TSTP Solution File: NUM925+8 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM925+8 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 12:31:42 EDT 2022
% Result : Theorem 68.14s 68.29s
% Output : CNFRefutation 68.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 48
% Number of leaves : 170
% Syntax : Number of formulae : 636 ( 381 unt; 0 def)
% Number of atoms : 1012 (1011 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 763 ( 387 ~; 366 |; 4 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 0 usr; 1 prp; 0-2 aty)
% Number of functors : 34 ( 34 usr; 18 con; 0-4 aty)
% Number of variables : 547 ( 10 sgn 156 !; 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(fact_20_zpower__int,axiom,
! [M,N] : hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M)),N) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)) ).
fof(fact_27_int__eq__0__conv,axiom,
! [Na] :
( hAPP(nat,int,semiring_1_of_nat(int),Na) = zero_zero(int)
<=> Na = zero_zero(nat) ) ).
fof(fact_47_zadd__commute,axiom,
! [Z_1,W] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),W) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z_1) ).
fof(fact_76_Pls__def,axiom,
pls = zero_zero(int) ).
fof(fact_123_number__of__is__id,axiom,
! [K_4] : hAPP(int,int,number_number_of(int),K_4) = ti(int,K_4) ).
fof(fact_303_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(fact_984_nat__int,axiom,
! [N] : hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),N)) = N ).
fof(fact_997_nat__0,axiom,
hAPP(int,nat,nat_1,zero_zero(int)) = zero_zero(nat) ).
fof(fact_1004_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_1312_Zero__not__Suc,axiom,
! [M] : zero_zero(nat) != hAPP(nat,nat,suc,M) ).
fof(fact_1316_Zero__neq__Suc,axiom,
! [M] : zero_zero(nat) != hAPP(nat,nat,suc,M) ).
fof(fact_1382_One__nat__def,axiom,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)) ).
fof(fact_1450_int__Suc,axiom,
! [M] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M)) ).
fof(fact_1483_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_2127_real__sqrt__zero,axiom,
hAPP(real,real,sqrt,zero_zero(real)) = zero_zero(real) ).
fof(fact_2130_real__sqrt__power,axiom,
! [X,K_4] : hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),K_4)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),K_4) ).
fof(fact_2166_real__sqrt__abs,axiom,
! [X] : hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(real,real,abs_abs(real),X) ).
fof(fact_2373_abs__real__of__nat__cancel,axiom,
! [X] : hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X)) = hAPP(nat,real,real_1(nat),X) ).
fof(fact_2378_real__of__nat__def,axiom,
real_1(nat) = semiring_1_of_nat(real) ).
fof(fact_2379_real__eq__of__nat,axiom,
real_1(nat) = semiring_1_of_nat(real) ).
fof(fact_2380_real__of__nat__zero,axiom,
hAPP(nat,real,real_1(nat),zero_zero(nat)) = zero_zero(real) ).
fof(fact_2388_power__real__of__nat,axiom,
! [M,N] : hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),M)),N) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)) ).
fof(fact_2760_Complex__eq__number__of,axiom,
! [A_3,B_2,Wa] :
( hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_3),B_2) = hAPP(int,complex,number_number_of(complex),Wa)
<=> ( A_3 = hAPP(int,real,number_number_of(real),Wa)
& B_2 = zero_zero(real) ) ) ).
fof(fact_2802_complex__of__real__def,axiom,
! [R_3] : hAPP(real,complex,of_real(complex),R_3) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,R_3),zero_zero(real)) ).
fof(fact_2952_complex__mod__mult__cnj,axiom,
! [Z_1] : hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) ).
fof(fact_2954_complex__cnj__complex__of__real,axiom,
! [X] : hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X)) = hAPP(real,complex,of_real(complex),X) ).
fof(fact_2958_cnj_Ominus,axiom,
! [X] : hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,cnj,X)) ).
fof(fact_2962_complex__cnj__of__nat,axiom,
! [N] : hAPP(complex,complex,cnj,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = hAPP(nat,complex,semiring_1_of_nat(complex),N) ).
fof(fact_2998_complex__Im__cnj,axiom,
! [X] : hAPP(complex,real,im,hAPP(complex,complex,cnj,X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)) ).
fof(fact_2999_Im__complex__of__real,axiom,
! [Z_1] : hAPP(complex,real,im,hAPP(real,complex,of_real(complex),Z_1)) = zero_zero(real) ).
fof(fact_3005_Im_Ominus,axiom,
! [X] : hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)) ).
fof(fact_3007_complex__Im__of__nat,axiom,
! [N] : hAPP(complex,real,im,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = zero_zero(real) ).
fof(fact_3018_Re__complex__of__real,axiom,
! [Z_1] : hAPP(complex,real,re,hAPP(real,complex,of_real(complex),Z_1)) = Z_1 ).
fof(fact_3025_complex__surj,axiom,
! [Z_1] : hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,Z_1)),hAPP(complex,real,im,Z_1)) = Z_1 ).
fof(fact_3029_Re_Ominus,axiom,
! [X] : hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,X)) ).
fof(fact_3032_complex__Re__of__nat,axiom,
! [N] : hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = hAPP(nat,real,semiring_1_of_nat(real),N) ).
fof(fact_3190_rcis__zero__arg,axiom,
! [R_3] : hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_3),zero_zero(real)) = hAPP(real,complex,of_real(complex),R_3) ).
fof(fact_3191_complex__mod__rcis,axiom,
! [R_3,A_1] : hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_3),A_1)) = hAPP(real,real,abs_abs(real),R_3) ).
fof(fact_3303_ceiling__real__of__nat,axiom,
! [N] : hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),N)) = hAPP(nat,int,semiring_1_of_nat(int),N) ).
fof(fact_3346_real__number__of,axiom,
! [V] : hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) = hAPP(int,real,number_number_of(real),V) ).
fof(fact_3348_real__of__int__zero,axiom,
hAPP(int,real,real_1(int),zero_zero(int)) = zero_zero(real) ).
fof(fact_3363_real__of__int__of__nat__eq,axiom,
! [N] : hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,real,real_1(nat),N) ).
fof(fact_3366_ceiling__real__of__int,axiom,
! [N] : hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)) = ti(int,N) ).
fof(fact_3367_real__of__int__minus,axiom,
! [X] : hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)) ).
fof(fact_3368_real__of__int__abs,axiom,
! [X] : hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)) ).
fof(fact_3468_zgcd__zminus,axiom,
! [I_1,J_2] : hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),I_1)),J_2) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2) ).
fof(fact_3478_zgcd__0,axiom,
! [M] : hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)) = hAPP(int,int,abs_abs(int),M) ).
fof(conj_0,conjecture,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) ).
fof(subgoal_0,plain,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int),
inference(strip,[],[conj_0]) ).
fof(negate_0_0,plain,
~ ( hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [N] : hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),N)) = hAPP(nat,int,semiring_1_of_nat(int),N),
inference(canonicalize,[],[fact_3303_ceiling__real__of__nat]) ).
fof(normalize_0_1,plain,
! [N] : hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),N)) = hAPP(nat,int,semiring_1_of_nat(int),N),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [K_4,X] : hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),K_4)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),K_4),
inference(canonicalize,[],[fact_2130_real__sqrt__power]) ).
fof(normalize_0_3,plain,
! [K_4,X] : hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),K_4)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),K_4),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [Z_1] : hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
inference(canonicalize,[],[fact_2952_complex__mod__mult__cnj]) ).
fof(normalize_0_5,plain,
! [Z_1] : hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,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_1483_numeral__2__eq__2]) ).
fof(normalize_0_7,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_1004_nat__number__of__def]) ).
fof(normalize_0_8,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_7]) ).
fof(normalize_0_9,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_10,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_9]) ).
fof(normalize_0_11,plain,
! [K_4] : hAPP(int,int,number_number_of(int),K_4) = ti(int,K_4),
inference(canonicalize,[],[fact_123_number__of__is__id]) ).
fof(normalize_0_12,plain,
! [K_4] : hAPP(int,int,number_number_of(int),K_4) = ti(int,K_4),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(canonicalize,[],[fact_1382_One__nat__def]) ).
fof(normalize_0_14,plain,
! [X] : hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(real,real,abs_abs(real),X),
inference(canonicalize,[],[fact_2166_real__sqrt__abs]) ).
fof(normalize_0_15,plain,
! [X] : hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(real,real,abs_abs(real),X),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X] : hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,cnj,X)),
inference(canonicalize,[],[fact_2958_cnj_Ominus]) ).
fof(normalize_0_17,plain,
! [X] : hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,cnj,X)),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [N] : hAPP(complex,complex,cnj,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = hAPP(nat,complex,semiring_1_of_nat(complex),N),
inference(canonicalize,[],[fact_2962_complex__cnj__of__nat]) ).
fof(normalize_0_19,plain,
! [N] : hAPP(complex,complex,cnj,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = hAPP(nat,complex,semiring_1_of_nat(complex),N),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [M,N] : hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),M)),N) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)),
inference(canonicalize,[],[fact_2388_power__real__of__nat]) ).
fof(normalize_0_21,plain,
! [M,N] : hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),M)),N) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [A_1,R_3] : hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_3),A_1)) = hAPP(real,real,abs_abs(real),R_3),
inference(canonicalize,[],[fact_3191_complex__mod__rcis]) ).
fof(normalize_0_23,plain,
! [A_1,R_3] : hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_3),A_1)) = hAPP(real,real,abs_abs(real),R_3),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [R_3] : hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_3),zero_zero(real)) = hAPP(real,complex,of_real(complex),R_3),
inference(canonicalize,[],[fact_3190_rcis__zero__arg]) ).
fof(normalize_0_25,plain,
! [R_3] : hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_3),zero_zero(real)) = hAPP(real,complex,of_real(complex),R_3),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [A_3,B_2,Wa] :
( hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_3),B_2) != hAPP(int,complex,number_number_of(complex),Wa)
<=> ( A_3 != hAPP(int,real,number_number_of(real),Wa)
| B_2 != zero_zero(real) ) ),
inference(canonicalize,[],[fact_2760_Complex__eq__number__of]) ).
fof(normalize_0_27,plain,
! [A_3,B_2,Wa] :
( hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_3),B_2) != hAPP(int,complex,number_number_of(complex),Wa)
<=> ( A_3 != hAPP(int,real,number_number_of(real),Wa)
| B_2 != zero_zero(real) ) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,plain,
! [A_3,B_2,Wa] :
( ( hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_3),B_2) != hAPP(int,complex,number_number_of(complex),Wa)
| A_3 = hAPP(int,real,number_number_of(real),Wa) )
& ( hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_3),B_2) != hAPP(int,complex,number_number_of(complex),Wa)
| B_2 = zero_zero(real) )
& ( A_3 != hAPP(int,real,number_number_of(real),Wa)
| B_2 != zero_zero(real)
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_3),B_2) = hAPP(int,complex,number_number_of(complex),Wa) ) ),
inference(clausify,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [A_3,B_2,Wa] :
( A_3 != hAPP(int,real,number_number_of(real),Wa)
| B_2 != zero_zero(real)
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_3),B_2) = hAPP(int,complex,number_number_of(complex),Wa) ),
inference(conjunct,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [R_3] : hAPP(real,complex,of_real(complex),R_3) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,R_3),zero_zero(real)),
inference(canonicalize,[],[fact_2802_complex__of__real__def]) ).
fof(normalize_0_31,plain,
! [R_3] : hAPP(real,complex,of_real(complex),R_3) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,R_3),zero_zero(real)),
inference(specialize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [X] : hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)),
inference(canonicalize,[],[fact_3368_real__of__int__abs]) ).
fof(normalize_0_33,plain,
! [X] : hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)),
inference(specialize,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [V] : hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) = hAPP(int,real,number_number_of(real),V),
inference(canonicalize,[],[fact_3346_real__number__of]) ).
fof(normalize_0_35,plain,
! [V] : hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) = hAPP(int,real,number_number_of(real),V),
inference(specialize,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
! [M] : hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)) = hAPP(int,int,abs_abs(int),M),
inference(canonicalize,[],[fact_3478_zgcd__0]) ).
fof(normalize_0_37,plain,
! [M] : hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)) = hAPP(int,int,abs_abs(int),M),
inference(specialize,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
pls = zero_zero(int),
inference(canonicalize,[],[fact_76_Pls__def]) ).
fof(normalize_0_39,plain,
! [I_1,J_2] : hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),I_1)),J_2) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2),
inference(canonicalize,[],[fact_3468_zgcd__zminus]) ).
fof(normalize_0_40,plain,
! [I_1,J_2] : hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),I_1)),J_2) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2),
inference(specialize,[],[normalize_0_39]) ).
fof(normalize_0_41,plain,
! [Z_1] : hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,Z_1)),hAPP(complex,real,im,Z_1)) = Z_1,
inference(canonicalize,[],[fact_3025_complex__surj]) ).
fof(normalize_0_42,plain,
! [Z_1] : hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,Z_1)),hAPP(complex,real,im,Z_1)) = Z_1,
inference(specialize,[],[normalize_0_41]) ).
fof(normalize_0_43,plain,
! [X] : hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,X)),
inference(canonicalize,[],[fact_3029_Re_Ominus]) ).
fof(normalize_0_44,plain,
! [X] : hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,X)),
inference(specialize,[],[normalize_0_43]) ).
fof(normalize_0_45,plain,
! [Z_1] : hAPP(complex,real,re,hAPP(real,complex,of_real(complex),Z_1)) = Z_1,
inference(canonicalize,[],[fact_3018_Re__complex__of__real]) ).
fof(normalize_0_46,plain,
! [Z_1] : hAPP(complex,real,re,hAPP(real,complex,of_real(complex),Z_1)) = Z_1,
inference(specialize,[],[normalize_0_45]) ).
fof(normalize_0_47,plain,
! [Z_1] : hAPP(complex,real,im,hAPP(real,complex,of_real(complex),Z_1)) = zero_zero(real),
inference(canonicalize,[],[fact_2999_Im__complex__of__real]) ).
fof(normalize_0_48,plain,
! [Z_1] : hAPP(complex,real,im,hAPP(real,complex,of_real(complex),Z_1)) = zero_zero(real),
inference(specialize,[],[normalize_0_47]) ).
fof(normalize_0_49,plain,
! [X] : hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X)) = hAPP(real,complex,of_real(complex),X),
inference(canonicalize,[],[fact_2954_complex__cnj__complex__of__real]) ).
fof(normalize_0_50,plain,
! [X] : hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X)) = hAPP(real,complex,of_real(complex),X),
inference(specialize,[],[normalize_0_49]) ).
fof(normalize_0_51,plain,
! [X] : hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)),
inference(canonicalize,[],[fact_3005_Im_Ominus]) ).
fof(normalize_0_52,plain,
! [X] : hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)),
inference(specialize,[],[normalize_0_51]) ).
fof(normalize_0_53,plain,
! [X] : hAPP(complex,real,im,hAPP(complex,complex,cnj,X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)),
inference(canonicalize,[],[fact_2998_complex__Im__cnj]) ).
fof(normalize_0_54,plain,
! [X] : hAPP(complex,real,im,hAPP(complex,complex,cnj,X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)),
inference(specialize,[],[normalize_0_53]) ).
fof(normalize_0_55,plain,
! [X] : hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)),
inference(canonicalize,[],[fact_3367_real__of__int__minus]) ).
fof(normalize_0_56,plain,
! [X] : hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)),
inference(specialize,[],[normalize_0_55]) ).
fof(normalize_0_57,plain,
! [N] : hAPP(complex,real,im,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = zero_zero(real),
inference(canonicalize,[],[fact_3007_complex__Im__of__nat]) ).
fof(normalize_0_58,plain,
! [N] : hAPP(complex,real,im,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = zero_zero(real),
inference(specialize,[],[normalize_0_57]) ).
fof(normalize_0_59,plain,
! [N] : hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,real,real_1(nat),N),
inference(canonicalize,[],[fact_3363_real__of__int__of__nat__eq]) ).
fof(normalize_0_60,plain,
! [N] : hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,real,real_1(nat),N),
inference(specialize,[],[normalize_0_59]) ).
fof(normalize_0_61,plain,
! [N] : hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = hAPP(nat,real,semiring_1_of_nat(real),N),
inference(canonicalize,[],[fact_3032_complex__Re__of__nat]) ).
fof(normalize_0_62,plain,
! [N] : hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = hAPP(nat,real,semiring_1_of_nat(real),N),
inference(specialize,[],[normalize_0_61]) ).
fof(normalize_0_63,plain,
real_1(nat) = semiring_1_of_nat(real),
inference(canonicalize,[],[fact_2379_real__eq__of__nat]) ).
fof(normalize_0_64,plain,
! [X] : hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X)) = hAPP(nat,real,real_1(nat),X),
inference(canonicalize,[],[fact_2373_abs__real__of__nat__cancel]) ).
fof(normalize_0_65,plain,
! [X] : hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X)) = hAPP(nat,real,real_1(nat),X),
inference(specialize,[],[normalize_0_64]) ).
fof(normalize_0_66,plain,
! [N] : hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),N)) = N,
inference(canonicalize,[],[fact_984_nat__int]) ).
fof(normalize_0_67,plain,
! [N] : hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),N)) = N,
inference(specialize,[],[normalize_0_66]) ).
fof(normalize_0_68,plain,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_69,plain,
! [M,N] : hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M)),N) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)),
inference(canonicalize,[],[fact_20_zpower__int]) ).
fof(normalize_0_70,plain,
! [M,N] : hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M)),N) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)),
inference(specialize,[],[normalize_0_69]) ).
fof(normalize_0_71,plain,
! [M] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M)),
inference(canonicalize,[],[fact_1450_int__Suc]) ).
fof(normalize_0_72,plain,
! [M] : hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M)),
inference(specialize,[],[normalize_0_71]) ).
fof(normalize_0_73,plain,
hAPP(int,nat,nat_1,zero_zero(int)) = zero_zero(nat),
inference(canonicalize,[],[fact_997_nat__0]) ).
fof(normalize_0_74,plain,
hAPP(real,real,sqrt,zero_zero(real)) = zero_zero(real),
inference(canonicalize,[],[fact_2127_real__sqrt__zero]) ).
fof(normalize_0_75,plain,
hAPP(nat,real,real_1(nat),zero_zero(nat)) = zero_zero(real),
inference(canonicalize,[],[fact_2380_real__of__nat__zero]) ).
fof(normalize_0_76,plain,
! [N] : hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)) = ti(int,N),
inference(canonicalize,[],[fact_3366_ceiling__real__of__int]) ).
fof(normalize_0_77,plain,
! [N] : hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)) = ti(int,N),
inference(specialize,[],[normalize_0_76]) ).
fof(normalize_0_78,plain,
hAPP(int,real,real_1(int),zero_zero(int)) = zero_zero(real),
inference(canonicalize,[],[fact_3348_real__of__int__zero]) ).
fof(normalize_0_79,plain,
ti(int,pls) = pls,
inference(canonicalize,[],[tsy_c_Int_OPls_res]) ).
fof(normalize_0_80,plain,
! [W,Z_1] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),W) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z_1),
inference(canonicalize,[],[fact_47_zadd__commute]) ).
fof(normalize_0_81,plain,
! [W,Z_1] : hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),W) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z_1),
inference(specialize,[],[normalize_0_80]) ).
fof(normalize_0_82,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_303_succ__def]) ).
fof(normalize_0_83,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_82]) ).
fof(normalize_0_84,plain,
! [Na] :
( Na != zero_zero(nat)
<=> hAPP(nat,int,semiring_1_of_nat(int),Na) != zero_zero(int) ),
inference(canonicalize,[],[fact_27_int__eq__0__conv]) ).
fof(normalize_0_85,plain,
! [Na] :
( Na != zero_zero(nat)
<=> hAPP(nat,int,semiring_1_of_nat(int),Na) != zero_zero(int) ),
inference(specialize,[],[normalize_0_84]) ).
fof(normalize_0_86,plain,
! [Na] :
( ( Na != zero_zero(nat)
| hAPP(nat,int,semiring_1_of_nat(int),Na) = zero_zero(int) )
& ( hAPP(nat,int,semiring_1_of_nat(int),Na) != zero_zero(int)
| Na = zero_zero(nat) ) ),
inference(clausify,[],[normalize_0_85]) ).
fof(normalize_0_87,plain,
! [Na] :
( hAPP(nat,int,semiring_1_of_nat(int),Na) != zero_zero(int)
| Na = zero_zero(nat) ),
inference(conjunct,[],[normalize_0_86]) ).
fof(normalize_0_88,plain,
! [M] : zero_zero(nat) != hAPP(nat,nat,suc,M),
inference(canonicalize,[],[fact_1316_Zero__neq__Suc]) ).
fof(normalize_0_89,plain,
! [M] : zero_zero(nat) != hAPP(nat,nat,suc,M),
inference(specialize,[],[normalize_0_88]) ).
cnf(refute_0_0,plain,
hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),N)) = hAPP(nat,int,semiring_1_of_nat(int),N),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n))) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)),
inference(subst,[],[refute_0_0:[bind(N,$fot(hAPP(nat,nat,suc,n)))]]) ).
cnf(refute_0_2,plain,
hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),K_4)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),K_4),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),Z_1))),hAPP(nat,nat,suc,one_one(nat))),
inference(subst,[],[refute_0_2:[bind(K_4,$fot(hAPP(nat,nat,suc,one_one(nat)))),bind(X,$fot(hAPP(complex,real,norm_norm(complex),Z_1)))]]) ).
cnf(refute_0_4,plain,
hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_6,plain,
hAPP(int,nat,number_number_of(nat),V) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1)) = hAPP(X_a,X_c,B_1_1,B_2_1),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
hAPP(int,nat,nat_1,ti(int,V)) = hAPP(int,nat,nat_1,V),
inference(subst,[],[refute_0_7:[bind(B_1_1,$fot(nat_1)),bind(B_2_1,$fot(V)),bind(X_a,$fot(int)),bind(X_c,$fot(nat))]]) ).
cnf(refute_0_9,plain,
hAPP(int,int,number_number_of(int),K_4) = ti(int,K_4),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
hAPP(int,int,number_number_of(int),V) = ti(int,V),
inference(subst,[],[refute_0_9:[bind(K_4,$fot(V))]]) ).
cnf(refute_0_11,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,[$fot(hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)))]]) ).
cnf(refute_0_12,plain,
( hAPP(int,int,number_number_of(int),V) != ti(int,V)
| hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) != hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V))
| hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) = hAPP(int,nat,nat_1,ti(int,V)) ),
introduced(tautology,[equality,[$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_13,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( $equal(hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V))) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) = hAPP(int,nat,nat_1,ti(int,V)),
inference(resolve,[$cnf( $equal(hAPP(int,int,number_number_of(int),V),ti(int,V)) )],[refute_0_10,refute_0_13]) ).
cnf(refute_0_15,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_16,plain,
( X0 != X0
| X0 != Y
| Y = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).
cnf(refute_0_17,plain,
( X0 != Y
| Y = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
( Y != X0
| Y != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_19,plain,
( X0 != Y
| Y != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y,X0) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) != hAPP(int,nat,nat_1,ti(int,V))
| hAPP(int,nat,nat_1,ti(int,V)) != hAPP(int,nat,nat_1,V)
| hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) = hAPP(int,nat,nat_1,V) ),
inference(subst,[],[refute_0_19:[bind(X0,$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_21,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( $equal(hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)),hAPP(int,nat,nat_1,ti(int,V))) )],[refute_0_14,refute_0_20]) ).
cnf(refute_0_22,plain,
hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) = hAPP(int,nat,nat_1,V),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,ti(int,V)),hAPP(int,nat,nat_1,V)) )],[refute_0_8,refute_0_21]) ).
cnf(refute_0_23,plain,
( hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)) != hAPP(int,nat,nat_1,V)
| hAPP(int,nat,number_number_of(nat),V) != hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V))
| hAPP(int,nat,number_number_of(nat),V) = hAPP(int,nat,nat_1,V) ),
introduced(tautology,[equality,[$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_24,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( $equal(hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V)),hAPP(int,nat,nat_1,V)) )],[refute_0_22,refute_0_23]) ).
cnf(refute_0_25,plain,
hAPP(int,nat,number_number_of(nat),V) = hAPP(int,nat,nat_1,V),
inference(resolve,[$cnf( $equal(hAPP(int,nat,number_number_of(nat),V),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V))) )],[refute_0_6,refute_0_24]) ).
cnf(refute_0_26,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),
inference(subst,[],[refute_0_25:[bind(V,$fot(hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))]]) ).
cnf(refute_0_27,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)))
| 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,hAPP(int,int,bit1,pls))) = 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,hAPP(int,int,bit1,pls))))]]) ).
cnf(refute_0_28,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,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) ),
inference(resolve,[$cnf( $equal(hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
one_one(nat) = hAPP(nat,nat,suc,zero_zero(nat)),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_30,plain,
( one_one(nat) != hAPP(nat,nat,suc,zero_zero(nat))
| hAPP(nat,nat,suc,zero_zero(nat)) = one_one(nat) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(one_one(nat))),bind(Y,$fot(hAPP(nat,nat,suc,zero_zero(nat))))]]) ).
cnf(refute_0_31,plain,
hAPP(nat,nat,suc,zero_zero(nat)) = one_one(nat),
inference(resolve,[$cnf( $equal(one_one(nat),hAPP(nat,nat,suc,zero_zero(nat))) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),
introduced(tautology,[refl,[$fot(hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))]]) ).
cnf(refute_0_33,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_34,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( $equal(hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(nat,nat,suc,one_one(nat)),
inference(resolve,[$cnf( $equal(hAPP(nat,nat,suc,zero_zero(nat)),one_one(nat)) )],[refute_0_31,refute_0_34]) ).
cnf(refute_0_36,plain,
( hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))
| hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))) != hAPP(nat,nat,suc,one_one(nat))
| hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,one_one(nat)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(nat,nat,suc,one_one(nat))) ),[0],$fot(hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))]]) ).
cnf(refute_0_37,plain,
( hAPP(int,nat,nat_1,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,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,one_one(nat)) ),
inference(resolve,[$cnf( $equal(hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,suc,one_one(nat))) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
( hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))
| hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,one_one(nat)) ),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) )],[refute_0_28,refute_0_37]) ).
cnf(refute_0_39,plain,
hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,one_one(nat)),
inference(resolve,[$cnf( $equal(hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) )],[refute_0_5,refute_0_38]) ).
cnf(refute_0_40,plain,
( hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(nat,nat,suc,one_one(nat))
| hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) != hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))
| hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,one_one(nat)) ),
inference(subst,[],[refute_0_19:[bind(X0,$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_41,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( $equal(hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) )],[refute_0_26,refute_0_40]) ).
cnf(refute_0_42,plain,
hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,suc,one_one(nat)),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(nat,nat,suc,one_one(nat))) )],[refute_0_39,refute_0_41]) ).
cnf(refute_0_43,plain,
hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
introduced(tautology,[refl,[$fot(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))]]) ).
cnf(refute_0_44,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,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) ),[1,3],$fot(hAPP(nat,nat,suc,one_one(nat)))]]) ).
cnf(refute_0_45,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,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) )],[refute_0_43,refute_0_44]) ).
cnf(refute_0_46,plain,
hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat))),
inference(resolve,[$cnf( $equal(hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(nat,nat,suc,one_one(nat))) )],[refute_0_42,refute_0_45]) ).
cnf(refute_0_47,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat)))) ),[0],$fot(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))]]) ).
cnf(refute_0_48,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat)))) )],[refute_0_46,refute_0_47]) ).
cnf(refute_0_49,plain,
hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat))),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) )],[refute_0_4,refute_0_48]) ).
cnf(refute_0_50,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat))) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))))),bind(Y,$fot(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat)))))]]) ).
cnf(refute_0_51,plain,
hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat))) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat)))) )],[refute_0_49,refute_0_50]) ).
cnf(refute_0_52,plain,
( hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat))) != hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1)))
| hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat)))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),Z_1))),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),Z_1))),hAPP(nat,nat,suc,one_one(nat))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),Z_1))),hAPP(nat,nat,suc,one_one(nat)))) ),[0,3],$fot(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))))]]) ).
cnf(refute_0_53,plain,
( hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat)))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),Z_1))),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),Z_1))),hAPP(nat,nat,suc,one_one(nat))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat))),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1)))) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),Z_1))),hAPP(nat,nat,suc,one_one(nat))),
inference(resolve,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(nat,nat,suc,one_one(nat)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),Z_1))),hAPP(nat,nat,suc,one_one(nat)))) )],[refute_0_3,refute_0_53]) ).
cnf(refute_0_55,plain,
hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(real,real,abs_abs(real),X),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_56,plain,
hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
introduced(tautology,[refl,[$fot(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))]]) ).
cnf(refute_0_57,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,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(nat,nat,suc,one_one(nat))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) ),[1,3],$fot(hAPP(nat,nat,suc,one_one(nat)))]]) ).
cnf(refute_0_58,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,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(nat,nat,suc,one_one(nat))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(nat,nat,suc,one_one(nat))),
inference(resolve,[$cnf( $equal(hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(nat,nat,suc,one_one(nat))) )],[refute_0_42,refute_0_58]) ).
cnf(refute_0_60,plain,
hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
inference(subst,[],[refute_0_2:[bind(K_4,$fot(hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))]]) ).
cnf(refute_0_61,plain,
( hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(nat,nat,suc,one_one(nat))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),bind(Y,$fot(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),bind(Z,$fot(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(nat,nat,suc,one_one(nat)))))]]) ).
cnf(refute_0_62,plain,
( hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(nat,nat,suc,one_one(nat))) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(nat,nat,suc,one_one(nat))),
inference(resolve,[$cnf( $equal(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(nat,nat,suc,one_one(nat)))) )],[refute_0_59,refute_0_62]) ).
cnf(refute_0_64,plain,
( hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != hAPP(real,real,abs_abs(real),X)
| hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(nat,nat,suc,one_one(nat))) = hAPP(real,real,abs_abs(real),X) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(real,real,abs_abs(real),X)) ),[0],$fot(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(nat,nat,suc,one_one(nat))))]]) ).
cnf(refute_0_65,plain,
( hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != hAPP(real,real,abs_abs(real),X)
| hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(nat,nat,suc,one_one(nat))) = hAPP(real,real,abs_abs(real),X) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(nat,nat,suc,one_one(nat)))) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(nat,nat,suc,one_one(nat))) = hAPP(real,real,abs_abs(real),X),
inference(resolve,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(real,real,abs_abs(real),X)) )],[refute_0_55,refute_0_65]) ).
cnf(refute_0_67,plain,
hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),Z_1))),hAPP(nat,nat,suc,one_one(nat))) = hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),Z_1)),
inference(subst,[],[refute_0_66:[bind(X,$fot(hAPP(complex,real,norm_norm(complex),Z_1)))]]) ).
cnf(refute_0_68,plain,
( hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),Z_1))),hAPP(nat,nat,suc,one_one(nat))) != hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),Z_1))
| hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1)))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),Z_1))),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1)))) = hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),Z_1)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),Z_1))),hAPP(nat,nat,suc,one_one(nat)))) ),[1],$fot(hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),Z_1)))]]) ).
cnf(refute_0_69,plain,
( hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1)))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),Z_1))),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1)))) = hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),Z_1)) ),
inference(resolve,[$cnf( $equal(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),Z_1))),hAPP(nat,nat,suc,one_one(nat))),hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),Z_1))) )],[refute_0_67,refute_0_68]) ).
cnf(refute_0_70,plain,
hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1)))) = hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),Z_1)),
inference(resolve,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),Z_1))),hAPP(nat,nat,suc,one_one(nat)))) )],[refute_0_54,refute_0_69]) ).
cnf(refute_0_71,plain,
hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))))) = hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),
inference(subst,[],[refute_0_70:[bind(Z_1,$fot(hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))]]) ).
cnf(refute_0_72,plain,
hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,cnj,X)),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_73,plain,
hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,cnj,hAPP(nat,complex,semiring_1_of_nat(complex),N))),
inference(subst,[],[refute_0_72:[bind(X,$fot(hAPP(nat,complex,semiring_1_of_nat(complex),N)))]]) ).
cnf(refute_0_74,plain,
hAPP(complex,complex,cnj,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = hAPP(nat,complex,semiring_1_of_nat(complex),N),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_75,plain,
( hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) != hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,cnj,hAPP(nat,complex,semiring_1_of_nat(complex),N)))
| hAPP(complex,complex,cnj,hAPP(nat,complex,semiring_1_of_nat(complex),N)) != hAPP(nat,complex,semiring_1_of_nat(complex),N)
| hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,cnj,hAPP(nat,complex,semiring_1_of_nat(complex),N)))) ),[1,3],$fot(hAPP(nat,complex,semiring_1_of_nat(complex),N))]]) ).
cnf(refute_0_76,plain,
( hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) != hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,cnj,hAPP(nat,complex,semiring_1_of_nat(complex),N)))
| hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)) ),
inference(resolve,[$cnf( $equal(hAPP(complex,complex,cnj,hAPP(nat,complex,semiring_1_of_nat(complex),N)),hAPP(nat,complex,semiring_1_of_nat(complex),N)) )],[refute_0_74,refute_0_75]) ).
cnf(refute_0_77,plain,
hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)),
inference(resolve,[$cnf( $equal(hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,cnj,hAPP(nat,complex,semiring_1_of_nat(complex),N)))) )],[refute_0_73,refute_0_76]) ).
cnf(refute_0_78,plain,
( hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) != hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))
| hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))))) != hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))
| hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) = hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))))),hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) ),[0,3,3,3],$fot(hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))]]) ).
cnf(refute_0_79,plain,
( hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))))) != hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))
| hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) = hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) ),
inference(resolve,[$cnf( $equal(hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) )],[refute_0_77,refute_0_78]) ).
cnf(refute_0_80,plain,
hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) = hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),
inference(resolve,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))))),hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) )],[refute_0_71,refute_0_79]) ).
cnf(refute_0_81,plain,
hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))),
inference(subst,[],[refute_0_49:[bind(Z_1,$fot(hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))]]) ).
cnf(refute_0_82,plain,
( hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) != hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))
| hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat)))) ),[0,3,3],$fot(hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))]]) ).
cnf(refute_0_83,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))) ),
inference(resolve,[$cnf( $equal(hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) )],[refute_0_77,refute_0_82]) ).
cnf(refute_0_84,plain,
hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat)))) )],[refute_0_81,refute_0_83]) ).
cnf(refute_0_85,plain,
hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),M)),N) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_86,plain,
hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,nat,suc,one_one(nat))) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat)))),
inference(subst,[],[refute_0_85:[bind(M,$fot(N)),bind(N,$fot(hAPP(nat,nat,suc,one_one(nat))))]]) ).
cnf(refute_0_87,plain,
hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_3),A_1)) = hAPP(real,real,abs_abs(real),R_3),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_88,plain,
hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,X_500),zero_zero(real))) = hAPP(real,real,abs_abs(real),X_500),
inference(subst,[],[refute_0_87:[bind(A_1,$fot(zero_zero(real))),bind(R_3,$fot(X_500))]]) ).
cnf(refute_0_89,plain,
hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_3),zero_zero(real)) = hAPP(real,complex,of_real(complex),R_3),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_90,plain,
hAPP(real,complex,hAPP(real,fun(real,complex),rcis,X_500),zero_zero(real)) = hAPP(real,complex,of_real(complex),X_500),
inference(subst,[],[refute_0_89:[bind(R_3,$fot(X_500))]]) ).
cnf(refute_0_91,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,X_500),zero_zero(real))) != hAPP(real,real,abs_abs(real),X_500)
| hAPP(real,complex,hAPP(real,fun(real,complex),rcis,X_500),zero_zero(real)) != hAPP(real,complex,of_real(complex),X_500)
| hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),X_500)) = hAPP(real,real,abs_abs(real),X_500) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,X_500),zero_zero(real))),hAPP(real,real,abs_abs(real),X_500)) ),[0,3],$fot(hAPP(real,complex,of_real(complex),X_500))]]) ).
cnf(refute_0_92,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,X_500),zero_zero(real))) != hAPP(real,real,abs_abs(real),X_500)
| hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),X_500)) = hAPP(real,real,abs_abs(real),X_500) ),
inference(resolve,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),rcis,X_500),zero_zero(real)),hAPP(real,complex,of_real(complex),X_500)) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),X_500)) = hAPP(real,real,abs_abs(real),X_500),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,X_500),zero_zero(real))),hAPP(real,real,abs_abs(real),X_500)) )],[refute_0_88,refute_0_92]) ).
cnf(refute_0_94,plain,
hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),Wa))) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),Wa)),
inference(subst,[],[refute_0_93:[bind(X_500,$fot(hAPP(int,real,number_number_of(real),Wa)))]]) ).
cnf(refute_0_95,plain,
( A_3 != hAPP(int,real,number_number_of(real),Wa)
| B_2 != zero_zero(real)
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_3),B_2) = hAPP(int,complex,number_number_of(complex),Wa) ),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_96,plain,
( hAPP(int,real,number_number_of(real),Wa) != hAPP(int,real,number_number_of(real),Wa)
| zero_zero(real) != zero_zero(real)
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(int,real,number_number_of(real),Wa)),zero_zero(real)) = hAPP(int,complex,number_number_of(complex),Wa) ),
inference(subst,[],[refute_0_95:[bind(A_3,$fot(hAPP(int,real,number_number_of(real),Wa))),bind(B_2,$fot(zero_zero(real)))]]) ).
cnf(refute_0_97,plain,
hAPP(int,real,number_number_of(real),Wa) = hAPP(int,real,number_number_of(real),Wa),
introduced(tautology,[refl,[$fot(hAPP(int,real,number_number_of(real),Wa))]]) ).
cnf(refute_0_98,plain,
( zero_zero(real) != zero_zero(real)
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(int,real,number_number_of(real),Wa)),zero_zero(real)) = hAPP(int,complex,number_number_of(complex),Wa) ),
inference(resolve,[$cnf( $equal(hAPP(int,real,number_number_of(real),Wa),hAPP(int,real,number_number_of(real),Wa)) )],[refute_0_97,refute_0_96]) ).
cnf(refute_0_99,plain,
zero_zero(real) = zero_zero(real),
introduced(tautology,[refl,[$fot(zero_zero(real))]]) ).
cnf(refute_0_100,plain,
hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(int,real,number_number_of(real),Wa)),zero_zero(real)) = hAPP(int,complex,number_number_of(complex),Wa),
inference(resolve,[$cnf( $equal(zero_zero(real),zero_zero(real)) )],[refute_0_99,refute_0_98]) ).
cnf(refute_0_101,plain,
hAPP(real,complex,of_real(complex),R_3) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,R_3),zero_zero(real)),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_102,plain,
( hAPP(real,complex,of_real(complex),R_3) != hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,R_3),zero_zero(real))
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,R_3),zero_zero(real)) = hAPP(real,complex,of_real(complex),R_3) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(hAPP(real,complex,of_real(complex),R_3))),bind(Y,$fot(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,R_3),zero_zero(real))))]]) ).
cnf(refute_0_103,plain,
hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,R_3),zero_zero(real)) = hAPP(real,complex,of_real(complex),R_3),
inference(resolve,[$cnf( $equal(hAPP(real,complex,of_real(complex),R_3),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,R_3),zero_zero(real))) )],[refute_0_101,refute_0_102]) ).
cnf(refute_0_104,plain,
hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(int,real,number_number_of(real),Wa)),zero_zero(real)) = hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),Wa)),
inference(subst,[],[refute_0_103:[bind(R_3,$fot(hAPP(int,real,number_number_of(real),Wa)))]]) ).
cnf(refute_0_105,plain,
( hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(int,real,number_number_of(real),Wa)),zero_zero(real)) != hAPP(int,complex,number_number_of(complex),Wa)
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(int,real,number_number_of(real),Wa)),zero_zero(real)) != hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),Wa))
| hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),Wa)) = hAPP(int,complex,number_number_of(complex),Wa) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(int,real,number_number_of(real),Wa)),zero_zero(real)),hAPP(int,complex,number_number_of(complex),Wa)) ),[0],$fot(hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),Wa)))]]) ).
cnf(refute_0_106,plain,
( hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(int,real,number_number_of(real),Wa)),zero_zero(real)) != hAPP(int,complex,number_number_of(complex),Wa)
| hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),Wa)) = hAPP(int,complex,number_number_of(complex),Wa) ),
inference(resolve,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(int,real,number_number_of(real),Wa)),zero_zero(real)),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),Wa))) )],[refute_0_104,refute_0_105]) ).
cnf(refute_0_107,plain,
hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),Wa)) = hAPP(int,complex,number_number_of(complex),Wa),
inference(resolve,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(int,real,number_number_of(real),Wa)),zero_zero(real)),hAPP(int,complex,number_number_of(complex),Wa)) )],[refute_0_100,refute_0_106]) ).
cnf(refute_0_108,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),Wa))) != hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),Wa))
| hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),Wa)) != hAPP(int,complex,number_number_of(complex),Wa)
| hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),Wa)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),Wa)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),Wa))),hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),Wa))) ),[0,3],$fot(hAPP(int,complex,number_number_of(complex),Wa))]]) ).
cnf(refute_0_109,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),Wa))) != hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),Wa))
| hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),Wa)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),Wa)) ),
inference(resolve,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),Wa)),hAPP(int,complex,number_number_of(complex),Wa)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),Wa)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),Wa)),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),Wa))),hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),Wa))) )],[refute_0_94,refute_0_109]) ).
cnf(refute_0_111,plain,
hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_112,plain,
hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) = hAPP(int,real,number_number_of(real),V),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_113,plain,
hAPP(int,real,real_1(int),ti(int,V)) = hAPP(int,real,real_1(int),V),
inference(subst,[],[refute_0_7:[bind(B_1_1,$fot(real_1(int))),bind(B_2_1,$fot(V)),bind(X_a,$fot(int)),bind(X_c,$fot(real))]]) ).
cnf(refute_0_114,plain,
hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) = hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)),
introduced(tautology,[refl,[$fot(hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)))]]) ).
cnf(refute_0_115,plain,
( hAPP(int,int,number_number_of(int),V) != ti(int,V)
| hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) != hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V))
| hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) = hAPP(int,real,real_1(int),ti(int,V)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V))) ),[1,3],$fot(ti(int,V))]]) ).
cnf(refute_0_116,plain,
( hAPP(int,int,number_number_of(int),V) != ti(int,V)
| hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) = hAPP(int,real,real_1(int),ti(int,V)) ),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V))) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) = hAPP(int,real,real_1(int),ti(int,V)),
inference(resolve,[$cnf( $equal(hAPP(int,int,number_number_of(int),V),ti(int,V)) )],[refute_0_10,refute_0_116]) ).
cnf(refute_0_118,plain,
( hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) != hAPP(int,real,real_1(int),ti(int,V))
| hAPP(int,real,real_1(int),ti(int,V)) != hAPP(int,real,real_1(int),V)
| hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) = hAPP(int,real,real_1(int),V) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)))),bind(Y,$fot(hAPP(int,real,real_1(int),ti(int,V)))),bind(Z,$fot(hAPP(int,real,real_1(int),V)))]]) ).
cnf(refute_0_119,plain,
( hAPP(int,real,real_1(int),ti(int,V)) != hAPP(int,real,real_1(int),V)
| hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) = hAPP(int,real,real_1(int),V) ),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,real,real_1(int),ti(int,V))) )],[refute_0_117,refute_0_118]) ).
cnf(refute_0_120,plain,
hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) = hAPP(int,real,real_1(int),V),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),ti(int,V)),hAPP(int,real,real_1(int),V)) )],[refute_0_113,refute_0_119]) ).
cnf(refute_0_121,plain,
( hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) != hAPP(int,real,number_number_of(real),V)
| hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) != hAPP(int,real,real_1(int),V)
| hAPP(int,real,real_1(int),V) = hAPP(int,real,number_number_of(real),V) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,real,number_number_of(real),V)) ),[0],$fot(hAPP(int,real,real_1(int),V))]]) ).
cnf(refute_0_122,plain,
( hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)) != hAPP(int,real,number_number_of(real),V)
| hAPP(int,real,real_1(int),V) = hAPP(int,real,number_number_of(real),V) ),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,real,real_1(int),V)) )],[refute_0_120,refute_0_121]) ).
cnf(refute_0_123,plain,
hAPP(int,real,real_1(int),V) = hAPP(int,real,number_number_of(real),V),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,real,number_number_of(real),V)) )],[refute_0_112,refute_0_122]) ).
cnf(refute_0_124,plain,
hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)) = hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)),
inference(subst,[],[refute_0_123:[bind(V,$fot(hAPP(int,int,abs_abs(int),X)))]]) ).
cnf(refute_0_125,plain,
( hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)) != hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X))
| hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)) != hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))
| hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)),hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))) ),[0],$fot(hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)))]]) ).
cnf(refute_0_126,plain,
( hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)) != hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))
| hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)) ),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)),hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X))) )],[refute_0_124,refute_0_125]) ).
cnf(refute_0_127,plain,
hAPP(int,real,real_1(int),X) = hAPP(int,real,number_number_of(real),X),
inference(subst,[],[refute_0_123:[bind(V,$fot(X))]]) ).
cnf(refute_0_128,plain,
hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)),
introduced(tautology,[refl,[$fot(hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)))]]) ).
cnf(refute_0_129,plain,
( hAPP(int,real,real_1(int),X) != hAPP(int,real,number_number_of(real),X)
| hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)) != hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))
| hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),X)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)),hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))) ),[1,3],$fot(hAPP(int,real,number_number_of(real),X))]]) ).
cnf(refute_0_130,plain,
( hAPP(int,real,real_1(int),X) != hAPP(int,real,number_number_of(real),X)
| hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),X)) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)),hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))) )],[refute_0_128,refute_0_129]) ).
cnf(refute_0_131,plain,
hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),X)),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),X),hAPP(int,real,number_number_of(real),X)) )],[refute_0_127,refute_0_130]) ).
cnf(refute_0_132,plain,
( hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)) != hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))
| hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)) != hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),X))
| hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)),hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),X))) ),[0],$fot(hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)))]]) ).
cnf(refute_0_133,plain,
( hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)) != hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))
| hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),X)) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X)),hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),X))) )],[refute_0_131,refute_0_132]) ).
cnf(refute_0_134,plain,
( hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)) != hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))
| hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),X)) ),
inference(resolve,[$cnf( $equal(hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)),hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))) )],[refute_0_126,refute_0_133]) ).
cnf(refute_0_135,plain,
hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),X)),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)),hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))) )],[refute_0_111,refute_0_134]) ).
cnf(refute_0_136,plain,
( hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)) != hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),X))
| hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),X)) = hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)))),bind(Y,$fot(hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),X))))]]) ).
cnf(refute_0_137,plain,
hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),X)) = hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)),
inference(resolve,[$cnf( $equal(hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X)),hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),X))) )],[refute_0_135,refute_0_136]) ).
cnf(refute_0_138,plain,
hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),Wa)) = hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),Wa)),
inference(subst,[],[refute_0_137:[bind(X,$fot(Wa))]]) ).
cnf(refute_0_139,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),Wa)) != hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),Wa))
| hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),Wa)) != hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),Wa))
| hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),Wa)) = hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),Wa)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),Wa)),hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),Wa))) ),[0],$fot(hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),Wa)))]]) ).
cnf(refute_0_140,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),Wa)) != hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),Wa))
| hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),Wa)) = hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),Wa)) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),Wa)),hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),Wa))) )],[refute_0_138,refute_0_139]) ).
cnf(refute_0_141,plain,
hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),Wa)) = hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),Wa)),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),Wa)),hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),Wa))) )],[refute_0_110,refute_0_140]) ).
cnf(refute_0_142,plain,
hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))) = hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1143))),
inference(subst,[],[refute_0_141:[bind(Wa,$fot(hAPP(int,int,uminus_uminus(int),X_1143)))]]) ).
cnf(refute_0_143,plain,
hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)) = hAPP(int,int,abs_abs(int),M),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_144,plain,
pls = zero_zero(int),
inference(canonicalize,[],[normalize_0_38]) ).
cnf(refute_0_145,plain,
( pls != zero_zero(int)
| zero_zero(int) = pls ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(pls)),bind(Y,$fot(zero_zero(int)))]]) ).
cnf(refute_0_146,plain,
zero_zero(int) = pls,
inference(resolve,[$cnf( $equal(pls,zero_zero(int)) )],[refute_0_144,refute_0_145]) ).
cnf(refute_0_147,plain,
hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)),
introduced(tautology,[refl,[$fot(hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)))]]) ).
cnf(refute_0_148,plain,
( hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)) != hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int))
| zero_zero(int) != pls
| hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),pls) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int))) ),[1,3],$fot(pls)]]) ).
cnf(refute_0_149,plain,
( zero_zero(int) != pls
| hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int))) )],[refute_0_147,refute_0_148]) ).
cnf(refute_0_150,plain,
hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),pls),
inference(resolve,[$cnf( $equal(zero_zero(int),pls) )],[refute_0_146,refute_0_149]) ).
cnf(refute_0_151,plain,
( hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)) != hAPP(int,int,abs_abs(int),M)
| hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)) != hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),pls)
| hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),pls) = hAPP(int,int,abs_abs(int),M) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)),hAPP(int,int,abs_abs(int),M)) ),[0],$fot(hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),pls))]]) ).
cnf(refute_0_152,plain,
( hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)) != hAPP(int,int,abs_abs(int),M)
| hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),pls) = hAPP(int,int,abs_abs(int),M) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),pls)) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),pls) = hAPP(int,int,abs_abs(int),M),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int)),hAPP(int,int,abs_abs(int),M)) )],[refute_0_143,refute_0_152]) ).
cnf(refute_0_154,plain,
hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),X_1139)),pls) = hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1139)),
inference(subst,[],[refute_0_153:[bind(M,$fot(hAPP(int,int,uminus_uminus(int),X_1139)))]]) ).
cnf(refute_0_155,plain,
hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),I_1)),J_2) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2),
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_156,plain,
hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),X_1139)),pls) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1139),pls),
inference(subst,[],[refute_0_155:[bind(I_1,$fot(X_1139)),bind(J_2,$fot(pls))]]) ).
cnf(refute_0_157,plain,
( hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),X_1139)),pls) != hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1139))
| hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),X_1139)),pls) != hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1139),pls)
| hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1139),pls) = hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1139)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),X_1139)),pls),hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1139))) ),[0],$fot(hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1139),pls))]]) ).
cnf(refute_0_158,plain,
( hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),X_1139)),pls) != hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1139))
| hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1139),pls) = hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1139)) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),X_1139)),pls),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1139),pls)) )],[refute_0_156,refute_0_157]) ).
cnf(refute_0_159,plain,
hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1139),pls) = hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1139)),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),X_1139)),pls),hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1139))) )],[refute_0_154,refute_0_158]) ).
cnf(refute_0_160,plain,
hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1139),pls) = hAPP(int,int,abs_abs(int),X_1139),
inference(subst,[],[refute_0_153:[bind(M,$fot(X_1139))]]) ).
cnf(refute_0_161,plain,
( hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1139),pls) != hAPP(int,int,abs_abs(int),X_1139)
| hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1139),pls) != hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1139))
| hAPP(int,int,abs_abs(int),X_1139) = hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1139)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1139),pls),hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1139))) ),[0],$fot(hAPP(int,int,abs_abs(int),X_1139))]]) ).
cnf(refute_0_162,plain,
( hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1139),pls) != hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1139))
| hAPP(int,int,abs_abs(int),X_1139) = hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1139)) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1139),pls),hAPP(int,int,abs_abs(int),X_1139)) )],[refute_0_160,refute_0_161]) ).
cnf(refute_0_163,plain,
hAPP(int,int,abs_abs(int),X_1139) = hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1139)),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1139),pls),hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1139))) )],[refute_0_159,refute_0_162]) ).
cnf(refute_0_164,plain,
hAPP(int,int,abs_abs(int),X_1143) = hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1143)),
inference(subst,[],[refute_0_163:[bind(X_1139,$fot(X_1143))]]) ).
cnf(refute_0_165,plain,
( hAPP(int,int,abs_abs(int),X_1143) != hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1143))
| hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1143)) = hAPP(int,int,abs_abs(int),X_1143) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(hAPP(int,int,abs_abs(int),X_1143))),bind(Y,$fot(hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1143))))]]) ).
cnf(refute_0_166,plain,
hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1143)) = hAPP(int,int,abs_abs(int),X_1143),
inference(resolve,[$cnf( $equal(hAPP(int,int,abs_abs(int),X_1143),hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1143))) )],[refute_0_164,refute_0_165]) ).
cnf(refute_0_167,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))) != hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1143)))
| hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1143)) != hAPP(int,int,abs_abs(int),X_1143)
| hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))) = hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))),hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1143)))) ),[1,3],$fot(hAPP(int,int,abs_abs(int),X_1143))]]) ).
cnf(refute_0_168,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))) != hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1143)))
| hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))) = hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143)) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1143)),hAPP(int,int,abs_abs(int),X_1143)) )],[refute_0_166,refute_0_167]) ).
cnf(refute_0_169,plain,
hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))) = hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143)),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))),hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),X_1143)))) )],[refute_0_142,refute_0_168]) ).
cnf(refute_0_170,plain,
hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,Z_1)),hAPP(complex,real,im,Z_1)) = Z_1,
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_171,plain,
hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)),
inference(subst,[],[refute_0_170:[bind(Z_1,$fot(hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))))]]) ).
cnf(refute_0_172,plain,
hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,X)),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_173,plain,
hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),Z_1))) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,hAPP(real,complex,of_real(complex),Z_1))),
inference(subst,[],[refute_0_172:[bind(X,$fot(hAPP(real,complex,of_real(complex),Z_1)))]]) ).
cnf(refute_0_174,plain,
hAPP(complex,real,re,hAPP(real,complex,of_real(complex),Z_1)) = Z_1,
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_175,plain,
( hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),Z_1))) != hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,hAPP(real,complex,of_real(complex),Z_1)))
| hAPP(complex,real,re,hAPP(real,complex,of_real(complex),Z_1)) != Z_1
| hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),Z_1))) = hAPP(real,real,uminus_uminus(real),Z_1) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),Z_1))),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,hAPP(real,complex,of_real(complex),Z_1)))) ),[1,3],$fot(Z_1)]]) ).
cnf(refute_0_176,plain,
( hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),Z_1))) != hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,hAPP(real,complex,of_real(complex),Z_1)))
| hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),Z_1))) = hAPP(real,real,uminus_uminus(real),Z_1) ),
inference(resolve,[$cnf( $equal(hAPP(complex,real,re,hAPP(real,complex,of_real(complex),Z_1)),Z_1) )],[refute_0_174,refute_0_175]) ).
cnf(refute_0_177,plain,
hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),Z_1))) = hAPP(real,real,uminus_uminus(real),Z_1),
inference(resolve,[$cnf( $equal(hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),Z_1))),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,hAPP(real,complex,of_real(complex),Z_1)))) )],[refute_0_173,refute_0_176]) ).
cnf(refute_0_178,plain,
hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))) = hAPP(real,real,uminus_uminus(real),X_311),
inference(subst,[],[refute_0_177:[bind(Z_1,$fot(X_311))]]) ).
cnf(refute_0_179,plain,
( hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))) != hAPP(real,real,uminus_uminus(real),X_311)
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) != hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))),hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))) ),[0,2,3],$fot(hAPP(real,real,uminus_uminus(real),X_311))]]) ).
cnf(refute_0_180,plain,
( hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) != hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)) ),
inference(resolve,[$cnf( $equal(hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))),hAPP(real,real,uminus_uminus(real),X_311)) )],[refute_0_178,refute_0_179]) ).
cnf(refute_0_181,plain,
hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)),
inference(resolve,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))),hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))) )],[refute_0_171,refute_0_180]) ).
cnf(refute_0_182,plain,
hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),zero_zero(real)) = hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),X_311)),
inference(subst,[],[refute_0_103:[bind(R_3,$fot(hAPP(real,real,uminus_uminus(real),X_311)))]]) ).
cnf(refute_0_183,plain,
hAPP(complex,real,im,hAPP(real,complex,of_real(complex),Z_1)) = zero_zero(real),
inference(canonicalize,[],[normalize_0_48]) ).
cnf(refute_0_184,plain,
hAPP(complex,real,im,hAPP(real,complex,of_real(complex),X_311)) = zero_zero(real),
inference(subst,[],[refute_0_183:[bind(Z_1,$fot(X_311))]]) ).
cnf(refute_0_185,plain,
hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X)) = hAPP(real,complex,of_real(complex),X),
inference(canonicalize,[],[normalize_0_50]) ).
cnf(refute_0_186,plain,
hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311)) = hAPP(real,complex,of_real(complex),X_311),
inference(subst,[],[refute_0_185:[bind(X,$fot(X_311))]]) ).
cnf(refute_0_187,plain,
hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))) = hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))),
introduced(tautology,[refl,[$fot(hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))))]]) ).
cnf(refute_0_188,plain,
( hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311)) != hAPP(real,complex,of_real(complex),X_311)
| hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))) != hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311)))
| hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))) = hAPP(complex,real,im,hAPP(real,complex,of_real(complex),X_311)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))),hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311)))) ),[1,3],$fot(hAPP(real,complex,of_real(complex),X_311))]]) ).
cnf(refute_0_189,plain,
( hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311)) != hAPP(real,complex,of_real(complex),X_311)
| hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))) = hAPP(complex,real,im,hAPP(real,complex,of_real(complex),X_311)) ),
inference(resolve,[$cnf( $equal(hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))),hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311)))) )],[refute_0_187,refute_0_188]) ).
cnf(refute_0_190,plain,
hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))) = hAPP(complex,real,im,hAPP(real,complex,of_real(complex),X_311)),
inference(resolve,[$cnf( $equal(hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311)),hAPP(real,complex,of_real(complex),X_311)) )],[refute_0_186,refute_0_189]) ).
cnf(refute_0_191,plain,
( hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))) != hAPP(complex,real,im,hAPP(real,complex,of_real(complex),X_311))
| hAPP(complex,real,im,hAPP(real,complex,of_real(complex),X_311)) != zero_zero(real)
| hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))) = zero_zero(real) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))))),bind(Y,$fot(hAPP(complex,real,im,hAPP(real,complex,of_real(complex),X_311)))),bind(Z,$fot(zero_zero(real)))]]) ).
cnf(refute_0_192,plain,
( hAPP(complex,real,im,hAPP(real,complex,of_real(complex),X_311)) != zero_zero(real)
| hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))) = zero_zero(real) ),
inference(resolve,[$cnf( $equal(hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))),hAPP(complex,real,im,hAPP(real,complex,of_real(complex),X_311))) )],[refute_0_190,refute_0_191]) ).
cnf(refute_0_193,plain,
hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))) = zero_zero(real),
inference(resolve,[$cnf( $equal(hAPP(complex,real,im,hAPP(real,complex,of_real(complex),X_311)),zero_zero(real)) )],[refute_0_184,refute_0_192]) ).
cnf(refute_0_194,plain,
hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)),
inference(canonicalize,[],[normalize_0_52]) ).
cnf(refute_0_195,plain,
hAPP(complex,real,im,hAPP(complex,complex,cnj,X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)),
inference(canonicalize,[],[normalize_0_54]) ).
cnf(refute_0_196,plain,
( hAPP(complex,real,im,hAPP(complex,complex,cnj,X)) != hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))
| hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)) = hAPP(complex,real,im,hAPP(complex,complex,cnj,X)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(hAPP(complex,real,im,hAPP(complex,complex,cnj,X)))),bind(Y,$fot(hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))))]]) ).
cnf(refute_0_197,plain,
hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)) = hAPP(complex,real,im,hAPP(complex,complex,cnj,X)),
inference(resolve,[$cnf( $equal(hAPP(complex,real,im,hAPP(complex,complex,cnj,X)),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))) )],[refute_0_195,refute_0_196]) ).
cnf(refute_0_198,plain,
( hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),X)) != hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))
| hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)) != hAPP(complex,real,im,hAPP(complex,complex,cnj,X))
| hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(complex,real,im,hAPP(complex,complex,cnj,X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),X)),hAPP(complex,real,im,hAPP(complex,complex,cnj,X))) ),[0],$fot(hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)))]]) ).
cnf(refute_0_199,plain,
( hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),X)) != hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))
| hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(complex,real,im,hAPP(complex,complex,cnj,X)) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,hAPP(complex,complex,cnj,X))) )],[refute_0_197,refute_0_198]) ).
cnf(refute_0_200,plain,
hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(complex,real,im,hAPP(complex,complex,cnj,X)),
inference(resolve,[$cnf( $equal(hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),X)),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))) )],[refute_0_194,refute_0_199]) ).
cnf(refute_0_201,plain,
hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))) = hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))),
inference(subst,[],[refute_0_200:[bind(X,$fot(hAPP(real,complex,of_real(complex),X_311)))]]) ).
cnf(refute_0_202,plain,
( hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))) != zero_zero(real)
| hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))) != hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311)))
| hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))) = zero_zero(real) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))))),bind(Y,$fot(hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))))),bind(Z,$fot(zero_zero(real)))]]) ).
cnf(refute_0_203,plain,
( hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))) != zero_zero(real)
| hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))) = zero_zero(real) ),
inference(resolve,[$cnf( $equal(hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))),hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311)))) )],[refute_0_201,refute_0_202]) ).
cnf(refute_0_204,plain,
hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))) = zero_zero(real),
inference(resolve,[$cnf( $equal(hAPP(complex,real,im,hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X_311))),zero_zero(real)) )],[refute_0_193,refute_0_203]) ).
cnf(refute_0_205,plain,
hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))),
introduced(tautology,[refl,[$fot(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))))]]) ).
cnf(refute_0_206,plain,
( hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))) != zero_zero(real)
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) != hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))))
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),zero_zero(real)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))))) ),[1,3],$fot(zero_zero(real))]]) ).
cnf(refute_0_207,plain,
( hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))) != zero_zero(real)
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),zero_zero(real)) ),
inference(resolve,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))))) )],[refute_0_205,refute_0_206]) ).
cnf(refute_0_208,plain,
hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),zero_zero(real)),
inference(resolve,[$cnf( $equal(hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))),zero_zero(real)) )],[refute_0_204,refute_0_207]) ).
cnf(refute_0_209,plain,
( hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) != hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),zero_zero(real))
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),zero_zero(real)) != hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),X_311))
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) = hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),X_311)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))))),bind(Y,$fot(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),zero_zero(real)))),bind(Z,$fot(hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),X_311))))]]) ).
cnf(refute_0_210,plain,
( hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),zero_zero(real)) != hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),X_311))
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) = hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),X_311)) ),
inference(resolve,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),zero_zero(real))) )],[refute_0_208,refute_0_209]) ).
cnf(refute_0_211,plain,
hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) = hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),X_311)),
inference(resolve,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),zero_zero(real)),hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),X_311))) )],[refute_0_182,refute_0_210]) ).
cnf(refute_0_212,plain,
( hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) != hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) != hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),X_311))
| hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),X_311)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))),hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))) ),[0],$fot(hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),X_311)))]]) ).
cnf(refute_0_213,plain,
( hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))) != hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))
| hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),X_311)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)) ),
inference(resolve,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))),hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),X_311))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),X_311)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)),
inference(resolve,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),X_311)),hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311)))),hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),X_311))) )],[refute_0_181,refute_0_213]) ).
cnf(refute_0_215,plain,
hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X))) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))),
inference(subst,[],[refute_0_214:[bind(X_311,$fot(hAPP(int,real,number_number_of(real),X)))]]) ).
cnf(refute_0_216,plain,
hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)),
inference(canonicalize,[],[normalize_0_56]) ).
cnf(refute_0_217,plain,
hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X)) = hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)),
inference(subst,[],[refute_0_123:[bind(V,$fot(hAPP(int,int,uminus_uminus(int),X)))]]) ).
cnf(refute_0_218,plain,
( hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X)) != hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X))
| hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X)) != hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X))
| hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X)),hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X))) ),[0],$fot(hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)))]]) ).
cnf(refute_0_219,plain,
( hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X)) != hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X))
| hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)) ),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X)),hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X))) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)),
introduced(tautology,[refl,[$fot(hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)))]]) ).
cnf(refute_0_221,plain,
( hAPP(int,real,real_1(int),X) != hAPP(int,real,number_number_of(real),X)
| hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)) != hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X))
| hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)),hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X))) ),[1,3],$fot(hAPP(int,real,number_number_of(real),X))]]) ).
cnf(refute_0_222,plain,
( hAPP(int,real,real_1(int),X) != hAPP(int,real,number_number_of(real),X)
| hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X)) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)),hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X))) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X)),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),X),hAPP(int,real,number_number_of(real),X)) )],[refute_0_127,refute_0_222]) ).
cnf(refute_0_224,plain,
( hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)) != hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X))
| hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)) != hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X))
| hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)),hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X))) ),[0],$fot(hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)))]]) ).
cnf(refute_0_225,plain,
( hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)) != hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X))
| hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X)) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)),hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
( hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X)) != hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X))
| hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X)) ),
inference(resolve,[$cnf( $equal(hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)),hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X))) )],[refute_0_219,refute_0_225]) ).
cnf(refute_0_227,plain,
hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)) = hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X)),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X)),hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X))) )],[refute_0_216,refute_0_226]) ).
cnf(refute_0_228,plain,
( hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)) != hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X))
| hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X)) = hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)))),bind(Y,$fot(hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X))))]]) ).
cnf(refute_0_229,plain,
hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X)) = hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)),
inference(resolve,[$cnf( $equal(hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)),hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X))) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
( hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X))) != hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)))
| hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X)) != hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X))
| hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X))) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X))),hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)))) ),[0,3],$fot(hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X)))]]) ).
cnf(refute_0_231,plain,
( hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X))) != hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)))
| hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X))) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X)),hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X))) )],[refute_0_229,refute_0_230]) ).
cnf(refute_0_232,plain,
hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X))) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))),
inference(resolve,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),hAPP(int,real,number_number_of(real),X))),hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)))) )],[refute_0_215,refute_0_231]) ).
cnf(refute_0_233,plain,
hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X))) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X)),
inference(subst,[],[refute_0_107:[bind(Wa,$fot(hAPP(int,int,uminus_uminus(int),X)))]]) ).
cnf(refute_0_234,plain,
( hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X))) != hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)))
| hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X))) != hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X))
| hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X))),hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)))) ),[0],$fot(hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X)))]]) ).
cnf(refute_0_235,plain,
( hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X))) != hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)))
| hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))) ),
inference(resolve,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X))),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X))) )],[refute_0_233,refute_0_234]) ).
cnf(refute_0_236,plain,
hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)) = hAPP(int,complex,number_number_of(complex),X),
inference(subst,[],[refute_0_107:[bind(Wa,$fot(X))]]) ).
cnf(refute_0_237,plain,
hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))),
introduced(tautology,[refl,[$fot(hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))))]]) ).
cnf(refute_0_238,plain,
( hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))) != hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)))
| hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)) != hAPP(int,complex,number_number_of(complex),X)
| hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))) = hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))),hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)))) ),[1,3],$fot(hAPP(int,complex,number_number_of(complex),X))]]) ).
cnf(refute_0_239,plain,
( hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)) != hAPP(int,complex,number_number_of(complex),X)
| hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))) = hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X)) ),
inference(resolve,[$cnf( $equal(hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))),hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)))) )],[refute_0_237,refute_0_238]) ).
cnf(refute_0_240,plain,
hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))) = hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X)),
inference(resolve,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)),hAPP(int,complex,number_number_of(complex),X)) )],[refute_0_236,refute_0_239]) ).
cnf(refute_0_241,plain,
( hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))) != hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X))
| hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X)) != hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)))
| hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X)),hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)))) ),[1],$fot(hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X)))]]) ).
cnf(refute_0_242,plain,
( hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X)) != hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)))
| hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X)) ),
inference(resolve,[$cnf( $equal(hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X))),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X))) )],[refute_0_240,refute_0_241]) ).
cnf(refute_0_243,plain,
( hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X))) != hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)))
| hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X)) ),
inference(resolve,[$cnf( $equal(hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X)),hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)))) )],[refute_0_235,refute_0_242]) ).
cnf(refute_0_244,plain,
hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X)),
inference(resolve,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),hAPP(int,int,uminus_uminus(int),X))),hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),X)))) )],[refute_0_232,refute_0_243]) ).
cnf(refute_0_245,plain,
hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143)),
inference(subst,[],[refute_0_244:[bind(X,$fot(X_1143))]]) ).
cnf(refute_0_246,plain,
hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))),
introduced(tautology,[refl,[$fot(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))))]]) ).
cnf(refute_0_247,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))) != hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143)))
| hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143)) != hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))
| hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))),hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143)))) ),[1,3],$fot(hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143)))]]) ).
cnf(refute_0_248,plain,
( hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143)) != hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))
| hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))) ),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))),hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143)))) )],[refute_0_246,refute_0_247]) ).
cnf(refute_0_249,plain,
hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))),
inference(resolve,[$cnf( $equal(hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143)),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))) )],[refute_0_245,refute_0_248]) ).
cnf(refute_0_250,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))) != hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143)))
| hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))) != hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143))
| hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))) = hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))),hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143))) ),[0],$fot(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))))]]) ).
cnf(refute_0_251,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))) != hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143))
| hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))) = hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143)) ),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143)))) )],[refute_0_249,refute_0_250]) ).
cnf(refute_0_252,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),Wa)) != hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),Wa))
| hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),Wa)) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),Wa)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),Wa)))),bind(Y,$fot(hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),Wa))))]]) ).
cnf(refute_0_253,plain,
hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),Wa)) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),Wa)),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),Wa)),hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),Wa))) )],[refute_0_141,refute_0_252]) ).
cnf(refute_0_254,plain,
hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143)) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),X_1143)),
inference(subst,[],[refute_0_253:[bind(Wa,$fot(X_1143))]]) ).
cnf(refute_0_255,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))) != hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143))
| hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143)) != hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),X_1143))
| hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),X_1143)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))),hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),X_1143))) ),[0],$fot(hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143)))]]) ).
cnf(refute_0_256,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))) != hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143))
| hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),X_1143)) ),
inference(resolve,[$cnf( $equal(hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143)),hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),X_1143))) )],[refute_0_254,refute_0_255]) ).
cnf(refute_0_257,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))) != hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143))
| hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),X_1143)) ),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))),hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143))) )],[refute_0_251,refute_0_256]) ).
cnf(refute_0_258,plain,
hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),X_1143))) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),X_1143)),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,uminus_uminus(int),X_1143))),hAPP(int,real,number_number_of(real),hAPP(int,int,abs_abs(int),X_1143))) )],[refute_0_169,refute_0_257]) ).
cnf(refute_0_259,plain,
hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)))) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))),
inference(subst,[],[refute_0_258:[bind(X_1143,$fot(hAPP(nat,int,semiring_1_of_nat(int),N)))]]) ).
cnf(refute_0_260,plain,
hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,real,im,hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(nat,complex,semiring_1_of_nat(complex),N),
inference(subst,[],[refute_0_170:[bind(Z_1,$fot(hAPP(nat,complex,semiring_1_of_nat(complex),N)))]]) ).
cnf(refute_0_261,plain,
hAPP(complex,real,im,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = zero_zero(real),
inference(canonicalize,[],[normalize_0_58]) ).
cnf(refute_0_262,plain,
( hAPP(complex,real,im,hAPP(nat,complex,semiring_1_of_nat(complex),N)) != zero_zero(real)
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,real,im,hAPP(nat,complex,semiring_1_of_nat(complex),N))) != hAPP(nat,complex,semiring_1_of_nat(complex),N)
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),zero_zero(real)) = hAPP(nat,complex,semiring_1_of_nat(complex),N) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,real,im,hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(nat,complex,semiring_1_of_nat(complex),N)) ),[0,3],$fot(zero_zero(real))]]) ).
cnf(refute_0_263,plain,
( hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,real,im,hAPP(nat,complex,semiring_1_of_nat(complex),N))) != hAPP(nat,complex,semiring_1_of_nat(complex),N)
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),zero_zero(real)) = hAPP(nat,complex,semiring_1_of_nat(complex),N) ),
inference(resolve,[$cnf( $equal(hAPP(complex,real,im,hAPP(nat,complex,semiring_1_of_nat(complex),N)),zero_zero(real)) )],[refute_0_261,refute_0_262]) ).
cnf(refute_0_264,plain,
hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),zero_zero(real)) = hAPP(nat,complex,semiring_1_of_nat(complex),N),
inference(resolve,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,real,im,hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(nat,complex,semiring_1_of_nat(complex),N)) )],[refute_0_260,refute_0_263]) ).
cnf(refute_0_265,plain,
hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),X_130))) = hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),X_130)),
inference(subst,[],[refute_0_107:[bind(Wa,$fot(hAPP(nat,int,semiring_1_of_nat(int),X_130)))]]) ).
cnf(refute_0_266,plain,
hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,real,real_1(nat),N),
inference(canonicalize,[],[normalize_0_60]) ).
cnf(refute_0_267,plain,
hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),N)),
inference(subst,[],[refute_0_123:[bind(V,$fot(hAPP(nat,int,semiring_1_of_nat(int),N)))]]) ).
cnf(refute_0_268,plain,
( hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N)) != hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),N))
| hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N)) != hAPP(nat,real,real_1(nat),N)
| hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,real,real_1(nat),N) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N)),hAPP(nat,real,real_1(nat),N)) ),[0],$fot(hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),N)))]]) ).
cnf(refute_0_269,plain,
( hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N)) != hAPP(nat,real,real_1(nat),N)
| hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,real,real_1(nat),N) ),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N)),hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),N))) )],[refute_0_267,refute_0_268]) ).
cnf(refute_0_270,plain,
hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,real,real_1(nat),N),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N)),hAPP(nat,real,real_1(nat),N)) )],[refute_0_266,refute_0_269]) ).
cnf(refute_0_271,plain,
hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),X_130)) = hAPP(nat,real,real_1(nat),X_130),
inference(subst,[],[refute_0_270:[bind(N,$fot(X_130))]]) ).
cnf(refute_0_272,plain,
( hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),X_130)) != hAPP(nat,real,real_1(nat),X_130)
| hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),X_130))) != hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),X_130))
| hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130)) = hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),X_130)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),X_130))),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),X_130))) ),[0,3],$fot(hAPP(nat,real,real_1(nat),X_130))]]) ).
cnf(refute_0_273,plain,
( hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),X_130))) != hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),X_130))
| hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130)) = hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),X_130)) ),
inference(resolve,[$cnf( $equal(hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),X_130)),hAPP(nat,real,real_1(nat),X_130)) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130)) = hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),X_130)),
inference(resolve,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),X_130))),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),X_130))) )],[refute_0_265,refute_0_273]) ).
cnf(refute_0_275,plain,
hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),N)) = hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)),
inference(subst,[],[refute_0_274:[bind(X_130,$fot(N))]]) ).
cnf(refute_0_276,plain,
hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = hAPP(nat,real,semiring_1_of_nat(real),N),
inference(canonicalize,[],[normalize_0_62]) ).
cnf(refute_0_277,plain,
real_1(nat) = semiring_1_of_nat(real),
inference(canonicalize,[],[normalize_0_63]) ).
cnf(refute_0_278,plain,
( real_1(nat) != semiring_1_of_nat(real)
| semiring_1_of_nat(real) = real_1(nat) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(real_1(nat))),bind(Y,$fot(semiring_1_of_nat(real)))]]) ).
cnf(refute_0_279,plain,
semiring_1_of_nat(real) = real_1(nat),
inference(resolve,[$cnf( $equal(real_1(nat),semiring_1_of_nat(real)) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
hAPP(nat,real,semiring_1_of_nat(real),N) = hAPP(nat,real,semiring_1_of_nat(real),N),
introduced(tautology,[refl,[$fot(hAPP(nat,real,semiring_1_of_nat(real),N))]]) ).
cnf(refute_0_281,plain,
( hAPP(nat,real,semiring_1_of_nat(real),N) != hAPP(nat,real,semiring_1_of_nat(real),N)
| semiring_1_of_nat(real) != real_1(nat)
| hAPP(nat,real,semiring_1_of_nat(real),N) = hAPP(nat,real,real_1(nat),N) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,real,semiring_1_of_nat(real),N),hAPP(nat,real,semiring_1_of_nat(real),N)) ),[1,2],$fot(real_1(nat))]]) ).
cnf(refute_0_282,plain,
( semiring_1_of_nat(real) != real_1(nat)
| hAPP(nat,real,semiring_1_of_nat(real),N) = hAPP(nat,real,real_1(nat),N) ),
inference(resolve,[$cnf( $equal(hAPP(nat,real,semiring_1_of_nat(real),N),hAPP(nat,real,semiring_1_of_nat(real),N)) )],[refute_0_280,refute_0_281]) ).
cnf(refute_0_283,plain,
hAPP(nat,real,semiring_1_of_nat(real),N) = hAPP(nat,real,real_1(nat),N),
inference(resolve,[$cnf( $equal(semiring_1_of_nat(real),real_1(nat)) )],[refute_0_279,refute_0_282]) ).
cnf(refute_0_284,plain,
( hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)) != hAPP(nat,real,semiring_1_of_nat(real),N)
| hAPP(nat,real,semiring_1_of_nat(real),N) != hAPP(nat,real,real_1(nat),N)
| hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = hAPP(nat,real,real_1(nat),N) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)),hAPP(nat,real,real_1(nat),N)) ),[0],$fot(hAPP(nat,real,semiring_1_of_nat(real),N))]]) ).
cnf(refute_0_285,plain,
( hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)) != hAPP(nat,real,semiring_1_of_nat(real),N)
| hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = hAPP(nat,real,real_1(nat),N) ),
inference(resolve,[$cnf( $equal(hAPP(nat,real,semiring_1_of_nat(real),N),hAPP(nat,real,real_1(nat),N)) )],[refute_0_283,refute_0_284]) ).
cnf(refute_0_286,plain,
hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = hAPP(nat,real,real_1(nat),N),
inference(resolve,[$cnf( $equal(hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)),hAPP(nat,real,semiring_1_of_nat(real),N)) )],[refute_0_276,refute_0_285]) ).
cnf(refute_0_287,plain,
hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),
introduced(tautology,[refl,[$fot(hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))))]]) ).
cnf(refute_0_288,plain,
( hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)) != hAPP(nat,real,real_1(nat),N)
| hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))) != hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)))
| hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),N)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)))) ),[1,3],$fot(hAPP(nat,real,real_1(nat),N))]]) ).
cnf(refute_0_289,plain,
( hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)) != hAPP(nat,real,real_1(nat),N)
| hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),N)) ),
inference(resolve,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)))) )],[refute_0_287,refute_0_288]) ).
cnf(refute_0_290,plain,
hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),N)),
inference(resolve,[$cnf( $equal(hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)),hAPP(nat,real,real_1(nat),N)) )],[refute_0_286,refute_0_289]) ).
cnf(refute_0_291,plain,
( hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))) != hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),N))
| hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),N)) != hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))
| hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))))),bind(Y,$fot(hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),N)))),bind(Z,$fot(hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))))]]) ).
cnf(refute_0_292,plain,
( hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),N)) != hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))
| hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)) ),
inference(resolve,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),N))) )],[refute_0_290,refute_0_291]) ).
cnf(refute_0_293,plain,
hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)),
inference(resolve,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),N)),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))) )],[refute_0_275,refute_0_292]) ).
cnf(refute_0_294,plain,
hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),zero_zero(real)) = hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),
inference(subst,[],[refute_0_103:[bind(R_3,$fot(hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))))]]) ).
cnf(refute_0_295,plain,
( hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),zero_zero(real)) != hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)))
| hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))) != hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),zero_zero(real)) = hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),zero_zero(real)))),bind(Y,$fot(hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))))),bind(Z,$fot(hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))))]]) ).
cnf(refute_0_296,plain,
( hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))) != hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),zero_zero(real)) = hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)) ),
inference(resolve,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),zero_zero(real)),hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N)))) )],[refute_0_294,refute_0_295]) ).
cnf(refute_0_297,plain,
hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),zero_zero(real)) = hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)),
inference(resolve,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))) )],[refute_0_293,refute_0_296]) ).
cnf(refute_0_298,plain,
( hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),zero_zero(real)) != hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))
| hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),zero_zero(real)) != hAPP(nat,complex,semiring_1_of_nat(complex),N)
| hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,complex,semiring_1_of_nat(complex),N) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),zero_zero(real)),hAPP(nat,complex,semiring_1_of_nat(complex),N)) ),[0],$fot(hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)))]]) ).
cnf(refute_0_299,plain,
( hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),zero_zero(real)) != hAPP(nat,complex,semiring_1_of_nat(complex),N)
| hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,complex,semiring_1_of_nat(complex),N) ),
inference(resolve,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),zero_zero(real)),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))) )],[refute_0_297,refute_0_298]) ).
cnf(refute_0_300,plain,
hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,complex,semiring_1_of_nat(complex),N),
inference(resolve,[$cnf( $equal(hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,hAPP(nat,complex,semiring_1_of_nat(complex),N))),zero_zero(real)),hAPP(nat,complex,semiring_1_of_nat(complex),N)) )],[refute_0_264,refute_0_299]) ).
cnf(refute_0_301,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)))) != hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)))
| hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)) != hAPP(nat,complex,semiring_1_of_nat(complex),N)
| hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)))),hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)))) ),[0,3,3],$fot(hAPP(nat,complex,semiring_1_of_nat(complex),N))]]) ).
cnf(refute_0_302,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)))) != hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)))
| hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))) ),
inference(resolve,[$cnf( $equal(hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)),hAPP(nat,complex,semiring_1_of_nat(complex),N)) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)))),hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)))) )],[refute_0_259,refute_0_302]) ).
cnf(refute_0_304,plain,
hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130))) = hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X_130)),
inference(subst,[],[refute_0_93:[bind(X_500,$fot(hAPP(nat,real,real_1(nat),X_130)))]]) ).
cnf(refute_0_305,plain,
hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),X_130)) = hAPP(nat,complex,semiring_1_of_nat(complex),X_130),
inference(subst,[],[refute_0_300:[bind(N,$fot(X_130))]]) ).
cnf(refute_0_306,plain,
( hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),X_130)) != hAPP(nat,complex,semiring_1_of_nat(complex),X_130)
| hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130)) != hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),X_130))
| hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130)) = hAPP(nat,complex,semiring_1_of_nat(complex),X_130) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130)),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),X_130))) ),[1],$fot(hAPP(nat,complex,semiring_1_of_nat(complex),X_130))]]) ).
cnf(refute_0_307,plain,
( hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130)) != hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),X_130))
| hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130)) = hAPP(nat,complex,semiring_1_of_nat(complex),X_130) ),
inference(resolve,[$cnf( $equal(hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),X_130)),hAPP(nat,complex,semiring_1_of_nat(complex),X_130)) )],[refute_0_305,refute_0_306]) ).
cnf(refute_0_308,plain,
hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130)) = hAPP(nat,complex,semiring_1_of_nat(complex),X_130),
inference(resolve,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130)),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),X_130))) )],[refute_0_274,refute_0_307]) ).
cnf(refute_0_309,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130))) != hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X_130))
| hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130)) != hAPP(nat,complex,semiring_1_of_nat(complex),X_130)
| hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),X_130)) = hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X_130)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130))),hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X_130))) ),[0,3],$fot(hAPP(nat,complex,semiring_1_of_nat(complex),X_130))]]) ).
cnf(refute_0_310,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130))) != hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X_130))
| hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),X_130)) = hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X_130)) ),
inference(resolve,[$cnf( $equal(hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130)),hAPP(nat,complex,semiring_1_of_nat(complex),X_130)) )],[refute_0_308,refute_0_309]) ).
cnf(refute_0_311,plain,
hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),X_130)) = hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X_130)),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),hAPP(nat,real,real_1(nat),X_130))),hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X_130))) )],[refute_0_304,refute_0_310]) ).
cnf(refute_0_312,plain,
hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X)) = hAPP(nat,real,real_1(nat),X),
inference(canonicalize,[],[normalize_0_65]) ).
cnf(refute_0_313,plain,
hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X_130)) = hAPP(nat,real,real_1(nat),X_130),
inference(subst,[],[refute_0_312:[bind(X,$fot(X_130))]]) ).
cnf(refute_0_314,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),X_130)) != hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X_130))
| hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X_130)) != hAPP(nat,real,real_1(nat),X_130)
| hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),X_130)) = hAPP(nat,real,real_1(nat),X_130) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),X_130)),hAPP(nat,real,real_1(nat),X_130)) ),[0],$fot(hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X_130)))]]) ).
cnf(refute_0_315,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),X_130)) != hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X_130))
| hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),X_130)) = hAPP(nat,real,real_1(nat),X_130) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X_130)),hAPP(nat,real,real_1(nat),X_130)) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),X_130)) = hAPP(nat,real,real_1(nat),X_130),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),X_130)),hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X_130))) )],[refute_0_311,refute_0_315]) ).
cnf(refute_0_317,plain,
hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)) = hAPP(nat,real,real_1(nat),N),
inference(subst,[],[refute_0_316:[bind(X_130,$fot(N))]]) ).
cnf(refute_0_318,plain,
hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))),
introduced(tautology,[refl,[$fot(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))))]]) ).
cnf(refute_0_319,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))) != hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)))
| hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)) != hAPP(nat,complex,semiring_1_of_nat(complex),N)
| hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))) = hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))),hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)))) ),[1,3],$fot(hAPP(nat,complex,semiring_1_of_nat(complex),N))]]) ).
cnf(refute_0_320,plain,
( hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)) != hAPP(nat,complex,semiring_1_of_nat(complex),N)
| hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))) = hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)) ),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))),hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)))) )],[refute_0_318,refute_0_319]) ).
cnf(refute_0_321,plain,
hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))) = hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)),
inference(resolve,[$cnf( $equal(hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)),hAPP(nat,complex,semiring_1_of_nat(complex),N)) )],[refute_0_300,refute_0_320]) ).
cnf(refute_0_322,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))) != hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))
| hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)) != hAPP(nat,real,real_1(nat),N)
| hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))) = hAPP(nat,real,real_1(nat),N) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))))),bind(Y,$fot(hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),bind(Z,$fot(hAPP(nat,real,real_1(nat),N)))]]) ).
cnf(refute_0_323,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)) != hAPP(nat,real,real_1(nat),N)
| hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))) = hAPP(nat,real,real_1(nat),N) ),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))),hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) )],[refute_0_321,refute_0_322]) ).
cnf(refute_0_324,plain,
hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))) = hAPP(nat,real,real_1(nat),N),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)),hAPP(nat,real,real_1(nat),N)) )],[refute_0_317,refute_0_323]) ).
cnf(refute_0_325,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) != hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)))
| hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))) != hAPP(nat,real,real_1(nat),N)
| hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(nat,real,real_1(nat),N) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(nat,real,real_1(nat),N)) ),[0],$fot(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))))]]) ).
cnf(refute_0_326,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) != hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)))
| hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(nat,real,real_1(nat),N) ),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N))),hAPP(nat,real,real_1(nat),N)) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) = hAPP(nat,real,real_1(nat),N),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),N)))) )],[refute_0_303,refute_0_326]) ).
cnf(refute_0_328,plain,
hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),
introduced(tautology,[refl,[$fot(hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))))]]) ).
cnf(refute_0_329,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) != hAPP(nat,real,real_1(nat),N)
| hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) != hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))
| hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) ),[1,3],$fot(hAPP(nat,real,real_1(nat),N))]]) ).
cnf(refute_0_330,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) != hAPP(nat,real,real_1(nat),N)
| hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N)) ),
inference(resolve,[$cnf( $equal(hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) )],[refute_0_328,refute_0_329]) ).
cnf(refute_0_331,plain,
hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N)),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(nat,real,real_1(nat),N)) )],[refute_0_327,refute_0_330]) ).
cnf(refute_0_332,plain,
hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))),
introduced(tautology,[refl,[$fot(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))))]]) ).
cnf(refute_0_333,plain,
( hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) != hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N))
| hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,nat,suc,one_one(nat))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat)))) ),[1,2],$fot(hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N)))]]) ).
cnf(refute_0_334,plain,
( hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) != hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N))
| hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,nat,suc,one_one(nat))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat)))) )],[refute_0_332,refute_0_333]) ).
cnf(refute_0_335,plain,
hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,nat,suc,one_one(nat))),
inference(resolve,[$cnf( $equal(hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N))) )],[refute_0_331,refute_0_334]) ).
cnf(refute_0_336,plain,
( hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,nat,suc,one_one(nat))) != hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))
| hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat)))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))))),bind(Y,$fot(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,nat,suc,one_one(nat))))),bind(Z,$fot(hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))))]]) ).
cnf(refute_0_337,plain,
( hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,nat,suc,one_one(nat))) != hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))
| hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat)))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,nat,suc,one_one(nat)))) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat)))),
inference(resolve,[$cnf( $equal(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,nat,suc,one_one(nat))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))) )],[refute_0_86,refute_0_337]) ).
cnf(refute_0_339,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))) != hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))
| hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat)))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))) ),[0],$fot(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))))]]) ).
cnf(refute_0_340,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat)))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))) )],[refute_0_338,refute_0_339]) ).
cnf(refute_0_341,plain,
hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat)))),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,nat,suc,one_one(nat)))) )],[refute_0_84,refute_0_340]) ).
cnf(refute_0_342,plain,
hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) = hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))),
introduced(tautology,[refl,[$fot(hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))))]]) ).
cnf(refute_0_343,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) != hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))
| hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) != hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))))
| hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) = hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))))) ),[1,3],$fot(hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat)))))]]) ).
cnf(refute_0_344,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) != hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))
| hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) = hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))),hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))))) )],[refute_0_342,refute_0_343]) ).
cnf(refute_0_345,plain,
hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) = hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))) )],[refute_0_341,refute_0_344]) ).
cnf(refute_0_346,plain,
( hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) != hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))
| hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) != hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat)))))
| hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))) = hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))),hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) ),[0],$fot(hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))))]]) ).
cnf(refute_0_347,plain,
( hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) != hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))
| hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))) = hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))),hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat)))))) )],[refute_0_345,refute_0_346]) ).
cnf(refute_0_348,plain,
hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),N)) = hAPP(nat,real,real_1(nat),N),
inference(subst,[],[refute_0_312:[bind(X,$fot(N))]]) ).
cnf(refute_0_349,plain,
hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),
introduced(tautology,[refl,[$fot(hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))))]]) ).
cnf(refute_0_350,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) != hAPP(nat,real,real_1(nat),N)
| hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) != hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))
| hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),N)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) ),[1,3],$fot(hAPP(nat,real,real_1(nat),N))]]) ).
cnf(refute_0_351,plain,
( hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))) != hAPP(nat,real,real_1(nat),N)
| hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),N)) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) )],[refute_0_349,refute_0_350]) ).
cnf(refute_0_352,plain,
hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),N)),
inference(resolve,[$cnf( $equal(hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(nat,real,real_1(nat),N)) )],[refute_0_327,refute_0_351]) ).
cnf(refute_0_353,plain,
( hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) != hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),N))
| hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),N)) != hAPP(nat,real,real_1(nat),N)
| hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(nat,real,real_1(nat),N) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))))),bind(Y,$fot(hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),N)))),bind(Z,$fot(hAPP(nat,real,real_1(nat),N)))]]) ).
cnf(refute_0_354,plain,
( hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),N)) != hAPP(nat,real,real_1(nat),N)
| hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(nat,real,real_1(nat),N) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),N))) )],[refute_0_352,refute_0_353]) ).
cnf(refute_0_355,plain,
hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) = hAPP(nat,real,real_1(nat),N),
inference(resolve,[$cnf( $equal(hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,real_1(nat),N)) )],[refute_0_348,refute_0_354]) ).
cnf(refute_0_356,plain,
( hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))) != hAPP(nat,real,real_1(nat),N)
| hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))) != hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))
| hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))) = hAPP(nat,real,real_1(nat),N) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))),hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) ),[1],$fot(hAPP(nat,real,real_1(nat),N))]]) ).
cnf(refute_0_357,plain,
( hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))) != hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))
| hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))) = hAPP(nat,real,real_1(nat),N) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N)))),hAPP(nat,real,real_1(nat),N)) )],[refute_0_355,refute_0_356]) ).
cnf(refute_0_358,plain,
( hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) != hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))
| hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))) = hAPP(nat,real,real_1(nat),N) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))),hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) )],[refute_0_347,refute_0_357]) ).
cnf(refute_0_359,plain,
hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(nat,nat,suc,one_one(nat))))) = hAPP(nat,real,real_1(nat),N),
inference(resolve,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))),hAPP(real,real,abs_abs(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,semiring_1_of_nat(complex),N))))) )],[refute_0_80,refute_0_358]) ).
cnf(refute_0_360,plain,
hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))))) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n)),
inference(subst,[],[refute_0_359:[bind(N,$fot(hAPP(nat,nat,suc,n)))]]) ).
cnf(refute_0_361,plain,
hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),N)) = N,
inference(canonicalize,[],[normalize_0_67]) ).
cnf(refute_0_362,plain,
hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))),
inference(subst,[],[refute_0_361:[bind(N,$fot(hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))))]]) ).
cnf(refute_0_363,plain,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int),
inference(canonicalize,[],[normalize_0_68]) ).
cnf(refute_0_364,plain,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M)),N) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)),
inference(canonicalize,[],[normalize_0_70]) ).
cnf(refute_0_365,plain,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat))) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))),
inference(subst,[],[refute_0_364:[bind(M,$fot(hAPP(nat,nat,suc,n))),bind(N,$fot(hAPP(nat,nat,suc,one_one(nat))))]]) ).
cnf(refute_0_366,plain,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
introduced(tautology,[refl,[$fot(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))]]) ).
cnf(refute_0_367,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),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),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),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),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),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),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),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) ),[1,3],$fot(hAPP(nat,nat,suc,one_one(nat)))]]) ).
cnf(refute_0_368,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),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),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),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) )],[refute_0_366,refute_0_367]) ).
cnf(refute_0_369,plain,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat))),
inference(resolve,[$cnf( $equal(hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))),hAPP(nat,nat,suc,one_one(nat))) )],[refute_0_42,refute_0_368]) ).
cnf(refute_0_370,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M)),
inference(canonicalize,[],[normalize_0_72]) ).
cnf(refute_0_371,plain,
( hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M))
| hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)))),bind(Y,$fot(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M))))]]) ).
cnf(refute_0_372,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)),
inference(resolve,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M))) )],[refute_0_370,refute_0_371]) ).
cnf(refute_0_373,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)),
inference(subst,[],[refute_0_372:[bind(M,$fot(n))]]) ).
cnf(refute_0_374,plain,
hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),
introduced(tautology,[refl,[$fot(hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))))]]) ).
cnf(refute_0_375,plain,
( hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) != hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))
| hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)) != hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))
| hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) ),[1,3],$fot(hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)))]]) ).
cnf(refute_0_376,plain,
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)) != hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))
| hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))) ),
inference(resolve,[$cnf( $equal(hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)))) )],[refute_0_374,refute_0_375]) ).
cnf(refute_0_377,plain,
hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) = hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n)),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))) )],[refute_0_373,refute_0_376]) ).
cnf(refute_0_378,plain,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
introduced(tautology,[refl,[$fot(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))]]) ).
cnf(refute_0_379,plain,
( hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) != hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)))
| hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),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),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),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),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),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),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) ),[1,2],$fot(hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))))]]) ).
cnf(refute_0_380,plain,
( hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))) != hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)))
| hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),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),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) )],[refute_0_378,refute_0_379]) ).
cnf(refute_0_381,plain,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),
inference(resolve,[$cnf( $equal(hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)))) )],[refute_0_377,refute_0_380]) ).
cnf(refute_0_382,plain,
( hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))
| hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),bind(Y,$fot(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),bind(Z,$fot(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat)))))]]) ).
cnf(refute_0_383,plain,
( hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),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),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),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),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) )],[refute_0_381,refute_0_382]) ).
cnf(refute_0_384,plain,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat))),
inference(resolve,[$cnf( $equal(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat)))) )],[refute_0_369,refute_0_383]) ).
cnf(refute_0_385,plain,
( hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat))) != hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))))
| hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),bind(Y,$fot(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat))))),bind(Z,$fot(hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))))))]]) ).
cnf(refute_0_386,plain,
( hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat))) != hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))))
| hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat)))) )],[refute_0_384,refute_0_385]) ).
cnf(refute_0_387,plain,
hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))),
inference(resolve,[$cnf( $equal(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))),hAPP(nat,nat,suc,one_one(nat))),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))))) )],[refute_0_365,refute_0_386]) ).
cnf(refute_0_388,plain,
( hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))))
| hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int)
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))) = zero_zero(int) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),zero_zero(int)) ),[0],$fot(hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))))]]) ).
cnf(refute_0_389,plain,
( hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int)
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))) = zero_zero(int) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))))) )],[refute_0_387,refute_0_388]) ).
cnf(refute_0_390,plain,
( hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))) != zero_zero(int)
| zero_zero(int) != pls
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))) = pls ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))),pls) ),[0],$fot(zero_zero(int))]]) ).
cnf(refute_0_391,plain,
( hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))) != zero_zero(int)
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))) = pls ),
inference(resolve,[$cnf( $equal(zero_zero(int),pls) )],[refute_0_146,refute_0_390]) ).
cnf(refute_0_392,plain,
( hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int)
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))) = pls ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))),zero_zero(int)) )],[refute_0_389,refute_0_391]) ).
cnf(refute_0_393,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))) = pls,
inference(resolve,[$cnf( $equal(hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),n))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),zero_zero(int)) )],[refute_0_363,refute_0_392]) ).
cnf(refute_0_394,plain,
( hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))))) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))) != pls
| hAPP(int,nat,nat_1,pls) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))) ),[0,3],$fot(pls)]]) ).
cnf(refute_0_395,plain,
( hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))))) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(int,nat,nat_1,pls) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))),pls) )],[refute_0_393,refute_0_394]) ).
cnf(refute_0_396,plain,
hAPP(int,nat,nat_1,pls) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))) )],[refute_0_362,refute_0_395]) ).
cnf(refute_0_397,plain,
hAPP(int,nat,nat_1,zero_zero(int)) = zero_zero(nat),
inference(canonicalize,[],[normalize_0_73]) ).
cnf(refute_0_398,plain,
hAPP(int,nat,nat_1,zero_zero(int)) = hAPP(int,nat,nat_1,zero_zero(int)),
introduced(tautology,[refl,[$fot(hAPP(int,nat,nat_1,zero_zero(int)))]]) ).
cnf(refute_0_399,plain,
( hAPP(int,nat,nat_1,zero_zero(int)) != hAPP(int,nat,nat_1,zero_zero(int))
| zero_zero(int) != pls
| hAPP(int,nat,nat_1,zero_zero(int)) = hAPP(int,nat,nat_1,pls) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,nat,nat_1,zero_zero(int)),hAPP(int,nat,nat_1,zero_zero(int))) ),[1,3],$fot(pls)]]) ).
cnf(refute_0_400,plain,
( zero_zero(int) != pls
| hAPP(int,nat,nat_1,zero_zero(int)) = hAPP(int,nat,nat_1,pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,zero_zero(int)),hAPP(int,nat,nat_1,zero_zero(int))) )],[refute_0_398,refute_0_399]) ).
cnf(refute_0_401,plain,
hAPP(int,nat,nat_1,zero_zero(int)) = hAPP(int,nat,nat_1,pls),
inference(resolve,[$cnf( $equal(zero_zero(int),pls) )],[refute_0_146,refute_0_400]) ).
cnf(refute_0_402,plain,
( hAPP(int,nat,nat_1,zero_zero(int)) != hAPP(int,nat,nat_1,pls)
| hAPP(int,nat,nat_1,zero_zero(int)) != zero_zero(nat)
| hAPP(int,nat,nat_1,pls) = zero_zero(nat) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,nat,nat_1,zero_zero(int)),zero_zero(nat)) ),[0],$fot(hAPP(int,nat,nat_1,pls))]]) ).
cnf(refute_0_403,plain,
( hAPP(int,nat,nat_1,zero_zero(int)) != zero_zero(nat)
| hAPP(int,nat,nat_1,pls) = zero_zero(nat) ),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,zero_zero(int)),hAPP(int,nat,nat_1,pls)) )],[refute_0_401,refute_0_402]) ).
cnf(refute_0_404,plain,
hAPP(int,nat,nat_1,pls) = zero_zero(nat),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,zero_zero(int)),zero_zero(nat)) )],[refute_0_397,refute_0_403]) ).
cnf(refute_0_405,plain,
( hAPP(int,nat,nat_1,pls) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(int,nat,nat_1,pls) != zero_zero(nat)
| zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,nat,nat_1,pls),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))) ),[0],$fot(zero_zero(nat))]]) ).
cnf(refute_0_406,plain,
( hAPP(int,nat,nat_1,pls) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))
| zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))) ),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,pls),zero_zero(nat)) )],[refute_0_404,refute_0_405]) ).
cnf(refute_0_407,plain,
zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))),
inference(resolve,[$cnf( $equal(hAPP(int,nat,nat_1,pls),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))) )],[refute_0_396,refute_0_406]) ).
cnf(refute_0_408,plain,
( zero_zero(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))
| hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))) = zero_zero(nat) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(zero_zero(nat))),bind(Y,$fot(hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))))]]) ).
cnf(refute_0_409,plain,
hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))) = zero_zero(nat),
inference(resolve,[$cnf( $equal(zero_zero(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat)))) )],[refute_0_407,refute_0_408]) ).
cnf(refute_0_410,plain,
( hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))) != zero_zero(nat)
| hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))))) != hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n))
| hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n))) ),[0,3,3],$fot(zero_zero(nat))]]) ).
cnf(refute_0_411,plain,
( hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))))) != hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n))
| hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n)) ),
inference(resolve,[$cnf( $equal(hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))),zero_zero(nat)) )],[refute_0_409,refute_0_410]) ).
cnf(refute_0_412,plain,
hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n)),
inference(resolve,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,n)),hAPP(nat,nat,suc,one_one(nat))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n))) )],[refute_0_360,refute_0_411]) ).
cnf(refute_0_413,plain,
hAPP(real,real,sqrt,zero_zero(real)) = zero_zero(real),
inference(canonicalize,[],[normalize_0_74]) ).
cnf(refute_0_414,plain,
hAPP(nat,real,real_1(nat),zero_zero(nat)) = zero_zero(real),
inference(canonicalize,[],[normalize_0_75]) ).
cnf(refute_0_415,plain,
hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))) = hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))),
introduced(tautology,[refl,[$fot(hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))))]]) ).
cnf(refute_0_416,plain,
( hAPP(nat,real,real_1(nat),zero_zero(nat)) != zero_zero(real)
| hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))) != hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat)))
| hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))) = hAPP(real,real,sqrt,zero_zero(real)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))),hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat)))) ),[1,3],$fot(zero_zero(real))]]) ).
cnf(refute_0_417,plain,
( hAPP(nat,real,real_1(nat),zero_zero(nat)) != zero_zero(real)
| hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))) = hAPP(real,real,sqrt,zero_zero(real)) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))),hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat)))) )],[refute_0_415,refute_0_416]) ).
cnf(refute_0_418,plain,
hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))) = hAPP(real,real,sqrt,zero_zero(real)),
inference(resolve,[$cnf( $equal(hAPP(nat,real,real_1(nat),zero_zero(nat)),zero_zero(real)) )],[refute_0_414,refute_0_417]) ).
cnf(refute_0_419,plain,
( hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))) != hAPP(real,real,sqrt,zero_zero(real))
| hAPP(real,real,sqrt,zero_zero(real)) != zero_zero(real)
| hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))) = zero_zero(real) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))))),bind(Y,$fot(hAPP(real,real,sqrt,zero_zero(real)))),bind(Z,$fot(zero_zero(real)))]]) ).
cnf(refute_0_420,plain,
( hAPP(real,real,sqrt,zero_zero(real)) != zero_zero(real)
| hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))) = zero_zero(real) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))),hAPP(real,real,sqrt,zero_zero(real))) )],[refute_0_418,refute_0_419]) ).
cnf(refute_0_421,plain,
hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))) = zero_zero(real),
inference(resolve,[$cnf( $equal(hAPP(real,real,sqrt,zero_zero(real)),zero_zero(real)) )],[refute_0_413,refute_0_420]) ).
cnf(refute_0_422,plain,
( hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))) != hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n))
| hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))) != zero_zero(real)
| zero_zero(real) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n))) ),[0],$fot(zero_zero(real))]]) ).
cnf(refute_0_423,plain,
( hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))) != hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n))
| zero_zero(real) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n)) ),
inference(resolve,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))),zero_zero(real)) )],[refute_0_421,refute_0_422]) ).
cnf(refute_0_424,plain,
zero_zero(real) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n)),
inference(resolve,[$cnf( $equal(hAPP(real,real,sqrt,hAPP(nat,real,real_1(nat),zero_zero(nat))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n))) )],[refute_0_412,refute_0_423]) ).
cnf(refute_0_425,plain,
( zero_zero(real) != hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n))
| hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n)) = zero_zero(real) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(zero_zero(real))),bind(Y,$fot(hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n))))]]) ).
cnf(refute_0_426,plain,
hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n)) = zero_zero(real),
inference(resolve,[$cnf( $equal(zero_zero(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n))) )],[refute_0_424,refute_0_425]) ).
cnf(refute_0_427,plain,
( hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n)) != zero_zero(real)
| hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n))) != hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))
| hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n))),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))) ),[0,3],$fot(zero_zero(real))]]) ).
cnf(refute_0_428,plain,
( hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n))) != hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))
| hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)) ),
inference(resolve,[$cnf( $equal(hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n)),zero_zero(real)) )],[refute_0_426,refute_0_427]) ).
cnf(refute_0_429,plain,
hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)),
inference(resolve,[$cnf( $equal(hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,n))),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))) )],[refute_0_1,refute_0_428]) ).
cnf(refute_0_430,plain,
hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)) = ti(int,N),
inference(canonicalize,[],[normalize_0_77]) ).
cnf(refute_0_431,plain,
hAPP(int,real,real_1(int),N) = hAPP(int,real,number_number_of(real),N),
inference(subst,[],[refute_0_123:[bind(V,$fot(N))]]) ).
cnf(refute_0_432,plain,
hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)),
introduced(tautology,[refl,[$fot(hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)))]]) ).
cnf(refute_0_433,plain,
( hAPP(int,real,real_1(int),N) != hAPP(int,real,number_number_of(real),N)
| hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)) != hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N))
| hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),N)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)),hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N))) ),[1,3],$fot(hAPP(int,real,number_number_of(real),N))]]) ).
cnf(refute_0_434,plain,
( hAPP(int,real,real_1(int),N) != hAPP(int,real,number_number_of(real),N)
| hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),N)) ),
inference(resolve,[$cnf( $equal(hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)),hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N))) )],[refute_0_432,refute_0_433]) ).
cnf(refute_0_435,plain,
hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),N)),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),N),hAPP(int,real,number_number_of(real),N)) )],[refute_0_431,refute_0_434]) ).
cnf(refute_0_436,plain,
( hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)) != hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),N))
| hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)) != ti(int,N)
| hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),N)) = ti(int,N) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)),ti(int,N)) ),[0],$fot(hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),N)))]]) ).
cnf(refute_0_437,plain,
( hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)) != ti(int,N)
| hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),N)) = ti(int,N) ),
inference(resolve,[$cnf( $equal(hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)),hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),N))) )],[refute_0_435,refute_0_436]) ).
cnf(refute_0_438,plain,
hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),N)) = ti(int,N),
inference(resolve,[$cnf( $equal(hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)),ti(int,N)) )],[refute_0_430,refute_0_437]) ).
cnf(refute_0_439,plain,
hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),pls)) = ti(int,pls),
inference(subst,[],[refute_0_438:[bind(N,$fot(pls))]]) ).
cnf(refute_0_440,plain,
hAPP(int,real,real_1(int),zero_zero(int)) = zero_zero(real),
inference(canonicalize,[],[normalize_0_78]) ).
cnf(refute_0_441,plain,
hAPP(int,real,number_number_of(real),zero_zero(int)) = hAPP(int,real,number_number_of(real),zero_zero(int)),
introduced(tautology,[refl,[$fot(hAPP(int,real,number_number_of(real),zero_zero(int)))]]) ).
cnf(refute_0_442,plain,
( hAPP(int,real,number_number_of(real),zero_zero(int)) != hAPP(int,real,number_number_of(real),zero_zero(int))
| zero_zero(int) != pls
| hAPP(int,real,number_number_of(real),zero_zero(int)) = hAPP(int,real,number_number_of(real),pls) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,real,number_number_of(real),zero_zero(int)),hAPP(int,real,number_number_of(real),zero_zero(int))) ),[1,3],$fot(pls)]]) ).
cnf(refute_0_443,plain,
( zero_zero(int) != pls
| hAPP(int,real,number_number_of(real),zero_zero(int)) = hAPP(int,real,number_number_of(real),pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,real,number_number_of(real),zero_zero(int)),hAPP(int,real,number_number_of(real),zero_zero(int))) )],[refute_0_441,refute_0_442]) ).
cnf(refute_0_444,plain,
hAPP(int,real,number_number_of(real),zero_zero(int)) = hAPP(int,real,number_number_of(real),pls),
inference(resolve,[$cnf( $equal(zero_zero(int),pls) )],[refute_0_146,refute_0_443]) ).
cnf(refute_0_445,plain,
hAPP(int,real,real_1(int),zero_zero(int)) = hAPP(int,real,number_number_of(real),zero_zero(int)),
inference(subst,[],[refute_0_123:[bind(V,$fot(zero_zero(int)))]]) ).
cnf(refute_0_446,plain,
( hAPP(int,real,number_number_of(real),zero_zero(int)) != hAPP(int,real,number_number_of(real),pls)
| hAPP(int,real,real_1(int),zero_zero(int)) != hAPP(int,real,number_number_of(real),zero_zero(int))
| hAPP(int,real,real_1(int),zero_zero(int)) = hAPP(int,real,number_number_of(real),pls) ),
inference(subst,[],[refute_0_19:[bind(X0,$fot(hAPP(int,real,real_1(int),zero_zero(int)))),bind(Y,$fot(hAPP(int,real,number_number_of(real),zero_zero(int)))),bind(Z,$fot(hAPP(int,real,number_number_of(real),pls)))]]) ).
cnf(refute_0_447,plain,
( hAPP(int,real,number_number_of(real),zero_zero(int)) != hAPP(int,real,number_number_of(real),pls)
| hAPP(int,real,real_1(int),zero_zero(int)) = hAPP(int,real,number_number_of(real),pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),zero_zero(int)),hAPP(int,real,number_number_of(real),zero_zero(int))) )],[refute_0_445,refute_0_446]) ).
cnf(refute_0_448,plain,
hAPP(int,real,real_1(int),zero_zero(int)) = hAPP(int,real,number_number_of(real),pls),
inference(resolve,[$cnf( $equal(hAPP(int,real,number_number_of(real),zero_zero(int)),hAPP(int,real,number_number_of(real),pls)) )],[refute_0_444,refute_0_447]) ).
cnf(refute_0_449,plain,
( hAPP(int,real,real_1(int),zero_zero(int)) != hAPP(int,real,number_number_of(real),pls)
| hAPP(int,real,real_1(int),zero_zero(int)) != zero_zero(real)
| hAPP(int,real,number_number_of(real),pls) = zero_zero(real) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,real,real_1(int),zero_zero(int)),zero_zero(real)) ),[0],$fot(hAPP(int,real,number_number_of(real),pls))]]) ).
cnf(refute_0_450,plain,
( hAPP(int,real,real_1(int),zero_zero(int)) != zero_zero(real)
| hAPP(int,real,number_number_of(real),pls) = zero_zero(real) ),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),zero_zero(int)),hAPP(int,real,number_number_of(real),pls)) )],[refute_0_448,refute_0_449]) ).
cnf(refute_0_451,plain,
hAPP(int,real,number_number_of(real),pls) = zero_zero(real),
inference(resolve,[$cnf( $equal(hAPP(int,real,real_1(int),zero_zero(int)),zero_zero(real)) )],[refute_0_440,refute_0_450]) ).
cnf(refute_0_452,plain,
( hAPP(int,real,number_number_of(real),pls) != zero_zero(real)
| hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),pls)) != ti(int,pls)
| hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) = ti(int,pls) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),pls)),ti(int,pls)) ),[0,3],$fot(zero_zero(real))]]) ).
cnf(refute_0_453,plain,
( hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),pls)) != ti(int,pls)
| hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) = ti(int,pls) ),
inference(resolve,[$cnf( $equal(hAPP(int,real,number_number_of(real),pls),zero_zero(real)) )],[refute_0_451,refute_0_452]) ).
cnf(refute_0_454,plain,
hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) = ti(int,pls),
inference(resolve,[$cnf( $equal(hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),pls)),ti(int,pls)) )],[refute_0_439,refute_0_453]) ).
cnf(refute_0_455,plain,
ti(int,pls) = pls,
inference(canonicalize,[],[normalize_0_79]) ).
cnf(refute_0_456,plain,
( hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) != ti(int,pls)
| ti(int,pls) != pls
| hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) = pls ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(real,int,archimedean_ceiling(real),zero_zero(real)),pls) ),[0],$fot(ti(int,pls))]]) ).
cnf(refute_0_457,plain,
( hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) != ti(int,pls)
| hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) = pls ),
inference(resolve,[$cnf( $equal(ti(int,pls),pls) )],[refute_0_455,refute_0_456]) ).
cnf(refute_0_458,plain,
hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) = pls,
inference(resolve,[$cnf( $equal(hAPP(real,int,archimedean_ceiling(real),zero_zero(real)),ti(int,pls)) )],[refute_0_454,refute_0_457]) ).
cnf(refute_0_459,plain,
( hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) != hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))
| hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) != pls
| pls = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(real,int,archimedean_ceiling(real),zero_zero(real)),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))) ),[0],$fot(pls)]]) ).
cnf(refute_0_460,plain,
( hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) != hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))
| pls = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)) ),
inference(resolve,[$cnf( $equal(hAPP(real,int,archimedean_ceiling(real),zero_zero(real)),pls) )],[refute_0_458,refute_0_459]) ).
cnf(refute_0_461,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),W) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z_1),
inference(canonicalize,[],[normalize_0_81]) ).
cnf(refute_0_462,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),one_one(int)),
inference(subst,[],[refute_0_461:[bind(W,$fot(hAPP(nat,int,semiring_1_of_nat(int),M))),bind(Z_1,$fot(one_one(int)))]]) ).
cnf(refute_0_463,plain,
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),one_one(int))
| hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M)) != hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M))
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),one_one(int)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),one_one(int))) ),[0],$fot(hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)))]]) ).
cnf(refute_0_464,plain,
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),one_one(int))
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),one_one(int)) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M))) )],[refute_0_372,refute_0_463]) ).
cnf(refute_0_465,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),one_one(int)),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),one_one(int))) )],[refute_0_462,refute_0_464]) ).
cnf(refute_0_466,plain,
hAPP(int,int,succ,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int)),
inference(canonicalize,[],[normalize_0_83]) ).
cnf(refute_0_467,plain,
( hAPP(int,int,succ,K_4) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int))
| hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int)) = hAPP(int,int,succ,K_4) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(hAPP(int,int,succ,K_4))),bind(Y,$fot(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int))))]]) ).
cnf(refute_0_468,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int)) = hAPP(int,int,succ,K_4),
inference(resolve,[$cnf( $equal(hAPP(int,int,succ,K_4),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int))) )],[refute_0_466,refute_0_467]) ).
cnf(refute_0_469,plain,
hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),one_one(int)) = hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M)),
inference(subst,[],[refute_0_468:[bind(K_4,$fot(hAPP(nat,int,semiring_1_of_nat(int),M)))]]) ).
cnf(refute_0_470,plain,
( hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),one_one(int)) != hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M))
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),one_one(int))
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) = hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),one_one(int))) ),[1],$fot(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M)))]]) ).
cnf(refute_0_471,plain,
( hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),one_one(int))
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) = hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M)) ),
inference(resolve,[$cnf( $equal(hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),one_one(int)),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M))) )],[refute_0_469,refute_0_470]) ).
cnf(refute_0_472,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) = hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M)),
inference(resolve,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),one_one(int))) )],[refute_0_465,refute_0_471]) ).
cnf(refute_0_473,plain,
hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)) = hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)),
inference(subst,[],[refute_0_472:[bind(M,$fot(n))]]) ).
cnf(refute_0_474,plain,
( hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)) != hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))
| pls != hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))
| pls = hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) ),
introduced(tautology,[equality,[$cnf( $equal(pls,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))) ),[1],$fot(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)))]]) ).
cnf(refute_0_475,plain,
( pls != hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))
| pls = hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n)),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) )],[refute_0_473,refute_0_474]) ).
cnf(refute_0_476,plain,
( hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) != hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))
| pls = hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)) ),
inference(resolve,[$cnf( $equal(pls,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))) )],[refute_0_460,refute_0_475]) ).
cnf(refute_0_477,plain,
pls = hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)),
inference(resolve,[$cnf( $equal(hAPP(real,int,archimedean_ceiling(real),zero_zero(real)),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,n))) )],[refute_0_429,refute_0_476]) ).
cnf(refute_0_478,plain,
( hAPP(nat,int,semiring_1_of_nat(int),Na) != zero_zero(int)
| Na = zero_zero(nat) ),
inference(canonicalize,[],[normalize_0_87]) ).
cnf(refute_0_479,plain,
( hAPP(nat,int,semiring_1_of_nat(int),Na) != pls
| zero_zero(int) != pls
| hAPP(nat,int,semiring_1_of_nat(int),Na) = zero_zero(int) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP(nat,int,semiring_1_of_nat(int),Na),zero_zero(int)) ),[1],$fot(pls)]]) ).
cnf(refute_0_480,plain,
( hAPP(nat,int,semiring_1_of_nat(int),Na) != pls
| hAPP(nat,int,semiring_1_of_nat(int),Na) = zero_zero(int) ),
inference(resolve,[$cnf( $equal(zero_zero(int),pls) )],[refute_0_146,refute_0_479]) ).
cnf(refute_0_481,plain,
( hAPP(nat,int,semiring_1_of_nat(int),Na) != pls
| Na = zero_zero(nat) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),Na),zero_zero(int)) )],[refute_0_480,refute_0_478]) ).
cnf(refute_0_482,plain,
( hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) != pls
| hAPP(nat,nat,suc,M) = zero_zero(nat) ),
inference(subst,[],[refute_0_481:[bind(Na,$fot(hAPP(nat,nat,suc,M)))]]) ).
cnf(refute_0_483,plain,
( hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M)) != pls
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) != hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M))
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) = pls ),
introduced(tautology,[equality,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M))) ),[1],$fot(pls)]]) ).
cnf(refute_0_484,plain,
( hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M)) != pls
| hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)) = pls ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)),hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M))) )],[refute_0_472,refute_0_483]) ).
cnf(refute_0_485,plain,
( hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M)) != pls
| hAPP(nat,nat,suc,M) = zero_zero(nat) ),
inference(resolve,[$cnf( $equal(hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,M)),pls) )],[refute_0_484,refute_0_482]) ).
cnf(refute_0_486,plain,
zero_zero(nat) != hAPP(nat,nat,suc,M),
inference(canonicalize,[],[normalize_0_89]) ).
cnf(refute_0_487,plain,
( hAPP(nat,nat,suc,M) != zero_zero(nat)
| zero_zero(nat) = hAPP(nat,nat,suc,M) ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(hAPP(nat,nat,suc,M))),bind(Y,$fot(zero_zero(nat)))]]) ).
cnf(refute_0_488,plain,
hAPP(nat,nat,suc,M) != zero_zero(nat),
inference(resolve,[$cnf( $equal(zero_zero(nat),hAPP(nat,nat,suc,M)) )],[refute_0_487,refute_0_486]) ).
cnf(refute_0_489,plain,
hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M)) != pls,
inference(resolve,[$cnf( $equal(hAPP(nat,nat,suc,M),zero_zero(nat)) )],[refute_0_485,refute_0_488]) ).
cnf(refute_0_490,plain,
( pls != hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M))
| hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M)) = pls ),
inference(subst,[],[refute_0_17:[bind(X0,$fot(pls)),bind(Y,$fot(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M))))]]) ).
cnf(refute_0_491,plain,
pls != hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M)),
inference(resolve,[$cnf( $equal(hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),M)),pls) )],[refute_0_490,refute_0_489]) ).
cnf(refute_0_492,plain,
pls != hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n)),
inference(subst,[],[refute_0_491:[bind(M,$fot(n))]]) ).
cnf(refute_0_493,plain,
$false,
inference(resolve,[$cnf( $equal(pls,hAPP(int,int,succ,hAPP(nat,int,semiring_1_of_nat(int),n))) )],[refute_0_477,refute_0_492]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM925+8 : TPTP v8.1.0. Released v5.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n025.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 : Fri Jul 8 02:21:29 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 68.14/68.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 68.14/68.29
% 68.14/68.29 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 68.24/68.42
%------------------------------------------------------------------------------