%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM925+2 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 12:31:39 EDT 2022
% Result : Theorem 10.07s 10.29s
% Output : CNFRefutation 10.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 52
% Syntax : Number of formulae : 184 ( 113 unt; 0 def)
% Number of atoms : 284 ( 241 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 207 ( 107 ~; 96 |; 1 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 25 ( 25 usr; 10 con; 0-2 aty)
% Number of variables : 135 ( 3 sgn 44 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_25_semiring__norm_I110_J,axiom,
one_one_int = number_number_of_int(bit1(pls)) ).
fof(fact_39_zadd__int,axiom,
! [M_1,N_1] : hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(M_1),N_1)) ).
fof(fact_40_int__1,axiom,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int ).
fof(fact_53_one__is__num__one,axiom,
one_one_int = number_number_of_int(bit1(pls)) ).
fof(fact_98_Pls__def,axiom,
pls = zero_zero_int ).
fof(fact_130_number__of__int,axiom,
! [N_29] : number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,N_29)) = hAPP_nat_nat(semiri984289939at_nat,N_29) ).
fof(fact_176_number__of__is__id,axiom,
! [K] : number_number_of_int(K) = K ).
fof(fact_178_nat__add__commute,axiom,
! [M_1,N_1] : hAPP_nat_nat(plus_plus_nat(M_1),N_1) = hAPP_nat_nat(plus_plus_nat(N_1),M_1) ).
fof(fact_245_of__nat__add,axiom,
! [M_7,N_19] : hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(M_7),N_19)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,M_7)),hAPP_nat_nat(semiri984289939at_nat,N_19)) ).
fof(fact_248_of__nat__1,axiom,
hAPP_nat_nat(semiri984289939at_nat,one_one_nat) = one_one_nat ).
fof(fact_249_of__nat__1,axiom,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int ).
fof(fact_493_not__one__le__zero,axiom,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)) ).
fof(fact_557_eq__0__number__of,axiom,
! [Va] :
( zero_zero_nat = number_number_of_nat(Va)
<=> hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Va),pls)) ) ).
fof(fact_573_succ__def,axiom,
! [K] : succ(K) = hAPP_int_int(plus_plus_int(K),one_one_int) ).
fof(fact_583_number__of__succ,axiom,
! [K_3] : number_number_of_int(succ(K_3)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)) ).
fof(fact_589_power2__ge__self,axiom,
! [X] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))))) ).
fof(fact_628_le__add1,axiom,
! [N_1,M_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(plus_plus_nat(N_1),M_1))) ).
fof(conj_0,conjecture,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(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(semiri1621563631at_int,n))),number_number_of_nat(bit0(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(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [M_1,N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(plus_plus_nat(N_1),M_1))),
inference(canonicalize,[],[fact_628_le__add1]) ).
fof(normalize_0_1,plain,
! [M_1,N_1] : hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(plus_plus_nat(N_1),M_1))),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [M_7,N_19] : hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(M_7),N_19)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,M_7)),hAPP_nat_nat(semiri984289939at_nat,N_19)),
inference(canonicalize,[],[fact_245_of__nat__add]) ).
fof(normalize_0_3,plain,
! [M_7,N_19] : hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(M_7),N_19)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,M_7)),hAPP_nat_nat(semiri984289939at_nat,N_19)),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
hAPP_nat_nat(semiri984289939at_nat,one_one_nat) = one_one_nat,
inference(canonicalize,[],[fact_248_of__nat__1]) ).
fof(normalize_0_5,plain,
! [N_29] : number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,N_29)) = hAPP_nat_nat(semiri984289939at_nat,N_29),
inference(canonicalize,[],[fact_130_number__of__int]) ).
fof(normalize_0_6,plain,
! [N_29] : number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,N_29)) = hAPP_nat_nat(semiri984289939at_nat,N_29),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [M_1,N_1] : hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(M_1),N_1)),
inference(canonicalize,[],[fact_39_zadd__int]) ).
fof(normalize_0_8,plain,
! [M_1,N_1] : hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(M_1),N_1)),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
inference(canonicalize,[],[fact_249_of__nat__1]) ).
fof(normalize_0_10,plain,
! [K] : succ(K) = hAPP_int_int(plus_plus_int(K),one_one_int),
inference(canonicalize,[],[fact_573_succ__def]) ).
fof(normalize_0_11,plain,
! [K] : succ(K) = hAPP_int_int(plus_plus_int(K),one_one_int),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [M_1,N_1] : hAPP_nat_nat(plus_plus_nat(M_1),N_1) = hAPP_nat_nat(plus_plus_nat(N_1),M_1),
inference(canonicalize,[],[fact_178_nat__add__commute]) ).
fof(normalize_0_13,plain,
! [M_1,N_1] : hAPP_nat_nat(plus_plus_nat(M_1),N_1) = hAPP_nat_nat(plus_plus_nat(N_1),M_1),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))))),
inference(canonicalize,[],[fact_589_power2__ge__self]) ).
fof(normalize_0_15,plain,
! [X] : hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))))),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(canonicalize,[],[fact_53_one__is__num__one]) ).
fof(normalize_0_17,plain,
! [K] : number_number_of_int(K) = K,
inference(canonicalize,[],[fact_176_number__of__is__id]) ).
fof(normalize_0_18,plain,
! [K] : number_number_of_int(K) = K,
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_20,plain,
! [K_3] : number_number_of_int(succ(K_3)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)),
inference(canonicalize,[],[fact_583_number__of__succ]) ).
fof(normalize_0_21,plain,
! [K_3] : number_number_of_int(succ(K_3)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
pls = zero_zero_int,
inference(canonicalize,[],[fact_98_Pls__def]) ).
fof(normalize_0_23,plain,
! [Va] :
( zero_zero_nat != number_number_of_nat(Va)
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Va),pls)) ),
inference(canonicalize,[],[fact_557_eq__0__number__of]) ).
fof(normalize_0_24,plain,
! [Va] :
( zero_zero_nat != number_number_of_nat(Va)
<=> ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Va),pls)) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [Va] :
( ( zero_zero_nat != number_number_of_nat(Va)
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Va),pls)) )
& ( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Va),pls))
| zero_zero_nat = number_number_of_nat(Va) ) ),
inference(clausify,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [Va] :
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Va),pls))
| zero_zero_nat = number_number_of_nat(Va) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)),
inference(canonicalize,[],[fact_493_not__one__le__zero]) ).
cnf(refute_0_0,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,N_1),hAPP_nat_nat(plus_plus_nat(N_1),M_1))),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144)))),
inference(subst,[],[refute_0_0:[bind(M_1,$fot(hAPP_nat_nat(semiri984289939at_nat,X_144))),bind(N_1,$fot(one_one_nat))]]) ).
cnf(refute_0_2,plain,
hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(M_7),N_19)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,M_7)),hAPP_nat_nat(semiri984289939at_nat,N_19)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_144),one_one_nat)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),hAPP_nat_nat(semiri984289939at_nat,one_one_nat)),
inference(subst,[],[refute_0_2:[bind(M_7,$fot(X_144)),bind(N_19,$fot(one_one_nat))]]) ).
cnf(refute_0_4,plain,
hAPP_nat_nat(semiri984289939at_nat,one_one_nat) = one_one_nat,
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_5,plain,
( hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_144),one_one_nat)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),hAPP_nat_nat(semiri984289939at_nat,one_one_nat))
| hAPP_nat_nat(semiri984289939at_nat,one_one_nat) != one_one_nat
| hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_144),one_one_nat)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_144),one_one_nat)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),hAPP_nat_nat(semiri984289939at_nat,one_one_nat))) ),[1,1],$fot(one_one_nat)]]) ).
cnf(refute_0_6,plain,
( hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_144),one_one_nat)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),hAPP_nat_nat(semiri984289939at_nat,one_one_nat))
| hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_144),one_one_nat)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat) ),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(semiri984289939at_nat,one_one_nat),one_one_nat) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_144),one_one_nat)) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_144),one_one_nat)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),hAPP_nat_nat(semiri984289939at_nat,one_one_nat))) )],[refute_0_3,refute_0_6]) ).
cnf(refute_0_8,plain,
number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,N_29)) = hAPP_nat_nat(semiri984289939at_nat,N_29),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_9,plain,
number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat))) = hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat)),
inference(subst,[],[refute_0_8:[bind(N_29,$fot(hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat)))]]) ).
cnf(refute_0_10,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,M_1)),hAPP_nat_int(semiri1621563631at_int,N_1)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(M_1),N_1)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_11,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X_132)),hAPP_nat_int(semiri1621563631at_int,one_one_nat)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_132),one_one_nat)),
inference(subst,[],[refute_0_10:[bind(M_1,$fot(X_132)),bind(N_1,$fot(one_one_nat))]]) ).
cnf(refute_0_12,plain,
hAPP_nat_int(semiri1621563631at_int,one_one_nat) = one_one_int,
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_13,plain,
( hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X_132)),hAPP_nat_int(semiri1621563631at_int,one_one_nat)) != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_132),one_one_nat))
| hAPP_nat_int(semiri1621563631at_int,one_one_nat) != one_one_int
| hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X_132)),one_one_int) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_132),one_one_nat)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X_132)),hAPP_nat_int(semiri1621563631at_int,one_one_nat)),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_132),one_one_nat))) ),[0,1],$fot(one_one_int)]]) ).
cnf(refute_0_14,plain,
( hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X_132)),hAPP_nat_int(semiri1621563631at_int,one_one_nat)) != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_132),one_one_nat))
| hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X_132)),one_one_int) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_132),one_one_nat)) ),
inference(resolve,[$cnf( $equal(hAPP_nat_int(semiri1621563631at_int,one_one_nat),one_one_int) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X_132)),one_one_int) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_132),one_one_nat)),
inference(resolve,[$cnf( $equal(hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X_132)),hAPP_nat_int(semiri1621563631at_int,one_one_nat)),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_132),one_one_nat))) )],[refute_0_11,refute_0_14]) ).
cnf(refute_0_16,plain,
succ(K) = hAPP_int_int(plus_plus_int(K),one_one_int),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_17,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_18,plain,
( X0 != X0
| X0 != Y
| Y = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).
cnf(refute_0_19,plain,
( X0 != Y
| Y = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( succ(K) != hAPP_int_int(plus_plus_int(K),one_one_int)
| hAPP_int_int(plus_plus_int(K),one_one_int) = succ(K) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(succ(K))),bind(Y,$fot(hAPP_int_int(plus_plus_int(K),one_one_int)))]]) ).
cnf(refute_0_21,plain,
hAPP_int_int(plus_plus_int(K),one_one_int) = succ(K),
inference(resolve,[$cnf( $equal(succ(K),hAPP_int_int(plus_plus_int(K),one_one_int)) )],[refute_0_16,refute_0_20]) ).
cnf(refute_0_22,plain,
hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X_132)),one_one_int) = succ(hAPP_nat_int(semiri1621563631at_int,X_132)),
inference(subst,[],[refute_0_21:[bind(K,$fot(hAPP_nat_int(semiri1621563631at_int,X_132)))]]) ).
cnf(refute_0_23,plain,
( hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X_132)),one_one_int) != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_132),one_one_nat))
| hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X_132)),one_one_int) != succ(hAPP_nat_int(semiri1621563631at_int,X_132))
| succ(hAPP_nat_int(semiri1621563631at_int,X_132)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_132),one_one_nat)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X_132)),one_one_int),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_132),one_one_nat))) ),[0],$fot(succ(hAPP_nat_int(semiri1621563631at_int,X_132)))]]) ).
cnf(refute_0_24,plain,
( hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X_132)),one_one_int) != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_132),one_one_nat))
| succ(hAPP_nat_int(semiri1621563631at_int,X_132)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_132),one_one_nat)) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X_132)),one_one_int),succ(hAPP_nat_int(semiri1621563631at_int,X_132))) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
succ(hAPP_nat_int(semiri1621563631at_int,X_132)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_132),one_one_nat)),
inference(resolve,[$cnf( $equal(hAPP_int_int(plus_plus_int(hAPP_nat_int(semiri1621563631at_int,X_132)),one_one_int),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_132),one_one_nat))) )],[refute_0_15,refute_0_24]) ).
cnf(refute_0_26,plain,
succ(hAPP_nat_int(semiri1621563631at_int,X_134)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat)),
inference(subst,[],[refute_0_25:[bind(X_132,$fot(X_134))]]) ).
cnf(refute_0_27,plain,
( succ(hAPP_nat_int(semiri1621563631at_int,X_134)) != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat))
| hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat)) = succ(hAPP_nat_int(semiri1621563631at_int,X_134)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(succ(hAPP_nat_int(semiri1621563631at_int,X_134)))),bind(Y,$fot(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat))))]]) ).
cnf(refute_0_28,plain,
hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat)) = succ(hAPP_nat_int(semiri1621563631at_int,X_134)),
inference(resolve,[$cnf( $equal(succ(hAPP_nat_int(semiri1621563631at_int,X_134)),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat)) != succ(hAPP_nat_int(semiri1621563631at_int,X_134))
| number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat))) != hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat))
| number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_134))) = hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat)) ),
introduced(tautology,[equality,[$cnf( $equal(number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat))),hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat))) ),[0,0],$fot(succ(hAPP_nat_int(semiri1621563631at_int,X_134)))]]) ).
cnf(refute_0_30,plain,
( number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat))) != hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat))
| number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_134))) = hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat)) ),
inference(resolve,[$cnf( $equal(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat)),succ(hAPP_nat_int(semiri1621563631at_int,X_134))) )],[refute_0_28,refute_0_29]) ).
cnf(refute_0_31,plain,
number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_134))) = hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat)),
inference(resolve,[$cnf( $equal(number_number_of_nat(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat))),hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat))) )],[refute_0_9,refute_0_30]) ).
cnf(refute_0_32,plain,
( number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_134))) != hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat))
| hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat)) = number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_134))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_134))))),bind(Y,$fot(hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat))))]]) ).
cnf(refute_0_33,plain,
hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat)) = number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_134))),
inference(resolve,[$cnf( $equal(number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_134))),hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_134),one_one_nat))) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,plain,
hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_144),one_one_nat)) = number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))),
inference(subst,[],[refute_0_33:[bind(X_134,$fot(X_144))]]) ).
cnf(refute_0_35,plain,
( hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_144),one_one_nat)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat)
| hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_144),one_one_nat)) != number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144)))
| number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_144),one_one_nat)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat)) ),[0],$fot(number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))))]]) ).
cnf(refute_0_36,plain,
( hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_144),one_one_nat)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat)
| number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))) = hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat) ),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_144),one_one_nat)),number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144)))) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
hAPP_nat_nat(plus_plus_nat(M_1),N_1) = hAPP_nat_nat(plus_plus_nat(N_1),M_1),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_38,plain,
( hAPP_nat_nat(plus_plus_nat(M_1),N_1) != hAPP_nat_nat(plus_plus_nat(N_1),M_1)
| hAPP_nat_nat(plus_plus_nat(N_1),M_1) = hAPP_nat_nat(plus_plus_nat(M_1),N_1) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(hAPP_nat_nat(plus_plus_nat(M_1),N_1))),bind(Y,$fot(hAPP_nat_nat(plus_plus_nat(N_1),M_1)))]]) ).
cnf(refute_0_39,plain,
hAPP_nat_nat(plus_plus_nat(N_1),M_1) = hAPP_nat_nat(plus_plus_nat(M_1),N_1),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(plus_plus_nat(M_1),N_1),hAPP_nat_nat(plus_plus_nat(N_1),M_1)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat) = hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144)),
inference(subst,[],[refute_0_39:[bind(M_1,$fot(one_one_nat)),bind(N_1,$fot(hAPP_nat_nat(semiri984289939at_nat,X_144)))]]) ).
cnf(refute_0_41,plain,
( hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat) != hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144))
| number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat)
| number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144)) ),
introduced(tautology,[equality,[$cnf( $equal(number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat)) ),[1],$fot(hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144)))]]) ).
cnf(refute_0_42,plain,
( number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat)
| number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144)) ),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat),hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144))) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_144),one_one_nat)) != hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat)
| number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144)) ),
inference(resolve,[$cnf( $equal(number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat)) )],[refute_0_36,refute_0_42]) ).
cnf(refute_0_44,plain,
number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))) = hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144)),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(semiri984289939at_nat,hAPP_nat_nat(plus_plus_nat(X_144),one_one_nat)),hAPP_nat_nat(plus_plus_nat(hAPP_nat_nat(semiri984289939at_nat,X_144)),one_one_nat)) )],[refute_0_7,refute_0_43]) ).
cnf(refute_0_45,plain,
( number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))) != hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144))
| hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144)) = number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))))),bind(Y,$fot(hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144))))]]) ).
cnf(refute_0_46,plain,
hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144)) = number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))),
inference(resolve,[$cnf( $equal(number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))),hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144)) != number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144)))
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144))))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))))) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144)))) ),[0,1],$fot(number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))))]]) ).
cnf(refute_0_48,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144))))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))))) ),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144)),number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144)))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,X_144))))),
inference(resolve,[$cnf( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),hAPP_nat_nat(plus_plus_nat(one_one_nat),hAPP_nat_nat(semiri984289939at_nat,X_144)))) )],[refute_0_1,refute_0_48]) ).
cnf(refute_0_50,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,n))))),
inference(subst,[],[refute_0_49:[bind(X_144,$fot(n))]]) ).
cnf(refute_0_51,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))))),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_52,plain,
one_one_int = number_number_of_int(bit1(pls)),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_53,plain,
number_number_of_int(K) = K,
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_54,plain,
number_number_of_int(bit1(pls)) = bit1(pls),
inference(subst,[],[refute_0_53:[bind(K,$fot(bit1(pls)))]]) ).
cnf(refute_0_55,plain,
( number_number_of_int(bit1(pls)) != bit1(pls)
| one_one_int != number_number_of_int(bit1(pls))
| one_one_int = bit1(pls) ),
introduced(tautology,[equality,[$cnf( $equal(one_one_int,number_number_of_int(bit1(pls))) ),[1],$fot(bit1(pls))]]) ).
cnf(refute_0_56,plain,
( one_one_int != number_number_of_int(bit1(pls))
| one_one_int = bit1(pls) ),
inference(resolve,[$cnf( $equal(number_number_of_int(bit1(pls)),bit1(pls)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
one_one_int = bit1(pls),
inference(resolve,[$cnf( $equal(one_one_int,number_number_of_int(bit1(pls))) )],[refute_0_52,refute_0_56]) ).
cnf(refute_0_58,plain,
( one_one_int != bit1(pls)
| bit1(pls) = one_one_int ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(one_one_int)),bind(Y,$fot(bit1(pls)))]]) ).
cnf(refute_0_59,plain,
bit1(pls) = one_one_int,
inference(resolve,[$cnf( $equal(one_one_int,bit1(pls)) )],[refute_0_57,refute_0_58]) ).
cnf(refute_0_60,plain,
bit0(bit1(pls)) = bit0(bit1(pls)),
introduced(tautology,[refl,[$fot(bit0(bit1(pls)))]]) ).
cnf(refute_0_61,plain,
( bit0(bit1(pls)) != bit0(bit1(pls))
| bit1(pls) != one_one_int
| bit0(bit1(pls)) = bit0(one_one_int) ),
introduced(tautology,[equality,[$cnf( $equal(bit0(bit1(pls)),bit0(bit1(pls))) ),[1,0],$fot(one_one_int)]]) ).
cnf(refute_0_62,plain,
( bit1(pls) != one_one_int
| bit0(bit1(pls)) = bit0(one_one_int) ),
inference(resolve,[$cnf( $equal(bit0(bit1(pls)),bit0(bit1(pls))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
bit0(bit1(pls)) = bit0(one_one_int),
inference(resolve,[$cnf( $equal(bit1(pls),one_one_int) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
number_number_of_nat(bit0(bit1(pls))) = number_number_of_nat(bit0(bit1(pls))),
introduced(tautology,[refl,[$fot(number_number_of_nat(bit0(bit1(pls))))]]) ).
cnf(refute_0_65,plain,
( bit0(bit1(pls)) != bit0(one_one_int)
| number_number_of_nat(bit0(bit1(pls))) != number_number_of_nat(bit0(bit1(pls)))
| number_number_of_nat(bit0(bit1(pls))) = number_number_of_nat(bit0(one_one_int)) ),
introduced(tautology,[equality,[$cnf( $equal(number_number_of_nat(bit0(bit1(pls))),number_number_of_nat(bit0(bit1(pls)))) ),[1,0],$fot(bit0(one_one_int))]]) ).
cnf(refute_0_66,plain,
( bit0(bit1(pls)) != bit0(one_one_int)
| number_number_of_nat(bit0(bit1(pls))) = number_number_of_nat(bit0(one_one_int)) ),
inference(resolve,[$cnf( $equal(number_number_of_nat(bit0(bit1(pls))),number_number_of_nat(bit0(bit1(pls)))) )],[refute_0_64,refute_0_65]) ).
cnf(refute_0_67,plain,
number_number_of_nat(bit0(bit1(pls))) = number_number_of_nat(bit0(one_one_int)),
inference(resolve,[$cnf( $equal(bit0(bit1(pls)),bit0(one_one_int)) )],[refute_0_63,refute_0_66]) ).
cnf(refute_0_68,plain,
hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))),
introduced(tautology,[refl,[$fot(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))))]]) ).
cnf(refute_0_69,plain,
( hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))
| number_number_of_nat(bit0(bit1(pls))) != number_number_of_nat(bit0(one_one_int))
| hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(one_one_int))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))) ),[1,1],$fot(number_number_of_nat(bit0(one_one_int)))]]) ).
cnf(refute_0_70,plain,
( number_number_of_nat(bit0(bit1(pls))) != number_number_of_nat(bit0(one_one_int))
| hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(one_one_int))) ),
inference(resolve,[$cnf( $equal(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(one_one_int))),
inference(resolve,[$cnf( $equal(number_number_of_nat(bit0(bit1(pls))),number_number_of_nat(bit0(one_one_int))) )],[refute_0_67,refute_0_70]) ).
cnf(refute_0_72,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),
introduced(tautology,[refl,[$fot(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))))]]) ).
cnf(refute_0_73,plain,
( hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))) != hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))))
| hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(one_one_int)))
| hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(one_one_int)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))))) ),[1,1],$fot(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(one_one_int))))]]) ).
cnf(refute_0_74,plain,
( hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(one_one_int)))
| hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(one_one_int)))) ),
inference(resolve,[$cnf( $equal(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(one_one_int)))),
inference(resolve,[$cnf( $equal(hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(one_one_int)))) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
( hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))) != hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(one_one_int))))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(one_one_int))))) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))))) ),[0],$fot(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(one_one_int)))))]]) ).
cnf(refute_0_77,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(one_one_int))))) ),
inference(resolve,[$cnf( $equal(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls))))),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(one_one_int))))) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(one_one_int))))),
inference(resolve,[$cnf( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,X),hAPP_nat_int(power_power_int(X),number_number_of_nat(bit0(bit1(pls)))))) )],[refute_0_51,refute_0_77]) ).
cnf(refute_0_79,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,succ(hAPP_nat_int(semiri1621563631at_int,n))),hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))))),
inference(subst,[],[refute_0_78:[bind(X,$fot(succ(hAPP_nat_int(semiri1621563631at_int,n))))]]) ).
cnf(refute_0_80,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = zero_zero_int,
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_81,plain,
hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
introduced(tautology,[refl,[$fot(hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))))]]) ).
cnf(refute_0_82,plain,
( hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls))))
| number_number_of_nat(bit0(bit1(pls))) != number_number_of_nat(bit0(one_one_int))
| hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls))))) ),[1,1],$fot(number_number_of_nat(bit0(one_one_int)))]]) ).
cnf(refute_0_83,plain,
( number_number_of_nat(bit0(bit1(pls))) != number_number_of_nat(bit0(one_one_int))
| hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))) ),
inference(resolve,[$cnf( $equal(hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls))))) )],[refute_0_81,refute_0_82]) ).
cnf(refute_0_84,plain,
hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))),
inference(resolve,[$cnf( $equal(number_number_of_nat(bit0(bit1(pls))),number_number_of_nat(bit0(one_one_int))) )],[refute_0_67,refute_0_83]) ).
cnf(refute_0_85,plain,
number_number_of_int(succ(K_3)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_86,plain,
number_number_of_int(succ(K_3)) = succ(K_3),
inference(subst,[],[refute_0_53:[bind(K,$fot(succ(K_3)))]]) ).
cnf(refute_0_87,plain,
( number_number_of_int(succ(K_3)) != hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3))
| number_number_of_int(succ(K_3)) != succ(K_3)
| succ(K_3) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)) ),
introduced(tautology,[equality,[$cnf( $equal(number_number_of_int(succ(K_3)),hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3))) ),[0],$fot(succ(K_3))]]) ).
cnf(refute_0_88,plain,
( number_number_of_int(succ(K_3)) != hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3))
| succ(K_3) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)) ),
inference(resolve,[$cnf( $equal(number_number_of_int(succ(K_3)),succ(K_3)) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
number_number_of_int(K_3) = K_3,
inference(subst,[],[refute_0_53:[bind(K,$fot(K_3))]]) ).
cnf(refute_0_90,plain,
hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)) = hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)),
introduced(tautology,[refl,[$fot(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)))]]) ).
cnf(refute_0_91,plain,
( hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)) != hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3))
| number_number_of_int(K_3) != K_3
| hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)) = hAPP_int_int(plus_plus_int(one_one_int),K_3) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)),hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3))) ),[1,1],$fot(K_3)]]) ).
cnf(refute_0_92,plain,
( number_number_of_int(K_3) != K_3
| hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)) = hAPP_int_int(plus_plus_int(one_one_int),K_3) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)),hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)) = hAPP_int_int(plus_plus_int(one_one_int),K_3),
inference(resolve,[$cnf( $equal(number_number_of_int(K_3),K_3) )],[refute_0_89,refute_0_92]) ).
cnf(refute_0_94,plain,
( hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)) != hAPP_int_int(plus_plus_int(one_one_int),K_3)
| succ(K_3) != hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3))
| succ(K_3) = hAPP_int_int(plus_plus_int(one_one_int),K_3) ),
introduced(tautology,[equality,[$cnf( $equal(succ(K_3),hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3))) ),[1],$fot(hAPP_int_int(plus_plus_int(one_one_int),K_3))]]) ).
cnf(refute_0_95,plain,
( succ(K_3) != hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3))
| succ(K_3) = hAPP_int_int(plus_plus_int(one_one_int),K_3) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3)),hAPP_int_int(plus_plus_int(one_one_int),K_3)) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
( number_number_of_int(succ(K_3)) != hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3))
| succ(K_3) = hAPP_int_int(plus_plus_int(one_one_int),K_3) ),
inference(resolve,[$cnf( $equal(succ(K_3),hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3))) )],[refute_0_88,refute_0_95]) ).
cnf(refute_0_97,plain,
succ(K_3) = hAPP_int_int(plus_plus_int(one_one_int),K_3),
inference(resolve,[$cnf( $equal(number_number_of_int(succ(K_3)),hAPP_int_int(plus_plus_int(one_one_int),number_number_of_int(K_3))) )],[refute_0_85,refute_0_96]) ).
cnf(refute_0_98,plain,
( succ(K_3) != hAPP_int_int(plus_plus_int(one_one_int),K_3)
| hAPP_int_int(plus_plus_int(one_one_int),K_3) = succ(K_3) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(succ(K_3))),bind(Y,$fot(hAPP_int_int(plus_plus_int(one_one_int),K_3)))]]) ).
cnf(refute_0_99,plain,
hAPP_int_int(plus_plus_int(one_one_int),K_3) = succ(K_3),
inference(resolve,[$cnf( $equal(succ(K_3),hAPP_int_int(plus_plus_int(one_one_int),K_3)) )],[refute_0_97,refute_0_98]) ).
cnf(refute_0_100,plain,
hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = succ(hAPP_nat_int(semiri1621563631at_int,n)),
inference(subst,[],[refute_0_99:[bind(K_3,$fot(hAPP_nat_int(semiri1621563631at_int,n)))]]) ).
cnf(refute_0_101,plain,
power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),
introduced(tautology,[refl,[$fot(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))]]) ).
cnf(refute_0_102,plain,
( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) != succ(hAPP_nat_int(semiri1621563631at_int,n))
| power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) != power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))
| power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))) ),
introduced(tautology,[equality,[$cnf( $equal(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),[1,0],$fot(succ(hAPP_nat_int(semiri1621563631at_int,n)))]]) ).
cnf(refute_0_103,plain,
( hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) != succ(hAPP_nat_int(semiri1621563631at_int,n))
| power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(resolve,[$cnf( $equal(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),
inference(resolve,[$cnf( $equal(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n)),succ(hAPP_nat_int(semiri1621563631at_int,n))) )],[refute_0_100,refute_0_103]) ).
cnf(refute_0_105,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
introduced(tautology,[refl,[$fot(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))))]]) ).
cnf(refute_0_106,plain,
( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls))))
| power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) != power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n)))
| hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls))))) ),[1,0],$fot(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))))]]) ).
cnf(refute_0_107,plain,
( power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) != power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n)))
| hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) ),
inference(resolve,[$cnf( $equal(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls))))) )],[refute_0_105,refute_0_106]) ).
cnf(refute_0_108,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),
inference(resolve,[$cnf( $equal(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n)))) )],[refute_0_104,refute_0_107]) ).
cnf(refute_0_109,plain,
( Y != X0
| Y != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_110,plain,
( X0 != Y
| Y != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y,X0) )],[refute_0_19,refute_0_109]) ).
cnf(refute_0_111,plain,
( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls))))
| hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int)))
| hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))) ),
inference(subst,[],[refute_0_110:[bind(X0,$fot(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))))),bind(Y,$fot(hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))))),bind(Z,$fot(hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int)))))]]) ).
cnf(refute_0_112,plain,
( hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int)))
| hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))) ),
inference(resolve,[$cnf( $equal(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls))))) )],[refute_0_108,refute_0_111]) ).
cnf(refute_0_113,plain,
hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) = hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))),
inference(resolve,[$cnf( $equal(hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int)))) )],[refute_0_84,refute_0_112]) ).
cnf(refute_0_114,plain,
( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int)))
| hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int
| hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))) = zero_zero_int ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),zero_zero_int) ),[0],$fot(hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))))]]) ).
cnf(refute_0_115,plain,
( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int
| hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))) = zero_zero_int ),
inference(resolve,[$cnf( $equal(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int)))) )],[refute_0_113,refute_0_114]) ).
cnf(refute_0_116,plain,
pls = zero_zero_int,
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_117,plain,
( pls != zero_zero_int
| zero_zero_int = pls ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(pls)),bind(Y,$fot(zero_zero_int))]]) ).
cnf(refute_0_118,plain,
zero_zero_int = pls,
inference(resolve,[$cnf( $equal(pls,zero_zero_int) )],[refute_0_116,refute_0_117]) ).
cnf(refute_0_119,plain,
( hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))) != zero_zero_int
| zero_zero_int != pls
| hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))) = pls ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))),pls) ),[0],$fot(zero_zero_int)]]) ).
cnf(refute_0_120,plain,
( hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))) != zero_zero_int
| hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))) = pls ),
inference(resolve,[$cnf( $equal(zero_zero_int,pls) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
( hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))) != zero_zero_int
| hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))) = pls ),
inference(resolve,[$cnf( $equal(hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))),zero_zero_int) )],[refute_0_115,refute_0_120]) ).
cnf(refute_0_122,plain,
hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))) = pls,
inference(resolve,[$cnf( $equal(hAPP_nat_int(power_power_int(hAPP_int_int(plus_plus_int(one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(bit1(pls)))),zero_zero_int) )],[refute_0_80,refute_0_121]) ).
cnf(refute_0_123,plain,
( hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))) != pls
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,succ(hAPP_nat_int(semiri1621563631at_int,n))),hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int)))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,succ(hAPP_nat_int(semiri1621563631at_int,n))),pls)) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,succ(hAPP_nat_int(semiri1621563631at_int,n))),hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))))) ),[0,1],$fot(pls)]]) ).
cnf(refute_0_124,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,succ(hAPP_nat_int(semiri1621563631at_int,n))),hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int)))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,succ(hAPP_nat_int(semiri1621563631at_int,n))),pls)) ),
inference(resolve,[$cnf( $equal(hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))),pls) )],[refute_0_122,refute_0_123]) ).
cnf(refute_0_125,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,succ(hAPP_nat_int(semiri1621563631at_int,n))),pls)),
inference(resolve,[$cnf( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,succ(hAPP_nat_int(semiri1621563631at_int,n))),hAPP_nat_int(power_power_int(succ(hAPP_nat_int(semiri1621563631at_int,n))),number_number_of_nat(bit0(one_one_int))))) )],[refute_0_79,refute_0_124]) ).
cnf(refute_0_126,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,Va),pls))
| zero_zero_nat = number_number_of_nat(Va) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_127,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,succ(hAPP_nat_int(semiri1621563631at_int,n))),pls))
| zero_zero_nat = number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(subst,[],[refute_0_126:[bind(Va,$fot(succ(hAPP_nat_int(semiri1621563631at_int,n))))]]) ).
cnf(refute_0_128,plain,
zero_zero_nat = number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,n))),
inference(resolve,[$cnf( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_eq_int,succ(hAPP_nat_int(semiri1621563631at_int,n))),pls)) )],[refute_0_125,refute_0_127]) ).
cnf(refute_0_129,plain,
( zero_zero_nat != number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,n)))
| number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,n))) = zero_zero_nat ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(zero_zero_nat)),bind(Y,$fot(number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,n)))))]]) ).
cnf(refute_0_130,plain,
number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,n))) = zero_zero_nat,
inference(resolve,[$cnf( $equal(zero_zero_nat,number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,n)))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
( number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,n))) != zero_zero_nat
| ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,n)))))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,n))))) ),[0,1],$fot(zero_zero_nat)]]) ).
cnf(refute_0_132,plain,
( ~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,n)))))
| hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)) ),
inference(resolve,[$cnf( $equal(number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,n))),zero_zero_nat) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)),
inference(resolve,[$cnf( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),number_number_of_nat(succ(hAPP_nat_int(semiri1621563631at_int,n))))) )],[refute_0_50,refute_0_132]) ).
cnf(refute_0_134,plain,
~ hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_135,plain,
$false,
inference(resolve,[$cnf( hBOOL(hAPP_nat_bool(hAPP_n1699378549t_bool(ord_less_eq_nat,one_one_nat),zero_zero_nat)) )],[refute_0_133,refute_0_134]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM925+2 : TPTP v8.1.0. Released v5.3.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n029.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Wed Jul 6 19:27:13 EDT 2022
% 0.20/0.34 % CPUTime :
% 0.20/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 10.07/10.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 10.07/10.29
% 10.07/10.29 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.14/10.31
%------------------------------------------------------------------------------