%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SWC173+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 : n014.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 02:40:15 PM UTC 2026
% Result : Theorem 53.88s 7.22s
% Output : CNFRefutation 53.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 72
% Syntax : Number of formulae : 327 ( 19 unt; 49 def)
% Number of atoms : 1258 ( 201 equ)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 1607 ( 676 ~; 688 |; 110 &)
% ( 60 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 5 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 57 ( 55 usr; 48 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 10 con; 0-5 aty)
% Number of variables : 319 ( 280 !; 39 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [U] :
( ssItem(U)
=> ! [V] :
( ssItem(V)
=> ( neq(U,V)
<=> U != V ) ) ),
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(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(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(f79,axiom,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ( app(W,V) = app(U,V)
=> W = 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(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(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(f96,conjecture,
! [U] :
( ssList(U)
=> ! [V] :
( ssList(V)
=> ! [W] :
( ssList(W)
=> ! [X] :
( ssList(X)
=> ( ( ( nil != W
| nil != X )
& ! [X3] :
( ssItem(X3)
=> ! [X4] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X7] :
( lt(X7,X3)
& memberP(X5,X7)
& ssItem(X7) )
| ? [X6] :
( lt(X3,X6)
& memberP(X4,X6)
& ssItem(X6) )
| app(app(X4,W),X5) != X
| cons(X3,nil) != W ) ) ) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssItem(Z)
=> ( neq(Y,Z)
| ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) != 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] :
( ssList(X4)
=> ! [X5] :
( ssList(X5)
=> ( ? [X7] :
( lt(X7,X3)
& memberP(X5,X7)
& ssItem(X7) )
| ? [X6] :
( lt(X3,X6)
& memberP(X4,X6)
& ssItem(X6) )
| app(app(X4,W),X5) != X
| cons(X3,nil) != W ) ) ) ) )
| ! [Y] :
( ssItem(Y)
=> ! [Z] :
( ssItem(Z)
=> ( neq(Y,Z)
| ! [X1] :
( ssList(X1)
=> ! [X2] :
( ssList(X2)
=> app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) != U ) ) ) ) )
| U != W
| V != X ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f96]) ).
fof(f98,plain,
! [U] :
( ! [V] :
( ( neq(U,V)
<=> U != V )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f99,plain,
! [U] :
( ! [V] :
( ( ( U = V
| neq(U,V) )
& ( U != V
| ~ neq(U,V) ) )
| ~ ssItem(V) )
| ~ ssItem(U) ),
inference(NNF_transformation,[status(thm)],[f98]) ).
fof(f101,plain,
! [X0,X1] :
( X0 = X1
| neq(X0,X1)
| ~ ssItem(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f99]) ).
fof(f119,plain,
! [U] :
( ! [V] :
( ( frontsegP(U,V)
<=> ? [W] :
( app(V,W) = U
& ssList(W) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f5]) ).
fof(f120,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ? [W] :
( app(V,W) = U
& ssList(W) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(NNF_transformation,[status(thm)],[f119]) ).
fof(f121,plain,
! [U] :
( ! [V] :
( ( ( ! [W] :
( app(V,W) != U
| ~ ssList(W) )
| frontsegP(U,V) )
& ( ( app(V,sK5_skl(V,U)) = U
& ssList(sK5_skl(V,U)) )
| ~ frontsegP(U,V) ) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK5_skl]),skolemize(W,sK5_skl(V,U))],[f120]) ).
fof(f122,plain,
! [X0,X1] :
( ssList(sK5_skl(X1,X0))
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f123,plain,
! [X0,X1] :
( app(X1,sK5_skl(X1,X0)) = X0
| ~ frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(f124,plain,
! [X0,X1,X2] :
( app(X1,X2) != X0
| ~ ssList(X2)
| frontsegP(X0,X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f121]) ).
fof(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(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(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(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(f375,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(W,V) != app(U,V)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f79]) ).
fof(f376,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X2,X1) != app(X0,X1)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f375]) ).
fof(f377,plain,
! [U] :
( ! [V] :
( ! [W] :
( W = U
| app(V,W) != app(V,U)
| ~ ssList(W) )
| ~ ssList(V) )
| ~ ssList(U) ),
inference(pre_NNF_transformation,[status(thm)],[f80]) ).
fof(f378,plain,
! [X0,X1,X2] :
( X2 = X0
| app(X1,X2) != app(X1,X0)
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f377]) ).
fof(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(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(f415,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X3] :
( ? [X4] :
( ? [X5] :
( ! [X7] :
( ~ lt(X7,X3)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& ! [X6] :
( ~ lt(X3,X6)
| ~ memberP(X4,X6)
| ~ ssItem(X6) )
& app(app(X4,W),X5) = X
& cons(X3,nil) = W
& ssList(X5) )
& ssList(X4) )
& ssItem(X3) ) )
& ? [Y] :
( ? [Z] :
( ~ neq(Y,Z)
& ? [X1] :
( ? [X2] :
( app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) = U
& ssList(X2) )
& ssList(X1) )
& ssItem(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,X3] :
( sP0_prd(X3,X,W)
<=> ( ? [X4] :
( ? [X5] :
( ! [X7] :
( ~ lt(X7,X3)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& ! [X6] :
( ~ lt(X3,X6)
| ~ memberP(X4,X6)
| ~ ssItem(X6) )
& app(app(X4,W),X5) = X
& cons(X3,nil) = W
& ssList(X5) )
& ssList(X4) )
& ssItem(X3) ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f417,plain,
? [U] :
( ? [V] :
( ? [W] :
( ? [X] :
( ( ( nil = W
& nil = X )
| ? [X3] : sP0_prd(X3,X,W) )
& ? [Y] :
( ? [Z] :
( ~ neq(Y,Z)
& ? [X1] :
( ? [X2] :
( app(app(app(X1,cons(Y,nil)),cons(Z,nil)),X2) = U
& ssList(X2) )
& ssList(X1) )
& ssItem(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(sK55_skl,sK50_skl,sK49_skl) )
& ~ neq(sK51_skl,sK52_skl)
& app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),sK54_skl) = sK47_skl
& ssList(sK54_skl)
& ssList(sK53_skl)
& ssItem(sK52_skl)
& ssItem(sK51_skl)
& sK47_skl = sK49_skl
& sK48_skl = sK50_skl
& ssList(sK50_skl)
& ssList(sK49_skl)
& ssList(sK48_skl)
& ssList(sK47_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK47_skl,sK48_skl,sK49_skl,sK50_skl,sK51_skl,sK52_skl,sK53_skl,sK54_skl,sK55_skl]),skolemize(U,sK47_skl),skolemize(V,sK48_skl),skolemize(W,sK49_skl),skolemize(X,sK50_skl),skolemize(Y,sK51_skl),skolemize(Z,sK52_skl),skolemize(X1,sK53_skl),skolemize(X2,sK54_skl),skolemize(X3,sK55_skl)],[f417]) ).
fof(f419,plain,
ssList(sK47_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f423,plain,
sK48_skl = sK50_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f424,plain,
sK47_skl = sK49_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f425,plain,
ssItem(sK51_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f426,plain,
ssItem(sK52_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f427,plain,
ssList(sK53_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f428,plain,
ssList(sK54_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f429,plain,
app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),sK54_skl) = sK47_skl,
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f430,plain,
~ neq(sK51_skl,sK52_skl),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f432,plain,
( nil = sK49_skl
| sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
inference(cnf_transformation,[status(thm)],[f418]) ).
fof(f433,definition,
! [X3,X4,X6] :
( sP1_prd(X6,X4,X3)
<=> ( ~ lt(X3,X6)
| ~ memberP(X4,X6)
| ~ ssItem(X6) ) ),
introduced(definition,[new_symbols(definition,[sP1_prd])],[]) ).
fof(f434,plain,
! [W,X,X3] :
( sP0_prd(X3,X,W)
<=> ( ? [X4] :
( ? [X5] :
( ! [X7] :
( ~ lt(X7,X3)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& ! [X6] : sP1_prd(X6,X4,X3)
& app(app(X4,W),X5) = X
& cons(X3,nil) = W
& ssList(X5) )
& ssList(X4) )
& ssItem(X3) ) ),
inference(formula_renaming,[status(thm)],[f416,f433]) ).
fof(f435,plain,
! [W,X,X3] :
( ( ! [X4] :
( ! [X5] :
( ? [X7] :
( lt(X7,X3)
& memberP(X5,X7)
& ssItem(X7) )
| ? [X6] : ~ sP1_prd(X6,X4,X3)
| app(app(X4,W),X5) != X
| cons(X3,nil) != W
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ( ( ? [X4] :
( ? [X5] :
( ! [X7] :
( ~ lt(X7,X3)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& ! [X6] : sP1_prd(X6,X4,X3)
& app(app(X4,W),X5) = X
& cons(X3,nil) = W
& ssList(X5) )
& ssList(X4) )
& ssItem(X3) )
| ~ sP0_prd(X3,X,W) ) ),
inference(NNF_transformation,[status(thm)],[f434]) ).
fof(f436,plain,
( ! [W,X,X3] :
( ! [X4] :
( ! [X5] :
( ? [X7] :
( lt(X7,X3)
& memberP(X5,X7)
& ssItem(X7) )
| ? [X6] : ~ sP1_prd(X6,X4,X3)
| app(app(X4,W),X5) != X
| cons(X3,nil) != W
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ! [W,X,X3] :
( ( ? [X4] :
( ? [X5] :
( ! [X7] :
( ~ lt(X7,X3)
| ~ memberP(X5,X7)
| ~ ssItem(X7) )
& ! [X6] : sP1_prd(X6,X4,X3)
& app(app(X4,W),X5) = X
& cons(X3,nil) = W
& ssList(X5) )
& ssList(X4) )
& ssItem(X3) )
| ~ sP0_prd(X3,X,W) ) ),
inference(miniscoping,[status(thm)],[f435]) ).
fof(f437,plain,
( ! [W,X,X3] :
( ! [X4] :
( ! [X5] :
( ( lt(sK59_skl(X5,X4,X3,X,W),X3)
& memberP(X5,sK59_skl(X5,X4,X3,X,W))
& ssItem(sK59_skl(X5,X4,X3,X,W)) )
| ~ sP1_prd(sK58_skl(X5,X4,X3,X,W),X4,X3)
| app(app(X4,W),X5) != X
| cons(X3,nil) != W
| ~ ssList(X5) )
| ~ ssList(X4) )
| ~ ssItem(X3)
| sP0_prd(X3,X,W) )
& ! [W,X,X3] :
( ( ! [X7] :
( ~ lt(X7,X3)
| ~ memberP(sK57_skl(X3,X,W),X7)
| ~ ssItem(X7) )
& ! [X6] : sP1_prd(X6,sK56_skl(X3,X,W),X3)
& app(app(sK56_skl(X3,X,W),W),sK57_skl(X3,X,W)) = X
& cons(X3,nil) = W
& ssList(sK57_skl(X3,X,W))
& ssList(sK56_skl(X3,X,W))
& ssItem(X3) )
| ~ sP0_prd(X3,X,W) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK56_skl,sK57_skl,sK58_skl,sK59_skl]),skolemize(X4,sK56_skl(X3,X,W)),skolemize(X5,sK57_skl(X3,X,W)),skolemize(X6,sK58_skl(X5,X4,X3,X,W)),skolemize(X7,sK59_skl(X5,X4,X3,X,W))],[f436]) ).
fof(f438,plain,
! [X0,X1,X2] :
( ssItem(X0)
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f437]) ).
fof(f441,plain,
! [X0,X1,X2] :
( cons(X0,nil) = X2
| ~ sP0_prd(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f437]) ).
fof(f454,definition,
( sQ0_spl
<=> sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f455,plain,
( ~ sQ0_spl
| sP0_prd(sK55_skl,sK50_skl,sK49_skl) ),
inference(component_clause,[status(thm)],[f454]) ).
fof(f461,definition,
( sQ2_spl
<=> nil = sK49_skl ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f462,plain,
( ~ sQ2_spl
| nil = sK49_skl ),
inference(component_clause,[status(thm)],[f461]) ).
fof(f464,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f432,f454,f461]) ).
fof(f469,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0)
| ~ ssList(app(X0,X1)) ),
inference(destructive_equality_resolution,[status(thm)],[f124]) ).
fof(f482,plain,
! [X1,X2] :
( memberP(cons(X1,X2),X1)
| ~ ssList(X2)
| ~ ssItem(X1)
| ~ ssItem(X1) ),
inference(destructive_equality_resolution,[status(thm)],[f276]) ).
fof(f483,plain,
! [X0,X1] :
( memberP(cons(X0,X1),X0)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f482]) ).
fof(f484,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(f485,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)],[f484]) ).
fof(f500,plain,
( sK51_skl = sK52_skl
| ~ ssItem(sK52_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f101,f430]) ).
fof(f503,definition,
( sQ3_spl
<=> ssItem(sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f505,plain,
( sQ3_spl
| ~ ssItem(sK51_skl) ),
inference(component_clause,[status(thm)],[f503]) ).
fof(f506,definition,
( sQ4_spl
<=> ssItem(sK52_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f508,plain,
( sQ4_spl
| ~ ssItem(sK52_skl) ),
inference(component_clause,[status(thm)],[f506]) ).
fof(f509,definition,
( sQ5_spl
<=> sK51_skl = sK52_skl ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f510,plain,
( ~ sQ5_spl
| sK51_skl = sK52_skl ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f512,plain,
( sQ5_spl
| ~ sQ4_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f500,f503,f506,f509]) ).
fof(f520,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f505,f425]) ).
fof(f521,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f520]) ).
fof(f537,plain,
( ssList(sK47_skl)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil))) ),
inference(paramodulation,[status(thm)],[f429,f245]) ).
fof(f538,definition,
( sQ9_spl
<=> ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f540,plain,
( sQ9_spl
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil))) ),
inference(component_clause,[status(thm)],[f538]) ).
fof(f541,definition,
( sQ10_spl
<=> ssList(sK54_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f543,plain,
( sQ10_spl
| ~ ssList(sK54_skl) ),
inference(component_clause,[status(thm)],[f541]) ).
fof(f544,definition,
( sQ11_spl
<=> ssList(sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f547,plain,
( sQ11_spl
| ~ sQ10_spl
| ~ sQ9_spl ),
inference(split_clause,[status(thm)],[f537,f538,f541,f544]) ).
fof(f548,plain,
( sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f543,f428]) ).
fof(f549,plain,
sQ10_spl,
inference(contradiction_clause,[status(thm)],[f548]) ).
fof(f550,plain,
! [X0] :
( ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssList(sK54_skl)
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)))
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f429,f271]) ).
fof(f551,definition,
! [X0] :
( sQ12_spl
<=> ( ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f552,plain,
! [X0] :
( ~ sQ12_spl
| ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK52_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f551]) ).
fof(f554,plain,
( ~ sQ10_spl
| ~ sQ9_spl
| sQ12_spl ),
inference(split_clause,[status(thm)],[f550,f551,f538,f541]) ).
fof(f594,definition,
( sQ18_spl
<=> ssList(nil) ),
introduced(definition,[new_symbols(definition,[sQ18_spl])],[split_symbol_definition]) ).
fof(f596,plain,
( sQ18_spl
| ~ ssList(nil) ),
inference(component_clause,[status(thm)],[f594]) ).
fof(f604,plain,
( sQ18_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f596,f223]) ).
fof(f605,plain,
sQ18_spl,
inference(contradiction_clause,[status(thm)],[f604]) ).
fof(f623,plain,
( sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f508,f426]) ).
fof(f624,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f623]) ).
fof(f626,plain,
( ~ sQ5_spl
| app(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),sK54_skl) = sK47_skl ),
inference(backward_demodulation,[status(thm)],[f510,f429]) ).
fof(f656,plain,
! [X0,X1] :
( ~ ssList(X1)
| frontsegP(app(X0,X1),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f469,f245]) ).
fof(f663,plain,
( ~ sQ0_spl
| sP0_prd(sK55_skl,sK48_skl,sK49_skl) ),
inference(forward_demodulation,[status(thm)],[f423,f455]) ).
fof(f664,plain,
( ~ sQ0_spl
| sP0_prd(sK55_skl,sK48_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f424,f663]) ).
fof(f665,plain,
( ~ sQ0_spl
| cons(sK55_skl,nil) = sK47_skl ),
inference(resolution,[status(thm)],[f664,f441]) ).
fof(f666,plain,
( ~ sQ0_spl
| ssItem(sK55_skl) ),
inference(resolution,[status(thm)],[f664,f438]) ).
fof(f668,plain,
! [X0] :
( ~ sQ0_spl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssList(nil)
| ~ ssItem(sK55_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f665,f275]) ).
fof(f681,definition,
( sQ24_spl
<=> ssItem(sK55_skl) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f683,plain,
( sQ24_spl
| ~ ssItem(sK55_skl) ),
inference(component_clause,[status(thm)],[f681]) ).
fof(f685,definition,
! [X0] :
( sQ25_spl
<=> ( memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ25_spl])],[split_symbol_definition]) ).
fof(f686,plain,
! [X0] :
( ~ sQ25_spl
| memberP(nil,X0)
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f685]) ).
fof(f688,plain,
( ~ sQ0_spl
| ~ sQ18_spl
| ~ sQ24_spl
| sQ25_spl ),
inference(split_clause,[status(thm)],[f668,f685,f681,f594,f454]) ).
fof(f702,definition,
( sQ29_spl
<=> nil = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ29_spl])],[split_symbol_definition]) ).
fof(f704,plain,
( sQ29_spl
| nil != sK47_skl ),
inference(component_clause,[status(thm)],[f702]) ).
fof(f707,plain,
( sQ24_spl
| ~ sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f683,f666]) ).
fof(f708,plain,
( sQ24_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f707]) ).
fof(f710,plain,
( ~ sQ2_spl
| nil = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f424,f462]) ).
fof(f777,plain,
! [X0] :
( ~ sQ25_spl
| X0 = sK55_skl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f686,f279]) ).
fof(f779,plain,
! [X0,X1] :
( ~ frontsegP(app(X1,X0),X1)
| ~ ssList(X1)
| ~ ssList(app(X1,X0))
| sK5_skl(X1,app(X1,X0)) = X0
| ~ ssList(sK5_skl(X1,app(X1,X0)))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(resolution,[status(thm)],[f378,f123]) ).
fof(f787,plain,
! [X0,X1] :
( ~ frontsegP(app(X1,X0),X1)
| ~ ssList(app(X1,X0))
| sK5_skl(X1,app(X1,X0)) = X0
| ~ ssList(sK5_skl(X1,app(X1,X0)))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f779]) ).
fof(f788,plain,
! [X0,X1] :
( ~ frontsegP(app(X1,X0),X1)
| ~ ssList(app(X1,X0))
| sK5_skl(X1,app(X1,X0)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f787,f122]) ).
fof(f942,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ ssList(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil))) ),
inference(forward_demodulation,[status(thm)],[f510,f540]) ).
fof(f943,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(resolution,[status(thm)],[f942,f245]) ).
fof(f944,definition,
( sQ44_spl
<=> ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
introduced(definition,[new_symbols(definition,[sQ44_spl])],[split_symbol_definition]) ).
fof(f945,plain,
( ~ sQ44_spl
| ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f944]) ).
fof(f946,plain,
( sQ44_spl
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(component_clause,[status(thm)],[f944]) ).
fof(f947,definition,
( sQ45_spl
<=> ssList(cons(sK51_skl,nil)) ),
introduced(definition,[new_symbols(definition,[sQ45_spl])],[split_symbol_definition]) ).
fof(f949,plain,
( sQ45_spl
| ~ ssList(cons(sK51_skl,nil)) ),
inference(component_clause,[status(thm)],[f947]) ).
fof(f950,plain,
( sQ9_spl
| ~ sQ5_spl
| ~ sQ45_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f943,f944,f947,f509,f538]) ).
fof(f951,plain,
( sQ44_spl
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f946,f245]) ).
fof(f952,definition,
( sQ46_spl
<=> ssList(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ46_spl])],[split_symbol_definition]) ).
fof(f954,plain,
( sQ46_spl
| ~ ssList(sK53_skl) ),
inference(component_clause,[status(thm)],[f952]) ).
fof(f955,plain,
( sQ44_spl
| ~ sQ45_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f951,f952,f947,f944]) ).
fof(f956,plain,
( sQ45_spl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f949,f222]) ).
fof(f957,plain,
( sQ45_spl
| ~ sQ3_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f956,f594,f503,f947]) ).
fof(f963,plain,
( sQ46_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f954,f427]) ).
fof(f964,plain,
sQ46_spl,
inference(contradiction_clause,[status(thm)],[f963]) ).
fof(f1265,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ memberP(app(app(sK53_skl,cons(sK51_skl,nil)),cons(sK51_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_demodulation,[status(thm)],[f510,f552]) ).
fof(f1282,plain,
( ~ sQ0_spl
| hd(sK47_skl) = sK55_skl
| ~ ssItem(sK55_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f665,f239]) ).
fof(f1348,definition,
( sQ118_spl
<=> hd(sK47_skl) = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ118_spl])],[split_symbol_definition]) ).
fof(f1349,plain,
( ~ sQ118_spl
| hd(sK47_skl) = sK55_skl ),
inference(component_clause,[status(thm)],[f1348]) ).
fof(f1351,plain,
( ~ sQ0_spl
| sQ118_spl
| ~ sQ24_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f1282,f594,f681,f1348,f454]) ).
fof(f1400,plain,
! [X0] :
( ~ sQ12_spl
| ~ sQ5_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil)))
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1265,f271]) ).
fof(f1402,definition,
( sQ120_spl
<=> memberP(sK47_skl,sK51_skl) ),
introduced(definition,[new_symbols(definition,[sQ120_spl])],[split_symbol_definition]) ).
fof(f1403,plain,
( ~ sQ120_spl
| memberP(sK47_skl,sK51_skl) ),
inference(component_clause,[status(thm)],[f1402]) ).
fof(f1406,definition,
! [X0] :
( sQ121_spl
<=> ( ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ121_spl])],[split_symbol_definition]) ).
fof(f1407,plain,
! [X0] :
( ~ sQ121_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1406]) ).
fof(f1409,plain,
( ~ sQ12_spl
| ~ sQ5_spl
| ~ sQ45_spl
| ~ sQ44_spl
| sQ121_spl ),
inference(split_clause,[status(thm)],[f1400,f1406,f944,f947,f509,f551]) ).
fof(f1410,definition,
! [X0] :
( sQ122_spl
<=> ( ~ memberP(cons(sK51_skl,nil),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ122_spl])],[split_symbol_definition]) ).
fof(f1411,plain,
! [X0] :
( ~ sQ122_spl
| ~ memberP(cons(sK51_skl,nil),X0)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f1410]) ).
fof(f1414,plain,
! [X0] :
( ~ sQ121_spl
| ~ memberP(app(sK53_skl,cons(sK51_skl,nil)),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1407]) ).
fof(f1415,plain,
! [X0] :
( ~ sQ122_spl
| ~ memberP(cons(sK51_skl,nil),X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(duplicate_literals_removal,[status(thm)],[f1411]) ).
fof(f1416,plain,
( ~ sQ25_spl
| ~ sQ120_spl
| sK51_skl = sK55_skl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1403,f777]) ).
fof(f1417,definition,
( sQ123_spl
<=> sK51_skl = sK55_skl ),
introduced(definition,[new_symbols(definition,[sQ123_spl])],[split_symbol_definition]) ).
fof(f1418,plain,
( ~ sQ123_spl
| sK51_skl = sK55_skl ),
inference(component_clause,[status(thm)],[f1417]) ).
fof(f1420,plain,
( ~ sQ25_spl
| ~ sQ120_spl
| sQ123_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1416,f503,f1417,f1402,f685]) ).
fof(f1446,plain,
( ~ sQ5_spl
| sK47_skl = app(app(sK53_skl,cons(sK51_skl,nil)),app(cons(sK51_skl,nil),sK54_skl))
| ~ ssList(sK54_skl)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(app(sK53_skl,cons(sK51_skl,nil))) ),
inference(paramodulation,[status(thm)],[f626,f382]) ).
fof(f1471,definition,
( sQ128_spl
<=> sK47_skl = app(app(sK53_skl,cons(sK51_skl,nil)),app(cons(sK51_skl,nil),sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ128_spl])],[split_symbol_definition]) ).
fof(f1472,plain,
( ~ sQ128_spl
| sK47_skl = app(app(sK53_skl,cons(sK51_skl,nil)),app(cons(sK51_skl,nil),sK54_skl)) ),
inference(component_clause,[status(thm)],[f1471]) ).
fof(f1474,plain,
( ~ sQ5_spl
| sQ128_spl
| ~ sQ10_spl
| ~ sQ45_spl
| ~ sQ44_spl ),
inference(split_clause,[status(thm)],[f1446,f944,f947,f541,f1471,f509]) ).
fof(f1522,plain,
( ~ sQ0_spl
| ~ sQ123_spl
| cons(sK51_skl,nil) = sK47_skl ),
inference(backward_demodulation,[status(thm)],[f1418,f665]) ).
fof(f1528,plain,
( ~ sQ44_spl
| ~ sQ0_spl
| ~ sQ123_spl
| ssList(app(sK53_skl,sK47_skl)) ),
inference(backward_demodulation,[status(thm)],[f1522,f945]) ).
fof(f1554,plain,
( ~ sQ0_spl
| ~ sQ123_spl
| nil != sK47_skl
| ~ ssItem(sK51_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f1522,f235]) ).
fof(f1631,plain,
( ~ sQ0_spl
| ~ sQ123_spl
| ~ sQ29_spl
| ~ sQ3_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f1554,f594,f503,f702,f1417,f454]) ).
fof(f1653,plain,
( ~ sQ122_spl
| ~ ssList(nil)
| ~ ssItem(sK51_skl)
| memberP(sK47_skl,sK51_skl)
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f1415,f483]) ).
fof(f1658,plain,
( ~ sQ122_spl
| ~ sQ18_spl
| sQ120_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f1653,f503,f1402,f594,f1410]) ).
fof(f1767,plain,
( ~ sQ118_spl
| ~ sQ123_spl
| hd(sK47_skl) = sK51_skl ),
inference(forward_demodulation,[status(thm)],[f1418,f1349]) ).
fof(f1858,definition,
( sQ159_spl
<=> ssList(app(sK53_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ159_spl])],[split_symbol_definition]) ).
fof(f1860,plain,
( sQ159_spl
| ~ ssList(app(sK53_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f1858]) ).
fof(f1876,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ123_spl
| app(app(app(sK53_skl,sK47_skl),cons(sK51_skl,nil)),sK54_skl) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f1522,f626]) ).
fof(f1877,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ123_spl
| app(app(app(sK53_skl,sK47_skl),sK47_skl),sK54_skl) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f1522,f1876]) ).
fof(f1964,plain,
( sQ159_spl
| ~ sQ44_spl
| ~ sQ0_spl
| ~ sQ123_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f1860,f1528]) ).
fof(f1965,plain,
( sQ159_spl
| ~ sQ44_spl
| ~ sQ0_spl
| ~ sQ123_spl ),
inference(contradiction_clause,[status(thm)],[f1964]) ).
fof(f2446,definition,
( sQ235_spl
<=> nil = app(sK53_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ235_spl])],[split_symbol_definition]) ).
fof(f2447,plain,
( ~ sQ235_spl
| nil = app(sK53_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f2446]) ).
fof(f2463,plain,
! [X0] :
( ~ sQ235_spl
| ~ memberP(sK47_skl,X0)
| memberP(nil,X0)
| ~ ssList(sK47_skl)
| ~ ssList(sK53_skl)
| ~ ssItem(X0) ),
inference(paramodulation,[status(thm)],[f2447,f272]) ).
fof(f2468,definition,
( sQ236_spl
<=> nil = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ236_spl])],[split_symbol_definition]) ).
fof(f2469,plain,
( ~ sQ236_spl
| nil = sK53_skl ),
inference(component_clause,[status(thm)],[f2468]) ).
fof(f2474,definition,
! [X0] :
( sQ237_spl
<=> ( ~ memberP(sK47_skl,X0)
| memberP(nil,X0)
| ~ ssItem(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ237_spl])],[split_symbol_definition]) ).
fof(f2475,plain,
! [X0] :
( ~ sQ237_spl
| ~ memberP(sK47_skl,X0)
| memberP(nil,X0)
| ~ ssItem(X0) ),
inference(component_clause,[status(thm)],[f2474]) ).
fof(f2477,plain,
( ~ sQ235_spl
| ~ sQ11_spl
| ~ sQ46_spl
| sQ237_spl ),
inference(split_clause,[status(thm)],[f2463,f2474,f952,f544,f2446]) ).
fof(f2488,plain,
! [X0] :
( ~ sQ237_spl
| ~ memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2475,f279]) ).
fof(f2489,plain,
( ~ sQ120_spl
| ~ sQ237_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f2488,f1403]) ).
fof(f2490,plain,
( ~ sQ120_spl
| ~ sQ237_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f2489,f503,f2474,f1402]) ).
fof(f2637,definition,
( sQ243_spl
<=> ssList(app(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ243_spl])],[split_symbol_definition]) ).
fof(f2639,plain,
( sQ243_spl
| ~ ssList(app(sK47_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f2637]) ).
fof(f2775,plain,
( sQ243_spl
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f2639,f245]) ).
fof(f2776,plain,
( sQ243_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f2775,f544,f2637]) ).
fof(f2826,definition,
( sQ259_spl
<=> frontsegP(sK47_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ259_spl])],[split_symbol_definition]) ).
fof(f2827,plain,
( ~ sQ259_spl
| frontsegP(sK47_skl,sK47_skl) ),
inference(component_clause,[status(thm)],[f2826]) ).
fof(f2945,definition,
( sQ274_spl
<=> frontsegP(sK47_skl,app(sK53_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ274_spl])],[split_symbol_definition]) ).
fof(f2946,plain,
( ~ sQ274_spl
| frontsegP(sK47_skl,app(sK53_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f2945]) ).
fof(f2968,plain,
( ~ sQ274_spl
| app(sK53_skl,sK47_skl) = sK47_skl
| ~ frontsegP(app(sK53_skl,sK47_skl),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK53_skl,sK47_skl)) ),
inference(resolution,[status(thm)],[f2946,f284]) ).
fof(f2970,definition,
( sQ278_spl
<=> frontsegP(app(sK53_skl,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ278_spl])],[split_symbol_definition]) ).
fof(f2972,plain,
( sQ278_spl
| ~ frontsegP(app(sK53_skl,sK47_skl),sK47_skl) ),
inference(component_clause,[status(thm)],[f2970]) ).
fof(f2973,definition,
( sQ279_spl
<=> app(sK53_skl,sK47_skl) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ279_spl])],[split_symbol_definition]) ).
fof(f2974,plain,
( ~ sQ279_spl
| app(sK53_skl,sK47_skl) = sK47_skl ),
inference(component_clause,[status(thm)],[f2973]) ).
fof(f2976,plain,
( ~ sQ274_spl
| sQ279_spl
| ~ sQ278_spl
| ~ sQ11_spl
| ~ sQ159_spl ),
inference(split_clause,[status(thm)],[f2968,f1858,f544,f2970,f2973,f2945]) ).
fof(f3027,definition,
( sQ286_spl
<=> frontsegP(sK53_skl,sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ286_spl])],[split_symbol_definition]) ).
fof(f3166,plain,
! [X0] :
( ~ sQ279_spl
| sK53_skl = X0
| sK47_skl != app(X0,sK47_skl)
| ~ ssList(sK53_skl)
| ~ ssList(sK47_skl)
| ~ ssList(X0) ),
inference(paramodulation,[status(thm)],[f2974,f376]) ).
fof(f3175,definition,
! [X0] :
( sQ299_spl
<=> ( sK53_skl = X0
| sK47_skl != app(X0,sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ299_spl])],[split_symbol_definition]) ).
fof(f3176,plain,
! [X0] :
( ~ sQ299_spl
| sK53_skl = X0
| sK47_skl != app(X0,sK47_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3175]) ).
fof(f3178,plain,
( ~ sQ279_spl
| ~ sQ46_spl
| ~ sQ11_spl
| sQ299_spl ),
inference(split_clause,[status(thm)],[f3166,f3175,f544,f952,f2973]) ).
fof(f3277,plain,
! [X0] :
( ~ sQ0_spl
| ~ sQ123_spl
| ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK47_skl)
| ~ ssList(nil)
| ~ ssList(X0)
| ~ ssItem(sK51_skl) ),
inference(paramodulation,[status(thm)],[f1522,f485]) ).
fof(f3298,definition,
! [X0] :
( sQ310_spl
<=> ( ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK47_skl)
| ~ ssList(X0) ) ),
introduced(definition,[new_symbols(definition,[sQ310_spl])],[split_symbol_definition]) ).
fof(f3299,plain,
! [X0] :
( ~ sQ310_spl
| ~ frontsegP(X0,nil)
| frontsegP(cons(sK51_skl,X0),sK47_skl)
| ~ ssList(X0) ),
inference(component_clause,[status(thm)],[f3298]) ).
fof(f3301,plain,
( ~ sQ0_spl
| ~ sQ123_spl
| ~ sQ18_spl
| sQ310_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3277,f503,f3298,f594,f1417,f454]) ).
fof(f3302,plain,
! [X0] :
( ~ sQ310_spl
| frontsegP(cons(sK51_skl,X0),sK47_skl)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f3299,f295]) ).
fof(f3674,plain,
! [X0] :
( ~ sQ121_spl
| ~ memberP(cons(sK51_skl,nil),X0)
| ~ ssList(cons(sK51_skl,nil))
| ~ ssList(sK53_skl)
| ~ ssItem(X0)
| memberP(sK47_skl,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1414,f272]) ).
fof(f3676,plain,
( ~ sQ121_spl
| ~ sQ45_spl
| ~ sQ46_spl
| sQ122_spl ),
inference(split_clause,[status(thm)],[f3674,f1410,f952,f947,f1406]) ).
fof(f3695,plain,
( ~ sQ120_spl
| ~ sQ2_spl
| memberP(nil,sK51_skl) ),
inference(backward_demodulation,[status(thm)],[f710,f1403]) ).
fof(f3706,plain,
( ~ sQ120_spl
| ~ sQ2_spl
| ~ ssItem(sK51_skl) ),
inference(resolution,[status(thm)],[f3695,f279]) ).
fof(f3707,plain,
( ~ sQ120_spl
| ~ sQ2_spl
| ~ sQ3_spl ),
inference(split_clause,[status(thm)],[f3706,f503,f461,f1402]) ).
fof(f7228,plain,
! [X0,X1] :
( ~ frontsegP(app(X1,X0),X1)
| sK5_skl(X1,app(X1,X0)) = X0
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f788,f245]) ).
fof(f7232,definition,
( sQ618_spl
<=> sK5_skl(sK47_skl,sK47_skl) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ618_spl])],[split_symbol_definition]) ).
fof(f7233,plain,
( ~ sQ618_spl
| sK5_skl(sK47_skl,sK47_skl) = sK47_skl ),
inference(component_clause,[status(thm)],[f7232]) ).
fof(f7235,definition,
( sQ619_spl
<=> frontsegP(app(sK47_skl,sK47_skl),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ619_spl])],[split_symbol_definition]) ).
fof(f7237,plain,
( sQ619_spl
| ~ frontsegP(app(sK47_skl,sK47_skl),sK47_skl) ),
inference(component_clause,[status(thm)],[f7235]) ).
fof(f7239,definition,
( sQ620_spl
<=> sK5_skl(sK47_skl,sK47_skl) = nil ),
introduced(definition,[new_symbols(definition,[sQ620_spl])],[split_symbol_definition]) ).
fof(f7240,plain,
( ~ sQ620_spl
| sK5_skl(sK47_skl,sK47_skl) = nil ),
inference(component_clause,[status(thm)],[f7239]) ).
fof(f7242,definition,
( sQ621_spl
<=> frontsegP(app(sK47_skl,nil),sK47_skl) ),
introduced(definition,[new_symbols(definition,[sQ621_spl])],[split_symbol_definition]) ).
fof(f7244,plain,
( sQ621_spl
| ~ frontsegP(app(sK47_skl,nil),sK47_skl) ),
inference(component_clause,[status(thm)],[f7242]) ).
fof(f7329,definition,
( sQ629_spl
<=> app(nil,sK47_skl) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ629_spl])],[split_symbol_definition]) ).
fof(f7330,plain,
( ~ sQ629_spl
| app(nil,sK47_skl) = sK47_skl ),
inference(component_clause,[status(thm)],[f7329]) ).
fof(f7331,plain,
( sQ629_spl
| app(nil,sK47_skl) != sK47_skl ),
inference(component_clause,[status(thm)],[f7329]) ).
fof(f7336,definition,
( sQ630_spl
<=> app(sK47_skl,sK47_skl) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ630_spl])],[split_symbol_definition]) ).
fof(f7337,plain,
( ~ sQ630_spl
| app(sK47_skl,sK47_skl) = sK47_skl ),
inference(component_clause,[status(thm)],[f7336]) ).
fof(f7436,plain,
( sQ629_spl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f7331,f249]) ).
fof(f7437,plain,
( sQ629_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7436,f419]) ).
fof(f7438,plain,
sQ629_spl,
inference(contradiction_clause,[status(thm)],[f7437]) ).
fof(f7632,plain,
( ~ sQ630_spl
| ~ frontsegP(app(sK47_skl,sK47_skl),sK47_skl)
| sK5_skl(sK47_skl,sK47_skl) = sK47_skl
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f7337,f7228]) ).
fof(f7651,plain,
( ~ sQ630_spl
| ~ sQ619_spl
| sQ618_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f7632,f544,f7232,f7235,f7336]) ).
fof(f7778,definition,
( sQ646_spl
<=> app(sK47_skl,nil) = sK47_skl ),
introduced(definition,[new_symbols(definition,[sQ646_spl])],[split_symbol_definition]) ).
fof(f7779,plain,
( ~ sQ646_spl
| app(sK47_skl,nil) = sK47_skl ),
inference(component_clause,[status(thm)],[f7778]) ).
fof(f7780,plain,
( sQ646_spl
| app(sK47_skl,nil) != sK47_skl ),
inference(component_clause,[status(thm)],[f7778]) ).
fof(f7953,plain,
( ~ sQ618_spl
| ~ sQ620_spl
| nil = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f7240,f7233]) ).
fof(f7954,plain,
( ~ sQ618_spl
| ~ sQ620_spl
| sQ29_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f7953,f704]) ).
fof(f7955,plain,
( ~ sQ618_spl
| ~ sQ620_spl
| sQ29_spl ),
inference(contradiction_clause,[status(thm)],[f7954]) ).
fof(f8011,plain,
( ~ sQ646_spl
| ~ frontsegP(app(sK47_skl,nil),sK47_skl)
| sK5_skl(sK47_skl,sK47_skl) = nil
| ~ ssList(sK47_skl)
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f7779,f7228]) ).
fof(f8021,plain,
( ~ sQ646_spl
| ~ ssList(nil)
| frontsegP(sK47_skl,sK47_skl)
| ~ ssList(sK47_skl) ),
inference(paramodulation,[status(thm)],[f7779,f656]) ).
fof(f8031,plain,
( ~ sQ646_spl
| ~ sQ621_spl
| sQ620_spl
| ~ sQ11_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f8011,f594,f544,f7239,f7242,f7778]) ).
fof(f8041,plain,
( ~ sQ646_spl
| ~ sQ18_spl
| sQ259_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f8021,f544,f2826,f594,f7778]) ).
fof(f8064,plain,
( sQ646_spl
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f7780,f389]) ).
fof(f8065,plain,
( sQ646_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8064,f419]) ).
fof(f8066,plain,
sQ646_spl,
inference(contradiction_clause,[status(thm)],[f8065]) ).
fof(f8240,plain,
( sQ621_spl
| ~ sQ646_spl
| ~ frontsegP(sK47_skl,sK47_skl) ),
inference(forward_demodulation,[status(thm)],[f7779,f7244]) ).
fof(f8241,plain,
( sQ621_spl
| ~ sQ646_spl
| ~ sQ259_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f8240,f2827]) ).
fof(f8242,plain,
( sQ621_spl
| ~ sQ646_spl
| ~ sQ259_spl ),
inference(contradiction_clause,[status(thm)],[f8241]) ).
fof(f9905,definition,
( sQ798_spl
<=> frontsegP(sK47_skl,app(sK47_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ798_spl])],[split_symbol_definition]) ).
fof(f9906,plain,
( ~ sQ798_spl
| frontsegP(sK47_skl,app(sK47_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f9905]) ).
fof(f9923,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ123_spl
| ~ sQ236_spl
| app(app(app(nil,sK47_skl),sK47_skl),sK54_skl) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f2469,f1877]) ).
fof(f9924,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ123_spl
| ~ sQ236_spl
| ~ sQ629_spl
| app(app(sK47_skl,sK47_skl),sK54_skl) = sK47_skl ),
inference(forward_demodulation,[status(thm)],[f7330,f9923]) ).
fof(f9993,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ123_spl
| ~ sQ236_spl
| ~ sQ629_spl
| ~ ssList(sK54_skl)
| frontsegP(sK47_skl,app(sK47_skl,sK47_skl))
| ~ ssList(app(sK47_skl,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f9924,f656]) ).
fof(f10049,plain,
( ~ sQ5_spl
| ~ sQ0_spl
| ~ sQ123_spl
| ~ sQ236_spl
| ~ sQ629_spl
| ~ sQ10_spl
| sQ798_spl
| ~ sQ243_spl ),
inference(split_clause,[status(thm)],[f9993,f2637,f9905,f541,f7329,f2468,f1417,f454,f509]) ).
fof(f10219,plain,
( ~ sQ798_spl
| app(sK47_skl,sK47_skl) = sK47_skl
| ~ frontsegP(app(sK47_skl,sK47_skl),sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(app(sK47_skl,sK47_skl)) ),
inference(resolution,[status(thm)],[f284,f9906]) ).
fof(f10232,plain,
( ~ sQ798_spl
| sQ630_spl
| ~ sQ619_spl
| ~ sQ11_spl
| ~ sQ243_spl ),
inference(split_clause,[status(thm)],[f10219,f2637,f544,f7235,f7336,f9905]) ).
fof(f10462,plain,
( sQ619_spl
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f7237,f656]) ).
fof(f10465,plain,
( sQ619_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f10462,f544,f7235]) ).
fof(f10920,plain,
( sQ278_spl
| ~ frontsegP(sK53_skl,sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK47_skl)
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f2972,f288]) ).
fof(f10922,plain,
( sQ278_spl
| ~ sQ286_spl
| ~ sQ11_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f10920,f952,f544,f3027,f2970]) ).
fof(f12384,plain,
( ~ sQ629_spl
| ~ sQ299_spl
| sK53_skl = nil
| ~ ssList(nil) ),
inference(resolution,[status(thm)],[f3176,f7330]) ).
fof(f12391,plain,
( ~ sQ629_spl
| ~ sQ299_spl
| sQ236_spl
| ~ sQ18_spl ),
inference(split_clause,[status(thm)],[f12384,f594,f2468,f3175,f7329]) ).
fof(f12532,plain,
( ~ sQ128_spl
| ~ sQ0_spl
| ~ sQ123_spl
| sK47_skl = app(app(sK53_skl,sK47_skl),app(cons(sK51_skl,nil),sK54_skl)) ),
inference(forward_demodulation,[status(thm)],[f1522,f1472]) ).
fof(f12533,plain,
( ~ sQ128_spl
| ~ sQ0_spl
| ~ sQ123_spl
| sK47_skl = app(app(sK53_skl,sK47_skl),app(sK47_skl,sK54_skl)) ),
inference(forward_demodulation,[status(thm)],[f1522,f12532]) ).
fof(f12541,plain,
( ~ sQ128_spl
| ~ sQ0_spl
| ~ sQ123_spl
| hd(sK47_skl) = hd(app(sK53_skl,sK47_skl))
| nil = app(sK53_skl,sK47_skl)
| ~ ssList(app(sK47_skl,sK54_skl))
| ~ ssList(app(sK53_skl,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f12533,f391]) ).
fof(f12549,plain,
( ~ sQ128_spl
| ~ sQ0_spl
| ~ sQ123_spl
| ~ ssList(app(sK47_skl,sK54_skl))
| frontsegP(sK47_skl,app(sK53_skl,sK47_skl))
| ~ ssList(app(sK53_skl,sK47_skl)) ),
inference(paramodulation,[status(thm)],[f12533,f656]) ).
fof(f12560,definition,
( sQ1040_spl
<=> ssList(app(sK47_skl,sK54_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1040_spl])],[split_symbol_definition]) ).
fof(f12562,plain,
( sQ1040_spl
| ~ ssList(app(sK47_skl,sK54_skl)) ),
inference(component_clause,[status(thm)],[f12560]) ).
fof(f12588,definition,
( sQ1047_spl
<=> hd(sK47_skl) = hd(app(sK53_skl,sK47_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1047_spl])],[split_symbol_definition]) ).
fof(f12589,plain,
( ~ sQ1047_spl
| hd(sK47_skl) = hd(app(sK53_skl,sK47_skl)) ),
inference(component_clause,[status(thm)],[f12588]) ).
fof(f12591,plain,
( ~ sQ128_spl
| ~ sQ0_spl
| ~ sQ123_spl
| sQ1047_spl
| sQ235_spl
| ~ sQ1040_spl
| ~ sQ159_spl ),
inference(split_clause,[status(thm)],[f12541,f1858,f12560,f2446,f12588,f1417,f454,f1471]) ).
fof(f12614,plain,
( ~ sQ128_spl
| ~ sQ0_spl
| ~ sQ123_spl
| ~ sQ1040_spl
| sQ274_spl
| ~ sQ159_spl ),
inference(split_clause,[status(thm)],[f12549,f1858,f2945,f12560,f1417,f454,f1471]) ).
fof(f12634,plain,
( ~ sQ1047_spl
| ~ sQ118_spl
| ~ sQ123_spl
| sK51_skl = hd(app(sK53_skl,sK47_skl)) ),
inference(forward_demodulation,[status(thm)],[f1767,f12589]) ).
fof(f13059,plain,
( sQ1040_spl
| ~ ssList(sK54_skl)
| ~ ssList(sK47_skl) ),
inference(resolution,[status(thm)],[f12562,f245]) ).
fof(f13060,plain,
( sQ1040_spl
| ~ sQ10_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f13059,f544,f541,f12560]) ).
fof(f14161,plain,
( ~ sQ1047_spl
| ~ sQ118_spl
| ~ sQ123_spl
| sK51_skl = hd(sK53_skl)
| nil = sK53_skl
| ~ ssList(sK47_skl)
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f12634,f391]) ).
fof(f14168,definition,
( sQ1255_spl
<=> sK51_skl = hd(sK53_skl) ),
introduced(definition,[new_symbols(definition,[sQ1255_spl])],[split_symbol_definition]) ).
fof(f14169,plain,
( ~ sQ1255_spl
| sK51_skl = hd(sK53_skl) ),
inference(component_clause,[status(thm)],[f14168]) ).
fof(f14171,plain,
( ~ sQ1047_spl
| ~ sQ118_spl
| ~ sQ123_spl
| sQ1255_spl
| sQ236_spl
| ~ sQ11_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f14161,f952,f544,f2468,f14168,f1417,f1348,f12588]) ).
fof(f14202,plain,
( ~ sQ1255_spl
| cons(sK51_skl,tl(sK53_skl)) = sK53_skl
| nil = sK53_skl
| ~ ssList(sK53_skl) ),
inference(paramodulation,[status(thm)],[f14169,f374]) ).
fof(f14208,definition,
( sQ1263_spl
<=> cons(sK51_skl,tl(sK53_skl)) = sK53_skl ),
introduced(definition,[new_symbols(definition,[sQ1263_spl])],[split_symbol_definition]) ).
fof(f14209,plain,
( ~ sQ1263_spl
| cons(sK51_skl,tl(sK53_skl)) = sK53_skl ),
inference(component_clause,[status(thm)],[f14208]) ).
fof(f14211,plain,
( ~ sQ1255_spl
| sQ1263_spl
| sQ236_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f14202,f952,f2468,f14208,f14168]) ).
fof(f14453,plain,
( ~ sQ1263_spl
| ~ sQ310_spl
| frontsegP(sK53_skl,sK47_skl)
| ~ ssList(tl(sK53_skl)) ),
inference(paramodulation,[status(thm)],[f14209,f3302]) ).
fof(f14493,definition,
( sQ1284_spl
<=> ssList(tl(sK53_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1284_spl])],[split_symbol_definition]) ).
fof(f14495,plain,
( sQ1284_spl
| ~ ssList(tl(sK53_skl)) ),
inference(component_clause,[status(thm)],[f14493]) ).
fof(f14496,plain,
( ~ sQ1263_spl
| ~ sQ310_spl
| sQ286_spl
| ~ sQ1284_spl ),
inference(split_clause,[status(thm)],[f14453,f14493,f3027,f3298,f14208]) ).
fof(f15186,plain,
( sQ1284_spl
| nil = sK53_skl
| ~ ssList(sK53_skl) ),
inference(resolution,[status(thm)],[f14495,f241]) ).
fof(f15187,plain,
( sQ1284_spl
| sQ236_spl
| ~ sQ46_spl ),
inference(split_clause,[status(thm)],[f15186,f952,f2468,f14493]) ).
fof(f15188,plain,
$false,
inference(sat_refutation,[status(thm)],[f464,f512,f521,f547,f549,f554,f605,f624,f688,f708,f950,f955,f957,f964,f1351,f1409,f1420,f1474,f1631,f1658,f1965,f2477,f2490,f2776,f2976,f3178,f3301,f3676,f3707,f7438,f7651,f7955,f8031,f8041,f8066,f8242,f10049,f10232,f10465,f10922,f12391,f12591,f12614,f13060,f14171,f14211,f14496,f15187]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC173+1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n014.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 08:00:51 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.12/0.38 % Drodi V4.1.1
% 53.88/7.22 % Refutation found
% 53.88/7.22 % SZS status Theorem for theBenchmark: Theorem is valid
% 53.88/7.22 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 53.88/7.27 % Elapsed time: 6.889098 seconds
% 53.88/7.27 % CPU time: 54.287783 seconds
% 53.88/7.27 % Total memory used: 388.906 MB
% 53.88/7.27 % Net memory used: 366.587 MB
%------------------------------------------------------------------------------