%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM925+6 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.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 : 600s
% DateTime : Mon Jul 18 12:31:41 EDT 2022
% Result : Theorem 3.37s 3.59s
% Output : CNFRefutation 3.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 76
% Syntax : Number of formulae : 239 ( 108 unt; 0 def)
% Number of atoms : 429 ( 322 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 382 ( 192 ~; 170 |; 9 &)
% ( 9 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 8 con; 0-4 aty)
% Number of variables : 134 ( 0 sgn 48 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_0_n1pos,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) ).
fof(fact_27_int__eq__0__conv,axiom,
! [Na] :
( hAPP(nat,int,semiring_1_of_nat(int),Na) = zero_zero(int)
<=> Na = zero_zero(nat) ) ).
fof(fact_29_nat__1__add__1,axiom,
hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) ).
fof(fact_37_one__is__num__one,axiom,
one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)) ).
fof(fact_47_zadd__commute,axiom,
! [Z_1,W_1] : hAPP(int,int,plus_plus(int,Z_1),W_1) = hAPP(int,int,plus_plus(int,W_1),Z_1) ).
fof(fact_73_Pls__def,axiom,
pls = zero_zero(int) ).
fof(fact_119_number__of__is__id,axiom,
! [K] : number_number_of(int,K) = K ).
fof(fact_190_zero__less__imp__eq__int,axiom,
! [K] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))
=> ? [N_1] :
( hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1))
& K = hAPP(nat,int,semiring_1_of_nat(int),N_1) ) ) ).
fof(fact_248_zle__refl,axiom,
! [W_1] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),W_1)) ).
fof(fact_254_zless__le,axiom,
! [Z_2,Wa] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),Wa))
<=> ( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),Wa))
& Z_2 != Wa ) ) ).
fof(fact_313_int__le__0__conv,axiom,
! [Na] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)))
<=> Na = zero_zero(nat) ) ).
fof(fact_320_succ__def,axiom,
! [K] : hAPP(int,int,succ,K) = hAPP(int,int,plus_plus(int,K),one_one(int)) ).
fof(fact_329_power2__ge__self,axiom,
! [X] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ).
fof(fact_376_nonneg__eq__int,axiom,
! [Z_1] :
( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1))
=> ~ ! [M] : Z_1 != hAPP(nat,int,semiring_1_of_nat(int),M) ) ).
fof(conj_0,conjecture,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) ).
fof(subgoal_0,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int),
inference(strip,[],[conj_0]) ).
fof(negate_0_0,plain,
~ ( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(canonicalize,[],[fact_0_n1pos]) ).
fof(normalize_0_1,plain,
pls = zero_zero(int),
inference(canonicalize,[],[fact_73_Pls__def]) ).
fof(normalize_0_2,plain,
! [K] : hAPP(int,int,succ,K) = hAPP(int,int,plus_plus(int,K),one_one(int)),
inference(canonicalize,[],[fact_320_succ__def]) ).
fof(normalize_0_3,plain,
! [K] : hAPP(int,int,succ,K) = hAPP(int,int,plus_plus(int,K),one_one(int)),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [W_1,Z_1] : hAPP(int,int,plus_plus(int,Z_1),W_1) = hAPP(int,int,plus_plus(int,W_1),Z_1),
inference(canonicalize,[],[fact_47_zadd__commute]) ).
fof(normalize_0_5,plain,
! [W_1,Z_1] : hAPP(int,int,plus_plus(int,Z_1),W_1) = hAPP(int,int,plus_plus(int,W_1),Z_1),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [K] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))
| ? [N_1] :
( K = hAPP(nat,int,semiring_1_of_nat(int),N_1)
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) ) ),
inference(canonicalize,[],[fact_190_zero__less__imp__eq__int]) ).
fof(normalize_0_7,plain,
! [K] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))
| ? [N_1] :
( K = hAPP(nat,int,semiring_1_of_nat(int),N_1)
& hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) ) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [K] :
( ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))
| K = hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(K)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))
| hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),skolemFOFtoCNF_N_1(K))) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [K] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))
| K = hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(K)) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [W_1] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),W_1)),
inference(canonicalize,[],[fact_248_zle__refl]) ).
fof(normalize_0_11,plain,
! [W_1] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),W_1)),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [Z_1] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1))
| ? [M] : Z_1 = hAPP(nat,int,semiring_1_of_nat(int),M) ),
inference(canonicalize,[],[fact_376_nonneg__eq__int]) ).
fof(normalize_0_13,plain,
! [Z_1] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1))
| ? [M] : Z_1 = hAPP(nat,int,semiring_1_of_nat(int),M) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [Z_1] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1))
| Z_1 = hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(Z_1)) ),
inference(clausify,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [Na] :
( Na != zero_zero(nat)
<=> ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int))) ),
inference(canonicalize,[],[fact_313_int__le__0__conv]) ).
fof(normalize_0_16,plain,
! [Na] :
( Na != zero_zero(nat)
<=> ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int))) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [Na] :
( ( Na != zero_zero(nat)
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int))) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)))
| Na = zero_zero(nat) ) ),
inference(clausify,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [Na] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)))
| Na = zero_zero(nat) ),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [Na] :
( Na != zero_zero(nat)
<=> hAPP(nat,int,semiring_1_of_nat(int),Na) != zero_zero(int) ),
inference(canonicalize,[],[fact_27_int__eq__0__conv]) ).
fof(normalize_0_20,plain,
! [Na] :
( Na != zero_zero(nat)
<=> hAPP(nat,int,semiring_1_of_nat(int),Na) != zero_zero(int) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [Na] :
( ( Na != zero_zero(nat)
| hAPP(nat,int,semiring_1_of_nat(int),Na) = zero_zero(int) )
& ( hAPP(nat,int,semiring_1_of_nat(int),Na) != zero_zero(int)
| Na = zero_zero(nat) ) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [Na] :
( hAPP(nat,int,semiring_1_of_nat(int),Na) != zero_zero(int)
| Na = zero_zero(nat) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),
inference(canonicalize,[],[fact_329_power2__ge__self]) ).
fof(normalize_0_24,plain,
! [X] : hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
inference(canonicalize,[],[fact_29_nat__1__add__1]) ).
fof(normalize_0_26,plain,
one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)),
inference(canonicalize,[],[fact_37_one__is__num__one]) ).
fof(normalize_0_27,plain,
! [K] : number_number_of(int,K) = K,
inference(canonicalize,[],[fact_119_number__of__is__id]) ).
fof(normalize_0_28,plain,
! [K] : number_number_of(int,K) = K,
inference(specialize,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_30,plain,
! [Wa,Z_2] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),Wa))
<=> ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),Wa))
| Z_2 = Wa ) ),
inference(canonicalize,[],[fact_254_zless__le]) ).
fof(normalize_0_31,plain,
! [Wa,Z_2] :
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),Wa))
<=> ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),Wa))
| Z_2 = Wa ) ),
inference(specialize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [Wa,Z_2] :
( ( Z_2 != Wa
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),Wa)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),Wa))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),Wa)) )
& ( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_2),Wa))
| Z_2 = Wa
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),Wa)) ) ),
inference(clausify,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [Wa,Z_2] :
( Z_2 != Wa
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),Wa)) ),
inference(conjunct,[],[normalize_0_32]) ).
cnf(refute_0_0,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
pls = zero_zero(int),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_2,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_3,plain,
( X0 != X0
| X0 != Y
| Y = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X0 != Y
| Y = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( pls != zero_zero(int)
| zero_zero(int) = pls ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(pls)),bind(Y,$fot(zero_zero(int)))]]) ).
cnf(refute_0_6,plain,
zero_zero(int) = pls,
inference(resolve,[$cnf( $equal(pls,zero_zero(int)) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)) = hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),
introduced(tautology,[refl,[$fot(hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))]]) ).
cnf(refute_0_8,plain,
( hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)) != hAPP(int,fun(int,bool),ord_less(int),zero_zero(int))
| zero_zero(int) != pls
| hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)) = hAPP(int,fun(int,bool),ord_less(int),pls) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int))) ),[1,3],$fot(pls)]]) ).
cnf(refute_0_9,plain,
( zero_zero(int) != pls
| hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)) = hAPP(int,fun(int,bool),ord_less(int),pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int))) )],[refute_0_7,refute_0_8]) ).
cnf(refute_0_10,plain,
hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)) = hAPP(int,fun(int,bool),ord_less(int),pls),
inference(resolve,[$cnf( $equal(zero_zero(int),pls) )],[refute_0_6,refute_0_9]) ).
cnf(refute_0_11,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),
introduced(tautology,[refl,[$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))))]]) ).
cnf(refute_0_12,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))
| hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)) != hAPP(int,fun(int,bool),ord_less(int),pls)
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) ),[1,2],$fot(hAPP(int,fun(int,bool),ord_less(int),pls))]]) ).
cnf(refute_0_13,plain,
( hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)) != hAPP(int,fun(int,bool),ord_less(int),pls)
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),
inference(resolve,[$cnf( $equal(hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,fun(int,bool),ord_less(int),pls)) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) ),[0],$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))))]]) ).
cnf(refute_0_16,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) )],[refute_0_0,refute_0_16]) ).
cnf(refute_0_18,plain,
hAPP(int,int,succ,K) = hAPP(int,int,plus_plus(int,K),one_one(int)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_19,plain,
hAPP(int,int,plus_plus(int,Z_1),W_1) = hAPP(int,int,plus_plus(int,W_1),Z_1),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_20,plain,
hAPP(int,int,plus_plus(int,K),one_one(int)) = hAPP(int,int,plus_plus(int,one_one(int)),K),
inference(subst,[],[refute_0_19:[bind(W_1,$fot(one_one(int))),bind(Z_1,$fot(K))]]) ).
cnf(refute_0_21,plain,
( hAPP(int,int,plus_plus(int,K),one_one(int)) != hAPP(int,int,plus_plus(int,one_one(int)),K)
| hAPP(int,int,succ,K) != hAPP(int,int,plus_plus(int,K),one_one(int))
| hAPP(int,int,succ,K) = hAPP(int,int,plus_plus(int,one_one(int)),K) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,succ,K),hAPP(int,int,plus_plus(int,K),one_one(int))) ),[1],$fot(hAPP(int,int,plus_plus(int,one_one(int)),K))]]) ).
cnf(refute_0_22,plain,
( hAPP(int,int,succ,K) != hAPP(int,int,plus_plus(int,K),one_one(int))
| hAPP(int,int,succ,K) = hAPP(int,int,plus_plus(int,one_one(int)),K) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,K),one_one(int)),hAPP(int,int,plus_plus(int,one_one(int)),K)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
hAPP(int,int,succ,K) = hAPP(int,int,plus_plus(int,one_one(int)),K),
inference(resolve,[$cnf( $equal(hAPP(int,int,succ,K),hAPP(int,int,plus_plus(int,K),one_one(int))) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
( hAPP(int,int,succ,K) != hAPP(int,int,plus_plus(int,one_one(int)),K)
| hAPP(int,int,plus_plus(int,one_one(int)),K) = hAPP(int,int,succ,K) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(hAPP(int,int,succ,K))),bind(Y,$fot(hAPP(int,int,plus_plus(int,one_one(int)),K)))]]) ).
cnf(refute_0_25,plain,
hAPP(int,int,plus_plus(int,one_one(int)),K) = hAPP(int,int,succ,K),
inference(resolve,[$cnf( $equal(hAPP(int,int,succ,K),hAPP(int,int,plus_plus(int,one_one(int)),K)) )],[refute_0_23,refute_0_24]) ).
cnf(refute_0_26,plain,
hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)) = hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)),
inference(subst,[],[refute_0_25:[bind(K,$fot(hAPP(nat,int,semiring_1_of_nat(int),n)))]]) ).
cnf(refute_0_27,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),
introduced(tautology,[refl,[$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))))]]) ).
cnf(refute_0_28,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))
| hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)) != hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) ),[1,3],$fot(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))]]) ).
cnf(refute_0_29,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)) != hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) )],[refute_0_26,refute_0_29]) ).
cnf(refute_0_31,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) ),[0],$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))]]) ).
cnf(refute_0_32,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) )],[refute_0_17,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))
| K = hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(K)) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_35,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K),
introduced(tautology,[refl,[$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K))]]) ).
cnf(refute_0_36,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)
| hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)) != hAPP(int,fun(int,bool),ord_less(int),pls)
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) ),[1,2],$fot(hAPP(int,fun(int,bool),ord_less(int),pls))]]) ).
cnf(refute_0_37,plain,
( hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)) != hAPP(int,fun(int,bool),ord_less(int),pls)
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K),
inference(resolve,[$cnf( $equal(hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,fun(int,bool),ord_less(int),pls)) )],[refute_0_10,refute_0_37]) ).
cnf(refute_0_39,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) ),
introduced(tautology,[equality,[$cnf( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) ),[0],$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K))]]) ).
cnf(refute_0_40,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K)) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K))
| K = hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(K)) ),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) )],[refute_0_40,refute_0_34]) ).
cnf(refute_0_42,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))
| hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) = hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) ),
inference(subst,[],[refute_0_41:[bind(K,$fot(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))]]) ).
cnf(refute_0_43,plain,
hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) = hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) )],[refute_0_33,refute_0_42]) ).
cnf(refute_0_44,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),W_1)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_45,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),pls)),
inference(subst,[],[refute_0_44:[bind(W_1,$fot(pls))]]) ).
cnf(refute_0_46,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1))
| Z_1 = hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(Z_1)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_47,plain,
hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)) = hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),
introduced(tautology,[refl,[$fot(hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))]]) ).
cnf(refute_0_48,plain,
( hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)) != hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int))
| zero_zero(int) != pls
| hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)) = hAPP(int,fun(int,bool),ord_less_eq(int),pls) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int))) ),[1,3],$fot(pls)]]) ).
cnf(refute_0_49,plain,
( zero_zero(int) != pls
| hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)) = hAPP(int,fun(int,bool),ord_less_eq(int),pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)) = hAPP(int,fun(int,bool),ord_less_eq(int),pls),
inference(resolve,[$cnf( $equal(zero_zero(int),pls) )],[refute_0_6,refute_0_49]) ).
cnf(refute_0_51,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1),
introduced(tautology,[refl,[$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1))]]) ).
cnf(refute_0_52,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)
| hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)) != hAPP(int,fun(int,bool),ord_less_eq(int),pls)
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),Z_1) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) ),[1,2],$fot(hAPP(int,fun(int,bool),ord_less_eq(int),pls))]]) ).
cnf(refute_0_53,plain,
( hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)) != hAPP(int,fun(int,bool),ord_less_eq(int),pls)
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),Z_1) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),Z_1),
inference(resolve,[$cnf( $equal(hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,fun(int,bool),ord_less_eq(int),pls)) )],[refute_0_50,refute_0_53]) ).
cnf(refute_0_55,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),Z_1)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),Z_1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) ),
introduced(tautology,[equality,[$cnf( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) ),[0],$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),Z_1))]]) ).
cnf(refute_0_56,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),Z_1))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),Z_1)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),Z_1))
| Z_1 = hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(Z_1)) ),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) )],[refute_0_56,refute_0_46]) ).
cnf(refute_0_58,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),pls))
| pls = hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)) ),
inference(subst,[],[refute_0_57:[bind(Z_1,$fot(pls))]]) ).
cnf(refute_0_59,plain,
pls = hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),pls)) )],[refute_0_45,refute_0_58]) ).
cnf(refute_0_60,plain,
( pls != hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls))
| hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)) = pls ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(pls)),bind(Y,$fot(hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls))))]]) ).
cnf(refute_0_61,plain,
hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)) = pls,
inference(resolve,[$cnf( $equal(pls,hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)))
| Na = zero_zero(nat) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_63,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)),
introduced(tautology,[refl,[$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)))]]) ).
cnf(refute_0_64,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int))
| zero_zero(int) != pls
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),pls) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int))) ),[1,3],$fot(pls)]]) ).
cnf(refute_0_65,plain,
( zero_zero(int) != pls
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),pls),
inference(resolve,[$cnf( $equal(zero_zero(int),pls) )],[refute_0_6,refute_0_65]) ).
cnf(refute_0_67,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),pls)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int))) ),
introduced(tautology,[equality,[$cnf( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int))) ),[0],$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),pls))]]) ).
cnf(refute_0_68,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),pls)) )],[refute_0_66,refute_0_67]) ).
cnf(refute_0_69,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),pls))
| Na = zero_zero(nat) ),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),zero_zero(int))) )],[refute_0_68,refute_0_62]) ).
cnf(refute_0_70,plain,
( hAPP(nat,int,semiring_1_of_nat(int),Na) != zero_zero(int)
| Na = zero_zero(nat) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_71,plain,
( hAPP(nat,int,semiring_1_of_nat(int),Na) != pls
| zero_zero(int) != pls
| hAPP(nat,int,semiring_1_of_nat(int),Na) = zero_zero(int) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(nat,int,semiring_1_of_nat(int),Na),zero_zero(int)) ),[1],$fot(pls)]]) ).
cnf(refute_0_72,plain,
( hAPP(nat,int,semiring_1_of_nat(int),Na) != pls
| hAPP(nat,int,semiring_1_of_nat(int),Na) = zero_zero(int) ),
inference(resolve,[$cnf( $equal(zero_zero(int),pls) )],[refute_0_6,refute_0_71]) ).
cnf(refute_0_73,plain,
( hAPP(nat,int,semiring_1_of_nat(int),Na) != pls
| Na = zero_zero(nat) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),Na),zero_zero(int)) )],[refute_0_72,refute_0_70]) ).
cnf(refute_0_74,plain,
( hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)) != pls
| skolemFOFtoCNF_M(pls) = zero_zero(nat) ),
inference(subst,[],[refute_0_73:[bind(Na,$fot(skolemFOFtoCNF_M(pls)))]]) ).
cnf(refute_0_75,plain,
( hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)) != pls
| pls != pls
| hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)) = pls ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)),pls) ),[0],$fot(pls)]]) ).
cnf(refute_0_76,plain,
( pls != pls
| hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)) = pls ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)),pls) )],[refute_0_61,refute_0_75]) ).
cnf(refute_0_77,plain,
( pls != pls
| skolemFOFtoCNF_M(pls) = zero_zero(nat) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)),pls) )],[refute_0_76,refute_0_74]) ).
cnf(refute_0_78,plain,
pls = pls,
introduced(tautology,[refl,[$fot(pls)]]) ).
cnf(refute_0_79,plain,
skolemFOFtoCNF_M(pls) = zero_zero(nat),
inference(resolve,[$cnf( $equal(pls,pls) )],[refute_0_78,refute_0_77]) ).
cnf(refute_0_80,plain,
( skolemFOFtoCNF_M(pls) != zero_zero(nat)
| zero_zero(nat) = skolemFOFtoCNF_M(pls) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(skolemFOFtoCNF_M(pls))),bind(Y,$fot(zero_zero(nat)))]]) ).
cnf(refute_0_81,plain,
zero_zero(nat) = skolemFOFtoCNF_M(pls),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_M(pls),zero_zero(nat)) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
( Na != zero_zero(nat)
| zero_zero(nat) != skolemFOFtoCNF_M(pls)
| Na = skolemFOFtoCNF_M(pls) ),
introduced(tautology,[equality,[$cnf( ~ $equal(Na,skolemFOFtoCNF_M(pls)) ),[0],$fot(zero_zero(nat))]]) ).
cnf(refute_0_83,plain,
( Na != zero_zero(nat)
| Na = skolemFOFtoCNF_M(pls) ),
inference(resolve,[$cnf( $equal(zero_zero(nat),skolemFOFtoCNF_M(pls)) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Na)),pls))
| Na = skolemFOFtoCNF_M(pls) ),
inference(resolve,[$cnf( $equal(Na,zero_zero(nat)) )],[refute_0_69,refute_0_83]) ).
cnf(refute_0_85,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))),pls))
| skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) = skolemFOFtoCNF_M(pls) ),
inference(subst,[],[refute_0_84:[bind(Na,$fot(skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))))]]) ).
cnf(refute_0_86,plain,
( hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) != hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))
| hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) = hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))),bind(Y,$fot(hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))))]]) ).
cnf(refute_0_87,plain,
hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) = hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)),
inference(resolve,[$cnf( $equal(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)),hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))) )],[refute_0_43,refute_0_86]) ).
cnf(refute_0_88,plain,
( hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) != hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))),pls)) ),
introduced(tautology,[equality,[$cnf( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))),pls)) ),[0,2,3],$fot(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))]]) ).
cnf(refute_0_89,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))),pls)) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) )],[refute_0_87,refute_0_88]) ).
cnf(refute_0_90,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),pls))
| skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) = skolemFOFtoCNF_M(pls) ),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))),pls)) )],[refute_0_89,refute_0_85]) ).
cnf(refute_0_91,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_92,plain,
hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_93,plain,
( hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) != number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),bind(Y,$fot(number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))]]) ).
cnf(refute_0_94,plain,
number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)),
inference(resolve,[$cnf( $equal(hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) )],[refute_0_92,refute_0_93]) ).
cnf(refute_0_95,plain,
hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
introduced(tautology,[refl,[$fot(hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))]]) ).
cnf(refute_0_96,plain,
( hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))
| hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) ),[1,3],$fot(hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))]]) ).
cnf(refute_0_97,plain,
( number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))
| hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))),
inference(resolve,[$cnf( $equal(number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
introduced(tautology,[refl,[$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))]]) ).
cnf(refute_0_100,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))
| hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),[1,3],$fot(hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))))]]) ).
cnf(refute_0_101,plain,
( hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) )],[refute_0_99,refute_0_100]) ).
cnf(refute_0_102,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),
inference(resolve,[$cnf( $equal(hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))) )],[refute_0_98,refute_0_101]) ).
cnf(refute_0_103,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))))) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),[0],$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))))]]) ).
cnf(refute_0_104,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))))),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) )],[refute_0_91,refute_0_104]) ).
cnf(refute_0_106,plain,
one_one(int) = number_number_of(int,hAPP(int,int,bit1,pls)),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_107,plain,
number_number_of(int,K) = K,
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_108,plain,
number_number_of(int,hAPP(int,int,bit1,pls)) = hAPP(int,int,bit1,pls),
inference(subst,[],[refute_0_107:[bind(K,$fot(hAPP(int,int,bit1,pls)))]]) ).
cnf(refute_0_109,plain,
( number_number_of(int,hAPP(int,int,bit1,pls)) != hAPP(int,int,bit1,pls)
| one_one(int) != number_number_of(int,hAPP(int,int,bit1,pls))
| one_one(int) = hAPP(int,int,bit1,pls) ),
introduced(tautology,[equality,[$cnf( $equal(one_one(int),number_number_of(int,hAPP(int,int,bit1,pls))) ),[1],$fot(hAPP(int,int,bit1,pls))]]) ).
cnf(refute_0_110,plain,
( one_one(int) != number_number_of(int,hAPP(int,int,bit1,pls))
| one_one(int) = hAPP(int,int,bit1,pls) ),
inference(resolve,[$cnf( $equal(number_number_of(int,hAPP(int,int,bit1,pls)),hAPP(int,int,bit1,pls)) )],[refute_0_108,refute_0_109]) ).
cnf(refute_0_111,plain,
one_one(int) = hAPP(int,int,bit1,pls),
inference(resolve,[$cnf( $equal(one_one(int),number_number_of(int,hAPP(int,int,bit1,pls))) )],[refute_0_106,refute_0_110]) ).
cnf(refute_0_112,plain,
( one_one(int) != hAPP(int,int,bit1,pls)
| hAPP(int,int,bit1,pls) = one_one(int) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(one_one(int))),bind(Y,$fot(hAPP(int,int,bit1,pls)))]]) ).
cnf(refute_0_113,plain,
hAPP(int,int,bit1,pls) = one_one(int),
inference(resolve,[$cnf( $equal(one_one(int),hAPP(int,int,bit1,pls)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
hAPP(int,int,bit0,hAPP(int,int,bit1,pls)) = hAPP(int,int,bit0,hAPP(int,int,bit1,pls)),
introduced(tautology,[refl,[$fot(hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))]]) ).
cnf(refute_0_115,plain,
( hAPP(int,int,bit0,hAPP(int,int,bit1,pls)) != hAPP(int,int,bit0,hAPP(int,int,bit1,pls))
| hAPP(int,int,bit1,pls) != one_one(int)
| hAPP(int,int,bit0,hAPP(int,int,bit1,pls)) = hAPP(int,int,bit0,one_one(int)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,bit0,hAPP(int,int,bit1,pls)),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) ),[1,3],$fot(one_one(int))]]) ).
cnf(refute_0_116,plain,
( hAPP(int,int,bit1,pls) != one_one(int)
| hAPP(int,int,bit0,hAPP(int,int,bit1,pls)) = hAPP(int,int,bit0,one_one(int)) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,bit0,hAPP(int,int,bit1,pls)),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
hAPP(int,int,bit0,hAPP(int,int,bit1,pls)) = hAPP(int,int,bit0,one_one(int)),
inference(resolve,[$cnf( $equal(hAPP(int,int,bit1,pls),one_one(int)) )],[refute_0_113,refute_0_116]) ).
cnf(refute_0_118,plain,
number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
introduced(tautology,[refl,[$fot(number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))]]) ).
cnf(refute_0_119,plain,
( hAPP(int,int,bit0,hAPP(int,int,bit1,pls)) != hAPP(int,int,bit0,one_one(int))
| number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = number_number_of(nat,hAPP(int,int,bit0,one_one(int))) ),
introduced(tautology,[equality,[$cnf( $equal(number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) ),[1,1],$fot(hAPP(int,int,bit0,one_one(int)))]]) ).
cnf(refute_0_120,plain,
( hAPP(int,int,bit0,hAPP(int,int,bit1,pls)) != hAPP(int,int,bit0,one_one(int))
| number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = number_number_of(nat,hAPP(int,int,bit0,one_one(int))) ),
inference(resolve,[$cnf( $equal(number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = number_number_of(nat,hAPP(int,int,bit0,one_one(int))),
inference(resolve,[$cnf( $equal(hAPP(int,int,bit0,hAPP(int,int,bit1,pls)),hAPP(int,int,bit0,one_one(int))) )],[refute_0_117,refute_0_120]) ).
cnf(refute_0_122,plain,
( hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) != number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != number_number_of(nat,hAPP(int,int,bit0,one_one(int)))
| hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,bit0,one_one(int))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) ),[0],$fot(number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))]]) ).
cnf(refute_0_123,plain,
( hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) != number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,bit0,one_one(int))) ),
inference(resolve,[$cnf( $equal(number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) )],[refute_0_121,refute_0_122]) ).
cnf(refute_0_124,plain,
hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) = number_number_of(nat,hAPP(int,int,bit0,one_one(int))),
inference(resolve,[$cnf( $equal(hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) )],[refute_0_92,refute_0_123]) ).
cnf(refute_0_125,plain,
hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))) = hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))),
introduced(tautology,[refl,[$fot(hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))))]]) ).
cnf(refute_0_126,plain,
( hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))) != hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))
| hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) != number_number_of(nat,hAPP(int,int,bit0,one_one(int)))
| hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))) = hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))) ),[1,3],$fot(number_number_of(nat,hAPP(int,int,bit0,one_one(int))))]]) ).
cnf(refute_0_127,plain,
( hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)) != number_number_of(nat,hAPP(int,int,bit0,one_one(int)))
| hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))) = hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))) )],[refute_0_125,refute_0_126]) ).
cnf(refute_0_128,plain,
hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))) = hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))),
inference(resolve,[$cnf( $equal(hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) )],[refute_0_124,refute_0_127]) ).
cnf(refute_0_129,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),
introduced(tautology,[refl,[$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))))]]) ).
cnf(refute_0_130,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))))
| hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))) != hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))))) ),[1,3],$fot(hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))))]]) ).
cnf(refute_0_131,plain,
( hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))) != hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))),
inference(resolve,[$cnf( $equal(hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))) )],[refute_0_128,refute_0_131]) ).
cnf(refute_0_133,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))))
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))))) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))))) ),[0],$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))))]]) ).
cnf(refute_0_134,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat)))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))))) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))))),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,power_power(int,X),hAPP(nat,nat,plus_plus(nat,one_one(nat)),one_one(nat))))) )],[refute_0_105,refute_0_134]) ).
cnf(refute_0_136,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))))),
inference(subst,[],[refute_0_135:[bind(X,$fot(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))]]) ).
cnf(refute_0_137,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_138,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
introduced(tautology,[refl,[$fot(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))]]) ).
cnf(refute_0_139,plain,
( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != number_number_of(nat,hAPP(int,int,bit0,one_one(int)))
| hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) ),[1,3],$fot(number_number_of(nat,hAPP(int,int,bit0,one_one(int))))]]) ).
cnf(refute_0_140,plain,
( number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != number_number_of(nat,hAPP(int,int,bit0,one_one(int)))
| hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))),
inference(resolve,[$cnf( $equal(number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) )],[refute_0_121,refute_0_140]) ).
cnf(refute_0_142,plain,
( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))
| hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int)
| hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = zero_zero(int) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),zero_zero(int)) ),[0],$fot(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))))]]) ).
cnf(refute_0_143,plain,
( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int)
| hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = zero_zero(int) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))) )],[refute_0_141,refute_0_142]) ).
cnf(refute_0_144,plain,
( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) != zero_zero(int)
| zero_zero(int) != pls
| hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = pls ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))),pls) ),[0],$fot(zero_zero(int))]]) ).
cnf(refute_0_145,plain,
( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) != zero_zero(int)
| hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = pls ),
inference(resolve,[$cnf( $equal(zero_zero(int),pls) )],[refute_0_6,refute_0_144]) ).
cnf(refute_0_146,plain,
( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int)
| hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = pls ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))),zero_zero(int)) )],[refute_0_143,refute_0_145]) ).
cnf(refute_0_147,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = pls,
inference(resolve,[$cnf( $equal(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),zero_zero(int)) )],[refute_0_137,refute_0_146]) ).
cnf(refute_0_148,plain,
power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),
introduced(tautology,[refl,[$fot(power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))))]]) ).
cnf(refute_0_149,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)) != hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))
| power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) != power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))
| power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) ),
introduced(tautology,[equality,[$cnf( $equal(power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) ),[1,1],$fot(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))]]) ).
cnf(refute_0_150,plain,
( hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)) != hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))
| power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) ),
inference(resolve,[$cnf( $equal(power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),
inference(resolve,[$cnf( $equal(hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) )],[refute_0_26,refute_0_150]) ).
cnf(refute_0_152,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))),
introduced(tautology,[refl,[$fot(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))))]]) ).
cnf(refute_0_153,plain,
( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) != hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))
| power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) != power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))
| hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))) ),[1,2],$fot(power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))]]) ).
cnf(refute_0_154,plain,
( power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) != power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))
| hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))),hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))) )],[refute_0_152,refute_0_153]) ).
cnf(refute_0_155,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))),
inference(resolve,[$cnf( $equal(power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) )],[refute_0_151,refute_0_154]) ).
cnf(refute_0_156,plain,
( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) != hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))
| hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) != pls
| hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = pls ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))),pls) ),[0],$fot(hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))))]]) ).
cnf(refute_0_157,plain,
( hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) != pls
| hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = pls ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))),hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))) )],[refute_0_155,refute_0_156]) ).
cnf(refute_0_158,plain,
hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) = pls,
inference(resolve,[$cnf( $equal(hAPP(nat,int,power_power(int,hAPP(int,int,plus_plus(int,one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))),pls) )],[refute_0_147,refute_0_157]) ).
cnf(refute_0_159,plain,
( hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))) != pls
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),pls)) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))))) ),[0,3],$fot(pls)]]) ).
cnf(refute_0_160,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int))))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),pls)) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))),pls) )],[refute_0_158,refute_0_159]) ).
cnf(refute_0_161,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),pls)),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(nat,int,power_power(int,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),number_number_of(nat,hAPP(int,int,bit0,one_one(int)))))) )],[refute_0_136,refute_0_160]) ).
cnf(refute_0_162,plain,
skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) = skolemFOFtoCNF_M(pls),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),pls)) )],[refute_0_161,refute_0_90]) ).
cnf(refute_0_163,plain,
hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) = hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))),
introduced(tautology,[refl,[$fot(hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))))]]) ).
cnf(refute_0_164,plain,
( hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) != hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))
| skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) != skolemFOFtoCNF_M(pls)
| hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) = hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))),hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))) ),[1,3],$fot(skolemFOFtoCNF_M(pls))]]) ).
cnf(refute_0_165,plain,
( skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) != skolemFOFtoCNF_M(pls)
| hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) = hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))),hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) = hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),skolemFOFtoCNF_M(pls)) )],[refute_0_162,refute_0_165]) ).
cnf(refute_0_167,plain,
( Y != X0
| Y != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_168,plain,
( X0 != Y
| Y != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y,X0) )],[refute_0_4,refute_0_167]) ).
cnf(refute_0_169,plain,
( hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)) != pls
| hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) != hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls))
| hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) = pls ),
inference(subst,[],[refute_0_168:[bind(X0,$fot(hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))))),bind(Y,$fot(hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)))),bind(Z,$fot(pls))]]) ).
cnf(refute_0_170,plain,
( hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)) != pls
| hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) = pls ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))),hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls))) )],[refute_0_166,refute_0_169]) ).
cnf(refute_0_171,plain,
hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) = pls,
inference(resolve,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_M(pls)),pls) )],[refute_0_61,refute_0_170]) ).
cnf(refute_0_172,plain,
( hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) != hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))
| hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) != pls
| hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) = pls ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)),pls) ),[0],$fot(hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))))]]) ).
cnf(refute_0_173,plain,
( hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) != hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))
| hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) = pls ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))),pls) )],[refute_0_171,refute_0_172]) ).
cnf(refute_0_174,plain,
hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) = pls,
inference(resolve,[$cnf( $equal(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)),hAPP(nat,int,semiring_1_of_nat(int),skolemFOFtoCNF_N_1(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))) )],[refute_0_43,refute_0_173]) ).
cnf(refute_0_175,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),
introduced(tautology,[refl,[$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))]]) ).
cnf(refute_0_176,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))
| hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) != pls
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) ),[1,3],$fot(pls)]]) ).
cnf(refute_0_177,plain,
( hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) != pls
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) )],[refute_0_175,refute_0_176]) ).
cnf(refute_0_178,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls),
inference(resolve,[$cnf( $equal(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)),pls) )],[refute_0_174,refute_0_177]) ).
cnf(refute_0_179,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) ),[0],$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls))]]) ).
cnf(refute_0_180,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))) )],[refute_0_33,refute_0_180]) ).
cnf(refute_0_182,plain,
( Z_2 != Wa
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),Wa)) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_183,plain,
( Wa != Wa
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Wa)) ),
inference(subst,[],[refute_0_182:[bind(Z_2,$fot(Wa))]]) ).
cnf(refute_0_184,plain,
Wa = Wa,
introduced(tautology,[refl,[$fot(Wa)]]) ).
cnf(refute_0_185,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Wa),Wa)),
inference(resolve,[$cnf( $equal(Wa,Wa) )],[refute_0_184,refute_0_183]) ).
cnf(refute_0_186,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)),
inference(subst,[],[refute_0_185:[bind(Wa,$fot(pls))]]) ).
cnf(refute_0_187,plain,
$false,
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),pls)) )],[refute_0_181,refute_0_186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM925+6 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n023.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jul 7 09:49:56 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 3.37/3.59 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 3.37/3.59
% 3.37/3.59 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 3.45/3.61
%------------------------------------------------------------------------------