%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC187+1 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n011.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 02:40:19 PM UTC 2026
% Result : Theorem 14.26s 2.26s
% Output : CNFRefutation 14.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 62
% Number of leaves : 23
% Syntax : Number of formulae : 219 ( 27 unt; 1 def)
% Number of atoms : 826 ( 245 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 1021 ( 414 ~; 462 |; 70 &)
% ( 11 <=>; 64 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 251 ( 232 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> ssList(cons(V,U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> nil != cons(V,U) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> hd(cons(V,U)) = V ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> ssList(tl(U)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssItem(V)
=> tl(cons(V,U)) = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ssList(app(U,V)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( memberP(app(V,W),U)
<=> ( memberP(W,U)
| memberP(V,U) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f37,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ( memberP(cons(V,W),U)
<=> ( memberP(W,U)
| U = V ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [U] :
( ssItem(U)
=> ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( ( frontsegP(V,W)
& frontsegP(U,V) )
=> frontsegP(U,W) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( ( frontsegP(V,U)
& frontsegP(U,V) )
=> U = V ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f44,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( frontsegP(cons(U,W),cons(V,X))
<=> ( frontsegP(W,X)
& U = V ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f45,axiom,
! [U] :
( ssList(U)
=> frontsegP(U,nil) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [U] :
( ssList(U)
=> ( nil != U
=> cons(hd(U),tl(U)) = U ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f80,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(V,W) = app(V,U)
=> W = U ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f83,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil = app(U,V)
<=> ( nil = U
& nil = V ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f84,axiom,
! [U] :
( ssList(U)
=> app(U,nil) = U ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ( nil != U
=> hd(app(U,V)) = hd(U) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p') ).
fof(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [X2] :
( ssItem(X2)
=> ( ~ memberP(X,X2)
| cons(X2,nil) != W ) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ( ~ memberP(X1,Y)
& ~ memberP(Z,Y) )
| app(app(Z,cons(Y,nil)),X1) != U ) ) ) )
| U != W
| V != X ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,negated_conjecture,
~ ! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [X2] :
( ssItem(X2)
=> ( ~ memberP(X,X2)
| cons(X2,nil) != W ) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssList(Z)
=> ! [X1] :
( ssList(X1)
=> ( ( ~ memberP(X1,Y)
& ~ memberP(Z,Y) )
| app(app(Z,cons(Y,nil)),X1) != U ) ) ) )
| U != W
| V != 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(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(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(f281,plain,
! [U] :
( ! [V] :
( ! [W] :
( frontsegP(U,W)
| ~ frontsegP(V,W)
| ~ frontsegP(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f40]) ).
fof(f282,plain,
! [X0,X1,X2] :
( frontsegP(X0,X2)
| ~ frontsegP(X1,X2)
| ~ frontsegP(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f281]) ).
fof(f283,plain,
! [U] :
( ! [V] :
( U = V
| ~ frontsegP(V,U)
| ~ frontsegP(U,V)
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f41]) ).
fof(f284,plain,
! [X0,X1] :
( X0 = X1
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f283]) ).
fof(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(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 )
| ? [X2] :
( 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)
<=> ( 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] :
( ( ~ memberP(X,X2)
| cons(X2,nil) != W
| ~ ssItem(X2)
| sP0_prd(X2,X,W) )
& ( ( 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] :
( ~ memberP(X,X2)
| cons(X2,nil) != W
| ~ ssItem(X2)
| sP0_prd(X2,X,W) )
& ! [W,X,X2] :
( ( memberP(X,X2)
& cons(X2,nil) = W
& ssItem(X2) )
| ~ sP0_prd(X2,X,W) ) ),
inference(miniscoping,[status(thm)],[f432]) ).
fof(f434,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f435,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f433]) ).
fof(f442,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f457,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(f458,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)],[f457]) ).
fof(f472,plain,
app(app(sK52_skl,cons(sK51_skl,nil)),sK53_skl) = sK49_skl,
inference(forward_demodulation,[status(thm)],[f424,f428]) ).
fof(f480,plain,
( cons(sK54_skl,nil) = sK49_skl
| nil = sK49_skl ),
inference(resolution,[status(thm)],[f431,f435]) ).
fof(f482,plain,
( ssItem(sK54_skl)
| nil = sK49_skl ),
inference(resolution,[status(thm)],[f431,f434]) ).
fof(f564,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)],[f472,f386]) ).
fof(f565,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)],[f564,f427]) ).
fof(f574,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)],[f472,f271]) ).
fof(f575,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)],[f574,f427]) ).
fof(f577,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)],[f472,f272]) ).
fof(f578,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)],[f577,f427]) ).
fof(f597,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f442,f245]) ).
fof(f598,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)],[f472,f597]) ).
fof(f599,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)],[f598,f427]) ).
fof(f620,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)],[f480,f275]) ).
fof(f622,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)],[f620,f482]) ).
fof(f682,plain,
! [X0] :
( sK53_skl = X0
| sK49_skl != app(app(sK52_skl,cons(sK51_skl,nil)),X0)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f472,f378]) ).
fof(f691,plain,
! [X0] :
( sK53_skl = X0
| sK49_skl != app(app(sK52_skl,cons(sK51_skl,nil)),X0)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f682,f427]) ).
fof(f716,plain,
( ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| nil = app(sK52_skl,cons(sK51_skl,nil))
| nil != sK49_skl ),
inference(resolution,[status(thm)],[f565,f245]) ).
fof(f717,plain,
( ~ ssList(cons(sK51_skl,nil))
| nil = app(sK52_skl,cons(sK51_skl,nil))
| nil != sK49_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f716,f426]) ).
fof(f752,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)],[f575,f271]) ).
fof(f757,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)],[f752]) ).
fof(f758,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)],[f757,f245]) ).
fof(f766,plain,
! [X0] :
( nil = sK49_skl
| memberP(nil,X0)
| X0 = sK54_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f622,f223]) ).
fof(f774,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)],[f717,f385]) ).
fof(f777,plain,
( nil = cons(sK51_skl,nil)
| ~ ssList(sK52_skl)
| ~ ssList(cons(sK51_skl,nil))
| nil != sK49_skl ),
inference(duplicate_literals_removal,[status(thm)],[f774]) ).
fof(f778,plain,
( nil = cons(sK51_skl,nil)
| ~ ssList(cons(sK51_skl,nil))
| nil != sK49_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f777,f426]) ).
fof(f806,plain,
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| nil = cons(sK51_skl,nil)
| nil != sK49_skl ),
inference(resolution,[status(thm)],[f778,f222]) ).
fof(f807,plain,
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| nil != sK49_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f806,f235]) ).
fof(f808,plain,
! [X0] :
( ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK52_skl)
| ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f578,f245]) ).
fof(f809,plain,
! [X0] :
( ~ ssList(cons(sK51_skl,nil))
| ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f808,f426]) ).
fof(f810,plain,
( ~ ssItem(sK51_skl)
| nil != sK49_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f807,f223]) ).
fof(f811,plain,
nil != sK49_skl,
inference(resolution,[status(thm)],[f810,f425]) ).
fof(f812,plain,
! [X0] :
( memberP(nil,X0)
| X0 = sK54_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f766,f811]) ).
fof(f826,plain,
cons(sK54_skl,nil) = sK49_skl,
inference(backward_subsumption_resolution,[status(thm)],[f480,f811]) ).
fof(f828,plain,
ssItem(sK54_skl),
inference(backward_subsumption_resolution,[status(thm)],[f482,f811]) ).
fof(f830,plain,
! [X0] :
( X0 = sK54_skl
| ~ memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f812,f279]) ).
fof(f942,plain,
! [X0] :
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f809,f222]) ).
fof(f943,plain,
! [X0] :
( ~ ssItem(sK51_skl)
| ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f942,f223]) ).
fof(f949,plain,
! [X0] :
( ~ memberP(sK53_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f943,f425]) ).
fof(f950,plain,
( memberP(sK52_skl,sK51_skl)
| memberP(sK49_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f949,f429]) ).
fof(f951,plain,
( memberP(sK52_skl,sK51_skl)
| memberP(sK49_skl,sK51_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f950,f425]) ).
fof(f962,plain,
( hd(sK49_skl) = sK54_skl
| ~ ssItem(sK54_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f826,f239]) ).
fof(f963,plain,
( hd(sK49_skl) = sK54_skl
| ~ ssItem(sK54_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f962,f223]) ).
fof(f964,plain,
hd(sK49_skl) = sK54_skl,
inference(forward_subsumption_resolution,[status(thm)],[f963,f828]) ).
fof(f966,plain,
( tl(sK49_skl) = nil
| ~ ssItem(sK54_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f826,f243]) ).
fof(f967,plain,
( tl(sK49_skl) = nil
| ~ ssItem(sK54_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f966,f223]) ).
fof(f968,plain,
tl(sK49_skl) = nil,
inference(forward_subsumption_resolution,[status(thm)],[f967,f828]) ).
fof(f986,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| ~ ssList(cons(sK51_skl,nil))
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f758,f426]) ).
fof(f987,plain,
! [X0] :
( ~ ssItem(sK51_skl)
| ~ ssList(nil)
| ~ memberP(sK52_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f986,f222]) ).
fof(f988,plain,
! [X0] :
( ~ ssItem(sK51_skl)
| ~ memberP(sK52_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f987,f223]) ).
fof(f989,plain,
! [X0] :
( ~ memberP(sK52_skl,X0)
| memberP(sK49_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f988,f425]) ).
fof(f990,plain,
( memberP(sK49_skl,sK51_skl)
| memberP(sK49_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f989,f951]) ).
fof(f991,plain,
( memberP(sK49_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f990]) ).
fof(f992,plain,
memberP(sK49_skl,sK51_skl),
inference(forward_subsumption_resolution,[status(thm)],[f991,f425]) ).
fof(f993,plain,
( sK51_skl = sK54_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f992,f830]) ).
fof(f994,plain,
sK51_skl = sK54_skl,
inference(forward_subsumption_resolution,[status(thm)],[f993,f425]) ).
fof(f995,plain,
hd(sK49_skl) = sK51_skl,
inference(backward_demodulation,[status(thm)],[f994,f964]) ).
fof(f1005,plain,
cons(sK51_skl,nil) = sK49_skl,
inference(backward_demodulation,[status(thm)],[f994,f826]) ).
fof(f1018,plain,
! [X0] :
( sK53_skl = X0
| sK49_skl != app(app(sK52_skl,sK49_skl),X0)
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil)))
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f1005,f691]) ).
fof(f1020,plain,
( frontsegP(sK49_skl,app(sK52_skl,sK49_skl))
| ~ ssList(app(sK52_skl,cons(sK51_skl,nil))) ),
inference(backward_demodulation,[status(thm)],[f1005,f599]) ).
fof(f1023,plain,
app(app(sK52_skl,sK49_skl),sK53_skl) = sK49_skl,
inference(backward_demodulation,[status(thm)],[f1005,f472]) ).
fof(f1064,plain,
! [X0] :
( sK53_skl = X0
| sK49_skl != app(app(sK52_skl,sK49_skl),X0)
| ~ ssList(app(sK52_skl,sK49_skl))
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f1005,f1018]) ).
fof(f1066,plain,
( frontsegP(sK49_skl,app(sK52_skl,sK49_skl))
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f1005,f1020]) ).
fof(f1457,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| ~ ssList(X1)
| frontsegP(X0,X1)
| ~ frontsegP(X0,app(X1,X2))
| ~ ssList(X1)
| ~ ssList(app(X1,X2))
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f282,f597]) ).
fof(f1466,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| frontsegP(X0,X1)
| ~ frontsegP(X0,app(X1,X2))
| ~ ssList(X1)
| ~ ssList(app(X1,X2))
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1457]) ).
fof(f1467,plain,
! [X0,X1,X2] :
( ~ ssList(X2)
| frontsegP(X0,X1)
| ~ frontsegP(X0,app(X1,X2))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1466,f245]) ).
fof(f1521,plain,
( ~ ssList(app(sK52_skl,sK49_skl))
| ~ ssList(sK49_skl)
| frontsegP(sK49_skl,sK52_skl)
| ~ ssList(sK52_skl)
| ~ ssList(sK49_skl) ),
inference(resolution,[status(thm)],[f1467,f1066]) ).
fof(f1527,plain,
( ~ ssList(app(sK52_skl,sK49_skl))
| frontsegP(sK49_skl,sK52_skl)
| ~ ssList(sK52_skl)
| ~ ssList(sK49_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f1521]) ).
fof(f1528,plain,
( ~ ssList(app(sK52_skl,sK49_skl))
| frontsegP(sK49_skl,sK52_skl)
| ~ ssList(sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1527,f421]) ).
fof(f1535,plain,
( ~ ssList(app(sK52_skl,sK49_skl))
| frontsegP(sK49_skl,sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1528,f426]) ).
fof(f1536,plain,
( ~ ssList(sK49_skl)
| ~ ssList(sK52_skl)
| frontsegP(sK49_skl,sK52_skl) ),
inference(resolution,[status(thm)],[f1535,f245]) ).
fof(f1537,plain,
( ~ ssList(sK49_skl)
| frontsegP(sK49_skl,sK52_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1536,f426]) ).
fof(f1545,plain,
frontsegP(sK49_skl,sK52_skl),
inference(forward_subsumption_resolution,[status(thm)],[f1537,f421]) ).
fof(f1547,plain,
( sK52_skl = sK49_skl
| ~ frontsegP(sK52_skl,sK49_skl)
| ~ ssList(sK49_skl)
| ~ ssList(sK52_skl) ),
inference(resolution,[status(thm)],[f1545,f284]) ).
fof(f1549,plain,
( sK52_skl = sK49_skl
| ~ frontsegP(sK52_skl,sK49_skl)
| ~ ssList(sK49_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1547,f426]) ).
fof(f1550,plain,
( sK52_skl = sK49_skl
| ~ frontsegP(sK52_skl,sK49_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f1549,f421]) ).
fof(f1609,plain,
! [X0] :
( ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK49_skl)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1005,f458]) ).
fof(f1615,plain,
! [X0] :
( ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK49_skl)
| ~ ssList(nil)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1609,f425]) ).
fof(f1758,plain,
( tl(sK49_skl) = app(tl(app(sK52_skl,sK49_skl)),sK53_skl)
| nil = app(sK52_skl,sK49_skl)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f1023,f393]) ).
fof(f1759,plain,
( nil = app(tl(app(sK52_skl,sK49_skl)),sK53_skl)
| nil = app(sK52_skl,sK49_skl)
| ~ ssList(sK53_skl)
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(forward_demodulation,[status(thm)],[f968,f1758]) ).
fof(f1760,plain,
( nil = app(tl(app(sK52_skl,sK49_skl)),sK53_skl)
| nil = app(sK52_skl,sK49_skl)
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1759,f427]) ).
fof(f1827,plain,
! [X0] :
( ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK49_skl)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1615,f223]) ).
fof(f2624,plain,
( nil = sK53_skl
| ~ ssList(sK53_skl)
| ~ ssList(tl(app(sK52_skl,sK49_skl)))
| nil = app(sK52_skl,sK49_skl)
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(resolution,[status(thm)],[f1760,f385]) ).
fof(f2626,plain,
( nil = sK53_skl
| ~ ssList(sK53_skl)
| nil = app(sK52_skl,sK49_skl)
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2624,f241]) ).
fof(f3341,plain,
( nil = sK53_skl
| nil = app(sK52_skl,sK49_skl)
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f2626,f427]) ).
fof(f3342,plain,
( ~ ssList(sK49_skl)
| ~ ssList(sK52_skl)
| nil = sK53_skl
| nil = app(sK52_skl,sK49_skl) ),
inference(resolution,[status(thm)],[f3341,f245]) ).
fof(f3343,plain,
( ~ ssList(sK49_skl)
| nil = sK53_skl
| nil = app(sK52_skl,sK49_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f3342,f426]) ).
fof(f3344,plain,
( nil = sK53_skl
| nil = app(sK52_skl,sK49_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f3343,f421]) ).
fof(f3346,plain,
( nil = sK49_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK52_skl)
| nil = sK53_skl ),
inference(resolution,[status(thm)],[f3344,f385]) ).
fof(f3392,plain,
( nil = sK49_skl
| ~ ssList(sK49_skl)
| nil = sK53_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f3346,f426]) ).
fof(f3457,plain,
( nil = sK49_skl
| nil = sK53_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f3392,f421]) ).
fof(f3475,plain,
( nil = sK49_skl
| app(app(sK52_skl,sK49_skl),nil) = sK49_skl ),
inference(paramodulation,[status(thm)],[f3457,f1023]) ).
fof(f3478,plain,
( nil = sK49_skl
| memberP(nil,sK51_skl)
| memberP(sK52_skl,sK51_skl) ),
inference(paramodulation,[status(thm)],[f3457,f429]) ).
fof(f3485,plain,
app(app(sK52_skl,sK49_skl),nil) = sK49_skl,
inference(forward_subsumption_resolution,[status(thm)],[f3475,f811]) ).
fof(f3486,plain,
( memberP(nil,sK51_skl)
| memberP(sK52_skl,sK51_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f3478,f811]) ).
fof(f3579,plain,
( sK53_skl = nil
| ~ ssList(app(sK52_skl,sK49_skl))
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3485,f1064]) ).
fof(f3585,plain,
( sK49_skl = app(sK52_skl,sK49_skl)
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(paramodulation,[status(thm)],[f3485,f389]) ).
fof(f3619,plain,
( sK53_skl = nil
| ~ ssList(app(sK52_skl,sK49_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f3579,f223]) ).
fof(f3909,plain,
( nil = sK53_skl
| sK53_skl = nil
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f3344,f3619]) ).
fof(f3911,plain,
( sK53_skl = nil
| ~ ssList(nil) ),
inference(duplicate_literals_removal,[status(thm)],[f3909]) ).
fof(f3912,plain,
sK53_skl = nil,
inference(forward_subsumption_resolution,[status(thm)],[f3911,f223]) ).
fof(f3934,plain,
! [X0] :
( nil = X0
| sK49_skl != app(app(sK52_skl,sK49_skl),X0)
| ~ ssList(app(sK52_skl,sK49_skl))
| ~ ssList(X0) ),
inference(backward_demodulation,[status(thm)],[f3912,f1064]) ).
fof(f4042,plain,
( ~ ssList(sK49_skl)
| ~ ssList(sK52_skl)
| sK49_skl = app(sK52_skl,sK49_skl) ),
inference(resolution,[status(thm)],[f3585,f245]) ).
fof(f4043,plain,
( ~ ssList(sK49_skl)
| sK49_skl = app(sK52_skl,sK49_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f4042,f426]) ).
fof(f4053,plain,
sK49_skl = app(sK52_skl,sK49_skl),
inference(forward_subsumption_resolution,[status(thm)],[f4043,f421]) ).
fof(f4068,plain,
( hd(sK49_skl) = hd(sK52_skl)
| nil = sK52_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f4053,f391]) ).
fof(f4109,plain,
( sK51_skl = hd(sK52_skl)
| nil = sK52_skl
| ~ ssList(sK49_skl)
| ~ ssList(sK52_skl) ),
inference(forward_demodulation,[status(thm)],[f995,f4068]) ).
fof(f4110,plain,
( sK51_skl = hd(sK52_skl)
| nil = sK52_skl
| ~ ssList(sK49_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f4109,f426]) ).
fof(f4264,plain,
( sK51_skl = hd(sK52_skl)
| nil = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f4110,f421]) ).
fof(f4267,plain,
( nil = sK52_skl
| cons(sK51_skl,tl(sK52_skl)) = sK52_skl
| nil = sK52_skl
| ~ ssList(sK52_skl) ),
inference(paramodulation,[status(thm)],[f4264,f374]) ).
fof(f4274,plain,
( cons(sK51_skl,tl(sK52_skl)) = sK52_skl
| nil = sK52_skl
| ~ ssList(sK52_skl) ),
inference(duplicate_literals_removal,[status(thm)],[f4267]) ).
fof(f4275,plain,
( cons(sK51_skl,tl(sK52_skl)) = sK52_skl
| nil = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f4274,f426]) ).
fof(f4277,plain,
! [X0] :
( nil = X0
| sK49_skl != app(app(sK52_skl,sK49_skl),X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f4053,f3934]) ).
fof(f4278,plain,
! [X0] :
( nil = X0
| sK49_skl != app(sK49_skl,X0)
| ~ ssList(sK49_skl)
| ~ ssList(X0) ),
inference(forward_demodulation,[status(thm)],[f4053,f4277]) ).
fof(f4279,plain,
! [X0] :
( nil = X0
| sK49_skl != app(sK49_skl,X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f4278,f421]) ).
fof(f4287,plain,
( nil = sK52_skl
| ~ frontsegP(tl(sK52_skl),nil)
| frontsegP(sK52_skl,sK49_skl)
| ~ ssList(tl(sK52_skl)) ),
inference(paramodulation,[status(thm)],[f4275,f1827]) ).
fof(f4346,plain,
( nil = sK52_skl
| frontsegP(sK52_skl,sK49_skl)
| ~ ssList(tl(sK52_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f4287,f295]) ).
fof(f4396,plain,
( sK52_skl = sK49_skl
| nil = sK52_skl
| ~ ssList(tl(sK52_skl)) ),
inference(resolution,[status(thm)],[f4346,f1550]) ).
fof(f4421,plain,
( nil = sK52_skl
| ~ ssList(sK52_skl)
| sK52_skl = sK49_skl
| nil = sK52_skl ),
inference(resolution,[status(thm)],[f4396,f241]) ).
fof(f4422,plain,
( ~ ssList(sK52_skl)
| sK52_skl = sK49_skl
| nil = sK52_skl ),
inference(duplicate_literals_removal,[status(thm)],[f4421]) ).
fof(f4423,plain,
( sK52_skl = sK49_skl
| nil = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f4422,f426]) ).
fof(f4427,plain,
( nil = sK52_skl
| sK49_skl = app(sK49_skl,sK49_skl) ),
inference(paramodulation,[status(thm)],[f4423,f4053]) ).
fof(f4482,plain,
( nil = sK49_skl
| ~ ssList(sK49_skl)
| nil = sK52_skl ),
inference(resolution,[status(thm)],[f4427,f4279]) ).
fof(f4523,plain,
( nil = sK49_skl
| nil = sK52_skl ),
inference(forward_subsumption_resolution,[status(thm)],[f4482,f421]) ).
fof(f4573,plain,
( memberP(nil,sK51_skl)
| memberP(nil,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f4587,f3486]) ).
fof(f4587,plain,
nil = sK52_skl,
inference(forward_subsumption_resolution,[status(thm)],[f4523,f811]) ).
fof(f4588,plain,
memberP(nil,sK51_skl),
inference(duplicate_literals_removal,[status(thm)],[f4573]) ).
fof(f4595,plain,
~ ssItem(sK51_skl),
inference(resolution,[status(thm)],[f4588,f279]) ).
fof(f4596,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4595,f425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWC187+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n011.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 08:02:55 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.13/0.37 % Drodi V4.1.1
% 14.26/2.26 % Refutation found
% 14.26/2.26 % SZS status Theorem for theBenchmark: Theorem is valid
% 14.26/2.26 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 14.26/2.29 % Elapsed time: 1.921623 seconds
% 14.26/2.29 % CPU time: 14.879750 seconds
% 14.26/2.29 % Total memory used: 192.816 MB
% 14.26/2.29 % Net memory used: 183.244 MB
%------------------------------------------------------------------------------