%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : SWX217+1 : TPTP v9.3.0. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n007.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 07:04:35 PM UTC 2026
% Result : Theorem 1.89s 2.06s
% Output : CNFRefutation 1.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 74
% Number of leaves : 255
% Syntax : Number of formulae : 854 ( 407 unt; 0 def)
% Number of atoms : 1496 (1424 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1286 ( 644 ~; 636 |; 1 &)
% ( 3 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 9 ( 3 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 15 ( 15 usr; 4 con; 0-2 aty)
% Number of variables : 307 ( 1 sgn 64 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(axiom_001,axiom,
! [X,X2] : head(cons(X,X2)) = X ).
fof(axiom_004,axiom,
! [X] : proj1Suc(suc(X)) = X ).
fof(axiom_006,axiom,
i != o ).
fof(axiom_007,axiom,
half(zero) = zero ).
fof(axiom_008,axiom,
half(suc(zero)) = zero ).
fof(axiom_009,axiom,
! [N] : half(suc(suc(N))) = suc(half(N)) ).
fof(axiom_010,axiom,
evenNat(zero) ).
fof(axiom_011,axiom,
! [N] :
( evenNat(suc(N))
<=> ~ evenNat(N) ) ).
fof(axiom_012,axiom,
shw(zero) = nil ).
fof(axiom_013,axiom,
! [Y] :
( evenNat(suc(Y))
=> shw(suc(Y)) = cons(o,shw(half(suc(Y)))) ) ).
fof(axiom_014,axiom,
! [Y] :
( ~ evenNat(suc(Y))
=> shw(suc(Y)) = cons(i,shw(half(suc(Y)))) ) ).
fof(axiom_015,axiom,
! [Y] : append(nil,Y) = Y ).
fof(axiom_016,axiom,
! [Y,Z,Xs] : append(cons(Z,Xs),Y) = cons(Z,append(Xs,Y)) ).
fof(axiom_017,axiom,
! [Y] : addNat(zero,Y) = Y ).
fof(axiom_018,axiom,
! [Y,Z] : addNat(suc(Z),Y) = suc(addNat(Z,Y)) ).
fof(axiom_019,axiom,
! [X] : double(X) = addNat(X,X) ).
fof(axiom_020,axiom,
rd(nil) = zero ).
fof(axiom_021,axiom,
! [Xs] : rd(cons(i,Xs)) = suc(double(rd(Xs))) ).
fof(axiom_022,axiom,
! [Xs] : rd(cons(o,Xs)) = double(rd(Xs)) ).
fof(axiom_023,axiom,
! [X,Y] : x(X,Y) = rd(append(shw(X),shw(Y))) ).
fof(goal_024,conjecture,
? [X,Y] : x(X,Y) != x(Y,X) ).
fof(subgoal_0,plain,
? [X,Y] : x(X,Y) != x(Y,X),
inference(strip,[],[goal_024]) ).
fof(negate_0_0,plain,
~ ? [X,Y] : x(X,Y) != x(Y,X),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,X2] : head(cons(X,X2)) = X,
inference(canonicalize,[],[axiom_001]) ).
fof(normalize_0_1,plain,
! [X,X2] : head(cons(X,X2)) = X,
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [N] :
( ~ evenNat(N)
<=> evenNat(suc(N)) ),
inference(canonicalize,[],[axiom_011]) ).
fof(normalize_0_3,plain,
! [N] :
( ~ evenNat(N)
<=> evenNat(suc(N)) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [N] :
( ( ~ evenNat(N)
| ~ evenNat(suc(N)) )
& ( evenNat(N)
| evenNat(suc(N)) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [N] :
( evenNat(N)
| evenNat(suc(N)) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X] : double(X) = addNat(X,X),
inference(canonicalize,[],[axiom_019]) ).
fof(normalize_0_7,plain,
! [X] : double(X) = addNat(X,X),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [Y,Z] : addNat(suc(Z),Y) = suc(addNat(Z,Y)),
inference(canonicalize,[],[axiom_018]) ).
fof(normalize_0_9,plain,
! [Y,Z] : addNat(suc(Z),Y) = suc(addNat(Z,Y)),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [Y] : addNat(zero,Y) = Y,
inference(canonicalize,[],[axiom_017]) ).
fof(normalize_0_11,plain,
! [Y] : addNat(zero,Y) = Y,
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [Y] :
( ~ evenNat(suc(Y))
| shw(suc(Y)) = cons(o,shw(half(suc(Y)))) ),
inference(canonicalize,[],[axiom_013]) ).
fof(normalize_0_13,plain,
! [Y] :
( ~ evenNat(suc(Y))
| shw(suc(Y)) = cons(o,shw(half(suc(Y)))) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
half(zero) = zero,
inference(canonicalize,[],[axiom_007]) ).
fof(normalize_0_15,plain,
! [N] : half(suc(suc(N))) = suc(half(N)),
inference(canonicalize,[],[axiom_009]) ).
fof(normalize_0_16,plain,
! [N] : half(suc(suc(N))) = suc(half(N)),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [N] :
( ~ evenNat(N)
| ~ evenNat(suc(N)) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_18,plain,
! [Xs] : rd(cons(i,Xs)) = suc(double(rd(Xs))),
inference(canonicalize,[],[axiom_021]) ).
fof(normalize_0_19,plain,
! [Xs] : rd(cons(i,Xs)) = suc(double(rd(Xs))),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
rd(nil) = zero,
inference(canonicalize,[],[axiom_020]) ).
fof(normalize_0_21,plain,
evenNat(zero),
inference(canonicalize,[],[axiom_010]) ).
fof(normalize_0_22,plain,
! [Y] :
( shw(suc(Y)) = cons(i,shw(half(suc(Y))))
| evenNat(suc(Y)) ),
inference(canonicalize,[],[axiom_014]) ).
fof(normalize_0_23,plain,
! [Y] :
( shw(suc(Y)) = cons(i,shw(half(suc(Y))))
| evenNat(suc(Y)) ),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
half(suc(zero)) = zero,
inference(canonicalize,[],[axiom_008]) ).
fof(normalize_0_25,plain,
shw(zero) = nil,
inference(canonicalize,[],[axiom_012]) ).
fof(normalize_0_26,plain,
! [X] : proj1Suc(suc(X)) = X,
inference(canonicalize,[],[axiom_004]) ).
fof(normalize_0_27,plain,
! [X] : proj1Suc(suc(X)) = X,
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [X,Y] : x(X,Y) = rd(append(shw(X),shw(Y))),
inference(canonicalize,[],[axiom_023]) ).
fof(normalize_0_29,plain,
! [X,Y] : x(X,Y) = rd(append(shw(X),shw(Y))),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [Xs,Y,Z] : append(cons(Z,Xs),Y) = cons(Z,append(Xs,Y)),
inference(canonicalize,[],[axiom_016]) ).
fof(normalize_0_31,plain,
! [Xs,Y,Z] : append(cons(Z,Xs),Y) = cons(Z,append(Xs,Y)),
inference(specialize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [Y] : append(nil,Y) = Y,
inference(canonicalize,[],[axiom_015]) ).
fof(normalize_0_33,plain,
! [Y] : append(nil,Y) = Y,
inference(specialize,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [X,Y] : x(X,Y) = x(Y,X),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_35,plain,
! [X,Y] : x(X,Y) = x(Y,X),
inference(specialize,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
! [Xs] : rd(cons(o,Xs)) = double(rd(Xs)),
inference(canonicalize,[],[axiom_022]) ).
fof(normalize_0_37,plain,
! [Xs] : rd(cons(o,Xs)) = double(rd(Xs)),
inference(specialize,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
i != o,
inference(canonicalize,[],[axiom_006]) ).
cnf(refute_0_0,plain,
head(cons(X,X2)) = X,
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
head(cons(o,shw(suc(zero)))) = o,
inference(subst,[],[refute_0_0:[bind(X,$fot(o)),bind(X2,$fot(shw(suc(zero))))]]) ).
cnf(refute_0_2,plain,
( evenNat(N)
| evenNat(suc(N)) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( evenNat(suc(suc(zero)))
| evenNat(suc(zero)) ),
inference(subst,[],[refute_0_2:[bind(N,$fot(suc(zero)))]]) ).
cnf(refute_0_4,plain,
double(X) = addNat(X,X),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
double(suc(X_21)) = addNat(suc(X_21),suc(X_21)),
inference(subst,[],[refute_0_4:[bind(X,$fot(suc(X_21)))]]) ).
cnf(refute_0_6,plain,
addNat(suc(Z),Y) = suc(addNat(Z,Y)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
addNat(suc(X_21),suc(X_21)) = suc(addNat(X_21,suc(X_21))),
inference(subst,[],[refute_0_6:[bind(Y,$fot(suc(X_21))),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_8,plain,
( addNat(suc(X_21),suc(X_21)) != suc(addNat(X_21,suc(X_21)))
| double(suc(X_21)) != addNat(suc(X_21),suc(X_21))
| double(suc(X_21)) = suc(addNat(X_21,suc(X_21))) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(X_21)),addNat(suc(X_21),suc(X_21))) ),[1],$fot(suc(addNat(X_21,suc(X_21))))]]) ).
cnf(refute_0_9,plain,
( double(suc(X_21)) != addNat(suc(X_21),suc(X_21))
| double(suc(X_21)) = suc(addNat(X_21,suc(X_21))) ),
inference(resolve,[$cnf( $equal(addNat(suc(X_21),suc(X_21)),suc(addNat(X_21,suc(X_21)))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
double(suc(X_21)) = suc(addNat(X_21,suc(X_21))),
inference(resolve,[$cnf( $equal(double(suc(X_21)),addNat(suc(X_21),suc(X_21))) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
double(suc(zero)) = suc(addNat(zero,suc(zero))),
inference(subst,[],[refute_0_10:[bind(X_21,$fot(zero))]]) ).
cnf(refute_0_12,plain,
addNat(zero,Y) = Y,
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_13,plain,
addNat(zero,suc(zero)) = suc(zero),
inference(subst,[],[refute_0_12:[bind(Y,$fot(suc(zero)))]]) ).
cnf(refute_0_14,plain,
( addNat(zero,suc(zero)) != suc(zero)
| double(suc(zero)) != suc(addNat(zero,suc(zero)))
| double(suc(zero)) = suc(suc(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(zero)),suc(addNat(zero,suc(zero)))) ),[1,0],$fot(suc(zero))]]) ).
cnf(refute_0_15,plain,
( double(suc(zero)) != suc(addNat(zero,suc(zero)))
| double(suc(zero)) = suc(suc(zero)) ),
inference(resolve,[$cnf( $equal(addNat(zero,suc(zero)),suc(zero)) )],[refute_0_13,refute_0_14]) ).
cnf(refute_0_16,plain,
double(suc(zero)) = suc(suc(zero)),
inference(resolve,[$cnf( $equal(double(suc(zero)),suc(addNat(zero,suc(zero)))) )],[refute_0_11,refute_0_15]) ).
cnf(refute_0_17,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_18,plain,
( X0 != X0
| X0 != Y0
| Y0 = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y0)]]) ).
cnf(refute_0_19,plain,
( X0 != Y0
| Y0 = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( double(suc(zero)) != suc(suc(zero))
| suc(suc(zero)) = double(suc(zero)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(double(suc(zero)))),bind(Y0,$fot(suc(suc(zero))))]]) ).
cnf(refute_0_21,plain,
suc(suc(zero)) = double(suc(zero)),
inference(resolve,[$cnf( $equal(double(suc(zero)),suc(suc(zero))) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
( suc(suc(zero)) != double(suc(zero))
| ~ evenNat(suc(suc(zero)))
| evenNat(double(suc(zero))) ),
introduced(tautology,[equality,[$cnf( evenNat(suc(suc(zero))) ),[0],$fot(double(suc(zero)))]]) ).
cnf(refute_0_23,plain,
( ~ evenNat(suc(suc(zero)))
| evenNat(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(suc(suc(zero)),double(suc(zero))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
( evenNat(double(suc(zero)))
| evenNat(suc(zero)) ),
inference(resolve,[$cnf( evenNat(suc(suc(zero))) )],[refute_0_3,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ evenNat(suc(Y))
| shw(suc(Y)) = cons(o,shw(half(suc(Y)))) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_26,plain,
( ~ evenNat(suc(suc(zero)))
| shw(suc(suc(zero))) = cons(o,shw(half(suc(suc(zero))))) ),
inference(subst,[],[refute_0_25:[bind(Y,$fot(suc(zero)))]]) ).
cnf(refute_0_27,plain,
( suc(suc(zero)) != double(suc(zero))
| ~ evenNat(double(suc(zero)))
| evenNat(suc(suc(zero))) ),
introduced(tautology,[equality,[$cnf( ~ evenNat(suc(suc(zero))) ),[0],$fot(double(suc(zero)))]]) ).
cnf(refute_0_28,plain,
( ~ evenNat(double(suc(zero)))
| evenNat(suc(suc(zero))) ),
inference(resolve,[$cnf( $equal(suc(suc(zero)),double(suc(zero))) )],[refute_0_21,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ evenNat(double(suc(zero)))
| shw(suc(suc(zero))) = cons(o,shw(half(suc(suc(zero))))) ),
inference(resolve,[$cnf( evenNat(suc(suc(zero))) )],[refute_0_28,refute_0_26]) ).
cnf(refute_0_30,plain,
shw(suc(suc(zero))) = shw(suc(suc(zero))),
introduced(tautology,[refl,[$fot(shw(suc(suc(zero))))]]) ).
cnf(refute_0_31,plain,
( shw(suc(suc(zero))) != shw(suc(suc(zero)))
| suc(suc(zero)) != double(suc(zero))
| shw(suc(suc(zero))) = shw(double(suc(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(shw(suc(suc(zero))),shw(suc(suc(zero)))) ),[1,0],$fot(double(suc(zero)))]]) ).
cnf(refute_0_32,plain,
( suc(suc(zero)) != double(suc(zero))
| shw(suc(suc(zero))) = shw(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(shw(suc(suc(zero))),shw(suc(suc(zero)))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
shw(suc(suc(zero))) = shw(double(suc(zero))),
inference(resolve,[$cnf( $equal(suc(suc(zero)),double(suc(zero))) )],[refute_0_21,refute_0_32]) ).
cnf(refute_0_34,plain,
( shw(suc(suc(zero))) != cons(o,shw(half(suc(suc(zero)))))
| shw(suc(suc(zero))) != shw(double(suc(zero)))
| shw(double(suc(zero))) = cons(o,shw(half(suc(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(shw(suc(suc(zero))),cons(o,shw(half(suc(suc(zero)))))) ),[0],$fot(shw(double(suc(zero))))]]) ).
cnf(refute_0_35,plain,
( shw(suc(suc(zero))) != cons(o,shw(half(suc(suc(zero)))))
| shw(double(suc(zero))) = cons(o,shw(half(suc(suc(zero))))) ),
inference(resolve,[$cnf( $equal(shw(suc(suc(zero))),shw(double(suc(zero)))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
half(zero) = zero,
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_37,plain,
suc(half(zero)) = suc(half(zero)),
introduced(tautology,[refl,[$fot(suc(half(zero)))]]) ).
cnf(refute_0_38,plain,
( half(zero) != zero
| suc(half(zero)) != suc(half(zero))
| suc(half(zero)) = suc(zero) ),
introduced(tautology,[equality,[$cnf( $equal(suc(half(zero)),suc(half(zero))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_39,plain,
( half(zero) != zero
| suc(half(zero)) = suc(zero) ),
inference(resolve,[$cnf( $equal(suc(half(zero)),suc(half(zero))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
suc(half(zero)) = suc(zero),
inference(resolve,[$cnf( $equal(half(zero),zero) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
half(suc(suc(N))) = suc(half(N)),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_42,plain,
half(suc(suc(zero))) = suc(half(zero)),
inference(subst,[],[refute_0_41:[bind(N,$fot(zero))]]) ).
cnf(refute_0_43,plain,
( Y0 != X0
| Y0 != Z0
| X0 = Z0 ),
introduced(tautology,[equality,[$cnf( $equal(Y0,Z0) ),[0],$fot(X0)]]) ).
cnf(refute_0_44,plain,
( X0 != Y0
| Y0 != Z0
| X0 = Z0 ),
inference(resolve,[$cnf( $equal(Y0,X0) )],[refute_0_19,refute_0_43]) ).
cnf(refute_0_45,plain,
( half(suc(suc(zero))) != suc(half(zero))
| suc(half(zero)) != suc(zero)
| half(suc(suc(zero))) = suc(zero) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(half(suc(suc(zero))))),bind(Y0,$fot(suc(half(zero)))),bind(Z0,$fot(suc(zero)))]]) ).
cnf(refute_0_46,plain,
( suc(half(zero)) != suc(zero)
| half(suc(suc(zero))) = suc(zero) ),
inference(resolve,[$cnf( $equal(half(suc(suc(zero))),suc(half(zero))) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
half(suc(suc(zero))) = suc(zero),
inference(resolve,[$cnf( $equal(suc(half(zero)),suc(zero)) )],[refute_0_40,refute_0_46]) ).
cnf(refute_0_48,plain,
shw(half(suc(suc(zero)))) = shw(half(suc(suc(zero)))),
introduced(tautology,[refl,[$fot(shw(half(suc(suc(zero)))))]]) ).
cnf(refute_0_49,plain,
( half(suc(suc(zero))) != suc(zero)
| shw(half(suc(suc(zero)))) != shw(half(suc(suc(zero))))
| shw(half(suc(suc(zero)))) = shw(suc(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(shw(half(suc(suc(zero)))),shw(half(suc(suc(zero))))) ),[1,0],$fot(suc(zero))]]) ).
cnf(refute_0_50,plain,
( half(suc(suc(zero))) != suc(zero)
| shw(half(suc(suc(zero)))) = shw(suc(zero)) ),
inference(resolve,[$cnf( $equal(shw(half(suc(suc(zero)))),shw(half(suc(suc(zero))))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
shw(half(suc(suc(zero)))) = shw(suc(zero)),
inference(resolve,[$cnf( $equal(half(suc(suc(zero))),suc(zero)) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
cons(o,shw(half(suc(suc(zero))))) = cons(o,shw(half(suc(suc(zero))))),
introduced(tautology,[refl,[$fot(cons(o,shw(half(suc(suc(zero))))))]]) ).
cnf(refute_0_53,plain,
( cons(o,shw(half(suc(suc(zero))))) != cons(o,shw(half(suc(suc(zero)))))
| shw(half(suc(suc(zero)))) != shw(suc(zero))
| cons(o,shw(half(suc(suc(zero))))) = cons(o,shw(suc(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(cons(o,shw(half(suc(suc(zero))))),cons(o,shw(half(suc(suc(zero)))))) ),[1,1],$fot(shw(suc(zero)))]]) ).
cnf(refute_0_54,plain,
( shw(half(suc(suc(zero)))) != shw(suc(zero))
| cons(o,shw(half(suc(suc(zero))))) = cons(o,shw(suc(zero))) ),
inference(resolve,[$cnf( $equal(cons(o,shw(half(suc(suc(zero))))),cons(o,shw(half(suc(suc(zero)))))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
cons(o,shw(half(suc(suc(zero))))) = cons(o,shw(suc(zero))),
inference(resolve,[$cnf( $equal(shw(half(suc(suc(zero)))),shw(suc(zero))) )],[refute_0_51,refute_0_54]) ).
cnf(refute_0_56,plain,
( cons(o,shw(half(suc(suc(zero))))) != cons(o,shw(suc(zero)))
| shw(double(suc(zero))) != cons(o,shw(half(suc(suc(zero)))))
| shw(double(suc(zero))) = cons(o,shw(suc(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(shw(double(suc(zero))),cons(o,shw(half(suc(suc(zero)))))) ),[1],$fot(cons(o,shw(suc(zero))))]]) ).
cnf(refute_0_57,plain,
( shw(double(suc(zero))) != cons(o,shw(half(suc(suc(zero)))))
| shw(double(suc(zero))) = cons(o,shw(suc(zero))) ),
inference(resolve,[$cnf( $equal(cons(o,shw(half(suc(suc(zero))))),cons(o,shw(suc(zero)))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
( shw(suc(suc(zero))) != cons(o,shw(half(suc(suc(zero)))))
| shw(double(suc(zero))) = cons(o,shw(suc(zero))) ),
inference(resolve,[$cnf( $equal(shw(double(suc(zero))),cons(o,shw(half(suc(suc(zero)))))) )],[refute_0_35,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ evenNat(double(suc(zero)))
| shw(double(suc(zero))) = cons(o,shw(suc(zero))) ),
inference(resolve,[$cnf( $equal(shw(suc(suc(zero))),cons(o,shw(half(suc(suc(zero)))))) )],[refute_0_29,refute_0_58]) ).
cnf(refute_0_60,plain,
( shw(double(suc(zero))) = cons(o,shw(suc(zero)))
| evenNat(suc(zero)) ),
inference(resolve,[$cnf( evenNat(double(suc(zero))) )],[refute_0_24,refute_0_59]) ).
cnf(refute_0_61,plain,
( ~ evenNat(N)
| ~ evenNat(suc(N)) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_62,plain,
( ~ evenNat(double(rd(Xs)))
| ~ evenNat(suc(double(rd(Xs)))) ),
inference(subst,[],[refute_0_61:[bind(N,$fot(double(rd(Xs))))]]) ).
cnf(refute_0_63,plain,
rd(cons(i,Xs)) = suc(double(rd(Xs))),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_64,plain,
( rd(cons(i,Xs)) != suc(double(rd(Xs)))
| suc(double(rd(Xs))) = rd(cons(i,Xs)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(rd(cons(i,Xs)))),bind(Y0,$fot(suc(double(rd(Xs)))))]]) ).
cnf(refute_0_65,plain,
suc(double(rd(Xs))) = rd(cons(i,Xs)),
inference(resolve,[$cnf( $equal(rd(cons(i,Xs)),suc(double(rd(Xs)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( suc(double(rd(Xs))) != rd(cons(i,Xs))
| ~ evenNat(rd(cons(i,Xs)))
| evenNat(suc(double(rd(Xs)))) ),
introduced(tautology,[equality,[$cnf( ~ evenNat(suc(double(rd(Xs)))) ),[0],$fot(rd(cons(i,Xs)))]]) ).
cnf(refute_0_67,plain,
( ~ evenNat(rd(cons(i,Xs)))
| evenNat(suc(double(rd(Xs)))) ),
inference(resolve,[$cnf( $equal(suc(double(rd(Xs))),rd(cons(i,Xs))) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ evenNat(double(rd(Xs)))
| ~ evenNat(rd(cons(i,Xs))) ),
inference(resolve,[$cnf( evenNat(suc(double(rd(Xs)))) )],[refute_0_67,refute_0_62]) ).
cnf(refute_0_69,plain,
( ~ evenNat(double(rd(nil)))
| ~ evenNat(rd(cons(i,nil))) ),
inference(subst,[],[refute_0_68:[bind(Xs,$fot(nil))]]) ).
cnf(refute_0_70,plain,
rd(cons(i,nil)) = suc(double(rd(nil))),
inference(subst,[],[refute_0_63:[bind(Xs,$fot(nil))]]) ).
cnf(refute_0_71,plain,
rd(nil) = zero,
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_72,plain,
( rd(cons(i,nil)) != suc(double(rd(nil)))
| rd(nil) != zero
| rd(cons(i,nil)) = suc(double(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(rd(cons(i,nil)),suc(double(rd(nil)))) ),[1,0,0],$fot(zero)]]) ).
cnf(refute_0_73,plain,
( rd(cons(i,nil)) != suc(double(rd(nil)))
| rd(cons(i,nil)) = suc(double(zero)) ),
inference(resolve,[$cnf( $equal(rd(nil),zero) )],[refute_0_71,refute_0_72]) ).
cnf(refute_0_74,plain,
rd(cons(i,nil)) = suc(double(zero)),
inference(resolve,[$cnf( $equal(rd(cons(i,nil)),suc(double(rd(nil)))) )],[refute_0_70,refute_0_73]) ).
cnf(refute_0_75,plain,
addNat(zero,zero) = zero,
inference(subst,[],[refute_0_12:[bind(Y,$fot(zero))]]) ).
cnf(refute_0_76,plain,
double(zero) = addNat(zero,zero),
inference(subst,[],[refute_0_4:[bind(X,$fot(zero))]]) ).
cnf(refute_0_77,plain,
( double(zero) != addNat(zero,zero)
| addNat(zero,zero) = double(zero) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(double(zero))),bind(Y0,$fot(addNat(zero,zero)))]]) ).
cnf(refute_0_78,plain,
addNat(zero,zero) = double(zero),
inference(resolve,[$cnf( $equal(double(zero),addNat(zero,zero)) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( addNat(zero,zero) != double(zero)
| addNat(zero,zero) != zero
| double(zero) = zero ),
introduced(tautology,[equality,[$cnf( $equal(addNat(zero,zero),zero) ),[0],$fot(double(zero))]]) ).
cnf(refute_0_80,plain,
( addNat(zero,zero) != zero
| double(zero) = zero ),
inference(resolve,[$cnf( $equal(addNat(zero,zero),double(zero)) )],[refute_0_78,refute_0_79]) ).
cnf(refute_0_81,plain,
double(zero) = zero,
inference(resolve,[$cnf( $equal(addNat(zero,zero),zero) )],[refute_0_75,refute_0_80]) ).
cnf(refute_0_82,plain,
suc(double(zero)) = suc(double(zero)),
introduced(tautology,[refl,[$fot(suc(double(zero)))]]) ).
cnf(refute_0_83,plain,
( double(zero) != zero
| suc(double(zero)) != suc(double(zero))
| suc(double(zero)) = suc(zero) ),
introduced(tautology,[equality,[$cnf( $equal(suc(double(zero)),suc(double(zero))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_84,plain,
( double(zero) != zero
| suc(double(zero)) = suc(zero) ),
inference(resolve,[$cnf( $equal(suc(double(zero)),suc(double(zero))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
suc(double(zero)) = suc(zero),
inference(resolve,[$cnf( $equal(double(zero),zero) )],[refute_0_81,refute_0_84]) ).
cnf(refute_0_86,plain,
( rd(cons(i,nil)) != suc(double(zero))
| suc(double(zero)) != suc(zero)
| rd(cons(i,nil)) = suc(zero) ),
introduced(tautology,[equality,[$cnf( ~ $equal(rd(cons(i,nil)),suc(zero)) ),[0],$fot(suc(double(zero)))]]) ).
cnf(refute_0_87,plain,
( rd(cons(i,nil)) != suc(double(zero))
| rd(cons(i,nil)) = suc(zero) ),
inference(resolve,[$cnf( $equal(suc(double(zero)),suc(zero)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
rd(cons(i,nil)) = suc(zero),
inference(resolve,[$cnf( $equal(rd(cons(i,nil)),suc(double(zero))) )],[refute_0_74,refute_0_87]) ).
cnf(refute_0_89,plain,
( rd(cons(i,nil)) != suc(zero)
| ~ evenNat(suc(zero))
| evenNat(rd(cons(i,nil))) ),
introduced(tautology,[equality,[$cnf( ~ evenNat(rd(cons(i,nil))) ),[0],$fot(suc(zero))]]) ).
cnf(refute_0_90,plain,
( ~ evenNat(suc(zero))
| evenNat(rd(cons(i,nil))) ),
inference(resolve,[$cnf( $equal(rd(cons(i,nil)),suc(zero)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
( ~ evenNat(double(rd(nil)))
| ~ evenNat(suc(zero)) ),
inference(resolve,[$cnf( evenNat(rd(cons(i,nil))) )],[refute_0_90,refute_0_69]) ).
cnf(refute_0_92,plain,
double(rd(nil)) = double(rd(nil)),
introduced(tautology,[refl,[$fot(double(rd(nil)))]]) ).
cnf(refute_0_93,plain,
( double(rd(nil)) != double(rd(nil))
| rd(nil) != zero
| double(rd(nil)) = double(zero) ),
introduced(tautology,[equality,[$cnf( $equal(double(rd(nil)),double(rd(nil))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_94,plain,
( rd(nil) != zero
| double(rd(nil)) = double(zero) ),
inference(resolve,[$cnf( $equal(double(rd(nil)),double(rd(nil))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
double(rd(nil)) = double(zero),
inference(resolve,[$cnf( $equal(rd(nil),zero) )],[refute_0_71,refute_0_94]) ).
cnf(refute_0_96,plain,
( double(rd(nil)) != double(zero)
| double(zero) != zero
| double(rd(nil)) = zero ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(double(rd(nil)))),bind(Y0,$fot(double(zero))),bind(Z0,$fot(zero))]]) ).
cnf(refute_0_97,plain,
( double(zero) != zero
| double(rd(nil)) = zero ),
inference(resolve,[$cnf( $equal(double(rd(nil)),double(zero)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
double(rd(nil)) = zero,
inference(resolve,[$cnf( $equal(double(zero),zero) )],[refute_0_81,refute_0_97]) ).
cnf(refute_0_99,plain,
( double(rd(nil)) != zero
| ~ evenNat(zero)
| evenNat(double(rd(nil))) ),
introduced(tautology,[equality,[$cnf( ~ evenNat(double(rd(nil))) ),[0],$fot(zero)]]) ).
cnf(refute_0_100,plain,
( ~ evenNat(zero)
| evenNat(double(rd(nil))) ),
inference(resolve,[$cnf( $equal(double(rd(nil)),zero) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
( ~ evenNat(suc(zero))
| ~ evenNat(zero) ),
inference(resolve,[$cnf( evenNat(double(rd(nil))) )],[refute_0_100,refute_0_91]) ).
cnf(refute_0_102,plain,
evenNat(zero),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_103,plain,
~ evenNat(suc(zero)),
inference(resolve,[$cnf( evenNat(zero) )],[refute_0_102,refute_0_101]) ).
cnf(refute_0_104,plain,
shw(double(suc(zero))) = cons(o,shw(suc(zero))),
inference(resolve,[$cnf( evenNat(suc(zero)) )],[refute_0_60,refute_0_103]) ).
cnf(refute_0_105,plain,
( shw(double(suc(zero))) != cons(o,shw(suc(zero)))
| cons(o,shw(suc(zero))) = shw(double(suc(zero))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(shw(double(suc(zero))))),bind(Y0,$fot(cons(o,shw(suc(zero)))))]]) ).
cnf(refute_0_106,plain,
cons(o,shw(suc(zero))) = shw(double(suc(zero))),
inference(resolve,[$cnf( $equal(shw(double(suc(zero))),cons(o,shw(suc(zero)))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
( cons(o,shw(suc(zero))) != shw(double(suc(zero)))
| head(cons(o,shw(suc(zero)))) != o
| head(shw(double(suc(zero)))) = o ),
introduced(tautology,[equality,[$cnf( $equal(head(cons(o,shw(suc(zero)))),o) ),[0,0],$fot(shw(double(suc(zero))))]]) ).
cnf(refute_0_108,plain,
( head(cons(o,shw(suc(zero)))) != o
| head(shw(double(suc(zero)))) = o ),
inference(resolve,[$cnf( $equal(cons(o,shw(suc(zero))),shw(double(suc(zero)))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
head(shw(double(suc(zero)))) = o,
inference(resolve,[$cnf( $equal(head(cons(o,shw(suc(zero)))),o) )],[refute_0_1,refute_0_108]) ).
cnf(refute_0_110,plain,
head(cons(i,nil)) = i,
inference(subst,[],[refute_0_0:[bind(X,$fot(i)),bind(X2,$fot(nil))]]) ).
cnf(refute_0_111,plain,
( shw(suc(Y)) = cons(i,shw(half(suc(Y))))
| evenNat(suc(Y)) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_112,plain,
( shw(suc(zero)) = cons(i,shw(half(suc(zero))))
| evenNat(suc(zero)) ),
inference(subst,[],[refute_0_111:[bind(Y,$fot(zero))]]) ).
cnf(refute_0_113,plain,
half(suc(zero)) = zero,
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_114,plain,
( half(suc(zero)) != zero
| shw(suc(zero)) != cons(i,shw(half(suc(zero))))
| shw(suc(zero)) = cons(i,shw(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(shw(suc(zero)),cons(i,shw(half(suc(zero))))) ),[1,1,0],$fot(zero)]]) ).
cnf(refute_0_115,plain,
( shw(suc(zero)) != cons(i,shw(half(suc(zero))))
| shw(suc(zero)) = cons(i,shw(zero)) ),
inference(resolve,[$cnf( $equal(half(suc(zero)),zero) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
( shw(suc(zero)) = cons(i,shw(zero))
| evenNat(suc(zero)) ),
inference(resolve,[$cnf( $equal(shw(suc(zero)),cons(i,shw(half(suc(zero))))) )],[refute_0_112,refute_0_115]) ).
cnf(refute_0_117,plain,
shw(zero) = nil,
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_118,plain,
cons(i,shw(zero)) = cons(i,shw(zero)),
introduced(tautology,[refl,[$fot(cons(i,shw(zero)))]]) ).
cnf(refute_0_119,plain,
( cons(i,shw(zero)) != cons(i,shw(zero))
| shw(zero) != nil
| cons(i,shw(zero)) = cons(i,nil) ),
introduced(tautology,[equality,[$cnf( $equal(cons(i,shw(zero)),cons(i,shw(zero))) ),[1,1],$fot(nil)]]) ).
cnf(refute_0_120,plain,
( shw(zero) != nil
| cons(i,shw(zero)) = cons(i,nil) ),
inference(resolve,[$cnf( $equal(cons(i,shw(zero)),cons(i,shw(zero))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
cons(i,shw(zero)) = cons(i,nil),
inference(resolve,[$cnf( $equal(shw(zero),nil) )],[refute_0_117,refute_0_120]) ).
cnf(refute_0_122,plain,
( cons(i,shw(zero)) != cons(i,nil)
| shw(suc(zero)) != cons(i,shw(zero))
| shw(suc(zero)) = cons(i,nil) ),
introduced(tautology,[equality,[$cnf( $equal(shw(suc(zero)),cons(i,shw(zero))) ),[1],$fot(cons(i,nil))]]) ).
cnf(refute_0_123,plain,
( shw(suc(zero)) != cons(i,shw(zero))
| shw(suc(zero)) = cons(i,nil) ),
inference(resolve,[$cnf( $equal(cons(i,shw(zero)),cons(i,nil)) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
( shw(suc(zero)) = cons(i,nil)
| evenNat(suc(zero)) ),
inference(resolve,[$cnf( $equal(shw(suc(zero)),cons(i,shw(zero))) )],[refute_0_116,refute_0_123]) ).
cnf(refute_0_125,plain,
shw(suc(zero)) = cons(i,nil),
inference(resolve,[$cnf( evenNat(suc(zero)) )],[refute_0_124,refute_0_103]) ).
cnf(refute_0_126,plain,
( shw(suc(zero)) != cons(i,nil)
| cons(i,nil) = shw(suc(zero)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(shw(suc(zero)))),bind(Y0,$fot(cons(i,nil)))]]) ).
cnf(refute_0_127,plain,
cons(i,nil) = shw(suc(zero)),
inference(resolve,[$cnf( $equal(shw(suc(zero)),cons(i,nil)) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
( cons(i,nil) != shw(suc(zero))
| head(cons(i,nil)) != i
| head(shw(suc(zero))) = i ),
introduced(tautology,[equality,[$cnf( $equal(head(cons(i,nil)),i) ),[0,0],$fot(shw(suc(zero)))]]) ).
cnf(refute_0_129,plain,
( head(cons(i,nil)) != i
| head(shw(suc(zero))) = i ),
inference(resolve,[$cnf( $equal(cons(i,nil),shw(suc(zero))) )],[refute_0_127,refute_0_128]) ).
cnf(refute_0_130,plain,
head(shw(suc(zero))) = i,
inference(resolve,[$cnf( $equal(head(cons(i,nil)),i) )],[refute_0_110,refute_0_129]) ).
cnf(refute_0_131,plain,
proj1Suc(suc(X)) = X,
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_132,plain,
proj1Suc(suc(suc(zero))) = suc(zero),
inference(subst,[],[refute_0_131:[bind(X,$fot(suc(zero)))]]) ).
cnf(refute_0_133,plain,
( proj1Suc(suc(suc(zero))) != suc(zero)
| suc(suc(zero)) != double(suc(zero))
| proj1Suc(double(suc(zero))) = suc(zero) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(suc(suc(zero))),suc(zero)) ),[0,0],$fot(double(suc(zero)))]]) ).
cnf(refute_0_134,plain,
( proj1Suc(suc(suc(zero))) != suc(zero)
| proj1Suc(double(suc(zero))) = suc(zero) ),
inference(resolve,[$cnf( $equal(suc(suc(zero)),double(suc(zero))) )],[refute_0_21,refute_0_133]) ).
cnf(refute_0_135,plain,
proj1Suc(double(suc(zero))) = suc(zero),
inference(resolve,[$cnf( $equal(proj1Suc(suc(suc(zero))),suc(zero)) )],[refute_0_132,refute_0_134]) ).
cnf(refute_0_136,plain,
proj1Suc(suc(zero)) = zero,
inference(subst,[],[refute_0_131:[bind(X,$fot(zero))]]) ).
cnf(refute_0_137,plain,
half(suc(suc(suc(zero)))) = suc(half(suc(zero))),
inference(subst,[],[refute_0_41:[bind(N,$fot(suc(zero)))]]) ).
cnf(refute_0_138,plain,
( half(suc(suc(suc(zero)))) != suc(half(suc(zero)))
| suc(suc(zero)) != double(suc(zero))
| half(suc(double(suc(zero)))) = suc(half(suc(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(half(suc(suc(suc(zero)))),suc(half(suc(zero)))) ),[0,0,0],$fot(double(suc(zero)))]]) ).
cnf(refute_0_139,plain,
( half(suc(suc(suc(zero)))) != suc(half(suc(zero)))
| half(suc(double(suc(zero)))) = suc(half(suc(zero))) ),
inference(resolve,[$cnf( $equal(suc(suc(zero)),double(suc(zero))) )],[refute_0_21,refute_0_138]) ).
cnf(refute_0_140,plain,
half(suc(double(suc(zero)))) = suc(half(suc(zero))),
inference(resolve,[$cnf( $equal(half(suc(suc(suc(zero)))),suc(half(suc(zero)))) )],[refute_0_137,refute_0_139]) ).
cnf(refute_0_141,plain,
suc(half(suc(zero))) = suc(half(suc(zero))),
introduced(tautology,[refl,[$fot(suc(half(suc(zero))))]]) ).
cnf(refute_0_142,plain,
( half(suc(zero)) != zero
| suc(half(suc(zero))) != suc(half(suc(zero)))
| suc(half(suc(zero))) = suc(zero) ),
introduced(tautology,[equality,[$cnf( $equal(suc(half(suc(zero))),suc(half(suc(zero)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_143,plain,
( half(suc(zero)) != zero
| suc(half(suc(zero))) = suc(zero) ),
inference(resolve,[$cnf( $equal(suc(half(suc(zero))),suc(half(suc(zero)))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
suc(half(suc(zero))) = suc(zero),
inference(resolve,[$cnf( $equal(half(suc(zero)),zero) )],[refute_0_113,refute_0_143]) ).
cnf(refute_0_145,plain,
( half(suc(double(suc(zero)))) != suc(half(suc(zero)))
| suc(half(suc(zero))) != suc(zero)
| half(suc(double(suc(zero)))) = suc(zero) ),
introduced(tautology,[equality,[$cnf( ~ $equal(half(suc(double(suc(zero)))),suc(zero)) ),[0],$fot(suc(half(suc(zero))))]]) ).
cnf(refute_0_146,plain,
( half(suc(double(suc(zero)))) != suc(half(suc(zero)))
| half(suc(double(suc(zero)))) = suc(zero) ),
inference(resolve,[$cnf( $equal(suc(half(suc(zero))),suc(zero)) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
half(suc(double(suc(zero)))) = suc(zero),
inference(resolve,[$cnf( $equal(half(suc(double(suc(zero)))),suc(half(suc(zero)))) )],[refute_0_140,refute_0_146]) ).
cnf(refute_0_148,plain,
half(suc(suc(double(suc(zero))))) = suc(half(double(suc(zero)))),
inference(subst,[],[refute_0_41:[bind(N,$fot(double(suc(zero))))]]) ).
cnf(refute_0_149,plain,
double(double(suc(zero))) = addNat(double(suc(zero)),double(suc(zero))),
inference(subst,[],[refute_0_4:[bind(X,$fot(double(suc(zero))))]]) ).
cnf(refute_0_150,plain,
addNat(suc(suc(zero)),Y) = suc(addNat(suc(zero),Y)),
inference(subst,[],[refute_0_6:[bind(Z,$fot(suc(zero)))]]) ).
cnf(refute_0_151,plain,
( addNat(suc(suc(zero)),Y) != suc(addNat(suc(zero),Y))
| suc(suc(zero)) != double(suc(zero))
| addNat(double(suc(zero)),Y) = suc(addNat(suc(zero),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(addNat(suc(suc(zero)),Y),suc(addNat(suc(zero),Y))) ),[0,0],$fot(double(suc(zero)))]]) ).
cnf(refute_0_152,plain,
( addNat(suc(suc(zero)),Y) != suc(addNat(suc(zero),Y))
| addNat(double(suc(zero)),Y) = suc(addNat(suc(zero),Y)) ),
inference(resolve,[$cnf( $equal(suc(suc(zero)),double(suc(zero))) )],[refute_0_21,refute_0_151]) ).
cnf(refute_0_153,plain,
addNat(double(suc(zero)),Y) = suc(addNat(suc(zero),Y)),
inference(resolve,[$cnf( $equal(addNat(suc(suc(zero)),Y),suc(addNat(suc(zero),Y))) )],[refute_0_150,refute_0_152]) ).
cnf(refute_0_154,plain,
suc(addNat(zero,Y)) = suc(addNat(zero,Y)),
introduced(tautology,[refl,[$fot(suc(addNat(zero,Y)))]]) ).
cnf(refute_0_155,plain,
( addNat(zero,Y) != Y
| suc(addNat(zero,Y)) != suc(addNat(zero,Y))
| suc(addNat(zero,Y)) = suc(Y) ),
introduced(tautology,[equality,[$cnf( $equal(suc(addNat(zero,Y)),suc(addNat(zero,Y))) ),[1,0],$fot(Y)]]) ).
cnf(refute_0_156,plain,
( addNat(zero,Y) != Y
| suc(addNat(zero,Y)) = suc(Y) ),
inference(resolve,[$cnf( $equal(suc(addNat(zero,Y)),suc(addNat(zero,Y))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
suc(addNat(zero,Y)) = suc(Y),
inference(resolve,[$cnf( $equal(addNat(zero,Y),Y) )],[refute_0_12,refute_0_156]) ).
cnf(refute_0_158,plain,
addNat(suc(zero),Y) = suc(addNat(zero,Y)),
inference(subst,[],[refute_0_6:[bind(Z,$fot(zero))]]) ).
cnf(refute_0_159,plain,
( addNat(suc(zero),Y) != suc(addNat(zero,Y))
| suc(addNat(zero,Y)) != suc(Y)
| addNat(suc(zero),Y) = suc(Y) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(addNat(suc(zero),Y))),bind(Y0,$fot(suc(addNat(zero,Y)))),bind(Z0,$fot(suc(Y)))]]) ).
cnf(refute_0_160,plain,
( suc(addNat(zero,Y)) != suc(Y)
| addNat(suc(zero),Y) = suc(Y) ),
inference(resolve,[$cnf( $equal(addNat(suc(zero),Y),suc(addNat(zero,Y))) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
addNat(suc(zero),Y) = suc(Y),
inference(resolve,[$cnf( $equal(suc(addNat(zero,Y)),suc(Y)) )],[refute_0_157,refute_0_160]) ).
cnf(refute_0_162,plain,
suc(addNat(suc(zero),Y)) = suc(addNat(suc(zero),Y)),
introduced(tautology,[refl,[$fot(suc(addNat(suc(zero),Y)))]]) ).
cnf(refute_0_163,plain,
( addNat(suc(zero),Y) != suc(Y)
| suc(addNat(suc(zero),Y)) != suc(addNat(suc(zero),Y))
| suc(addNat(suc(zero),Y)) = suc(suc(Y)) ),
introduced(tautology,[equality,[$cnf( $equal(suc(addNat(suc(zero),Y)),suc(addNat(suc(zero),Y))) ),[1,0],$fot(suc(Y))]]) ).
cnf(refute_0_164,plain,
( addNat(suc(zero),Y) != suc(Y)
| suc(addNat(suc(zero),Y)) = suc(suc(Y)) ),
inference(resolve,[$cnf( $equal(suc(addNat(suc(zero),Y)),suc(addNat(suc(zero),Y))) )],[refute_0_162,refute_0_163]) ).
cnf(refute_0_165,plain,
suc(addNat(suc(zero),Y)) = suc(suc(Y)),
inference(resolve,[$cnf( $equal(addNat(suc(zero),Y),suc(Y)) )],[refute_0_161,refute_0_164]) ).
cnf(refute_0_166,plain,
( addNat(double(suc(zero)),Y) != suc(addNat(suc(zero),Y))
| suc(addNat(suc(zero),Y)) != suc(suc(Y))
| addNat(double(suc(zero)),Y) = suc(suc(Y)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addNat(double(suc(zero)),Y),suc(suc(Y))) ),[0],$fot(suc(addNat(suc(zero),Y)))]]) ).
cnf(refute_0_167,plain,
( addNat(double(suc(zero)),Y) != suc(addNat(suc(zero),Y))
| addNat(double(suc(zero)),Y) = suc(suc(Y)) ),
inference(resolve,[$cnf( $equal(suc(addNat(suc(zero),Y)),suc(suc(Y))) )],[refute_0_165,refute_0_166]) ).
cnf(refute_0_168,plain,
addNat(double(suc(zero)),Y) = suc(suc(Y)),
inference(resolve,[$cnf( $equal(addNat(double(suc(zero)),Y),suc(addNat(suc(zero),Y))) )],[refute_0_153,refute_0_167]) ).
cnf(refute_0_169,plain,
addNat(double(suc(zero)),double(suc(zero))) = suc(suc(double(suc(zero)))),
inference(subst,[],[refute_0_168:[bind(Y,$fot(double(suc(zero))))]]) ).
cnf(refute_0_170,plain,
( addNat(double(suc(zero)),double(suc(zero))) != suc(suc(double(suc(zero))))
| double(double(suc(zero))) != addNat(double(suc(zero)),double(suc(zero)))
| double(double(suc(zero))) = suc(suc(double(suc(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(double(double(suc(zero))),addNat(double(suc(zero)),double(suc(zero)))) ),[1],$fot(suc(suc(double(suc(zero)))))]]) ).
cnf(refute_0_171,plain,
( double(double(suc(zero))) != addNat(double(suc(zero)),double(suc(zero)))
| double(double(suc(zero))) = suc(suc(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(addNat(double(suc(zero)),double(suc(zero))),suc(suc(double(suc(zero))))) )],[refute_0_169,refute_0_170]) ).
cnf(refute_0_172,plain,
double(double(suc(zero))) = suc(suc(double(suc(zero)))),
inference(resolve,[$cnf( $equal(double(double(suc(zero))),addNat(double(suc(zero)),double(suc(zero)))) )],[refute_0_149,refute_0_171]) ).
cnf(refute_0_173,plain,
( double(double(suc(zero))) != suc(suc(double(suc(zero))))
| suc(suc(double(suc(zero)))) = double(double(suc(zero))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(double(double(suc(zero))))),bind(Y0,$fot(suc(suc(double(suc(zero))))))]]) ).
cnf(refute_0_174,plain,
suc(suc(double(suc(zero)))) = double(double(suc(zero))),
inference(resolve,[$cnf( $equal(double(double(suc(zero))),suc(suc(double(suc(zero))))) )],[refute_0_172,refute_0_173]) ).
cnf(refute_0_175,plain,
( half(suc(suc(double(suc(zero))))) != suc(half(double(suc(zero))))
| suc(suc(double(suc(zero)))) != double(double(suc(zero)))
| half(double(double(suc(zero)))) = suc(half(double(suc(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(half(suc(suc(double(suc(zero))))),suc(half(double(suc(zero))))) ),[0,0],$fot(double(double(suc(zero))))]]) ).
cnf(refute_0_176,plain,
( half(suc(suc(double(suc(zero))))) != suc(half(double(suc(zero))))
| half(double(double(suc(zero)))) = suc(half(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(suc(suc(double(suc(zero)))),double(double(suc(zero)))) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
half(double(double(suc(zero)))) = suc(half(double(suc(zero)))),
inference(resolve,[$cnf( $equal(half(suc(suc(double(suc(zero))))),suc(half(double(suc(zero))))) )],[refute_0_148,refute_0_176]) ).
cnf(refute_0_178,plain,
( half(suc(suc(zero))) != suc(half(zero))
| suc(suc(zero)) != double(suc(zero))
| half(double(suc(zero))) = suc(half(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(half(suc(suc(zero))),suc(half(zero))) ),[0,0],$fot(double(suc(zero)))]]) ).
cnf(refute_0_179,plain,
( half(suc(suc(zero))) != suc(half(zero))
| half(double(suc(zero))) = suc(half(zero)) ),
inference(resolve,[$cnf( $equal(suc(suc(zero)),double(suc(zero))) )],[refute_0_21,refute_0_178]) ).
cnf(refute_0_180,plain,
half(double(suc(zero))) = suc(half(zero)),
inference(resolve,[$cnf( $equal(half(suc(suc(zero))),suc(half(zero))) )],[refute_0_42,refute_0_179]) ).
cnf(refute_0_181,plain,
( half(double(suc(zero))) != suc(half(zero))
| suc(half(zero)) != suc(zero)
| half(double(suc(zero))) = suc(zero) ),
introduced(tautology,[equality,[$cnf( ~ $equal(half(double(suc(zero))),suc(zero)) ),[0],$fot(suc(half(zero)))]]) ).
cnf(refute_0_182,plain,
( half(double(suc(zero))) != suc(half(zero))
| half(double(suc(zero))) = suc(zero) ),
inference(resolve,[$cnf( $equal(suc(half(zero)),suc(zero)) )],[refute_0_40,refute_0_181]) ).
cnf(refute_0_183,plain,
half(double(suc(zero))) = suc(zero),
inference(resolve,[$cnf( $equal(half(double(suc(zero))),suc(half(zero))) )],[refute_0_180,refute_0_182]) ).
cnf(refute_0_184,plain,
suc(half(double(suc(zero)))) = suc(half(double(suc(zero)))),
introduced(tautology,[refl,[$fot(suc(half(double(suc(zero)))))]]) ).
cnf(refute_0_185,plain,
( half(double(suc(zero))) != suc(zero)
| suc(half(double(suc(zero)))) != suc(half(double(suc(zero))))
| suc(half(double(suc(zero)))) = suc(suc(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(suc(half(double(suc(zero)))),suc(half(double(suc(zero))))) ),[1,0],$fot(suc(zero))]]) ).
cnf(refute_0_186,plain,
( half(double(suc(zero))) != suc(zero)
| suc(half(double(suc(zero)))) = suc(suc(zero)) ),
inference(resolve,[$cnf( $equal(suc(half(double(suc(zero)))),suc(half(double(suc(zero))))) )],[refute_0_184,refute_0_185]) ).
cnf(refute_0_187,plain,
suc(half(double(suc(zero)))) = suc(suc(zero)),
inference(resolve,[$cnf( $equal(half(double(suc(zero))),suc(zero)) )],[refute_0_183,refute_0_186]) ).
cnf(refute_0_188,plain,
( suc(half(double(suc(zero)))) != suc(suc(zero))
| suc(suc(zero)) != double(suc(zero))
| suc(half(double(suc(zero)))) = double(suc(zero)) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(suc(half(double(suc(zero)))))),bind(Y0,$fot(suc(suc(zero)))),bind(Z0,$fot(double(suc(zero))))]]) ).
cnf(refute_0_189,plain,
( suc(suc(zero)) != double(suc(zero))
| suc(half(double(suc(zero)))) = double(suc(zero)) ),
inference(resolve,[$cnf( $equal(suc(half(double(suc(zero)))),suc(suc(zero))) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
suc(half(double(suc(zero)))) = double(suc(zero)),
inference(resolve,[$cnf( $equal(suc(suc(zero)),double(suc(zero))) )],[refute_0_21,refute_0_189]) ).
cnf(refute_0_191,plain,
( half(double(double(suc(zero)))) != suc(half(double(suc(zero))))
| suc(half(double(suc(zero)))) != double(suc(zero))
| half(double(double(suc(zero)))) = double(suc(zero)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(half(double(double(suc(zero)))),double(suc(zero))) ),[0],$fot(suc(half(double(suc(zero)))))]]) ).
cnf(refute_0_192,plain,
( half(double(double(suc(zero)))) != suc(half(double(suc(zero))))
| half(double(double(suc(zero)))) = double(suc(zero)) ),
inference(resolve,[$cnf( $equal(suc(half(double(suc(zero)))),double(suc(zero))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
half(double(double(suc(zero)))) = double(suc(zero)),
inference(resolve,[$cnf( $equal(half(double(double(suc(zero)))),suc(half(double(suc(zero))))) )],[refute_0_177,refute_0_192]) ).
cnf(refute_0_194,plain,
half(suc(suc(addNat(X_22,suc(X_22))))) = suc(half(addNat(X_22,suc(X_22)))),
inference(subst,[],[refute_0_41:[bind(N,$fot(addNat(X_22,suc(X_22))))]]) ).
cnf(refute_0_195,plain,
double(suc(X_22)) = suc(addNat(X_22,suc(X_22))),
inference(subst,[],[refute_0_10:[bind(X_21,$fot(X_22))]]) ).
cnf(refute_0_196,plain,
( double(suc(X_22)) != suc(addNat(X_22,suc(X_22)))
| suc(addNat(X_22,suc(X_22))) = double(suc(X_22)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(double(suc(X_22)))),bind(Y0,$fot(suc(addNat(X_22,suc(X_22)))))]]) ).
cnf(refute_0_197,plain,
suc(addNat(X_22,suc(X_22))) = double(suc(X_22)),
inference(resolve,[$cnf( $equal(double(suc(X_22)),suc(addNat(X_22,suc(X_22)))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
( half(suc(suc(addNat(X_22,suc(X_22))))) != suc(half(addNat(X_22,suc(X_22))))
| suc(addNat(X_22,suc(X_22))) != double(suc(X_22))
| half(suc(double(suc(X_22)))) = suc(half(addNat(X_22,suc(X_22)))) ),
introduced(tautology,[equality,[$cnf( $equal(half(suc(suc(addNat(X_22,suc(X_22))))),suc(half(addNat(X_22,suc(X_22))))) ),[0,0,0],$fot(double(suc(X_22)))]]) ).
cnf(refute_0_199,plain,
( half(suc(suc(addNat(X_22,suc(X_22))))) != suc(half(addNat(X_22,suc(X_22))))
| half(suc(double(suc(X_22)))) = suc(half(addNat(X_22,suc(X_22)))) ),
inference(resolve,[$cnf( $equal(suc(addNat(X_22,suc(X_22))),double(suc(X_22))) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
half(suc(double(suc(X_22)))) = suc(half(addNat(X_22,suc(X_22)))),
inference(resolve,[$cnf( $equal(half(suc(suc(addNat(X_22,suc(X_22))))),suc(half(addNat(X_22,suc(X_22))))) )],[refute_0_194,refute_0_199]) ).
cnf(refute_0_201,plain,
proj1Suc(suc(addNat(X_22,suc(X_22)))) = addNat(X_22,suc(X_22)),
inference(subst,[],[refute_0_131:[bind(X,$fot(addNat(X_22,suc(X_22))))]]) ).
cnf(refute_0_202,plain,
( proj1Suc(suc(addNat(X_22,suc(X_22)))) != addNat(X_22,suc(X_22))
| suc(addNat(X_22,suc(X_22))) != double(suc(X_22))
| proj1Suc(double(suc(X_22))) = addNat(X_22,suc(X_22)) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(suc(addNat(X_22,suc(X_22)))),addNat(X_22,suc(X_22))) ),[0,0],$fot(double(suc(X_22)))]]) ).
cnf(refute_0_203,plain,
( proj1Suc(suc(addNat(X_22,suc(X_22)))) != addNat(X_22,suc(X_22))
| proj1Suc(double(suc(X_22))) = addNat(X_22,suc(X_22)) ),
inference(resolve,[$cnf( $equal(suc(addNat(X_22,suc(X_22))),double(suc(X_22))) )],[refute_0_197,refute_0_202]) ).
cnf(refute_0_204,plain,
proj1Suc(double(suc(X_22))) = addNat(X_22,suc(X_22)),
inference(resolve,[$cnf( $equal(proj1Suc(suc(addNat(X_22,suc(X_22)))),addNat(X_22,suc(X_22))) )],[refute_0_201,refute_0_203]) ).
cnf(refute_0_205,plain,
( proj1Suc(double(suc(X_22))) != addNat(X_22,suc(X_22))
| addNat(X_22,suc(X_22)) = proj1Suc(double(suc(X_22))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(proj1Suc(double(suc(X_22))))),bind(Y0,$fot(addNat(X_22,suc(X_22))))]]) ).
cnf(refute_0_206,plain,
addNat(X_22,suc(X_22)) = proj1Suc(double(suc(X_22))),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(X_22))),addNat(X_22,suc(X_22))) )],[refute_0_204,refute_0_205]) ).
cnf(refute_0_207,plain,
half(addNat(X_22,suc(X_22))) = half(addNat(X_22,suc(X_22))),
introduced(tautology,[refl,[$fot(half(addNat(X_22,suc(X_22))))]]) ).
cnf(refute_0_208,plain,
( addNat(X_22,suc(X_22)) != proj1Suc(double(suc(X_22)))
| half(addNat(X_22,suc(X_22))) != half(addNat(X_22,suc(X_22)))
| half(addNat(X_22,suc(X_22))) = half(proj1Suc(double(suc(X_22)))) ),
introduced(tautology,[equality,[$cnf( $equal(half(addNat(X_22,suc(X_22))),half(addNat(X_22,suc(X_22)))) ),[1,0],$fot(proj1Suc(double(suc(X_22))))]]) ).
cnf(refute_0_209,plain,
( addNat(X_22,suc(X_22)) != proj1Suc(double(suc(X_22)))
| half(addNat(X_22,suc(X_22))) = half(proj1Suc(double(suc(X_22)))) ),
inference(resolve,[$cnf( $equal(half(addNat(X_22,suc(X_22))),half(addNat(X_22,suc(X_22)))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
half(addNat(X_22,suc(X_22))) = half(proj1Suc(double(suc(X_22)))),
inference(resolve,[$cnf( $equal(addNat(X_22,suc(X_22)),proj1Suc(double(suc(X_22)))) )],[refute_0_206,refute_0_209]) ).
cnf(refute_0_211,plain,
suc(half(addNat(X_22,suc(X_22)))) = suc(half(addNat(X_22,suc(X_22)))),
introduced(tautology,[refl,[$fot(suc(half(addNat(X_22,suc(X_22)))))]]) ).
cnf(refute_0_212,plain,
( half(addNat(X_22,suc(X_22))) != half(proj1Suc(double(suc(X_22))))
| suc(half(addNat(X_22,suc(X_22)))) != suc(half(addNat(X_22,suc(X_22))))
| suc(half(addNat(X_22,suc(X_22)))) = suc(half(proj1Suc(double(suc(X_22))))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(half(addNat(X_22,suc(X_22)))),suc(half(addNat(X_22,suc(X_22))))) ),[1,0],$fot(half(proj1Suc(double(suc(X_22)))))]]) ).
cnf(refute_0_213,plain,
( half(addNat(X_22,suc(X_22))) != half(proj1Suc(double(suc(X_22))))
| suc(half(addNat(X_22,suc(X_22)))) = suc(half(proj1Suc(double(suc(X_22))))) ),
inference(resolve,[$cnf( $equal(suc(half(addNat(X_22,suc(X_22)))),suc(half(addNat(X_22,suc(X_22))))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
suc(half(addNat(X_22,suc(X_22)))) = suc(half(proj1Suc(double(suc(X_22))))),
inference(resolve,[$cnf( $equal(half(addNat(X_22,suc(X_22))),half(proj1Suc(double(suc(X_22))))) )],[refute_0_210,refute_0_213]) ).
cnf(refute_0_215,plain,
( half(suc(double(suc(X_22)))) != suc(half(addNat(X_22,suc(X_22))))
| suc(half(addNat(X_22,suc(X_22)))) != suc(half(proj1Suc(double(suc(X_22)))))
| half(suc(double(suc(X_22)))) = suc(half(proj1Suc(double(suc(X_22))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(half(suc(double(suc(X_22)))),suc(half(proj1Suc(double(suc(X_22)))))) ),[0],$fot(suc(half(addNat(X_22,suc(X_22)))))]]) ).
cnf(refute_0_216,plain,
( half(suc(double(suc(X_22)))) != suc(half(addNat(X_22,suc(X_22))))
| half(suc(double(suc(X_22)))) = suc(half(proj1Suc(double(suc(X_22))))) ),
inference(resolve,[$cnf( $equal(suc(half(addNat(X_22,suc(X_22)))),suc(half(proj1Suc(double(suc(X_22)))))) )],[refute_0_214,refute_0_215]) ).
cnf(refute_0_217,plain,
half(suc(double(suc(X_22)))) = suc(half(proj1Suc(double(suc(X_22))))),
inference(resolve,[$cnf( $equal(half(suc(double(suc(X_22)))),suc(half(addNat(X_22,suc(X_22))))) )],[refute_0_200,refute_0_216]) ).
cnf(refute_0_218,plain,
half(suc(double(suc(suc(double(suc(zero))))))) = suc(half(proj1Suc(double(suc(suc(double(suc(zero)))))))),
inference(subst,[],[refute_0_217:[bind(X_22,$fot(suc(double(suc(zero)))))]]) ).
cnf(refute_0_219,plain,
( half(suc(double(suc(suc(double(suc(zero))))))) != suc(half(proj1Suc(double(suc(suc(double(suc(zero))))))))
| suc(suc(double(suc(zero)))) != double(double(suc(zero)))
| half(suc(double(suc(suc(double(suc(zero))))))) = suc(half(proj1Suc(double(double(double(suc(zero))))))) ),
introduced(tautology,[equality,[$cnf( $equal(half(suc(double(suc(suc(double(suc(zero))))))),suc(half(proj1Suc(double(suc(suc(double(suc(zero))))))))) ),[1,0,0,0,0],$fot(double(double(suc(zero))))]]) ).
cnf(refute_0_220,plain,
( half(suc(double(suc(suc(double(suc(zero))))))) != suc(half(proj1Suc(double(suc(suc(double(suc(zero))))))))
| half(suc(double(suc(suc(double(suc(zero))))))) = suc(half(proj1Suc(double(double(double(suc(zero))))))) ),
inference(resolve,[$cnf( $equal(suc(suc(double(suc(zero)))),double(double(suc(zero)))) )],[refute_0_174,refute_0_219]) ).
cnf(refute_0_221,plain,
half(suc(double(suc(suc(double(suc(zero))))))) = suc(half(proj1Suc(double(double(double(suc(zero))))))),
inference(resolve,[$cnf( $equal(half(suc(double(suc(suc(double(suc(zero))))))),suc(half(proj1Suc(double(suc(suc(double(suc(zero))))))))) )],[refute_0_218,refute_0_220]) ).
cnf(refute_0_222,plain,
double(suc(suc(double(suc(zero))))) = double(suc(suc(double(suc(zero))))),
introduced(tautology,[refl,[$fot(double(suc(suc(double(suc(zero))))))]]) ).
cnf(refute_0_223,plain,
( double(suc(suc(double(suc(zero))))) != double(suc(suc(double(suc(zero)))))
| suc(suc(double(suc(zero)))) != double(double(suc(zero)))
| double(suc(suc(double(suc(zero))))) = double(double(double(suc(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(suc(double(suc(zero))))),double(suc(suc(double(suc(zero)))))) ),[1,0],$fot(double(double(suc(zero))))]]) ).
cnf(refute_0_224,plain,
( suc(suc(double(suc(zero)))) != double(double(suc(zero)))
| double(suc(suc(double(suc(zero))))) = double(double(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(double(suc(suc(double(suc(zero))))),double(suc(suc(double(suc(zero)))))) )],[refute_0_222,refute_0_223]) ).
cnf(refute_0_225,plain,
double(suc(suc(double(suc(zero))))) = double(double(double(suc(zero)))),
inference(resolve,[$cnf( $equal(suc(suc(double(suc(zero)))),double(double(suc(zero)))) )],[refute_0_174,refute_0_224]) ).
cnf(refute_0_226,plain,
suc(double(suc(suc(double(suc(zero)))))) = suc(double(suc(suc(double(suc(zero)))))),
introduced(tautology,[refl,[$fot(suc(double(suc(suc(double(suc(zero)))))))]]) ).
cnf(refute_0_227,plain,
( double(suc(suc(double(suc(zero))))) != double(double(double(suc(zero))))
| suc(double(suc(suc(double(suc(zero)))))) != suc(double(suc(suc(double(suc(zero))))))
| suc(double(suc(suc(double(suc(zero)))))) = suc(double(double(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(double(suc(suc(double(suc(zero)))))),suc(double(suc(suc(double(suc(zero))))))) ),[1,0],$fot(double(double(double(suc(zero)))))]]) ).
cnf(refute_0_228,plain,
( double(suc(suc(double(suc(zero))))) != double(double(double(suc(zero))))
| suc(double(suc(suc(double(suc(zero)))))) = suc(double(double(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(suc(double(suc(suc(double(suc(zero)))))),suc(double(suc(suc(double(suc(zero))))))) )],[refute_0_226,refute_0_227]) ).
cnf(refute_0_229,plain,
suc(double(suc(suc(double(suc(zero)))))) = suc(double(double(double(suc(zero))))),
inference(resolve,[$cnf( $equal(double(suc(suc(double(suc(zero))))),double(double(double(suc(zero))))) )],[refute_0_225,refute_0_228]) ).
cnf(refute_0_230,plain,
half(suc(double(suc(suc(double(suc(zero))))))) = half(suc(double(suc(suc(double(suc(zero))))))),
introduced(tautology,[refl,[$fot(half(suc(double(suc(suc(double(suc(zero))))))))]]) ).
cnf(refute_0_231,plain,
( half(suc(double(suc(suc(double(suc(zero))))))) != half(suc(double(suc(suc(double(suc(zero)))))))
| suc(double(suc(suc(double(suc(zero)))))) != suc(double(double(double(suc(zero)))))
| half(suc(double(suc(suc(double(suc(zero))))))) = half(suc(double(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(half(suc(double(suc(suc(double(suc(zero))))))),half(suc(double(suc(suc(double(suc(zero)))))))) ),[1,0],$fot(suc(double(double(double(suc(zero))))))]]) ).
cnf(refute_0_232,plain,
( suc(double(suc(suc(double(suc(zero)))))) != suc(double(double(double(suc(zero)))))
| half(suc(double(suc(suc(double(suc(zero))))))) = half(suc(double(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(half(suc(double(suc(suc(double(suc(zero))))))),half(suc(double(suc(suc(double(suc(zero)))))))) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
half(suc(double(suc(suc(double(suc(zero))))))) = half(suc(double(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(suc(double(suc(suc(double(suc(zero)))))),suc(double(double(double(suc(zero)))))) )],[refute_0_229,refute_0_232]) ).
cnf(refute_0_234,plain,
( half(suc(double(suc(suc(double(suc(zero))))))) != half(suc(double(double(double(suc(zero))))))
| half(suc(double(suc(suc(double(suc(zero))))))) != suc(half(proj1Suc(double(double(double(suc(zero)))))))
| half(suc(double(double(double(suc(zero)))))) = suc(half(proj1Suc(double(double(double(suc(zero))))))) ),
introduced(tautology,[equality,[$cnf( $equal(half(suc(double(suc(suc(double(suc(zero))))))),suc(half(proj1Suc(double(double(double(suc(zero)))))))) ),[0],$fot(half(suc(double(double(double(suc(zero)))))))]]) ).
cnf(refute_0_235,plain,
( half(suc(double(suc(suc(double(suc(zero))))))) != suc(half(proj1Suc(double(double(double(suc(zero)))))))
| half(suc(double(double(double(suc(zero)))))) = suc(half(proj1Suc(double(double(double(suc(zero))))))) ),
inference(resolve,[$cnf( $equal(half(suc(double(suc(suc(double(suc(zero))))))),half(suc(double(double(double(suc(zero))))))) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
half(suc(suc(suc(double(double(suc(zero))))))) = suc(half(suc(double(double(suc(zero)))))),
inference(subst,[],[refute_0_41:[bind(N,$fot(suc(double(double(suc(zero))))))]]) ).
cnf(refute_0_237,plain,
addNat(X_21,suc(X_21)) = proj1Suc(double(suc(X_21))),
inference(subst,[],[refute_0_206:[bind(X_22,$fot(X_21))]]) ).
cnf(refute_0_238,plain,
suc(addNat(X_21,suc(X_21))) = suc(addNat(X_21,suc(X_21))),
introduced(tautology,[refl,[$fot(suc(addNat(X_21,suc(X_21))))]]) ).
cnf(refute_0_239,plain,
( addNat(X_21,suc(X_21)) != proj1Suc(double(suc(X_21)))
| suc(addNat(X_21,suc(X_21))) != suc(addNat(X_21,suc(X_21)))
| suc(addNat(X_21,suc(X_21))) = suc(proj1Suc(double(suc(X_21)))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(addNat(X_21,suc(X_21))),suc(addNat(X_21,suc(X_21)))) ),[1,0],$fot(proj1Suc(double(suc(X_21))))]]) ).
cnf(refute_0_240,plain,
( addNat(X_21,suc(X_21)) != proj1Suc(double(suc(X_21)))
| suc(addNat(X_21,suc(X_21))) = suc(proj1Suc(double(suc(X_21)))) ),
inference(resolve,[$cnf( $equal(suc(addNat(X_21,suc(X_21))),suc(addNat(X_21,suc(X_21)))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
suc(addNat(X_21,suc(X_21))) = suc(proj1Suc(double(suc(X_21)))),
inference(resolve,[$cnf( $equal(addNat(X_21,suc(X_21)),proj1Suc(double(suc(X_21)))) )],[refute_0_237,refute_0_240]) ).
cnf(refute_0_242,plain,
( double(suc(X_21)) != suc(addNat(X_21,suc(X_21)))
| suc(addNat(X_21,suc(X_21))) != suc(proj1Suc(double(suc(X_21))))
| double(suc(X_21)) = suc(proj1Suc(double(suc(X_21)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(double(suc(X_21)),suc(proj1Suc(double(suc(X_21))))) ),[0],$fot(suc(addNat(X_21,suc(X_21))))]]) ).
cnf(refute_0_243,plain,
( double(suc(X_21)) != suc(addNat(X_21,suc(X_21)))
| double(suc(X_21)) = suc(proj1Suc(double(suc(X_21)))) ),
inference(resolve,[$cnf( $equal(suc(addNat(X_21,suc(X_21))),suc(proj1Suc(double(suc(X_21))))) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
double(suc(X_21)) = suc(proj1Suc(double(suc(X_21)))),
inference(resolve,[$cnf( $equal(double(suc(X_21)),suc(addNat(X_21,suc(X_21)))) )],[refute_0_10,refute_0_243]) ).
cnf(refute_0_245,plain,
double(suc(double(suc(zero)))) = suc(proj1Suc(double(suc(double(suc(zero)))))),
inference(subst,[],[refute_0_244:[bind(X_21,$fot(double(suc(zero))))]]) ).
cnf(refute_0_246,plain,
proj1Suc(double(suc(double(suc(zero))))) = addNat(double(suc(zero)),suc(double(suc(zero)))),
inference(subst,[],[refute_0_204:[bind(X_22,$fot(double(suc(zero))))]]) ).
cnf(refute_0_247,plain,
addNat(double(suc(zero)),suc(double(suc(zero)))) = suc(suc(suc(double(suc(zero))))),
inference(subst,[],[refute_0_168:[bind(Y,$fot(suc(double(suc(zero)))))]]) ).
cnf(refute_0_248,plain,
( addNat(double(suc(zero)),suc(double(suc(zero)))) != suc(suc(suc(double(suc(zero)))))
| proj1Suc(double(suc(double(suc(zero))))) != addNat(double(suc(zero)),suc(double(suc(zero))))
| proj1Suc(double(suc(double(suc(zero))))) = suc(suc(suc(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(suc(double(suc(zero))))),addNat(double(suc(zero)),suc(double(suc(zero))))) ),[1],$fot(suc(suc(suc(double(suc(zero))))))]]) ).
cnf(refute_0_249,plain,
( proj1Suc(double(suc(double(suc(zero))))) != addNat(double(suc(zero)),suc(double(suc(zero))))
| proj1Suc(double(suc(double(suc(zero))))) = suc(suc(suc(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(addNat(double(suc(zero)),suc(double(suc(zero)))),suc(suc(suc(double(suc(zero)))))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
proj1Suc(double(suc(double(suc(zero))))) = suc(suc(suc(double(suc(zero))))),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(double(suc(zero))))),addNat(double(suc(zero)),suc(double(suc(zero))))) )],[refute_0_246,refute_0_249]) ).
cnf(refute_0_251,plain,
suc(suc(suc(double(suc(zero))))) = suc(suc(suc(double(suc(zero))))),
introduced(tautology,[refl,[$fot(suc(suc(suc(double(suc(zero))))))]]) ).
cnf(refute_0_252,plain,
( suc(suc(double(suc(zero)))) != double(double(suc(zero)))
| suc(suc(suc(double(suc(zero))))) != suc(suc(suc(double(suc(zero)))))
| suc(suc(suc(double(suc(zero))))) = suc(double(double(suc(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(suc(suc(double(suc(zero))))),suc(suc(suc(double(suc(zero)))))) ),[1,0],$fot(double(double(suc(zero))))]]) ).
cnf(refute_0_253,plain,
( suc(suc(double(suc(zero)))) != double(double(suc(zero)))
| suc(suc(suc(double(suc(zero))))) = suc(double(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(suc(suc(suc(double(suc(zero))))),suc(suc(suc(double(suc(zero)))))) )],[refute_0_251,refute_0_252]) ).
cnf(refute_0_254,plain,
suc(suc(suc(double(suc(zero))))) = suc(double(double(suc(zero)))),
inference(resolve,[$cnf( $equal(suc(suc(double(suc(zero)))),double(double(suc(zero)))) )],[refute_0_174,refute_0_253]) ).
cnf(refute_0_255,plain,
( proj1Suc(double(suc(double(suc(zero))))) != suc(suc(suc(double(suc(zero)))))
| suc(suc(suc(double(suc(zero))))) != suc(double(double(suc(zero))))
| proj1Suc(double(suc(double(suc(zero))))) = suc(double(double(suc(zero)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(proj1Suc(double(suc(double(suc(zero))))),suc(double(double(suc(zero))))) ),[0],$fot(suc(suc(suc(double(suc(zero))))))]]) ).
cnf(refute_0_256,plain,
( proj1Suc(double(suc(double(suc(zero))))) != suc(suc(suc(double(suc(zero)))))
| proj1Suc(double(suc(double(suc(zero))))) = suc(double(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(suc(suc(suc(double(suc(zero))))),suc(double(double(suc(zero))))) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
proj1Suc(double(suc(double(suc(zero))))) = suc(double(double(suc(zero)))),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(double(suc(zero))))),suc(suc(suc(double(suc(zero)))))) )],[refute_0_250,refute_0_256]) ).
cnf(refute_0_258,plain,
( double(suc(double(suc(zero)))) != suc(proj1Suc(double(suc(double(suc(zero))))))
| proj1Suc(double(suc(double(suc(zero))))) != suc(double(double(suc(zero))))
| double(suc(double(suc(zero)))) = suc(suc(double(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(double(suc(zero)))),suc(proj1Suc(double(suc(double(suc(zero))))))) ),[1,0],$fot(suc(double(double(suc(zero)))))]]) ).
cnf(refute_0_259,plain,
( double(suc(double(suc(zero)))) != suc(proj1Suc(double(suc(double(suc(zero))))))
| double(suc(double(suc(zero)))) = suc(suc(double(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(double(suc(zero))))),suc(double(double(suc(zero))))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
double(suc(double(suc(zero)))) = suc(suc(double(double(suc(zero))))),
inference(resolve,[$cnf( $equal(double(suc(double(suc(zero)))),suc(proj1Suc(double(suc(double(suc(zero))))))) )],[refute_0_245,refute_0_259]) ).
cnf(refute_0_261,plain,
( double(suc(double(suc(zero)))) != suc(suc(double(double(suc(zero)))))
| suc(suc(double(double(suc(zero))))) = double(suc(double(suc(zero)))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(double(suc(double(suc(zero)))))),bind(Y0,$fot(suc(suc(double(double(suc(zero)))))))]]) ).
cnf(refute_0_262,plain,
suc(suc(double(double(suc(zero))))) = double(suc(double(suc(zero)))),
inference(resolve,[$cnf( $equal(double(suc(double(suc(zero)))),suc(suc(double(double(suc(zero)))))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
( half(suc(suc(suc(double(double(suc(zero))))))) != suc(half(suc(double(double(suc(zero))))))
| suc(suc(double(double(suc(zero))))) != double(suc(double(suc(zero))))
| half(suc(double(suc(double(suc(zero)))))) = suc(half(suc(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(half(suc(suc(suc(double(double(suc(zero))))))),suc(half(suc(double(double(suc(zero))))))) ),[0,0,0],$fot(double(suc(double(suc(zero)))))]]) ).
cnf(refute_0_264,plain,
( half(suc(suc(suc(double(double(suc(zero))))))) != suc(half(suc(double(double(suc(zero))))))
| half(suc(double(suc(double(suc(zero)))))) = suc(half(suc(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(suc(suc(double(double(suc(zero))))),double(suc(double(suc(zero))))) )],[refute_0_262,refute_0_263]) ).
cnf(refute_0_265,plain,
half(suc(double(suc(double(suc(zero)))))) = suc(half(suc(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(half(suc(suc(suc(double(double(suc(zero))))))),suc(half(suc(double(double(suc(zero))))))) )],[refute_0_236,refute_0_264]) ).
cnf(refute_0_266,plain,
proj1Suc(double(suc(suc(double(suc(zero)))))) = addNat(suc(double(suc(zero))),suc(suc(double(suc(zero))))),
inference(subst,[],[refute_0_204:[bind(X_22,$fot(suc(double(suc(zero)))))]]) ).
cnf(refute_0_267,plain,
( proj1Suc(double(suc(suc(double(suc(zero)))))) != addNat(suc(double(suc(zero))),suc(suc(double(suc(zero)))))
| suc(suc(double(suc(zero)))) != double(double(suc(zero)))
| proj1Suc(double(suc(suc(double(suc(zero)))))) = addNat(suc(double(suc(zero))),double(double(suc(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(suc(suc(double(suc(zero)))))),addNat(suc(double(suc(zero))),suc(suc(double(suc(zero)))))) ),[1,1],$fot(double(double(suc(zero))))]]) ).
cnf(refute_0_268,plain,
( proj1Suc(double(suc(suc(double(suc(zero)))))) != addNat(suc(double(suc(zero))),suc(suc(double(suc(zero)))))
| proj1Suc(double(suc(suc(double(suc(zero)))))) = addNat(suc(double(suc(zero))),double(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(suc(suc(double(suc(zero)))),double(double(suc(zero)))) )],[refute_0_174,refute_0_267]) ).
cnf(refute_0_269,plain,
proj1Suc(double(suc(suc(double(suc(zero)))))) = addNat(suc(double(suc(zero))),double(double(suc(zero)))),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(suc(double(suc(zero)))))),addNat(suc(double(suc(zero))),suc(suc(double(suc(zero)))))) )],[refute_0_266,refute_0_268]) ).
cnf(refute_0_270,plain,
proj1Suc(double(suc(suc(double(suc(zero)))))) = proj1Suc(double(suc(suc(double(suc(zero)))))),
introduced(tautology,[refl,[$fot(proj1Suc(double(suc(suc(double(suc(zero)))))))]]) ).
cnf(refute_0_271,plain,
( double(suc(suc(double(suc(zero))))) != double(double(double(suc(zero))))
| proj1Suc(double(suc(suc(double(suc(zero)))))) != proj1Suc(double(suc(suc(double(suc(zero))))))
| proj1Suc(double(suc(suc(double(suc(zero)))))) = proj1Suc(double(double(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(suc(suc(double(suc(zero)))))),proj1Suc(double(suc(suc(double(suc(zero))))))) ),[1,0],$fot(double(double(double(suc(zero)))))]]) ).
cnf(refute_0_272,plain,
( double(suc(suc(double(suc(zero))))) != double(double(double(suc(zero))))
| proj1Suc(double(suc(suc(double(suc(zero)))))) = proj1Suc(double(double(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(suc(double(suc(zero)))))),proj1Suc(double(suc(suc(double(suc(zero))))))) )],[refute_0_270,refute_0_271]) ).
cnf(refute_0_273,plain,
proj1Suc(double(suc(suc(double(suc(zero)))))) = proj1Suc(double(double(double(suc(zero))))),
inference(resolve,[$cnf( $equal(double(suc(suc(double(suc(zero))))),double(double(double(suc(zero))))) )],[refute_0_225,refute_0_272]) ).
cnf(refute_0_274,plain,
( proj1Suc(double(suc(suc(double(suc(zero)))))) != addNat(suc(double(suc(zero))),double(double(suc(zero))))
| proj1Suc(double(suc(suc(double(suc(zero)))))) != proj1Suc(double(double(double(suc(zero)))))
| proj1Suc(double(double(double(suc(zero))))) = addNat(suc(double(suc(zero))),double(double(suc(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(suc(suc(double(suc(zero)))))),addNat(suc(double(suc(zero))),double(double(suc(zero))))) ),[0],$fot(proj1Suc(double(double(double(suc(zero))))))]]) ).
cnf(refute_0_275,plain,
( proj1Suc(double(suc(suc(double(suc(zero)))))) != addNat(suc(double(suc(zero))),double(double(suc(zero))))
| proj1Suc(double(double(double(suc(zero))))) = addNat(suc(double(suc(zero))),double(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(suc(double(suc(zero)))))),proj1Suc(double(double(double(suc(zero)))))) )],[refute_0_273,refute_0_274]) ).
cnf(refute_0_276,plain,
addNat(double(suc(zero)),double(double(suc(zero)))) = suc(suc(double(double(suc(zero))))),
inference(subst,[],[refute_0_168:[bind(Y,$fot(double(double(suc(zero)))))]]) ).
cnf(refute_0_277,plain,
suc(addNat(double(suc(zero)),double(double(suc(zero))))) = suc(addNat(double(suc(zero)),double(double(suc(zero))))),
introduced(tautology,[refl,[$fot(suc(addNat(double(suc(zero)),double(double(suc(zero))))))]]) ).
cnf(refute_0_278,plain,
( addNat(double(suc(zero)),double(double(suc(zero)))) != suc(suc(double(double(suc(zero)))))
| suc(addNat(double(suc(zero)),double(double(suc(zero))))) != suc(addNat(double(suc(zero)),double(double(suc(zero)))))
| suc(addNat(double(suc(zero)),double(double(suc(zero))))) = suc(suc(suc(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(addNat(double(suc(zero)),double(double(suc(zero))))),suc(addNat(double(suc(zero)),double(double(suc(zero)))))) ),[1,0],$fot(suc(suc(double(double(suc(zero))))))]]) ).
cnf(refute_0_279,plain,
( addNat(double(suc(zero)),double(double(suc(zero)))) != suc(suc(double(double(suc(zero)))))
| suc(addNat(double(suc(zero)),double(double(suc(zero))))) = suc(suc(suc(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(suc(addNat(double(suc(zero)),double(double(suc(zero))))),suc(addNat(double(suc(zero)),double(double(suc(zero)))))) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
suc(addNat(double(suc(zero)),double(double(suc(zero))))) = suc(suc(suc(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(addNat(double(suc(zero)),double(double(suc(zero)))),suc(suc(double(double(suc(zero)))))) )],[refute_0_276,refute_0_279]) ).
cnf(refute_0_281,plain,
addNat(suc(double(suc(zero))),double(double(suc(zero)))) = suc(addNat(double(suc(zero)),double(double(suc(zero))))),
inference(subst,[],[refute_0_6:[bind(Y,$fot(double(double(suc(zero))))),bind(Z,$fot(double(suc(zero))))]]) ).
cnf(refute_0_282,plain,
( addNat(suc(double(suc(zero))),double(double(suc(zero)))) != suc(addNat(double(suc(zero)),double(double(suc(zero)))))
| suc(addNat(double(suc(zero)),double(double(suc(zero))))) != suc(suc(suc(double(double(suc(zero))))))
| addNat(suc(double(suc(zero))),double(double(suc(zero)))) = suc(suc(suc(double(double(suc(zero)))))) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(addNat(suc(double(suc(zero))),double(double(suc(zero)))))),bind(Y0,$fot(suc(addNat(double(suc(zero)),double(double(suc(zero))))))),bind(Z0,$fot(suc(suc(suc(double(double(suc(zero))))))))]]) ).
cnf(refute_0_283,plain,
( suc(addNat(double(suc(zero)),double(double(suc(zero))))) != suc(suc(suc(double(double(suc(zero))))))
| addNat(suc(double(suc(zero))),double(double(suc(zero)))) = suc(suc(suc(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(addNat(suc(double(suc(zero))),double(double(suc(zero)))),suc(addNat(double(suc(zero)),double(double(suc(zero)))))) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
addNat(suc(double(suc(zero))),double(double(suc(zero)))) = suc(suc(suc(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(suc(addNat(double(suc(zero)),double(double(suc(zero))))),suc(suc(suc(double(double(suc(zero))))))) )],[refute_0_280,refute_0_283]) ).
cnf(refute_0_285,plain,
( addNat(suc(double(suc(zero))),double(double(suc(zero)))) != suc(suc(suc(double(double(suc(zero))))))
| proj1Suc(double(double(double(suc(zero))))) != addNat(suc(double(suc(zero))),double(double(suc(zero))))
| proj1Suc(double(double(double(suc(zero))))) = suc(suc(suc(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(double(double(suc(zero))))),addNat(suc(double(suc(zero))),double(double(suc(zero))))) ),[1],$fot(suc(suc(suc(double(double(suc(zero)))))))]]) ).
cnf(refute_0_286,plain,
( proj1Suc(double(double(double(suc(zero))))) != addNat(suc(double(suc(zero))),double(double(suc(zero))))
| proj1Suc(double(double(double(suc(zero))))) = suc(suc(suc(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(addNat(suc(double(suc(zero))),double(double(suc(zero)))),suc(suc(suc(double(double(suc(zero))))))) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
( proj1Suc(double(suc(suc(double(suc(zero)))))) != addNat(suc(double(suc(zero))),double(double(suc(zero))))
| proj1Suc(double(double(double(suc(zero))))) = suc(suc(suc(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(double(double(suc(zero))))),addNat(suc(double(suc(zero))),double(double(suc(zero))))) )],[refute_0_275,refute_0_286]) ).
cnf(refute_0_288,plain,
proj1Suc(double(double(double(suc(zero))))) = suc(suc(suc(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(suc(double(suc(zero)))))),addNat(suc(double(suc(zero))),double(double(suc(zero))))) )],[refute_0_269,refute_0_287]) ).
cnf(refute_0_289,plain,
suc(suc(suc(double(double(suc(zero)))))) = suc(suc(suc(double(double(suc(zero)))))),
introduced(tautology,[refl,[$fot(suc(suc(suc(double(double(suc(zero)))))))]]) ).
cnf(refute_0_290,plain,
( suc(suc(double(double(suc(zero))))) != double(suc(double(suc(zero))))
| suc(suc(suc(double(double(suc(zero)))))) != suc(suc(suc(double(double(suc(zero))))))
| suc(suc(suc(double(double(suc(zero)))))) = suc(double(suc(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(suc(suc(double(double(suc(zero)))))),suc(suc(suc(double(double(suc(zero))))))) ),[1,0],$fot(double(suc(double(suc(zero)))))]]) ).
cnf(refute_0_291,plain,
( suc(suc(double(double(suc(zero))))) != double(suc(double(suc(zero))))
| suc(suc(suc(double(double(suc(zero)))))) = suc(double(suc(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(suc(suc(suc(double(double(suc(zero)))))),suc(suc(suc(double(double(suc(zero))))))) )],[refute_0_289,refute_0_290]) ).
cnf(refute_0_292,plain,
suc(suc(suc(double(double(suc(zero)))))) = suc(double(suc(double(suc(zero))))),
inference(resolve,[$cnf( $equal(suc(suc(double(double(suc(zero))))),double(suc(double(suc(zero))))) )],[refute_0_262,refute_0_291]) ).
cnf(refute_0_293,plain,
( proj1Suc(double(double(double(suc(zero))))) != suc(suc(suc(double(double(suc(zero))))))
| suc(suc(suc(double(double(suc(zero)))))) != suc(double(suc(double(suc(zero)))))
| proj1Suc(double(double(double(suc(zero))))) = suc(double(suc(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(proj1Suc(double(double(double(suc(zero))))),suc(double(suc(double(suc(zero)))))) ),[0],$fot(suc(suc(suc(double(double(suc(zero)))))))]]) ).
cnf(refute_0_294,plain,
( proj1Suc(double(double(double(suc(zero))))) != suc(suc(suc(double(double(suc(zero))))))
| proj1Suc(double(double(double(suc(zero))))) = suc(double(suc(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(suc(suc(suc(double(double(suc(zero)))))),suc(double(suc(double(suc(zero)))))) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
proj1Suc(double(double(double(suc(zero))))) = suc(double(suc(double(suc(zero))))),
inference(resolve,[$cnf( $equal(proj1Suc(double(double(double(suc(zero))))),suc(suc(suc(double(double(suc(zero))))))) )],[refute_0_288,refute_0_294]) ).
cnf(refute_0_296,plain,
( proj1Suc(double(double(double(suc(zero))))) != suc(double(suc(double(suc(zero)))))
| suc(double(suc(double(suc(zero))))) = proj1Suc(double(double(double(suc(zero))))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(proj1Suc(double(double(double(suc(zero))))))),bind(Y0,$fot(suc(double(suc(double(suc(zero)))))))]]) ).
cnf(refute_0_297,plain,
suc(double(suc(double(suc(zero))))) = proj1Suc(double(double(double(suc(zero))))),
inference(resolve,[$cnf( $equal(proj1Suc(double(double(double(suc(zero))))),suc(double(suc(double(suc(zero)))))) )],[refute_0_295,refute_0_296]) ).
cnf(refute_0_298,plain,
half(suc(double(suc(double(suc(zero)))))) = half(suc(double(suc(double(suc(zero)))))),
introduced(tautology,[refl,[$fot(half(suc(double(suc(double(suc(zero)))))))]]) ).
cnf(refute_0_299,plain,
( half(suc(double(suc(double(suc(zero)))))) != half(suc(double(suc(double(suc(zero))))))
| suc(double(suc(double(suc(zero))))) != proj1Suc(double(double(double(suc(zero)))))
| half(suc(double(suc(double(suc(zero)))))) = half(proj1Suc(double(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(half(suc(double(suc(double(suc(zero)))))),half(suc(double(suc(double(suc(zero))))))) ),[1,0],$fot(proj1Suc(double(double(double(suc(zero))))))]]) ).
cnf(refute_0_300,plain,
( suc(double(suc(double(suc(zero))))) != proj1Suc(double(double(double(suc(zero)))))
| half(suc(double(suc(double(suc(zero)))))) = half(proj1Suc(double(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(half(suc(double(suc(double(suc(zero)))))),half(suc(double(suc(double(suc(zero))))))) )],[refute_0_298,refute_0_299]) ).
cnf(refute_0_301,plain,
half(suc(double(suc(double(suc(zero)))))) = half(proj1Suc(double(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(suc(double(suc(double(suc(zero))))),proj1Suc(double(double(double(suc(zero)))))) )],[refute_0_297,refute_0_300]) ).
cnf(refute_0_302,plain,
( half(suc(double(suc(double(suc(zero)))))) != half(proj1Suc(double(double(double(suc(zero))))))
| half(suc(double(suc(double(suc(zero)))))) != suc(half(suc(double(double(suc(zero))))))
| half(proj1Suc(double(double(double(suc(zero)))))) = suc(half(suc(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(half(suc(double(suc(double(suc(zero)))))),suc(half(suc(double(double(suc(zero))))))) ),[0],$fot(half(proj1Suc(double(double(double(suc(zero)))))))]]) ).
cnf(refute_0_303,plain,
( half(suc(double(suc(double(suc(zero)))))) != suc(half(suc(double(double(suc(zero))))))
| half(proj1Suc(double(double(double(suc(zero)))))) = suc(half(suc(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(half(suc(double(suc(double(suc(zero)))))),half(proj1Suc(double(double(double(suc(zero))))))) )],[refute_0_301,refute_0_302]) ).
cnf(refute_0_304,plain,
half(suc(suc(suc(double(suc(zero)))))) = suc(half(suc(double(suc(zero))))),
inference(subst,[],[refute_0_41:[bind(N,$fot(suc(double(suc(zero)))))]]) ).
cnf(refute_0_305,plain,
( half(suc(suc(suc(double(suc(zero)))))) != suc(half(suc(double(suc(zero)))))
| suc(suc(double(suc(zero)))) != double(double(suc(zero)))
| half(suc(double(double(suc(zero))))) = suc(half(suc(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(half(suc(suc(suc(double(suc(zero)))))),suc(half(suc(double(suc(zero)))))) ),[0,0,0],$fot(double(double(suc(zero))))]]) ).
cnf(refute_0_306,plain,
( half(suc(suc(suc(double(suc(zero)))))) != suc(half(suc(double(suc(zero)))))
| half(suc(double(double(suc(zero))))) = suc(half(suc(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(suc(suc(double(suc(zero)))),double(double(suc(zero)))) )],[refute_0_174,refute_0_305]) ).
cnf(refute_0_307,plain,
half(suc(double(double(suc(zero))))) = suc(half(suc(double(suc(zero))))),
inference(resolve,[$cnf( $equal(half(suc(suc(suc(double(suc(zero)))))),suc(half(suc(double(suc(zero)))))) )],[refute_0_304,refute_0_306]) ).
cnf(refute_0_308,plain,
suc(half(suc(double(suc(zero))))) = suc(half(suc(double(suc(zero))))),
introduced(tautology,[refl,[$fot(suc(half(suc(double(suc(zero))))))]]) ).
cnf(refute_0_309,plain,
( half(suc(double(suc(zero)))) != suc(zero)
| suc(half(suc(double(suc(zero))))) != suc(half(suc(double(suc(zero)))))
| suc(half(suc(double(suc(zero))))) = suc(suc(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(suc(half(suc(double(suc(zero))))),suc(half(suc(double(suc(zero)))))) ),[1,0],$fot(suc(zero))]]) ).
cnf(refute_0_310,plain,
( half(suc(double(suc(zero)))) != suc(zero)
| suc(half(suc(double(suc(zero))))) = suc(suc(zero)) ),
inference(resolve,[$cnf( $equal(suc(half(suc(double(suc(zero))))),suc(half(suc(double(suc(zero)))))) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
suc(half(suc(double(suc(zero))))) = suc(suc(zero)),
inference(resolve,[$cnf( $equal(half(suc(double(suc(zero)))),suc(zero)) )],[refute_0_147,refute_0_310]) ).
cnf(refute_0_312,plain,
( suc(half(suc(double(suc(zero))))) != suc(suc(zero))
| suc(suc(zero)) != double(suc(zero))
| suc(half(suc(double(suc(zero))))) = double(suc(zero)) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(suc(half(suc(double(suc(zero))))))),bind(Y0,$fot(suc(suc(zero)))),bind(Z0,$fot(double(suc(zero))))]]) ).
cnf(refute_0_313,plain,
( suc(suc(zero)) != double(suc(zero))
| suc(half(suc(double(suc(zero))))) = double(suc(zero)) ),
inference(resolve,[$cnf( $equal(suc(half(suc(double(suc(zero))))),suc(suc(zero))) )],[refute_0_311,refute_0_312]) ).
cnf(refute_0_314,plain,
suc(half(suc(double(suc(zero))))) = double(suc(zero)),
inference(resolve,[$cnf( $equal(suc(suc(zero)),double(suc(zero))) )],[refute_0_21,refute_0_313]) ).
cnf(refute_0_315,plain,
( half(suc(double(double(suc(zero))))) != suc(half(suc(double(suc(zero)))))
| suc(half(suc(double(suc(zero))))) != double(suc(zero))
| half(suc(double(double(suc(zero))))) = double(suc(zero)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(half(suc(double(double(suc(zero))))),double(suc(zero))) ),[0],$fot(suc(half(suc(double(suc(zero))))))]]) ).
cnf(refute_0_316,plain,
( half(suc(double(double(suc(zero))))) != suc(half(suc(double(suc(zero)))))
| half(suc(double(double(suc(zero))))) = double(suc(zero)) ),
inference(resolve,[$cnf( $equal(suc(half(suc(double(suc(zero))))),double(suc(zero))) )],[refute_0_314,refute_0_315]) ).
cnf(refute_0_317,plain,
half(suc(double(double(suc(zero))))) = double(suc(zero)),
inference(resolve,[$cnf( $equal(half(suc(double(double(suc(zero))))),suc(half(suc(double(suc(zero)))))) )],[refute_0_307,refute_0_316]) ).
cnf(refute_0_318,plain,
suc(half(suc(double(double(suc(zero)))))) = suc(half(suc(double(double(suc(zero)))))),
introduced(tautology,[refl,[$fot(suc(half(suc(double(double(suc(zero)))))))]]) ).
cnf(refute_0_319,plain,
( half(suc(double(double(suc(zero))))) != double(suc(zero))
| suc(half(suc(double(double(suc(zero)))))) != suc(half(suc(double(double(suc(zero))))))
| suc(half(suc(double(double(suc(zero)))))) = suc(double(suc(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(half(suc(double(double(suc(zero)))))),suc(half(suc(double(double(suc(zero))))))) ),[1,0],$fot(double(suc(zero)))]]) ).
cnf(refute_0_320,plain,
( half(suc(double(double(suc(zero))))) != double(suc(zero))
| suc(half(suc(double(double(suc(zero)))))) = suc(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(suc(half(suc(double(double(suc(zero)))))),suc(half(suc(double(double(suc(zero))))))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
suc(half(suc(double(double(suc(zero)))))) = suc(double(suc(zero))),
inference(resolve,[$cnf( $equal(half(suc(double(double(suc(zero))))),double(suc(zero))) )],[refute_0_317,refute_0_320]) ).
cnf(refute_0_322,plain,
( half(proj1Suc(double(double(double(suc(zero)))))) != suc(half(suc(double(double(suc(zero))))))
| suc(half(suc(double(double(suc(zero)))))) != suc(double(suc(zero)))
| half(proj1Suc(double(double(double(suc(zero)))))) = suc(double(suc(zero))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(half(proj1Suc(double(double(double(suc(zero)))))),suc(double(suc(zero)))) ),[0],$fot(suc(half(suc(double(double(suc(zero)))))))]]) ).
cnf(refute_0_323,plain,
( half(proj1Suc(double(double(double(suc(zero)))))) != suc(half(suc(double(double(suc(zero))))))
| half(proj1Suc(double(double(double(suc(zero)))))) = suc(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(suc(half(suc(double(double(suc(zero)))))),suc(double(suc(zero)))) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
( half(suc(double(suc(double(suc(zero)))))) != suc(half(suc(double(double(suc(zero))))))
| half(proj1Suc(double(double(double(suc(zero)))))) = suc(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(half(proj1Suc(double(double(double(suc(zero)))))),suc(half(suc(double(double(suc(zero))))))) )],[refute_0_303,refute_0_323]) ).
cnf(refute_0_325,plain,
half(proj1Suc(double(double(double(suc(zero)))))) = suc(double(suc(zero))),
inference(resolve,[$cnf( $equal(half(suc(double(suc(double(suc(zero)))))),suc(half(suc(double(double(suc(zero))))))) )],[refute_0_265,refute_0_324]) ).
cnf(refute_0_326,plain,
suc(half(proj1Suc(double(double(double(suc(zero))))))) = suc(half(proj1Suc(double(double(double(suc(zero))))))),
introduced(tautology,[refl,[$fot(suc(half(proj1Suc(double(double(double(suc(zero))))))))]]) ).
cnf(refute_0_327,plain,
( half(proj1Suc(double(double(double(suc(zero)))))) != suc(double(suc(zero)))
| suc(half(proj1Suc(double(double(double(suc(zero))))))) != suc(half(proj1Suc(double(double(double(suc(zero)))))))
| suc(half(proj1Suc(double(double(double(suc(zero))))))) = suc(suc(double(suc(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(half(proj1Suc(double(double(double(suc(zero))))))),suc(half(proj1Suc(double(double(double(suc(zero)))))))) ),[1,0],$fot(suc(double(suc(zero))))]]) ).
cnf(refute_0_328,plain,
( half(proj1Suc(double(double(double(suc(zero)))))) != suc(double(suc(zero)))
| suc(half(proj1Suc(double(double(double(suc(zero))))))) = suc(suc(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(suc(half(proj1Suc(double(double(double(suc(zero))))))),suc(half(proj1Suc(double(double(double(suc(zero)))))))) )],[refute_0_326,refute_0_327]) ).
cnf(refute_0_329,plain,
suc(half(proj1Suc(double(double(double(suc(zero))))))) = suc(suc(double(suc(zero)))),
inference(resolve,[$cnf( $equal(half(proj1Suc(double(double(double(suc(zero)))))),suc(double(suc(zero)))) )],[refute_0_325,refute_0_328]) ).
cnf(refute_0_330,plain,
( suc(half(proj1Suc(double(double(double(suc(zero))))))) != suc(suc(double(suc(zero))))
| suc(suc(double(suc(zero)))) != double(double(suc(zero)))
| suc(half(proj1Suc(double(double(double(suc(zero))))))) = double(double(suc(zero))) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(suc(half(proj1Suc(double(double(double(suc(zero))))))))),bind(Y0,$fot(suc(suc(double(suc(zero)))))),bind(Z0,$fot(double(double(suc(zero)))))]]) ).
cnf(refute_0_331,plain,
( suc(suc(double(suc(zero)))) != double(double(suc(zero)))
| suc(half(proj1Suc(double(double(double(suc(zero))))))) = double(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(suc(half(proj1Suc(double(double(double(suc(zero))))))),suc(suc(double(suc(zero))))) )],[refute_0_329,refute_0_330]) ).
cnf(refute_0_332,plain,
suc(half(proj1Suc(double(double(double(suc(zero))))))) = double(double(suc(zero))),
inference(resolve,[$cnf( $equal(suc(suc(double(suc(zero)))),double(double(suc(zero)))) )],[refute_0_174,refute_0_331]) ).
cnf(refute_0_333,plain,
( half(suc(double(double(double(suc(zero)))))) != suc(half(proj1Suc(double(double(double(suc(zero)))))))
| suc(half(proj1Suc(double(double(double(suc(zero))))))) != double(double(suc(zero)))
| half(suc(double(double(double(suc(zero)))))) = double(double(suc(zero))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(half(suc(double(double(double(suc(zero)))))),double(double(suc(zero)))) ),[0],$fot(suc(half(proj1Suc(double(double(double(suc(zero))))))))]]) ).
cnf(refute_0_334,plain,
( half(suc(double(double(double(suc(zero)))))) != suc(half(proj1Suc(double(double(double(suc(zero)))))))
| half(suc(double(double(double(suc(zero)))))) = double(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(suc(half(proj1Suc(double(double(double(suc(zero))))))),double(double(suc(zero)))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
( half(suc(double(suc(suc(double(suc(zero))))))) != suc(half(proj1Suc(double(double(double(suc(zero)))))))
| half(suc(double(double(double(suc(zero)))))) = double(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(half(suc(double(double(double(suc(zero)))))),suc(half(proj1Suc(double(double(double(suc(zero)))))))) )],[refute_0_235,refute_0_334]) ).
cnf(refute_0_336,plain,
half(suc(double(double(double(suc(zero)))))) = double(double(suc(zero))),
inference(resolve,[$cnf( $equal(half(suc(double(suc(suc(double(suc(zero))))))),suc(half(proj1Suc(double(double(double(suc(zero)))))))) )],[refute_0_221,refute_0_335]) ).
cnf(refute_0_337,plain,
proj1Suc(double(suc(suc(double(double(suc(zero))))))) = addNat(suc(double(double(suc(zero)))),suc(suc(double(double(suc(zero)))))),
inference(subst,[],[refute_0_204:[bind(X_22,$fot(suc(double(double(suc(zero))))))]]) ).
cnf(refute_0_338,plain,
( proj1Suc(double(suc(suc(double(double(suc(zero))))))) != addNat(suc(double(double(suc(zero)))),suc(suc(double(double(suc(zero))))))
| suc(suc(double(double(suc(zero))))) != double(suc(double(suc(zero))))
| proj1Suc(double(suc(suc(double(double(suc(zero))))))) = addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(suc(suc(double(double(suc(zero))))))),addNat(suc(double(double(suc(zero)))),suc(suc(double(double(suc(zero))))))) ),[1,1],$fot(double(suc(double(suc(zero)))))]]) ).
cnf(refute_0_339,plain,
( proj1Suc(double(suc(suc(double(double(suc(zero))))))) != addNat(suc(double(double(suc(zero)))),suc(suc(double(double(suc(zero))))))
| proj1Suc(double(suc(suc(double(double(suc(zero))))))) = addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(suc(suc(double(double(suc(zero))))),double(suc(double(suc(zero))))) )],[refute_0_262,refute_0_338]) ).
cnf(refute_0_340,plain,
proj1Suc(double(suc(suc(double(double(suc(zero))))))) = addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero))))),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(suc(double(double(suc(zero))))))),addNat(suc(double(double(suc(zero)))),suc(suc(double(double(suc(zero))))))) )],[refute_0_337,refute_0_339]) ).
cnf(refute_0_341,plain,
double(suc(suc(double(double(suc(zero)))))) = double(suc(suc(double(double(suc(zero)))))),
introduced(tautology,[refl,[$fot(double(suc(suc(double(double(suc(zero)))))))]]) ).
cnf(refute_0_342,plain,
( double(suc(suc(double(double(suc(zero)))))) != double(suc(suc(double(double(suc(zero))))))
| suc(suc(double(double(suc(zero))))) != double(suc(double(suc(zero))))
| double(suc(suc(double(double(suc(zero)))))) = double(double(suc(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(suc(double(double(suc(zero)))))),double(suc(suc(double(double(suc(zero))))))) ),[1,0],$fot(double(suc(double(suc(zero)))))]]) ).
cnf(refute_0_343,plain,
( suc(suc(double(double(suc(zero))))) != double(suc(double(suc(zero))))
| double(suc(suc(double(double(suc(zero)))))) = double(double(suc(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(double(suc(suc(double(double(suc(zero)))))),double(suc(suc(double(double(suc(zero))))))) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
double(suc(suc(double(double(suc(zero)))))) = double(double(suc(double(suc(zero))))),
inference(resolve,[$cnf( $equal(suc(suc(double(double(suc(zero))))),double(suc(double(suc(zero))))) )],[refute_0_262,refute_0_343]) ).
cnf(refute_0_345,plain,
proj1Suc(double(suc(suc(double(double(suc(zero))))))) = proj1Suc(double(suc(suc(double(double(suc(zero))))))),
introduced(tautology,[refl,[$fot(proj1Suc(double(suc(suc(double(double(suc(zero))))))))]]) ).
cnf(refute_0_346,plain,
( double(suc(suc(double(double(suc(zero)))))) != double(double(suc(double(suc(zero)))))
| proj1Suc(double(suc(suc(double(double(suc(zero))))))) != proj1Suc(double(suc(suc(double(double(suc(zero)))))))
| proj1Suc(double(suc(suc(double(double(suc(zero))))))) = proj1Suc(double(double(suc(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(suc(suc(double(double(suc(zero))))))),proj1Suc(double(suc(suc(double(double(suc(zero)))))))) ),[1,0],$fot(double(double(suc(double(suc(zero))))))]]) ).
cnf(refute_0_347,plain,
( double(suc(suc(double(double(suc(zero)))))) != double(double(suc(double(suc(zero)))))
| proj1Suc(double(suc(suc(double(double(suc(zero))))))) = proj1Suc(double(double(suc(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(suc(double(double(suc(zero))))))),proj1Suc(double(suc(suc(double(double(suc(zero)))))))) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
proj1Suc(double(suc(suc(double(double(suc(zero))))))) = proj1Suc(double(double(suc(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(double(suc(suc(double(double(suc(zero)))))),double(double(suc(double(suc(zero)))))) )],[refute_0_344,refute_0_347]) ).
cnf(refute_0_349,plain,
( proj1Suc(double(suc(suc(double(double(suc(zero))))))) != addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero)))))
| proj1Suc(double(suc(suc(double(double(suc(zero))))))) != proj1Suc(double(double(suc(double(suc(zero))))))
| proj1Suc(double(double(suc(double(suc(zero)))))) = addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(suc(suc(double(double(suc(zero))))))),addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero)))))) ),[0],$fot(proj1Suc(double(double(suc(double(suc(zero)))))))]]) ).
cnf(refute_0_350,plain,
( proj1Suc(double(suc(suc(double(double(suc(zero))))))) != addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero)))))
| proj1Suc(double(double(suc(double(suc(zero)))))) = addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(suc(double(double(suc(zero))))))),proj1Suc(double(double(suc(double(suc(zero))))))) )],[refute_0_348,refute_0_349]) ).
cnf(refute_0_351,plain,
double(suc(suc(double(suc(zero))))) = suc(proj1Suc(double(suc(suc(double(suc(zero))))))),
inference(subst,[],[refute_0_244:[bind(X_21,$fot(suc(double(suc(zero)))))]]) ).
cnf(refute_0_352,plain,
( double(suc(suc(double(suc(zero))))) != suc(proj1Suc(double(suc(suc(double(suc(zero)))))))
| suc(suc(double(suc(zero)))) != double(double(suc(zero)))
| double(suc(suc(double(suc(zero))))) = suc(proj1Suc(double(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(suc(double(suc(zero))))),suc(proj1Suc(double(suc(suc(double(suc(zero)))))))) ),[1,0,0,0],$fot(double(double(suc(zero))))]]) ).
cnf(refute_0_353,plain,
( double(suc(suc(double(suc(zero))))) != suc(proj1Suc(double(suc(suc(double(suc(zero)))))))
| double(suc(suc(double(suc(zero))))) = suc(proj1Suc(double(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(suc(suc(double(suc(zero)))),double(double(suc(zero)))) )],[refute_0_174,refute_0_352]) ).
cnf(refute_0_354,plain,
double(suc(suc(double(suc(zero))))) = suc(proj1Suc(double(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(double(suc(suc(double(suc(zero))))),suc(proj1Suc(double(suc(suc(double(suc(zero)))))))) )],[refute_0_351,refute_0_353]) ).
cnf(refute_0_355,plain,
( double(suc(suc(double(suc(zero))))) != double(double(double(suc(zero))))
| double(suc(suc(double(suc(zero))))) != suc(proj1Suc(double(double(double(suc(zero))))))
| double(double(double(suc(zero)))) = suc(proj1Suc(double(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(suc(double(suc(zero))))),suc(proj1Suc(double(double(double(suc(zero))))))) ),[0],$fot(double(double(double(suc(zero)))))]]) ).
cnf(refute_0_356,plain,
( double(suc(suc(double(suc(zero))))) != suc(proj1Suc(double(double(double(suc(zero))))))
| double(double(double(suc(zero)))) = suc(proj1Suc(double(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(double(suc(suc(double(suc(zero))))),double(double(double(suc(zero))))) )],[refute_0_225,refute_0_355]) ).
cnf(refute_0_357,plain,
double(double(double(suc(zero)))) = suc(proj1Suc(double(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(double(suc(suc(double(suc(zero))))),suc(proj1Suc(double(double(double(suc(zero))))))) )],[refute_0_354,refute_0_356]) ).
cnf(refute_0_358,plain,
( double(double(double(suc(zero)))) != suc(proj1Suc(double(double(double(suc(zero))))))
| suc(proj1Suc(double(double(double(suc(zero)))))) = double(double(double(suc(zero)))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(double(double(double(suc(zero)))))),bind(Y0,$fot(suc(proj1Suc(double(double(double(suc(zero))))))))]]) ).
cnf(refute_0_359,plain,
suc(proj1Suc(double(double(double(suc(zero)))))) = double(double(double(suc(zero)))),
inference(resolve,[$cnf( $equal(double(double(double(suc(zero)))),suc(proj1Suc(double(double(double(suc(zero))))))) )],[refute_0_357,refute_0_358]) ).
cnf(refute_0_360,plain,
suc(suc(double(suc(double(suc(zero)))))) = suc(suc(double(suc(double(suc(zero)))))),
introduced(tautology,[refl,[$fot(suc(suc(double(suc(double(suc(zero)))))))]]) ).
cnf(refute_0_361,plain,
( suc(double(suc(double(suc(zero))))) != proj1Suc(double(double(double(suc(zero)))))
| suc(suc(double(suc(double(suc(zero)))))) != suc(suc(double(suc(double(suc(zero))))))
| suc(suc(double(suc(double(suc(zero)))))) = suc(proj1Suc(double(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(suc(double(suc(double(suc(zero)))))),suc(suc(double(suc(double(suc(zero))))))) ),[1,0],$fot(proj1Suc(double(double(double(suc(zero))))))]]) ).
cnf(refute_0_362,plain,
( suc(double(suc(double(suc(zero))))) != proj1Suc(double(double(double(suc(zero)))))
| suc(suc(double(suc(double(suc(zero)))))) = suc(proj1Suc(double(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(suc(suc(double(suc(double(suc(zero)))))),suc(suc(double(suc(double(suc(zero))))))) )],[refute_0_360,refute_0_361]) ).
cnf(refute_0_363,plain,
suc(suc(double(suc(double(suc(zero)))))) = suc(proj1Suc(double(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(suc(double(suc(double(suc(zero))))),proj1Suc(double(double(double(suc(zero)))))) )],[refute_0_297,refute_0_362]) ).
cnf(refute_0_364,plain,
( suc(proj1Suc(double(double(double(suc(zero)))))) != double(double(double(suc(zero))))
| suc(suc(double(suc(double(suc(zero)))))) != suc(proj1Suc(double(double(double(suc(zero))))))
| suc(suc(double(suc(double(suc(zero)))))) = double(double(double(suc(zero)))) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(suc(suc(double(suc(double(suc(zero)))))))),bind(Y0,$fot(suc(proj1Suc(double(double(double(suc(zero)))))))),bind(Z0,$fot(double(double(double(suc(zero))))))]]) ).
cnf(refute_0_365,plain,
( suc(proj1Suc(double(double(double(suc(zero)))))) != double(double(double(suc(zero))))
| suc(suc(double(suc(double(suc(zero)))))) = double(double(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(suc(suc(double(suc(double(suc(zero)))))),suc(proj1Suc(double(double(double(suc(zero))))))) )],[refute_0_363,refute_0_364]) ).
cnf(refute_0_366,plain,
suc(suc(double(suc(double(suc(zero)))))) = double(double(double(suc(zero)))),
inference(resolve,[$cnf( $equal(suc(proj1Suc(double(double(double(suc(zero)))))),double(double(double(suc(zero))))) )],[refute_0_359,refute_0_365]) ).
cnf(refute_0_367,plain,
suc(suc(suc(double(suc(double(suc(zero))))))) = suc(suc(suc(double(suc(double(suc(zero))))))),
introduced(tautology,[refl,[$fot(suc(suc(suc(double(suc(double(suc(zero))))))))]]) ).
cnf(refute_0_368,plain,
( suc(suc(double(suc(double(suc(zero)))))) != double(double(double(suc(zero))))
| suc(suc(suc(double(suc(double(suc(zero))))))) != suc(suc(suc(double(suc(double(suc(zero)))))))
| suc(suc(suc(double(suc(double(suc(zero))))))) = suc(double(double(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(suc(suc(double(suc(double(suc(zero))))))),suc(suc(suc(double(suc(double(suc(zero)))))))) ),[1,0],$fot(double(double(double(suc(zero)))))]]) ).
cnf(refute_0_369,plain,
( suc(suc(double(suc(double(suc(zero)))))) != double(double(double(suc(zero))))
| suc(suc(suc(double(suc(double(suc(zero))))))) = suc(double(double(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(suc(suc(suc(double(suc(double(suc(zero))))))),suc(suc(suc(double(suc(double(suc(zero)))))))) )],[refute_0_367,refute_0_368]) ).
cnf(refute_0_370,plain,
suc(suc(suc(double(suc(double(suc(zero))))))) = suc(double(double(double(suc(zero))))),
inference(resolve,[$cnf( $equal(suc(suc(double(suc(double(suc(zero)))))),double(double(double(suc(zero))))) )],[refute_0_366,refute_0_369]) ).
cnf(refute_0_371,plain,
suc(suc(suc(suc(double(suc(double(suc(zero)))))))) = suc(suc(suc(suc(double(suc(double(suc(zero)))))))),
introduced(tautology,[refl,[$fot(suc(suc(suc(suc(double(suc(double(suc(zero)))))))))]]) ).
cnf(refute_0_372,plain,
( suc(suc(suc(double(suc(double(suc(zero))))))) != suc(double(double(double(suc(zero)))))
| suc(suc(suc(suc(double(suc(double(suc(zero)))))))) != suc(suc(suc(suc(double(suc(double(suc(zero))))))))
| suc(suc(suc(suc(double(suc(double(suc(zero)))))))) = suc(suc(double(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(suc(suc(suc(double(suc(double(suc(zero)))))))),suc(suc(suc(suc(double(suc(double(suc(zero))))))))) ),[1,0],$fot(suc(double(double(double(suc(zero))))))]]) ).
cnf(refute_0_373,plain,
( suc(suc(suc(double(suc(double(suc(zero))))))) != suc(double(double(double(suc(zero)))))
| suc(suc(suc(suc(double(suc(double(suc(zero)))))))) = suc(suc(double(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(suc(suc(suc(suc(double(suc(double(suc(zero)))))))),suc(suc(suc(suc(double(suc(double(suc(zero))))))))) )],[refute_0_371,refute_0_372]) ).
cnf(refute_0_374,plain,
suc(suc(suc(suc(double(suc(double(suc(zero)))))))) = suc(suc(double(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(suc(suc(suc(double(suc(double(suc(zero))))))),suc(double(double(double(suc(zero)))))) )],[refute_0_370,refute_0_373]) ).
cnf(refute_0_375,plain,
addNat(suc(suc(double(suc(zero)))),Y) = suc(addNat(suc(double(suc(zero))),Y)),
inference(subst,[],[refute_0_6:[bind(Z,$fot(suc(double(suc(zero)))))]]) ).
cnf(refute_0_376,plain,
( addNat(suc(suc(double(suc(zero)))),Y) != suc(addNat(suc(double(suc(zero))),Y))
| suc(suc(double(suc(zero)))) != double(double(suc(zero)))
| addNat(double(double(suc(zero))),Y) = suc(addNat(suc(double(suc(zero))),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(addNat(suc(suc(double(suc(zero)))),Y),suc(addNat(suc(double(suc(zero))),Y))) ),[0,0],$fot(double(double(suc(zero))))]]) ).
cnf(refute_0_377,plain,
( addNat(suc(suc(double(suc(zero)))),Y) != suc(addNat(suc(double(suc(zero))),Y))
| addNat(double(double(suc(zero))),Y) = suc(addNat(suc(double(suc(zero))),Y)) ),
inference(resolve,[$cnf( $equal(suc(suc(double(suc(zero)))),double(double(suc(zero)))) )],[refute_0_174,refute_0_376]) ).
cnf(refute_0_378,plain,
addNat(double(double(suc(zero))),Y) = suc(addNat(suc(double(suc(zero))),Y)),
inference(resolve,[$cnf( $equal(addNat(suc(suc(double(suc(zero)))),Y),suc(addNat(suc(double(suc(zero))),Y))) )],[refute_0_375,refute_0_377]) ).
cnf(refute_0_379,plain,
suc(addNat(double(suc(zero)),Y)) = suc(addNat(double(suc(zero)),Y)),
introduced(tautology,[refl,[$fot(suc(addNat(double(suc(zero)),Y)))]]) ).
cnf(refute_0_380,plain,
( addNat(double(suc(zero)),Y) != suc(suc(Y))
| suc(addNat(double(suc(zero)),Y)) != suc(addNat(double(suc(zero)),Y))
| suc(addNat(double(suc(zero)),Y)) = suc(suc(suc(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(addNat(double(suc(zero)),Y)),suc(addNat(double(suc(zero)),Y))) ),[1,0],$fot(suc(suc(Y)))]]) ).
cnf(refute_0_381,plain,
( addNat(double(suc(zero)),Y) != suc(suc(Y))
| suc(addNat(double(suc(zero)),Y)) = suc(suc(suc(Y))) ),
inference(resolve,[$cnf( $equal(suc(addNat(double(suc(zero)),Y)),suc(addNat(double(suc(zero)),Y))) )],[refute_0_379,refute_0_380]) ).
cnf(refute_0_382,plain,
suc(addNat(double(suc(zero)),Y)) = suc(suc(suc(Y))),
inference(resolve,[$cnf( $equal(addNat(double(suc(zero)),Y),suc(suc(Y))) )],[refute_0_168,refute_0_381]) ).
cnf(refute_0_383,plain,
addNat(suc(double(suc(zero))),Y) = suc(addNat(double(suc(zero)),Y)),
inference(subst,[],[refute_0_6:[bind(Z,$fot(double(suc(zero))))]]) ).
cnf(refute_0_384,plain,
( addNat(suc(double(suc(zero))),Y) != suc(addNat(double(suc(zero)),Y))
| suc(addNat(double(suc(zero)),Y)) != suc(suc(suc(Y)))
| addNat(suc(double(suc(zero))),Y) = suc(suc(suc(Y))) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(addNat(suc(double(suc(zero))),Y))),bind(Y0,$fot(suc(addNat(double(suc(zero)),Y)))),bind(Z0,$fot(suc(suc(suc(Y)))))]]) ).
cnf(refute_0_385,plain,
( suc(addNat(double(suc(zero)),Y)) != suc(suc(suc(Y)))
| addNat(suc(double(suc(zero))),Y) = suc(suc(suc(Y))) ),
inference(resolve,[$cnf( $equal(addNat(suc(double(suc(zero))),Y),suc(addNat(double(suc(zero)),Y))) )],[refute_0_383,refute_0_384]) ).
cnf(refute_0_386,plain,
addNat(suc(double(suc(zero))),Y) = suc(suc(suc(Y))),
inference(resolve,[$cnf( $equal(suc(addNat(double(suc(zero)),Y)),suc(suc(suc(Y)))) )],[refute_0_382,refute_0_385]) ).
cnf(refute_0_387,plain,
suc(addNat(suc(double(suc(zero))),Y)) = suc(addNat(suc(double(suc(zero))),Y)),
introduced(tautology,[refl,[$fot(suc(addNat(suc(double(suc(zero))),Y)))]]) ).
cnf(refute_0_388,plain,
( addNat(suc(double(suc(zero))),Y) != suc(suc(suc(Y)))
| suc(addNat(suc(double(suc(zero))),Y)) != suc(addNat(suc(double(suc(zero))),Y))
| suc(addNat(suc(double(suc(zero))),Y)) = suc(suc(suc(suc(Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(addNat(suc(double(suc(zero))),Y)),suc(addNat(suc(double(suc(zero))),Y))) ),[1,0],$fot(suc(suc(suc(Y))))]]) ).
cnf(refute_0_389,plain,
( addNat(suc(double(suc(zero))),Y) != suc(suc(suc(Y)))
| suc(addNat(suc(double(suc(zero))),Y)) = suc(suc(suc(suc(Y)))) ),
inference(resolve,[$cnf( $equal(suc(addNat(suc(double(suc(zero))),Y)),suc(addNat(suc(double(suc(zero))),Y))) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
suc(addNat(suc(double(suc(zero))),Y)) = suc(suc(suc(suc(Y)))),
inference(resolve,[$cnf( $equal(addNat(suc(double(suc(zero))),Y),suc(suc(suc(Y)))) )],[refute_0_386,refute_0_389]) ).
cnf(refute_0_391,plain,
( addNat(double(double(suc(zero))),Y) != suc(addNat(suc(double(suc(zero))),Y))
| suc(addNat(suc(double(suc(zero))),Y)) != suc(suc(suc(suc(Y))))
| addNat(double(double(suc(zero))),Y) = suc(suc(suc(suc(Y)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(addNat(double(double(suc(zero))),Y),suc(suc(suc(suc(Y))))) ),[0],$fot(suc(addNat(suc(double(suc(zero))),Y)))]]) ).
cnf(refute_0_392,plain,
( addNat(double(double(suc(zero))),Y) != suc(addNat(suc(double(suc(zero))),Y))
| addNat(double(double(suc(zero))),Y) = suc(suc(suc(suc(Y)))) ),
inference(resolve,[$cnf( $equal(suc(addNat(suc(double(suc(zero))),Y)),suc(suc(suc(suc(Y))))) )],[refute_0_390,refute_0_391]) ).
cnf(refute_0_393,plain,
addNat(double(double(suc(zero))),Y) = suc(suc(suc(suc(Y)))),
inference(resolve,[$cnf( $equal(addNat(double(double(suc(zero))),Y),suc(addNat(suc(double(suc(zero))),Y))) )],[refute_0_378,refute_0_392]) ).
cnf(refute_0_394,plain,
addNat(double(double(suc(zero))),double(suc(double(suc(zero))))) = suc(suc(suc(suc(double(suc(double(suc(zero)))))))),
inference(subst,[],[refute_0_393:[bind(Y,$fot(double(suc(double(suc(zero))))))]]) ).
cnf(refute_0_395,plain,
( addNat(double(double(suc(zero))),double(suc(double(suc(zero))))) != suc(suc(suc(suc(double(suc(double(suc(zero))))))))
| suc(suc(suc(suc(double(suc(double(suc(zero)))))))) != suc(suc(double(double(double(suc(zero))))))
| addNat(double(double(suc(zero))),double(suc(double(suc(zero))))) = suc(suc(double(double(double(suc(zero)))))) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(addNat(double(double(suc(zero))),double(suc(double(suc(zero))))))),bind(Y0,$fot(suc(suc(suc(suc(double(suc(double(suc(zero)))))))))),bind(Z0,$fot(suc(suc(double(double(double(suc(zero))))))))]]) ).
cnf(refute_0_396,plain,
( suc(suc(suc(suc(double(suc(double(suc(zero)))))))) != suc(suc(double(double(double(suc(zero))))))
| addNat(double(double(suc(zero))),double(suc(double(suc(zero))))) = suc(suc(double(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(addNat(double(double(suc(zero))),double(suc(double(suc(zero))))),suc(suc(suc(suc(double(suc(double(suc(zero))))))))) )],[refute_0_394,refute_0_395]) ).
cnf(refute_0_397,plain,
addNat(double(double(suc(zero))),double(suc(double(suc(zero))))) = suc(suc(double(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(suc(suc(suc(suc(double(suc(double(suc(zero)))))))),suc(suc(double(double(double(suc(zero))))))) )],[refute_0_374,refute_0_396]) ).
cnf(refute_0_398,plain,
suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero)))))) = suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero)))))),
introduced(tautology,[refl,[$fot(suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero)))))))]]) ).
cnf(refute_0_399,plain,
( addNat(double(double(suc(zero))),double(suc(double(suc(zero))))) != suc(suc(double(double(double(suc(zero))))))
| suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero)))))) != suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero))))))
| suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero)))))) = suc(suc(suc(double(double(double(suc(zero))))))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero)))))),suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero))))))) ),[1,0],$fot(suc(suc(double(double(double(suc(zero)))))))]]) ).
cnf(refute_0_400,plain,
( addNat(double(double(suc(zero))),double(suc(double(suc(zero))))) != suc(suc(double(double(double(suc(zero))))))
| suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero)))))) = suc(suc(suc(double(double(double(suc(zero))))))) ),
inference(resolve,[$cnf( $equal(suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero)))))),suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero))))))) )],[refute_0_398,refute_0_399]) ).
cnf(refute_0_401,plain,
suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero)))))) = suc(suc(suc(double(double(double(suc(zero))))))),
inference(resolve,[$cnf( $equal(addNat(double(double(suc(zero))),double(suc(double(suc(zero))))),suc(suc(double(double(double(suc(zero))))))) )],[refute_0_397,refute_0_400]) ).
cnf(refute_0_402,plain,
addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero))))) = suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero)))))),
inference(subst,[],[refute_0_6:[bind(Y,$fot(double(suc(double(suc(zero)))))),bind(Z,$fot(double(double(suc(zero)))))]]) ).
cnf(refute_0_403,plain,
( addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero))))) != suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero))))))
| suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero)))))) != suc(suc(suc(double(double(double(suc(zero)))))))
| addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero))))) = suc(suc(suc(double(double(double(suc(zero))))))) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero))))))),bind(Y0,$fot(suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero)))))))),bind(Z0,$fot(suc(suc(suc(double(double(double(suc(zero)))))))))]]) ).
cnf(refute_0_404,plain,
( suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero)))))) != suc(suc(suc(double(double(double(suc(zero)))))))
| addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero))))) = suc(suc(suc(double(double(double(suc(zero))))))) ),
inference(resolve,[$cnf( $equal(addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero))))),suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero))))))) )],[refute_0_402,refute_0_403]) ).
cnf(refute_0_405,plain,
addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero))))) = suc(suc(suc(double(double(double(suc(zero))))))),
inference(resolve,[$cnf( $equal(suc(addNat(double(double(suc(zero))),double(suc(double(suc(zero)))))),suc(suc(suc(double(double(double(suc(zero)))))))) )],[refute_0_401,refute_0_404]) ).
cnf(refute_0_406,plain,
( addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero))))) != suc(suc(suc(double(double(double(suc(zero)))))))
| proj1Suc(double(double(suc(double(suc(zero)))))) != addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero)))))
| proj1Suc(double(double(suc(double(suc(zero)))))) = suc(suc(suc(double(double(double(suc(zero))))))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(double(suc(double(suc(zero)))))),addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero)))))) ),[1],$fot(suc(suc(suc(double(double(double(suc(zero))))))))]]) ).
cnf(refute_0_407,plain,
( proj1Suc(double(double(suc(double(suc(zero)))))) != addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero)))))
| proj1Suc(double(double(suc(double(suc(zero)))))) = suc(suc(suc(double(double(double(suc(zero))))))) ),
inference(resolve,[$cnf( $equal(addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero))))),suc(suc(suc(double(double(double(suc(zero)))))))) )],[refute_0_405,refute_0_406]) ).
cnf(refute_0_408,plain,
( proj1Suc(double(suc(suc(double(double(suc(zero))))))) != addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero)))))
| proj1Suc(double(double(suc(double(suc(zero)))))) = suc(suc(suc(double(double(double(suc(zero))))))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(double(suc(double(suc(zero)))))),addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero)))))) )],[refute_0_350,refute_0_407]) ).
cnf(refute_0_409,plain,
proj1Suc(double(double(suc(double(suc(zero)))))) = suc(suc(suc(double(double(double(suc(zero))))))),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(suc(double(double(suc(zero))))))),addNat(suc(double(double(suc(zero)))),double(suc(double(suc(zero)))))) )],[refute_0_340,refute_0_408]) ).
cnf(refute_0_410,plain,
double(suc(double(double(suc(zero))))) = suc(proj1Suc(double(suc(double(double(suc(zero))))))),
inference(subst,[],[refute_0_244:[bind(X_21,$fot(double(double(suc(zero)))))]]) ).
cnf(refute_0_411,plain,
addNat(suc(Z),suc(suc(Z))) = suc(addNat(Z,suc(suc(Z)))),
inference(subst,[],[refute_0_6:[bind(Y,$fot(suc(suc(Z))))]]) ).
cnf(refute_0_412,plain,
proj1Suc(double(suc(suc(Z)))) = addNat(suc(Z),suc(suc(Z))),
inference(subst,[],[refute_0_204:[bind(X_22,$fot(suc(Z)))]]) ).
cnf(refute_0_413,plain,
( proj1Suc(double(suc(suc(Z)))) != addNat(suc(Z),suc(suc(Z)))
| addNat(suc(Z),suc(suc(Z))) = proj1Suc(double(suc(suc(Z)))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(proj1Suc(double(suc(suc(Z)))))),bind(Y0,$fot(addNat(suc(Z),suc(suc(Z)))))]]) ).
cnf(refute_0_414,plain,
addNat(suc(Z),suc(suc(Z))) = proj1Suc(double(suc(suc(Z)))),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(suc(Z)))),addNat(suc(Z),suc(suc(Z)))) )],[refute_0_412,refute_0_413]) ).
cnf(refute_0_415,plain,
( addNat(suc(Z),suc(suc(Z))) != proj1Suc(double(suc(suc(Z))))
| addNat(suc(Z),suc(suc(Z))) != suc(addNat(Z,suc(suc(Z))))
| proj1Suc(double(suc(suc(Z)))) = suc(addNat(Z,suc(suc(Z)))) ),
introduced(tautology,[equality,[$cnf( $equal(addNat(suc(Z),suc(suc(Z))),suc(addNat(Z,suc(suc(Z))))) ),[0],$fot(proj1Suc(double(suc(suc(Z)))))]]) ).
cnf(refute_0_416,plain,
( addNat(suc(Z),suc(suc(Z))) != suc(addNat(Z,suc(suc(Z))))
| proj1Suc(double(suc(suc(Z)))) = suc(addNat(Z,suc(suc(Z)))) ),
inference(resolve,[$cnf( $equal(addNat(suc(Z),suc(suc(Z))),proj1Suc(double(suc(suc(Z))))) )],[refute_0_414,refute_0_415]) ).
cnf(refute_0_417,plain,
proj1Suc(double(suc(suc(Z)))) = suc(addNat(Z,suc(suc(Z)))),
inference(resolve,[$cnf( $equal(addNat(suc(Z),suc(suc(Z))),suc(addNat(Z,suc(suc(Z))))) )],[refute_0_411,refute_0_416]) ).
cnf(refute_0_418,plain,
proj1Suc(double(suc(suc(suc(double(suc(zero))))))) = suc(addNat(suc(double(suc(zero))),suc(suc(suc(double(suc(zero))))))),
inference(subst,[],[refute_0_417:[bind(Z,$fot(suc(double(suc(zero)))))]]) ).
cnf(refute_0_419,plain,
( proj1Suc(double(suc(suc(suc(double(suc(zero))))))) != suc(addNat(suc(double(suc(zero))),suc(suc(suc(double(suc(zero)))))))
| suc(suc(double(suc(zero)))) != double(double(suc(zero)))
| proj1Suc(double(suc(suc(suc(double(suc(zero))))))) = suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(suc(suc(suc(double(suc(zero))))))),suc(addNat(suc(double(suc(zero))),suc(suc(suc(double(suc(zero)))))))) ),[1,0,1,0],$fot(double(double(suc(zero))))]]) ).
cnf(refute_0_420,plain,
( proj1Suc(double(suc(suc(suc(double(suc(zero))))))) != suc(addNat(suc(double(suc(zero))),suc(suc(suc(double(suc(zero)))))))
| proj1Suc(double(suc(suc(suc(double(suc(zero))))))) = suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(suc(suc(double(suc(zero)))),double(double(suc(zero)))) )],[refute_0_174,refute_0_419]) ).
cnf(refute_0_421,plain,
proj1Suc(double(suc(suc(suc(double(suc(zero))))))) = suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(suc(suc(double(suc(zero))))))),suc(addNat(suc(double(suc(zero))),suc(suc(suc(double(suc(zero)))))))) )],[refute_0_418,refute_0_420]) ).
cnf(refute_0_422,plain,
double(suc(suc(suc(double(suc(zero)))))) = double(suc(suc(suc(double(suc(zero)))))),
introduced(tautology,[refl,[$fot(double(suc(suc(suc(double(suc(zero)))))))]]) ).
cnf(refute_0_423,plain,
( double(suc(suc(suc(double(suc(zero)))))) != double(suc(suc(suc(double(suc(zero))))))
| suc(suc(suc(double(suc(zero))))) != suc(double(double(suc(zero))))
| double(suc(suc(suc(double(suc(zero)))))) = double(suc(double(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(suc(suc(double(suc(zero)))))),double(suc(suc(suc(double(suc(zero))))))) ),[1,0],$fot(suc(double(double(suc(zero)))))]]) ).
cnf(refute_0_424,plain,
( suc(suc(suc(double(suc(zero))))) != suc(double(double(suc(zero))))
| double(suc(suc(suc(double(suc(zero)))))) = double(suc(double(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(double(suc(suc(suc(double(suc(zero)))))),double(suc(suc(suc(double(suc(zero))))))) )],[refute_0_422,refute_0_423]) ).
cnf(refute_0_425,plain,
double(suc(suc(suc(double(suc(zero)))))) = double(suc(double(double(suc(zero))))),
inference(resolve,[$cnf( $equal(suc(suc(suc(double(suc(zero))))),suc(double(double(suc(zero))))) )],[refute_0_254,refute_0_424]) ).
cnf(refute_0_426,plain,
proj1Suc(double(suc(suc(suc(double(suc(zero))))))) = proj1Suc(double(suc(suc(suc(double(suc(zero))))))),
introduced(tautology,[refl,[$fot(proj1Suc(double(suc(suc(suc(double(suc(zero))))))))]]) ).
cnf(refute_0_427,plain,
( double(suc(suc(suc(double(suc(zero)))))) != double(suc(double(double(suc(zero)))))
| proj1Suc(double(suc(suc(suc(double(suc(zero))))))) != proj1Suc(double(suc(suc(suc(double(suc(zero)))))))
| proj1Suc(double(suc(suc(suc(double(suc(zero))))))) = proj1Suc(double(suc(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(suc(suc(suc(double(suc(zero))))))),proj1Suc(double(suc(suc(suc(double(suc(zero)))))))) ),[1,0],$fot(double(suc(double(double(suc(zero))))))]]) ).
cnf(refute_0_428,plain,
( double(suc(suc(suc(double(suc(zero)))))) != double(suc(double(double(suc(zero)))))
| proj1Suc(double(suc(suc(suc(double(suc(zero))))))) = proj1Suc(double(suc(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(suc(suc(double(suc(zero))))))),proj1Suc(double(suc(suc(suc(double(suc(zero)))))))) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
proj1Suc(double(suc(suc(suc(double(suc(zero))))))) = proj1Suc(double(suc(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(double(suc(suc(suc(double(suc(zero)))))),double(suc(double(double(suc(zero)))))) )],[refute_0_425,refute_0_428]) ).
cnf(refute_0_430,plain,
( proj1Suc(double(suc(suc(suc(double(suc(zero))))))) != proj1Suc(double(suc(double(double(suc(zero))))))
| proj1Suc(double(suc(suc(suc(double(suc(zero))))))) != suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))))
| proj1Suc(double(suc(double(double(suc(zero)))))) = suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(suc(suc(suc(double(suc(zero))))))),suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))))) ),[0],$fot(proj1Suc(double(suc(double(double(suc(zero)))))))]]) ).
cnf(refute_0_431,plain,
( proj1Suc(double(suc(suc(suc(double(suc(zero))))))) != suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))))
| proj1Suc(double(suc(double(double(suc(zero)))))) = suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(suc(suc(double(suc(zero))))))),proj1Suc(double(suc(double(double(suc(zero))))))) )],[refute_0_429,refute_0_430]) ).
cnf(refute_0_432,plain,
( suc(double(suc(double(suc(zero))))) != proj1Suc(double(double(double(suc(zero)))))
| suc(suc(suc(double(double(suc(zero)))))) != suc(double(suc(double(suc(zero)))))
| suc(suc(suc(double(double(suc(zero)))))) = proj1Suc(double(double(double(suc(zero))))) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(suc(suc(suc(double(double(suc(zero)))))))),bind(Y0,$fot(suc(double(suc(double(suc(zero))))))),bind(Z0,$fot(proj1Suc(double(double(double(suc(zero)))))))]]) ).
cnf(refute_0_433,plain,
( suc(double(suc(double(suc(zero))))) != proj1Suc(double(double(double(suc(zero)))))
| suc(suc(suc(double(double(suc(zero)))))) = proj1Suc(double(double(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(suc(suc(suc(double(double(suc(zero)))))),suc(double(suc(double(suc(zero)))))) )],[refute_0_292,refute_0_432]) ).
cnf(refute_0_434,plain,
suc(suc(suc(double(double(suc(zero)))))) = proj1Suc(double(double(double(suc(zero))))),
inference(resolve,[$cnf( $equal(suc(double(suc(double(suc(zero))))),proj1Suc(double(double(double(suc(zero)))))) )],[refute_0_297,refute_0_433]) ).
cnf(refute_0_435,plain,
addNat(double(suc(zero)),suc(double(double(suc(zero))))) = suc(suc(suc(double(double(suc(zero)))))),
inference(subst,[],[refute_0_168:[bind(Y,$fot(suc(double(double(suc(zero))))))]]) ).
cnf(refute_0_436,plain,
( addNat(double(suc(zero)),suc(double(double(suc(zero))))) != suc(suc(suc(double(double(suc(zero))))))
| suc(suc(suc(double(double(suc(zero)))))) != proj1Suc(double(double(double(suc(zero)))))
| addNat(double(suc(zero)),suc(double(double(suc(zero))))) = proj1Suc(double(double(double(suc(zero))))) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(addNat(double(suc(zero)),suc(double(double(suc(zero))))))),bind(Y0,$fot(suc(suc(suc(double(double(suc(zero)))))))),bind(Z0,$fot(proj1Suc(double(double(double(suc(zero)))))))]]) ).
cnf(refute_0_437,plain,
( suc(suc(suc(double(double(suc(zero)))))) != proj1Suc(double(double(double(suc(zero)))))
| addNat(double(suc(zero)),suc(double(double(suc(zero))))) = proj1Suc(double(double(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(addNat(double(suc(zero)),suc(double(double(suc(zero))))),suc(suc(suc(double(double(suc(zero))))))) )],[refute_0_435,refute_0_436]) ).
cnf(refute_0_438,plain,
addNat(double(suc(zero)),suc(double(double(suc(zero))))) = proj1Suc(double(double(double(suc(zero))))),
inference(resolve,[$cnf( $equal(suc(suc(suc(double(double(suc(zero)))))),proj1Suc(double(double(double(suc(zero)))))) )],[refute_0_434,refute_0_437]) ).
cnf(refute_0_439,plain,
suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))) = suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))),
introduced(tautology,[refl,[$fot(suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))))]]) ).
cnf(refute_0_440,plain,
( addNat(double(suc(zero)),suc(double(double(suc(zero))))) != proj1Suc(double(double(double(suc(zero)))))
| suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))) != suc(addNat(double(suc(zero)),suc(double(double(suc(zero))))))
| suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))) = suc(proj1Suc(double(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))),suc(addNat(double(suc(zero)),suc(double(double(suc(zero))))))) ),[1,0],$fot(proj1Suc(double(double(double(suc(zero))))))]]) ).
cnf(refute_0_441,plain,
( addNat(double(suc(zero)),suc(double(double(suc(zero))))) != proj1Suc(double(double(double(suc(zero)))))
| suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))) = suc(proj1Suc(double(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))),suc(addNat(double(suc(zero)),suc(double(double(suc(zero))))))) )],[refute_0_439,refute_0_440]) ).
cnf(refute_0_442,plain,
suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))) = suc(proj1Suc(double(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(addNat(double(suc(zero)),suc(double(double(suc(zero))))),proj1Suc(double(double(double(suc(zero)))))) )],[refute_0_438,refute_0_441]) ).
cnf(refute_0_443,plain,
( suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))) != suc(proj1Suc(double(double(double(suc(zero))))))
| suc(proj1Suc(double(double(double(suc(zero)))))) != double(double(double(suc(zero))))
| suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))) = double(double(double(suc(zero)))) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))))),bind(Y0,$fot(suc(proj1Suc(double(double(double(suc(zero)))))))),bind(Z0,$fot(double(double(double(suc(zero))))))]]) ).
cnf(refute_0_444,plain,
( suc(proj1Suc(double(double(double(suc(zero)))))) != double(double(double(suc(zero))))
| suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))) = double(double(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))),suc(proj1Suc(double(double(double(suc(zero))))))) )],[refute_0_442,refute_0_443]) ).
cnf(refute_0_445,plain,
suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))) = double(double(double(suc(zero)))),
inference(resolve,[$cnf( $equal(suc(proj1Suc(double(double(double(suc(zero)))))),double(double(double(suc(zero))))) )],[refute_0_359,refute_0_444]) ).
cnf(refute_0_446,plain,
addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))) = suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))),
inference(subst,[],[refute_0_6:[bind(Y,$fot(suc(double(double(suc(zero)))))),bind(Z,$fot(double(suc(zero))))]]) ).
cnf(refute_0_447,plain,
( addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))) != suc(addNat(double(suc(zero)),suc(double(double(suc(zero))))))
| suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))) != double(double(double(suc(zero))))
| addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))) = double(double(double(suc(zero)))) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))))),bind(Y0,$fot(suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))))),bind(Z0,$fot(double(double(double(suc(zero))))))]]) ).
cnf(refute_0_448,plain,
( suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))) != double(double(double(suc(zero))))
| addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))) = double(double(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))),suc(addNat(double(suc(zero)),suc(double(double(suc(zero))))))) )],[refute_0_446,refute_0_447]) ).
cnf(refute_0_449,plain,
addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))) = double(double(double(suc(zero)))),
inference(resolve,[$cnf( $equal(suc(addNat(double(suc(zero)),suc(double(double(suc(zero)))))),double(double(double(suc(zero))))) )],[refute_0_445,refute_0_448]) ).
cnf(refute_0_450,plain,
suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))) = suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))),
introduced(tautology,[refl,[$fot(suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))))]]) ).
cnf(refute_0_451,plain,
( addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))) != double(double(double(suc(zero))))
| suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))) != suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))))
| suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))) = suc(double(double(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))),suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))))) ),[1,0],$fot(double(double(double(suc(zero)))))]]) ).
cnf(refute_0_452,plain,
( addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))) != double(double(double(suc(zero))))
| suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))) = suc(double(double(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))),suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))))) )],[refute_0_450,refute_0_451]) ).
cnf(refute_0_453,plain,
suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))) = suc(double(double(double(suc(zero))))),
inference(resolve,[$cnf( $equal(addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))),double(double(double(suc(zero))))) )],[refute_0_449,refute_0_452]) ).
cnf(refute_0_454,plain,
( proj1Suc(double(suc(double(double(suc(zero)))))) != suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))))
| suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))) != suc(double(double(double(suc(zero)))))
| proj1Suc(double(suc(double(double(suc(zero)))))) = suc(double(double(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(proj1Suc(double(suc(double(double(suc(zero)))))),suc(double(double(double(suc(zero)))))) ),[0],$fot(suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))))]]) ).
cnf(refute_0_455,plain,
( proj1Suc(double(suc(double(double(suc(zero)))))) != suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))))
| proj1Suc(double(suc(double(double(suc(zero)))))) = suc(double(double(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero)))))),suc(double(double(double(suc(zero)))))) )],[refute_0_453,refute_0_454]) ).
cnf(refute_0_456,plain,
( proj1Suc(double(suc(suc(suc(double(suc(zero))))))) != suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))))
| proj1Suc(double(suc(double(double(suc(zero)))))) = suc(double(double(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(double(double(suc(zero)))))),suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))))) )],[refute_0_431,refute_0_455]) ).
cnf(refute_0_457,plain,
proj1Suc(double(suc(double(double(suc(zero)))))) = suc(double(double(double(suc(zero))))),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(suc(suc(double(suc(zero))))))),suc(addNat(suc(double(suc(zero))),suc(double(double(suc(zero))))))) )],[refute_0_421,refute_0_456]) ).
cnf(refute_0_458,plain,
( double(suc(double(double(suc(zero))))) != suc(proj1Suc(double(suc(double(double(suc(zero)))))))
| proj1Suc(double(suc(double(double(suc(zero)))))) != suc(double(double(double(suc(zero)))))
| double(suc(double(double(suc(zero))))) = suc(suc(double(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(double(double(suc(zero))))),suc(proj1Suc(double(suc(double(double(suc(zero)))))))) ),[1,0],$fot(suc(double(double(double(suc(zero))))))]]) ).
cnf(refute_0_459,plain,
( double(suc(double(double(suc(zero))))) != suc(proj1Suc(double(suc(double(double(suc(zero)))))))
| double(suc(double(double(suc(zero))))) = suc(suc(double(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(double(double(suc(zero)))))),suc(double(double(double(suc(zero)))))) )],[refute_0_457,refute_0_458]) ).
cnf(refute_0_460,plain,
double(suc(double(double(suc(zero))))) = suc(suc(double(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(double(suc(double(double(suc(zero))))),suc(proj1Suc(double(suc(double(double(suc(zero)))))))) )],[refute_0_410,refute_0_459]) ).
cnf(refute_0_461,plain,
( double(suc(double(double(suc(zero))))) != suc(suc(double(double(double(suc(zero))))))
| suc(suc(double(double(double(suc(zero)))))) = double(suc(double(double(suc(zero))))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(double(suc(double(double(suc(zero))))))),bind(Y0,$fot(suc(suc(double(double(double(suc(zero))))))))]]) ).
cnf(refute_0_462,plain,
suc(suc(double(double(double(suc(zero)))))) = double(suc(double(double(suc(zero))))),
inference(resolve,[$cnf( $equal(double(suc(double(double(suc(zero))))),suc(suc(double(double(double(suc(zero))))))) )],[refute_0_460,refute_0_461]) ).
cnf(refute_0_463,plain,
suc(suc(suc(double(double(double(suc(zero))))))) = suc(suc(suc(double(double(double(suc(zero))))))),
introduced(tautology,[refl,[$fot(suc(suc(suc(double(double(double(suc(zero))))))))]]) ).
cnf(refute_0_464,plain,
( suc(suc(double(double(double(suc(zero)))))) != double(suc(double(double(suc(zero)))))
| suc(suc(suc(double(double(double(suc(zero))))))) != suc(suc(suc(double(double(double(suc(zero)))))))
| suc(suc(suc(double(double(double(suc(zero))))))) = suc(double(suc(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(suc(suc(double(double(double(suc(zero))))))),suc(suc(suc(double(double(double(suc(zero)))))))) ),[1,0],$fot(double(suc(double(double(suc(zero))))))]]) ).
cnf(refute_0_465,plain,
( suc(suc(double(double(double(suc(zero)))))) != double(suc(double(double(suc(zero)))))
| suc(suc(suc(double(double(double(suc(zero))))))) = suc(double(suc(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(suc(suc(suc(double(double(double(suc(zero))))))),suc(suc(suc(double(double(double(suc(zero)))))))) )],[refute_0_463,refute_0_464]) ).
cnf(refute_0_466,plain,
suc(suc(suc(double(double(double(suc(zero))))))) = suc(double(suc(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(suc(suc(double(double(double(suc(zero)))))),double(suc(double(double(suc(zero)))))) )],[refute_0_462,refute_0_465]) ).
cnf(refute_0_467,plain,
( proj1Suc(double(double(suc(double(suc(zero)))))) != suc(suc(suc(double(double(double(suc(zero)))))))
| suc(suc(suc(double(double(double(suc(zero))))))) != suc(double(suc(double(double(suc(zero))))))
| proj1Suc(double(double(suc(double(suc(zero)))))) = suc(double(suc(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(proj1Suc(double(double(suc(double(suc(zero)))))),suc(double(suc(double(double(suc(zero))))))) ),[0],$fot(suc(suc(suc(double(double(double(suc(zero))))))))]]) ).
cnf(refute_0_468,plain,
( proj1Suc(double(double(suc(double(suc(zero)))))) != suc(suc(suc(double(double(double(suc(zero)))))))
| proj1Suc(double(double(suc(double(suc(zero)))))) = suc(double(suc(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(suc(suc(suc(double(double(double(suc(zero))))))),suc(double(suc(double(double(suc(zero))))))) )],[refute_0_466,refute_0_467]) ).
cnf(refute_0_469,plain,
proj1Suc(double(double(suc(double(suc(zero)))))) = suc(double(suc(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(proj1Suc(double(double(suc(double(suc(zero)))))),suc(suc(suc(double(double(double(suc(zero)))))))) )],[refute_0_409,refute_0_468]) ).
cnf(refute_0_470,plain,
double(suc(double(rd(Xs)))) = suc(proj1Suc(double(suc(double(rd(Xs)))))),
inference(subst,[],[refute_0_244:[bind(X_21,$fot(double(rd(Xs))))]]) ).
cnf(refute_0_471,plain,
( double(suc(double(rd(Xs)))) != suc(proj1Suc(double(suc(double(rd(Xs))))))
| suc(double(rd(Xs))) != rd(cons(i,Xs))
| double(suc(double(rd(Xs)))) = suc(proj1Suc(double(rd(cons(i,Xs))))) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(double(rd(Xs)))),suc(proj1Suc(double(suc(double(rd(Xs))))))) ),[1,0,0,0],$fot(rd(cons(i,Xs)))]]) ).
cnf(refute_0_472,plain,
( double(suc(double(rd(Xs)))) != suc(proj1Suc(double(suc(double(rd(Xs))))))
| double(suc(double(rd(Xs)))) = suc(proj1Suc(double(rd(cons(i,Xs))))) ),
inference(resolve,[$cnf( $equal(suc(double(rd(Xs))),rd(cons(i,Xs))) )],[refute_0_65,refute_0_471]) ).
cnf(refute_0_473,plain,
double(suc(double(rd(Xs)))) = suc(proj1Suc(double(rd(cons(i,Xs))))),
inference(resolve,[$cnf( $equal(double(suc(double(rd(Xs)))),suc(proj1Suc(double(suc(double(rd(Xs))))))) )],[refute_0_470,refute_0_472]) ).
cnf(refute_0_474,plain,
double(suc(double(rd(Xs)))) = double(suc(double(rd(Xs)))),
introduced(tautology,[refl,[$fot(double(suc(double(rd(Xs)))))]]) ).
cnf(refute_0_475,plain,
( double(suc(double(rd(Xs)))) != double(suc(double(rd(Xs))))
| suc(double(rd(Xs))) != rd(cons(i,Xs))
| double(suc(double(rd(Xs)))) = double(rd(cons(i,Xs))) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(double(rd(Xs)))),double(suc(double(rd(Xs))))) ),[1,0],$fot(rd(cons(i,Xs)))]]) ).
cnf(refute_0_476,plain,
( suc(double(rd(Xs))) != rd(cons(i,Xs))
| double(suc(double(rd(Xs)))) = double(rd(cons(i,Xs))) ),
inference(resolve,[$cnf( $equal(double(suc(double(rd(Xs)))),double(suc(double(rd(Xs))))) )],[refute_0_474,refute_0_475]) ).
cnf(refute_0_477,plain,
double(suc(double(rd(Xs)))) = double(rd(cons(i,Xs))),
inference(resolve,[$cnf( $equal(suc(double(rd(Xs))),rd(cons(i,Xs))) )],[refute_0_65,refute_0_476]) ).
cnf(refute_0_478,plain,
( double(suc(double(rd(Xs)))) != double(rd(cons(i,Xs)))
| double(suc(double(rd(Xs)))) != suc(proj1Suc(double(rd(cons(i,Xs)))))
| double(rd(cons(i,Xs))) = suc(proj1Suc(double(rd(cons(i,Xs))))) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(double(rd(Xs)))),suc(proj1Suc(double(rd(cons(i,Xs)))))) ),[0],$fot(double(rd(cons(i,Xs))))]]) ).
cnf(refute_0_479,plain,
( double(suc(double(rd(Xs)))) != suc(proj1Suc(double(rd(cons(i,Xs)))))
| double(rd(cons(i,Xs))) = suc(proj1Suc(double(rd(cons(i,Xs))))) ),
inference(resolve,[$cnf( $equal(double(suc(double(rd(Xs)))),double(rd(cons(i,Xs)))) )],[refute_0_477,refute_0_478]) ).
cnf(refute_0_480,plain,
double(rd(cons(i,Xs))) = suc(proj1Suc(double(rd(cons(i,Xs))))),
inference(resolve,[$cnf( $equal(double(suc(double(rd(Xs)))),suc(proj1Suc(double(rd(cons(i,Xs)))))) )],[refute_0_473,refute_0_479]) ).
cnf(refute_0_481,plain,
double(rd(cons(i,shw(X_69)))) = suc(proj1Suc(double(rd(cons(i,shw(X_69)))))),
inference(subst,[],[refute_0_480:[bind(Xs,$fot(shw(X_69)))]]) ).
cnf(refute_0_482,plain,
x(X,Y) = rd(append(shw(X),shw(Y))),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_483,plain,
x(suc(zero),Y) = rd(append(shw(suc(zero)),shw(Y))),
inference(subst,[],[refute_0_482:[bind(X,$fot(suc(zero)))]]) ).
cnf(refute_0_484,plain,
append(cons(Z,Xs),Y) = cons(Z,append(Xs,Y)),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_485,plain,
append(cons(i,nil),X_66) = cons(i,append(nil,X_66)),
inference(subst,[],[refute_0_484:[bind(Xs,$fot(nil)),bind(Y,$fot(X_66)),bind(Z,$fot(i))]]) ).
cnf(refute_0_486,plain,
( cons(i,nil) != shw(suc(zero))
| append(cons(i,nil),X_66) != cons(i,append(nil,X_66))
| append(shw(suc(zero)),X_66) = cons(i,append(nil,X_66)) ),
introduced(tautology,[equality,[$cnf( $equal(append(cons(i,nil),X_66),cons(i,append(nil,X_66))) ),[0,0],$fot(shw(suc(zero)))]]) ).
cnf(refute_0_487,plain,
( append(cons(i,nil),X_66) != cons(i,append(nil,X_66))
| append(shw(suc(zero)),X_66) = cons(i,append(nil,X_66)) ),
inference(resolve,[$cnf( $equal(cons(i,nil),shw(suc(zero))) )],[refute_0_127,refute_0_486]) ).
cnf(refute_0_488,plain,
append(shw(suc(zero)),X_66) = cons(i,append(nil,X_66)),
inference(resolve,[$cnf( $equal(append(cons(i,nil),X_66),cons(i,append(nil,X_66))) )],[refute_0_485,refute_0_487]) ).
cnf(refute_0_489,plain,
append(nil,Y) = Y,
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_490,plain,
append(nil,X_66) = X_66,
inference(subst,[],[refute_0_489:[bind(Y,$fot(X_66))]]) ).
cnf(refute_0_491,plain,
cons(i,append(nil,X_66)) = cons(i,append(nil,X_66)),
introduced(tautology,[refl,[$fot(cons(i,append(nil,X_66)))]]) ).
cnf(refute_0_492,plain,
( cons(i,append(nil,X_66)) != cons(i,append(nil,X_66))
| append(nil,X_66) != X_66
| cons(i,append(nil,X_66)) = cons(i,X_66) ),
introduced(tautology,[equality,[$cnf( $equal(cons(i,append(nil,X_66)),cons(i,append(nil,X_66))) ),[1,1],$fot(X_66)]]) ).
cnf(refute_0_493,plain,
( append(nil,X_66) != X_66
| cons(i,append(nil,X_66)) = cons(i,X_66) ),
inference(resolve,[$cnf( $equal(cons(i,append(nil,X_66)),cons(i,append(nil,X_66))) )],[refute_0_491,refute_0_492]) ).
cnf(refute_0_494,plain,
cons(i,append(nil,X_66)) = cons(i,X_66),
inference(resolve,[$cnf( $equal(append(nil,X_66),X_66) )],[refute_0_490,refute_0_493]) ).
cnf(refute_0_495,plain,
( cons(i,append(nil,X_66)) != cons(i,X_66)
| append(shw(suc(zero)),X_66) != cons(i,append(nil,X_66))
| append(shw(suc(zero)),X_66) = cons(i,X_66) ),
introduced(tautology,[equality,[$cnf( $equal(append(shw(suc(zero)),X_66),cons(i,append(nil,X_66))) ),[1],$fot(cons(i,X_66))]]) ).
cnf(refute_0_496,plain,
( append(shw(suc(zero)),X_66) != cons(i,append(nil,X_66))
| append(shw(suc(zero)),X_66) = cons(i,X_66) ),
inference(resolve,[$cnf( $equal(cons(i,append(nil,X_66)),cons(i,X_66)) )],[refute_0_494,refute_0_495]) ).
cnf(refute_0_497,plain,
append(shw(suc(zero)),X_66) = cons(i,X_66),
inference(resolve,[$cnf( $equal(append(shw(suc(zero)),X_66),cons(i,append(nil,X_66))) )],[refute_0_488,refute_0_496]) ).
cnf(refute_0_498,plain,
append(shw(suc(zero)),shw(Y)) = cons(i,shw(Y)),
inference(subst,[],[refute_0_497:[bind(X_66,$fot(shw(Y)))]]) ).
cnf(refute_0_499,plain,
( append(shw(suc(zero)),shw(Y)) != cons(i,shw(Y))
| x(suc(zero),Y) != rd(append(shw(suc(zero)),shw(Y)))
| x(suc(zero),Y) = rd(cons(i,shw(Y))) ),
introduced(tautology,[equality,[$cnf( $equal(x(suc(zero),Y),rd(append(shw(suc(zero)),shw(Y)))) ),[1,0],$fot(cons(i,shw(Y)))]]) ).
cnf(refute_0_500,plain,
( x(suc(zero),Y) != rd(append(shw(suc(zero)),shw(Y)))
| x(suc(zero),Y) = rd(cons(i,shw(Y))) ),
inference(resolve,[$cnf( $equal(append(shw(suc(zero)),shw(Y)),cons(i,shw(Y))) )],[refute_0_498,refute_0_499]) ).
cnf(refute_0_501,plain,
x(suc(zero),Y) = rd(cons(i,shw(Y))),
inference(resolve,[$cnf( $equal(x(suc(zero),Y),rd(append(shw(suc(zero)),shw(Y)))) )],[refute_0_483,refute_0_500]) ).
cnf(refute_0_502,plain,
x(suc(zero),X_69) = rd(cons(i,shw(X_69))),
inference(subst,[],[refute_0_501:[bind(Y,$fot(X_69))]]) ).
cnf(refute_0_503,plain,
( x(suc(zero),X_69) != rd(cons(i,shw(X_69)))
| rd(cons(i,shw(X_69))) = x(suc(zero),X_69) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(x(suc(zero),X_69))),bind(Y0,$fot(rd(cons(i,shw(X_69)))))]]) ).
cnf(refute_0_504,plain,
rd(cons(i,shw(X_69))) = x(suc(zero),X_69),
inference(resolve,[$cnf( $equal(x(suc(zero),X_69),rd(cons(i,shw(X_69)))) )],[refute_0_502,refute_0_503]) ).
cnf(refute_0_505,plain,
( double(rd(cons(i,shw(X_69)))) != suc(proj1Suc(double(rd(cons(i,shw(X_69))))))
| rd(cons(i,shw(X_69))) != x(suc(zero),X_69)
| double(rd(cons(i,shw(X_69)))) = suc(proj1Suc(double(x(suc(zero),X_69)))) ),
introduced(tautology,[equality,[$cnf( $equal(double(rd(cons(i,shw(X_69)))),suc(proj1Suc(double(rd(cons(i,shw(X_69))))))) ),[1,0,0,0],$fot(x(suc(zero),X_69))]]) ).
cnf(refute_0_506,plain,
( double(rd(cons(i,shw(X_69)))) != suc(proj1Suc(double(rd(cons(i,shw(X_69))))))
| double(rd(cons(i,shw(X_69)))) = suc(proj1Suc(double(x(suc(zero),X_69)))) ),
inference(resolve,[$cnf( $equal(rd(cons(i,shw(X_69))),x(suc(zero),X_69)) )],[refute_0_504,refute_0_505]) ).
cnf(refute_0_507,plain,
double(rd(cons(i,shw(X_69)))) = suc(proj1Suc(double(x(suc(zero),X_69)))),
inference(resolve,[$cnf( $equal(double(rd(cons(i,shw(X_69)))),suc(proj1Suc(double(rd(cons(i,shw(X_69))))))) )],[refute_0_481,refute_0_506]) ).
cnf(refute_0_508,plain,
double(rd(cons(i,shw(X_69)))) = double(rd(cons(i,shw(X_69)))),
introduced(tautology,[refl,[$fot(double(rd(cons(i,shw(X_69)))))]]) ).
cnf(refute_0_509,plain,
( double(rd(cons(i,shw(X_69)))) != double(rd(cons(i,shw(X_69))))
| rd(cons(i,shw(X_69))) != x(suc(zero),X_69)
| double(rd(cons(i,shw(X_69)))) = double(x(suc(zero),X_69)) ),
introduced(tautology,[equality,[$cnf( $equal(double(rd(cons(i,shw(X_69)))),double(rd(cons(i,shw(X_69))))) ),[1,0],$fot(x(suc(zero),X_69))]]) ).
cnf(refute_0_510,plain,
( rd(cons(i,shw(X_69))) != x(suc(zero),X_69)
| double(rd(cons(i,shw(X_69)))) = double(x(suc(zero),X_69)) ),
inference(resolve,[$cnf( $equal(double(rd(cons(i,shw(X_69)))),double(rd(cons(i,shw(X_69))))) )],[refute_0_508,refute_0_509]) ).
cnf(refute_0_511,plain,
double(rd(cons(i,shw(X_69)))) = double(x(suc(zero),X_69)),
inference(resolve,[$cnf( $equal(rd(cons(i,shw(X_69))),x(suc(zero),X_69)) )],[refute_0_504,refute_0_510]) ).
cnf(refute_0_512,plain,
( double(rd(cons(i,shw(X_69)))) != double(x(suc(zero),X_69))
| double(rd(cons(i,shw(X_69)))) != suc(proj1Suc(double(x(suc(zero),X_69))))
| double(x(suc(zero),X_69)) = suc(proj1Suc(double(x(suc(zero),X_69)))) ),
introduced(tautology,[equality,[$cnf( $equal(double(rd(cons(i,shw(X_69)))),suc(proj1Suc(double(x(suc(zero),X_69))))) ),[0],$fot(double(x(suc(zero),X_69)))]]) ).
cnf(refute_0_513,plain,
( double(rd(cons(i,shw(X_69)))) != suc(proj1Suc(double(x(suc(zero),X_69))))
| double(x(suc(zero),X_69)) = suc(proj1Suc(double(x(suc(zero),X_69)))) ),
inference(resolve,[$cnf( $equal(double(rd(cons(i,shw(X_69)))),double(x(suc(zero),X_69))) )],[refute_0_511,refute_0_512]) ).
cnf(refute_0_514,plain,
double(x(suc(zero),X_69)) = suc(proj1Suc(double(x(suc(zero),X_69)))),
inference(resolve,[$cnf( $equal(double(rd(cons(i,shw(X_69)))),suc(proj1Suc(double(x(suc(zero),X_69))))) )],[refute_0_507,refute_0_513]) ).
cnf(refute_0_515,plain,
double(x(suc(zero),X_78)) = suc(proj1Suc(double(x(suc(zero),X_78)))),
inference(subst,[],[refute_0_514:[bind(X_69,$fot(X_78))]]) ).
cnf(refute_0_516,plain,
x(X,Y) = x(Y,X),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_517,plain,
x(X_78,suc(zero)) = x(suc(zero),X_78),
inference(subst,[],[refute_0_516:[bind(X,$fot(X_78)),bind(Y,$fot(suc(zero)))]]) ).
cnf(refute_0_518,plain,
( x(X_78,suc(zero)) != x(suc(zero),X_78)
| x(suc(zero),X_78) = x(X_78,suc(zero)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(x(X_78,suc(zero)))),bind(Y0,$fot(x(suc(zero),X_78)))]]) ).
cnf(refute_0_519,plain,
x(suc(zero),X_78) = x(X_78,suc(zero)),
inference(resolve,[$cnf( $equal(x(X_78,suc(zero)),x(suc(zero),X_78)) )],[refute_0_517,refute_0_518]) ).
cnf(refute_0_520,plain,
( double(x(suc(zero),X_78)) != suc(proj1Suc(double(x(suc(zero),X_78))))
| x(suc(zero),X_78) != x(X_78,suc(zero))
| double(x(suc(zero),X_78)) = suc(proj1Suc(double(x(X_78,suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(double(x(suc(zero),X_78)),suc(proj1Suc(double(x(suc(zero),X_78))))) ),[1,0,0,0],$fot(x(X_78,suc(zero)))]]) ).
cnf(refute_0_521,plain,
( double(x(suc(zero),X_78)) != suc(proj1Suc(double(x(suc(zero),X_78))))
| double(x(suc(zero),X_78)) = suc(proj1Suc(double(x(X_78,suc(zero))))) ),
inference(resolve,[$cnf( $equal(x(suc(zero),X_78),x(X_78,suc(zero))) )],[refute_0_519,refute_0_520]) ).
cnf(refute_0_522,plain,
double(x(suc(zero),X_78)) = suc(proj1Suc(double(x(X_78,suc(zero))))),
inference(resolve,[$cnf( $equal(double(x(suc(zero),X_78)),suc(proj1Suc(double(x(suc(zero),X_78))))) )],[refute_0_515,refute_0_521]) ).
cnf(refute_0_523,plain,
double(x(suc(zero),double(suc(zero)))) = suc(proj1Suc(double(x(double(suc(zero)),suc(zero))))),
inference(subst,[],[refute_0_522:[bind(X_78,$fot(double(suc(zero))))]]) ).
cnf(refute_0_524,plain,
x(double(suc(zero)),Y) = rd(append(shw(double(suc(zero))),shw(Y))),
inference(subst,[],[refute_0_482:[bind(X,$fot(double(suc(zero))))]]) ).
cnf(refute_0_525,plain,
append(cons(o,shw(suc(zero))),Y) = cons(o,append(shw(suc(zero)),Y)),
inference(subst,[],[refute_0_484:[bind(Xs,$fot(shw(suc(zero)))),bind(Z,$fot(o))]]) ).
cnf(refute_0_526,plain,
( cons(o,shw(suc(zero))) != shw(double(suc(zero)))
| append(cons(o,shw(suc(zero))),Y) != cons(o,append(shw(suc(zero)),Y))
| append(shw(double(suc(zero))),Y) = cons(o,append(shw(suc(zero)),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(append(cons(o,shw(suc(zero))),Y),cons(o,append(shw(suc(zero)),Y))) ),[0,0],$fot(shw(double(suc(zero))))]]) ).
cnf(refute_0_527,plain,
( append(cons(o,shw(suc(zero))),Y) != cons(o,append(shw(suc(zero)),Y))
| append(shw(double(suc(zero))),Y) = cons(o,append(shw(suc(zero)),Y)) ),
inference(resolve,[$cnf( $equal(cons(o,shw(suc(zero))),shw(double(suc(zero)))) )],[refute_0_106,refute_0_526]) ).
cnf(refute_0_528,plain,
append(shw(double(suc(zero))),Y) = cons(o,append(shw(suc(zero)),Y)),
inference(resolve,[$cnf( $equal(append(cons(o,shw(suc(zero))),Y),cons(o,append(shw(suc(zero)),Y))) )],[refute_0_525,refute_0_527]) ).
cnf(refute_0_529,plain,
append(shw(suc(zero)),Y) = cons(i,Y),
inference(subst,[],[refute_0_497:[bind(X_66,$fot(Y))]]) ).
cnf(refute_0_530,plain,
cons(o,append(shw(suc(zero)),Y)) = cons(o,append(shw(suc(zero)),Y)),
introduced(tautology,[refl,[$fot(cons(o,append(shw(suc(zero)),Y)))]]) ).
cnf(refute_0_531,plain,
( cons(o,append(shw(suc(zero)),Y)) != cons(o,append(shw(suc(zero)),Y))
| append(shw(suc(zero)),Y) != cons(i,Y)
| cons(o,append(shw(suc(zero)),Y)) = cons(o,cons(i,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(cons(o,append(shw(suc(zero)),Y)),cons(o,append(shw(suc(zero)),Y))) ),[1,1],$fot(cons(i,Y))]]) ).
cnf(refute_0_532,plain,
( append(shw(suc(zero)),Y) != cons(i,Y)
| cons(o,append(shw(suc(zero)),Y)) = cons(o,cons(i,Y)) ),
inference(resolve,[$cnf( $equal(cons(o,append(shw(suc(zero)),Y)),cons(o,append(shw(suc(zero)),Y))) )],[refute_0_530,refute_0_531]) ).
cnf(refute_0_533,plain,
cons(o,append(shw(suc(zero)),Y)) = cons(o,cons(i,Y)),
inference(resolve,[$cnf( $equal(append(shw(suc(zero)),Y),cons(i,Y)) )],[refute_0_529,refute_0_532]) ).
cnf(refute_0_534,plain,
( cons(o,append(shw(suc(zero)),Y)) != cons(o,cons(i,Y))
| append(shw(double(suc(zero))),Y) != cons(o,append(shw(suc(zero)),Y))
| append(shw(double(suc(zero))),Y) = cons(o,cons(i,Y)) ),
introduced(tautology,[equality,[$cnf( $equal(append(shw(double(suc(zero))),Y),cons(o,append(shw(suc(zero)),Y))) ),[1],$fot(cons(o,cons(i,Y)))]]) ).
cnf(refute_0_535,plain,
( append(shw(double(suc(zero))),Y) != cons(o,append(shw(suc(zero)),Y))
| append(shw(double(suc(zero))),Y) = cons(o,cons(i,Y)) ),
inference(resolve,[$cnf( $equal(cons(o,append(shw(suc(zero)),Y)),cons(o,cons(i,Y))) )],[refute_0_533,refute_0_534]) ).
cnf(refute_0_536,plain,
append(shw(double(suc(zero))),Y) = cons(o,cons(i,Y)),
inference(resolve,[$cnf( $equal(append(shw(double(suc(zero))),Y),cons(o,append(shw(suc(zero)),Y))) )],[refute_0_528,refute_0_535]) ).
cnf(refute_0_537,plain,
append(shw(double(suc(zero))),shw(Y)) = cons(o,cons(i,shw(Y))),
inference(subst,[],[refute_0_536:[bind(Y,$fot(shw(Y)))]]) ).
cnf(refute_0_538,plain,
( append(shw(double(suc(zero))),shw(Y)) != cons(o,cons(i,shw(Y)))
| x(double(suc(zero)),Y) != rd(append(shw(double(suc(zero))),shw(Y)))
| x(double(suc(zero)),Y) = rd(cons(o,cons(i,shw(Y)))) ),
introduced(tautology,[equality,[$cnf( $equal(x(double(suc(zero)),Y),rd(append(shw(double(suc(zero))),shw(Y)))) ),[1,0],$fot(cons(o,cons(i,shw(Y))))]]) ).
cnf(refute_0_539,plain,
( x(double(suc(zero)),Y) != rd(append(shw(double(suc(zero))),shw(Y)))
| x(double(suc(zero)),Y) = rd(cons(o,cons(i,shw(Y)))) ),
inference(resolve,[$cnf( $equal(append(shw(double(suc(zero))),shw(Y)),cons(o,cons(i,shw(Y)))) )],[refute_0_537,refute_0_538]) ).
cnf(refute_0_540,plain,
x(double(suc(zero)),Y) = rd(cons(o,cons(i,shw(Y)))),
inference(resolve,[$cnf( $equal(x(double(suc(zero)),Y),rd(append(shw(double(suc(zero))),shw(Y)))) )],[refute_0_524,refute_0_539]) ).
cnf(refute_0_541,plain,
( x(suc(zero),Y) != rd(cons(i,shw(Y)))
| rd(cons(i,shw(Y))) = x(suc(zero),Y) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(x(suc(zero),Y))),bind(Y0,$fot(rd(cons(i,shw(Y)))))]]) ).
cnf(refute_0_542,plain,
rd(cons(i,shw(Y))) = x(suc(zero),Y),
inference(resolve,[$cnf( $equal(x(suc(zero),Y),rd(cons(i,shw(Y)))) )],[refute_0_501,refute_0_541]) ).
cnf(refute_0_543,plain,
double(rd(cons(i,shw(Y)))) = double(rd(cons(i,shw(Y)))),
introduced(tautology,[refl,[$fot(double(rd(cons(i,shw(Y)))))]]) ).
cnf(refute_0_544,plain,
( double(rd(cons(i,shw(Y)))) != double(rd(cons(i,shw(Y))))
| rd(cons(i,shw(Y))) != x(suc(zero),Y)
| double(rd(cons(i,shw(Y)))) = double(x(suc(zero),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(double(rd(cons(i,shw(Y)))),double(rd(cons(i,shw(Y))))) ),[1,0],$fot(x(suc(zero),Y))]]) ).
cnf(refute_0_545,plain,
( rd(cons(i,shw(Y))) != x(suc(zero),Y)
| double(rd(cons(i,shw(Y)))) = double(x(suc(zero),Y)) ),
inference(resolve,[$cnf( $equal(double(rd(cons(i,shw(Y)))),double(rd(cons(i,shw(Y))))) )],[refute_0_543,refute_0_544]) ).
cnf(refute_0_546,plain,
double(rd(cons(i,shw(Y)))) = double(x(suc(zero),Y)),
inference(resolve,[$cnf( $equal(rd(cons(i,shw(Y))),x(suc(zero),Y)) )],[refute_0_542,refute_0_545]) ).
cnf(refute_0_547,plain,
rd(cons(o,Xs)) = double(rd(Xs)),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_548,plain,
rd(cons(o,cons(i,shw(Y)))) = double(rd(cons(i,shw(Y)))),
inference(subst,[],[refute_0_547:[bind(Xs,$fot(cons(i,shw(Y))))]]) ).
cnf(refute_0_549,plain,
( double(rd(cons(i,shw(Y)))) != double(x(suc(zero),Y))
| rd(cons(o,cons(i,shw(Y)))) != double(rd(cons(i,shw(Y))))
| rd(cons(o,cons(i,shw(Y)))) = double(x(suc(zero),Y)) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(rd(cons(o,cons(i,shw(Y)))))),bind(Y0,$fot(double(rd(cons(i,shw(Y)))))),bind(Z0,$fot(double(x(suc(zero),Y))))]]) ).
cnf(refute_0_550,plain,
( double(rd(cons(i,shw(Y)))) != double(x(suc(zero),Y))
| rd(cons(o,cons(i,shw(Y)))) = double(x(suc(zero),Y)) ),
inference(resolve,[$cnf( $equal(rd(cons(o,cons(i,shw(Y)))),double(rd(cons(i,shw(Y))))) )],[refute_0_548,refute_0_549]) ).
cnf(refute_0_551,plain,
rd(cons(o,cons(i,shw(Y)))) = double(x(suc(zero),Y)),
inference(resolve,[$cnf( $equal(double(rd(cons(i,shw(Y)))),double(x(suc(zero),Y))) )],[refute_0_546,refute_0_550]) ).
cnf(refute_0_552,plain,
( rd(cons(o,cons(i,shw(Y)))) != double(x(suc(zero),Y))
| x(double(suc(zero)),Y) != rd(cons(o,cons(i,shw(Y))))
| x(double(suc(zero)),Y) = double(x(suc(zero),Y)) ),
introduced(tautology,[equality,[$cnf( $equal(x(double(suc(zero)),Y),rd(cons(o,cons(i,shw(Y))))) ),[1],$fot(double(x(suc(zero),Y)))]]) ).
cnf(refute_0_553,plain,
( x(double(suc(zero)),Y) != rd(cons(o,cons(i,shw(Y))))
| x(double(suc(zero)),Y) = double(x(suc(zero),Y)) ),
inference(resolve,[$cnf( $equal(rd(cons(o,cons(i,shw(Y)))),double(x(suc(zero),Y))) )],[refute_0_551,refute_0_552]) ).
cnf(refute_0_554,plain,
x(double(suc(zero)),Y) = double(x(suc(zero),Y)),
inference(resolve,[$cnf( $equal(x(double(suc(zero)),Y),rd(cons(o,cons(i,shw(Y))))) )],[refute_0_540,refute_0_553]) ).
cnf(refute_0_555,plain,
x(double(suc(zero)),suc(zero)) = double(x(suc(zero),suc(zero))),
inference(subst,[],[refute_0_554:[bind(Y,$fot(suc(zero)))]]) ).
cnf(refute_0_556,plain,
( double(x(suc(zero),double(suc(zero)))) != suc(proj1Suc(double(x(double(suc(zero)),suc(zero)))))
| x(double(suc(zero)),suc(zero)) != double(x(suc(zero),suc(zero)))
| double(x(suc(zero),double(suc(zero)))) = suc(proj1Suc(double(double(x(suc(zero),suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(double(x(suc(zero),double(suc(zero)))),suc(proj1Suc(double(x(double(suc(zero)),suc(zero)))))) ),[1,0,0,0],$fot(double(x(suc(zero),suc(zero))))]]) ).
cnf(refute_0_557,plain,
( double(x(suc(zero),double(suc(zero)))) != suc(proj1Suc(double(x(double(suc(zero)),suc(zero)))))
| double(x(suc(zero),double(suc(zero)))) = suc(proj1Suc(double(double(x(suc(zero),suc(zero)))))) ),
inference(resolve,[$cnf( $equal(x(double(suc(zero)),suc(zero)),double(x(suc(zero),suc(zero)))) )],[refute_0_555,refute_0_556]) ).
cnf(refute_0_558,plain,
double(x(suc(zero),double(suc(zero)))) = suc(proj1Suc(double(double(x(suc(zero),suc(zero)))))),
inference(resolve,[$cnf( $equal(double(x(suc(zero),double(suc(zero)))),suc(proj1Suc(double(x(double(suc(zero)),suc(zero)))))) )],[refute_0_523,refute_0_557]) ).
cnf(refute_0_559,plain,
rd(cons(i,cons(o,Xs))) = suc(double(rd(cons(o,Xs)))),
inference(subst,[],[refute_0_63:[bind(Xs,$fot(cons(o,Xs)))]]) ).
cnf(refute_0_560,plain,
( rd(cons(i,cons(o,Xs))) != suc(double(rd(cons(o,Xs))))
| rd(cons(o,Xs)) != double(rd(Xs))
| rd(cons(i,cons(o,Xs))) = suc(double(double(rd(Xs)))) ),
introduced(tautology,[equality,[$cnf( $equal(rd(cons(i,cons(o,Xs))),suc(double(rd(cons(o,Xs))))) ),[1,0,0],$fot(double(rd(Xs)))]]) ).
cnf(refute_0_561,plain,
( rd(cons(i,cons(o,Xs))) != suc(double(rd(cons(o,Xs))))
| rd(cons(i,cons(o,Xs))) = suc(double(double(rd(Xs)))) ),
inference(resolve,[$cnf( $equal(rd(cons(o,Xs)),double(rd(Xs))) )],[refute_0_547,refute_0_560]) ).
cnf(refute_0_562,plain,
rd(cons(i,cons(o,Xs))) = suc(double(double(rd(Xs)))),
inference(resolve,[$cnf( $equal(rd(cons(i,cons(o,Xs))),suc(double(rd(cons(o,Xs))))) )],[refute_0_559,refute_0_561]) ).
cnf(refute_0_563,plain,
rd(cons(i,cons(o,shw(suc(zero))))) = suc(double(double(rd(shw(suc(zero)))))),
inference(subst,[],[refute_0_562:[bind(Xs,$fot(shw(suc(zero))))]]) ).
cnf(refute_0_564,plain,
( cons(o,shw(suc(zero))) != shw(double(suc(zero)))
| rd(cons(i,cons(o,shw(suc(zero))))) != suc(double(double(rd(shw(suc(zero))))))
| rd(cons(i,shw(double(suc(zero))))) = suc(double(double(rd(shw(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(rd(cons(i,cons(o,shw(suc(zero))))),suc(double(double(rd(shw(suc(zero))))))) ),[0,0,1],$fot(shw(double(suc(zero))))]]) ).
cnf(refute_0_565,plain,
( rd(cons(i,cons(o,shw(suc(zero))))) != suc(double(double(rd(shw(suc(zero))))))
| rd(cons(i,shw(double(suc(zero))))) = suc(double(double(rd(shw(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(cons(o,shw(suc(zero))),shw(double(suc(zero)))) )],[refute_0_106,refute_0_564]) ).
cnf(refute_0_566,plain,
rd(cons(i,shw(double(suc(zero))))) = suc(double(double(rd(shw(suc(zero)))))),
inference(resolve,[$cnf( $equal(rd(cons(i,cons(o,shw(suc(zero))))),suc(double(double(rd(shw(suc(zero))))))) )],[refute_0_563,refute_0_565]) ).
cnf(refute_0_567,plain,
rd(cons(i,shw(double(suc(zero))))) = x(suc(zero),double(suc(zero))),
inference(subst,[],[refute_0_542:[bind(Y,$fot(double(suc(zero))))]]) ).
cnf(refute_0_568,plain,
( rd(cons(i,shw(double(suc(zero))))) != suc(double(double(rd(shw(suc(zero))))))
| rd(cons(i,shw(double(suc(zero))))) != x(suc(zero),double(suc(zero)))
| x(suc(zero),double(suc(zero))) = suc(double(double(rd(shw(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(rd(cons(i,shw(double(suc(zero))))),suc(double(double(rd(shw(suc(zero))))))) ),[0],$fot(x(suc(zero),double(suc(zero))))]]) ).
cnf(refute_0_569,plain,
( rd(cons(i,shw(double(suc(zero))))) != suc(double(double(rd(shw(suc(zero))))))
| x(suc(zero),double(suc(zero))) = suc(double(double(rd(shw(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(rd(cons(i,shw(double(suc(zero))))),x(suc(zero),double(suc(zero)))) )],[refute_0_567,refute_0_568]) ).
cnf(refute_0_570,plain,
rd(cons(i,nil)) = rd(cons(i,nil)),
introduced(tautology,[refl,[$fot(rd(cons(i,nil)))]]) ).
cnf(refute_0_571,plain,
( cons(i,nil) != shw(suc(zero))
| rd(cons(i,nil)) != rd(cons(i,nil))
| rd(cons(i,nil)) = rd(shw(suc(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(rd(cons(i,nil)),rd(cons(i,nil))) ),[1,0],$fot(shw(suc(zero)))]]) ).
cnf(refute_0_572,plain,
( cons(i,nil) != shw(suc(zero))
| rd(cons(i,nil)) = rd(shw(suc(zero))) ),
inference(resolve,[$cnf( $equal(rd(cons(i,nil)),rd(cons(i,nil))) )],[refute_0_570,refute_0_571]) ).
cnf(refute_0_573,plain,
rd(cons(i,nil)) = rd(shw(suc(zero))),
inference(resolve,[$cnf( $equal(cons(i,nil),shw(suc(zero))) )],[refute_0_127,refute_0_572]) ).
cnf(refute_0_574,plain,
( rd(cons(i,nil)) != rd(shw(suc(zero)))
| rd(cons(i,nil)) != suc(zero)
| rd(shw(suc(zero))) = suc(zero) ),
introduced(tautology,[equality,[$cnf( $equal(rd(cons(i,nil)),suc(zero)) ),[0],$fot(rd(shw(suc(zero))))]]) ).
cnf(refute_0_575,plain,
( rd(cons(i,nil)) != suc(zero)
| rd(shw(suc(zero))) = suc(zero) ),
inference(resolve,[$cnf( $equal(rd(cons(i,nil)),rd(shw(suc(zero)))) )],[refute_0_573,refute_0_574]) ).
cnf(refute_0_576,plain,
rd(shw(suc(zero))) = suc(zero),
inference(resolve,[$cnf( $equal(rd(cons(i,nil)),suc(zero)) )],[refute_0_88,refute_0_575]) ).
cnf(refute_0_577,plain,
double(rd(shw(suc(zero)))) = double(rd(shw(suc(zero)))),
introduced(tautology,[refl,[$fot(double(rd(shw(suc(zero)))))]]) ).
cnf(refute_0_578,plain,
( double(rd(shw(suc(zero)))) != double(rd(shw(suc(zero))))
| rd(shw(suc(zero))) != suc(zero)
| double(rd(shw(suc(zero)))) = double(suc(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(double(rd(shw(suc(zero)))),double(rd(shw(suc(zero))))) ),[1,0],$fot(suc(zero))]]) ).
cnf(refute_0_579,plain,
( rd(shw(suc(zero))) != suc(zero)
| double(rd(shw(suc(zero)))) = double(suc(zero)) ),
inference(resolve,[$cnf( $equal(double(rd(shw(suc(zero)))),double(rd(shw(suc(zero))))) )],[refute_0_577,refute_0_578]) ).
cnf(refute_0_580,plain,
double(rd(shw(suc(zero)))) = double(suc(zero)),
inference(resolve,[$cnf( $equal(rd(shw(suc(zero))),suc(zero)) )],[refute_0_576,refute_0_579]) ).
cnf(refute_0_581,plain,
double(double(rd(shw(suc(zero))))) = double(double(rd(shw(suc(zero))))),
introduced(tautology,[refl,[$fot(double(double(rd(shw(suc(zero))))))]]) ).
cnf(refute_0_582,plain,
( double(double(rd(shw(suc(zero))))) != double(double(rd(shw(suc(zero)))))
| double(rd(shw(suc(zero)))) != double(suc(zero))
| double(double(rd(shw(suc(zero))))) = double(double(suc(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(double(double(rd(shw(suc(zero))))),double(double(rd(shw(suc(zero)))))) ),[1,0],$fot(double(suc(zero)))]]) ).
cnf(refute_0_583,plain,
( double(rd(shw(suc(zero)))) != double(suc(zero))
| double(double(rd(shw(suc(zero))))) = double(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(double(double(rd(shw(suc(zero))))),double(double(rd(shw(suc(zero)))))) )],[refute_0_581,refute_0_582]) ).
cnf(refute_0_584,plain,
double(double(rd(shw(suc(zero))))) = double(double(suc(zero))),
inference(resolve,[$cnf( $equal(double(rd(shw(suc(zero)))),double(suc(zero))) )],[refute_0_580,refute_0_583]) ).
cnf(refute_0_585,plain,
suc(double(double(rd(shw(suc(zero)))))) = suc(double(double(rd(shw(suc(zero)))))),
introduced(tautology,[refl,[$fot(suc(double(double(rd(shw(suc(zero)))))))]]) ).
cnf(refute_0_586,plain,
( double(double(rd(shw(suc(zero))))) != double(double(suc(zero)))
| suc(double(double(rd(shw(suc(zero)))))) != suc(double(double(rd(shw(suc(zero))))))
| suc(double(double(rd(shw(suc(zero)))))) = suc(double(double(suc(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(double(double(rd(shw(suc(zero)))))),suc(double(double(rd(shw(suc(zero))))))) ),[1,0],$fot(double(double(suc(zero))))]]) ).
cnf(refute_0_587,plain,
( double(double(rd(shw(suc(zero))))) != double(double(suc(zero)))
| suc(double(double(rd(shw(suc(zero)))))) = suc(double(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(suc(double(double(rd(shw(suc(zero)))))),suc(double(double(rd(shw(suc(zero))))))) )],[refute_0_585,refute_0_586]) ).
cnf(refute_0_588,plain,
suc(double(double(rd(shw(suc(zero)))))) = suc(double(double(suc(zero)))),
inference(resolve,[$cnf( $equal(double(double(rd(shw(suc(zero))))),double(double(suc(zero)))) )],[refute_0_584,refute_0_587]) ).
cnf(refute_0_589,plain,
( suc(double(double(rd(shw(suc(zero)))))) != suc(double(double(suc(zero))))
| x(suc(zero),double(suc(zero))) != suc(double(double(rd(shw(suc(zero))))))
| x(suc(zero),double(suc(zero))) = suc(double(double(suc(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(x(suc(zero),double(suc(zero))),suc(double(double(rd(shw(suc(zero))))))) ),[1],$fot(suc(double(double(suc(zero)))))]]) ).
cnf(refute_0_590,plain,
( x(suc(zero),double(suc(zero))) != suc(double(double(rd(shw(suc(zero))))))
| x(suc(zero),double(suc(zero))) = suc(double(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(suc(double(double(rd(shw(suc(zero)))))),suc(double(double(suc(zero))))) )],[refute_0_588,refute_0_589]) ).
cnf(refute_0_591,plain,
( rd(cons(i,shw(double(suc(zero))))) != suc(double(double(rd(shw(suc(zero))))))
| x(suc(zero),double(suc(zero))) = suc(double(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(x(suc(zero),double(suc(zero))),suc(double(double(rd(shw(suc(zero))))))) )],[refute_0_569,refute_0_590]) ).
cnf(refute_0_592,plain,
x(suc(zero),double(suc(zero))) = suc(double(double(suc(zero)))),
inference(resolve,[$cnf( $equal(rd(cons(i,shw(double(suc(zero))))),suc(double(double(rd(shw(suc(zero))))))) )],[refute_0_566,refute_0_591]) ).
cnf(refute_0_593,plain,
double(x(suc(zero),double(suc(zero)))) = double(x(suc(zero),double(suc(zero)))),
introduced(tautology,[refl,[$fot(double(x(suc(zero),double(suc(zero)))))]]) ).
cnf(refute_0_594,plain,
( double(x(suc(zero),double(suc(zero)))) != double(x(suc(zero),double(suc(zero))))
| x(suc(zero),double(suc(zero))) != suc(double(double(suc(zero))))
| double(x(suc(zero),double(suc(zero)))) = double(suc(double(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(double(x(suc(zero),double(suc(zero)))),double(x(suc(zero),double(suc(zero))))) ),[1,0],$fot(suc(double(double(suc(zero)))))]]) ).
cnf(refute_0_595,plain,
( x(suc(zero),double(suc(zero))) != suc(double(double(suc(zero))))
| double(x(suc(zero),double(suc(zero)))) = double(suc(double(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(double(x(suc(zero),double(suc(zero)))),double(x(suc(zero),double(suc(zero))))) )],[refute_0_593,refute_0_594]) ).
cnf(refute_0_596,plain,
double(x(suc(zero),double(suc(zero)))) = double(suc(double(double(suc(zero))))),
inference(resolve,[$cnf( $equal(x(suc(zero),double(suc(zero))),suc(double(double(suc(zero))))) )],[refute_0_592,refute_0_595]) ).
cnf(refute_0_597,plain,
( double(x(suc(zero),double(suc(zero)))) != double(suc(double(double(suc(zero)))))
| double(x(suc(zero),double(suc(zero)))) != suc(proj1Suc(double(double(x(suc(zero),suc(zero))))))
| double(suc(double(double(suc(zero))))) = suc(proj1Suc(double(double(x(suc(zero),suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(double(x(suc(zero),double(suc(zero)))),suc(proj1Suc(double(double(x(suc(zero),suc(zero))))))) ),[0],$fot(double(suc(double(double(suc(zero))))))]]) ).
cnf(refute_0_598,plain,
( double(x(suc(zero),double(suc(zero)))) != suc(proj1Suc(double(double(x(suc(zero),suc(zero))))))
| double(suc(double(double(suc(zero))))) = suc(proj1Suc(double(double(x(suc(zero),suc(zero)))))) ),
inference(resolve,[$cnf( $equal(double(x(suc(zero),double(suc(zero)))),double(suc(double(double(suc(zero)))))) )],[refute_0_596,refute_0_597]) ).
cnf(refute_0_599,plain,
rd(cons(i,cons(i,nil))) = suc(double(rd(cons(i,nil)))),
inference(subst,[],[refute_0_63:[bind(Xs,$fot(cons(i,nil)))]]) ).
cnf(refute_0_600,plain,
( rd(cons(i,cons(i,nil))) != suc(double(rd(cons(i,nil))))
| rd(cons(i,nil)) != suc(zero)
| rd(cons(i,cons(i,nil))) = suc(double(suc(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(rd(cons(i,cons(i,nil))),suc(double(rd(cons(i,nil))))) ),[1,0,0],$fot(suc(zero))]]) ).
cnf(refute_0_601,plain,
( rd(cons(i,cons(i,nil))) != suc(double(rd(cons(i,nil))))
| rd(cons(i,cons(i,nil))) = suc(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(rd(cons(i,nil)),suc(zero)) )],[refute_0_88,refute_0_600]) ).
cnf(refute_0_602,plain,
rd(cons(i,cons(i,nil))) = suc(double(suc(zero))),
inference(resolve,[$cnf( $equal(rd(cons(i,cons(i,nil))),suc(double(rd(cons(i,nil))))) )],[refute_0_599,refute_0_601]) ).
cnf(refute_0_603,plain,
cons(i,cons(i,nil)) = cons(i,cons(i,nil)),
introduced(tautology,[refl,[$fot(cons(i,cons(i,nil)))]]) ).
cnf(refute_0_604,plain,
( cons(i,cons(i,nil)) != cons(i,cons(i,nil))
| cons(i,nil) != shw(suc(zero))
| cons(i,cons(i,nil)) = cons(i,shw(suc(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(cons(i,cons(i,nil)),cons(i,cons(i,nil))) ),[1,1],$fot(shw(suc(zero)))]]) ).
cnf(refute_0_605,plain,
( cons(i,nil) != shw(suc(zero))
| cons(i,cons(i,nil)) = cons(i,shw(suc(zero))) ),
inference(resolve,[$cnf( $equal(cons(i,cons(i,nil)),cons(i,cons(i,nil))) )],[refute_0_603,refute_0_604]) ).
cnf(refute_0_606,plain,
cons(i,cons(i,nil)) = cons(i,shw(suc(zero))),
inference(resolve,[$cnf( $equal(cons(i,nil),shw(suc(zero))) )],[refute_0_127,refute_0_605]) ).
cnf(refute_0_607,plain,
rd(cons(i,cons(i,nil))) = rd(cons(i,cons(i,nil))),
introduced(tautology,[refl,[$fot(rd(cons(i,cons(i,nil))))]]) ).
cnf(refute_0_608,plain,
( cons(i,cons(i,nil)) != cons(i,shw(suc(zero)))
| rd(cons(i,cons(i,nil))) != rd(cons(i,cons(i,nil)))
| rd(cons(i,cons(i,nil))) = rd(cons(i,shw(suc(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(rd(cons(i,cons(i,nil))),rd(cons(i,cons(i,nil)))) ),[1,0],$fot(cons(i,shw(suc(zero))))]]) ).
cnf(refute_0_609,plain,
( cons(i,cons(i,nil)) != cons(i,shw(suc(zero)))
| rd(cons(i,cons(i,nil))) = rd(cons(i,shw(suc(zero)))) ),
inference(resolve,[$cnf( $equal(rd(cons(i,cons(i,nil))),rd(cons(i,cons(i,nil)))) )],[refute_0_607,refute_0_608]) ).
cnf(refute_0_610,plain,
rd(cons(i,cons(i,nil))) = rd(cons(i,shw(suc(zero)))),
inference(resolve,[$cnf( $equal(cons(i,cons(i,nil)),cons(i,shw(suc(zero)))) )],[refute_0_606,refute_0_609]) ).
cnf(refute_0_611,plain,
( rd(cons(i,cons(i,nil))) != rd(cons(i,shw(suc(zero))))
| rd(cons(i,cons(i,nil))) != suc(double(suc(zero)))
| rd(cons(i,shw(suc(zero)))) = suc(double(suc(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(rd(cons(i,cons(i,nil))),suc(double(suc(zero)))) ),[0],$fot(rd(cons(i,shw(suc(zero)))))]]) ).
cnf(refute_0_612,plain,
( rd(cons(i,cons(i,nil))) != suc(double(suc(zero)))
| rd(cons(i,shw(suc(zero)))) = suc(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(rd(cons(i,cons(i,nil))),rd(cons(i,shw(suc(zero))))) )],[refute_0_610,refute_0_611]) ).
cnf(refute_0_613,plain,
rd(cons(i,shw(suc(zero)))) = suc(double(suc(zero))),
inference(resolve,[$cnf( $equal(rd(cons(i,cons(i,nil))),suc(double(suc(zero)))) )],[refute_0_602,refute_0_612]) ).
cnf(refute_0_614,plain,
rd(cons(i,shw(suc(zero)))) = x(suc(zero),suc(zero)),
inference(subst,[],[refute_0_542:[bind(Y,$fot(suc(zero)))]]) ).
cnf(refute_0_615,plain,
( rd(cons(i,shw(suc(zero)))) != suc(double(suc(zero)))
| rd(cons(i,shw(suc(zero)))) != x(suc(zero),suc(zero))
| x(suc(zero),suc(zero)) = suc(double(suc(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(rd(cons(i,shw(suc(zero)))),suc(double(suc(zero)))) ),[0],$fot(x(suc(zero),suc(zero)))]]) ).
cnf(refute_0_616,plain,
( rd(cons(i,shw(suc(zero)))) != suc(double(suc(zero)))
| x(suc(zero),suc(zero)) = suc(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(rd(cons(i,shw(suc(zero)))),x(suc(zero),suc(zero))) )],[refute_0_614,refute_0_615]) ).
cnf(refute_0_617,plain,
x(suc(zero),suc(zero)) = suc(double(suc(zero))),
inference(resolve,[$cnf( $equal(rd(cons(i,shw(suc(zero)))),suc(double(suc(zero)))) )],[refute_0_613,refute_0_616]) ).
cnf(refute_0_618,plain,
double(x(suc(zero),suc(zero))) = double(x(suc(zero),suc(zero))),
introduced(tautology,[refl,[$fot(double(x(suc(zero),suc(zero))))]]) ).
cnf(refute_0_619,plain,
( double(x(suc(zero),suc(zero))) != double(x(suc(zero),suc(zero)))
| x(suc(zero),suc(zero)) != suc(double(suc(zero)))
| double(x(suc(zero),suc(zero))) = double(suc(double(suc(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(double(x(suc(zero),suc(zero))),double(x(suc(zero),suc(zero)))) ),[1,0],$fot(suc(double(suc(zero))))]]) ).
cnf(refute_0_620,plain,
( x(suc(zero),suc(zero)) != suc(double(suc(zero)))
| double(x(suc(zero),suc(zero))) = double(suc(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(double(x(suc(zero),suc(zero))),double(x(suc(zero),suc(zero)))) )],[refute_0_618,refute_0_619]) ).
cnf(refute_0_621,plain,
double(x(suc(zero),suc(zero))) = double(suc(double(suc(zero)))),
inference(resolve,[$cnf( $equal(x(suc(zero),suc(zero)),suc(double(suc(zero)))) )],[refute_0_617,refute_0_620]) ).
cnf(refute_0_622,plain,
double(double(x(suc(zero),suc(zero)))) = double(double(x(suc(zero),suc(zero)))),
introduced(tautology,[refl,[$fot(double(double(x(suc(zero),suc(zero)))))]]) ).
cnf(refute_0_623,plain,
( double(double(x(suc(zero),suc(zero)))) != double(double(x(suc(zero),suc(zero))))
| double(x(suc(zero),suc(zero))) != double(suc(double(suc(zero))))
| double(double(x(suc(zero),suc(zero)))) = double(double(suc(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(double(double(x(suc(zero),suc(zero)))),double(double(x(suc(zero),suc(zero))))) ),[1,0],$fot(double(suc(double(suc(zero)))))]]) ).
cnf(refute_0_624,plain,
( double(x(suc(zero),suc(zero))) != double(suc(double(suc(zero))))
| double(double(x(suc(zero),suc(zero)))) = double(double(suc(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(double(double(x(suc(zero),suc(zero)))),double(double(x(suc(zero),suc(zero))))) )],[refute_0_622,refute_0_623]) ).
cnf(refute_0_625,plain,
double(double(x(suc(zero),suc(zero)))) = double(double(suc(double(suc(zero))))),
inference(resolve,[$cnf( $equal(double(x(suc(zero),suc(zero))),double(suc(double(suc(zero))))) )],[refute_0_621,refute_0_624]) ).
cnf(refute_0_626,plain,
double(suc(proj1Suc(double(x(suc(zero),X_78))))) = suc(proj1Suc(double(suc(proj1Suc(double(x(suc(zero),X_78))))))),
inference(subst,[],[refute_0_244:[bind(X_21,$fot(proj1Suc(double(x(suc(zero),X_78)))))]]) ).
cnf(refute_0_627,plain,
( double(x(suc(zero),X_78)) != suc(proj1Suc(double(x(suc(zero),X_78))))
| suc(proj1Suc(double(x(suc(zero),X_78)))) = double(x(suc(zero),X_78)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(double(x(suc(zero),X_78)))),bind(Y0,$fot(suc(proj1Suc(double(x(suc(zero),X_78))))))]]) ).
cnf(refute_0_628,plain,
suc(proj1Suc(double(x(suc(zero),X_78)))) = double(x(suc(zero),X_78)),
inference(resolve,[$cnf( $equal(double(x(suc(zero),X_78)),suc(proj1Suc(double(x(suc(zero),X_78))))) )],[refute_0_515,refute_0_627]) ).
cnf(refute_0_629,plain,
( double(suc(proj1Suc(double(x(suc(zero),X_78))))) != suc(proj1Suc(double(suc(proj1Suc(double(x(suc(zero),X_78)))))))
| suc(proj1Suc(double(x(suc(zero),X_78)))) != double(x(suc(zero),X_78))
| double(suc(proj1Suc(double(x(suc(zero),X_78))))) = suc(proj1Suc(double(double(x(suc(zero),X_78))))) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(proj1Suc(double(x(suc(zero),X_78))))),suc(proj1Suc(double(suc(proj1Suc(double(x(suc(zero),X_78)))))))) ),[1,0,0,0],$fot(double(x(suc(zero),X_78)))]]) ).
cnf(refute_0_630,plain,
( double(suc(proj1Suc(double(x(suc(zero),X_78))))) != suc(proj1Suc(double(suc(proj1Suc(double(x(suc(zero),X_78)))))))
| double(suc(proj1Suc(double(x(suc(zero),X_78))))) = suc(proj1Suc(double(double(x(suc(zero),X_78))))) ),
inference(resolve,[$cnf( $equal(suc(proj1Suc(double(x(suc(zero),X_78)))),double(x(suc(zero),X_78))) )],[refute_0_628,refute_0_629]) ).
cnf(refute_0_631,plain,
double(suc(proj1Suc(double(x(suc(zero),X_78))))) = suc(proj1Suc(double(double(x(suc(zero),X_78))))),
inference(resolve,[$cnf( $equal(double(suc(proj1Suc(double(x(suc(zero),X_78))))),suc(proj1Suc(double(suc(proj1Suc(double(x(suc(zero),X_78)))))))) )],[refute_0_626,refute_0_630]) ).
cnf(refute_0_632,plain,
double(suc(proj1Suc(double(x(suc(zero),X_78))))) = double(suc(proj1Suc(double(x(suc(zero),X_78))))),
introduced(tautology,[refl,[$fot(double(suc(proj1Suc(double(x(suc(zero),X_78))))))]]) ).
cnf(refute_0_633,plain,
( double(suc(proj1Suc(double(x(suc(zero),X_78))))) != double(suc(proj1Suc(double(x(suc(zero),X_78)))))
| suc(proj1Suc(double(x(suc(zero),X_78)))) != double(x(suc(zero),X_78))
| double(suc(proj1Suc(double(x(suc(zero),X_78))))) = double(double(x(suc(zero),X_78))) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(proj1Suc(double(x(suc(zero),X_78))))),double(suc(proj1Suc(double(x(suc(zero),X_78)))))) ),[1,0],$fot(double(x(suc(zero),X_78)))]]) ).
cnf(refute_0_634,plain,
( suc(proj1Suc(double(x(suc(zero),X_78)))) != double(x(suc(zero),X_78))
| double(suc(proj1Suc(double(x(suc(zero),X_78))))) = double(double(x(suc(zero),X_78))) ),
inference(resolve,[$cnf( $equal(double(suc(proj1Suc(double(x(suc(zero),X_78))))),double(suc(proj1Suc(double(x(suc(zero),X_78)))))) )],[refute_0_632,refute_0_633]) ).
cnf(refute_0_635,plain,
double(suc(proj1Suc(double(x(suc(zero),X_78))))) = double(double(x(suc(zero),X_78))),
inference(resolve,[$cnf( $equal(suc(proj1Suc(double(x(suc(zero),X_78)))),double(x(suc(zero),X_78))) )],[refute_0_628,refute_0_634]) ).
cnf(refute_0_636,plain,
( double(suc(proj1Suc(double(x(suc(zero),X_78))))) != double(double(x(suc(zero),X_78)))
| double(suc(proj1Suc(double(x(suc(zero),X_78))))) != suc(proj1Suc(double(double(x(suc(zero),X_78)))))
| double(double(x(suc(zero),X_78))) = suc(proj1Suc(double(double(x(suc(zero),X_78))))) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(proj1Suc(double(x(suc(zero),X_78))))),suc(proj1Suc(double(double(x(suc(zero),X_78)))))) ),[0],$fot(double(double(x(suc(zero),X_78))))]]) ).
cnf(refute_0_637,plain,
( double(suc(proj1Suc(double(x(suc(zero),X_78))))) != suc(proj1Suc(double(double(x(suc(zero),X_78)))))
| double(double(x(suc(zero),X_78))) = suc(proj1Suc(double(double(x(suc(zero),X_78))))) ),
inference(resolve,[$cnf( $equal(double(suc(proj1Suc(double(x(suc(zero),X_78))))),double(double(x(suc(zero),X_78)))) )],[refute_0_635,refute_0_636]) ).
cnf(refute_0_638,plain,
double(double(x(suc(zero),X_78))) = suc(proj1Suc(double(double(x(suc(zero),X_78))))),
inference(resolve,[$cnf( $equal(double(suc(proj1Suc(double(x(suc(zero),X_78))))),suc(proj1Suc(double(double(x(suc(zero),X_78)))))) )],[refute_0_631,refute_0_637]) ).
cnf(refute_0_639,plain,
( double(double(x(suc(zero),X_78))) != suc(proj1Suc(double(double(x(suc(zero),X_78)))))
| suc(proj1Suc(double(double(x(suc(zero),X_78))))) = double(double(x(suc(zero),X_78))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(double(double(x(suc(zero),X_78))))),bind(Y0,$fot(suc(proj1Suc(double(double(x(suc(zero),X_78)))))))]]) ).
cnf(refute_0_640,plain,
suc(proj1Suc(double(double(x(suc(zero),X_78))))) = double(double(x(suc(zero),X_78))),
inference(resolve,[$cnf( $equal(double(double(x(suc(zero),X_78))),suc(proj1Suc(double(double(x(suc(zero),X_78)))))) )],[refute_0_638,refute_0_639]) ).
cnf(refute_0_641,plain,
suc(proj1Suc(double(double(x(suc(zero),suc(zero)))))) = double(double(x(suc(zero),suc(zero)))),
inference(subst,[],[refute_0_640:[bind(X_78,$fot(suc(zero)))]]) ).
cnf(refute_0_642,plain,
( double(double(x(suc(zero),suc(zero)))) != double(double(suc(double(suc(zero)))))
| suc(proj1Suc(double(double(x(suc(zero),suc(zero)))))) != double(double(x(suc(zero),suc(zero))))
| suc(proj1Suc(double(double(x(suc(zero),suc(zero)))))) = double(double(suc(double(suc(zero))))) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(suc(proj1Suc(double(double(x(suc(zero),suc(zero)))))))),bind(Y0,$fot(double(double(x(suc(zero),suc(zero)))))),bind(Z0,$fot(double(double(suc(double(suc(zero)))))))]]) ).
cnf(refute_0_643,plain,
( double(double(x(suc(zero),suc(zero)))) != double(double(suc(double(suc(zero)))))
| suc(proj1Suc(double(double(x(suc(zero),suc(zero)))))) = double(double(suc(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(suc(proj1Suc(double(double(x(suc(zero),suc(zero)))))),double(double(x(suc(zero),suc(zero))))) )],[refute_0_641,refute_0_642]) ).
cnf(refute_0_644,plain,
suc(proj1Suc(double(double(x(suc(zero),suc(zero)))))) = double(double(suc(double(suc(zero))))),
inference(resolve,[$cnf( $equal(double(double(x(suc(zero),suc(zero)))),double(double(suc(double(suc(zero)))))) )],[refute_0_625,refute_0_643]) ).
cnf(refute_0_645,plain,
( double(suc(double(double(suc(zero))))) != suc(proj1Suc(double(double(x(suc(zero),suc(zero))))))
| suc(proj1Suc(double(double(x(suc(zero),suc(zero)))))) != double(double(suc(double(suc(zero)))))
| double(suc(double(double(suc(zero))))) = double(double(suc(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(double(suc(double(double(suc(zero))))),double(double(suc(double(suc(zero)))))) ),[0],$fot(suc(proj1Suc(double(double(x(suc(zero),suc(zero)))))))]]) ).
cnf(refute_0_646,plain,
( double(suc(double(double(suc(zero))))) != suc(proj1Suc(double(double(x(suc(zero),suc(zero))))))
| double(suc(double(double(suc(zero))))) = double(double(suc(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(suc(proj1Suc(double(double(x(suc(zero),suc(zero)))))),double(double(suc(double(suc(zero)))))) )],[refute_0_644,refute_0_645]) ).
cnf(refute_0_647,plain,
( double(x(suc(zero),double(suc(zero)))) != suc(proj1Suc(double(double(x(suc(zero),suc(zero))))))
| double(suc(double(double(suc(zero))))) = double(double(suc(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(double(suc(double(double(suc(zero))))),suc(proj1Suc(double(double(x(suc(zero),suc(zero))))))) )],[refute_0_598,refute_0_646]) ).
cnf(refute_0_648,plain,
double(suc(double(double(suc(zero))))) = double(double(suc(double(suc(zero))))),
inference(resolve,[$cnf( $equal(double(x(suc(zero),double(suc(zero)))),suc(proj1Suc(double(double(x(suc(zero),suc(zero))))))) )],[refute_0_558,refute_0_647]) ).
cnf(refute_0_649,plain,
proj1Suc(suc(double(rd(X_7)))) = double(rd(X_7)),
inference(subst,[],[refute_0_131:[bind(X,$fot(double(rd(X_7))))]]) ).
cnf(refute_0_650,plain,
rd(cons(i,X_7)) = suc(double(rd(X_7))),
inference(subst,[],[refute_0_63:[bind(Xs,$fot(X_7))]]) ).
cnf(refute_0_651,plain,
( rd(cons(i,X_7)) != suc(double(rd(X_7)))
| suc(double(rd(X_7))) = rd(cons(i,X_7)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(rd(cons(i,X_7)))),bind(Y0,$fot(suc(double(rd(X_7)))))]]) ).
cnf(refute_0_652,plain,
suc(double(rd(X_7))) = rd(cons(i,X_7)),
inference(resolve,[$cnf( $equal(rd(cons(i,X_7)),suc(double(rd(X_7)))) )],[refute_0_650,refute_0_651]) ).
cnf(refute_0_653,plain,
( proj1Suc(suc(double(rd(X_7)))) != double(rd(X_7))
| suc(double(rd(X_7))) != rd(cons(i,X_7))
| proj1Suc(rd(cons(i,X_7))) = double(rd(X_7)) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(suc(double(rd(X_7)))),double(rd(X_7))) ),[0,0],$fot(rd(cons(i,X_7)))]]) ).
cnf(refute_0_654,plain,
( proj1Suc(suc(double(rd(X_7)))) != double(rd(X_7))
| proj1Suc(rd(cons(i,X_7))) = double(rd(X_7)) ),
inference(resolve,[$cnf( $equal(suc(double(rd(X_7))),rd(cons(i,X_7))) )],[refute_0_652,refute_0_653]) ).
cnf(refute_0_655,plain,
proj1Suc(rd(cons(i,X_7))) = double(rd(X_7)),
inference(resolve,[$cnf( $equal(proj1Suc(suc(double(rd(X_7)))),double(rd(X_7))) )],[refute_0_649,refute_0_654]) ).
cnf(refute_0_656,plain,
proj1Suc(rd(cons(i,shw(X_69)))) = double(rd(shw(X_69))),
inference(subst,[],[refute_0_655:[bind(X_7,$fot(shw(X_69)))]]) ).
cnf(refute_0_657,plain,
( proj1Suc(rd(cons(i,shw(X_69)))) != double(rd(shw(X_69)))
| rd(cons(i,shw(X_69))) != x(suc(zero),X_69)
| proj1Suc(x(suc(zero),X_69)) = double(rd(shw(X_69))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(rd(cons(i,shw(X_69)))),double(rd(shw(X_69)))) ),[0,0],$fot(x(suc(zero),X_69))]]) ).
cnf(refute_0_658,plain,
( proj1Suc(rd(cons(i,shw(X_69)))) != double(rd(shw(X_69)))
| proj1Suc(x(suc(zero),X_69)) = double(rd(shw(X_69))) ),
inference(resolve,[$cnf( $equal(rd(cons(i,shw(X_69))),x(suc(zero),X_69)) )],[refute_0_504,refute_0_657]) ).
cnf(refute_0_659,plain,
proj1Suc(x(suc(zero),X_69)) = double(rd(shw(X_69))),
inference(resolve,[$cnf( $equal(proj1Suc(rd(cons(i,shw(X_69)))),double(rd(shw(X_69)))) )],[refute_0_656,refute_0_658]) ).
cnf(refute_0_660,plain,
proj1Suc(x(suc(zero),X_73)) = double(rd(shw(X_73))),
inference(subst,[],[refute_0_659:[bind(X_69,$fot(X_73))]]) ).
cnf(refute_0_661,plain,
x(X_73,suc(zero)) = x(suc(zero),X_73),
inference(subst,[],[refute_0_516:[bind(X,$fot(X_73)),bind(Y,$fot(suc(zero)))]]) ).
cnf(refute_0_662,plain,
( x(X_73,suc(zero)) != x(suc(zero),X_73)
| x(suc(zero),X_73) = x(X_73,suc(zero)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(x(X_73,suc(zero)))),bind(Y0,$fot(x(suc(zero),X_73)))]]) ).
cnf(refute_0_663,plain,
x(suc(zero),X_73) = x(X_73,suc(zero)),
inference(resolve,[$cnf( $equal(x(X_73,suc(zero)),x(suc(zero),X_73)) )],[refute_0_661,refute_0_662]) ).
cnf(refute_0_664,plain,
( proj1Suc(x(suc(zero),X_73)) != double(rd(shw(X_73)))
| x(suc(zero),X_73) != x(X_73,suc(zero))
| proj1Suc(x(X_73,suc(zero))) = double(rd(shw(X_73))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(x(suc(zero),X_73)),double(rd(shw(X_73)))) ),[0,0],$fot(x(X_73,suc(zero)))]]) ).
cnf(refute_0_665,plain,
( proj1Suc(x(suc(zero),X_73)) != double(rd(shw(X_73)))
| proj1Suc(x(X_73,suc(zero))) = double(rd(shw(X_73))) ),
inference(resolve,[$cnf( $equal(x(suc(zero),X_73),x(X_73,suc(zero))) )],[refute_0_663,refute_0_664]) ).
cnf(refute_0_666,plain,
proj1Suc(x(X_73,suc(zero))) = double(rd(shw(X_73))),
inference(resolve,[$cnf( $equal(proj1Suc(x(suc(zero),X_73)),double(rd(shw(X_73)))) )],[refute_0_660,refute_0_665]) ).
cnf(refute_0_667,plain,
proj1Suc(x(double(suc(zero)),suc(zero))) = double(rd(shw(double(suc(zero))))),
inference(subst,[],[refute_0_666:[bind(X_73,$fot(double(suc(zero))))]]) ).
cnf(refute_0_668,plain,
( proj1Suc(x(double(suc(zero)),suc(zero))) != double(rd(shw(double(suc(zero)))))
| x(double(suc(zero)),suc(zero)) != double(x(suc(zero),suc(zero)))
| proj1Suc(double(x(suc(zero),suc(zero)))) = double(rd(shw(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(x(double(suc(zero)),suc(zero))),double(rd(shw(double(suc(zero)))))) ),[0,0],$fot(double(x(suc(zero),suc(zero))))]]) ).
cnf(refute_0_669,plain,
( proj1Suc(x(double(suc(zero)),suc(zero))) != double(rd(shw(double(suc(zero)))))
| proj1Suc(double(x(suc(zero),suc(zero)))) = double(rd(shw(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(x(double(suc(zero)),suc(zero)),double(x(suc(zero),suc(zero)))) )],[refute_0_555,refute_0_668]) ).
cnf(refute_0_670,plain,
proj1Suc(double(x(suc(zero),suc(zero)))) = double(rd(shw(double(suc(zero))))),
inference(resolve,[$cnf( $equal(proj1Suc(x(double(suc(zero)),suc(zero))),double(rd(shw(double(suc(zero)))))) )],[refute_0_667,refute_0_669]) ).
cnf(refute_0_671,plain,
proj1Suc(double(x(suc(zero),suc(zero)))) = proj1Suc(double(x(suc(zero),suc(zero)))),
introduced(tautology,[refl,[$fot(proj1Suc(double(x(suc(zero),suc(zero)))))]]) ).
cnf(refute_0_672,plain,
( double(x(suc(zero),suc(zero))) != double(suc(double(suc(zero))))
| proj1Suc(double(x(suc(zero),suc(zero)))) != proj1Suc(double(x(suc(zero),suc(zero))))
| proj1Suc(double(x(suc(zero),suc(zero)))) = proj1Suc(double(suc(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(x(suc(zero),suc(zero)))),proj1Suc(double(x(suc(zero),suc(zero))))) ),[1,0],$fot(double(suc(double(suc(zero)))))]]) ).
cnf(refute_0_673,plain,
( double(x(suc(zero),suc(zero))) != double(suc(double(suc(zero))))
| proj1Suc(double(x(suc(zero),suc(zero)))) = proj1Suc(double(suc(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(x(suc(zero),suc(zero)))),proj1Suc(double(x(suc(zero),suc(zero))))) )],[refute_0_671,refute_0_672]) ).
cnf(refute_0_674,plain,
proj1Suc(double(x(suc(zero),suc(zero)))) = proj1Suc(double(suc(double(suc(zero))))),
inference(resolve,[$cnf( $equal(double(x(suc(zero),suc(zero))),double(suc(double(suc(zero))))) )],[refute_0_621,refute_0_673]) ).
cnf(refute_0_675,plain,
( proj1Suc(double(suc(double(suc(zero))))) != suc(double(double(suc(zero))))
| proj1Suc(double(x(suc(zero),suc(zero)))) != proj1Suc(double(suc(double(suc(zero)))))
| proj1Suc(double(x(suc(zero),suc(zero)))) = suc(double(double(suc(zero)))) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(proj1Suc(double(x(suc(zero),suc(zero)))))),bind(Y0,$fot(proj1Suc(double(suc(double(suc(zero))))))),bind(Z0,$fot(suc(double(double(suc(zero))))))]]) ).
cnf(refute_0_676,plain,
( proj1Suc(double(suc(double(suc(zero))))) != suc(double(double(suc(zero))))
| proj1Suc(double(x(suc(zero),suc(zero)))) = suc(double(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(x(suc(zero),suc(zero)))),proj1Suc(double(suc(double(suc(zero)))))) )],[refute_0_674,refute_0_675]) ).
cnf(refute_0_677,plain,
proj1Suc(double(x(suc(zero),suc(zero)))) = suc(double(double(suc(zero)))),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(double(suc(zero))))),suc(double(double(suc(zero))))) )],[refute_0_257,refute_0_676]) ).
cnf(refute_0_678,plain,
( proj1Suc(double(x(suc(zero),suc(zero)))) != double(rd(shw(double(suc(zero)))))
| proj1Suc(double(x(suc(zero),suc(zero)))) != suc(double(double(suc(zero))))
| suc(double(double(suc(zero)))) = double(rd(shw(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(x(suc(zero),suc(zero)))),double(rd(shw(double(suc(zero)))))) ),[0],$fot(suc(double(double(suc(zero)))))]]) ).
cnf(refute_0_679,plain,
( proj1Suc(double(x(suc(zero),suc(zero)))) != double(rd(shw(double(suc(zero)))))
| suc(double(double(suc(zero)))) = double(rd(shw(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(x(suc(zero),suc(zero)))),suc(double(double(suc(zero))))) )],[refute_0_677,refute_0_678]) ).
cnf(refute_0_680,plain,
rd(cons(o,shw(suc(zero)))) = double(rd(shw(suc(zero)))),
inference(subst,[],[refute_0_547:[bind(Xs,$fot(shw(suc(zero))))]]) ).
cnf(refute_0_681,plain,
( cons(o,shw(suc(zero))) != shw(double(suc(zero)))
| rd(cons(o,shw(suc(zero)))) != double(rd(shw(suc(zero))))
| rd(shw(double(suc(zero)))) = double(rd(shw(suc(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(rd(cons(o,shw(suc(zero)))),double(rd(shw(suc(zero))))) ),[0,0],$fot(shw(double(suc(zero))))]]) ).
cnf(refute_0_682,plain,
( rd(cons(o,shw(suc(zero)))) != double(rd(shw(suc(zero))))
| rd(shw(double(suc(zero)))) = double(rd(shw(suc(zero)))) ),
inference(resolve,[$cnf( $equal(cons(o,shw(suc(zero))),shw(double(suc(zero)))) )],[refute_0_106,refute_0_681]) ).
cnf(refute_0_683,plain,
rd(shw(double(suc(zero)))) = double(rd(shw(suc(zero)))),
inference(resolve,[$cnf( $equal(rd(cons(o,shw(suc(zero)))),double(rd(shw(suc(zero))))) )],[refute_0_680,refute_0_682]) ).
cnf(refute_0_684,plain,
( double(rd(shw(suc(zero)))) != double(suc(zero))
| rd(shw(double(suc(zero)))) != double(rd(shw(suc(zero))))
| rd(shw(double(suc(zero)))) = double(suc(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(rd(shw(double(suc(zero)))),double(rd(shw(suc(zero))))) ),[1],$fot(double(suc(zero)))]]) ).
cnf(refute_0_685,plain,
( rd(shw(double(suc(zero)))) != double(rd(shw(suc(zero))))
| rd(shw(double(suc(zero)))) = double(suc(zero)) ),
inference(resolve,[$cnf( $equal(double(rd(shw(suc(zero)))),double(suc(zero))) )],[refute_0_580,refute_0_684]) ).
cnf(refute_0_686,plain,
rd(shw(double(suc(zero)))) = double(suc(zero)),
inference(resolve,[$cnf( $equal(rd(shw(double(suc(zero)))),double(rd(shw(suc(zero))))) )],[refute_0_683,refute_0_685]) ).
cnf(refute_0_687,plain,
double(rd(shw(double(suc(zero))))) = double(rd(shw(double(suc(zero))))),
introduced(tautology,[refl,[$fot(double(rd(shw(double(suc(zero))))))]]) ).
cnf(refute_0_688,plain,
( double(rd(shw(double(suc(zero))))) != double(rd(shw(double(suc(zero)))))
| rd(shw(double(suc(zero)))) != double(suc(zero))
| double(rd(shw(double(suc(zero))))) = double(double(suc(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(double(rd(shw(double(suc(zero))))),double(rd(shw(double(suc(zero)))))) ),[1,0],$fot(double(suc(zero)))]]) ).
cnf(refute_0_689,plain,
( rd(shw(double(suc(zero)))) != double(suc(zero))
| double(rd(shw(double(suc(zero))))) = double(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(double(rd(shw(double(suc(zero))))),double(rd(shw(double(suc(zero)))))) )],[refute_0_687,refute_0_688]) ).
cnf(refute_0_690,plain,
double(rd(shw(double(suc(zero))))) = double(double(suc(zero))),
inference(resolve,[$cnf( $equal(rd(shw(double(suc(zero)))),double(suc(zero))) )],[refute_0_686,refute_0_689]) ).
cnf(refute_0_691,plain,
( double(rd(shw(double(suc(zero))))) != double(double(suc(zero)))
| suc(double(double(suc(zero)))) != double(rd(shw(double(suc(zero)))))
| suc(double(double(suc(zero)))) = double(double(suc(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(double(double(suc(zero)))),double(rd(shw(double(suc(zero)))))) ),[1],$fot(double(double(suc(zero))))]]) ).
cnf(refute_0_692,plain,
( suc(double(double(suc(zero)))) != double(rd(shw(double(suc(zero)))))
| suc(double(double(suc(zero)))) = double(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(double(rd(shw(double(suc(zero))))),double(double(suc(zero)))) )],[refute_0_690,refute_0_691]) ).
cnf(refute_0_693,plain,
( proj1Suc(double(x(suc(zero),suc(zero)))) != double(rd(shw(double(suc(zero)))))
| suc(double(double(suc(zero)))) = double(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(suc(double(double(suc(zero)))),double(rd(shw(double(suc(zero)))))) )],[refute_0_679,refute_0_692]) ).
cnf(refute_0_694,plain,
suc(double(double(suc(zero)))) = double(double(suc(zero))),
inference(resolve,[$cnf( $equal(proj1Suc(double(x(suc(zero),suc(zero)))),double(rd(shw(double(suc(zero)))))) )],[refute_0_670,refute_0_693]) ).
cnf(refute_0_695,plain,
double(suc(double(double(suc(zero))))) = double(suc(double(double(suc(zero))))),
introduced(tautology,[refl,[$fot(double(suc(double(double(suc(zero))))))]]) ).
cnf(refute_0_696,plain,
( double(suc(double(double(suc(zero))))) != double(suc(double(double(suc(zero)))))
| suc(double(double(suc(zero)))) != double(double(suc(zero)))
| double(suc(double(double(suc(zero))))) = double(double(double(suc(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(double(double(suc(zero))))),double(suc(double(double(suc(zero)))))) ),[1,0],$fot(double(double(suc(zero))))]]) ).
cnf(refute_0_697,plain,
( suc(double(double(suc(zero)))) != double(double(suc(zero)))
| double(suc(double(double(suc(zero))))) = double(double(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(double(suc(double(double(suc(zero))))),double(suc(double(double(suc(zero)))))) )],[refute_0_695,refute_0_696]) ).
cnf(refute_0_698,plain,
double(suc(double(double(suc(zero))))) = double(double(double(suc(zero)))),
inference(resolve,[$cnf( $equal(suc(double(double(suc(zero)))),double(double(suc(zero)))) )],[refute_0_694,refute_0_697]) ).
cnf(refute_0_699,plain,
( double(suc(double(double(suc(zero))))) != double(double(double(suc(zero))))
| double(suc(double(double(suc(zero))))) != double(double(suc(double(suc(zero)))))
| double(double(double(suc(zero)))) = double(double(suc(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(double(double(suc(zero))))),double(double(suc(double(suc(zero)))))) ),[0],$fot(double(double(double(suc(zero)))))]]) ).
cnf(refute_0_700,plain,
( double(suc(double(double(suc(zero))))) != double(double(suc(double(suc(zero)))))
| double(double(double(suc(zero)))) = double(double(suc(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(double(suc(double(double(suc(zero))))),double(double(double(suc(zero))))) )],[refute_0_698,refute_0_699]) ).
cnf(refute_0_701,plain,
double(double(double(suc(zero)))) = double(double(suc(double(suc(zero))))),
inference(resolve,[$cnf( $equal(double(suc(double(double(suc(zero))))),double(double(suc(double(suc(zero)))))) )],[refute_0_648,refute_0_700]) ).
cnf(refute_0_702,plain,
( double(double(double(suc(zero)))) != double(double(suc(double(suc(zero)))))
| double(double(suc(double(suc(zero))))) = double(double(double(suc(zero)))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(double(double(double(suc(zero)))))),bind(Y0,$fot(double(double(suc(double(suc(zero)))))))]]) ).
cnf(refute_0_703,plain,
double(double(suc(double(suc(zero))))) = double(double(double(suc(zero)))),
inference(resolve,[$cnf( $equal(double(double(double(suc(zero)))),double(double(suc(double(suc(zero)))))) )],[refute_0_701,refute_0_702]) ).
cnf(refute_0_704,plain,
proj1Suc(double(double(suc(double(suc(zero)))))) = proj1Suc(double(double(suc(double(suc(zero)))))),
introduced(tautology,[refl,[$fot(proj1Suc(double(double(suc(double(suc(zero)))))))]]) ).
cnf(refute_0_705,plain,
( double(double(suc(double(suc(zero))))) != double(double(double(suc(zero))))
| proj1Suc(double(double(suc(double(suc(zero)))))) != proj1Suc(double(double(suc(double(suc(zero))))))
| proj1Suc(double(double(suc(double(suc(zero)))))) = proj1Suc(double(double(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(double(suc(double(suc(zero)))))),proj1Suc(double(double(suc(double(suc(zero))))))) ),[1,0],$fot(double(double(double(suc(zero)))))]]) ).
cnf(refute_0_706,plain,
( double(double(suc(double(suc(zero))))) != double(double(double(suc(zero))))
| proj1Suc(double(double(suc(double(suc(zero)))))) = proj1Suc(double(double(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(double(suc(double(suc(zero)))))),proj1Suc(double(double(suc(double(suc(zero))))))) )],[refute_0_704,refute_0_705]) ).
cnf(refute_0_707,plain,
proj1Suc(double(double(suc(double(suc(zero)))))) = proj1Suc(double(double(double(suc(zero))))),
inference(resolve,[$cnf( $equal(double(double(suc(double(suc(zero))))),double(double(double(suc(zero))))) )],[refute_0_703,refute_0_706]) ).
cnf(refute_0_708,plain,
( proj1Suc(double(double(suc(double(suc(zero)))))) != proj1Suc(double(double(double(suc(zero)))))
| proj1Suc(double(double(suc(double(suc(zero)))))) != suc(double(suc(double(double(suc(zero))))))
| proj1Suc(double(double(double(suc(zero))))) = suc(double(suc(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(double(suc(double(suc(zero)))))),suc(double(suc(double(double(suc(zero))))))) ),[0],$fot(proj1Suc(double(double(double(suc(zero))))))]]) ).
cnf(refute_0_709,plain,
( proj1Suc(double(double(suc(double(suc(zero)))))) != suc(double(suc(double(double(suc(zero))))))
| proj1Suc(double(double(double(suc(zero))))) = suc(double(suc(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(double(suc(double(suc(zero)))))),proj1Suc(double(double(double(suc(zero)))))) )],[refute_0_707,refute_0_708]) ).
cnf(refute_0_710,plain,
suc(double(suc(double(double(suc(zero)))))) = suc(double(suc(double(double(suc(zero)))))),
introduced(tautology,[refl,[$fot(suc(double(suc(double(double(suc(zero)))))))]]) ).
cnf(refute_0_711,plain,
( double(suc(double(double(suc(zero))))) != double(double(double(suc(zero))))
| suc(double(suc(double(double(suc(zero)))))) != suc(double(suc(double(double(suc(zero))))))
| suc(double(suc(double(double(suc(zero)))))) = suc(double(double(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( $equal(suc(double(suc(double(double(suc(zero)))))),suc(double(suc(double(double(suc(zero))))))) ),[1,0],$fot(double(double(double(suc(zero)))))]]) ).
cnf(refute_0_712,plain,
( double(suc(double(double(suc(zero))))) != double(double(double(suc(zero))))
| suc(double(suc(double(double(suc(zero)))))) = suc(double(double(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(suc(double(suc(double(double(suc(zero)))))),suc(double(suc(double(double(suc(zero))))))) )],[refute_0_710,refute_0_711]) ).
cnf(refute_0_713,plain,
suc(double(suc(double(double(suc(zero)))))) = suc(double(double(double(suc(zero))))),
inference(resolve,[$cnf( $equal(double(suc(double(double(suc(zero))))),double(double(double(suc(zero))))) )],[refute_0_698,refute_0_712]) ).
cnf(refute_0_714,plain,
( proj1Suc(double(double(double(suc(zero))))) != suc(double(suc(double(double(suc(zero))))))
| suc(double(suc(double(double(suc(zero)))))) != suc(double(double(double(suc(zero)))))
| proj1Suc(double(double(double(suc(zero))))) = suc(double(double(double(suc(zero))))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(proj1Suc(double(double(double(suc(zero))))),suc(double(double(double(suc(zero)))))) ),[0],$fot(suc(double(suc(double(double(suc(zero)))))))]]) ).
cnf(refute_0_715,plain,
( proj1Suc(double(double(double(suc(zero))))) != suc(double(suc(double(double(suc(zero))))))
| proj1Suc(double(double(double(suc(zero))))) = suc(double(double(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(suc(double(suc(double(double(suc(zero)))))),suc(double(double(double(suc(zero)))))) )],[refute_0_713,refute_0_714]) ).
cnf(refute_0_716,plain,
( proj1Suc(double(double(suc(double(suc(zero)))))) != suc(double(suc(double(double(suc(zero))))))
| proj1Suc(double(double(double(suc(zero))))) = suc(double(double(double(suc(zero))))) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(double(double(suc(zero))))),suc(double(suc(double(double(suc(zero))))))) )],[refute_0_709,refute_0_715]) ).
cnf(refute_0_717,plain,
proj1Suc(double(double(double(suc(zero))))) = suc(double(double(double(suc(zero))))),
inference(resolve,[$cnf( $equal(proj1Suc(double(double(suc(double(suc(zero)))))),suc(double(suc(double(double(suc(zero))))))) )],[refute_0_469,refute_0_716]) ).
cnf(refute_0_718,plain,
( proj1Suc(double(double(double(suc(zero))))) != suc(double(double(double(suc(zero)))))
| suc(double(double(double(suc(zero))))) = proj1Suc(double(double(double(suc(zero))))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(proj1Suc(double(double(double(suc(zero))))))),bind(Y0,$fot(suc(double(double(double(suc(zero)))))))]]) ).
cnf(refute_0_719,plain,
suc(double(double(double(suc(zero))))) = proj1Suc(double(double(double(suc(zero))))),
inference(resolve,[$cnf( $equal(proj1Suc(double(double(double(suc(zero))))),suc(double(double(double(suc(zero)))))) )],[refute_0_717,refute_0_718]) ).
cnf(refute_0_720,plain,
half(suc(double(double(double(suc(zero)))))) = half(suc(double(double(double(suc(zero)))))),
introduced(tautology,[refl,[$fot(half(suc(double(double(double(suc(zero)))))))]]) ).
cnf(refute_0_721,plain,
( half(suc(double(double(double(suc(zero)))))) != half(suc(double(double(double(suc(zero))))))
| suc(double(double(double(suc(zero))))) != proj1Suc(double(double(double(suc(zero)))))
| half(suc(double(double(double(suc(zero)))))) = half(proj1Suc(double(double(double(suc(zero)))))) ),
introduced(tautology,[equality,[$cnf( $equal(half(suc(double(double(double(suc(zero)))))),half(suc(double(double(double(suc(zero))))))) ),[1,0],$fot(proj1Suc(double(double(double(suc(zero))))))]]) ).
cnf(refute_0_722,plain,
( suc(double(double(double(suc(zero))))) != proj1Suc(double(double(double(suc(zero)))))
| half(suc(double(double(double(suc(zero)))))) = half(proj1Suc(double(double(double(suc(zero)))))) ),
inference(resolve,[$cnf( $equal(half(suc(double(double(double(suc(zero)))))),half(suc(double(double(double(suc(zero))))))) )],[refute_0_720,refute_0_721]) ).
cnf(refute_0_723,plain,
half(suc(double(double(double(suc(zero)))))) = half(proj1Suc(double(double(double(suc(zero)))))),
inference(resolve,[$cnf( $equal(suc(double(double(double(suc(zero))))),proj1Suc(double(double(double(suc(zero)))))) )],[refute_0_719,refute_0_722]) ).
cnf(refute_0_724,plain,
( half(proj1Suc(double(double(double(suc(zero)))))) != suc(double(suc(zero)))
| half(suc(double(double(double(suc(zero)))))) != half(proj1Suc(double(double(double(suc(zero))))))
| half(suc(double(double(double(suc(zero)))))) = suc(double(suc(zero))) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(half(suc(double(double(double(suc(zero)))))))),bind(Y0,$fot(half(proj1Suc(double(double(double(suc(zero)))))))),bind(Z0,$fot(suc(double(suc(zero)))))]]) ).
cnf(refute_0_725,plain,
( half(proj1Suc(double(double(double(suc(zero)))))) != suc(double(suc(zero)))
| half(suc(double(double(double(suc(zero)))))) = suc(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(half(suc(double(double(double(suc(zero)))))),half(proj1Suc(double(double(double(suc(zero))))))) )],[refute_0_723,refute_0_724]) ).
cnf(refute_0_726,plain,
half(suc(double(double(double(suc(zero)))))) = suc(double(suc(zero))),
inference(resolve,[$cnf( $equal(half(proj1Suc(double(double(double(suc(zero)))))),suc(double(suc(zero)))) )],[refute_0_325,refute_0_725]) ).
cnf(refute_0_727,plain,
( half(suc(double(double(double(suc(zero)))))) != double(double(suc(zero)))
| half(suc(double(double(double(suc(zero)))))) != suc(double(suc(zero)))
| suc(double(suc(zero))) = double(double(suc(zero))) ),
introduced(tautology,[equality,[$cnf( $equal(half(suc(double(double(double(suc(zero)))))),double(double(suc(zero)))) ),[0],$fot(suc(double(suc(zero))))]]) ).
cnf(refute_0_728,plain,
( half(suc(double(double(double(suc(zero)))))) != double(double(suc(zero)))
| suc(double(suc(zero))) = double(double(suc(zero))) ),
inference(resolve,[$cnf( $equal(half(suc(double(double(double(suc(zero)))))),suc(double(suc(zero)))) )],[refute_0_726,refute_0_727]) ).
cnf(refute_0_729,plain,
suc(double(suc(zero))) = double(double(suc(zero))),
inference(resolve,[$cnf( $equal(half(suc(double(double(double(suc(zero)))))),double(double(suc(zero)))) )],[refute_0_336,refute_0_728]) ).
cnf(refute_0_730,plain,
half(suc(double(suc(zero)))) = half(suc(double(suc(zero)))),
introduced(tautology,[refl,[$fot(half(suc(double(suc(zero)))))]]) ).
cnf(refute_0_731,plain,
( half(suc(double(suc(zero)))) != half(suc(double(suc(zero))))
| suc(double(suc(zero))) != double(double(suc(zero)))
| half(suc(double(suc(zero)))) = half(double(double(suc(zero)))) ),
introduced(tautology,[equality,[$cnf( $equal(half(suc(double(suc(zero)))),half(suc(double(suc(zero))))) ),[1,0],$fot(double(double(suc(zero))))]]) ).
cnf(refute_0_732,plain,
( suc(double(suc(zero))) != double(double(suc(zero)))
| half(suc(double(suc(zero)))) = half(double(double(suc(zero)))) ),
inference(resolve,[$cnf( $equal(half(suc(double(suc(zero)))),half(suc(double(suc(zero))))) )],[refute_0_730,refute_0_731]) ).
cnf(refute_0_733,plain,
half(suc(double(suc(zero)))) = half(double(double(suc(zero)))),
inference(resolve,[$cnf( $equal(suc(double(suc(zero))),double(double(suc(zero)))) )],[refute_0_729,refute_0_732]) ).
cnf(refute_0_734,plain,
( half(double(double(suc(zero)))) != double(suc(zero))
| half(suc(double(suc(zero)))) != half(double(double(suc(zero))))
| half(suc(double(suc(zero)))) = double(suc(zero)) ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(half(suc(double(suc(zero)))))),bind(Y0,$fot(half(double(double(suc(zero)))))),bind(Z0,$fot(double(suc(zero))))]]) ).
cnf(refute_0_735,plain,
( half(double(double(suc(zero)))) != double(suc(zero))
| half(suc(double(suc(zero)))) = double(suc(zero)) ),
inference(resolve,[$cnf( $equal(half(suc(double(suc(zero)))),half(double(double(suc(zero))))) )],[refute_0_733,refute_0_734]) ).
cnf(refute_0_736,plain,
half(suc(double(suc(zero)))) = double(suc(zero)),
inference(resolve,[$cnf( $equal(half(double(double(suc(zero)))),double(suc(zero))) )],[refute_0_193,refute_0_735]) ).
cnf(refute_0_737,plain,
( half(suc(double(suc(zero)))) != double(suc(zero))
| half(suc(double(suc(zero)))) != suc(zero)
| double(suc(zero)) = suc(zero) ),
introduced(tautology,[equality,[$cnf( $equal(half(suc(double(suc(zero)))),suc(zero)) ),[0],$fot(double(suc(zero)))]]) ).
cnf(refute_0_738,plain,
( half(suc(double(suc(zero)))) != suc(zero)
| double(suc(zero)) = suc(zero) ),
inference(resolve,[$cnf( $equal(half(suc(double(suc(zero)))),double(suc(zero))) )],[refute_0_736,refute_0_737]) ).
cnf(refute_0_739,plain,
double(suc(zero)) = suc(zero),
inference(resolve,[$cnf( $equal(half(suc(double(suc(zero)))),suc(zero)) )],[refute_0_147,refute_0_738]) ).
cnf(refute_0_740,plain,
proj1Suc(double(suc(zero))) = proj1Suc(double(suc(zero))),
introduced(tautology,[refl,[$fot(proj1Suc(double(suc(zero))))]]) ).
cnf(refute_0_741,plain,
( double(suc(zero)) != suc(zero)
| proj1Suc(double(suc(zero))) != proj1Suc(double(suc(zero)))
| proj1Suc(double(suc(zero))) = proj1Suc(suc(zero)) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(suc(zero))),proj1Suc(double(suc(zero)))) ),[1,0],$fot(suc(zero))]]) ).
cnf(refute_0_742,plain,
( double(suc(zero)) != suc(zero)
| proj1Suc(double(suc(zero))) = proj1Suc(suc(zero)) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(zero))),proj1Suc(double(suc(zero)))) )],[refute_0_740,refute_0_741]) ).
cnf(refute_0_743,plain,
proj1Suc(double(suc(zero))) = proj1Suc(suc(zero)),
inference(resolve,[$cnf( $equal(double(suc(zero)),suc(zero)) )],[refute_0_739,refute_0_742]) ).
cnf(refute_0_744,plain,
( proj1Suc(double(suc(zero))) != proj1Suc(suc(zero))
| proj1Suc(suc(zero)) != zero
| proj1Suc(double(suc(zero))) = zero ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(proj1Suc(double(suc(zero))))),bind(Y0,$fot(proj1Suc(suc(zero)))),bind(Z0,$fot(zero))]]) ).
cnf(refute_0_745,plain,
( proj1Suc(suc(zero)) != zero
| proj1Suc(double(suc(zero))) = zero ),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(zero))),proj1Suc(suc(zero))) )],[refute_0_743,refute_0_744]) ).
cnf(refute_0_746,plain,
proj1Suc(double(suc(zero))) = zero,
inference(resolve,[$cnf( $equal(proj1Suc(suc(zero)),zero) )],[refute_0_136,refute_0_745]) ).
cnf(refute_0_747,plain,
( proj1Suc(double(suc(zero))) != suc(zero)
| proj1Suc(double(suc(zero))) != zero
| zero = suc(zero) ),
introduced(tautology,[equality,[$cnf( $equal(proj1Suc(double(suc(zero))),suc(zero)) ),[0],$fot(zero)]]) ).
cnf(refute_0_748,plain,
( proj1Suc(double(suc(zero))) != suc(zero)
| zero = suc(zero) ),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(zero))),zero) )],[refute_0_746,refute_0_747]) ).
cnf(refute_0_749,plain,
zero = suc(zero),
inference(resolve,[$cnf( $equal(proj1Suc(double(suc(zero))),suc(zero)) )],[refute_0_135,refute_0_748]) ).
cnf(refute_0_750,plain,
( zero != suc(zero)
| suc(zero) = zero ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(zero)),bind(Y0,$fot(suc(zero)))]]) ).
cnf(refute_0_751,plain,
suc(zero) = zero,
inference(resolve,[$cnf( $equal(zero,suc(zero)) )],[refute_0_749,refute_0_750]) ).
cnf(refute_0_752,plain,
shw(suc(zero)) = shw(suc(zero)),
introduced(tautology,[refl,[$fot(shw(suc(zero)))]]) ).
cnf(refute_0_753,plain,
( shw(suc(zero)) != shw(suc(zero))
| suc(zero) != zero
| shw(suc(zero)) = shw(zero) ),
introduced(tautology,[equality,[$cnf( $equal(shw(suc(zero)),shw(suc(zero))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_754,plain,
( suc(zero) != zero
| shw(suc(zero)) = shw(zero) ),
inference(resolve,[$cnf( $equal(shw(suc(zero)),shw(suc(zero))) )],[refute_0_752,refute_0_753]) ).
cnf(refute_0_755,plain,
shw(suc(zero)) = shw(zero),
inference(resolve,[$cnf( $equal(suc(zero),zero) )],[refute_0_751,refute_0_754]) ).
cnf(refute_0_756,plain,
( shw(suc(zero)) != shw(zero)
| shw(zero) != nil
| shw(suc(zero)) = nil ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(shw(suc(zero)))),bind(Y0,$fot(shw(zero))),bind(Z0,$fot(nil))]]) ).
cnf(refute_0_757,plain,
( shw(zero) != nil
| shw(suc(zero)) = nil ),
inference(resolve,[$cnf( $equal(shw(suc(zero)),shw(zero)) )],[refute_0_755,refute_0_756]) ).
cnf(refute_0_758,plain,
shw(suc(zero)) = nil,
inference(resolve,[$cnf( $equal(shw(zero),nil) )],[refute_0_117,refute_0_757]) ).
cnf(refute_0_759,plain,
head(shw(suc(zero))) = head(shw(suc(zero))),
introduced(tautology,[refl,[$fot(head(shw(suc(zero))))]]) ).
cnf(refute_0_760,plain,
( head(shw(suc(zero))) != head(shw(suc(zero)))
| shw(suc(zero)) != nil
| head(shw(suc(zero))) = head(nil) ),
introduced(tautology,[equality,[$cnf( $equal(head(shw(suc(zero))),head(shw(suc(zero)))) ),[1,0],$fot(nil)]]) ).
cnf(refute_0_761,plain,
( shw(suc(zero)) != nil
| head(shw(suc(zero))) = head(nil) ),
inference(resolve,[$cnf( $equal(head(shw(suc(zero))),head(shw(suc(zero)))) )],[refute_0_759,refute_0_760]) ).
cnf(refute_0_762,plain,
head(shw(suc(zero))) = head(nil),
inference(resolve,[$cnf( $equal(shw(suc(zero)),nil) )],[refute_0_758,refute_0_761]) ).
cnf(refute_0_763,plain,
( head(shw(suc(zero))) != head(nil)
| head(shw(suc(zero))) != i
| head(nil) = i ),
introduced(tautology,[equality,[$cnf( $equal(head(shw(suc(zero))),i) ),[0],$fot(head(nil))]]) ).
cnf(refute_0_764,plain,
( head(shw(suc(zero))) != i
| head(nil) = i ),
inference(resolve,[$cnf( $equal(head(shw(suc(zero))),head(nil)) )],[refute_0_762,refute_0_763]) ).
cnf(refute_0_765,plain,
head(nil) = i,
inference(resolve,[$cnf( $equal(head(shw(suc(zero))),i) )],[refute_0_130,refute_0_764]) ).
cnf(refute_0_766,plain,
double(suc(zero)) = double(suc(zero)),
introduced(tautology,[refl,[$fot(double(suc(zero)))]]) ).
cnf(refute_0_767,plain,
( double(suc(zero)) != double(suc(zero))
| suc(zero) != zero
| double(suc(zero)) = double(zero) ),
introduced(tautology,[equality,[$cnf( $equal(double(suc(zero)),double(suc(zero))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_768,plain,
( suc(zero) != zero
| double(suc(zero)) = double(zero) ),
inference(resolve,[$cnf( $equal(double(suc(zero)),double(suc(zero))) )],[refute_0_766,refute_0_767]) ).
cnf(refute_0_769,plain,
double(suc(zero)) = double(zero),
inference(resolve,[$cnf( $equal(suc(zero),zero) )],[refute_0_751,refute_0_768]) ).
cnf(refute_0_770,plain,
( double(suc(zero)) != double(zero)
| double(zero) != zero
| double(suc(zero)) = zero ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(double(suc(zero)))),bind(Y0,$fot(double(zero))),bind(Z0,$fot(zero))]]) ).
cnf(refute_0_771,plain,
( double(zero) != zero
| double(suc(zero)) = zero ),
inference(resolve,[$cnf( $equal(double(suc(zero)),double(zero)) )],[refute_0_769,refute_0_770]) ).
cnf(refute_0_772,plain,
double(suc(zero)) = zero,
inference(resolve,[$cnf( $equal(double(zero),zero) )],[refute_0_81,refute_0_771]) ).
cnf(refute_0_773,plain,
shw(double(suc(zero))) = shw(double(suc(zero))),
introduced(tautology,[refl,[$fot(shw(double(suc(zero))))]]) ).
cnf(refute_0_774,plain,
( double(suc(zero)) != zero
| shw(double(suc(zero))) != shw(double(suc(zero)))
| shw(double(suc(zero))) = shw(zero) ),
introduced(tautology,[equality,[$cnf( $equal(shw(double(suc(zero))),shw(double(suc(zero)))) ),[1,0],$fot(zero)]]) ).
cnf(refute_0_775,plain,
( double(suc(zero)) != zero
| shw(double(suc(zero))) = shw(zero) ),
inference(resolve,[$cnf( $equal(shw(double(suc(zero))),shw(double(suc(zero)))) )],[refute_0_773,refute_0_774]) ).
cnf(refute_0_776,plain,
shw(double(suc(zero))) = shw(zero),
inference(resolve,[$cnf( $equal(double(suc(zero)),zero) )],[refute_0_772,refute_0_775]) ).
cnf(refute_0_777,plain,
( shw(double(suc(zero))) != shw(zero)
| shw(zero) != nil
| shw(double(suc(zero))) = nil ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(shw(double(suc(zero))))),bind(Y0,$fot(shw(zero))),bind(Z0,$fot(nil))]]) ).
cnf(refute_0_778,plain,
( shw(zero) != nil
| shw(double(suc(zero))) = nil ),
inference(resolve,[$cnf( $equal(shw(double(suc(zero))),shw(zero)) )],[refute_0_776,refute_0_777]) ).
cnf(refute_0_779,plain,
shw(double(suc(zero))) = nil,
inference(resolve,[$cnf( $equal(shw(zero),nil) )],[refute_0_117,refute_0_778]) ).
cnf(refute_0_780,plain,
head(shw(double(suc(zero)))) = head(shw(double(suc(zero)))),
introduced(tautology,[refl,[$fot(head(shw(double(suc(zero)))))]]) ).
cnf(refute_0_781,plain,
( head(shw(double(suc(zero)))) != head(shw(double(suc(zero))))
| shw(double(suc(zero))) != nil
| head(shw(double(suc(zero)))) = head(nil) ),
introduced(tautology,[equality,[$cnf( $equal(head(shw(double(suc(zero)))),head(shw(double(suc(zero))))) ),[1,0],$fot(nil)]]) ).
cnf(refute_0_782,plain,
( shw(double(suc(zero))) != nil
| head(shw(double(suc(zero)))) = head(nil) ),
inference(resolve,[$cnf( $equal(head(shw(double(suc(zero)))),head(shw(double(suc(zero))))) )],[refute_0_780,refute_0_781]) ).
cnf(refute_0_783,plain,
head(shw(double(suc(zero)))) = head(nil),
inference(resolve,[$cnf( $equal(shw(double(suc(zero))),nil) )],[refute_0_779,refute_0_782]) ).
cnf(refute_0_784,plain,
( head(nil) != i
| head(shw(double(suc(zero)))) != head(nil)
| head(shw(double(suc(zero)))) = i ),
inference(subst,[],[refute_0_44:[bind(X0,$fot(head(shw(double(suc(zero)))))),bind(Y0,$fot(head(nil))),bind(Z0,$fot(i))]]) ).
cnf(refute_0_785,plain,
( head(nil) != i
| head(shw(double(suc(zero)))) = i ),
inference(resolve,[$cnf( $equal(head(shw(double(suc(zero)))),head(nil)) )],[refute_0_783,refute_0_784]) ).
cnf(refute_0_786,plain,
head(shw(double(suc(zero)))) = i,
inference(resolve,[$cnf( $equal(head(nil),i) )],[refute_0_765,refute_0_785]) ).
cnf(refute_0_787,plain,
( head(shw(double(suc(zero)))) != i
| head(shw(double(suc(zero)))) != o
| i = o ),
introduced(tautology,[equality,[$cnf( $equal(head(shw(double(suc(zero)))),o) ),[0],$fot(i)]]) ).
cnf(refute_0_788,plain,
( head(shw(double(suc(zero)))) != o
| i = o ),
inference(resolve,[$cnf( $equal(head(shw(double(suc(zero)))),i) )],[refute_0_786,refute_0_787]) ).
cnf(refute_0_789,plain,
i = o,
inference(resolve,[$cnf( $equal(head(shw(double(suc(zero)))),o) )],[refute_0_109,refute_0_788]) ).
cnf(refute_0_790,plain,
i != o,
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_791,plain,
$false,
inference(resolve,[$cnf( $equal(i,o) )],[refute_0_789,refute_0_790]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWX217+1 : TPTP v9.3.0. Released v9.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.18/0.35 % Computer : n007.cluster.edu
% 0.18/0.35 % Model : x86_64 x86_64
% 0.18/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35 % Memory : 8042.1875MB
% 0.18/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35 % CPULimit : 300
% 0.18/0.35 % WCLimit : 300
% 0.18/0.35 % DateTime : Tue May 5 12:13:38 EDT 2026
% 0.18/0.35 % CPUTime :
% 0.18/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.89/2.06 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.89/2.06
% 1.89/2.06 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.99/2.16
%------------------------------------------------------------------------------