TSTP Solution File: NUM924+8 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM924+8 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.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 12:31:37 EDT 2022
% Result : Theorem 31.46s 31.66s
% Output : CNFRefutation 31.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 70
% Syntax : Number of formulae : 249 ( 142 unt; 0 def)
% Number of atoms : 407 ( 383 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 320 ( 162 ~; 158 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 2 avg)
% Maximal term depth : 13 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 22 ( 22 usr; 12 con; 0-4 aty)
% Number of variables : 85 ( 1 sgn 42 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(tsy_c_Int_OPls_res,hypothesis,
ti(int,pls) = pls ).
fof(tsy_c_hAPP_arg2,axiom,
! [X_a,X_c,B_1_1,B_2_1] : hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ).
fof(tsy_c_hAPP_res,axiom,
! [X_c,X_a,B_1_1,B_2_1] : ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1) ).
fof(fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096,axiom,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))) ).
fof(fact_3_t,axiom,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) ).
fof(fact_22_number__of__is__id,axiom,
! [K_4] : hAPP(int,int,number_number_of(int),K_4) = ti(int,K_4) ).
fof(fact_23_zmult__commute,axiom,
! [Z_1,W] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1) ).
fof(fact_62_mult__Pls,axiom,
! [W] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W) = pls ).
fof(fact_100_zero__is__num__zero,axiom,
zero_zero(int) = hAPP(int,int,number_number_of(int),pls) ).
fof(fact_112_one__is__num__one,axiom,
one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)) ).
fof(fact_1112_nat__number__of__def,axiom,
! [V] : hAPP(int,nat,number_number_of(nat),V) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) ).
fof(fact_1330_One__nat__def,axiom,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)) ).
fof(fact_1426_numeral__2__eq__2,axiom,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) ).
fof(fact_1528_succ__def,axiom,
! [K_4] : hAPP(int,int,succ,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int)) ).
fof(conj_0,conjecture,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))) ).
fof(subgoal_0,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))),
inference(strip,[],[conj_0]) ).
fof(negate_0_0,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))),
inference(canonicalize,[],[fact_2__096_I4_A_K_Am_A_L_A1_J_A_K_At_A_060_A_I4_A_K_Am_A_L_A1_J_A_K_A0_096]) ).
fof(normalize_0_1,plain,
! [W] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W) = pls,
inference(canonicalize,[],[fact_62_mult__Pls]) ).
fof(normalize_0_2,plain,
! [W] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W) = pls,
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),
inference(canonicalize,[],[fact_112_one__is__num__one]) ).
fof(normalize_0_4,plain,
! [B_1_1,B_2_1,X_a,X_c] : ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1),
inference(canonicalize,[],[tsy_c_hAPP_res]) ).
fof(normalize_0_5,plain,
! [B_1_1,B_2_1,X_a,X_c] : ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [K_4] : hAPP(int,int,number_number_of(int),K_4) = ti(int,K_4),
inference(canonicalize,[],[fact_22_number__of__is__id]) ).
fof(normalize_0_7,plain,
! [K_4] : hAPP(int,int,number_number_of(int),K_4) = ti(int,K_4),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [W,Z_1] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1),
inference(canonicalize,[],[fact_23_zmult__commute]) ).
fof(normalize_0_9,plain,
! [W,Z_1] : hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [K_4] : hAPP(int,int,succ,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int)),
inference(canonicalize,[],[fact_1528_succ__def]) ).
fof(normalize_0_11,plain,
! [K_4] : hAPP(int,int,succ,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int)),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
zero_zero(int) = hAPP(int,int,number_number_of(int),pls),
inference(canonicalize,[],[fact_100_zero__is__num__zero]) ).
fof(normalize_0_13,plain,
ti(int,pls) = pls,
inference(canonicalize,[],[tsy_c_Int_OPls_res]) ).
fof(normalize_0_14,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t),
inference(canonicalize,[],[fact_3_t]) ).
fof(normalize_0_15,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),
inference(canonicalize,[],[fact_1426_numeral__2__eq__2]) ).
fof(normalize_0_16,plain,
! [V] : hAPP(int,nat,number_number_of(nat),V) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)),
inference(canonicalize,[],[fact_1112_nat__number__of__def]) ).
fof(normalize_0_17,plain,
! [V] : hAPP(int,nat,number_number_of(nat),V) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [B_1_1,B_2_1,X_a,X_c] : hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1),
inference(canonicalize,[],[tsy_c_hAPP_arg2]) ).
fof(normalize_0_19,plain,
! [B_1_1,B_2_1,X_a,X_c] : hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(canonicalize,[],[fact_1330_One__nat__def]) ).
fof(normalize_0_21,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))),
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W) = pls,
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) = pls,
inference(subst,[],[refute_0_1:[bind(W,$fot(hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))))]]) ).
cnf(refute_0_3,plain,
one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_4,plain,
ti(X_c,hAPP(X_a,X_c,B_1_1,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
ti(int,hAPP(int,int,bit1,pls)) = hAPP(int,int,bit1,pls),
inference(subst,[],[refute_0_4:[bind(B_1_1,$fot(bit1)),bind(B_2_1,$fot(pls)),bind(X_a,$fot(int)),bind(X_c,$fot(int))]]) ).
cnf(refute_0_6,plain,
hAPP(int,int,number_number_of(int),K_4) = ti(int,K_4),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)) = ti(int,hAPP(int,int,bit1,pls)),
inference(subst,[],[refute_0_6:[bind(K_4,$fot(hAPP(int,int,bit1,pls)))]]) ).
cnf(refute_0_8,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_9,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_10,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
( Y != X
| Y != Z
| X = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X)]]) ).
cnf(refute_0_12,plain,
( X != Y
| Y != Z
| X = Z ),
inference(resolve,[$cnf( $equal(Y,X) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)) != ti(int,hAPP(int,int,bit1,pls))
| ti(int,hAPP(int,int,bit1,pls)) != hAPP(int,int,bit1,pls)
| hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)) = hAPP(int,int,bit1,pls) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)))),bind(Y,$fot(ti(int,hAPP(int,int,bit1,pls)))),bind(Z,$fot(hAPP(int,int,bit1,pls)))]]) ).
cnf(refute_0_14,plain,
( ti(int,hAPP(int,int,bit1,pls)) != hAPP(int,int,bit1,pls)
| hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)) = hAPP(int,int,bit1,pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),ti(int,hAPP(int,int,bit1,pls))) )],[refute_0_7,refute_0_13]) ).
cnf(refute_0_15,plain,
hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)) = hAPP(int,int,bit1,pls),
inference(resolve,[$cnf( $equal(ti(int,hAPP(int,int,bit1,pls)),hAPP(int,int,bit1,pls)) )],[refute_0_5,refute_0_14]) ).
cnf(refute_0_16,plain,
( hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)) != hAPP(int,int,bit1,pls)
| one_one(int) != hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls))
| one_one(int) = hAPP(int,int,bit1,pls) ),
introduced(tautology,[equality,[$cnf( $equal(one_one(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls))) ),[1],$fot(hAPP(int,int,bit1,pls))]]) ).
cnf(refute_0_17,plain,
( one_one(int) != hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls))
| one_one(int) = hAPP(int,int,bit1,pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)),hAPP(int,int,bit1,pls)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
one_one(int) = hAPP(int,int,bit1,pls),
inference(resolve,[$cnf( $equal(one_one(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls))) )],[refute_0_3,refute_0_17]) ).
cnf(refute_0_19,plain,
( one_one(int) != hAPP(int,int,bit1,pls)
| hAPP(int,int,bit1,pls) = one_one(int) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(one_one(int))),bind(Y,$fot(hAPP(int,int,bit1,pls)))]]) ).
cnf(refute_0_20,plain,
hAPP(int,int,bit1,pls) = one_one(int),
inference(resolve,[$cnf( $equal(one_one(int),hAPP(int,int,bit1,pls)) )],[refute_0_18,refute_0_19]) ).
cnf(refute_0_21,plain,
hAPP(int,int,bit0,hAPP(int,int,bit1,pls)) = hAPP(int,int,bit0,hAPP(int,int,bit1,pls)),
introduced(tautology,[refl,[$fot(hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))]]) ).
cnf(refute_0_22,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_23,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( $equal(hAPP(int,int,bit0,hAPP(int,int,bit1,pls)),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) )],[refute_0_21,refute_0_22]) ).
cnf(refute_0_24,plain,
hAPP(int,int,bit0,hAPP(int,int,bit1,pls)) = hAPP(int,int,bit0,one_one(int)),
inference(resolve,[$cnf( $equal(hAPP(int,int,bit1,pls),one_one(int)) )],[refute_0_20,refute_0_23]) ).
cnf(refute_0_25,plain,
hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
introduced(tautology,[refl,[$fot(hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))]]) ).
cnf(refute_0_26,plain,
( hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| hAPP(int,int,bit0,hAPP(int,int,bit1,pls)) != hAPP(int,int,bit0,one_one(int))
| hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) ),[1,3],$fot(hAPP(int,int,bit0,one_one(int)))]]) ).
cnf(refute_0_27,plain,
( hAPP(int,int,bit0,hAPP(int,int,bit1,pls)) != hAPP(int,int,bit0,one_one(int))
| hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) )],[refute_0_25,refute_0_26]) ).
cnf(refute_0_28,plain,
hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))),
inference(resolve,[$cnf( $equal(hAPP(int,int,bit0,hAPP(int,int,bit1,pls)),hAPP(int,int,bit0,one_one(int))) )],[refute_0_24,refute_0_27]) ).
cnf(refute_0_29,plain,
ti(int,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
inference(subst,[],[refute_0_4:[bind(B_1_1,$fot(bit0)),bind(B_2_1,$fot(hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),bind(X_a,$fot(int)),bind(X_c,$fot(int))]]) ).
cnf(refute_0_30,plain,
hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = ti(int,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
inference(subst,[],[refute_0_6:[bind(K_4,$fot(hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))]]) ).
cnf(refute_0_31,plain,
( hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != ti(int,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| ti(int,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),bind(Y,$fot(ti(int,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),bind(Z,$fot(hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))]]) ).
cnf(refute_0_32,plain,
( ti(int,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),ti(int,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
inference(resolve,[$cnf( $equal(ti(int,hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) )],[refute_0_29,refute_0_32]) ).
cnf(refute_0_34,plain,
( hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))
| hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),bind(Y,$fot(hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),bind(Z,$fot(hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))]]) ).
cnf(refute_0_35,plain,
( hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))
| hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))),
inference(resolve,[$cnf( $equal(hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))) )],[refute_0_28,refute_0_35]) ).
cnf(refute_0_37,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
introduced(tautology,[refl,[$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))]]) ).
cnf(refute_0_38,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))
| hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),[1,3],$fot(hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))]]) ).
cnf(refute_0_39,plain,
( hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))),
inference(resolve,[$cnf( $equal(hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))) )],[refute_0_36,refute_0_39]) ).
cnf(refute_0_41,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_42,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1)
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W))),bind(Y,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1)))]]) ).
cnf(refute_0_43,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1)) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
inference(subst,[],[refute_0_43:[bind(W,$fot(hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),bind(Z_1,$fot(m))]]) ).
cnf(refute_0_45,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m))),bind(Y,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),bind(Z,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))]]) ).
cnf(refute_0_46,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))) )],[refute_0_40,refute_0_46]) ).
cnf(refute_0_48,plain,
hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)) = hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),
introduced(tautology,[refl,[$fot(hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)))]]) ).
cnf(refute_0_49,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))
| hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)) != hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m))
| hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)) = hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m))) ),[1,3],$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))]]) ).
cnf(refute_0_50,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))
| hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)) = hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m))) )],[refute_0_48,refute_0_49]) ).
cnf(refute_0_51,plain,
hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)) = hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))) )],[refute_0_47,refute_0_50]) ).
cnf(refute_0_52,plain,
hAPP(int,int,succ,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int)),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_53,plain,
( hAPP(int,int,succ,K_4) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int))
| hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int)) = hAPP(int,int,succ,K_4) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(hAPP(int,int,succ,K_4))),bind(Y,$fot(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int))))]]) ).
cnf(refute_0_54,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int)) = hAPP(int,int,succ,K_4),
inference(resolve,[$cnf( $equal(hAPP(int,int,succ,K_4),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int))) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)) = hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),
inference(subst,[],[refute_0_54:[bind(K_4,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)))]]) ).
cnf(refute_0_56,plain,
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)) != hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m))
| hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)) != hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))
| hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)) = hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))),bind(Y,$fot(hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)))),bind(Z,$fot(hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))))]]) ).
cnf(refute_0_57,plain,
( hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)) != hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))
| hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)) = hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m))) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)) = hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) )],[refute_0_51,refute_0_57]) ).
cnf(refute_0_59,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),
introduced(tautology,[refl,[$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))))]]) ).
cnf(refute_0_60,plain,
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)) != hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) ),[1,3],$fot(hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))]]) ).
cnf(refute_0_61,plain,
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)) != hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) )],[refute_0_58,refute_0_61]) ).
cnf(refute_0_63,plain,
zero_zero(int) = hAPP(int,int,number_number_of(int),pls),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_64,plain,
ti(int,pls) = pls,
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_65,plain,
hAPP(int,int,number_number_of(int),pls) = ti(int,pls),
inference(subst,[],[refute_0_6:[bind(K_4,$fot(pls))]]) ).
cnf(refute_0_66,plain,
( hAPP(int,int,number_number_of(int),pls) != ti(int,pls)
| ti(int,pls) != pls
| hAPP(int,int,number_number_of(int),pls) = pls ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,int,number_number_of(int),pls))),bind(Y,$fot(ti(int,pls))),bind(Z,$fot(pls))]]) ).
cnf(refute_0_67,plain,
( ti(int,pls) != pls
| hAPP(int,int,number_number_of(int),pls) = pls ),
inference(resolve,[$cnf( $equal(hAPP(int,int,number_number_of(int),pls),ti(int,pls)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
hAPP(int,int,number_number_of(int),pls) = pls,
inference(resolve,[$cnf( $equal(ti(int,pls),pls) )],[refute_0_64,refute_0_67]) ).
cnf(refute_0_69,plain,
( hAPP(int,int,number_number_of(int),pls) != pls
| zero_zero(int) != hAPP(int,int,number_number_of(int),pls)
| zero_zero(int) = pls ),
introduced(tautology,[equality,[$cnf( $equal(zero_zero(int),hAPP(int,int,number_number_of(int),pls)) ),[1],$fot(pls)]]) ).
cnf(refute_0_70,plain,
( zero_zero(int) != hAPP(int,int,number_number_of(int),pls)
| zero_zero(int) = pls ),
inference(resolve,[$cnf( $equal(hAPP(int,int,number_number_of(int),pls),pls) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
zero_zero(int) = pls,
inference(resolve,[$cnf( $equal(zero_zero(int),hAPP(int,int,number_number_of(int),pls)) )],[refute_0_63,refute_0_70]) ).
cnf(refute_0_72,plain,
hAPP(int,fun(int,int),times_times(int),zero_zero(int)) = hAPP(int,fun(int,int),times_times(int),zero_zero(int)),
introduced(tautology,[refl,[$fot(hAPP(int,fun(int,int),times_times(int),zero_zero(int)))]]) ).
cnf(refute_0_73,plain,
( hAPP(int,fun(int,int),times_times(int),zero_zero(int)) != hAPP(int,fun(int,int),times_times(int),zero_zero(int))
| zero_zero(int) != pls
| hAPP(int,fun(int,int),times_times(int),zero_zero(int)) = hAPP(int,fun(int,int),times_times(int),pls) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,fun(int,int),times_times(int),zero_zero(int))) ),[1,3],$fot(pls)]]) ).
cnf(refute_0_74,plain,
( zero_zero(int) != pls
| hAPP(int,fun(int,int),times_times(int),zero_zero(int)) = hAPP(int,fun(int,int),times_times(int),pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,fun(int,int),times_times(int),zero_zero(int))) )],[refute_0_72,refute_0_73]) ).
cnf(refute_0_75,plain,
hAPP(int,fun(int,int),times_times(int),zero_zero(int)) = hAPP(int,fun(int,int),times_times(int),pls),
inference(resolve,[$cnf( $equal(zero_zero(int),pls) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),
introduced(tautology,[refl,[$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))))]]) ).
cnf(refute_0_77,plain,
( hAPP(int,fun(int,int),times_times(int),zero_zero(int)) != hAPP(int,fun(int,int),times_times(int),pls)
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) ),[1,2],$fot(hAPP(int,fun(int,int),times_times(int),pls))]]) ).
cnf(refute_0_78,plain,
( hAPP(int,fun(int,int),times_times(int),zero_zero(int)) != hAPP(int,fun(int,int),times_times(int),pls)
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),
inference(resolve,[$cnf( $equal(hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,fun(int,int),times_times(int),pls)) )],[refute_0_75,refute_0_78]) ).
cnf(refute_0_80,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))))),bind(Y,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))))),bind(Z,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))))]]) ).
cnf(refute_0_81,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) )],[refute_0_79,refute_0_80]) ).
cnf(refute_0_82,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))) )],[refute_0_62,refute_0_81]) ).
cnf(refute_0_83,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) != pls
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = pls ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))))),bind(Y,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))))),bind(Z,$fot(pls))]]) ).
cnf(refute_0_84,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) != pls
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = pls ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = pls,
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))),pls) )],[refute_0_2,refute_0_84]) ).
cnf(refute_0_86,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),
inference(subst,[],[refute_0_43:[bind(W,$fot(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))),bind(Z_1,$fot(zero_zero(int)))]]) ).
cnf(refute_0_87,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) != pls
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)) = pls ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))),bind(Y,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))))),bind(Z,$fot(pls))]]) ).
cnf(refute_0_88,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) != pls
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)) = pls ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)) = pls,
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),pls) )],[refute_0_85,refute_0_88]) ).
cnf(refute_0_90,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))),
introduced(tautology,[refl,[$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))))]]) ).
cnf(refute_0_91,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)) != pls
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))) ),[1,3],$fot(pls)]]) ).
cnf(refute_0_92,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)) != pls
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)),pls) )],[refute_0_89,refute_0_92]) ).
cnf(refute_0_94,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),
introduced(tautology,[refl,[$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))))]]) ).
cnf(refute_0_95,plain,
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)) != hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) ),[1,3],$fot(hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))]]) ).
cnf(refute_0_96,plain,
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)) != hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) )],[refute_0_94,refute_0_95]) ).
cnf(refute_0_97,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) )],[refute_0_58,refute_0_96]) ).
cnf(refute_0_98,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),
inference(subst,[],[refute_0_43:[bind(W,$fot(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))),bind(Z_1,$fot(t))]]) ).
cnf(refute_0_99,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t))),bind(Y,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))))),bind(Z,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))))]]) ).
cnf(refute_0_100,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))) )],[refute_0_97,refute_0_100]) ).
cnf(refute_0_102,plain,
hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)) = hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),
introduced(tautology,[refl,[$fot(hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)))]]) ).
cnf(refute_0_103,plain,
( hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)) != hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))
| hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)) = hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t))) ),[1,3],$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))))]]) ).
cnf(refute_0_104,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))
| hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)) = hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t))) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)) = hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))) )],[refute_0_101,refute_0_104]) ).
cnf(refute_0_106,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))),
introduced(tautology,[refl,[$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))))]]) ).
cnf(refute_0_107,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))
| hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)) != hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))) ),[1,2],$fot(hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))))]]) ).
cnf(refute_0_108,plain,
( hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)) != hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))),
inference(resolve,[$cnf( $equal(hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))))) )],[refute_0_105,refute_0_108]) ).
cnf(refute_0_110,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls)
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))))),bind(Y,$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))))),bind(Z,$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls)))]]) ).
cnf(refute_0_111,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls)
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))) )],[refute_0_109,refute_0_110]) ).
cnf(refute_0_112,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls)) )],[refute_0_93,refute_0_111]) ).
cnf(refute_0_113,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls)) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))) ),[0],$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls))]]) ).
cnf(refute_0_114,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls)) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls)) )],[refute_0_112,refute_0_113]) ).
cnf(refute_0_115,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls)),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),zero_zero(int)))) )],[refute_0_0,refute_0_114]) ).
cnf(refute_0_116,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_117,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_118,plain,
hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
introduced(tautology,[refl,[$fot(hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))]]) ).
cnf(refute_0_119,plain,
( hAPP(int,int,bit0,hAPP(int,int,bit1,pls)) != hAPP(int,int,bit0,one_one(int))
| hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) ),[1,3],$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))
| hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))) ),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) )],[refute_0_118,refute_0_119]) ).
cnf(refute_0_121,plain,
hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))),
inference(resolve,[$cnf( $equal(hAPP(int,int,bit0,hAPP(int,int,bit1,pls)),hAPP(int,int,bit0,one_one(int))) )],[refute_0_24,refute_0_120]) ).
cnf(refute_0_122,plain,
hAPP(int,nat,number_number_of(nat),V) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_123,plain,
hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_124,plain,
hAPP(int,nat,nat_1,ti(int,V)) = hAPP(int,nat,nat_1,V),
inference(subst,[],[refute_0_123:[bind(B_1_1,$fot(nat_1)),bind(B_2_1,$fot(V)),bind(X_a,$fot(int)),bind(X_c,$fot(nat))]]) ).
cnf(refute_0_125,plain,
hAPP(int,int,number_number_of(int),V) = ti(int,V),
inference(subst,[],[refute_0_6:[bind(K_4,$fot(V))]]) ).
cnf(refute_0_126,plain,
hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)),
introduced(tautology,[refl,[$fot(hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)))]]) ).
cnf(refute_0_127,plain,
( hAPP(int,int,number_number_of(int),V) != ti(int,V)
| hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) != hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V))
| hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) = hAPP(int,nat,nat_1,ti(int,V)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V))) ),[1,3],$fot(ti(int,V))]]) ).
cnf(refute_0_128,plain,
( hAPP(int,int,number_number_of(int),V) != ti(int,V)
| hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) = hAPP(int,nat,nat_1,ti(int,V)) ),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) = hAPP(int,nat,nat_1,ti(int,V)),
inference(resolve,[$cnf( $equal(hAPP(int,int,number_number_of(int),V),ti(int,V)) )],[refute_0_125,refute_0_128]) ).
cnf(refute_0_130,plain,
( hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) != hAPP(int,nat,nat_1,ti(int,V))
| hAPP(int,nat,nat_1,ti(int,V)) != hAPP(int,nat,nat_1,V)
| hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) = hAPP(int,nat,nat_1,V) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)))),bind(Y,$fot(hAPP(int,nat,nat_1,ti(int,V)))),bind(Z,$fot(hAPP(int,nat,nat_1,V)))]]) ).
cnf(refute_0_131,plain,
( hAPP(int,nat,nat_1,ti(int,V)) != hAPP(int,nat,nat_1,V)
| hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) = hAPP(int,nat,nat_1,V) ),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)),hAPP(int,nat,nat_1,ti(int,V))) )],[refute_0_129,refute_0_130]) ).
cnf(refute_0_132,plain,
hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) = hAPP(int,nat,nat_1,V),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,ti(int,V)),hAPP(int,nat,nat_1,V)) )],[refute_0_124,refute_0_131]) ).
cnf(refute_0_133,plain,
( hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) != hAPP(int,nat,nat_1,V)
| hAPP(int,nat,number_number_of(nat),V) != hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V))
| hAPP(int,nat,number_number_of(nat),V) = hAPP(int,nat,nat_1,V) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,nat,number_number_of(nat),V),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V))) ),[1],$fot(hAPP(int,nat,nat_1,V))]]) ).
cnf(refute_0_134,plain,
( hAPP(int,nat,number_number_of(nat),V) != hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V))
| hAPP(int,nat,number_number_of(nat),V) = hAPP(int,nat,nat_1,V) ),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)),hAPP(int,nat,nat_1,V)) )],[refute_0_132,refute_0_133]) ).
cnf(refute_0_135,plain,
hAPP(int,nat,number_number_of(nat),V) = hAPP(int,nat,nat_1,V),
inference(resolve,[$cnf( $equal(hAPP(int,nat,number_number_of(nat),V),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V))) )],[refute_0_122,refute_0_134]) ).
cnf(refute_0_136,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
inference(subst,[],[refute_0_135:[bind(V,$fot(hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))]]) ).
cnf(refute_0_137,plain,
( hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int)))
| hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),bind(Y,$fot(hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),bind(Z,$fot(hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int)))))]]) ).
cnf(refute_0_138,plain,
( hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int)))
| hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))) ),
inference(resolve,[$cnf( $equal(hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) )],[refute_0_136,refute_0_137]) ).
cnf(refute_0_139,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int)))) )],[refute_0_121,refute_0_138]) ).
cnf(refute_0_140,plain,
( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int)))
| hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))
| hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) ),[0],$fot(hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))))]]) ).
cnf(refute_0_141,plain,
( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))
| hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) ),
inference(resolve,[$cnf( $equal(hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int)))) )],[refute_0_139,refute_0_140]) ).
cnf(refute_0_142,plain,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_143,plain,
( one_one(nat) != hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,suc,zero_zero(nat)) = one_one(nat) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(one_one(nat))),bind(Y,$fot(hAPP(nat,nat,suc,zero_zero(nat))))]]) ).
cnf(refute_0_144,plain,
hAPP(nat,nat,suc,zero_zero(nat)) = one_one(nat),
inference(resolve,[$cnf( $equal(one_one(nat),hAPP(nat,nat,suc,zero_zero(nat))) )],[refute_0_142,refute_0_143]) ).
cnf(refute_0_145,plain,
hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),
introduced(tautology,[refl,[$fot(hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))]]) ).
cnf(refute_0_146,plain,
( hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) != hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))
| hAPP(nat,nat,suc,zero_zero(nat)) != one_one(nat)
| hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(nat,nat,suc,one_one(nat)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) ),[1,3],$fot(one_one(nat))]]) ).
cnf(refute_0_147,plain,
( hAPP(nat,nat,suc,zero_zero(nat)) != one_one(nat)
| hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(nat,nat,suc,one_one(nat)) ),
inference(resolve,[$cnf( $equal(hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) )],[refute_0_145,refute_0_146]) ).
cnf(refute_0_148,plain,
hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(nat,nat,suc,one_one(nat)),
inference(resolve,[$cnf( $equal(hAPP(nat,nat,suc,zero_zero(nat)),one_one(nat)) )],[refute_0_144,refute_0_147]) ).
cnf(refute_0_149,plain,
( hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))) != hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))
| hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) != hAPP(nat,nat,suc,one_one(nat))
| hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))) = hAPP(nat,nat,suc,one_one(nat)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))),hAPP(nat,nat,suc,one_one(nat))) ),[0],$fot(hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))]]) ).
cnf(refute_0_150,plain,
( hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))) != hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))
| hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))) = hAPP(nat,nat,suc,one_one(nat)) ),
inference(resolve,[$cnf( $equal(hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,suc,one_one(nat))) )],[refute_0_148,refute_0_149]) ).
cnf(refute_0_151,plain,
( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))
| hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))) = hAPP(nat,nat,suc,one_one(nat)) ),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) )],[refute_0_141,refute_0_150]) ).
cnf(refute_0_152,plain,
hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))) = hAPP(nat,nat,suc,one_one(nat)),
inference(resolve,[$cnf( $equal(hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) )],[refute_0_117,refute_0_151]) ).
cnf(refute_0_153,plain,
( hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int)))
| hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))) != hAPP(nat,nat,suc,one_one(nat))
| hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,one_one(nat)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),bind(Y,$fot(hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))))),bind(Z,$fot(hAPP(nat,nat,suc,one_one(nat))))]]) ).
cnf(refute_0_154,plain,
( hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))) != hAPP(nat,nat,suc,one_one(nat))
| hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,one_one(nat)) ),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int)))) )],[refute_0_121,refute_0_153]) ).
cnf(refute_0_155,plain,
hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,one_one(nat)),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,hAPP(int,int,bit0,one_one(int))),hAPP(nat,nat,suc,one_one(nat))) )],[refute_0_152,refute_0_154]) ).
cnf(refute_0_156,plain,
( hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(nat,nat,suc,one_one(nat))
| hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,one_one(nat)) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),bind(Y,$fot(hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),bind(Z,$fot(hAPP(nat,nat,suc,one_one(nat))))]]) ).
cnf(refute_0_157,plain,
( hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(nat,nat,suc,one_one(nat))
| hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,one_one(nat)) ),
inference(resolve,[$cnf( $equal(hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) )],[refute_0_136,refute_0_156]) ).
cnf(refute_0_158,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,one_one(nat)),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(nat,nat,suc,one_one(nat))) )],[refute_0_155,refute_0_157]) ).
cnf(refute_0_159,plain,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
introduced(tautology,[refl,[$fot(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))]]) ).
cnf(refute_0_160,plain,
( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(nat,nat,suc,one_one(nat))
| hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) ),[1,3],$fot(hAPP(nat,nat,suc,one_one(nat)))]]) ).
cnf(refute_0_161,plain,
( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(nat,nat,suc,one_one(nat))
| hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) )],[refute_0_159,refute_0_160]) ).
cnf(refute_0_162,plain,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))),
inference(resolve,[$cnf( $equal(hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(nat,nat,suc,one_one(nat))) )],[refute_0_158,refute_0_161]) ).
cnf(refute_0_163,plain,
hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
introduced(tautology,[refl,[$fot(hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))]]) ).
cnf(refute_0_164,plain,
( hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))
| hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) ),[1,3],$fot(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))]]) ).
cnf(refute_0_165,plain,
( hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))),
inference(resolve,[$cnf( $equal(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))) )],[refute_0_162,refute_0_165]) ).
cnf(refute_0_167,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) = hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),
inference(subst,[],[refute_0_54:[bind(K_4,$fot(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))]]) ).
cnf(refute_0_168,plain,
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) != hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))
| hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))
| hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) = hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)))),bind(Y,$fot(hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),bind(Z,$fot(hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))))]]) ).
cnf(refute_0_169,plain,
( hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))
| hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) = hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) )],[refute_0_167,refute_0_168]) ).
cnf(refute_0_170,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) = hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))),
inference(resolve,[$cnf( $equal(hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))) )],[refute_0_166,refute_0_169]) ).
cnf(refute_0_171,plain,
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)
| hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) != hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))
| hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)) ),[0],$fot(hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))))]]) ).
cnf(refute_0_172,plain,
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)
| hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))) )],[refute_0_170,refute_0_171]) ).
cnf(refute_0_173,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))
| hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)
| hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)) ),[1],$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))))]]) ).
cnf(refute_0_174,plain,
( hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)
| hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))) )],[refute_0_101,refute_0_173]) ).
cnf(refute_0_175,plain,
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)
| hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)) )],[refute_0_172,refute_0_174]) ).
cnf(refute_0_176,plain,
hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),t)) )],[refute_0_116,refute_0_175]) ).
cnf(refute_0_177,plain,
( hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) = hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))))),bind(Y,$fot(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))))]]) ).
cnf(refute_0_178,plain,
hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) = hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))),
inference(resolve,[$cnf( $equal(hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))) = hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),
introduced(tautology,[refl,[$fot(hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))))]]) ).
cnf(refute_0_180,plain,
( hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))) != hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))))
| hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) != hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))
| hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))) = hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))))) ),[1,3],$fot(hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))))]]) ).
cnf(refute_0_181,plain,
( hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))) != hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))
| hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))) = hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))))) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))) = hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int)))))),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))) )],[refute_0_178,refute_0_181]) ).
cnf(refute_0_183,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls),
introduced(tautology,[refl,[$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls))]]) ).
cnf(refute_0_184,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls)
| hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))) != hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls)) ),[1,2],$fot(hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))))]]) ).
cnf(refute_0_185,plain,
( hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))) != hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls)) )],[refute_0_183,refute_0_184]) ).
cnf(refute_0_186,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls),
inference(resolve,[$cnf( $equal(hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))))) )],[refute_0_182,refute_0_185]) ).
cnf(refute_0_187,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls)) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls)) ),[0],$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls))]]) ).
cnf(refute_0_188,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls)) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls)) )],[refute_0_186,refute_0_187]) ).
cnf(refute_0_189,plain,
hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls)),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),t),hAPP(int,int,succ,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),m),hAPP(int,int,bit0,hAPP(int,int,bit0,one_one(int))))))),pls)) )],[refute_0_115,refute_0_188]) ).
cnf(refute_0_190,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_191,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int)),
introduced(tautology,[refl,[$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int)))]]) ).
cnf(refute_0_192,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int)) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int))
| zero_zero(int) != pls
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int))) ),[1,3],$fot(pls)]]) ).
cnf(refute_0_193,plain,
( zero_zero(int) != pls
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int))) )],[refute_0_191,refute_0_192]) ).
cnf(refute_0_194,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls),
inference(resolve,[$cnf( $equal(zero_zero(int),pls) )],[refute_0_71,refute_0_193]) ).
cnf(refute_0_195,plain,
hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))) = hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),
introduced(tautology,[refl,[$fot(hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))))]]) ).
cnf(refute_0_196,plain,
( hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))) != hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)))
| hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) != hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))
| hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))) = hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)))) ),[1,3],$fot(hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))))]]) ).
cnf(refute_0_197,plain,
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) != hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))
| hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))) = hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))) ),
inference(resolve,[$cnf( $equal(hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))) = hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))) )],[refute_0_170,refute_0_197]) ).
cnf(refute_0_199,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)),
introduced(tautology,[refl,[$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)))]]) ).
cnf(refute_0_200,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))
| hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))) != hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))) ),[1,2],$fot(hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))))]]) ).
cnf(refute_0_201,plain,
( hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))) != hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int)) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))) )],[refute_0_199,refute_0_200]) ).
cnf(refute_0_202,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int)),
inference(resolve,[$cnf( $equal(hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat)))))) )],[refute_0_198,refute_0_201]) ).
cnf(refute_0_203,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int))
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int)) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls)
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)))),bind(Y,$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int)))),bind(Z,$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls)))]]) ).
cnf(refute_0_204,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int)) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls)
| hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int))) )],[refute_0_202,refute_0_203]) ).
cnf(refute_0_205,plain,
hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)) = hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),zero_zero(int)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls)) )],[refute_0_194,refute_0_204]) ).
cnf(refute_0_206,plain,
( hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)) != hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls)
| ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))) ),
introduced(tautology,[equality,[$cnf( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))) ),[0],$fot(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls))]]) ).
cnf(refute_0_207,plain,
( ~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls))
| hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))) ),
inference(resolve,[$cnf( $equal(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls)) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
~ hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls)),
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int))),zero_zero(int))) )],[refute_0_207,refute_0_190]) ).
cnf(refute_0_209,plain,
$false,
inference(resolve,[$cnf( hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,succ,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(nat,nat,suc,one_one(nat))))),pls)) )],[refute_0_189,refute_0_208]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM924+8 : TPTP v8.1.0. Released v5.3.0.
% 0.08/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n027.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jul 7 08:43:59 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 31.46/31.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 31.46/31.66
% 31.46/31.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 31.53/31.74
%------------------------------------------------------------------------------