%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC295+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n001.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 02:40:41 PM UTC 2026
% Result : Theorem 90.33s 11.96s
% Output : CNFRefutation 81.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 73
% Number of leaves : 27
% Syntax : Number of formulae : 301 ( 27 unt; 2 def)
% Number of atoms : 1228 ( 304 equ)
% Maximal formula atoms : 24 ( 4 avg)
% Number of connectives : 1563 ( 636 ~; 716 |; 121 &)
% ( 16 <=>; 74 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-3 aty)
% Number of variables : 383 ( 349 !; 34 ?)
% 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/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> hd(cons(V,U)) = V ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssList(tl(U)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> tl(cons(V,U)) = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( frontsegP(V,U)
& frontsegP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( frontsegP(U,V)
=> frontsegP(app(U,W),V) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( frontsegP(cons(U,W),cons(V,X))
<=> ( frontsegP(W,X)
& U = V ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f47,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( rearsegP(V,W)
& rearsegP(U,V) )
=> rearsegP(U,W) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> cons(hd(U),tl(U)) = U ) ),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = V ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil != U
=> hd(app(U,V)) = hd(U) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil != U
=> tl(app(U,V)) = app(tl(U),V) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [X3] :
( ssItem(X3)
=> ( ? [X4] :
( leq(X3,X4)
& memberP(X,X4)
& X3 != X4
& ssItem(X4) )
| ~ memberP(X,X3)
| cons(X3,nil) != W ) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ! [X2] :
( ssItem(X2)
=> ( ( lt(Y,X2)
| ~ memberP(X1,X2) )
& ( lt(X2,Y)
| ~ memberP(Z,X2) ) ) )
| app(app(Z,cons(Y,nil)),X1) != U ) ) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [X3] :
( ssItem(X3)
=> ( ? [X4] :
( leq(X3,X4)
& memberP(X,X4)
& X3 != X4
& ssItem(X4) )
| ~ memberP(X,X3)
| cons(X3,nil) != W ) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ! [X2] :
( ssItem(X2)
=> ( ( lt(Y,X2)
| ~ memberP(X1,X2) )
& ( lt(X2,Y)
| ~ memberP(Z,X2) ) ) )
| app(app(Z,cons(Y,nil)),X1) != U ) ) ) )
| U != W
| V != 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(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(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(f124,plain,
! [X0,X1,X2] :
( app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f125,plain,
! [U] :
( ! [V] :
( ( rearsegP(U,V)
<=> ? [W] :
( app(W,V) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f126,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ? [W] :
( app(W,V) = U
& ssList(W) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f125]) ).
fof(f127,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(W,V) != U
| ~ ssList(W) )
| rearsegP(U,V) )
& ( ( app(sK6_skl(V,U),V) = U
& ssList(sK6_skl(V,U)) )
| ~ rearsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(W,sK6_skl(V,U))],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ssList(sK6_skl(X1,X0))
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f129,plain,
! [X0,X1] :
( app(sK6_skl(X1,X0),X1) = X0
| ~ rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(f130,plain,
! [X0,X1,X2] :
( app(X2,X1) != X0
| ~ ssList(X2)
| rearsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f127]) ).
fof(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(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(f240,plain,
! [U] :
( ssList(tl(U))
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f241,plain,
! [X0] :
( ssList(tl(X0))
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f240]) ).
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(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(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(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(f283,plain,
! [U] :
( ! [V] :
( U = V
| ~ frontsegP(V,U)
| ~ frontsegP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f284,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(f287,plain,
! [U] :
( ! [V] :
( ! [W] :
( frontsegP(app(U,W),V)
| ~ frontsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f43]) ).
fof(f288,plain,
! [X0,X1,X2] :
( frontsegP(app(X0,X2),X1)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f287]) ).
fof(f289,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( frontsegP(cons(U,W),cons(V,X))
<=> ( frontsegP(W,X)
& U = V ) )
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f44]) ).
fof(f290,plain,
! [U] :
( ! [V] :
( ! [W] :
( ! [X] :
( ( ( ~ frontsegP(W,X)
| U != V
| frontsegP(cons(U,W),cons(V,X)) )
& ( ( frontsegP(W,X)
& U = V )
| ~ frontsegP(cons(U,W),cons(V,X)) ) )
| ~ ssList(X) )
| ~ ssList(W) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f289]) ).
fof(f293,plain,
! [X0,X1,X2,X3] :
( ~ frontsegP(X2,X3)
| X0 != X1
| frontsegP(cons(X0,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f290]) ).
fof(f294,plain,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f295,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f294]) ).
fof(f300,plain,
! [U] :
( ! [V] :
( ! [W] :
( rearsegP(U,W)
| ~ rearsegP(V,W)
| ~ rearsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f301,plain,
! [X0,X1,X2] :
( rearsegP(X0,X2)
| ~ rearsegP(X1,X2)
| ~ rearsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f300]) ).
fof(f373,plain,
! [U] :
( cons(hd(U),tl(U)) = U
| nil = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f78]) ).
fof(f374,plain,
! [X0] :
( cons(hd(X0),tl(X0)) = X0
| nil = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f373]) ).
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(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(f390,plain,
! [U] :
( ! [V] :
( hd(app(U,V)) = hd(U)
| nil = U
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f85]) ).
fof(f391,plain,
! [X0,X1] :
( hd(app(X0,X1)) = hd(X0)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f390]) ).
fof(f392,plain,
! [U] :
( ! [V] :
( tl(app(U,V)) = app(tl(U),V)
| nil = U
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f86]) ).
fof(f393,plain,
! [X0,X1] :
( tl(app(X0,X1)) = app(tl(X0),X1)
| nil = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f392]) ).
fof(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X3] :
( ! [X4] :
( ~ leq(X3,X4)
| ~ memberP(X,X4)
| X3 = X4
| ~ ssItem(X4) )
& memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) ) )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ( ( ~ lt(Y,X2)
& memberP(X1,X2) )
| ( ~ lt(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)
<=> ( ~ lt(X2,Y)
& memberP(Z,X2) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,definition,
! [W,X,X3] :
( sP1_prd(X3,X,W)
<=> ( ! [X4] :
( ~ leq(X3,X4)
| ~ memberP(X,X4)
| X3 = X4
| ~ ssItem(X4) )
& memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f418,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X3] : sP1_prd(X3,X,W) )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ? [X2] :
( ( ( ~ lt(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,f417,f416]) ).
fof(f419,plain,
( ( ( nil = sK49_skl
& nil = sK50_skl )
| sP1_prd(sK55_skl,sK50_skl,sK49_skl) )
& ( ( ~ lt(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)],[f418]) ).
fof(f420,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f424,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f425,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f426,plain,
ssItem(sK51_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f427,plain,
ssList(sK52_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f428,plain,
ssList(sK53_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f429,plain,
app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK47_skl,
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f430,plain,
ssItem(sK54_skl),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f431,plain,
( memberP(sK53_skl,sK54_skl)
| sP0_prd(sK54_skl,sK52_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f434,plain,
( nil = sK49_skl
| sP1_prd(sK55_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f419]) ).
fof(f435,plain,
! [Y,Z,X2] :
( ( lt(X2,Y)
| ~ memberP(Z,X2)
| sP0_prd(X2,Z,Y) )
& ( ( ~ lt(X2,Y)
& memberP(Z,X2) )
| ~ sP0_prd(X2,Z,Y) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f436,plain,
( ! [Y,Z,X2] :
( lt(X2,Y)
| ~ memberP(Z,X2)
| sP0_prd(X2,Z,Y) )
& ! [Y,Z,X2] :
( ( ~ lt(X2,Y)
& memberP(Z,X2) )
| ~ sP0_prd(X2,Z,Y) ) ),
inference(miniscoping,[status(thm)],[f435]) ).
fof(f437,plain,
! [X0,X1,X2] :
( memberP(X1,X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f436]) ).
fof(f440,plain,
! [W,X,X3] :
( ( ? [X4] :
( leq(X3,X4)
& memberP(X,X4)
& X3 != X4
& ssItem(X4) )
| ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3)
| sP1_prd(X3,X,W) )
& ( ( ! [X4] :
( ~ leq(X3,X4)
| ~ memberP(X,X4)
| X3 = X4
| ~ ssItem(X4) )
& memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) )
| ~ sP1_prd(X3,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f417]) ).
fof(f441,plain,
( ! [W,X,X3] :
( ? [X4] :
( leq(X3,X4)
& memberP(X,X4)
& X3 != X4
& ssItem(X4) )
| ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3)
| sP1_prd(X3,X,W) )
& ! [W,X,X3] :
( ( ! [X4] :
( ~ leq(X3,X4)
| ~ memberP(X,X4)
| X3 = X4
| ~ ssItem(X4) )
& memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) )
| ~ sP1_prd(X3,X,W) ) ),
inference(miniscoping,[status(thm)],[f440]) ).
fof(f442,plain,
( ! [W,X,X3] :
( ( leq(X3,sK56_skl(X3,X,W))
& memberP(X,sK56_skl(X3,X,W))
& X3 != sK56_skl(X3,X,W)
& ssItem(sK56_skl(X3,X,W)) )
| ~ memberP(X,X3)
| cons(X3,nil) != W
| ~ ssItem(X3)
| sP1_prd(X3,X,W) )
& ! [W,X,X3] :
( ( ! [X4] :
( ~ leq(X3,X4)
| ~ memberP(X,X4)
| X3 = X4
| ~ ssItem(X4) )
& memberP(X,X3)
& cons(X3,nil) = W
& ssItem(X3) )
| ~ sP1_prd(X3,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56_skl]),skolemize(X4,sK56_skl(X3,X,W))],[f441]) ).
fof(f443,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
fof(f444,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
fof(f447,plain,
! [X0,X1,X2] :
( ssItem(sK56_skl(X0,X1,X2))
| ~ memberP(X1,X0)
| cons(X0,nil) != X2
| ~ ssItem(X0)
| sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
fof(f448,plain,
! [X0,X1,X2] :
( X0 != sK56_skl(X0,X1,X2)
| ~ memberP(X1,X0)
| cons(X0,nil) != X2
| ~ ssItem(X0)
| sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
fof(f449,plain,
! [X0,X1,X2] :
( memberP(X1,sK56_skl(X0,X1,X2))
| ~ memberP(X1,X0)
| cons(X0,nil) != X2
| ~ ssItem(X0)
| sP1_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f442]) ).
fof(f453,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(f455,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f456,plain,
! [X0,X1] :
( ~ ssList(X0)
| rearsegP(app(X0,X1),X1)
| ~ ssList(X1)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f130]) ).
fof(f468,plain,
! [X1,X2] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f276]) ).
fof(f469,plain,
! [X0,X1] :
( memberP(cons(X0,X1),X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f468]) ).
fof(f470,plain,
! [X1,X2,X3] :
( ~ frontsegP(X2,X3)
| frontsegP(cons(X1,X2),cons(X1,X3))
| ~ ssList(X3)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f293]) ).
fof(f471,plain,
! [X0,X1,X2] :
( ~ frontsegP(X1,X2)
| frontsegP(cons(X0,X1),cons(X0,X2))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f470]) ).
fof(f481,plain,
! [X0,X1] :
( ssItem(sK56_skl(X0,X1,cons(X0,nil)))
| ~ memberP(X1,X0)
| ~ ssItem(X0)
| sP1_prd(X0,X1,cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f447]) ).
fof(f482,plain,
! [X0,X1] :
( X0 != sK56_skl(X0,X1,cons(X0,nil))
| ~ memberP(X1,X0)
| ~ ssItem(X0)
| sP1_prd(X0,X1,cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f448]) ).
fof(f483,plain,
! [X0,X1] :
( memberP(X1,sK56_skl(X0,X1,cons(X0,nil)))
| ~ memberP(X1,X0)
| ~ ssItem(X0)
| sP1_prd(X0,X1,cons(X0,nil)) ),
inference(destructive_equality_resolution,[status(thm)],[f449]) ).
fof(f499,plain,
( nil = sK49_skl
| sP1_prd(sK55_skl,sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f434]) ).
fof(f500,plain,
( nil = sK49_skl
| sP1_prd(sK55_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f499]) ).
fof(f501,plain,
( nil = sK47_skl
| sP1_prd(sK55_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f425,f500]) ).
fof(f502,plain,
( cons(sK55_skl,nil) = sK47_skl
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f501,f444]) ).
fof(f504,plain,
( ssItem(sK55_skl)
| nil = sK47_skl ),
inference(resolution,[status(thm)],[f501,f443]) ).
fof(f685,plain,
( memberP(sK52_skl,sK54_skl)
| memberP(sK53_skl,sK54_skl) ),
inference(resolution,[status(thm)],[f431,f437]) ).
fof(f714,plain,
( nil = app(sK52_skl,cons(sK51_skl,nil))
| nil != sK47_skl
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f429,f386]) ).
fof(f715,plain,
( nil = app(sK52_skl,cons(sK51_skl,nil))
| nil != sK47_skl
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(forward_subsumption_resolution,[status(thm)],[f714,f428]) ).
fof(f884,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f455,f245]) ).
fof(f888,plain,
! [X0] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f129,f385]) ).
fof(f891,plain,
! [X0] :
( nil = X0
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(duplicate_literals_removal,[status(thm)],[f888]) ).
fof(f892,plain,
! [X0] :
( nil = X0
| ~ ssList(sK6_skl(X0,nil))
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f891,f223]) ).
fof(f927,plain,
! [X0] :
( ~ rearsegP(nil,X0)
| ~ ssList(X0)
| ~ ssList(nil)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f892,f128]) ).
fof(f928,plain,
! [X0] :
( ~ ssList(nil)
| nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f927]) ).
fof(f929,plain,
! [X0] :
( nil = X0
| ~ rearsegP(nil,X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f928,f223]) ).
fof(f963,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)],[f429,f271]) ).
fof(f964,plain,
! [X0] :
( ~ memberP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f963,f428]) ).
fof(f966,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)],[f429,f272]) ).
fof(f967,plain,
! [X0] :
( ~ memberP(sK53_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f966,f428]) ).
fof(f972,plain,
! [X0] :
( nil = sK47_skl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK55_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f502,f275]) ).
fof(f974,plain,
! [X0] :
( nil = sK47_skl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f972,f504]) ).
fof(f989,plain,
! [X0,X1] :
( ~ ssList(X1)
| rearsegP(app(X1,X0),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f456,f245]) ).
fof(f990,plain,
( ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| rearsegP(sK47_skl,sK53_skl)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f429,f989]) ).
fof(f991,plain,
( ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| rearsegP(sK47_skl,sK53_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f990,f428]) ).
fof(f992,plain,
( ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| rearsegP(sK47_skl,sK53_skl) ),
inference(resolution,[status(thm)],[f991,f245]) ).
fof(f993,plain,
( ~ ssList(cons(sK51_skl,nil))
| rearsegP(sK47_skl,sK53_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f992,f427]) ).
fof(f994,plain,
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| rearsegP(sK47_skl,sK53_skl) ),
inference(resolution,[status(thm)],[f993,f222]) ).
fof(f995,plain,
( ~ ssItem(sK51_skl)
| rearsegP(sK47_skl,sK53_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f994,f223]) ).
fof(f996,plain,
rearsegP(sK47_skl,sK53_skl),
inference(forward_subsumption_resolution,[status(thm)],[f995,f426]) ).
fof(f1018,plain,
! [X0,X1,X2] :
( memberP(X2,sK56_skl(X0,cons(X1,X2),cons(X0,nil)))
| sK56_skl(X0,cons(X1,X2),cons(X0,nil)) = X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(sK56_skl(X0,cons(X1,X2),cons(X0,nil)))
| ~ memberP(cons(X1,X2),X0)
| ~ ssItem(X0)
| sP1_prd(X0,cons(X1,X2),cons(X0,nil)) ),
inference(resolution,[status(thm)],[f483,f275]) ).
fof(f1023,plain,
! [X0,X1,X2] :
( memberP(X2,sK56_skl(X0,cons(X1,X2),cons(X0,nil)))
| sK56_skl(X0,cons(X1,X2),cons(X0,nil)) = X1
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ memberP(cons(X1,X2),X0)
| ~ ssItem(X0)
| sP1_prd(X0,cons(X1,X2),cons(X0,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1018,f481]) ).
fof(f1380,plain,
( nil = sK52_skl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| nil != sK47_skl
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(resolution,[status(thm)],[f715,f386]) ).
fof(f1381,plain,
( nil = cons(sK51_skl,nil)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| nil != sK47_skl
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(resolution,[status(thm)],[f715,f385]) ).
fof(f1382,plain,
( nil = sK52_skl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| nil != sK47_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f1380,f245]) ).
fof(f1383,plain,
( nil = cons(sK51_skl,nil)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| nil != sK47_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f1381,f245]) ).
fof(f2700,plain,
! [X0] :
( frontsegP(sK47_skl,X0)
| ~ frontsegP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| ~ ssList(sK53_skl)
| ~ ssList(X0)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f429,f288]) ).
fof(f2705,plain,
! [X0] :
( frontsegP(sK47_skl,X0)
| ~ frontsegP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| ~ ssList(X0)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(forward_subsumption_resolution,[status(thm)],[f2700,f428]) ).
fof(f2707,plain,
( ~ ssList(nil)
| ~ ssList(sK52_skl)
| ~ ssItem(sK51_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| memberP(sK47_skl,sK51_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f964,f453]) ).
fof(f2709,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f964,f271]) ).
fof(f2711,plain,
( ~ ssList(nil)
| ~ ssList(sK52_skl)
| memberP(sK47_skl,sK51_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(sK51_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f2707]) ).
fof(f2712,plain,
( ~ ssList(nil)
| ~ ssList(sK52_skl)
| memberP(sK47_skl,sK51_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(forward_subsumption_resolution,[status(thm)],[f2711,f426]) ).
fof(f2715,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| memberP(sK47_skl,X0)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f2709]) ).
fof(f2716,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2715,f245]) ).
fof(f2718,plain,
! [X0] :
( ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| ~ memberP(sK53_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f967,f245]) ).
fof(f2719,plain,
! [X0] :
( ~ ssList(cons(sK51_skl,nil))
| ~ memberP(sK53_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2718,f427]) ).
fof(f2795,plain,
! [X0,X1] :
( ~ ssItem(sK56_skl(X0,cons(X1,nil),cons(X0,nil)))
| sK56_skl(X0,cons(X1,nil),cons(X0,nil)) = X1
| ~ ssList(nil)
| ~ ssItem(X1)
| ~ memberP(cons(X1,nil),X0)
| ~ ssItem(X0)
| sP1_prd(X0,cons(X1,nil),cons(X0,nil)) ),
inference(resolution,[status(thm)],[f1023,f279]) ).
fof(f2807,plain,
! [X0,X1] :
( ~ ssItem(sK56_skl(X0,cons(X1,nil),cons(X0,nil)))
| sK56_skl(X0,cons(X1,nil),cons(X0,nil)) = X1
| ~ ssItem(X1)
| ~ memberP(cons(X1,nil),X0)
| ~ ssItem(X0)
| sP1_prd(X0,cons(X1,nil),cons(X0,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2795,f223]) ).
fof(f2956,plain,
! [X0] :
( rearsegP(X0,sK53_skl)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(sK53_skl)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f301,f996]) ).
fof(f2978,plain,
! [X0] :
( rearsegP(X0,sK53_skl)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(sK53_skl)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2956,f420]) ).
fof(f2997,plain,
! [X0] :
( rearsegP(X0,sK53_skl)
| ~ rearsegP(X0,sK47_skl)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2978,f428]) ).
fof(f3017,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK47_skl)
| rearsegP(app(X0,sK47_skl),sK53_skl)
| ~ ssList(app(X0,sK47_skl)) ),
inference(resolution,[status(thm)],[f2997,f989]) ).
fof(f3029,plain,
! [X0] :
( ~ ssList(X0)
| ~ ssList(sK47_skl)
| rearsegP(app(X0,sK47_skl),sK53_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f3017,f245]) ).
fof(f5863,plain,
! [X0] :
( ~ ssList(X0)
| rearsegP(app(X0,sK47_skl),sK53_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f3029,f420]) ).
fof(f5920,plain,
( tl(sK47_skl) = app(tl(app(sK52_skl,cons(sK51_skl,nil))),sK53_skl)
| nil = app(sK52_skl,cons(sK51_skl,nil))
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f429,f393]) ).
fof(f5921,plain,
( tl(sK47_skl) = app(tl(app(sK52_skl,cons(sK51_skl,nil))),sK53_skl)
| nil = app(sK52_skl,cons(sK51_skl,nil))
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(forward_subsumption_resolution,[status(thm)],[f5920,f428]) ).
fof(f5927,plain,
( ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| frontsegP(sK47_skl,sK52_skl)
| ~ ssList(sK52_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(resolution,[status(thm)],[f2705,f884]) ).
fof(f5932,plain,
( ~ ssList(cons(sK51_skl,nil))
| frontsegP(sK47_skl,sK52_skl)
| ~ ssList(sK52_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(duplicate_literals_removal,[status(thm)],[f5927]) ).
fof(f5933,plain,
( ~ ssList(cons(sK51_skl,nil))
| frontsegP(sK47_skl,sK52_skl)
| ~ ssList(sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f5932,f245]) ).
fof(f6819,plain,
( ~ ssList(cons(sK51_skl,nil))
| frontsegP(sK47_skl,sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f5933,f427]) ).
fof(f6820,plain,
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| frontsegP(sK47_skl,sK52_skl) ),
inference(resolution,[status(thm)],[f6819,f222]) ).
fof(f6821,plain,
( ~ ssItem(sK51_skl)
| frontsegP(sK47_skl,sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f6820,f223]) ).
fof(f6822,plain,
frontsegP(sK47_skl,sK52_skl),
inference(forward_subsumption_resolution,[status(thm)],[f6821,f426]) ).
fof(f6824,plain,
( sK52_skl = sK47_skl
| ~ frontsegP(sK52_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK52_skl) ),
inference(resolution,[status(thm)],[f6822,f284]) ).
fof(f6835,plain,
( sK52_skl = sK47_skl
| ~ frontsegP(sK52_skl,sK47_skl)
| ~ ssList(sK47_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f6824,f427]) ).
fof(f7611,plain,
( sK52_skl = sK47_skl
| ~ frontsegP(sK52_skl,sK47_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f6835,f420]) ).
fof(f7669,plain,
! [X0] :
( nil = sK47_skl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f974,f223]) ).
fof(f7821,plain,
( nil = sK52_skl
| ~ ssList(cons(sK51_skl,nil))
| nil != sK47_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f1382,f427]) ).
fof(f7878,plain,
( nil = cons(sK51_skl,nil)
| ~ ssList(cons(sK51_skl,nil))
| nil != sK47_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f1383,f427]) ).
fof(f7879,plain,
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| ~ ssList(cons(sK51_skl,nil))
| nil != sK47_skl ),
inference(resolution,[status(thm)],[f7878,f235]) ).
fof(f7881,plain,
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| nil != sK47_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f7879,f222]) ).
fof(f7897,plain,
( ~ ssItem(sK51_skl)
| nil != sK47_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f7881,f223]) ).
fof(f8264,plain,
( ~ ssList(nil)
| memberP(sK47_skl,sK51_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(forward_subsumption_resolution,[status(thm)],[f2712,f427]) ).
fof(f8265,plain,
( ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| ~ ssList(nil)
| memberP(sK47_skl,sK51_skl) ),
inference(resolution,[status(thm)],[f8264,f245]) ).
fof(f8266,plain,
( ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| memberP(sK47_skl,sK51_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f8265,f223]) ).
fof(f8267,plain,
( ~ ssList(cons(sK51_skl,nil))
| memberP(sK47_skl,sK51_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f8266,f427]) ).
fof(f8268,plain,
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| memberP(sK47_skl,sK51_skl) ),
inference(resolution,[status(thm)],[f8267,f222]) ).
fof(f8269,plain,
( ~ ssItem(sK51_skl)
| memberP(sK47_skl,sK51_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f8268,f223]) ).
fof(f8270,plain,
memberP(sK47_skl,sK51_skl),
inference(forward_subsumption_resolution,[status(thm)],[f8269,f426]) ).
fof(f8272,plain,
( nil = sK47_skl
| memberP(nil,sK51_skl)
| sK51_skl = sK55_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f8270,f7669]) ).
fof(f8274,plain,
( nil = sK47_skl
| memberP(nil,sK51_skl)
| sK51_skl = sK55_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f8272,f426]) ).
fof(f8484,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| ~ ssList(cons(sK51_skl,nil))
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2716,f427]) ).
fof(f8485,plain,
! [X0] :
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| ~ memberP(sK52_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f8484,f222]) ).
fof(f8486,plain,
! [X0] :
( ~ ssItem(sK51_skl)
| ~ memberP(sK52_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f8485,f223]) ).
fof(f8709,plain,
! [X0] :
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| ~ memberP(sK53_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f2719,f222]) ).
fof(f8711,plain,
! [X0] :
( ~ ssItem(sK51_skl)
| ~ memberP(sK53_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f8709,f223]) ).
fof(f8713,plain,
( ~ ssItem(sK51_skl)
| nil = sK47_skl
| sK51_skl = sK55_skl ),
inference(resolution,[status(thm)],[f8274,f279]) ).
fof(f8714,plain,
( ~ ssItem(sK51_skl)
| sK51_skl = sK55_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f8713,f7897]) ).
fof(f8786,plain,
( cons(sK51_skl,nil) = sK47_skl
| nil = sK47_skl ),
inference(backward_demodulation,[status(thm)],[f8792,f502]) ).
fof(f8792,plain,
sK51_skl = sK55_skl,
inference(forward_subsumption_resolution,[status(thm)],[f8714,f426]) ).
fof(f9486,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f8486,f426]) ).
fof(f9493,plain,
! [X0] :
( ~ memberP(sK53_skl,X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f8711,f426]) ).
fof(f9494,plain,
( memberP(sK52_skl,sK54_skl)
| memberP(sK47_skl,sK54_skl)
| ~ ssItem(sK54_skl) ),
inference(resolution,[status(thm)],[f9493,f685]) ).
fof(f9498,plain,
( memberP(sK52_skl,sK54_skl)
| memberP(sK47_skl,sK54_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f9494,f430]) ).
fof(f9520,plain,
( memberP(sK47_skl,sK54_skl)
| ~ ssItem(sK54_skl)
| memberP(sK47_skl,sK54_skl) ),
inference(resolution,[status(thm)],[f9498,f9486]) ).
fof(f9521,plain,
( ~ ssItem(sK54_skl)
| memberP(sK47_skl,sK54_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f9520]) ).
fof(f9522,plain,
memberP(sK47_skl,sK54_skl),
inference(forward_subsumption_resolution,[status(thm)],[f9521,f430]) ).
fof(f9868,plain,
! [X0,X1] :
( sK56_skl(X0,cons(X1,nil),cons(X0,nil)) = X1
| ~ ssItem(X1)
| ~ memberP(cons(X1,nil),X0)
| ~ ssItem(X0)
| sP1_prd(X0,cons(X1,nil),cons(X0,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2807,f481]) ).
fof(f9869,plain,
! [X0] :
( ~ memberP(cons(X0,nil),X0)
| ~ ssItem(X0)
| sP1_prd(X0,cons(X0,nil),cons(X0,nil))
| ~ ssItem(X0)
| ~ memberP(cons(X0,nil),X0)
| ~ ssItem(X0)
| sP1_prd(X0,cons(X0,nil),cons(X0,nil)) ),
inference(resolution,[status(thm)],[f9868,f482]) ).
fof(f9876,plain,
! [X0] :
( ~ memberP(cons(X0,nil),X0)
| ~ ssItem(X0)
| sP1_prd(X0,cons(X0,nil),cons(X0,nil)) ),
inference(duplicate_literals_removal,[status(thm)],[f9869]) ).
fof(f13561,plain,
( nil = sK47_skl
| ~ memberP(cons(sK51_skl,nil),sK51_skl)
| ~ ssItem(sK51_skl)
| sP1_prd(sK51_skl,sK47_skl,cons(sK51_skl,nil)) ),
inference(paramodulation,[status(thm)],[f8786,f9876]) ).
fof(f13569,plain,
( nil = sK47_skl
| ~ memberP(cons(sK51_skl,nil),sK51_skl)
| sP1_prd(sK51_skl,sK47_skl,cons(sK51_skl,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f13561,f426]) ).
fof(f14853,plain,
( nil = sK47_skl
| nil = sK47_skl
| ~ memberP(cons(sK51_skl,nil),sK51_skl)
| sP1_prd(sK51_skl,sK47_skl,sK47_skl) ),
inference(paramodulation,[status(thm)],[f8786,f13569]) ).
fof(f14855,plain,
( nil = sK47_skl
| ~ memberP(cons(sK51_skl,nil),sK51_skl)
| sP1_prd(sK51_skl,sK47_skl,sK47_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f14853]) ).
fof(f14859,plain,
( ~ ssList(nil)
| ~ ssItem(sK51_skl)
| nil = sK47_skl
| sP1_prd(sK51_skl,sK47_skl,sK47_skl) ),
inference(resolution,[status(thm)],[f14855,f469]) ).
fof(f14863,plain,
( ~ ssList(nil)
| ~ ssItem(sK51_skl)
| sP1_prd(sK51_skl,sK47_skl,sK47_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f14859,f7897]) ).
fof(f14871,plain,
( ~ ssList(nil)
| sP1_prd(sK51_skl,sK47_skl,sK47_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f14863,f426]) ).
fof(f14873,plain,
( cons(sK51_skl,nil) = sK47_skl
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f14871,f444]) ).
fof(f14877,plain,
cons(sK51_skl,nil) = sK47_skl,
inference(forward_subsumption_resolution,[status(thm)],[f14873,f223]) ).
fof(f15000,plain,
( nil = sK52_skl
| ~ ssList(sK47_skl)
| nil != sK47_skl ),
inference(backward_demodulation,[status(thm)],[f14877,f7821]) ).
fof(f15001,plain,
( tl(sK47_skl) = app(tl(app(sK52_skl,sK47_skl)),sK53_skl)
| nil = app(sK52_skl,cons(sK51_skl,nil))
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(backward_demodulation,[status(thm)],[f14877,f5921]) ).
fof(f15015,plain,
app(app(sK52_skl,sK47_skl),sK53_skl) = sK47_skl,
inference(backward_demodulation,[status(thm)],[f14877,f429]) ).
fof(f15110,plain,
! [X0] :
( ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK47_skl)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f14877,f471]) ).
fof(f15128,plain,
( tl(sK47_skl) = nil
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f14877,f243]) ).
fof(f15129,plain,
( hd(sK47_skl) = sK51_skl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f14877,f239]) ).
fof(f15132,plain,
! [X0] :
( memberP(nil,X0)
| X0 = sK51_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK51_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f14877,f275]) ).
fof(f15216,plain,
( nil = sK52_skl
| nil != sK47_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f15000,f420]) ).
fof(f15217,plain,
( tl(sK47_skl) = app(tl(app(sK52_skl,sK47_skl)),sK53_skl)
| nil = app(sK52_skl,cons(sK51_skl,nil))
| ~ ssList(app(sK52_skl,sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f14877,f15001]) ).
fof(f15218,plain,
( tl(sK47_skl) = app(tl(app(sK52_skl,sK47_skl)),sK53_skl)
| nil = app(sK52_skl,sK47_skl)
| ~ ssList(app(sK52_skl,sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f14877,f15217]) ).
fof(f15370,plain,
! [X0] :
( ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK47_skl)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f15110,f426]) ).
fof(f15397,plain,
( tl(sK47_skl) = nil
| ~ ssItem(sK51_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f15128,f223]) ).
fof(f15398,plain,
( hd(sK47_skl) = sK51_skl
| ~ ssItem(sK51_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f15129,f223]) ).
fof(f15403,plain,
! [X0] :
( memberP(nil,X0)
| X0 = sK51_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f15132,f426]) ).
fof(f15433,plain,
tl(sK47_skl) = nil,
inference(forward_subsumption_resolution,[status(thm)],[f15397,f426]) ).
fof(f15506,plain,
hd(sK47_skl) = sK51_skl,
inference(forward_subsumption_resolution,[status(thm)],[f15398,f426]) ).
fof(f15623,plain,
! [X0] :
( X0 = sK53_skl
| app(app(sK52_skl,sK47_skl),X0) != sK47_skl
| ~ ssList(X0)
| ~ ssList(app(sK52_skl,sK47_skl))
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f15015,f378]) ).
fof(f15766,plain,
! [X0] :
( X0 = sK53_skl
| app(app(sK52_skl,sK47_skl),X0) != sK47_skl
| ~ ssList(X0)
| ~ ssList(app(sK52_skl,sK47_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f15623,f428]) ).
fof(f15969,plain,
( nil = app(tl(app(sK52_skl,sK47_skl)),sK53_skl)
| nil = app(sK52_skl,sK47_skl)
| ~ ssList(app(sK52_skl,sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f15433,f15218]) ).
fof(f15971,plain,
( nil = sK53_skl
| ~ ssList(sK53_skl)
| ~ ssList(tl(app(sK52_skl,sK47_skl)))
| nil = app(sK52_skl,sK47_skl)
| ~ ssList(app(sK52_skl,sK47_skl)) ),
inference(resolution,[status(thm)],[f15969,f385]) ).
fof(f15973,plain,
( nil = sK53_skl
| ~ ssList(sK53_skl)
| nil = app(sK52_skl,sK47_skl)
| ~ ssList(app(sK52_skl,sK47_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f15971,f241]) ).
fof(f16127,plain,
! [X0] :
( memberP(nil,X0)
| X0 = sK51_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f15403,f223]) ).
fof(f16129,plain,
( memberP(nil,sK54_skl)
| sK54_skl = sK51_skl
| ~ ssItem(sK54_skl) ),
inference(resolution,[status(thm)],[f16127,f9522]) ).
fof(f16145,plain,
( memberP(nil,sK54_skl)
| sK54_skl = sK51_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f16129,f430]) ).
fof(f16159,plain,
( ~ ssItem(sK54_skl)
| sK54_skl = sK51_skl ),
inference(resolution,[status(thm)],[f16145,f279]) ).
fof(f16162,plain,
sK54_skl = sK51_skl,
inference(forward_subsumption_resolution,[status(thm)],[f16159,f430]) ).
fof(f16180,plain,
( memberP(sK52_skl,sK51_skl)
| memberP(sK53_skl,sK54_skl) ),
inference(backward_demodulation,[status(thm)],[f16162,f685]) ).
fof(f16189,plain,
( memberP(sK52_skl,sK51_skl)
| memberP(sK53_skl,sK51_skl) ),
inference(forward_demodulation,[status(thm)],[f16162,f16180]) ).
fof(f16255,plain,
! [X0] :
( ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK47_skl)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f15370,f223]) ).
fof(f16453,plain,
( nil = sK53_skl
| nil = app(sK52_skl,sK47_skl)
| ~ ssList(app(sK52_skl,sK47_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f15973,f428]) ).
fof(f16454,plain,
( ~ ssList(sK47_skl)
| ~ ssList(sK52_skl)
| nil = sK53_skl
| nil = app(sK52_skl,sK47_skl) ),
inference(resolution,[status(thm)],[f16453,f245]) ).
fof(f16455,plain,
( ~ ssList(sK47_skl)
| nil = sK53_skl
| nil = app(sK52_skl,sK47_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f16454,f427]) ).
fof(f16456,plain,
( nil = sK53_skl
| nil = app(sK52_skl,sK47_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f16455,f420]) ).
fof(f16483,plain,
( nil = sK53_skl
| ~ ssList(sK52_skl)
| rearsegP(nil,sK53_skl) ),
inference(paramodulation,[status(thm)],[f16456,f5863]) ).
fof(f16561,plain,
( nil = sK53_skl
| rearsegP(nil,sK53_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f16483,f427]) ).
fof(f16630,plain,
( nil = sK53_skl
| ~ ssList(sK53_skl)
| nil = sK53_skl ),
inference(resolution,[status(thm)],[f16561,f929]) ).
fof(f16633,plain,
( ~ ssList(sK53_skl)
| nil = sK53_skl ),
inference(duplicate_literals_removal,[status(thm)],[f16630]) ).
fof(f16634,plain,
nil = sK53_skl,
inference(forward_subsumption_resolution,[status(thm)],[f16633,f428]) ).
fof(f16647,plain,
( memberP(sK52_skl,sK51_skl)
| memberP(nil,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f16634,f16189]) ).
fof(f16660,plain,
app(app(sK52_skl,sK47_skl),nil) = sK47_skl,
inference(backward_demodulation,[status(thm)],[f16634,f15015]) ).
fof(f16700,plain,
( sK47_skl = app(sK52_skl,sK47_skl)
| ~ ssList(app(sK52_skl,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f16660,f389]) ).
fof(f16917,plain,
( ~ ssList(sK47_skl)
| ~ ssList(sK52_skl)
| sK47_skl = app(sK52_skl,sK47_skl) ),
inference(resolution,[status(thm)],[f16700,f245]) ).
fof(f16918,plain,
( ~ ssList(sK47_skl)
| sK47_skl = app(sK52_skl,sK47_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f16917,f427]) ).
fof(f16930,plain,
sK47_skl = app(sK52_skl,sK47_skl),
inference(forward_subsumption_resolution,[status(thm)],[f16918,f420]) ).
fof(f16982,plain,
( hd(sK47_skl) = hd(sK52_skl)
| nil = sK52_skl
| ~ ssList(sK47_skl)
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f16930,f391]) ).
fof(f17078,plain,
( sK51_skl = hd(sK52_skl)
| nil = sK52_skl
| ~ ssList(sK47_skl)
| ~ ssList(sK52_skl) ),
inference(forward_demodulation,[status(thm)],[f15506,f16982]) ).
fof(f17079,plain,
( sK51_skl = hd(sK52_skl)
| nil = sK52_skl
| ~ ssList(sK47_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f17078,f427]) ).
fof(f17267,plain,
! [X0] :
( X0 = sK53_skl
| app(app(sK52_skl,sK47_skl),X0) != sK47_skl
| ~ ssList(X0)
| ~ ssList(sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f16930,f15766]) ).
fof(f17268,plain,
! [X0] :
( X0 = sK53_skl
| app(sK47_skl,X0) != sK47_skl
| ~ ssList(X0)
| ~ ssList(sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f16930,f17267]) ).
fof(f17269,plain,
! [X0] :
( X0 = nil
| app(sK47_skl,X0) != sK47_skl
| ~ ssList(X0)
| ~ ssList(sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f16634,f17268]) ).
fof(f17270,plain,
! [X0] :
( X0 = nil
| app(sK47_skl,X0) != sK47_skl
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f17269,f420]) ).
fof(f17277,plain,
( sK51_skl = hd(sK52_skl)
| nil = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f17079,f420]) ).
fof(f17285,plain,
( nil = sK52_skl
| cons(sK51_skl,tl(sK52_skl)) = sK52_skl
| nil = sK52_skl
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f17277,f374]) ).
fof(f17303,plain,
( cons(sK51_skl,tl(sK52_skl)) = sK52_skl
| nil = sK52_skl
| ~ ssList(sK52_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f17285]) ).
fof(f17304,plain,
( cons(sK51_skl,tl(sK52_skl)) = sK52_skl
| nil = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f17303,f427]) ).
fof(f17309,plain,
( nil = sK52_skl
| ~ frontsegP(tl(sK52_skl),nil)
| frontsegP(sK52_skl,sK47_skl)
| ~ ssList(tl(sK52_skl)) ),
inference(paramodulation,[status(thm)],[f17304,f16255]) ).
fof(f17382,plain,
( nil = sK52_skl
| frontsegP(sK52_skl,sK47_skl)
| ~ ssList(tl(sK52_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f17309,f295]) ).
fof(f17449,plain,
( nil = sK52_skl
| ~ ssList(sK52_skl)
| nil = sK52_skl
| frontsegP(sK52_skl,sK47_skl) ),
inference(resolution,[status(thm)],[f17382,f241]) ).
fof(f17450,plain,
( ~ ssList(sK52_skl)
| nil = sK52_skl
| frontsegP(sK52_skl,sK47_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f17449]) ).
fof(f17451,plain,
( nil = sK52_skl
| frontsegP(sK52_skl,sK47_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f17450,f427]) ).
fof(f17454,plain,
( sK52_skl = sK47_skl
| nil = sK52_skl ),
inference(resolution,[status(thm)],[f17451,f7611]) ).
fof(f17465,plain,
( nil = sK52_skl
| sK47_skl = app(sK47_skl,sK47_skl) ),
inference(paramodulation,[status(thm)],[f17454,f16930]) ).
fof(f17497,plain,
( sK47_skl = nil
| ~ ssList(sK47_skl)
| nil = sK52_skl ),
inference(resolution,[status(thm)],[f17465,f17270]) ).
fof(f17579,plain,
( sK47_skl = nil
| nil = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f17497,f420]) ).
fof(f17689,plain,
( memberP(nil,sK51_skl)
| memberP(nil,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f17710,f16647]) ).
fof(f17710,plain,
nil = sK52_skl,
inference(forward_subsumption_resolution,[status(thm)],[f17579,f15216]) ).
fof(f17713,plain,
memberP(nil,sK51_skl),
inference(duplicate_literals_removal,[status(thm)],[f17689]) ).
fof(f17732,plain,
~ ssItem(sK51_skl),
inference(resolution,[status(thm)],[f17713,f279]) ).
fof(f17733,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f17732,f426]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC295+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n001.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 08:18:44 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.08/0.38 % Drodi V4.1.1
% 90.33/11.96 % Refutation found
% 90.33/11.96 % SZS status Theorem for theBenchmark: Theorem is valid
% 90.33/11.96 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 17.69/12.01 % Elapsed time: 11.640047 seconds
% 17.69/12.01 % CPU time: 91.546801 seconds
% 17.69/12.01 % Total memory used: 382.182 MB
% 17.69/12.01 % Net memory used: 358.707 MB
%------------------------------------------------------------------------------