%------------------------------------------------------------------------------
% 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 : n009.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 : Unsatisfiable 10.33s 1.79s
% Output : CNFRefutation 10.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 84
% Number of leaves : 37
% Syntax : Number of formulae : 243 ( 36 unt; 0 def)
% Number of atoms : 761 ( 275 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 950 ( 432 ~; 518 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 197 ( 197 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
ssList(nil),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [U] : ssItem(skaf83(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [U] : ssList(skaf82(U)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [U] :
( frontsegP(U,nil)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f71,axiom,
! [U] :
( ~ ssItem(U)
| ~ memberP(nil,U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f74,axiom,
! [U] :
( app(nil,U) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,axiom,
! [U] :
( nil = U
| ssList(tl(U))
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f85,axiom,
! [U,V] :
( ssList(app(V,U))
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [U,V] :
( ssList(cons(U,V))
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,axiom,
! [U,V] :
( tl(cons(U,V)) = V
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f97,axiom,
! [U,V] :
( hd(cons(U,V)) = U
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f98,axiom,
! [U,V] :
( ~ ssList(V)
| ~ ssItem(U)
| cons(U,V) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f104,axiom,
! [U] :
( nil = U
| cons(hd(U),tl(U)) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f109,axiom,
! [U] :
( nil = U
| cons(skaf83(U),skaf82(U)) = U
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f118,axiom,
! [U,V] :
( nil = U
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f119,axiom,
! [U,V] :
( nil = V
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f120,axiom,
! [U,V] :
( app(cons(U,nil),V) = cons(U,V)
| ~ ssList(V)
| ~ ssItem(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f123,axiom,
! [U,V] :
( hd(app(V,U)) = hd(V)
| nil = V
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f129,axiom,
! [U,V] :
( V = U
| ~ ssList(V)
| ~ ssList(U)
| ~ frontsegP(V,U)
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f140,axiom,
! [U,V,W] :
( memberP(app(U,W),V)
| ~ ssItem(V)
| ~ ssList(U)
| ~ ssList(W)
| ~ memberP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f141,axiom,
! [U,V,W] :
( memberP(app(W,U),V)
| ~ ssItem(V)
| ~ ssList(W)
| ~ ssList(U)
| ~ memberP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f144,axiom,
! [U,V,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != W ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f149,axiom,
! [U,V,W] :
( app(app(W,V),U) = app(W,app(V,U))
| ~ ssList(W)
| ~ ssList(V)
| ~ ssList(U) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f150,axiom,
! [U,V,W] :
( V = W
| ~ ssList(W)
| ~ ssList(U)
| ~ ssList(V)
| app(U,V) != app(U,W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f161,axiom,
! [U,V,W] :
( W = U
| memberP(V,W)
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f170,axiom,
! [U,V,W,X] :
( U = W
| ~ ssList(V)
| ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| cons(U,V) != cons(W,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f171,axiom,
! [U,V,W,X] :
( X = V
| ~ ssList(V)
| ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| cons(U,V) != cons(W,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f178,axiom,
! [U,V,W,X] :
( frontsegP(cons(W,U),cons(X,V))
| ~ ssItem(W)
| ~ ssItem(X)
| ~ ssList(U)
| ~ ssList(V)
| W != X
| ~ frontsegP(U,V) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f188,negated_conjecture,
ssList(sk3),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f191,negated_conjecture,
sk1 = sk3,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f192,negated_conjecture,
ssItem(sk5),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f193,negated_conjecture,
ssList(sk6),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f194,negated_conjecture,
ssList(sk7),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f195,negated_conjecture,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f196,negated_conjecture,
( memberP(sk7,sk5)
| memberP(sk6,sk5) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f198,negated_conjecture,
( nil = sk3
| ssItem(sk8) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f201,negated_conjecture,
( nil = sk3
| cons(sk8,nil) = sk3 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f210,plain,
ssList(nil),
inference(cnf_transformation,[status(thm)],[f8]) ).
fof(f214,plain,
! [X0] : ssItem(skaf83(X0)),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f215,plain,
! [X0] : ssList(skaf82(X0)),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f262,plain,
! [X0] :
( frontsegP(X0,nil)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
fof(f273,plain,
! [X0] :
( ~ ssItem(X0)
| ~ memberP(nil,X0) ),
inference(cnf_transformation,[status(thm)],[f71]) ).
fof(f277,plain,
! [X0] :
( app(nil,X0) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
fof(f278,plain,
! [X0] :
( nil = X0
| ssList(tl(X0))
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
fof(f288,plain,
! [X0,X1] :
( ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f85]) ).
fof(f289,plain,
! [X0,X1] :
( ssList(cons(X0,X1))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f299,plain,
! [X0,X1] :
( tl(cons(X0,X1)) = X1
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f300,plain,
! [X0,X1] :
( hd(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f97]) ).
fof(f301,plain,
! [V] :
( ~ ssList(V)
| ! [U] :
( ~ ssItem(U)
| cons(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f98]) ).
fof(f302,plain,
! [X0,X1] :
( ~ ssList(X1)
| ~ ssItem(X0)
| cons(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f301]) ).
fof(f309,plain,
! [X0] :
( nil = X0
| cons(hd(X0),tl(X0)) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f104]) ).
fof(f314,plain,
! [X0] :
( nil = X0
| cons(skaf83(X0),skaf82(X0)) = X0
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f109]) ).
fof(f329,plain,
! [U] :
( nil = U
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f118]) ).
fof(f330,plain,
! [X0,X1] :
( nil = X0
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f329]) ).
fof(f331,plain,
! [V] :
( nil = V
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != nil ) ),
inference(miniscoping,[status(thm)],[f119]) ).
fof(f332,plain,
! [X0,X1] :
( nil = X1
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != nil ),
inference(cnf_transformation,[status(thm)],[f331]) ).
fof(f333,plain,
! [X0,X1] :
( app(cons(X0,nil),X1) = cons(X0,X1)
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(cnf_transformation,[status(thm)],[f120]) ).
fof(f336,plain,
! [X0,X1] :
( hd(app(X1,X0)) = hd(X1)
| nil = X1
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f123]) ).
fof(f344,plain,
! [X0,X1] :
( X1 = X0
| ~ ssList(X1)
| ~ ssList(X0)
| ~ frontsegP(X1,X0)
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f129]) ).
fof(f357,plain,
! [X0,X1,X2] :
( memberP(app(X0,X2),X1)
| ~ ssItem(X1)
| ~ ssList(X0)
| ~ ssList(X2)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f358,plain,
! [X0,X1,X2] :
( memberP(app(X2,X0),X1)
| ~ ssItem(X1)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ memberP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f141]) ).
fof(f362,plain,
! [U,W] :
( frontsegP(W,U)
| ~ ssList(W)
| ~ ssList(U)
| ! [V] :
( ~ ssList(V)
| app(U,V) != W ) ),
inference(miniscoping,[status(thm)],[f144]) ).
fof(f363,plain,
! [X0,X1,X2] :
( frontsegP(X2,X0)
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != X2 ),
inference(cnf_transformation,[status(thm)],[f362]) ).
fof(f371,plain,
! [X0,X1,X2] :
( app(app(X2,X1),X0) = app(X2,app(X1,X0))
| ~ ssList(X2)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(cnf_transformation,[status(thm)],[f149]) ).
fof(f372,plain,
! [V,W] :
( V = W
| ~ ssList(W)
| ! [U] :
( ~ ssList(U)
| ~ ssList(V)
| app(U,V) != app(U,W) ) ),
inference(miniscoping,[status(thm)],[f150]) ).
fof(f373,plain,
! [X0,X1,X2] :
( X1 = X2
| ~ ssList(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| app(X0,X1) != app(X0,X2) ),
inference(cnf_transformation,[status(thm)],[f372]) ).
fof(f393,plain,
! [U,W] :
( W = U
| ! [V] :
( memberP(V,W)
| ~ ssItem(W)
| ~ ssItem(U)
| ~ ssList(V)
| ~ memberP(cons(U,V),W) ) ),
inference(miniscoping,[status(thm)],[f161]) ).
fof(f394,plain,
! [X0,X1,X2] :
( X2 = X0
| memberP(X1,X2)
| ~ ssItem(X2)
| ~ ssItem(X0)
| ~ ssList(X1)
| ~ memberP(cons(X0,X1),X2) ),
inference(cnf_transformation,[status(thm)],[f393]) ).
fof(f403,plain,
! [U,W] :
( U = W
| ! [V] :
( ~ ssList(V)
| ! [X] :
( ~ ssList(X)
| ~ ssItem(U)
| ~ ssItem(W)
| cons(U,V) != cons(W,X) ) ) ),
inference(miniscoping,[status(thm)],[f170]) ).
fof(f404,plain,
! [X0,X1,X2,X3] :
( X0 = X2
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| cons(X0,X1) != cons(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f403]) ).
fof(f405,plain,
! [V,X] :
( X = V
| ~ ssList(V)
| ~ ssList(X)
| ! [U] :
( ~ ssItem(U)
| ! [W] :
( ~ ssItem(W)
| cons(U,V) != cons(W,X) ) ) ),
inference(miniscoping,[status(thm)],[f171]) ).
fof(f406,plain,
! [X0,X1,X2,X3] :
( X3 = X1
| ~ ssList(X1)
| ~ ssList(X3)
| ~ ssItem(X0)
| ~ ssItem(X2)
| cons(X0,X1) != cons(X2,X3) ),
inference(cnf_transformation,[status(thm)],[f405]) ).
fof(f418,plain,
! [X0,X1,X2,X3] :
( frontsegP(cons(X2,X0),cons(X3,X1))
| ~ ssItem(X2)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X1)
| X2 != X3
| ~ frontsegP(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f435,plain,
ssList(sk3),
inference(cnf_transformation,[status(thm)],[f188]) ).
fof(f438,plain,
sk1 = sk3,
inference(cnf_transformation,[status(thm)],[f191]) ).
fof(f439,plain,
ssItem(sk5),
inference(cnf_transformation,[status(thm)],[f192]) ).
fof(f440,plain,
ssList(sk6),
inference(cnf_transformation,[status(thm)],[f193]) ).
fof(f441,plain,
ssList(sk7),
inference(cnf_transformation,[status(thm)],[f194]) ).
fof(f442,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk1,
inference(cnf_transformation,[status(thm)],[f195]) ).
fof(f443,plain,
( memberP(sk7,sk5)
| memberP(sk6,sk5) ),
inference(cnf_transformation,[status(thm)],[f196]) ).
fof(f445,plain,
( nil = sk3
| ssItem(sk8) ),
inference(cnf_transformation,[status(thm)],[f198]) ).
fof(f448,plain,
( nil = sk3
| cons(sk8,nil) = sk3 ),
inference(cnf_transformation,[status(thm)],[f201]) ).
fof(f465,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(app(X1,X0))
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(destructive_equality_resolution,[status(thm)],[f363]) ).
fof(f470,plain,
! [X0,X1,X3] :
( frontsegP(cons(X3,X0),cons(X3,X1))
| ~ ssItem(X3)
| ~ ssItem(X3)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(destructive_equality_resolution,[status(thm)],[f418]) ).
fof(f471,plain,
! [X0,X1,X2] :
( frontsegP(cons(X2,X0),cons(X2,X1))
| ~ ssItem(X2)
| ~ ssList(X0)
| ~ ssList(X1)
| ~ frontsegP(X0,X1) ),
inference(duplicate_literals_removal,[status(thm)],[f470]) ).
fof(f481,plain,
app(app(sk6,cons(sk5,nil)),sk7) = sk3,
inference(forward_demodulation,[status(thm)],[f438,f442]) ).
fof(f485,plain,
( nil = app(sk6,cons(sk5,nil))
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| sk3 != nil ),
inference(paramodulation,[status(thm)],[f481,f330]) ).
fof(f486,plain,
( nil = app(sk6,cons(sk5,nil))
| ~ ssList(app(sk6,cons(sk5,nil)))
| sk3 != nil ),
inference(forward_subsumption_resolution,[status(thm)],[f485,f441]) ).
fof(f501,plain,
( ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| nil = app(sk6,cons(sk5,nil))
| sk3 != nil ),
inference(resolution,[status(thm)],[f486,f288]) ).
fof(f502,plain,
( ~ ssList(cons(sk5,nil))
| nil = app(sk6,cons(sk5,nil))
| sk3 != nil ),
inference(forward_subsumption_resolution,[status(thm)],[f501,f440]) ).
fof(f510,plain,
! [X0] :
( nil = sk3
| app(sk3,X0) = cons(sk8,X0)
| ~ ssList(X0)
| ~ ssItem(sk8) ),
inference(paramodulation,[status(thm)],[f448,f333]) ).
fof(f512,plain,
! [X0] :
( nil = sk3
| app(sk3,X0) = cons(sk8,X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f510,f445]) ).
fof(f518,plain,
( nil = cons(sk5,nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(cons(sk5,nil))
| sk3 != nil ),
inference(resolution,[status(thm)],[f502,f332]) ).
fof(f520,plain,
( nil = cons(sk5,nil)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| sk3 != nil ),
inference(duplicate_literals_removal,[status(thm)],[f518]) ).
fof(f521,plain,
( nil = cons(sk5,nil)
| ~ ssList(cons(sk5,nil))
| sk3 != nil ),
inference(forward_subsumption_resolution,[status(thm)],[f520,f440]) ).
fof(f548,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| ~ memberP(app(sk6,cons(sk5,nil)),X0) ),
inference(paramodulation,[status(thm)],[f481,f357]) ).
fof(f549,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ memberP(app(sk6,cons(sk5,nil)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f548,f441]) ).
fof(f550,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ ssList(sk7)
| ~ memberP(sk7,X0) ),
inference(paramodulation,[status(thm)],[f481,f358]) ).
fof(f551,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(app(sk6,cons(sk5,nil)))
| ~ memberP(sk7,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f550,f441]) ).
fof(f552,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| nil = cons(sk5,nil)
| sk3 != nil ),
inference(resolution,[status(thm)],[f521,f289]) ).
fof(f553,plain,
( ~ ssList(nil)
| ~ ssItem(sk5)
| sk3 != nil ),
inference(forward_subsumption_resolution,[status(thm)],[f552,f302]) ).
fof(f554,plain,
( ~ ssList(nil)
| sk3 != nil ),
inference(forward_subsumption_resolution,[status(thm)],[f553,f439]) ).
fof(f555,plain,
sk3 != nil,
inference(resolution,[status(thm)],[f554,f210]) ).
fof(f556,plain,
! [X0] :
( app(sk3,X0) = cons(sk8,X0)
| ~ ssList(X0) ),
inference(backward_subsumption_resolution,[status(thm)],[f512,f555]) ).
fof(f558,plain,
cons(sk8,nil) = sk3,
inference(backward_subsumption_resolution,[status(thm)],[f448,f555]) ).
fof(f560,plain,
ssItem(sk8),
inference(backward_subsumption_resolution,[status(thm)],[f445,f555]) ).
fof(f569,plain,
( sk3 = app(sk6,app(cons(sk5,nil),sk7))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f481,f371]) ).
fof(f571,plain,
( sk3 = app(sk6,app(cons(sk5,nil),sk7))
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f569,f441]) ).
fof(f576,plain,
! [X0] :
( ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ),
inference(resolution,[status(thm)],[f551,f288]) ).
fof(f577,plain,
! [X0] :
( ~ ssList(cons(sk5,nil))
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f576,f440]) ).
fof(f578,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssItem(sk5)
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ),
inference(resolution,[status(thm)],[f577,f289]) ).
fof(f579,plain,
! [X0] :
( ~ ssList(nil)
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f578,f439]) ).
fof(f582,plain,
! [X0] :
( memberP(sk3,X0)
| ~ ssItem(X0)
| ~ memberP(sk7,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f579,f210]) ).
fof(f583,plain,
( memberP(sk6,sk5)
| memberP(sk3,sk5)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f582,f443]) ).
fof(f584,plain,
( memberP(sk6,sk5)
| memberP(sk3,sk5) ),
inference(forward_subsumption_resolution,[status(thm)],[f583,f439]) ).
fof(f587,plain,
! [X0] :
( X0 = sk8
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssItem(sk8)
| ~ ssList(nil)
| ~ memberP(sk3,X0) ),
inference(paramodulation,[status(thm)],[f558,f394]) ).
fof(f588,plain,
! [X0] :
( X0 = sk8
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ ssItem(sk8)
| ~ memberP(sk3,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f587,f210]) ).
fof(f589,plain,
! [X0] :
( X0 = sk8
| memberP(nil,X0)
| ~ ssItem(X0)
| ~ memberP(sk3,X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f588,f560]) ).
fof(f603,plain,
! [X0,X1] :
( X1 = nil
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssItem(sk8)
| ~ ssItem(X0)
| sk3 != cons(X0,X1) ),
inference(paramodulation,[status(thm)],[f558,f406]) ).
fof(f606,plain,
! [X0,X1] :
( X1 = nil
| ~ ssList(nil)
| ~ ssList(X1)
| ~ ssItem(X0)
| sk3 != cons(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f603,f560]) ).
fof(f618,plain,
! [X0,X1] :
( X1 = nil
| ~ ssList(X1)
| ~ ssItem(X0)
| sk3 != cons(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f606,f210]) ).
fof(f637,plain,
( sk3 = app(sk6,app(cons(sk5,nil),sk7))
| ~ ssList(cons(sk5,nil)) ),
inference(forward_subsumption_resolution,[status(thm)],[f571,f440]) ).
fof(f663,plain,
! [X0] :
( ~ ssItem(X0)
| ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ memberP(sk6,X0)
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(app(sk6,cons(sk5,nil))) ),
inference(resolution,[status(thm)],[f549,f357]) ).
fof(f668,plain,
! [X0] :
( ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ memberP(sk6,X0)
| memberP(sk3,X0)
| ~ ssItem(X0)
| ~ ssList(app(sk6,cons(sk5,nil))) ),
inference(duplicate_literals_removal,[status(thm)],[f663]) ).
fof(f669,plain,
! [X0] :
( ~ ssList(sk6)
| ~ ssList(cons(sk5,nil))
| ~ memberP(sk6,X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f668,f288]) ).
fof(f671,plain,
! [X0] :
( ~ ssList(cons(sk5,nil))
| ~ memberP(sk6,X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f669,f440]) ).
fof(f672,plain,
! [X0] :
( ~ ssList(nil)
| ~ ssItem(sk5)
| ~ memberP(sk6,X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f671,f289]) ).
fof(f673,plain,
! [X0] :
( ~ ssList(nil)
| ~ memberP(sk6,X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f672,f439]) ).
fof(f674,plain,
! [X0] :
( ~ memberP(sk6,X0)
| memberP(sk3,X0)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f673,f210]) ).
fof(f675,plain,
( memberP(sk3,sk5)
| memberP(sk3,sk5)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f674,f584]) ).
fof(f676,plain,
( memberP(sk3,sk5)
| ~ ssItem(sk5) ),
inference(duplicate_literals_removal,[status(thm)],[f675]) ).
fof(f677,plain,
memberP(sk3,sk5),
inference(forward_subsumption_resolution,[status(thm)],[f676,f439]) ).
fof(f678,plain,
( sk5 = sk8
| memberP(nil,sk5)
| ~ ssItem(sk5) ),
inference(resolution,[status(thm)],[f677,f589]) ).
fof(f679,plain,
( sk5 = sk8
| memberP(nil,sk5) ),
inference(forward_subsumption_resolution,[status(thm)],[f678,f439]) ).
fof(f680,plain,
( ~ ssItem(sk5)
| sk5 = sk8 ),
inference(resolution,[status(thm)],[f679,f273]) ).
fof(f681,plain,
sk5 = sk8,
inference(forward_subsumption_resolution,[status(thm)],[f680,f439]) ).
fof(f686,plain,
( sk3 = app(sk6,app(cons(sk8,nil),sk7))
| ~ ssList(cons(sk5,nil)) ),
inference(backward_demodulation,[status(thm)],[f681,f637]) ).
fof(f689,plain,
( memberP(sk7,sk8)
| memberP(sk6,sk5) ),
inference(backward_demodulation,[status(thm)],[f681,f443]) ).
fof(f699,plain,
( sk3 = app(sk6,app(cons(sk8,nil),sk7))
| ~ ssList(cons(sk8,nil)) ),
inference(forward_demodulation,[status(thm)],[f681,f686]) ).
fof(f700,plain,
( sk3 = app(sk6,app(cons(sk8,nil),sk7))
| ~ ssList(sk3) ),
inference(forward_demodulation,[status(thm)],[f558,f699]) ).
fof(f701,plain,
( sk3 = app(sk6,app(sk3,sk7))
| ~ ssList(sk3) ),
inference(forward_demodulation,[status(thm)],[f558,f700]) ).
fof(f702,plain,
sk3 = app(sk6,app(sk3,sk7)),
inference(forward_subsumption_resolution,[status(thm)],[f701,f435]) ).
fof(f709,plain,
( memberP(sk7,sk8)
| memberP(sk6,sk8) ),
inference(forward_demodulation,[status(thm)],[f681,f689]) ).
fof(f746,plain,
! [X0] :
( X0 = app(sk3,sk7)
| ~ ssList(app(sk3,sk7))
| ~ ssList(sk6)
| ~ ssList(X0)
| app(sk6,X0) != sk3 ),
inference(paramodulation,[status(thm)],[f702,f373]) ).
fof(f756,plain,
! [X0] :
( X0 = app(sk3,sk7)
| ~ ssList(app(sk3,sk7))
| ~ ssList(X0)
| app(sk6,X0) != sk3 ),
inference(forward_subsumption_resolution,[status(thm)],[f746,f440]) ).
fof(f762,plain,
( hd(sk3) = sk8
| ~ ssList(nil)
| ~ ssItem(sk8) ),
inference(paramodulation,[status(thm)],[f558,f300]) ).
fof(f763,plain,
( hd(sk3) = sk8
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f762,f560]) ).
fof(f764,plain,
hd(sk3) = sk8,
inference(forward_subsumption_resolution,[status(thm)],[f763,f210]) ).
fof(f825,plain,
! [X0] :
( ~ ssList(sk3)
| ~ ssList(sk7)
| X0 = app(sk3,sk7)
| ~ ssList(X0)
| app(sk6,X0) != sk3 ),
inference(resolution,[status(thm)],[f756,f288]) ).
fof(f826,plain,
! [X0] :
( ~ ssList(sk3)
| X0 = app(sk3,sk7)
| ~ ssList(X0)
| app(sk6,X0) != sk3 ),
inference(forward_subsumption_resolution,[status(thm)],[f825,f441]) ).
fof(f827,plain,
! [X0] :
( X0 = app(sk3,sk7)
| ~ ssList(X0)
| app(sk6,X0) != sk3 ),
inference(forward_subsumption_resolution,[status(thm)],[f826,f435]) ).
fof(f841,plain,
! [X0,X1] :
( skaf83(cons(X0,X1)) = X0
| ~ ssList(skaf82(cons(X0,X1)))
| ~ ssList(X1)
| ~ ssItem(skaf83(cons(X0,X1)))
| ~ ssItem(X0)
| nil = cons(X0,X1)
| ~ ssList(cons(X0,X1)) ),
inference(resolution,[status(thm)],[f314,f404]) ).
fof(f843,plain,
( skaf82(sk3) = nil
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| nil = sk3
| ~ ssList(sk3) ),
inference(resolution,[status(thm)],[f314,f618]) ).
fof(f848,plain,
! [X0,X1] :
( skaf83(cons(X0,X1)) = X0
| ~ ssList(skaf82(cons(X0,X1)))
| ~ ssList(X1)
| ~ ssItem(skaf83(cons(X0,X1)))
| ~ ssItem(X0)
| nil = cons(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f841,f289]) ).
fof(f849,plain,
( skaf82(sk3) = nil
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3))
| nil = sk3 ),
inference(forward_subsumption_resolution,[status(thm)],[f843,f435]) ).
fof(f870,plain,
( hd(sk3) = hd(sk6)
| nil = sk6
| ~ ssList(sk6)
| ~ ssList(app(sk3,sk7)) ),
inference(paramodulation,[status(thm)],[f702,f336]) ).
fof(f872,plain,
( sk8 = hd(sk6)
| nil = sk6
| ~ ssList(sk6)
| ~ ssList(app(sk3,sk7)) ),
inference(forward_demodulation,[status(thm)],[f764,f870]) ).
fof(f873,plain,
( sk8 = hd(sk6)
| nil = sk6
| ~ ssList(app(sk3,sk7)) ),
inference(forward_subsumption_resolution,[status(thm)],[f872,f440]) ).
fof(f883,plain,
( ~ ssList(sk3)
| ~ ssList(sk7)
| sk8 = hd(sk6)
| nil = sk6 ),
inference(resolution,[status(thm)],[f873,f288]) ).
fof(f884,plain,
( ~ ssList(sk3)
| sk8 = hd(sk6)
| nil = sk6 ),
inference(forward_subsumption_resolution,[status(thm)],[f883,f441]) ).
fof(f885,plain,
( sk8 = hd(sk6)
| nil = sk6 ),
inference(forward_subsumption_resolution,[status(thm)],[f884,f435]) ).
fof(f886,plain,
( nil = sk6
| nil = sk6
| cons(sk8,tl(sk6)) = sk6
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f885,f309]) ).
fof(f888,plain,
( nil = sk6
| cons(sk8,tl(sk6)) = sk6
| ~ ssList(sk6) ),
inference(duplicate_literals_removal,[status(thm)],[f886]) ).
fof(f889,plain,
( nil = sk6
| cons(sk8,tl(sk6)) = sk6 ),
inference(forward_subsumption_resolution,[status(thm)],[f888,f440]) ).
fof(f996,plain,
( skaf82(sk3) = nil
| ~ ssList(skaf82(sk3))
| ~ ssItem(skaf83(sk3)) ),
inference(forward_subsumption_resolution,[status(thm)],[f849,f555]) ).
fof(f997,plain,
( skaf82(sk3) = nil
| ~ ssList(skaf82(sk3)) ),
inference(resolution,[status(thm)],[f996,f214]) ).
fof(f999,plain,
skaf82(sk3) = nil,
inference(forward_subsumption_resolution,[status(thm)],[f997,f215]) ).
fof(f1080,plain,
! [X0,X1] :
( skaf83(cons(X0,X1)) = X0
| ~ ssList(skaf82(cons(X0,X1)))
| ~ ssList(X1)
| ~ ssItem(skaf83(cons(X0,X1)))
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f848,f302]) ).
fof(f1081,plain,
! [X0,X1] :
( skaf83(cons(X0,X1)) = X0
| ~ ssList(skaf82(cons(X0,X1)))
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(resolution,[status(thm)],[f1080,f214]) ).
fof(f1085,plain,
! [X0,X1] :
( skaf83(cons(X0,X1)) = X0
| ~ ssList(X1)
| ~ ssItem(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f1081,f215]) ).
fof(f1095,plain,
( nil = sk6
| skaf83(sk6) = sk8
| ~ ssList(tl(sk6))
| ~ ssItem(sk8) ),
inference(paramodulation,[status(thm)],[f889,f1085]) ).
fof(f1097,plain,
( nil = sk6
| skaf83(sk6) = sk8
| ~ ssList(tl(sk6)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1095,f560]) ).
fof(f1099,plain,
( nil = sk6
| ~ ssList(sk6)
| nil = sk6
| skaf83(sk6) = sk8 ),
inference(resolution,[status(thm)],[f1097,f278]) ).
fof(f1100,plain,
( ~ ssList(sk6)
| nil = sk6
| skaf83(sk6) = sk8 ),
inference(duplicate_literals_removal,[status(thm)],[f1099]) ).
fof(f1101,plain,
( nil = sk6
| skaf83(sk6) = sk8 ),
inference(forward_subsumption_resolution,[status(thm)],[f1100,f440]) ).
fof(f1102,plain,
( nil = sk6
| nil = sk6
| cons(sk8,skaf82(sk6)) = sk6
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f1101,f314]) ).
fof(f1104,plain,
( nil = sk6
| cons(sk8,skaf82(sk6)) = sk6
| ~ ssList(sk6) ),
inference(duplicate_literals_removal,[status(thm)],[f1102]) ).
fof(f1105,plain,
( nil = sk6
| cons(sk8,skaf82(sk6)) = sk6 ),
inference(forward_subsumption_resolution,[status(thm)],[f1104,f440]) ).
fof(f1114,plain,
( nil = sk6
| tl(sk6) = skaf82(sk6)
| ~ ssList(skaf82(sk6))
| ~ ssItem(sk8) ),
inference(paramodulation,[status(thm)],[f1105,f299]) ).
fof(f1134,plain,
( nil = sk6
| tl(sk6) = skaf82(sk6)
| ~ ssList(skaf82(sk6)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1114,f560]) ).
fof(f1169,plain,
( nil = sk6
| tl(sk6) = skaf82(sk6) ),
inference(forward_subsumption_resolution,[status(thm)],[f1134,f215]) ).
fof(f1172,plain,
( nil = sk6
| nil = sk6
| cons(skaf83(sk6),tl(sk6)) = sk6
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f1169,f314]) ).
fof(f1173,plain,
( nil = sk6
| ssList(tl(sk6)) ),
inference(paramodulation,[status(thm)],[f1169,f215]) ).
fof(f1176,plain,
( nil = sk6
| cons(skaf83(sk6),tl(sk6)) = sk6
| ~ ssList(sk6) ),
inference(duplicate_literals_removal,[status(thm)],[f1172]) ).
fof(f1177,plain,
( nil = sk6
| cons(skaf83(sk6),tl(sk6)) = sk6 ),
inference(forward_subsumption_resolution,[status(thm)],[f1176,f440]) ).
fof(f1187,plain,
( nil = sk6
| hd(sk6) = skaf83(sk6)
| ~ ssList(tl(sk6))
| ~ ssItem(skaf83(sk6)) ),
inference(paramodulation,[status(thm)],[f1177,f300]) ).
fof(f1210,plain,
( nil = sk6
| hd(sk6) = skaf83(sk6)
| ~ ssList(tl(sk6)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1187,f214]) ).
fof(f1233,plain,
( nil = sk6
| hd(sk6) = skaf83(sk6) ),
inference(forward_subsumption_resolution,[status(thm)],[f1210,f1173]) ).
fof(f1237,plain,
( nil = sk6
| nil = sk6
| cons(hd(sk6),skaf82(sk6)) = sk6
| ~ ssList(sk6) ),
inference(paramodulation,[status(thm)],[f1233,f314]) ).
fof(f1238,plain,
( nil = sk6
| ssItem(hd(sk6)) ),
inference(paramodulation,[status(thm)],[f1233,f214]) ).
fof(f1242,plain,
( nil = sk6
| cons(hd(sk6),skaf82(sk6)) = sk6
| ~ ssList(sk6) ),
inference(duplicate_literals_removal,[status(thm)],[f1237]) ).
fof(f1243,plain,
( nil = sk6
| cons(hd(sk6),skaf82(sk6)) = sk6 ),
inference(forward_subsumption_resolution,[status(thm)],[f1242,f440]) ).
fof(f1360,plain,
! [X0,X1] :
( frontsegP(app(X1,X0),X1)
| ~ ssList(X1)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f465,f288]) ).
fof(f1362,plain,
( frontsegP(sk3,sk6)
| ~ ssList(sk6)
| ~ ssList(app(sk3,sk7)) ),
inference(paramodulation,[status(thm)],[f702,f1360]) ).
fof(f1366,plain,
( frontsegP(sk3,sk6)
| ~ ssList(app(sk3,sk7)) ),
inference(forward_subsumption_resolution,[status(thm)],[f1362,f440]) ).
fof(f1368,plain,
( ~ ssList(sk3)
| ~ ssList(sk7)
| frontsegP(sk3,sk6) ),
inference(resolution,[status(thm)],[f1366,f288]) ).
fof(f1369,plain,
( ~ ssList(sk3)
| frontsegP(sk3,sk6) ),
inference(forward_subsumption_resolution,[status(thm)],[f1368,f441]) ).
fof(f1370,plain,
frontsegP(sk3,sk6),
inference(forward_subsumption_resolution,[status(thm)],[f1369,f435]) ).
fof(f1371,plain,
( sk3 = sk6
| ~ ssList(sk3)
| ~ ssList(sk6)
| ~ frontsegP(sk6,sk3) ),
inference(resolution,[status(thm)],[f1370,f344]) ).
fof(f1372,plain,
( sk3 = sk6
| ~ ssList(sk3)
| ~ frontsegP(sk6,sk3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1371,f440]) ).
fof(f1373,plain,
( sk3 = sk6
| ~ frontsegP(sk6,sk3) ),
inference(forward_subsumption_resolution,[status(thm)],[f1372,f435]) ).
fof(f2262,plain,
! [X0] :
( frontsegP(cons(sk8,X0),sk3)
| ~ ssItem(sk8)
| ~ ssList(X0)
| ~ ssList(nil)
| ~ frontsegP(X0,nil) ),
inference(paramodulation,[status(thm)],[f558,f471]) ).
fof(f2276,plain,
! [X0] :
( frontsegP(cons(sk8,X0),sk3)
| ~ ssItem(sk8)
| ~ ssList(X0)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f2262,f262]) ).
fof(f2277,plain,
! [X0] :
( frontsegP(cons(sk8,X0),sk3)
| ~ ssItem(sk8)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2276,f210]) ).
fof(f2280,plain,
( nil = sk6
| frontsegP(sk6,sk3)
| ~ ssItem(sk8)
| ~ ssList(skaf82(sk6)) ),
inference(paramodulation,[status(thm)],[f1105,f2277]) ).
fof(f2285,plain,
( nil = sk6
| frontsegP(sk6,sk3)
| ~ ssItem(sk8) ),
inference(forward_subsumption_resolution,[status(thm)],[f2280,f215]) ).
fof(f2341,plain,
( nil = sk6
| frontsegP(sk6,sk3) ),
inference(forward_subsumption_resolution,[status(thm)],[f2285,f560]) ).
fof(f2342,plain,
( sk3 = sk6
| nil = sk6 ),
inference(resolution,[status(thm)],[f2341,f1373]) ).
fof(f2384,plain,
( nil = sk6
| nil = sk6
| cons(hd(sk6),skaf82(sk3)) = sk6 ),
inference(paramodulation,[status(thm)],[f2342,f1243]) ).
fof(f2428,plain,
( nil = sk6
| nil = sk6
| cons(hd(sk6),nil) = sk6 ),
inference(forward_demodulation,[status(thm)],[f999,f2384]) ).
fof(f2429,plain,
( nil = sk6
| cons(hd(sk6),nil) = sk6 ),
inference(duplicate_literals_removal,[status(thm)],[f2428]) ).
fof(f2590,plain,
! [X0] :
( nil = sk6
| app(sk6,X0) = cons(hd(sk6),X0)
| ~ ssList(X0)
| ~ ssItem(hd(sk6)) ),
inference(paramodulation,[status(thm)],[f2429,f333]) ).
fof(f2639,plain,
! [X0] :
( nil = sk6
| app(sk6,X0) = cons(hd(sk6),X0)
| ~ ssList(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f2590,f1238]) ).
fof(f3011,plain,
( nil = sk6
| nil = sk6
| app(sk6,nil) = sk6
| ~ ssList(nil) ),
inference(paramodulation,[status(thm)],[f2429,f2639]) ).
fof(f3016,plain,
( nil = sk6
| app(sk6,nil) = sk6
| ~ ssList(nil) ),
inference(duplicate_literals_removal,[status(thm)],[f3011]) ).
fof(f3017,plain,
( nil = sk6
| app(sk6,nil) = sk6 ),
inference(forward_subsumption_resolution,[status(thm)],[f3016,f210]) ).
fof(f3111,plain,
( nil = sk6
| nil = app(sk3,sk7)
| ~ ssList(nil)
| sk6 != sk3 ),
inference(paramodulation,[status(thm)],[f3017,f827]) ).
fof(f3145,plain,
( nil = sk6
| nil = app(sk3,sk7)
| ~ ssList(nil) ),
inference(forward_subsumption_resolution,[status(thm)],[f3111,f2342]) ).
fof(f3556,plain,
( nil = sk6
| nil = app(sk3,sk7) ),
inference(forward_subsumption_resolution,[status(thm)],[f3145,f210]) ).
fof(f3558,plain,
( nil = sk3
| ~ ssList(sk3)
| ~ ssList(sk7)
| nil = sk6 ),
inference(resolution,[status(thm)],[f3556,f330]) ).
fof(f3570,plain,
( nil = sk6
| nil = cons(sk8,sk7)
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f3556,f556]) ).
fof(f3604,plain,
( nil = sk3
| ~ ssList(sk3)
| nil = sk6 ),
inference(forward_subsumption_resolution,[status(thm)],[f3558,f441]) ).
fof(f3610,plain,
( nil = sk6
| nil = cons(sk8,sk7) ),
inference(forward_subsumption_resolution,[status(thm)],[f3570,f441]) ).
fof(f3677,plain,
( nil = sk3
| nil = sk6 ),
inference(forward_subsumption_resolution,[status(thm)],[f3604,f435]) ).
fof(f3749,plain,
( nil = sk3
| sk3 = app(nil,app(sk3,sk7)) ),
inference(paramodulation,[status(thm)],[f3677,f702]) ).
fof(f3768,plain,
sk3 = app(nil,app(sk3,sk7)),
inference(forward_subsumption_resolution,[status(thm)],[f3749,f555]) ).
fof(f3884,plain,
( ~ ssList(sk7)
| ~ ssItem(sk8)
| nil = sk6 ),
inference(resolution,[status(thm)],[f3610,f302]) ).
fof(f3936,plain,
( ~ ssList(sk7)
| nil = sk6 ),
inference(forward_subsumption_resolution,[status(thm)],[f3884,f560]) ).
fof(f4053,plain,
( memberP(sk7,sk8)
| memberP(nil,sk8) ),
inference(backward_demodulation,[status(thm)],[f4057,f709]) ).
fof(f4057,plain,
nil = sk6,
inference(forward_subsumption_resolution,[status(thm)],[f3936,f441]) ).
fof(f4160,plain,
( sk3 = app(sk3,sk7)
| ~ ssList(app(sk3,sk7)) ),
inference(paramodulation,[status(thm)],[f3768,f277]) ).
fof(f4265,plain,
( ~ ssList(sk3)
| ~ ssList(sk7)
| sk3 = app(sk3,sk7) ),
inference(resolution,[status(thm)],[f4160,f288]) ).
fof(f4266,plain,
( ~ ssList(sk3)
| sk3 = app(sk3,sk7) ),
inference(forward_subsumption_resolution,[status(thm)],[f4265,f441]) ).
fof(f4271,plain,
sk3 = app(sk3,sk7),
inference(forward_subsumption_resolution,[status(thm)],[f4266,f435]) ).
fof(f4273,plain,
( sk3 = cons(sk8,sk7)
| ~ ssList(sk7) ),
inference(paramodulation,[status(thm)],[f4271,f556]) ).
fof(f4306,plain,
sk3 = cons(sk8,sk7),
inference(forward_subsumption_resolution,[status(thm)],[f4273,f441]) ).
fof(f4378,plain,
( sk7 = nil
| ~ ssList(sk7)
| ~ ssItem(sk8) ),
inference(resolution,[status(thm)],[f4306,f618]) ).
fof(f4439,plain,
( sk7 = nil
| ~ ssList(sk7) ),
inference(forward_subsumption_resolution,[status(thm)],[f4378,f560]) ).
fof(f4614,plain,
( memberP(nil,sk8)
| memberP(nil,sk8) ),
inference(backward_demodulation,[status(thm)],[f4627,f4053]) ).
fof(f4627,plain,
sk7 = nil,
inference(forward_subsumption_resolution,[status(thm)],[f4439,f441]) ).
fof(f4628,plain,
memberP(nil,sk8),
inference(duplicate_literals_removal,[status(thm)],[f4614]) ).
fof(f4634,plain,
~ ssItem(sk8),
inference(resolution,[status(thm)],[f4628,f273]) ).
fof(f4635,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f4634,f560]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWC187-1 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n009.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 08:02:57 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 10.33/1.79 % Refutation found
% 10.33/1.79 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 10.33/1.79 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.72/1.83 % Elapsed time: 1.465927 seconds
% 0.72/1.83 % CPU time: 11.149279 seconds
% 0.72/1.83 % Total memory used: 201.452 MB
% 0.72/1.83 % Net memory used: 194.313 MB
%------------------------------------------------------------------------------