%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC183+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 : n007.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 02:40:18 PM UTC 2026
% Result : Theorem 17.40s 2.85s
% Output : CNFRefutation 18.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 65
% Number of leaves : 24
% Syntax : Number of formulae : 224 ( 27 unt; 1 def)
% Number of atoms : 886 ( 253 equ)
% Maximal formula atoms : 21 ( 3 avg)
% Number of connectives : 1118 ( 456 ~; 496 |; 94 &)
% ( 11 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 9 con; 0-3 aty)
% Number of variables : 283 ( 260 !; 23 ?)
% Comments :
%------------------------------------------------------------------------------
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(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(f18,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) != U ) ),
file('/export/starexec/sandbox2/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/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(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,axiom,
! [U] :
( ssList(U)
=> app(nil,U) = U ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(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(f78,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> cons(hd(U),tl(U)) = U ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f81,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> cons(V,U) = app(cons(V,nil),U) ) ),
file('/export/starexec/sandbox2/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/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(f85,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil != U
=> hd(app(U,V)) = hd(U) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( nil != W
| nil != X )
& ! [X2] :
( ? [X3] :
( leq(X2,X3)
& memberP(X,X3)
& X2 != X3
& ssItem(X3) )
| ~ memberP(X,X2)
| cons(X2,nil) != W
| ~ ssItem(X2) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ( ~ memberP(X1,Y)
& ~ memberP(Z,Y) )
| app(app(Z,cons(Y,nil)),X1) != U
| ~ ssList(X1) ) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ( ( nil != W
| nil != X )
& ! [X2] :
( ? [X3] :
( leq(X2,X3)
& memberP(X,X3)
& X2 != X3
& ssItem(X3) )
| ~ memberP(X,X2)
| cons(X2,nil) != W
| ~ ssItem(X2) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ( ~ memberP(X1,Y)
& ~ memberP(Z,Y) )
| app(app(Z,cons(Y,nil)),X1) != U
| ~ ssList(X1) ) ) )
| U != W
| V != X
| ~ ssList(X) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
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(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(f224,plain,
! [U] :
( ! [V] :
( cons(V,U) != U
| ~ ssItem(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f18]) ).
fof(f225,plain,
! [X0,X1] :
( cons(X1,X0) != X0
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f224]) ).
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(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(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(f244,plain,
! [U] :
( ! [V] :
( ssList(app(U,V))
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f26]) ).
fof(f245,plain,
! [X0,X1] :
( ssList(app(X0,X1))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f244]) ).
fof(f248,plain,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f28]) ).
fof(f249,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
fof(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(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(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(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(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(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X2] :
( ! [X3] :
( ~ leq(X2,X3)
| ~ memberP(X,X3)
| X2 = X3
| ~ ssItem(X3) )
& memberP(X,X2)
& cons(X2,nil) = W
& ssItem(X2) ) )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ( memberP(X1,Y)
| memberP(Z,Y) )
& 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,
! [W,X,X2] :
( sP0_prd(X2,X,W)
<=> ( ! [X3] :
( ~ leq(X2,X3)
| ~ memberP(X,X3)
| X2 = X3
| ~ ssItem(X3) )
& memberP(X,X2)
& cons(X2,nil) = W
& ssItem(X2) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X2] : sP0_prd(X2,X,W) )
& ? [Y] :
( ? [Z] :
( ? [X1] :
( ( memberP(X1,Y)
| memberP(Z,Y) )
& 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,
( ( ( nil = sK49_skl
& nil = sK50_skl )
| sP0_prd(sK54_skl,sK50_skl,sK49_skl) )
& ( memberP(sK53_skl,sK51_skl)
| memberP(sK52_skl,sK51_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]),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)],[f417]) ).
fof(f421,plain,
ssList(sK49_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,
( memberP(sK53_skl,sK51_skl)
| memberP(sK52_skl,sK51_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f431,plain,
( nil = sK49_skl
| sP0_prd(sK54_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f432,plain,
! [W,X,X2] :
( ( ? [X3] :
( leq(X2,X3)
& memberP(X,X3)
& X2 != X3
& ssItem(X3) )
| ~ memberP(X,X2)
| cons(X2,nil) != W
| ~ ssItem(X2)
| sP0_prd(X2,X,W) )
& ( ( ! [X3] :
( ~ leq(X2,X3)
| ~ memberP(X,X3)
| X2 = X3
| ~ ssItem(X3) )
& memberP(X,X2)
& cons(X2,nil) = W
& ssItem(X2) )
| ~ sP0_prd(X2,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f416]) ).
fof(f433,plain,
( ! [W,X,X2] :
( ? [X3] :
( leq(X2,X3)
& memberP(X,X3)
& X2 != X3
& ssItem(X3) )
| ~ memberP(X,X2)
| cons(X2,nil) != W
| ~ ssItem(X2)
| sP0_prd(X2,X,W) )
& ! [W,X,X2] :
( ( ! [X3] :
( ~ leq(X2,X3)
| ~ memberP(X,X3)
| X2 = X3
| ~ ssItem(X3) )
& memberP(X,X2)
& cons(X2,nil) = W
& ssItem(X2) )
| ~ sP0_prd(X2,X,W) ) ),
inference(miniscoping,[status(thm)],[f432]) ).
fof(f434,plain,
( ! [W,X,X2] :
( ( leq(X2,sK55_skl(X2,X,W))
& memberP(X,sK55_skl(X2,X,W))
& X2 != sK55_skl(X2,X,W)
& ssItem(sK55_skl(X2,X,W)) )
| ~ memberP(X,X2)
| cons(X2,nil) != W
| ~ ssItem(X2)
| sP0_prd(X2,X,W) )
& ! [W,X,X2] :
( ( ! [X3] :
( ~ leq(X2,X3)
| ~ memberP(X,X3)
| X2 = X3
| ~ ssItem(X3) )
& memberP(X,X2)
& cons(X2,nil) = W
& ssItem(X2) )
| ~ sP0_prd(X2,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK55_skl]),skolemize(X3,sK55_skl(X2,X,W))],[f433]) ).
fof(f435,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f436,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f434]) ).
fof(f447,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f462,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(f463,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)],[f462]) ).
fof(f480,plain,
app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK49_skl,
inference(forward_demodulation,[status(thm)],[f424,f428]) ).
fof(f487,plain,
( cons(sK54_skl,nil) = sK49_skl
| nil = sK49_skl ),
inference(resolution,[status(thm)],[f431,f436]) ).
fof(f489,plain,
( ssItem(sK54_skl)
| nil = sK49_skl ),
inference(resolution,[status(thm)],[f431,f435]) ).
fof(f533,plain,
! [X0,X1] :
( nil = sK49_skl
| nil = X0
| cons(X1,X0) != sK49_skl
| ~ ssItem(sK54_skl)
| ~ ssItem(X1)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f487,f228]) ).
fof(f545,plain,
! [X0,X1] :
( nil = sK49_skl
| nil = X0
| cons(X1,X0) != sK49_skl
| ~ ssItem(sK54_skl)
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f533,f223]) ).
fof(f582,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f447,f245]) ).
fof(f583,plain,
( ~ ssList(sK53_skl)
| frontsegP(sK49_skl,app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f480,f582]) ).
fof(f584,plain,
( frontsegP(sK49_skl,app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(forward_subsumption_resolution,[status(thm)],[f583,f427]) ).
fof(f608,plain,
( nil = app(sK52_skl,cons(sK51_skl,nil))
| nil != sK49_skl
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f480,f386]) ).
fof(f611,plain,
( nil = app(sK52_skl,cons(sK51_skl,nil))
| nil != sK49_skl
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(forward_subsumption_resolution,[status(thm)],[f608,f427]) ).
fof(f622,plain,
! [X0] :
( ~ memberP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| memberP(sK49_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f480,f271]) ).
fof(f623,plain,
! [X0] :
( ~ memberP(app(sK52_skl,cons(sK51_skl,nil)),X0)
| memberP(sK49_skl,X0)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f622,f427]) ).
fof(f625,plain,
! [X0] :
( ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f480,f272]) ).
fof(f626,plain,
! [X0] :
( ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f625,f427]) ).
fof(f653,plain,
! [X0] :
( nil = sK49_skl
| cons(sK54_skl,X0) = app(sK49_skl,X0)
| ~ ssItem(sK54_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f487,f380]) ).
fof(f655,plain,
! [X0] :
( nil = sK49_skl
| cons(sK54_skl,X0) = app(sK49_skl,X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f653,f489]) ).
fof(f663,plain,
! [X0] :
( nil = sK49_skl
| memberP(nil,X0)
| X0 = sK54_skl
| ~ memberP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK54_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f487,f275]) ).
fof(f665,plain,
! [X0] :
( nil = sK49_skl
| memberP(nil,X0)
| X0 = sK54_skl
| ~ memberP(sK49_skl,X0)
| ~ ssList(nil)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f663,f489]) ).
fof(f736,plain,
( sK49_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)],[f480,f382]) ).
fof(f738,plain,
( sK49_skl = app(sK52_skl,app(cons(sK51_skl,nil),sK53_skl))
| ~ ssList(sK53_skl)
| ~ ssList(cons(sK51_skl,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f736,f426]) ).
fof(f784,plain,
! [X0,X1] :
( nil = sK49_skl
| nil = X0
| cons(X1,X0) != sK49_skl
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f545,f489]) ).
fof(f825,plain,
! [X0] :
( nil = sK49_skl
| memberP(nil,X0)
| X0 = sK54_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f665,f223]) ).
fof(f877,plain,
( ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| nil = app(sK52_skl,cons(sK51_skl,nil))
| nil != sK49_skl ),
inference(resolution,[status(thm)],[f611,f245]) ).
fof(f878,plain,
( ~ ssList(cons(sK51_skl,nil))
| nil = app(sK52_skl,cons(sK51_skl,nil))
| nil != sK49_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f877,f426]) ).
fof(f904,plain,
( nil = cons(sK51_skl,nil)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| ~ ssList(cons(sK51_skl,nil))
| nil != sK49_skl ),
inference(resolution,[status(thm)],[f878,f385]) ).
fof(f907,plain,
( nil = cons(sK51_skl,nil)
| ~ ssList(sK52_skl)
| ~ ssList(cons(sK51_skl,nil))
| nil != sK49_skl ),
inference(duplicate_literals_removal,[status(thm)],[f904]) ).
fof(f908,plain,
( nil = cons(sK51_skl,nil)
| ~ ssList(cons(sK51_skl,nil))
| nil != sK49_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f907,f426]) ).
fof(f912,plain,
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| nil = cons(sK51_skl,nil)
| nil != sK49_skl ),
inference(resolution,[status(thm)],[f908,f222]) ).
fof(f913,plain,
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| nil != sK49_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f912,f235]) ).
fof(f976,plain,
( ~ ssItem(sK51_skl)
| nil != sK49_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f913,f223]) ).
fof(f977,plain,
nil != sK49_skl,
inference(resolution,[status(thm)],[f976,f425]) ).
fof(f979,plain,
! [X0] :
( memberP(nil,X0)
| X0 = sK54_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f825,f977]) ).
fof(f981,plain,
! [X0,X1] :
( nil = X0
| cons(X1,X0) != sK49_skl
| ~ ssItem(X1)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f784,f977]) ).
fof(f983,plain,
! [X0] :
( cons(sK54_skl,X0) = app(sK49_skl,X0)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f655,f977]) ).
fof(f993,plain,
cons(sK54_skl,nil) = sK49_skl,
inference(backward_subsumption_resolution,[status(thm)],[f487,f977]) ).
fof(f995,plain,
ssItem(sK54_skl),
inference(backward_subsumption_resolution,[status(thm)],[f489,f977]) ).
fof(f997,plain,
! [X0] :
( X0 = sK54_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f979,f279]) ).
fof(f1005,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| ~ ssItem(X0)
| memberP(sK49_skl,X0)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f623,f271]) ).
fof(f1011,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| memberP(sK49_skl,X0)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1005]) ).
fof(f1012,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1011,f245]) ).
fof(f1014,plain,
! [X0] :
( ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f626,f245]) ).
fof(f1015,plain,
! [X0] :
( ~ ssList(cons(sK51_skl,nil))
| ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1014,f426]) ).
fof(f1130,plain,
( hd(sK49_skl) = sK54_skl
| ~ ssItem(sK54_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f993,f239]) ).
fof(f1131,plain,
( hd(sK49_skl) = sK54_skl
| ~ ssItem(sK54_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1130,f223]) ).
fof(f1132,plain,
hd(sK49_skl) = sK54_skl,
inference(forward_subsumption_resolution,[status(thm)],[f1131,f995]) ).
fof(f1157,plain,
! [X0] :
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1015,f222]) ).
fof(f1158,plain,
! [X0] :
( ~ ssItem(sK51_skl)
| ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1157,f223]) ).
fof(f1159,plain,
! [X0] :
( ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1158,f425]) ).
fof(f1160,plain,
( memberP(sK52_skl,sK51_skl)
| memberP(sK49_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1159,f429]) ).
fof(f1162,plain,
( memberP(sK52_skl,sK51_skl)
| memberP(sK49_skl,sK51_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1160,f425]) ).
fof(f1242,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssList(X0)
| X0 = app(X0,X1)
| ~ frontsegP(X0,app(X0,X1))
| ~ ssList(app(X0,X1))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f284,f582]) ).
fof(f1247,plain,
! [X0,X1] :
( ~ ssList(X1)
| X0 = app(X0,X1)
| ~ frontsegP(X0,app(X0,X1))
| ~ ssList(app(X0,X1))
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1242]) ).
fof(f1248,plain,
! [X0,X1] :
( ~ ssList(X1)
| X0 = app(X0,X1)
| ~ frontsegP(X0,app(X0,X1))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1247,f245]) ).
fof(f1542,plain,
! [X0] :
( frontsegP(sK49_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)],[f480,f288]) ).
fof(f1548,plain,
! [X0] :
( frontsegP(sK49_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)],[f1542,f427]) ).
fof(f1673,plain,
! [X0] :
( ~ frontsegP(X0,nil)
| frontsegP(cons(sK54_skl,X0),sK49_skl)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK54_skl) ),
inference(paramodulation,[status(thm)],[f993,f463]) ).
fof(f1679,plain,
! [X0] :
( ~ frontsegP(X0,nil)
| frontsegP(cons(sK54_skl,X0),sK49_skl)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1673,f995]) ).
fof(f1710,plain,
! [X0] :
( ~ frontsegP(X0,nil)
| frontsegP(cons(sK54_skl,X0),sK49_skl)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1679,f223]) ).
fof(f1758,plain,
( sK49_skl = app(sK52_skl,app(cons(sK51_skl,nil),sK53_skl))
| ~ ssList(cons(sK51_skl,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f738,f427]) ).
fof(f2126,plain,
( ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| frontsegP(sK49_skl,sK52_skl)
| ~ ssList(sK52_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(resolution,[status(thm)],[f1548,f582]) ).
fof(f2132,plain,
( ~ ssList(cons(sK51_skl,nil))
| frontsegP(sK49_skl,sK52_skl)
| ~ ssList(sK52_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(duplicate_literals_removal,[status(thm)],[f2126]) ).
fof(f2133,plain,
( ~ ssList(cons(sK51_skl,nil))
| frontsegP(sK49_skl,sK52_skl)
| ~ ssList(sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f2132,f245]) ).
fof(f2138,plain,
( ~ ssList(cons(sK51_skl,nil))
| frontsegP(sK49_skl,sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f2133,f426]) ).
fof(f2139,plain,
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| frontsegP(sK49_skl,sK52_skl) ),
inference(resolution,[status(thm)],[f2138,f222]) ).
fof(f2140,plain,
( ~ ssItem(sK51_skl)
| frontsegP(sK49_skl,sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f2139,f223]) ).
fof(f2141,plain,
frontsegP(sK49_skl,sK52_skl),
inference(forward_subsumption_resolution,[status(thm)],[f2140,f425]) ).
fof(f2143,plain,
( sK52_skl = sK49_skl
| ~ frontsegP(sK52_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK52_skl) ),
inference(resolution,[status(thm)],[f2141,f284]) ).
fof(f2145,plain,
( sK52_skl = sK49_skl
| ~ frontsegP(sK52_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f2143,f426]) ).
fof(f2146,plain,
( sK52_skl = sK49_skl
| ~ frontsegP(sK52_skl,sK49_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f2145,f421]) ).
fof(f4364,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| ~ ssList(cons(sK51_skl,nil))
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1012,f426]) ).
fof(f4365,plain,
! [X0] :
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| ~ memberP(sK52_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f4364,f222]) ).
fof(f4366,plain,
! [X0] :
( ~ ssItem(sK51_skl)
| ~ memberP(sK52_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4365,f223]) ).
fof(f4367,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4366,f425]) ).
fof(f4368,plain,
( memberP(sK49_skl,sK51_skl)
| memberP(sK49_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f4367,f1162]) ).
fof(f4373,plain,
( memberP(sK49_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f4368]) ).
fof(f4374,plain,
memberP(sK49_skl,sK51_skl),
inference(forward_subsumption_resolution,[status(thm)],[f4373,f425]) ).
fof(f4379,plain,
( sK51_skl = sK54_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f4374,f997]) ).
fof(f4380,plain,
sK51_skl = sK54_skl,
inference(forward_subsumption_resolution,[status(thm)],[f4379,f425]) ).
fof(f4387,plain,
! [X0] :
( ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK49_skl)
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f4380,f1710]) ).
fof(f4399,plain,
hd(sK49_skl) = sK51_skl,
inference(backward_demodulation,[status(thm)],[f4380,f1132]) ).
fof(f4402,plain,
! [X0] :
( cons(sK51_skl,X0) = app(sK49_skl,X0)
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f4380,f983]) ).
fof(f4404,plain,
cons(sK51_skl,nil) = sK49_skl,
inference(backward_demodulation,[status(thm)],[f4380,f993]) ).
fof(f4415,plain,
! [X0] :
( frontsegP(cons(sK51_skl,X0),sK49_skl)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4387,f295]) ).
fof(f4463,plain,
( sK49_skl = app(sK52_skl,app(sK49_skl,sK53_skl))
| ~ ssList(cons(sK51_skl,nil)) ),
inference(backward_demodulation,[status(thm)],[f4404,f1758]) ).
fof(f4468,plain,
( frontsegP(sK49_skl,app(sK52_skl,sK49_skl))
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(backward_demodulation,[status(thm)],[f4404,f584]) ).
fof(f4549,plain,
( sK49_skl = app(sK52_skl,app(sK49_skl,sK53_skl))
| ~ ssList(sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f4404,f4463]) ).
fof(f4550,plain,
sK49_skl = app(sK52_skl,app(sK49_skl,sK53_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f4549,f421]) ).
fof(f4554,plain,
( frontsegP(sK49_skl,app(sK52_skl,sK49_skl))
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f4404,f4468]) ).
fof(f4903,plain,
( hd(sK49_skl) = hd(sK52_skl)
| nil = sK52_skl
| ~ ssList(app(sK49_skl,sK53_skl))
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f4550,f391]) ).
fof(f4941,plain,
( sK51_skl = hd(sK52_skl)
| nil = sK52_skl
| ~ ssList(app(sK49_skl,sK53_skl))
| ~ ssList(sK52_skl) ),
inference(forward_demodulation,[status(thm)],[f4399,f4903]) ).
fof(f4942,plain,
( sK51_skl = hd(sK52_skl)
| nil = sK52_skl
| ~ ssList(app(sK49_skl,sK53_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f4941,f426]) ).
fof(f5127,plain,
( ~ ssList(sK53_skl)
| ~ ssList(sK49_skl)
| sK51_skl = hd(sK52_skl)
| nil = sK52_skl ),
inference(resolution,[status(thm)],[f4942,f245]) ).
fof(f5128,plain,
( ~ ssList(sK53_skl)
| sK51_skl = hd(sK52_skl)
| nil = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f5127,f421]) ).
fof(f5129,plain,
( sK51_skl = hd(sK52_skl)
| nil = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f5128,f427]) ).
fof(f5130,plain,
( nil = sK52_skl
| cons(sK51_skl,tl(sK52_skl)) = sK52_skl
| nil = sK52_skl
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f5129,f374]) ).
fof(f5132,plain,
( cons(sK51_skl,tl(sK52_skl)) = sK52_skl
| nil = sK52_skl
| ~ ssList(sK52_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f5130]) ).
fof(f5133,plain,
( cons(sK51_skl,tl(sK52_skl)) = sK52_skl
| nil = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f5132,f426]) ).
fof(f5136,plain,
( nil = sK52_skl
| frontsegP(sK52_skl,sK49_skl)
| ~ ssList(tl(sK52_skl)) ),
inference(paramodulation,[status(thm)],[f5133,f4415]) ).
fof(f5269,plain,
( sK52_skl = sK49_skl
| nil = sK52_skl
| ~ ssList(tl(sK52_skl)) ),
inference(resolution,[status(thm)],[f5136,f2146]) ).
fof(f5296,plain,
( nil = sK52_skl
| ~ ssList(sK52_skl)
| sK52_skl = sK49_skl
| nil = sK52_skl ),
inference(resolution,[status(thm)],[f5269,f241]) ).
fof(f5297,plain,
( ~ ssList(sK52_skl)
| sK52_skl = sK49_skl
| nil = sK52_skl ),
inference(duplicate_literals_removal,[status(thm)],[f5296]) ).
fof(f5298,plain,
( sK52_skl = sK49_skl
| nil = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f5297,f426]) ).
fof(f5303,plain,
( nil = sK52_skl
| frontsegP(sK49_skl,app(sK49_skl,sK49_skl))
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f5298,f4554]) ).
fof(f6756,plain,
( ~ ssList(sK49_skl)
| sK49_skl = app(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| nil = sK52_skl
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(resolution,[status(thm)],[f5303,f1248]) ).
fof(f6768,plain,
( sK49_skl = app(sK49_skl,sK49_skl)
| ~ ssList(sK49_skl)
| nil = sK52_skl
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(duplicate_literals_removal,[status(thm)],[f6756]) ).
fof(f6769,plain,
( sK49_skl = app(sK49_skl,sK49_skl)
| nil = sK52_skl
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f6768,f421]) ).
fof(f6776,plain,
( ~ ssList(sK49_skl)
| ~ ssList(sK52_skl)
| sK49_skl = app(sK49_skl,sK49_skl)
| nil = sK52_skl ),
inference(resolution,[status(thm)],[f6769,f245]) ).
fof(f6778,plain,
( ~ ssList(sK49_skl)
| sK49_skl = app(sK49_skl,sK49_skl)
| nil = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f6776,f426]) ).
fof(f6788,plain,
( sK49_skl = app(sK49_skl,sK49_skl)
| nil = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f6778,f421]) ).
fof(f6793,plain,
( nil = sK52_skl
| cons(sK51_skl,sK49_skl) = sK49_skl
| ~ ssList(sK49_skl) ),
inference(paramodulation,[status(thm)],[f6788,f4402]) ).
fof(f6837,plain,
( nil = sK52_skl
| cons(sK51_skl,sK49_skl) = sK49_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f6793,f421]) ).
fof(f6958,plain,
( ~ ssItem(sK51_skl)
| ~ ssList(sK49_skl)
| nil = sK52_skl ),
inference(resolution,[status(thm)],[f6837,f225]) ).
fof(f7020,plain,
( ~ ssItem(sK51_skl)
| nil = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f6958,f421]) ).
fof(f7110,plain,
sK49_skl = app(nil,app(sK49_skl,sK53_skl)),
inference(backward_demodulation,[status(thm)],[f7125,f4550]) ).
fof(f7123,plain,
( memberP(sK53_skl,sK51_skl)
| memberP(nil,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f7125,f429]) ).
fof(f7125,plain,
nil = sK52_skl,
inference(forward_subsumption_resolution,[status(thm)],[f7020,f425]) ).
fof(f7245,plain,
( sK49_skl = app(sK49_skl,sK53_skl)
| ~ ssList(app(sK49_skl,sK53_skl)) ),
inference(paramodulation,[status(thm)],[f7110,f249]) ).
fof(f7321,plain,
( ~ ssList(sK53_skl)
| ~ ssList(sK49_skl)
| sK49_skl = app(sK49_skl,sK53_skl) ),
inference(resolution,[status(thm)],[f7245,f245]) ).
fof(f7322,plain,
( ~ ssList(sK53_skl)
| sK49_skl = app(sK49_skl,sK53_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f7321,f421]) ).
fof(f7326,plain,
sK49_skl = app(sK49_skl,sK53_skl),
inference(forward_subsumption_resolution,[status(thm)],[f7322,f427]) ).
fof(f7327,plain,
( cons(sK51_skl,sK53_skl) = sK49_skl
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f7326,f4402]) ).
fof(f7366,plain,
cons(sK51_skl,sK53_skl) = sK49_skl,
inference(forward_subsumption_resolution,[status(thm)],[f7327,f427]) ).
fof(f7490,plain,
( nil = sK53_skl
| ~ ssItem(sK51_skl)
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f7366,f981]) ).
fof(f7551,plain,
( nil = sK53_skl
| ~ ssItem(sK51_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f7490,f427]) ).
fof(f7621,plain,
( memberP(nil,sK51_skl)
| memberP(nil,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f7636,f7123]) ).
fof(f7636,plain,
nil = sK53_skl,
inference(forward_subsumption_resolution,[status(thm)],[f7551,f425]) ).
fof(f7638,plain,
memberP(nil,sK51_skl),
inference(duplicate_literals_removal,[status(thm)],[f7621]) ).
fof(f7646,plain,
~ ssItem(sK51_skl),
inference(resolution,[status(thm)],[f7638,f279]) ).
fof(f7647,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f7646,f425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWC183+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.07 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.45 % Computer : n007.cluster.edu
% 0.20/0.45 % Model : x86_64 x86_64
% 0.20/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.45 % Memory : 8046.5625MB
% 0.20/0.45 % OS : Linux 6.8.0-71-generic
% 0.20/0.45 % CPULimit : 300
% 0.20/0.45 % WCLimit : 300
% 0.20/0.45 % DateTime : Mon Sep 21 08:00:21 UTC 2026
% 0.20/0.45 % CPUTime :
% 0.20/0.50 % Drodi V4.1.1
% 17.40/2.85 % Refutation found
% 17.40/2.85 % SZS status Theorem for theBenchmark: Theorem is valid
% 17.40/2.85 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 18.19/2.90 % Elapsed time: 2.428631 seconds
% 18.19/2.90 % CPU time: 18.452527 seconds
% 18.19/2.90 % Total memory used: 205.667 MB
% 18.19/2.90 % Net memory used: 197.288 MB
%------------------------------------------------------------------------------