%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC284+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 : n004.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 02:40:38 PM UTC 2026
% Result : Theorem 3.94s 0.97s
% Output : CNFRefutation 3.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 147
% Syntax : Number of formulae : 571 ( 20 unt; 117 def)
% Number of atoms : 2664 ( 270 equ)
% Maximal formula atoms : 21 ( 4 avg)
% Number of connectives : 3841 (1748 ~;1723 |; 144 &)
% ( 139 <=>; 87 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 130 ( 128 usr; 117 prp; 0-3 aty)
% Number of functors : 31 ( 31 usr; 10 con; 0-2 aty)
% Number of variables : 726 ( 677 !; 49 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ( memberP(U,V)
<=> ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [U] :
( ssList(U)
=> ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [U] :
( ssList(U)
=> ( cyclefreeP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ~ ( leq(W,V)
& leq(V,W) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [U] :
( ssList(U)
=> ( totalorderP(U)
<=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssList(X)
=> ! [Y] :
( ssList(Y)
=> ! [Z] :
( ssList(Z)
=> ( app(app(X,cons(V,Y)),cons(W,Z)) = U
=> ( leq(W,V)
| leq(V,W) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( neq(U,V)
<=> U != V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> ! [X] :
( ssItem(X)
=> ( cons(W,U) = cons(X,V)
=> ( V = U
& W = X ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> hd(cons(V,U)) = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> tl(cons(V,U)) = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssItem(W)
=> cons(W,app(V,U)) = app(cons(W,V),U) ) ) ),
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(f29,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( ( leq(V,U)
& leq(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssItem(W)
=> ( ( leq(V,W)
& leq(U,V) )
=> leq(U,W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [U] :
( ssItem(U)
=> leq(U,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f79,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(W,V) = app(U,V)
=> W = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(V,W) = app(V,U)
=> W = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) = app(cons(V,nil),U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f82,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> app(app(U,V),W) = app(U,app(V,W)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( neq(X,nil)
& ! [X3] :
( ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3) ) )
| ( nil = X
& nil != W )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ! [X2] :
( ssItem(X2)
=> ( ( leq(Y,X2)
| ~ memberP(X1,X2) )
& ( leq(X2,Y)
| ~ memberP(Z,X2) ) ) )
| app(app(Z,cons(Y,nil)),X1) != U
| ~ ssList(X1) ) ) )
| 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] :
( ( neq(X,nil)
& ! [X3] :
( ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3) ) )
| ( nil = X
& nil != W )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ! [X2] :
( ssItem(X2)
=> ( ( leq(Y,X2)
| ~ memberP(X1,X2) )
& ( leq(X2,Y)
| ~ memberP(Z,X2) ) ) )
| app(app(Z,cons(Y,nil)),X1) != U
| ~ ssList(X1) ) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f106,plain,
! [U] :
( ! [V] :
( ( memberP(U,V)
<=> ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f107,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(W,cons(V,X)) != U
| ~ ssList(X) )
| ~ ssList(W) )
| memberP(U,V) )
& ( ? [W] :
( ? [X] :
( app(W,cons(V,X)) = U
& ssList(X) )
& ssList(W) )
| ~ memberP(U,V) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f106]) ).
fof(f108,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(W,cons(V,X)) != U
| ~ ssList(X) )
| ~ ssList(W) )
| memberP(U,V) )
& ( ( app(sK2_skl(V,U),cons(V,sK3_skl(V,U))) = U
& ssList(sK3_skl(V,U))
& ssList(sK2_skl(V,U)) )
| ~ memberP(U,V) ) )
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(W,sK2_skl(V,U)),skolemize(X,sK3_skl(V,U))],[f107]) ).
fof(f111,plain,
! [X0,X1] :
( app(sK2_skl(X1,X0),cons(X1,sK3_skl(X1,X0))) = X0
| ~ memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f112,plain,
! [X0,X1,X2,X3] :
( app(X2,cons(X1,X3)) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| memberP(X0,X1)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
fof(f113,plain,
! [U] :
( ( singletonP(U)
<=> ? [V] :
( cons(V,nil) = U
& ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f114,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ? [V] :
( cons(V,nil) = U
& ssItem(V) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f113]) ).
fof(f115,plain,
! [U] :
( ( ( ! [V] :
( cons(V,nil) != U
| ~ ssItem(V) )
| singletonP(U) )
& ( ( cons(sK4_skl(U),nil) = U
& ssItem(sK4_skl(U)) )
| ~ singletonP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl]),skolemize(V,sK4_skl(U))],[f114]) ).
fof(f117,plain,
! [X0] :
( cons(sK4_skl(X0),nil) = X0
| ~ singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f118,plain,
! [X0,X1] :
( cons(X1,nil) != X0
| ~ ssItem(X1)
| singletonP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f115]) ).
fof(f119,plain,
! [U] :
( ! [V] :
( ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f120,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ? [W] :
( app(V,W) = U
& ssList(W) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ( app(V,sK5_skl(V,U)) = U
& ssList(sK5_skl(V,U)) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120]) ).
fof(f123,plain,
! [X0,X1] :
( app(X1,sK5_skl(X1,X0)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f124,plain,
! [X0,X1,X2] :
( app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f125,plain,
! [U] :
( ! [V] :
( ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f126,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ? [W] :
( app(W,V) = U
& ssList(W) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ( app(sK6_skl(V,U),V) = U
& ssList(sK6_skl(V,U)) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126]) ).
fof(f129,plain,
! [X0,X1] :
( app(sK6_skl(X1,X0),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f130,plain,
! [X0,X1,X2] :
( app(X2,X1) != X0
| ~ ssList(X2)
| rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f131,plain,
! [U] :
( ! [V] :
( ( segmentP(U,V)
<=> ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f132,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ? [W] :
( ? [X] :
( app(app(W,V),X) = U
& ssList(X) )
& ssList(W) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f131]) ).
fof(f133,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( ! [X] :
( app(app(W,V),X) != U
| ~ ssList(X) )
| ~ ssList(W) )
| segmentP(U,V) )
& ( ( app(app(sK7_skl(V,U),V),sK8_skl(V,U)) = U
& ssList(sK8_skl(V,U))
& ssList(sK7_skl(V,U)) )
| ~ segmentP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl]),skolemize(W,sK7_skl(V,U)),skolemize(X,sK8_skl(V,U))],[f132]) ).
fof(f136,plain,
! [X0,X1] :
( app(app(sK7_skl(X1,X0),X1),sK8_skl(X1,X0)) = X0
| ~ segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f137,plain,
! [X0,X1,X2,X3] :
( app(app(X2,X1),X3) != X0
| ~ ssList(X3)
| ~ ssList(X2)
| segmentP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f138,plain,
! [U] :
( ( cyclefreeP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f139,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( leq(W,V)
& leq(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| cyclefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ cyclefreeP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f138]) ).
fof(f140,plain,
! [U] :
( ( ( ( leq(sK10_skl(U),sK9_skl(U))
& leq(sK9_skl(U),sK10_skl(U))
& app(app(sK11_skl(U),cons(sK9_skl(U),sK12_skl(U))),cons(sK10_skl(U),sK13_skl(U))) = U
& ssList(sK13_skl(U))
& ssList(sK12_skl(U))
& ssList(sK11_skl(U))
& ssItem(sK10_skl(U))
& ssItem(sK9_skl(U)) )
| cyclefreeP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( ~ leq(W,V)
| ~ leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ cyclefreeP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK9_skl,sK10_skl,sK11_skl,sK12_skl,sK13_skl]),skolemize(V,sK9_skl(U)),skolemize(W,sK10_skl(U)),skolemize(X,sK11_skl(U)),skolemize(Y,sK12_skl(U)),skolemize(Z,sK13_skl(U))],[f139]) ).
fof(f141,plain,
! [X0,X1,X2,X3,X4,X5] :
( ~ leq(X2,X1)
| ~ leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ cyclefreeP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f150,plain,
! [U] :
( ( totalorderP(U)
<=> ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(W,V)
| leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) ) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f151,plain,
! [U] :
( ( ( ? [V] :
( ? [W] :
( ? [X] :
( ? [Y] :
( ? [Z] :
( ~ leq(W,V)
& ~ leq(V,W)
& app(app(X,cons(V,Y)),cons(W,Z)) = U
& ssList(Z) )
& ssList(Y) )
& ssList(X) )
& ssItem(W) )
& ssItem(V) )
| totalorderP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(W,V)
| leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderP(U) ) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f150]) ).
fof(f152,plain,
! [U] :
( ( ( ( ~ leq(sK15_skl(U),sK14_skl(U))
& ~ leq(sK14_skl(U),sK15_skl(U))
& app(app(sK16_skl(U),cons(sK14_skl(U),sK17_skl(U))),cons(sK15_skl(U),sK18_skl(U))) = U
& ssList(sK18_skl(U))
& ssList(sK17_skl(U))
& ssList(sK16_skl(U))
& ssItem(sK15_skl(U))
& ssItem(sK14_skl(U)) )
| totalorderP(U) )
& ( ! [V] :
( ! [W] :
( ! [X] :
( ! [Y] :
( ! [Z] :
( leq(W,V)
| leq(V,W)
| app(app(X,cons(V,Y)),cons(W,Z)) != U
| ~ ssList(Z) )
| ~ ssList(Y) )
| ~ ssList(X) )
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ totalorderP(U) ) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK14_skl,sK15_skl,sK16_skl,sK17_skl,sK18_skl]),skolemize(V,sK14_skl(U)),skolemize(W,sK15_skl(U)),skolemize(X,sK16_skl(U)),skolemize(Y,sK17_skl(U)),skolemize(Z,sK18_skl(U))],[f151]) ).
fof(f153,plain,
! [X0,X1,X2,X3,X4,X5] :
( leq(X2,X1)
| leq(X1,X2)
| app(app(X3,cons(X1,X4)),cons(X2,X5)) != X0
| ~ ssList(X5)
| ~ ssList(X4)
| ~ ssList(X3)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ totalorderP(X0)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f152]) ).
fof(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(f221,plain,
! [U] :
( ! [V] :
( ssList(cons(V,U))
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f222,plain,
! [X0,X1] :
( ssList(cons(X1,X0))
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f221]) ).
fof(f223,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f226,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( V = U
& W = X )
| cons(W,U) != cons(X,V)
| ~ ssItem(X) )
| ~ ssItem(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f227,plain,
! [X0,X1,X2,X3] :
( X2 = X3
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f228,plain,
! [X0,X1,X2,X3] :
( X1 = X0
| cons(X2,X0) != cons(X3,X1)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f226]) ).
fof(f234,plain,
! [U] :
( ! [V] :
( nil != cons(V,U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f235,plain,
! [X0,X1] :
( nil != cons(X1,X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f234]) ).
fof(f238,plain,
! [U] :
( ! [V] :
( hd(cons(V,U)) = V
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f23]) ).
fof(f239,plain,
! [X0,X1] :
( hd(cons(X1,X0)) = X1
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f238]) ).
fof(f242,plain,
! [U] :
( ! [V] :
( tl(cons(V,U)) = U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f25]) ).
fof(f243,plain,
! [X0,X1] :
( tl(cons(X1,X0)) = X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f242]) ).
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(f246,plain,
! [U] :
( ! [V] :
( ! [W] :
( cons(W,app(V,U)) = app(cons(W,V),U)
| ~ ssItem(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f27]) ).
fof(f247,plain,
! [X0,X1,X2] :
( cons(X2,app(X1,X0)) = app(cons(X2,X1),X0)
| ~ ssItem(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f246]) ).
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(f250,plain,
! [U] :
( ! [V] :
( U = V
| ~ leq(V,U)
| ~ leq(U,V)
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f29]) ).
fof(f251,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X1,X0)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f250]) ).
fof(f252,plain,
! [U] :
( ! [V] :
( ! [W] :
( leq(U,W)
| ~ leq(V,W)
| ~ leq(U,V)
| ~ ssItem(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f253,plain,
! [X0,X1,X2] :
( leq(X0,X2)
| ~ leq(X1,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f252]) ).
fof(f254,plain,
! [U] :
( leq(U,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f31]) ).
fof(f255,plain,
! [X0] :
( leq(X0,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f254]) ).
fof(f268,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f269,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& ~ memberP(V,U) )
| memberP(app(V,W),U) )
& ( memberP(W,U)
| memberP(V,U)
| ~ memberP(app(V,W),U) ) )
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f268]) ).
fof(f270,plain,
! [X0,X1,X2] :
( memberP(X2,X0)
| memberP(X1,X0)
| ~ memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f271,plain,
! [X0,X1,X2] :
( ~ memberP(X1,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f272,plain,
! [X0,X1,X2] :
( ~ memberP(X2,X0)
| memberP(app(X1,X2),X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
fof(f273,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f37]) ).
fof(f274,plain,
! [U] :
( ! [V] :
( ! [W] :
( ( ( ( ~ memberP(W,U)
& U != V )
| memberP(cons(V,W),U) )
& ( memberP(W,U)
| U = V
| ~ memberP(cons(V,W),U) ) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f273]) ).
fof(f275,plain,
! [X0,X1,X2] :
( memberP(X2,X0)
| X0 = X1
| ~ memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f276,plain,
! [X0,X1,X2] :
( X0 != X1
| memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f277,plain,
! [X0,X1,X2] :
( ~ memberP(X2,X0)
| memberP(cons(X1,X2),X0)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f274]) ).
fof(f278,plain,
! [U] :
( ~ memberP(nil,U)
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f38]) ).
fof(f279,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f278]) ).
fof(f375,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(W,V) != app(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f79]) ).
fof(f376,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f375]) ).
fof(f377,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(V,W) != app(V,U)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f80]) ).
fof(f378,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f377]) ).
fof(f379,plain,
! [U] :
( ! [V] :
( cons(V,U) = app(cons(V,nil),U)
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f81]) ).
fof(f380,plain,
! [X0,X1] :
( cons(X1,X0) = app(cons(X1,nil),X0)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f379]) ).
fof(f381,plain,
! [U] :
( ! [V] :
( ! [W] :
( app(app(U,V),W) = app(U,app(V,W))
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f82]) ).
fof(f382,plain,
! [X0,X1,X2] :
( app(app(X0,X1),X2) = app(X0,app(X1,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f381]) ).
fof(f383,plain,
! [U] :
( ! [V] :
( ( nil = app(U,V)
<=> ( nil = U
& nil = V ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f83]) ).
fof(f384,plain,
! [U] :
( ! [V] :
( ( ( nil != U
| nil != V
| nil = app(U,V) )
& ( ( nil = U
& nil = V )
| nil != app(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f383]) ).
fof(f385,plain,
! [X0,X1] :
( nil = X1
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f386,plain,
! [X0,X1] :
( nil = X0
| nil != app(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f384]) ).
fof(f388,plain,
! [U] :
( app(U,nil) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f84]) ).
fof(f389,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f388]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [X3] :
( memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) ) )
& ( nil != X
| nil = W )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ( ( ~ leq(Y,X2)
& memberP(X1,X2) )
| ( ~ leq(X2,Y)
& memberP(Z,X2) ) )
& ssItem(X2) )
& app(app(Z,cons(Y,nil)),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f97]) ).
fof(f416,definition,
! [Y,Z,X2] :
( sP0_prd(X2,Z,Y)
<=> ( ~ leq(X2,Y)
& memberP(Z,X2) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ~ neq(X,nil)
| ? [X3] :
( memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) ) )
& ( nil != X
| nil = W )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ( ( ~ leq(Y,X2)
& memberP(X1,X2) )
| sP0_prd(X2,Z,Y) )
& ssItem(X2) )
& app(app(Z,cons(Y,nil)),X1) = U
& ssList(X1) )
& ssList(Z) )
& ssItem(Y) )
& U = W
& V = X
& ssList(X) )
& ssList(W) )
& ssList(V) )
& ssList(U) ),
inference(formula_renaming,[status(thm)],[f415,f416]) ).
fof(f418,plain,
( ( ~ neq(sK50_skl,nil)
| ( memberP(sK50_skl,sK55_skl)
& cons(sK55_skl,nil) = sK49_skl
& ssItem(sK55_skl) ) )
& ( nil != sK50_skl
| nil = sK49_skl )
& ( ( ~ leq(sK51_skl,sK54_skl)
& memberP(sK53_skl,sK54_skl) )
| sP0_prd(sK54_skl,sK52_skl,sK51_skl) )
& ssItem(sK54_skl)
& app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK47_skl
& ssList(sK53_skl)
& ssList(sK52_skl)
& ssItem(sK51_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,sK52_skl,sK53_skl,sK54_skl,sK55_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl),skolemize(X1,sK53_skl),skolemize(X2,sK54_skl),skolemize(X3,sK55_skl)],[f417]) ).
fof(f419,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f420,plain,
ssList(sK48_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
ssItem(sK51_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
ssList(sK53_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK47_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
ssItem(sK54_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f430,plain,
( memberP(sK53_skl,sK54_skl)
| sP0_prd(sK54_skl,sK52_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f431,plain,
( ~ leq(sK51_skl,sK54_skl)
| sP0_prd(sK54_skl,sK52_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f432,plain,
( nil != sK50_skl
| nil = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f433,plain,
( ~ neq(sK50_skl,nil)
| ssItem(sK55_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f434,plain,
( ~ neq(sK50_skl,nil)
| cons(sK55_skl,nil) = sK49_skl ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f435,plain,
( ~ neq(sK50_skl,nil)
| memberP(sK50_skl,sK55_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f436,plain,
! [Y,Z,X2] :
( ( leq(X2,Y)
| ~ memberP(Z,X2)
| sP0_prd(X2,Z,Y) )
& ( ( ~ leq(X2,Y)
& memberP(Z,X2) )
| ~ sP0_prd(X2,Z,Y) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f437,plain,
( ! [Y,Z,X2] :
( leq(X2,Y)
| ~ memberP(Z,X2)
| sP0_prd(X2,Z,Y) )
& ! [Y,Z,X2] :
( ( ~ leq(X2,Y)
& memberP(Z,X2) )
| ~ sP0_prd(X2,Z,Y) ) ),
inference(miniscoping,[status(thm)],[f436]) ).
fof(f438,plain,
! [X0,X1,X2] :
( memberP(X1,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f437]) ).
fof(f439,plain,
! [X0,X1,X2] :
( ~ leq(X0,X2)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f437]) ).
fof(f441,definition,
( sQ0_spl
<=> sP0_prd(sK54_skl,sK52_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f442,plain,
( ~ sQ0_spl
| sP0_prd(sK54_skl,sK52_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f441]) ).
fof(f444,definition,
( sQ1_spl
<=> memberP(sK53_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f445,plain,
( ~ sQ1_spl
| memberP(sK53_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f444]) ).
fof(f447,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f430,f441,f444]) ).
fof(f448,definition,
( sQ2_spl
<=> leq(sK51_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f450,plain,
( sQ2_spl
| ~ leq(sK51_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f448]) ).
fof(f451,plain,
( ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f431,f441,f448]) ).
fof(f452,definition,
( sQ3_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f453,plain,
( ~ sQ3_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f452]) ).
fof(f455,definition,
( sQ4_spl
<=> nil = sK50_skl ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f457,plain,
( sQ4_spl
| nil != sK50_skl ),
inference(component_clause,[status(thm)],[f455]) ).
fof(f458,plain,
( ~ sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f432,f452,f455]) ).
fof(f459,definition,
( sQ5_spl
<=> ssItem(sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f462,definition,
( sQ6_spl
<=> neq(sK50_skl,nil) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f464,plain,
( sQ6_spl
| ~ neq(sK50_skl,nil) ),
inference(component_clause,[status(thm)],[f462]) ).
fof(f465,plain,
( ~ sQ6_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f433,f459,f462]) ).
fof(f466,definition,
( sQ7_spl
<=> cons(sK55_skl,nil) = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f467,plain,
( ~ sQ7_spl
| cons(sK55_skl,nil) = sK49_skl ),
inference(component_clause,[status(thm)],[f466]) ).
fof(f469,plain,
( ~ sQ6_spl
| sQ7_spl ),
inference(split_clause,[status(thm)],[f434,f466,f462]) ).
fof(f470,definition,
( sQ8_spl
<=> memberP(sK50_skl,sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f473,plain,
( ~ sQ6_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f435,f470,f462]) ).
fof(f476,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X0)
| memberP(app(X0,cons(X1,X2)),X1)
| ~ ssItem(X1)
| ~ ssList(app(X0,cons(X1,X2))) ),
inference(destructive_equality_resolution,[status(thm)],[f112]) ).
fof(f477,plain,
! [X0] :
( ~ ssItem(X0)
| singletonP(cons(X0,nil))
| ~ ssList(cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f118]) ).
fof(f478,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f479,plain,
! [X0,X1] :
( ~ ssList(X0)
| rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f480,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(f481,plain,
! [X0,X1,X2,X3,X4] :
( ~ leq(X3,X1)
| ~ leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
inference(destructive_equality_resolution,[status(thm)],[f141]) ).
fof(f482,plain,
! [X0,X1,X2,X3,X4] :
( leq(X3,X1)
| leq(X1,X3)
| ~ ssList(X4)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X3)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),cons(X3,X4)))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(X3,X4))) ),
inference(destructive_equality_resolution,[status(thm)],[f153]) ).
fof(f491,plain,
! [X1,X2] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f276]) ).
fof(f492,plain,
! [X0,X1] :
( memberP(cons(X0,X1),X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f491]) ).
fof(f506,plain,
( sQ6_spl
| ~ neq(sK48_skl,nil) ),
inference(forward_demodulation,[status(thm)],[f423,f464]) ).
fof(f516,definition,
( sQ11_spl
<=> sK48_skl = nil ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f517,plain,
( ~ sQ11_spl
| sK48_skl = nil ),
inference(component_clause,[status(thm)],[f516]) ).
fof(f524,plain,
( ~ sQ3_spl
| nil = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f424,f453]) ).
fof(f529,definition,
( sQ12_spl
<=> nil = nil ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f535,plain,
! [X0] :
( ~ sQ7_spl
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(app(X0,sK49_skl),sK55_skl)
| ~ ssItem(sK55_skl)
| ~ ssList(app(X0,cons(sK55_skl,nil))) ),
inference(paramodulation,[status(thm)],[f467,f476]) ).
fof(f536,definition,
! [X0] :
( sQ13_spl
<=> ( ~ ssList(X0)
| memberP(app(X0,sK49_skl),sK55_skl)
| ~ ssList(app(X0,cons(sK55_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ13_spl])],[split_symbol_definition]) ).
fof(f539,definition,
( sQ14_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ14_spl])],[split_symbol_definition]) ).
fof(f541,plain,
( sQ14_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f539]) ).
fof(f542,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ5_spl
| sQ13_spl ),
inference(split_clause,[status(thm)],[f535,f536,f459,f539,f466]) ).
fof(f543,plain,
( sQ14_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f541,f223]) ).
fof(f544,plain,
sQ14_spl,
inference(contradiction_clause,[status(thm)],[f543]) ).
fof(f547,plain,
( sQ6_spl
| sK48_skl = nil
| ~ ssList(nil)
| ~ ssList(sK48_skl) ),
inference(resolution,[status(thm)],[f220,f506]) ).
fof(f550,definition,
( sQ15_spl
<=> ssList(sK48_skl) ),
introduced(definition,[new_symbols(definition,[sQ15_spl])],[split_symbol_definition]) ).
fof(f552,plain,
( sQ15_spl
| ~ ssList(sK48_skl) ),
inference(component_clause,[status(thm)],[f550]) ).
fof(f553,plain,
( sQ6_spl
| sQ11_spl
| ~ sQ14_spl
| ~ sQ15_spl ),
inference(split_clause,[status(thm)],[f547,f550,f539,f516,f462]) ).
fof(f554,plain,
( sQ15_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f552,f420]) ).
fof(f555,plain,
sQ15_spl,
inference(contradiction_clause,[status(thm)],[f554]) ).
fof(f557,plain,
! [X0,X1] :
( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(equality_resolution,[status(thm)],[f227]) ).
fof(f558,definition,
! [X0] :
( sQ16_spl
<=> ( ~ ssList(X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ16_spl])],[split_symbol_definition]) ).
fof(f559,plain,
! [X0] :
( ~ sQ16_spl
| ~ ssList(X0)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f558]) ).
fof(f561,definition,
! [X1] :
( sQ17_spl
<=> ( X1 = X1
| ~ ssItem(X1)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ17_spl])],[split_symbol_definition]) ).
fof(f564,plain,
( sQ17_spl
| sQ16_spl ),
inference(split_clause,[status(thm)],[f557,f558,f561]) ).
fof(f565,plain,
! [X0] :
( ~ sQ16_spl
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f559]) ).
fof(f566,plain,
( ~ sQ16_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f420,f565]) ).
fof(f570,plain,
~ sQ16_spl,
inference(contradiction_clause,[status(thm)],[f566]) ).
fof(f572,plain,
( ~ sQ7_spl
| ~ ssItem(sK55_skl)
| singletonP(sK49_skl)
| ~ ssList(cons(sK55_skl,nil)) ),
inference(paramodulation,[status(thm)],[f467,f477]) ).
fof(f573,definition,
( sQ18_spl
<=> ssList(cons(sK55_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f575,plain,
( sQ18_spl
| ~ ssList(cons(sK55_skl,nil)) ),
inference(component_clause,[status(thm)],[f573]) ).
fof(f576,definition,
( sQ19_spl
<=> singletonP(sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ19_spl])],[split_symbol_definition]) ).
fof(f579,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| sQ19_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f572,f573,f576,f459,f466]) ).
fof(f584,plain,
( ~ sQ11_spl
| nil = sK50_skl ),
inference(backward_demodulation,[status(thm)],[f517,f423]) ).
fof(f591,plain,
( ~ sQ0_spl
| ~ leq(sK54_skl,sK51_skl) ),
inference(resolution,[status(thm)],[f442,f439]) ).
fof(f592,plain,
( ~ sQ0_spl
| memberP(sK52_skl,sK54_skl) ),
inference(resolution,[status(thm)],[f442,f438]) ).
fof(f604,definition,
( sQ22_spl
<=> ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ22_spl])],[split_symbol_definition]) ).
fof(f606,plain,
( sQ22_spl
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f604]) ).
fof(f607,definition,
( sQ23_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ23_spl])],[split_symbol_definition]) ).
fof(f609,plain,
( sQ23_spl
| ~ ssList(sK53_skl) ),
inference(component_clause,[status(thm)],[f607]) ).
fof(f615,plain,
! [X0,X1] :
( ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| X0 = nil
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f228,f117]) ).
fof(f618,definition,
! [X0,X1] :
( sQ24_spl
<=> ( ~ singletonP(cons(X1,X0))
| ~ ssList(cons(X1,X0))
| X0 = nil
| ~ ssItem(X1)
| ~ ssItem(sK4_skl(cons(X1,X0)))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f621,plain,
( sQ24_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f615,f539,f618]) ).
fof(f631,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f478,f245]) ).
fof(f632,plain,
( sQ4_spl
| ~ sQ11_spl
| nil != nil ),
inference(forward_demodulation,[status(thm)],[f584,f457]) ).
fof(f633,plain,
( sQ4_spl
| ~ sQ11_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f632]) ).
fof(f634,plain,
( sQ4_spl
| ~ sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f633]) ).
fof(f638,plain,
( ~ sQ3_spl
| app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = nil ),
inference(forward_demodulation,[status(thm)],[f524,f428]) ).
fof(f646,plain,
( sQ23_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f609,f427]) ).
fof(f647,plain,
sQ23_spl,
inference(contradiction_clause,[status(thm)],[f646]) ).
fof(f649,plain,
! [X0] :
( ~ sQ3_spl
| ~ memberP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| memberP(nil,X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f638,f271]) ).
fof(f650,definition,
! [X0] :
( sQ28_spl
<=> ( ~ memberP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ28_spl])],[split_symbol_definition]) ).
fof(f651,plain,
! [X0] :
( ~ sQ28_spl
| ~ memberP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| memberP(nil,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f650]) ).
fof(f653,plain,
( ~ sQ3_spl
| ~ sQ23_spl
| ~ sQ22_spl
| sQ28_spl ),
inference(split_clause,[status(thm)],[f649,f650,f604,f607,f452]) ).
fof(f659,plain,
! [X0,X1,X2,X3] :
( ~ leq(X3,X2)
| ~ leq(X1,X3)
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssItem(X1)
| leq(X0,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f253,f253]) ).
fof(f661,plain,
! [X0] :
( ~ sQ0_spl
| ~ leq(X0,sK51_skl)
| ~ leq(sK54_skl,X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0)
| ~ ssItem(sK54_skl) ),
inference(resolution,[status(thm)],[f253,f591]) ).
fof(f664,plain,
! [X0,X1,X2,X3] :
( ~ leq(X3,X2)
| ~ leq(X1,X3)
| ~ ssItem(X3)
| leq(X0,X2)
| ~ leq(X0,X1)
| ~ ssItem(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f659]) ).
fof(f665,definition,
( sQ30_spl
<=> ssItem(sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ30_spl])],[split_symbol_definition]) ).
fof(f667,plain,
( sQ30_spl
| ~ ssItem(sK54_skl) ),
inference(component_clause,[status(thm)],[f665]) ).
fof(f668,definition,
! [X0] :
( sQ31_spl
<=> ( ~ leq(X0,sK51_skl)
| ~ leq(sK54_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ31_spl])],[split_symbol_definition]) ).
fof(f669,plain,
! [X0] :
( ~ sQ31_spl
| ~ leq(X0,sK51_skl)
| ~ leq(sK54_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f668]) ).
fof(f671,definition,
( sQ32_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ32_spl])],[split_symbol_definition]) ).
fof(f673,plain,
( sQ32_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f671]) ).
fof(f674,plain,
( ~ sQ0_spl
| ~ sQ32_spl
| sQ31_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f661,f665,f668,f671,f441]) ).
fof(f677,plain,
( sQ32_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f673,f425]) ).
fof(f678,plain,
sQ32_spl,
inference(contradiction_clause,[status(thm)],[f677]) ).
fof(f679,plain,
( sQ30_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f667,f429]) ).
fof(f680,plain,
sQ30_spl,
inference(contradiction_clause,[status(thm)],[f679]) ).
fof(f682,plain,
( ~ sQ31_spl
| ~ ssItem(sK54_skl)
| ~ leq(sK54_skl,sK51_skl)
| ~ ssItem(sK54_skl) ),
inference(resolution,[status(thm)],[f669,f255]) ).
fof(f687,definition,
( sQ34_spl
<=> leq(sK54_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ34_spl])],[split_symbol_definition]) ).
fof(f689,plain,
( sQ34_spl
| ~ leq(sK54_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f687]) ).
fof(f690,plain,
( ~ sQ31_spl
| ~ sQ34_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f682,f665,f687,f668]) ).
fof(f700,plain,
! [X0] :
( sQ2_spl
| ~ leq(X0,sK54_skl)
| ~ leq(sK51_skl,X0)
| ~ ssItem(sK54_skl)
| ~ ssItem(X0)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f450,f253]) ).
fof(f701,definition,
! [X0] :
( sQ36_spl
<=> ( ~ leq(X0,sK54_skl)
| ~ leq(sK51_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ36_spl])],[split_symbol_definition]) ).
fof(f702,plain,
! [X0] :
( ~ sQ36_spl
| ~ leq(X0,sK54_skl)
| ~ leq(sK51_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f701]) ).
fof(f704,plain,
( sQ2_spl
| ~ sQ30_spl
| sQ36_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f700,f671,f701,f665,f448]) ).
fof(f714,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(app(X1,X0),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f479,f245]) ).
fof(f720,plain,
! [X0,X1] :
( ~ sQ36_spl
| ~ leq(X1,X0)
| ~ leq(sK51_skl,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f702,f253]) ).
fof(f722,definition,
! [X0,X1] :
( sQ39_spl
<=> ( ~ leq(X1,X0)
| ~ leq(sK51_skl,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ39_spl])],[split_symbol_definition]) ).
fof(f723,plain,
! [X0,X1] :
( ~ sQ39_spl
| ~ leq(X1,X0)
| ~ leq(sK51_skl,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f722]) ).
fof(f725,plain,
( ~ sQ36_spl
| ~ sQ32_spl
| sQ39_spl ),
inference(split_clause,[status(thm)],[f720,f722,f671,f701]) ).
fof(f727,plain,
! [X0,X1] :
( ~ sQ39_spl
| ~ leq(X1,X0)
| ~ leq(sK51_skl,X1)
| ~ ssItem(X1)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f723]) ).
fof(f743,definition,
( sQ42_spl
<=> sK54_skl = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ42_spl])],[split_symbol_definition]) ).
fof(f744,plain,
( ~ sQ42_spl
| sK54_skl = sK51_skl ),
inference(component_clause,[status(thm)],[f743]) ).
fof(f863,definition,
! [X0] :
( sQ55_spl
<=> ( leq(X0,sK54_skl)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ55_spl])],[split_symbol_definition]) ).
fof(f1208,definition,
! [X2,X3] :
( sQ89_spl
<=> ( ~ leq(X2,X3)
| ~ leq(X3,sK51_skl)
| ~ ssItem(X3)
| ~ leq(sK51_skl,X2)
| ~ ssItem(X2) ) ),
introduced(definition,[new_symbols(definition,[sQ89_spl])],[split_symbol_definition]) ).
fof(f1209,plain,
! [X0,X1] :
( ~ sQ89_spl
| ~ leq(X0,X1)
| ~ leq(X1,sK51_skl)
| ~ ssItem(X1)
| ~ leq(sK51_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1208]) ).
fof(f1213,definition,
! [X2] :
( sQ90_spl
<=> ( ~ leq(X2,sK51_skl)
| ~ leq(sK51_skl,X2)
| ~ ssItem(X2) ) ),
introduced(definition,[new_symbols(definition,[sQ90_spl])],[split_symbol_definition]) ).
fof(f1214,plain,
! [X0] :
( ~ sQ90_spl
| ~ leq(X0,sK51_skl)
| ~ leq(sK51_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1213]) ).
fof(f1399,definition,
! [X0] :
( sQ103_spl
<=> ( leq(X0,sK51_skl)
| ~ leq(X0,sK51_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ103_spl])],[split_symbol_definition]) ).
fof(f1410,definition,
! [X3] :
( sQ104_spl
<=> ( ~ leq(X3,sK54_skl)
| ~ leq(sK54_skl,X3)
| ~ ssItem(X3) ) ),
introduced(definition,[new_symbols(definition,[sQ104_spl])],[split_symbol_definition]) ).
fof(f1411,plain,
! [X0] :
( ~ sQ104_spl
| ~ leq(X0,sK54_skl)
| ~ leq(sK54_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1410]) ).
fof(f1415,definition,
( sQ105_spl
<=> leq(sK54_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ105_spl])],[split_symbol_definition]) ).
fof(f1416,plain,
( ~ sQ105_spl
| leq(sK54_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f1415]) ).
fof(f1417,plain,
( sQ105_spl
| ~ leq(sK54_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f1415]) ).
fof(f1454,plain,
! [X0] :
( app(X0,nil) = X0
| ~ ssList(app(X0,nil))
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssList(app(X0,nil)) ),
inference(resolution,[status(thm)],[f389,f376]) ).
fof(f1456,definition,
! [X0] :
( sQ109_spl
<=> ( app(X0,nil) = X0
| ~ ssList(app(X0,nil))
| ~ ssList(X0)
| ~ ssList(app(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ109_spl])],[split_symbol_definition]) ).
fof(f1459,plain,
( ~ sQ14_spl
| sQ109_spl ),
inference(split_clause,[status(thm)],[f1454,f1456,f539]) ).
fof(f1462,plain,
( sQ22_spl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl) ),
inference(resolution,[status(thm)],[f606,f245]) ).
fof(f1463,definition,
( sQ110_spl
<=> ssList(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ110_spl])],[split_symbol_definition]) ).
fof(f1465,plain,
( sQ110_spl
| ~ ssList(sK52_skl) ),
inference(component_clause,[status(thm)],[f1463]) ).
fof(f1466,definition,
( sQ111_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ111_spl])],[split_symbol_definition]) ).
fof(f1468,plain,
( sQ111_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f1466]) ).
fof(f1469,plain,
( sQ22_spl
| ~ sQ111_spl
| ~ sQ110_spl ),
inference(split_clause,[status(thm)],[f1462,f1463,f1466,f604]) ).
fof(f1470,plain,
( sQ110_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1465,f426]) ).
fof(f1471,plain,
sQ110_spl,
inference(contradiction_clause,[status(thm)],[f1470]) ).
fof(f1472,plain,
( sQ111_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f1468,f222]) ).
fof(f1473,plain,
( sQ111_spl
| ~ sQ32_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1472,f539,f671,f1466]) ).
fof(f1474,plain,
! [X0] :
( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(app(nil,X0))
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f378,f249]) ).
fof(f1479,definition,
! [X0] :
( sQ112_spl
<=> ( ~ ssList(app(nil,X0))
| app(nil,X0) = X0
| ~ ssList(app(nil,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ112_spl])],[split_symbol_definition]) ).
fof(f1482,plain,
( ~ sQ14_spl
| sQ112_spl ),
inference(split_clause,[status(thm)],[f1474,f1479,f539]) ).
fof(f1491,plain,
( sQ18_spl
| ~ ssItem(sK55_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f575,f222]) ).
fof(f1492,plain,
( sQ18_spl
| ~ sQ5_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1491,f539,f459,f573]) ).
fof(f1494,plain,
( ~ sQ7_spl
| cons(sK55_skl,nil) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f424,f467]) ).
fof(f1495,plain,
! [X0] :
( ~ sQ7_spl
| cons(sK55_skl,X0) = app(sK47_skl,X0)
| ~ ssItem(sK55_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1494,f380]) ).
fof(f1496,plain,
( ~ sQ7_spl
| ~ ssItem(sK55_skl)
| singletonP(sK47_skl)
| ~ ssList(cons(sK55_skl,nil)) ),
inference(paramodulation,[status(thm)],[f1494,f477]) ).
fof(f1497,plain,
( ~ sQ7_spl
| tl(sK47_skl) = nil
| ~ ssItem(sK55_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1494,f243]) ).
fof(f1498,plain,
( ~ sQ7_spl
| hd(sK47_skl) = sK55_skl
| ~ ssItem(sK55_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1494,f239]) ).
fof(f1499,plain,
! [X0] :
( ~ sQ7_spl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK55_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1494,f275]) ).
fof(f1501,plain,
( ~ sQ7_spl
| memberP(sK47_skl,sK55_skl)
| ~ ssList(nil)
| ~ ssItem(sK55_skl) ),
inference(paramodulation,[status(thm)],[f1494,f492]) ).
fof(f1502,plain,
! [X0] :
( ~ sQ7_spl
| cons(sK55_skl,app(nil,X0)) = app(sK47_skl,X0)
| ~ ssItem(sK55_skl)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f1494,f247]) ).
fof(f1508,definition,
! [X0] :
( sQ113_spl
<=> ( cons(sK55_skl,X0) = app(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ113_spl])],[split_symbol_definition]) ).
fof(f1511,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| sQ113_spl ),
inference(split_clause,[status(thm)],[f1495,f1508,f459,f466]) ).
fof(f1512,definition,
( sQ114_spl
<=> singletonP(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ114_spl])],[split_symbol_definition]) ).
fof(f1515,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| sQ114_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f1496,f573,f1512,f459,f466]) ).
fof(f1516,definition,
( sQ115_spl
<=> tl(sK47_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ115_spl])],[split_symbol_definition]) ).
fof(f1519,plain,
( ~ sQ7_spl
| sQ115_spl
| ~ sQ5_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1497,f539,f459,f1516,f466]) ).
fof(f1520,definition,
( sQ116_spl
<=> hd(sK47_skl) = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ116_spl])],[split_symbol_definition]) ).
fof(f1523,plain,
( ~ sQ7_spl
| sQ116_spl
| ~ sQ5_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f1498,f539,f459,f1520,f466]) ).
fof(f1524,definition,
! [X0] :
( sQ117_spl
<=> ( memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ117_spl])],[split_symbol_definition]) ).
fof(f1525,plain,
! [X0] :
( ~ sQ117_spl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1524]) ).
fof(f1527,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ5_spl
| sQ117_spl ),
inference(split_clause,[status(thm)],[f1499,f1524,f459,f539,f466]) ).
fof(f1528,definition,
! [X0] :
( sQ118_spl
<=> ( ~ memberP(nil,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1532,definition,
( sQ119_spl
<=> memberP(sK47_skl,sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ119_spl])],[split_symbol_definition]) ).
fof(f1533,plain,
( ~ sQ119_spl
| memberP(sK47_skl,sK55_skl) ),
inference(component_clause,[status(thm)],[f1532]) ).
fof(f1535,plain,
( ~ sQ7_spl
| sQ119_spl
| ~ sQ14_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1501,f459,f539,f1532,f466]) ).
fof(f1536,definition,
! [X0] :
( sQ120_spl
<=> ( cons(sK55_skl,app(nil,X0)) = app(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1539,plain,
( ~ sQ7_spl
| ~ sQ5_spl
| ~ sQ14_spl
| sQ120_spl ),
inference(split_clause,[status(thm)],[f1502,f1536,f539,f459,f466]) ).
fof(f1540,definition,
! [X0,X1] :
( sQ121_spl
<=> ( nil = X0
| cons(X1,X0) != sK47_skl
| ~ ssItem(X1)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1545,definition,
( sQ122_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1549,definition,
( sQ123_spl
<=> nil = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1554,plain,
! [X0] :
( ~ sQ117_spl
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1525,f279]) ).
fof(f1555,plain,
( ~ sQ119_spl
| ~ sQ117_spl
| sK55_skl = sK55_skl
| ~ ssItem(sK55_skl) ),
inference(resolution,[status(thm)],[f1554,f1533]) ).
fof(f1556,definition,
( sQ124_spl
<=> sK55_skl = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ124_spl])],[split_symbol_definition]) ).
fof(f1559,plain,
( ~ sQ119_spl
| ~ sQ117_spl
| sQ124_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f1555,f459,f1556,f1524,f1532]) ).
fof(f1631,definition,
! [X1,X2] :
( sQ131_spl
<=> ( ~ leq(sK51_skl,X2)
| leq(X1,X2)
| ~ leq(X1,sK51_skl)
| ~ ssItem(X2)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ131_spl])],[split_symbol_definition]) ).
fof(f1632,plain,
! [X0,X1] :
( ~ sQ131_spl
| ~ leq(sK51_skl,X1)
| leq(X0,X1)
| ~ leq(X0,sK51_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1631]) ).
fof(f1636,definition,
! [X1,X2] :
( sQ132_spl
<=> ( ~ leq(X2,sK51_skl)
| leq(X1,sK51_skl)
| ~ leq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1) ) ),
introduced(definition,[new_symbols(definition,[sQ132_spl])],[split_symbol_definition]) ).
fof(f1637,plain,
! [X0,X1] :
( ~ sQ132_spl
| ~ leq(X1,sK51_skl)
| leq(X0,sK51_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1636]) ).
fof(f1643,definition,
( sQ133_spl
<=> leq(sK51_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ133_spl])],[split_symbol_definition]) ).
fof(f1644,plain,
( ~ sQ133_spl
| leq(sK51_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1643]) ).
fof(f1645,plain,
( sQ133_spl
| ~ leq(sK51_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1643]) ).
fof(f1662,definition,
! [X0,X1,X2,X3] :
( sQ136_spl
<=> ( ~ leq(sK54_skl,X3)
| leq(X2,X3)
| ~ leq(X2,X0)
| ~ ssItem(X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ leq(X1,sK54_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ136_spl])],[split_symbol_definition]) ).
fof(f1688,definition,
! [X0,X1,X2] :
( sQ141_spl
<=> ( ~ leq(X2,sK51_skl)
| ~ leq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1)
| leq(X0,sK51_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ141_spl])],[split_symbol_definition]) ).
fof(f1692,definition,
! [X0,X1,X2,X3] :
( sQ142_spl
<=> ( ~ leq(X2,X3)
| ~ leq(X3,sK51_skl)
| ~ ssItem(X3)
| ~ leq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1)
| leq(X0,sK51_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ142_spl])],[split_symbol_definition]) ).
fof(f1711,plain,
( sQ105_spl
| ~ ssItem(sK54_skl) ),
inference(resolution,[status(thm)],[f1417,f255]) ).
fof(f1720,plain,
( sQ105_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1711,f665,f1415]) ).
fof(f1726,plain,
( sQ133_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1645,f255]) ).
fof(f1732,plain,
( sQ133_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f1726,f671,f1643]) ).
fof(f1749,plain,
! [X0] :
( ~ sQ105_spl
| ~ ssItem(sK54_skl)
| leq(X0,sK54_skl)
| ~ leq(X0,sK54_skl)
| ~ ssItem(sK54_skl)
| ~ ssItem(sK54_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1416,f664]) ).
fof(f1750,plain,
! [X0,X1] :
( ~ sQ105_spl
| ~ leq(X1,sK54_skl)
| ~ ssItem(sK54_skl)
| leq(X0,sK54_skl)
| ~ leq(X0,X1)
| ~ ssItem(sK54_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1416,f664]) ).
fof(f1752,plain,
! [X0,X1] :
( ~ sQ105_spl
| ~ leq(sK54_skl,X1)
| ~ ssItem(sK54_skl)
| leq(X0,X1)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X1)
| ~ ssItem(sK54_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1416,f664]) ).
fof(f1754,plain,
( ~ sQ105_spl
| sK54_skl = sK54_skl
| ~ leq(sK54_skl,sK54_skl)
| ~ ssItem(sK54_skl)
| ~ ssItem(sK54_skl) ),
inference(resolution,[status(thm)],[f1416,f251]) ).
fof(f1770,definition,
! [X0,X1] :
( sQ144_spl
<=> ( ~ leq(sK54_skl,X1)
| leq(X0,X1)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ144_spl])],[split_symbol_definition]) ).
fof(f1771,plain,
! [X0,X1] :
( ~ sQ144_spl
| ~ leq(sK54_skl,X1)
| leq(X0,X1)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1770]) ).
fof(f1774,plain,
( ~ sQ105_spl
| ~ sQ30_spl
| sQ55_spl ),
inference(split_clause,[status(thm)],[f1749,f863,f665,f1415]) ).
fof(f1775,definition,
! [X0,X1] :
( sQ145_spl
<=> ( ~ leq(X1,sK54_skl)
| leq(X0,sK54_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ145_spl])],[split_symbol_definition]) ).
fof(f1776,plain,
! [X0,X1] :
( ~ sQ145_spl
| ~ leq(X1,sK54_skl)
| leq(X0,sK54_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1775]) ).
fof(f1778,plain,
( ~ sQ105_spl
| ~ sQ30_spl
| sQ145_spl ),
inference(split_clause,[status(thm)],[f1750,f1775,f665,f1415]) ).
fof(f1780,plain,
( ~ sQ105_spl
| ~ sQ30_spl
| sQ144_spl ),
inference(split_clause,[status(thm)],[f1752,f1770,f665,f1415]) ).
fof(f1782,definition,
( sQ146_spl
<=> sK54_skl = sK54_skl ),
introduced(definition,[new_symbols(definition,[sQ146_spl])],[split_symbol_definition]) ).
fof(f1785,plain,
( sQ146_spl
| ~ sQ105_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1754,f665,f1415,f1782]) ).
fof(f1786,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| ~ leq(X1,sK55_skl)
| ~ leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK55_skl)
| ~ cyclefreeP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f1494,f481]) ).
fof(f1787,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| ~ leq(sK55_skl,X1)
| ~ leq(X1,sK55_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil))) ),
inference(paramodulation,[status(thm)],[f1494,f481]) ).
fof(f1788,definition,
! [X0,X1,X2] :
( sQ147_spl
<=> ( ~ leq(X1,sK55_skl)
| ~ leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ147_spl])],[split_symbol_definition]) ).
fof(f1791,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ5_spl
| sQ147_spl ),
inference(split_clause,[status(thm)],[f1786,f1788,f459,f539,f466]) ).
fof(f1792,definition,
! [X0,X1,X2] :
( sQ148_spl
<=> ( ~ leq(sK55_skl,X1)
| ~ leq(X1,sK55_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ148_spl])],[split_symbol_definition]) ).
fof(f1795,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ5_spl
| sQ148_spl ),
inference(split_clause,[status(thm)],[f1787,f1792,f459,f539,f466]) ).
fof(f1807,plain,
! [X0] :
( ~ sQ133_spl
| ~ ssItem(sK51_skl)
| leq(X0,sK51_skl)
| ~ leq(X0,sK51_skl)
| ~ ssItem(sK51_skl)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1644,f664]) ).
fof(f1808,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ leq(X1,sK51_skl)
| ~ ssItem(sK51_skl)
| leq(X0,sK51_skl)
| ~ leq(X0,X1)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1644,f664]) ).
fof(f1810,plain,
! [X0,X1] :
( ~ sQ133_spl
| ~ leq(sK51_skl,X1)
| ~ ssItem(sK51_skl)
| leq(X0,X1)
| ~ leq(X0,sK51_skl)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1644,f664]) ).
fof(f1822,plain,
( ~ sQ133_spl
| ~ sQ32_spl
| sQ103_spl ),
inference(split_clause,[status(thm)],[f1807,f1399,f671,f1643]) ).
fof(f1823,plain,
( ~ sQ133_spl
| ~ sQ32_spl
| sQ132_spl ),
inference(split_clause,[status(thm)],[f1808,f1636,f671,f1643]) ).
fof(f1825,plain,
( ~ sQ133_spl
| ~ sQ32_spl
| sQ131_spl ),
inference(split_clause,[status(thm)],[f1810,f1631,f671,f1643]) ).
fof(f1827,definition,
( sQ149_spl
<=> sK51_skl = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ149_spl])],[split_symbol_definition]) ).
fof(f1831,plain,
( ~ sQ105_spl
| ~ sQ104_spl
| ~ leq(sK54_skl,sK54_skl)
| ~ ssItem(sK54_skl) ),
inference(resolution,[status(thm)],[f1411,f1416]) ).
fof(f1841,plain,
( ~ sQ104_spl
| ~ sQ105_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1831,f665,f1415,f1410]) ).
fof(f1845,definition,
! [X0,X2] :
( sQ150_spl
<=> ( ~ leq(X2,X0)
| ~ leq(sK54_skl,X2)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ150_spl])],[split_symbol_definition]) ).
fof(f1846,plain,
! [X0,X1] :
( ~ sQ150_spl
| ~ leq(X1,X0)
| ~ leq(sK54_skl,X1)
| ~ ssItem(X1)
| ~ ssItem(X0)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1845]) ).
fof(f1849,definition,
! [X0] :
( sQ151_spl
<=> ( ~ leq(sK54_skl,X0)
| ~ ssItem(X0)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ151_spl])],[split_symbol_definition]) ).
fof(f1850,plain,
! [X0] :
( ~ sQ151_spl
| ~ leq(sK54_skl,X0)
| ~ ssItem(X0)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1849]) ).
fof(f1883,plain,
( ~ ssList(sK53_skl)
| ~ ssList(sK52_skl)
| segmentP(sK47_skl,cons(sK51_skl,nil))
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl)) ),
inference(paramodulation,[status(thm)],[f428,f480]) ).
fof(f1884,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| segmentP(app(sK47_skl,X0),sK53_skl)
| ~ ssList(sK53_skl)
| ~ ssList(app(app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl),X0)) ),
inference(paramodulation,[status(thm)],[f428,f480]) ).
fof(f1885,plain,
! [X0] :
( X0 = sK53_skl
| app(app(sK52_skl,cons(sK51_skl,nil)),X0) != sK47_skl
| ~ ssList(X0)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f428,f378]) ).
fof(f1887,plain,
! [X0] :
( X0 = app(sK52_skl,cons(sK51_skl,nil))
| app(X0,sK53_skl) != sK47_skl
| ~ ssList(X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f428,f376]) ).
fof(f1889,plain,
( ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| rearsegP(sK47_skl,sK53_skl)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f428,f714]) ).
fof(f1890,plain,
! [X0] :
( memberP(sK53_skl,X0)
| memberP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| ~ memberP(sK47_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f428,f270]) ).
fof(f1891,plain,
! [X0] :
( ~ memberP(sK53_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f428,f272]) ).
fof(f1892,plain,
! [X0] :
( ~ memberP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f428,f271]) ).
fof(f1893,plain,
( ~ ssList(sK53_skl)
| frontsegP(sK47_skl,app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f428,f631]) ).
fof(f1894,plain,
( ssList(sK47_skl)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f428,f245]) ).
fof(f1895,definition,
( sQ154_spl
<=> ssList(app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f1897,plain,
( sQ154_spl
| ~ ssList(app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl)) ),
inference(component_clause,[status(thm)],[f1895]) ).
fof(f1898,definition,
( sQ155_spl
<=> segmentP(sK47_skl,cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ155_spl])],[split_symbol_definition]) ).
fof(f1901,plain,
( ~ sQ23_spl
| ~ sQ110_spl
| sQ155_spl
| ~ sQ111_spl
| ~ sQ154_spl ),
inference(split_clause,[status(thm)],[f1883,f1895,f1466,f1898,f1463,f607]) ).
fof(f1902,definition,
! [X0] :
( sQ156_spl
<=> ( ~ ssList(X0)
| segmentP(app(sK47_skl,X0),sK53_skl)
| ~ ssList(app(app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ156_spl])],[split_symbol_definition]) ).
fof(f1905,plain,
( ~ sQ22_spl
| ~ sQ23_spl
| sQ156_spl ),
inference(split_clause,[status(thm)],[f1884,f1902,f607,f604]) ).
fof(f1906,definition,
! [X0] :
( sQ157_spl
<=> ( X0 = sK53_skl
| app(app(sK52_skl,cons(sK51_skl,nil)),X0) != sK47_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ157_spl])],[split_symbol_definition]) ).
fof(f1909,plain,
( sQ157_spl
| ~ sQ22_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1885,f607,f604,f1906]) ).
fof(f1911,definition,
! [X0] :
( sQ158_spl
<=> ( X0 = app(sK52_skl,cons(sK51_skl,nil))
| app(X0,sK53_skl) != sK47_skl
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ158_spl])],[split_symbol_definition]) ).
fof(f1914,plain,
( sQ158_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f1887,f604,f607,f1911]) ).
fof(f1916,definition,
( sQ159_spl
<=> rearsegP(sK47_skl,sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f1919,plain,
( ~ sQ22_spl
| sQ159_spl
| ~ sQ23_spl ),
inference(split_clause,[status(thm)],[f1889,f607,f1916,f604]) ).
fof(f1920,definition,
! [X0] :
( sQ160_spl
<=> ( memberP(sK53_skl,X0)
| memberP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ160_spl])],[split_symbol_definition]) ).
fof(f1923,plain,
( ~ sQ23_spl
| ~ sQ22_spl
| sQ160_spl ),
inference(split_clause,[status(thm)],[f1890,f1920,f604,f607]) ).
fof(f1924,definition,
! [X0] :
( sQ161_spl
<=> ( ~ memberP(sK53_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ161_spl])],[split_symbol_definition]) ).
fof(f1925,plain,
! [X0] :
( ~ sQ161_spl
| ~ memberP(sK53_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1924]) ).
fof(f1927,plain,
( ~ sQ23_spl
| ~ sQ22_spl
| sQ161_spl ),
inference(split_clause,[status(thm)],[f1891,f1924,f604,f607]) ).
fof(f1928,definition,
! [X0] :
( sQ162_spl
<=> ( ~ memberP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ162_spl])],[split_symbol_definition]) ).
fof(f1929,plain,
! [X0] :
( ~ sQ162_spl
| ~ memberP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1928]) ).
fof(f1931,plain,
( ~ sQ23_spl
| ~ sQ22_spl
| sQ162_spl ),
inference(split_clause,[status(thm)],[f1892,f1928,f604,f607]) ).
fof(f1932,definition,
( sQ163_spl
<=> frontsegP(sK47_skl,app(sK52_skl,cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ163_spl])],[split_symbol_definition]) ).
fof(f1935,plain,
( ~ sQ23_spl
| sQ163_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f1893,f604,f1932,f607]) ).
fof(f1936,plain,
( sQ122_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f1894,f604,f607,f1545]) ).
fof(f1938,plain,
( sQ154_spl
| ~ ssList(sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f428,f1897]) ).
fof(f1939,plain,
( sQ154_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1938,f419]) ).
fof(f1940,plain,
sQ154_spl,
inference(contradiction_clause,[status(thm)],[f1939]) ).
fof(f1958,plain,
( ~ sQ133_spl
| ~ sQ90_spl
| ~ leq(sK51_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1214,f1644]) ).
fof(f1962,plain,
( ~ sQ90_spl
| ~ sQ133_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f1958,f671,f1643,f1213]) ).
fof(f1984,plain,
( ~ sQ1_spl
| ~ sQ161_spl
| memberP(sK47_skl,sK54_skl)
| ~ ssItem(sK54_skl) ),
inference(resolution,[status(thm)],[f1925,f445]) ).
fof(f1985,definition,
( sQ169_spl
<=> memberP(sK47_skl,sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ169_spl])],[split_symbol_definition]) ).
fof(f1986,plain,
( ~ sQ169_spl
| memberP(sK47_skl,sK54_skl) ),
inference(component_clause,[status(thm)],[f1985]) ).
fof(f1988,plain,
( ~ sQ1_spl
| ~ sQ161_spl
| sQ169_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1984,f665,f1985,f1924,f444]) ).
fof(f1989,plain,
( ~ sQ117_spl
| ~ sQ169_spl
| sK54_skl = sK55_skl
| ~ ssItem(sK54_skl) ),
inference(resolution,[status(thm)],[f1986,f1554]) ).
fof(f1990,definition,
( sQ170_spl
<=> sK54_skl = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ170_spl])],[split_symbol_definition]) ).
fof(f1991,plain,
( ~ sQ170_spl
| sK54_skl = sK55_skl ),
inference(component_clause,[status(thm)],[f1990]) ).
fof(f1993,plain,
( ~ sQ117_spl
| ~ sQ169_spl
| sQ170_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f1989,f665,f1990,f1985,f1524]) ).
fof(f1996,plain,
( ~ sQ7_spl
| ~ sQ170_spl
| cons(sK54_skl,nil) = sK47_skl ),
inference(backward_demodulation,[status(thm)],[f1991,f1494]) ).
fof(f2005,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ170_spl
| memberP(nil,X0)
| X0 = sK54_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK54_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f1996,f275]) ).
fof(f2035,definition,
! [X0] :
( sQ176_spl
<=> ( memberP(nil,X0)
| X0 = sK54_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ176_spl])],[split_symbol_definition]) ).
fof(f2036,plain,
! [X0] :
( ~ sQ176_spl
| memberP(nil,X0)
| X0 = sK54_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f2035]) ).
fof(f2038,plain,
( ~ sQ7_spl
| ~ sQ170_spl
| ~ sQ14_spl
| ~ sQ30_spl
| sQ176_spl ),
inference(split_clause,[status(thm)],[f2005,f2035,f665,f539,f1990,f466]) ).
fof(f2050,plain,
! [X0] :
( ~ sQ28_spl
| ~ memberP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f651,f279]) ).
fof(f2061,plain,
! [X0,X1] :
( ~ sQ150_spl
| ~ leq(X1,X0)
| ~ leq(sK54_skl,X1)
| ~ ssItem(X1)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1846]) ).
fof(f2062,plain,
! [X0] :
( ~ sQ151_spl
| ~ leq(sK54_skl,X0)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1850]) ).
fof(f2073,plain,
! [X0] :
( ~ sQ176_spl
| X0 = sK54_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2036,f279]) ).
fof(f2082,plain,
( sK47_skl = app(sK52_skl,app(cons(sK51_skl,nil),sK53_skl))
| ~ ssList(sK53_skl)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f428,f382]) ).
fof(f2083,plain,
! [X0] :
( app(sK47_skl,X0) = app(app(sK52_skl,cons(sK51_skl,nil)),app(sK53_skl,X0))
| ~ ssList(X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f428,f382]) ).
fof(f2084,definition,
( sQ178_spl
<=> sK47_skl = app(sK52_skl,app(cons(sK51_skl,nil),sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ178_spl])],[split_symbol_definition]) ).
fof(f2087,plain,
( sQ178_spl
| ~ sQ23_spl
| ~ sQ111_spl
| ~ sQ110_spl ),
inference(split_clause,[status(thm)],[f2082,f1463,f1466,f607,f2084]) ).
fof(f2088,definition,
! [X0] :
( sQ179_spl
<=> ( app(sK47_skl,X0) = app(app(sK52_skl,cons(sK51_skl,nil)),app(sK53_skl,X0))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ179_spl])],[split_symbol_definition]) ).
fof(f2091,plain,
( sQ179_spl
| ~ sQ23_spl
| ~ sQ22_spl ),
inference(split_clause,[status(thm)],[f2083,f604,f607,f2088]) ).
fof(f2092,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ),
inference(resolution,[status(thm)],[f385,f129]) ).
fof(f2093,plain,
( ~ ssList(nil)
| nil = nil
| ~ ssList(nil)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f385,f249]) ).
fof(f2095,plain,
! [X0] :
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = sK8_skl(X0,nil)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0)) ),
inference(resolution,[status(thm)],[f385,f136]) ).
fof(f2096,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(nil)
| nil = cons(X0,sK3_skl(X0,nil))
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil)) ),
inference(resolution,[status(thm)],[f385,f111]) ).
fof(f2098,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = sK5_skl(X0,nil)
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f385,f123]) ).
fof(f2100,definition,
! [X0] :
( sQ180_spl
<=> ( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| nil = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ180_spl])],[split_symbol_definition]) ).
fof(f2103,plain,
( ~ sQ14_spl
| sQ180_spl ),
inference(split_clause,[status(thm)],[f2092,f2100,f539]) ).
fof(f2104,plain,
( sQ12_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f2093,f539,f529]) ).
fof(f2118,definition,
! [X0] :
( sQ185_spl
<=> ( ~ segmentP(nil,X0)
| ~ ssList(X0)
| nil = sK8_skl(X0,nil)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ185_spl])],[split_symbol_definition]) ).
fof(f2121,plain,
( ~ sQ14_spl
| sQ185_spl ),
inference(split_clause,[status(thm)],[f2095,f2118,f539]) ).
fof(f2122,definition,
! [X0] :
( sQ186_spl
<=> ( ~ memberP(nil,X0)
| ~ ssItem(X0)
| nil = cons(X0,sK3_skl(X0,nil))
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ186_spl])],[split_symbol_definition]) ).
fof(f2125,plain,
( ~ sQ14_spl
| sQ186_spl ),
inference(split_clause,[status(thm)],[f2096,f2122,f539]) ).
fof(f2127,definition,
! [X0] :
( sQ187_spl
<=> ( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| nil = sK5_skl(X0,nil)
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ187_spl])],[split_symbol_definition]) ).
fof(f2130,plain,
( ~ sQ14_spl
| sQ187_spl ),
inference(split_clause,[status(thm)],[f2098,f2127,f539]) ).
fof(f2195,plain,
! [X0,X1] :
( ~ sQ151_spl
| ~ leq(X1,X0)
| ~ leq(sK54_skl,X1)
| ~ ssItem(X0)
| ~ ssItem(X1)
| ~ ssItem(sK54_skl)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2062,f253]) ).
fof(f2200,plain,
( ~ sQ151_spl
| ~ sQ30_spl
| sQ150_spl ),
inference(split_clause,[status(thm)],[f2195,f1845,f665,f1849]) ).
fof(f2243,plain,
! [X0] :
( ~ sQ28_spl
| ~ memberP(cons(sK51_skl,nil),X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2050,f272]) ).
fof(f2245,definition,
! [X0] :
( sQ191_spl
<=> ( ~ memberP(cons(sK51_skl,nil),X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ191_spl])],[split_symbol_definition]) ).
fof(f2246,plain,
! [X0] :
( ~ sQ191_spl
| ~ memberP(cons(sK51_skl,nil),X0)
| ~ ssItem(X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f2245]) ).
fof(f2248,plain,
( ~ sQ28_spl
| ~ sQ111_spl
| ~ sQ110_spl
| sQ191_spl ),
inference(split_clause,[status(thm)],[f2243,f2245,f1463,f1466,f650]) ).
fof(f2253,plain,
! [X0] :
( ~ sQ191_spl
| ~ memberP(cons(sK51_skl,nil),X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2246]) ).
fof(f2256,plain,
( ~ sQ191_spl
| ~ ssList(nil)
| ~ ssItem(sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f2253,f492]) ).
fof(f2261,plain,
( ~ sQ191_spl
| ~ sQ14_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f2256,f671,f539,f2245]) ).
fof(f2281,plain,
! [X0,X1,X2,X3] :
( ~ sQ144_spl
| ~ leq(X3,X1)
| ~ leq(X2,X3)
| ~ ssItem(X3)
| ~ leq(sK54_skl,X2)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssItem(sK54_skl)
| leq(X0,X1)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1771,f664]) ).
fof(f2282,plain,
! [X0,X1,X2] :
( ~ sQ144_spl
| ~ leq(X2,X1)
| ~ leq(sK54_skl,X2)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssItem(sK54_skl)
| leq(X0,X1)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1771,f253]) ).
fof(f2286,definition,
! [X0,X1,X2,X3] :
( sQ196_spl
<=> ( ~ leq(X3,X1)
| ~ leq(X2,X3)
| ~ ssItem(X3)
| ~ leq(sK54_skl,X2)
| ~ ssItem(X1)
| ~ ssItem(X2)
| leq(X0,X1)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ196_spl])],[split_symbol_definition]) ).
fof(f2289,plain,
( ~ sQ144_spl
| ~ sQ30_spl
| sQ196_spl ),
inference(split_clause,[status(thm)],[f2281,f2286,f665,f1770]) ).
fof(f2290,definition,
! [X0,X1,X2] :
( sQ197_spl
<=> ( ~ leq(X2,X1)
| ~ leq(sK54_skl,X2)
| ~ ssItem(X1)
| ~ ssItem(X2)
| leq(X0,X1)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ197_spl])],[split_symbol_definition]) ).
fof(f2293,plain,
( ~ sQ144_spl
| ~ sQ30_spl
| sQ197_spl ),
inference(split_clause,[status(thm)],[f2282,f2290,f665,f1770]) ).
fof(f2309,plain,
! [X0,X1,X2,X3] :
( ~ sQ145_spl
| ~ leq(X3,X0)
| ~ ssItem(X0)
| leq(X2,sK54_skl)
| ~ leq(X2,X3)
| ~ ssItem(sK54_skl)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ leq(X1,sK54_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1776,f664]) ).
fof(f2311,plain,
! [X0,X1,X2,X3] :
( ~ sQ145_spl
| ~ leq(sK54_skl,X3)
| ~ ssItem(sK54_skl)
| leq(X2,X3)
| ~ leq(X2,X0)
| ~ ssItem(X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ leq(X1,sK54_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1776,f664]) ).
fof(f2312,plain,
! [X0,X1,X2] :
( ~ sQ145_spl
| leq(X2,sK54_skl)
| ~ leq(X2,X0)
| ~ ssItem(sK54_skl)
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ leq(X1,sK54_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1776,f253]) ).
fof(f2313,plain,
! [X0,X1] :
( ~ sQ145_spl
| sK54_skl = X0
| ~ leq(sK54_skl,X0)
| ~ ssItem(X0)
| ~ ssItem(sK54_skl)
| ~ leq(X1,sK54_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1776,f251]) ).
fof(f2316,plain,
! [X0,X1,X2,X3] :
( ~ sQ145_spl
| ~ leq(X3,sK54_skl)
| ~ leq(X2,X3)
| ~ ssItem(X3)
| ~ leq(X1,X2)
| ~ ssItem(sK54_skl)
| ~ ssItem(X2)
| ~ ssItem(X1)
| leq(X0,sK54_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1776,f664]) ).
fof(f2326,definition,
! [X0,X1,X2,X3] :
( sQ199_spl
<=> ( ~ leq(X3,X0)
| ~ ssItem(X0)
| leq(X2,sK54_skl)
| ~ leq(X2,X3)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ leq(X1,sK54_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ199_spl])],[split_symbol_definition]) ).
fof(f2329,plain,
( ~ sQ145_spl
| ~ sQ30_spl
| sQ199_spl ),
inference(split_clause,[status(thm)],[f2309,f2326,f665,f1775]) ).
fof(f2331,plain,
( ~ sQ145_spl
| ~ sQ30_spl
| sQ136_spl ),
inference(split_clause,[status(thm)],[f2311,f1662,f665,f1775]) ).
fof(f2332,definition,
! [X0,X1,X2] :
( sQ200_spl
<=> ( leq(X2,sK54_skl)
| ~ leq(X2,X0)
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ leq(X1,sK54_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ200_spl])],[split_symbol_definition]) ).
fof(f2335,plain,
( ~ sQ145_spl
| ~ sQ30_spl
| sQ200_spl ),
inference(split_clause,[status(thm)],[f2312,f2332,f665,f1775]) ).
fof(f2336,definition,
! [X0,X1] :
( sQ201_spl
<=> ( sK54_skl = X0
| ~ leq(sK54_skl,X0)
| ~ ssItem(X0)
| ~ leq(X1,sK54_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ201_spl])],[split_symbol_definition]) ).
fof(f2339,plain,
( ~ sQ145_spl
| ~ sQ30_spl
| sQ201_spl ),
inference(split_clause,[status(thm)],[f2313,f2336,f665,f1775]) ).
fof(f2342,definition,
! [X0,X1,X2,X3] :
( sQ202_spl
<=> ( ~ leq(X3,sK54_skl)
| ~ leq(X2,X3)
| ~ ssItem(X3)
| ~ leq(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X1)
| leq(X0,sK54_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ202_spl])],[split_symbol_definition]) ).
fof(f2345,plain,
( ~ sQ145_spl
| ~ sQ30_spl
| sQ202_spl ),
inference(split_clause,[status(thm)],[f2316,f2342,f665,f1775]) ).
fof(f2358,plain,
! [X0,X1,X2,X3] :
( ~ sQ132_spl
| ~ leq(X3,X0)
| ~ ssItem(X0)
| leq(X2,sK51_skl)
| ~ leq(X2,X3)
| ~ ssItem(sK51_skl)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ leq(X1,sK51_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1637,f664]) ).
fof(f2360,plain,
! [X0,X1,X2,X3] :
( ~ sQ132_spl
| ~ leq(sK51_skl,X3)
| ~ ssItem(sK51_skl)
| leq(X2,X3)
| ~ leq(X2,X0)
| ~ ssItem(X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ leq(X1,sK51_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1637,f664]) ).
fof(f2361,plain,
! [X0,X1,X2] :
( ~ sQ132_spl
| leq(X2,sK51_skl)
| ~ leq(X2,X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ leq(X1,sK51_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1637,f253]) ).
fof(f2362,plain,
! [X0,X1] :
( ~ sQ132_spl
| sK51_skl = X0
| ~ leq(sK51_skl,X0)
| ~ ssItem(X0)
| ~ ssItem(sK51_skl)
| ~ leq(X1,sK51_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1637,f251]) ).
fof(f2366,plain,
! [X0,X1,X2,X3] :
( ~ sQ132_spl
| ~ leq(X3,sK51_skl)
| ~ leq(X2,X3)
| ~ ssItem(X3)
| ~ leq(X1,X2)
| ~ ssItem(sK51_skl)
| ~ ssItem(X2)
| ~ ssItem(X1)
| leq(X0,sK51_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1637,f664]) ).
fof(f2374,definition,
! [X0,X1,X2,X3] :
( sQ203_spl
<=> ( ~ leq(X3,X0)
| ~ ssItem(X0)
| leq(X2,sK51_skl)
| ~ leq(X2,X3)
| ~ ssItem(X3)
| ~ ssItem(X2)
| ~ leq(X1,sK51_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ203_spl])],[split_symbol_definition]) ).
fof(f2377,plain,
( ~ sQ132_spl
| ~ sQ32_spl
| sQ203_spl ),
inference(split_clause,[status(thm)],[f2358,f2374,f671,f1636]) ).
fof(f2379,definition,
! [X0,X1,X2,X3] :
( sQ204_spl
<=> ( ~ leq(sK51_skl,X3)
| leq(X2,X3)
| ~ leq(X2,X0)
| ~ ssItem(X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| ~ leq(X1,sK51_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ204_spl])],[split_symbol_definition]) ).
fof(f2382,plain,
( ~ sQ132_spl
| ~ sQ32_spl
| sQ204_spl ),
inference(split_clause,[status(thm)],[f2360,f2379,f671,f1636]) ).
fof(f2383,plain,
( ~ sQ132_spl
| ~ sQ32_spl
| sQ141_spl ),
inference(split_clause,[status(thm)],[f2361,f1688,f671,f1636]) ).
fof(f2384,definition,
! [X0,X1] :
( sQ205_spl
<=> ( sK51_skl = X0
| ~ leq(sK51_skl,X0)
| ~ ssItem(X0)
| ~ leq(X1,sK51_skl)
| ~ leq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ205_spl])],[split_symbol_definition]) ).
fof(f2387,plain,
( ~ sQ132_spl
| ~ sQ32_spl
| sQ205_spl ),
inference(split_clause,[status(thm)],[f2362,f2384,f671,f1636]) ).
fof(f2391,plain,
( ~ sQ132_spl
| ~ sQ32_spl
| sQ142_spl ),
inference(split_clause,[status(thm)],[f2366,f1692,f671,f1636]) ).
fof(f2401,plain,
! [X0,X1,X2,X3] :
( ~ sQ131_spl
| ~ leq(X3,X1)
| ~ leq(X2,X3)
| ~ ssItem(X3)
| ~ leq(sK51_skl,X2)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssItem(sK51_skl)
| leq(X0,X1)
| ~ leq(X0,sK51_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1632,f664]) ).
fof(f2402,plain,
! [X0,X1,X2] :
( ~ sQ131_spl
| ~ leq(X2,X1)
| ~ leq(sK51_skl,X2)
| ~ ssItem(X1)
| ~ ssItem(X2)
| ~ ssItem(sK51_skl)
| leq(X0,X1)
| ~ leq(X0,sK51_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1632,f253]) ).
fof(f2407,definition,
! [X0,X1,X2,X3] :
( sQ206_spl
<=> ( ~ leq(X3,X1)
| ~ leq(X2,X3)
| ~ ssItem(X3)
| ~ leq(sK51_skl,X2)
| ~ ssItem(X1)
| ~ ssItem(X2)
| leq(X0,X1)
| ~ leq(X0,sK51_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ206_spl])],[split_symbol_definition]) ).
fof(f2410,plain,
( ~ sQ131_spl
| ~ sQ32_spl
| sQ206_spl ),
inference(split_clause,[status(thm)],[f2401,f2407,f671,f1631]) ).
fof(f2411,definition,
! [X0,X1,X2] :
( sQ207_spl
<=> ( ~ leq(X2,X1)
| ~ leq(sK51_skl,X2)
| ~ ssItem(X1)
| ~ ssItem(X2)
| leq(X0,X1)
| ~ leq(X0,sK51_skl)
| ~ ssItem(X1)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ207_spl])],[split_symbol_definition]) ).
fof(f2414,plain,
( ~ sQ131_spl
| ~ sQ32_spl
| sQ207_spl ),
inference(split_clause,[status(thm)],[f2402,f2411,f671,f1631]) ).
fof(f2528,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ),
inference(resolution,[status(thm)],[f386,f129]) ).
fof(f2531,plain,
! [X0] :
( ~ segmentP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = app(sK7_skl(X0,nil),X0)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0)) ),
inference(resolution,[status(thm)],[f386,f136]) ).
fof(f2532,plain,
! [X0] :
( ~ memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssList(nil)
| nil = sK2_skl(X0,nil)
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil)) ),
inference(resolution,[status(thm)],[f386,f111]) ).
fof(f2534,plain,
! [X0] :
( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f386,f123]) ).
fof(f2536,definition,
! [X0] :
( sQ209_spl
<=> ( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| nil = sK6_skl(X0,nil)
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ209_spl])],[split_symbol_definition]) ).
fof(f2539,plain,
( ~ sQ14_spl
| sQ209_spl ),
inference(split_clause,[status(thm)],[f2528,f2536,f539]) ).
fof(f2545,definition,
! [X0] :
( sQ211_spl
<=> ( ~ segmentP(nil,X0)
| ~ ssList(X0)
| nil = app(sK7_skl(X0,nil),X0)
| ~ ssList(sK8_skl(X0,nil))
| ~ ssList(app(sK7_skl(X0,nil),X0)) ) ),
introduced(definition,[new_symbols(definition,[sQ211_spl])],[split_symbol_definition]) ).
fof(f2548,plain,
( ~ sQ14_spl
| sQ211_spl ),
inference(split_clause,[status(thm)],[f2531,f2545,f539]) ).
fof(f2549,definition,
! [X0] :
( sQ212_spl
<=> ( ~ memberP(nil,X0)
| ~ ssItem(X0)
| nil = sK2_skl(X0,nil)
| ~ ssList(cons(X0,sK3_skl(X0,nil)))
| ~ ssList(sK2_skl(X0,nil)) ) ),
introduced(definition,[new_symbols(definition,[sQ212_spl])],[split_symbol_definition]) ).
fof(f2552,plain,
( ~ sQ14_spl
| sQ212_spl ),
inference(split_clause,[status(thm)],[f2532,f2549,f539]) ).
fof(f2554,definition,
! [X0] :
( sQ213_spl
<=> ( ~ frontsegP(nil,X0)
| ~ ssList(X0)
| nil = X0
| ~ ssList(sK5_skl(X0,nil))
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ213_spl])],[split_symbol_definition]) ).
fof(f2557,plain,
( ~ sQ14_spl
| sQ213_spl ),
inference(split_clause,[status(thm)],[f2534,f2554,f539]) ).
fof(f2578,plain,
! [X0] :
( ~ sQ89_spl
| ~ ssItem(sK51_skl)
| ~ leq(sK51_skl,X0)
| ~ leq(X0,sK51_skl)
| ~ ssItem(X0)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1209,f255]) ).
fof(f2591,plain,
( ~ sQ89_spl
| sQ90_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f2578,f671,f1213,f1208]) ).
fof(f2599,plain,
! [X0] :
( ~ sQ150_spl
| ~ ssItem(sK54_skl)
| ~ leq(sK54_skl,X0)
| ~ ssItem(sK54_skl)
| ~ leq(X0,sK54_skl)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2061,f255]) ).
fof(f2613,plain,
( ~ sQ150_spl
| ~ sQ30_spl
| sQ104_spl ),
inference(split_clause,[status(thm)],[f2599,f1410,f665,f1845]) ).
fof(f2614,plain,
( ~ sQ162_spl
| ~ ssList(nil)
| ~ ssList(sK52_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| memberP(sK47_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1929,f476]) ).
fof(f2615,plain,
! [X0] :
( ~ sQ162_spl
| ~ memberP(cons(sK51_skl,nil),X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1929,f272]) ).
fof(f2616,plain,
! [X0] :
( ~ sQ162_spl
| ~ memberP(sK52_skl,X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1929,f271]) ).
fof(f2617,definition,
( sQ220_spl
<=> memberP(sK47_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ220_spl])],[split_symbol_definition]) ).
fof(f2618,plain,
( ~ sQ220_spl
| memberP(sK47_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f2617]) ).
fof(f2620,plain,
( ~ sQ162_spl
| ~ sQ14_spl
| ~ sQ110_spl
| ~ sQ22_spl
| sQ220_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f2614,f671,f2617,f604,f1463,f539,f1928]) ).
fof(f2621,definition,
! [X0] :
( sQ221_spl
<=> ( ~ memberP(cons(sK51_skl,nil),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ221_spl])],[split_symbol_definition]) ).
fof(f2624,plain,
( ~ sQ162_spl
| ~ sQ111_spl
| ~ sQ110_spl
| sQ221_spl ),
inference(split_clause,[status(thm)],[f2615,f2621,f1463,f1466,f1928]) ).
fof(f2625,definition,
! [X0] :
( sQ222_spl
<=> ( ~ memberP(sK52_skl,X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ222_spl])],[split_symbol_definition]) ).
fof(f2626,plain,
! [X0] :
( ~ sQ222_spl
| ~ memberP(sK52_skl,X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f2625]) ).
fof(f2628,plain,
( ~ sQ162_spl
| ~ sQ111_spl
| ~ sQ110_spl
| sQ222_spl ),
inference(split_clause,[status(thm)],[f2616,f2625,f1463,f1466,f1928]) ).
fof(f2630,plain,
! [X0] :
( ~ sQ222_spl
| ~ memberP(sK52_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2626]) ).
fof(f2631,plain,
( ~ sQ176_spl
| ~ sQ220_spl
| sK51_skl = sK54_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f2618,f2073]) ).
fof(f2632,plain,
( ~ sQ176_spl
| ~ sQ220_spl
| sQ42_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f2631,f671,f743,f2617,f2035]) ).
fof(f2634,plain,
! [X0,X1] :
( ~ sQ39_spl
| ~ sQ42_spl
| ~ leq(X1,X0)
| ~ leq(sK51_skl,X1)
| ~ ssItem(X1)
| ~ leq(X0,sK51_skl)
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f744,f727]) ).
fof(f2651,plain,
( ~ sQ39_spl
| ~ sQ42_spl
| sQ89_spl ),
inference(split_clause,[status(thm)],[f2634,f1208,f743,f722]) ).
fof(f2701,plain,
( sQ34_spl
| ~ sQ42_spl
| ~ leq(sK51_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f744,f689]) ).
fof(f2702,plain,
( sQ34_spl
| ~ sQ42_spl
| ~ sQ133_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f2701,f1644]) ).
fof(f2703,plain,
( sQ34_spl
| ~ sQ42_spl
| ~ sQ133_spl ),
inference(contradiction_clause,[status(thm)],[f2702]) ).
fof(f2762,plain,
! [X0] :
( ~ sQ7_spl
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(app(X0,sK47_skl),sK55_skl)
| ~ ssItem(sK55_skl)
| ~ ssList(app(X0,cons(sK55_skl,nil))) ),
inference(paramodulation,[status(thm)],[f1494,f476]) ).
fof(f2763,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| leq(sK55_skl,X1)
| leq(X1,sK55_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK55_skl)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil))) ),
inference(paramodulation,[status(thm)],[f1494,f482]) ).
fof(f2764,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| leq(X1,sK55_skl)
| leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK55_skl)
| ~ totalorderP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f1494,f482]) ).
fof(f2780,definition,
! [X0] :
( sQ228_spl
<=> ( ~ ssList(X0)
| memberP(app(X0,sK47_skl),sK55_skl)
| ~ ssList(app(X0,cons(sK55_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ228_spl])],[split_symbol_definition]) ).
fof(f2783,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ5_spl
| sQ228_spl ),
inference(split_clause,[status(thm)],[f2762,f2780,f459,f539,f466]) ).
fof(f2784,definition,
! [X0,X1,X2] :
( sQ229_spl
<=> ( leq(sK55_skl,X1)
| leq(X1,sK55_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK55_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ229_spl])],[split_symbol_definition]) ).
fof(f2787,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ5_spl
| sQ229_spl ),
inference(split_clause,[status(thm)],[f2763,f2784,f459,f539,f466]) ).
fof(f2788,definition,
! [X0,X1,X2] :
( sQ230_spl
<=> ( leq(X1,sK55_skl)
| leq(sK55_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK55_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ230_spl])],[split_symbol_definition]) ).
fof(f2791,plain,
( ~ sQ7_spl
| ~ sQ14_spl
| ~ sQ5_spl
| sQ230_spl ),
inference(split_clause,[status(thm)],[f2764,f2788,f459,f539,f466]) ).
fof(f2809,plain,
( ~ sQ220_spl
| ~ sQ117_spl
| sK51_skl = sK55_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1554,f2618]) ).
fof(f2811,definition,
( sQ231_spl
<=> sK51_skl = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ231_spl])],[split_symbol_definition]) ).
fof(f2812,plain,
( ~ sQ231_spl
| sK51_skl = sK55_skl ),
inference(component_clause,[status(thm)],[f2811]) ).
fof(f2814,plain,
( ~ sQ220_spl
| ~ sQ117_spl
| sQ231_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f2809,f671,f2811,f1524,f2617]) ).
fof(f2815,plain,
! [X0] :
( ~ sQ117_spl
| ~ sQ231_spl
| X0 = sK51_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(backward_demodulation,[status(thm)],[f2812,f1554]) ).
fof(f2816,plain,
( ~ sQ7_spl
| ~ sQ231_spl
| cons(sK51_skl,nil) = sK47_skl ),
inference(backward_demodulation,[status(thm)],[f2812,f1494]) ).
fof(f2822,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ231_spl
| cons(sK51_skl,X0) = app(sK47_skl,X0)
| ~ ssItem(sK51_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f2816,f380]) ).
fof(f2824,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ231_spl
| ~ ssList(nil)
| ~ ssList(X0)
| memberP(app(X0,sK47_skl),sK51_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(app(X0,cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f2816,f476]) ).
fof(f2825,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| ~ sQ231_spl
| leq(sK51_skl,X1)
| leq(X1,sK51_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f2816,f482]) ).
fof(f2826,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| ~ sQ231_spl
| leq(X1,sK51_skl)
| leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ totalorderP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2816,f482]) ).
fof(f2827,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| ~ sQ231_spl
| ~ leq(sK51_skl,X1)
| ~ leq(X1,sK51_skl)
| ~ ssList(nil)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f2816,f481]) ).
fof(f2828,plain,
! [X0,X1,X2] :
( ~ sQ7_spl
| ~ sQ231_spl
| ~ leq(X1,sK51_skl)
| ~ leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ ssItem(sK51_skl)
| ~ cyclefreeP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ),
inference(paramodulation,[status(thm)],[f2816,f481]) ).
fof(f2830,plain,
( ~ sQ7_spl
| ~ sQ231_spl
| hd(sK47_skl) = sK51_skl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2816,f239]) ).
fof(f2831,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ231_spl
| memberP(nil,X0)
| X0 = sK51_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f2816,f275]) ).
fof(f2832,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ231_spl
| ~ memberP(nil,X0)
| memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f2816,f277]) ).
fof(f2834,plain,
! [X0] :
( ~ sQ7_spl
| ~ sQ231_spl
| cons(sK51_skl,app(nil,X0)) = app(sK47_skl,X0)
| ~ ssItem(sK51_skl)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f2816,f247]) ).
fof(f2835,plain,
! [X0,X1] :
( ~ sQ7_spl
| ~ sQ231_spl
| nil = X0
| cons(X1,X0) != sK47_skl
| ~ ssItem(sK51_skl)
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f2816,f228]) ).
fof(f2838,plain,
( ~ sQ7_spl
| ~ sQ231_spl
| nil != sK47_skl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2816,f235]) ).
fof(f2840,definition,
! [X0] :
( sQ232_spl
<=> ( cons(sK51_skl,X0) = app(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ232_spl])],[split_symbol_definition]) ).
fof(f2843,plain,
( ~ sQ7_spl
| ~ sQ231_spl
| ~ sQ32_spl
| sQ232_spl ),
inference(split_clause,[status(thm)],[f2822,f2840,f671,f2811,f466]) ).
fof(f2845,definition,
! [X0] :
( sQ233_spl
<=> ( ~ ssList(X0)
| memberP(app(X0,sK47_skl),sK51_skl)
| ~ ssList(app(X0,cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ233_spl])],[split_symbol_definition]) ).
fof(f2848,plain,
( ~ sQ7_spl
| ~ sQ231_spl
| ~ sQ14_spl
| ~ sQ32_spl
| sQ233_spl ),
inference(split_clause,[status(thm)],[f2824,f2845,f671,f539,f2811,f466]) ).
fof(f2849,definition,
! [X0,X1,X2] :
( sQ234_spl
<=> ( leq(sK51_skl,X1)
| leq(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ234_spl])],[split_symbol_definition]) ).
fof(f2852,plain,
( ~ sQ7_spl
| ~ sQ231_spl
| ~ sQ14_spl
| ~ sQ32_spl
| sQ234_spl ),
inference(split_clause,[status(thm)],[f2825,f2849,f671,f539,f2811,f466]) ).
fof(f2853,definition,
! [X0,X1,X2] :
( sQ235_spl
<=> ( leq(X1,sK51_skl)
| leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ totalorderP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f2856,plain,
( ~ sQ7_spl
| ~ sQ231_spl
| ~ sQ14_spl
| ~ sQ32_spl
| sQ235_spl ),
inference(split_clause,[status(thm)],[f2826,f2853,f671,f539,f2811,f466]) ).
fof(f2857,definition,
! [X0,X1,X2] :
( sQ236_spl
<=> ( ~ leq(sK51_skl,X1)
| ~ leq(X1,sK51_skl)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,cons(X1,X2)),sK47_skl))
| ~ ssList(app(app(X0,cons(X1,X2)),cons(sK51_skl,nil))) ) ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f2860,plain,
( ~ sQ7_spl
| ~ sQ231_spl
| ~ sQ14_spl
| ~ sQ32_spl
| sQ236_spl ),
inference(split_clause,[status(thm)],[f2827,f2857,f671,f539,f2811,f466]) ).
fof(f2861,definition,
! [X0,X1,X2] :
( sQ237_spl
<=> ( ~ leq(X1,sK51_skl)
| ~ leq(sK51_skl,X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssItem(X1)
| ~ cyclefreeP(app(app(X0,sK47_skl),cons(X1,X2)))
| ~ ssList(app(app(X0,cons(sK51_skl,nil)),cons(X1,X2))) ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f2864,plain,
( ~ sQ7_spl
| ~ sQ231_spl
| ~ sQ14_spl
| ~ sQ32_spl
| sQ237_spl ),
inference(split_clause,[status(thm)],[f2828,f2861,f671,f539,f2811,f466]) ).
fof(f2866,definition,
( sQ238_spl
<=> hd(sK47_skl) = sK51_skl ),
introduced(definition,[new_symbols(definition,[sQ238_spl])],[split_symbol_definition]) ).
fof(f2869,plain,
( ~ sQ7_spl
| ~ sQ231_spl
| sQ238_spl
| ~ sQ32_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f2830,f539,f671,f2866,f2811,f466]) ).
fof(f2870,definition,
! [X0] :
( sQ239_spl
<=> ( memberP(nil,X0)
| X0 = sK51_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ239_spl])],[split_symbol_definition]) ).
fof(f2873,plain,
( ~ sQ7_spl
| ~ sQ231_spl
| ~ sQ14_spl
| ~ sQ32_spl
| sQ239_spl ),
inference(split_clause,[status(thm)],[f2831,f2870,f671,f539,f2811,f466]) ).
fof(f2874,plain,
( ~ sQ7_spl
| ~ sQ231_spl
| ~ sQ14_spl
| ~ sQ32_spl
| sQ118_spl ),
inference(split_clause,[status(thm)],[f2832,f1528,f671,f539,f2811,f466]) ).
fof(f2876,definition,
! [X0] :
( sQ240_spl
<=> ( cons(sK51_skl,app(nil,X0)) = app(sK47_skl,X0)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ240_spl])],[split_symbol_definition]) ).
fof(f2879,plain,
( ~ sQ7_spl
| ~ sQ231_spl
| ~ sQ32_spl
| ~ sQ14_spl
| sQ240_spl ),
inference(split_clause,[status(thm)],[f2834,f2876,f539,f671,f2811,f466]) ).
fof(f2880,plain,
( ~ sQ7_spl
| ~ sQ231_spl
| ~ sQ32_spl
| ~ sQ14_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f2835,f1540,f539,f671,f2811,f466]) ).
fof(f2883,plain,
( ~ sQ7_spl
| ~ sQ231_spl
| ~ sQ123_spl
| ~ sQ32_spl
| ~ sQ14_spl ),
inference(split_clause,[status(thm)],[f2838,f539,f671,f1549,f2811,f466]) ).
fof(f2891,plain,
( ~ sQ220_spl
| ~ sQ117_spl
| ~ sQ231_spl
| sK51_skl = sK51_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f2815,f2618]) ).
fof(f2892,plain,
( ~ sQ220_spl
| ~ sQ117_spl
| ~ sQ231_spl
| sQ149_spl
| ~ sQ32_spl ),
inference(split_clause,[status(thm)],[f2891,f671,f1827,f2811,f1524,f2617]) ).
fof(f2893,plain,
( ~ sQ0_spl
| ~ sQ222_spl
| memberP(sK47_skl,sK54_skl)
| ~ ssItem(sK54_skl) ),
inference(resolution,[status(thm)],[f2630,f592]) ).
fof(f2894,plain,
( ~ sQ0_spl
| ~ sQ222_spl
| sQ169_spl
| ~ sQ30_spl ),
inference(split_clause,[status(thm)],[f2893,f665,f1985,f2625,f441]) ).
fof(f2895,plain,
$false,
inference(sat_refutation,[status(thm)],[f447,f451,f458,f465,f469,f473,f542,f544,f553,f555,f564,f570,f579,f621,f634,f647,f653,f674,f678,f680,f690,f704,f725,f1459,f1469,f1471,f1473,f1482,f1492,f1511,f1515,f1519,f1523,f1527,f1535,f1539,f1559,f1720,f1732,f1774,f1778,f1780,f1785,f1791,f1795,f1822,f1823,f1825,f1841,f1901,f1905,f1909,f1914,f1919,f1923,f1927,f1931,f1935,f1936,f1940,f1962,f1988,f1993,f2038,f2087,f2091,f2103,f2104,f2121,f2125,f2130,f2200,f2248,f2261,f2289,f2293,f2329,f2331,f2335,f2339,f2345,f2377,f2382,f2383,f2387,f2391,f2410,f2414,f2539,f2548,f2552,f2557,f2591,f2613,f2620,f2624,f2628,f2632,f2651,f2703,f2783,f2787,f2791,f2814,f2843,f2848,f2852,f2856,f2860,f2864,f2869,f2873,f2874,f2879,f2880,f2883,f2892,f2894]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC284+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n004.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 08:12:05 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 3.94/0.97 % Refutation found
% 3.94/0.97 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.94/0.97 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.81/1.02 % Elapsed time: 0.656086 seconds
% 0.81/1.02 % CPU time: 4.735847 seconds
% 0.81/1.02 % Total memory used: 155.008 MB
% 0.81/1.02 % Net memory used: 150.763 MB
%------------------------------------------------------------------------------