%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWX187+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 5 07:04:30 PM UTC 2026
% Result : Theorem 7.03s 7.20s
% Output : CNFRefutation 7.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 53
% Syntax : Number of formulae : 220 ( 113 unt; 0 def)
% Number of atoms : 424 ( 352 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 394 ( 190 ~; 185 |; 1 &)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 2 con; 0-2 aty)
% Number of variables : 611 ( 28 sgn 66 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_001,axiom,
! [X,X2] : head(cons(X,X2)) = X ).
fof(axiom_003,axiom,
! [X,X2] : nil != cons(X,X2) ).
fof(axiom_005,axiom,
! [X] : s(X) != z ).
fof(axiom_007,axiom,
! [Y,Xs] : length(cons(Y,Xs)) = s(length(Xs)) ).
fof(axiom_008,axiom,
! [Z,Y2] :
( x2(s(Z),s(Y2))
<=> x2(Z,Y2) ) ).
fof(axiom_010,axiom,
! [X2] : x2(z,s(X2)) ).
fof(axiom_012,axiom,
! [Y] : x(nil,Y) = Y ).
fof(axiom_013,axiom,
! [Y,Z,Xs] : x(cons(Z,Xs),Y) = cons(Z,x(Xs,Y)) ).
fof(axiom_015,axiom,
! [Z,X2,X3] : rotate(s(Z),cons(X2,X3)) = rotate(Z,x(X3,cons(X2,nil))) ).
fof(axiom_016,axiom,
! [Y] : rotate(z,Y) = Y ).
fof(goal_017,conjecture,
? [N,M,Ys,Xs] :
~ ( x2(N,length(Xs))
=> ( x2(M,length(Ys))
=> ( Xs = Ys
=> ( rotate(s(z),Xs) != Xs
=> ( rotate(N,Xs) = rotate(M,Ys)
=> N = M ) ) ) ) ) ).
fof(subgoal_0,plain,
? [N,M,Ys,Xs] :
~ ( x2(N,length(Xs))
=> ( x2(M,length(Ys))
=> ( Xs = Ys
=> ( rotate(s(z),Xs) != Xs
=> ( rotate(N,Xs) = rotate(M,Ys)
=> N = M ) ) ) ) ),
inference(strip,[],[goal_017]) ).
fof(negate_0_0,plain,
~ ? [N,M,Ys,Xs] :
~ ( x2(N,length(Xs))
=> ( x2(M,length(Ys))
=> ( Xs = Ys
=> ( rotate(s(z),Xs) != Xs
=> ( rotate(N,Xs) = rotate(M,Ys)
=> N = M ) ) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,X2] : nil != cons(X,X2),
inference(canonicalize,[],[axiom_003]) ).
fof(normalize_0_1,plain,
! [X,X2] : nil != cons(X,X2),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,X2] : head(cons(X,X2)) = X,
inference(canonicalize,[],[axiom_001]) ).
fof(normalize_0_3,plain,
! [X,X2] : head(cons(X,X2)) = X,
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X2] : x2(z,s(X2)),
inference(canonicalize,[],[axiom_010]) ).
fof(normalize_0_5,plain,
! [X2] : x2(z,s(X2)),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [M,N,Xs,Ys] :
( Xs != Ys
| rotate(N,Xs) != rotate(M,Ys)
| ~ x2(M,length(Ys))
| ~ x2(N,length(Xs))
| N = M
| rotate(s(z),Xs) = Xs ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
! [M,N,Xs,Ys] :
( Xs != Ys
| rotate(N,Xs) != rotate(M,Ys)
| ~ x2(M,length(Ys))
| ~ x2(N,length(Xs))
| N = M
| rotate(s(z),Xs) = Xs ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [Xs,Y] : length(cons(Y,Xs)) = s(length(Xs)),
inference(canonicalize,[],[axiom_007]) ).
fof(normalize_0_9,plain,
! [Xs,Y] : length(cons(Y,Xs)) = s(length(Xs)),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [Y] : rotate(z,Y) = Y,
inference(canonicalize,[],[axiom_016]) ).
fof(normalize_0_11,plain,
! [Y] : rotate(z,Y) = Y,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X2,X3,Z] : rotate(s(Z),cons(X2,X3)) = rotate(Z,x(X3,cons(X2,nil))),
inference(canonicalize,[],[axiom_015]) ).
fof(normalize_0_13,plain,
! [X2,X3,Z] : rotate(s(Z),cons(X2,X3)) = rotate(Z,x(X3,cons(X2,nil))),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [Xs,Y,Z] : x(cons(Z,Xs),Y) = cons(Z,x(Xs,Y)),
inference(canonicalize,[],[axiom_013]) ).
fof(normalize_0_15,plain,
! [Xs,Y,Z] : x(cons(Z,Xs),Y) = cons(Z,x(Xs,Y)),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [Y2,Z] :
( ~ x2(Z,Y2)
<=> ~ x2(s(Z),s(Y2)) ),
inference(canonicalize,[],[axiom_008]) ).
fof(normalize_0_17,plain,
! [Y2,Z] :
( ~ x2(Z,Y2)
<=> ~ x2(s(Z),s(Y2)) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [Y2,Z] :
( ( ~ x2(Z,Y2)
| x2(s(Z),s(Y2)) )
& ( ~ x2(s(Z),s(Y2))
| x2(Z,Y2) ) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [Y2,Z] :
( ~ x2(Z,Y2)
| x2(s(Z),s(Y2)) ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X] : s(X) != z,
inference(canonicalize,[],[axiom_005]) ).
fof(normalize_0_21,plain,
! [X] : s(X) != z,
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [Y] : x(nil,Y) = Y,
inference(canonicalize,[],[axiom_012]) ).
fof(normalize_0_23,plain,
! [Y] : x(nil,Y) = Y,
inference(specialize,[],[normalize_0_22]) ).
cnf(refute_0_0,plain,
nil != cons(X,X2),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
head(cons(X,X2)) = X,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
head(cons(X,cons(X_674,cons(X,cons(X_674,nil))))) = X,
inference(subst,[],[refute_0_1:[bind(X2,$fot(cons(X_674,cons(X,cons(X_674,nil)))))]]) ).
cnf(refute_0_3,plain,
x2(z,s(X2)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
x2(z,s(length(X_455))),
inference(subst,[],[refute_0_3:[bind(X2,$fot(length(X_455)))]]) ).
cnf(refute_0_5,plain,
( Xs != Ys
| rotate(N,Xs) != rotate(M,Ys)
| ~ x2(M,length(Ys))
| ~ x2(N,length(Xs))
| N = M
| rotate(s(z),Xs) = Xs ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
( Ys != Ys
| rotate(N,Ys) != rotate(M,Ys)
| ~ x2(M,length(Ys))
| ~ x2(N,length(Ys))
| N = M
| rotate(s(z),Ys) = Ys ),
inference(subst,[],[refute_0_5:[bind(Xs,$fot(Ys))]]) ).
cnf(refute_0_7,plain,
Ys = Ys,
introduced(tautology,[refl,[$fot(Ys)]]) ).
cnf(refute_0_8,plain,
( rotate(N,Ys) != rotate(M,Ys)
| ~ x2(M,length(Ys))
| ~ x2(N,length(Ys))
| N = M
| rotate(s(z),Ys) = Ys ),
inference(resolve,[$cnf( $equal(Ys,Ys) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
( rotate(X_269,cons(Y,Xs)) != rotate(X_268,cons(Y,Xs))
| ~ x2(X_268,length(cons(Y,Xs)))
| ~ x2(X_269,length(cons(Y,Xs)))
| X_269 = X_268
| rotate(s(z),cons(Y,Xs)) = cons(Y,Xs) ),
inference(subst,[],[refute_0_8:[bind(M,$fot(X_268)),bind(N,$fot(X_269)),bind(Ys,$fot(cons(Y,Xs)))]]) ).
cnf(refute_0_10,plain,
length(cons(Y,Xs)) = s(length(Xs)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_11,plain,
( length(cons(Y,Xs)) != s(length(Xs))
| ~ x2(X_269,s(length(Xs)))
| x2(X_269,length(cons(Y,Xs))) ),
introduced(tautology,[equality,[$cnf( ~ x2(X_269,length(cons(Y,Xs))) ),[1],$fot(s(length(Xs)))]]) ).
cnf(refute_0_12,plain,
( ~ x2(X_269,s(length(Xs)))
| x2(X_269,length(cons(Y,Xs))) ),
inference(resolve,[$cnf( $equal(length(cons(Y,Xs)),s(length(Xs))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( rotate(X_269,cons(Y,Xs)) != rotate(X_268,cons(Y,Xs))
| ~ x2(X_268,length(cons(Y,Xs)))
| ~ x2(X_269,s(length(Xs)))
| X_269 = X_268
| rotate(s(z),cons(Y,Xs)) = cons(Y,Xs) ),
inference(resolve,[$cnf( x2(X_269,length(cons(Y,Xs))) )],[refute_0_12,refute_0_9]) ).
cnf(refute_0_14,plain,
( length(cons(Y,Xs)) != s(length(Xs))
| ~ x2(X_268,s(length(Xs)))
| x2(X_268,length(cons(Y,Xs))) ),
introduced(tautology,[equality,[$cnf( ~ x2(X_268,length(cons(Y,Xs))) ),[1],$fot(s(length(Xs)))]]) ).
cnf(refute_0_15,plain,
( ~ x2(X_268,s(length(Xs)))
| x2(X_268,length(cons(Y,Xs))) ),
inference(resolve,[$cnf( $equal(length(cons(Y,Xs)),s(length(Xs))) )],[refute_0_10,refute_0_14]) ).
cnf(refute_0_16,plain,
( rotate(X_269,cons(Y,Xs)) != rotate(X_268,cons(Y,Xs))
| ~ x2(X_268,s(length(Xs)))
| ~ x2(X_269,s(length(Xs)))
| X_269 = X_268
| rotate(s(z),cons(Y,Xs)) = cons(Y,Xs) ),
inference(resolve,[$cnf( x2(X_268,length(cons(Y,Xs))) )],[refute_0_15,refute_0_13]) ).
cnf(refute_0_17,plain,
rotate(z,Y) = Y,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_18,plain,
rotate(z,x(X_33,cons(X_32,nil))) = x(X_33,cons(X_32,nil)),
inference(subst,[],[refute_0_17:[bind(Y,$fot(x(X_33,cons(X_32,nil))))]]) ).
cnf(refute_0_19,plain,
rotate(s(Z),cons(X2,X3)) = rotate(Z,x(X3,cons(X2,nil))),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_20,plain,
rotate(s(z),cons(X_32,X_33)) = rotate(z,x(X_33,cons(X_32,nil))),
inference(subst,[],[refute_0_19:[bind(X2,$fot(X_32)),bind(X3,$fot(X_33)),bind(Z,$fot(z))]]) ).
cnf(refute_0_21,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_22,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_23,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( rotate(s(z),cons(X_32,X_33)) != rotate(z,x(X_33,cons(X_32,nil)))
| rotate(z,x(X_33,cons(X_32,nil))) = rotate(s(z),cons(X_32,X_33)) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(rotate(s(z),cons(X_32,X_33)))),bind(Y0,$fot(rotate(z,x(X_33,cons(X_32,nil)))))]]) ).
cnf(refute_0_25,plain,
rotate(z,x(X_33,cons(X_32,nil))) = rotate(s(z),cons(X_32,X_33)),
inference(resolve,[$cnf( $equal(rotate(s(z),cons(X_32,X_33)),rotate(z,x(X_33,cons(X_32,nil)))) )],[refute_0_20,refute_0_24]) ).
cnf(refute_0_26,plain,
( rotate(z,x(X_33,cons(X_32,nil))) != rotate(s(z),cons(X_32,X_33))
| rotate(z,x(X_33,cons(X_32,nil))) != x(X_33,cons(X_32,nil))
| rotate(s(z),cons(X_32,X_33)) = x(X_33,cons(X_32,nil)) ),
introduced(tautology,[equality,[$cnf( $equal(rotate(z,x(X_33,cons(X_32,nil))),x(X_33,cons(X_32,nil))) ),[0],$fot(rotate(s(z),cons(X_32,X_33)))]]) ).
cnf(refute_0_27,plain,
( rotate(z,x(X_33,cons(X_32,nil))) != x(X_33,cons(X_32,nil))
| rotate(s(z),cons(X_32,X_33)) = x(X_33,cons(X_32,nil)) ),
inference(resolve,[$cnf( $equal(rotate(z,x(X_33,cons(X_32,nil))),rotate(s(z),cons(X_32,X_33))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
rotate(s(z),cons(X_32,X_33)) = x(X_33,cons(X_32,nil)),
inference(resolve,[$cnf( $equal(rotate(z,x(X_33,cons(X_32,nil))),x(X_33,cons(X_32,nil))) )],[refute_0_18,refute_0_27]) ).
cnf(refute_0_29,plain,
rotate(s(z),cons(Y,Xs)) = x(Xs,cons(Y,nil)),
inference(subst,[],[refute_0_28:[bind(X_32,$fot(Y)),bind(X_33,$fot(Xs))]]) ).
cnf(refute_0_30,plain,
( rotate(s(z),cons(Y,Xs)) != cons(Y,Xs)
| rotate(s(z),cons(Y,Xs)) != x(Xs,cons(Y,nil))
| x(Xs,cons(Y,nil)) = cons(Y,Xs) ),
introduced(tautology,[equality,[$cnf( $equal(rotate(s(z),cons(Y,Xs)),cons(Y,Xs)) ),[0],$fot(x(Xs,cons(Y,nil)))]]) ).
cnf(refute_0_31,plain,
( rotate(s(z),cons(Y,Xs)) != cons(Y,Xs)
| x(Xs,cons(Y,nil)) = cons(Y,Xs) ),
inference(resolve,[$cnf( $equal(rotate(s(z),cons(Y,Xs)),x(Xs,cons(Y,nil))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( rotate(X_269,cons(Y,Xs)) != rotate(X_268,cons(Y,Xs))
| ~ x2(X_268,s(length(Xs)))
| ~ x2(X_269,s(length(Xs)))
| X_269 = X_268
| x(Xs,cons(Y,nil)) = cons(Y,Xs) ),
inference(resolve,[$cnf( $equal(rotate(s(z),cons(Y,Xs)),cons(Y,Xs)) )],[refute_0_16,refute_0_31]) ).
cnf(refute_0_33,plain,
( rotate(X_458,cons(X_456,X_455)) != rotate(z,cons(X_456,X_455))
| ~ x2(X_458,s(length(X_455)))
| ~ x2(z,s(length(X_455)))
| X_458 = z
| x(X_455,cons(X_456,nil)) = cons(X_456,X_455) ),
inference(subst,[],[refute_0_32:[bind(Xs,$fot(X_455)),bind(Y,$fot(X_456)),bind(X_268,$fot(z)),bind(X_269,$fot(X_458))]]) ).
cnf(refute_0_34,plain,
( rotate(X_458,cons(X_456,X_455)) != rotate(z,cons(X_456,X_455))
| ~ x2(X_458,s(length(X_455)))
| X_458 = z
| x(X_455,cons(X_456,nil)) = cons(X_456,X_455) ),
inference(resolve,[$cnf( x2(z,s(length(X_455))) )],[refute_0_4,refute_0_33]) ).
cnf(refute_0_35,plain,
rotate(z,cons(X_456,X_455)) = cons(X_456,X_455),
inference(subst,[],[refute_0_17:[bind(Y,$fot(cons(X_456,X_455)))]]) ).
cnf(refute_0_36,plain,
( rotate(X_458,cons(X_456,X_455)) != cons(X_456,X_455)
| rotate(z,cons(X_456,X_455)) != cons(X_456,X_455)
| rotate(X_458,cons(X_456,X_455)) = rotate(z,cons(X_456,X_455)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(rotate(X_458,cons(X_456,X_455)),rotate(z,cons(X_456,X_455))) ),[1],$fot(cons(X_456,X_455))]]) ).
cnf(refute_0_37,plain,
( rotate(X_458,cons(X_456,X_455)) != cons(X_456,X_455)
| rotate(X_458,cons(X_456,X_455)) = rotate(z,cons(X_456,X_455)) ),
inference(resolve,[$cnf( $equal(rotate(z,cons(X_456,X_455)),cons(X_456,X_455)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( rotate(X_458,cons(X_456,X_455)) != cons(X_456,X_455)
| ~ x2(X_458,s(length(X_455)))
| X_458 = z
| x(X_455,cons(X_456,nil)) = cons(X_456,X_455) ),
inference(resolve,[$cnf( $equal(rotate(X_458,cons(X_456,X_455)),rotate(z,cons(X_456,X_455))) )],[refute_0_37,refute_0_34]) ).
cnf(refute_0_39,plain,
( rotate(s(s(z)),cons(X_512,cons(X_47,cons(Z,Xs)))) != cons(X_512,cons(X_47,cons(Z,Xs)))
| ~ x2(s(s(z)),s(length(cons(X_47,cons(Z,Xs)))))
| s(s(z)) = z
| x(cons(X_47,cons(Z,Xs)),cons(X_512,nil)) = cons(X_512,cons(X_47,cons(Z,Xs))) ),
inference(subst,[],[refute_0_38:[bind(X_455,$fot(cons(X_47,cons(Z,Xs)))),bind(X_456,$fot(X_512)),bind(X_458,$fot(s(s(z))))]]) ).
cnf(refute_0_40,plain,
rotate(s(z),cons(X_32,x(X_42,cons(X_44,nil)))) = x(x(X_42,cons(X_44,nil)),cons(X_32,nil)),
inference(subst,[],[refute_0_28:[bind(X_33,$fot(x(X_42,cons(X_44,nil))))]]) ).
cnf(refute_0_41,plain,
rotate(s(X_34),cons(X_32,cons(Z,Xs))) = rotate(X_34,x(cons(Z,Xs),cons(X_32,nil))),
inference(subst,[],[refute_0_19:[bind(X2,$fot(X_32)),bind(X3,$fot(cons(Z,Xs))),bind(Z,$fot(X_34))]]) ).
cnf(refute_0_42,plain,
x(cons(Z,Xs),Y) = cons(Z,x(Xs,Y)),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_43,plain,
x(cons(Z,Xs),cons(X_32,nil)) = cons(Z,x(Xs,cons(X_32,nil))),
inference(subst,[],[refute_0_42:[bind(Y,$fot(cons(X_32,nil)))]]) ).
cnf(refute_0_44,plain,
( rotate(s(X_34),cons(X_32,cons(Z,Xs))) != rotate(X_34,x(cons(Z,Xs),cons(X_32,nil)))
| x(cons(Z,Xs),cons(X_32,nil)) != cons(Z,x(Xs,cons(X_32,nil)))
| rotate(s(X_34),cons(X_32,cons(Z,Xs))) = rotate(X_34,cons(Z,x(Xs,cons(X_32,nil)))) ),
introduced(tautology,[equality,[$cnf( $equal(rotate(s(X_34),cons(X_32,cons(Z,Xs))),rotate(X_34,x(cons(Z,Xs),cons(X_32,nil)))) ),[1,1],$fot(cons(Z,x(Xs,cons(X_32,nil))))]]) ).
cnf(refute_0_45,plain,
( rotate(s(X_34),cons(X_32,cons(Z,Xs))) != rotate(X_34,x(cons(Z,Xs),cons(X_32,nil)))
| rotate(s(X_34),cons(X_32,cons(Z,Xs))) = rotate(X_34,cons(Z,x(Xs,cons(X_32,nil)))) ),
inference(resolve,[$cnf( $equal(x(cons(Z,Xs),cons(X_32,nil)),cons(Z,x(Xs,cons(X_32,nil)))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
rotate(s(X_34),cons(X_32,cons(Z,Xs))) = rotate(X_34,cons(Z,x(Xs,cons(X_32,nil)))),
inference(resolve,[$cnf( $equal(rotate(s(X_34),cons(X_32,cons(Z,Xs))),rotate(X_34,x(cons(Z,Xs),cons(X_32,nil)))) )],[refute_0_41,refute_0_45]) ).
cnf(refute_0_47,plain,
rotate(s(s(z)),cons(X_44,cons(X_32,X_42))) = rotate(s(z),cons(X_32,x(X_42,cons(X_44,nil)))),
inference(subst,[],[refute_0_46:[bind(Xs,$fot(X_42)),bind(Z,$fot(X_32)),bind(X_32,$fot(X_44)),bind(X_34,$fot(s(z)))]]) ).
cnf(refute_0_48,plain,
( rotate(s(s(z)),cons(X_44,cons(X_32,X_42))) != rotate(s(z),cons(X_32,x(X_42,cons(X_44,nil))))
| rotate(s(z),cons(X_32,x(X_42,cons(X_44,nil)))) = rotate(s(s(z)),cons(X_44,cons(X_32,X_42))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(rotate(s(s(z)),cons(X_44,cons(X_32,X_42))))),bind(Y0,$fot(rotate(s(z),cons(X_32,x(X_42,cons(X_44,nil))))))]]) ).
cnf(refute_0_49,plain,
rotate(s(z),cons(X_32,x(X_42,cons(X_44,nil)))) = rotate(s(s(z)),cons(X_44,cons(X_32,X_42))),
inference(resolve,[$cnf( $equal(rotate(s(s(z)),cons(X_44,cons(X_32,X_42))),rotate(s(z),cons(X_32,x(X_42,cons(X_44,nil))))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
( rotate(s(z),cons(X_32,x(X_42,cons(X_44,nil)))) != rotate(s(s(z)),cons(X_44,cons(X_32,X_42)))
| rotate(s(z),cons(X_32,x(X_42,cons(X_44,nil)))) != x(x(X_42,cons(X_44,nil)),cons(X_32,nil))
| rotate(s(s(z)),cons(X_44,cons(X_32,X_42))) = x(x(X_42,cons(X_44,nil)),cons(X_32,nil)) ),
introduced(tautology,[equality,[$cnf( $equal(rotate(s(z),cons(X_32,x(X_42,cons(X_44,nil)))),x(x(X_42,cons(X_44,nil)),cons(X_32,nil))) ),[0],$fot(rotate(s(s(z)),cons(X_44,cons(X_32,X_42))))]]) ).
cnf(refute_0_51,plain,
( rotate(s(z),cons(X_32,x(X_42,cons(X_44,nil)))) != x(x(X_42,cons(X_44,nil)),cons(X_32,nil))
| rotate(s(s(z)),cons(X_44,cons(X_32,X_42))) = x(x(X_42,cons(X_44,nil)),cons(X_32,nil)) ),
inference(resolve,[$cnf( $equal(rotate(s(z),cons(X_32,x(X_42,cons(X_44,nil)))),rotate(s(s(z)),cons(X_44,cons(X_32,X_42)))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
rotate(s(s(z)),cons(X_44,cons(X_32,X_42))) = x(x(X_42,cons(X_44,nil)),cons(X_32,nil)),
inference(resolve,[$cnf( $equal(rotate(s(z),cons(X_32,x(X_42,cons(X_44,nil)))),x(x(X_42,cons(X_44,nil)),cons(X_32,nil))) )],[refute_0_40,refute_0_51]) ).
cnf(refute_0_53,plain,
rotate(s(s(z)),cons(X_49,cons(X_47,cons(Z,Xs)))) = x(x(cons(Z,Xs),cons(X_49,nil)),cons(X_47,nil)),
inference(subst,[],[refute_0_52:[bind(X_32,$fot(X_47)),bind(X_42,$fot(cons(Z,Xs))),bind(X_44,$fot(X_49))]]) ).
cnf(refute_0_54,plain,
x(cons(Z,Xs),cons(X_49,nil)) = cons(Z,x(Xs,cons(X_49,nil))),
inference(subst,[],[refute_0_42:[bind(Y,$fot(cons(X_49,nil)))]]) ).
cnf(refute_0_55,plain,
( rotate(s(s(z)),cons(X_49,cons(X_47,cons(Z,Xs)))) != x(x(cons(Z,Xs),cons(X_49,nil)),cons(X_47,nil))
| x(cons(Z,Xs),cons(X_49,nil)) != cons(Z,x(Xs,cons(X_49,nil)))
| rotate(s(s(z)),cons(X_49,cons(X_47,cons(Z,Xs)))) = x(cons(Z,x(Xs,cons(X_49,nil))),cons(X_47,nil)) ),
introduced(tautology,[equality,[$cnf( $equal(rotate(s(s(z)),cons(X_49,cons(X_47,cons(Z,Xs)))),x(x(cons(Z,Xs),cons(X_49,nil)),cons(X_47,nil))) ),[1,0],$fot(cons(Z,x(Xs,cons(X_49,nil))))]]) ).
cnf(refute_0_56,plain,
( rotate(s(s(z)),cons(X_49,cons(X_47,cons(Z,Xs)))) != x(x(cons(Z,Xs),cons(X_49,nil)),cons(X_47,nil))
| rotate(s(s(z)),cons(X_49,cons(X_47,cons(Z,Xs)))) = x(cons(Z,x(Xs,cons(X_49,nil))),cons(X_47,nil)) ),
inference(resolve,[$cnf( $equal(x(cons(Z,Xs),cons(X_49,nil)),cons(Z,x(Xs,cons(X_49,nil)))) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
rotate(s(s(z)),cons(X_49,cons(X_47,cons(Z,Xs)))) = x(cons(Z,x(Xs,cons(X_49,nil))),cons(X_47,nil)),
inference(resolve,[$cnf( $equal(rotate(s(s(z)),cons(X_49,cons(X_47,cons(Z,Xs)))),x(x(cons(Z,Xs),cons(X_49,nil)),cons(X_47,nil))) )],[refute_0_53,refute_0_56]) ).
cnf(refute_0_58,plain,
( rotate(s(s(z)),cons(X_44,cons(X_32,X_42))) != x(x(X_42,cons(X_44,nil)),cons(X_32,nil))
| x(x(X_42,cons(X_44,nil)),cons(X_32,nil)) = rotate(s(s(z)),cons(X_44,cons(X_32,X_42))) ),
inference(subst,[],[refute_0_23:[bind(X0,$fot(rotate(s(s(z)),cons(X_44,cons(X_32,X_42))))),bind(Y0,$fot(x(x(X_42,cons(X_44,nil)),cons(X_32,nil))))]]) ).
cnf(refute_0_59,plain,
x(x(X_42,cons(X_44,nil)),cons(X_32,nil)) = rotate(s(s(z)),cons(X_44,cons(X_32,X_42))),
inference(resolve,[$cnf( $equal(rotate(s(s(z)),cons(X_44,cons(X_32,X_42))),x(x(X_42,cons(X_44,nil)),cons(X_32,nil))) )],[refute_0_52,refute_0_58]) ).
cnf(refute_0_60,plain,
x(x(Xs,cons(X_49,nil)),cons(X_47,nil)) = rotate(s(s(z)),cons(X_49,cons(X_47,Xs))),
inference(subst,[],[refute_0_59:[bind(X_32,$fot(X_47)),bind(X_42,$fot(Xs)),bind(X_44,$fot(X_49))]]) ).
cnf(refute_0_61,plain,
cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil))) = cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil))),
introduced(tautology,[refl,[$fot(cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil))))]]) ).
cnf(refute_0_62,plain,
( cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil))) != cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil)))
| x(x(Xs,cons(X_49,nil)),cons(X_47,nil)) != rotate(s(s(z)),cons(X_49,cons(X_47,Xs)))
| cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil))) = cons(Z,rotate(s(s(z)),cons(X_49,cons(X_47,Xs)))) ),
introduced(tautology,[equality,[$cnf( $equal(cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil))),cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil)))) ),[1,1],$fot(rotate(s(s(z)),cons(X_49,cons(X_47,Xs))))]]) ).
cnf(refute_0_63,plain,
( x(x(Xs,cons(X_49,nil)),cons(X_47,nil)) != rotate(s(s(z)),cons(X_49,cons(X_47,Xs)))
| cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil))) = cons(Z,rotate(s(s(z)),cons(X_49,cons(X_47,Xs)))) ),
inference(resolve,[$cnf( $equal(cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil))),cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil)))) )],[refute_0_61,refute_0_62]) ).
cnf(refute_0_64,plain,
cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil))) = cons(Z,rotate(s(s(z)),cons(X_49,cons(X_47,Xs)))),
inference(resolve,[$cnf( $equal(x(x(Xs,cons(X_49,nil)),cons(X_47,nil)),rotate(s(s(z)),cons(X_49,cons(X_47,Xs)))) )],[refute_0_60,refute_0_63]) ).
cnf(refute_0_65,plain,
x(cons(Z,x(Xs,cons(X_49,nil))),cons(X_47,nil)) = cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil))),
inference(subst,[],[refute_0_42:[bind(Xs,$fot(x(Xs,cons(X_49,nil)))),bind(Y,$fot(cons(X_47,nil)))]]) ).
cnf(refute_0_66,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_67,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_23,refute_0_66]) ).
cnf(refute_0_68,plain,
( cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil))) != cons(Z,rotate(s(s(z)),cons(X_49,cons(X_47,Xs))))
| x(cons(Z,x(Xs,cons(X_49,nil))),cons(X_47,nil)) != cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil)))
| x(cons(Z,x(Xs,cons(X_49,nil))),cons(X_47,nil)) = cons(Z,rotate(s(s(z)),cons(X_49,cons(X_47,Xs)))) ),
inference(subst,[],[refute_0_67:[bind(X0,$fot(x(cons(Z,x(Xs,cons(X_49,nil))),cons(X_47,nil)))),bind(Y0,$fot(cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil))))),bind(Z0,$fot(cons(Z,rotate(s(s(z)),cons(X_49,cons(X_47,Xs))))))]]) ).
cnf(refute_0_69,plain,
( cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil))) != cons(Z,rotate(s(s(z)),cons(X_49,cons(X_47,Xs))))
| x(cons(Z,x(Xs,cons(X_49,nil))),cons(X_47,nil)) = cons(Z,rotate(s(s(z)),cons(X_49,cons(X_47,Xs)))) ),
inference(resolve,[$cnf( $equal(x(cons(Z,x(Xs,cons(X_49,nil))),cons(X_47,nil)),cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil)))) )],[refute_0_65,refute_0_68]) ).
cnf(refute_0_70,plain,
x(cons(Z,x(Xs,cons(X_49,nil))),cons(X_47,nil)) = cons(Z,rotate(s(s(z)),cons(X_49,cons(X_47,Xs)))),
inference(resolve,[$cnf( $equal(cons(Z,x(x(Xs,cons(X_49,nil)),cons(X_47,nil))),cons(Z,rotate(s(s(z)),cons(X_49,cons(X_47,Xs))))) )],[refute_0_64,refute_0_69]) ).
cnf(refute_0_71,plain,
( rotate(s(s(z)),cons(X_49,cons(X_47,cons(Z,Xs)))) != x(cons(Z,x(Xs,cons(X_49,nil))),cons(X_47,nil))
| x(cons(Z,x(Xs,cons(X_49,nil))),cons(X_47,nil)) != cons(Z,rotate(s(s(z)),cons(X_49,cons(X_47,Xs))))
| rotate(s(s(z)),cons(X_49,cons(X_47,cons(Z,Xs)))) = cons(Z,rotate(s(s(z)),cons(X_49,cons(X_47,Xs)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(rotate(s(s(z)),cons(X_49,cons(X_47,cons(Z,Xs)))),cons(Z,rotate(s(s(z)),cons(X_49,cons(X_47,Xs))))) ),[0],$fot(x(cons(Z,x(Xs,cons(X_49,nil))),cons(X_47,nil)))]]) ).
cnf(refute_0_72,plain,
( rotate(s(s(z)),cons(X_49,cons(X_47,cons(Z,Xs)))) != x(cons(Z,x(Xs,cons(X_49,nil))),cons(X_47,nil))
| rotate(s(s(z)),cons(X_49,cons(X_47,cons(Z,Xs)))) = cons(Z,rotate(s(s(z)),cons(X_49,cons(X_47,Xs)))) ),
inference(resolve,[$cnf( $equal(x(cons(Z,x(Xs,cons(X_49,nil))),cons(X_47,nil)),cons(Z,rotate(s(s(z)),cons(X_49,cons(X_47,Xs))))) )],[refute_0_70,refute_0_71]) ).
cnf(refute_0_73,plain,
rotate(s(s(z)),cons(X_49,cons(X_47,cons(Z,Xs)))) = cons(Z,rotate(s(s(z)),cons(X_49,cons(X_47,Xs)))),
inference(resolve,[$cnf( $equal(rotate(s(s(z)),cons(X_49,cons(X_47,cons(Z,Xs)))),x(cons(Z,x(Xs,cons(X_49,nil))),cons(X_47,nil))) )],[refute_0_57,refute_0_72]) ).
cnf(refute_0_74,plain,
rotate(s(s(z)),cons(X_512,cons(X_47,cons(Z,Xs)))) = cons(Z,rotate(s(s(z)),cons(X_512,cons(X_47,Xs)))),
inference(subst,[],[refute_0_73:[bind(X_49,$fot(X_512))]]) ).
cnf(refute_0_75,plain,
( cons(Z,rotate(s(s(z)),cons(X_512,cons(X_47,Xs)))) != cons(X_512,cons(X_47,cons(Z,Xs)))
| rotate(s(s(z)),cons(X_512,cons(X_47,cons(Z,Xs)))) != cons(Z,rotate(s(s(z)),cons(X_512,cons(X_47,Xs))))
| rotate(s(s(z)),cons(X_512,cons(X_47,cons(Z,Xs)))) = cons(X_512,cons(X_47,cons(Z,Xs))) ),
introduced(tautology,[equality,[$cnf( $equal(rotate(s(s(z)),cons(X_512,cons(X_47,cons(Z,Xs)))),cons(Z,rotate(s(s(z)),cons(X_512,cons(X_47,Xs))))) ),[1],$fot(cons(X_512,cons(X_47,cons(Z,Xs))))]]) ).
cnf(refute_0_76,plain,
( cons(Z,rotate(s(s(z)),cons(X_512,cons(X_47,Xs)))) != cons(X_512,cons(X_47,cons(Z,Xs)))
| rotate(s(s(z)),cons(X_512,cons(X_47,cons(Z,Xs)))) = cons(X_512,cons(X_47,cons(Z,Xs))) ),
inference(resolve,[$cnf( $equal(rotate(s(s(z)),cons(X_512,cons(X_47,cons(Z,Xs)))),cons(Z,rotate(s(s(z)),cons(X_512,cons(X_47,Xs))))) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
( cons(Z,rotate(s(s(z)),cons(X_512,cons(X_47,Xs)))) != cons(X_512,cons(X_47,cons(Z,Xs)))
| ~ x2(s(s(z)),s(length(cons(X_47,cons(Z,Xs)))))
| s(s(z)) = z
| x(cons(X_47,cons(Z,Xs)),cons(X_512,nil)) = cons(X_512,cons(X_47,cons(Z,Xs))) ),
inference(resolve,[$cnf( $equal(rotate(s(s(z)),cons(X_512,cons(X_47,cons(Z,Xs)))),cons(X_512,cons(X_47,cons(Z,Xs)))) )],[refute_0_76,refute_0_39]) ).
cnf(refute_0_78,plain,
length(cons(Z,Xs)) = s(length(Xs)),
inference(subst,[],[refute_0_10:[bind(Y,$fot(Z))]]) ).
cnf(refute_0_79,plain,
s(length(cons(Z,Xs))) = s(length(cons(Z,Xs))),
introduced(tautology,[refl,[$fot(s(length(cons(Z,Xs))))]]) ).
cnf(refute_0_80,plain,
( length(cons(Z,Xs)) != s(length(Xs))
| s(length(cons(Z,Xs))) != s(length(cons(Z,Xs)))
| s(length(cons(Z,Xs))) = s(s(length(Xs))) ),
introduced(tautology,[equality,[$cnf( $equal(s(length(cons(Z,Xs))),s(length(cons(Z,Xs)))) ),[1,0],$fot(s(length(Xs)))]]) ).
cnf(refute_0_81,plain,
( length(cons(Z,Xs)) != s(length(Xs))
| s(length(cons(Z,Xs))) = s(s(length(Xs))) ),
inference(resolve,[$cnf( $equal(s(length(cons(Z,Xs))),s(length(cons(Z,Xs)))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
s(length(cons(Z,Xs))) = s(s(length(Xs))),
inference(resolve,[$cnf( $equal(length(cons(Z,Xs)),s(length(Xs))) )],[refute_0_78,refute_0_81]) ).
cnf(refute_0_83,plain,
length(cons(X_47,cons(Z,Xs))) = s(length(cons(Z,Xs))),
inference(subst,[],[refute_0_10:[bind(Xs,$fot(cons(Z,Xs))),bind(Y,$fot(X_47))]]) ).
cnf(refute_0_84,plain,
( length(cons(X_47,cons(Z,Xs))) != s(length(cons(Z,Xs)))
| s(length(cons(Z,Xs))) != s(s(length(Xs)))
| length(cons(X_47,cons(Z,Xs))) = s(s(length(Xs))) ),
inference(subst,[],[refute_0_67:[bind(X0,$fot(length(cons(X_47,cons(Z,Xs))))),bind(Y0,$fot(s(length(cons(Z,Xs))))),bind(Z0,$fot(s(s(length(Xs)))))]]) ).
cnf(refute_0_85,plain,
( s(length(cons(Z,Xs))) != s(s(length(Xs)))
| length(cons(X_47,cons(Z,Xs))) = s(s(length(Xs))) ),
inference(resolve,[$cnf( $equal(length(cons(X_47,cons(Z,Xs))),s(length(cons(Z,Xs)))) )],[refute_0_83,refute_0_84]) ).
cnf(refute_0_86,plain,
length(cons(X_47,cons(Z,Xs))) = s(s(length(Xs))),
inference(resolve,[$cnf( $equal(s(length(cons(Z,Xs))),s(s(length(Xs)))) )],[refute_0_82,refute_0_85]) ).
cnf(refute_0_87,plain,
s(length(cons(X_47,cons(Z,Xs)))) = s(length(cons(X_47,cons(Z,Xs)))),
introduced(tautology,[refl,[$fot(s(length(cons(X_47,cons(Z,Xs)))))]]) ).
cnf(refute_0_88,plain,
( length(cons(X_47,cons(Z,Xs))) != s(s(length(Xs)))
| s(length(cons(X_47,cons(Z,Xs)))) != s(length(cons(X_47,cons(Z,Xs))))
| s(length(cons(X_47,cons(Z,Xs)))) = s(s(s(length(Xs)))) ),
introduced(tautology,[equality,[$cnf( $equal(s(length(cons(X_47,cons(Z,Xs)))),s(length(cons(X_47,cons(Z,Xs))))) ),[1,0],$fot(s(s(length(Xs))))]]) ).
cnf(refute_0_89,plain,
( length(cons(X_47,cons(Z,Xs))) != s(s(length(Xs)))
| s(length(cons(X_47,cons(Z,Xs)))) = s(s(s(length(Xs)))) ),
inference(resolve,[$cnf( $equal(s(length(cons(X_47,cons(Z,Xs)))),s(length(cons(X_47,cons(Z,Xs))))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
s(length(cons(X_47,cons(Z,Xs)))) = s(s(s(length(Xs)))),
inference(resolve,[$cnf( $equal(length(cons(X_47,cons(Z,Xs))),s(s(length(Xs)))) )],[refute_0_86,refute_0_89]) ).
cnf(refute_0_91,plain,
( s(length(cons(X_47,cons(Z,Xs)))) != s(s(s(length(Xs))))
| ~ x2(s(s(z)),s(s(s(length(Xs)))))
| x2(s(s(z)),s(length(cons(X_47,cons(Z,Xs))))) ),
introduced(tautology,[equality,[$cnf( ~ x2(s(s(z)),s(length(cons(X_47,cons(Z,Xs))))) ),[1],$fot(s(s(s(length(Xs)))))]]) ).
cnf(refute_0_92,plain,
( ~ x2(s(s(z)),s(s(s(length(Xs)))))
| x2(s(s(z)),s(length(cons(X_47,cons(Z,Xs))))) ),
inference(resolve,[$cnf( $equal(s(length(cons(X_47,cons(Z,Xs)))),s(s(s(length(Xs))))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
( cons(Z,rotate(s(s(z)),cons(X_512,cons(X_47,Xs)))) != cons(X_512,cons(X_47,cons(Z,Xs)))
| ~ x2(s(s(z)),s(s(s(length(Xs)))))
| s(s(z)) = z
| x(cons(X_47,cons(Z,Xs)),cons(X_512,nil)) = cons(X_512,cons(X_47,cons(Z,Xs))) ),
inference(resolve,[$cnf( x2(s(s(z)),s(length(cons(X_47,cons(Z,Xs))))) )],[refute_0_92,refute_0_77]) ).
cnf(refute_0_94,plain,
x(cons(Z,Xs),cons(X_512,nil)) = cons(Z,x(Xs,cons(X_512,nil))),
inference(subst,[],[refute_0_42:[bind(Y,$fot(cons(X_512,nil)))]]) ).
cnf(refute_0_95,plain,
cons(X_47,x(cons(Z,Xs),cons(X_512,nil))) = cons(X_47,x(cons(Z,Xs),cons(X_512,nil))),
introduced(tautology,[refl,[$fot(cons(X_47,x(cons(Z,Xs),cons(X_512,nil))))]]) ).
cnf(refute_0_96,plain,
( cons(X_47,x(cons(Z,Xs),cons(X_512,nil))) != cons(X_47,x(cons(Z,Xs),cons(X_512,nil)))
| x(cons(Z,Xs),cons(X_512,nil)) != cons(Z,x(Xs,cons(X_512,nil)))
| cons(X_47,x(cons(Z,Xs),cons(X_512,nil))) = cons(X_47,cons(Z,x(Xs,cons(X_512,nil)))) ),
introduced(tautology,[equality,[$cnf( $equal(cons(X_47,x(cons(Z,Xs),cons(X_512,nil))),cons(X_47,x(cons(Z,Xs),cons(X_512,nil)))) ),[1,1],$fot(cons(Z,x(Xs,cons(X_512,nil))))]]) ).
cnf(refute_0_97,plain,
( x(cons(Z,Xs),cons(X_512,nil)) != cons(Z,x(Xs,cons(X_512,nil)))
| cons(X_47,x(cons(Z,Xs),cons(X_512,nil))) = cons(X_47,cons(Z,x(Xs,cons(X_512,nil)))) ),
inference(resolve,[$cnf( $equal(cons(X_47,x(cons(Z,Xs),cons(X_512,nil))),cons(X_47,x(cons(Z,Xs),cons(X_512,nil)))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
cons(X_47,x(cons(Z,Xs),cons(X_512,nil))) = cons(X_47,cons(Z,x(Xs,cons(X_512,nil)))),
inference(resolve,[$cnf( $equal(x(cons(Z,Xs),cons(X_512,nil)),cons(Z,x(Xs,cons(X_512,nil)))) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
x(cons(X_47,cons(Z,Xs)),cons(X_512,nil)) = cons(X_47,x(cons(Z,Xs),cons(X_512,nil))),
inference(subst,[],[refute_0_42:[bind(Xs,$fot(cons(Z,Xs))),bind(Y,$fot(cons(X_512,nil))),bind(Z,$fot(X_47))]]) ).
cnf(refute_0_100,plain,
( cons(X_47,x(cons(Z,Xs),cons(X_512,nil))) != cons(X_47,cons(Z,x(Xs,cons(X_512,nil))))
| x(cons(X_47,cons(Z,Xs)),cons(X_512,nil)) != cons(X_47,x(cons(Z,Xs),cons(X_512,nil)))
| x(cons(X_47,cons(Z,Xs)),cons(X_512,nil)) = cons(X_47,cons(Z,x(Xs,cons(X_512,nil)))) ),
inference(subst,[],[refute_0_67:[bind(X0,$fot(x(cons(X_47,cons(Z,Xs)),cons(X_512,nil)))),bind(Y0,$fot(cons(X_47,x(cons(Z,Xs),cons(X_512,nil))))),bind(Z0,$fot(cons(X_47,cons(Z,x(Xs,cons(X_512,nil))))))]]) ).
cnf(refute_0_101,plain,
( cons(X_47,x(cons(Z,Xs),cons(X_512,nil))) != cons(X_47,cons(Z,x(Xs,cons(X_512,nil))))
| x(cons(X_47,cons(Z,Xs)),cons(X_512,nil)) = cons(X_47,cons(Z,x(Xs,cons(X_512,nil)))) ),
inference(resolve,[$cnf( $equal(x(cons(X_47,cons(Z,Xs)),cons(X_512,nil)),cons(X_47,x(cons(Z,Xs),cons(X_512,nil)))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
x(cons(X_47,cons(Z,Xs)),cons(X_512,nil)) = cons(X_47,cons(Z,x(Xs,cons(X_512,nil)))),
inference(resolve,[$cnf( $equal(cons(X_47,x(cons(Z,Xs),cons(X_512,nil))),cons(X_47,cons(Z,x(Xs,cons(X_512,nil))))) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
( x(cons(X_47,cons(Z,Xs)),cons(X_512,nil)) != cons(X_47,cons(Z,x(Xs,cons(X_512,nil))))
| x(cons(X_47,cons(Z,Xs)),cons(X_512,nil)) != cons(X_512,cons(X_47,cons(Z,Xs)))
| cons(X_47,cons(Z,x(Xs,cons(X_512,nil)))) = cons(X_512,cons(X_47,cons(Z,Xs))) ),
introduced(tautology,[equality,[$cnf( $equal(x(cons(X_47,cons(Z,Xs)),cons(X_512,nil)),cons(X_512,cons(X_47,cons(Z,Xs)))) ),[0],$fot(cons(X_47,cons(Z,x(Xs,cons(X_512,nil)))))]]) ).
cnf(refute_0_104,plain,
( x(cons(X_47,cons(Z,Xs)),cons(X_512,nil)) != cons(X_512,cons(X_47,cons(Z,Xs)))
| cons(X_47,cons(Z,x(Xs,cons(X_512,nil)))) = cons(X_512,cons(X_47,cons(Z,Xs))) ),
inference(resolve,[$cnf( $equal(x(cons(X_47,cons(Z,Xs)),cons(X_512,nil)),cons(X_47,cons(Z,x(Xs,cons(X_512,nil))))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
( cons(Z,rotate(s(s(z)),cons(X_512,cons(X_47,Xs)))) != cons(X_512,cons(X_47,cons(Z,Xs)))
| ~ x2(s(s(z)),s(s(s(length(Xs)))))
| cons(X_47,cons(Z,x(Xs,cons(X_512,nil)))) = cons(X_512,cons(X_47,cons(Z,Xs)))
| s(s(z)) = z ),
inference(resolve,[$cnf( $equal(x(cons(X_47,cons(Z,Xs)),cons(X_512,nil)),cons(X_512,cons(X_47,cons(Z,Xs)))) )],[refute_0_93,refute_0_104]) ).
cnf(refute_0_106,plain,
( ~ x2(Z,Y2)
| x2(s(Z),s(Y2)) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_107,plain,
( ~ x2(s(z),s(s(X_17)))
| x2(s(s(z)),s(s(s(X_17)))) ),
inference(subst,[],[refute_0_106:[bind(Y2,$fot(s(s(X_17)))),bind(Z,$fot(s(z)))]]) ).
cnf(refute_0_108,plain,
( ~ x2(z,s(X2))
| x2(s(z),s(s(X2))) ),
inference(subst,[],[refute_0_106:[bind(Y2,$fot(s(X2))),bind(Z,$fot(z))]]) ).
cnf(refute_0_109,plain,
x2(s(z),s(s(X2))),
inference(resolve,[$cnf( x2(z,s(X2)) )],[refute_0_3,refute_0_108]) ).
cnf(refute_0_110,plain,
x2(s(z),s(s(X_17))),
inference(subst,[],[refute_0_109:[bind(X2,$fot(X_17))]]) ).
cnf(refute_0_111,plain,
x2(s(s(z)),s(s(s(X_17)))),
inference(resolve,[$cnf( x2(s(z),s(s(X_17))) )],[refute_0_110,refute_0_107]) ).
cnf(refute_0_112,plain,
x2(s(s(z)),s(s(s(length(Xs))))),
inference(subst,[],[refute_0_111:[bind(X_17,$fot(length(Xs)))]]) ).
cnf(refute_0_113,plain,
( cons(Z,rotate(s(s(z)),cons(X_512,cons(X_47,Xs)))) != cons(X_512,cons(X_47,cons(Z,Xs)))
| cons(X_47,cons(Z,x(Xs,cons(X_512,nil)))) = cons(X_512,cons(X_47,cons(Z,Xs)))
| s(s(z)) = z ),
inference(resolve,[$cnf( x2(s(s(z)),s(s(s(length(Xs))))) )],[refute_0_112,refute_0_105]) ).
cnf(refute_0_114,plain,
s(X) != z,
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_115,plain,
s(s(z)) != z,
inference(subst,[],[refute_0_114:[bind(X,$fot(s(z)))]]) ).
cnf(refute_0_116,plain,
( cons(Z,rotate(s(s(z)),cons(X_512,cons(X_47,Xs)))) != cons(X_512,cons(X_47,cons(Z,Xs)))
| cons(X_47,cons(Z,x(Xs,cons(X_512,nil)))) = cons(X_512,cons(X_47,cons(Z,Xs))) ),
inference(resolve,[$cnf( $equal(s(s(z)),z) )],[refute_0_113,refute_0_115]) ).
cnf(refute_0_117,plain,
( cons(X_670,rotate(s(s(z)),cons(X_672,cons(X_671,cons(X_82,nil))))) != cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil))))
| cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))) = cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil)))) ),
inference(subst,[],[refute_0_116:[bind(Xs,$fot(cons(X_82,nil))),bind(Z,$fot(X_670)),bind(X_47,$fot(X_671)),bind(X_512,$fot(X_672))]]) ).
cnf(refute_0_118,plain,
rotate(s(X_45),cons(X_44,cons(X_43,cons(Z,Xs)))) = rotate(X_45,cons(X_43,x(cons(Z,Xs),cons(X_44,nil)))),
inference(subst,[],[refute_0_46:[bind(Xs,$fot(cons(Z,Xs))),bind(Z,$fot(X_43)),bind(X_32,$fot(X_44)),bind(X_34,$fot(X_45))]]) ).
cnf(refute_0_119,plain,
x(cons(Z,Xs),cons(X_44,nil)) = cons(Z,x(Xs,cons(X_44,nil))),
inference(subst,[],[refute_0_42:[bind(Y,$fot(cons(X_44,nil)))]]) ).
cnf(refute_0_120,plain,
( rotate(s(X_45),cons(X_44,cons(X_43,cons(Z,Xs)))) != rotate(X_45,cons(X_43,x(cons(Z,Xs),cons(X_44,nil))))
| x(cons(Z,Xs),cons(X_44,nil)) != cons(Z,x(Xs,cons(X_44,nil)))
| rotate(s(X_45),cons(X_44,cons(X_43,cons(Z,Xs)))) = rotate(X_45,cons(X_43,cons(Z,x(Xs,cons(X_44,nil))))) ),
introduced(tautology,[equality,[$cnf( $equal(rotate(s(X_45),cons(X_44,cons(X_43,cons(Z,Xs)))),rotate(X_45,cons(X_43,x(cons(Z,Xs),cons(X_44,nil))))) ),[1,1,1],$fot(cons(Z,x(Xs,cons(X_44,nil))))]]) ).
cnf(refute_0_121,plain,
( rotate(s(X_45),cons(X_44,cons(X_43,cons(Z,Xs)))) != rotate(X_45,cons(X_43,x(cons(Z,Xs),cons(X_44,nil))))
| rotate(s(X_45),cons(X_44,cons(X_43,cons(Z,Xs)))) = rotate(X_45,cons(X_43,cons(Z,x(Xs,cons(X_44,nil))))) ),
inference(resolve,[$cnf( $equal(x(cons(Z,Xs),cons(X_44,nil)),cons(Z,x(Xs,cons(X_44,nil)))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
rotate(s(X_45),cons(X_44,cons(X_43,cons(Z,Xs)))) = rotate(X_45,cons(X_43,cons(Z,x(Xs,cons(X_44,nil))))),
inference(resolve,[$cnf( $equal(rotate(s(X_45),cons(X_44,cons(X_43,cons(Z,Xs)))),rotate(X_45,cons(X_43,x(cons(Z,Xs),cons(X_44,nil))))) )],[refute_0_118,refute_0_121]) ).
cnf(refute_0_123,plain,
rotate(s(X_85),cons(X_84,cons(X_83,cons(X_82,nil)))) = rotate(X_85,cons(X_83,cons(X_82,x(nil,cons(X_84,nil))))),
inference(subst,[],[refute_0_122:[bind(Xs,$fot(nil)),bind(Z,$fot(X_82)),bind(X_43,$fot(X_83)),bind(X_44,$fot(X_84)),bind(X_45,$fot(X_85))]]) ).
cnf(refute_0_124,plain,
x(nil,Y) = Y,
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_125,plain,
x(nil,cons(X_84,nil)) = cons(X_84,nil),
inference(subst,[],[refute_0_124:[bind(Y,$fot(cons(X_84,nil)))]]) ).
cnf(refute_0_126,plain,
( rotate(s(X_85),cons(X_84,cons(X_83,cons(X_82,nil)))) != rotate(X_85,cons(X_83,cons(X_82,x(nil,cons(X_84,nil)))))
| x(nil,cons(X_84,nil)) != cons(X_84,nil)
| rotate(s(X_85),cons(X_84,cons(X_83,cons(X_82,nil)))) = rotate(X_85,cons(X_83,cons(X_82,cons(X_84,nil)))) ),
introduced(tautology,[equality,[$cnf( $equal(rotate(s(X_85),cons(X_84,cons(X_83,cons(X_82,nil)))),rotate(X_85,cons(X_83,cons(X_82,x(nil,cons(X_84,nil)))))) ),[1,1,1,1],$fot(cons(X_84,nil))]]) ).
cnf(refute_0_127,plain,
( rotate(s(X_85),cons(X_84,cons(X_83,cons(X_82,nil)))) != rotate(X_85,cons(X_83,cons(X_82,x(nil,cons(X_84,nil)))))
| rotate(s(X_85),cons(X_84,cons(X_83,cons(X_82,nil)))) = rotate(X_85,cons(X_83,cons(X_82,cons(X_84,nil)))) ),
inference(resolve,[$cnf( $equal(x(nil,cons(X_84,nil)),cons(X_84,nil)) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
rotate(s(X_85),cons(X_84,cons(X_83,cons(X_82,nil)))) = rotate(X_85,cons(X_83,cons(X_82,cons(X_84,nil)))),
inference(resolve,[$cnf( $equal(rotate(s(X_85),cons(X_84,cons(X_83,cons(X_82,nil)))),rotate(X_85,cons(X_83,cons(X_82,x(nil,cons(X_84,nil)))))) )],[refute_0_123,refute_0_127]) ).
cnf(refute_0_129,plain,
rotate(s(s(z)),cons(X_672,cons(X_671,cons(X_82,nil)))) = rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil)))),
inference(subst,[],[refute_0_128:[bind(X_83,$fot(X_671)),bind(X_84,$fot(X_672)),bind(X_85,$fot(s(z)))]]) ).
cnf(refute_0_130,plain,
( cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))) != cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil))))
| rotate(s(s(z)),cons(X_672,cons(X_671,cons(X_82,nil)))) != rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))
| cons(X_670,rotate(s(s(z)),cons(X_672,cons(X_671,cons(X_82,nil))))) = cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(cons(X_670,rotate(s(s(z)),cons(X_672,cons(X_671,cons(X_82,nil))))),cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil))))) ),[0,1],$fot(rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil)))))]]) ).
cnf(refute_0_131,plain,
( cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))) != cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil))))
| cons(X_670,rotate(s(s(z)),cons(X_672,cons(X_671,cons(X_82,nil))))) = cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil)))) ),
inference(resolve,[$cnf( $equal(rotate(s(s(z)),cons(X_672,cons(X_671,cons(X_82,nil)))),rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
( cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))) != cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil))))
| cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))) = cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil)))) ),
inference(resolve,[$cnf( $equal(cons(X_670,rotate(s(s(z)),cons(X_672,cons(X_671,cons(X_82,nil))))),cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil))))) )],[refute_0_131,refute_0_117]) ).
cnf(refute_0_133,plain,
rotate(z,cons(X_82,cons(X_672,cons(X_671,nil)))) = cons(X_82,cons(X_672,cons(X_671,nil))),
inference(subst,[],[refute_0_17:[bind(Y,$fot(cons(X_82,cons(X_672,cons(X_671,nil)))))]]) ).
cnf(refute_0_134,plain,
rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil)))) = rotate(z,cons(X_82,cons(X_672,cons(X_671,nil)))),
inference(subst,[],[refute_0_128:[bind(X_82,$fot(X_672)),bind(X_83,$fot(X_82)),bind(X_84,$fot(X_671)),bind(X_85,$fot(z))]]) ).
cnf(refute_0_135,plain,
( rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil)))) != rotate(z,cons(X_82,cons(X_672,cons(X_671,nil))))
| rotate(z,cons(X_82,cons(X_672,cons(X_671,nil)))) != cons(X_82,cons(X_672,cons(X_671,nil)))
| rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil)))) = cons(X_82,cons(X_672,cons(X_671,nil))) ),
inference(subst,[],[refute_0_67:[bind(X0,$fot(rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil)))))),bind(Y0,$fot(rotate(z,cons(X_82,cons(X_672,cons(X_671,nil)))))),bind(Z0,$fot(cons(X_82,cons(X_672,cons(X_671,nil)))))]]) ).
cnf(refute_0_136,plain,
( rotate(z,cons(X_82,cons(X_672,cons(X_671,nil)))) != cons(X_82,cons(X_672,cons(X_671,nil)))
| rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil)))) = cons(X_82,cons(X_672,cons(X_671,nil))) ),
inference(resolve,[$cnf( $equal(rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil)))),rotate(z,cons(X_82,cons(X_672,cons(X_671,nil))))) )],[refute_0_134,refute_0_135]) ).
cnf(refute_0_137,plain,
rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil)))) = cons(X_82,cons(X_672,cons(X_671,nil))),
inference(resolve,[$cnf( $equal(rotate(z,cons(X_82,cons(X_672,cons(X_671,nil)))),cons(X_82,cons(X_672,cons(X_671,nil)))) )],[refute_0_133,refute_0_136]) ).
cnf(refute_0_138,plain,
cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))) = cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))),
introduced(tautology,[refl,[$fot(cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))))]]) ).
cnf(refute_0_139,plain,
( cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))) != cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil)))))
| rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil)))) != cons(X_82,cons(X_672,cons(X_671,nil)))
| cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))) = cons(X_670,cons(X_82,cons(X_672,cons(X_671,nil)))) ),
introduced(tautology,[equality,[$cnf( $equal(cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))),cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil)))))) ),[1,1],$fot(cons(X_82,cons(X_672,cons(X_671,nil))))]]) ).
cnf(refute_0_140,plain,
( rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil)))) != cons(X_82,cons(X_672,cons(X_671,nil)))
| cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))) = cons(X_670,cons(X_82,cons(X_672,cons(X_671,nil)))) ),
inference(resolve,[$cnf( $equal(cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))),cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil)))))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))) = cons(X_670,cons(X_82,cons(X_672,cons(X_671,nil)))),
inference(resolve,[$cnf( $equal(rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil)))),cons(X_82,cons(X_672,cons(X_671,nil)))) )],[refute_0_137,refute_0_140]) ).
cnf(refute_0_142,plain,
( cons(X_670,cons(X_82,cons(X_672,cons(X_671,nil)))) != cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil))))
| cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))) != cons(X_670,cons(X_82,cons(X_672,cons(X_671,nil))))
| cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))) = cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil)))) ),
introduced(tautology,[equality,[$cnf( $equal(cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))),cons(X_670,cons(X_82,cons(X_672,cons(X_671,nil))))) ),[1],$fot(cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil)))))]]) ).
cnf(refute_0_143,plain,
( cons(X_670,cons(X_82,cons(X_672,cons(X_671,nil)))) != cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil))))
| cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))) = cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil)))) ),
inference(resolve,[$cnf( $equal(cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))),cons(X_670,cons(X_82,cons(X_672,cons(X_671,nil))))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
( cons(X_670,cons(X_82,cons(X_672,cons(X_671,nil)))) != cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil))))
| cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))) = cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil)))) ),
inference(resolve,[$cnf( $equal(cons(X_670,rotate(s(z),cons(X_671,cons(X_82,cons(X_672,nil))))),cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil))))) )],[refute_0_143,refute_0_132]) ).
cnf(refute_0_145,plain,
x(nil,cons(X_672,nil)) = cons(X_672,nil),
inference(subst,[],[refute_0_124:[bind(Y,$fot(cons(X_672,nil)))]]) ).
cnf(refute_0_146,plain,
cons(X_82,x(nil,cons(X_672,nil))) = cons(X_82,x(nil,cons(X_672,nil))),
introduced(tautology,[refl,[$fot(cons(X_82,x(nil,cons(X_672,nil))))]]) ).
cnf(refute_0_147,plain,
( cons(X_82,x(nil,cons(X_672,nil))) != cons(X_82,x(nil,cons(X_672,nil)))
| x(nil,cons(X_672,nil)) != cons(X_672,nil)
| cons(X_82,x(nil,cons(X_672,nil))) = cons(X_82,cons(X_672,nil)) ),
introduced(tautology,[equality,[$cnf( $equal(cons(X_82,x(nil,cons(X_672,nil))),cons(X_82,x(nil,cons(X_672,nil)))) ),[1,1],$fot(cons(X_672,nil))]]) ).
cnf(refute_0_148,plain,
( x(nil,cons(X_672,nil)) != cons(X_672,nil)
| cons(X_82,x(nil,cons(X_672,nil))) = cons(X_82,cons(X_672,nil)) ),
inference(resolve,[$cnf( $equal(cons(X_82,x(nil,cons(X_672,nil))),cons(X_82,x(nil,cons(X_672,nil)))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
cons(X_82,x(nil,cons(X_672,nil))) = cons(X_82,cons(X_672,nil)),
inference(resolve,[$cnf( $equal(x(nil,cons(X_672,nil)),cons(X_672,nil)) )],[refute_0_145,refute_0_148]) ).
cnf(refute_0_150,plain,
x(cons(X_82,nil),cons(X_672,nil)) = cons(X_82,x(nil,cons(X_672,nil))),
inference(subst,[],[refute_0_42:[bind(Xs,$fot(nil)),bind(Y,$fot(cons(X_672,nil))),bind(Z,$fot(X_82))]]) ).
cnf(refute_0_151,plain,
( cons(X_82,x(nil,cons(X_672,nil))) != cons(X_82,cons(X_672,nil))
| x(cons(X_82,nil),cons(X_672,nil)) != cons(X_82,x(nil,cons(X_672,nil)))
| x(cons(X_82,nil),cons(X_672,nil)) = cons(X_82,cons(X_672,nil)) ),
inference(subst,[],[refute_0_67:[bind(X0,$fot(x(cons(X_82,nil),cons(X_672,nil)))),bind(Y0,$fot(cons(X_82,x(nil,cons(X_672,nil))))),bind(Z0,$fot(cons(X_82,cons(X_672,nil))))]]) ).
cnf(refute_0_152,plain,
( cons(X_82,x(nil,cons(X_672,nil))) != cons(X_82,cons(X_672,nil))
| x(cons(X_82,nil),cons(X_672,nil)) = cons(X_82,cons(X_672,nil)) ),
inference(resolve,[$cnf( $equal(x(cons(X_82,nil),cons(X_672,nil)),cons(X_82,x(nil,cons(X_672,nil)))) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
x(cons(X_82,nil),cons(X_672,nil)) = cons(X_82,cons(X_672,nil)),
inference(resolve,[$cnf( $equal(cons(X_82,x(nil,cons(X_672,nil))),cons(X_82,cons(X_672,nil))) )],[refute_0_149,refute_0_152]) ).
cnf(refute_0_154,plain,
cons(X_670,x(cons(X_82,nil),cons(X_672,nil))) = cons(X_670,x(cons(X_82,nil),cons(X_672,nil))),
introduced(tautology,[refl,[$fot(cons(X_670,x(cons(X_82,nil),cons(X_672,nil))))]]) ).
cnf(refute_0_155,plain,
( cons(X_670,x(cons(X_82,nil),cons(X_672,nil))) != cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))
| x(cons(X_82,nil),cons(X_672,nil)) != cons(X_82,cons(X_672,nil))
| cons(X_670,x(cons(X_82,nil),cons(X_672,nil))) = cons(X_670,cons(X_82,cons(X_672,nil))) ),
introduced(tautology,[equality,[$cnf( $equal(cons(X_670,x(cons(X_82,nil),cons(X_672,nil))),cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))) ),[1,1],$fot(cons(X_82,cons(X_672,nil)))]]) ).
cnf(refute_0_156,plain,
( x(cons(X_82,nil),cons(X_672,nil)) != cons(X_82,cons(X_672,nil))
| cons(X_670,x(cons(X_82,nil),cons(X_672,nil))) = cons(X_670,cons(X_82,cons(X_672,nil))) ),
inference(resolve,[$cnf( $equal(cons(X_670,x(cons(X_82,nil),cons(X_672,nil))),cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
cons(X_670,x(cons(X_82,nil),cons(X_672,nil))) = cons(X_670,cons(X_82,cons(X_672,nil))),
inference(resolve,[$cnf( $equal(x(cons(X_82,nil),cons(X_672,nil)),cons(X_82,cons(X_672,nil))) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))) = cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))),
introduced(tautology,[refl,[$fot(cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))))]]) ).
cnf(refute_0_159,plain,
( cons(X_670,x(cons(X_82,nil),cons(X_672,nil))) != cons(X_670,cons(X_82,cons(X_672,nil)))
| cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))) != cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil))))
| cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))) = cons(X_671,cons(X_670,cons(X_82,cons(X_672,nil)))) ),
introduced(tautology,[equality,[$cnf( $equal(cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))),cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil))))) ),[1,1],$fot(cons(X_670,cons(X_82,cons(X_672,nil))))]]) ).
cnf(refute_0_160,plain,
( cons(X_670,x(cons(X_82,nil),cons(X_672,nil))) != cons(X_670,cons(X_82,cons(X_672,nil)))
| cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))) = cons(X_671,cons(X_670,cons(X_82,cons(X_672,nil)))) ),
inference(resolve,[$cnf( $equal(cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))),cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil))))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))) = cons(X_671,cons(X_670,cons(X_82,cons(X_672,nil)))),
inference(resolve,[$cnf( $equal(cons(X_670,x(cons(X_82,nil),cons(X_672,nil))),cons(X_670,cons(X_82,cons(X_672,nil)))) )],[refute_0_157,refute_0_160]) ).
cnf(refute_0_162,plain,
( cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))) != cons(X_671,cons(X_670,cons(X_82,cons(X_672,nil))))
| cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))) != cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil))))
| cons(X_671,cons(X_670,cons(X_82,cons(X_672,nil)))) = cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil)))) ),
introduced(tautology,[equality,[$cnf( $equal(cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))),cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil))))) ),[0],$fot(cons(X_671,cons(X_670,cons(X_82,cons(X_672,nil)))))]]) ).
cnf(refute_0_163,plain,
( cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))) != cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil))))
| cons(X_671,cons(X_670,cons(X_82,cons(X_672,nil)))) = cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil)))) ),
inference(resolve,[$cnf( $equal(cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))),cons(X_671,cons(X_670,cons(X_82,cons(X_672,nil))))) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
( cons(X_670,cons(X_82,cons(X_672,cons(X_671,nil)))) != cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil))))
| cons(X_671,cons(X_670,cons(X_82,cons(X_672,nil)))) = cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil)))) ),
inference(resolve,[$cnf( $equal(cons(X_671,cons(X_670,x(cons(X_82,nil),cons(X_672,nil)))),cons(X_672,cons(X_671,cons(X_670,cons(X_82,nil))))) )],[refute_0_144,refute_0_163]) ).
cnf(refute_0_165,plain,
( cons(X_672,cons(X_671,cons(X_672,cons(X_671,nil)))) != cons(X_672,cons(X_671,cons(X_672,cons(X_671,nil))))
| cons(X_671,cons(X_672,cons(X_671,cons(X_672,nil)))) = cons(X_672,cons(X_671,cons(X_672,cons(X_671,nil)))) ),
inference(subst,[],[refute_0_164:[bind(X_670,$fot(X_672)),bind(X_82,$fot(X_671))]]) ).
cnf(refute_0_166,plain,
cons(X_672,cons(X_671,cons(X_672,cons(X_671,nil)))) = cons(X_672,cons(X_671,cons(X_672,cons(X_671,nil)))),
introduced(tautology,[refl,[$fot(cons(X_672,cons(X_671,cons(X_672,cons(X_671,nil)))))]]) ).
cnf(refute_0_167,plain,
cons(X_671,cons(X_672,cons(X_671,cons(X_672,nil)))) = cons(X_672,cons(X_671,cons(X_672,cons(X_671,nil)))),
inference(resolve,[$cnf( $equal(cons(X_672,cons(X_671,cons(X_672,cons(X_671,nil)))),cons(X_672,cons(X_671,cons(X_672,cons(X_671,nil))))) )],[refute_0_166,refute_0_165]) ).
cnf(refute_0_168,plain,
cons(X,cons(X_674,cons(X,cons(X_674,nil)))) = cons(X_674,cons(X,cons(X_674,cons(X,nil)))),
inference(subst,[],[refute_0_167:[bind(X_671,$fot(X)),bind(X_672,$fot(X_674))]]) ).
cnf(refute_0_169,plain,
( cons(X,cons(X_674,cons(X,cons(X_674,nil)))) != cons(X_674,cons(X,cons(X_674,cons(X,nil))))
| head(cons(X,cons(X_674,cons(X,cons(X_674,nil))))) != X
| head(cons(X_674,cons(X,cons(X_674,cons(X,nil))))) = X ),
introduced(tautology,[equality,[$cnf( $equal(head(cons(X,cons(X_674,cons(X,cons(X_674,nil))))),X) ),[0,0],$fot(cons(X_674,cons(X,cons(X_674,cons(X,nil)))))]]) ).
cnf(refute_0_170,plain,
( head(cons(X,cons(X_674,cons(X,cons(X_674,nil))))) != X
| head(cons(X_674,cons(X,cons(X_674,cons(X,nil))))) = X ),
inference(resolve,[$cnf( $equal(cons(X,cons(X_674,cons(X,cons(X_674,nil)))),cons(X_674,cons(X,cons(X_674,cons(X,nil))))) )],[refute_0_168,refute_0_169]) ).
cnf(refute_0_171,plain,
head(cons(X_674,cons(X,cons(X_674,cons(X,nil))))) = X,
inference(resolve,[$cnf( $equal(head(cons(X,cons(X_674,cons(X,cons(X_674,nil))))),X) )],[refute_0_2,refute_0_170]) ).
cnf(refute_0_172,plain,
head(cons(X_674,cons(X,cons(X_674,cons(X,nil))))) = X_674,
inference(subst,[],[refute_0_1:[bind(X,$fot(X_674)),bind(X2,$fot(cons(X,cons(X_674,cons(X,nil)))))]]) ).
cnf(refute_0_173,plain,
( head(cons(X_674,cons(X,cons(X_674,cons(X,nil))))) != X
| head(cons(X_674,cons(X,cons(X_674,cons(X,nil))))) != X_674
| X_674 = X ),
introduced(tautology,[equality,[$cnf( $equal(head(cons(X_674,cons(X,cons(X_674,cons(X,nil))))),X) ),[0],$fot(X_674)]]) ).
cnf(refute_0_174,plain,
( head(cons(X_674,cons(X,cons(X_674,cons(X,nil))))) != X
| X_674 = X ),
inference(resolve,[$cnf( $equal(head(cons(X_674,cons(X,cons(X_674,cons(X,nil))))),X_674) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
X_674 = X,
inference(resolve,[$cnf( $equal(head(cons(X_674,cons(X,cons(X_674,cons(X,nil))))),X) )],[refute_0_171,refute_0_174]) ).
cnf(refute_0_176,plain,
cons(X,X2) = X,
inference(subst,[],[refute_0_175:[bind(X_674,$fot(cons(X,X2)))]]) ).
cnf(refute_0_177,plain,
( cons(X,X2) != X
| nil != X
| nil = cons(X,X2) ),
introduced(tautology,[equality,[$cnf( ~ $equal(nil,cons(X,X2)) ),[1],$fot(X)]]) ).
cnf(refute_0_178,plain,
( nil != X
| nil = cons(X,X2) ),
inference(resolve,[$cnf( $equal(cons(X,X2),X) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
nil != X,
inference(resolve,[$cnf( $equal(nil,cons(X,X2)) )],[refute_0_178,refute_0_0]) ).
cnf(refute_0_180,plain,
nil != nil,
inference(subst,[],[refute_0_179:[bind(X,$fot(nil))]]) ).
cnf(refute_0_181,plain,
nil = nil,
introduced(tautology,[refl,[$fot(nil)]]) ).
cnf(refute_0_182,plain,
$false,
inference(resolve,[$cnf( $equal(nil,nil) )],[refute_0_181,refute_0_180]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SWX187+1 : TPTP v9.3.0. Released v9.3.0.
% 0.11/0.14 % Command : metis --show proof --show saturation %s
% 0.16/0.35 % Computer : n008.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue May 5 09:39:58 EDT 2026
% 0.16/0.35 % CPUTime :
% 0.20/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 7.03/7.20 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.03/7.20
% 7.03/7.20 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.03/7.23
%------------------------------------------------------------------------------