ156_spl
<=> sK5_skl(sK51_skl,sK47_skl) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f2660,plain,
( ~ sQ156_spl
| sK5_skl(sK51_skl,sK47_skl) = sK47_skl ),
inference(component_clause,[status(thm)],[f2659]) ).
fof(f2662,plain,
( ~ sQ150_spl
| sQ156_spl
| ~ sQ155_spl
| ~ sQ19_spl
| ~ sQ51_spl ),
inference(split_clause,[status(thm)],[f2649,f1085,f828,f2656,f2659,f2616]) ).
fof(f2663,definition,
! [X0] :
( sQ157_spl
<=> ( segmentP(X0,sK5_skl(sK51_skl,sK47_skl))
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f2666,plain,
( ~ sQ150_spl
| ~ sQ51_spl
| ~ sQ19_spl
| sQ157_spl ),
inference(split_clause,[status(thm)],[f2650,f2663,f828,f1085,f2616]) ).
fof(f2667,definition,
( sQ158_spl
<=> app(app(sK7_skl(sK5_skl(sK51_skl,sK47_skl),sK47_skl),sK5_skl(sK51_skl,sK47_skl)),sK8_skl(sK5_skl(sK51_skl,sK47_skl),sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f2670,plain,
( ~ sQ150_spl
| sQ158_spl
| ~ sQ51_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2651,f828,f1085,f2667,f2616]) ).
fof(f2686,plain,
( ~ sQ107_spl
| ~ sQ38_spl
| ~ frontsegP(nil,sK48_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f999,f1544]) ).
fof(f2690,plain,
! [X0,X1] :
( ~ sQ38_spl
| ~ frontsegP(X1,X0)
| ~ frontsegP(sK51_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ ssList(sK51_skl)
| ~ frontsegP(X0,sK48_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f999,f282]) ).
fof(f2691,plain,
( ~ sQ107_spl
| ~ sQ38_spl
| ~ sQ83_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f2686,f852,f1316,f998,f1543]) ).
fof(f2695,definition,
! [X0,X1] :
( sQ159_spl
<=> ( ~ frontsegP(X1,X0)
| ~ frontsegP(sK51_skl,X1)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,sK48_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f2698,plain,
( ~ sQ38_spl
| ~ sQ2_spl
| sQ159_spl ),
inference(split_clause,[status(thm)],[f2690,f2695,f445,f998]) ).
fof(f2700,plain,
( sQ86_spl
| ~ sQ54_spl
| ~ frontsegP(sK51_skl,sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1105,f1333]) ).
fof(f2702,plain,
! [X0] :
( ~ sQ54_spl
| app(X0,sK5_skl(X0,sK48_skl)) = sK48_skl
| ~ ssList(X0)
| ~ ssList(sK48_skl)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1105,f123]) ).
fof(f2703,plain,
! [X0] :
( ~ sQ54_spl
| X0 = sK48_skl
| ~ frontsegP(X0,sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(X0)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1105,f284]) ).
fof(f2704,plain,
( sQ86_spl
| ~ sQ54_spl
| ~ sQ28_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2700,f828,f880,f1104,f1331]) ).
fof(f2706,definition,
! [X0] :
( sQ160_spl
<=> ( app(X0,sK5_skl(X0,sK48_skl)) = sK48_skl
| ~ ssList(X0)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f2709,plain,
( ~ sQ54_spl
| ~ sQ20_spl
| sQ160_spl ),
inference(split_clause,[status(thm)],[f2702,f2706,f831,f1104]) ).
fof(f2710,definition,
! [X0] :
( sQ161_spl
<=> ( X0 = sK48_skl
| ~ frontsegP(X0,sK48_skl)
| ~ ssList(X0)
| ~ frontsegP(sK51_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f2713,plain,
( ~ sQ54_spl
| ~ sQ20_spl
| sQ161_spl ),
inference(split_clause,[status(thm)],[f2703,f2710,f831,f1104]) ).
fof(f2884,plain,
( sQ22_spl
| ~ sQ33_spl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f915,f319]) ).
fof(f2885,plain,
( sQ22_spl
| ~ sQ33_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f2884,f828,f911,f847]) ).
fof(f2906,plain,
( sQ141_spl
| ~ sQ156_spl
| ~ frontsegP(sK47_skl,sK5_skl(sK51_skl,sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f2660,f2473]) ).
fof(f2907,plain,
( sQ141_spl
| ~ sQ156_spl
| ~ frontsegP(sK47_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f2660,f2906]) ).
fof(f2908,plain,
( sQ141_spl
| ~ sQ156_spl
| ~ sQ125_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2907,f2330]) ).
fof(f2909,plain,
( sQ141_spl
| ~ sQ156_spl
| ~ sQ125_spl ),
inference(contradiction_clause,[status(thm)],[f2908]) ).
fof(f3036,plain,
( ~ sQ101_spl
| ~ sQ103_spl
| frontsegP(sK48_skl,sK48_skl) ),
inference(forward_demodulation,[status(thm)],[f1522,f1512]) ).
fof(f3037,plain,
( sQ83_spl
| ~ sQ103_spl
| ~ frontsegP(sK48_skl,sK48_skl) ),
inference(forward_demodulation,[status(thm)],[f1522,f1318]) ).
fof(f3038,plain,
( sQ83_spl
| ~ sQ103_spl
| ~ sQ101_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3037,f3036]) ).
fof(f3039,plain,
( sQ83_spl
| ~ sQ103_spl
| ~ sQ101_spl ),
inference(contradiction_clause,[status(thm)],[f3038]) ).
fof(f3052,plain,
( ~ sQ50_spl
| sQ32_spl
| ~ frontsegP(sK51_skl,sK48_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f910,f1083]) ).
fof(f3054,plain,
( ~ sQ50_spl
| sQ32_spl
| ~ sQ26_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3052,f831,f873,f908,f1082]) ).
fof(f3122,plain,
( sQ114_spl
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1716,f323]) ).
fof(f3123,plain,
( sQ114_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3122,f831,f1714]) ).
fof(f3130,plain,
! [X0,X1] :
( ~ sQ114_spl
| segmentP(app(app(X0,sK48_skl),X1),nil)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1715,f321]) ).
fof(f3131,plain,
( ~ sQ114_spl
| nil = sK48_skl
| ~ segmentP(nil,sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1715,f317]) ).
fof(f3132,plain,
! [X0] :
( ~ sQ114_spl
| segmentP(X0,nil)
| ~ segmentP(X0,sK48_skl)
| ~ ssList(nil)
| ~ ssList(sK48_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1715,f315]) ).
fof(f3133,plain,
( ~ sQ114_spl
| app(app(sK7_skl(nil,sK48_skl),nil),sK8_skl(nil,sK48_skl)) = sK48_skl
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f1715,f136]) ).
fof(f3134,definition,
! [X0,X1] :
( sQ162_spl
<=> ( segmentP(app(app(X0,sK48_skl),X1),nil)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f3137,plain,
( ~ sQ114_spl
| sQ162_spl
| ~ sQ23_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3130,f831,f852,f3134,f1714]) ).
fof(f3138,definition,
( sQ163_spl
<=> segmentP(nil,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f3141,plain,
( ~ sQ114_spl
| sQ103_spl
| ~ sQ163_spl
| ~ sQ20_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f3131,f852,f831,f3138,f1521,f1714]) ).
fof(f3142,definition,
! [X0] :
( sQ164_spl
<=> ( segmentP(X0,nil)
| ~ segmentP(X0,sK48_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ164_spl])],[split_symbol_definition]) ).
fof(f3145,plain,
( ~ sQ114_spl
| ~ sQ23_spl
| ~ sQ20_spl
| sQ164_spl ),
inference(split_clause,[status(thm)],[f3132,f3142,f831,f852,f1714]) ).
fof(f3146,definition,
( sQ165_spl
<=> app(app(sK7_skl(nil,sK48_skl),nil),sK8_skl(nil,sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ165_spl])],[split_symbol_definition]) ).
fof(f3149,plain,
( ~ sQ114_spl
| sQ165_spl
| ~ sQ23_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3133,f831,f852,f3146,f1714]) ).
fof(f3150,plain,
( sQ95_spl
| ~ frontsegP(sK47_skl,sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f1459,f122]) ).
fof(f3151,plain,
( sQ95_spl
| ~ sQ32_spl
| ~ sQ20_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f3150,f828,f831,f908,f1457]) ).
fof(f3217,plain,
! [X0] :
( ~ sQ95_spl
| ~ frontsegP(sK5_skl(sK48_skl,sK47_skl),X0)
| ~ frontsegP(sK5_skl(sK48_skl,sK47_skl),sK5_skl(sK48_skl,sK47_skl))
| X0 = sK5_skl(sK48_skl,sK47_skl)
| ~ frontsegP(X0,sK5_skl(sK48_skl,sK47_skl))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f1458,f891]) ).
fof(f3223,definition,
! [X0] :
( sQ166_spl
<=> ( ~ frontsegP(sK5_skl(sK48_skl,sK47_skl),X0)
| X0 = sK5_skl(sK48_skl,sK47_skl)
| ~ frontsegP(X0,sK5_skl(sK48_skl,sK47_skl))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ166_spl])],[split_symbol_definition]) ).
fof(f3226,definition,
( sQ167_spl
<=> frontsegP(sK5_skl(sK48_skl,sK47_skl),sK5_skl(sK48_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ167_spl])],[split_symbol_definition]) ).
fof(f3229,plain,
( ~ sQ95_spl
| ~ sQ167_spl
| sQ166_spl ),
inference(split_clause,[status(thm)],[f3217,f3223,f3226,f1457]) ).
fof(f3369,plain,
( ~ sQ2_spl
| ~ sQ72_spl
| ~ ssList(nil)
| segmentP(app(sK51_skl,nil),sK51_skl)
| ~ ssList(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1013,f1248]) ).
fof(f3370,plain,
( ~ sQ35_spl
| ~ sQ72_spl
| ~ sQ2_spl
| ~ ssList(sK5_skl(sK51_skl,sK47_skl))
| segmentP(app(sK51_skl,sK5_skl(sK51_skl,sK47_skl)),sK51_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f945,f1248]) ).
fof(f3371,plain,
( ~ sQ37_spl
| ~ sQ72_spl
| ~ sQ2_spl
| ~ ssList(sK5_skl(sK51_skl,sK48_skl))
| segmentP(app(sK51_skl,sK5_skl(sK51_skl,sK48_skl)),sK51_skl)
| ~ ssList(sK48_skl) ),
inference(paramodulation,[status(thm)],[f989,f1248]) ).
fof(f3372,plain,
( ~ sQ2_spl
| ~ sQ72_spl
| ~ ssList(sK5_skl(sK51_skl,sK51_skl))
| segmentP(app(sK51_skl,sK5_skl(sK51_skl,sK51_skl)),sK51_skl)
| ~ ssList(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1155,f1248]) ).
fof(f3373,definition,
( sQ168_spl
<=> segmentP(app(sK51_skl,nil),sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ168_spl])],[split_symbol_definition]) ).
fof(f3374,plain,
( ~ sQ168_spl
| segmentP(app(sK51_skl,nil),sK51_skl) ),
inference(component_clause,[status(thm)],[f3373]) ).
fof(f3376,plain,
( ~ sQ72_spl
| ~ sQ23_spl
| sQ168_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f3369,f445,f3373,f852,f1244]) ).
fof(f3377,definition,
( sQ169_spl
<=> segmentP(app(sK51_skl,sK5_skl(sK51_skl,sK47_skl)),sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f3378,plain,
( ~ sQ169_spl
| segmentP(app(sK51_skl,sK5_skl(sK51_skl,sK47_skl)),sK51_skl) ),
inference(component_clause,[status(thm)],[f3377]) ).
fof(f3380,plain,
( ~ sQ35_spl
| ~ sQ72_spl
| ~ sQ2_spl
| ~ sQ51_spl
| sQ169_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f3370,f828,f3377,f1085,f445,f1244,f944]) ).
fof(f3381,definition,
( sQ170_spl
<=> segmentP(app(sK51_skl,sK5_skl(sK51_skl,sK48_skl)),sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f3382,plain,
( ~ sQ170_spl
| segmentP(app(sK51_skl,sK5_skl(sK51_skl,sK48_skl)),sK51_skl) ),
inference(component_clause,[status(thm)],[f3381]) ).
fof(f3384,plain,
( ~ sQ37_spl
| ~ sQ72_spl
| ~ sQ2_spl
| ~ sQ55_spl
| sQ170_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3371,f831,f3381,f1107,f445,f1244,f988]) ).
fof(f3385,definition,
( sQ171_spl
<=> segmentP(app(sK51_skl,sK5_skl(sK51_skl,sK51_skl)),sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ171_spl])],[split_symbol_definition]) ).
fof(f3388,plain,
( ~ sQ72_spl
| ~ sQ64_spl
| sQ171_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f3372,f445,f3385,f1181,f1244]) ).
fof(f3389,plain,
( ~ sQ168_spl
| ~ sQ2_spl
| segmentP(sK51_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f1013,f3374]) ).
fof(f3391,plain,
( ~ sQ169_spl
| ~ sQ35_spl
| segmentP(sK47_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f945,f3378]) ).
fof(f3392,plain,
( ~ sQ170_spl
| ~ sQ37_spl
| segmentP(sK48_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f989,f3382]) ).
fof(f3393,plain,
! [X0,X1] :
( ~ sQ168_spl
| ~ sQ2_spl
| segmentP(app(app(X0,sK51_skl),X1),sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK51_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f3389,f321]) ).
fof(f3395,plain,
! [X0] :
( ~ sQ168_spl
| ~ sQ2_spl
| segmentP(X0,sK51_skl)
| ~ segmentP(X0,sK51_skl)
| ~ ssList(sK51_skl)
| ~ ssList(sK51_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3389,f315]) ).
fof(f3396,plain,
( ~ sQ168_spl
| ~ sQ2_spl
| app(app(sK7_skl(sK51_skl,sK51_skl),sK51_skl),sK8_skl(sK51_skl,sK51_skl)) = sK51_skl
| ~ ssList(sK51_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f3389,f136]) ).
fof(f3397,definition,
! [X0,X1] :
( sQ172_spl
<=> ( segmentP(app(app(X0,sK51_skl),X1),sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ172_spl])],[split_symbol_definition]) ).
fof(f3400,plain,
( ~ sQ168_spl
| sQ172_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f3393,f445,f3397,f3373]) ).
fof(f3405,definition,
! [X0] :
( sQ174_spl
<=> ( segmentP(X0,sK51_skl)
| ~ segmentP(X0,sK51_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ174_spl])],[split_symbol_definition]) ).
fof(f3408,plain,
( ~ sQ168_spl
| ~ sQ2_spl
| sQ174_spl ),
inference(split_clause,[status(thm)],[f3395,f3405,f445,f3373]) ).
fof(f3409,definition,
( sQ175_spl
<=> app(app(sK7_skl(sK51_skl,sK51_skl),sK51_skl),sK8_skl(sK51_skl,sK51_skl)) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ175_spl])],[split_symbol_definition]) ).
fof(f3412,plain,
( ~ sQ168_spl
| sQ175_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f3396,f445,f3409,f3373]) ).
fof(f3413,plain,
! [X0,X1] :
( ~ sQ169_spl
| ~ sQ35_spl
| segmentP(app(app(X0,sK47_skl),X1),sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK51_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f3391,f321]) ).
fof(f3414,plain,
( ~ sQ169_spl
| ~ sQ35_spl
| sK51_skl = sK47_skl
| ~ segmentP(sK51_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f3391,f317]) ).
fof(f3415,plain,
! [X0] :
( ~ sQ169_spl
| ~ sQ35_spl
| segmentP(X0,sK51_skl)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(sK51_skl)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3391,f315]) ).
fof(f3416,plain,
( ~ sQ169_spl
| ~ sQ35_spl
| app(app(sK7_skl(sK51_skl,sK47_skl),sK51_skl),sK8_skl(sK51_skl,sK47_skl)) = sK47_skl
| ~ ssList(sK51_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f3391,f136]) ).
fof(f3417,definition,
! [X0,X1] :
( sQ176_spl
<=> ( segmentP(app(app(X0,sK47_skl),X1),sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f3420,plain,
( ~ sQ169_spl
| ~ sQ35_spl
| sQ176_spl
| ~ sQ2_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f3413,f828,f445,f3417,f944,f3377]) ).
fof(f3421,definition,
( sQ177_spl
<=> segmentP(sK51_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ177_spl])],[split_symbol_definition]) ).
fof(f3424,plain,
( ~ sQ169_spl
| ~ sQ35_spl
| sQ29_spl
| ~ sQ177_spl
| ~ sQ19_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f3414,f445,f828,f3421,f883,f944,f3377]) ).
fof(f3425,definition,
! [X0] :
( sQ178_spl
<=> ( segmentP(X0,sK51_skl)
| ~ segmentP(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f3428,plain,
( ~ sQ169_spl
| ~ sQ35_spl
| ~ sQ2_spl
| ~ sQ19_spl
| sQ178_spl ),
inference(split_clause,[status(thm)],[f3415,f3425,f828,f445,f944,f3377]) ).
fof(f3429,definition,
( sQ179_spl
<=> app(app(sK7_skl(sK51_skl,sK47_skl),sK51_skl),sK8_skl(sK51_skl,sK47_skl)) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f3432,plain,
( ~ sQ169_spl
| ~ sQ35_spl
| sQ179_spl
| ~ sQ2_spl
| ~ sQ19_spl ),
inference(split_clause,[status(thm)],[f3416,f828,f445,f3429,f944,f3377]) ).
fof(f3433,plain,
( ~ sQ9_spl
| ~ sQ170_spl
| ~ sQ37_spl
| ~ segmentP(sK47_skl,sK51_skl)
| ~ neq(sK51_skl,nil)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f3392,f472]) ).
fof(f3434,plain,
! [X0,X1] :
( ~ sQ170_spl
| ~ sQ37_spl
| segmentP(app(app(X0,sK48_skl),X1),sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0)
| ~ ssList(sK51_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f3392,f321]) ).
fof(f3435,plain,
( ~ sQ170_spl
| ~ sQ37_spl
| sK51_skl = sK48_skl
| ~ segmentP(sK51_skl,sK48_skl)
| ~ ssList(sK48_skl)
| ~ ssList(sK51_skl) ),
inference(resolution,[status(thm)],[f3392,f317]) ).
fof(f3436,plain,
! [X0] :
( ~ sQ170_spl
| ~ sQ37_spl
| segmentP(X0,sK51_skl)
| ~ segmentP(X0,sK48_skl)
| ~ ssList(sK51_skl)
| ~ ssList(sK48_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f3392,f315]) ).
fof(f3437,plain,
( ~ sQ170_spl
| ~ sQ37_spl
| app(app(sK7_skl(sK51_skl,sK48_skl),sK51_skl),sK8_skl(sK51_skl,sK48_skl)) = sK48_skl
| ~ ssList(sK51_skl)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f3392,f136]) ).
fof(f3438,definition,
( sQ180_spl
<=> segmentP(sK47_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f3440,plain,
( sQ180_spl
| ~ segmentP(sK47_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f3438]) ).
fof(f3441,plain,
( ~ sQ9_spl
| ~ sQ170_spl
| ~ sQ37_spl
| ~ sQ180_spl
| ~ sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f3433,f445,f452,f3438,f988,f3381,f471]) ).
fof(f3442,definition,
! [X0,X1] :
( sQ181_spl
<=> ( segmentP(app(app(X0,sK48_skl),X1),sK51_skl)
| ~ ssList(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ181_spl])],[split_symbol_definition]) ).
fof(f3445,plain,
( ~ sQ170_spl
| ~ sQ37_spl
| sQ181_spl
| ~ sQ2_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3434,f831,f445,f3442,f988,f3381]) ).
fof(f3446,definition,
( sQ182_spl
<=> segmentP(sK51_skl,sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ182_spl])],[split_symbol_definition]) ).
fof(f3449,plain,
( ~ sQ170_spl
| ~ sQ37_spl
| sQ27_spl
| ~ sQ182_spl
| ~ sQ20_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f3435,f445,f831,f3446,f876,f988,f3381]) ).
fof(f3450,definition,
! [X0] :
( sQ183_spl
<=> ( segmentP(X0,sK51_skl)
| ~ segmentP(X0,sK48_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ183_spl])],[split_symbol_definition]) ).
fof(f3453,plain,
( ~ sQ170_spl
| ~ sQ37_spl
| ~ sQ2_spl
| ~ sQ20_spl
| sQ183_spl ),
inference(split_clause,[status(thm)],[f3436,f3450,f831,f445,f988,f3381]) ).
fof(f3454,definition,
( sQ184_spl
<=> app(app(sK7_skl(sK51_skl,sK48_skl),sK51_skl),sK8_skl(sK51_skl,sK48_skl)) = sK48_skl ),
introduced(definition,[new_symbols(definition,[sQ184_spl])],[split_symbol_definition]) ).
fof(f3457,plain,
( ~ sQ170_spl
| ~ sQ37_spl
| sQ184_spl
| ~ sQ2_spl
| ~ sQ20_spl ),
inference(split_clause,[status(thm)],[f3437,f831,f445,f3454,f988,f3381]) ).
fof(f3458,plain,
( sQ180_spl
| ~ sQ169_spl
| ~ sQ35_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f3440,f3391]) ).
fof(f3459,plain,
( sQ180_spl
| ~ sQ169_spl
| ~ sQ35_spl ),
inference(contradiction_clause,[status(thm)],[f3458]) ).
fof(f3460,plain,
$false,
inference(sat_refutation,[status(thm)],[f444,f451,f455,f459,f463,f470,f474,f576,f579,f592,f836,f845,f850,f861,f863,f865,f879,f890,f900,f914,f934,f956,f971,f973,f978,f991,f995,f1001,f1008,f1026,f1030,f1037,f1041,f1048,f1052,f1059,f1063,f1073,f1077,f1088,f1092,f1097,f1100,f1110,f1114,f1119,f1122,f1136,f1150,f1152,f1168,f1173,f1188,f1197,f1201,f1207,f1212,f1218,f1222,f1243,f1247,f1254,f1258,f1265,f1269,f1284,f1289,f1293,f1303,f1307,f1319,f1320,f1324,f1330,f1334,f1375,f1402,f1406,f1414,f1418,f1425,f1460,f1467,f1468,f1472,f1514,f1520,f1524,f1529,f1552,f1559,f1564,f1684,f1694,f1726,f1728,f1821,f1827,f1831,f2057,f2181,f2328,f2332,f2339,f2340,f2348,f2373,f2377,f2391,f2438,f2442,f2446,f2474,f2478,f2559,f2563,f2571,f2576,f2583,f2588,f2600,f2607,f2611,f2619,f2623,f2626,f2646,f2655,f2662,f2666,f2670,f2691,f2698,f2704,f2709,f2713,f2885,f2909,f3039,f3054,f3123,f3137,f3141,f3145,f3149,f3151,f3229,f3376,f3380,f3384,f3388,f3400,f3408,f3412,f3420,f3424,f3428,f3432,f3441,f3445,f3449,f3453,f3457,f3459]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC052+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.56 % Computer : n007.cluster.edu
% 0.09/0.56 % Model : x86_64 x86_64
% 0.09/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.56 % Memory : 8046.5625MB
% 0.09/0.56 % OS : Linux 6.8.0-71-generic
% 0.09/0.56 % CPULimit : 300
% 0.09/0.56 % WCLimit : 300
% 0.09/0.56 % DateTime : Mon Sep 21 07:49:36 UTC 2026
% 0.09/0.57 % CPUTime :
% 0.14/0.58 % Drodi V4.1.1
% 9.40/1.88 % Refutation found
% 9.40/1.88 % SZS status Theorem for theBenchmark: Theorem is valid
% 9.40/1.88 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 9.40/1.90 % Elapsed time: 1.324835 seconds
% 9.40/1.90 % CPU time: 10.148976 seconds
% 9.40/1.90 % Total memory used: 181.880 MB
% 9.40/1.90 % Net memory used: 174.746 MB
%------------------------------------------------------------------------------