TSTP Solution File: NUM925+4 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM925+4 : TPTP v8.1.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Mon Jul 18 12:31:40 EDT 2022
% Result : Theorem 24.06s 24.29s
% Output : CNFRefutation 24.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 52
% Number of leaves : 141
% Syntax : Number of formulae : 492 ( 294 unt; 0 def)
% Number of atoms : 784 ( 760 equ)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 591 ( 299 ~; 286 |; 3 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 4 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 56 ( 56 usr; 34 con; 0-2 aty)
% Number of variables : 294 ( 1 sgn 99 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(fact_0_n1pos,axiom,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ).
fof(fact_34_one__add__one__is__two,axiom,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) ).
fof(fact_38_semiring__one__add__one__is__two,axiom,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) ).
fof(fact_39_semiring__one__add__one__is__two,axiom,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) ).
fof(fact_51_semiring__norm_I110_J,axiom,
one_one_int = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) ).
fof(fact_63_zero__is__num__zero,axiom,
zero_zero_int = hAPP_int_int(number_number_of_int,pls) ).
fof(fact_64_zpower__int,axiom,
! [M,N] : hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,M)),N) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,M),N)) ).
fof(fact_72_int__0,axiom,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int ).
fof(fact_73_nat__1__add__1,axiom,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) ).
fof(fact_81_one__is__num__one,axiom,
one_one_int = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) ).
fof(fact_102_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_151_Pls__def,axiom,
pls = zero_zero_int ).
fof(fact_156_Bit0__def,axiom,
! [K_2] : hAPP_int_int(bit0,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),K_2) ).
fof(fact_171_semiring__norm_I112_J,axiom,
zero_zero_int = hAPP_int_int(number_number_of_int,pls) ).
fof(fact_201_Bit1__def,axiom,
! [K_2] : hAPP_int_int(bit1,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)),K_2) ).
fof(fact_204_number__of__int,axiom,
! [N_58] : hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58)) = hAPP_nat_complex(semiri2020571505omplex,N_58) ).
fof(fact_205_number__of__int,axiom,
! [N_58] : hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58)) = hAPP_nat_real(semiri132038758t_real,N_58) ).
fof(fact_227_number__of__Bit1,axiom,
! [W_10] : hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,W_10)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10)) ).
fof(fact_471_of__nat__0,axiom,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int ).
fof(fact_857_succ__def,axiom,
! [K_2] : hAPP_int_int(succ,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),one_one_int) ).
fof(fact_1102_of__nat__mult,axiom,
! [M_18,N_30] : hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_18),N_30)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,M_18)),hAPP_nat_complex(semiri2020571505omplex,N_30)) ).
fof(fact_1476_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J,axiom,
! [M_15] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_15),M_15) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15) ).
fof(fact_1856_order__less__irrefl,axiom,
! [X_29] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),X_29)) ).
fof(fact_1869_double__number__of__Bit0,axiom,
! [W_5] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_5)) ).
fof(fact_1900_power2__eq__square,axiom,
! [A_59] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59) ).
fof(fact_2703_nat__int,axiom,
! [N] : hAPP_int_nat(nat,hAPP_nat_int(semiri1621563631at_int,N)) = N ).
fof(fact_2738_nat__0,axiom,
hAPP_int_nat(nat,zero_zero_int) = zero_zero_nat ).
fof(fact_3064_Suc__eq__plus1__left,axiom,
! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N) ).
fof(fact_3105_int__Suc,axiom,
! [M] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M)) ).
fof(fact_3514_real__sqrt__zero,axiom,
hAPP_real_real(sqrt,zero_zero_real) = zero_zero_real ).
fof(fact_3692_abs__real__of__nat__cancel,axiom,
! [X] : hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,X)) = hAPP_nat_real(real_nat,X) ).
fof(fact_3697_real__of__nat__def,axiom,
real_nat = semiri132038758t_real ).
fof(fact_3698_real__eq__of__nat,axiom,
real_nat = semiri132038758t_real ).
fof(fact_3699_real__of__nat__zero,axiom,
hAPP_nat_real(real_nat,zero_zero_nat) = zero_zero_real ).
fof(fact_3954_Complex__eq__number__of,axiom,
! [A_1,B_1,Wa] :
( hAPP_real_complex(hAPP_r265291036omplex(complex,A_1),B_1) = hAPP_int_complex(number528085621omplex,Wa)
<=> ( A_1 = hAPP_int_real(number267125858f_real,Wa)
& B_1 = zero_zero_real ) ) ).
fof(fact_3984_complex__of__real__def,axiom,
! [R_2] : of_real_complex(R_2) = hAPP_real_complex(hAPP_r265291036omplex(complex,R_2),zero_zero_real) ).
fof(fact_4019_floor__real__of__nat,axiom,
! [N] : archim1246769320r_real(hAPP_nat_real(real_nat,N)) = hAPP_nat_int(semiri1621563631at_int,N) ).
fof(fact_4071_complex__cnj__of__nat,axiom,
! [N] : hAPP_complex_complex(cnj,hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_nat_complex(semiri2020571505omplex,N) ).
fof(fact_4126_complex__Re__of__nat,axiom,
! [N] : hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_nat_real(semiri132038758t_real,N) ).
fof(fact_4132_complex__mod__sqrt__Re__mult__cnj,axiom,
! [Z_1] : hAPP_complex_real(norm_norm_complex,Z_1) = hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Z_1),hAPP_complex_complex(cnj,Z_1)))) ).
fof(fact_4257_rcis__zero__arg,axiom,
! [R_2] : rcis(R_2,zero_zero_real) = of_real_complex(R_2) ).
fof(fact_4258_complex__mod__rcis,axiom,
! [R_2,A_3] : hAPP_complex_real(norm_norm_complex,rcis(R_2,A_3)) = hAPP_real_real(abs_abs_real,R_2) ).
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(semiri1621563631at_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(semiri1621563631at_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(semiri1621563631at_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,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(canonicalize,[],[fact_0_n1pos]) ).
fof(normalize_0_1,plain,
! [M] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M)),
inference(canonicalize,[],[fact_3105_int__Suc]) ).
fof(normalize_0_2,plain,
! [M] : hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M)),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
pls = zero_zero_int,
inference(canonicalize,[],[fact_151_Pls__def]) ).
fof(normalize_0_4,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_102_zadd__commute]) ).
fof(normalize_0_5,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_4]) ).
fof(normalize_0_6,plain,
! [K_2] : hAPP_int_int(succ,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),one_one_int),
inference(canonicalize,[],[fact_857_succ__def]) ).
fof(normalize_0_7,plain,
! [K_2] : hAPP_int_int(succ,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),one_one_int),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [N] : archim1246769320r_real(hAPP_nat_real(real_nat,N)) = hAPP_nat_int(semiri1621563631at_int,N),
inference(canonicalize,[],[fact_4019_floor__real__of__nat]) ).
fof(normalize_0_9,plain,
! [N] : archim1246769320r_real(hAPP_nat_real(real_nat,N)) = hAPP_nat_int(semiri1621563631at_int,N),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [Z_1] : hAPP_complex_real(norm_norm_complex,Z_1) = hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Z_1),hAPP_complex_complex(cnj,Z_1)))),
inference(canonicalize,[],[fact_4132_complex__mod__sqrt__Re__mult__cnj]) ).
fof(normalize_0_11,plain,
! [Z_1] : hAPP_complex_real(norm_norm_complex,Z_1) = hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Z_1),hAPP_complex_complex(cnj,Z_1)))),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [N] : hAPP_complex_complex(cnj,hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_nat_complex(semiri2020571505omplex,N),
inference(canonicalize,[],[fact_4071_complex__cnj__of__nat]) ).
fof(normalize_0_13,plain,
! [N] : hAPP_complex_complex(cnj,hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_nat_complex(semiri2020571505omplex,N),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A_3,R_2] : hAPP_complex_real(norm_norm_complex,rcis(R_2,A_3)) = hAPP_real_real(abs_abs_real,R_2),
inference(canonicalize,[],[fact_4258_complex__mod__rcis]) ).
fof(normalize_0_15,plain,
! [A_3,R_2] : hAPP_complex_real(norm_norm_complex,rcis(R_2,A_3)) = hAPP_real_real(abs_abs_real,R_2),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [R_2] : rcis(R_2,zero_zero_real) = of_real_complex(R_2),
inference(canonicalize,[],[fact_4257_rcis__zero__arg]) ).
fof(normalize_0_17,plain,
! [R_2] : rcis(R_2,zero_zero_real) = of_real_complex(R_2),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [A_1,B_1,Wa] :
( hAPP_real_complex(hAPP_r265291036omplex(complex,A_1),B_1) != hAPP_int_complex(number528085621omplex,Wa)
<=> ( A_1 != hAPP_int_real(number267125858f_real,Wa)
| B_1 != zero_zero_real ) ),
inference(canonicalize,[],[fact_3954_Complex__eq__number__of]) ).
fof(normalize_0_19,plain,
! [A_1,B_1,Wa] :
( hAPP_real_complex(hAPP_r265291036omplex(complex,A_1),B_1) != hAPP_int_complex(number528085621omplex,Wa)
<=> ( A_1 != hAPP_int_real(number267125858f_real,Wa)
| B_1 != zero_zero_real ) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [A_1,B_1,Wa] :
( ( hAPP_real_complex(hAPP_r265291036omplex(complex,A_1),B_1) != hAPP_int_complex(number528085621omplex,Wa)
| A_1 = hAPP_int_real(number267125858f_real,Wa) )
& ( hAPP_real_complex(hAPP_r265291036omplex(complex,A_1),B_1) != hAPP_int_complex(number528085621omplex,Wa)
| B_1 = zero_zero_real )
& ( A_1 != hAPP_int_real(number267125858f_real,Wa)
| B_1 != zero_zero_real
| hAPP_real_complex(hAPP_r265291036omplex(complex,A_1),B_1) = hAPP_int_complex(number528085621omplex,Wa) ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A_1,B_1,Wa] :
( A_1 != hAPP_int_real(number267125858f_real,Wa)
| B_1 != zero_zero_real
| hAPP_real_complex(hAPP_r265291036omplex(complex,A_1),B_1) = hAPP_int_complex(number528085621omplex,Wa) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [R_2] : of_real_complex(R_2) = hAPP_real_complex(hAPP_r265291036omplex(complex,R_2),zero_zero_real),
inference(canonicalize,[],[fact_3984_complex__of__real__def]) ).
fof(normalize_0_23,plain,
! [R_2] : of_real_complex(R_2) = hAPP_real_complex(hAPP_r265291036omplex(complex,R_2),zero_zero_real),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [N_58] : hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58)) = hAPP_nat_real(semiri132038758t_real,N_58),
inference(canonicalize,[],[fact_205_number__of__int]) ).
fof(normalize_0_25,plain,
! [N_58] : hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58)) = hAPP_nat_real(semiri132038758t_real,N_58),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
real_nat = semiri132038758t_real,
inference(canonicalize,[],[fact_3698_real__eq__of__nat]) ).
fof(normalize_0_27,plain,
! [N_58] : hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58)) = hAPP_nat_complex(semiri2020571505omplex,N_58),
inference(canonicalize,[],[fact_204_number__of__int]) ).
fof(normalize_0_28,plain,
! [N_58] : hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58)) = hAPP_nat_complex(semiri2020571505omplex,N_58),
inference(specialize,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [X] : hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,X)) = hAPP_nat_real(real_nat,X),
inference(canonicalize,[],[fact_3692_abs__real__of__nat__cancel]) ).
fof(normalize_0_30,plain,
! [X] : hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,X)) = hAPP_nat_real(real_nat,X),
inference(specialize,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [N] : hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_nat_real(semiri132038758t_real,N),
inference(canonicalize,[],[fact_4126_complex__Re__of__nat]) ).
fof(normalize_0_32,plain,
! [N] : hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_nat_real(semiri132038758t_real,N),
inference(specialize,[],[normalize_0_31]) ).
fof(normalize_0_33,plain,
! [M_18,N_30] : hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_18),N_30)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,M_18)),hAPP_nat_complex(semiri2020571505omplex,N_30)),
inference(canonicalize,[],[fact_1102_of__nat__mult]) ).
fof(normalize_0_34,plain,
! [M_18,N_30] : hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_18),N_30)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,M_18)),hAPP_nat_complex(semiri2020571505omplex,N_30)),
inference(specialize,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [A_59] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59),
inference(canonicalize,[],[fact_1900_power2__eq__square]) ).
fof(normalize_0_36,plain,
! [A_59] : hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59),
inference(specialize,[],[normalize_0_35]) ).
fof(normalize_0_37,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),
inference(canonicalize,[],[fact_73_nat__1__add__1]) ).
fof(normalize_0_38,plain,
! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N),
inference(canonicalize,[],[fact_3064_Suc__eq__plus1__left]) ).
fof(normalize_0_39,plain,
! [N] : hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N),
inference(specialize,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
! [N] : hAPP_int_nat(nat,hAPP_nat_int(semiri1621563631at_int,N)) = N,
inference(canonicalize,[],[fact_2703_nat__int]) ).
fof(normalize_0_41,plain,
! [N] : hAPP_int_nat(nat,hAPP_nat_int(semiri1621563631at_int,N)) = N,
inference(specialize,[],[normalize_0_40]) ).
fof(normalize_0_42,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(semiri1621563631at_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_43,plain,
! [M,N] : hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,M)),N) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,M),N)),
inference(canonicalize,[],[fact_64_zpower__int]) ).
fof(normalize_0_44,plain,
! [M,N] : hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,M)),N) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,M),N)),
inference(specialize,[],[normalize_0_43]) ).
fof(normalize_0_45,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),
inference(canonicalize,[],[fact_39_semiring__one__add__one__is__two]) ).
fof(normalize_0_46,plain,
zero_zero_int = hAPP_int_int(number_number_of_int,pls),
inference(canonicalize,[],[fact_171_semiring__norm_I112_J]) ).
fof(normalize_0_47,plain,
! [W_10] : hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,W_10)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10)),
inference(canonicalize,[],[fact_227_number__of__Bit1]) ).
fof(normalize_0_48,plain,
! [W_10] : hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,W_10)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10)),
inference(specialize,[],[normalize_0_47]) ).
fof(normalize_0_49,plain,
! [K_2] : hAPP_int_int(bit1,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)),K_2),
inference(canonicalize,[],[fact_201_Bit1__def]) ).
fof(normalize_0_50,plain,
! [K_2] : hAPP_int_int(bit1,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)),K_2),
inference(specialize,[],[normalize_0_49]) ).
fof(normalize_0_51,plain,
! [W_5] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_5)),
inference(canonicalize,[],[fact_1869_double__number__of__Bit0]) ).
fof(normalize_0_52,plain,
! [W_5] : hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_5)),
inference(specialize,[],[normalize_0_51]) ).
fof(normalize_0_53,plain,
! [M_15] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_15),M_15) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15),
inference(canonicalize,[],[fact_1476_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J]) ).
fof(normalize_0_54,plain,
! [M_15] : hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_15),M_15) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15),
inference(specialize,[],[normalize_0_53]) ).
fof(normalize_0_55,plain,
! [K_2] : hAPP_int_int(bit0,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),K_2),
inference(canonicalize,[],[fact_156_Bit0__def]) ).
fof(normalize_0_56,plain,
! [K_2] : hAPP_int_int(bit0,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),K_2),
inference(specialize,[],[normalize_0_55]) ).
fof(normalize_0_57,plain,
one_one_int = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)),
inference(canonicalize,[],[fact_81_one__is__num__one]) ).
fof(normalize_0_58,plain,
hAPP_int_nat(nat,zero_zero_int) = zero_zero_nat,
inference(canonicalize,[],[fact_2738_nat__0]) ).
fof(normalize_0_59,plain,
hAPP_real_real(sqrt,zero_zero_real) = zero_zero_real,
inference(canonicalize,[],[fact_3514_real__sqrt__zero]) ).
fof(normalize_0_60,plain,
hAPP_nat_real(real_nat,zero_zero_nat) = zero_zero_real,
inference(canonicalize,[],[fact_3699_real__of__nat__zero]) ).
fof(normalize_0_61,plain,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
inference(canonicalize,[],[fact_471_of__nat__0]) ).
fof(normalize_0_62,plain,
! [X_29] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),X_29)),
inference(canonicalize,[],[fact_1856_order__less__irrefl]) ).
fof(normalize_0_63,plain,
! [X_29] : ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),X_29)),
inference(specialize,[],[normalize_0_62]) ).
cnf(refute_0_0,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))),
inference(canonicalize,[],[normalize_0_0]) ).
cnf(refute_0_1,plain,
hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M)),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
X0 = X0,
introduced(tautology,[refl,[$fot(X0)]]) ).
cnf(refute_0_3,plain,
( X0 != X0
| X0 != Y
| Y = X0 ),
introduced(tautology,[equality,[$cnf( $equal(X0,X0) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X0 != Y
| Y = X0 ),
inference(resolve,[$cnf( $equal(X0,X0) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M))
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)))),bind(Y,$fot(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M))))]]) ).
cnf(refute_0_6,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)),
inference(resolve,[$cnf( $equal(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)),
inference(subst,[],[refute_0_6:[bind(M,$fot(n))]]) ).
cnf(refute_0_8,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),
introduced(tautology,[refl,[$fot(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))]]) ).
cnf(refute_0_9,plain,
( hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) != hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))
| hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),[1,1],$fot(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))]]) ).
cnf(refute_0_10,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))
| hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) ),
inference(resolve,[$cnf( $equal(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) )],[refute_0_8,refute_0_9]) ).
cnf(refute_0_11,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) )],[refute_0_7,refute_0_10]) ).
cnf(refute_0_12,plain,
pls = zero_zero_int,
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_13,plain,
( pls != zero_zero_int
| zero_zero_int = pls ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(pls)),bind(Y,$fot(zero_zero_int))]]) ).
cnf(refute_0_14,plain,
zero_zero_int = pls,
inference(resolve,[$cnf( $equal(pls,zero_zero_int) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
hAPP_i1948725293t_bool(ord_less_int,zero_zero_int) = hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),
introduced(tautology,[refl,[$fot(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int))]]) ).
cnf(refute_0_16,plain,
( hAPP_i1948725293t_bool(ord_less_int,zero_zero_int) != hAPP_i1948725293t_bool(ord_less_int,zero_zero_int)
| zero_zero_int != pls
| hAPP_i1948725293t_bool(ord_less_int,zero_zero_int) = hAPP_i1948725293t_bool(ord_less_int,pls) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_i1948725293t_bool(ord_less_int,zero_zero_int)) ),[1,1],$fot(pls)]]) ).
cnf(refute_0_17,plain,
( zero_zero_int != pls
| hAPP_i1948725293t_bool(ord_less_int,zero_zero_int) = hAPP_i1948725293t_bool(ord_less_int,pls) ),
inference(resolve,[$cnf( $equal(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_i1948725293t_bool(ord_less_int,zero_zero_int)) )],[refute_0_15,refute_0_16]) ).
cnf(refute_0_18,plain,
hAPP_i1948725293t_bool(ord_less_int,zero_zero_int) = hAPP_i1948725293t_bool(ord_less_int,pls),
inference(resolve,[$cnf( $equal(zero_zero_int,pls) )],[refute_0_14,refute_0_17]) ).
cnf(refute_0_19,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),
introduced(tautology,[refl,[$fot(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))]]) ).
cnf(refute_0_20,plain,
( hAPP_i1948725293t_bool(ord_less_int,zero_zero_int) != hAPP_i1948725293t_bool(ord_less_int,pls)
| hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) != hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))
| hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),[1,0],$fot(hAPP_i1948725293t_bool(ord_less_int,pls))]]) ).
cnf(refute_0_21,plain,
( hAPP_i1948725293t_bool(ord_less_int,zero_zero_int) != hAPP_i1948725293t_bool(ord_less_int,pls)
| hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(resolve,[$cnf( $equal(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),
inference(resolve,[$cnf( $equal(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_i1948725293t_bool(ord_less_int,pls)) )],[refute_0_18,refute_0_21]) ).
cnf(refute_0_23,plain,
( Y != X0
| Y != Z
| X0 = Z ),
introduced(tautology,[equality,[$cnf( $equal(Y,Z) ),[0],$fot(X0)]]) ).
cnf(refute_0_24,plain,
( X0 != Y
| Y != Z
| X0 = Z ),
inference(resolve,[$cnf( $equal(Y,X0) )],[refute_0_4,refute_0_23]) ).
cnf(refute_0_25,plain,
( hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) != hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))
| hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) != hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))
| hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))),bind(Y,$fot(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))),bind(Z,$fot(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))))]]) ).
cnf(refute_0_26,plain,
( hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) != hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))
| hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) ),
inference(resolve,[$cnf( $equal(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) )],[refute_0_22,refute_0_25]) ).
cnf(refute_0_27,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),
inference(resolve,[$cnf( $equal(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))) )],[refute_0_11,refute_0_26]) ).
cnf(refute_0_28,plain,
( hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) != hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),[0],$fot(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))))]]) ).
cnf(refute_0_29,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))) ),
inference(resolve,[$cnf( $equal(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))) )],[refute_0_27,refute_0_28]) ).
cnf(refute_0_30,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))),
inference(resolve,[$cnf( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,zero_zero_int),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) )],[refute_0_0,refute_0_29]) ).
cnf(refute_0_31,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_5]) ).
cnf(refute_0_32,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),one_one_int),
inference(subst,[],[refute_0_31:[bind(W,$fot(hAPP_nat_int(semiri1621563631at_int,M))),bind(Z_1,$fot(one_one_int))]]) ).
cnf(refute_0_33,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M)) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),one_one_int)
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M)) != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M))
| hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),one_one_int) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),one_one_int)) ),[0],$fot(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)))]]) ).
cnf(refute_0_34,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M)) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),one_one_int)
| hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),one_one_int) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M)),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M))) )],[refute_0_6,refute_0_33]) ).
cnf(refute_0_35,plain,
hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),one_one_int),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,M)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),one_one_int)) )],[refute_0_32,refute_0_34]) ).
cnf(refute_0_36,plain,
hAPP_int_int(succ,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),one_one_int),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_37,plain,
( hAPP_int_int(succ,K_2) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),one_one_int)
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),one_one_int) = hAPP_int_int(succ,K_2) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(hAPP_int_int(succ,K_2))),bind(Y,$fot(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),one_one_int)))]]) ).
cnf(refute_0_38,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),one_one_int) = hAPP_int_int(succ,K_2),
inference(resolve,[$cnf( $equal(hAPP_int_int(succ,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),one_one_int)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),one_one_int) = hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,M)),
inference(subst,[],[refute_0_38:[bind(K_2,$fot(hAPP_nat_int(semiri1621563631at_int,M)))]]) ).
cnf(refute_0_40,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),one_one_int) != hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,M))
| hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),one_one_int)
| hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)) = hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,M)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),one_one_int)) ),[1],$fot(hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,M)))]]) ).
cnf(refute_0_41,plain,
( hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),one_one_int)
| hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)) = hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,M)) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),one_one_int),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,M))) )],[refute_0_39,refute_0_40]) ).
cnf(refute_0_42,plain,
hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)) = hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,M)),
inference(resolve,[$cnf( $equal(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,M)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_nat_int(semiri1621563631at_int,M)),one_one_int)) )],[refute_0_35,refute_0_41]) ).
cnf(refute_0_43,plain,
hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)) = hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)),
inference(subst,[],[refute_0_42:[bind(M,$fot(n))]]) ).
cnf(refute_0_44,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),
introduced(tautology,[refl,[$fot(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))))]]) ).
cnf(refute_0_45,plain,
( hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) != hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))
| hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)) != hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))
| hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))) ),[1,1],$fot(hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)))]]) ).
cnf(refute_0_46,plain,
( hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)) != hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))
| hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))) ),
inference(resolve,[$cnf( $equal(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))),
inference(resolve,[$cnf( $equal(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))) )],[refute_0_43,refute_0_46]) ).
cnf(refute_0_48,plain,
( hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) != hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)))
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)))) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))) ),[0],$fot(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))))]]) ).
cnf(refute_0_49,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)))) ),
inference(resolve,[$cnf( $equal(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)))) )],[refute_0_47,refute_0_48]) ).
cnf(refute_0_50,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)))),
inference(resolve,[$cnf( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))) )],[refute_0_30,refute_0_49]) ).
cnf(refute_0_51,plain,
archim1246769320r_real(hAPP_nat_real(real_nat,N)) = hAPP_nat_int(semiri1621563631at_int,N),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_52,plain,
archim1246769320r_real(hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n))) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)),
inference(subst,[],[refute_0_51:[bind(N,$fot(hAPP_nat_nat(suc,n)))]]) ).
cnf(refute_0_53,plain,
hAPP_complex_real(norm_norm_complex,Z_1) = hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,Z_1),hAPP_complex_complex(cnj,Z_1)))),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_54,plain,
hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_complex_complex(cnj,hAPP_nat_complex(semiri2020571505omplex,N))))),
inference(subst,[],[refute_0_53:[bind(Z_1,$fot(hAPP_nat_complex(semiri2020571505omplex,N)))]]) ).
cnf(refute_0_55,plain,
hAPP_complex_complex(cnj,hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_nat_complex(semiri2020571505omplex,N),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_56,plain,
( hAPP_complex_complex(cnj,hAPP_nat_complex(semiri2020571505omplex,N)) != hAPP_nat_complex(semiri2020571505omplex,N)
| hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N)) != hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_complex_complex(cnj,hAPP_nat_complex(semiri2020571505omplex,N)))))
| hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_complex_complex(cnj,hAPP_nat_complex(semiri2020571505omplex,N)))))) ),[1,1,1,1],$fot(hAPP_nat_complex(semiri2020571505omplex,N))]]) ).
cnf(refute_0_57,plain,
( hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N)) != hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_complex_complex(cnj,hAPP_nat_complex(semiri2020571505omplex,N)))))
| hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))) ),
inference(resolve,[$cnf( $equal(hAPP_complex_complex(cnj,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)) )],[refute_0_55,refute_0_56]) ).
cnf(refute_0_58,plain,
hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))),
inference(resolve,[$cnf( $equal(hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_complex_complex(cnj,hAPP_nat_complex(semiri2020571505omplex,N)))))) )],[refute_0_54,refute_0_57]) ).
cnf(refute_0_59,plain,
hAPP_complex_real(norm_norm_complex,rcis(R_2,A_3)) = hAPP_real_real(abs_abs_real,R_2),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_60,plain,
hAPP_complex_real(norm_norm_complex,rcis(X_505,zero_zero_real)) = hAPP_real_real(abs_abs_real,X_505),
inference(subst,[],[refute_0_59:[bind(A_3,$fot(zero_zero_real)),bind(R_2,$fot(X_505))]]) ).
cnf(refute_0_61,plain,
rcis(R_2,zero_zero_real) = of_real_complex(R_2),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_62,plain,
rcis(X_505,zero_zero_real) = of_real_complex(X_505),
inference(subst,[],[refute_0_61:[bind(R_2,$fot(X_505))]]) ).
cnf(refute_0_63,plain,
( hAPP_complex_real(norm_norm_complex,rcis(X_505,zero_zero_real)) != hAPP_real_real(abs_abs_real,X_505)
| rcis(X_505,zero_zero_real) != of_real_complex(X_505)
| hAPP_complex_real(norm_norm_complex,of_real_complex(X_505)) = hAPP_real_real(abs_abs_real,X_505) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_complex_real(norm_norm_complex,rcis(X_505,zero_zero_real)),hAPP_real_real(abs_abs_real,X_505)) ),[0,1],$fot(of_real_complex(X_505))]]) ).
cnf(refute_0_64,plain,
( hAPP_complex_real(norm_norm_complex,rcis(X_505,zero_zero_real)) != hAPP_real_real(abs_abs_real,X_505)
| hAPP_complex_real(norm_norm_complex,of_real_complex(X_505)) = hAPP_real_real(abs_abs_real,X_505) ),
inference(resolve,[$cnf( $equal(rcis(X_505,zero_zero_real),of_real_complex(X_505)) )],[refute_0_62,refute_0_63]) ).
cnf(refute_0_65,plain,
hAPP_complex_real(norm_norm_complex,of_real_complex(X_505)) = hAPP_real_real(abs_abs_real,X_505),
inference(resolve,[$cnf( $equal(hAPP_complex_real(norm_norm_complex,rcis(X_505,zero_zero_real)),hAPP_real_real(abs_abs_real,X_505)) )],[refute_0_60,refute_0_64]) ).
cnf(refute_0_66,plain,
hAPP_complex_real(norm_norm_complex,of_real_complex(hAPP_nat_real(real_nat,N_58))) = hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,N_58)),
inference(subst,[],[refute_0_65:[bind(X_505,$fot(hAPP_nat_real(real_nat,N_58)))]]) ).
cnf(refute_0_67,plain,
( A_1 != hAPP_int_real(number267125858f_real,Wa)
| B_1 != zero_zero_real
| hAPP_real_complex(hAPP_r265291036omplex(complex,A_1),B_1) = hAPP_int_complex(number528085621omplex,Wa) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_68,plain,
( hAPP_int_real(number267125858f_real,Wa) != hAPP_int_real(number267125858f_real,Wa)
| zero_zero_real != zero_zero_real
| hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_int_real(number267125858f_real,Wa)),zero_zero_real) = hAPP_int_complex(number528085621omplex,Wa) ),
inference(subst,[],[refute_0_67:[bind(A_1,$fot(hAPP_int_real(number267125858f_real,Wa))),bind(B_1,$fot(zero_zero_real))]]) ).
cnf(refute_0_69,plain,
hAPP_int_real(number267125858f_real,Wa) = hAPP_int_real(number267125858f_real,Wa),
introduced(tautology,[refl,[$fot(hAPP_int_real(number267125858f_real,Wa))]]) ).
cnf(refute_0_70,plain,
( zero_zero_real != zero_zero_real
| hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_int_real(number267125858f_real,Wa)),zero_zero_real) = hAPP_int_complex(number528085621omplex,Wa) ),
inference(resolve,[$cnf( $equal(hAPP_int_real(number267125858f_real,Wa),hAPP_int_real(number267125858f_real,Wa)) )],[refute_0_69,refute_0_68]) ).
cnf(refute_0_71,plain,
zero_zero_real = zero_zero_real,
introduced(tautology,[refl,[$fot(zero_zero_real)]]) ).
cnf(refute_0_72,plain,
hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_int_real(number267125858f_real,Wa)),zero_zero_real) = hAPP_int_complex(number528085621omplex,Wa),
inference(resolve,[$cnf( $equal(zero_zero_real,zero_zero_real) )],[refute_0_71,refute_0_70]) ).
cnf(refute_0_73,plain,
of_real_complex(R_2) = hAPP_real_complex(hAPP_r265291036omplex(complex,R_2),zero_zero_real),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_74,plain,
( of_real_complex(R_2) != hAPP_real_complex(hAPP_r265291036omplex(complex,R_2),zero_zero_real)
| hAPP_real_complex(hAPP_r265291036omplex(complex,R_2),zero_zero_real) = of_real_complex(R_2) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(of_real_complex(R_2))),bind(Y,$fot(hAPP_real_complex(hAPP_r265291036omplex(complex,R_2),zero_zero_real)))]]) ).
cnf(refute_0_75,plain,
hAPP_real_complex(hAPP_r265291036omplex(complex,R_2),zero_zero_real) = of_real_complex(R_2),
inference(resolve,[$cnf( $equal(of_real_complex(R_2),hAPP_real_complex(hAPP_r265291036omplex(complex,R_2),zero_zero_real)) )],[refute_0_73,refute_0_74]) ).
cnf(refute_0_76,plain,
hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_int_real(number267125858f_real,Wa)),zero_zero_real) = of_real_complex(hAPP_int_real(number267125858f_real,Wa)),
inference(subst,[],[refute_0_75:[bind(R_2,$fot(hAPP_int_real(number267125858f_real,Wa)))]]) ).
cnf(refute_0_77,plain,
( hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_int_real(number267125858f_real,Wa)),zero_zero_real) != hAPP_int_complex(number528085621omplex,Wa)
| hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_int_real(number267125858f_real,Wa)),zero_zero_real) != of_real_complex(hAPP_int_real(number267125858f_real,Wa))
| of_real_complex(hAPP_int_real(number267125858f_real,Wa)) = hAPP_int_complex(number528085621omplex,Wa) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_int_real(number267125858f_real,Wa)),zero_zero_real),hAPP_int_complex(number528085621omplex,Wa)) ),[0],$fot(of_real_complex(hAPP_int_real(number267125858f_real,Wa)))]]) ).
cnf(refute_0_78,plain,
( hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_int_real(number267125858f_real,Wa)),zero_zero_real) != hAPP_int_complex(number528085621omplex,Wa)
| of_real_complex(hAPP_int_real(number267125858f_real,Wa)) = hAPP_int_complex(number528085621omplex,Wa) ),
inference(resolve,[$cnf( $equal(hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_int_real(number267125858f_real,Wa)),zero_zero_real),of_real_complex(hAPP_int_real(number267125858f_real,Wa))) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
of_real_complex(hAPP_int_real(number267125858f_real,Wa)) = hAPP_int_complex(number528085621omplex,Wa),
inference(resolve,[$cnf( $equal(hAPP_real_complex(hAPP_r265291036omplex(complex,hAPP_int_real(number267125858f_real,Wa)),zero_zero_real),hAPP_int_complex(number528085621omplex,Wa)) )],[refute_0_72,refute_0_78]) ).
cnf(refute_0_80,plain,
of_real_complex(hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58))) = hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58)),
inference(subst,[],[refute_0_79:[bind(Wa,$fot(hAPP_nat_int(semiri1621563631at_int,N_58)))]]) ).
cnf(refute_0_81,plain,
hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58)) = hAPP_nat_real(semiri132038758t_real,N_58),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_82,plain,
real_nat = semiri132038758t_real,
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_83,plain,
( real_nat != semiri132038758t_real
| semiri132038758t_real = real_nat ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(real_nat)),bind(Y,$fot(semiri132038758t_real))]]) ).
cnf(refute_0_84,plain,
semiri132038758t_real = real_nat,
inference(resolve,[$cnf( $equal(real_nat,semiri132038758t_real) )],[refute_0_82,refute_0_83]) ).
cnf(refute_0_85,plain,
hAPP_nat_real(semiri132038758t_real,N_58) = hAPP_nat_real(semiri132038758t_real,N_58),
introduced(tautology,[refl,[$fot(hAPP_nat_real(semiri132038758t_real,N_58))]]) ).
cnf(refute_0_86,plain,
( hAPP_nat_real(semiri132038758t_real,N_58) != hAPP_nat_real(semiri132038758t_real,N_58)
| semiri132038758t_real != real_nat
| hAPP_nat_real(semiri132038758t_real,N_58) = hAPP_nat_real(real_nat,N_58) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_real(semiri132038758t_real,N_58),hAPP_nat_real(semiri132038758t_real,N_58)) ),[1,0],$fot(real_nat)]]) ).
cnf(refute_0_87,plain,
( semiri132038758t_real != real_nat
| hAPP_nat_real(semiri132038758t_real,N_58) = hAPP_nat_real(real_nat,N_58) ),
inference(resolve,[$cnf( $equal(hAPP_nat_real(semiri132038758t_real,N_58),hAPP_nat_real(semiri132038758t_real,N_58)) )],[refute_0_85,refute_0_86]) ).
cnf(refute_0_88,plain,
hAPP_nat_real(semiri132038758t_real,N_58) = hAPP_nat_real(real_nat,N_58),
inference(resolve,[$cnf( $equal(semiri132038758t_real,real_nat) )],[refute_0_84,refute_0_87]) ).
cnf(refute_0_89,plain,
( hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58)) != hAPP_nat_real(semiri132038758t_real,N_58)
| hAPP_nat_real(semiri132038758t_real,N_58) != hAPP_nat_real(real_nat,N_58)
| hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58)) = hAPP_nat_real(real_nat,N_58) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58)),hAPP_nat_real(real_nat,N_58)) ),[0],$fot(hAPP_nat_real(semiri132038758t_real,N_58))]]) ).
cnf(refute_0_90,plain,
( hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58)) != hAPP_nat_real(semiri132038758t_real,N_58)
| hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58)) = hAPP_nat_real(real_nat,N_58) ),
inference(resolve,[$cnf( $equal(hAPP_nat_real(semiri132038758t_real,N_58),hAPP_nat_real(real_nat,N_58)) )],[refute_0_88,refute_0_89]) ).
cnf(refute_0_91,plain,
hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58)) = hAPP_nat_real(real_nat,N_58),
inference(resolve,[$cnf( $equal(hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58)),hAPP_nat_real(semiri132038758t_real,N_58)) )],[refute_0_81,refute_0_90]) ).
cnf(refute_0_92,plain,
( hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58)) != hAPP_nat_real(real_nat,N_58)
| of_real_complex(hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58))) != hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58))
| of_real_complex(hAPP_nat_real(real_nat,N_58)) = hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58)) ),
introduced(tautology,[equality,[$cnf( $equal(of_real_complex(hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58))),hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58))) ),[0,0],$fot(hAPP_nat_real(real_nat,N_58))]]) ).
cnf(refute_0_93,plain,
( of_real_complex(hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58))) != hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58))
| of_real_complex(hAPP_nat_real(real_nat,N_58)) = hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58)) ),
inference(resolve,[$cnf( $equal(hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58)),hAPP_nat_real(real_nat,N_58)) )],[refute_0_91,refute_0_92]) ).
cnf(refute_0_94,plain,
of_real_complex(hAPP_nat_real(real_nat,N_58)) = hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58)),
inference(resolve,[$cnf( $equal(of_real_complex(hAPP_int_real(number267125858f_real,hAPP_nat_int(semiri1621563631at_int,N_58))),hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58))) )],[refute_0_80,refute_0_93]) ).
cnf(refute_0_95,plain,
hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58)) = hAPP_nat_complex(semiri2020571505omplex,N_58),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_96,plain,
( hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58)) != hAPP_nat_complex(semiri2020571505omplex,N_58)
| of_real_complex(hAPP_nat_real(real_nat,N_58)) != hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58))
| of_real_complex(hAPP_nat_real(real_nat,N_58)) = hAPP_nat_complex(semiri2020571505omplex,N_58) ),
introduced(tautology,[equality,[$cnf( $equal(of_real_complex(hAPP_nat_real(real_nat,N_58)),hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58))) ),[1],$fot(hAPP_nat_complex(semiri2020571505omplex,N_58))]]) ).
cnf(refute_0_97,plain,
( of_real_complex(hAPP_nat_real(real_nat,N_58)) != hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58))
| of_real_complex(hAPP_nat_real(real_nat,N_58)) = hAPP_nat_complex(semiri2020571505omplex,N_58) ),
inference(resolve,[$cnf( $equal(hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58)),hAPP_nat_complex(semiri2020571505omplex,N_58)) )],[refute_0_95,refute_0_96]) ).
cnf(refute_0_98,plain,
of_real_complex(hAPP_nat_real(real_nat,N_58)) = hAPP_nat_complex(semiri2020571505omplex,N_58),
inference(resolve,[$cnf( $equal(of_real_complex(hAPP_nat_real(real_nat,N_58)),hAPP_int_complex(number528085621omplex,hAPP_nat_int(semiri1621563631at_int,N_58))) )],[refute_0_94,refute_0_97]) ).
cnf(refute_0_99,plain,
( hAPP_complex_real(norm_norm_complex,of_real_complex(hAPP_nat_real(real_nat,N_58))) != hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,N_58))
| of_real_complex(hAPP_nat_real(real_nat,N_58)) != hAPP_nat_complex(semiri2020571505omplex,N_58)
| hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N_58)) = hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,N_58)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_complex_real(norm_norm_complex,of_real_complex(hAPP_nat_real(real_nat,N_58))),hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,N_58))) ),[0,1],$fot(hAPP_nat_complex(semiri2020571505omplex,N_58))]]) ).
cnf(refute_0_100,plain,
( hAPP_complex_real(norm_norm_complex,of_real_complex(hAPP_nat_real(real_nat,N_58))) != hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,N_58))
| hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N_58)) = hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,N_58)) ),
inference(resolve,[$cnf( $equal(of_real_complex(hAPP_nat_real(real_nat,N_58)),hAPP_nat_complex(semiri2020571505omplex,N_58)) )],[refute_0_98,refute_0_99]) ).
cnf(refute_0_101,plain,
hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N_58)) = hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,N_58)),
inference(resolve,[$cnf( $equal(hAPP_complex_real(norm_norm_complex,of_real_complex(hAPP_nat_real(real_nat,N_58))),hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,N_58))) )],[refute_0_66,refute_0_100]) ).
cnf(refute_0_102,plain,
hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,X)) = hAPP_nat_real(real_nat,X),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_103,plain,
hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,N_58)) = hAPP_nat_real(real_nat,N_58),
inference(subst,[],[refute_0_102:[bind(X,$fot(N_58))]]) ).
cnf(refute_0_104,plain,
( hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N_58)) != hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,N_58))
| hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,N_58)) != hAPP_nat_real(real_nat,N_58)
| hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N_58)) = hAPP_nat_real(real_nat,N_58) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N_58)),hAPP_nat_real(real_nat,N_58)) ),[0],$fot(hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,N_58)))]]) ).
cnf(refute_0_105,plain,
( hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N_58)) != hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,N_58))
| hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N_58)) = hAPP_nat_real(real_nat,N_58) ),
inference(resolve,[$cnf( $equal(hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,N_58)),hAPP_nat_real(real_nat,N_58)) )],[refute_0_103,refute_0_104]) ).
cnf(refute_0_106,plain,
hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N_58)) = hAPP_nat_real(real_nat,N_58),
inference(resolve,[$cnf( $equal(hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N_58)),hAPP_real_real(abs_abs_real,hAPP_nat_real(real_nat,N_58))) )],[refute_0_101,refute_0_105]) ).
cnf(refute_0_107,plain,
hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_nat_real(real_nat,N),
inference(subst,[],[refute_0_106:[bind(N_58,$fot(N))]]) ).
cnf(refute_0_108,plain,
( hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N)) != hAPP_nat_real(real_nat,N)
| hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N)) != hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))))
| hAPP_nat_real(real_nat,N) = hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))))) ),[0],$fot(hAPP_nat_real(real_nat,N))]]) ).
cnf(refute_0_109,plain,
( hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N)) != hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))))
| hAPP_nat_real(real_nat,N) = hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))) ),
inference(resolve,[$cnf( $equal(hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_real(real_nat,N)) )],[refute_0_107,refute_0_108]) ).
cnf(refute_0_110,plain,
hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_nat_real(semiri132038758t_real,N),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_111,plain,
hAPP_nat_real(semiri132038758t_real,N) = hAPP_nat_real(semiri132038758t_real,N),
introduced(tautology,[refl,[$fot(hAPP_nat_real(semiri132038758t_real,N))]]) ).
cnf(refute_0_112,plain,
( hAPP_nat_real(semiri132038758t_real,N) != hAPP_nat_real(semiri132038758t_real,N)
| semiri132038758t_real != real_nat
| hAPP_nat_real(semiri132038758t_real,N) = hAPP_nat_real(real_nat,N) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_real(semiri132038758t_real,N),hAPP_nat_real(semiri132038758t_real,N)) ),[1,0],$fot(real_nat)]]) ).
cnf(refute_0_113,plain,
( semiri132038758t_real != real_nat
| hAPP_nat_real(semiri132038758t_real,N) = hAPP_nat_real(real_nat,N) ),
inference(resolve,[$cnf( $equal(hAPP_nat_real(semiri132038758t_real,N),hAPP_nat_real(semiri132038758t_real,N)) )],[refute_0_111,refute_0_112]) ).
cnf(refute_0_114,plain,
hAPP_nat_real(semiri132038758t_real,N) = hAPP_nat_real(real_nat,N),
inference(resolve,[$cnf( $equal(semiri132038758t_real,real_nat) )],[refute_0_84,refute_0_113]) ).
cnf(refute_0_115,plain,
( hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,N)) != hAPP_nat_real(semiri132038758t_real,N)
| hAPP_nat_real(semiri132038758t_real,N) != hAPP_nat_real(real_nat,N)
| hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_nat_real(real_nat,N) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_real(real_nat,N)) ),[0],$fot(hAPP_nat_real(semiri132038758t_real,N))]]) ).
cnf(refute_0_116,plain,
( hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,N)) != hAPP_nat_real(semiri132038758t_real,N)
| hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_nat_real(real_nat,N) ),
inference(resolve,[$cnf( $equal(hAPP_nat_real(semiri132038758t_real,N),hAPP_nat_real(real_nat,N)) )],[refute_0_114,refute_0_115]) ).
cnf(refute_0_117,plain,
hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_nat_real(real_nat,N),
inference(resolve,[$cnf( $equal(hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_real(semiri132038758t_real,N)) )],[refute_0_110,refute_0_116]) ).
cnf(refute_0_118,plain,
hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))) = hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N)),
inference(subst,[],[refute_0_117:[bind(N,$fot(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N)))]]) ).
cnf(refute_0_119,plain,
hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_18),N_30)) = hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,M_18)),hAPP_nat_complex(semiri2020571505omplex,N_30)),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_120,plain,
( hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_18),N_30)) != hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,M_18)),hAPP_nat_complex(semiri2020571505omplex,N_30))
| hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,M_18)),hAPP_nat_complex(semiri2020571505omplex,N_30)) = hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_18),N_30)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_18),N_30)))),bind(Y,$fot(hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,M_18)),hAPP_nat_complex(semiri2020571505omplex,N_30))))]]) ).
cnf(refute_0_121,plain,
hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,M_18)),hAPP_nat_complex(semiri2020571505omplex,N_30)) = hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_18),N_30)),
inference(resolve,[$cnf( $equal(hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,M_18),N_30)),hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,M_18)),hAPP_nat_complex(semiri2020571505omplex,N_30))) )],[refute_0_119,refute_0_120]) ).
cnf(refute_0_122,plain,
hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)) = hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N)),
inference(subst,[],[refute_0_121:[bind(M_18,$fot(N)),bind(N_30,$fot(N))]]) ).
cnf(refute_0_123,plain,
hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))) = hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))),
introduced(tautology,[refl,[$fot(hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))))]]) ).
cnf(refute_0_124,plain,
( hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)) != hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))
| hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))) != hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))
| hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))) = hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))),hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))) ),[1,1],$fot(hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N)))]]) ).
cnf(refute_0_125,plain,
( hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)) != hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))
| hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))) = hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))) ),
inference(resolve,[$cnf( $equal(hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))),hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))) )],[refute_0_123,refute_0_124]) ).
cnf(refute_0_126,plain,
hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))) = hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))),
inference(resolve,[$cnf( $equal(hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))) )],[refute_0_122,refute_0_125]) ).
cnf(refute_0_127,plain,
( hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))) != hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N)))
| hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))) != hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))
| hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))) = hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N)) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))))),bind(Y,$fot(hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))))),bind(Z,$fot(hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))))]]) ).
cnf(refute_0_128,plain,
( hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))) != hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))
| hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))) = hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N)) ),
inference(resolve,[$cnf( $equal(hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))),hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N)))) )],[refute_0_126,refute_0_127]) ).
cnf(refute_0_129,plain,
hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))) = hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N)),
inference(resolve,[$cnf( $equal(hAPP_complex_real(re,hAPP_nat_complex(semiri2020571505omplex,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))),hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))) )],[refute_0_118,refute_0_128]) ).
cnf(refute_0_130,plain,
hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))) = hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))),
introduced(tautology,[refl,[$fot(hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))))]]) ).
cnf(refute_0_131,plain,
( hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))) != hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))
| hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))) != hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))))
| hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))) = hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))),hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))))) ),[1,1],$fot(hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N)))]]) ).
cnf(refute_0_132,plain,
( hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))) != hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))
| hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))) = hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))) ),
inference(resolve,[$cnf( $equal(hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))),hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))))) )],[refute_0_130,refute_0_131]) ).
cnf(refute_0_133,plain,
hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))) = hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))),
inference(resolve,[$cnf( $equal(hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))),hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))) )],[refute_0_129,refute_0_132]) ).
cnf(refute_0_134,plain,
( hAPP_nat_real(real_nat,N) != hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))))
| hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))) != hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N)))
| hAPP_nat_real(real_nat,N) = hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP_nat_real(real_nat,N),hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N)))) ),[0],$fot(hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))))]]) ).
cnf(refute_0_135,plain,
( hAPP_nat_real(real_nat,N) != hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))))
| hAPP_nat_real(real_nat,N) = hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))) ),
inference(resolve,[$cnf( $equal(hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N)))),hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N)))) )],[refute_0_133,refute_0_134]) ).
cnf(refute_0_136,plain,
( hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N)) != hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))))
| hAPP_nat_real(real_nat,N) = hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))) ),
inference(resolve,[$cnf( $equal(hAPP_nat_real(real_nat,N),hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))))) )],[refute_0_109,refute_0_135]) ).
cnf(refute_0_137,plain,
hAPP_nat_real(real_nat,N) = hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,N),N))),
inference(resolve,[$cnf( $equal(hAPP_complex_real(norm_norm_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_real_real(sqrt,hAPP_complex_real(re,hAPP_complex_complex(hAPP_c172932010omplex(times_times_complex,hAPP_nat_complex(semiri2020571505omplex,N)),hAPP_nat_complex(semiri2020571505omplex,N))))) )],[refute_0_58,refute_0_136]) ).
cnf(refute_0_138,plain,
hAPP_nat_real(real_nat,X_839) = hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_839),X_839))),
inference(subst,[],[refute_0_137:[bind(N,$fot(X_839))]]) ).
cnf(refute_0_139,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59),
inference(canonicalize,[],[normalize_0_36]) ).
cnf(refute_0_140,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),
inference(canonicalize,[],[normalize_0_37]) ).
cnf(refute_0_141,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat) != hAPP_int_nat(number_number_of_nat,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(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat))),bind(Y,$fot(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))]]) ).
cnf(refute_0_142,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )],[refute_0_140,refute_0_141]) ).
cnf(refute_0_143,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
introduced(tautology,[refl,[$fot(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))]]) ).
cnf(refute_0_144,plain,
( hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) ),[1,1],$fot(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat))]]) ).
cnf(refute_0_145,plain,
( hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)) ),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) )],[refute_0_143,refute_0_144]) ).
cnf(refute_0_146,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)),
inference(resolve,[$cnf( $equal(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)) )],[refute_0_142,refute_0_145]) ).
cnf(refute_0_147,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59)) ),[0],$fot(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)))]]) ).
cnf(refute_0_148,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59) ),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat))) )],[refute_0_146,refute_0_147]) ).
cnf(refute_0_149,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59)) )],[refute_0_139,refute_0_148]) ).
cnf(refute_0_150,plain,
hAPP_nat_nat(suc,N) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N),
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_151,plain,
( hAPP_nat_nat(suc,N) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N) = hAPP_nat_nat(suc,N) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(hAPP_nat_nat(suc,N))),bind(Y,$fot(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N)))]]) ).
cnf(refute_0_152,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N) = hAPP_nat_nat(suc,N),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(suc,N),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),N)) )],[refute_0_150,refute_0_151]) ).
cnf(refute_0_153,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat) = hAPP_nat_nat(suc,one_one_nat),
inference(subst,[],[refute_0_152:[bind(N,$fot(one_one_nat))]]) ).
cnf(refute_0_154,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)),
introduced(tautology,[refl,[$fot(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)))]]) ).
cnf(refute_0_155,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat) != hAPP_nat_nat(suc,one_one_nat)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(suc,one_one_nat)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat))) ),[1,1],$fot(hAPP_nat_nat(suc,one_one_nat))]]) ).
cnf(refute_0_156,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat) != hAPP_nat_nat(suc,one_one_nat)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(suc,one_one_nat)) ),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat))) )],[refute_0_154,refute_0_155]) ).
cnf(refute_0_157,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(suc,one_one_nat)),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat),hAPP_nat_nat(suc,one_one_nat)) )],[refute_0_153,refute_0_156]) ).
cnf(refute_0_158,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(suc,one_one_nat))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(suc,one_one_nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59)) ),[0],$fot(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(suc,one_one_nat)))]]) ).
cnf(refute_0_159,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(suc,one_one_nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59) ),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(suc,one_one_nat))) )],[refute_0_157,refute_0_158]) ).
cnf(refute_0_160,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(suc,one_one_nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,A_59),hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,A_59),A_59)) )],[refute_0_149,refute_0_159]) ).
cnf(refute_0_161,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_839),hAPP_nat_nat(suc,one_one_nat)) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_839),X_839),
inference(subst,[],[refute_0_160:[bind(A_59,$fot(X_839))]]) ).
cnf(refute_0_162,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_839),hAPP_nat_nat(suc,one_one_nat)) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_839),X_839)
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_839),X_839) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_839),hAPP_nat_nat(suc,one_one_nat)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_839),hAPP_nat_nat(suc,one_one_nat)))),bind(Y,$fot(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_839),X_839)))]]) ).
cnf(refute_0_163,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_839),X_839) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_839),hAPP_nat_nat(suc,one_one_nat)),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_839),hAPP_nat_nat(suc,one_one_nat)),hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_839),X_839)) )],[refute_0_161,refute_0_162]) ).
cnf(refute_0_164,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_839),X_839) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_839),hAPP_nat_nat(suc,one_one_nat))
| hAPP_nat_real(real_nat,X_839) != hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_839),X_839)))
| hAPP_nat_real(real_nat,X_839) = hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_839),hAPP_nat_nat(suc,one_one_nat)))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_real(real_nat,X_839),hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_839),X_839)))) ),[1,1,1],$fot(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_839),hAPP_nat_nat(suc,one_one_nat)))]]) ).
cnf(refute_0_165,plain,
( hAPP_nat_real(real_nat,X_839) != hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_839),X_839)))
| hAPP_nat_real(real_nat,X_839) = hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_839),hAPP_nat_nat(suc,one_one_nat)))) ),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_839),X_839),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_839),hAPP_nat_nat(suc,one_one_nat))) )],[refute_0_163,refute_0_164]) ).
cnf(refute_0_166,plain,
hAPP_nat_real(real_nat,X_839) = hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,X_839),hAPP_nat_nat(suc,one_one_nat)))),
inference(resolve,[$cnf( $equal(hAPP_nat_real(real_nat,X_839),hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(times_times_nat,X_839),X_839)))) )],[refute_0_138,refute_0_165]) ).
cnf(refute_0_167,plain,
hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n)) = hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)))),
inference(subst,[],[refute_0_166:[bind(X_839,$fot(hAPP_nat_nat(suc,n)))]]) ).
cnf(refute_0_168,plain,
hAPP_int_nat(nat,hAPP_nat_int(semiri1621563631at_int,N)) = N,
inference(canonicalize,[],[normalize_0_41]) ).
cnf(refute_0_169,plain,
hAPP_int_nat(nat,hAPP_nat_int(semiri1621563631at_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_168:[bind(N,$fot(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))))]]) ).
cnf(refute_0_170,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = zero_zero_int,
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_171,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,M)),N) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,M),N)),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_172,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat)) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))),
inference(subst,[],[refute_0_171:[bind(M,$fot(hAPP_nat_nat(suc,n))),bind(N,$fot(hAPP_nat_nat(suc,one_one_nat)))]]) ).
cnf(refute_0_173,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat) != hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat) != hAPP_nat_nat(suc,one_one_nat)
| hAPP_nat_nat(suc,one_one_nat) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ),[0],$fot(hAPP_nat_nat(suc,one_one_nat))]]) ).
cnf(refute_0_174,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),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) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) ),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat),hAPP_nat_nat(suc,one_one_nat)) )],[refute_0_153,refute_0_173]) ).
cnf(refute_0_175,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),
inference(canonicalize,[],[normalize_0_45]) ).
cnf(refute_0_176,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int) = hAPP_int_int(succ,one_one_int),
inference(subst,[],[refute_0_38:[bind(K_2,$fot(one_one_int))]]) ).
cnf(refute_0_177,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int) != hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int) != hAPP_int_int(succ,one_one_int)
| hAPP_int_int(succ,one_one_int) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ),[0],$fot(hAPP_int_int(succ,one_one_int))]]) ).
cnf(refute_0_178,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int) != hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))
| hAPP_int_int(succ,one_one_int) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int),hAPP_int_int(succ,one_one_int)) )],[refute_0_176,refute_0_177]) ).
cnf(refute_0_179,plain,
zero_zero_int = hAPP_int_int(number_number_of_int,pls),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_180,plain,
( zero_zero_int != hAPP_int_int(number_number_of_int,pls)
| hAPP_int_int(number_number_of_int,pls) = zero_zero_int ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(zero_zero_int)),bind(Y,$fot(hAPP_int_int(number_number_of_int,pls)))]]) ).
cnf(refute_0_181,plain,
hAPP_int_int(number_number_of_int,pls) = zero_zero_int,
inference(resolve,[$cnf( $equal(zero_zero_int,hAPP_int_int(number_number_of_int,pls)) )],[refute_0_179,refute_0_180]) ).
cnf(refute_0_182,plain,
( hAPP_int_int(number_number_of_int,pls) != zero_zero_int
| zero_zero_int != pls
| hAPP_int_int(number_number_of_int,pls) = pls ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(hAPP_int_int(number_number_of_int,pls))),bind(Y,$fot(zero_zero_int)),bind(Z,$fot(pls))]]) ).
cnf(refute_0_183,plain,
( zero_zero_int != pls
| hAPP_int_int(number_number_of_int,pls) = pls ),
inference(resolve,[$cnf( $equal(hAPP_int_int(number_number_of_int,pls),zero_zero_int) )],[refute_0_181,refute_0_182]) ).
cnf(refute_0_184,plain,
hAPP_int_int(number_number_of_int,pls) = pls,
inference(resolve,[$cnf( $equal(zero_zero_int,pls) )],[refute_0_14,refute_0_183]) ).
cnf(refute_0_185,plain,
hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls)) = hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls)),
introduced(tautology,[refl,[$fot(hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls)))]]) ).
cnf(refute_0_186,plain,
( hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls)) != hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls))
| hAPP_int_int(number_number_of_int,pls) != pls
| hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls)) = hAPP_int_int(bit1,pls) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls)),hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls))) ),[1,1],$fot(pls)]]) ).
cnf(refute_0_187,plain,
( hAPP_int_int(number_number_of_int,pls) != pls
| hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls)) = hAPP_int_int(bit1,pls) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls)),hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls))) )],[refute_0_185,refute_0_186]) ).
cnf(refute_0_188,plain,
hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls)) = hAPP_int_int(bit1,pls),
inference(resolve,[$cnf( $equal(hAPP_int_int(number_number_of_int,pls),pls) )],[refute_0_184,refute_0_187]) ).
cnf(refute_0_189,plain,
hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,W_10)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10)),
inference(canonicalize,[],[normalize_0_48]) ).
cnf(refute_0_190,plain,
hAPP_int_int(bit1,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)),K_2),
inference(canonicalize,[],[normalize_0_50]) ).
cnf(refute_0_191,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_1),W) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),Z_1)
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),Z_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_1),W) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_1),W))),bind(Y,$fot(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),Z_1)))]]) ).
cnf(refute_0_192,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),Z_1) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_1),W),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,Z_1),W),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,W),Z_1)) )],[refute_0_31,refute_0_191]) ).
cnf(refute_0_193,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)),K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)),
inference(subst,[],[refute_0_192:[bind(W,$fot(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2))),bind(Z_1,$fot(K_2))]]) ).
cnf(refute_0_194,plain,
( hAPP_int_int(bit1,K_2) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)),K_2)
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)),K_2) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2))
| hAPP_int_int(bit1,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP_int_int(bit1,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2))) ),[0],$fot(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)),K_2))]]) ).
cnf(refute_0_195,plain,
( hAPP_int_int(bit1,K_2) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)),K_2)
| hAPP_int_int(bit1,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)),K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2))) )],[refute_0_193,refute_0_194]) ).
cnf(refute_0_196,plain,
hAPP_int_int(bit1,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)),
inference(resolve,[$cnf( $equal(hAPP_int_int(bit1,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)),K_2)) )],[refute_0_190,refute_0_195]) ).
cnf(refute_0_197,plain,
( hAPP_int_int(bit1,K_2) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2))
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)) = hAPP_int_int(bit1,K_2) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(hAPP_int_int(bit1,K_2))),bind(Y,$fot(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2))))]]) ).
cnf(refute_0_198,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2)) = hAPP_int_int(bit1,K_2),
inference(resolve,[$cnf( $equal(hAPP_int_int(bit1,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),K_2))) )],[refute_0_196,refute_0_197]) ).
cnf(refute_0_199,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,W_10)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))) = hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,W_10)),
inference(subst,[],[refute_0_198:[bind(K_2,$fot(hAPP_int_int(number_number_of_int,W_10)))]]) ).
cnf(refute_0_200,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10)) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,W_10)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),
inference(subst,[],[refute_0_192:[bind(W,$fot(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10)))),bind(Z_1,$fot(hAPP_int_int(number_number_of_int,W_10)))]]) ).
cnf(refute_0_201,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10)) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,W_10)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10)))
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,W_10)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))) != hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,W_10))
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10)) = hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,W_10)) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10)))),bind(Y,$fot(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,W_10)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))))),bind(Z,$fot(hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,W_10))))]]) ).
cnf(refute_0_202,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,W_10)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))) != hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,W_10))
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10)) = hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,W_10)) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,W_10)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10)))) )],[refute_0_200,refute_0_201]) ).
cnf(refute_0_203,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10)) = hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,W_10)),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(number_number_of_int,W_10)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,W_10))) )],[refute_0_199,refute_0_202]) ).
cnf(refute_0_204,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10)) != hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,W_10))
| hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,W_10)) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10))
| hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,W_10)) = hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,W_10)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,W_10)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10))) ),[1],$fot(hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,W_10)))]]) ).
cnf(refute_0_205,plain,
( hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,W_10)) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10))
| hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,W_10)) = hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,W_10)) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10)),hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,W_10))) )],[refute_0_203,refute_0_204]) ).
cnf(refute_0_206,plain,
hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,W_10)) = hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,W_10)),
inference(resolve,[$cnf( $equal(hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,W_10)),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_int_int(number_number_of_int,W_10))),hAPP_int_int(number_number_of_int,W_10))) )],[refute_0_189,refute_0_205]) ).
cnf(refute_0_207,plain,
hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) = hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls)),
inference(subst,[],[refute_0_206:[bind(W_10,$fot(pls))]]) ).
cnf(refute_0_208,plain,
( hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls)) != hAPP_int_int(bit1,pls)
| hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) != hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls))
| hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) = hAPP_int_int(bit1,pls) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)))),bind(Y,$fot(hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls)))),bind(Z,$fot(hAPP_int_int(bit1,pls)))]]) ).
cnf(refute_0_209,plain,
( hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls)) != hAPP_int_int(bit1,pls)
| hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) = hAPP_int_int(bit1,pls) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)),hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls))) )],[refute_0_207,refute_0_208]) ).
cnf(refute_0_210,plain,
hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) = hAPP_int_int(bit1,pls),
inference(resolve,[$cnf( $equal(hAPP_int_int(bit1,hAPP_int_int(number_number_of_int,pls)),hAPP_int_int(bit1,pls)) )],[refute_0_188,refute_0_209]) ).
cnf(refute_0_211,plain,
hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))) = hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),
introduced(tautology,[refl,[$fot(hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))))]]) ).
cnf(refute_0_212,plain,
( hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))) != hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)))
| hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) != hAPP_int_int(bit1,pls)
| hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))) = hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)))) ),[1,1],$fot(hAPP_int_int(bit1,pls))]]) ).
cnf(refute_0_213,plain,
( hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) != hAPP_int_int(bit1,pls)
| hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))) = hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)))) )],[refute_0_211,refute_0_212]) ).
cnf(refute_0_214,plain,
hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))) = hAPP_int_int(bit0,hAPP_int_int(bit1,pls)),
inference(resolve,[$cnf( $equal(hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)),hAPP_int_int(bit1,pls)) )],[refute_0_210,refute_0_213]) ).
cnf(refute_0_215,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_5)),
inference(canonicalize,[],[normalize_0_52]) ).
cnf(refute_0_216,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_15),M_15) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15),
inference(canonicalize,[],[normalize_0_54]) ).
cnf(refute_0_217,plain,
hAPP_int_int(bit0,K_2) = hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),K_2),
inference(canonicalize,[],[normalize_0_56]) ).
cnf(refute_0_218,plain,
( hAPP_int_int(bit0,K_2) != hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),K_2)
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),K_2) = hAPP_int_int(bit0,K_2) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(hAPP_int_int(bit0,K_2))),bind(Y,$fot(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),K_2)))]]) ).
cnf(refute_0_219,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),K_2) = hAPP_int_int(bit0,K_2),
inference(resolve,[$cnf( $equal(hAPP_int_int(bit0,K_2),hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,K_2),K_2)) )],[refute_0_217,refute_0_218]) ).
cnf(refute_0_220,plain,
hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_15),M_15) = hAPP_int_int(bit0,M_15),
inference(subst,[],[refute_0_219:[bind(K_2,$fot(M_15))]]) ).
cnf(refute_0_221,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_15),M_15) != hAPP_int_int(bit0,M_15)
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_15),M_15) != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15)
| hAPP_int_int(bit0,M_15) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_15),M_15),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15)) ),[0],$fot(hAPP_int_int(bit0,M_15))]]) ).
cnf(refute_0_222,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_15),M_15) != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15)
| hAPP_int_int(bit0,M_15) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_15),M_15),hAPP_int_int(bit0,M_15)) )],[refute_0_220,refute_0_221]) ).
cnf(refute_0_223,plain,
hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)) = hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),
introduced(tautology,[refl,[$fot(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)))]]) ).
cnf(refute_0_224,plain,
( hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)) != hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int))
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int) != hAPP_int_int(succ,one_one_int)
| hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)) = hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int))) ),[1,1],$fot(hAPP_int_int(succ,one_one_int))]]) ).
cnf(refute_0_225,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int) != hAPP_int_int(succ,one_one_int)
| hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)) = hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)) ),
inference(resolve,[$cnf( $equal(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int))) )],[refute_0_223,refute_0_224]) ).
cnf(refute_0_226,plain,
hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)) = hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int),hAPP_int_int(succ,one_one_int)) )],[refute_0_176,refute_0_225]) ).
cnf(refute_0_227,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15),
introduced(tautology,[refl,[$fot(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15))]]) ).
cnf(refute_0_228,plain,
( hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)) != hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int))
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15) != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15)
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),M_15) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15)) ),[1,0],$fot(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)))]]) ).
cnf(refute_0_229,plain,
( hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)) != hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int))
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),M_15) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15)) )],[refute_0_227,refute_0_228]) ).
cnf(refute_0_230,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),M_15),
inference(resolve,[$cnf( $equal(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int))) )],[refute_0_226,refute_0_229]) ).
cnf(refute_0_231,plain,
( hAPP_int_int(bit0,M_15) != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15)
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15) != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),M_15)
| hAPP_int_int(bit0,M_15) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),M_15) ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP_int_int(bit0,M_15),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),M_15)) ),[0],$fot(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15))]]) ).
cnf(refute_0_232,plain,
( hAPP_int_int(bit0,M_15) != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15)
| hAPP_int_int(bit0,M_15) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),M_15) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),M_15)) )],[refute_0_230,refute_0_231]) ).
cnf(refute_0_233,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_15),M_15) != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15)
| hAPP_int_int(bit0,M_15) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),M_15) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(bit0,M_15),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15)) )],[refute_0_222,refute_0_232]) ).
cnf(refute_0_234,plain,
hAPP_int_int(bit0,M_15) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),M_15),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,M_15),M_15),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),M_15)) )],[refute_0_216,refute_0_233]) ).
cnf(refute_0_235,plain,
( hAPP_int_int(bit0,M_15) != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),M_15)
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),M_15) = hAPP_int_int(bit0,M_15) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(hAPP_int_int(bit0,M_15))),bind(Y,$fot(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),M_15)))]]) ).
cnf(refute_0_236,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),M_15) = hAPP_int_int(bit0,M_15),
inference(resolve,[$cnf( $equal(hAPP_int_int(bit0,M_15),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),M_15)) )],[refute_0_234,refute_0_235]) ).
cnf(refute_0_237,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),hAPP_int_int(number_number_of_int,W_5)) = hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5)),
inference(subst,[],[refute_0_236:[bind(M_15,$fot(hAPP_int_int(number_number_of_int,W_5)))]]) ).
cnf(refute_0_238,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)),
introduced(tautology,[refl,[$fot(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)))]]) ).
cnf(refute_0_239,plain,
( hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)) != hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int))
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)) != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5))
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),hAPP_int_int(number_number_of_int,W_5)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5))) ),[1,0],$fot(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)))]]) ).
cnf(refute_0_240,plain,
( hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)) != hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int))
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),hAPP_int_int(number_number_of_int,W_5)) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5))) )],[refute_0_238,refute_0_239]) ).
cnf(refute_0_241,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)) = hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),hAPP_int_int(number_number_of_int,W_5)),
inference(resolve,[$cnf( $equal(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int))) )],[refute_0_226,refute_0_240]) ).
cnf(refute_0_242,plain,
( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)) != hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),hAPP_int_int(number_number_of_int,W_5))
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),hAPP_int_int(number_number_of_int,W_5)) != hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5))
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)) = hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5)) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)))),bind(Y,$fot(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),hAPP_int_int(number_number_of_int,W_5)))),bind(Z,$fot(hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5))))]]) ).
cnf(refute_0_243,plain,
( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),hAPP_int_int(number_number_of_int,W_5)) != hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5))
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)) = hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5)) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)),hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),hAPP_int_int(number_number_of_int,W_5))) )],[refute_0_241,refute_0_242]) ).
cnf(refute_0_244,plain,
hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)) = hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5)),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(succ,one_one_int)),hAPP_int_int(number_number_of_int,W_5)),hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5))) )],[refute_0_237,refute_0_243]) ).
cnf(refute_0_245,plain,
( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)) != hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5))
| hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)) != hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_5))
| hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5)) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_5)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_5))) ),[0],$fot(hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5)))]]) ).
cnf(refute_0_246,plain,
( hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)) != hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_5))
| hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5)) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_5)) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)),hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5))) )],[refute_0_244,refute_0_245]) ).
cnf(refute_0_247,plain,
hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5)) = hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_5)),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(times_times_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int)),hAPP_int_int(number_number_of_int,W_5)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_5))) )],[refute_0_215,refute_0_246]) ).
cnf(refute_0_248,plain,
( hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5)) != hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_5))
| hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_5)) = hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5)) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5)))),bind(Y,$fot(hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_5))))]]) ).
cnf(refute_0_249,plain,
hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_5)) = hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5)),
inference(resolve,[$cnf( $equal(hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,W_5)),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,W_5))) )],[refute_0_247,refute_0_248]) ).
cnf(refute_0_250,plain,
hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),
inference(subst,[],[refute_0_249:[bind(W_5,$fot(hAPP_int_int(bit1,pls)))]]) ).
cnf(refute_0_251,plain,
( hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))) != hAPP_int_int(bit0,hAPP_int_int(bit1,pls))
| hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) != hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)))
| hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),bind(Y,$fot(hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))))),bind(Z,$fot(hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))]]) ).
cnf(refute_0_252,plain,
( hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))) != hAPP_int_int(bit0,hAPP_int_int(bit1,pls))
| hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)))) )],[refute_0_250,refute_0_251]) ).
cnf(refute_0_253,plain,
hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_int_int(bit0,hAPP_int_int(bit1,pls)),
inference(resolve,[$cnf( $equal(hAPP_int_int(bit0,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))),hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) )],[refute_0_214,refute_0_252]) ).
cnf(refute_0_254,plain,
( hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) != hAPP_int_int(bit0,hAPP_int_int(bit1,pls))
| hAPP_int_int(succ,one_one_int) != hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))
| hAPP_int_int(succ,one_one_int) = hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_int(succ,one_one_int),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ),[1],$fot(hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))]]) ).
cnf(refute_0_255,plain,
( hAPP_int_int(succ,one_one_int) != hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))
| hAPP_int_int(succ,one_one_int) = hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) )],[refute_0_253,refute_0_254]) ).
cnf(refute_0_256,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int) != hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))
| hAPP_int_int(succ,one_one_int) = hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(succ,one_one_int),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )],[refute_0_178,refute_0_255]) ).
cnf(refute_0_257,plain,
hAPP_int_int(succ,one_one_int) = hAPP_int_int(bit0,hAPP_int_int(bit1,pls)),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),one_one_int),hAPP_int_int(number_number_of_int,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )],[refute_0_175,refute_0_256]) ).
cnf(refute_0_258,plain,
( hAPP_int_int(succ,one_one_int) != hAPP_int_int(bit0,hAPP_int_int(bit1,pls))
| hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) = hAPP_int_int(succ,one_one_int) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(hAPP_int_int(succ,one_one_int))),bind(Y,$fot(hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))]]) ).
cnf(refute_0_259,plain,
hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) = hAPP_int_int(succ,one_one_int),
inference(resolve,[$cnf( $equal(hAPP_int_int(succ,one_one_int),hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) )],[refute_0_257,refute_0_258]) ).
cnf(refute_0_260,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),
introduced(tautology,[refl,[$fot(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))]]) ).
cnf(refute_0_261,plain,
( hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) != hAPP_int_int(succ,one_one_int)
| hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) != hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))
| hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ),[1,1],$fot(hAPP_int_int(succ,one_one_int))]]) ).
cnf(refute_0_262,plain,
( hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) != hAPP_int_int(succ,one_one_int)
| hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)) ),
inference(resolve,[$cnf( $equal(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )],[refute_0_260,refute_0_261]) ).
cnf(refute_0_263,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)),
inference(resolve,[$cnf( $equal(hAPP_int_int(bit0,hAPP_int_int(bit1,pls)),hAPP_int_int(succ,one_one_int)) )],[refute_0_259,refute_0_262]) ).
cnf(refute_0_264,plain,
( hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) != hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int))
| hAPP_nat_nat(suc,one_one_nat) != hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))
| hAPP_nat_nat(suc,one_one_nat) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_nat(suc,one_one_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ),[1],$fot(hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)))]]) ).
cnf(refute_0_265,plain,
( 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) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)) ),
inference(resolve,[$cnf( $equal(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int))) )],[refute_0_263,refute_0_264]) ).
cnf(refute_0_266,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat) != hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))
| hAPP_nat_nat(suc,one_one_nat) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)) ),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(suc,one_one_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )],[refute_0_174,refute_0_265]) ).
cnf(refute_0_267,plain,
hAPP_nat_nat(suc,one_one_nat) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(plus_plus_nat,one_one_nat),one_one_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )],[refute_0_140,refute_0_266]) ).
cnf(refute_0_268,plain,
one_one_int = hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)),
inference(canonicalize,[],[normalize_0_57]) ).
cnf(refute_0_269,plain,
( hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)) != hAPP_int_int(bit1,pls)
| one_one_int != hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))
| one_one_int = hAPP_int_int(bit1,pls) ),
introduced(tautology,[equality,[$cnf( $equal(one_one_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))) ),[1],$fot(hAPP_int_int(bit1,pls))]]) ).
cnf(refute_0_270,plain,
( one_one_int != hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))
| one_one_int = hAPP_int_int(bit1,pls) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls)),hAPP_int_int(bit1,pls)) )],[refute_0_210,refute_0_269]) ).
cnf(refute_0_271,plain,
one_one_int = hAPP_int_int(bit1,pls),
inference(resolve,[$cnf( $equal(one_one_int,hAPP_int_int(number_number_of_int,hAPP_int_int(bit1,pls))) )],[refute_0_268,refute_0_270]) ).
cnf(refute_0_272,plain,
( one_one_int != hAPP_int_int(bit1,pls)
| hAPP_int_int(bit1,pls) = one_one_int ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(one_one_int)),bind(Y,$fot(hAPP_int_int(bit1,pls)))]]) ).
cnf(refute_0_273,plain,
hAPP_int_int(bit1,pls) = one_one_int,
inference(resolve,[$cnf( $equal(one_one_int,hAPP_int_int(bit1,pls)) )],[refute_0_271,refute_0_272]) ).
cnf(refute_0_274,plain,
hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) = hAPP_int_int(bit0,hAPP_int_int(bit1,pls)),
introduced(tautology,[refl,[$fot(hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))]]) ).
cnf(refute_0_275,plain,
( hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) != hAPP_int_int(bit0,hAPP_int_int(bit1,pls))
| hAPP_int_int(bit1,pls) != one_one_int
| hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) = hAPP_int_int(bit0,one_one_int) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_int(bit0,hAPP_int_int(bit1,pls)),hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) ),[1,1],$fot(one_one_int)]]) ).
cnf(refute_0_276,plain,
( hAPP_int_int(bit1,pls) != one_one_int
| hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) = hAPP_int_int(bit0,one_one_int) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(bit0,hAPP_int_int(bit1,pls)),hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) )],[refute_0_274,refute_0_275]) ).
cnf(refute_0_277,plain,
hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) = hAPP_int_int(bit0,one_one_int),
inference(resolve,[$cnf( $equal(hAPP_int_int(bit1,pls),one_one_int) )],[refute_0_273,refute_0_276]) ).
cnf(refute_0_278,plain,
( hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) != hAPP_int_int(bit0,one_one_int)
| hAPP_int_int(succ,one_one_int) != hAPP_int_int(bit0,hAPP_int_int(bit1,pls))
| hAPP_int_int(succ,one_one_int) = hAPP_int_int(bit0,one_one_int) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_int(succ,one_one_int),hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) ),[1],$fot(hAPP_int_int(bit0,one_one_int))]]) ).
cnf(refute_0_279,plain,
( hAPP_int_int(succ,one_one_int) != hAPP_int_int(bit0,hAPP_int_int(bit1,pls))
| hAPP_int_int(succ,one_one_int) = hAPP_int_int(bit0,one_one_int) ),
inference(resolve,[$cnf( $equal(hAPP_int_int(bit0,hAPP_int_int(bit1,pls)),hAPP_int_int(bit0,one_one_int)) )],[refute_0_277,refute_0_278]) ).
cnf(refute_0_280,plain,
hAPP_int_int(succ,one_one_int) = hAPP_int_int(bit0,one_one_int),
inference(resolve,[$cnf( $equal(hAPP_int_int(succ,one_one_int),hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) )],[refute_0_257,refute_0_279]) ).
cnf(refute_0_281,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)),
introduced(tautology,[refl,[$fot(hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)))]]) ).
cnf(refute_0_282,plain,
( hAPP_int_int(succ,one_one_int) != hAPP_int_int(bit0,one_one_int)
| hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)) != hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int))
| hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int))) ),[1,1],$fot(hAPP_int_int(bit0,one_one_int))]]) ).
cnf(refute_0_283,plain,
( hAPP_int_int(succ,one_one_int) != hAPP_int_int(bit0,one_one_int)
| hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)) ),
inference(resolve,[$cnf( $equal(hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int))) )],[refute_0_281,refute_0_282]) ).
cnf(refute_0_284,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)),
inference(resolve,[$cnf( $equal(hAPP_int_int(succ,one_one_int),hAPP_int_int(bit0,one_one_int)) )],[refute_0_280,refute_0_283]) ).
cnf(refute_0_285,plain,
( hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)) != hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int))
| hAPP_nat_nat(suc,one_one_nat) != hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int))
| hAPP_nat_nat(suc,one_one_nat) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_nat(suc,one_one_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int))) ),[1],$fot(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)))]]) ).
cnf(refute_0_286,plain,
( hAPP_nat_nat(suc,one_one_nat) != hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int))
| hAPP_nat_nat(suc,one_one_nat) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)) ),
inference(resolve,[$cnf( $equal(hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int)),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int))) )],[refute_0_284,refute_0_285]) ).
cnf(refute_0_287,plain,
hAPP_nat_nat(suc,one_one_nat) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(suc,one_one_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(succ,one_one_int))) )],[refute_0_267,refute_0_286]) ).
cnf(refute_0_288,plain,
( hAPP_nat_nat(suc,one_one_nat) != hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int))
| hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)) = hAPP_nat_nat(suc,one_one_nat) ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(hAPP_nat_nat(suc,one_one_nat))),bind(Y,$fot(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int))))]]) ).
cnf(refute_0_289,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)) = hAPP_nat_nat(suc,one_one_nat),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(suc,one_one_nat),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int))) )],[refute_0_287,refute_0_288]) ).
cnf(refute_0_290,plain,
( hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) != hAPP_int_int(bit0,one_one_int)
| hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) != hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))
| hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) ),[1,1],$fot(hAPP_int_int(bit0,one_one_int))]]) ).
cnf(refute_0_291,plain,
( hAPP_int_int(bit0,hAPP_int_int(bit1,pls)) != hAPP_int_int(bit0,one_one_int)
| hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)) ),
inference(resolve,[$cnf( $equal(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) )],[refute_0_260,refute_0_290]) ).
cnf(refute_0_292,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)),
inference(resolve,[$cnf( $equal(hAPP_int_int(bit0,hAPP_int_int(bit1,pls)),hAPP_int_int(bit0,one_one_int)) )],[refute_0_277,refute_0_291]) ).
cnf(refute_0_293,plain,
( hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) != hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int))
| hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)) != hAPP_nat_nat(suc,one_one_nat)
| hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_nat_nat(suc,one_one_nat) ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))),bind(Y,$fot(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)))),bind(Z,$fot(hAPP_nat_nat(suc,one_one_nat)))]]) ).
cnf(refute_0_294,plain,
( hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)) != 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( $equal(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int))) )],[refute_0_292,refute_0_293]) ).
cnf(refute_0_295,plain,
hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))) = hAPP_nat_nat(suc,one_one_nat),
inference(resolve,[$cnf( $equal(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,one_one_int)),hAPP_nat_nat(suc,one_one_nat)) )],[refute_0_289,refute_0_294]) ).
cnf(refute_0_296,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
introduced(tautology,[refl,[$fot(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_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_297,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(semiri1621563631at_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(semiri1621563631at_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(semiri1621563631at_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(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) ),[1,1],$fot(hAPP_nat_nat(suc,one_one_nat))]]) ).
cnf(refute_0_298,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(semiri1621563631at_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(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat)) ),
inference(resolve,[$cnf( $equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) )],[refute_0_296,refute_0_297]) ).
cnf(refute_0_299,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat)),
inference(resolve,[$cnf( $equal(hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))),hAPP_nat_nat(suc,one_one_nat)) )],[refute_0_295,refute_0_298]) ).
cnf(refute_0_300,plain,
hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),
introduced(tautology,[refl,[$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(semiri1621563631at_int,n))))]]) ).
cnf(refute_0_301,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(semiri1621563631at_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(semiri1621563631at_int,n)))
| hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) != hAPP_nat_int(semiri1621563631at_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(semiri1621563631at_int,n))) = hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) ),[1,1],$fot(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))]]) ).
cnf(refute_0_302,plain,
( hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)) != hAPP_nat_int(semiri1621563631at_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(semiri1621563631at_int,n))) = hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) ),
inference(resolve,[$cnf( $equal(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)))) )],[refute_0_300,refute_0_301]) ).
cnf(refute_0_303,plain,
hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),
inference(resolve,[$cnf( $equal(hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n)),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) )],[refute_0_7,refute_0_302]) ).
cnf(refute_0_304,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
introduced(tautology,[refl,[$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(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))]]) ).
cnf(refute_0_305,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(semiri1621563631at_int,n))) != hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_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(semiri1621563631at_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(semiri1621563631at_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(semiri1621563631at_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(semiri1621563631at_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( $equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) ),[1,0],$fot(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))))]]) ).
cnf(refute_0_306,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(semiri1621563631at_int,n))) != hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_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(semiri1621563631at_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(semiri1621563631at_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( $equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) )],[refute_0_304,refute_0_305]) ).
cnf(refute_0_307,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),
inference(resolve,[$cnf( $equal(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)))) )],[refute_0_303,refute_0_306]) ).
cnf(refute_0_308,plain,
( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))
| hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat))
| hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat)) ),
inference(subst,[],[refute_0_24:[bind(X0,$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(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),bind(Y,$fot(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),bind(Z,$fot(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat))))]]) ).
cnf(refute_0_309,plain,
( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_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(semiri1621563631at_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(semiri1621563631at_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(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat)) ),
inference(resolve,[$cnf( $equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls))))) )],[refute_0_307,refute_0_308]) ).
cnf(refute_0_310,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat)),
inference(resolve,[$cnf( $equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat))) )],[refute_0_299,refute_0_309]) ).
cnf(refute_0_311,plain,
( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat))
| hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat)) != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)))
| hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))) ),
inference(subst,[],[refute_0_24:[bind(X0,$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(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))))),bind(Y,$fot(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat)))),bind(Z,$fot(hAPP_nat_int(semiri1621563631at_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_312,plain,
( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat)) != hAPP_nat_int(semiri1621563631at_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(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_int(semiri1621563631at_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( $equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat))) )],[refute_0_310,refute_0_311]) ).
cnf(refute_0_313,plain,
hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))),
inference(resolve,[$cnf( $equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))),hAPP_nat_nat(suc,one_one_nat)),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)))) )],[refute_0_172,refute_0_312]) ).
cnf(refute_0_314,plain,
( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)))
| hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != zero_zero_int
| hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))) = zero_zero_int ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),zero_zero_int) ),[0],$fot(hAPP_nat_int(semiri1621563631at_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_315,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(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != zero_zero_int
| hAPP_nat_int(semiri1621563631at_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( $equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)))) )],[refute_0_313,refute_0_314]) ).
cnf(refute_0_316,plain,
( hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))) != zero_zero_int
| zero_zero_int != pls
| hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))) = pls ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))),pls) ),[0],$fot(zero_zero_int)]]) ).
cnf(refute_0_317,plain,
( hAPP_nat_int(semiri1621563631at_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(semiri1621563631at_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( $equal(zero_zero_int,pls) )],[refute_0_14,refute_0_316]) ).
cnf(refute_0_318,plain,
( hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))) != zero_zero_int
| hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))) = pls ),
inference(resolve,[$cnf( $equal(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))),zero_zero_int) )],[refute_0_315,refute_0_317]) ).
cnf(refute_0_319,plain,
hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))) = pls,
inference(resolve,[$cnf( $equal(hAPP_nat_int(hAPP_int_fun_nat_int(power_power_int,hAPP_int_int(hAPP_int_fun_int_int(plus_plus_int,one_one_int),hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_nat(number_number_of_nat,hAPP_int_int(bit0,hAPP_int_int(bit1,pls)))),zero_zero_int) )],[refute_0_170,refute_0_318]) ).
cnf(refute_0_320,plain,
( hAPP_int_nat(nat,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)))) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))
| hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))) != pls
| hAPP_int_nat(nat,pls) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_nat(nat,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))) ),[0,1],$fot(pls)]]) ).
cnf(refute_0_321,plain,
( hAPP_int_nat(nat,hAPP_nat_int(semiri1621563631at_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,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( $equal(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))),pls) )],[refute_0_319,refute_0_320]) ).
cnf(refute_0_322,plain,
hAPP_int_nat(nat,pls) = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)),
inference(resolve,[$cnf( $equal(hAPP_int_nat(nat,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)))),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))) )],[refute_0_169,refute_0_321]) ).
cnf(refute_0_323,plain,
hAPP_int_nat(nat,zero_zero_int) = zero_zero_nat,
inference(canonicalize,[],[normalize_0_58]) ).
cnf(refute_0_324,plain,
hAPP_int_nat(nat,zero_zero_int) = hAPP_int_nat(nat,zero_zero_int),
introduced(tautology,[refl,[$fot(hAPP_int_nat(nat,zero_zero_int))]]) ).
cnf(refute_0_325,plain,
( hAPP_int_nat(nat,zero_zero_int) != hAPP_int_nat(nat,zero_zero_int)
| zero_zero_int != pls
| hAPP_int_nat(nat,zero_zero_int) = hAPP_int_nat(nat,pls) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_nat(nat,zero_zero_int),hAPP_int_nat(nat,zero_zero_int)) ),[1,1],$fot(pls)]]) ).
cnf(refute_0_326,plain,
( zero_zero_int != pls
| hAPP_int_nat(nat,zero_zero_int) = hAPP_int_nat(nat,pls) ),
inference(resolve,[$cnf( $equal(hAPP_int_nat(nat,zero_zero_int),hAPP_int_nat(nat,zero_zero_int)) )],[refute_0_324,refute_0_325]) ).
cnf(refute_0_327,plain,
hAPP_int_nat(nat,zero_zero_int) = hAPP_int_nat(nat,pls),
inference(resolve,[$cnf( $equal(zero_zero_int,pls) )],[refute_0_14,refute_0_326]) ).
cnf(refute_0_328,plain,
( hAPP_int_nat(nat,zero_zero_int) != hAPP_int_nat(nat,pls)
| hAPP_int_nat(nat,zero_zero_int) != zero_zero_nat
| hAPP_int_nat(nat,pls) = zero_zero_nat ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_nat(nat,zero_zero_int),zero_zero_nat) ),[0],$fot(hAPP_int_nat(nat,pls))]]) ).
cnf(refute_0_329,plain,
( hAPP_int_nat(nat,zero_zero_int) != zero_zero_nat
| hAPP_int_nat(nat,pls) = zero_zero_nat ),
inference(resolve,[$cnf( $equal(hAPP_int_nat(nat,zero_zero_int),hAPP_int_nat(nat,pls)) )],[refute_0_327,refute_0_328]) ).
cnf(refute_0_330,plain,
hAPP_int_nat(nat,pls) = zero_zero_nat,
inference(resolve,[$cnf( $equal(hAPP_int_nat(nat,zero_zero_int),zero_zero_nat) )],[refute_0_323,refute_0_329]) ).
cnf(refute_0_331,plain,
( hAPP_int_nat(nat,pls) != hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))
| hAPP_int_nat(nat,pls) != zero_zero_nat
| zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_nat(nat,pls),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))) ),[0],$fot(zero_zero_nat)]]) ).
cnf(refute_0_332,plain,
( hAPP_int_nat(nat,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( $equal(hAPP_int_nat(nat,pls),zero_zero_nat) )],[refute_0_330,refute_0_331]) ).
cnf(refute_0_333,plain,
zero_zero_nat = hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)),
inference(resolve,[$cnf( $equal(hAPP_int_nat(nat,pls),hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))) )],[refute_0_322,refute_0_332]) ).
cnf(refute_0_334,plain,
( zero_zero_nat != hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))
| hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)) = zero_zero_nat ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(zero_zero_nat)),bind(Y,$fot(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))))]]) ).
cnf(refute_0_335,plain,
hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)) = zero_zero_nat,
inference(resolve,[$cnf( $equal(zero_zero_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))) )],[refute_0_333,refute_0_334]) ).
cnf(refute_0_336,plain,
( hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)) != zero_zero_nat
| hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n)) != hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))))
| hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n)) = hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n)),hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))))) ),[1,1,1],$fot(zero_zero_nat)]]) ).
cnf(refute_0_337,plain,
( hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n)) != hAPP_real_real(sqrt,hAPP_nat_real(real_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_nat,hAPP_nat_nat(suc,n)) = hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)) ),
inference(resolve,[$cnf( $equal(hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat)),zero_zero_nat) )],[refute_0_335,refute_0_336]) ).
cnf(refute_0_338,plain,
hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n)) = hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)),
inference(resolve,[$cnf( $equal(hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n)),hAPP_real_real(sqrt,hAPP_nat_real(real_nat,hAPP_nat_nat(hAPP_nat_fun_nat_nat(power_power_nat,hAPP_nat_nat(suc,n)),hAPP_nat_nat(suc,one_one_nat))))) )],[refute_0_167,refute_0_337]) ).
cnf(refute_0_339,plain,
hAPP_real_real(sqrt,zero_zero_real) = zero_zero_real,
inference(canonicalize,[],[normalize_0_59]) ).
cnf(refute_0_340,plain,
hAPP_nat_real(real_nat,zero_zero_nat) = zero_zero_real,
inference(canonicalize,[],[normalize_0_60]) ).
cnf(refute_0_341,plain,
hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)) = hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)),
introduced(tautology,[refl,[$fot(hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)))]]) ).
cnf(refute_0_342,plain,
( hAPP_nat_real(real_nat,zero_zero_nat) != zero_zero_real
| hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)) != hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat))
| hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)) = hAPP_real_real(sqrt,zero_zero_real) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)),hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat))) ),[1,1],$fot(zero_zero_real)]]) ).
cnf(refute_0_343,plain,
( hAPP_nat_real(real_nat,zero_zero_nat) != zero_zero_real
| hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)) = hAPP_real_real(sqrt,zero_zero_real) ),
inference(resolve,[$cnf( $equal(hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)),hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat))) )],[refute_0_341,refute_0_342]) ).
cnf(refute_0_344,plain,
hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)) = hAPP_real_real(sqrt,zero_zero_real),
inference(resolve,[$cnf( $equal(hAPP_nat_real(real_nat,zero_zero_nat),zero_zero_real) )],[refute_0_340,refute_0_343]) ).
cnf(refute_0_345,plain,
( hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)) != hAPP_real_real(sqrt,zero_zero_real)
| hAPP_real_real(sqrt,zero_zero_real) != zero_zero_real
| hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)) = zero_zero_real ),
inference(subst,[],[refute_0_24:[bind(X0,$fot(hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)))),bind(Y,$fot(hAPP_real_real(sqrt,zero_zero_real))),bind(Z,$fot(zero_zero_real))]]) ).
cnf(refute_0_346,plain,
( hAPP_real_real(sqrt,zero_zero_real) != zero_zero_real
| hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)) = zero_zero_real ),
inference(resolve,[$cnf( $equal(hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)),hAPP_real_real(sqrt,zero_zero_real)) )],[refute_0_344,refute_0_345]) ).
cnf(refute_0_347,plain,
hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)) = zero_zero_real,
inference(resolve,[$cnf( $equal(hAPP_real_real(sqrt,zero_zero_real),zero_zero_real) )],[refute_0_339,refute_0_346]) ).
cnf(refute_0_348,plain,
( hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n)) != hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat))
| hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)) != zero_zero_real
| hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n)) = zero_zero_real ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n)),zero_zero_real) ),[0],$fot(hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)))]]) ).
cnf(refute_0_349,plain,
( hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n)) != hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat))
| hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n)) = zero_zero_real ),
inference(resolve,[$cnf( $equal(hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat)),zero_zero_real) )],[refute_0_347,refute_0_348]) ).
cnf(refute_0_350,plain,
hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n)) = zero_zero_real,
inference(resolve,[$cnf( $equal(hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n)),hAPP_real_real(sqrt,hAPP_nat_real(real_nat,zero_zero_nat))) )],[refute_0_338,refute_0_349]) ).
cnf(refute_0_351,plain,
( archim1246769320r_real(hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n))) != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))
| hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n)) != zero_zero_real
| archim1246769320r_real(zero_zero_real) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)) ),
introduced(tautology,[equality,[$cnf( $equal(archim1246769320r_real(hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n))),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) ),[0,0],$fot(zero_zero_real)]]) ).
cnf(refute_0_352,plain,
( archim1246769320r_real(hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n))) != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))
| archim1246769320r_real(zero_zero_real) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)) ),
inference(resolve,[$cnf( $equal(hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n)),zero_zero_real) )],[refute_0_350,refute_0_351]) ).
cnf(refute_0_353,plain,
archim1246769320r_real(zero_zero_real) = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)),
inference(resolve,[$cnf( $equal(archim1246769320r_real(hAPP_nat_real(real_nat,hAPP_nat_nat(suc,n))),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) )],[refute_0_52,refute_0_352]) ).
cnf(refute_0_354,plain,
archim1246769320r_real(hAPP_nat_real(real_nat,zero_zero_nat)) = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
inference(subst,[],[refute_0_51:[bind(N,$fot(zero_zero_nat))]]) ).
cnf(refute_0_355,plain,
( archim1246769320r_real(hAPP_nat_real(real_nat,zero_zero_nat)) != hAPP_nat_int(semiri1621563631at_int,zero_zero_nat)
| hAPP_nat_real(real_nat,zero_zero_nat) != zero_zero_real
| archim1246769320r_real(zero_zero_real) = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) ),
introduced(tautology,[equality,[$cnf( $equal(archim1246769320r_real(hAPP_nat_real(real_nat,zero_zero_nat)),hAPP_nat_int(semiri1621563631at_int,zero_zero_nat)) ),[0,0],$fot(zero_zero_real)]]) ).
cnf(refute_0_356,plain,
( archim1246769320r_real(hAPP_nat_real(real_nat,zero_zero_nat)) != hAPP_nat_int(semiri1621563631at_int,zero_zero_nat)
| archim1246769320r_real(zero_zero_real) = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) ),
inference(resolve,[$cnf( $equal(hAPP_nat_real(real_nat,zero_zero_nat),zero_zero_real) )],[refute_0_340,refute_0_355]) ).
cnf(refute_0_357,plain,
archim1246769320r_real(zero_zero_real) = hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),
inference(resolve,[$cnf( $equal(archim1246769320r_real(hAPP_nat_real(real_nat,zero_zero_nat)),hAPP_nat_int(semiri1621563631at_int,zero_zero_nat)) )],[refute_0_354,refute_0_356]) ).
cnf(refute_0_358,plain,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = zero_zero_int,
inference(canonicalize,[],[normalize_0_61]) ).
cnf(refute_0_359,plain,
( hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) != zero_zero_int
| zero_zero_int != pls
| hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = pls ),
introduced(tautology,[equality,[$cnf( ~ $equal(hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),pls) ),[0],$fot(zero_zero_int)]]) ).
cnf(refute_0_360,plain,
( hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) != zero_zero_int
| hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = pls ),
inference(resolve,[$cnf( $equal(zero_zero_int,pls) )],[refute_0_14,refute_0_359]) ).
cnf(refute_0_361,plain,
hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) = pls,
inference(resolve,[$cnf( $equal(hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),zero_zero_int) )],[refute_0_358,refute_0_360]) ).
cnf(refute_0_362,plain,
( archim1246769320r_real(zero_zero_real) != hAPP_nat_int(semiri1621563631at_int,zero_zero_nat)
| hAPP_nat_int(semiri1621563631at_int,zero_zero_nat) != pls
| archim1246769320r_real(zero_zero_real) = pls ),
introduced(tautology,[equality,[$cnf( ~ $equal(archim1246769320r_real(zero_zero_real),pls) ),[0],$fot(hAPP_nat_int(semiri1621563631at_int,zero_zero_nat))]]) ).
cnf(refute_0_363,plain,
( archim1246769320r_real(zero_zero_real) != hAPP_nat_int(semiri1621563631at_int,zero_zero_nat)
| archim1246769320r_real(zero_zero_real) = pls ),
inference(resolve,[$cnf( $equal(hAPP_nat_int(semiri1621563631at_int,zero_zero_nat),pls) )],[refute_0_361,refute_0_362]) ).
cnf(refute_0_364,plain,
archim1246769320r_real(zero_zero_real) = pls,
inference(resolve,[$cnf( $equal(archim1246769320r_real(zero_zero_real),hAPP_nat_int(semiri1621563631at_int,zero_zero_nat)) )],[refute_0_357,refute_0_363]) ).
cnf(refute_0_365,plain,
( archim1246769320r_real(zero_zero_real) != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))
| archim1246769320r_real(zero_zero_real) != pls
| pls = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)) ),
introduced(tautology,[equality,[$cnf( $equal(archim1246769320r_real(zero_zero_real),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) ),[0],$fot(pls)]]) ).
cnf(refute_0_366,plain,
( archim1246769320r_real(zero_zero_real) != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))
| pls = hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)) ),
inference(resolve,[$cnf( $equal(archim1246769320r_real(zero_zero_real),pls) )],[refute_0_364,refute_0_365]) ).
cnf(refute_0_367,plain,
( hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)) != hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))
| pls != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))
| pls = hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)) ),
introduced(tautology,[equality,[$cnf( $equal(pls,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) ),[1],$fot(hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)))]]) ).
cnf(refute_0_368,plain,
( pls != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))
| pls = hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)) ),
inference(resolve,[$cnf( $equal(hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n)),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))) )],[refute_0_43,refute_0_367]) ).
cnf(refute_0_369,plain,
( archim1246769320r_real(zero_zero_real) != hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))
| pls = hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)) ),
inference(resolve,[$cnf( $equal(pls,hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) )],[refute_0_366,refute_0_368]) ).
cnf(refute_0_370,plain,
pls = hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)),
inference(resolve,[$cnf( $equal(archim1246769320r_real(zero_zero_real),hAPP_nat_int(semiri1621563631at_int,hAPP_nat_nat(suc,n))) )],[refute_0_353,refute_0_369]) ).
cnf(refute_0_371,plain,
( pls != hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))
| hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)) = pls ),
inference(subst,[],[refute_0_4:[bind(X0,$fot(pls)),bind(Y,$fot(hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))))]]) ).
cnf(refute_0_372,plain,
hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)) = pls,
inference(resolve,[$cnf( $equal(pls,hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))) )],[refute_0_370,refute_0_371]) ).
cnf(refute_0_373,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))),
introduced(tautology,[refl,[$fot(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))))]]) ).
cnf(refute_0_374,plain,
( hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))) != hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)))
| hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)) != pls
| hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls) ),
introduced(tautology,[equality,[$cnf( $equal(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)))) ),[1,1],$fot(pls)]]) ).
cnf(refute_0_375,plain,
( hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)) != pls
| hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls) ),
inference(resolve,[$cnf( $equal(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)))) )],[refute_0_373,refute_0_374]) ).
cnf(refute_0_376,plain,
hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))) = hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls),
inference(resolve,[$cnf( $equal(hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)),pls) )],[refute_0_372,refute_0_375]) ).
cnf(refute_0_377,plain,
( hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))) != hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)
| ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)) ),
introduced(tautology,[equality,[$cnf( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)))) ),[0],$fot(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls))]]) ).
cnf(refute_0_378,plain,
( ~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))))
| hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)) ),
inference(resolve,[$cnf( $equal(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n))),hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)) )],[refute_0_376,refute_0_377]) ).
cnf(refute_0_379,plain,
hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(resolve,[$cnf( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),hAPP_int_int(succ,hAPP_nat_int(semiri1621563631at_int,n)))) )],[refute_0_50,refute_0_378]) ).
cnf(refute_0_380,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,X_29),X_29)),
inference(canonicalize,[],[normalize_0_63]) ).
cnf(refute_0_381,plain,
~ hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)),
inference(subst,[],[refute_0_380:[bind(X_29,$fot(pls))]]) ).
cnf(refute_0_382,plain,
$false,
inference(resolve,[$cnf( hBOOL(hAPP_int_bool(hAPP_i1948725293t_bool(ord_less_int,pls),pls)) )],[refute_0_379,refute_0_381]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM925+4 : TPTP v8.1.0. Released v5.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.32 % Computer : n027.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 600
% 0.12/0.32 % DateTime : Thu Jul 7 13:31:59 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 24.06/24.29 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 24.06/24.29
% 24.06/24.29 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 24.15/24.35
%------------------------------------------------------------------------------